Finite Group Databasebeta

← C2×#22602828 #32905172

Subgroups — C2×#22602828 #32905172

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#22602828C2132yesmaximal, direct product factor
2C2×#17986750C214yesmaximal, complemented
3C2×Q8×Dic142C211yesmaximal, characteristic, complemented
4C2×#17986728C211yesmaximal, characteristic, complemented
5C2×#17986727C212yesmaximal, complemented
6C2×#17986722C212yesmaximal, complemented
7C2×#17986722C211yesmaximal, characteristic, complemented
8C2×#17986720C212yesmaximal, complemented
9C2×#17986709C211yesmaximal, characteristic, complemented
10C2×#17986683C212yesmaximal, complemented
11C2×#17986626C212yesmaximal, complemented
12C2×#17986620C212yesmaximal
13C2×#17986611C212yesmaximal, complemented
14C2×#17986610C212yesmaximal, complemented
15C2×#17986608C214yesmaximal, complemented
16C2×#17986556C211yesmaximal, characteristic, complemented
17C2×#17986533C211yesmaximal, characteristic
18C2×#533×C71C211yesmaximal, characteristic, complemented
19#17986750C22164yescomplemented
20Q8×Dic142C22116yescomplemented
21#17986728C22116yescomplemented
22#17986727C22132yescomplemented
23#17986722C22132yescomplemented
24#17986722C22116yescomplemented
25#17986720C22132yescomplemented
26#17986709C22116yescomplemented
27#17986683C22132yescomplemented
28#17986626C22132yescomplemented
29#17986620C22132yes—
30#17986611C22132yescomplemented
31#17986610C22132yescomplemented
32#17986608C22164yescomplemented
33#17986556C22116yescomplemented
34C2×#14556128C2211yescharacteristic
35C2×#14556128C2211yescharacteristic
36C2×#14556128C2212yes—
37C2×#14556128C2212yes—
38C2×#14556127C2212yes—
39C2×#14556127C2214yes—
40C2×#14556126C2214yes—
41#17986533C22116yes—
42C2×#14556123C2214yes—
43C2×#14556123C2214yes—
44C2×#14556123C2214yes—
45C2×#14556123C2214yes—
46C2×#14556122C2212yes—
47C2×#14556121C2214yes—
48C2×#14556121C2214yes—
49C2×#14556120C2212yes—
50C2×#14556120C2211yescharacteristic
51C2×#14556120C2212yes—
52C2×#14556119C2212yes—
53C2×#14556119C2214yes—
54C2×#14556118C2214yes—
55C2×#14556118C2214yes—
56C2×#14556118C2214yes—
57C2×#14556118C2214yes—
58C2×#14556116C2211yescharacteristic
59C2×#14556116C2212yes—
60C2×#14556114C2214yes—
61C2×#14556111C2212yes—
62C2×#14556110C2214yes—
63C2×#14556107C2211yescharacteristic
64C2×#14556107C2212yes—
65C2×#14556107C2212yes—
66C2×#14556106C2214yes—
67C2×#14556106C2214yes—
68C2×#14556104C2214yes—
69C2×#14556104C2212yes—
70C2×#14556104C2212yes—
71C2×#14556102C2211yescharacteristic
72C2×Q8×Dic71C2212yes—
73C2×Q8×Dic71C2212yes—
74C2×C4×Dic142C2211yescharacteristic
75C2×C4×Dic142C2212yes—
76C2×C4×Dic142C2212yes—
77C2×C4×Dic142C2212yes—
78C2×C4×Dic142C2212yes—
79C2×C4×Dic142C2212yes—
80C2×#14556093C2214yes—
81C2×C4×D284C2211yescharacteristic
82C2×C4×D284C2212yes—
83C2×C4×C22⋊D71C2212yes—
84C2×#14556087C2212yes—
