Finite Group Databasebeta

← C2×#22602824 #32905173

Subgroups — C2×#22602824 #32905173

Order 18176.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602824C2132yesmaximal, direct product factor
2C2×#17986753C214yesmaximal, complemented
3C2×Q8×Dic142C211yesmaximal, characteristic, complemented
4C2×#17986725C212yesmaximal, complemented
5C2×#17986723C211yesmaximal, characteristic, complemented
6C2×#17986723C212yesmaximal, complemented
7C2×#17986722C212yesmaximal, complemented
8C2×#17986709C211yesmaximal, characteristic, complemented
9C2×#17986687C212yesmaximal, complemented
10C2×#17986629C212yesmaximal, complemented
11C2×#17986621C212yesmaximal
12C2×#17986610C212yesmaximal, complemented
13C2×#17986608C214yesmaximal, complemented
14C2×#17986607C212yesmaximal, complemented
15C2×#17986554C211yesmaximal, characteristic, complemented
16C2×#17986553C211yesmaximal, characteristic, complemented
17C2×#17986536C211yesmaximal, characteristic
18C2×#557×C71C211yesmaximal, characteristic, complemented
19#17986753C22164yescomplemented
20Q8×Dic142C22116yescomplemented
21#17986725C22132yescomplemented
22#17986723C22132yescomplemented
23#17986723C22116yescomplemented
24#17986722C22132yescomplemented
25#17986709C22116yescomplemented
26#17986687C22132yescomplemented
27#17986629C22132yescomplemented
28#17986621C22132yes—
29#17986610C22132yescomplemented
30#17986608C22164yescomplemented
31#17986607C22132yescomplemented
32#17986554C22116yescomplemented
33#17986553C22116yescomplemented
34C2×#14556128C2212yes—
35C2×#14556128C2211yescharacteristic
36C2×#14556127C2211yescharacteristic
37C2×#14556127C2214yes—
38C2×#14556127C2212yes—
39C2×#14556127C2214yes—
40C2×#14556126C2211yescharacteristic
41#17986536C22116yes—
42C2×#14556123C2214yes—
43C2×#14556123C2212yes—
44C2×#14556123C2214yes—
45C2×#14556123C2214yes—
46C2×#14556123C2214yes—
47C2×#14556123C2214yes—
48C2×#14556122C2214yes—
49C2×#14556120C2212yes—
50C2×#14556120C2214yes—
51C2×#14556119C2212yes—
52C2×#14556119C2214yes—
53C2×#14556119C2211yescharacteristic
54C2×#14556118C2214yes—
55C2×#14556118C2212yes—
56C2×#14556118C2214yes—
57C2×#14556117C2211yescharacteristic
58C2×#14556117C2212yes—
59C2×#14556116C2214yes—
60C2×#14556113C2214yes—
61C2×#14556113C2212yes—
62C2×#14556108C2214yes—
63C2×#14556108C2211yescharacteristic
64C2×#14556108C2212yes—
65C2×#14556108C2212yes—
66C2×#14556106C2214yes—
67C2×#14556106C2214yes—
68C2×#14556106C2212yes—
69C2×#14556104C2211yescharacteristic
70C2×#14556104C2212yes—
71C2×#14556104C2211yescharacteristic
72C2×#14556104C2212yes—
73C2×#14556103C2211yescharacteristic
74C2×Q8×Dic71C2212yes—
75C2×Q8×Dic71C2212yes—
76C2×Q8×Dic71C2212yes—
77C2×C4×Dic142C2212yes—
78C2×C4×Dic142C2212yes—
79C2×C4×Dic142C2211yescharacteristic
80C2×C4×Dic142C2214yes—
81C2×#14556093C2212yes—
