Finite Group Databasebeta

← C2×#22600400 #32874180

Subgroups — C2×#22600400 #32874180

Order 18176.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986658C211yesmaximal, characteristic
2#22600400C2116yesmaximal, direct product factor
3C2×#17986361C211yesmaximal, characteristic, complemented
4C2×#17986340C211yesmaximal, characteristic, complemented
5C2×#17986323C211yesmaximal, characteristic, complemented
6C2×#17986291C211yesmaximal, characteristic, complemented
7C2×#17986247C211yesmaximal, characteristic, complemented
8C2×#17986238C211yesmaximal, characteristic, complemented
9C2×#17986221C211yesmaximal, characteristic, complemented
10C2×#17986159C211yesmaximal, characteristic, complemented
11C2×#17986154C211yesmaximal, characteristic, complemented
12C2×#17986104C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986007C211yesmaximal, characteristic, complemented
15C2×#17985993C211yesmaximal, characteristic, complemented
16C2×#556×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C23×Dic142C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765855C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22C22×#11765849C2211yescharacteristic
23C23×C71⋊C8C2211yescharacteristic
24#17986658—24no—
25#17986658C2218yes—
26C2×#14556116C2211yescharacteristic
27C2×#14556114—21no—
28C2×#14556107C2211yescharacteristic
29C2×#14556106—21no—
30C2×#14556102C2211yescharacteristic
31C2×#14556100—21no—
32C2×C4×Dic142C2211yescharacteristic
33C2×(C22⋊D71)⋊C4—21no—
34#17986361C2218yescomplemented
35#17986340C2218yescomplemented
36#17986323C2218yescomplemented
37#17986291C2218yescomplemented
38#17986247C2218yescomplemented
39#17986238C2218yescomplemented
40#17986221C2218yescomplemented
41#17986159C2218yescomplemented
42#17986154C2218yescomplemented
43#17986104C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986007C2218yescomplemented
50#17985993C2218yescomplemented
51C2×#14556052C2211yescharacteristic
52C2×#14556051C2211yescharacteristic
53C2×#14556051C2211yescharacteristic
54C2×#14556051C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#556×C71—24no—
65#556×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#124×C71—21no—
70C2×C22⋊Q8×C71C2211yescharacteristic
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×C4×Q8×C71—21no—
73C2×C4×Q8×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C2×#11765865—24no—
78C2×#11765865—22no—
79C2×#11765865—42no—
80C2×#11765865C2314yes—
81C22×Dic142—24no—
82C22×Dic142—22no—
83C22×Dic142—21no—
84C22×Dic142—42no—
85C22×Dic142C2311yescharacteristic
86C22×Dic142C2314yes—
87C22×Dic142C2311yescharacteristic
88C22×D284C2311yescharacteristic
89C22×C22⋊D71—21no—
90C22×C22⋊D71—21no—
91C23×Dic71—21no—
92C22×C4×D71—21no—
93C2×#11765855—24no—
94C2×#11765855—42no—
95C2×#11765855C2314yes—
96C2×#11765855C2314yes—
97C2×#11765852—42no—
98C2×#11765852C2314yes—
99C2×#11765849—42no—
100C2×#11765849C2314yes—
101C22×C71⋊C8—42no—
102C22×C71⋊C8C2311yescharacteristic
103C22×C71⋊C8C2311yescharacteristic
104C22×C71⋊C8C2311yescharacteristic
105C22×C71⋊C8C2311yescharacteristic
106C22×C71⋊C8C2314yes—
107#14556116—22no—
108#14556116C2314yes—
109#14556114—28no—
110#14556107—22no—
111#14556107C2314yes—
112#14556106—28no—
113#14556102—22no—
114#14556102C2314yes—
115#14556100—28no—
116C4×Dic142—22no—
117C4×Dic142C2314yes—
118(C22⋊D71)⋊C4—28no—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×Dic71⋊C4—21no—