85C2×#14556086C2212yes—
86C2×#14556086C2214yes—
87C2×#14556085C2212yes—
88C2×C4⋊C4×D71C2212yes—
89#533×C71C22116yescomplemented
90C2×C4⋊Q8×C71C2211yescharacteristic
91C2×C4⋊Q8×C71C2211yescharacteristic
92C2×#125×C71C2212yes—
93C2×C22⋊Q8×C71C2211yescharacteristic
94C2×C22⋊Q8×C71C2211yescharacteristic
95C2×C22⋊Q8×C71C2212yes—
96C2×C4×Q8×C71C2211yescharacteristic
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2211yescharacteristic
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C22×Dic142C2311yescharacteristic
102C22×Dic142C2312yes—
103C22×Dic142C2314yes—
104C22×Dic142C2312yes—
105C22×D284C2311yescharacteristic
106C22×C22⋊D71C2312yes—
107C22×C4×D71C2312yes—
108C22×C4×D71C2314yes—
109#14556128C23116yes—
110#14556128C23116yes—
111#14556128C2318yes—
112#14556128C2318yes—
113#14556127C23132yes—
114#14556127C23116yes—
115#14556126C23132yes—
116#14556123C23132yes—
117#14556123C23132yes—
118#14556123C23132yes—
119#14556123C23132yes—
120#14556122C23116yes—
121#14556121C23132yes—
122#14556121C23132yes—
123#14556120C23116yes—
124#14556120C23116yes—
125#14556120C2318yes—
126#14556119C23132yes—
127#14556119C23116yes—
128#14556118C23132yes—
129#14556118C23132yes—
130#14556118C23132yes—
131#14556118C23132yes—
132#14556116C23116yes—
133#14556116C2318yes—
134#14556114C23132yes—
135#14556111C23116yes—
136#14556110C23132yes—
137#14556107C2318yes—
138#14556107C23116yes—
139#14556107C23116yes—
140#14556106C23132yes—
141#14556106C23132yes—
142#14556104C23116yes—
143#14556104C23116yes—
144#14556104C23132yes—
145#14556102C2318yes—
146Q8×Dic71C23116yes—
147Q8×Dic71C23116yes—
148C4×Dic142C23116yes—
149C4×Dic142C23116yes—
150C4×Dic142C23116yes—
151C4×Dic142C23116yes—
152C4×Dic142C23116yes—
153C4×Dic142C2318yes—
154#14556093C23132yes—
155C4×D284C23116yes—
156C4×D284C2318yes—
157C4×C22⋊D71C23116yes—
158#14556087C23116yes—
159#14556086C23132yes—
160#14556086C23116yes—
161#14556085C23116yes—
162C2×C4⋊Dic71C2312yes—
163C2×C4⋊Dic71C2312yes—
164C2×C4⋊Dic71C2314yes—
165C2×C4⋊Dic71C2311yescharacteristic
166C2×C4⋊Dic71C2312yes—
167C2×C4⋊Dic71C2311yescharacteristic
168C2×C4⋊Dic71C2312yes—
169C2×C4⋊Dic71C2314yes—
170C2×C4⋊Dic71C2314yes—
171C2×Dic71⋊C4C2314yes—
172C2×Dic71⋊C4C2312yes—
173C2×Dic71⋊C4C2312yes—
174C2×Dic71⋊C4C2312yes—
175C2×Dic71⋊C4C2314yes—
176C2×Dic71⋊C4C2314yes—
177C2×Dic71⋊C4C2314yes—
178C2×Dic71⋊C4C2314yes—
179C2×Dic71⋊C4C2314yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2312yes—
182C4⋊C4×D71C23116yes—
183C2×C22⋊Dic71C2314yes—
184C2×C22⋊Dic71C2312yes—
185C2×(C2×D71)⋊C4C2312yes—
186C2×(C2×D71)⋊C4C2312yes—
187C2×(C2×D71)⋊C4C2312yes—
188C2×(C2×D71)⋊C4C2314yes—
189C2×(C2×D71)⋊C4C2314yes—
190C2×(C2×D71)⋊C4C2314yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×C4×Dic71C2312yes—
193C2×C4×Dic71C2314yes—
194C2×C4×Dic71C2314yes—
195C2×C4×Dic71C2314yes—
196C2×C4×Dic71C2314yes—
