Finite Group Databasebeta

← C2×#22591340 #32156964

Subgroups — C2×#22591340 #32156964

Order 18176.

3614 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556105C211yesmaximal, characteristic
2C22×#14556093C211yesmaximal, characteristic, complemented
3C23×Dic71⋊C4C211yesmaximal, characteristic
4#22591340C2116yesmaximal, direct product factor
5C2×#17985903C211yesmaximal, characteristic, complemented
6C2×#17985895C211yesmaximal, characteristic, complemented
7C2×#17985894C211yesmaximal, characteristic, complemented
8C2×#17985894C211yesmaximal, characteristic, complemented
9C2×#17985884C211yesmaximal, characteristic, complemented
10C2×#17985881C211yesmaximal, characteristic, complemented
11C2×#17985871C211yesmaximal, characteristic
12C2×#17985850C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic71C211yesmaximal, characteristic
14C2×C22⋊C4×Dic71C211yesmaximal, characteristic
15C2×C4×C22⋊Dic71C211yesmaximal, characteristic
16C2×#385×C71C211yesmaximal, characteristic
17C23×Dic142C2211yescharacteristic
18C24×Dic71C2211yescharacteristic
19C24×Dic71C2211yescharacteristic
20C2×#14556105C4116yescomplemented
21C2×#14556105C2218yes—
22C2×#14556093—28no—
23C2×#14556093C2218yescomplemented
24C22×C4⋊Dic71C2211yescharacteristic
25C22×Dic71⋊C4—28no—
26C22×Dic71⋊C4C2211yescharacteristic
27C22×Dic71⋊C4C2211yescharacteristic
28C22×Dic71⋊C4C2211yescharacteristic
29C22×Dic71⋊C4C2218yes—
30C22×Dic71⋊C4C2211yescharacteristic
31C22×Dic71⋊C4C2211yescharacteristic
32C22×Dic71⋊C4C2211yescharacteristic
33C22×Dic71⋊C4C2211yescharacteristic
34C22×Dic71⋊C4C2211yescharacteristic
35C22×C22⋊Dic71C2211yescharacteristic
36C22×C22⋊Dic71C2211yescharacteristic
37C22×C4×Dic71C2211yescharacteristic
38C22×C4×Dic71C2211yescharacteristic
39C22×C4×Dic71C2211yescharacteristic
40C22×C4×Dic71C2211yescharacteristic
41C22×C4×Dic71C2211yescharacteristic
42C22×C4×Dic71C2211yescharacteristic
43#17985903C2218yescomplemented
44#17985895C2218yescomplemented
45#17985894C2218yescomplemented
46#17985894C2218yescomplemented
47#17985884C2218yescomplemented
48#17985881C2218yescomplemented
49#17985871C2218yes—
50#17985850C2218yescomplemented
51C22⋊C4×Dic71C2218yes—
52C22⋊C4×Dic71C2218yes—
53C4×C22⋊Dic71C2218yes—
54C2×C71⋊#95C2211yescharacteristic
55C2×C71⋊#95C2211yescharacteristic
56C2×C71⋊#95C2211yescharacteristic
57C2×C71⋊#95C2211yescharacteristic
58C2×C71⋊#95C2211yescharacteristic
59C2×C71⋊#95C2211yescharacteristic
60C2×C71⋊#95C2211yescharacteristic
61C2×C71⋊#95C2211yescharacteristic
62C24×C4×C71C2211yescharacteristic
63C22×C4⋊C4×C71C2211yescharacteristic
64C22×C4⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C22⋊C4×C71C2211yescharacteristic
67#385×C71C2218yes—
68C2×#95×C71C2211yescharacteristic
69C2×#95×C71C2211yescharacteristic
70C22×Dic142—24no—
71C22×Dic142—24no—
72C22×Dic142C2×C418yescomplemented
73C22×Dic142C2314yes—
74C23×Dic71—24no—
75C23×Dic71—24no—
76C23×Dic71—24no—
77C23×Dic71—24no—
78C23×Dic71—42no—
79C23×Dic71C2×C418yes—
80C23×Dic71C2311yescharacteristic
