Finite Group Databasebeta

← C73×#59912 #32969316

Subgroups — C73×#59912 #32969316

Order 18688.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2806C211yesmaximal, characteristic, complemented
2C73×#2788C211yesmaximal, characteristic, complemented
3C73×#2774C211yesmaximal, characteristic, complemented
4C73×#2729C211yesmaximal, characteristic, complemented
5C73×#2589C211yesmaximal, characteristic, complemented
6C73×#2588C211yesmaximal, characteristic, complemented
7C73×#2588C211yesmaximal, characteristic, complemented
8C73×#2586C211yesmaximal, characteristic, complemented
9C73×#2574C211yesmaximal, characteristic, complemented
10C73×#2556C211yesmaximal, characteristic, complemented
11C73×#2550C211yesmaximal, characteristic, complemented
12C73×#2549C211yesmaximal, characteristic, complemented
13C73×#2520C211yesmaximal, characteristic, complemented
14C73×#2505C211yesmaximal, characteristic, complemented
15C73×#2492C211yesmaximal, characteristic, complemented
16C73×#2473C211yesmaximal, characteristic, complemented
17C73×#2450C211yesmaximal, characteristic
18C73×#2449C211yesmaximal, characteristic
19C73×#2438C211yesmaximal, characteristic, complemented
20C73×#2438C211yesmaximal, characteristic, complemented
21C73×#2434C211yesmaximal, characteristic, complemented
22C73×#2409C211yesmaximal, characteristic
23C73×#2369C211yesmaximal, characteristic, complemented
24C73×#2368C211yesmaximal, characteristic, complemented
25C73×#2368C211yesmaximal, characteristic, complemented
26C73×#2359C211yesmaximal, characteristic
27C73×#2359C211yesmaximal, characteristic
28C73×#2349C211yesmaximal, characteristic
29C4×#123×C73C211yesmaximal, characteristic
30C73×#2296C211yesmaximal, characteristic, complemented
31C2×#391×C73C211yesmaximal, characteristic, complemented
32C23×Q8×C73C2211yescharacteristic
33C2×C4⋊Q8×C73C2211yescharacteristic
34C2×C4⋊Q8×C73C2211yescharacteristic
35C2×#125×C73C2211yescharacteristic
36C2×#123×C73C2211yescharacteristic
37C2×C22⋊Q8×C73C2211yescharacteristic
38C2×C22⋊Q8×C73C2211yescharacteristic
39C2×C22⋊Q8×C73C2211yescharacteristic
40C2×C22⋊Q8×C73C2211yescharacteristic
41C2×C22⋊Q8×C73C2211yescharacteristic
42C2×C4×D4×C73C2211yescharacteristic
43C2×C4×D4×C73C2211yescharacteristic
44C2×C4×D4×C73C2211yescharacteristic
45C2×#117×C73C2211yescharacteristic
46C2×#117×C73C2211yescharacteristic
47C22×C4⋊C4×C73C2211yescharacteristic
48C22×C42×C73C2211yescharacteristic
49#400×C73C2211yescharacteristic
50#400×C73C2211yescharacteristic
51#400×C73C2211yescharacteristic
52#400×C73C2211yescharacteristic
53#400×C73C2211yescharacteristic
54#400×C73C2211yescharacteristic
55#400×C73C2211yescharacteristic
56#399×C73C2211yescharacteristic
57#398×C73C2211yescharacteristic
58#398×C73C2211yescharacteristic
59#398×C73C2211yescharacteristic
60#398×C73C2211yescharacteristic
61#398×C73C2211yescharacteristic
62#398×C73C2211yescharacteristic
63#398×C73C2211yescharacteristic
64#398×C73C2211yescharacteristic
65#398×C73C2211yescharacteristic
66#398×C73C2211yescharacteristic
67#396×C73C2211yescharacteristic
68#396×C73C2211yescharacteristic
69#395×C73C2211yescharacteristic
70#395×C73C2211yescharacteristic
71#395×C73C2211yescharacteristic
72#395×C73C2211yescharacteristic
73#395×C73C2211yescharacteristic
74#395×C73C2211yescharacteristic
75#395×C73C2211yescharacteristic
76#395×C73C2211yescharacteristic
77#395×C73C2211yescharacteristic
78#393×C73C2211yescharacteristic
79#393×C73C2211yescharacteristic
80#393×C73C2211yescharacteristic
81#391×C73C2211yescharacteristic
82#391×C73C2211yescharacteristic
83#391×C73C2211yescharacteristic
84#391×C73C2211yescharacteristic
85#391×C73C2211yescharacteristic
86#391×C73C2211yescharacteristic
87#391×C73C2211yescharacteristic
88#391×C73C2211yescharacteristic
