Finite Group Databasebeta

← C2×#22602223 #32905891

Subgroups — C2×#22602223 #32905891

Order 18176.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602223C2132yesmaximal, direct product factor
2C2×#17986727C211yesmaximal, characteristic, complemented
3C2×#17986724C212yesmaximal, complemented
4C2×#17986723C211yesmaximal, characteristic, complemented
5C2×#17986722C211yesmaximal, characteristic, complemented
6C2×#17986721C212yesmaximal, complemented
7C2×#17986690C212yesmaximal, complemented
8C2×#17986687C212yesmaximal, complemented
9C2×#17986681C214yesmaximal, complemented
10C2×#17986608C214yesmaximal, complemented
11C2×#17986574C212yesmaximal
12C2×#17986555C212yesmaximal, complemented
13C2×#17986553C212yesmaximal, complemented
14C2×#17986553C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986475C212yesmaximal, complemented
17C2×C4×#11765866C211yesmaximal, characteristic
18C2×#557×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2211yescharacteristic
20C22×Q8×D71C2212yes—
21#17986727C22116yescomplemented
22#17986724C22132yescomplemented
23#17986723C22116yescomplemented
24#17986722C22116yescomplemented
25#17986721C22132yescomplemented
26#17986690C22132yescomplemented
27#17986687C22132yescomplemented
28#17986681C22164yescomplemented
29#17986608C22164yescomplemented
30#17986574C22132yes—
31#17986555C22132yescomplemented
32#17986553C22132yescomplemented
33#17986553C22116yescomplemented
34C2×#14556128C2211yescharacteristic
35C2×#14556127C2212yes—
36C2×#14556127C2212yes—
37C2×#14556127C2211yescharacteristic
38C2×#14556126C2212yes—
39C2×#14556126C2211yescharacteristic
40C2×#14556126C2212yes—
41C4⋊Q8×D71C22116yescomplemented
42C2×#14556123C2214yes—
43C2×#14556123C2214yes—
44C2×#14556123C2214yes—
45C2×#14556122C2214yes—
46C2×#14556120C2212yes—
47C2×#14556119C2214yes—
48C2×#14556118C2214yes—
49C2×#14556118C2214yes—
50C2×#14556118C2214yes—
51C2×#14556118C2212yes—
52C2×#14556117C2212yes—
53C2×#14556116C2212yes—
54C2×#14556113C2214yes—
55C2×#14556113C2214yes—
56C2×#14556108C2211yescharacteristic
57C2×#14556108C2212yes—
58C2×#14556106C2212yes—
59C2×#14556106C2214yes—
60C2×#14556106C2214yes—
61C2×#14556106C2214yes—
62C2×#14556104C2211yescharacteristic
63C2×#14556104C2212yes—
64#17986475C22132yescomplemented
65C4×#11765866C22116yes—
66C2×Q8×Dic71C2211yescharacteristic
67C2×Q8×Dic71C2212yes—
68C2×C4×Dic142C2214yes—
69C2×C4×Dic142C2212yes—
70C2×C4×Dic142C2212yes—
71C2×C4×Dic142C2212yes—
72C2×C4×Dic142C2211yescharacteristic
73C2×#14556093C2214yes—
74C2×#14556093C2212yes—
75C2×#14556093C2214yes—
76C2×C4×D284C2212yes—
77C2×C4×D284C2211yescharacteristic
78C2×#14556090C2212yes—
79C2×#14556090C2211yescharacteristic
80C2×#14556086C2211yescharacteristic
81C2×#14556086C2212yes—
82C2×#14556086C2214yes—
83C2×#14556086C2212yes—
84C2×#14556086C2212yes—