81C23×Dic71C2314yes—
82C23×Dic71C2311yescharacteristic
83C23×Dic71C2314yes—
84C23×Dic71C2311yescharacteristic
85C23×Dic71C2311yescharacteristic
86C23×Dic71C2311yescharacteristic
87C23×Dic71C2311yescharacteristic
88C23×Dic71C2311yescharacteristic
89C23×Dic71C2311yescharacteristic
90#14556105C2×C4164yescomplemented
91#14556093—232no—
92C2×C4⋊Dic71C2×C418yescomplemented
93C2×C4⋊Dic71C2314yes—
94C2×Dic71⋊C4—24no—
95C2×Dic71⋊C4—24no—
96C2×Dic71⋊C4—24no—
97C2×Dic71⋊C4—232no—
98C2×Dic71⋊C4—24no—
99C2×Dic71⋊C4—42no—
100C2×Dic71⋊C4C2×C418yescomplemented
101C2×Dic71⋊C4C2×C418yescomplemented
102C2×Dic71⋊C4D418yes—
103C2×Dic71⋊C4C2314yes—
104C2×Dic71⋊C4C2314yes—
105C2×Dic71⋊C4C2314yes—
106C2×Dic71⋊C4C2314yes—
107C2×Dic71⋊C4C2314yes—
108C2×Dic71⋊C4C2314yes—
109C2×Dic71⋊C4C2314yes—
110C2×Dic71⋊C4C2314yes—
111C2×C22⋊Dic71C2×C418yes—
112C2×C22⋊Dic71Q818yescomplemented
113C2×C22⋊Dic71C2314yes—
114C2×C22⋊Dic71C2314yes—
115C2×C4×Dic71—24no—
116C2×C4×Dic71—24no—
117C2×C4×Dic71—24no—
118C2×C4×Dic71—24no—
119C2×C4×Dic71—42no—
120C2×C4×Dic71—42no—
121C2×C4×Dic71C2314yes—
122C2×C4×Dic71C2314yes—
123C2×C4×Dic71C2314yes—
124C2×C4×Dic71C2314yes—
125C2×C4×Dic71C2314yes—
126C2×C4×Dic71C2314yes—
127C71⋊#95C2314yes—
128C71⋊#95C2314yes—
129C71⋊#95C2314yes—
130C71⋊#95C2314yes—
131C71⋊#95C2314yes—
132C71⋊#95C2314yes—
133C71⋊#95C2314yes—
134C71⋊#95C2314yes—
135C25×C71C2311yescharacteristic
136C23×C4×C71—24no—
137C23×C4×C71—24no—
138C23×C4×C71—42no—
139C23×C4×C71C2311yescharacteristic
140C23×C4×C71C2311yescharacteristic
141C23×C4×C71C2311yescharacteristic
142C23×C4×C71C2314yes—
143C23×C4×C71C2311yescharacteristic
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146C2×C4⋊C4×C71—24no—
147C2×C4⋊C4×C71—42no—
148C2×C4⋊C4×C71C2314yes—
149C2×C4⋊C4×C71C2314yes—
150C2×C22⋊C4×C71—24no—
151C2×C22⋊C4×C71C2×C418yes—
152C2×C22⋊C4×C71C2314yes—
153C2×C22⋊C4×C71C2314yes—
154#95×C71C2314yes—
155#95×C71C2314yes—
156C2×Dic142—232no—
157C2×Dic142—28no—
158C2×Dic142—28no—
159C2×Dic142C22×C4116yescomplemented
160C22×Dic71—22no—
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—22no—
164C22×Dic71—22no—
165C22×Dic71—22no—
166C22×Dic71—22no—
167C22×Dic71—22no—
168C22×Dic71—22no—
169C22×Dic71—22no—
170C22×Dic71—22no—
171C22×Dic71—22no—
172C22×Dic71—232no—
173C22×Dic71—28no—
174C22×Dic71—28no—
175C22×Dic71—22no—
176C22×Dic71—28no—
177C22×Dic71—22no—
178C22×Dic71—22no—
179C22×Dic71—28no—
180C22×Dic71—44no—
181C22×Dic71—416no—
182C22×Dic71C22×C414yes—
183C22×Dic71C22×C4116yes—
184C22×Dic71C22×C414yes—
185C22×Dic71C22×C414yes—
186C22×Dic71C22×C414yes—
187C22×Dic71C2×D414yes—
188C22×Dic71C2×D414yes—
189C22×Dic71C2×Q814yes—
190C22×Dic71C2×Q814yes—
191C22×Dic71#4114yes—
192C22×Dic71C2412yes—
193C22×Dic71C2412yes—
194C22×Dic71C2412yes—
195C22×Dic71C2412yes—
196C22×Dic71C2412yes—
197C22×Dic71C2412yes—
198C22×Dic71C2412yes—
199C22×Dic71C2412yes—
200C4⋊Dic71C22×C4116yescomplemented
201Dic71⋊C4—28no—
202Dic71⋊C4—28no—
203Dic71⋊C4—28no—
204Dic71⋊C4—28no—
205Dic71⋊C4—44no—
206Dic71⋊C4C22×C4116yescomplemented
