Finite Group Databasebeta

← C2×#22602681 #32905135

Subgroups — C2×#22602681 #32905135

Order 18176.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602681C2132yesmaximal, direct product factor
2C2×#17986750C214yesmaximal, complemented
3C2×Q8×Dic142C211yesmaximal, characteristic, complemented
4C2×#17986714C211yesmaximal, characteristic, complemented
5C2×#17986710C211yesmaximal, characteristic, complemented
6C2×#17986687C212yesmaximal, complemented
7C2×#17986683C212yesmaximal, complemented
8C2×#17986654C212yesmaximal, complemented
9C2×#17986650C212yesmaximal, complemented
10C2×#17986630C212yesmaximal, complemented
11C2×#17986629C212yesmaximal, complemented
12C2×#17986622C212yesmaximal, complemented
13C2×#17986614C212yesmaximal, complemented
14C2×#17986572C214yesmaximal, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986536C211yesmaximal, characteristic, complemented
17C2×#17986531C211yesmaximal, characteristic, complemented
18C2×#554×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2214yes—
20C22×Q8×D71C2212yes—
21#17986750C22164yescomplemented
22Q8×Dic142C22116yescomplemented
23#17986714C22116yescomplemented
24#17986710C22116yescomplemented
25#17986687C22132yescomplemented
26#17986683C22132yescomplemented
27#17986654C22132yescomplemented
28#17986650C22132yescomplemented
29#17986630C22132yescomplemented
30#17986629C22132yescomplemented
31#17986622C22132yescomplemented
32#17986614C22132yescomplemented
33#17986572C22164yescomplemented
34C2×#14556128C2212yes—
35C2×#14556128C2211yescharacteristic
36C2×#14556127C2214yes—
37C2×#14556127C2212yes—
38C2×#14556127C2212yes—
39C2×#14556127C2212yes—
40C2×#14556127C2214yes—
41C2×#14556126C2212yes—
42C4⋊Q8×D71C22116yescomplemented
43#17986536C22116yescomplemented
44#17986531C22116yescomplemented
45C2×#14556123C2214yes—
46C2×#14556123C2212yes—
47C2×#14556121C2214yes—
48C2×#14556121C2212yes—
49C2×#14556119C2211yescharacteristic
50C2×#14556119C2211yescharacteristic
51C2×#14556119C2212yes—
52C2×#14556119C2214yes—
53C2×#14556118C2214yes—
54C2×#14556117C2211yescharacteristic
55C2×#14556115C2211yescharacteristic
56C2×#14556114C2214yes—
57C2×#14556114C2214yes—
58C2×#14556113C2214yes—
59C2×#14556113C2212yes—
60C2×#14556111C2214yes—
61C2×#14556110C2214yes—
62C2×#14556110C2214yes—
63C2×#14556110C2212yes—
64C2×#14556108C2214yes—
65C2×#14556108C2211yescharacteristic
66C2×#14556108C2212yes—
67C2×#14556107C2214yes—
68C2×#14556107C2214yes—
69C2×#14556106C2214yes—
70C2×#14556104C2211yescharacteristic
71C2×#14556104C2214yes—
72C2×#14556103C2211yescharacteristic
73C2×#14556102C2212yes—
74C2×#14556099C2211yescharacteristic
75C2×#14556099C2212yes—
76C2×Q8×Dic71C2212yes—
77C2×C4×Dic142C2212yes—
78C2×C4×Dic142C2211yescharacteristic
79C2×C4×D284C2212yes—
80C2×C4×D284C2211yescharacteristic
81C2×#14556090C2212yes—
82C2×C4×C22⋊D71C2212yes—
83C2×#14556087C2212yes—
84C2×#14556087C2212yes—
85C2×#14556086C2212yes—
86C2×#14556086C2214yes—
