Finite Group Databasebeta

← C2×#22602220 #32905889

Subgroups — C2×#22602220 #32905889

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#22602220C2132yesmaximal, direct product factor
2C2×#17986728C211yesmaximal, characteristic, complemented
3C2×#17986727C212yesmaximal, complemented
4C2×#17986724C211yesmaximal, characteristic, complemented
5C2×#17986719C211yesmaximal, characteristic, complemented
6C2×#17986718C212yesmaximal, complemented
7C2×#17986688C212yesmaximal, complemented
8C2×#17986685C214yesmaximal, complemented
9C2×#17986683C212yesmaximal, complemented
10C2×#17986606C214yesmaximal, complemented
11C2×#17986569C212yesmaximal
12C2×#17986553C211yesmaximal, characteristic, complemented
13C2×#17986552C212yesmaximal, complemented
14C2×#17986551C212yesmaximal, complemented
15C2×C4⋊Q8×D71C211yesmaximal, characteristic, complemented
16C2×#17986475C212yesmaximal, complemented
17C2×C4×#11765864C211yesmaximal, characteristic
18C2×#556×C71C211yesmaximal, characteristic, complemented
19C22×#11765864C2211yescharacteristic
20C22×Q8×D71C2212yes—
21#17986728C22116yescomplemented
22#17986727C22132yescomplemented
23#17986724C22116yescomplemented
24#17986719C22116yescomplemented
25#17986718C22132yescomplemented
26#17986688C22132yescomplemented
27#17986685C22164yescomplemented
28#17986683C22132yescomplemented
29#17986606C22164yescomplemented
30#17986569C22132yes—
31#17986553C22116yescomplemented
32#17986552C22132yescomplemented
33#17986551C22132yescomplemented
34C2×#14556128C2211yescharacteristic
35C2×#14556128C2212yes—
36C2×#14556127C2212yes—
37C2×#14556127C2212yes—
38C2×#14556127C2211yescharacteristic
39C2×#14556126C2212yes—
40C2×#14556126C2211yescharacteristic
41C2×#14556126C2212yes—
42C4⋊Q8×D71C22116yescomplemented
43C2×#14556121C2214yes—
44C2×#14556121C2214yes—
45C2×#14556121C2214yes—
46C2×#14556120C2214yes—
47C2×#14556119C2212yes—
48C2×#14556119C2214yes—
49C2×#14556119C2212yes—
50C2×#14556118C2214yes—
51C2×#14556118C2214yes—
52C2×#14556118C2214yes—
53C2×#14556118C2212yes—
54C2×#14556115C2212yes—
55C2×#14556110C2214yes—
56C2×#14556110C2214yes—
57C2×#14556108C2211yescharacteristic
58C2×#14556107C2212yes—
59C2×#14556106C2212yes—
60C2×#14556105C2214yes—
61C2×#14556105C2214yes—
62C2×#14556105C2214yes—
63C2×#14556104C2211yescharacteristic
64#17986475C22132yescomplemented
65C4×#11765864C22116yes—
66C2×Q8×Dic71C2212yes—
67C2×Q8×Dic71C2212yes—
68C2×C4×Dic142C2211yescharacteristic
69C2×C4×Dic142C2214yes—
70C2×C4×Dic142C2212yes—
71C2×C4×Dic142C2214yes—
72C2×C4×Dic142C2212yes—
73C2×C4×Dic142C2211yescharacteristic
74C2×#14556093C2211yescharacteristic
75C2×#14556093C2214yes—
76C2×#14556093C2212yes—
77C2×#14556093C2212yes—
78C2×D4×Dic71C2211yescharacteristic
79C2×C4×C22⋊D71C2212yes—
80C2×(C22⋊D71)⋊C4C2212yes—