207Dic71⋊C4C22×C4116yescomplemented
208Dic71⋊C4C2×D4116yes—
209C22⋊Dic71C22×C4116yes—
210C22⋊Dic71C2×Q8116yescomplemented
211C4×Dic71—28no—
212C4×Dic71—28no—
213C4×Dic71—28no—
214C4×Dic71—28no—
215C4×Dic71—44no—
216C4×Dic71—44no—
217C24×C71—22no—
218C24×C71—22no—
219C24×C71—22no—
220C24×C71—22no—
221C24×C71C22×C414yes—
222C24×C71C2×Q814yes—
223C24×C71#4114yes—
224C24×C71C2412yes—
225C24×C71C2411yescharacteristic
226C22×C4×C71—22no—
227C22×C4×C71—22no—
228C22×C4×C71—22no—
229C22×C4×C71—22no—
230C22×C4×C71—22no—
231C22×C4×C71—22no—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—28no—
237C22×C4×C71—22no—
238C22×C4×C71—22no—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—22no—
242C22×C4×C71—28no—
243C22×C4×C71—44no—
244C22×C4×C71—416no—
245C22×C4×C71C22×C414yes—
246C22×C4×C71C22×C414yes—
247C22×C4×C71C2×D414yes—
248C22×C4×C71C2412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2412yes—
253C22×C4×C71C2412yes—
254C4⋊C4×C71—28no—
255C4⋊C4×C71—44no—
256C22⋊C4×C71—28no—
257C22⋊C4×C71C22×C4116yes—
258C23×C71—28no—
259C23×C71—28no—
260C23×C71—28no—
261C23×C71—28no—
262C23×C71—28no—
263C23×C71—28no—
264C23×C71—22no—
265C23×C71—22no—
266C23×C71—22no—
267C23×C71—22no—
268C23×C71C4×Q8116yescomplemented
269C23×C71C23×C414yes—
270C23×C71C23×C412yes—
271C23×C71C22×D412yes—
272C23×C71C22×Q814yes—
273C23×C71C22×Q812yes—
274C23×C71C2×#4112yes—
275C23×C71C2×#4114yes—
276C23×C71C2×#4112yes—
277C23×C71H(5,𝔽2)12yes—
278C23×C712−1+412yes—
279C23×C71C2511yescharacteristic
280C2×C4×C71—28no—
281C2×C4×C71—28no—
282C2×C4×C71—28no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—416no—
299C2×C4×C71—44no—
300C2×C4×C71—44no—
301C2×C4×C71—44no—
302C2×C4×C71C23×C414yes—
303C2×C4×C71C23×C414yes—
304C2×C4×C71C22×D414yes—
305C2×Dic71—28no—
306C2×Dic71—28no—
307C2×Dic71—28no—
308C2×Dic71—28no—
309C2×Dic71—28no—
310C2×Dic71—28no—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—232no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—416no—
328C2×Dic71—44no—
329C2×Dic71C4×D4116yes—
330C2×Dic71C23×C414yes—
331C2×Dic71C23×C414yes—
332C2×Dic71C23×C414yes—
333C2×Dic71C23×C414yes—
334C2×Dic71C22×D414yes—
335C2×Dic71C22×D414yes—
336C2×Dic71C22×Q814yes—
337C2×Dic71C22×Q814yes—
338C2×Dic71C2×#4114yes—
339Dic142—232no—
340C22×C71—232no—
341C22×C71—24no—
342C22×C71—24no—
343C22×C71—24no—
344C22×C71—24no—
345C22×C71—24no—
346C22×C71—24no—
347C22×C71C2×C4×D414yes—
348C22×C71C2×C4×Q814yes—
349C22×C71C2×C4×Q818yescomplemented
350C22×C71#52014yes—
351C22×C71#54614yes—
352C22×C71D4×Q814yes—
353C22×C71#55214yes—
354C22×C71#55414yes—
355C22×C71C24×C411yescharacteristic
356C22×C71C23×D411yescharacteristic
357C22×C71C23×Q811yescharacteristic
358C22×C71C22×#4111yescharacteristic
359C22×C71C22×#4111yescharacteristic
360C22×C71C2×H(5,𝔽2)11yescharacteristic
361C22×C71C2×2−1+411yescharacteristic
362C4×C71—24no—
363C4×C71—24no—
364C4×C71—24no—
365C4×C71—42no—
366C4×C71—42no—
367C4×C71—42no—
368Dic71—24no—
369Dic71—24no—
370Dic71—24no—
371Dic71—24no—
