Finite Group Databasebeta

← C2×#22601955 #32904548

Subgroups — C2×#22601955 #32904548

Order 18176.

7706 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22601955C2132yesmaximal, direct product factor
2C2×#17986727C211yesmaximal, characteristic, complemented
3C2×#17986722C211yesmaximal, characteristic, complemented
4C2×#17986717C212yesmaximal, complemented
5C2×#17986689C212yesmaximal, complemented
6C2×#17986682C214yesmaximal, complemented
7C2×D4×Dic142C211yesmaximal, characteristic, complemented
8C2×#17986658C212yesmaximal, complemented
9C2×#17986653C211yesmaximal, characteristic, complemented
10C2×#17986648C212yesmaximal, complemented
11C2×#17986556C211yesmaximal, characteristic, complemented
12C2×#17986553C212yesmaximal, complemented
13C2×#17986533C212yesmaximal, complemented
14C2×#17986529C214yesmaximal, complemented
15C2×C4×#11765865C211yesmaximal, characteristic, complemented
16C2×C4×#11765864C212yesmaximal, complemented
17C22×C4×Dic142C212yesmaximal, complemented
18C2×C4×#41×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2211yescharacteristic
20C22×#11765864C2212yes—
21C23×Dic142C2212yes—
22#17986727C22116yescomplemented
23#17986722C22116yescomplemented
24#17986717C22132yescomplemented
25#17986689C22132yescomplemented
26#17986682C22164yescomplemented
27D4×Dic142C22116yescomplemented
28#17986658C22132yescomplemented
29#17986653C22116yescomplemented
30#17986648C22132yescomplemented
31#17986556C22116yescomplemented
32#17986553C22132yescomplemented
33C2×#14556128C2211yescharacteristic
34C2×#14556128C2211yescharacteristic
35C2×#14556127C2212yes—
36C2×#14556126C2212yes—
37#17986533C22132yescomplemented
38#17986529C22164yescomplemented
39C2×#14556123C2214yes—
40C2×#14556122C2214yes—
41C2×#14556121C2214yes—
42C2×#14556120C2212yes—
43C2×#14556120C2212yes—
44C2×#14556118C2214yes—
45C2×#14556118C2214yes—
46C2×#14556116C2212yes—
47C2×#14556114C2214yes—
48C2×#14556112C2214yes—
49C2×#14556111C2214yes—
50C2×#14556109C2214yes—
51C2×#14556108C2212yes—
52C2×#14556107C2212yes—
53C2×#14556107C2212yes—
54C2×#14556107C2212yes—
55C2×#14556106C2214yes—
56C2×#14556105C2214yes—
57C2×#14556104C2212yes—
58C2×#14556102C2212yes—
59C2×#14556100C2214yes—
60C4×#11765865C22116yescomplemented
61C4×#11765864C22132yescomplemented
62C2×C4×Dic142C2211yescharacteristic
63C2×C4×Dic142C2212yes—
64C2×C4×Dic142C2214yes—
65C2×C4×Dic142C2212yes—
66C2×C4×Dic142C2214yes—
67C2×C4×Dic142C2212yes—
68C2×C4×Dic142C2212yes—
69C2×C4×Dic142C2211yescharacteristic
70C2×C4×Dic142C22132yescomplemented
71C2×#14556093C2212yes—
72C2×C4×D284C2211yescharacteristic
73C2×C4×D284C2211yescharacteristic
74C2×D4×Dic71C2212yes—
75C2×C4×C22⋊D71C2214yes—
76C2×C4×C22⋊D71C2212yes—
77C2×C4×C22⋊D71C2212yes—