82C2×C4×D284C2212yes—
83C2×C4×D284C2211yescharacteristic
84C2×C4×D284C2212yes—
85C2×#14556086C2212yes—
86C2×#14556086C2212yes—
87C2×#14556086C2214yes—
88C2×#14556085C2212yes—
89C2×#14556085C2212yes—
90C2×C4⋊C4×D71C2212yes—
91C2×C42×D71C2211yescharacteristic
92#557×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×C4⋊Q8×C71C2212yes—
95C2×#125×C71C2212yes—
96C2×#125×C71C2214yes—
97C2×C4×Q8×C71C2211yescharacteristic
98C2×C4×Q8×C71C2211yescharacteristic
99C2×C4×Q8×C71C2212yes—
100C2×C4×Q8×C71C2212yes—
101C22×Dic142C2311yescharacteristic
102C22×Dic142C2312yes—
103C22×Dic142C2312yes—
104C22×Dic142C2314yes—
105C22×D284C2311yescharacteristic
106C22×D284C2312yes—
107C22×C4×D71C2311yescharacteristic
108C22×C4×D71C2311yescharacteristic
109C22×C4×D71C2312yes—
110C22×C4×D71C2311yescharacteristic
111C22×C4×D71C2314yes—
112#14556128C23116yes—
113#14556128C2318yes—
114#14556127C23132yes—
115#14556127C23116yes—
116#14556127C2318yes—
117#14556127C23132yes—
118#14556126C2318yes—
119#14556123C23132yes—
120#14556123C23116yes—
121#14556123C23132yes—
122#14556123C23132yes—
123#14556123C23132yes—
124#14556123C23132yes—
125#14556122C23132yes—
126#14556120C23132yes—
127#14556120C23116yes—
128#14556119C23116yes—
129#14556119C23132yes—
130#14556119C2318yes—
131#14556118C23132yes—
132#14556118C23116yes—
133#14556118C23132yes—
134#14556117C23116yes—
135#14556117C2318yes—
136#14556116C23132yes—
137#14556113C23132yes—
138#14556113C23116yes—
139#14556108C23116yes—
140#14556108C23132yes—
141#14556108C2318yes—
142#14556108C23116yes—
143#14556106C23132yes—
144#14556106C23132yes—
145#14556106C23116yes—
146#14556104C23116yes—
147#14556104C2318yes—
148#14556104C23116yes—
149#14556104C2318yes—
150#14556103C2318yes—
151Q8×Dic71C23116yes—
152Q8×Dic71C23116yes—
153Q8×Dic71C23116yes—
154C4×Dic142C23116yes—
155C4×Dic142C23132yes—
156C4×Dic142C23116yes—
157C4×Dic142C2318yes—
158#14556093C23116yes—
159C4×D284C23116yes—
160C4×D284C23116yes—
161C4×D284C2318yes—
162#14556086C23132yes—
163#14556086C23116yes—
164#14556086C23116yes—
165#14556085C23116yes—
166#14556085C23116yes—
167C2×C4⋊Dic71C2312yes—
168C2×C4⋊Dic71C2311yescharacteristic
169C2×C4⋊Dic71C2312yes—
170C2×C4⋊Dic71C2312yes—
171C2×C4⋊Dic71C2311yescharacteristic
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2314yes—
175C2×C4⋊Dic71C2314yes—
176C2×Dic71⋊C4C2314yes—
177C2×Dic71⋊C4C2312yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2312yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C4⋊C4×D71C23116yes—
188C2×(C2×D71)⋊C4C2312yes—
189C2×(C2×D71)⋊C4C2312yes—
190C2×(C2×D71)⋊C4C2312yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×(C2×D71)⋊C4C2312yes—
199C2×C4×Dic71C2311yescharacteristic
200C2×C4×Dic71C2311yescharacteristic
201C2×C4×Dic71C2311yescharacteristic
202C2×C4×Dic71C2312yes—
