Finite Group Databasebeta

← C2×#22602786 #32905062

Subgroups — C2×#22602786 #32905062

Order 18176.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602786C2132yesmaximal, direct product factor
2C2×#17986753C214yesmaximal, complemented
3C2×#17986722C211yesmaximal, characteristic, complemented
4C2×#17986709C212yesmaximal, complemented
5C2×#17986702C212yesmaximal, complemented
6C2×Q8×D284C211yesmaximal, characteristic, complemented
7C2×#17986664C212yesmaximal, complemented
8C2×#17986661C212yesmaximal, complemented
9C2×#17986652C211yesmaximal, characteristic, complemented
10C2×#17986629C212yesmaximal, complemented
11C2×#17986621C212yesmaximal, complemented
12C2×#17986607C212yesmaximal, complemented
13C2×#17986597C214yesmaximal, complemented
14C2×#17986574C212yesmaximal, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986536C211yesmaximal, characteristic, complemented
17C2×#17986536C211yesmaximal, characteristic, complemented
18C2×#557×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×Q8×D71C2212yes—
21C22×Q8×D71C2212yes—
22#17986753C22164yescomplemented
23#17986722C22116yescomplemented
24#17986709C22132yescomplemented
25#17986702C22132yescomplemented
26Q8×D284C22116yescomplemented
27#17986664C22132yescomplemented
28#17986661C22132yescomplemented
29#17986652C22116yescomplemented
30#17986629C22132yescomplemented
31#17986621C22132yescomplemented
32#17986607C22132yescomplemented
33#17986597C22164yescomplemented
34#17986574C22132yescomplemented
35C2×#14556128C2212yes—
36C2×#14556128C2211yescharacteristic
37C2×#14556127C2214yes—
38C2×#14556127C2212yes—
39C2×#14556127C2212yes—
40C2×#14556126C2212yes—
41C4⋊Q8×D71C22116yescomplemented
42#17986536C22116yescomplemented
43#17986536C22116yescomplemented
44C2×#14556123C2212yes—
45C2×#14556123C2212yes—
46C2×#14556123C2214yes—
47C2×#14556123C2214yes—
48C2×#14556122C2214yes—
49C2×#14556120C2214yes—
50C2×#14556119C2211yescharacteristic
51C2×#14556119C2211yescharacteristic
52C2×#14556118C2214yes—
53C2×#14556117C2211yescharacteristic
54C2×#14556117C2211yescharacteristic
55C2×#14556116C2212yes—
56C2×#14556116C2214yes—
57C2×#14556113C2214yes—
58C2×#14556113C2212yes—
59C2×#14556113C2212yes—
60C2×#14556113C2214yes—
61C2×#14556113C2214yes—
62C2×#14556108C2214yes—
63C2×#14556108C2212yes—
64C2×#14556108C2214yes—
65C2×#14556106C2214yes—
66C2×#14556106C2214yes—
67C2×#14556106C2214yes—
68C2×#14556106C2214yes—
69C2×#14556104C2212yes—
70C2×#14556104C2211yescharacteristic
71C2×#14556104C2211yescharacteristic
72C2×#14556104C2212yes—
73C2×#14556103C2212yes—
74C2×#14556103C2211yescharacteristic
75C2×#14556103C2214yes—
76C2×#14556103C2211yescharacteristic
77C2×C4×Dic142C2212yes—
78C2×C4×D284C2211yescharacteristic
79C2×C4×D284C2211yescharacteristic
80C2×C4×D284C2212yes—
81C2×C4×D284C2214yes—
82C2×C4×D284C2212yes—
83C2×C4×D284C2212yes—
84C2×#14556090C2214yes—
85C2×#14556086C2212yes—
86C2×#14556085C2212yes—