78C2×(C22⋊D71)⋊C4C2214yes—
79C2×#14556087C2211yescharacteristic
80C2×#14556087C2212yes—
81C2×#14556086C2212yes—
82C2×#14556085C2212yes—
83C2×#14556085C2214yes—
84C2×#14556084C2214yes—
85C22×C4⋊Dic71C2212yes—
86C22×Dic71⋊C4C2214yes—
87C22×C4×Dic71C2214yes—
88C2×C42×D71C2212yes—
89C22×#41×C71C2211yescharacteristic
90C4×#41×C71C22116yescomplemented
91C2×C4×Q8×C71C2211yescharacteristic
92C2×C4×Q8×C71C2211yescharacteristic
93C2×C4×D4×C71C2211yescharacteristic
94C2×C4×D4×C71C2211yescharacteristic
95C2×C4×D4×C71C2212yes—
96C2×C4×D4×C71C2212yes—
97C2×#117×C71C2212yes—
98C2×#117×C71C2211yescharacteristic
99C22×C42×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765865—28no—
102C2×#11765865C2318yes—
103C2×#11765864—216no—
104C2×#11765864C23116yes—
105C22×Dic142—216no—
106C22×Dic142C23116yes—
107C22×Dic142C2314yes—
108C22×Dic142C2312yes—
109C22×Dic142C2312yes—
110C22×Dic142C2311yescharacteristic
111C22×D284C2311yescharacteristic
112C22×C22⋊D71C2314yes—
113C22×C22⋊D71C2312yes—
114C23×Dic71C2314yes—
115C23×Dic71C2314yes—
116C22×C4×D71C2312yes—
117C22×C4×D71C2312yes—
118C22×C4×D71C2312yes—
119#14556128C2318yes—
120#14556128C2318yes—
121#14556127C23116yes—
122#14556126C23116yes—
123#14556123C23132yes—
124#14556122C23132yes—
125#14556121C23132yes—
126#14556120C23116yes—
127#14556120C23116yes—
128#14556118C23132yes—
129#14556118C23132yes—
130#14556116C23116yes—
131#14556114C23132yes—
132#14556112C23132yes—
133#14556111C23132yes—
134#14556109C23132yes—
135#14556108C23116yes—
136#14556107C23116yes—
137#14556107C23116yes—
138#14556107C23116yes—
139#14556106C23132yes—
140#14556105C23132yes—
141#14556104C23116yes—
142#14556102C23116yes—
143#14556100C23132yes—
144C4×Dic142C23116yes—
145C4×Dic142C2318yes—
146C4×Dic142C23132yes—
147C4×Dic142C23116yes—
148C4×Dic142C2318yes—
149C4×Dic142C23132yes—
150C4×Dic142C23116yes—
151C4×Dic142C23116yes—
152#14556093C23116yes—
153C4×D284C2318yes—
154C4×D284C2318yes—
155D4×Dic71C23116yes—
156C4×C22⋊D71C23116yes—
157C4×C22⋊D71C23132yes—
158C4×C22⋊D71C23116yes—
159(C22⋊D71)⋊C4C23132yes—
160#14556087C2318yes—
161#14556087C23116yes—
162#14556086C23116yes—
163#14556085C23116yes—
164#14556085C23132yes—
165#14556084C23132yes—
166C2×C4⋊Dic71C23116yes—
167C2×C4⋊Dic71C2311yescharacteristic
168C2×C4⋊Dic71C2312yes—
169C2×C4⋊Dic71C2314yes—
170C2×C4⋊Dic71C2312yes—
171C2×C4⋊Dic71C2311yescharacteristic
172C2×C4⋊Dic71C2312yes—
173C2×C4⋊Dic71C2312yes—
174C2×Dic71⋊C4C23132yes—
175C2×Dic71⋊C4C2312yes—
176C2×Dic71⋊C4C2314yes—
177C2×Dic71⋊C4C2314yes—
178C2×Dic71⋊C4C2314yes—
179C2×Dic71⋊C4C2314yes—
180C2×Dic71⋊C4C2314yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×C22⋊Dic71C2314yes—
185C2×C22⋊Dic71C2312yes—
186C2×C22⋊Dic71C2314yes—
187C2×(C2×D71)⋊C4C2312yes—