197C22×Q8×C71C2311yescharacteristic
198C22×Q8×C71C2311yescharacteristic
199C22×Q8×C71C2312yes—
200C23×C4×C71C2311yescharacteristic
201C23×C4×C71C2311yescharacteristic
202C23×C4×C71C2311yescharacteristic
203C4⋊Q8×C71C2318yes—
204C4⋊Q8×C71C2318yes—
205#125×C71C23116yes—
206C22⋊Q8×C71C2318yes—
207C22⋊Q8×C71C2318yes—
208C22⋊Q8×C71C23116yes—
209C4×Q8×C71C2318yes—
210C4×Q8×C71C23116yes—
211C4×Q8×C71C2318yes—
212#117×C71C23116yes—
213C2×C4⋊C4×C71C2312yes—
214C2×C4⋊C4×C71C2312yes—
215C2×C4⋊C4×C71C2312yes—
216C2×C4⋊C4×C71C2312yes—
217C2×C4⋊C4×C71C2312yes—
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2311yescharacteristic
221C2×C4⋊C4×C71C2312yes—
222C2×C22⋊C4×C71C2312yes—
223C2×C22⋊C4×C71C2312yes—
224C2×C42×C71C2311yescharacteristic
225C2×C42×C71C2311yescharacteristic
226C2×C42×C71C2311yescharacteristic
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2318yes—
229C2×C42×C71C2312yes—
230C2×C42×C71C2312yes—
231C23×D71C2412yes—
232C2×Dic142—24no—
233C2×Dic142—28no—
234C2×Dic142—44no—
235C2×Dic142—48no—
236C2×Dic142C2418yes—
237C2×Dic142C2414yes—
238C2×Dic142C24116yes—
239C2×Dic142C2418yes—
240C2×D284—24no—
241C2×D284C2414yes—
242C2×C22⋊D71—44no—
243C2×C22⋊D71C2418yes—
244C22×Dic71C2414yes—
245C22×Dic71C2412yes—
246C22×Dic71C2412yes—
247C22×Dic71C2412yes—
248C22×Dic71C2414yes—
249C2×C4×D71—28no—
250C2×C4×D71—48no—
251C2×C4×D71C2418yes—
252C2×C4×D71C24116yes—
253C4⋊Dic71C2418yes—
254C4⋊Dic71C2418yes—
255C4⋊Dic71C24116yes—
256C4⋊Dic71C2414yes—
257C4⋊Dic71C2418yes—
258C4⋊Dic71C2414yes—
259C4⋊Dic71C2418yes—
260C4⋊Dic71C24116yes—
261C4⋊Dic71C24116yes—
262Dic71⋊C4C24116yes—
263Dic71⋊C4C2418yes—
264Dic71⋊C4C2418yes—
265Dic71⋊C4C2418yes—
266Dic71⋊C4C24116yes—
267Dic71⋊C4C24116yes—
268Dic71⋊C4C24116yes—
269Dic71⋊C4C24116yes—
270Dic71⋊C4C24116yes—
271Dic71⋊C4C24116yes—
272Dic71⋊C4C2418yes—
273C22⋊Dic71C24116yes—
274C22⋊Dic71C2418yes—
275(C2×D71)⋊C4C2418yes—
276(C2×D71)⋊C4C2418yes—
277(C2×D71)⋊C4C2418yes—
278(C2×D71)⋊C4C24116yes—
279(C2×D71)⋊C4C24116yes—
280(C2×D71)⋊C4C24116yes—
281(C2×D71)⋊C4C2418yes—
282C4×Dic71C2418yes—
283C4×Dic71C24116yes—
284C4×Dic71C24116yes—
285C4×Dic71C24116yes—
286C4×Dic71C24116yes—
287C24×C71C2411yescharacteristic
288C2×Q8×C71—24no—
289C2×Q8×C71—24no—
290C2×Q8×C71—44no—
291C2×Q8×C71C2414yes—
292C2×Q8×C71C2414yes—
293C2×Q8×C71C2418yes—
294C22×C4×C71—24no—
295C22×C4×C71—24no—
296C22×C4×C71—42no—
297C22×C4×C71C2412yes—
298C22×C4×C71C2411yescharacteristic
299C22×C4×C71C2412yes—
300C22×C4×C71C2411yescharacteristic
301C22×C4×C71C2411yescharacteristic
302C22×C4×C71C2411yescharacteristic
303C22×C4×C71C2414yes—
304C22×C4×C71C2414yes—
305C22×C4×C71C2412yes—
306C22×C4×C71C2412yes—
307C22×C4×C71C2414yes—
308C22×C4×C71C2411yescharacteristic
309C22×C4×C71C2411yescharacteristic
310C4⋊C4×C71C2418yes—
311C4⋊C4×C71C2418yes—
312C4⋊C4×C71C2418yes—
