Finite Group Databasebeta

← C73×#36797 #32946201

Subgroups — C73×#36797 #32946201

Order 18688.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2852C211yesmaximal, characteristic, complemented
2C73×#2850C211yesmaximal, characteristic, complemented
3C73×#2796C211yesmaximal, characteristic, complemented
4C73×#2775C211yesmaximal, characteristic, complemented
5C73×#2773C211yesmaximal, characteristic, complemented
6C73×#2772C211yesmaximal, characteristic, complemented
7C73×#2770C211yesmaximal, characteristic, complemented
8C73×#2767C211yesmaximal, characteristic, complemented
9C73×#2762C211yesmaximal, characteristic, complemented
10C73×#2754C211yesmaximal, characteristic, complemented
11C73×#2751C211yesmaximal, characteristic, complemented
12C73×#2746C211yesmaximal, characteristic, complemented
13C73×#2741C211yesmaximal, characteristic, complemented
14C73×#2737C211yesmaximal, characteristic, complemented
15C73×#2730C211yesmaximal, characteristic, complemented
16C73×#2717C211yesmaximal, characteristic, complemented
17C73×#2705C211yesmaximal, characteristic, complemented
18C73×#2698C211yesmaximal, characteristic, complemented
19C73×#2643C211yesmaximal, characteristic, complemented
20C73×#2639C211yesmaximal, characteristic, complemented
21C73×#2549C211yesmaximal, characteristic, complemented
22C73×#2543C211yesmaximal, characteristic
23C73×#2504C211yesmaximal, characteristic, complemented
24C73×#2487C211yesmaximal, characteristic, complemented
25C73×#2450C211yesmaximal, characteristic, complemented
26C73×#2449C211yesmaximal, characteristic, complemented
27C73×#2444C211yesmaximal, characteristic, complemented
28C73×#2443C211yesmaximal, characteristic, complemented
29C73×#2325C211yesmaximal, characteristic, complemented
30C73×#2318C211yesmaximal, characteristic, complemented
31C2×#387×C73C211yesmaximal, characteristic, complemented
32C2×#126×C73C2211yescharacteristic
33C2×#124×C73C2211yescharacteristic
34C2×#123×C73C2211yescharacteristic
35C2×C22⋊Q8×C73C2211yescharacteristic
36C2×C22⋊Q8×C73C2211yescharacteristic
37C2×C22⋊Q8×C73C2211yescharacteristic
38C2×#121×C73C2211yescharacteristic
39C2×#121×C73C2211yescharacteristic
40C2×#121×C73C2211yescharacteristic
41C2×C4×D4×C73C2211yescharacteristic
42C2×C4×D4×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C22×C4⋊C4×C73C2211yescharacteristic
45C22×C4⋊C4×C73C2211yescharacteristic
46C22×C42×C73C2211yescharacteristic
47#401×C73C2211yescharacteristic
48#400×C73C2211yescharacteristic
49#400×C73C2211yescharacteristic
50#400×C73C2211yescharacteristic
51#400×C73C2211yescharacteristic
52#400×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic
54#400×C73C2211yescharacteristic
55#400×C73C2211yescharacteristic
56#400×C73C2211yescharacteristic
57#399×C73C2211yescharacteristic
58#399×C73C2211yescharacteristic
59#399×C73C2211yescharacteristic
60#399×C73C2211yescharacteristic
61#398×C73C2211yescharacteristic
62#398×C73C2211yescharacteristic
63#398×C73C2211yescharacteristic
64#398×C73C2211yescharacteristic
65#398×C73C2211yescharacteristic
66#398×C73C2211yescharacteristic
67#397×C73C2211yescharacteristic