81C2×#14556087C2212yes—
82C2×#14556086C2211yescharacteristic
83C2×#14556086C2214yes—
84C2×#14556085C2214yes—
85C2×#14556085C2212yes—
86C2×#14556084C2212yes—
87C2×#14556084C2214yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C22×C4×Dic71C2212yes—
91C2×C42×D71C2211yescharacteristic
92#556×C71C22116yescomplemented
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#126×C71C2214yes—
95C2×#124×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2211yescharacteristic
99C2×C4×D4×C71C2211yescharacteristic
100C2×#117×C71C2212yes—
101C2×#11765864—28no—
102C2×#11765864C2318yes—
103C22×Dic142C2314yes—
104C22×Dic142C2312yes—
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2311yescharacteristic
107C22×Dic142C2312yes—
108C2×Q8×D71—216no—
109C2×Q8×D71C23116yes—
110C22×C22⋊D71C2312yes—
111C23×Dic71C2312yes—
112C23×Dic71C2312yes—
113C22×C4×D71C2314yes—
114C22×C4×D71C2311yescharacteristic
115C22×C4×D71C2311yescharacteristic
116C22×C4×D71C2311yescharacteristic
117#14556128C23116yes—
118#14556128C2318yes—
119#14556127C23116yes—
120#14556127C23116yes—
121#14556127C2318yes—
122#14556126C23116yes—
123#14556126C23116yes—
124#14556126C2318yes—
125#14556121C23132yes—
126#14556121C23132yes—
127#14556121C23132yes—
128#14556120C23132yes—
129#14556119C23132yes—
130#14556119C23116yes—
131#14556119C23116yes—
132#14556118C23116yes—
133#14556118C23132yes—
134#14556118C23132yes—
135#14556118C23132yes—
136#14556115C23116yes—
137#14556110C23132yes—
138#14556110C23132yes—
139#14556108C2318yes—
140#14556107C23116yes—
141#14556106C23116yes—
142#14556105C23132yes—
143#14556105C23132yes—
144#14556105C23132yes—
145#14556104C2318yes—
146Q8×Dic71C23116yes—
147Q8×Dic71C23116yes—
148C4×Dic142C23132yes—
149C4×Dic142C23132yes—
150C4×Dic142C23116yes—
151C4×Dic142C23116yes—
152C4×Dic142C2318yes—
153C4×Dic142C2318yes—
154#14556093C23132yes—
155#14556093C23116yes—
156#14556093C23116yes—
157#14556093C2318yes—
158D4×Dic71C2318yes—
159C4×C22⋊D71C23116yes—
160(C22⋊D71)⋊C4C23116yes—
161#14556087C23116yes—
162#14556086C23132yes—
163#14556086C2318yes—
164#14556085C23116yes—
165#14556085C23132yes—
166#14556084C23116yes—
167#14556084C23132yes—
168C2×C4⋊Dic71C2312yes—
169C2×C4⋊Dic71C2312yes—
170C2×C4⋊Dic71C2311yescharacteristic
171C2×C4⋊Dic71C2314yes—
172C2×C4⋊Dic71C2311yescharacteristic
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2314yes—
176C2×Dic71⋊C4C2314yes—
177C2×Dic71⋊C4C2314yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2312yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2312yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2314yes—
186C2×Dic71⋊C4C2312yes—
187C2×Dic71⋊C4C2314yes—
188C2×Dic71⋊C4C2312yes—
189C4⋊C4×D71C23116yes—
190C4⋊C4×D71C23116yes—
191C2×C22⋊Dic71C2312yes—
192C2×C22⋊Dic71C2314yes—