313C4⋊C4×C71C2418yes—
314C4⋊C4×C71C2418yes—
315C4⋊C4×C71C2418yes—
316C4⋊C4×C71C2414yes—
317C4⋊C4×C71C2414yes—
318C4⋊C4×C71C2418yes—
319C22⋊C4×C71C2418yes—
320C22⋊C4×C71C2418yes—
321C42×C71C2414yes—
322C42×C71C2414yes—
323C42×C71C2414yes—
324C42×C71C2414yes—
325C42×C71C2418yes—
326C42×C71C2418yes—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—22no—
330C23×C71C2512yes—
331C23×C71C2511yescharacteristic
332C22×D71—24no—
333C22×D71—24no—
334C22×D71—24no—
335C22×D71C2514yes—
336Q8×C71—28no—
337Q8×C71—28no—
338Q8×C71—48no—
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—24no—
342C2×C4×C71—24no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—24no—
346C2×C4×C71—24no—
347C2×C4×C71—28no—
348C2×C4×C71—28no—
349C2×C4×C71—44no—
350C2×C4×C712−1+414yes—
351C2×C4×C712−1+414yes—
352C2×C4×C71C2512yes—
353C2×C4×C71C2512yes—
354C2×C4×C71C2512yes—
355C2×C4×C71C2512yes—
356C2×C4×C71C2514yes—
357C2×C4×C71C2514yes—
358C2×C4×C71C2514yes—
359C2×C4×C71C2514yes—
360C2×C4×C71C2512yes—
361C2×C4×C71C2512yes—
362C22⋊D71—48no—
363C2×Dic71—24no—
364C2×Dic71—24no—
365C2×Dic71—28no—
366C2×Dic71—28no—
367C2×Dic71—24no—
368C2×Dic71C2514yes—
369C2×Dic71C2518yes—
370C2×Dic71C2514yes—
371C2×Dic71C2514yes—
372C2×Dic71C2518yes—
373D284—28no—
374C4×D71—216no—
375C4×D71—416no—
376Dic142—216no—
377Dic142—28no—
378Dic142—48no—
379Dic142—416no—
380C22×C71—22no—
381C22×C71—22no—
382C22×C71—22no—
383C22×C71—44no—
384C22×C71C2×2−1+412yes—
385C22×C71C2×2−1+412yes—
386C22×C71#58512yes—
387C22×C71C2611yescharacteristic
388C2×D71—24no—
389C2×D71—24no—
390C2×D71—24no—
391C2×D71—48no—
392C4×C71—22no—
393C4×C71—22no—
394C4×C71—24no—
395C4×C71—24no—
396C4×C71—22no—
397C4×C71—24no—
398C4×C71—24no—
399C4×C71—22no—
400C4×C71C2×2−1+414yes—
401C4×C71C2×2−1+414yes—
402Dic71—24no—
403Dic71—28no—
404Dic71—24no—
405Dic71—28no—
406Dic71—24no—
407C2×#3555—711nomaximal, Sylow
408C2×C71—42no—
409C2×C71#355514yescomplemented
410C2×C71C22×2−1+411yescharacteristic
411C2×C71C22×2−1+411yescharacteristic
412C2×C71C2×#58511yescharacteristic
413D71—44no—
414#3555—7132no—
415C2×#563—714no—
416C2×Q82—711no—
417C2×#557—712no—
418C2×#557—711no—
419C2×#556—712no—
420C2×#556—712no—
421C2×#556—711no—
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×#533D7111yescharacteristic, complemented
431C2×#529—711no—
432C71C2×#355511yescharacteristic, complemented, Sylow
433#563—7164no—
434Q82—7116no—
435#557—7132no—
436#557—7116no—
437#556—7132no—
438#556—7132no—
439#556—7116no—
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#533C2×D71116yescomplemented
449C2×C4⋊Q8—714no—
450C2×C4⋊Q8—714no—
451C2×C4⋊Q8—712no—
452C2×C4⋊Q8—711no—
453C2×C4⋊Q8—711no—
454C2×C4⋊Q8—712no—
455C2×C4⋊Q8—712no—
456C2×C4⋊Q8C2×D7111yescharacteristic
457C2×C4⋊Q8C2×D7111yescharacteristic
458#529—7116no—
459C2×#126—714no—
460C2×#126—714no—
461C2×#126—714no—