372Dic71—24no—
373Dic71—24no—
374Dic71—42no—
375Dic71C2×C4×D418yes—
376C2×#2360—711nomaximal, Sylow
377C2×C71—28no—
378C2×C71#236018yescomplemented
379C2×C71C22×C4×D411yescharacteristic
380C2×C71C22×C4×Q811yescharacteristic
381C2×C71C2×#52011yescharacteristic
382C2×C71C2×#54611yescharacteristic
383C2×C71C2×D4×Q811yescharacteristic
384C2×C71C2×#55211yescharacteristic
385C2×C71C2×#55411yescharacteristic
386C22×C22⋊Q8—711no—
387C22×C4×Q8—711no—
388C23×C4⋊C4—711no—
389#2360—7116no—
390C2×#391—711no—
391C2×#389—711no—
392C2×#389—711no—
393C2×#389—711no—
394C2×#387—711no—
395C2×#387—711no—
396C2×#385—711no—
397C2×#385D7111yescharacteristic
398C2×C4×C4⋊C4—711no—
399C2×C4×C22⋊C4—711no—
400C2×C4×C22⋊C4—711no—
401C2×C4×C22⋊C4—711no—
402C71C2×#236011yescharacteristic, complemented, Sylow
403C23×Q8—711no—
404C24×C4—711no—
405C24×C4—711no—
406C24×C4C2×D7111yescharacteristic
407C2×C22⋊Q8—7116no—
408C2×C22⋊Q8—718no—
409C2×C4×Q8—718no—
410C2×C4×Q8—1428no—
411C22×C4⋊C4—711no—
412C22×C4⋊C4—711no—
413C22×C4⋊C4—711no—
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4—718no—
417C22×C4⋊C4—711no—
418C22×C4⋊C4—711no—
419C22×C4⋊C4—711no—
420C22×C4⋊C4—711no—
421C22×C4⋊C4—1428no—
422C22×C4⋊C4C2×D7111yescharacteristic
423C22×C4⋊C4C2×D7111yescharacteristic
424C22×C22⋊C4—711no—
425C22×C22⋊C4—711no—
426C22×C22⋊C4C2×D7111yescharacteristic
427C22×C22⋊C4C2×D7111yescharacteristic
428C22×C42—711no—
429C22×C42—711no—
430C22×C42—711no—
431C22×C42—711no—
432C22×C42—711no—
433C22×C42—711no—
434#391—718no—
435#389—718no—
436#389—718no—
437#389—718no—
438#387—718no—
439#387—718no—
440#385—718no—
441#385C2×D7118yes—
442C4×C4⋊C4—718no—
443C4×C22⋊C4—718no—
444C4×C22⋊C4—718no—
445C4×C22⋊C4—718no—
446C2×#95—711no—
447C2×#95—711no—
448C2×#95—711no—
449C2×#95—711no—
450C2×#95—711no—
451C2×#95—711no—
452C2×#95—711no—
453C2×#95—711no—
454C2×#95C2×D7111yescharacteristic
455C2×#95C2×D7111yescharacteristic
456C25C22×D7111yescharacteristic
457C22×Q8—718no—
458C22×Q8—714no—
459C22×Q8—1424no—
460C22×Q8—1424no—
461C23×C4—24no—
462C23×C4—24no—
463C23×C4—42no—
464C23×C4—2842no—
465C23×C4—714no—
466C23×C4—711no—
467C23×C4—718no—
468C23×C4—714no—
469C23×C4—711no—
470C23×C4—711no—
471C23×C4—711no—
472C23×C4—711no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—1424no—
477C23×C4—1424no—
478C23×C4—1424no—
479C23×C4—1424no—
480C23×C4C22×D7111yescharacteristic
481C23×C4C22×D7111yescharacteristic
482C23×C4C22×D7111yescharacteristic
483C23×C4C22×D7114yes—
484C23×C4C22×D7111yescharacteristic
485C23×C4C22×D7111yescharacteristic
486C23×C4C22×D7111yescharacteristic
487C22⋊Q8—7164no—
488C4×Q8—14232no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—42no—
491C2×C4⋊C4—2842no—
492C2×C4⋊C4—714no—
493C2×C4⋊C4—718no—
494C2×C4⋊C4—718no—
495C2×C4⋊C4—718no—
496C2×C4⋊C4—718no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—714no—
499C2×C4⋊C4—714no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—714no—
504C2×C4⋊C4—714no—
505C2×C4⋊C4—14232no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1424no—