188C2×(C2×D71)⋊C4C2312yes—
189C2×(C2×D71)⋊C4C2314yes—
190C2×(C2×D71)⋊C4C2314yes—
191C2×(C2×D71)⋊C4C2314yes—
192C2×C4×Dic71C2312yes—
193C2×C4×Dic71C2312yes—
194C2×C4×Dic71C2312yes—
195C2×C4×Dic71C2314yes—
196C2×C4×Dic71C2314yes—
197C2×C4×Dic71C2314yes—
198C2×C4×Dic71C23132yes—
199C42×D71C23116yes—
200C2×#41×C71—28no—
201C2×#41×C71C2318yes—
202C22×Q8×C71C2311yescharacteristic
203C22×D4×C71C2312yes—
204C22×D4×C71C2311yescharacteristic
205C23×C4×C71C2312yes—
206C23×C4×C71C2311yescharacteristic
207C23×C4×C71C2312yes—
208C23×C4×C71C2311yescharacteristic
209C23×C4×C71C2312yes—
210C23×C4×C71C2311yescharacteristic
211C4×Q8×C71C2318yes—
212C4×Q8×C71C2318yes—
213C4×D4×C71C2318yes—
214C4×D4×C71C23116yes—
215C4×D4×C71C2318yes—
216C4×D4×C71C23116yes—
217#117×C71C23116yes—
218#117×C71C2318yes—
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2311yescharacteristic
222C2×C4⋊C4×C71C2312yes—
223C2×C22⋊C4×C71C2312yes—
224C2×C22⋊C4×C71C2312yes—
225C2×C22⋊C4×C71C2312yes—
226C2×C42×C71C2311yescharacteristic
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2312yes—
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2312yes—
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2312yes—
233C2×C42×C71C23116yes—
234C2×C42×C71C2318yes—
235C23×D71C2412yes—
236#11765865—232no—
237#11765864—264no—
238C2×Dic142—28no—
239C2×Dic142—28no—
240C2×Dic142—216no—
241C2×Dic142—264no—
242C2×Dic142#4118yescomplemented
243C2×Dic142C24116yes—
244C2×Dic142C2418yes—
245C2×Dic142C2418yes—
246C2×Dic142C2414yes—
247C2×D284—24no—
248C2×D284C2414yes—
249C2×C22⋊D71—216no—
250C2×C22⋊D71—28no—
251C2×C22⋊D71C24116yes—
252C2×C22⋊D71C2418yes—
253C22×Dic71—216no—
254C22×Dic71—216no—
255C22×Dic71C2412yes—
256C22×Dic71C2412yes—
257C22×Dic71C2414yes—
258C22×Dic71C2414yes—
259C22×Dic71C24116yes—
260C22×Dic71C24116yes—
261C22×Dic71C2412yes—
262C2×C4×D71—28no—
263C2×C4×D71—28no—
264C2×C4×D71—28no—
265C2×C4×D71C2418yes—
266C2×C4×D71C2418yes—
267C2×C4×D71C2418yes—
268C4⋊Dic71C2414yes—
269C4⋊Dic71C2418yes—
270C4⋊Dic71C24116yes—
271C4⋊Dic71C2418yes—
272C4⋊Dic71C2414yes—
273C4⋊Dic71C2418yes—
274C4⋊Dic71C2418yes—
275Dic71⋊C4C2418yes—
276Dic71⋊C4C24116yes—
277Dic71⋊C4C24116yes—
278Dic71⋊C4C24116yes—
279Dic71⋊C4C24116yes—
280Dic71⋊C4C24116yes—
281Dic71⋊C4C2418yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C24116yes—
284C22⋊Dic71C24116yes—
285C22⋊Dic71C2418yes—
286C22⋊Dic71C24116yes—
287(C2×D71)⋊C4C2418yes—
288(C2×D71)⋊C4C2418yes—
289(C2×D71)⋊C4C24116yes—
290(C2×D71)⋊C4C24116yes—
291(C2×D71)⋊C4C24116yes—
292C4×Dic71C2418yes—
293C4×Dic71C2418yes—
294C4×Dic71C2418yes—
295C4×Dic71C24116yes—
296C4×Dic71C24116yes—
297C4×Dic71C24116yes—
298C24×C71C2411yescharacteristic
299C24×C71C2412yes—
300#41×C71—232no—