87C2×#14556085C2212yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C4⋊C4×D71C2212yes—
91C2×C42×D71C2211yescharacteristic
92#554×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#125×C71C2212yes—
95C2×C22⋊Q8×C71C2212yes—
96C2×C22⋊Q8×C71C2214yes—
97C2×C4×Q8×C71C2211yescharacteristic
98C2×C4×D4×C71C2212yes—
99C2×C4×D4×C71C2211yescharacteristic
100C22×C4⋊C4×C71C2212yes—
101C2×#11765865—416no—
102C2×#11765865C23132yes—
103C22×Dic142C2311yescharacteristic
104C22×Dic142C2314yes—
105C22×Dic142C2312yes—
106C22×Dic142C2314yes—
107C2×Q8×D71—48no—
108C2×Q8×D71C23116yes—
109C22×D284C2312yes—
110C22×D284C2311yescharacteristic
111C22×C22⋊D71C2312yes—
112C22×C22⋊D71C2314yes—
113C22×C4×D71C2311yescharacteristic
114C22×C4×D71C2314yes—
115C22×C4×D71C2311yescharacteristic
116C22×C4×D71C2311yescharacteristic
117C22×C4×D71C2312yes—
118C22×C4×D71C2314yes—
119#14556128C23116yes—
120#14556128C2318yes—
121#14556127C23132yes—
122#14556127C23132yes—
123#14556127C23116yes—
124#14556127C23116yes—
125#14556127C23116yes—
126#14556126C23116yes—
127#14556123C23132yes—
128#14556123C23116yes—
129#14556121C23132yes—
130#14556121C23116yes—
131#14556119C2318yes—
132#14556119C2318yes—
133#14556119C23116yes—
134#14556119C23132yes—
135#14556118C23132yes—
136#14556117C2318yes—
137#14556115C2318yes—
138#14556114C23132yes—
139#14556114C23132yes—
140#14556113C23116yes—
141#14556113C23132yes—
142#14556111C23132yes—
143#14556110C23116yes—
144#14556110C23132yes—
145#14556110C23132yes—
146#14556108C23132yes—
147#14556108C23116yes—
148#14556108C2318yes—
149#14556107C23132yes—
150#14556107C23132yes—
151#14556106C23132yes—
152#14556104C23132yes—
153#14556104C2318yes—
154#14556103C2318yes—
155#14556102C23116yes—
156#14556099C23116yes—
157#14556099C2318yes—
158Q8×Dic71C23116yes—
159C4×Dic142C23116yes—
160C4×Dic142C2318yes—
161C4×D284C23116yes—
162C4×D284C2318yes—
163#14556090C23116yes—
164C4×C22⋊D71C23116yes—
165#14556087C23116yes—
166#14556087C23116yes—
167#14556086C23132yes—
168#14556086C23116yes—
169#14556085C23116yes—
170C2×C4⋊Dic71C2311yescharacteristic
171C2×C4⋊Dic71C2312yes—
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2311yescharacteristic
175C2×C4⋊Dic71C2312yes—
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2312yes—
178C2×C4⋊Dic71C2314yes—
179C2×Dic71⋊C4C2314yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2312yes—
183C2×Dic71⋊C4C2312yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C4⋊C4×D71C23116yes—
188C4⋊C4×D71C23116yes—
189C4⋊C4×D71C23116yes—
190C2×C22⋊Dic71C2312yes—
191C2×C22⋊Dic71C2314yes—
192C2×C22⋊Dic71C2312yes—
193C2×C22⋊Dic71C2312yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×(C2×D71)⋊C4C2314yes—
200C2×(C2×D71)⋊C4C2312yes—
201C2×(C2×D71)⋊C4C2312yes—
202C2×C4×Dic71C2311yescharacteristic
203C2×C4×Dic71C2311yescharacteristic
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2314yes—
206C2×C4×Dic71C2314yes—
207C2×C4×Dic71C2312yes—
208C42×D71C2318yes—