121C2×Dic71⋊C4—21no—
122C2×C22⋊Dic71—21no—
123C2×(C2×D71)⋊C4—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×C4×Dic71—21no—
127#14556061C2314yes—
128#14556061C2314yes—
129#14556059C2314yes—
130C4⋊(C71⋊C8)C2314yes—
131#14556052C2314yes—
132#14556051C2314yes—
133#14556051C2314yes—
134#14556051C2314yes—
135#14556051C2314yes—
136#14556051C2314yes—
137#14556051C2314yes—
138#14556048C2314yes—
139#14556048C2314yes—
140#14556048C2314yes—
141C22⋊(C71⋊C8)C2314yes—
142C22⋊(C71⋊C8)C2314yes—
143#14556039C2314yes—
144C22×Q8×C71—21no—
145C22×Q8×C71C2311yescharacteristic
146C22×D4×C71D411yescharacteristic
147C23×C4×C71C2311yescharacteristic
148C23×C4×C71C2311yescharacteristic
149C4⋊Q8×C71—22no—
150C4⋊Q8×C71C2314yes—
151#126×C71—28no—
152#126×C71—28no—
153#124×C71—28no—
154C22⋊Q8×C71—22no—
155C22⋊Q8×C71—22no—
156C22⋊Q8×C71C2314yes—
157C22⋊Q8×C71C2314yes—
158C4×Q8×C71—28no—
159C4×Q8×C71—22no—
160C4×Q8×C71C2314yes—
161C4×D4×C71D414yes—
162C4×D4×C71C2314yes—
163#117×C71—22no—
164#117×C71—22no—
165#117×C71C2314yes—
166#117×C71C2314yes—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71—21no—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71—21no—
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71D411yescharacteristic
180C2×C22⋊C4×C71D411yescharacteristic
181C2×C42×C71—21no—
182C2×C42×C71—21no—
183C2×C42×C71—21no—
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186#11765865—28no—
187#11765865—44no—
188#11765865—48no—
189C2×Dic142—21no—
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—22no—
193C2×Dic142—28no—
194C2×Dic142—24no—
195C2×Dic142—21no—
196C2×Dic142—44no—
197C2×Dic142—48no—
198C2×Dic142—44no—
199C2×Dic142#4114yes—
200C2×Dic142C2412yes—
201C2×Dic142C2412yes—
202C2×D284—22no—
203C2×D284—22no—
204C2×D284—21no—
205C2×D284C2412yes—
206C2×C22⋊D71—24no—
207C2×C22⋊D71—24no—
208C2×C22⋊D71—44no—
209C2×C22⋊D71—44no—
210C22×Dic71—21no—
211C22×Dic71—21no—
212C22×Dic71—24no—
213C22×Dic71—21no—
214C22×Dic71—44no—
215C2×C4×D71—24no—
216C2×C4×D71—44no—
217#11765855—28no—
218#11765855—44no—
219#11765852—44no—
220#11765849—44no—
221C2×C71⋊C8—22no—
222C2×C71⋊C8—22no—
223C2×C71⋊C8—22no—
224C2×C71⋊C8—22no—
225C2×C71⋊C8—44no—
226C2×C71⋊C8C2412yes—
227C2×C71⋊C8C2412yes—
228C2×C71⋊C8C2412yes—
229C2×C71⋊C8C2412yes—
230C4⋊Dic71—21no—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234C22⋊Dic71—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238C4×Dic71—24no—
239C24×C71C2×D411yescharacteristic
240C24×C71C2×D411yescharacteristic
241C2×Q8×C71—21no—
242C2×Q8×C71—24no—
243C2×Q8×C71—22no—
244C2×Q8×C71—22no—
245C2×Q8×C71—44no—
246C2×Q8×C71C2412yes—
247C2×D4×C71—42no—
248C2×D4×C71C2×D414yes—
249C22×C4×C71—22no—
250C22×C4×C71—22no—
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2×D412yes—
260C22×C4×C71C2×D412yes—
261C22×C4×C71C2×D411yescharacteristic
262C22×C4×C71C2×D411yescharacteristic
263C22×C4×C71C2412yes—
264C22×C4×C71C2412yes—
265C22×C4×C71C2411yescharacteristic
266C4⋊C4×C71—24no—
267C4⋊C4×C71—24no—
268C4⋊C4×C71—24no—
269C4⋊C4×C71—24no—
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71C2×D414yes—
274C4⋊C4×C71C2412yes—
275C4⋊C4×C71C2412yes—
276C4⋊C4×C71C2412yes—
277C22⋊C4×C71—24no—
278C22⋊C4×C71—24no—
279C22⋊C4×C71—24no—
280C22⋊C4×C71—24no—
281C22⋊C4×C71C2×D414yes—
282C22⋊C4×C71C2×D414yes—
283C42×C71—24no—
284C42×C71—24no—
285C42×C71—24no—
286C42×C71C2×D412yes—