301C2×Q8×C71—24no—
302C2×Q8×C71C2414yes—
303C2×D4×C71—28no—
304C2×D4×C71#4118yescomplemented
305C2×D4×C71C2418yes—
306C2×D4×C71C2414yes—
307C22×C4×C71—28no—
308C22×C4×C71—28no—
309C22×C4×C71—24no—
310C22×C4×C71—24no—
311C22×C4×C71—28no—
312C22×C4×C71—24no—
313C22×C4×C71C2411yescharacteristic
314C22×C4×C71C2412yes—
315C22×C4×C71C2418yes—
316C22×C4×C71C2414yes—
317C22×C4×C71C2411yescharacteristic
318C22×C4×C71C2412yes—
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2412yes—
321C22×C4×C71C2418yes—
322C22×C4×C71C2414yes—
323C22×C4×C71C2418yes—
324C22×C4×C71C2414yes—
325C22×C4×C71C2411yescharacteristic
326C22×C4×C71C2411yescharacteristic
327C22×C4×C71C2411yescharacteristic
328C4⋊C4×C71C2414yes—
329C4⋊C4×C71C2418yes—
330C4⋊C4×C71C2414yes—
331C4⋊C4×C71C2418yes—
332C22⋊C4×C71C2418yes—
333C22⋊C4×C71C2418yes—
334C22⋊C4×C71C2418yes—
335C42×C71C2414yes—
336C42×C71C2414yes—
337C42×C71C2418yes—
338C42×C71C2414yes—
339C42×C71C2418yes—
340C42×C71C2414yes—
341C42×C71C2418yes—
342C23×C71—24no—
343C23×C71—24no—
344C23×C71—22no—
345C23×C71—22no—
346C23×C71—22no—
347C23×C71C2×#4118yes—
348C23×C71C2512yes—
349C23×C71C2514yes—
350C23×C71C2511yescharacteristic
351C22×D71—24no—
352C22×D71—24no—
353C22×D71—24no—
354C22×D71C2514yes—
355Q8×C71—28no—
356D4×C71—216no—
357D4×C71C2×#41116yescomplemented
358C2×C4×C71—22no—
359C2×C4×C71—24no—
360C2×C4×C71—216no—
361C2×C4×C71—22no—
362C2×C4×C71—24no—
363C2×C4×C71—24no—
364C2×C4×C71—22no—
365C2×C4×C71—28no—
366C2×C4×C71—216no—
367C2×C4×C71—28no—
368C2×C4×C71—216no—
369C2×C4×C71—28no—
370C2×C4×C71C2×#4114yes—
371C2×C4×C71C2×#4114yes—
372C2×C4×C712−1+414yes—
373C2×C4×C71C2512yes—
374C2×C4×C71C2514yes—
375C2×C4×C71C2512yes—
376C2×C4×C71C2512yes—
377C2×C4×C71C2514yes—
378C2×C4×C71C2514yes—
379C2×C4×C71C2512yes—
380C2×C4×C71C2512yes—
381C2×C4×C71C2512yes—
382C22⋊D71—232no—
383C22⋊D71—216no—
384C2×Dic71—24no—
385C2×Dic71—28no—
386C2×Dic71—28no—
387C2×Dic71—232no—
388C2×Dic71—24no—
389C2×Dic71—232no—
390C2×Dic71C2×#4118yes—
391C2×Dic71C2514yes—
392C2×Dic71C2518yes—
393C2×Dic71C2514yes—
394C2×Dic71C2518yes—
395C2×Dic71C2514yes—
396D284—28no—
397C4×D71—216no—
398C4×D71—216no—
399C4×D71—216no—
400Dic142—216no—
401Dic142—216no—
402Dic142—232no—
403Dic142C2×#41116yescomplemented
404C22×C71—24no—
405C22×C71—24no—
406C22×C71—216no—
407C22×C71—22no—
408C22×C71—22no—
409C22×C71—22no—
410C22×C71—44no—
411C22×C71C22×#4112yes—
412C22×C71C22×#4118yes—
413C22×C71C22×#4112yes—
414C22×C71C2×2−1+412yes—
415C22×C71C2611yescharacteristic
416C2×D71—24no—
417C2×D71—24no—
418C2×D71—24no—
419C2×D71—48no—
420C4×C71—24no—
421C4×C71—22no—
422C4×C71—22no—
423C4×C71—24no—
424C4×C71—24no—
425C4×C71—22no—
426C4×C71C22×#4114yes—
427C4×C71C22×#4114yes—
428C4×C71C2×2−1+414yes—