68#397×C73C2211yescharacteristic
69#397×C73C2211yescharacteristic
70#397×C73C2211yescharacteristic
71#397×C73C2211yescharacteristic
72#397×C73C2211yescharacteristic
73#397×C73C2211yescharacteristic
74#397×C73C2211yescharacteristic
75#397×C73C2211yescharacteristic
76#397×C73C2211yescharacteristic
77#397×C73C2211yescharacteristic
78#397×C73C2211yescharacteristic
79#397×C73C2211yescharacteristic
80#396×C73C2211yescharacteristic
81#396×C73C2211yescharacteristic
82#396×C73C2211yescharacteristic
83#395×C73C2211yescharacteristic
84#395×C73C2211yescharacteristic
85#395×C73C2211yescharacteristic
86#394×C73C2211yescharacteristic
87#394×C73C2211yescharacteristic
88#394×C73C2211yescharacteristic
89#394×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#393×C73C2211yescharacteristic
92#393×C73C2211yescharacteristic
93#393×C73C2211yescharacteristic
94#392×C73C2211yescharacteristic
95#391×C73C2211yescharacteristic
96#391×C73C2211yescharacteristic
97#391×C73C2211yescharacteristic
98#391×C73C2211yescharacteristic
99#390×C73C2211yescharacteristic
100#390×C73C2211yescharacteristic
101#390×C73C2211yescharacteristic
102#389×C73C2211yescharacteristic
103#389×C73C2211yescharacteristic
104#389×C73C2211yescharacteristic
105#389×C73C2211yescharacteristic
106#389×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#387×C73C2211yescharacteristic
123#387×C73C2211yescharacteristic
124#387×C73C2211yescharacteristic
125#387×C73C2211yescharacteristic
126#387×C73C2211yescharacteristic
127#387×C73C2211yescharacteristic
128#387×C73C2211yescharacteristic
129#387×C73C2211yescharacteristic
130#387×C73C2211yescharacteristic
131#387×C73C2211yescharacteristic
132#387×C73C2211yescharacteristic
133#387×C73C2211yescharacteristic
134#387×C73C2211yescharacteristic
135#387×C73C2211yescharacteristic
136#387×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×C73C2211yescharacteristic
141#386×C73C2211yescharacteristic
142#386×C73C2211yescharacteristic
143#386×C73C2211yescharacteristic
144#386×C73C2211yescharacteristic
145#386×C73C2211yescharacteristic
146#386×C73C2211yescharacteristic
147#386×C73C2211yescharacteristic
148#386×C73C2211yescharacteristic
149#386×C73C2211yescharacteristic
150#386×C73C2211yescharacteristic
151#386×C73C2211yescharacteristic
152#386×C73C2211yescharacteristic
153#386×C73C2211yescharacteristic
154#386×C73C2211yescharacteristic
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic
157#386×C73C2211yescharacteristic
158#385×C73C2211yescharacteristic
159#385×C73C2211yescharacteristic
160#385×C73C2211yescharacteristic
161#385×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic
165#385×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic
167#385×C73C2211yescharacteristic
168#385×C73C2211yescharacteristic
169#383×C73C2211yescharacteristic
170#383×C73C2211yescharacteristic
171#382×C73C2211yescharacteristic
172#382×C73C2211yescharacteristic
173#382×C73C2211yescharacteristic
174#382×C73C2211yescharacteristic
175#381×C73C2211yescharacteristic
176#381×C73C2211yescharacteristic
177#380×C73C2211yescharacteristic
178#380×C73C2211yescharacteristic
