Finite Group Databasebeta

← C73×#36733 #32946137

Subgroups — C73×#36733 #32946137

Order 18688.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2849C211yesmaximal, characteristic
2C73×#2848C211yesmaximal, characteristic, complemented
3C73×#2745C211yesmaximal, characteristic, complemented
4C73×#2745C211yesmaximal, characteristic, complemented
5C73×#2744C211yesmaximal, characteristic, complemented
6C73×#2743C211yesmaximal, characteristic, complemented
7C73×#2742C211yesmaximal, characteristic, complemented
8C73×#2741C211yesmaximal, characteristic, complemented
9C73×#2736C211yesmaximal, characteristic, complemented
10C73×#2735C211yesmaximal, characteristic, complemented
11C73×#2707C211yesmaximal, characteristic, complemented
12C73×#2700C211yesmaximal, characteristic, complemented
13C73×#2698C211yesmaximal, characteristic, complemented
14C73×#2692C211yesmaximal, characteristic, complemented
15C73×#2690C211yesmaximal, characteristic, complemented
16C73×#2687C211yesmaximal, characteristic, complemented
17C73×#2685C211yesmaximal, characteristic
18C73×#2684C211yesmaximal, characteristic
19C73×#2665C211yesmaximal, characteristic, complemented
20C73×#2663C211yesmaximal, characteristic, complemented
21C73×#2595C211yesmaximal, characteristic, complemented
22C73×#2589C211yesmaximal, characteristic, complemented
23C73×#2589C211yesmaximal, characteristic, complemented
24C73×#2576C211yesmaximal, characteristic, complemented
25C73×#2478C211yesmaximal, characteristic, complemented
26C73×#2477C211yesmaximal, characteristic, complemented
27C73×#2475C211yesmaximal, characteristic, complemented
28C73×#2474C211yesmaximal, characteristic, complemented
29C73×#2335C211yesmaximal, characteristic, complemented
30C73×#2332C211yesmaximal, characteristic, complemented
31C73×#2280C211yesmaximal, characteristic, complemented
32C24×C4×C73C2211yescharacteristic
33C2×#126×C73C2211yescharacteristic
34C2×#125×C73C2211yescharacteristic, complemented
35C2×#124×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic
37C2×#123×C73C2211yescharacteristic
38C2×C22⋊Q8×C73C2211yescharacteristic
39C2×C22⋊Q8×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×C22⋊Q8×C73C2211yescharacteristic, complemented
42C2×#120×C73C2211yescharacteristic
43C2×#117×C73C2211yescharacteristic
44C2×#117×C73C2211yescharacteristic
45#401×C73C2211yescharacteristic, complemented
46#400×C73C2211yescharacteristic, complemented
47#400×C73C2211yescharacteristic, complemented
48#400×C73C2211yescharacteristic, complemented
49#400×C73C2211yescharacteristic, complemented
50#400×C73C2211yescharacteristic, complemented
51#400×C73C2211yescharacteristic, complemented
52#400×C73C2211yescharacteristic, complemented
53#400×C73C2211yescharacteristic, complemented
54#399×C73C2211yescharacteristic
55#399×C73C2211yescharacteristic
56#399×C73C2211yescharacteristic, complemented
57#398×C73C2211yescharacteristic, complemented
58#398×C73C2211yescharacteristic, complemented
59#398×C73C2211yescharacteristic, complemented
60#398×C73C2211yescharacteristic, complemented
61#398×C73C2211yescharacteristic, complemented
62#397×C73C2211yescharacteristic
63#397×C73C2211yescharacteristic
64#397×C73C2211yescharacteristic
65#397×C73C2211yescharacteristic
66#397×C73C2211yescharacteristic
67#397×C73C2211yescharacteristic
68#397×C73C2211yescharacteristic
69#397×C73C2211yescharacteristic
70#397×C73C2211yescharacteristic, complemented
71#397×C73C2211yescharacteristic, complemented
72#396×C73C2211yescharacteristic
73#396×C73C2211yescharacteristic
74#396×C73C2211yescharacteristic
75#396×C73C2211yescharacteristic, complemented
76#396×C73C2211yescharacteristic, complemented
77#395×C73C2211yescharacteristic, complemented
78#395×C73C2211yescharacteristic, complemented
79#395×C73C2211yescharacteristic, complemented
80#395×C73C2211yescharacteristic, complemented
81#394×C73C2211yescharacteristic
82#394×C73C2211yescharacteristic
83#394×C73C2211yescharacteristic
84#394×C73C2211yescharacteristic
85#394×C73C2211yescharacteristic
86#394×C73C2211yescharacteristic
87#393×C73C2211yescharacteristic
88#393×C73C2211yescharacteristic
89#393×C73C2211yescharacteristic
90#393×C73C2211yescharacteristic
91#393×C73C2211yescharacteristic
92#393×C73C2211yescharacteristic, complemented
93#391×C73C2211yescharacteristic, complemented
94#391×C73C2211yescharacteristic, complemented
95#391×C73C2211yescharacteristic, complemented
96#391×C73C2211yescharacteristic, complemented
97#391×C73C2211yescharacteristic, complemented
98#391×C73C2211yescharacteristic, complemented
99#390×C73C2211yescharacteristic
100#390×C73C2211yescharacteristic
101#389×C73C2211yescharacteristic, complemented
102#389×C73C2211yescharacteristic, complemented
103#389×C73C2211yescharacteristic, complemented
104#389×C73C2211yescharacteristic, complemented
105#388×C73C2211yescharacteristic
106#388×C73C2211yescharacteristic
107#388×C73C2211yescharacteristic
108#388×C73C2211yescharacteristic
109#388×C73C2211yescharacteristic
110#388×C73C2211yescharacteristic
111#388×C73C2211yescharacteristic
112#388×C73C2211yescharacteristic
113#388×C73C2211yescharacteristic
114#388×C73C2211yescharacteristic
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic
117#388×C73C2211yescharacteristic
118#388×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic
122#388×C73C2211yescharacteristic, complemented
123#388×C73C2211yescharacteristic, complemented
124#388×C73C2211yescharacteristic, complemented
125#388×C73C2211yescharacteristic, complemented
126#388×C73C2211yescharacteristic, complemented
127#388×C73C2211yescharacteristic, complemented
128#387×C73C2211yescharacteristic, complemented