429Dic71—28no—
430Dic71—28no—
431Dic71—24no—
432Dic71—24no—
433Dic71C22×#4118yes—
434C2×#3482—711nomaximal, Sylow
435C2×C71—28no—
436C2×C71—42no—
437C2×C71#348214yescomplemented
438C2×C71C23×#4111yescharacteristic
439C2×C71C23×#4111yescharacteristic
440C2×C71C22×2−1+411yescharacteristic
441D71—44no—
442#3482—7132no—
443C2×#557—711no—
444C2×#556—711no—
445C2×#556—712no—
446C2×#552—712no—
447C2×#552—714no—
448C2×D4×Q8—711no—
449C2×#548—712no—
450C2×#547—712no—
451C2×#547—711no—
452C2×#533—711no—
453C2×#533—712no—
454C2×#529—712no—
455C2×#529—714no—
456C2×C4×#41—711no—
457C2×C4×#41—712no—
458C2×C4×#41D7111yescharacteristic, complemented
459C22×C4×Q8—712no—
460C71C2×#348211yescharacteristic, complemented, Sylow
461C22×#41—712no—
462C22×#41—711no—
463C22×#41C2×D7111yescharacteristic
464C23×Q8—712no—
465#557—7116no—
466#556—7116no—
467#556—7132no—
468#552—7132no—
469#552—7164no—
470D4×Q8—7116no—
471#548—7132no—
472#547—7132no—
473#547—7116no—
474#533—7132no—
475#533—7116no—
476C2×C4⋊Q8—712no—
477C2×C4⋊Q8—712no—
478C2×C4⋊Q8—711no—
479C2×C4⋊Q8—711no—
480#529—7164no—
481#529—7132no—
482C2×#126—714no—
483C2×#126—714no—
484C2×#126—714no—
485C2×#125—714no—
486C2×#125—714no—
487C2×#125—712no—
488C2×#125—712no—
489C2×#124—714no—
490C2×#124—712no—
491C2×#123—714no—
492C2×#123—714no—
493C2×#123—714no—
494C2×C22⋊Q8—712no—
495C2×C22⋊Q8—712no—
496C2×C22⋊Q8—712no—
497C2×C22⋊Q8—712no—
498C2×C22⋊Q8—712no—
499C2×C22⋊Q8—714no—
500C2×C22⋊Q8—714no—
501C2×#121—714no—
502C2×#121—712no—
503C4×#41—7132no—
504C4×#41—7116no—
505C4×#41C2×D71116yescomplemented
506C2×C4×Q8—712no—
507C2×C4×Q8—711no—
508C2×C4×Q8—712no—
509C2×C4×Q8—714no—
510C2×C4×Q8—712no—
511C2×C4×Q8—712no—
512C2×C4×Q8—714no—
513C2×C4×Q8—7132no—
514C2×C4×Q8—712no—
515C2×C4×Q8—711no—
516C2×C4×Q8C2×D7111yescharacteristic
517C2×C4×Q8C2×D7111yescharacteristic
518C2×C4×D4—712no—
519C2×C4×D4—714no—
520C2×C4×D4—712no—
521C2×C4×D4—712no—
522C2×C4×D4—714no—
523C2×C4×D4—711no—
524C2×C4×D4—711no—
525C2×C4×D4C2×D7111yescharacteristic
526C2×C4×D4C2×D7112yes—
527C2×C4×D4C2×D7111yescharacteristic
528C2×C4×D4C2×D7112yes—
529C2×#117—711no—
530C2×#117—712no—
531C2×#117—712no—
532C2×#117—714no—
533C2×#117—712no—
534C2×#117—714no—
535C2×#117C2×D7112yes—
536C2×#117C2×D7111yescharacteristic
537C22×C4⋊C4—714no—
538C22×C4⋊C4—712no—
539C22×C42—714no—
540C22×C42—712no—
541C22×C42C2×D7112yes—
542C22×C42C2×D7111yescharacteristic
543C2×#41—28no—
544C2×#41—7116no—
545C2×#41—718no—
546C2×#41—1428no—
547C2×#41—14216no—
548C2×#41C22×D7118yes—
549C22×Q8—711no—
550C22×Q8—714no—
551C22×Q8—712no—
552C22×Q8—712no—
553C22×Q8—7116no—
554C22×Q8—14216no—
555C22×Q8C22×D7111yescharacteristic
556C22×D4—714no—
557C22×D4—712no—
558C22×D4—711no—
559C22×D4C22×D7112yes—