508C2×C4⋊C4—1424no—
509C2×C4⋊C4—1424no—
510C2×C4⋊C4C22×D7114yes—
511C2×C4⋊C4C22×D7114yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—718no—
514C2×C22⋊C4—718no—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—714no—
517C2×C22⋊C4C4×D7118yes—
518C2×C22⋊C4C22×D7114yes—
519C2×C22⋊C4C22×D7114yes—
520C2×C42—2842no—
521C2×C42—2842no—
522C2×C42—714no—
523C2×C42—714no—
524C2×C42—714no—
525C2×C42—714no—
526C2×C42—714no—
527C2×C42—714no—
528C2×C42—1424no—
529C2×C42—1424no—
530C2×C42—1424no—
531C2×C42—1424no—
532#95—714no—
533#95—714no—
534#95—714no—
535#95—714no—
536#95—714no—
537#95—714no—
538#95—714no—
539#95—714no—
540#95C22×D7114yes—
541#95C22×D7114yes—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24C2×C4×D7114yes—
547C24Q8×D7114yes—
548C24#1176586414yes—
549C24C23×D7112yes—
550C24C23×D7111yescharacteristic
551C2×Q8—7116no—
552C2×Q8—1428no—
553C2×Q8—1428no—
554C2×Q8—14232no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—44no—
573C22×C4—416no—
574C22×C4—28416no—
575C22×C4—2844no—
576C22×C4—714no—
577C22×C4—714no—
578C22×C4—714no—
579C22×C4—712no—
580C22×C4—714no—
581C22×C4—714no—
582C22×C4—714no—
583C22×C4—7116no—
584C22×C4—714no—
585C22×C4—714no—
586C22×C4—714no—
587C22×C4—712no—
588C22×C4—712no—
589C22×C4—712no—
590C22×C4—712no—
591C22×C4—712no—
592C22×C4—712no—
593C22×C4—712no—
594C22×C4—1428no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1428no—
598C22×C4—1422no—
599C22×C4—1428no—
600C22×C4—1428no—
601C22×C4—14232no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1422no—
607C22×C4—1422no—
608C22×C4—1422no—
609C22×C4—1422no—
610C22×C4—1422no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4C2×C4×D7114yes—
615C22×C4C2×C4×D7114yes—
616C22×C4D4×D7114yes—
617C22×C4C23×D7112yes—
618C22×C4C23×D7112yes—
619C22×C4C23×D7112yes—
620C22×C4C23×D7112yes—
621C22×C4C23×D7112yes—
622C22×C4C23×D7112yes—
623C4⋊C4—28no—
624C4⋊C4—44no—
625C4⋊C4—2844no—
626C4⋊C4—7116no—
627C4⋊C4—7116no—
628C4⋊C4—7116no—
629C4⋊C4—7116no—
630C4⋊C4—1428no—
631C4⋊C4—1428no—
632C4⋊C4—1428no—
633C4⋊C4—1428no—
634C22⋊C4—28no—
635C22⋊C4—7116no—
636C22⋊C4—7116no—
637C22⋊C4C2×C4×D71116yes—
638C42—2844no—
639C42—2844no—
640C42—1428no—
641C42—1428no—
642C42—1428no—
643C42—1428no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—28no—
649C23—28no—
650C23—28no—
651C23—28no—
652C23—28no—
653C23—28no—
654C23#14556093116yescomplemented
655C23C22×C4×D7114yes—
656C23C22×C4×D7112yes—
657C23C2×D4×D7112yes—
658C23C2×Q8×D7114yes—
659C23C2×Q8×D7112yes—
660C23#41×D7112yes—
661C23C2×#1176586414yes—
662C23C2×#1176586412yes—
663C23#1455617312yes—
664C23#1455617512yes—
665C23C24×D7111yescharacteristic
666Q8—14232no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—28no—
674C2×C4—28no—
675C2×C4—28no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—416no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—2844no—
690C2×C4—28416no—
691C2×C4—714no—
692C2×C4—714no—
693C2×C4—714no—
694C2×C4—7116no—
695C2×C4—714no—
696C2×C4—714no—
697C2×C4—714no—
