Finite Group Databasebeta

← C2×#22602206 #32905533

Subgroups — C2×#22602206 #32905533

Order 18176.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602206C2132yesmaximal, direct product factor
2C2×#17986734C211yesmaximal, characteristic, complemented
3C2×#17986734C211yesmaximal, characteristic, complemented
4C2×#17986724C211yesmaximal, characteristic, complemented
5C2×#17986723C212yesmaximal, complemented
6C2×#17986721C212yesmaximal, complemented
7C2×#17986721C212yesmaximal, complemented
8C2×#17986705C212yesmaximal, complemented
9C2×#17986681C214yesmaximal, complemented
10C2×#17986597C214yesmaximal, complemented
11C2×#17986574C212yesmaximal, complemented
12C2×#17986553C211yesmaximal, characteristic, complemented
13C2×#17986550C211yesmaximal, characteristic
14C2×#17986536C212yesmaximal, complemented
15C2×#17986534C212yesmaximal, complemented
16C2×#17986481C212yesmaximal, complemented
17C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
18C2×#557×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×Q8×D71C2211yescharacteristic
21#17986734C22116yescomplemented
22#17986734C22116yescomplemented
23#17986724C22116yescomplemented
24#17986723C22132yescomplemented
25#17986721C22132yescomplemented
26#17986721C22132yescomplemented
27#17986705C22132yescomplemented
28#17986681C22164yescomplemented
29#17986597C22164yescomplemented
30#17986574C22132yescomplemented
31#17986553C22116yescomplemented
32#17986550C22116yes—
33C2×#14556127C2211yescharacteristic
34C2×#14556126C2211yescharacteristic
35C2×#14556126C2212yes—
36C2×#14556125C2211yescharacteristic
37#17986536C22132yescomplemented
38#17986534C22132yescomplemented
39C2×#14556123C2214yes—
40C2×#14556123C2214yes—
41C2×#14556123C2214yes—
42C2×#14556122C2214yes—
43C2×#14556119C2212yes—
44C2×#14556118C2212yes—
45C2×#14556118C2214yes—
46C2×#14556117C2212yes—
47C2×#14556117C2212yes—
48C2×#14556117C2212yes—
49C2×#14556116C2212yes—
50C2×#14556116C2212yes—
51C2×#14556113C2214yes—
52C2×#14556113C2214yes—
53C2×#14556113C2214yes—
54C2×#14556113C2214yes—
55C2×#14556108C2211yescharacteristic
56C2×#14556108C2214yes—
57C2×#14556106C2214yes—
58C2×#14556106C2214yes—
59C2×#14556106C2214yes—
60C2×#14556106C2212yes—
61C2×#14556104C2211yescharacteristic
62C2×#14556103C2212yes—
63C2×#14556103C2212yes—
64#17986481C22132yescomplemented
65C2×Q8×Dic71C2211yescharacteristic
66C2×Q8×Dic71C2212yes—
67C2×C4×Dic142C2212yes—
68C2×C4×Dic142C2211yescharacteristic
69C2×C4×Dic142C2212yes—
70C2×C4×Dic142C2211yescharacteristic
71C2×#14556093C2212yes—
72C2×#14556093C2211yescharacteristic
73C2×#14556093C2212yes—
74C4×Q8×D71C22116yescomplemented
75C2×C4×D284C2214yes—
76C2×C4×D284C2212yes—
77C2×C4×D284C2212yes—
78C2×#14556090C2214yes—
79C2×#14556090C2212yes—
80C2×#14556090C2212yes—
81C2×#14556090C2212yes—
82C2×#14556090C2212yes—
83C2×#14556086C2214yes—
84C2×#14556085C2214yes—