560C22×D4C22×D7111yescharacteristic
561C23×C4—714no—
562C23×C4—714no—
563C23×C4—712no—
564C23×C4—712no—
565C23×C4—712no—
566C23×C4C22×D7112yes—
567C23×C4C22×D7112yes—
568C23×C4C22×D7111yescharacteristic
569C23×C4C22×D7111yescharacteristic
570C23×C4C22×D7111yescharacteristic
571C23×C4C22×D7112yes—
572C4⋊Q8—7116no—
573C4⋊Q8—7116no—
574C4⋊Q8—718no—
575C4⋊Q8—718no—
576#126—7132no—
577#126—7132no—
578#126—7132no—
579#125—7132no—
580#125—7132no—
581#125—7116no—
582#125—7116no—
583#124—7132no—
584#124—7116no—
585#123—7132no—
586#123—7132no—
587#123—7132no—
588C22⋊Q8—7116no—
589C22⋊Q8—7116no—
590C22⋊Q8—7116no—
591C22⋊Q8—7116no—
592C22⋊Q8—7116no—
593C22⋊Q8—7132no—
594C22⋊Q8—7132no—
595#121—7132no—
596#121—7116no—
597C4×Q8—7116no—
598C4×Q8—718no—
599C4×Q8—7132no—
600C4×Q8—7116no—
601C4×Q8—7116no—
602C4×Q8—7116no—
603C4×Q8—7132no—
604C4×Q8—7116no—
605C4×Q8—718no—
606C4×Q8C22×D7118yes—
607C4×Q8C22×D7118yes—
608C4×D4—7116no—
609C4×D4—7116no—
610C4×D4—7132no—
611C4×D4—7116no—
612C4×D4—7132no—
613C4×D4—718no—
614C4×D4—718no—
615C4×D4C22×D7118yes—
616C4×D4C22×D71116yes—
617C4×D4C22×D7118yes—
618C4×D4C22×D71116yes—
619#117—718no—
620#117—7116no—
621#117—7116no—
622#117—7132no—
623#117—7116no—
624#117—7132no—
625#117C22×D71116yes—
626#117C22×D7118yes—
627C2×C4⋊C4—712no—
628C2×C4⋊C4—711no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—712no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—714no—
633C2×C4⋊C4—714no—
634C2×C4⋊C4—7132no—
635C2×C4⋊C4—7116no—
636C2×C4⋊C4—712no—
637C2×C4⋊C4—714no—
638C2×C4⋊C4—711no—
639C2×C4⋊C4—712no—
640C2×C4⋊C4—714no—
641C2×C4⋊C4—714no—
642C2×C4⋊C4—712no—
643C2×C4⋊C4—714no—
644C2×C4⋊C4—712no—
645C2×C4⋊C4C22×D7111yescharacteristic
646C2×C4⋊C4C22×D7112yes—
647C2×C4⋊C4C22×D7111yescharacteristic
648C2×C4⋊C4C22×D7112yes—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—714no—
652C2×C22⋊C4—712no—
653C2×C22⋊C4—712no—
654C2×C22⋊C4—714no—
655C2×C22⋊C4—714no—
656C2×C22⋊C4—714no—
657C2×C22⋊C4C22×D7112yes—
658C2×C22⋊C4C22×D7112yes—
659C2×C22⋊C4C22×D7112yes—
660C2×C42—712no—
661C2×C42—714no—
662C2×C42—712no—
663C2×C42—714no—
664C2×C42—7132no—
665C2×C42—714no—
666C2×C42—712no—
667C2×C42—7116no—
668C2×C42C22×D7111yescharacteristic
669C2×C42C22×D7112yes—
670C2×C42C22×D7111yescharacteristic
671C2×C42C22×D7112yes—
672C2×C42C22×D71116yes—
673C2×C42C22×D7118yes—
674C2×C42C22×D7112yes—
675C2×C42C22×D7111yescharacteristic
676C2×C42C22×D7111yescharacteristic
677C24—712no—
678C24C23×D7111yescharacteristic
679C24C23×D7112yes—
680#41—232no—
681#41—14232no—
682#41—14264no—
683C2×Q8—24no—
684C2×Q8—718no—
685C2×Q8—714no—
686C2×Q8—7116no—
687C2×Q8—718no—
688C2×Q8—718no—
689C2×Q8—14216no—
690C2×Q8—14264no—
691C2×Q8—1428no—
692C2×Q8—1428no—