203C2×C4×Dic71C2314yes—
204C2×C4×Dic71C2314yes—
205C2×C4×Dic71C2314yes—
206C42×D71C2318yes—
207C22×Q8×C71C2311yescharacteristic
208C22×Q8×C71C2311yescharacteristic
209C22×Q8×C71C2312yes—
210C4⋊Q8×C71C23116yes—
211C4⋊Q8×C71C2318yes—
212#125×C71C23132yes—
213#125×C71C23116yes—
214C4×Q8×C71C23116yes—
215C4×Q8×C71C23116yes—
216C4×Q8×C71C2318yes—
217C4×Q8×C71C2318yes—
218C2×C4⋊C4×C71C2311yescharacteristic
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2314yes—
222C2×C4⋊C4×C71C2312yes—
223C2×C4⋊C4×C71C2312yes—
224C2×C4⋊C4×C71C2314yes—
225C2×C4⋊C4×C71C2314yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C42×C71C2312yes—
228C2×C42×C71C2314yes—
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2312yes—
231C23×D71C2411yescharacteristic
232C23×D71C2412yes—
233C2×Dic142—24no—
234C2×Dic142—44no—
235C2×Dic142—44no—
236C2×Dic142—48no—
237C2×Dic142C2414yes—
238C2×Dic142C2418yes—
239C2×Dic142C2418yes—
240C2×Dic142C24116yes—
241C2×D284—24no—
242C2×D284—44no—
243C2×D284C2414yes—
244C2×D284C2418yes—
245C22×Dic71C2411yescharacteristic
246C22×Dic71C2414yes—
247C22×Dic71C2411yescharacteristic
248C22×Dic71C2411yescharacteristic
249C22×Dic71C2412yes—
250C22×Dic71C2412yes—
251C22×Dic71C2412yes—
252C2×C4×D71—24no—
253C2×C4×D71—24no—
254C2×C4×D71—28no—
255C2×C4×D71—48no—
256C2×C4×D71—42no—
257C2×C4×D71C2414yes—
258C2×C4×D71C2414yes—
259C2×C4×D71C2418yes—
260C2×C4×D71C2414yes—
261C2×C4×D71C24116yes—
262C4⋊Dic71C2418yes—
263C4⋊Dic71C2414yes—
264C4⋊Dic71C2418yes—
265C4⋊Dic71C2418yes—
266C4⋊Dic71C2414yes—
267C4⋊Dic71C2418yes—
268C4⋊Dic71C24116yes—
269C4⋊Dic71C24116yes—
270C4⋊Dic71C24116yes—
271Dic71⋊C4C24116yes—
272Dic71⋊C4C2418yes—
273Dic71⋊C4C2418yes—
274Dic71⋊C4C2418yes—
275Dic71⋊C4C2418yes—
276Dic71⋊C4C24116yes—
277Dic71⋊C4C2418yes—
278Dic71⋊C4C24116yes—
279Dic71⋊C4C2418yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C24116yes—
282(C2×D71)⋊C4C2418yes—
283(C2×D71)⋊C4C2418yes—
284(C2×D71)⋊C4C2418yes—
285(C2×D71)⋊C4C2418yes—
286(C2×D71)⋊C4C2418yes—
287(C2×D71)⋊C4C24116yes—
288(C2×D71)⋊C4C24116yes—
289(C2×D71)⋊C4C24116yes—
290(C2×D71)⋊C4C24116yes—
291(C2×D71)⋊C4C2418yes—
292(C2×D71)⋊C4C2418yes—
293C4×Dic71C2414yes—
294C4×Dic71C2414yes—
295C4×Dic71C2414yes—
296C4×Dic71C2418yes—
297C4×Dic71C24116yes—
298C4×Dic71C24116yes—
299C4×Dic71C24116yes—
300C2×Q8×C71—24no—
301C2×Q8×C71—28no—
302C2×Q8×C71—24no—
303C2×Q8×C71C2414yes—
304C2×Q8×C71C2418yes—
305C2×Q8×C71C2414yes—
306C22×C4×C71C2412yes—
307C22×C4×C71C2411yescharacteristic
308C22×C4×C71C2412yes—
309C22×C4×C71C2412yes—
310C22×C4×C71C2412yes—
311C22×C4×C71C2414yes—
312C22×C4×C71C2411yescharacteristic
313C22×C4×C71C2411yescharacteristic
314C4⋊C4×C71C2414yes—
315C4⋊C4×C71C2414yes—
316C4⋊C4×C71C2418yes—
317C4⋊C4×C71C24116yes—
318C4⋊C4×C71C2418yes—
319C4⋊C4×C71C2418yes—
320C4⋊C4×C71C24116yes—