193C2×C22⋊Dic71C2314yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2312yes—
197C2×C4×Dic71C2311yescharacteristic
198C2×C4×Dic71C2311yescharacteristic
199C2×C4×Dic71C2311yescharacteristic
200C2×C4×Dic71C2312yes—
201C2×C4×Dic71C2312yes—
202C2×C4×Dic71C2312yes—
203C2×C4×Dic71C23116yes—
204C2×C4×Dic71C2314yes—
205C2×C4×Dic71C2314yes—
206C2×C4×Dic71C2312yes—
207C2×C4×Dic71C2314yes—
208C42×D71C2318yes—
209C22×Q8×C71C2312yes—
210C22×Q8×C71C2311yescharacteristic
211C22×D4×C71C2311yescharacteristic
212C23×C4×C71C2312yes—
213C4⋊Q8×C71C2318yes—
214#126×C71C23132yes—
215#124×C71C23116yes—
216C22⋊Q8×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C2318yes—
219C4×D4×C71C2318yes—
220#117×C71C23116yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2312yes—
223C2×C4⋊C4×C71C2311yescharacteristic
224C2×C4⋊C4×C71C2314yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C22⋊C4×C71C2314yes—
228C2×C22⋊C4×C71C2312yes—
229C2×C22⋊C4×C71C2314yes—
230C2×C42×C71C2314yes—
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2312yes—
233C23×D71C2411yescharacteristic
234#11765864—232no—
235C2×Dic142—28no—
236C2×Dic142—24no—
237C2×Dic142—24no—
238C2×Dic142—216no—
239C2×Dic142—28no—
240C2×Dic142C24116yes—
241C2×Dic142C2418yes—
242C2×Dic142C2414yes—
243C2×Dic142C2414yes—
244C2×Dic142C2418yes—
245Q8×D71—264no—
246C2×C22⋊D71—28no—
247C2×C22⋊D71C2418yes—
248C22×Dic71—28no—
249C22×Dic71—28no—
250C22×Dic71C2414yes—
251C22×Dic71C2411yescharacteristic
252C22×Dic71C2412yes—
253C22×Dic71C2418yes—
254C22×Dic71C2412yes—
255C22×Dic71C2418yes—
256C22×Dic71C2412yes—
257C22×Dic71C2412yes—
258C22×Dic71C2411yescharacteristic
259C22×Dic71C2411yescharacteristic
260C2×C4×D71—216no—
261C2×C4×D71—24no—
262C2×C4×D71—24no—
263C2×C4×D71#4118yes—
264C2×C4×D71C24116yes—
265C2×C4×D71C2414yes—
266C2×C4×D71C2414yes—
267C2×C4×D71C2414yes—
268C4⋊Dic71C2418yes—
269C4⋊Dic71C2418yes—
270C4⋊Dic71C2414yes—
271C4⋊Dic71C24116yes—
272C4⋊Dic71C2414yes—
273C4⋊Dic71C24116yes—
274C4⋊Dic71C2418yes—
275C4⋊Dic71C24116yes—
276Dic71⋊C4C24116yes—
277Dic71⋊C4C24116yes—
278Dic71⋊C4C2418yes—
279Dic71⋊C4C2418yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C2418yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C2418yes—
284Dic71⋊C4C24116yes—
285Dic71⋊C4C24116yes—
286Dic71⋊C4C2418yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C2418yes—
289C22⋊Dic71C2418yes—
290C22⋊Dic71C24116yes—
291C22⋊Dic71C24116yes—
292(C2×D71)⋊C4C2418yes—
293(C2×D71)⋊C4C2418yes—
294(C2×D71)⋊C4C2418yes—
295C4×Dic71C2414yes—
296C4×Dic71C2414yes—
297C4×Dic71C2414yes—
298C4×Dic71C2418yes—
299C4×Dic71C2418yes—
300C4×Dic71C2418yes—
301C4×Dic71C24116yes—
302C4×Dic71C24116yes—
303C4×Dic71C2418yes—
304C4×Dic71C24116yes—
305C24×C71C2412yes—
306C2×Q8×C71—28no—