209C22×Q8×C71C2311yescharacteristic
210C22×Q8×C71C2312yes—
211C22×D4×C71C2311yescharacteristic
212C23×C4×C71C2312yes—
213C23×C4×C71C2314yes—
214C4⋊Q8×C71C2318yes—
215#125×C71C23116yes—
216C22⋊Q8×C71C23132yes—
217C22⋊Q8×C71C23116yes—
218C4×Q8×C71C2318yes—
219C4×D4×C71C23116yes—
220C4×D4×C71C2318yes—
221C2×C4⋊C4×C71C23116yes—
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2311yescharacteristic
226C2×C4⋊C4×C71C2312yes—
227C2×C4⋊C4×C71C2312yes—
228C2×C4⋊C4×C71C2314yes—
229C2×C22⋊C4×C71C2314yes—
230C2×C22⋊C4×C71C2312yes—
231C2×C42×C71C2312yes—
232C2×C42×C71C2311yescharacteristic
233C23×D71C2412yes—
234C23×D71C2411yescharacteristic
235#11765865—464no—
236C2×Dic142—24no—
237C2×Dic142—44no—
238C2×Dic142—48no—
239C2×Dic142—48no—
240C2×Dic142C2414yes—
241C2×Dic142C24116yes—
242C2×Dic142C2418yes—
243C2×Dic142C24116yes—
244Q8×D71—432no—
245C2×D284—28no—
246C2×D284—24no—
247C2×D284C2418yes—
248C2×D284C2414yes—
249C2×C22⋊D71—28no—
250C2×C22⋊D71—48no—
251C2×C22⋊D71C2418yes—
252C2×C22⋊D71C24116yes—
253C22×Dic71C2412yes—
254C22×Dic71C2414yes—
255C22×Dic71C2411yescharacteristic
256C22×Dic71C2411yescharacteristic
257C22×Dic71C2411yescharacteristic
258C22×Dic71C2412yes—
259C22×Dic71C2412yes—
260C2×C4×D71—24no—
261C2×C4×D71—216no—
262C2×C4×D71—24no—
263C2×C4×D71—24no—
264C2×C4×D71—28no—
265C2×C4×D71—48no—
266C2×C4×D71C2414yes—
267C2×C4×D71C24116yes—
268C2×C4×D71C2414yes—
269C2×C4×D71C2414yes—
270C2×C4×D71C2418yes—
271C2×C4×D71C24116yes—
272C4⋊Dic71C2414yes—
273C4⋊Dic71C2418yes—
274C4⋊Dic71C2418yes—
275C4⋊Dic71C24116yes—
276C4⋊Dic71C2414yes—
277C4⋊Dic71C2418yes—
278C4⋊Dic71C2418yes—
279C4⋊Dic71C2418yes—
280C4⋊Dic71C24116yes—
281Dic71⋊C4C24116yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C24116yes—
284Dic71⋊C4C2418yes—
285Dic71⋊C4C2418yes—
286Dic71⋊C4C2418yes—
287Dic71⋊C4C2418yes—
288Dic71⋊C4C24116yes—
289C22⋊Dic71C2418yes—
290C22⋊Dic71C24116yes—
291C22⋊Dic71C2418yes—
292C22⋊Dic71C2418yes—
293(C2×D71)⋊C4C2418yes—
294(C2×D71)⋊C4C2418yes—
295(C2×D71)⋊C4C2418yes—
296(C2×D71)⋊C4C2418yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C24116yes—
299(C2×D71)⋊C4C2418yes—
300(C2×D71)⋊C4C2418yes—
301C4×Dic71C2414yes—
302C4×Dic71C2414yes—
303C4×Dic71C2414yes—
304C4×Dic71C24116yes—
305C4×Dic71C24116yes—
306C4×Dic71C2418yes—
307C24×C71C2412yes—
308C2×Q8×C71—24no—
309C2×Q8×C71—44no—
310C2×Q8×C71C2414yes—
311C2×Q8×C71C2418yes—
312C2×D4×C71—24no—
313C2×D4×C71C2414yes—
314C22×C4×C71—28no—
315C22×C4×C71—48no—
316C22×C4×C71C2414yes—
317C22×C4×C71C2411yescharacteristic
318C22×C4×C71C2412yes—
319C22×C4×C71C2412yes—
320C22×C4×C71C2412yes—
321C22×C4×C71C2418yes—
322C22×C4×C71C24116yes—
323C22×C4×C71C2411yescharacteristic
324C22×C4×C71C2411yescharacteristic
325C4⋊C4×C71C2414yes—
326C4⋊C4×C71C24116yes—
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C2414yes—
329C4⋊C4×C71C2418yes—
330C4⋊C4×C71C2418yes—
331C4⋊C4×C71C24116yes—
332C22⋊C4×C71C24116yes—
333C22⋊C4×C71C2418yes—
334C42×C71C2418yes—
335C42×C71C2414yes—
