Finite Group Databasebeta

← C2×#22602313 #32905557

Subgroups — C2×#22602313 #32905557

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#22602313C2132yesmaximal, direct product factor
2C2×#17986724C211yesmaximal, characteristic, complemented
3C2×#17986710C211yesmaximal, characteristic, complemented
4C2×#17986710C211yesmaximal, characteristic, complemented
5C2×#17986693C212yesmaximal, complemented
6C2×#17986690C214yesmaximal, complemented
7C2×#17986688C212yesmaximal, complemented
8C2×#17986683C212yesmaximal, complemented
9C2×#17986652C211yesmaximal, characteristic, complemented
10C2×#17986651C212yesmaximal, complemented
11C2×#17986607C212yesmaximal, complemented
12C2×#17986595C214yesmaximal, complemented
13C2×#17986534C212yesmaximal, complemented
14C2×#17986533C211yesmaximal, characteristic, complemented
15C2×#125×D71C212yesmaximal, complemented
16C2×#17986481C212yesmaximal, complemented
17C2×C4×#11765865C211yesmaximal, characteristic, complemented
18C2×#533×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×#11765865C2211yescharacteristic
21#17986724C22116yescomplemented
22#17986710C22116yescomplemented
23#17986710C22116yescomplemented
24#17986693C22132yescomplemented
25#17986690C22164yescomplemented
26#17986688C22132yescomplemented
27#17986683C22132yescomplemented
28#17986652C22116yescomplemented
29#17986651C22132yescomplemented
30#17986607C22132yescomplemented
31#17986595C22164yescomplemented
32C2×#14556126C2212yes—
33#17986534C22132yescomplemented
34#17986533C22116yescomplemented
35C2×#14556123C2214yes—
36C2×#14556122C2212yes—
37C2×#14556122C2214yes—
38C2×#14556121C2214yes—
39C2×#14556120C2211yescharacteristic
40C2×#14556120C2214yes—
41C2×#14556119C2212yes—
42C2×#14556119C2212yes—
43C2×#14556119C2212yes—
44C2×#14556118C2214yes—
45C2×#14556118C2214yes—
46C2×#14556118C2214yes—
47#125×D71C22132yescomplemented
48C2×#14556116C2211yescharacteristic
49C2×#14556113C2214yes—
50C2×#14556113C2214yes—
51C2×#14556111C2212yes—
52C2×#14556110C2214yes—
53C2×#14556110C2214yes—
54C2×#14556108C2212yes—
55C2×#14556108C2212yes—
56C2×#14556107C2211yescharacteristic
57C2×#14556104C2212yes—
58C2×#14556104C2214yes—
59C2×#14556104C2214yes—
60C2×#14556103C2212yes—
61C2×#14556102C2211yescharacteristic
62C2×#14556101C2214yes—
63#17986481C22132yescomplemented
64C4×#11765865C22116yescomplemented
65C2×Q8×Dic71C2212yes—
66C2×C4×Dic142C2211yescharacteristic
67C2×C4×Dic142C2211yescharacteristic
68C2×C4×Dic142C2211yescharacteristic
69C2×#14556093C2212yes—
70C2×C4×D284C2211yescharacteristic
71C2×C4×D284C2211yescharacteristic
72C2×C4×D284C2214yes—
73C2×C4×D284C2211yescharacteristic
74C2×#14556090C2212yes—
75C2×#14556090C2214yes—
76C2×#14556090C2212yes—
77C2×C4×C22⋊D71C2212yes—
78C2×C4×C22⋊D71C2212yes—
79C2×C4×C22⋊D71C2212yes—
80C2×#14556087C2211yescharacteristic
81C2×#14556086C2214yes—
82C2×#14556085C2212yes—
83C2×#14556085C2214yes—
84C2×#14556085C2212yes—
85C2×C4⋊C4×D71C2214yes—