85C2×#14556085C2212yes—
86C2×#14556085C2214yes—
87C2×C4⋊C4×D71C2211yescharacteristic
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2214yes—
90C2×C42×D71C2212yes—
91C2×C42×D71C2211yescharacteristic
92#557×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×C4⋊Q8×C71C2212yes—
95C2×#125×C71C2214yes—
96C2×#125×C71C2212yes—
97C2×C4×Q8×C71C2211yescharacteristic
98C2×C4×Q8×C71C2212yes—
99C2×C4×Q8×C71C2212yes—
100C2×C4×Q8×C71C2211yescharacteristic
101C2×#11765866—216no—
102C2×#11765866C23116yes—
103C22×Dic142C2312yes—
104C22×Dic142C2311yescharacteristic
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2312yes—
107C2×Q8×D71—28no—
108C2×Q8×D71C2318yes—
109C22×D284C2314yes—
110C22×D284C2312yes—
111C22×D284C2312yes—
112C22×D284C2312yes—
113C22×C4×D71C2312yes—
114C22×C4×D71C2314yes—
115C22×C4×D71C2311yescharacteristic
116C22×C4×D71C2312yes—
117C22×C4×D71C2311yescharacteristic
118C22×C4×D71C2314yes—
119C22×C4×D71C2314yes—
120C22×C4×D71C2311yescharacteristic
121#14556127C2318yes—
122#14556126C23116yes—
123#14556126C2318yes—
124#14556125C2318yes—
125#14556123C23132yes—
126#14556123C23132yes—
127#14556123C23132yes—
128#14556122C23132yes—
129#14556119C23116yes—
130#14556118C23132yes—
131#14556118C23116yes—
132#14556117C23116yes—
133#14556117C23116yes—
134#14556117C23116yes—
135#14556116C23116yes—
136#14556116C23116yes—
137#14556113C23132yes—
138#14556113C23132yes—
139#14556113C23132yes—
140#14556113C23132yes—
141#14556108C23132yes—
142#14556108C2318yes—
143#14556106C23132yes—
144#14556106C23132yes—
145#14556106C23116yes—
146#14556106C23132yes—
147#14556104C2318yes—
148#14556103C23116yes—
149#14556103C23116yes—
150Q8×Dic71C2318yes—
151Q8×Dic71C23116yes—
152C4×Dic142C23116yes—
153C4×Dic142C2318yes—
154C4×Dic142C23116yes—
155C4×Dic142C2318yes—
156#14556093C23116yes—
157#14556093C2318yes—
158#14556093C23116yes—
159C4×D284C23132yes—
160C4×D284C23116yes—
161C4×D284C23116yes—
162#14556090C23132yes—
163#14556090C23116yes—
164#14556090C23116yes—
165#14556090C23116yes—
166#14556090C23116yes—
167#14556086C23132yes—
168#14556085C23116yes—
169#14556085C23132yes—
170#14556085C23132yes—
171C2×C4⋊Dic71C2311yescharacteristic
172C2×C4⋊Dic71C2314yes—
173C2×C4⋊Dic71C2312yes—
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2311yescharacteristic
176C2×Dic71⋊C4C2312yes—
177C2×Dic71⋊C4C2312yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C4⋊C4×D71C23116yes—
187C4⋊C4×D71C23132yes—
188C4⋊C4×D71C2318yes—
189C2×(C2×D71)⋊C4C2314yes—
190C2×(C2×D71)⋊C4C2312yes—
191C2×(C2×D71)⋊C4C2314yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×C4×Dic71C2312yes—
200C2×C4×Dic71C2312yes—
201C2×C4×Dic71C2311yescharacteristic
202C2×C4×Dic71C2311yescharacteristic
203C2×C4×Dic71C2312yes—
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2314yes—
206C2×C4×Dic71C2312yes—
207C42×D71C23116yes—
208C42×D71C2318yes—
209C22×Q8×C71C2311yescharacteristic