87C2×#14556085C2212yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
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×C71C2212yes—
98C2×C4×Q8×C71C2211yescharacteristic
99C2×C4×Q8×C71C2211yescharacteristic
100C2×C4×Q8×C71C2212yes—
101C2×#11765866—48no—
102C2×#11765866C23116yes—
103C22×Dic142C2312yes—
104C22×Dic142C2314yes—
105C22×Dic142C2314yes—
106C2×Q8×D71—48no—
107C2×Q8×D71—48no—
108C2×Q8×D71C23116yes—
109C2×Q8×D71C23116yes—
110C22×D284C2311yescharacteristic
111C22×D284C2312yes—
112C22×D284C2312yes—
113C22×D284C2311yescharacteristic
114C22×D284C2314yes—
115C22×C4×D71C2311yescharacteristic
116C22×C4×D71C2312yes—
117C22×C4×D71C2311yescharacteristic
118C22×C4×D71C2311yescharacteristic
119C22×C4×D71C2312yes—
120C22×C4×D71C2314yes—
121C22×C4×D71C2314yes—
122C22×C4×D71C2314yes—
123#14556128C23116yes—
124#14556128C2318yes—
125#14556127C23116yes—
126#14556127C23132yes—
127#14556127C23116yes—
128#14556126C23116yes—
129#14556123C23132yes—
130#14556123C23132yes—
131#14556123C23116yes—
132#14556123C23116yes—
133#14556122C23132yes—
134#14556120C23132yes—
135#14556119C2318yes—
136#14556119C2318yes—
137#14556118C23132yes—
138#14556117C2318yes—
139#14556117C2318yes—
140#14556116C23116yes—
141#14556116C23132yes—
142#14556113C23132yes—
143#14556113C23132yes—
144#14556113C23116yes—
145#14556113C23116yes—
146#14556113C23132yes—
147#14556108C23132yes—
148#14556108C23116yes—
149#14556108C23132yes—
150#14556106C23132yes—
151#14556106C23132yes—
152#14556106C23132yes—
153#14556106C23132yes—
154#14556104C23116yes—
155#14556104C23116yes—
156#14556104C2318yes—
157#14556104C2318yes—
158#14556103C23132yes—
159#14556103C23116yes—
160#14556103C2318yes—
161#14556103C2318yes—
162C4×Dic142C23116yes—
163C4×D284C23132yes—
164C4×D284C23116yes—
165C4×D284C2318yes—
166C4×D284C2318yes—
167C4×D284C23116yes—
168C4×D284C23116yes—
169#14556090C23132yes—
170#14556086C23116yes—
171#14556085C23116yes—
172#14556085C23116yes—
173C2×C4⋊Dic71C2311yescharacteristic
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2312yes—
176C2×C4⋊Dic71C2311yescharacteristic
177C2×C4⋊Dic71C2314yes—
178C2×C4⋊Dic71C2312yes—
179C2×C4⋊Dic71C2312yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2312yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2312yes—
187C2×Dic71⋊C4C2314yes—
188C4⋊C4×D71C23116yes—
189C4⋊C4×D71C23116yes—
190C4⋊C4×D71C23116yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2312yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×(C2×D71)⋊C4C2312yes—
199C2×(C2×D71)⋊C4C2314yes—
200C2×(C2×D71)⋊C4C2314yes—
201C2×(C2×D71)⋊C4C2312yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2312yes—
204C2×(C2×D71)⋊C4C2312yes—
205C2×C4×Dic71C2311yescharacteristic
206C2×C4×Dic71C2311yescharacteristic
207C2×C4×Dic71C2311yescharacteristic
208C2×C4×Dic71C2314yes—
209C42×D71C2318yes—
210C22×Q8×C71C2311yescharacteristic
211C22×Q8×C71C2312yes—
212C22×Q8×C71C2311yescharacteristic