85C2×#14556085C2214yes—
86C2×#14556085C2212yes—
87C2×#14556085C2214yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C42×D71C2211yescharacteristic
91C2×C42×D71C2212yes—
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—28no—
102C2×#11765866C2318yes—
103C22×Dic142C2314yes—
104C22×Dic142C2312yes—
105C22×Dic142C2312yes—
106C22×Dic142C2311yescharacteristic
107C2×Q8×D71—216no—
108C2×Q8×D71C23116yes—
109C22×D284C2312yes—
110C22×D284C2311yescharacteristic
111C22×C4×D71C2314yes—
112C22×C4×D71C2312yes—
113C22×C4×D71C2311yescharacteristic
114C22×C4×D71C2311yescharacteristic
115C22×C4×D71C2312yes—
116C22×C4×D71C2312yes—
117C22×C4×D71C2311yescharacteristic
118#14556128C2318yes—
119#14556127C23116yes—
120#14556127C23116yes—
121#14556127C2318yes—
122#14556126C23116yes—
123#14556126C23116yes—
124#14556126C2318yes—
125#14556123C23132yes—
126#14556123C23132yes—
127#14556123C23132yes—
128#14556122C23132yes—
129#14556120C23116yes—
130#14556119C23132yes—
131#14556118C23116yes—
132#14556118C23132yes—
133#14556118C23132yes—
134#14556118C23132yes—
135#14556117C23116yes—
136#14556116C23116yes—
137#14556113C23132yes—
138#14556113C23132yes—
139#14556108C2318yes—
140#14556108C23116yes—
141#14556106C23132yes—
142#14556106C23132yes—
143#14556106C23116yes—
144#14556106C23132yes—
145#14556104C2318yes—
146#14556104C23116yes—
147Q8×Dic71C23116yes—
148Q8×Dic71C2318yes—
149C4×Dic142C23132yes—
150C4×Dic142C23116yes—
151C4×Dic142C23116yes—
152C4×Dic142C23116yes—
153C4×Dic142C2318yes—
154#14556093C23132yes—
155#14556093C23132yes—
156#14556093C23116yes—
157C4×D284C23116yes—
158C4×D284C2318yes—
159#14556090C23116yes—
160#14556090C2318yes—
161#14556086C23116yes—
162#14556086C23132yes—
163#14556086C23116yes—
164#14556086C23116yes—
165#14556086C2318yes—
166#14556085C23116yes—
167#14556085C23132yes—
168#14556085C23132yes—
169C2×C4⋊Dic71C2312yes—
170C2×C4⋊Dic71C2312yes—
171C2×C4⋊Dic71C2311yescharacteristic
172C2×C4⋊Dic71C2311yescharacteristic
173C2×C4⋊Dic71C2312yes—
174C2×C4⋊Dic71C2314yes—
175C2×C4⋊Dic71C2312yes—
176C2×Dic71⋊C4C2314yes—
177C2×Dic71⋊C4C2314yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2312yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2314yes—
186C2×Dic71⋊C4C2312yes—
187C4⋊C4×D71C23116yes—
188C4⋊C4×D71C23116yes—
189C2×(C2×D71)⋊C4C2312yes—
190C2×(C2×D71)⋊C4C2312yes—
191C2×(C2×D71)⋊C4C2312yes—
192C2×(C2×D71)⋊C4C2314yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×C4×Dic71C2311yescharacteristic
199C2×C4×Dic71C2312yes—
200C2×C4×Dic71C2311yescharacteristic
201C2×C4×Dic71C2312yes—
202C2×C4×Dic71C2311yescharacteristic
203C2×C4×Dic71C2314yes—
204C2×C4×Dic71C2314yes—
205C2×C4×Dic71C2312yes—
206C2×C4×Dic71C2314yes—
207C42×D71C2318yes—
208C42×D71C23116yes—
209C22×Q8×C71C2312yes—
210C22×Q8×C71C2311yescharacteristic
211C22×Q8×C71C2311yescharacteristic
