Finite Group Databasebeta

← C2×#22602318 #32905566

Subgroups — C2×#22602318 #32905566

Order 18176.

7142 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#22602318C2132yesmaximal, direct product factor
2C2×#17986727C211yesmaximal, characteristic, complemented
3C2×#17986709C211yesmaximal, characteristic, complemented
4C2×#17986706C211yesmaximal, characteristic, complemented
5C2×#17986695C212yesmaximal, complemented
6C2×#17986689C212yesmaximal, complemented
7C2×#17986688C212yesmaximal, complemented
8C2×#17986682C214yesmaximal, complemented
9C2×#17986653C211yesmaximal, characteristic, complemented
10C2×#17986648C212yesmaximal, complemented
11C2×#17986607C212yesmaximal, complemented
12C2×#17986591C214yesmaximal, complemented
13C2×#17986556C211yesmaximal, characteristic, complemented
14C2×#17986533C212yesmaximal, complemented
15C2×#17986533C211yesmaximal, characteristic, complemented
16C22×#14556120C212yesmaximal, complemented
17C2×#17986478C212yesmaximal, complemented
18C2×C4×#41×C71C211yesmaximal, characteristic, complemented
19C22×#11765864C2212yes—
20#17986727C22116yescomplemented
21#17986709C22116yescomplemented
22#17986706C22116yescomplemented
23#17986695C22132yescomplemented
24#17986689C22132yescomplemented
25#17986688C22132yescomplemented
26#17986682C22164yescomplemented
27#17986653C22116yescomplemented
28#17986648C22132yescomplemented
29#17986607C22132yescomplemented
30#17986591C22164yescomplemented
31#17986556C22116yescomplemented
32C2×#14556128C2211yescharacteristic
33C2×#14556128C2211yescharacteristic
34C2×#14556126C2212yes—
35#17986533C22132yescomplemented
36#17986533C22116yescomplemented
37C2×#14556123C2214yes—
38C2×#14556122C2212yes—
39C2×#14556122C2214yes—
40C2×#14556121C2214yes—
41C2×#14556120C2214yes—
42C2×#14556120C2211yescharacteristic
43C2×#14556120C2212yes—
44C2×#14556120C2212yes—
45C2×#14556120C2212yes—
46C2×#14556120C2214yes—
47C2×#14556120C22132yescomplemented
48C2×#14556119C2212yes—
49C2×#14556118C2214yes—
50C2×#14556118C2214yes—
51C2×#14556116C2211yescharacteristic
52C2×#14556112C2214yes—
53C2×#14556111C2214yes—
54C2×#14556111C2212yes—
55C2×#14556110C2214yes—
56C2×#14556109C2214yes—
57C2×#14556108C2212yes—
58C2×#14556107C2212yes—
59C2×#14556107C2211yescharacteristic
60C2×#14556107C2212yes—
61C2×#14556107C2212yes—
62C2×#14556106C2214yes—
63C2×#14556105C2214yes—
64C2×#14556104C2212yes—
65C2×#14556102C2212yes—
66C2×#14556102C2211yescharacteristic
67C2×#14556100C2214yes—
68#17986478C22132yescomplemented
69C2×C4×Dic142C2212yes—
70C2×C4×Dic142C2212yes—
71C2×C4×Dic142C2212yes—