336C23×C71—24no—
337C23×C71—24no—
338C23×C71—24no—
339C23×C71C2514yes—
340C23×C71C2511yescharacteristic
341C22×D71—22no—
342C22×D71—22no—
343C22×D71—24no—
344C22×D71—24no—
345C22×D71—24no—
346C22×D71H(5,𝔽2)14yes—
347C22×D71C2514yes—
348C22×D71C2512yes—
349Q8×C71—28no—
350Q8×C71—48no—
351D4×C71—28no—
352C2×C4×C71—24no—
353C2×C4×C71—28no—
354C2×C4×C71—22no—
355C2×C4×C71—24no—
356C2×C4×C71—24no—
357C2×C4×C71—216no—
358C2×C4×C71—416no—
359C2×C4×C712−1+414yes—
360C2×C4×C712−1+414yes—
361C2×C4×C71C2514yes—
362C2×C4×C71C2512yes—
363C2×C4×C71C2514yes—
364C2×C4×C71C2514yes—
365C2×C4×C71C2518yes—
366C2×C4×C71C2512yes—
367C2×C4×C71C2512yes—
368C22⋊D71—216no—
369C22⋊D71—416no—
370C2×Dic71—28no—
371C2×Dic71—22no—
372C2×Dic71—24no—
373C2×Dic71—22no—
374C2×Dic71—22no—
375C2×Dic71—24no—
376C2×Dic71—24no—
377C2×Dic71C2514yes—
378C2×Dic71C2512yes—
379C2×Dic71C2512yes—
380C2×Dic71C2514yes—
381C2×Dic71C2512yes—
382C2×Dic71C2518yes—
383C2×Dic71C2514yes—
384D284—216no—
385D284—28no—
386C4×D71—28no—
387C4×D71—232no—
388C4×D71—28no—
389C4×D71—28no—
390C4×D71—216no—
391C4×D71—416no—
392Dic142—28no—
393Dic142—416no—
394Dic142—48no—
395Dic142—416no—
396C22×C71—24no—
397C22×C71—24no—
398C22×C71—24no—
399C22×C71—48no—
400C22×C71C2×H(5,𝔽2)12yes—
401C22×C71C2×2−1+412yes—
402C22×C71C2×2−1+412yes—
403C22×C71C2611yescharacteristic
404C2×D71—22no—
405C2×D71—22no—
406C2×D71—28no—
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—48no—
411C2×D71C2×H(5,𝔽2)14yes—
412C4×C71—22no—
413C4×C71—24no—
414C4×C71—28no—
415C4×C71—24no—
416C4×C71—24no—
417C4×C71C2×2−1+414yes—
418C4×C71C2×2−1+414yes—
419Dic71—22no—
420Dic71—28no—
421Dic71—24no—
422Dic71—24no—
423Dic71—22no—
424Dic71—22no—
425Dic71—24no—
426C2×#3544—711nomaximal, Sylow
427C2×C71—44no—
428C2×C71#354414yescomplemented
429C2×C71C22×H(5,𝔽2)11yescharacteristic
430C2×C71C22×2−1+411yescharacteristic
431C2×C71C22×2−1+411yescharacteristic
432D71—24no—
433D71—44no—
434#3544—7132no—
435C2×#563—714no—
436C2×Q82—711no—
437C2×#555—711no—
438C2×#554—711no—
439C2×#554D7111yescharacteristic, complemented
440C2×#552—712no—
441C2×#552—712no—
442C2×#547—712no—
443C2×#547—712no—
444C2×#544—712no—
445C2×#544—712no—
446C2×#542—712no—
447C2×#542—712no—
448C2×#536—714no—
449C22×C4⋊Q8—711no—
450C2×#529—711no—
451C2×#529—711no—
452C71C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—714no—
454C23×Q8—712no—
455#563—7164no—
456Q82—7116no—
457#555—7116no—
458#554—7116no—
459#554C2×D71116yescomplemented
460#552—7132no—
461#552—7132no—
462#547—7132no—
463#547—7132no—
464#544—7132no—
465#544—7132no—
466#542—7132no—
467#542—7132no—
468#536—7164no—
469C2×C4⋊Q8—712no—
470C2×C4⋊Q8—7116no—
471C2×C4⋊Q8—712no—
472C2×C4⋊Q8—712no—
473C2×C4⋊Q8—714no—
474C2×C4⋊Q8—714no—
475C2×C4⋊Q8—712no—
476C2×C4⋊Q8—711no—
477C2×C4⋊Q8—712no—
478C2×C4⋊Q8C2×D7111yescharacteristic
479#529—7116no—
480#529—7116no—
481C2×#126—712no—
482C2×#126—714no—
483C2×#126—712no—
484C2×#126—714no—
485C2×#125—711no—