307C2×Q8×C71—24no—
308C2×Q8×C71C2418yes—
309C2×Q8×C71C2414yes—
310C2×D4×C71—24no—
311C2×D4×C71C2414yes—
312C22×C4×C71—28no—
313C22×C4×C71C2414yes—
314C22×C4×C71C2411yescharacteristic
315C22×C4×C71C2412yes—
316C22×C4×C71C2412yes—
317C22×C4×C71C2412yes—
318C22×C4×C71C2418yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2411yescharacteristic
321C4⋊C4×C71C2414yes—
322C4⋊C4×C71C2418yes—
323C4⋊C4×C71C2414yes—
324C4⋊C4×C71C24116yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2418yes—
327C22⋊C4×C71C24116yes—
328C22⋊C4×C71C2418yes—
329C22⋊C4×C71C24116yes—
330C42×C71C24116yes—
331C42×C71C2414yes—
332C42×C71C2418yes—
333C23×C71—24no—
334C23×C71—24no—
335C23×C71—24no—
336C23×C71C2514yes—
337C23×C71C2511yescharacteristic
338C22×D71—22no—
339C22×D71—22no—
340C22×D71C2×#4114yes—
341C22×D71C2512yes—
342Q8×C71—216no—
343Q8×C71—28no—
344D4×C71—28no—
345C2×C4×C71—28no—
346C2×C4×C71—24no—
347C2×C4×C71—24no—
348C2×C4×C71—22no—
349C2×C4×C71—24no—
350C2×C4×C71—216no—
351C2×C4×C71C2×#4114yes—
352C2×C4×C712−1+414yes—
353C2×C4×C71C2514yes—
354C2×C4×C71C2514yes—
355C2×C4×C71C2512yes—
356C2×C4×C71C2514yes—
357C2×C4×C71C2518yes—
358C2×C4×C71C2512yes—
359C2×C4×C71C2512yes—
360C22⋊D71—216no—
361C2×Dic71—28no—
362C2×Dic71—24no—
363C2×Dic71—22no—
364C2×Dic71—24no—
365C2×Dic71—24no—
366C2×Dic71—24no—
367C2×Dic71—216no—
368C2×Dic71—216no—
369C2×Dic71C2×#4114yes—
370C2×Dic712−1+414yes—
371C2×Dic71C2514yes—
372C2×Dic71C2514yes—
373C2×Dic71C2514yes—
374C2×Dic71C2512yes—
375C2×Dic71C2518yes—
376C2×Dic71C2514yes—
377C2×Dic71C2512yes—
378C2×Dic71C2512yes—
379C4×D71—232no—
380C4×D71—28no—
381C4×D71—28no—
382C4×D71C2×#41116yes—
383Dic142—216no—
384Dic142—28no—
385Dic142—28no—
386Dic142—232no—
387Dic142—216no—
388C22×C71—24no—
389C22×C71—24no—
390C22×C71—24no—
391C22×C71—48no—
392C22×C71C22×#4112yes—
393C22×C71C2×2−1+412yes—
394C22×C71C2×2−1+412yes—
395C22×C71C2611yescharacteristic
396C2×D71—22no—
397C2×D71—22no—
398C2×D71—28no—
399C2×D71C22×#4114yes—
400C4×C71—28no—
401C4×C71—24no—
402C4×C71—22no—
403C4×C71—24no—
404C4×C71—24no—
405C4×C71C22×#4114yes—
406C4×C71C2×2−1+414yes—
407Dic71—28no—
408Dic71—24no—
409Dic71—24no—
410Dic71—24no—
411Dic71—22no—
412Dic71—24no—
413Dic71C22×#4114yes—
414Dic71C2×2−1+414yes—
415C2×#3509—711nomaximal, Sylow
416C2×C71—44no—
417C2×C71#350914yescomplemented
418C2×C71C23×#4111yescharacteristic
419C2×C71C22×2−1+411yescharacteristic
420C2×C71C22×2−1+411yescharacteristic
421D71—24no—
422#3509—7132no—
423C2×#557—711no—
424C2×#557—712no—
425C2×#557—711no—
426C2×#556—712no—
427C2×#556—711no—
428C2×#556D7111yescharacteristic, complemented
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—7116no—
444#557—7132no—
445#557—7116no—
446#556—7132no—
447#556—7116no—
448#556C2×D71116yescomplemented