89#391×C73C2211yescharacteristic
90#391×C73C2211yescharacteristic
91#391×C73C2211yescharacteristic
92#391×C73C2211yescharacteristic
93#391×C73C2211yescharacteristic
94#391×C73C2211yescharacteristic
95#391×C73C2211yescharacteristic
96#391×C73C2211yescharacteristic
97#391×C73C2211yescharacteristic
98#389×C73C2211yescharacteristic
99#389×C73C2211yescharacteristic
100#389×C73C2211yescharacteristic
101#389×C73C2211yescharacteristic
102#389×C73C2211yescharacteristic
103#389×C73C2211yescharacteristic
104#389×C73C2211yescharacteristic
105#389×C73C2211yescharacteristic
106#389×C73C2211yescharacteristic
107#389×C73C2211yescharacteristic
108#389×C73C2211yescharacteristic
109#389×C73C2211yescharacteristic
110#389×C73C2211yescharacteristic
111#388×C73C2211yescharacteristic
112#388×C73C2211yescharacteristic
113#388×C73C2211yescharacteristic
114#388×C73C2211yescharacteristic
115#388×C73C2211yescharacteristic
116#388×C73C2211yescharacteristic
117#387×C73C2211yescharacteristic
118#387×C73C2211yescharacteristic
119#387×C73C2211yescharacteristic
120#387×C73C2211yescharacteristic
121#387×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#386×C73C2211yescharacteristic
138#386×C73C2211yescharacteristic
139#386×C73C2211yescharacteristic
140#385×C73C2211yescharacteristic
141#385×C73C2211yescharacteristic
142#385×C73C2211yescharacteristic
143#385×C73C2211yescharacteristic
144#385×C73C2211yescharacteristic
145#385×C73C2211yescharacteristic
146#385×C73C2211yescharacteristic
147#385×C73C2211yescharacteristic
148#385×C73C2211yescharacteristic
149#385×C73C2211yescharacteristic
150#385×C73C2211yescharacteristic
151#385×C73C2211yescharacteristic
152#385×C73C2211yescharacteristic
153#385×C73C2211yescharacteristic
154#385×C73C2211yescharacteristic
155#385×C73C2211yescharacteristic
156#385×C73C2211yescharacteristic
157#382×C73C2211yescharacteristic
158#382×C73C2211yescharacteristic
159#381×C73C2211yescharacteristic
160#380×C73C2211yescharacteristic
161#380×C73C2211yescharacteristic
162#380×C73C2211yescharacteristic
163#380×C73C2211yescharacteristic
164C4×C4⋊C4×C73C2211yescharacteristic
165C4×C4⋊C4×C73C2211yescharacteristic
166C4×C4⋊C4×C73C2211yescharacteristic
167C4×C4⋊C4×C73C2211yescharacteristic
168C4×C4⋊C4×C73C2211yescharacteristic
169C4×C4⋊C4×C73C2211yescharacteristic
170C4×C4⋊C4×C73C2211yescharacteristic
171C4×C4⋊C4×C73C2211yescharacteristic
172C4×C4⋊C4×C73C2211yescharacteristic
173C4×C4⋊C4×C73C2211yescharacteristic
174C4×C4⋊C4×C73C2211yescharacteristic
175C4×C22⋊C4×C73C2211yescharacteristic
176C4×C22⋊C4×C73C2211yescharacteristic
177C4×C22⋊C4×C73C2211yescharacteristic
178C4×C22⋊C4×C73C2211yescharacteristic
179C4×C22⋊C4×C73C2211yescharacteristic
180C4×C22⋊C4×C73C2211yescharacteristic
181C4×C22⋊C4×C73C2211yescharacteristic
182C2×#95×C73C2211yescharacteristic
183C2×#95×C73C2211yescharacteristic
184C2×#95×C73C2211yescharacteristic
185C2×#95×C73C2211yescharacteristic
186C2×#95×C73C2211yescharacteristic
187C22×Q8×C73—24no—
188C22×Q8×C73—42no—
189C22×Q8×C73—42no—
190C22×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×Q8×C73C2311yescharacteristic
193C22×Q8×C73C2311yescharacteristic
194C22×Q8×C73C2311yescharacteristic
195C22×Q8×C73C2311yescharacteristic
196C22×D4×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
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C4⋊Q8×C73—24no—
208C4⋊Q8×C73—42no—
209#125×C73—42no—
210#123×C73Q818yescomplemented
211C22⋊Q8×C73—24no—
212C22⋊Q8×C73—24no—
213C22⋊Q8×C73—42no—
214C22⋊Q8×C73—42no—
215C22⋊Q8×C73—42no—
216C4×D4×C73—24no—
217C4×D4×C73—42no—
218C4×D4×C73—42no—
219#117×C73—24no—
220#117×C73—42no—
221C2×C4⋊C4×C73—42no—
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×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C4⋊C4×C73C2311yescharacteristic