462C2×#126—714no—
463C2×#126—714no—
464C2×#126—714no—
465C2×#126—712no—
466C2×#125—714no—
467C2×#125—714no—
468C2×#125—714no—
469C2×#125—714no—
470C2×#125—714no—
471C2×#125—712no—
472C2×#125—711no—
473C2×#125—712no—
474C2×#125—712no—
475C2×#125C2×D7112yes—
476C2×#124—714no—
477C2×#124—711no—
478C2×#124—712no—
479C2×#123—712no—
480C2×#123—714no—
481C2×C22⋊Q8—712no—
482C2×C22⋊Q8—712no—
483C2×C22⋊Q8—714no—
484C2×C22⋊Q8—711no—
485C2×C22⋊Q8—712no—
486C2×C22⋊Q8—712no—
487C2×C22⋊Q8—714no—
488C2×C22⋊Q8—714no—
489C2×C22⋊Q8C2×D7111yescharacteristic
490C2×C22⋊Q8C2×D7111yescharacteristic
491C2×C22⋊Q8C2×D7112yes—
492C2×#121—711no—
493C2×C4×Q8—712no—
494C2×C4×Q8—712no—
495C2×C4×Q8—714no—
496C2×C4×Q8—711no—
497C2×C4×Q8—712no—
498C2×C4×Q8—712no—
499C2×C4×Q8—712no—
500C2×C4×Q8—712no—
501C2×C4×Q8—712no—
502C2×C4×Q8C2×D7111yescharacteristic
503C2×C4×Q8C2×D7112yes—
504C2×C4×Q8C2×D7111yescharacteristic
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×#117C2×D7112yes—
513C22×C4⋊C4—712no—
514C22×C42C2×D7111yescharacteristic
515C22×Q8—712no—
516C22×Q8—714no—
517C22×Q8—711no—
518C22×Q8—712no—
519C22×Q8C22×D7111yescharacteristic
520C22×Q8C22×D7111yescharacteristic
521C22×Q8C22×D7112yes—
522C22×D4—712no—
523C22×D4—711no—
524C23×C4—714no—
525C23×C4—712no—
526C23×C4C22×D7111yescharacteristic
527C23×C4C22×D7111yescharacteristic
528C23×C4C22×D7111yescharacteristic
529C4⋊Q8—7132no—
530C4⋊Q8—7132no—
531C4⋊Q8—7116no—
532C4⋊Q8—718no—
533C4⋊Q8—718no—
534C4⋊Q8—7116no—
535C4⋊Q8—7116no—
536C4⋊Q8C22×D7118yes—
537C4⋊Q8C22×D7118yes—
538#126—7132no—
539#126—7132no—
540#126—7132no—
541#126—7132no—
542#126—7132no—
543#126—7132no—
544#126—7116no—
545#125—7132no—
546#125—7132no—
547#125—7132no—
548#125—7132no—
549#125—7132no—
550#125—7116no—
551#125—718no—
552#125—7116no—
553#125—7116no—
554#125C22×D71116yes—
555#124—7132no—
556#124—718no—
557#124—7116no—
558#123—7116no—
559#123—7132no—
560C22⋊Q8—7116no—
561C22⋊Q8—7116no—
562C22⋊Q8—7132no—
563C22⋊Q8—718no—
564C22⋊Q8—7116no—
565C22⋊Q8—7116no—
566C22⋊Q8—7132no—
567C22⋊Q8—7132no—
568C22⋊Q8C22×D7118yes—
569C22⋊Q8C22×D7118yes—
570C22⋊Q8C22×D71116yes—
571#121—718no—
572C4×Q8—7116no—
573C4×Q8—7116no—
574C4×Q8—7132no—
575C4×Q8—718no—
576C4×Q8—7116no—
577C4×Q8—7116no—
578C4×Q8—7116no—
579C4×Q8—7116no—
580C4×Q8—7116no—
581C4×Q8C22×D7118yes—
582C4×Q8C22×D71116yes—
583C4×Q8C22×D7118yes—
584C4×D4—7116no—
585C4×D4—718no—
586C4×D4—7116no—
587#117—7116no—
588#117—7132no—
589#117—7116no—
590#117—7116no—
591#117C22×D71116yes—
592C2×C4⋊C4—712no—
593C2×C4⋊C4—714no—
594C2×C4⋊C4—712no—
595C2×C4⋊C4—712no—
596C2×C4⋊C4—714no—
597C2×C4⋊C4—712no—
598C2×C4⋊C4—711no—
599C2×C4⋊C4—712no—
600C2×C4⋊C4—712no—
601C2×C4⋊C4—711no—
602C2×C4⋊C4—714no—
603C2×C4⋊C4—714no—
604C2×C4⋊C4—714no—
605C2×C4⋊C4—714no—
606C2×C4⋊C4—714no—
607C2×C4⋊C4—712no—
608C2×C4⋊C4—714no—