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⋊Q8—712no—
466C2×C4⋊Q8C2×D7111yescharacteristic
467C2×#126—714no—
468C2×#126—714no—
469C2×#126—714no—
470C2×#126C2×D7114yes—
471C2×#125—712no—
472C2×#125—714no—
473C2×#125—712no—
474C2×#125—712no—
475C2×#125—714no—
476C2×#125—714no—
477C2×#125—714no—
478C2×#125—714no—
479C2×#124—712no—
480C2×#124C2×D7112yes—
481C2×#123—714no—
482C2×#123—714no—
483C2×C22⋊Q8—711no—
484C2×C22⋊Q8—712no—
485C2×C22⋊Q8—712no—
486C2×C22⋊Q8—711no—
487C2×C22⋊Q8—714no—
488C2×C22⋊Q8—714no—
489C2×C22⋊Q8—714no—
490C2×C22⋊Q8C2×D7112yes—
491#519—7132no—
492C4×#41—7116no—
493C2×C4×Q8—712no—
494C2×C4×Q8—712no—
495C2×C4×Q8—711no—
496C2×C4×Q8—714no—
497C2×C4×Q8—712no—
498C2×C4×Q8—712no—
499C2×C4×Q8—711no—
500C2×C4×Q8—714no—
501C2×C4×Q8—712no—
502C2×C4×Q8—714no—
503C2×C4×Q8—711no—
504C2×C4×Q8—712no—
505C2×C4×Q8C2×D7112yes—
506C2×C4×Q8C2×D7111yescharacteristic
507C2×C4×D4—711no—
508C2×C4×D4—712no—
509C2×C4×D4—712no—
510C2×C4×D4C2×D7111yescharacteristic
511C2×#117—712no—
512C2×#117—711no—
513C2×#117—714no—
514C2×#117—712no—
515C2×#117—714no—
516C2×#117—712no—
517C2×#117—714no—
518C2×#117C2×D7112yes—
519C22×C4⋊C4—712no—
520C22×C4⋊C4—712no—
521C22×C42—712no—
522C22×C42—711no—
523C2×#41—718no—
524C2×#41—1428no—
525C22×Q8—7116no—
526C22×Q8—712no—
527C22×Q8—711no—
528C22×Q8—714no—
529C22×Q8—712no—
530C22×Q8—711no—
531C22×Q8—14216no—
532C22×Q8C22×D7111yescharacteristic
533C22×Q8C22×D7112yes—
534C22×D4—712no—
535C22×D4C22×D7111yescharacteristic
536C23×C4—711no—
537C23×C4—712no—
538C23×C4—712no—
539C23×C4—714no—
540C23×C4—711no—
541C23×C4—711no—
542C23×C4C22×D7112yes—
543C4⋊Q8—7116no—
544C4⋊Q8—718no—
545C4⋊Q8—7116no—
546C4⋊Q8—7116no—
547C4⋊Q8—7116no—
548C4⋊Q8—718no—
549C4⋊Q8—718no—
550C4⋊Q8—7116no—
551C4⋊Q8C22×D7118yes—
552#126—7132no—
553#126—7132no—
554#126—7132no—
555#126C22×D71132yes—
556#125—7116no—
557#125—7132no—
558#125—7116no—
559#125—7116no—
560#125—7132no—
561#125—7132no—
562#125—7132no—
563#125—7132no—
564#124—7116no—
565#124C22×D71116yes—
566#123—7132no—
567#123—7132no—
568C22⋊Q8—718no—
569C22⋊Q8—7116no—
570C22⋊Q8—7116no—
571C22⋊Q8—718no—
572C22⋊Q8—7132no—
573C22⋊Q8—7132no—
574C22⋊Q8—7132no—
575C22⋊Q8C22×D71116yes—
576C4×Q8—7116no—
577C4×Q8—7116no—
578C4×Q8—718no—
579C4×Q8—7132no—
580C4×Q8—7116no—
581C4×Q8—7116no—
582C4×Q8—718no—
583C4×Q8—7132no—
584C4×Q8—7116no—
585C4×Q8—7132no—
586C4×Q8—7116no—
587C4×Q8—718no—
588C4×Q8C22×D71116yes—
589C4×Q8C22×D7118yes—
590C4×D4—718no—
591C4×D4—7116no—
592C4×D4—7116no—
593C4×D4C22×D7118yes—
594#117—7116no—
595#117—718no—
596#117—7132no—
597#117—7116no—
598#117—7132no—
599#117—7116no—
600#117—7132no—
601#117C22×D71116yes—
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—712no—
613C2×C4⋊C4—714no—
614C2×C4⋊C4—714no—
615C2×C4⋊C4—714no—