256C2×C4⋊C4×C73C2311yescharacteristic
257C2×C4⋊C4×C73C2311yescharacteristic
258C2×C4⋊C4×C73C2311yescharacteristic
259C2×C4⋊C4×C73C2311yescharacteristic
260C2×C4⋊C4×C73C2311yescharacteristic
261C2×C4⋊C4×C73C2311yescharacteristic
262C2×C4⋊C4×C73C2311yescharacteristic
263C2×C4⋊C4×C73C2311yescharacteristic
264C2×C4⋊C4×C73C2311yescharacteristic
265C2×C4⋊C4×C73C2311yescharacteristic
266C2×C4⋊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×C42×C73—42no—
286C2×C42×C73C2311yescharacteristic
287C2×C42×C73C2311yescharacteristic
288C2×C42×C73C2311yescharacteristic
289C2×C42×C73C2311yescharacteristic
290C2×C42×C73C2311yescharacteristic
291C2×C42×C73C2311yescharacteristic
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
301C2×C42×C73C2311yescharacteristic
302C2×C42×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
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361C24×C73C2411yescharacteristic
362C24×C73C2411yescharacteristic
363C2×Q8×C73—22no—
364C2×Q8×C73—22no—
365C2×Q8×C73—22no—
366C2×Q8×C73—22no—
367C2×Q8×C73—22no—
368C2×Q8×C73—22no—
369C2×Q8×C73—22no—
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×Q8×C73—41no—
378C2×Q8×C73—41no—
379C2×Q8×C73—41no—
380C2×Q8×C73—416no—
381C2×Q8×C73#4114yes—
382C2×D4×C73—22no—
383C2×D4×C73—22no—
384C2×D4×C73C2×Q814yes—
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—22no—
394C22×C4×C73—22no—
395C22×C4×C73—22no—
396C22×C4×C73—22no—
397C22×C4×C73—22no—
398C22×C4×C73—22no—
399C22×C4×C73—22no—
400C22×C4×C73—22no—
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×C73C2×Q814yes—
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
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
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—22no—
452C4⋊C4×C73—22no—
453C4⋊C4×C73—22no—
454C4⋊C4×C73—22no—
455C4⋊C4×C73—22no—
456C4⋊C4×C73—22no—
457C4⋊C4×C73—22no—
458C4⋊C4×C73—22no—
459C4⋊C4×C73—22no—
460C4⋊C4×C73—22no—
461C4⋊C4×C73—22no—
462C4⋊C4×C73—22no—
463C4⋊C4×C73—22no—
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—
476C4⋊C4×C73—41no—
477C4⋊C4×C73—41no—
478C4⋊C4×C73—41no—
479C4⋊C4×C73—41no—
480C4⋊C4×C73—41no—
481C4⋊C4×C73—41no—
482C4⋊C4×C73—41no—
483C4⋊C4×C73—41no—
484C4⋊C4×C73—41no—
485C4⋊C4×C73—41no—
486C4⋊C4×C73—41no—
487C4⋊C4×C73C2×Q814yescomplemented
488C4⋊C4×C73C2×Q814yescomplemented
489C22⋊C4×C73—22no—
490C22⋊C4×C73—22no—
491C22⋊C4×C73—22no—
492C22⋊C4×C73—22no—
493C22⋊C4×C73—22no—
494C22⋊C4×C73—22no—
495C22⋊C4×C73—22no—
496C22⋊C4×C73—22no—
497C22⋊C4×C73—22no—
498C22⋊C4×C73—41no—
499C22⋊C4×C73—41no—
500C22⋊C4×C73—41no—
501C22⋊C4×C73—41no—
502C22⋊C4×C73—41no—
503C22⋊C4×C73C2×Q814yes—
504C22⋊C4×C73C2×Q814yescomplemented
505C22⋊C4×C73C2×Q814yescomplemented
506C22⋊C4×C73#4114yes—
507C42×C73—22no—
508C42×C73—22no—
509C42×C73—22no—
510C42×C73—22no—
511C42×C73—22no—
512C42×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×C73C22×Q812yes—
535C23×C73C22×Q812yes—
536C23×C73C2×#4112yes—
537C23×C73H(5,𝔽2)12yes—
538C23×C73C2511yescharacteristic
539Q8×C73—44no—
540Q8×C73—44no—
541Q8×C73—44no—
542Q8×C73—44no—
543Q8×C73—82no—
544Q8×C73—82no—
545D4×C73—28no—
546C2×C4×C73—28no—
547C2×C4×C73—28no—
548C2×C4×C73—21no—
549C2×C4×C73—21no—
550C2×C4×C73—21no—
551C2×C4×C73—21no—
552C2×C4×C73—21no—
553C2×C4×C73—21no—
554C2×C4×C73—21no—
555C2×C4×C73—21no—
556C2×C4×C73—21no—
557C2×C4×C73—21no—
558C2×C4×C73—21no—
559C2×C4×C73—21no—
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—44no—
624C2×C4×C73—44no—
625C2×C4×C73—44no—
626C2×C4×C73—82no—
627C2×C4×C73—82no—
628C2×C4×C73—82no—
629C2×C4×C73—82no—
630C2×C4×C73—82no—
631C2×C4×C73C22×Q812yes—
632C2×C4×C73C22×Q812yes—
633C2×C4×C73C22×Q812yes—
634C2×C4×C73C22×Q812yes—
635C2×C4×C73C22×Q812yes—
636C2×C4×C73C2×#4112yes—
637C2×C4×C73C2×#4112yes—
638C2×C4×C73C2×#4112yes—