212C4⋊Q8×C71C23116yes—
213C4⋊Q8×C71C2318yes—
214#125×C71C23132yes—
215#125×C71C23116yes—
216C4×Q8×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C2318yes—
219C4×Q8×C71C2318yes—
220C2×C4⋊C4×C71C2311yescharacteristic
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2312yes—
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2314yes—
227C2×C4⋊C4×C71C2312yes—
228C2×C4⋊C4×C71C2314yes—
229C2×C42×C71C2312yes—
230C2×C42×C71C2314yes—
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2312yes—
233C23×D71C2412yes—
234C23×D71C2411yescharacteristic
235#11765866—232no—
236C2×Dic142—28no—
237C2×Dic142—24no—
238C2×Dic142—216no—
239C2×Dic142—28no—
240C2×Dic142C24116yes—
241C2×Dic142C2418yes—
242C2×Dic142C2418yes—
243C2×Dic142C2414yes—
244Q8×D71—264no—
245C2×D284—28no—
246C2×D284—24no—
247C2×D284C2418yes—
248C2×D284C2414yes—
249C22×Dic71C2414yes—
250C22×Dic71C2412yes—
251C22×Dic71C2411yescharacteristic
252C22×Dic71C2412yes—
253C22×Dic71C2412yes—
254C22×Dic71C2411yescharacteristic
255C22×Dic71C2411yescharacteristic
256C2×C4×D71—216no—
257C2×C4×D71—24no—
258C2×C4×D71—28no—
259C2×C4×D71—28no—
260C2×C4×D71—24no—
261C2×C4×D71—28no—
262C2×C4×D71#4118yes—
263C2×C4×D71C24116yes—
264C2×C4×D71C2418yes—
265C2×C4×D71C2414yes—
266C2×C4×D71C2414yes—
267C2×C4×D71C2418yes—
268C2×C4×D71C2418yes—
269C2×C4×D71C2414yes—
270C4⋊Dic71C2418yes—
271C4⋊Dic71C2418yes—
272C4⋊Dic71C2414yes—
273C4⋊Dic71C2414yes—
274C4⋊Dic71C2418yes—
275C4⋊Dic71C24116yes—
276C4⋊Dic71C2418yes—
277Dic71⋊C4C24116yes—
278Dic71⋊C4C24116yes—
279Dic71⋊C4C2418yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C24116yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C2418yes—
284Dic71⋊C4C24116yes—
285Dic71⋊C4C2418yes—
286Dic71⋊C4C24116yes—
287Dic71⋊C4C2418yes—
288(C2×D71)⋊C4C2418yes—
289(C2×D71)⋊C4C2418yes—
290(C2×D71)⋊C4C2418yes—
291(C2×D71)⋊C4C24116yes—
292(C2×D71)⋊C4C24116yes—
293(C2×D71)⋊C4C2418yes—
294(C2×D71)⋊C4C2418yes—
295(C2×D71)⋊C4C24116yes—
296(C2×D71)⋊C4C24116yes—
297C4×Dic71C2414yes—
298C4×Dic71C2418yes—
299C4×Dic71C2414yes—
300C4×Dic71C2418yes—
301C4×Dic71C2414yes—
302C4×Dic71C24116yes—
303C4×Dic71C24116yes—
304C4×Dic71C2418yes—
305C4×Dic71C24116yes—
306C2×Q8×C71—28no—
307C2×Q8×C71—24no—
308C2×Q8×C71—24no—
309C2×Q8×C71C2418yes—
310C2×Q8×C71C2414yes—
311C2×Q8×C71C2414yes—
312C22×C4×C71C2412yes—
313C22×C4×C71C2414yes—
314C22×C4×C71C2412yes—
315C22×C4×C71C2411yescharacteristic
316C22×C4×C71C2412yes—
317C22×C4×C71C2412yes—
318C22×C4×C71C2411yescharacteristic
319C22×C4×C71C2411yescharacteristic
320C4⋊C4×C71C2414yes—
321C4⋊C4×C71C2414yes—
322C4⋊C4×C71C2418yes—
323C4⋊C4×C71C24116yes—
324C4⋊C4×C71C2418yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C24116yes—
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C24116yes—
329C42×C71C2418yes—
330C42×C71C24116yes—
331C42×C71C2414yes—