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×D7111yescharacteristic
616C2×C4⋊C4C22×D7112yes—
617C2×C4⋊C4C22×D7112yes—
618C2×C4⋊C4C22×D7112yes—
619C2×C4⋊C4C22×D7112yes—
620C2×C4⋊C4C22×D7112yes—
621C2×C4⋊C4C22×D7112yes—
622C2×C22⋊C4—714no—
623C2×C22⋊C4—712no—
624C2×C22⋊C4—712no—
625C2×C22⋊C4—712no—
626C2×C22⋊C4—712no—
627C2×C22⋊C4—714no—
628C2×C22⋊C4—714no—
629C2×C22⋊C4—712no—
630C2×C22⋊C4—714no—
631C2×C22⋊C4C22×D7112yes—
632C2×C22⋊C4C22×D7112yes—
633C2×C42—714no—
634C2×C42—712no—
635C2×C42—714no—
636C2×C42—714no—
637C2×C42—714no—
638C2×C42C22×D7111yescharacteristic
639C2×C42C22×D7112yes—
640C2×C42C22×D7112yes—
641C2×C42C22×D7111yescharacteristic
642C2×C42C22×D7111yescharacteristic
643C2×C42C22×D7111yescharacteristic
644C2×C42C22×D7118yes—
645C24—712no—
646C24C23×D7111yescharacteristic
647C2×Q8—24no—
648C2×Q8—24no—
649C2×Q8—44no—
650C2×Q8—2844no—
651C2×Q8—2848no—
652C2×Q8—718no—
653C2×Q8—7116no—
654C2×Q8—714no—
655C2×Q8—718no—
656C2×Q8—1424no—
657C2×Q8—1428no—
658C2×Q8C23×D7114yes—
659C2×Q8C23×D7114yes—
660C2×Q8C23×D7118yes—
661C2×D4—2844no—
662C2×D4—718no—
663C2×D4—714no—
664C2×D4—1424no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—2848no—
669C22×C4—7116no—
670C22×C4—714no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—714no—
675C22×C4—718no—
676C22×C4—1428no—
677C22×C4C23×D7114yes—
678C22×C4C23×D7114yes—
679C22×C4C23×D7111yescharacteristic
680C22×C4C23×D7112yes—
681C22×C4C23×D7112yes—
682C22×C4C23×D7112yes—
683C22×C4C23×D7111yescharacteristic
684C22×C4C23×D7111yescharacteristic
685C22×C4C23×D7111yescharacteristic
686C22×C4C23×D7112yes—
687C22×C4C23×D7114yes—
688C22×C4C23×D7111yescharacteristic
689C22×C4C23×D7111yescharacteristic
690C4⋊C4—7116no—
691C4⋊C4—718no—
692C4⋊C4—718no—
693C4⋊C4—718no—
694C4⋊C4—7116no—
695C4⋊C4—7116no—
696C4⋊C4—7116no—
697C4⋊C4—7116no—
698C4⋊C4—7116no—
699C4⋊C4—7116no—
700C4⋊C4—718no—
701C4⋊C4—718no—
702C4⋊C4—718no—
703C4⋊C4—7116no—
704C4⋊C4—714no—
705C4⋊C4—718no—
706C4⋊C4—714no—
707C4⋊C4—718no—
708C4⋊C4—7116no—
709C4⋊C4—7116no—
710C4⋊C4C23×D7114yes—
711C4⋊C4C23×D7118yes—
712C4⋊C4C23×D7114yes—
713C4⋊C4C23×D7118yes—
714C4⋊C4C23×D7118yes—
715C4⋊C4C23×D7118yes—
716C4⋊C4C23×D7118yes—
717C4⋊C4C23×D7118yes—
718C4⋊C4C23×D7118yes—
719C22⋊C4—7116no—
720C22⋊C4—718no—
721C22⋊C4—718no—
722C22⋊C4—718no—
723C22⋊C4—718no—
724C22⋊C4—7116no—
725C22⋊C4—7116no—
726C22⋊C4—718no—
727C22⋊C4—7116no—
728C22⋊C4C23×D7118yes—
729C22⋊C4C23×D7118yes—
730C42—7116no—
731C42—718no—
732C42—7116no—
733C42—7116no—
734C42—7116no—
735C42C23×D7114yes—
736C42C23×D7114yes—
737C42C23×D7114yes—
738C42C23×D7114yes—
739C42C23×D7118yes—
740C42C23×D7118yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—714no—
745C23—1424no—
746C23—1424no—
747C23—1424no—
748C23C24×D7112yes—
749C23C24×D7111yescharacteristic
750Q8—28no—
751Q8—28no—
752Q8—48no—
753Q8—2848no—
754Q8—28416no—