639C2×C4×C73C2×#4112yes—
640C2×C4×C73C2×#4112yes—
641C2×C4×C73H(5,𝔽2)12yes—
642C2×C4×C732−1+412yes—
643C22×C73—22no—
644C22×C73—22no—
645C22×C73—22no—
646C22×C73—22no—
647C22×C73—22no—
648C22×C73—22no—
649C22×C73—22no—
650C22×C73—22no—
651C22×C73—22no—
652C22×C73—41no—
653C22×C73—41no—
654C22×C73—41no—
655C22×C73—41no—
656C22×C73#55414yes—
657C22×C73C23×Q811yescharacteristic
658C22×C73C22×#4111yescharacteristic
659C22×C73C22×#4111yescharacteristic
660C22×C73C2×H(5,𝔽2)11yescharacteristic
661C22×C73C2×H(5,𝔽2)11yescharacteristic
662C22×C73C2×2−1+411yescharacteristic
663C22×C73#58511yescharacteristic
664C4×C73—22no—
665C4×C73—22no—
666C4×C73—22no—
667C4×C73—22no—
668C4×C73—22no—
669C4×C73—22no—
670C4×C73—22no—
671C4×C73—22no—
672C4×C73—22no—
673C4×C73—22no—
674C4×C73—22no—
675C4×C73—22no—
676C4×C73—41no—
677C4×C73—41no—
678C4×C73—41no—
679C4×C73—41no—
680C4×C73—41no—
681C4×C73—41no—
682C4×C73—41no—
683C4×C73—41no—
684C4×C73—41no—
685C4×C73—41no—
686C4×C73—41no—
687C4×C73—41no—
688C4×C73—41no—
689C4×C73—41no—
690C4×C73—41no—
691C4×C73—41no—
692C4×C73—41no—
693#59912C7311yesmaximal, characteristic, direct product factor, Sylow
694C2×C73—24no—
695C2×C73—42no—
696C2×C73C2×#55411yescharacteristic
697C2×C73Q8×#4111yescharacteristic
698C2×C73#348211yescharacteristic
699C2×C73#349011yescharacteristic
700C2×C73#350311yescharacteristic
701C2×C73#351411yescharacteristic
702C2×C73#353511yescharacteristic
703#2806C2×C7311yescharacteristic, complemented
704#2788C2×C7311yescharacteristic, complemented
705#2774C2×C7311yescharacteristic, complemented
706#2729C2×C7311yescharacteristic, complemented
707#2589C2×C7311yescharacteristic, complemented
708#2588C2×C7311yescharacteristic, complemented
709#2588C2×C7311yescharacteristic, complemented
710#2586C2×C7311yescharacteristic, complemented
711#2574C2×C7311yescharacteristic, complemented
712#2556C2×C7311yescharacteristic, complemented
713#2550C2×C7311yescharacteristic, complemented
714#2549C2×C7311yescharacteristic, complemented
715#2520C2×C7311yescharacteristic, complemented
716#2505C2×C7311yescharacteristic, complemented
717#2492C2×C7311yescharacteristic, complemented
718#2473C2×C7311yescharacteristic, complemented
719#2450C2×C7311yescharacteristic
720#2449C2×C7311yescharacteristic
721#2438C2×C7311yescharacteristic, complemented
722#2438C2×C7311yescharacteristic, complemented
723#2434C2×C7311yescharacteristic, complemented
724#2409C2×C7311yescharacteristic
725#2369C2×C7311yescharacteristic, complemented
726#2368C2×C7311yescharacteristic, complemented
727#2368C2×C7311yescharacteristic, complemented
728#2359C2×C7311yescharacteristic
729#2359C2×C7311yescharacteristic
730#2349C2×C7311yescharacteristic
731C4×#123C2×C7311yescharacteristic
732#2296C2×C7311yescharacteristic, complemented
733C2×#391C2×C7311yescharacteristic, complemented
734C73#5991211yescharacteristic, direct product factor, Sylow
735C23×Q8C22×C7311yescharacteristic
736C2×C4⋊Q8C22×C7311yescharacteristic
737C2×C4⋊Q8C22×C7311yescharacteristic
738C2×#125C22×C7311yescharacteristic
739C2×#123C22×C7311yescharacteristic
740C2×C22⋊Q8C22×C7311yescharacteristic
741C2×C22⋊Q8C22×C7311yescharacteristic
742C2×C22⋊Q8C22×C7311yescharacteristic
743C2×C22⋊Q8C22×C7311yescharacteristic
744C2×C22⋊Q8C22×C7311yescharacteristic
745C2×C4×D4C22×C7311yescharacteristic
746C2×C4×D4C22×C7311yescharacteristic
747C2×C4×D4C22×C7311yescharacteristic
748C2×#117C22×C7311yescharacteristic
749C2×#117C22×C7311yescharacteristic
750C22×C4⋊C4C22×C7311yescharacteristic
751C22×C42C22×C7311yescharacteristic
752#400C22×C7311yescharacteristic
753#400C22×C7311yescharacteristic
754#400C22×C7311yescharacteristic
755#400C22×C7311yescharacteristic
756#400C22×C7311yescharacteristic
757#400C22×C7311yescharacteristic