616C2×C4⋊C4—714no—
617C2×C4⋊C4—714no—
618C2×C4⋊C4—714no—
619C2×C4⋊C4—714no—
620C2×C4⋊C4—712no—
621C2×C4⋊C4—712no—
622C2×C4⋊C4—712no—
623C2×C4⋊C4—7116no—
624C2×C4⋊C4—7116no—
625C2×C4⋊C4C22×D7112yes—
626C2×C4⋊C4C22×D7112yes—
627C2×C4⋊C4C22×D7111yescharacteristic
628C2×C4⋊C4C22×D7114yes—
629C2×C4⋊C4C22×D7111yescharacteristic
630C2×C4⋊C4C22×D7112yes—
631C2×C22⋊C4—712no—
632C2×C22⋊C4—714no—
633C2×C22⋊C4—714no—
634C2×C22⋊C4—712no—
635C2×C22⋊C4—712no—
636C2×C22⋊C4—712no—
637C2×C22⋊C4C22×D7112yes—
638C2×C22⋊C4C22×D7114yes—
639C2×C22⋊C4C22×D7114yes—
640C2×C42—712no—
641C2×C42—714no—
642C2×C42—714no—
643C2×C42—714no—
644C2×C42—711no—
645C2×C42—712no—
646C2×C42—712no—
647C2×C42—712no—
648C2×C42—711no—
649C2×C42—7116no—
650C2×C42—711no—
651C2×C42—718no—
652C2×C42C22×D7114yes—
653C2×C42C22×D7112yes—
654C2×C42C22×D7111yescharacteristic
655C24—711no—
656C24C23×D7112yes—
657#41—14232no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—718no—
661C2×Q8—714no—
662C2×Q8—7116no—
663C2×Q8—718no—
664C2×Q8—714no—
665C2×Q8—1428no—
666C2×Q8—14216no—
667C2×Q8—14264no—
668C2×Q8—1428no—
669C2×Q8—1424no—
670C2×Q8—1424no—
671C2×Q8C23×D7114yes—
672C2×Q8C23×D7118yes—
673C2×D4—24no—
674C2×D4—718no—
675C2×D4—1428no—
676C2×D4C23×D7114yes—
677C22×C4—28no—
678C22×C4—711no—
679C22×C4—711no—
680C22×C4—718no—
681C22×C4—714no—
682C22×C4—718no—
683C22×C4—718no—
684C22×C4—712no—
685C22×C4—712no—
686C22×C4—712no—
687C22×C4—711no—
688C22×C4—714no—
689C22×C4—712no—
690C22×C4—714no—
691C22×C4—714no—
692C22×C4—7116no—
693C22×C4—1424no—
694C22×C4—14216no—
695C22×C4—1428no—
696C22×C4—1428no—
697C22×C4—1424no—
698C22×C4C23×D7118yes—
699C22×C4C23×D7112yes—
700C22×C4C23×D7112yes—
701C22×C4C23×D7111yescharacteristic
702C22×C4C23×D7114yes—
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—718no—
712C4⋊C4—718no—
713C4⋊C4—7116no—
714C4⋊C4—7116no—
715C4⋊C4—7116no—
716C4⋊C4—7116no—
717C4⋊C4—718no—
718C4⋊C4—718no—
719C4⋊C4—718no—
720C4⋊C4—718no—
721C4⋊C4—714no—
722C4⋊C4—714no—
723C4⋊C4—7116no—
724C4⋊C4—7116no—
725C4⋊C4—7116no—
726C4⋊C4—718no—
727C4⋊C4C23×D7118yes—
728C4⋊C4C23×D7118yes—
729C4⋊C4C23×D7114yes—
730C4⋊C4C23×D71116yes—
731C4⋊C4C23×D7114yes—
732C4⋊C4C23×D7118yes—
733C22⋊C4—718no—
734C22⋊C4—7116no—
735C22⋊C4—7116no—
736C22⋊C4—718no—
737C22⋊C4—718no—
738C22⋊C4—718no—
739C22⋊C4C23×D7118yes—
740C22⋊C4C23×D71116yes—
741C22⋊C4C23×D71116yes—
742C42—714no—
743C42—718no—
744C42—714no—
745C42—718no—
746C42—718no—
747C42—714no—
748C42—7116no—
749C42—7116no—
750C42—7116no—
751C42—718no—
752C42C23×D7114yes—
753C42C23×D71116yes—
754C42C23×D7118yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—714no—
759C23—712no—
760C23—1422no—
761C23—1422no—
762C23C24×D7114yes—
763C23C24×D7111yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—14232no—