210C22×Q8×C71C2312yes—
211C22×Q8×C71C2311yescharacteristic
212C4⋊Q8×C71C23116yes—
213C4⋊Q8×C71C2318yes—
214#125×C71C23132yes—
215#125×C71C23116yes—
216C4×Q8×C71C2318yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219C4×Q8×C71C2318yes—
220C2×C4⋊C4×C71C2311yescharacteristic
221C2×C4⋊C4×C71C2314yes—
222C2×C4⋊C4×C71C2312yes—
223C2×C4⋊C4×C71C2311yescharacteristic
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2314yes—
227C2×C4⋊C4×C71C2314yes—
228C2×C4⋊C4×C71C2312yes—
229C2×C42×C71C2312yes—
230C2×C42×C71C2314yes—
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2312yes—
233C23×D71C2414yes—
234C23×D71C2411yescharacteristic
235#11765866—264no—
236C2×Dic142—24no—
237C2×Dic142—24no—
238C2×Dic142—28no—
239C2×Dic142—44no—
240C2×Dic142C2418yes—
241C2×Dic142C2414yes—
242C2×Dic142C2414yes—
243C2×Dic142C2418yes—
244Q8×D71—232no—
245C2×D284—216no—
246C2×D284—28no—
247C2×D284—28no—
248C2×D284—44no—
249C2×D284C24116yes—
250C2×D284C2418yes—
251C2×D284C2418yes—
252C2×D284C2418yes—
253C22×Dic71C2412yes—
254C22×Dic71C2412yes—
255C22×Dic71C2412yes—
256C22×Dic71C2411yescharacteristic
257C22×Dic71C2411yescharacteristic
258C22×Dic71C2412yes—
259C22×Dic71C2411yescharacteristic
260C2×C4×D71—28no—
261C2×C4×D71—24no—
262C2×C4×D71—216no—
263C2×C4×D71—44no—
264C2×C4×D71—48no—
265C2×C4×D71—48no—
266C2×C4×D71—42no—
267C2×C4×D71#4118yes—
268C2×C4×D71C2418yes—
269C2×C4×D71C24116yes—
270C2×C4×D71C2414yes—
271C2×C4×D71C2418yes—
272C2×C4×D71C2414yes—
273C2×C4×D71C24116yes—
274C2×C4×D71C24116yes—
275C2×C4×D71C2414yes—
276C4⋊Dic71C2414yes—
277C4⋊Dic71C24116yes—
278C4⋊Dic71C2418yes—
279C4⋊Dic71C2418yes—
280C4⋊Dic71C2414yes—
281Dic71⋊C4C2418yes—
282Dic71⋊C4C2418yes—
283Dic71⋊C4C2418yes—
284Dic71⋊C4C2418yes—
285Dic71⋊C4C2418yes—
286Dic71⋊C4C2418yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C24116yes—
289Dic71⋊C4C2418yes—
290Dic71⋊C4C2418yes—
291(C2×D71)⋊C4C24116yes—
292(C2×D71)⋊C4C2418yes—
293(C2×D71)⋊C4C24116yes—
294(C2×D71)⋊C4C2418yes—
295(C2×D71)⋊C4C24116yes—
296(C2×D71)⋊C4C24116yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C24116yes—
299(C2×D71)⋊C4C24116yes—
300(C2×D71)⋊C4C24116yes—
301C4×Dic71C2418yes—
302C4×Dic71C2418yes—
303C4×Dic71C2414yes—
304C4×Dic71C2414yes—
305C4×Dic71C2418yes—
306C4×Dic71C2414yes—
307C4×Dic71C24116yes—
308C4×Dic71C2418yes—
309C2×Q8×C71—24no—
310C2×Q8×C71—28no—
311C2×Q8×C71—24no—
312C2×Q8×C71C2414yes—
313C2×Q8×C71C2418yes—
314C2×Q8×C71C2414yes—
315C22×C4×C71C2412yes—
316C22×C4×C71C2412yes—
317C22×C4×C71C2411yescharacteristic
318C22×C4×C71C2414yes—
319C22×C4×C71C2412yes—
320C22×C4×C71C2412yes—
321C22×C4×C71C2411yescharacteristic
322C22×C4×C71C2411yescharacteristic
323C4⋊C4×C71C2414yes—
324C4⋊C4×C71C24116yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2414yes—
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C2418yes—
329C4⋊C4×C71C24116yes—