129#387×C73C2211yescharacteristic, complemented
130#387×C73C2211yescharacteristic, complemented
131#387×C73C2211yescharacteristic, complemented
132#387×C73C2211yescharacteristic, complemented
133#387×C73C2211yescharacteristic, complemented
134#387×C73C2211yescharacteristic, complemented
135#387×C73C2211yescharacteristic, complemented
136#387×C73C2211yescharacteristic, complemented
137#387×C73C2211yescharacteristic, complemented
138#387×C73C2211yescharacteristic, complemented
139#387×C73C2211yescharacteristic, complemented
140#387×C73C2211yescharacteristic, complemented
141#387×C73C2211yescharacteristic, complemented
142#387×C73C2211yescharacteristic, complemented
143#386×C73C2211yescharacteristic
144#386×C73C2211yescharacteristic
145#386×C73C2211yescharacteristic
146#386×C73C2211yescharacteristic
147#386×C73C2211yescharacteristic
148#386×C73C2211yescharacteristic
149#386×C73C2211yescharacteristic
150#385×C73C2211yescharacteristic
151#385×C73C2211yescharacteristic
152#385×C73C2211yescharacteristic
153#385×C73C2211yescharacteristic
154#385×C73C2211yescharacteristic
155#385×C73C2211yescharacteristic
156#385×C73C2211yescharacteristic
157#385×C73C2211yescharacteristic
158#385×C73C2211yescharacteristic
159#385×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic, complemented
161#382×C73C2211yescharacteristic, complemented
162#381×C73C2211yescharacteristic
163#381×C73C2211yescharacteristic
164#381×C73C2211yescharacteristic
165#381×C73C2211yescharacteristic
166#381×C73C2211yescharacteristic, complemented
167#380×C73C2211yescharacteristic
168#380×C73C2211yescharacteristic
169#380×C73C2211yescharacteristic
170#380×C73C2211yescharacteristic
171#380×C73C2211yescharacteristic
172#380×C73C2211yescharacteristic
173#380×C73C2211yescharacteristic
174#379×C73C2211yescharacteristic
175#379×C73C2211yescharacteristic
176#379×C73C2211yescharacteristic
177#379×C73C2211yescharacteristic
178#379×C73C2211yescharacteristic
179C4×C4⋊C4×C73C2211yescharacteristic, complemented
180C4×C4⋊C4×C73C2211yescharacteristic, complemented
181C4×C4⋊C4×C73C2211yescharacteristic, complemented
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic, complemented
187C25×C73C2311yescharacteristic
188C22×Q8×C73C2311yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×Q8×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C23×C4×C73—24no—
195C23×C4×C73—42no—
196C23×C4×C73—42no—
197C23×C4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204#126×C73—42no—
205#125×C73—42no—
206#124×C73—42no—
207#123×C73—24no—
208#123×C73—42no—
209C22⋊Q8×C73—24no—
210C22⋊Q8×C73—42no—
211C22⋊Q8×C73—42no—
212C22⋊Q8×C73—42no—
213#120×C73—42no—
214#117×C73—42no—
215#117×C73—42no—
216C2×C4⋊C4×C73C2311yescharacteristic
217C2×C4⋊C4×C73C2311yescharacteristic
218C2×C4⋊C4×C73C2311yescharacteristic
219C2×C4⋊C4×C73C2311yescharacteristic
220C2×C4⋊C4×C73C2311yescharacteristic
221C2×C4⋊C4×C73C2311yescharacteristic
222C2×C4⋊C4×C73C2311yescharacteristic
223C2×C4⋊C4×C73C2311yescharacteristic
224C2×C4⋊C4×C73C2311yescharacteristic
225C2×C4⋊C4×C73C2311yescharacteristic
226C2×C4⋊C4×C73C2311yescharacteristic
227C2×C4⋊C4×C73C2311yescharacteristic
228C2×C4⋊C4×C73C2311yescharacteristic
229C2×C4⋊C4×C73C2311yescharacteristic
230C2×C4⋊C4×C73C2311yescharacteristic
231C2×C4⋊C4×C73C2311yescharacteristic
232C2×C4⋊C4×C73C2311yescharacteristic
233C2×C4⋊C4×C73C2311yescharacteristic
234C2×C4⋊C4×C73C2311yescharacteristic
235C2×C4⋊C4×C73C2311yescharacteristic
236C2×C4⋊C4×C73C2311yescharacteristic
237C2×C4⋊C4×C73C2311yescharacteristic
238C2×C4⋊C4×C73C2311yescharacteristic
239C2×C4⋊C4×C73C2311yescharacteristic
240C2×C4⋊C4×C73C2311yescharacteristic
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C22⋊C4×C73C2311yescharacteristic
251C2×C22⋊C4×C73C2311yescharacteristic
252C2×C22⋊C4×C73C2311yescharacteristic
253C2×C22⋊C4×C73C2311yescharacteristic
254C2×C22⋊C4×C73C2311yescharacteristic
255C2×C22⋊C4×C73C2311yescharacteristic
256C2×C22⋊C4×C73C2311yescharacteristic
257C2×C22⋊C4×C73C2311yescharacteristic
258C2×C22⋊C4×C73C2311yescharacteristic
259C2×C22⋊C4×C73C2311yescharacteristic
260C2×C22⋊C4×C73C2311yescharacteristic
261C2×C22⋊C4×C73C2311yescharacteristic
262C2×C22⋊C4×C73C2311yescharacteristic
263C2×C22⋊C4×C73C2311yescharacteristic
264C2×C22⋊C4×C73C2311yescharacteristic
265C2×C22⋊C4×C73C2311yescharacteristic
266C2×C22⋊C4×C73C2311yescharacteristic
267C2×C22⋊C4×C73C2311yescharacteristic
268C2×C22⋊C4×C73C2311yescharacteristic
269C2×C22⋊C4×C73C2311yescharacteristic
270C2×C22⋊C4×C73C2311yescharacteristic
271C2×C22⋊C4×C73C2311yescharacteristic
272C2×C22⋊C4×C73C2311yescharacteristic
273C2×C22⋊C4×C73C2311yescharacteristic
274C2×C22⋊C4×C73C2311yescharacteristic
275C2×C22⋊C4×C73C2311yescharacteristic
276C2×C22⋊C4×C73C2311yescharacteristic
277C2×C22⋊C4×C73C2311yescharacteristic
278C2×C22⋊C4×C73C2311yescharacteristic
279C2×C22⋊C4×C73C2311yescharacteristic
280C2×C22⋊C4×C73C2311yescharacteristic
281C2×C22⋊C4×C73C2311yescharacteristic
282C2×C22⋊C4×C73C2311yescharacteristic
283C2×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C22⋊C4×C73C2311yescharacteristic
293C2×C22⋊C4×C73C2311yescharacteristic
294C2×C42×C73C2311yescharacteristic
295C2×C42×C73C2311yescharacteristic
296C2×C42×C73C2311yescharacteristic
297C2×C42×C73C2311yescharacteristic
298C2×C42×C73C2311yescharacteristic
299C2×C42×C73C2311yescharacteristic
300C2×C42×C73C2311yescharacteristic
301C2×C42×C73C2311yescharacteristic
302C2×C42×C73C2311yescharacteristic
303C2×C42×C73C2311yescharacteristic
304C2×C42×C73C2311yescharacteristic
305#95×C73C2311yescharacteristic
306#95×C73C2311yescharacteristic
307#95×C73C2311yescharacteristic
308#95×C73C2311yescharacteristic