72C2×C4×Dic142C2211yescharacteristic
73C2×#14556093C2212yes—
74C2×C4×D284C2211yescharacteristic
75C2×C4×D284C2212yes—
76C2×D4×Dic71C2212yes—
77C2×C4×C22⋊D71C2214yes—
78C2×C4×C22⋊D71C2212yes—
79C2×(C22⋊D71)⋊C4C2214yes—
80C2×#14556087C2212yes—
81C2×#14556085C2212yes—
82C2×#14556085C2214yes—
83C2×#14556084C2214yes—
84C22×C4⋊Dic71C2212yes—
85C22×C4⋊Dic71C2212yes—
86C22×Dic71⋊C4C2214yes—
87C22×Dic71⋊C4C2214yes—
88C2×C4⋊C4×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×#11765864—216no—
102C2×#11765864C23116yes—
103C22×Dic142C2312yes—
104C22×Dic142C2311yescharacteristic
105C22×Dic142C2312yes—
106C22×D284C2311yescharacteristic
107C22×C22⋊D71C2314yes—
108C22×C22⋊D71C2312yes—
109C23×Dic71C2314yes—
110C23×Dic71C2314yes—
111C22×C4×D71C2312yes—
112C22×C4×D71C2314yes—
113#14556128C2318yes—
114#14556128C2318yes—
115#14556126C23116yes—
116#14556123C23132yes—
117#14556122C23132yes—
118#14556122C23116yes—
119#14556121C23132yes—
120#14556120C23132yes—
121#14556120C23132yes—
122#14556120C23116yes—
123#14556120C23116yes—
124#14556120C2318yes—
125#14556120C23116yes—
126#14556119C23116yes—
127#14556118C23132yes—
128#14556118C23132yes—
129#14556116C2318yes—
130#14556112C23132yes—
131#14556111C23116yes—
132#14556111C23132yes—
133#14556110C23132yes—
134#14556109C23132yes—
135#14556108C23116yes—
136#14556107C23116yes—
137#14556107C23116yes—
138#14556107C2318yes—
139#14556107C23116yes—
140#14556106C23132yes—
141#14556105C23132yes—
142#14556104C23116yes—
143#14556102C23116yes—
144#14556102C2318yes—
145#14556100C23132yes—
146C4×Dic142C23116yes—
147C4×Dic142C23116yes—
148C4×Dic142C23116yes—
149C4×Dic142C2318yes—
150#14556093C23116yes—
151C4×D284C2318yes—
152C4×D284C23116yes—
153D4×Dic71C23116yes—
154C4×C22⋊D71C23132yes—
155C4×C22⋊D71C23116yes—
156(C22⋊D71)⋊C4C23132yes—
157#14556087C23116yes—
158#14556085C23116yes—
159#14556085C23132yes—
160#14556084C23132yes—
161C2×C4⋊Dic71C23116yes—
162C2×C4⋊Dic71C23116yes—
163C2×C4⋊Dic71C2312yes—
164C2×C4⋊Dic71C2311yescharacteristic
165C2×C4⋊Dic71C2311yescharacteristic
166C2×C4⋊Dic71C2312yes—
167C2×C4⋊Dic71C2312yes—
168C2×C4⋊Dic71C2314yes—
169C2×C4⋊Dic71C2314yes—
170C2×C4⋊Dic71C2312yes—
171C2×Dic71⋊C4C23132yes—
172C2×Dic71⋊C4C23132yes—
173C2×Dic71⋊C4C2314yes—
174C2×Dic71⋊C4C2312yes—
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⋊C4C2312yes—
184C2×Dic71⋊C4C2314yes—
185C4⋊C4×D71C23116yes—
186C2×C22⋊Dic71C2314yes—
187C2×C22⋊Dic71C2314yes—
188C2×C22⋊Dic71C2312yes—
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×C4×Dic71C2314yes—
196C2×C4×Dic71C2314yes—
197C2×C4×Dic71C2312yes—