330C4⋊C4×C71C24116yes—
331C4⋊C4×C71C2418yes—
332C42×C71C2418yes—
333C42×C71C24116yes—
334C42×C71C2414yes—
335C42×C71C2418yes—
336C23×C71C2511yescharacteristic
337C22×D71—22no—
338C22×D71—22no—
339C22×D71—28no—
340C22×D71—28no—
341C22×D71—28no—
342C22×D71C2×#4114yes—
343C22×D71C2518yes—
344C22×D71C2512yes—
345Q8×C71—28no—
346Q8×C71—216no—
347Q8×C71—28no—
348C2×C4×C71—28no—
349C2×C4×C71—24no—
350C2×C4×C71—24no—
351C2×C4×C71—24no—
352C2×C4×C71—24no—
353C2×C4×C71—22no—
354C2×C4×C71C2×#4114yes—
355C2×C4×C712−1+414yes—
356C2×C4×C71C2514yes—
357C2×C4×C71C2514yes—
358C2×C4×C71C2512yes—
359C2×C4×C71C2514yes—
360C2×C4×C71C2514yes—
361C2×C4×C71C2518yes—
362C2×C4×C71C2512yes—
363C2×C4×C71C2512yes—
364C2×Dic71—24no—
365C2×Dic71—22no—
366C2×Dic71—24no—
367C2×Dic71—24no—
368C2×Dic71—24no—
369C2×Dic71—22no—
370C2×Dic71C2×#4114yes—
371C2×Dic71C2512yes—
372C2×Dic71C2514yes—
373C2×Dic71C2514yes—
374C2×Dic71C2514yes—
375C2×Dic71C2512yes—
376C2×Dic71C2514yes—
377C2×Dic71C2512yes—
378D284—232no—
379D284—216no—
380D284—216no—
381D284—48no—
382C4×D71—216no—
383C4×D71—28no—
384C4×D71—232no—
385C4×D71—44no—
386C4×D71—416no—
387C4×D71—416no—
388C4×D71—48no—
389C4×D71C2×#41116yes—
390Dic142—28no—
391Dic142—28no—
392Dic142—216no—
393Dic142—48no—
394C22×C71C22×#4112yes—
395C22×C71C2×2−1+412yes—
396C22×C71#58512yes—
397C22×C71C2611yescharacteristic
398C2×D71—22no—
399C2×D71—22no—
400C2×D71—28no—
401C2×D71—28no—
402C2×D71—28no—
403C2×D71—28no—
404C2×D71—416no—
405C2×D71C22×#4114yes—
406C4×C71—24no—
407C4×C71—28no—
408C4×C71—24no—
409C4×C71—24no—
410C4×C71—24no—
411C4×C71—22no—
412C4×C71C22×#4114yes—
413C4×C71C2×2−1+414yes—
414Dic71—24no—
415Dic71—24no—
416Dic71—22no—
417Dic71—22no—
418Dic71—24no—
419Dic71—24no—
420Dic71C22×#4114yes—
421C2×#3507—711nomaximal, Sylow
422C2×C71#350714yescomplemented
423C2×C71C23×#4111yescharacteristic
424C2×C71C22×2−1+411yescharacteristic
425C2×C71C2×#58511yescharacteristic
426D71—24no—
427D71—48no—
428#3507—7132no—
429C2×#559—711no—
430C2×#559—711no—
431C2×#557—711no—
432C2×#557D7111yescharacteristic, complemented
433C2×#556—712no—
434C2×#556—712no—
435C2×#556—712no—
436C2×#554—712no—
437C2×#552—714no—
438C2×#539—714no—
439C2×#536—712no—
440C2×#533—711no—
441C2×#532—711no—
442C2×#529—712no—
443C2×#529—712no—
444C2×#520—712no—
445C22×C4×Q8—711no—
446C71C2×#350711yescharacteristic, complemented, Sylow
447C22×#41—712no—
448C23×Q8—711no—
449#559—7116no—
450#559—7116no—
451#557—7116no—
452#557C2×D71116yescomplemented
453#556—7132no—
454#556—7132no—
455#556—7132no—
456#554—7132no—
457#552—7164no—
458#539—7164no—
459#536—7132no—
460#533—7116no—
461#532—7116no—
462C2×C4⋊Q8—711no—
463C2×C4⋊Q8—712no—
464C2×C4⋊Q8—711no—
465C2×C4⋊Q8C2×D7111yescharacteristic
466C2×C4⋊Q8C2×D7112yes—
467C2×#127—711no—
468#529—7132no—
469#529—7132no—
470C2×#126—714no—
471C2×#126—714no—
472C2×#126—714no—
473C2×#126—714no—
474C2×#125—712no—