309#95×C73C2311yescharacteristic
310#95×C73C2311yescharacteristic
311#95×C73C2311yescharacteristic
312#95×C73C2311yescharacteristic
313#95×C73C2311yescharacteristic
314#95×C73C2311yescharacteristic
315#95×C73C2311yescharacteristic
316#95×C73C2311yescharacteristic
317#95×C73C2311yescharacteristic
318#95×C73C2311yescharacteristic
319#95×C73C2311yescharacteristic
320#95×C73C2311yescharacteristic
321#95×C73C2311yescharacteristic
322#95×C73C2311yescharacteristic
323#95×C73C2311yescharacteristic
324#95×C73C2311yescharacteristic
325#95×C73C2311yescharacteristic
326#95×C73C2311yescharacteristic
327#95×C73C2311yescharacteristic
328#95×C73C2311yescharacteristic
329#95×C73C2311yescharacteristic
330#95×C73C2311yescharacteristic
331#95×C73C2311yescharacteristic
332#95×C73C2311yescharacteristic
333#95×C73C2311yescharacteristic
334#95×C73C2311yescharacteristic
335#95×C73C2311yescharacteristic
336#95×C73C2311yescharacteristic
337#95×C73C2311yescharacteristic
338#95×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357C24×C73—22no—
358C24×C73—22no—
359C24×C73—22no—
360C24×C73—41no—
361C24×C73—41no—
362C24×C73—41no—
363C24×C73—41no—
364C24×C73C2411yescharacteristic
365C24×C73C2411yescharacteristic
366C24×C73C2411yescharacteristic
367C24×C73C2411yescharacteristic
368C2×Q8×C73—22no—
369C2×Q8×C73—41no—
370C2×Q8×C73—41no—
371C2×Q8×C73—41no—
372C2×Q8×C73—41no—
373C2×Q8×C73—41no—
374C2×Q8×C73—41no—
375C2×Q8×C73—41no—
376C2×Q8×C73—41no—
377C2×D4×C73—22no—
378C2×D4×C73—22no—
379C2×D4×C73—22no—
380C2×D4×C73—41no—
381C2×D4×C73—41no—
382C2×D4×C73—41no—
383C2×D4×C73—41no—
384C2×D4×C73—41no—
385C2×D4×C73—41no—
386C22×C4×C73—22no—
387C22×C4×C73—22no—
388C22×C4×C73—22no—
389C22×C4×C73—22no—
390C22×C4×C73—22no—
391C22×C4×C73—22no—
392C22×C4×C73—22no—
393C22×C4×C73—22no—
394C22×C4×C73—22no—
395C22×C4×C73—22no—
396C22×C4×C73—41no—
397C22×C4×C73—41no—
398C22×C4×C73—41no—
399C22×C4×C73—41no—
400C22×C4×C73—41no—
401C22×C4×C73—41no—
402C22×C4×C73—41no—
403C22×C4×C73—41no—
404C22×C4×C73—41no—
405C22×C4×C73—41no—
406C22×C4×C73—416no—
407C22×C4×C73#4114yes—
408C22×C4×C73C2411yescharacteristic
409C22×C4×C73C2411yescharacteristic
410C22×C4×C73C2411yescharacteristic
411C22×C4×C73C2411yescharacteristic
412C22×C4×C73C2411yescharacteristic
413C22×C4×C73C2411yescharacteristic
414C22×C4×C73C2411yescharacteristic
415C22×C4×C73C2411yescharacteristic
416C22×C4×C73C2411yescharacteristic
417C22×C4×C73C2411yescharacteristic
418C22×C4×C73C2411yescharacteristic
419C22×C4×C73C2411yescharacteristic
420C22×C4×C73C2411yescharacteristic
421C22×C4×C73C2411yescharacteristic
422C22×C4×C73C2411yescharacteristic
423C22×C4×C73C2411yescharacteristic
424C22×C4×C73C2411yescharacteristic
425C22×C4×C73C2411yescharacteristic
426C22×C4×C73C2411yescharacteristic
427C22×C4×C73C2411yescharacteristic
428C22×C4×C73C2411yescharacteristic
429C22×C4×C73C2411yescharacteristic
430C22×C4×C73C2411yescharacteristic
431C22×C4×C73C2411yescharacteristic
432C22×C4×C73C2411yescharacteristic
433C22×C4×C73C2411yescharacteristic
434C22×C4×C73C2411yescharacteristic
435C4⋊C4×C73—22no—
436C4⋊C4×C73—22no—
437C4⋊C4×C73—22no—
438C4⋊C4×C73—22no—
439C4⋊C4×C73—22no—
440C4⋊C4×C73—22no—
441C4⋊C4×C73—22no—
442C4⋊C4×C73—22no—
443C4⋊C4×C73—22no—
444C4⋊C4×C73—22no—
445C4⋊C4×C73—41no—
446C4⋊C4×C73—41no—
447C4⋊C4×C73—41no—
448C4⋊C4×C73—41no—
449C4⋊C4×C73—41no—
450C4⋊C4×C73—41no—
451C4⋊C4×C73—41no—
452C4⋊C4×C73—41no—
453C4⋊C4×C73—41no—
454C4⋊C4×C73—41no—
455C4⋊C4×C73—41no—
456C4⋊C4×C73—41no—
457C4⋊C4×C73—41no—
458C4⋊C4×C73—41no—
459C4⋊C4×C73—41no—
460C4⋊C4×C73—41no—
461C4⋊C4×C73—41no—
462C4⋊C4×C73—41no—
463C4⋊C4×C73—41no—
464C4⋊C4×C73—41no—
465C4⋊C4×C73—41no—
466C4⋊C4×C73—41no—
467C4⋊C4×C73—41no—
468C4⋊C4×C73—41no—
469C22⋊C4×C73—22no—
470C22⋊C4×C73—22no—
471C22⋊C4×C73—22no—
472C22⋊C4×C73—22no—
473C22⋊C4×C73—22no—
474C22⋊C4×C73—22no—
475C22⋊C4×C73—22no—
476C22⋊C4×C73—22no—
477C22⋊C4×C73—22no—
478C22⋊C4×C73—22no—
479C22⋊C4×C73—22no—
480C22⋊C4×C73—22no—
481C22⋊C4×C73—22no—
482C22⋊C4×C73—22no—
483C22⋊C4×C73—41no—
484C22⋊C4×C73—41no—
485C22⋊C4×C73—41no—
486C22⋊C4×C73—41no—
487C22⋊C4×C73—41no—
488C22⋊C4×C73—41no—
489C22⋊C4×C73—41no—
490C22⋊C4×C73—41no—
491C22⋊C4×C73—41no—
492C22⋊C4×C73—41no—
493C22⋊C4×C73—41no—
494C22⋊C4×C73—41no—
495C22⋊C4×C73—41no—
496C22⋊C4×C73—41no—
497C22⋊C4×C73—41no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73—41no—
500C22⋊C4×C73—41no—
501C22⋊C4×C73—41no—
502C22⋊C4×C73—41no—
503C22⋊C4×C73—41no—
504C22⋊C4×C73—41no—
505C22⋊C4×C73—41no—
506C22⋊C4×C73—41no—
507C22⋊C4×C73—41no—
508C22⋊C4×C73—41no—
509C22⋊C4×C73—41no—
510C22⋊C4×C73—41no—
511C22⋊C4×C73—41no—
512C22⋊C4×C73—41no—
513C42×C73—41no—
514C42×C73—41no—
515C42×C73—41no—
516C42×C73—41no—
517C42×C73—41no—
518C42×C73—41no—
519C42×C73—41no—
520C42×C73—41no—
521C42×C73—41no—
522C42×C73—41no—
523C42×C73—41no—
524C23×C73—21no—
525C23×C73—21no—
526C23×C73—21no—
527C23×C73—21no—
528C23×C73—21no—
529C23×C73—21no—
530C23×C73—21no—
531C23×C73—21no—
532C23×C73—21no—
533C23×C73—21no—
534C23×C73—21no—
535C23×C73—21no—
536C23×C73—21no—
537C23×C73—21no—
538C23×C73—21no—
539C23×C73—21no—
540C23×C73—21no—
541C23×C73—21no—
542C23×C73—21no—
543C23×C73—21no—
544C23×C73—21no—
545C23×C73—21no—
546C23×C73—21no—
547C23×C73—21no—
548C23×C73—21no—
549C23×C73—44no—
550C23×C73—44no—
551C23×C73—44no—
552C23×C73—44no—
553C23×C73—44no—
554C23×C73—44no—
555C23×C73—44no—
556C23×C73C2×#4112yes—
557C23×C73H(5,𝔽2)12yes—
558C23×C732−1+412yes—
559C23×C73C2511yescharacteristic
560Q8×C73—82no—
561Q8×C73—82no—
562Q8×C73—82no—
563D4×C73—82no—
564D4×C73—82no—
565D4×C73—82no—
566C2×C4×C73—28no—
567C2×C4×C73—21no—
568C2×C4×C73—21no—
569C2×C4×C73—21no—
570C2×C4×C73—21no—