287C42×C71C2412yes—
288C23×C71—22no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71C22×D412yes—
295C23×C71C22×D412yes—
296C23×C71C22×D411yescharacteristic
297C22×D71—22no—
298C22×D71—42no—
299C22×D71—42no—
300C22×D71—42no—
301Q8×C71—22no—
302Q8×C71—22no—
303Q8×C71—48no—
304Q8×C71—42no—
305D4×C71—44no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—24no—
311C2×C4×C71—24no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—22no—
319C2×C4×C71—22no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—42no—
323C2×C4×C71—42no—
324C2×C4×C71C22×D412yes—
325C2×C4×C71C22×D412yes—
326C2×C4×C71C22×D412yes—
327C2×C4×C71C22×D412yes—
328C2×C4×C71C22×D411yescharacteristic
329C2×C4×C71C2×#4112yes—
330C2×C4×C71H(5,𝔽2)12yes—
331C2×C4×C71C2511yescharacteristic
332C22⋊D71—48no—
333C22⋊D71—48no—
334C2×Dic71—24no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—48no—
339C2×Dic71—42no—
340C2×Dic71—42no—
341D284—22no—
342D284—22no—
343D284—42no—
344C4×D71—48no—
345Dic142—24no—
346Dic142—22no—
347Dic142—22no—
348Dic142—22no—
349Dic142—48no—
350Dic142—42no—
351Dic142C2×#4114yes—
352C71⋊C8—22no—
353C71⋊C8—22no—
354C71⋊C8—22no—
355C71⋊C8—22no—
356C22×C71—22no—
357C22×C71—22no—
358C22×C71—22no—
359C22×C71—22no—
360C22×C71—22no—
361C22×C71—22no—
362C22×C71—44no—
363C22×C71—44no—
364C22×C71#54612yes—
365C22×C71#57512yes—
366C22×C71#57812yes—
367C22×C71C23×D411yescharacteristic
368C2×D71—42no—
369C2×D71—42no—
370C2×D71—42no—
371C2×D71—84no—
372C4×C71—22no—
373C4×C71—22no—
374C4×C71—22no—
375C4×C71—22no—
376C4×C71—42no—
377C4×C71—42no—
378C4×C71—42no—
379C4×C71—42no—
380C4×C71#54612yes—
381C4×C71C22×#4111yescharacteristic
382C4×C71C2×H(5,𝔽2)11yescharacteristic
383Dic71—24no—
384Dic71—42no—
385Dic71—42no—
386C2×#3313—711nomaximal, Sylow
387C2×C71—42no—
388C2×C71—42no—
389C2×C71#331314yescomplemented
390C2×C71C2×#54611yescharacteristic
391C2×C71C2×#57511yescharacteristic
392C2×C71C2×#57811yescharacteristic
393D71—82no—
394C2×#556D7111yescharacteristic, complemented
395C2×#548—711no—
396#3313—7116no—
397C2×#489—711no—
398C2×#485—711no—
399C2×#482—711no—
400C2×#477—711no—
401C2×#468—711no—
402C2×#467—711no—
403C2×#464—711no—
404C2×#452—711no—
405C2×#451—711no—
406C2×#441—711no—
407C2×#435—711no—
408C2×#419—711no—
409C2×#416—711no—
410C71C2×#331311yescharacteristic, complemented, Sylow
411C22×#41—711no—
412C23×Q8—711no—
413C22×Q16—711no—
414C22×Q16—711no—
415C22×SD16—711no—
416C22×M16—711no—
417C23×C8—711no—
418#556—24no—
419#556C2×D7118yescomplemented
420#548—718no—
421#548—1424no—
422C2×C4⋊Q8C2×D7111yescharacteristic
423C2×#126—21no—
424C2×#126—21no—
425C2×#124—21no—
426C2×#124—711no—
427C2×#124—1421no—
428C2×C22⋊Q8—711no—
429C2×C22⋊Q8—1421no—
430C2×C22⋊Q8C2×D7111yescharacteristic
431C2×C22⋊Q8C2×D7111yescharacteristic
432C2×#121—711no—
433C2×#121—1421no—
434C2×C4×Q8—21no—
435C2×C4×Q8—711no—
436C2×C4×Q8C2×D7111yescharacteristic
437C2×C4×D4—1421no—
438C2×C4×D4C2×D7111yescharacteristic
439C2×#117C2×D7111yescharacteristic
440C2×#117C2×D7111yescharacteristic
441#489—718no—
442#485—718no—
443#482—718no—
444#477—718no—
445#468—718no—
446#467—718no—
447#464—718no—
448#452—718no—
449#451—718no—
450#441—718no—
451#435—718no—
452C2×#107—711no—
453C2×#107—711no—
454C2×#106—711no—
455C2×C4⋊C8—711no—
456#419—718no—
457#416—718no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103—711no—
461C2×#103—711no—
462C2×#103—711no—