758#400C22×C7311yescharacteristic
759#399C22×C7311yescharacteristic
760#398C22×C7311yescharacteristic
761#398C22×C7311yescharacteristic
762#398C22×C7311yescharacteristic
763#398C22×C7311yescharacteristic
764#398C22×C7311yescharacteristic
765#398C22×C7311yescharacteristic
766#398C22×C7311yescharacteristic
767#398C22×C7311yescharacteristic
768#398C22×C7311yescharacteristic
769#398C22×C7311yescharacteristic
770#396C22×C7311yescharacteristic
771#396C22×C7311yescharacteristic
772#395C22×C7311yescharacteristic
773#395C22×C7311yescharacteristic
774#395C22×C7311yescharacteristic
775#395C22×C7311yescharacteristic
776#395C22×C7311yescharacteristic
777#395C22×C7311yescharacteristic
778#395C22×C7311yescharacteristic
779#395C22×C7311yescharacteristic
780#395C22×C7311yescharacteristic
781#393C22×C7311yescharacteristic
782#393C22×C7311yescharacteristic
783#393C22×C7311yescharacteristic
784#391C22×C7311yescharacteristic
785#391C22×C7311yescharacteristic
786#391C22×C7311yescharacteristic
787#391C22×C7311yescharacteristic
788#391C22×C7311yescharacteristic
789#391C22×C7311yescharacteristic
790#391C22×C7311yescharacteristic
791#391C22×C7311yescharacteristic
792#391C22×C7311yescharacteristic
793#391C22×C7311yescharacteristic
794#391C22×C7311yescharacteristic
795#391C22×C7311yescharacteristic
796#391C22×C7311yescharacteristic
797#391C22×C7311yescharacteristic
798#391C22×C7311yescharacteristic
799#391C22×C7311yescharacteristic
800#391C22×C7311yescharacteristic
801#389C22×C7311yescharacteristic
802#389C22×C7311yescharacteristic
803#389C22×C7311yescharacteristic
804#389C22×C7311yescharacteristic
805#389C22×C7311yescharacteristic
806#389C22×C7311yescharacteristic
807#389C22×C7311yescharacteristic
808#389C22×C7311yescharacteristic
809#389C22×C7311yescharacteristic
810#389C22×C7311yescharacteristic
811#389C22×C7311yescharacteristic
812#389C22×C7311yescharacteristic
813#389C22×C7311yescharacteristic
814#388C22×C7311yescharacteristic
815#388C22×C7311yescharacteristic
816#388C22×C7311yescharacteristic
817#388C22×C7311yescharacteristic
818#388C22×C7311yescharacteristic
819#388C22×C7311yescharacteristic
820#387C22×C7311yescharacteristic
821#387C22×C7311yescharacteristic
822#387C22×C7311yescharacteristic
823#387C22×C7311yescharacteristic
824#387C22×C7311yescharacteristic
825#387C22×C7311yescharacteristic
826#387C22×C7311yescharacteristic
827#387C22×C7311yescharacteristic
828#387C22×C7311yescharacteristic
829#387C22×C7311yescharacteristic
830#387C22×C7311yescharacteristic
831#387C22×C7311yescharacteristic
832#387C22×C7311yescharacteristic
833#387C22×C7311yescharacteristic
834#387C22×C7311yescharacteristic
835#387C22×C7311yescharacteristic
836#387C22×C7311yescharacteristic
837#387C22×C7311yescharacteristic
838#387C22×C7311yescharacteristic
839#387C22×C7311yescharacteristic
840#386C22×C7311yescharacteristic
841#386C22×C7311yescharacteristic
842#386C22×C7311yescharacteristic
843#385C22×C7311yescharacteristic
844#385C22×C7311yescharacteristic
845#385C22×C7311yescharacteristic
846#385C22×C7311yescharacteristic
847#385C22×C7311yescharacteristic
848#385C22×C7311yescharacteristic
849#385C22×C7311yescharacteristic
850#385C22×C7311yescharacteristic
851#385C22×C7311yescharacteristic
852#385C22×C7311yescharacteristic
853#385C22×C7311yescharacteristic
854#385C22×C7311yescharacteristic
855#385C22×C7311yescharacteristic
856#385C22×C7311yescharacteristic
857#385C22×C7311yescharacteristic
858#385C22×C7311yescharacteristic
859#385C22×C7311yescharacteristic
860#382C22×C7311yescharacteristic
861#382C22×C7311yescharacteristic
862#381C22×C7311yescharacteristic
863#380C22×C7311yescharacteristic
864#380C22×C7311yescharacteristic
865#380C22×C7311yescharacteristic
866#380C22×C7311yescharacteristic
867C4×C4⋊C4C22×C7311yescharacteristic