86C2×C4⋊C4×D71C2212yes—
87C2×C4⋊C4×D71C2214yes—
88C2×C4⋊C4×D71C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C42×D71C2212yes—
91#533×C71C22116yescomplemented
92C2×C4⋊Q8×C71C2211yescharacteristic
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#125×C71C2212yes—
95C2×C22⋊Q8×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765866—216no—
102C2×#11765866C23116yes—
103C2×#11765865—28no—
104C2×#11765865C2318yes—
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2311yescharacteristic
107C22×D284C2314yes—
108C22×D284C2311yescharacteristic
109C22×D284C2311yescharacteristic
110C22×C22⋊D71C2312yes—
111C22×C22⋊D71C2312yes—
112C22×C4×D71C2312yes—
113C22×C4×D71C2314yes—
114C22×C4×D71C2312yes—
115C22×C4×D71C2312yes—
116C22×C4×D71C2312yes—
117C22×C4×D71C2314yes—
118C22×C4×D71C2314yes—
119#14556126C23116yes—
120#14556123C23132yes—
121#14556122C23132yes—
122#14556122C23116yes—
123#14556121C23132yes—
124#14556120C23132yes—
125#14556120C2318yes—
126#14556119C23116yes—
127#14556119C23116yes—
128#14556119C23116yes—
129#14556118C23132yes—
130#14556118C23132yes—
131#14556118C23132yes—
132#14556116C2318yes—
133#14556113C23132yes—
134#14556113C23132yes—
135#14556111C23116yes—
136#14556110C23132yes—
137#14556110C23132yes—
138#14556108C23116yes—
139#14556108C23116yes—
140#14556107C2318yes—
141#14556104C23132yes—
142#14556104C23132yes—
143#14556104C23116yes—
144#14556103C23116yes—
145#14556102C2318yes—
146#14556101C23132yes—
147Q8×Dic71C23116yes—
148C4×Dic142C2318yes—
149C4×Dic142C2318yes—
150C4×Dic142C2318yes—
151#14556093C23116yes—
152C4×D284C2318yes—
153C4×D284C2318yes—
154C4×D284C23132yes—
155C4×D284C2318yes—
156#14556090C23132yes—
157#14556090C23116yes—
158#14556090C23116yes—
159C4×C22⋊D71C23116yes—
160C4×C22⋊D71C23116yes—
161C4×C22⋊D71C23116yes—
162#14556087C2318yes—
163#14556086C23132yes—
164#14556085C23116yes—
165#14556085C23132yes—
166#14556085C23116yes—
167C2×C4⋊Dic71C2311yescharacteristic
168C2×C4⋊Dic71C2311yescharacteristic
169C2×C4⋊Dic71C2311yescharacteristic
170C2×C4⋊Dic71C2314yes—
171C2×C4⋊Dic71C2314yes—
172C2×C4⋊Dic71C2314yes—
173C2×C4⋊Dic71C2311yescharacteristic
174C2×Dic71⋊C4C2314yes—
175C2×Dic71⋊C4C2312yes—
176C2×Dic71⋊C4C2312yes—
177C2×Dic71⋊C4C2314yes—
178C2×Dic71⋊C4C2314yes—
179C2×Dic71⋊C4C2314yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2312yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C4⋊C4×D71C23132yes—
186C4⋊C4×D71C23132yes—
187C4⋊C4×D71C23116yes—
188C4⋊C4×D71C23116yes—
189C4⋊C4×D71C23116yes—
190C2×C22⋊Dic71C2312yes—
191C2×C22⋊Dic71C2312yes—
192C2×(C2×D71)⋊C4C2312yes—
193C2×(C2×D71)⋊C4C2312yes—
194C2×(C2×D71)⋊C4C2314yes—
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×C4×Dic71C2312yes—
202C2×C4×Dic71C2312yes—
203C2×C4×Dic71C2312yes—
204C2×C4×Dic71C2314yes—
205C2×C4×Dic71C2312yes—
206C42×D71C23116yes—
207C22×Q8×C71C2312yes—
208C22×Q8×C71C2312yes—
209C23×C4×C71C2311yescharacteristic
210C23×C4×C71C2311yescharacteristic