213C4⋊Q8×C71C23116yes—
214C4⋊Q8×C71C2318yes—
215#125×C71C23132yes—
216#125×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219C4×Q8×C71C2318yes—
220C4×Q8×C71C2318yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C4⋊C4×C71C2314yes—
228C2×C4⋊C4×C71C2312yes—
229C2×C4⋊C4×C71C2314yes—
230C2×C42×C71C2312yes—
231C2×C42×C71C2314yes—
232C2×C42×C71C2311yescharacteristic
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235C23×D71C2412yes—
236C23×D71C2411yescharacteristic
237#11765866—432no—
238C2×Dic142—28no—
239C2×Dic142—48no—
240C2×Dic142—48no—
241C2×Dic142C2418yes—
242C2×Dic142C24116yes—
243C2×Dic142C24116yes—
244Q8×D71—432no—
245Q8×D71—432no—
246C2×D284—28no—
247C2×D284—28no—
248C2×D284—24no—
249C2×D284—24no—
250C2×D284—48no—
251C2×D284C2414yes—
252C2×D284C2418yes—
253C2×D284C2418yes—
254C2×D284C2414yes—
255C2×D284C24116yes—
256C22×Dic71C2412yes—
257C22×Dic71C2414yes—
258C22×Dic71C2411yescharacteristic
259C22×Dic71C2411yescharacteristic
260C22×Dic71C2411yescharacteristic
261C22×Dic71C2412yes—
262C2×C4×D71—24no—
263C2×C4×D71—24no—
264C2×C4×D71—28no—
265C2×C4×D71—24no—
266C2×C4×D71—28no—
267C2×C4×D71—48no—
268C2×C4×D71—48no—
269C2×C4×D71—48no—
270C2×C4×D71C2414yes—
271C2×C4×D71C2418yes—
272C2×C4×D71C2414yes—
273C2×C4×D71C2414yes—
274C2×C4×D71C2418yes—
275C2×C4×D71C24116yes—
276C2×C4×D71C24116yes—
277C2×C4×D71C24116yes—
278C4⋊Dic71C2414yes—
279C4⋊Dic71C2418yes—
280C4⋊Dic71C2418yes—
281C4⋊Dic71C2414yes—
282C4⋊Dic71C24116yes—
283C4⋊Dic71C2418yes—
284C4⋊Dic71C2418yes—
285Dic71⋊C4C24116yes—
286Dic71⋊C4C24116yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C2418yes—
289Dic71⋊C4C2418yes—
290Dic71⋊C4C2418yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C24116yes—
293(C2×D71)⋊C4C2418yes—
294(C2×D71)⋊C4C2418yes—
295(C2×D71)⋊C4C2418yes—
296(C2×D71)⋊C4C2418yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C24116yes—
300(C2×D71)⋊C4C2418yes—
301(C2×D71)⋊C4C24116yes—
302(C2×D71)⋊C4C24116yes—
303(C2×D71)⋊C4C2418yes—
304(C2×D71)⋊C4C2418yes—
305(C2×D71)⋊C4C2418yes—
306(C2×D71)⋊C4C2418yes—
307C4×Dic71C2414yes—
308C4×Dic71C2414yes—
309C4×Dic71C2414yes—
310C4×Dic71C24116yes—
311C2×Q8×C71—24no—
312C2×Q8×C71—28no—
313C2×Q8×C71—24no—
314C2×Q8×C71C2414yes—
315C2×Q8×C71C2418yes—
316C2×Q8×C71C2414yes—
317C22×C4×C71C2414yes—
318C22×C4×C71C2412yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2412yes—
321C22×C4×C71C2412yes—
322C22×C4×C71C2412yes—
323C22×C4×C71C2411yescharacteristic
324C22×C4×C71C2411yescharacteristic
325C4⋊C4×C71C2414yes—
326C4⋊C4×C71C2414yes—
327C4⋊C4×C71C24116yes—
328C4⋊C4×C71C2418yes—
329C4⋊C4×C71C2418yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C24116yes—
332C4⋊C4×C71C2418yes—
333C4⋊C4×C71C24116yes—
334C42×C71C2418yes—
335C42×C71C24116yes—
336C42×C71C2414yes—
337C42×C71C2418yes—
338C23×C71C2511yescharacteristic
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—24no—
342C22×D71—24no—
343C22×D71—24no—
344C22×D71—24no—