332C42×C71C2418yes—
333C23×C71C2511yescharacteristic
334C22×D71—22no—
335C22×D71—22no—
336C22×D71—24no—
337C22×D71—24no—
338C22×D71—24no—
339C22×D71C2×#4114yes—
340C22×D71C2514yes—
341C22×D71C2512yes—
342Q8×C71—216no—
343Q8×C71—28no—
344Q8×C71—28no—
345C2×C4×C71—24no—
346C2×C4×C71—28no—
347C2×C4×C71—24no—
348C2×C4×C71—24no—
349C2×C4×C71—22no—
350C2×C4×C71—24no—
351C2×C4×C71C2×#4114yes—
352C2×C4×C712−1+414yes—
353C2×C4×C71C2514yes—
354C2×C4×C71C2514yes—
355C2×C4×C71C2514yes—
356C2×C4×C71C2512yes—
357C2×C4×C71C2518yes—
358C2×C4×C71C2514yes—
359C2×C4×C71C2512yes—
360C2×C4×C71C2512yes—
361C2×Dic71—28no—
362C2×Dic71—24no—
363C2×Dic71—22no—
364C2×Dic71—24no—
365C2×Dic71—24no—
366C2×Dic71C2×#4114yes—
367C2×Dic712−1+414yes—
368C2×Dic71C2514yes—
369C2×Dic71C2514yes—
370C2×Dic71C2514yes—
371C2×Dic71C2512yes—
372C2×Dic71C2518yes—
373C2×Dic71C2512yes—
374C2×Dic71C2512yes—
375D284—216no—
376D284—28no—
377C4×D71—232no—
378C4×D71—28no—
379C4×D71—216no—
380C4×D71—216no—
381C4×D71—28no—
382C4×D71—216no—
383C4×D71C2×#41116yes—
384Dic142—216no—
385Dic142—28no—
386Dic142—232no—
387Dic142—216no—
388C22×C71C22×#4112yes—
389C22×C71C2×2−1+412yes—
390C22×C71C2×2−1+412yes—
391C22×C71C2611yescharacteristic
392C2×D71—22no—
393C2×D71—22no—
394C2×D71—28no—
395C2×D71—24no—
396C2×D71—24no—
397C2×D71—24no—
398C2×D71—48no—
399C2×D71C22×#4114yes—
400C4×C71—28no—
401C4×C71—24no—
402C4×C71—24no—
403C4×C71—24no—
404C4×C71—22no—
405C4×C71—24no—
406C4×C71C22×#4114yes—
407C4×C71C2×2−1+414yes—
408Dic71—28no—
409Dic71—24no—
410Dic71—24no—
411Dic71—24no—
412Dic71—22no—
413Dic71C22×#4114yes—
414Dic71C2×2−1+414yes—
415C2×#3509—711nomaximal, Sylow
416C2×C71#350914yescomplemented
417C2×C71C23×#4111yescharacteristic
418C2×C71C22×2−1+411yescharacteristic
419C2×C71C22×2−1+411yescharacteristic
420D71—24no—
421D71—44no—
422#3509—7132no—
423C2×#557—712no—
424C2×#557—711no—
425C2×#557D7111yescharacteristic, complemented
426C2×#556—711no—
427C2×#556—712no—
428C2×#556—711no—
429C2×#552—714no—
430C2×#552—712no—
431C2×#552—712no—
432C2×#541—714no—
433C2×#536—712no—
434C2×#533—712no—
435C2×#533—711no—
436C2×#533—712no—
437C22×C4⋊Q8—711no—
438C2×#519—712no—
439C2×C4×#41—711no—
440C71C2×#350911yescharacteristic, complemented, Sylow
441C22×#41—711no—
442C23×Q8—712no—
443#557—7132no—
444#557—7116no—
445#557C2×D71116yescomplemented
446#556—7116no—
447#556—7132no—
448#556—7116no—
449#552—7164no—
450#552—7132no—
451#552—7132no—
452#541—7164no—
453#536—7132no—
454#533—7132no—
455#533—7116no—
456#533—7132no—
457C2×C4⋊Q8—712no—
458C2×C4⋊Q8—711no—
459C2×C4⋊Q8—712no—
460C2×C4⋊Q8—7116no—
461C2×C4⋊Q8—712no—
462C2×C4⋊Q8—712no—
463C2×C4⋊Q8—711no—
464C2×C4⋊Q8—711no—
465C2×C4⋊Q8C2×D7111yescharacteristic
466C2×C4⋊Q8C2×D7112yes—
467C2×#126—714no—
468C2×#126—714no—
469C2×#126—714no—
470C2×#126—714no—