198C2×#41×C71—28no—
199C2×#41×C71C2318yes—
200C22×Q8×C71C2311yescharacteristic
201C22×D4×C71C2312yes—
202C22×D4×C71C2311yescharacteristic
203C23×C4×C71C2312yes—
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2312yes—
206C23×C4×C71C2311yescharacteristic
207C23×C4×C71C2312yes—
208C23×C4×C71C2311yescharacteristic
209C4×Q8×C71C2318yes—
210C4×Q8×C71C2318yes—
211C4×D4×C71C23116yes—
212C4×D4×C71C2318yes—
213C4×D4×C71C23116yes—
214C4×D4×C71C2318yes—
215#117×C71C23116yes—
216#117×C71C2318yes—
217C2×C4⋊C4×C71C2311yescharacteristic
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2311yescharacteristic
220C2×C4⋊C4×C71C2312yes—
221C2×C22⋊C4×C71C2312yes—
222C2×C22⋊C4×C71C2312yes—
223C2×C22⋊C4×C71C2312yes—
224C2×C42×C71C2311yescharacteristic
225C2×C42×C71C2312yes—
226C2×C42×C71C2311yescharacteristic
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2312yes—
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2312yes—
231C2×C42×C71C23116yes—
232C2×C42×C71C2318yes—
233C23×D71C2412yes—
234#11765864—264no—
235C2×Dic142—28no—
236C2×Dic142—24no—
237C2×Dic142—44no—
238C2×Dic142C2418yes—
239C2×Dic142C2414yes—
240C2×Dic142C2418yes—
241C2×D284—24no—
242C2×D284C2414yes—
243C2×C22⋊D71—216no—
244C2×C22⋊D71—44no—
245C2×C22⋊D71C24116yes—
246C2×C22⋊D71C2418yes—
247C22×Dic71—216no—
248C22×Dic71—48no—
249C22×Dic71C2412yes—
250C22×Dic71C2414yes—
251C22×Dic71C2412yes—
252C22×Dic71C2414yes—
253C22×Dic71C24116yes—
254C22×Dic71C2412yes—
255C22×Dic71C24116yes—
256C2×C4×D71—28no—
257C2×C4×D71—48no—
258C2×C4×D71C2418yes—
259C2×C4×D71C24116yes—
260C4⋊Dic71C2418yes—
261C4⋊Dic71C2414yes—
262C4⋊Dic71C2414yes—
263C4⋊Dic71C2418yes—
264C4⋊Dic71C2418yes—
265C4⋊Dic71C24116yes—
266C4⋊Dic71C24116yes—
267C4⋊Dic71C2418yes—
268Dic71⋊C4C24116yes—
269Dic71⋊C4C2418yes—
270Dic71⋊C4C2418yes—
271Dic71⋊C4C24116yes—
272Dic71⋊C4C24116yes—
273Dic71⋊C4C24116yes—
274Dic71⋊C4C24116yes—
275Dic71⋊C4C24116yes—
276Dic71⋊C4C2418yes—
277Dic71⋊C4C24116yes—
278Dic71⋊C4C2418yes—
279Dic71⋊C4C24116yes—
280C22⋊Dic71C24116yes—
281C22⋊Dic71C24116yes—
282C22⋊Dic71C2418yes—
283(C2×D71)⋊C4C2418yes—
284(C2×D71)⋊C4C2418yes—
285(C2×D71)⋊C4C2418yes—
286(C2×D71)⋊C4C24116yes—
287(C2×D71)⋊C4C24116yes—
288(C2×D71)⋊C4C2418yes—
289C4×Dic71C24116yes—
290C4×Dic71C24116yes—
291C4×Dic71C2418yes—
292C24×C71C2411yescharacteristic
293C24×C71C2412yes—
294#41×C71—232no—
295C2×Q8×C71—24no—
296C2×Q8×C71C2414yes—
297C2×D4×C71—28no—
298C2×D4×C71#4118yes—
299C2×D4×C71C2418yes—
300C2×D4×C71C2414yes—
301C22×C4×C71—28no—
302C22×C4×C71—24no—
303C22×C4×C71—28no—
304C22×C4×C71—24no—
305C22×C4×C71—44no—