693C2×Q8C23×D7114yes—
694C2×D4—28no—
695C2×D4—7116no—
696C2×D4—718no—
697C2×D4—714no—
698C2×D4—1428no—
699C2×D4—14216no—
700C2×D4—1424no—
701C2×D4#1176586518yescomplemented
702C2×D4C23×D7118yes—
703C2×D4C23×D7114yes—
704C22×C4—28no—
705C22×C4—28no—
706C22×C4—24no—
707C22×C4—24no—
708C22×C4—28no—
709C22×C4—24no—
710C22×C4—712no—
711C22×C4—712no—
712C22×C4—712no—
713C22×C4—714no—
714C22×C4—714no—
715C22×C4—7116no—
716C22×C4—7116no—
717C22×C4—718no—
718C22×C4—718no—
719C22×C4—718no—
720C22×C4—1428no—
721C22×C4—14216no—
722C22×C4—14216no—
723C22×C4—1428no—
724C22×C4—1428no—
725C22×C4C23×D7112yes—
726C22×C4C23×D7118yes—
727C22×C4C23×D7111yescharacteristic
728C22×C4C23×D7111yescharacteristic
729C22×C4C23×D7111yescharacteristic
730C22×C4C23×D7112yes—
731C22×C4C23×D7112yes—
732C22×C4C23×D7118yes—
733C22×C4C23×D7118yes—
734C22×C4C23×D7114yes—
735C22×C4C23×D7114yes—
736C22×C4C23×D7114yes—
737C22×C4C23×D7111yescharacteristic
738C22×C4C23×D7111yescharacteristic
739C22×C4C23×D7111yescharacteristic
740C4⋊C4—718no—
741C4⋊C4—7116no—
742C4⋊C4—7116no—
743C4⋊C4—7116no—
744C4⋊C4—718no—
745C4⋊C4—7116no—
746C4⋊C4—7116no—
747C4⋊C4—7116no—
748C4⋊C4—7116no—
749C4⋊C4—714no—
750C4⋊C4—718no—
751C4⋊C4—7116no—
752C4⋊C4—714no—
753C4⋊C4—718no—
754C4⋊C4—718no—
755C4⋊C4—718no—
756C4⋊C4C23×D7114yes—
757C4⋊C4C23×D7118yes—
758C4⋊C4C23×D7114yes—
759C4⋊C4C23×D7118yes—
760C22⋊C4—7116no—
761C22⋊C4—718no—
762C22⋊C4—7116no—
763C22⋊C4—718no—
764C22⋊C4—718no—
765C22⋊C4—7116no—
766C22⋊C4—7116no—
767C22⋊C4—7116no—
768C22⋊C4C23×D7118yes—
769C22⋊C4C23×D7118yes—
770C22⋊C4C23×D7118yes—
771C42—718no—
772C42—718no—
773C42—7116no—
774C42—7116no—
775C42—718no—
776C42—7116no—
777C42C23×D7114yes—
778C42C23×D7114yes—
779C42C23×D7114yes—
780C42C23×D7118yes—
781C42C23×D7118yes—
782C42C23×D7114yes—
783C42C23×D7118yes—
784C23—24no—
785C23—24no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—714no—
790C23—1424no—
791C23—1424no—
792C23—1424no—
793C23C2×#1176586518yes—
794C23C24×D7112yes—
795C23C24×D7114yes—
796C23C24×D7111yescharacteristic
797Q8—28no—
798Q8—7116no—
799Q8—14232no—
800Q8—14216no—
801Q8—14216no—
802D4—216no—
803D4—14216no—
804D4—14232no—
805D4—1428no—
806D4C2×#11765865116yescomplemented
807C2×C4—22no—
808C2×C4—24no—
809C2×C4—22no—
810C2×C4—24no—
811C2×C4—216no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—216no—
815C2×C4—28no—
816C2×C4—28no—
817C2×C4—216no—
818C2×C4—28no—
819C2×C4—718no—
820C2×C4—714no—
821C2×C4—714no—
822C2×C4—714no—
823C2×C4—718no—
824C2×C4—718no—
825C2×C4—14216no—
826C2×C4—14232no—
827C2×C4—1428no—
828C2×C4—1424no—
829C2×C4—1428no—
830C2×C4—14232no—
831C2×C4—1424no—
832C2×C4—14216no—
833C2×C4—14216no—
834C2×C4#41×D7114yes—
835C2×C4C2×#1176586514yes—
836C2×C4#1455617514yes—