868C4×C4⋊C4C22×C7311yescharacteristic
869C4×C4⋊C4C22×C7311yescharacteristic
870C4×C4⋊C4C22×C7311yescharacteristic
871C4×C4⋊C4C22×C7311yescharacteristic
872C4×C4⋊C4C22×C7311yescharacteristic
873C4×C4⋊C4C22×C7311yescharacteristic
874C4×C4⋊C4C22×C7311yescharacteristic
875C4×C4⋊C4C22×C7311yescharacteristic
876C4×C4⋊C4C22×C7311yescharacteristic
877C4×C4⋊C4C22×C7311yescharacteristic
878C4×C22⋊C4C22×C7311yescharacteristic
879C4×C22⋊C4C22×C7311yescharacteristic
880C4×C22⋊C4C22×C7311yescharacteristic
881C4×C22⋊C4C22×C7311yescharacteristic
882C4×C22⋊C4C22×C7311yescharacteristic
883C4×C22⋊C4C22×C7311yescharacteristic
884C4×C22⋊C4C22×C7311yescharacteristic
885C2×#95C22×C7311yescharacteristic
886C2×#95C22×C7311yescharacteristic
887C2×#95C22×C7311yescharacteristic
888C2×#95C22×C7311yescharacteristic
889C2×#95C22×C7311yescharacteristic
890C22×Q8—24no—
891C22×Q8—42no—
892C22×Q8—42no—
893C22×Q8C23×C7311yescharacteristic
894C22×Q8C23×C7311yescharacteristic
895C22×Q8C23×C7311yescharacteristic
896C22×Q8C23×C7311yescharacteristic
897C22×Q8C23×C7311yescharacteristic
898C22×Q8C23×C7311yescharacteristic
899C22×D4C23×C7311yescharacteristic
900C23×C4C23×C7311yescharacteristic
901C23×C4C23×C7311yescharacteristic
902C23×C4C23×C7311yescharacteristic
903C23×C4C23×C7311yescharacteristic
904C23×C4C23×C7311yescharacteristic
905C23×C4C23×C7311yescharacteristic
906C23×C4C23×C7311yescharacteristic
907C23×C4C23×C7311yescharacteristic
908C23×C4C23×C7311yescharacteristic
909C23×C4C23×C7311yescharacteristic
910C4⋊Q8—24no—
911C4⋊Q8—42no—
912#125—42no—
913#123Q8×C7318yescomplemented
914C22⋊Q8—24no—
915C22⋊Q8—24no—
916C22⋊Q8—42no—
917C22⋊Q8—42no—
918C22⋊Q8—42no—
919C4×D4—24no—
920C4×D4—42no—
921C4×D4—42no—
922#117—24no—
923#117—42no—
924C2×C4⋊C4—42no—
925C2×C4⋊C4C23×C7311yescharacteristic
926C2×C4⋊C4C23×C7311yescharacteristic
927C2×C4⋊C4C23×C7311yescharacteristic
928C2×C4⋊C4C23×C7311yescharacteristic
929C2×C4⋊C4C23×C7311yescharacteristic
930C2×C4⋊C4C23×C7311yescharacteristic
931C2×C4⋊C4C23×C7311yescharacteristic
932C2×C4⋊C4C23×C7311yescharacteristic
933C2×C4⋊C4C23×C7311yescharacteristic
934C2×C4⋊C4C23×C7311yescharacteristic
935C2×C4⋊C4C23×C7311yescharacteristic
936C2×C4⋊C4C23×C7311yescharacteristic
937C2×C4⋊C4C23×C7311yescharacteristic
938C2×C4⋊C4C23×C7311yescharacteristic
939C2×C4⋊C4C23×C7311yescharacteristic
940C2×C4⋊C4C23×C7311yescharacteristic
941C2×C4⋊C4C23×C7311yescharacteristic
942C2×C4⋊C4C23×C7311yescharacteristic
943C2×C4⋊C4C23×C7311yescharacteristic
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×C22⋊C4C23×C7311yescharacteristic
971C2×C22⋊C4C23×C7311yescharacteristic
972C2×C22⋊C4C23×C7311yescharacteristic
973C2×C22⋊C4C23×C7311yescharacteristic
974C2×C22⋊C4C23×C7311yescharacteristic
975C2×C22⋊C4C23×C7311yescharacteristic
976C2×C22⋊C4C23×C7311yescharacteristic
977C2×C22⋊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×C42—42no—
989C2×C42C23×C7311yescharacteristic
990C2×C42C23×C7311yescharacteristic
991C2×C42C23×C7311yescharacteristic
992C2×C42C23×C7311yescharacteristic
993C2×C42C23×C7311yescharacteristic
994C2×C42C23×C7311yescharacteristic
995C2×C42C23×C7311yescharacteristic
996C2×C42C23×C7311yescharacteristic
997C2×C42C23×C7311yescharacteristic
998C2×C42C23×C7311yescharacteristic
999C2×C42C23×C7311yescharacteristic
1000C2×C42C23×C7311yescharacteristic
1001C2×C42C23×C7311yescharacteristic
1002C2×C42C23×C7311yescharacteristic
1003C2×C42C23×C7311yescharacteristic
1004C2×C42C23×C7311yescharacteristic
1005C2×C42C23×C7311yescharacteristic
1006#95C23×C7311yescharacteristic
1007#95C23×C7311yescharacteristic
1008#95C23×C7311yescharacteristic
1009#95C23×C7311yescharacteristic
1010#95C23×C7311yescharacteristic
1011#95C23×C7311yescharacteristic
1012#95C23×C7311yescharacteristic