306C22×C4×C71—42no—
307C22×C4×C71C2412yes—
308C22×C4×C71C2411yescharacteristic
309C22×C4×C71C2411yescharacteristic
310C22×C4×C71C2411yescharacteristic
311C22×C4×C71C2411yescharacteristic
312C22×C4×C71C2412yes—
313C22×C4×C71C2412yes—
314C22×C4×C71C2418yes—
315C22×C4×C71C2414yes—
316C22×C4×C71C2418yes—
317C22×C4×C71C2414yes—
318C22×C4×C71C2418yes—
319C22×C4×C71C2414yes—
320C22×C4×C71C2411yescharacteristic
321C22×C4×C71C2411yescharacteristic
322C4⋊C4×C71C2414yes—
323C4⋊C4×C71C2418yes—
324C4⋊C4×C71C2414yes—
325C4⋊C4×C71C2418yes—
326C22⋊C4×C71C2418yes—
327C22⋊C4×C71C2418yes—
328C22⋊C4×C71C2418yes—
329C42×C71C2414yes—
330C42×C71C2418yes—
331C42×C71C2414yes—
332C42×C71C2414yes—
333C42×C71C2418yes—
334C42×C71C2414yes—
335C42×C71C2418yes—
336C23×C71—24no—
337C23×C71—24no—
338C23×C71—22no—
339C23×C71—22no—
340C23×C71—22no—
341C23×C71C2×#4118yes—
342C23×C71C2512yes—
343C23×C71C2514yes—
344C23×C71C2511yescharacteristic
345C22×D71—24no—
346C22×D71—24no—
347C22×D71—24no—
348C22×D71C2514yes—
349Q8×C71—28no—
350D4×C71—216no—
351D4×C71C2×#41116yes—
352C2×C4×C71—22no—
353C2×C4×C71—24no—
354C2×C4×C71—216no—
355C2×C4×C71—22no—
356C2×C4×C71—24no—
357C2×C4×C71—22no—
358C2×C4×C71—24no—
359C2×C4×C71—22no—
360C2×C4×C71—28no—
361C2×C4×C71—216no—
362C2×C4×C71—28no—
363C2×C4×C71—44no—
364C2×C4×C71—48no—
365C2×C4×C71C2×#4114yes—
366C2×C4×C712−1+414yes—
367C2×C4×C71C2512yes—
368C2×C4×C71C2512yes—
369C2×C4×C71C2512yes—
370C2×C4×C71C2514yes—
371C2×C4×C71C2514yes—
372C2×C4×C71C2512yes—
373C2×C4×C71C2514yes—
374C2×C4×C71C2512yes—
375C2×C4×C71C2512yes—
376C22⋊D71—232no—
377C22⋊D71—48no—
378C2×Dic71—24no—
379C2×Dic71—28no—
380C2×Dic71—232no—
381C2×Dic71—24no—
382C2×Dic71—28no—
383C2×Dic71—24no—
384C2×Dic71—416no—
385C2×Dic71C2514yes—
386C2×Dic71C2518yes—
387C2×Dic71C2518yes—
388C2×Dic71C2514yes—
389C2×Dic71C2514yes—
390D284—28no—
391C4×D71—216no—
392C4×D71—416no—
393Dic142—216no—
394Dic142—28no—
395Dic142—48no—
396C22×C71—24no—
397C22×C71—24no—
398C22×C71—216no—
399C22×C71—22no—
400C22×C71—22no—
401C22×C71—22no—
402C22×C71—44no—
403C22×C71C22×#4118yes—
404C22×C71C22×#4112yes—
405C22×C71C2×2−1+412yes—
406C22×C71#58512yes—
407C22×C71C2611yescharacteristic
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71—48no—
412C4×C71—22no—
413C4×C71—24no—
414C4×C71—22no—
415C4×C71—24no—
416C4×C71—22no—
417C4×C71—24no—
418C4×C71—22no—
419C4×C71C22×#4114yes—
420C4×C71C2×2−1+414yes—
421Dic71—28no—
422Dic71—24no—
423Dic71—24no—
424Dic71—28no—
425Dic71—24no—
426C2×#3515—711nomaximal, Sylow
427C2×C71—28no—
428C2×C71—42no—
429C2×C71#351514yescomplemented