345C22×D71—24no—
346C22×D71—24no—
347C22×D712−1+414yes—
348C22×D71C2514yes—
349C22×D71C2514yes—
350C22×D71C2512yes—
351Q8×C71—28no—
352Q8×C71—216no—
353Q8×C71—28no—
354C2×C4×C71—28no—
355C2×C4×C71—24no—
356C2×C4×C71—24no—
357C2×C4×C71—22no—
358C2×C4×C71—24no—
359C2×C4×C71—24no—
360C2×C4×C71H(5,𝔽2)14yes—
361C2×C4×C712−1+414yes—
362C2×C4×C71C2514yes—
363C2×C4×C71C2514yes—
364C2×C4×C71C2514yes—
365C2×C4×C71C2512yes—
366C2×C4×C71C2514yes—
367C2×C4×C71C2518yes—
368C2×C4×C71C2512yes—
369C2×C4×C71C2512yes—
370C2×Dic71—24no—
371C2×Dic71—22no—
372C2×Dic71—28no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—24no—
376C2×Dic71C2512yes—
377C2×Dic71C2512yes—
378C2×Dic71C2514yes—
379C2×Dic71C2512yes—
380C2×Dic71C2518yes—
381C2×Dic71C2514yes—
382D284—216no—
383D284—216no—
384D284—28no—
385D284—28no—
386D284—416no—
387C4×D71—28no—
388C4×D71—28no—
389C4×D71—216no—
390C4×D71—28no—
391C4×D71—216no—
392C4×D71—416no—
393C4×D71—416no—
394C4×D71—416no—
395Dic142—216no—
396Dic142—416no—
397Dic142—416no—
398C22×C71C2×H(5,𝔽2)12yes—
399C22×C71C2×2−1+412yes—
400C22×C71C2×2−1+412yes—
401C22×C71C2611yescharacteristic
402C2×D71—22no—
403C2×D71—22no—
404C2×D71—28no—
405C2×D71—24no—
406C2×D71—24no—
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—48no—
412C2×D71—48no—
413C2×D71C2×2−1+414yes—
414C4×C71—24no—
415C4×C71—28no—
416C4×C71—22no—
417C4×C71—24no—
418C4×C71—24no—
419C4×C71—24no—
420C4×C71C2×H(5,𝔽2)14yes—
421C4×C71C2×2−1+414yes—
422Dic71—28no—
423Dic71—22no—
424Dic71—24no—
425Dic71—22no—
426Dic71—22no—
427Dic71—24no—
428C2×#3552—711nomaximal, Sylow
429C2×C71#355214yescomplemented
430C2×C71C22×H(5,𝔽2)11yescharacteristic
431C2×C71C22×2−1+411yescharacteristic
432C2×C71C22×2−1+411yescharacteristic
433D71—24no—
434D71—44no—
435D71—44no—
436#3552—7132no—
437C2×#563—714no—
438C2×#557D7111yescharacteristic, complemented
439C2×#556—711no—
440C2×#554—712no—
441C2×#553—712no—
442C2×D4×Q8—712no—
443C2×D4×Q8—711no—
444C2×#548—712no—
445C2×#547—711no—
446C2×#544—712no—
447C2×#542—712no—
448C2×#541—712no—
449C2×#539—714no—
450C2×#536—712no—
451C22×C4⋊Q8—711no—
452C2×#529—711no—
453C2×#529—711no—
454C71C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—712no—
456C23×Q8—712no—
457C23×Q8—712no—
458#563—7164no—
459#557C2×D71116yescomplemented
460#556—7116no—
461#554—7132no—
462#553—7132no—
463D4×Q8—7132no—
464D4×Q8—7116no—
465#548—7132no—
466#547—7116no—
467#544—7132no—
468#542—7132no—
469#541—7132no—
470#539—7164no—
471#536—7132no—
472C2×C4⋊Q8—712no—
473C2×C4⋊Q8—7116no—
474C2×C4⋊Q8—712no—
475C2×C4⋊Q8—712no—
476C2×C4⋊Q8—714no—
477C2×C4⋊Q8—711no—
478C2×C4⋊Q8—712no—
479C2×C4⋊Q8C2×D7111yescharacteristic
480C2×C4⋊Q8C2×D7112yes—
481#529—7116no—
482#529—7116no—
483C2×#126—712no—
484C2×#126—712no—
485C2×#126—714no—
486C2×#126—714no—
487C2×#126—714no—
488C2×#125—711no—
489C2×#125—711no—
490C2×#125—714no—
491C2×#125—714no—
492C2×#125C2×D7114yes—
493C2×#125C2×D7112yes—