1013#95C23×C7311yescharacteristic
1014#95C23×C7311yescharacteristic
1015#95C23×C7311yescharacteristic
1016#95C23×C7311yescharacteristic
1017#95C23×C7311yescharacteristic
1018#95C23×C7311yescharacteristic
1019#95C23×C7311yescharacteristic
1020#95C23×C7311yescharacteristic
1021#95C23×C7311yescharacteristic
1022#95C23×C7311yescharacteristic
1023#95C23×C7311yescharacteristic
1024#95C23×C7311yescharacteristic
1025#95C23×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
1064C24C24×C7311yescharacteristic
1065C24C24×C7311yescharacteristic
1066C2×Q8—22no—
1067C2×Q8—22no—
1068C2×Q8—22no—
1069C2×Q8—22no—
1070C2×Q8—22no—
1071C2×Q8—22no—
1072C2×Q8—22no—
1073C2×Q8—41no—
1074C2×Q8—41no—
1075C2×Q8—41no—
1076C2×Q8—41no—
1077C2×Q8—41no—
1078C2×Q8—41no—
1079C2×Q8—41no—
1080C2×Q8—41no—
1081C2×Q8—41no—
1082C2×Q8—41no—
1083C2×Q8—416no—
1084C2×Q8#41×C7314yes—
1085C2×D4—22no—
1086C2×D4—22no—
1087C2×D4C2×Q8×C7314yes—
1088C22×C4—22no—
1089C22×C4—22no—
1090C22×C4—22no—
1091C22×C4—22no—
1092C22×C4—22no—
1093C22×C4—22no—
1094C22×C4—22no—
1095C22×C4—22no—
1096C22×C4—22no—
1097C22×C4—22no—
1098C22×C4—22no—
1099C22×C4—22no—
1100C22×C4—22no—
1101C22×C4—22no—
1102C22×C4—22no—
1103C22×C4—22no—
1104C22×C4—41no—
1105C22×C4—41no—
1106C22×C4—41no—
1107C22×C4—41no—
1108C22×C4—41no—
1109C22×C4—41no—
1110C22×C4—41no—
1111C22×C4—41no—
1112C22×C4—41no—
1113C22×C4—41no—
1114C22×C4—41no—
1115C22×C4—41no—
1116C22×C4—41no—
1117C22×C4C2×Q8×C7314yes—
1118C22×C4C24×C7311yescharacteristic
1119C22×C4C24×C7311yescharacteristic
1120C22×C4C24×C7311yescharacteristic
1121C22×C4C24×C7311yescharacteristic
1122C22×C4C24×C7311yescharacteristic
1123C22×C4C24×C7311yescharacteristic
1124C22×C4C24×C7311yescharacteristic
1125C22×C4C24×C7311yescharacteristic
1126C22×C4C24×C7311yescharacteristic
1127C22×C4C24×C7311yescharacteristic
1128C22×C4C24×C7311yescharacteristic
1129C22×C4C24×C7311yescharacteristic
1130C22×C4C24×C7311yescharacteristic
1131C22×C4C24×C7311yescharacteristic
1132C22×C4C24×C7311yescharacteristic
1133C22×C4C24×C7311yescharacteristic
1134C22×C4C24×C7311yescharacteristic
1135C22×C4C24×C7311yescharacteristic
1136C22×C4C24×C7311yescharacteristic
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
1147C4⋊C4—22no—
1148C4⋊C4—22no—
1149C4⋊C4—22no—
1150C4⋊C4—22no—
1151C4⋊C4—22no—
1152C4⋊C4—22no—
1153C4⋊C4—22no—
1154C4⋊C4—22no—
1155C4⋊C4—22no—
1156C4⋊C4—22no—
1157C4⋊C4—22no—
1158C4⋊C4—22no—
1159C4⋊C4—22no—
1160C4⋊C4—22no—
1161C4⋊C4—22no—
1162C4⋊C4—22no—
1163C4⋊C4—22no—
1164C4⋊C4—22no—
1165C4⋊C4—22no—
1166C4⋊C4—22no—
1167C4⋊C4—41no—
1168C4⋊C4—41no—
1169C4⋊C4—41no—
1170C4⋊C4—41no—
1171C4⋊C4—41no—
1172C4⋊C4—41no—
1173C4⋊C4—41no—
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⋊C4C2×Q8×C7314yescomplemented
1191C4⋊C4C2×Q8×C7314yescomplemented
1192C22⋊C4—22no—
1193C22⋊C4—22no—
1194C22⋊C4—22no—
1195C22⋊C4—22no—
1196C22⋊C4—22no—
1197C22⋊C4—22no—
1198C22⋊C4—22no—
1199C22⋊C4—22no—
1200C22⋊C4—22no—
1201C22⋊C4—41no—
1202C22⋊C4—41no—
1203C22⋊C4—41no—
1204C22⋊C4—41no—
1205C22⋊C4—41no—
1206C22⋊C4C2×Q8×C7314yes—
1207C22⋊C4C2×Q8×C7314yescomplemented
1208C22⋊C4C2×Q8×C7314yescomplemented
1209C22⋊C4#41×C7314yes—
1210C42—22no—
1211C42—22no—
1212C42—22no—
1213C42—22no—
1214C42—22no—
1215C42—41no—
1216C42—41no—
1217C42—41no—
1218C42—41no—
1219C42—41no—
1220C42—41no—
1221C42—41no—
1222C42—41no—
1223C42—41no—
1224C42—41no—
1225C42—41no—
1226C42—41no—
1227C23—21no—
1228C23—21no—
1229C23—21no—
1230C23—21no—
1231C23—21no—
1232C23—21no—
1233C23—21no—
1234C23—21no—
1235C23—21no—
1236C23—21no—
1237C23C22×Q8×C7312yes—
1238C23C22×Q8×C7312yes—
1239C23C2×#41×C7312yes—
1240C23H(5,𝔽2)×C7312yes—
1241C23C25×C7311yescharacteristic
1242Q8—44no—
1243Q8—44no—
1244Q8—44no—
1245Q8—44no—
1246Q8—82no—
1247Q8—82no—
1248D4—28no—
1249C2×C4—28no—