430C2×C71C23×#4111yescharacteristic
431C2×C71C22×2−1+411yescharacteristic
432C2×C71C2×#58511yescharacteristic
433D71—44no—
434#3515—7132no—
435C2×#557—711no—
436C2×#554—711no—
437C2×#554—711no—
438C2×#553—712no—
439C2×#552—712no—
440C2×#552—714no—
441C2×#552—712no—
442C2×#547—712no—
443C2×#547—711no—
444C2×#541—712no—
445C2×#539—714no—
446C2×#533—711no—
447C2×#529—711no—
448C2×#529—712no—
449C22×#125—712no—
450C2×#520—712no—
451C2×C4×#41D7111yescharacteristic, complemented
452C71C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—712no—
454C22×#41C2×D7111yescharacteristic
455#557—7116no—
456#554—7116no—
457#554—7116no—
458#553—7132no—
459#552—7132no—
460#552—7164no—
461#552—7132no—
462#547—7132no—
463#547—7116no—
464#541—7132no—
465#539—7164no—
466#533—7116no—
467C2×C4⋊Q8—712no—
468C2×C4⋊Q8—711no—
469C2×C4⋊Q8—711no—
470#529—7132no—
471#529—7116no—
472C2×#126—714no—
473C2×#126—714no—
474C2×#126—714no—
475C2×#126—712no—
476C2×#125—714no—
477C2×#125—714no—
478C2×#125—712no—
479C2×#125—711no—
480C2×#125—712no—
481C2×#125—714no—
482C2×#125—714no—
483C2×#125—712no—
484C2×#125—712no—
485C2×#125—7132no—
486C2×#124—711no—
487C2×#123—714no—
488C2×#123—712no—
489C2×#123—714no—
490C2×#123—714no—
491C2×#123—714no—
492C2×C22⋊Q8—712no—
493C2×C22⋊Q8—711no—
494C2×C22⋊Q8—712no—
495C2×C22⋊Q8—712no—
496C2×C22⋊Q8—712no—
497C2×C22⋊Q8—714no—
498C2×C22⋊Q8—712no—
499C2×C22⋊Q8—714no—
500C2×#121—714no—
501C2×#121—712no—
502C2×#121—711no—
503#520—7132no—
504C4×#41C2×D71116yescomplemented
505C2×C4×Q8—712no—
506C2×C4×Q8—712no—
507C2×C4×Q8—712no—
508C2×C4×Q8—711no—
509C2×C4×Q8—712no—
510C2×C4×Q8C2×D7111yescharacteristic
511C2×C4×Q8C2×D7111yescharacteristic
512C2×C4×D4—712no—
513C2×C4×D4—714no—
514C2×C4×D4—712no—
515C2×C4×D4—714no—
516C2×C4×D4—711no—
517C2×C4×D4—712no—
518C2×C4×D4C2×D7111yescharacteristic
519C2×C4×D4C2×D7112yes—
520C2×C4×D4C2×D7111yescharacteristic
521C2×C4×D4C2×D7112yes—
522C2×#117—712no—
523C2×#117—714no—
524C2×#117—712no—
525C2×#117—714no—
526C2×#117C2×D7111yescharacteristic
527C2×#117C2×D7112yes—
528C22×C4⋊C4—714no—
529C22×C4⋊C4—714no—
530C22×C4⋊C4—712no—
531C22×C4⋊C4—712no—
532C22×C4⋊C4—712no—
533C22×C42C2×D7112yes—
534C22×C42C2×D7111yescharacteristic
535C2×#41—28no—
536C2×#41—7116no—
537C2×#41—14216no—
538C2×#41C22×D7118yes—
539C22×Q8—712no—
540C22×Q8—711no—
541C22×Q8—712no—
542C22×Q8C22×D7111yescharacteristic
543C22×D4—712no—
544C22×D4—714no—
545C22×D4—711no—
546C22×D4C22×D7112yes—
547C22×D4C22×D7111yescharacteristic
548C23×C4—714no—
549C23×C4—714no—
550C23×C4—714no—
551C23×C4—712no—
552C23×C4C22×D7112yes—