463C2×#103—711no—
464C2×#103—711no—
465C2×#102—711no—
466C2×#102—711no—
467C2×#102—711no—
468C2×C22⋊C8—711no—
469C2×C22⋊C8—711no—
470C2×#97—711no—
471C2×#41—2842no—
472C2×#41—714no—
473C2×#41—1424no—
474C2×#41—1422no—
475C22×Q8—21no—
476C22×Q8—2842no—
477C22×Q8—714no—
478C22×Q8—711no—
479C22×Q8—711no—
480C22×Q8—1424no—
481C22×Q8—1421no—
482C22×Q8—1422no—
483C22×Q8C22×D7111yescharacteristic
484C22×D4—711no—
485C22×D4—1421no—
486C22×D4—1421no—
487C22×D4C22⋊D7111yescharacteristic
488C23×C4—1421no—
489C23×C4—1421no—
490C23×C4C22×D7111yescharacteristic
491C23×C4C22×D7111yescharacteristic
492C2×Q16—2842no—
493C2×Q16—714no—
494C2×Q16—714no—
495C2×Q16—1424no—
496C2×SD16—2842no—
497C2×SD16—714no—
498C2×M16—2842no—
499C2×M16—714no—
500C22×C8—2842no—
501C22×C8—714no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—711no—
505C22×C8—711no—
506C4⋊Q8—22no—
507C4⋊Q8C22×D7114yes—
508#126—28no—
509#126—28no—
510#124—28no—
511#124—714no—
512#124—1428no—
513#124—1422no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—714no—
517C22⋊Q8—1422no—
518C22⋊Q8—1428no—
519C22⋊Q8C22×D7114yes—
520C22⋊Q8C22×D7114yes—
521#121—714no—
522#121—1428no—
523#121—1422no—
524C4×Q8—28no—
525C4×Q8—22no—
526C4×Q8—714no—
527C4×Q8—1422no—
528C4×Q8C22×D7114yes—
529C4×D4—1428no—
530C4×D4C22⋊D7114yes—
531C4×D4C22×D7114yes—
532#117—22no—
533#117—22no—
534#117C22×D7114yes—
535#117C22×D7114yes—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—711no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4C22⋊D7111yescharacteristic
544C2×C4⋊C4C22×D7111yescharacteristic
545C2×C4⋊C4C22×D7111yescharacteristic
546C2×C4⋊C4C22×D7111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4C22⋊D7111yescharacteristic
556C2×C22⋊C4C22⋊D7111yescharacteristic
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—1421no—
561C2×C42C22×D7111yescharacteristic
562#107—714no—
563#107—714no—
564#106—714no—
565C4⋊C8—714no—
566#103—714no—
567#103—714no—
568#103—714no—
569#103—714no—
570#103—714no—
571#103—714no—
572#103—714no—
573#102—714no—
574#102—714no—
575#102—714no—
576C22⋊C8—714no—
577C22⋊C8—714no—
578#97—714no—
579C24—1421no—
580C24C2×C22⋊D7111yescharacteristic
581C24C2×C22⋊D7111yescharacteristic
582#41—2848no—
583#41—2844no—
584#41—1428no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—22no—
588C2×Q8—22no—
589C2×Q8—44no—
590C2×Q8—2848no—
591C2×Q8—2844no—
592C2×Q8—2844no—
593C2×Q8—714no—
594C2×Q8—712no—
595C2×Q8—712no—
596C2×Q8—1428no—
597C2×Q8—1422no—
598C2×Q8—1422no—
599C2×Q8—1421no—
600C2×Q8—1424no—
601C2×Q8—1421no—
602C2×Q8—1422no—
603C2×Q8C23×D7112yes—
604C2×D4—42no—
605C2×D4—2844no—
606C2×D4—2844no—
607C2×D4—712no—
608C2×D4—1424no—
609C2×D4—1424no—
610C2×D4—1421no—
611C2×D4—1422no—
612C2×D4—1422no—
613C2×D4C2×C22⋊D7114yes—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—2844no—
623C22×C4—2844no—
624C22×C4—1424no—
625C22×C4—1421no—
626C22×C4—1421no—
627C22×C4—1424no—
628C22×C4—1421no—
629C22×C4C2×C22⋊D7112yes—
630C22×C4C2×C22⋊D7112yes—
631C22×C4C2×C22⋊D7111yescharacteristic
632C22×C4C2×C22⋊D7111yescharacteristic
633C22×C4C2×C22⋊D7111yescharacteristic
634C22×C4C2×C22⋊D7111yescharacteristic
635C22×C4C23×D7112yes—
636C22×C4C23×D7112yes—
637C22×C4C23×D7111yescharacteristic
638Q16—2844no—
639Q16—1428no—
640SD16—2844no—
641M16—2844no—
642C2×C8—2844no—
643C2×C8—712no—
644C2×C8—712no—
645C2×C8—712no—
646C2×C8—712no—
647C2×C8—1422no—