1250C2×C4—28no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—21no—
1268C2×C4—21no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—21no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
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—44no—
1327C2×C4—44no—
1328C2×C4—44no—
1329C2×C4—82no—
1330C2×C4—82no—
1331C2×C4—82no—
1332C2×C4—82no—
1333C2×C4—82no—
1334C2×C4C22×Q8×C7312yes—
1335C2×C4C22×Q8×C7312yes—
1336C2×C4C22×Q8×C7312yes—
1337C2×C4C22×Q8×C7312yes—
1338C2×C4C22×Q8×C7312yes—
1339C2×C4C2×#41×C7312yes—
1340C2×C4C2×#41×C7312yes—
1341C2×C4C2×#41×C7312yes—
1342C2×C4C2×#41×C7312yes—
1343C2×C4C2×#41×C7312yes—
1344C2×C4H(5,𝔽2)×C7312yes—
1345C2×C42−1+4×C7312yes—
1346C22—22no—
1347C22—22no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—22no—
1352C22—22no—
1353C22—22no—
1354C22—22no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22#554×C7314yes—
1360C22C23×Q8×C7311yescharacteristic
1361C22C22×#41×C7311yescharacteristic
1362C22C22×#41×C7311yescharacteristic
1363C22C2×H(5,𝔽2)×C7311yescharacteristic
1364C22C2×H(5,𝔽2)×C7311yescharacteristic
1365C22C2×2−1+4×C7311yescharacteristic
1366C22#585×C7311yescharacteristic
1367C4—22no—
1368C4—22no—
1369C4—22no—
1370C4—22no—
1371C4—22no—
1372C4—22no—
1373C4—22no—
1374C4—22no—
1375C4—22no—
1376C4—22no—
1377C4—22no—
1378C4—22no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—41no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C2—24no—
1397C2—42no—
1398C2C2×#554×C7311yescharacteristic
1399C2Q8×#41×C7311yescharacteristic
1400C2C73×#348211yescharacteristic
1401C2C73×#349011yescharacteristic
1402C2C73×#350311yescharacteristic
1403C2C73×#351411yescharacteristic
1404C2C73×#353511yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC22×D4×C73C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2806C2semidirect
2. C73×#2788C2semidirect
3. C73×#2774C2semidirect
4. C73×#2729C2semidirect
5. C73×#2589C2semidirect
6. C73×#2588C2semidirect
7. C73×#2588C2semidirect
8. C73×#2586C2semidirect
9. C73×#2574C2semidirect
10. C73×#2556C2semidirect
11. C73×#2550C2semidirect
12. C73×#2549C2semidirect
13. C73×#2520C2semidirect
14. C73×#2505C2semidirect
15. C73×#2492C2semidirect
16. C73×#2473C2semidirect
19. C73×#2438C2semidirect
20. C73×#2438C2semidirect
21. C73×#2434C2semidirect
23. C73×#2369C2semidirect
24. C73×#2368C2semidirect
25. C73×#2368C2semidirect
30. C73×#2296C2semidirect
31. C2×#391×C73C2semidirect
210. #123×C73Q8semidirect
487. C4⋊C4×C73C2×Q8semidirect
488. C4⋊C4×C73C2×Q8semidirect
504. C22⋊C4×C73C2×Q8semidirect
505. C22⋊C4×C73C2×Q8semidirect
693. #59912C73direct (N × H)
703. #2806C2×C73semidirect
704. #2788C2×C73semidirect
705. #2774C2×C73semidirect
706. #2729C2×C73semidirect
707. #2589C2×C73semidirect
708. #2588C2×C73semidirect
709. #2588C2×C73semidirect
710. #2586C2×C73semidirect
711. #2574C2×C73semidirect
712. #2556C2×C73semidirect
713. #2550C2×C73semidirect
714. #2549C2×C73semidirect
715. #2520C2×C73semidirect
716. #2505C2×C73semidirect
717. #2492C2×C73semidirect
718. #2473C2×C73semidirect
721. #2438C2×C73semidirect
722. #2438C2×C73semidirect
723. #2434C2×C73semidirect
725. #2369C2×C73semidirect
726. #2368C2×C73semidirect
727. #2368C2×C73semidirect
732. #2296C2×C73semidirect
733. C2×#391C2×C73semidirect
734. C73#59912direct (N × H)
913. #123Q8×C73semidirect
1190. C4⋊C4C2×Q8×C73semidirect
1191. C4⋊C4C2×Q8×C73semidirect
1207. C22⋊C4C2×Q8×C73semidirect
1208. C22⋊C4C2×Q8×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28062
C73×#27882
C73×#27742
C73×#27292
C73×#25892
C73×#25882
C73×#25862
C73×#25742
C73×#25562
C73×#25502
C73×#25492
C73×#25202
C73×#25052
C73×#24922
C73×#24732
C73×#24502
C73×#24492
C73×#24382
C73×#24342
C73×#24092
C73×#23692
C73×#23682
C73×#23592
C73×#23492
C4×#123×C732
C73×#22962
C2×#391×C732
#5991273