475C2×#125—712no—
476C2×#125—714no—
477C2×#125C2×D7112yes—
478C2×#125C2×D7114yes—
479C2×#124—712no—
480C2×#124—712no—
481C2×#124—712no—
482C2×#124—712no—
483C2×#124—712no—
484C2×#123—714no—
485C2×#123—714no—
486C2×#123—714no—
487C2×#123—714no—
488C2×C22⋊Q8—711no—
489C2×C22⋊Q8—711no—
490C2×C22⋊Q8—712no—
491C2×C22⋊Q8—714no—
492C2×C22⋊Q8—714no—
493C2×C22⋊Q8—714no—
494C2×C22⋊Q8—714no—
495C2×#121—712no—
496C2×#121—712no—
497#520—7132no—
498C2×C4×Q8—711no—
499C2×C4×Q8—712no—
500C2×C4×Q8—7116no—
501C2×C4×Q8—712no—
502C2×C4×Q8—711no—
503C2×C4×Q8—712no—
504C2×C4×Q8—712no—
505C2×C4×Q8—711no—
506C2×C4×Q8—712no—
507C2×C4×Q8—711no—
508C2×C4×Q8C2×D7111yescharacteristic
509C2×C4×Q8C2×D7112yes—
510C2×C4×Q8C2×D7112yes—
511C2×C4×Q8C2×D7111yescharacteristic
512C2×C4×D4—714no—
513C2×C4×D4—712no—
514C2×C4×D4—712no—
515C2×C4×D4—712no—
516C2×C4×D4—712no—
517C2×C4×D4—714no—
518C2×C4×D4—712no—
519C2×C4×D4—712no—
520C2×#117—714no—
521C2×#117—712no—
522C2×#117—714no—
523C2×#117—714no—
524C22×C4⋊C4—711no—
525C22×C4⋊C4—712no—
526C22×C4⋊C4—714no—
527C22×C42—712no—
528C22×C42—711no—
529C2×#41—7116no—
530C2×#41—14216no—
531C22×Q8—718no—
532C22×Q8—712no—
533C22×Q8—711no—
534C22×Q8—712no—
535C22×Q8—711no—
536C22×Q8—1428no—
537C22×Q8C22×D7111yescharacteristic
538C22×Q8C22×D7112yes—
539C22×Q8C22×D7111yescharacteristic
540C22×D4—712no—
541C22×D4—712no—
542C22×D4—714no—
543C22×D4—712no—
544C23×C4—712no—
545C23×C4—711no—
546C23×C4—714no—
547C23×C4—714no—
548C23×C4—711no—
549C23×C4—714no—
550C23×C4—712no—
551C23×C4—711no—
552C4⋊Q8—718no—
553C4⋊Q8—7116no—
554C4⋊Q8—718no—
555C4⋊Q8C22×D7118yes—
556C4⋊Q8C22×D71116yes—
557#127—718no—
558#126—7132no—
559#126—7132no—
560#126—7132no—
561#126—7132no—
562#125—7116no—
563#125—7116no—
564#125—7132no—
565#125C22×D71116yes—
566#125C22×D71132yes—
567#124—7116no—
568#124—7116no—
569#124—7116no—
570#124—7116no—
571#124—7116no—
572#123—7132no—
573#123—7132no—
574#123—7132no—
575#123—7132no—
576C22⋊Q8—718no—
577C22⋊Q8—718no—
578C22⋊Q8—7116no—
579C22⋊Q8—7132no—
580C22⋊Q8—7132no—
581C22⋊Q8—7132no—
582C22⋊Q8—7132no—
583#121—7116no—
584#121—7116no—
585C4×Q8—718no—
586C4×Q8—7116no—
587C4×Q8—7116no—
588C4×Q8—718no—
589C4×Q8—7116no—
590C4×Q8—7116no—
591C4×Q8—718no—
592C4×Q8—7116no—
593C4×Q8—718no—
594C4×Q8C22×D7118yes—
595C4×Q8C22×D71116yes—
596C4×Q8C22×D71116yes—
597C4×Q8C22×D7118yes—
598C4×D4—7132no—
599C4×D4—7116no—
600C4×D4—7116no—
601C4×D4—7116no—
602C4×D4—7116no—
603C4×D4—7132no—
604C4×D4—7116no—
605C4×D4—7116no—
606#117—7132no—
607#117—7116no—
608#117—7132no—
609#117—7132no—
610C2×C4⋊C4—712no—
611C2×C4⋊C4—712no—
612C2×C4⋊C4—711no—
613C2×C4⋊C4—714no—
614C2×C4⋊C4—712no—
615C2×C4⋊C4—712no—
616C2×C4⋊C4—712no—
617C2×C4⋊C4—712no—
618C2×C4⋊C4—712no—
619C2×C4⋊C4—712no—
620C2×C4⋊C4—714no—
621C2×C4⋊C4—711no—
622C2×C4⋊C4—712no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—712no—
625C2×C4⋊C4—718no—