648C2×C8—1422no—
649C2×C8—1422no—
650C2×C8—1422no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—712no—
659C4⋊C4—1424no—
660C4⋊C4—1424no—
661C4⋊C4—1421no—
662C4⋊C4C2×C22⋊D7114yes—
663C4⋊C4C23×D7112yes—
664C4⋊C4C23×D7112yes—
665C4⋊C4C23×D7112yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—1424no—
671C22⋊C4—1424no—
672C22⋊C4—1424no—
673C22⋊C4—1424no—
674C22⋊C4C2×C22⋊D7114yes—
675C22⋊C4C2×C22⋊D7114yes—
676C42—24no—
677C42—24no—
678C42—24no—
679C42—1424no—
680C42C2×C22⋊D7112yes—
681C42C23×D7112yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—2842no—
689C23—2842no—
690C23—2842no—
691C23—1422no—
692C23C22×C22⋊D7112yes—
693C23C22×C22⋊D7112yes—
694C23C22×C22⋊D7111yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—48no—
698Q8—42no—
699Q8—2848no—
700Q8—2842no—
701Q8—714no—
702Q8—1422no—
703Q8—1422no—
704Q8—1422no—
705Q8—1424no—
706D4—44no—
707D4—2848no—
708D4—2848no—
709D4—2842no—
710D4—1422no—
711D4—1422no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—2848no—
731C2×C4—2842no—
732C2×C4—2842no—
733C2×C4—2848no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1422no—
737C2×C4—1424no—
738C2×C4C22×C22⋊D7112yes—
739C2×C4C22×C22⋊D7112yes—
740C2×C4C22×C22⋊D7112yes—
741C2×C4C22×C22⋊D7112yes—
742C2×C4C22×C22⋊D7111yescharacteristic
743C2×C4#41×D7112yes—
744C2×C4#1455617412yes—
745C2×C4C24×D7111yescharacteristic
746C8—1422no—
747C8—1422no—
748C8—1422no—
749C8—1422no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—2842no—
759C22—2842no—
760C22—2842no—
761C22—5684no—
762C22#1798663712yes—
763C22#1798679712yes—
764C22#1798681412yes—
765C22C23×C22⋊D7111yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—2842no—
775C4—2842no—
776C4—1424no—
777C4#1798663712yes—
778C4C2×#41×D7111yescharacteristic
779C4C2×#1455617411yescharacteristic
780C2—42no—
781C2—42no—
782C2—5682no—
783C2#2260040014yesdirect product factor
784C2C2×#1798663711yescharacteristic
785C2C2×#1798679711yescharacteristic
786C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#556×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986658C2
hypercenterC2×#556D71
hypocenterC71C2×#3313
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #22600400C2direct (N × H)
3. C2×#17986361C2semidirect
4. C2×#17986340C2semidirect
5. C2×#17986323C2semidirect
6. C2×#17986291C2semidirect
7. C2×#17986247C2semidirect
8. C2×#17986238C2semidirect
9. C2×#17986221C2semidirect
10. C2×#17986159C2semidirect
11. C2×#17986154C2semidirect
12. C2×#17986104C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986007C2semidirect
15. C2×#17985993C2semidirect
16. C2×#556×C71C2semidirect
34. #17986361C22semidirect
35. #17986340C22semidirect
36. #17986323C22semidirect
37. #17986291C22semidirect
38. #17986247C22semidirect
39. #17986238C22semidirect
40. #17986221C22semidirect
41. #17986159C22semidirect
42. #17986154C22semidirect
43. #17986104C22semidirect
44. #17986071C22semidirect
49. #17986007C22semidirect
50. #17985993C22semidirect
65. #556×C71C22semidirect
389. C2×C71#3313semidirect
394. C2×#556D71semidirect
410. C71C2×#3313semidirect
419. #556C2×D71semidirect
783. C2#22600400direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866582
#226004002
C2×#179863612
C2×#179863402
C2×#179863232
C2×#179862912
C2×#179862472
C2×#179862382
C2×#179862212
C2×#179861592
C2×#179861542
C2×#179861042
C2×#179860712
C2×#179860072
C2×#179859932
C2×#556×C712
C2×#331371