494C2×#124—711no—
495C2×#124—711no—
496C2×#124—712no—
497C2×#124—714no—
498C2×#123—712no—
499C2×#123—712no—
500C2×#123—714no—
501C2×#123—714no—
502C2×#123—714no—
503C2×C22⋊Q8—711no—
504C2×C22⋊Q8—711no—
505C2×C22⋊Q8—712no—
506C2×C22⋊Q8—712no—
507C2×C22⋊Q8—714no—
508C2×C22⋊Q8—714no—
509C2×C22⋊Q8—714no—
510C2×C22⋊Q8—714no—
511C2×C22⋊Q8—712no—
512C2×C22⋊Q8—714no—
513C2×C22⋊Q8—714no—
514C2×#121—711no—
515C2×#121—711no—
516C2×#121—714no—
517C2×#121—712no—
518C2×C4×Q8—712no—
519C2×C4×Q8C2×D7111yescharacteristic
520C2×C4×Q8C2×D7111yescharacteristic
521C2×C4×Q8C2×D7112yes—
522C2×C4×Q8C2×D7112yes—
523C2×C4×D4—714no—
524C2×C4×D4—711no—
525C2×C4×D4—711no—
526C2×C4×D4—712no—
527C2×C4×D4—712no—
528C2×C4×D4—714no—
529C2×C4×D4—712no—
530C2×#117—712no—
531C2×#117—712no—
532C2×#117—712no—
533C22×C4⋊C4—712no—
534C22×C4⋊C4—712no—
535C22×C4⋊C4—712no—
536C22×C42—711no—
537C2×#41—2848no—
538C2×#41—7116no—
539C22×Q8—2848no—
540C22×Q8—2848no—
541C22×Q8—7116no—
542C22×Q8—7116no—
543C22×Q8—714no—
544C22×Q8—714no—
545C22×Q8—712no—
546C22×Q8C22×D7111yescharacteristic
547C22×Q8C22×D7111yescharacteristic
548C22×Q8C22×D7112yes—
549C22×D4—714no—
550C22×D4—712no—
551C22×D4—712no—
552C22×D4—711no—
553C22×D4—711no—
554C23×C4—714no—
555C23×C4—714no—
556C23×C4—714no—
557C23×C4—711no—
558C23×C4—711no—
559C23×C4—712no—
560C23×C4—712no—
561C23×C4—711no—
562C4⋊Q8—7116no—
563C4⋊Q8—7116no—
564C4⋊Q8—7116no—
565C4⋊Q8—7132no—
566C4⋊Q8—718no—
567C4⋊Q8—7116no—
568C4⋊Q8C22×D7118yes—
569C4⋊Q8C22×D71116yes—
570#126—7116no—
571#126—7116no—
572#126—7132no—
573#126—7132no—
574#126—7132no—
575#125—718no—
576#125—718no—
577#125—7132no—
578#125—7132no—
579#125C22×D71132yes—
580#125C22×D71116yes—
581#124—718no—
582#124—718no—
583#124—7116no—
584#124—7132no—
585#123—7116no—
586#123—7116no—
587#123—7132no—
588#123—7132no—
589#123—7132no—
590C22⋊Q8—718no—
591C22⋊Q8—718no—
592C22⋊Q8—7116no—
593C22⋊Q8—7116no—
594C22⋊Q8—7132no—
595C22⋊Q8—7132no—
596C22⋊Q8—7132no—
597C22⋊Q8—7132no—
598C22⋊Q8—7116no—
599C22⋊Q8—7132no—
600C22⋊Q8—7132no—
601#121—718no—
602#121—718no—
603#121—7132no—
604#121—7116no—
605C4×Q8—7116no—
606C4×Q8C22×D7118yes—
607C4×Q8C22×D7118yes—
608C4×Q8C22×D71116yes—
609C4×Q8C22×D71116yes—
610C4×D4—7132no—
611C4×D4—718no—
612C4×D4—718no—
613C4×D4—7116no—
614C4×D4—7116no—
615C4×D4—7132no—
616C4×D4—7116no—
617#117—7116no—
618#117—7116no—
619#117—7116no—
620C2×C4⋊C4—711no—
621C2×C4⋊C4—712no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—712no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—712no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—712no—
629C2×C4⋊C4—712no—
630C2×C4⋊C4—711no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—712no—
633C2×C4⋊C4—712no—
634C2×C4⋊C4—714no—
635C2×C4⋊C4—7116no—
636C2×C4⋊C4—7116no—
637C2×C4⋊C4—7116no—
638C2×C4⋊C4C22×D7112yes—
639C2×C4⋊C4C22×D7112yes—
640C2×C4⋊C4C22×D7111yescharacteristic
641C2×C4⋊C4C22×D7114yes—
642C2×C4⋊C4C22×D7111yescharacteristic