321C4⋊C4×C71C24116yes—
322C4⋊C4×C71C2418yes—
323C42×C71C2418yes—
324C42×C71C24116yes—
325C42×C71C2414yes—
326C42×C71C2418yes—
327C23×C71C2511yescharacteristic
328C22×D71—22no—
329C22×D71—22no—
330C22×D71—24no—
331C22×D71—24no—
332C22×D71—24no—
333C22×D71—22no—
334C22×D71C2512yes—
335C22×D71C2514yes—
336Q8×C71—216no—
337Q8×C71—28no—
338Q8×C71—28no—
339C2×C4×C71—24no—
340C2×C4×C71—28no—
341C2×C4×C71—24no—
342C2×C4×C71—24no—
343C2×C4×C71—22no—
344C2×C4×C71—24no—
345C2×C4×C712−1+414yes—
346C2×C4×C712−1+414yes—
347C2×C4×C71C2514yes—
348C2×C4×C71C2514yes—
349C2×C4×C71C2512yes—
350C2×C4×C71C2514yes—
351C2×C4×C71C2514yes—
352C2×C4×C71C2518yes—
353C2×C4×C71C2512yes—
354C2×C4×C71C2512yes—
355C2×Dic71—22no—
356C2×Dic71—22no—
357C2×Dic71—24no—
358C2×Dic71—24no—
359C2×Dic71—28no—
360C2×Dic71—22no—
361C2×Dic71—24no—
362C2×Dic71C2512yes—
363C2×Dic71C2514yes—
364C2×Dic71C2514yes—
365C2×Dic71C2512yes—
366C2×Dic71C2514yes—
367C2×Dic71C2512yes—
368C2×Dic71C2518yes—
369D284—28no—
370D284—48no—
371C4×D71—28no—
372C4×D71—28no—
373C4×D71—216no—
374C4×D71—44no—
375C4×D71—416no—
376Dic142—28no—
377Dic142—416no—
378Dic142—48no—
379Dic142—48no—
380C22×C71C2×2−1+412yes—
381C22×C71C2×2−1+412yes—
382C22×C71#58512yes—
383C22×C71C2611yescharacteristic
384C2×D71—22no—
385C2×D71—22no—
386C2×D71—24no—
387C2×D71—24no—
388C2×D71—24no—
389C2×D71—22no—
390C2×D71—44no—
391C2×D71—48no—
392C4×C71—24no—
393C4×C71—28no—
394C4×C71—24no—
395C4×C71—22no—
396C4×C71—24no—
397C4×C71—24no—
398C4×C71C2×2−1+414yes—
399C4×C71C2×2−1+414yes—
400Dic71—24no—
401Dic71—22no—
402Dic71—22no—
403Dic71—24no—
404Dic71—24no—
405Dic71—28no—
406Dic71—22no—
407C2×#3555—711nomaximal, Sylow
408C2×C71#355514yescomplemented
409C2×C71C22×2−1+411yescharacteristic
410C2×C71C22×2−1+411yescharacteristic
411C2×C71C2×#58511yescharacteristic
412D71—42no—
413D71—44no—
414#3555—7132no—
415C2×#563—714no—
416C2×Q82—711no—
417C2×#557—712no—
418C2×#557D7111yescharacteristic, complemented
419C2×#556—712no—
420C2×#556—711no—
421C2×#556—712no—
422C2×#554—711no—
423C2×#552—712no—
424C2×#544—712no—
425C2×#542—712no—
426C2×#541—712no—
427C2×#541—714no—
428C2×#541—712no—
429C2×#533—711no—
430C2×#533—711no—
431C2×#529—711no—
432C71C2×#355511yescharacteristic, complemented, Sylow
433#563—7164no—
434Q82—7116no—
435#557—7132no—
436#557C2×D71116yescomplemented
437#556—7132no—
438#556—7116no—
439#556—7132no—
440#554—7116no—
441#552—7132no—
442#544—7132no—
443#542—7132no—
444#541—7132no—
445#541—7164no—
446#541—7132no—
447#533—7116no—
448#533—7116no—
449C2×C4⋊Q8—711no—
450C2×C4⋊Q8—711no—
451C2×C4⋊Q8—714no—
452C2×C4⋊Q8—712no—
453C2×C4⋊Q8—714no—
454C2×C4⋊Q8—711no—
455C2×C4⋊Q8—712no—
456C2×C4⋊Q8C2×D7111yescharacteristic
457C2×C4⋊Q8C2×D7112yes—
458#529—7116no—
459C2×#126—712no—
460C2×#126—714no—
461C2×#126—714no—