571C2×C4×C73—21no—
572C2×C4×C73—21no—
573C2×C4×C73—21no—
574C2×C4×C73—21no—
575C2×C4×C73—21no—
576C2×C4×C73—21no—
577C2×C4×C73—21no—
578C2×C4×C73—21no—
579C2×C4×C73—21no—
580C2×C4×C73—21no—
581C2×C4×C73—21no—
582C2×C4×C73—21no—
583C2×C4×C73—21no—
584C2×C4×C73—21no—
585C2×C4×C73—21no—
586C2×C4×C73—21no—
587C2×C4×C73—21no—
588C2×C4×C73—21no—
589C2×C4×C73—21no—
590C2×C4×C73—21no—
591C2×C4×C73—21no—
592C2×C4×C73—21no—
593C2×C4×C73—21no—
594C2×C4×C73—21no—
595C2×C4×C73—21no—
596C2×C4×C73—21no—
597C2×C4×C73—21no—
598C2×C4×C73—21no—
599C2×C4×C73—21no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—44no—
646C2×C4×C73—44no—
647C2×C4×C73—44no—
648C2×C4×C73—44no—
649C2×C4×C73—44no—
650C2×C4×C73—82no—
651C2×C4×C73C2×#4112yes—
652C2×C4×C73C2×#4112yes—
653C2×C4×C73H(5,𝔽2)12yes—
654C22×C73—22no—
655C22×C73—22no—
656C22×C73—22no—
657C22×C73—22no—
658C22×C73—22no—
659C22×C73—22no—
660C22×C73—22no—
661C22×C73—22no—
662C22×C73—22no—
663C22×C73—416no—
664C22×C73—41no—
665C22×C73—41no—
666C22×C73—41no—
667C22×C73—41no—
668C22×C73—41no—
669C22×C73—41no—
670C22×C73—41no—
671C22×C73—41no—
672C22×C73—41no—
673C22×C73—41no—
674C22×C73—41no—
675C22×C73—41no—
676C22×C73—41no—
677C22×C73—41no—
678C22×C73—41no—
679C22×C73—41no—
680C22×C73—41no—
681C22×C73—41no—
682C22×C73—41no—
683C22×C73C22×#4111yescharacteristic
684C22×C73C2×H(5,𝔽2)11yescharacteristic
685C22×C73C2×H(5,𝔽2)11yescharacteristic
686C22×C73C2×2−1+411yescharacteristic
687C22×C73#58511yescharacteristic
688C22×C73#58511yescharacteristic
689C22×C73#58511yescharacteristic
690C4×C73—22no—
691C4×C73—22no—
692C4×C73—22no—
693C4×C73—41no—
694C4×C73—41no—
695C4×C73—41no—
696C4×C73—41no—
697C4×C73—41no—
698C4×C73—41no—
699C4×C73—41no—
700C4×C73—41no—
701C4×C73—41no—
702C4×C73—41no—
703C4×C73—41no—
704C4×C73—41no—
705C4×C73—41no—
706C4×C73—41no—
707C4×C73—41no—
708C4×C73—41no—
709C4×C73—41no—
710C4×C73—41no—
711C4×C73—41no—
712C4×C73—41no—
713C4×C73—41no—
714C4×C73—41no—
715C4×C73—41no—
716C4×C73—41no—
717#36733C7311yesmaximal, characteristic, direct product factor, Sylow
718C2×C73—42no—
719C2×C73—42no—
720C2×C73—42no—
721C2×C73—81no—
722C2×C73#345511yescharacteristic
723C2×C73#349011yescharacteristic
724C2×C73#349511yescharacteristic
725C2×C73#353311yescharacteristic
726C2×C73#353511yescharacteristic
727C2×C73#354011yescharacteristic
728C2×C73#354111yescharacteristic
729#2849C2×C7311yescharacteristic
730#2848C2×C7311yescharacteristic, complemented
731#2745C2×C7311yescharacteristic, complemented
732#2745C2×C7311yescharacteristic, complemented
733#2744C2×C7311yescharacteristic, complemented
734#2743C2×C7311yescharacteristic, complemented
735#2742C2×C7311yescharacteristic, complemented
736#2741C2×C7311yescharacteristic, complemented
737#2736C2×C7311yescharacteristic, complemented
738#2735C2×C7311yescharacteristic, complemented
739#2707C2×C7311yescharacteristic, complemented
740#2700C2×C7311yescharacteristic, complemented
741#2698C2×C7311yescharacteristic, complemented
742#2692C2×C7311yescharacteristic, complemented
743#2690C2×C7311yescharacteristic, complemented
744#2687C2×C7311yescharacteristic, complemented
745#2685C2×C7311yescharacteristic
746#2684C2×C7311yescharacteristic
747#2665C2×C7311yescharacteristic, complemented
748#2663C2×C7311yescharacteristic, complemented
749#2595C2×C7311yescharacteristic, complemented
750#2589C2×C7311yescharacteristic, complemented
751#2589C2×C7311yescharacteristic, complemented
752#2576C2×C7311yescharacteristic, complemented
753#2478C2×C7311yescharacteristic, complemented
754#2477C2×C7311yescharacteristic, complemented
755#2475C2×C7311yescharacteristic, complemented
756#2474C2×C7311yescharacteristic, complemented
757#2335C2×C7311yescharacteristic, complemented
758#2332C2×C7311yescharacteristic, complemented
759#2280C2×C7311yescharacteristic, complemented
760C73#3673311yescharacteristic, direct product factor, Sylow
761C24×C4C22×C7311yescharacteristic
762C2×#126C22×C7311yescharacteristic
763C2×#125C22×C7311yescharacteristic, complemented
764C2×#124C22×C7311yescharacteristic
765C2×#123C22×C7311yescharacteristic
766C2×#123C22×C7311yescharacteristic
767C2×C22⋊Q8C22×C7311yescharacteristic
768C2×C22⋊Q8C22×C7311yescharacteristic
769C2×C22⋊Q8C22×C7311yescharacteristic
770C2×C22⋊Q8C22×C7311yescharacteristic, complemented
771C2×#120C22×C7311yescharacteristic
772C2×#117C22×C7311yescharacteristic
773C2×#117C22×C7311yescharacteristic
774#401C22×C7311yescharacteristic, complemented
775#400C22×C7311yescharacteristic, complemented
776#400C22×C7311yescharacteristic, complemented
777#400C22×C7311yescharacteristic, complemented
778#400C22×C7311yescharacteristic, complemented
779#400C22×C7311yescharacteristic, complemented
780#400C22×C7311yescharacteristic, complemented
781#400C22×C7311yescharacteristic, complemented
782#400C22×C7311yescharacteristic, complemented
783#399C22×C7311yescharacteristic
784#399C22×C7311yescharacteristic
785#399C22×C7311yescharacteristic, complemented
786#398C22×C7311yescharacteristic, complemented
787#398C22×C7311yescharacteristic, complemented
788#398C22×C7311yescharacteristic, complemented
789#398C22×C7311yescharacteristic, complemented
790#398C22×C7311yescharacteristic, complemented
791#397C22×C7311yescharacteristic
792#397C22×C7311yescharacteristic
793#397C22×C7311yescharacteristic
794#397C22×C7311yescharacteristic
795#397C22×C7311yescharacteristic
796#397C22×C7311yescharacteristic
797#397C22×C7311yescharacteristic
798#397C22×C7311yescharacteristic
799#397C22×C7311yescharacteristic, complemented
800#397C22×C7311yescharacteristic, complemented
801#396C22×C7311yescharacteristic
802#396C22×C7311yescharacteristic
803#396C22×C7311yescharacteristic