755Q8—1428no—
756Q8—14216no—
757D4—2848no—
758D4—1428no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—24no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—24no—
766C2×C4—24no—
767C2×C4—28no—
768C2×C4—28no—
769C2×C4—44no—
770C2×C4—28416no—
771C2×C4—718no—
772C2×C4—714no—
773C2×C4—714no—
774C2×C4—714no—
775C2×C4—718no—
776C2×C4—1424no—
777C2×C4—1428no—
778C2×C4—1424no—
779C2×C4—1428no—
780C2×C4—1424no—
781C2×C4—14216no—
782C2×C4#1455617514yes—
783C2×C4#1455617614yes—
784C2×C4C24×D7112yes—
785C2×C4C24×D7114yes—
786C2×C4C24×D7114yes—
787C2×C4C24×D7114yes—
788C2×C4C24×D7112yes—
789C2×C4C24×D7112yes—
790C2×C4C24×D7112yes—
791C2×C4C24×D7114yes—
792C2×C4C24×D7112yes—
793C2×C4C24×D7112yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—2848no—
799C22—1424no—
800C22—1424no—
801C22—1424no—
802C22C2×#1455617512yes—
803C22C2×#1455617612yes—
804C22#1798683512yes—
805C22C25×D7111yescharacteristic
806C4—22no—
807C4—24no—
808C4—24no—
809C4—22no—
810C4—22no—
811C4—22no—
812C4—24no—
813C4—24no—
814C4—1424no—
815C4—1428no—
816C4—1424no—
817C4—1428no—
818C4—1424no—
819C4C2×#1455617514yes—
820C4C2×#1455617614yes—
821C2—42no—
822C2—2844no—
823C2#2260282814yesdirect product factor
824C2C22×#1455617511yescharacteristic
825C2C22×#1455617611yescharacteristic
826C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#533×C71C2
socleC23×C71C25
prime radicalC2×#14556102C22
hypercenterC2×#533D71
hypocenterC71C2×#3555
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22602828C2direct (N × H)
2. C2×#17986750C2semidirect
3. C2×Q8×Dic142C2semidirect
4. C2×#17986728C2semidirect
5. C2×#17986727C2semidirect
6. C2×#17986722C2semidirect
7. C2×#17986722C2semidirect
8. C2×#17986720C2semidirect
9. C2×#17986709C2semidirect
10. C2×#17986683C2semidirect
11. C2×#17986626C2semidirect
13. C2×#17986611C2semidirect
14. C2×#17986610C2semidirect
15. C2×#17986608C2semidirect
16. C2×#17986556C2semidirect
18. C2×#533×C71C2semidirect
19. #17986750C22semidirect
20. Q8×Dic142C22semidirect
21. #17986728C22semidirect
22. #17986727C22semidirect
23. #17986722C22semidirect
24. #17986722C22semidirect
25. #17986720C22semidirect
26. #17986709C22semidirect
27. #17986683C22semidirect
28. #17986626C22semidirect
30. #17986611C22semidirect
31. #17986610C22semidirect
32. #17986608C22semidirect
33. #17986556C22semidirect
89. #533×C71C22semidirect
409. C2×C71#3555semidirect
430. C2×#533D71semidirect
432. C71C2×#3555semidirect
448. #533C2×D71semidirect
823. C2#22602828direct (N × H)

Maximal subgroups

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

subgroupindex
#226028282
C2×#179867502
C2×Q8×Dic1422
C2×#179867282
C2×#179867272
C2×#179867222
C2×#179867202
C2×#179867092
C2×#179866832
C2×#179866262
C2×#179866202
C2×#179866112
C2×#179866102
C2×#179866082
C2×#179865562
C2×#179865332
C2×#533×C712
C2×#355571