553C23×C4C22×D7112yes—
554C23×C4C22×D7111yescharacteristic
555C23×C4C22×D7111yescharacteristic
556C23×C4C22×D7112yes—
557C23×C4C22×D7111yescharacteristic
558C4⋊Q8—7116no—
559C4⋊Q8—718no—
560C4⋊Q8—718no—
561#126—7132no—
562#126—7132no—
563#126—7132no—
564#126—7116no—
565#125—7132no—
566#125—7132no—
567#125—7116no—
568#125—718no—
569#125—7116no—
570#125—7132no—
571#125—7132no—
572#125—7116no—
573#125—7116no—
574#124—718no—
575#123—7132no—
576#123—7116no—
577#123—7132no—
578#123—7132no—
579#123—7132no—
580C22⋊Q8—7116no—
581C22⋊Q8—718no—
582C22⋊Q8—7116no—
583C22⋊Q8—7116no—
584C22⋊Q8—7116no—
585C22⋊Q8—7132no—
586C22⋊Q8—7116no—
587C22⋊Q8—7132no—
588#121—7132no—
589#121—7116no—
590#121—718no—
591C4×Q8—7116no—
592C4×Q8—7116no—
593C4×Q8—7116no—
594C4×Q8—718no—
595C4×Q8—7116no—
596C4×Q8C22×D7118yes—
597C4×Q8C22×D7118yes—
598C4×D4—7116no—
599C4×D4—7132no—
600C4×D4—7116no—
601C4×D4—7132no—
602C4×D4—718no—
603C4×D4—7116no—
604C4×D4C22×D7118yes—
605C4×D4C22×D71116yes—
606C4×D4C22×D7118yes—
607C4×D4C22×D71116yes—
608#117—7116no—
609#117—7132no—
610#117—7116no—
611#117—7132no—
612#117C22×D7118yes—
613#117C22×D71116yes—
614C2×C4⋊C4—714no—
615C2×C4⋊C4—712no—
616C2×C4⋊C4—711no—
617C2×C4⋊C4—712no—
618C2×C4⋊C4—711no—
619C2×C4⋊C4—712no—
620C2×C4⋊C4—712no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—712no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—7132no—
626C2×C4⋊C4—714no—
627C2×C4⋊C4—714no—
628C2×C4⋊C4—714no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—7132no—
631C2×C4⋊C4—7116no—
632C2×C4⋊C4—7116no—
633C2×C4⋊C4—712no—
634C2×C4⋊C4—714no—
635C2×C4⋊C4—712no—
636C2×C4⋊C4—712no—
637C2×C4⋊C4—714no—
638C2×C4⋊C4—7116no—
639C2×C4⋊C4C22×D7111yescharacteristic
640C2×C4⋊C4C22×D7112yes—
641C2×C4⋊C4C22×D7111yescharacteristic
642C2×C4⋊C4C22×D7112yes—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—712no—
646C2×C22⋊C4—712no—
647C2×C22⋊C4—712no—
648C2×C22⋊C4—712no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—714no—
651C2×C22⋊C4—712no—
652C2×C22⋊C4C22×D7112yes—
653C2×C22⋊C4C22×D7112yes—
654C2×C22⋊C4C22×D7112yes—
655C2×C42—714no—
656C2×C42—714no—
657C2×C42—712no—
658C2×C42C22×D7112yes—
659C2×C42C22×D7111yescharacteristic
660C2×C42C22×D7111yescharacteristic
661C2×C42C22×D7112yes—
662C2×C42C22×D7111yescharacteristic
663C2×C42C22×D7112yes—
664C2×C42C22×D71116yes—
665C2×C42C22×D7118yes—
666C2×C42C22×D7111yescharacteristic
667C24—712no—
668C24C23×D7111yescharacteristic
669C24C23×D7112yes—
670#41—232no—
671#41—14264no—
672C2×Q8—24no—
673C2×Q8—2844no—
674C2×Q8—718no—
675C2×Q8—714no—
676C2×Q8—718no—