179#380×C73C2211yescharacteristic
180#380×C73C2211yescharacteristic
181#380×C73C2211yescharacteristic
182C4×C22⋊C4×C73C2211yescharacteristic
183C2×#95×C73C2211yescharacteristic
184C2×#95×C73C2211yescharacteristic
185C2×#95×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic
187C22×Q8×C73C2311yescharacteristic
188C22×Q8×C73C2311yescharacteristic
189C22×D4×C73C2311yescharacteristic
190C22×D4×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C23×C4×C73C2311yescharacteristic
196C23×C4×C73C2311yescharacteristic
197C23×C4×C73C2311yescharacteristic
198C23×C4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205#126×C73—42no—
206#124×C73—42no—
207#123×C73—42no—
208C22⋊Q8×C73—42no—
209C22⋊Q8×C73—42no—
210C22⋊Q8×C73—42no—
211#121×C73—24no—
212#121×C73—42no—
213#121×C73—42no—
214C4×D4×C73—24no—
215C4×D4×C73—42no—
216C4×D4×C73—42no—
217C2×C4⋊C4×C73—24no—
218C2×C4⋊C4×C73—42no—
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×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊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×C42×C73—42no—
292C2×C42×C73C2311yescharacteristic
293C2×C42×C73C2311yescharacteristic
294C2×C42×C73C2311yescharacteristic
295C2×C42×C73C2311yescharacteristic
296C2×C42×C73C2311yescharacteristic
297C2×C42×C73C2311yescharacteristic
298C2×C42×C73C2311yescharacteristic
299C2×C42×C73C2311yescharacteristic
300C2×C42×C73C2311yescharacteristic
301#95×C73C2311yescharacteristic
302#95×C73C2311yescharacteristic
303#95×C73C2311yescharacteristic
304#95×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×C73C2411yescharacteristic
358C24×C73C2411yescharacteristic
359C24×C73C2411yescharacteristic
360C24×C73C2411yescharacteristic
361C2×Q8×C73—22no—
362C2×Q8×C73—41no—
363C2×Q8×C73—41no—
364C2×Q8×C73—41no—
365C2×Q8×C73—41no—
366C2×Q8×C73—41no—
367C2×D4×C73—22no—
368C2×D4×C73—22no—
369C2×D4×C73—22no—
370C2×D4×C73—22no—
371C2×D4×C73—22no—
372C2×D4×C73—22no—
373C2×D4×C73—22no—
374C2×D4×C73—22no—
375C2×D4×C73—22no—
376C2×D4×C73—22no—
377C2×D4×C73—22no—
378C2×D4×C73—41no—
379C2×D4×C73—41no—
380C2×D4×C73—41no—
381C2×D4×C73—41no—
382C2×D4×C73—41no—
383C2×D4×C73—41no—
384C2×D4×C73—41no—
385C22×C4×C73—22no—
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—41no—
394C22×C4×C73—41no—
395C22×C4×C73—41no—
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—41no—
407C22×C4×C73—41no—
408C22×C4×C73—41no—
409C22×C4×C73—41no—
410C22×C4×C73—41no—
411C22×C4×C73—41no—
412C22×C4×C73—41no—
413C22×C4×C73—41no—
414C22×C4×C73#4114yes—
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
435C22×C4×C73C2411yescharacteristic
436C22×C4×C73C2411yescharacteristic
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C22×C4×C73C2411yescharacteristic
441C22×C4×C73C2411yescharacteristic
442C4⋊C4×C73—22no—
443C4⋊C4×C73—22no—
444C4⋊C4×C73—22no—
445C4⋊C4×C73—22no—
446C4⋊C4×C73—22no—
447C4⋊C4×C73—22no—
448C4⋊C4×C73—22no—
449C4⋊C4×C73—22no—
450C4⋊C4×C73—22no—
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—
469C4⋊C4×C73—41no—
470C4⋊C4×C73—41no—
471C4⋊C4×C73—41no—
472C4⋊C4×C73—41no—
473C4⋊C4×C73—41no—
474C4⋊C4×C73—41no—
475C4⋊C4×C73—41no—