804#396C22×C7311yescharacteristic, complemented
805#396C22×C7311yescharacteristic, complemented
806#395C22×C7311yescharacteristic, complemented
807#395C22×C7311yescharacteristic, complemented
808#395C22×C7311yescharacteristic, complemented
809#395C22×C7311yescharacteristic, complemented
810#394C22×C7311yescharacteristic
811#394C22×C7311yescharacteristic
812#394C22×C7311yescharacteristic
813#394C22×C7311yescharacteristic
814#394C22×C7311yescharacteristic
815#394C22×C7311yescharacteristic
816#393C22×C7311yescharacteristic
817#393C22×C7311yescharacteristic
818#393C22×C7311yescharacteristic
819#393C22×C7311yescharacteristic
820#393C22×C7311yescharacteristic
821#393C22×C7311yescharacteristic, complemented
822#391C22×C7311yescharacteristic, complemented
823#391C22×C7311yescharacteristic, complemented
824#391C22×C7311yescharacteristic, complemented
825#391C22×C7311yescharacteristic, complemented
826#391C22×C7311yescharacteristic, complemented
827#391C22×C7311yescharacteristic, complemented
828#390C22×C7311yescharacteristic
829#390C22×C7311yescharacteristic
830#389C22×C7311yescharacteristic, complemented
831#389C22×C7311yescharacteristic, complemented
832#389C22×C7311yescharacteristic, complemented
833#389C22×C7311yescharacteristic, complemented
834#388C22×C7311yescharacteristic
835#388C22×C7311yescharacteristic
836#388C22×C7311yescharacteristic
837#388C22×C7311yescharacteristic
838#388C22×C7311yescharacteristic
839#388C22×C7311yescharacteristic
840#388C22×C7311yescharacteristic
841#388C22×C7311yescharacteristic
842#388C22×C7311yescharacteristic
843#388C22×C7311yescharacteristic
844#388C22×C7311yescharacteristic
845#388C22×C7311yescharacteristic
846#388C22×C7311yescharacteristic
847#388C22×C7311yescharacteristic
848#388C22×C7311yescharacteristic
849#388C22×C7311yescharacteristic
850#388C22×C7311yescharacteristic
851#388C22×C7311yescharacteristic, complemented
852#388C22×C7311yescharacteristic, complemented
853#388C22×C7311yescharacteristic, complemented
854#388C22×C7311yescharacteristic, complemented
855#388C22×C7311yescharacteristic, complemented
856#388C22×C7311yescharacteristic, complemented
857#387C22×C7311yescharacteristic, complemented
858#387C22×C7311yescharacteristic, complemented
859#387C22×C7311yescharacteristic, complemented
860#387C22×C7311yescharacteristic, complemented
861#387C22×C7311yescharacteristic, complemented
862#387C22×C7311yescharacteristic, complemented
863#387C22×C7311yescharacteristic, complemented
864#387C22×C7311yescharacteristic, complemented
865#387C22×C7311yescharacteristic, complemented
866#387C22×C7311yescharacteristic, complemented
867#387C22×C7311yescharacteristic, complemented
868#387C22×C7311yescharacteristic, complemented
869#387C22×C7311yescharacteristic, complemented
870#387C22×C7311yescharacteristic, complemented
871#387C22×C7311yescharacteristic, complemented
872#386C22×C7311yescharacteristic
873#386C22×C7311yescharacteristic
874#386C22×C7311yescharacteristic
875#386C22×C7311yescharacteristic
876#386C22×C7311yescharacteristic
877#386C22×C7311yescharacteristic
878#386C22×C7311yescharacteristic
879#385C22×C7311yescharacteristic
880#385C22×C7311yescharacteristic
881#385C22×C7311yescharacteristic
882#385C22×C7311yescharacteristic
883#385C22×C7311yescharacteristic
884#385C22×C7311yescharacteristic
885#385C22×C7311yescharacteristic
886#385C22×C7311yescharacteristic
887#385C22×C7311yescharacteristic
888#385C22×C7311yescharacteristic
889#385C22×C7311yescharacteristic, complemented
890#382C22×C7311yescharacteristic, complemented
891#381C22×C7311yescharacteristic
892#381C22×C7311yescharacteristic
893#381C22×C7311yescharacteristic
894#381C22×C7311yescharacteristic
895#381C22×C7311yescharacteristic, complemented
896#380C22×C7311yescharacteristic
897#380C22×C7311yescharacteristic
898#380C22×C7311yescharacteristic
899#380C22×C7311yescharacteristic
900#380C22×C7311yescharacteristic
901#380C22×C7311yescharacteristic
902#380C22×C7311yescharacteristic
903#379C22×C7311yescharacteristic
904#379C22×C7311yescharacteristic
905#379C22×C7311yescharacteristic
906#379C22×C7311yescharacteristic
907#379C22×C7311yescharacteristic
908C4×C4⋊C4C22×C7311yescharacteristic, complemented
909C4×C4⋊C4C22×C7311yescharacteristic, complemented
910C4×C4⋊C4C22×C7311yescharacteristic, complemented
911C4×C22⋊C4C22×C7311yescharacteristic
912C4×C22⋊C4C22×C7311yescharacteristic
913C4×C22⋊C4C22×C7311yescharacteristic
914C4×C22⋊C4C22×C7311yescharacteristic
915C4×C22⋊C4C22×C7311yescharacteristic, complemented
916C25C23×C7311yescharacteristic
917C22×Q8C23×C7311yescharacteristic
918C22×Q8C23×C7311yescharacteristic
919C22×Q8C23×C7311yescharacteristic
920C22×D4C23×C7311yescharacteristic
921C22×D4C23×C7311yescharacteristic
922C22×D4C23×C7311yescharacteristic
923C23×C4—24no—
924C23×C4—42no—
925C23×C4—42no—
926C23×C4C23×C7311yescharacteristic
927C23×C4C23×C7311yescharacteristic
928C23×C4C23×C7311yescharacteristic
929C23×C4C23×C7311yescharacteristic
930C23×C4C23×C7311yescharacteristic
931C23×C4C23×C7311yescharacteristic
932C23×C4C23×C7311yescharacteristic
933#126—42no—
934#125—42no—
935#124—42no—
936#123—24no—
937#123—42no—
938C22⋊Q8—24no—
939C22⋊Q8—42no—
940C22⋊Q8—42no—
941C22⋊Q8—42no—
942#120—42no—
943#117—42no—
944#117—42no—
945C2×C4⋊C4C23×C7311yescharacteristic
946C2×C4⋊C4C23×C7311yescharacteristic
947C2×C4⋊C4C23×C7311yescharacteristic
948C2×C4⋊C4C23×C7311yescharacteristic
949C2×C4⋊C4C23×C7311yescharacteristic
950C2×C4⋊C4C23×C7311yescharacteristic
951C2×C4⋊C4C23×C7311yescharacteristic
952C2×C4⋊C4C23×C7311yescharacteristic
953C2×C4⋊C4C23×C7311yescharacteristic
954C2×C4⋊C4C23×C7311yescharacteristic