767Q8—14216no—
768Q8—14216no—
769Q8—1428no—
770Q8—1428no—
771D4—28no—
772D4—14216no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—216no—
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—714no—
790C2×C4—1428no—
791C2×C4—14232no—
792C2×C4—14216no—
793C2×C4—14216no—
794C2×C4—1424no—
795C2×C4—1428no—
796C2×C4—1424no—
797C2×C4—1424no—
798C2×C4—1422no—
799C2×C4—1424no—
800C2×C4—1428no—
801C2×C4#41×D7114yes—
802C2×C4#1455617514yes—
803C2×C4C24×D7114yes—
804C2×C4C24×D7114yes—
805C2×C4C24×D7112yes—
806C2×C4C24×D7118yes—
807C2×C4C24×D7114yes—
808C2×C4C24×D7112yes—
809C2×C4C24×D7112yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—714no—
815C22—1422no—
816C22—1422no—
817C22—1428no—
818C22C2×#41×D7112yes—
819C222−1+4×D7112yes—
820C22C2×#1455617512yes—
821C22C25×D7111yescharacteristic
822C4—28no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—714no—
828C4—714no—
829C4—1424no—
830C4—1428no—
831C4—1424no—
832C4—1424no—
833C4—1422no—
834C4—1424no—
835C4C2×#41×D7114yes—
836C4C2×#1455617514yes—
837C2—44no—
838C2—1424no—
839C2#2260222014yesdirect product factor
840C2C22×#41×D7111yescharacteristic
841C2C2×2−1+4×D7111yescharacteristic
842C2C22×#1455617511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#556×C71C2
socleC23×C71C25
prime radicalC22×#11765864C22
hypercenterC2×#556D71
hypocenterC71C2×#3509
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #22602220C2direct (N × H)
2. C2×#17986728C2semidirect
3. C2×#17986727C2semidirect
4. C2×#17986724C2semidirect
5. C2×#17986719C2semidirect
6. C2×#17986718C2semidirect
7. C2×#17986688C2semidirect
8. C2×#17986685C2semidirect
9. C2×#17986683C2semidirect
10. C2×#17986606C2semidirect
12. C2×#17986553C2semidirect
13. C2×#17986552C2semidirect
14. C2×#17986551C2semidirect
15. C2×C4⋊Q8×D71C2semidirect
16. C2×#17986475C2semidirect
18. C2×#556×C71C2semidirect
21. #17986728C22semidirect
22. #17986727C22semidirect
23. #17986724C22semidirect
24. #17986719C22semidirect
25. #17986718C22semidirect
26. #17986688C22semidirect
27. #17986685C22semidirect
28. #17986683C22semidirect
29. #17986606C22semidirect
31. #17986553C22semidirect
32. #17986552C22semidirect
33. #17986551C22semidirect
42. C4⋊Q8×D71C22semidirect
64. #17986475C22semidirect
92. #556×C71C22semidirect
417. C2×C71#3509semidirect
428. C2×#556D71semidirect
440. C71C2×#3509semidirect
448. #556C2×D71semidirect
839. C2#22602220direct (N × H)

Maximal subgroups

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

subgroupindex
#226022202
C2×#179867282
C2×#179867272
C2×#179867242
C2×#179867192
C2×#179867182
C2×#179866882
C2×#179866852
C2×#179866832
C2×#179866062
C2×#179865692
C2×#179865532
C2×#179865522
C2×#179865512
C2×C4⋊Q8×D712
C2×#179864752
C2×C4×#117658642
C2×#556×C712
C2×#350971