698C2×C4—714no—
699C2×C4—714no—
700C2×C4—714no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—14232no—
705C2×C4—1422no—
706C2×C4—1422no—
707C2×C4—1422no—
708C2×C4—1422no—
709C2×C4—1422no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1428no—
718C2×C4—1428no—
719C2×C4—1428no—
720C2×C4—1428no—
721C2×C4—1428no—
722C2×C4—1428no—
723C2×C4C22×C4×D7114yes—
724C2×C4C22×C4×D7114yes—
725C2×C4C2×D4×D7114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—232no—
731C22—24no—
732C22—24no—
733C22C4×D4×D7114yes—
734C22C2×#1455609314yes—
735C22C2×#1455609318yescomplemented
736C22#1798647814yes—
737C22#1798663614yes—
738C22#1798666214yes—
739C22#1798668614yes—
740C22#1798670314yes—
741C22C23×C4×D7111yescharacteristic
742C22C22×D4×D7111yescharacteristic
743C22C22×Q8×D7111yescharacteristic
744C22C2×#41×D7111yescharacteristic
745C22C22×#1176586411yescharacteristic
746C22C2×#1455617311yescharacteristic
747C22C2×#1455617511yescharacteristic
748C4—24no—
749C4—24no—
750C4—24no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—2842no—
755C4—718no—
756C4—1424no—
757C4—1424no—
758C4—1424no—
759C4—1424no—
760C4—1424no—
761C4—1424no—
762C2—28no—
763C2#2259134018yesdirect product factor
764C2C2×C4×D4×D7111yescharacteristic
765C2C22×#1455609311yescharacteristic
766C2C2×#1798647811yescharacteristic
767C2C2×#1798663611yescharacteristic
768C2C2×#1798666211yescharacteristic
769C2C2×#1798668611yescharacteristic
770C2C2×#1798670311yescharacteristic
subgroupG/H
centerC24C23×D71
commutatorC22×C71C24×C4
FrattiniC23C24×D71
FittingC2×#385×C71C2
socleC24×C71C24
prime radicalC25×C71C23
cosocleC23×C71C25
hypercenterC2×#385D71
hypocenterC71C2×#2360
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C22×#14556093C2semidirect
4. #22591340C2direct (N × H)
5. C2×#17985903C2semidirect
6. C2×#17985895C2semidirect
7. C2×#17985894C2semidirect
8. C2×#17985894C2semidirect
9. C2×#17985884C2semidirect
10. C2×#17985881C2semidirect
12. C2×#17985850C2semidirect
20. C2×#14556105C4semidirect
23. C2×#14556093C22semidirect
43. #17985903C22semidirect
44. #17985895C22semidirect
45. #17985894C22semidirect
46. #17985894C22semidirect
47. #17985884C22semidirect
48. #17985881C22semidirect
50. #17985850C22semidirect
72. C22×Dic142C2×C4semidirect
90. #14556105C2×C4semidirect
92. C2×C4⋊Dic71C2×C4semidirect
100. C2×Dic71⋊C4C2×C4semidirect
101. C2×Dic71⋊C4C2×C4semidirect
112. C2×C22⋊Dic71Q8semidirect
159. C2×Dic142C22×C4semidirect
200. C4⋊Dic71C22×C4semidirect
206. Dic71⋊C4C22×C4semidirect
207. Dic71⋊C4C22×C4semidirect
210. C22⋊Dic71C2×Q8semidirect
268. C23×C71C4×Q8semidirect
349. C22×C71C2×C4×Q8semidirect
378. C2×C71#2360semidirect
402. C71C2×#2360semidirect
654. C23#14556093semidirect
735. C22C2×#14556093semidirect
763. C2#22591340direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561052
C22×#145560932
C23×Dic71⋊C42
#225913402
C2×#179859032
C2×#179858952
C2×#179858942
C2×#179858842
C2×#179858812
C2×#179858712
C2×#179858502
C2×C22⋊C4×Dic712
C2×C4×C22⋊Dic712
C2×#385×C712
C2×#236071