471C2×#125—712no—
472C2×#125—714no—
473C2×#125—714no—
474C2×#125—714no—
475C2×#125—714no—
476C2×#125—712no—
477C2×#125C2×D7112yes—
478C2×#125C2×D7114yes—
479C2×#124—712no—
480C2×#124—712no—
481C2×#123—714no—
482C2×#123—714no—
483C2×C22⋊Q8—711no—
484C2×C22⋊Q8—712no—
485C2×C22⋊Q8—714no—
486C2×C22⋊Q8—714no—
487C2×C22⋊Q8—712no—
488C2×C22⋊Q8—711no—
489C2×C22⋊Q8—714no—
490C2×C22⋊Q8—712no—
491#519—7132no—
492C4×#41—7116no—
493C2×C4×Q8—711no—
494C2×C4×Q8—712no—
495C2×C4×Q8—714no—
496C2×C4×Q8—712no—
497C2×C4×Q8—714no—
498C2×C4×Q8—714no—
499C2×C4×Q8—712no—
500C2×C4×Q8—712no—
501C2×C4×Q8—711no—
502C2×C4×Q8—712no—
503C2×C4×Q8C2×D7111yescharacteristic
504C2×C4×Q8C2×D7112yes—
505C2×C4×Q8C2×D7112yes—
506C2×C4×Q8C2×D7111yescharacteristic
507C2×C4×D4—712no—
508C2×C4×D4—711no—
509C2×C4×D4—712no—
510C2×C4×D4—711no—
511C2×#117—711no—
512C2×#117—712no—
513C2×#117—714no—
514C2×#117—712no—
515C2×#117—712no—
516C2×#117—712no—
517C2×#117—714no—
518C2×#117—714no—
519C22×C4⋊C4—712no—
520C22×C4⋊C4—712no—
521C22×C42—711no—
522C22×C42—712no—
523C2×#41—718no—
524C2×#41—1428no—
525C22×Q8—7116no—
526C22×Q8—712no—
527C22×Q8—711no—
528C22×Q8—714no—
529C22×Q8—712no—
530C22×Q8—14216no—
531C22×Q8C22×D7112yes—
532C22×Q8C22×D7111yescharacteristic
533C22×Q8C22×D7111yescharacteristic
534C22×D4—712no—
535C22×D4—711no—
536C23×C4—711no—
537C23×C4—714no—
538C23×C4—711no—
539C23×C4—711no—
540C23×C4—712no—
541C23×C4—712no—
542C23×C4—712no—
543C4⋊Q8—7116no—
544C4⋊Q8—718no—
545C4⋊Q8—7116no—
546C4⋊Q8—7116no—
547C4⋊Q8—7116no—
548C4⋊Q8—718no—
549C4⋊Q8—718no—
550C4⋊Q8C22×D7118yes—
551C4⋊Q8C22×D71116yes—
552#126—7132no—
553#126—7132no—
554#126—7132no—
555#126—7132no—
556#125—7116no—
557#125—7132no—
558#125—7132no—
559#125—7132no—
560#125—7132no—
561#125—7116no—
562#125C22×D71116yes—
563#125C22×D71132yes—
564#124—7116no—
565#124—7116no—
566#123—7132no—
567#123—7132no—
568C22⋊Q8—718no—
569C22⋊Q8—7116no—
570C22⋊Q8—7132no—
571C22⋊Q8—7132no—
572C22⋊Q8—7116no—
573C22⋊Q8—718no—
574C22⋊Q8—7132no—
575C22⋊Q8—7116no—
576C4×Q8—718no—
577C4×Q8—7116no—
578C4×Q8—7132no—
579C4×Q8—7116no—
580C4×Q8—7132no—
581C4×Q8—7132no—
582C4×Q8—7116no—
583C4×Q8—7116no—
584C4×Q8—7116no—
585C4×Q8—718no—
586C4×Q8C22×D7118yes—
587C4×Q8C22×D71116yes—
588C4×Q8C22×D71116yes—
589C4×Q8C22×D7118yes—
590C4×D4—7116no—
591C4×D4—718no—
592C4×D4—7116no—
593C4×D4—718no—
594#117—718no—
595#117—7116no—
596#117—7132no—
597#117—7116no—
598#117—7116no—
599#117—7116no—
600#117—7132no—
601#117—7132no—
602C2×C4⋊C4—714no—
603C2×C4⋊C4—712no—
604C2×C4⋊C4—714no—
605C2×C4⋊C4—712no—
606C2×C4⋊C4—712no—
607C2×C4⋊C4—711no—
608C2×C4⋊C4—711no—
609C2×C4⋊C4—712no—
610C2×C4⋊C4—712no—
611C2×C4⋊C4—712no—
612C2×C4⋊C4—714no—
613C2×C4⋊C4—714no—
614C2×C4⋊C4—714no—
615C2×C4⋊C4—714no—
616C2×C4⋊C4—714no—
617C2×C4⋊C4—712no—
618C2×C4⋊C4—712no—
619C2×C4⋊C4—712no—