643C2×C4⋊C4C22×D7114yes—
644C2×C4⋊C4C22×D7114yes—
645C2×C4⋊C4C22×D7112yes—
646C2×C4⋊C4C22×D7112yes—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—712no—
649C2×C22⋊C4—712no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—712no—
652C2×C22⋊C4—712no—
653C2×C22⋊C4—712no—
654C2×C22⋊C4—714no—
655C2×C22⋊C4—714no—
656C2×C22⋊C4—712no—
657C2×C22⋊C4—712no—
658C2×C22⋊C4—714no—
659C2×C22⋊C4—712no—
660C2×C22⋊C4—712no—
661C2×C42—711no—
662C2×C42—711no—
663C2×C42—714no—
664C2×C42—711no—
665C2×C42—718no—
666C2×C42C22×D7112yes—
667C2×C42C22×D7112yes—
668C2×C42C22×D7111yescharacteristic
669C2×C42C22×D7114yes—
670C24—711no—
671C24—712no—
672C24—712no—
673#41—28432no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—24no—
677C2×Q8—2848no—
678C2×Q8—2848no—
679C2×Q8—28432no—
680C2×Q8—28432no—
681C2×Q8—7116no—
682C2×Q8—7116no—
683C2×Q8—718no—
684C2×Q8—1428no—
685C2×Q8C23×D7114yes—
686C2×Q8C23×D7114yes—
687C2×Q8C23×D7118yes—
688C2×D4—2848no—
689C2×D4—7116no—
690C2×D4—718no—
691C2×D4—718no—
692C2×D4—714no—
693C2×D4—714no—
694C2×D4—1428no—
695C2×D4—1428no—
696C2×D4—1424no—
697C2×D4—1424no—
698C22×C4—2848no—
699C22×C4—2848no—
700C22×C4—2848no—
701C22×C4—7116no—
702C22×C4—7116no—
703C22×C4—7116no—
704C22×C4—711no—
705C22×C4—711no—
706C22×C4—712no—
707C22×C4—711no—
708C22×C4—714no—
709C22×C4—712no—
710C22×C4—714no—
711C22×C4—714no—
712C22×C4—714no—
713C22×C4—718no—
714C22×C4—718no—
715C22×C4—1424no—
716C22×C4—1424no—
717C22×C4—1428no—
718C22×C4—1428no—
719C22×C4—1424no—
720C22×C4C23×D7112yes—
721C22×C4C23×D7111yescharacteristic
722C22×C4C23×D7112yes—
723C22×C4C23×D7112yes—
724C22×C4C23×D7112yes—
725C22×C4C23×D7114yes—
726C22×C4C23×D7111yescharacteristic
727C22×C4C23×D7111yescharacteristic
728C4⋊C4—7116no—
729C4⋊C4—7116no—
730C4⋊C4—7116no—
731C4⋊C4—718no—
732C4⋊C4—718no—
733C4⋊C4—718no—
734C4⋊C4—718no—
735C4⋊C4—7116no—
736C4⋊C4—714no—
737C4⋊C4—718no—
738C4⋊C4—718no—
739C4⋊C4—714no—
740C4⋊C4—7116no—
741C4⋊C4—718no—
742C4⋊C4—718no—
743C4⋊C4C23×D7118yes—
744C4⋊C4C23×D7118yes—
745C4⋊C4C23×D7114yes—
746C4⋊C4C23×D71116yes—
747C4⋊C4C23×D7114yes—
748C4⋊C4C23×D71116yes—
749C4⋊C4C23×D71116yes—
750C4⋊C4C23×D7118yes—
751C4⋊C4C23×D7118yes—
752C22⋊C4—7116no—
753C22⋊C4—718no—
754C22⋊C4—718no—
755C22⋊C4—718no—
756C22⋊C4—718no—
757C22⋊C4—718no—
758C22⋊C4—718no—
759C22⋊C4—7116no—
760C22⋊C4—7116no—
761C22⋊C4—718no—
762C22⋊C4—718no—
763C22⋊C4—7116no—
764C22⋊C4—718no—
765C22⋊C4—718no—
766C42—714no—
767C42—714no—
768C42—714no—
769C42—7116no—
770C42C23×D7114yes—
771C42C23×D7118yes—
772C42C23×D7118yes—
773C42C23×D71116yes—
774C23—714no—
775C23—712no—
776C23—714no—
777C23—714no—
778C23—1424no—
779C23—1424no—
780C23—1424no—
781C23—1424no—
782C23—1424no—
783C23—1424no—
784C23—1422no—
785C23—1422no—
786C23C24×D7111yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—28no—
790Q8—28416no—
791Q8—28416no—
792Q8—14216no—
793D4—28416no—
794D4—14216no—
795D4—14216no—
796D4—1428no—