486C2×#125—711no—
487C2×#125—712no—
488C2×#125—714no—
489C2×#125—714no—
490C2×#125C2×D7112yes—
491C2×#124—711no—
492C2×#124—711no—
493C2×#124—714no—
494C2×#124—714no—
495C2×#123—714no—
496C2×#123—712no—
497C2×#123—714no—
498C2×#123—712no—
499C2×#123—714no—
500C2×#123—714no—
501C2×C22⋊Q8—711no—
502C2×C22⋊Q8—714no—
503C2×C22⋊Q8—714no—
504C2×C22⋊Q8—714no—
505C2×C22⋊Q8—711no—
506C2×C22⋊Q8—714no—
507C2×C22⋊Q8—712no—
508C2×C22⋊Q8—714no—
509C2×C22⋊Q8C2×D7114yes—
510C2×C22⋊Q8C2×D7112yes—
511C2×#121—711no—
512C2×#121—712no—
513C2×#121—712no—
514C2×#121—711no—
515C2×C4×Q8—712no—
516C2×C4×Q8—711no—
517C2×C4×Q8—712no—
518C2×C4×Q8C2×D7111yescharacteristic
519C2×C4×D4—712no—
520C2×C4×D4—712no—
521C2×C4×D4—712no—
522C2×C4×D4—711no—
523C2×C4×D4C2×D7111yescharacteristic
524C2×C4×D4C2×D7112yes—
525C2×#117—712no—
526C2×#117—712no—
527C2×#117—714no—
528C2×#117—712no—
529C2×#117—712no—
530C22×C4⋊C4—712no—
531C22×C4⋊C4—712no—
532C22×C4⋊C4—712no—
533C22×C4⋊C4C2×D7112yes—
534C22×C42—711no—
535C2×#41—28416no—
536C2×#41—7132no—
537C22×Q8—2848no—
538C22×Q8—7116no—
539C22×Q8—714no—
540C22×Q8—714no—
541C22×Q8—712no—
542C22×Q8—711no—
543C22×Q8C22×D7111yescharacteristic
544C22×Q8C22×D7112yes—
545C22×D4—714no—
546C22×D4—712no—
547C22×D4—711no—
548C22×D4—712no—
549C22×D4C22×D7111yescharacteristic
550C23×C4—714no—
551C23×C4—714no—
552C23×C4—711no—
553C23×C4—711no—
554C23×C4—712no—
555C23×C4—711no—
556C23×C4C22×D7112yes—
557C23×C4C22×D7114yes—
558C4⋊Q8—7116no—
559C4⋊Q8—7116no—
560C4⋊Q8—7116no—
561C4⋊Q8—7132no—
562C4⋊Q8—7132no—
563C4⋊Q8—7116no—
564C4⋊Q8—718no—
565C4⋊Q8—7116no—
566C4⋊Q8C22×D7118yes—
567#126—7116no—
568#126—7132no—
569#126—7116no—
570#126—7132no—
571#125—718no—
572#125—718no—
573#125—7116no—
574#125—7132no—
575#125—7132no—
576#125C22×D71116yes—
577#124—718no—
578#124—718no—
579#124—7132no—
580#124—7132no—
581#123—7132no—
582#123—7116no—
583#123—7132no—
584#123—7116no—
585#123—7132no—
586#123—7132no—
587C22⋊Q8—718no—
588C22⋊Q8—7132no—
589C22⋊Q8—7132no—
590C22⋊Q8—7132no—
591C22⋊Q8—718no—
592C22⋊Q8—7132no—
593C22⋊Q8—7116no—
594C22⋊Q8—7132no—
595C22⋊Q8C22×D71132yes—
596C22⋊Q8C22×D71116yes—
597#121—718no—
598#121—7116no—
599#121—7116no—
600#121—718no—
601C4×Q8—7116no—
602C4×Q8—718no—
603C4×Q8—7116no—
604C4×Q8C22×D7118yes—
605C4×D4—7116no—
606C4×D4—7116no—
607C4×D4—7116no—
608C4×D4—718no—
609C4×D4C22×D7118yes—
610C4×D4C22×D71116yes—
611#117—7116no—
612#117—7116no—
613#117—7132no—
614#117—7116no—
615#117—7116no—
616C2×C4⋊C4—711no—
617C2×C4⋊C4—712no—
618C2×C4⋊C4—712no—
619C2×C4⋊C4—714no—
620C2×C4⋊C4—714no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—711no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—712no—
625C2×C4⋊C4—712no—
626C2×C4⋊C4—712no—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—712no—
629C2×C4⋊C4—712no—
630C2×C4⋊C4—712no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—714no—
633C2×C4⋊C4—7116no—
634C2×C4⋊C4—7116no—
635C2×C4⋊C4—7116no—
636C2×C4⋊C4C22×D7112yes—