955C2×C4⋊C4C23×C7311yescharacteristic
956C2×C4⋊C4C23×C7311yescharacteristic
957C2×C4⋊C4C23×C7311yescharacteristic
958C2×C4⋊C4C23×C7311yescharacteristic
959C2×C4⋊C4C23×C7311yescharacteristic
960C2×C4⋊C4C23×C7311yescharacteristic
961C2×C4⋊C4C23×C7311yescharacteristic
962C2×C4⋊C4C23×C7311yescharacteristic
963C2×C4⋊C4C23×C7311yescharacteristic
964C2×C4⋊C4C23×C7311yescharacteristic
965C2×C4⋊C4C23×C7311yescharacteristic
966C2×C4⋊C4C23×C7311yescharacteristic
967C2×C4⋊C4C23×C7311yescharacteristic
968C2×C4⋊C4C23×C7311yescharacteristic
969C2×C4⋊C4C23×C7311yescharacteristic
970C2×C4⋊C4C23×C7311yescharacteristic
971C2×C4⋊C4C23×C7311yescharacteristic
972C2×C4⋊C4C23×C7311yescharacteristic
973C2×C4⋊C4C23×C7311yescharacteristic
974C2×C4⋊C4C23×C7311yescharacteristic
975C2×C4⋊C4C23×C7311yescharacteristic
976C2×C4⋊C4C23×C7311yescharacteristic
977C2×C4⋊C4C23×C7311yescharacteristic
978C2×C4⋊C4C23×C7311yescharacteristic
979C2×C22⋊C4C23×C7311yescharacteristic
980C2×C22⋊C4C23×C7311yescharacteristic
981C2×C22⋊C4C23×C7311yescharacteristic
982C2×C22⋊C4C23×C7311yescharacteristic
983C2×C22⋊C4C23×C7311yescharacteristic
984C2×C22⋊C4C23×C7311yescharacteristic
985C2×C22⋊C4C23×C7311yescharacteristic
986C2×C22⋊C4C23×C7311yescharacteristic
987C2×C22⋊C4C23×C7311yescharacteristic
988C2×C22⋊C4C23×C7311yescharacteristic
989C2×C22⋊C4C23×C7311yescharacteristic
990C2×C22⋊C4C23×C7311yescharacteristic
991C2×C22⋊C4C23×C7311yescharacteristic
992C2×C22⋊C4C23×C7311yescharacteristic
993C2×C22⋊C4C23×C7311yescharacteristic
994C2×C22⋊C4C23×C7311yescharacteristic
995C2×C22⋊C4C23×C7311yescharacteristic
996C2×C22⋊C4C23×C7311yescharacteristic
997C2×C22⋊C4C23×C7311yescharacteristic
998C2×C22⋊C4C23×C7311yescharacteristic
999C2×C22⋊C4C23×C7311yescharacteristic
1000C2×C22⋊C4C23×C7311yescharacteristic
1001C2×C22⋊C4C23×C7311yescharacteristic
1002C2×C22⋊C4C23×C7311yescharacteristic
1003C2×C22⋊C4C23×C7311yescharacteristic
1004C2×C22⋊C4C23×C7311yescharacteristic
1005C2×C22⋊C4C23×C7311yescharacteristic
1006C2×C22⋊C4C23×C7311yescharacteristic
1007C2×C22⋊C4C23×C7311yescharacteristic
1008C2×C22⋊C4C23×C7311yescharacteristic
1009C2×C22⋊C4C23×C7311yescharacteristic
1010C2×C22⋊C4C23×C7311yescharacteristic
1011C2×C22⋊C4C23×C7311yescharacteristic
1012C2×C22⋊C4C23×C7311yescharacteristic
1013C2×C22⋊C4C23×C7311yescharacteristic
1014C2×C22⋊C4C23×C7311yescharacteristic
1015C2×C22⋊C4C23×C7311yescharacteristic
1016C2×C22⋊C4C23×C7311yescharacteristic
1017C2×C22⋊C4C23×C7311yescharacteristic
1018C2×C22⋊C4C23×C7311yescharacteristic
1019C2×C22⋊C4C23×C7311yescharacteristic
1020C2×C22⋊C4C23×C7311yescharacteristic
1021C2×C22⋊C4C23×C7311yescharacteristic
1022C2×C22⋊C4C23×C7311yescharacteristic
1023C2×C42C23×C7311yescharacteristic
1024C2×C42C23×C7311yescharacteristic
1025C2×C42C23×C7311yescharacteristic
1026C2×C42C23×C7311yescharacteristic
1027C2×C42C23×C7311yescharacteristic
1028C2×C42C23×C7311yescharacteristic
1029C2×C42C23×C7311yescharacteristic
1030C2×C42C23×C7311yescharacteristic
1031C2×C42C23×C7311yescharacteristic
1032C2×C42C23×C7311yescharacteristic
1033C2×C42C23×C7311yescharacteristic
1034#95C23×C7311yescharacteristic
1035#95C23×C7311yescharacteristic
1036#95C23×C7311yescharacteristic
1037#95C23×C7311yescharacteristic
1038#95C23×C7311yescharacteristic
1039#95C23×C7311yescharacteristic
1040#95C23×C7311yescharacteristic
1041#95C23×C7311yescharacteristic
1042#95C23×C7311yescharacteristic
1043#95C23×C7311yescharacteristic
1044#95C23×C7311yescharacteristic
1045#95C23×C7311yescharacteristic
1046#95C23×C7311yescharacteristic
1047#95C23×C7311yescharacteristic
1048#95C23×C7311yescharacteristic
1049#95C23×C7311yescharacteristic
1050#95C23×C7311yescharacteristic
1051#95C23×C7311yescharacteristic
1052#95C23×C7311yescharacteristic
1053#95C23×C7311yescharacteristic
1054#95C23×C7311yescharacteristic
1055#95C23×C7311yescharacteristic
1056#95C23×C7311yescharacteristic
1057#95C23×C7311yescharacteristic
1058#95C23×C7311yescharacteristic
1059#95C23×C7311yescharacteristic
1060#95C23×C7311yescharacteristic
1061#95C23×C7311yescharacteristic
1062#95C23×C7311yescharacteristic
1063#95C23×C7311yescharacteristic
1064#95C23×C7311yescharacteristic
1065#95C23×C7311yescharacteristic
1066#95C23×C7311yescharacteristic
1067#95C23×C7311yescharacteristic
1068#95C23×C7311yescharacteristic
1069#95C23×C7311yescharacteristic
1070#95C23×C7311yescharacteristic
1071#95C23×C7311yescharacteristic
1072#95C23×C7311yescharacteristic
1073#95C23×C7311yescharacteristic
1074#95C23×C7311yescharacteristic
1075#95C23×C7311yescharacteristic
1076#95C23×C7311yescharacteristic
1077#95C23×C7311yescharacteristic
1078#95C23×C7311yescharacteristic
1079#95C23×C7311yescharacteristic
1080#95C23×C7311yescharacteristic
1081#95C23×C7311yescharacteristic
1082#95C23×C7311yescharacteristic
1083#95C23×C7311yescharacteristic
1084#95C23×C7311yescharacteristic
1085#95C23×C7311yescharacteristic
1086C24—22no—
1087C24—22no—
1088C24—22no—
1089C24—41no—
1090C24—41no—
1091C24—41no—
1092C24—41no—
1093C24C24×C7311yescharacteristic
1094C24C24×C7311yescharacteristic
1095C24C24×C7311yescharacteristic
1096C24C24×C7311yescharacteristic
1097C2×Q8—22no—
1098C2×Q8—41no—
1099C2×Q8—41no—
1100C2×Q8—41no—
1101C2×Q8—41no—
1102C2×Q8—41no—
1103C2×Q8—41no—
1104C2×Q8—41no—
1105C2×Q8—41no—
1106C2×D4—22no—
1107C2×D4—22no—
1108C2×D4—22no—
1109C2×D4—41no—
1110C2×D4—41no—
1111C2×D4—41no—
1112C2×D4—41no—
1113C2×D4—41no—
1114C2×D4—41no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—22no—
1118C22×C4—22no—
1119C22×C4—22no—
1120C22×C4—22no—
1121C22×C4—22no—
1122C22×C4—22no—
1123C22×C4—22no—
1124C22×C4—22no—
1125C22×C4—41no—
1126C22×C4—41no—
1127C22×C4—41no—
1128C22×C4—41no—
1129C22×C4—41no—
1130C22×C4—41no—