797D4—1428no—
798C2×C4—28no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28416no—
805C2×C4—28416no—
806C2×C4—28416no—
807C2×C4—712no—
808C2×C4—712no—
809C2×C4—714no—
810C2×C4—712no—
811C2×C4—718no—
812C2×C4—714no—
813C2×C4—1428no—
814C2×C4—1424no—
815C2×C4—1428no—
816C2×C4—1422no—
817C2×C4—1422no—
818C2×C4—1422no—
819C2×C4—1424no—
820C2×C4—1428no—
821C2×C4—14216no—
822C2×C4—14216no—
823C2×C4—1428no—
824C2×C4#1455617414yes—
825C2×C4#1455617614yes—
826C2×C4C24×D7114yes—
827C2×C4C24×D7112yes—
828C2×C4C24×D7114yes—
829C2×C4C24×D7114yes—
830C2×C4C24×D7114yes—
831C2×C4C24×D7118yes—
832C2×C4C24×D7112yes—
833C2×C4C24×D7112yes—
834C22—2848no—
835C22—2848no—
836C22—714no—
837C22—1424no—
838C22—1424no—
839C22—1424no—
840C22—1424no—
841C22—1424no—
842C22—1424no—
843C22—1428no—
844C22—1422no—
845C22—1422no—
846C22C2×#1455617412yes—
847C222−1+4×D7112yes—
848C22C2×#1455617612yes—
849C22C25×D7111yescharacteristic
850C4—28no—
851C4—24no—
852C4—22no—
853C4—24no—
854C4—24no—
855C4—24no—
856C4—1424no—
857C4—1428no—
858C4—1422no—
859C4—1422no—
860C4—1422no—
861C4—1424no—
862C4C2×#1455617414yes—
863C4C2×#1455617614yes—
864C2—2844no—
865C2—2844no—
866C2—1424no—
867C2#2260278614yesdirect product factor
868C2C22×#1455617411yescharacteristic
869C2C2×2−1+4×D7111yescharacteristic
870C2C22×#1455617611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
hypercenterC2×#557D71
hypocenterC71C2×#3552
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602786C2direct (N × H)
2. C2×#17986753C2semidirect
3. C2×#17986722C2semidirect
4. C2×#17986709C2semidirect
5. C2×#17986702C2semidirect
6. C2×Q8×D284C2semidirect
7. C2×#17986664C2semidirect
8. C2×#17986661C2semidirect
9. C2×#17986652C2semidirect
10. C2×#17986629C2semidirect
11. C2×#17986621C2semidirect
12. C2×#17986607C2semidirect
13. C2×#17986597C2semidirect
14. C2×#17986574C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986536C2semidirect
17. C2×#17986536C2semidirect
18. C2×#557×C71C2semidirect
22. #17986753C22semidirect
23. #17986722C22semidirect
24. #17986709C22semidirect
25. #17986702C22semidirect
26. Q8×D284C22semidirect
27. #17986664C22semidirect
28. #17986661C22semidirect
29. #17986652C22semidirect
30. #17986629C22semidirect
31. #17986621C22semidirect
32. #17986607C22semidirect
33. #17986597C22semidirect
34. #17986574C22semidirect
41. C4⋊Q8×D71C22semidirect
42. #17986536C22semidirect
43. #17986536C22semidirect
92. #557×C71C22semidirect
429. C2×C71#3552semidirect
438. C2×#557D71semidirect
454. C71C2×#3552semidirect
459. #557C2×D71semidirect
867. C2#22602786direct (N × H)

Maximal subgroups

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

subgroupindex
#226027862
C2×#179867532
C2×#179867222
C2×#179867092
C2×#179867022
C2×Q8×D2842
C2×#179866642
C2×#179866612
C2×#179866522
C2×#179866292
C2×#179866212
C2×#179866072
C2×#179865972
C2×#179865742
C2×C4⋊Q8×D712
C2×#179865362
C2×#557×C712
C2×#355271