626C2×C4⋊C4—7116no—
627C2×C4⋊C4—7132no—
628C2×C4⋊C4C22×D7111yescharacteristic
629C2×C4⋊C4C22×D7114yes—
630C2×C4⋊C4C22×D7112yes—
631C2×C4⋊C4C22×D7114yes—
632C2×C4⋊C4C22×D7111yescharacteristic
633C2×C4⋊C4C22×D7112yes—
634C2×C4⋊C4C22×D7112yes—
635C2×C4⋊C4C22×D7112yes—
636C2×C4⋊C4C22×D7114yes—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—712no—
639C2×C22⋊C4—712no—
640C2×C22⋊C4—714no—
641C2×C22⋊C4—714no—
642C2×C22⋊C4—714no—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—714no—
647C2×C42—714no—
648C2×C42—712no—
649C2×C42—712no—
650C2×C42—712no—
651C2×C42—711no—
652C2×C42—711no—
653C2×C42—712no—
654C2×C42—711no—
655C2×C42—7116no—
656C2×C42—718no—
657C2×C42C22×D7114yes—
658C2×C42C22×D7112yes—
659C2×C42C22×D7112yes—
660C2×C42C22×D7111yescharacteristic
661C24—711no—
662C24—714no—
663#41—14264no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—2844no—
668C2×Q8—718no—
669C2×Q8—714no—
670C2×Q8—718no—
671C2×Q8—714no—
672C2×Q8—1428no—
673C2×Q8—14232no—
674C2×Q8—1424no—
675C2×Q8—1424no—
676C2×Q8C23×D7114yes—
677C2×Q8C23×D7118yes—
678C2×Q8C23×D7114yes—
679C2×D4—2844no—
680C2×D4—718no—
681C2×D4—718no—
682C2×D4—7116no—
683C2×D4—718no—
684C2×D4—14216no—
685C2×D4—1428no—
686C2×D4—1428no—
687C22×C4—2844no—
688C22×C4—2848no—
689C22×C4—2848no—
690C22×C4—2842no—
691C22×C4—718no—
692C22×C4—714no—
693C22×C4—7116no—
694C22×C4—7116no—
695C22×C4—711no—
696C22×C4—718no—
697C22×C4—714no—
698C22×C4—711no—
699C22×C4—712no—
700C22×C4—712no—
701C22×C4—712no—
702C22×C4—711no—
703C22×C4—712no—
704C22×C4—714no—
705C22×C4—718no—
706C22×C4—7116no—
707C22×C4—14216no—
708C22×C4—1428no—
709C22×C4—1424no—
710C22×C4C23×D7112yes—
711C22×C4C23×D7112yes—
712C22×C4C23×D7114yes—
713C22×C4C23×D7111yescharacteristic
714C22×C4C23×D7112yes—
715C22×C4C23×D7112yes—
716C22×C4C23×D7111yescharacteristic
717C22×C4C23×D7111yescharacteristic
718C4⋊C4—718no—
719C4⋊C4—718no—
720C4⋊C4—718no—
721C4⋊C4—718no—
722C4⋊C4—718no—
723C4⋊C4—718no—
724C4⋊C4—7116no—
725C4⋊C4—718no—
726C4⋊C4—7116no—
727C4⋊C4—718no—
728C4⋊C4—714no—
729C4⋊C4—7116no—
730C4⋊C4—718no—
731C4⋊C4—718no—
732C4⋊C4—714no—
733C4⋊C4C23×D7114yes—
734C4⋊C4C23×D71116yes—
735C4⋊C4C23×D7118yes—
736C4⋊C4C23×D71116yes—
737C4⋊C4C23×D7114yes—
738C4⋊C4C23×D7118yes—
739C4⋊C4C23×D7118yes—
740C4⋊C4C23×D7118yes—
741C4⋊C4C23×D71116yes—
742C22⋊C4—7116no—
743C22⋊C4—718no—
744C22⋊C4—718no—
745C22⋊C4—7116no—
746C22⋊C4—7116no—
747C22⋊C4—7116no—
748C22⋊C4—7116no—
749C22⋊C4—7116no—
750C22⋊C4—7116no—
751C22⋊C4—7116no—
752C42—718no—
753C42—718no—
754C42—714no—
755C42—714no—
756C42—718no—
757C42—714no—
758C42—7116no—
759C42—718no—
760C42C23×D7118yes—
761C42C23×D7114yes—
762C42C23×D71116yes—
763C42C23×D7118yes—
764C23—714no—
765C23—712no—
766C23—718no—
767C23—1428no—
768C23—1428no—
769C23—1428no—
770C23—1422no—
771C23—1422no—
772C23C24×D7111yescharacteristic
773Q8—28no—
774Q8—216no—
775Q8—28no—