1131C22×C4—41no—
1132C22×C4—41no—
1133C22×C4—41no—
1134C22×C4—41no—
1135C22×C4—416no—
1136C22×C4#41×C7314yes—
1137C22×C4C24×C7311yescharacteristic
1138C22×C4C24×C7311yescharacteristic
1139C22×C4C24×C7311yescharacteristic
1140C22×C4C24×C7311yescharacteristic
1141C22×C4C24×C7311yescharacteristic
1142C22×C4C24×C7311yescharacteristic
1143C22×C4C24×C7311yescharacteristic
1144C22×C4C24×C7311yescharacteristic
1145C22×C4C24×C7311yescharacteristic
1146C22×C4C24×C7311yescharacteristic
1147C22×C4C24×C7311yescharacteristic
1148C22×C4C24×C7311yescharacteristic
1149C22×C4C24×C7311yescharacteristic
1150C22×C4C24×C7311yescharacteristic
1151C22×C4C24×C7311yescharacteristic
1152C22×C4C24×C7311yescharacteristic
1153C22×C4C24×C7311yescharacteristic
1154C22×C4C24×C7311yescharacteristic
1155C22×C4C24×C7311yescharacteristic
1156C22×C4C24×C7311yescharacteristic
1157C22×C4C24×C7311yescharacteristic
1158C22×C4C24×C7311yescharacteristic
1159C22×C4C24×C7311yescharacteristic
1160C22×C4C24×C7311yescharacteristic
1161C22×C4C24×C7311yescharacteristic
1162C22×C4C24×C7311yescharacteristic
1163C22×C4C24×C7311yescharacteristic
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—41no—
1175C4⋊C4—41no—
1176C4⋊C4—41no—
1177C4⋊C4—41no—
1178C4⋊C4—41no—
1179C4⋊C4—41no—
1180C4⋊C4—41no—
1181C4⋊C4—41no—
1182C4⋊C4—41no—
1183C4⋊C4—41no—
1184C4⋊C4—41no—
1185C4⋊C4—41no—
1186C4⋊C4—41no—
1187C4⋊C4—41no—
1188C4⋊C4—41no—
1189C4⋊C4—41no—
1190C4⋊C4—41no—
1191C4⋊C4—41no—
1192C4⋊C4—41no—
1193C4⋊C4—41no—
1194C4⋊C4—41no—
1195C4⋊C4—41no—
1196C4⋊C4—41no—
1197C4⋊C4—41no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—22no—
1202C22⋊C4—22no—
1203C22⋊C4—22no—
1204C22⋊C4—22no—
1205C22⋊C4—22no—
1206C22⋊C4—22no—
1207C22⋊C4—22no—
1208C22⋊C4—22no—
1209C22⋊C4—22no—
1210C22⋊C4—22no—
1211C22⋊C4—22no—
1212C22⋊C4—41no—
1213C22⋊C4—41no—
1214C22⋊C4—41no—
1215C22⋊C4—41no—
1216C22⋊C4—41no—
1217C22⋊C4—41no—
1218C22⋊C4—41no—
1219C22⋊C4—41no—
1220C22⋊C4—41no—
1221C22⋊C4—41no—
1222C22⋊C4—41no—
1223C22⋊C4—41no—
1224C22⋊C4—41no—
1225C22⋊C4—41no—
1226C22⋊C4—41no—
1227C22⋊C4—41no—
1228C22⋊C4—41no—
1229C22⋊C4—41no—
1230C22⋊C4—41no—
1231C22⋊C4—41no—
1232C22⋊C4—41no—
1233C22⋊C4—41no—
1234C22⋊C4—41no—
1235C22⋊C4—41no—
1236C22⋊C4—41no—
1237C22⋊C4—41no—
1238C22⋊C4—41no—
1239C22⋊C4—41no—
1240C22⋊C4—41no—
1241C22⋊C4—41no—
1242C42—41no—
1243C42—41no—
1244C42—41no—
1245C42—41no—
1246C42—41no—
1247C42—41no—
1248C42—41no—
1249C42—41no—
1250C42—41no—
1251C42—41no—
1252C42—41no—
1253C23—21no—
1254C23—21no—
1255C23—21no—
1256C23—21no—
1257C23—21no—
1258C23—21no—
1259C23—21no—
1260C23—21no—
1261C23—21no—
1262C23—21no—
1263C23—21no—
1264C23—21no—
1265C23—21no—
1266C23—21no—
1267C23—21no—
1268C23—21no—
1269C23—21no—
1270C23—21no—
1271C23—21no—
1272C23—21no—
1273C23—21no—
1274C23—21no—
1275C23—21no—
1276C23—21no—
1277C23—21no—
1278C23—44no—
1279C23—44no—
1280C23—44no—
1281C23—44no—
1282C23—44no—
1283C23—44no—
1284C23—44no—
1285C23C2×#41×C7312yes—
1286C23H(5,𝔽2)×C7312yes—
1287C232−1+4×C7312yes—
1288C23C25×C7311yescharacteristic
1289Q8—82no—
1290Q8—82no—
1291Q8—82no—
1292D4—82no—
1293D4—82no—
1294D4—82no—
1295C2×C4—28no—
1296C2×C4—21no—
1297C2×C4—21no—
1298C2×C4—21no—
1299C2×C4—21no—
1300C2×C4—21no—
1301C2×C4—21no—
1302C2×C4—21no—
1303C2×C4—21no—
1304C2×C4—21no—
1305C2×C4—21no—
1306C2×C4—21no—
1307C2×C4—21no—
1308C2×C4—21no—
1309C2×C4—21no—
1310C2×C4—21no—
1311C2×C4—21no—
1312C2×C4—21no—
1313C2×C4—21no—
1314C2×C4—21no—
1315C2×C4—21no—
1316C2×C4—21no—
1317C2×C4—21no—
1318C2×C4—21no—
1319C2×C4—21no—
1320C2×C4—21no—
1321C2×C4—21no—
1322C2×C4—21no—
1323C2×C4—21no—
1324C2×C4—21no—
1325C2×C4—21no—
1326C2×C4—21no—
1327C2×C4—21no—
1328C2×C4—21no—
1329C2×C4—21no—
1330C2×C4—21no—
1331C2×C4—21no—
1332C2×C4—21no—
1333C2×C4—21no—
1334C2×C4—21no—
1335C2×C4—21no—
1336C2×C4—21no—
1337C2×C4—21no—
1338C2×C4—21no—
1339C2×C4—21no—
1340C2×C4—21no—
1341C2×C4—21no—
1342C2×C4—21no—
1343C2×C4—21no—
1344C2×C4—21no—
1345C2×C4—21no—
1346C2×C4—21no—
1347C2×C4—21no—
1348C2×C4—21no—
1349C2×C4—21no—
1350C2×C4—21no—
1351C2×C4—21no—
1352C2×C4—21no—
1353C2×C4—21no—
1354C2×C4—21no—
1355C2×C4—21no—
1356C2×C4—21no—
1357C2×C4—21no—
1358C2×C4—21no—
1359C2×C4—21no—
1360C2×C4—21no—
1361C2×C4—21no—
1362C2×C4—21no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—44no—
1375C2×C4—44no—
1376C2×C4—44no—
1377C2×C4—44no—
1378C2×C4—44no—
1379C2×C4—82no—
1380C2×C4C2×#41×C7312yes—
1381C2×C4C2×#41×C7312yes—
1382C2×C4H(5,𝔽2)×C7312yes—
1383C22—22no—
1384C22—22no—
1385C22—22no—
1386C22—22no—
1387C22—22no—
1388C22—22no—
1389C22—22no—
1390C22—22no—
1391C22—22no—
1392C22—416no—
1393C22—41no—
1394C22—41no—
1395C22—41no—
1396C22—41no—
1397C22—41no—
1398C22—41no—
1399C22—41no—
1400C22—41no—
1401C22—41no—
1402C22—41no—
1403C22—41no—
1404C22—41no—
1405C22—41no—
1406C22—41no—
1407C22—41no—
1408C22—41no—
1409C22—41no—
1410C22—41no—
1411C22—41no—
1412C22C22×#41×C7311yescharacteristic
1413C22C2×H(5,𝔽2)×C7311yescharacteristic
1414C22C2×H(5,𝔽2)×C7311yescharacteristic
1415C22C2×2−1+4×C7311yescharacteristic
1416C22#585×C7311yescharacteristic
1417C22#585×C7311yescharacteristic
1418C22#585×C7311yescharacteristic
1419C4—22no—
1420C4—22no—
1421C4—22no—
1422C4—41no—
1423C4—41no—
1424C4—41no—
1425C4—41no—
1426C4—41no—
1427C4—41no—
1428C4—41no—
1429C4—41no—
1430C4—41no—
1431C4—41no—
1432C4—41no—
1433C4—41no—
1434C4—41no—
1435C4—41no—
1436C4—41no—
1437C4—41no—
1438C4—41no—
1439C4—41no—
1440C4—41no—
1441C4—41no—
1442C4—41no—
1443C4—41no—
1444C4—41no—
1445C4—41no—
1446C2—42no—
1447C2—42no—
1448C2—42no—
1449C2—81no—
1450C2C73×#345511yescharacteristic
1451C2C73×#349011yescharacteristic
1452C2C73×#349511yescharacteristic
1453C2C73×#353311yescharacteristic
1454C2C73×#353511yescharacteristic