211C23×C4×C71C2311yescharacteristic
212C4⋊Q8×C71C2318yes—
213C4⋊Q8×C71C2318yes—
214#125×C71C23116yes—
215C22⋊Q8×C71C23116yes—
216C22⋊Q8×C71C23116yes—
217C4×Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219#117×C71C23116yes—
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2314yes—
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2312yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2314yes—
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2318yes—
232C2×C42×C71C2314yes—
233C23×D71C2412yes—
234C23×D71C2412yes—
235#11765866—264no—
236#11765865—232no—
237C2×Dic142—24no—
238C2×Dic142—24no—
239C2×Dic142C2414yes—
240C2×Dic142C2414yes—
241C2×D284—216no—
242C2×D284—24no—
243C2×D284#4118yes—
244C2×D284C24116yes—
245C2×D284C2414yes—
246C2×D284C2414yes—
247C2×C22⋊D71—28no—
248C2×C22⋊D71—44no—
249C2×C22⋊D71C2418yes—
250C2×C22⋊D71C2418yes—
251C22×Dic71C2412yes—
252C22×Dic71C2412yes—
253C22×Dic71C2412yes—
254C22×Dic71C2412yes—
255C22×Dic71C2412yes—
256C22×Dic71C2412yes—
257C2×C4×D71—28no—
258C2×C4×D71—216no—
259C2×C4×D71—28no—
260C2×C4×D71—28no—
261C2×C4×D71—44no—
262C2×C4×D71—48no—
263C2×C4×D71—48no—
264C2×C4×D71C2418yes—
265C2×C4×D71C24116yes—
266C2×C4×D71C2418yes—
267C2×C4×D71C2418yes—
268C2×C4×D71C2418yes—
269C2×C4×D71C24116yes—
270C2×C4×D71C24116yes—
271C4⋊Dic71C2414yes—
272C4⋊Dic71C2414yes—
273C4⋊Dic71C2414yes—
274C4⋊Dic71C24116yes—
275C4⋊Dic71C24116yes—
276C4⋊Dic71C24116yes—
277C4⋊Dic71C2414yes—
278Dic71⋊C4C24116yes—
279Dic71⋊C4C2418yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C24116yes—
282Dic71⋊C4C24116yes—
283Dic71⋊C4C24116yes—
284Dic71⋊C4C2418yes—
285Dic71⋊C4C2418yes—
286Dic71⋊C4C2418yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C2418yes—
289C22⋊Dic71C2418yes—
290C22⋊Dic71C2418yes—
291(C2×D71)⋊C4C2418yes—
292(C2×D71)⋊C4C2418yes—
293(C2×D71)⋊C4C24116yes—
294(C2×D71)⋊C4C2418yes—
295(C2×D71)⋊C4C2418yes—
296(C2×D71)⋊C4C2418yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C24116yes—
299(C2×D71)⋊C4C2418yes—
300C4×Dic71C2418yes—
301C4×Dic71C2418yes—
302C4×Dic71C2418yes—
303C4×Dic71C24116yes—
304C4×Dic71C2418yes—
305C24×C71C2411yescharacteristic
306C2×Q8×C71—28no—
307C2×Q8×C71—44no—
308C2×Q8×C71C2418yes—
309C2×Q8×C71C2418yes—
310C22×C4×C71—24no—
311C22×C4×C71—24no—
312C22×C4×C71—42no—
313C22×C4×C71C2411yescharacteristic
314C22×C4×C71C2411yescharacteristic
315C22×C4×C71C2414yes—
316C22×C4×C71C2414yes—
317C22×C4×C71C2414yes—
318C22×C4×C71C2411yescharacteristic
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2414yes—
321C22×C4×C71C2414yes—
322C22×C4×C71C2411yescharacteristic
323C22×C4×C71C2411yescharacteristic
324C4⋊C4×C71C2418yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C24116yes—
327C4⋊C4×C71C24116yes—
328C4⋊C4×C71C2418yes—
329C4⋊C4×C71C2418yes—
330C22⋊C4×C71C24116yes—
331C42×C71C2414yes—
332C42×C71C2414yes—
333C42×C71C2414yes—
334C42×C71C2414yes—
335C42×C71C24116yes—
336C23×C71—22no—
337C23×C71—22no—