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—22no—
484C22⋊C4×C73—22no—
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—
513C22⋊C4×C73—41no—
514C42×C73—22no—
515C42×C73—22no—
516C42×C73—22no—
517C42×C73—41no—
518C42×C73—41no—
519C42×C73—41no—
520C42×C73—41no—
521C42×C73—41no—
522C42×C73—41no—
523C23×C73—21no—
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×C73C2×#4112yes—
549C23×C73H(5,𝔽2)12yes—
550C23×C732−1+412yes—
551C23×C73C2511yescharacteristic
552Q8×C73—82no—
553Q8×C73—82no—
554D4×C73—44no—
555D4×C73—44no—
556D4×C73—44no—
557D4×C73—82no—
558D4×C73—82no—
559D4×C73—82no—
560C2×C4×C73—21no—
561C2×C4×C73—21no—
562C2×C4×C73—21no—
563C2×C4×C73—21no—
564C2×C4×C73—21no—
565C2×C4×C73—21no—
566C2×C4×C73—21no—
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—44no—
639C2×C4×C73—44no—
640C2×C4×C73—44no—
641C2×C4×C73—44no—
642C2×C4×C73—44no—
643C2×C4×C73—82no—
644C2×C4×C73—82no—
645C2×C4×C73—82no—
646C2×C4×C73—82no—
647C2×C4×C73—82no—
648C2×C4×C73C2×#4112yes—
649C2×C4×C73C2×#4112yes—
650C2×C4×C73H(5,𝔽2)12yes—
651C22×C73—22no—
652C22×C73—22no—
653C22×C73—22no—
654C22×C73—22no—
655C22×C73—22no—
656C22×C73—22no—
657C22×C73—41no—
658C22×C73—41no—
659C22×C73—41no—
660C22×C73—41no—
661C22×C73—41no—
662C22×C73—41no—
663C22×C73—41no—
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#54214yes—
679C22×C73C22×#4111yescharacteristic
680C22×C73C2×H(5,𝔽2)11yescharacteristic
681C22×C73C2×H(5,𝔽2)11yescharacteristic
682C22×C73C2×2−1+411yescharacteristic
683C22×C73#58511yescharacteristic
684C22×C73#58511yescharacteristic
685C22×C73#58511yescharacteristic
686C4×C73—22no—
687C4×C73—22no—
688C4×C73—22no—
689C4×C73—41no—
690C4×C73—41no—
691C4×C73—41no—
692C4×C73—41no—
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—
713#36797C7311yesmaximal, characteristic, direct product factor, Sylow
714C2×C73—24no—
715C2×C73—81no—
716C2×C73—81no—
717C2×C73—81no—
718C2×C73C2×#54211yescharacteristic
719C2×C73#349111yescharacteristic
720C2×C73#350611yescharacteristic
721C2×C73#353411yescharacteristic
722C2×C73#354111yescharacteristic
723C2×C73#355311yescharacteristic
724C2×C73#356011yescharacteristic
725#2852C2×C7311yescharacteristic, complemented
726#2850C2×C7311yescharacteristic, complemented
727#2796C2×C7311yescharacteristic, complemented
728#2775C2×C7311yescharacteristic, complemented
729#2773C2×C7311yescharacteristic, complemented
730#2772C2×C7311yescharacteristic, complemented
731#2770C2×C7311yescharacteristic, complemented
732#2767C2×C7311yescharacteristic, complemented
733#2762C2×C7311yescharacteristic, complemented
734#2754C2×C7311yescharacteristic, complemented
735#2751C2×C7311yescharacteristic, complemented
736#2746C2×C7311yescharacteristic, complemented
737#2741C2×C7311yescharacteristic, complemented
738#2737C2×C7311yescharacteristic, complemented
739#2730C2×C7311yescharacteristic, complemented
740#2717C2×C7311yescharacteristic, complemented
741#2705C2×C7311yescharacteristic, complemented
742#2698C2×C7311yescharacteristic, complemented
743#2643C2×C7311yescharacteristic, complemented
744#2639C2×C7311yescharacteristic, complemented