462C2×#126—714no—
463C2×#126—714no—
464C2×#126—714no—
465C2×#126—714no—
466C2×#125—711no—
467C2×#125—712no—
468C2×#125—712no—
469C2×#125—714no—
470C2×#125—714no—
471C2×#125—714no—
472C2×#125—712no—
473C2×#125—714no—
474C2×#125C2×D7114yes—
475C2×#125C2×D7112yes—
476C2×#124—711no—
477C2×#124—712no—
478C2×#124—714no—
479C2×#123—712no—
480C2×#123—714no—
481C2×C22⋊Q8—711no—
482C2×C22⋊Q8—712no—
483C2×C22⋊Q8—711no—
484C2×C22⋊Q8—712no—
485C2×C22⋊Q8—711no—
486C2×C22⋊Q8—712no—
487C2×C22⋊Q8—712no—
488C2×C22⋊Q8—714no—
489C2×C22⋊Q8—712no—
490C2×C22⋊Q8—714no—
491C2×C22⋊Q8—714no—
492C2×#121—711no—
493C2×C4×Q8—712no—
494C2×C4×Q8—712no—
495C2×C4×Q8—712no—
496C2×C4×Q8—712no—
497C2×C4×Q8—712no—
498C2×C4×Q8—711no—
499C2×C4×Q8—712no—
500C2×C4×Q8—714no—
501C2×C4×Q8C2×D7111yescharacteristic
502C2×C4×Q8C2×D7111yescharacteristic
503C2×C4×Q8C2×D7112yes—
504C2×C4×Q8C2×D7112yes—
505C2×C4×D4—712no—
506C2×C4×D4—711no—
507C2×C4×D4—712no—
508C2×#117—712no—
509C2×#117—714no—
510C2×#117—712no—
511C2×#117—712no—
512C2×#117—712no—
513C22×C4⋊C4—712no—
514C22×C42—711no—
515C22×Q8—712no—
516C22×Q8—712no—
517C22×Q8—714no—
518C22×Q8—711no—
519C22×Q8C22×D7112yes—
520C22×Q8C22×D7111yescharacteristic
521C22×Q8C22×D7111yescharacteristic
522C22×D4—712no—
523C22×D4—711no—
524C23×C4—714no—
525C23×C4—711no—
526C23×C4—712no—
527C23×C4—711no—
528C23×C4—711no—
529C4⋊Q8—718no—
530C4⋊Q8—718no—
531C4⋊Q8—7132no—
532C4⋊Q8—7116no—
533C4⋊Q8—7132no—
534C4⋊Q8—718no—
535C4⋊Q8—7116no—
536C4⋊Q8C22×D7118yes—
537C4⋊Q8C22×D71116yes—
538#126—7116no—
539#126—7132no—
540#126—7132no—
541#126—7132no—
542#126—7132no—
543#126—7132no—
544#126—7132no—
545#125—718no—
546#125—7116no—
547#125—7116no—
548#125—7132no—
549#125—7132no—
550#125—7132no—
551#125—7116no—
552#125—7132no—
553#125C22×D71132yes—
554#125C22×D71116yes—
555#124—718no—
556#124—7116no—
557#124—7132no—
558#123—7116no—
559#123—7132no—
560C22⋊Q8—718no—
561C22⋊Q8—7116no—
562C22⋊Q8—718no—
563C22⋊Q8—7116no—
564C22⋊Q8—718no—
565C22⋊Q8—7116no—
566C22⋊Q8—7116no—
567C22⋊Q8—7132no—
568C22⋊Q8—7116no—
569C22⋊Q8—7132no—
570C22⋊Q8—7132no—
571#121—718no—
572C4×Q8—7116no—
573C4×Q8—7116no—
574C4×Q8—7116no—
575C4×Q8—7116no—
576C4×Q8—7116no—
577C4×Q8—718no—
578C4×Q8—7116no—
579C4×Q8—7132no—
580C4×Q8C22×D7118yes—
581C4×Q8C22×D7118yes—
582C4×Q8C22×D71116yes—
583C4×Q8C22×D71116yes—
584C4×D4—7116no—
585C4×D4—718no—
586C4×D4—7116no—
587#117—7116no—
588#117—7132no—
589#117—7116no—
590#117—7116no—
591#117—7116no—
592C2×C4⋊C4—712no—
593C2×C4⋊C4—714no—
594C2×C4⋊C4—712no—
595C2×C4⋊C4—711no—
596C2×C4⋊C4—712no—
597C2×C4⋊C4—712no—
598C2×C4⋊C4—712no—
599C2×C4⋊C4—712no—
600C2×C4⋊C4—711no—
601C2×C4⋊C4—712no—
602C2×C4⋊C4—712no—
603C2×C4⋊C4—712no—
604C2×C4⋊C4—714no—
605C2×C4⋊C4—714no—
606C2×C4⋊C4—714no—
607C2×C4⋊C4—714no—
608C2×C4⋊C4—712no—
609C2×C4⋊C4—712no—