620C2×C4⋊C4—7116no—
621C2×C4⋊C4—7116no—
622C2×C4⋊C4C22×D7112yes—
623C2×C4⋊C4C22×D7112yes—
624C2×C4⋊C4C22×D7111yescharacteristic
625C2×C4⋊C4C22×D7111yescharacteristic
626C2×C4⋊C4C22×D7112yes—
627C2×C4⋊C4C22×D7114yes—
628C2×C4⋊C4C22×D7114yes—
629C2×C4⋊C4C22×D7114yes—
630C2×C4⋊C4C22×D7112yes—
631C2×C22⋊C4—712no—
632C2×C22⋊C4—712no—
633C2×C22⋊C4—712no—
634C2×C22⋊C4—712no—
635C2×C22⋊C4—712no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—714no—
639C2×C22⋊C4—714no—
640C2×C42—712no—
641C2×C42—714no—
642C2×C42—714no—
643C2×C42—714no—
644C2×C42—711no—
645C2×C42—712no—
646C2×C42—712no—
647C2×C42—711no—
648C2×C42—711no—
649C2×C42—718no—
650C2×C42—7116no—
651C2×C42C22×D7114yes—
652C2×C42C22×D7112yes—
653C2×C42C22×D7112yes—
654C2×C42C22×D7111yescharacteristic
655C24—711no—
656C24—712no—
657#41—14232no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—718no—
662C2×Q8—714no—
663C2×Q8—7116no—
664C2×Q8—718no—
665C2×Q8—1428no—
666C2×Q8—14216no—
667C2×Q8—14264no—
668C2×Q8—1428no—
669C2×Q8—1424no—
670C2×Q8C23×D7118yes—
671C2×Q8C23×D7114yes—
672C2×Q8C23×D7114yes—
673C2×D4—718no—
674C2×D4—714no—
675C2×D4—1428no—
676C2×D4—1424no—
677C22×C4—711no—
678C22×C4—711no—
679C22×C4—718no—
680C22×C4—714no—
681C22×C4—712no—
682C22×C4—712no—
683C22×C4—712no—
684C22×C4—711no—
685C22×C4—714no—
686C22×C4—714no—
687C22×C4—714no—
688C22×C4—718no—
689C22×C4—718no—
690C22×C4—718no—
691C22×C4—7116no—
692C22×C4—1428no—
693C22×C4—1424no—
694C22×C4—1428no—
695C22×C4—14216no—
696C22×C4—1428no—
697C22×C4—1424no—
698C22×C4C23×D7112yes—
699C22×C4C23×D7112yes—
700C22×C4C23×D7111yescharacteristic
701C22×C4C23×D7114yes—
702C22×C4C23×D7112yes—
703C22×C4C23×D7112yes—
704C22×C4C23×D7111yescharacteristic
705C22×C4C23×D7111yescharacteristic
706C4⋊C4—7116no—
707C4⋊C4—7116no—
708C4⋊C4—718no—
709C4⋊C4—718no—
710C4⋊C4—718no—
711C4⋊C4—7116no—
712C4⋊C4—7116no—
713C4⋊C4—7116no—
714C4⋊C4—7116no—
715C4⋊C4—718no—
716C4⋊C4—718no—
717C4⋊C4—718no—
718C4⋊C4—718no—
719C4⋊C4—714no—
720C4⋊C4—714no—
721C4⋊C4—718no—
722C4⋊C4—7116no—
723C4⋊C4—718no—
724C4⋊C4C23×D7118yes—
725C4⋊C4C23×D7118yes—
726C4⋊C4C23×D7114yes—
727C4⋊C4C23×D7114yes—
728C4⋊C4C23×D7118yes—
729C4⋊C4C23×D71116yes—
730C4⋊C4C23×D71116yes—
731C4⋊C4C23×D71116yes—
732C4⋊C4C23×D7118yes—
733C22⋊C4—718no—
734C22⋊C4—718no—
735C22⋊C4—718no—
736C22⋊C4—718no—
737C22⋊C4—718no—
738C22⋊C4—7116no—
739C22⋊C4—7116no—
740C22⋊C4—7116no—
741C22⋊C4—7116no—
742C42—714no—
743C42—718no—
744C42—714no—
745C42—718no—
746C42—714no—
747C42—7116no—
748C42—7116no—
749C42—7116no—
750C42—718no—
751C42C23×D7118yes—
752C42C23×D7114yes—
753C42C23×D71116yes—
754C42C23×D7118yes—
755C23—714no—
756C23—712no—
757C23—714no—
758C23—1424no—
759C23—1424no—
760C23—1424no—
761C23—1422no—
762C23—1422no—
763C23C24×D7111yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—28no—
767Q8—14232no—