745#2549C2×C7311yescharacteristic, complemented
746#2543C2×C7311yescharacteristic
747#2504C2×C7311yescharacteristic, complemented
748#2487C2×C7311yescharacteristic, complemented
749#2450C2×C7311yescharacteristic, complemented
750#2449C2×C7311yescharacteristic, complemented
751#2444C2×C7311yescharacteristic, complemented
752#2443C2×C7311yescharacteristic, complemented
753#2325C2×C7311yescharacteristic, complemented
754#2318C2×C7311yescharacteristic, complemented
755C2×#387C2×C7311yescharacteristic, complemented
756C73#3679711yescharacteristic, direct product factor, Sylow
757C2×#126C22×C7311yescharacteristic
758C2×#124C22×C7311yescharacteristic
759C2×#123C22×C7311yescharacteristic
760C2×C22⋊Q8C22×C7311yescharacteristic
761C2×C22⋊Q8C22×C7311yescharacteristic
762C2×C22⋊Q8C22×C7311yescharacteristic
763C2×#121C22×C7311yescharacteristic
764C2×#121C22×C7311yescharacteristic
765C2×#121C22×C7311yescharacteristic
766C2×C4×D4C22×C7311yescharacteristic
767C2×C4×D4C22×C7311yescharacteristic
768C2×C4×D4C22×C7311yescharacteristic
769C22×C4⋊C4C22×C7311yescharacteristic
770C22×C4⋊C4C22×C7311yescharacteristic
771C22×C42C22×C7311yescharacteristic
772#401C22×C7311yescharacteristic
773#400C22×C7311yescharacteristic
774#400C22×C7311yescharacteristic
775#400C22×C7311yescharacteristic
776#400C22×C7311yescharacteristic
777#400C22×C7311yescharacteristic
778#400C22×C7311yescharacteristic
779#400C22×C7311yescharacteristic
780#400C22×C7311yescharacteristic
781#400C22×C7311yescharacteristic
782#399C22×C7311yescharacteristic
783#399C22×C7311yescharacteristic
784#399C22×C7311yescharacteristic
785#399C22×C7311yescharacteristic
786#398C22×C7311yescharacteristic
787#398C22×C7311yescharacteristic
788#398C22×C7311yescharacteristic
789#398C22×C7311yescharacteristic
790#398C22×C7311yescharacteristic
791#398C22×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
800#397C22×C7311yescharacteristic
801#397C22×C7311yescharacteristic
802#397C22×C7311yescharacteristic
803#397C22×C7311yescharacteristic
804#397C22×C7311yescharacteristic
805#396C22×C7311yescharacteristic
806#396C22×C7311yescharacteristic
807#396C22×C7311yescharacteristic
808#395C22×C7311yescharacteristic
809#395C22×C7311yescharacteristic
810#395C22×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#392C22×C7311yescharacteristic
820#391C22×C7311yescharacteristic
821#391C22×C7311yescharacteristic
822#391C22×C7311yescharacteristic
823#391C22×C7311yescharacteristic
824#390C22×C7311yescharacteristic
825#390C22×C7311yescharacteristic
826#390C22×C7311yescharacteristic
827#389C22×C7311yescharacteristic
828#389C22×C7311yescharacteristic
829#389C22×C7311yescharacteristic
830#389C22×C7311yescharacteristic
831#389C22×C7311yescharacteristic
832#388C22×C7311yescharacteristic
833#388C22×C7311yescharacteristic
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#387C22×C7311yescharacteristic
848#387C22×C7311yescharacteristic
849#387C22×C7311yescharacteristic
850#387C22×C7311yescharacteristic
851#387C22×C7311yescharacteristic
852#387C22×C7311yescharacteristic
853#387C22×C7311yescharacteristic
854#387C22×C7311yescharacteristic