637C2×C4⋊C4C22×D7112yes—
638C2×C4⋊C4C22×D7111yescharacteristic
639C2×C4⋊C4C22×D7114yes—
640C2×C4⋊C4C22×D71116yes—
641C2×C4⋊C4C22×D7111yescharacteristic
642C2×C4⋊C4C22×D7114yes—
643C2×C4⋊C4C22×D7112yes—
644C2×C22⋊C4—712no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—712no—
647C2×C22⋊C4—712no—
648C2×C22⋊C4—712no—
649C2×C22⋊C4—712no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—714no—
652C2×C22⋊C4—712no—
653C2×C22⋊C4—714no—
654C2×C22⋊C4—712no—
655C2×C22⋊C4—712no—
656C2×C22⋊C4C22×D7114yes—
657C2×C22⋊C4C22×D7112yes—
658C2×C42—714no—
659C2×C42—711no—
660C2×C42—711no—
661C2×C42—712no—
662C2×C42—714no—
663C2×C42—711no—
664C2×C42—718no—
665C2×C42C22×D7112yes—
666C2×C42C22×D7111yescharacteristic
667C24—711no—
668C24—712no—
669C24C23×D7112yes—
670#41—28464no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—2848no—
674C2×Q8—2844no—
675C2×Q8—2848no—
676C2×Q8—28432no—
677C2×Q8—7116no—
678C2×Q8—7116no—
679C2×Q8—718no—
680C2×Q8—714no—
681C2×Q8—1424no—
682C2×Q8C23×D7114yes—
683C2×Q8C23×D7118yes—
684C2×D4—24no—
685C2×D4—2848no—
686C2×D4—7116no—
687C2×D4—718no—
688C2×D4—714no—
689C2×D4—718no—
690C2×D4—1428no—
691C2×D4—1428no—
692C2×D4—1424no—
693C2×D4C23×D7114yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—2848no—
697C22×C4—7116no—
698C22×C4—712no—
699C22×C4—711no—
700C22×C4—712no—
701C22×C4—711no—
702C22×C4—711no—
703C22×C4—714no—
704C22×C4—712no—
705C22×C4—714no—
706C22×C4—714no—
707C22×C4—714no—
708C22×C4—7116no—
709C22×C4—718no—
710C22×C4—1424no—
711C22×C4—14216no—
712C22×C4—1424no—
713C22×C4—1428no—
714C22×C4—1424no—
715C22×C4C23×D7118yes—
716C22×C4C23×D7112yes—
717C22×C4C23×D7112yes—
718C22×C4C23×D7111yescharacteristic
719C22×C4C23×D7112yes—
720C22×C4C23×D7114yes—
721C22×C4C23×D71116yes—
722C22×C4C23×D7111yescharacteristic
723C22×C4C23×D7111yescharacteristic
724C4⋊C4—7116no—
725C4⋊C4—7116no—
726C4⋊C4—7116no—
727C4⋊C4—718no—
728C4⋊C4—718no—
729C4⋊C4—718no—
730C4⋊C4—718no—
731C4⋊C4—7116no—
732C4⋊C4—714no—
733C4⋊C4—718no—
734C4⋊C4—718no—
735C4⋊C4—714no—
736C4⋊C4—7116no—
737C4⋊C4—718no—
738C4⋊C4—718no—
739C4⋊C4—718no—
740C4⋊C4—7116no—
741C4⋊C4C23×D7118yes—
742C4⋊C4C23×D7118yes—
743C4⋊C4C23×D7114yes—
744C4⋊C4C23×D71116yes—
745C4⋊C4C23×D7114yes—
746C4⋊C4C23×D71116yes—
747C4⋊C4C23×D7118yes—
748C22⋊C4—718no—
749C22⋊C4—7116no—
750C22⋊C4—718no—
751C22⋊C4—718no—
752C22⋊C4—718no—
753C22⋊C4—718no—
754C22⋊C4—718no—
755C22⋊C4—7116no—
756C22⋊C4—718no—
757C22⋊C4—7116no—
758C22⋊C4—718no—
759C22⋊C4—718no—
760C22⋊C4C23×D71116yes—
761C22⋊C4C23×D7118yes—
762C42—714no—
763C42—714no—
764C42—714no—
765C42—7116no—
766C42—718no—
767C42—7116no—
768C42C23×D7114yes—
769C42C23×D7118yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—714no—
774C23—712no—
775C23—714no—
776C23—1424no—
777C23—1424no—
778C23—1424no—
779C23—1422no—
780C23—1422no—
781C23C24×D7114yes—
782C23C24×D7111yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—28416no—
786Q8—2848no—
787Q8—28416no—