610C2×C4⋊C4—714no—
611C2×C4⋊C4—714no—
612C2×C4⋊C4—7116no—
613C2×C4⋊C4C22×D7111yescharacteristic
614C2×C4⋊C4C22×D7112yes—
615C2×C4⋊C4C22×D7114yes—
616C2×C4⋊C4C22×D7112yes—
617C2×C4⋊C4C22×D7111yescharacteristic
618C2×C4⋊C4C22×D7112yes—
619C2×C4⋊C4C22×D7114yes—
620C2×C4⋊C4C22×D7112yes—
621C2×C4⋊C4C22×D7114yes—
622C2×C22⋊C4—712no—
623C2×C22⋊C4—712no—
624C2×C22⋊C4—712no—
625C2×C22⋊C4—714no—
626C2×C22⋊C4—712no—
627C2×C22⋊C4—714no—
628C2×C22⋊C4—712no—
629C2×C22⋊C4—714no—
630C2×C22⋊C4—712no—
631C2×C22⋊C4—714no—
632C2×C22⋊C4—712no—
633C2×C42—714no—
634C2×C42—711no—
635C2×C42—712no—
636C2×C42—714no—
637C2×C42—714no—
638C2×C42—711no—
639C2×C42—711no—
640C2×C42—718no—
641C2×C42C22×D7112yes—
642C2×C42C22×D7112yes—
643C2×C42C22×D7111yescharacteristic
644C2×C42C22×D7114yes—
645C24—711no—
646C24—712no—
647C2×Q8—28no—
648C2×Q8—24no—
649C2×Q8—24no—
650C2×Q8—2844no—
651C2×Q8—2844no—
652C2×Q8—2848no—
653C2×Q8—718no—
654C2×Q8—718no—
655C2×Q8—7116no—
656C2×Q8—714no—
657C2×Q8—1424no—
658C2×Q8C23×D7118yes—
659C2×Q8C23×D7114yes—
660C2×Q8C23×D7114yes—
661C2×D4—2844no—
662C2×D4—718no—
663C2×D4—714no—
664C2×D4—1424no—
665C22×C4—2848no—
666C22×C4—2842no—
667C22×C4—714no—
668C22×C4—7116no—
669C22×C4—711no—
670C22×C4—712no—
671C22×C4—712no—
672C22×C4—711no—
673C22×C4—712no—
674C22×C4—714no—
675C22×C4—711no—
676C22×C4—714no—
677C22×C4—714no—
678C22×C4—718no—
679C22×C4—1424no—
680C22×C4—1428no—
681C22×C4—1424no—
682C22×C4C23×D7114yes—
683C22×C4C23×D7112yes—
684C22×C4C23×D7111yescharacteristic
685C22×C4C23×D7112yes—
686C22×C4C23×D7112yes—
687C22×C4C23×D7112yes—
688C22×C4C23×D7111yescharacteristic
689C22×C4C23×D7111yescharacteristic
690C4⋊C4—7116no—
691C4⋊C4—718no—
692C4⋊C4—718no—
693C4⋊C4—718no—
694C4⋊C4—718no—
695C4⋊C4—718no—
696C4⋊C4—7116no—
697C4⋊C4—7116no—
698C4⋊C4—718no—
699C4⋊C4—718no—
700C4⋊C4—7116no—
701C4⋊C4—718no—
702C4⋊C4—718no—
703C4⋊C4—714no—
704C4⋊C4—714no—
705C4⋊C4—718no—
706C4⋊C4—718no—
707C4⋊C4—7116no—
708C4⋊C4—7116no—
709C4⋊C4—7116no—
710C4⋊C4C23×D7114yes—
711C4⋊C4C23×D7118yes—
712C4⋊C4C23×D71116yes—
713C4⋊C4C23×D7118yes—
714C4⋊C4C23×D7114yes—
715C4⋊C4C23×D7118yes—
716C4⋊C4C23×D71116yes—
717C4⋊C4C23×D7118yes—
718C4⋊C4C23×D71116yes—
719C22⋊C4—718no—
720C22⋊C4—718no—
721C22⋊C4—718no—
722C22⋊C4—718no—
723C22⋊C4—7116no—
724C22⋊C4—7116no—
725C22⋊C4—718no—
726C22⋊C4—7116no—
727C22⋊C4—718no—
728C22⋊C4—7116no—
729C22⋊C4—718no—
730C42—714no—
731C42—714no—
732C42—714no—
733C42—7116no—
734C42—718no—
735C42—7116no—
736C42—7116no—
737C42C23×D7114yes—
738C42C23×D7118yes—
739C42C23×D7118yes—
740C42C23×D71116yes—
741C23—712no—
742C23—714no—
743C23—1422no—
744C23—1424no—
745C23—1422no—
746C23—1424no—
747C23—1424no—
748C23—1422no—
749C23C24×D7111yescharacteristic
750Q8—216no—
751Q8—28no—
752Q8—28no—
753Q8—2848no—
754Q8—2848no—
755Q8—28416no—
756Q8—1428no—