855#387C22×C7311yescharacteristic
856#387C22×C7311yescharacteristic
857#387C22×C7311yescharacteristic
858#387C22×C7311yescharacteristic
859#387C22×C7311yescharacteristic
860#387C22×C7311yescharacteristic
861#387C22×C7311yescharacteristic
862#387C22×C7311yescharacteristic
863#387C22×C7311yescharacteristic
864#387C22×C7311yescharacteristic
865#387C22×C7311yescharacteristic
866#386C22×C7311yescharacteristic
867#386C22×C7311yescharacteristic
868#386C22×C7311yescharacteristic
869#386C22×C7311yescharacteristic
870#386C22×C7311yescharacteristic
871#386C22×C7311yescharacteristic
872#386C22×C7311yescharacteristic
873#386C22×C7311yescharacteristic
874#386C22×C7311yescharacteristic
875#386C22×C7311yescharacteristic
876#386C22×C7311yescharacteristic
877#386C22×C7311yescharacteristic
878#386C22×C7311yescharacteristic
879#386C22×C7311yescharacteristic
880#386C22×C7311yescharacteristic
881#386C22×C7311yescharacteristic
882#386C22×C7311yescharacteristic
883#385C22×C7311yescharacteristic
884#385C22×C7311yescharacteristic
885#385C22×C7311yescharacteristic
886#385C22×C7311yescharacteristic
887#385C22×C7311yescharacteristic
888#385C22×C7311yescharacteristic
889#385C22×C7311yescharacteristic
890#385C22×C7311yescharacteristic
891#385C22×C7311yescharacteristic
892#385C22×C7311yescharacteristic
893#385C22×C7311yescharacteristic
894#383C22×C7311yescharacteristic
895#383C22×C7311yescharacteristic
896#382C22×C7311yescharacteristic
897#382C22×C7311yescharacteristic
898#382C22×C7311yescharacteristic
899#382C22×C7311yescharacteristic
900#381C22×C7311yescharacteristic
901#381C22×C7311yescharacteristic
902#380C22×C7311yescharacteristic
903#380C22×C7311yescharacteristic
904#380C22×C7311yescharacteristic
905#380C22×C7311yescharacteristic
906#380C22×C7311yescharacteristic
907C4×C22⋊C4C22×C7311yescharacteristic
908C2×#95C22×C7311yescharacteristic
909C2×#95C22×C7311yescharacteristic
910C2×#95C22×C7311yescharacteristic
911C2×#95C22×C7311yescharacteristic
912C22×Q8C23×C7311yescharacteristic
913C22×Q8C23×C7311yescharacteristic
914C22×D4C23×C7311yescharacteristic
915C22×D4C23×C7311yescharacteristic
916C22×D4C23×C7311yescharacteristic
917C22×D4C23×C7311yescharacteristic
918C22×D4C23×C7311yescharacteristic
919C22×D4C23×C7311yescharacteristic
920C23×C4C23×C7311yescharacteristic
921C23×C4C23×C7311yescharacteristic
922C23×C4C23×C7311yescharacteristic
923C23×C4C23×C7311yescharacteristic
924C23×C4C23×C7311yescharacteristic
925C23×C4C23×C7311yescharacteristic
926C23×C4C23×C7311yescharacteristic
927C23×C4C23×C7311yescharacteristic
928C23×C4C23×C7311yescharacteristic
929C23×C4C23×C7311yescharacteristic
930#126—42no—
931#124—42no—
932#123—42no—
933C22⋊Q8—42no—
934C22⋊Q8—42no—
935C22⋊Q8—42no—
936#121—24no—
937#121—42no—
938#121—42no—
939C4×D4—24no—
940C4×D4—42no—
941C4×D4—42no—
942C2×C4⋊C4—24no—
943C2×C4⋊C4—42no—
944C2×C4⋊C4C23×C7311yescharacteristic
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×C22⋊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×C42—42no—
1017C2×C42C23×C7311yescharacteristic
1018C2×C42C23×C7311yescharacteristic
1019C2×C42C23×C7311yescharacteristic