788Q8—1428no—
789D4—28no—
790D4—28416no—
791D4—14216no—
792D4—14216no—
793D4—1428no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—28416no—
802C2×C4—714no—
803C2×C4—712no—
804C2×C4—712no—
805C2×C4—714no—
806C2×C4—712no—
807C2×C4—718no—
808C2×C4—714no—
809C2×C4—1428no—
810C2×C4—14232no—
811C2×C4—1424no—
812C2×C4—1428no—
813C2×C4—1422no—
814C2×C4—1422no—
815C2×C4—1424no—
816C2×C4—1422no—
817C2×C4—1424no—
818C2×C4—1428no—
819C2×C4—14216no—
820C2×C4—1428no—
821C2×C4#1455617514yes—
822C2×C4#1455617614yes—
823C2×C4C24×D7114yes—
824C2×C4C24×D7114yes—
825C2×C4C24×D7112yes—
826C2×C4C24×D7114yes—
827C2×C4C24×D7118yes—
828C2×C4C24×D7112yes—
829C2×C4C24×D7112yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—2848no—
835C22—714no—
836C22—1424no—
837C22—1424no—
838C22—1424no—
839C22—1422no—
840C22—1422no—
841C22—1428no—
842C22H(5,𝔽2)×D7112yes—
843C22C2×#1455617512yes—
844C22C2×#1455617612yes—
845C22C25×D7111yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1424no—
852C4—1428no—
853C4—1422no—
854C4—1422no—
855C4—1422no—
856C4—1424no—
857C4—1424no—
858C4C2×#1455617514yes—
859C4C2×#1455617614yes—
860C2—44no—
861C2—2844no—
862C2—1424no—
863C2#2260268114yesdirect product factor
864C2C2×H(5,𝔽2)×D7111yescharacteristic
865C2C22×#1455617511yescharacteristic
866C2C22×#1455617611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#554×C71C2
socleC23×C71C25
hypercenterC2×#554D71
hypocenterC71C2×#3544
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22602681C2direct (N × H)
2. C2×#17986750C2semidirect
3. C2×Q8×Dic142C2semidirect
4. C2×#17986714C2semidirect
5. C2×#17986710C2semidirect
6. C2×#17986687C2semidirect
7. C2×#17986683C2semidirect
8. C2×#17986654C2semidirect
9. C2×#17986650C2semidirect
10. C2×#17986630C2semidirect
11. C2×#17986629C2semidirect
12. C2×#17986622C2semidirect
13. C2×#17986614C2semidirect
14. C2×#17986572C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986536C2semidirect
17. C2×#17986531C2semidirect
18. C2×#554×C71C2semidirect
21. #17986750C22semidirect
22. Q8×Dic142C22semidirect
23. #17986714C22semidirect
24. #17986710C22semidirect
25. #17986687C22semidirect
26. #17986683C22semidirect
27. #17986654C22semidirect
28. #17986650C22semidirect
29. #17986630C22semidirect
30. #17986629C22semidirect
31. #17986622C22semidirect
32. #17986614C22semidirect
33. #17986572C22semidirect
42. C4⋊Q8×D71C22semidirect
43. #17986536C22semidirect
44. #17986531C22semidirect
92. #554×C71C22semidirect
428. C2×C71#3544semidirect
439. C2×#554D71semidirect
452. C71C2×#3544semidirect
459. #554C2×D71semidirect
863. C2#22602681direct (N × H)

Maximal subgroups

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

subgroupindex
#226026812
C2×#179867502
C2×Q8×Dic1422
C2×#179867142
C2×#179867102
C2×#179866872
C2×#179866832
C2×#179866542
C2×#179866502
C2×#179866302
C2×#179866292
C2×#179866222
C2×#179866142
C2×#179865722
C2×C4⋊Q8×D712
C2×#179865362
C2×#179865312
C2×#554×C712
C2×#354471