757D4—2848no—
758D4—1428no—
759C2×C4—28no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—24no—
763C2×C4—22no—
764C2×C4—24no—
765C2×C4—28416no—
766C2×C4—2844no—
767C2×C4—712no—
768C2×C4—714no—
769C2×C4—714no—
770C2×C4—712no—
771C2×C4—714no—
772C2×C4—712no—
773C2×C4—718no—
774C2×C4—1422no—
775C2×C4—1422no—
776C2×C4—1424no—
777C2×C4—1424no—
778C2×C4—1428no—
779C2×C4—1422no—
780C2×C4—1424no—
781C2×C4—1428no—
782C2×C4—1428no—
783C2×C4—14216no—
784C2×C4#1455617514yes—
785C2×C4#1455617614yes—
786C2×C4C24×D7118yes—
787C2×C4C24×D7114yes—
788C2×C4C24×D7112yes—
789C2×C4C24×D7114yes—
790C2×C4C24×D7114yes—
791C2×C4C24×D7114yes—
792C2×C4C24×D7112yes—
793C2×C4C24×D7112yes—
794C22—2844no—
795C22—2848no—
796C22—1422no—
797C22—1424no—
798C22—1422no—
799C22—1424no—
800C22—1424no—
801C22—1422no—
802C22C2×#1455617512yes—
803C22C2×#1455617612yes—
804C22#1798683612yes—
805C22C25×D7111yescharacteristic
806C4—28no—
807C4—24no—
808C4—24no—
809C4—24no—
810C4—22no—
811C4—24no—
812C4—1422no—
813C4—1422no—
814C4—1424no—
815C4—1424no—
816C4—1428no—
817C4—1422no—
818C4—1424no—
819C4C2×#1455617514yes—
820C4C2×#1455617614yes—
821C2—2842no—
822C2—2844no—
823C2#2260282414yesdirect product factor
824C2C22×#1455617511yescharacteristic
825C2C22×#1455617611yescharacteristic
826C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
prime radicalC2×#14556103C22
hypercenterC2×#557D71
hypocenterC71C2×#3555
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602824C2direct (N × H)
2. C2×#17986753C2semidirect
3. C2×Q8×Dic142C2semidirect
4. C2×#17986725C2semidirect
5. C2×#17986723C2semidirect
6. C2×#17986723C2semidirect
7. C2×#17986722C2semidirect
8. C2×#17986709C2semidirect
9. C2×#17986687C2semidirect
10. C2×#17986629C2semidirect
12. C2×#17986610C2semidirect
13. C2×#17986608C2semidirect
14. C2×#17986607C2semidirect
15. C2×#17986554C2semidirect
16. C2×#17986553C2semidirect
18. C2×#557×C71C2semidirect
19. #17986753C22semidirect
20. Q8×Dic142C22semidirect
21. #17986725C22semidirect
22. #17986723C22semidirect
23. #17986723C22semidirect
24. #17986722C22semidirect
25. #17986709C22semidirect
26. #17986687C22semidirect
27. #17986629C22semidirect
29. #17986610C22semidirect
30. #17986608C22semidirect
31. #17986607C22semidirect
32. #17986554C22semidirect
33. #17986553C22semidirect
92. #557×C71C22semidirect
408. C2×C71#3555semidirect
418. C2×#557D71semidirect
432. C71C2×#3555semidirect
436. #557C2×D71semidirect
823. C2#22602824direct (N × H)

Maximal subgroups

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

subgroupindex
#226028242
C2×#179867532
C2×Q8×Dic1422
C2×#179867252
C2×#179867232
C2×#179867222
C2×#179867092
C2×#179866872
C2×#179866292
C2×#179866212
C2×#179866102
C2×#179866082
C2×#179866072
C2×#179865542
C2×#179865532
C2×#179865362
C2×#557×C712
C2×#355571