768Q8—14216no—
769Q8—14216no—
770Q8—1428no—
771D4—14216no—
772D4—1428no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—714no—
780C2×C4—714no—
781C2×C4—712no—
782C2×C4—712no—
783C2×C4—7116no—
784C2×C4—714no—
785C2×C4—714no—
786C2×C4—714no—
787C2×C4—712no—
788C2×C4—718no—
789C2×C4—14216no—
790C2×C4—14216no—
791C2×C4—1428no—
792C2×C4—14232no—
793C2×C4—1428no—
794C2×C4—1424no—
795C2×C4—1424no—
796C2×C4—1422no—
797C2×C4—1424no—
798C2×C4—14216no—
799C2×C4—1428no—
800C2×C4#41×D7114yes—
801C2×C4#1455617614yes—
802C2×C4C24×D7114yes—
803C2×C4C24×D7114yes—
804C2×C4C24×D7112yes—
805C2×C4C24×D7118yes—
806C2×C4C24×D7114yes—
807C2×C4C24×D7114yes—
808C2×C4C24×D7112yes—
809C2×C4C24×D7112yes—
810C22—2848no—
811C22—714no—
812C22—1424no—
813C22—1424no—
814C22—1424no—
815C22—1422no—
816C22—1422no—
817C22—1428no—
818C22C2×#41×D7112yes—
819C222−1+4×D7112yes—
820C22C2×#1455617612yes—
821C22C25×D7111yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—714no—
829C4—714no—
830C4—1428no—
831C4—1424no—
832C4—1424no—
833C4—1422no—
834C4—1424no—
835C4C2×#41×D7114yes—
836C4C2×#1455617614yes—
837C2—2844no—
838C2—1424no—
839C2#2260222314yesdirect product factor
840C2C22×#41×D7111yescharacteristic
841C2C2×2−1+4×D7111yescharacteristic
842C2C22×#1455617611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#557×C71C2
socleC23×C71C25
prime radicalC22×#11765866C22
hypercenterC2×#557D71
hypocenterC71C2×#3509
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22602223C2direct (N × H)
2. C2×#17986727C2semidirect
3. C2×#17986724C2semidirect
4. C2×#17986723C2semidirect
5. C2×#17986722C2semidirect
6. C2×#17986721C2semidirect
7. C2×#17986690C2semidirect
8. C2×#17986687C2semidirect
9. C2×#17986681C2semidirect
10. C2×#17986608C2semidirect
12. C2×#17986555C2semidirect
13. C2×#17986553C2semidirect
14. C2×#17986553C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986475C2semidirect
18. C2×#557×C71C2semidirect
21. #17986727C22semidirect
22. #17986724C22semidirect
23. #17986723C22semidirect
24. #17986722C22semidirect
25. #17986721C22semidirect
26. #17986690C22semidirect
27. #17986687C22semidirect
28. #17986681C22semidirect
29. #17986608C22semidirect
31. #17986555C22semidirect
32. #17986553C22semidirect
33. #17986553C22semidirect
41. C4⋊Q8×D71C22semidirect
64. #17986475C22semidirect
92. #557×C71C22semidirect
416. C2×C71#3509semidirect
425. C2×#557D71semidirect
440. C71C2×#3509semidirect
445. #557C2×D71semidirect
839. C2#22602223direct (N × H)

Maximal subgroups

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

subgroupindex
#226022232
C2×#179867272
C2×#179867242
C2×#179867232
C2×#179867222
C2×#179867212
C2×#179866902
C2×#179866872
C2×#179866812
C2×#179866082
C2×#179865742
C2×#179865552
C2×#179865532
C2×C4⋊Q8×D712
C2×#179864752
C2×C4×#117658662
C2×#557×C712
C2×#350971