677C2×Q8—1428no—
678C2×Q8—1424no—
679C2×Q8C23×D7114yes—
680C2×D4—28no—
681C2×D4—2844no—
682C2×D4—718no—
683C2×D4—7116no—
684C2×D4—714no—
685C2×D4—14216no—
686C2×D4—1424no—
687C2×D4#1176586518yes—
688C2×D4C23×D7118yes—
689C2×D4C23×D7114yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—28no—
693C22×C4—24no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—2848no—
697C22×C4—2848no—
698C22×C4—7116no—
699C22×C4—7116no—
700C22×C4—7116no—
701C22×C4—712no—
702C22×C4—714no—
703C22×C4—714no—
704C22×C4—712no—
705C22×C4—712no—
706C22×C4—718no—
707C22×C4—14216no—
708C22×C4—1428no—
709C22×C4C23×D7118yes—
710C22×C4C23×D7118yes—
711C22×C4C23×D7114yes—
712C22×C4C23×D7114yes—
713C22×C4C23×D7111yescharacteristic
714C22×C4C23×D7112yes—
715C22×C4C23×D7111yescharacteristic
716C22×C4C23×D7111yescharacteristic
717C22×C4C23×D7112yes—
718C22×C4C23×D7111yescharacteristic
719C22×C4C23×D7112yes—
720C22×C4C23×D7118yes—
721C22×C4C23×D7114yes—
722C22×C4C23×D7111yescharacteristic
723C22×C4C23×D7111yescharacteristic
724C4⋊C4—7116no—
725C4⋊C4—718no—
726C4⋊C4—718no—
727C4⋊C4—7116no—
728C4⋊C4—7116no—
729C4⋊C4—7116no—
730C4⋊C4—7116no—
731C4⋊C4—7116no—
732C4⋊C4—718no—
733C4⋊C4—7116no—
734C4⋊C4—718no—
735C4⋊C4—7116no—
736C4⋊C4—714no—
737C4⋊C4—714no—
738C4⋊C4—718no—
739C4⋊C4—718no—
740C4⋊C4—718no—
741C4⋊C4—7116no—
742C4⋊C4—7116no—
743C4⋊C4—718no—
744C4⋊C4C23×D7114yes—
745C4⋊C4C23×D7118yes—
746C4⋊C4C23×D7114yes—
747C4⋊C4C23×D7118yes—
748C22⋊C4—7116no—
749C22⋊C4—7116no—
750C22⋊C4—718no—
751C22⋊C4—718no—
752C22⋊C4—718no—
753C22⋊C4—718no—
754C22⋊C4—7116no—
755C22⋊C4—7116no—
756C22⋊C4—718no—
757C22⋊C4C23×D7118yes—
758C22⋊C4C23×D7118yes—
759C22⋊C4C23×D7118yes—
760C42—7116no—
761C42—7116no—
762C42—718no—
763C42C23×D7114yes—
764C42C23×D7118yes—
765C42C23×D7114yes—
766C42C23×D7114yes—
767C42C23×D7118yes—
768C42C23×D7114yes—
769C42C23×D7118yes—
770C23—24no—
771C23—24no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—714no—
776C23—1424no—
777C23—1424no—
778C23—1424no—
779C23C2×#1176586518yes—
780C23C24×D7112yes—
781C23C24×D7114yes—
782C23C24×D7111yescharacteristic
783Q8—28no—
784Q8—2848no—
785Q8—14216no—
786Q8—1428no—
787D4—216no—
788D4—2848no—
789D4—14232no—
790D4—1428no—
791D4C2×#11765865116yes—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—216no—
795C2×C4—22no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—28no—
801C2×C4—216no—
802C2×C4—28no—
803C2×C4—48no—
804C2×C4—44no—
805C2×C4—28416no—
806C2×C4—28416no—
807C2×C4—714no—
808C2×C4—718no—
809C2×C4—718no—
810C2×C4—714no—
811C2×C4—714no—
812C2×C4—1424no—
813C2×C4—1428no—