1455C2C73×#354011yescharacteristic
1456C2C73×#354111yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC2×#120×C73C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C73×#2848C2semidirect
3. C73×#2745C2semidirect
4. C73×#2745C2semidirect
5. C73×#2744C2semidirect
6. C73×#2743C2semidirect
7. C73×#2742C2semidirect
8. C73×#2741C2semidirect
9. C73×#2736C2semidirect
10. C73×#2735C2semidirect
11. C73×#2707C2semidirect
12. C73×#2700C2semidirect
13. C73×#2698C2semidirect
14. C73×#2692C2semidirect
15. C73×#2690C2semidirect
16. C73×#2687C2semidirect
19. C73×#2665C2semidirect
20. C73×#2663C2semidirect
21. C73×#2595C2semidirect
22. C73×#2589C2semidirect
23. C73×#2589C2semidirect
24. C73×#2576C2semidirect
25. C73×#2478C2semidirect
26. C73×#2477C2semidirect
27. C73×#2475C2semidirect
28. C73×#2474C2semidirect
29. C73×#2335C2semidirect
30. C73×#2332C2semidirect
31. C73×#2280C2semidirect
34. C2×#125×C73C22semidirect
41. C2×C22⋊Q8×C73C22semidirect
45. #401×C73C22semidirect
46. #400×C73C22semidirect
47. #400×C73C22semidirect
48. #400×C73C22semidirect
49. #400×C73C22semidirect
50. #400×C73C22semidirect
51. #400×C73C22semidirect
52. #400×C73C22semidirect
53. #400×C73C22semidirect
56. #399×C73C22semidirect
57. #398×C73C22semidirect
58. #398×C73C22semidirect
59. #398×C73C22semidirect
60. #398×C73C22semidirect
61. #398×C73C22semidirect
70. #397×C73C22semidirect
71. #397×C73C22semidirect
75. #396×C73C22semidirect
76. #396×C73C22semidirect
77. #395×C73C22semidirect
78. #395×C73C22semidirect
79. #395×C73C22semidirect
80. #395×C73C22semidirect
92. #393×C73C22semidirect
93. #391×C73C22semidirect
94. #391×C73C22semidirect
95. #391×C73C22semidirect
96. #391×C73C22semidirect
97. #391×C73C22semidirect
98. #391×C73C22semidirect
101. #389×C73C22semidirect
102. #389×C73C22semidirect
103. #389×C73C22semidirect
104. #389×C73C22semidirect
122. #388×C73C22semidirect
123. #388×C73C22semidirect
124. #388×C73C22semidirect
125. #388×C73C22semidirect
126. #388×C73C22semidirect
127. #388×C73C22semidirect
128. #387×C73C22semidirect
129. #387×C73C22semidirect
130. #387×C73C22semidirect
131. #387×C73C22semidirect
132. #387×C73C22semidirect
133. #387×C73C22semidirect
134. #387×C73C22semidirect
135. #387×C73C22semidirect
136. #387×C73C22semidirect
137. #387×C73C22semidirect
138. #387×C73C22semidirect
139. #387×C73C22semidirect
140. #387×C73C22semidirect
141. #387×C73C22semidirect
142. #387×C73C22semidirect
160. #385×C73C22semidirect
161. #382×C73C22semidirect
166. #381×C73C22semidirect
179. C4×C4⋊C4×C73C22semidirect
180. C4×C4⋊C4×C73C22semidirect
181. C4×C4⋊C4×C73C22semidirect
186. C4×C22⋊C4×C73C22semidirect
717. #36733C73direct (N × H)
730. #2848C2×C73semidirect
731. #2745C2×C73semidirect
732. #2745C2×C73semidirect
733. #2744C2×C73semidirect
734. #2743C2×C73semidirect
735. #2742C2×C73semidirect
736. #2741C2×C73semidirect
737. #2736C2×C73semidirect
738. #2735C2×C73semidirect
739. #2707C2×C73semidirect
740. #2700C2×C73semidirect
741. #2698C2×C73semidirect
742. #2692C2×C73semidirect
743. #2690C2×C73semidirect
744. #2687C2×C73semidirect
747. #2665C2×C73semidirect
748. #2663C2×C73semidirect
749. #2595C2×C73semidirect
750. #2589C2×C73semidirect
751. #2589C2×C73semidirect
752. #2576C2×C73semidirect
753. #2478C2×C73semidirect
754. #2477C2×C73semidirect
755. #2475C2×C73semidirect
756. #2474C2×C73semidirect
757. #2335C2×C73semidirect
758. #2332C2×C73semidirect
759. #2280C2×C73semidirect
760. C73#36733direct (N × H)
763. C2×#125C22×C73semidirect
770. C2×C22⋊Q8C22×C73semidirect
774. #401C22×C73semidirect
775. #400C22×C73semidirect
776. #400C22×C73semidirect
777. #400C22×C73semidirect
778. #400C22×C73semidirect
779. #400C22×C73semidirect
780. #400C22×C73semidirect
781. #400C22×C73semidirect
782. #400C22×C73semidirect
785. #399C22×C73semidirect
786. #398C22×C73semidirect
787. #398C22×C73semidirect
788. #398C22×C73semidirect
789. #398C22×C73semidirect
790. #398C22×C73semidirect
799. #397C22×C73semidirect
800. #397C22×C73semidirect
804. #396C22×C73semidirect
805. #396C22×C73semidirect
806. #395C22×C73semidirect
807. #395C22×C73semidirect
808. #395C22×C73semidirect
809. #395C22×C73semidirect
821. #393C22×C73semidirect
822. #391C22×C73semidirect
823. #391C22×C73semidirect
824. #391C22×C73semidirect
825. #391C22×C73semidirect
826. #391C22×C73semidirect
827. #391C22×C73semidirect
830. #389C22×C73semidirect
831. #389C22×C73semidirect
832. #389C22×C73semidirect
833. #389C22×C73semidirect
851. #388C22×C73semidirect
852. #388C22×C73semidirect
853. #388C22×C73semidirect
854. #388C22×C73semidirect
855. #388C22×C73semidirect
856. #388C22×C73semidirect
857. #387C22×C73semidirect
858. #387C22×C73semidirect
859. #387C22×C73semidirect
860. #387C22×C73semidirect
861. #387C22×C73semidirect
862. #387C22×C73semidirect
863. #387C22×C73semidirect
864. #387C22×C73semidirect
865. #387C22×C73semidirect
866. #387C22×C73semidirect
867. #387C22×C73semidirect
868. #387C22×C73semidirect
869. #387C22×C73semidirect
870. #387C22×C73semidirect
871. #387C22×C73semidirect
889. #385C22×C73semidirect
890. #382C22×C73semidirect
895. #381C22×C73semidirect
908. C4×C4⋊C4C22×C73semidirect
909. C4×C4⋊C4C22×C73semidirect
910. C4×C4⋊C4C22×C73semidirect
915. C4×C22⋊C4C22×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C73×#28492
C73×#28482
C73×#27452
C73×#27442
C73×#27432
C73×#27422
C73×#27412
C73×#27362
C73×#27352
C73×#27072
C73×#27002
C73×#26982
C73×#26922
C73×#26902
C73×#26872
C73×#26852
C73×#26842
C73×#26652
C73×#26632
C73×#25952
C73×#25892
C73×#25762
C73×#24782
C73×#24772
C73×#24752
C73×#24742
C73×#23352
C73×#23322
C73×#22802
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