1020C2×C42C23×C7311yescharacteristic
1021C2×C42C23×C7311yescharacteristic
1022C2×C42C23×C7311yescharacteristic
1023C2×C42C23×C7311yescharacteristic
1024C2×C42C23×C7311yescharacteristic
1025C2×C42C23×C7311yescharacteristic
1026#95C23×C7311yescharacteristic
1027#95C23×C7311yescharacteristic
1028#95C23×C7311yescharacteristic
1029#95C23×C7311yescharacteristic
1030#95C23×C7311yescharacteristic
1031#95C23×C7311yescharacteristic
1032#95C23×C7311yescharacteristic
1033#95C23×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
1082C24C24×C7311yescharacteristic
1083C24C24×C7311yescharacteristic
1084C24C24×C7311yescharacteristic
1085C24C24×C7311yescharacteristic
1086C2×Q8—22no—
1087C2×Q8—41no—
1088C2×Q8—41no—
1089C2×Q8—41no—
1090C2×Q8—41no—
1091C2×Q8—41no—
1092C2×D4—22no—
1093C2×D4—22no—
1094C2×D4—22no—
1095C2×D4—22no—
1096C2×D4—22no—
1097C2×D4—22no—
1098C2×D4—22no—
1099C2×D4—22no—
1100C2×D4—22no—
1101C2×D4—22no—
1102C2×D4—22no—
1103C2×D4—41no—
1104C2×D4—41no—
1105C2×D4—41no—
1106C2×D4—41no—
1107C2×D4—41no—
1108C2×D4—41no—
1109C2×D4—41no—
1110C22×C4—22no—
1111C22×C4—22no—
1112C22×C4—22no—
1113C22×C4—22no—
1114C22×C4—22no—
1115C22×C4—22no—
1116C22×C4—22no—
1117C22×C4—22no—
1118C22×C4—41no—
1119C22×C4—41no—
1120C22×C4—41no—
1121C22×C4—41no—
1122C22×C4—41no—
1123C22×C4—41no—
1124C22×C4—41no—
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—41no—
1136C22×C4—41no—
1137C22×C4—41no—
1138C22×C4—41no—
1139C22×C4#41×C7314yes—
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
1164C22×C4C24×C7311yescharacteristic
1165C22×C4C24×C7311yescharacteristic
1166C22×C4C24×C7311yescharacteristic
1167C4⋊C4—22no—
1168C4⋊C4—22no—
1169C4⋊C4—22no—
1170C4⋊C4—22no—
1171C4⋊C4—22no—
1172C4⋊C4—22no—
1173C4⋊C4—22no—
1174C4⋊C4—22no—
1175C4⋊C4—22no—
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—
1198C4⋊C4—41no—
1199C4⋊C4—41no—
1200C4⋊C4—41no—
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—41no—
1211C22⋊C4—41no—
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—
1239C42—22no—
1240C42—22no—
1241C42—22no—
1242C42—41no—
1243C42—41no—
1244C42—41no—
1245C42—41no—
1246C42—41no—
1247C42—41no—
1248C23—21no—
1249C23—21no—
1250C23—21no—
1251C23—21no—
1252C23—21no—
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—
1273C23C2×#41×C7312yes—
1274C23H(5,𝔽2)×C7312yes—
1275C232−1+4×C7312yes—
1276C23C25×C7311yescharacteristic
1277Q8—82no—
1278Q8—82no—
1279D4—44no—
1280D4—44no—
1281D4—44no—
1282D4—82no—
1283D4—82no—
1284D4—82no—
1285C2×C4—21no—
1286C2×C4—21no—
1287C2×C4—21no—
1288C2×C4—21no—
1289C2×C4—21no—
1290C2×C4—21no—
1291C2×C4—21no—
1292C2×C4—21no—
1293C2×C4—21no—
1294C2×C4—21no—
1295C2×C4—21no—
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—44no—
1364C2×C4—44no—
1365C2×C4—44no—
1366C2×C4—44no—
1367C2×C4—44no—
1368C2×C4—82no—
1369C2×C4—82no—
1370C2×C4—82no—
1371C2×C4—82no—
1372C2×C4—82no—
1373C2×C4C2×#41×C7312yes—
1374C2×C4C2×#41×C7312yes—
1375C2×C4H(5,𝔽2)×C7312yes—
1376C22—22no—
1377C22—22no—
1378C22—22no—
1379C22—22no—
1380C22—22no—
1381C22—22no—
1382C22—41no—
1383C22—41no—
1384C22—41no—
1385C22—41no—
1386C22—41no—
1387C22—41no—
1388C22—41no—
1389C22—41no—