814C2×C4—14232no—
815C2×C4—1424no—
816C2×C4—1424no—
817C2×C4—1428no—
818C2×C4—14216no—
819C2×C4C2×#1176586514yes—
820C2×C4#1455617514yes—
821C2×C4C24×D7112yes—
822C2×C4C24×D7114yes—
823C2×C4C24×D7112yes—
824C2×C4C24×D7112yes—
825C2×C4C24×D7114yes—
826C2×C4C24×D7112yes—
827C2×C4C24×D7114yes—
828C2×C4C24×D7112yes—
829C2×C4C24×D7112yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—44no—
837C22—2848no—
838C22—1424no—
839C22—1424no—
840C22—1424no—
841C22C22×#1176586518yes—
842C22C22×#1176586512yes—
843C22C2×#1455617512yes—
844C22#1798683512yes—
845C22C25×D7111yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—24no—
852C4—22no—
853C4—1424no—
854C4—1428no—
855C4—1424no—
856C4—1424no—
857C4—1428no—
858C4C22×#1176586514yes—
859C4C2×#1455617514yes—
860C2—28no—
861C2—42no—
862C2—2844no—
863C2#2260231814yesdirect product factor
864C2C23×#1176586511yescharacteristic
865C2C22×#1455617511yescharacteristic
866C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×C4×#41×C71C2
socleC23×C71C25
hypercenterC2×C4×#41D71
hypocenterC71C2×#3515
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #22602318C2direct (N × H)
2. C2×#17986727C2semidirect
3. C2×#17986709C2semidirect
4. C2×#17986706C2semidirect
5. C2×#17986695C2semidirect
6. C2×#17986689C2semidirect
7. C2×#17986688C2semidirect
8. C2×#17986682C2semidirect
9. C2×#17986653C2semidirect
10. C2×#17986648C2semidirect
11. C2×#17986607C2semidirect
12. C2×#17986591C2semidirect
13. C2×#17986556C2semidirect
14. C2×#17986533C2semidirect
15. C2×#17986533C2semidirect
16. C22×#14556120C2semidirect
17. C2×#17986478C2semidirect
18. C2×C4×#41×C71C2semidirect
20. #17986727C22semidirect
21. #17986709C22semidirect
22. #17986706C22semidirect
23. #17986695C22semidirect
24. #17986689C22semidirect
25. #17986688C22semidirect
26. #17986682C22semidirect
27. #17986653C22semidirect
28. #17986648C22semidirect
29. #17986607C22semidirect
30. #17986591C22semidirect
31. #17986556C22semidirect
35. #17986533C22semidirect
36. #17986533C22semidirect
47. C2×#14556120C22semidirect
68. #17986478C22semidirect
90. C4×#41×C71C22semidirect
429. C2×C71#3515semidirect
451. C2×C4×#41D71semidirect
452. C71C2×#3515semidirect
504. C4×#41C2×D71semidirect
863. C2#22602318direct (N × H)

Maximal subgroups

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

subgroupindex
#226023182
C2×#179867272
C2×#179867092
C2×#179867062
C2×#179866952
C2×#179866892
C2×#179866882
C2×#179866822
C2×#179866532
C2×#179866482
C2×#179866072
C2×#179865912
C2×#179865562
C2×#179865332
C22×#145561202
C2×#179864782
C2×C4×#41×C712
C2×#351571