776Q8—2848no—
777Q8—14216no—
778Q8—1428no—
779Q8—1428no—
780D4—2848no—
781D4—14232no—
782D4—14216no—
783D4—14216no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—2848no—
791C2×C4—28416no—
792C2×C4—28416no—
793C2×C4—2844no—
794C2×C4—714no—
795C2×C4—712no—
796C2×C4—7116no—
797C2×C4—712no—
798C2×C4—714no—
799C2×C4—714no—
800C2×C4—714no—
801C2×C4—712no—
802C2×C4—714no—
803C2×C4—14232no—
804C2×C4—14216no—
805C2×C4—1424no—
806C2×C4—1422no—
807C2×C4—1424no—
808C2×C4—1424no—
809C2×C4—1424no—
810C2×C4—1422no—
811C2×C4—1428no—
812C2×C4#41×D7114yes—
813C2×C4#1455617614yes—
814C2×C4C24×D7114yes—
815C2×C4C24×D7114yes—
816C2×C4C24×D7118yes—
817C2×C4C24×D7112yes—
818C2×C4C24×D7114yes—
819C2×C4C24×D7114yes—
820C2×C4C24×D7112yes—
821C2×C4C24×D7112yes—
822C22—28416no—
823C22—714no—
824C22—1428no—
825C22—1428no—
826C22—1428no—
827C22—1422no—
828C22—1422no—
829C22—1428no—
830C22C2×#41×D7112yes—
831C22C2×#1455617612yes—
832C22#1798683612yes—
833C22C25×D7111yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—714no—
841C4—1424no—
842C4—1422no—
843C4—1424no—
844C4—1424no—
845C4—1424no—
846C4—1422no—
847C4C2×#41×D7114yes—
848C4C2×#1455617614yes—
849C2—2848no—
850C2—1424no—
851C2#2260220614yesdirect product factor
852C2C22×#41×D7111yescharacteristic
853C2C22×#1455617611yescharacteristic
854C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
prime radicalC2×#17986550C2
hypercenterC2×#557D71
hypocenterC71C2×#3507
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602206C2direct (N × H)
2. C2×#17986734C2semidirect
3. C2×#17986734C2semidirect
4. C2×#17986724C2semidirect
5. C2×#17986723C2semidirect
6. C2×#17986721C2semidirect
7. C2×#17986721C2semidirect
8. C2×#17986705C2semidirect
9. C2×#17986681C2semidirect
10. C2×#17986597C2semidirect
11. C2×#17986574C2semidirect
12. C2×#17986553C2semidirect
14. C2×#17986536C2semidirect
15. C2×#17986534C2semidirect
16. C2×#17986481C2semidirect
17. C2×C4×Q8×D71C2semidirect
18. C2×#557×C71C2semidirect
21. #17986734C22semidirect
22. #17986734C22semidirect
23. #17986724C22semidirect
24. #17986723C22semidirect
25. #17986721C22semidirect
26. #17986721C22semidirect
27. #17986705C22semidirect
28. #17986681C22semidirect
29. #17986597C22semidirect
30. #17986574C22semidirect
31. #17986553C22semidirect
37. #17986536C22semidirect
38. #17986534C22semidirect
64. #17986481C22semidirect
74. C4×Q8×D71C22semidirect
92. #557×C71C22semidirect
422. C2×C71#3507semidirect
432. C2×#557D71semidirect
446. C71C2×#3507semidirect
452. #557C2×D71semidirect
851. C2#22602206direct (N × H)

Maximal subgroups

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

subgroupindex
#226022062
C2×#179867342
C2×#179867242
C2×#179867232
C2×#179867212
C2×#179867052
C2×#179866812
C2×#179865972
C2×#179865742
C2×#179865532
C2×#179865502
C2×#179865362
C2×#179865342
C2×#179864812
C2×C4×Q8×D712
C2×#557×C712
C2×#350771