1390C22—41no—
1391C22—41no—
1392C22—41no—
1393C22—41no—
1394C22—41no—
1395C22—41no—
1396C22—41no—
1397C22—41no—
1398C22—41no—
1399C22—41no—
1400C22—41no—
1401C22—41no—
1402C22—41no—
1403C22#542×C7314yes—
1404C22C22×#41×C7311yescharacteristic
1405C22C2×H(5,𝔽2)×C7311yescharacteristic
1406C22C2×H(5,𝔽2)×C7311yescharacteristic
1407C22C2×2−1+4×C7311yescharacteristic
1408C22#585×C7311yescharacteristic
1409C22#585×C7311yescharacteristic
1410C22#585×C7311yescharacteristic
1411C4—22no—
1412C4—22no—
1413C4—22no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—41no—
1419C4—41no—
1420C4—41no—
1421C4—41no—
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—
1438C2—24no—
1439C2—81no—
1440C2—81no—
1441C2—81no—
1442C2C2×#542×C7311yescharacteristic
1443C2C73×#349111yescharacteristic
1444C2C73×#350611yescharacteristic
1445C2C73×#353411yescharacteristic
1446C2C73×#354111yescharacteristic
1447C2C73×#355311yescharacteristic
1448C2C73×#356011yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC73×#2543C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2852C2semidirect
2. C73×#2850C2semidirect
3. C73×#2796C2semidirect
4. C73×#2775C2semidirect
5. C73×#2773C2semidirect
6. C73×#2772C2semidirect
7. C73×#2770C2semidirect
8. C73×#2767C2semidirect
9. C73×#2762C2semidirect
10. C73×#2754C2semidirect
11. C73×#2751C2semidirect
12. C73×#2746C2semidirect
13. C73×#2741C2semidirect
14. C73×#2737C2semidirect
15. C73×#2730C2semidirect
16. C73×#2717C2semidirect
17. C73×#2705C2semidirect
18. C73×#2698C2semidirect
19. C73×#2643C2semidirect
20. C73×#2639C2semidirect
21. C73×#2549C2semidirect
23. C73×#2504C2semidirect
24. C73×#2487C2semidirect
25. C73×#2450C2semidirect
26. C73×#2449C2semidirect
27. C73×#2444C2semidirect
28. C73×#2443C2semidirect
29. C73×#2325C2semidirect
30. C73×#2318C2semidirect
31. C2×#387×C73C2semidirect
713. #36797C73direct (N × H)
725. #2852C2×C73semidirect
726. #2850C2×C73semidirect
727. #2796C2×C73semidirect
728. #2775C2×C73semidirect
729. #2773C2×C73semidirect
730. #2772C2×C73semidirect
731. #2770C2×C73semidirect
732. #2767C2×C73semidirect
733. #2762C2×C73semidirect
734. #2754C2×C73semidirect
735. #2751C2×C73semidirect
736. #2746C2×C73semidirect
737. #2741C2×C73semidirect
738. #2737C2×C73semidirect
739. #2730C2×C73semidirect
740. #2717C2×C73semidirect
741. #2705C2×C73semidirect
742. #2698C2×C73semidirect
743. #2643C2×C73semidirect
744. #2639C2×C73semidirect
745. #2549C2×C73semidirect
747. #2504C2×C73semidirect
748. #2487C2×C73semidirect
749. #2450C2×C73semidirect
750. #2449C2×C73semidirect
751. #2444C2×C73semidirect
752. #2443C2×C73semidirect
753. #2325C2×C73semidirect
754. #2318C2×C73semidirect
755. C2×#387C2×C73semidirect
756. C73#36797direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28522
C73×#28502
C73×#27962
C73×#27752
C73×#27732
C73×#27722
C73×#27702
C73×#27672
C73×#27622
C73×#27542
C73×#27512
C73×#27462
C73×#27412
C73×#27372
C73×#27302
C73×#27172
C73×#27052
C73×#26982
C73×#26432
C73×#26392
C73×#25492
C73×#25432
C73×#25042
C73×#24872
C73×#24502
C73×#24492
C73×#24442
C73×#24432
C73×#23252
C73×#23182
C2×#387×C732
#3679773