837C2×C4C24×D7114yes—
838C2×C4C24×D7112yes—
839C2×C4C24×D7112yes—
840C2×C4C24×D7112yes—
841C2×C4C24×D7114yes—
842C2×C4C24×D7114yes—
843C2×C4C24×D7112yes—
844C2×C4C24×D7112yes—
845C2×C4C24×D7112yes—
846C22—24no—
847C22—24no—
848C22—216no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—2848no—
854C22—1424no—
855C22—1424no—
856C22—1424no—
857C22C2×#41×D7112yes—
858C22C22×#1176586518yes—
859C22C22×#1176586512yes—
860C22C2×#1455617512yes—
861C22C25×D7111yescharacteristic
862C4—22no—
863C4—24no—
864C4—22no—
865C4—24no—
866C4—24no—
867C4—22no—
868C4—718no—
869C4—1428no—
870C4—1424no—
871C4—1428no—
872C4—1424no—
873C4C2×#41×D7114yes—
874C4C22×#1176586514yes—
875C4C2×#1455617514yes—
876C2—28no—
877C2—42no—
878C2—2844no—
879C2#2260195514yesdirect product factor
880C2C22×#41×D7111yescharacteristic
881C2C23×#1176586511yescharacteristic
882C2C22×#1455617511yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×C4×#41×C71C2
socleC23×C71C25
hypercenterC2×C4×#41D71
hypocenterC71C2×#3482
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22601955C2direct (N × H)
2. C2×#17986727C2semidirect
3. C2×#17986722C2semidirect
4. C2×#17986717C2semidirect
5. C2×#17986689C2semidirect
6. C2×#17986682C2semidirect
7. C2×D4×Dic142C2semidirect
8. C2×#17986658C2semidirect
9. C2×#17986653C2semidirect
10. C2×#17986648C2semidirect
11. C2×#17986556C2semidirect
12. C2×#17986553C2semidirect
13. C2×#17986533C2semidirect
14. C2×#17986529C2semidirect
15. C2×C4×#11765865C2semidirect
16. C2×C4×#11765864C2semidirect
17. C22×C4×Dic142C2semidirect
18. C2×C4×#41×C71C2semidirect
22. #17986727C22semidirect
23. #17986722C22semidirect
24. #17986717C22semidirect
25. #17986689C22semidirect
26. #17986682C22semidirect
27. D4×Dic142C22semidirect
28. #17986658C22semidirect
29. #17986653C22semidirect
30. #17986648C22semidirect
31. #17986556C22semidirect
32. #17986553C22semidirect
37. #17986533C22semidirect
38. #17986529C22semidirect
60. C4×#11765865C22semidirect
61. C4×#11765864C22semidirect
70. C2×C4×Dic142C22semidirect
90. C4×#41×C71C22semidirect
242. C2×Dic142#41semidirect
304. C2×D4×C71#41semidirect
357. D4×C71C2×#41semidirect
403. Dic142C2×#41semidirect
437. C2×C71#3482semidirect
458. C2×C4×#41D71semidirect
460. C71C2×#3482semidirect
505. C4×#41C2×D71semidirect
701. C2×D4#11765865semidirect
806. D4C2×#11765865semidirect
879. C2#22601955direct (N × H)

Maximal subgroups

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

subgroupindex
#226019552
C2×#179867272
C2×#179867222
C2×#179867172
C2×#179866892
C2×#179866822
C2×D4×Dic1422
C2×#179866582
C2×#179866532
C2×#179866482
C2×#179865562
C2×#179865532
C2×#179865332
C2×#179865292
C2×C4×#117658652
C2×C4×#117658642
C22×C4×Dic1422
C2×C4×#41×C712
C2×#348271