338C23×C71—22no—
339C23×C71C2512yes—
340C23×C71C2511yescharacteristic
341C22×D71—24no—
342C22×D71—24no—
343C22×D71—24no—
344C22×D71—24no—
345C22×D71—24no—
346C22×D71C2×#4118yes—
347C22×D71C2514yes—
348C22×D71C2514yes—
349Q8×C71—216no—
350Q8×C71—48no—
351C2×C4×C71—22no—
352C2×C4×C71—28no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—28no—
357C2×C4×C71—28no—
358C2×C4×C71—28no—
359C2×C4×C71—44no—
360C2×C4×C71C2×#4114yes—
361C2×C4×C712−1+414yes—
362C2×C4×C71C2512yes—
363C2×C4×C71C2512yes—
364C2×C4×C71C2512yes—
365C2×C4×C71C2512yes—
366C2×C4×C71C2518yes—
367C2×C4×C71C2518yes—
368C2×C4×C71C2512yes—
369C2×C4×C71C2512yes—
370C22⋊D71—216no—
371C22⋊D71—48no—
372C2×Dic71—24no—
373C2×Dic71—24no—
374C2×Dic71—24no—
375C2×Dic71—24no—
376C2×Dic71—24no—
377C2×Dic71—24no—
378C2×Dic71C2514yes—
379C2×Dic71C2514yes—
380C2×Dic71C2514yes—
381C2×Dic71C2514yes—
382C2×Dic71C2514yes—
383C2×Dic71C2514yes—
384D284—232no—
385D284—28no—
386D284C2×#41116yes—
387C4×D71—216no—
388C4×D71—232no—
389C4×D71—216no—
390C4×D71—216no—
391C4×D71—48no—
392C4×D71—416no—
393C4×D71—416no—
394Dic142—28no—
395Dic142—28no—
396C22×C71—22no—
397C22×C71—22no—
398C22×C71—22no—
399C22×C71—44no—
400C22×C71C22×#4112yes—
401C22×C71C2×2−1+412yes—
402C22×C71#58512yes—
403C22×C71C2611yescharacteristic
404C2×D71—24no—
405C2×D71—24no—
406C2×D71—216no—
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—48no—
411C2×D71C22×#4118yes—
412C4×C71—22no—
413C4×C71—28no—
414C4×C71—22no—
415C4×C71—22no—
416C4×C71—28no—
417C4×C71—22no—
418C4×C71C22×#4114yes—
419C4×C71C2×2−1+414yes—
420Dic71—24no—
421Dic71—24no—
422Dic71—24no—
423Dic71—24no—
424Dic71—24no—
425Dic71—24no—
426C2×#3515—711nomaximal, Sylow
427C2×C71—42no—
428C2×C71#351514yescomplemented
429C2×C71C23×#4111yescharacteristic
430C2×C71C22×2−1+411yescharacteristic
431C2×C71C2×#58511yescharacteristic
432D71—28no—
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—711no—
443C2×#547—712no—
444C2×#541—712no—
445C2×#539—714no—
446C2×#533D7111yescharacteristic, complemented
447C2×#529—711no—
448C2×#529—712no—
449C22×#125—712no—
450C2×#520—712no—
451C2×C4×#41—711no—
452C71C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—712no—
454C22×#41—711no—
455#557—7116no—
456#554—7116no—
457#554—7116no—
458#553—7132no—
459#552—7132no—
460#552—7164no—
461#552—7132no—
462#547—7116no—
463#547—7132no—
464#541—7132no—
465#539—7164no—
466#533C2×D71116yescomplemented
467C2×C4⋊Q8—712no—
468C2×C4⋊Q8C2×D7111yescharacteristic
469C2×C4⋊Q8C2×D7111yescharacteristic
470#529—7132no—
471#529—7116no—
472C2×#126—714no—
473C2×#126—714no—
474C2×#126—712no—
475C2×#126—714no—
476C2×#125—7132no—
477C2×#125—714no—
478C2×#125—714no—
479C2×#125—712no—
480C2×#125—712no—
481C2×#125—714no—
482C2×#125—712no—
483C2×#125—711no—
484C2×#125—714no—
485C2×#125C2×D7112yes—
486C2×#124—711no—
487C2×#123—712no—
488C2×#123—714no—
489C2×#123—714no—
490C2×#123—714no—
491C2×#123—714no—
492C2×C22⋊Q8—714no—
493C2×C22⋊Q8—714no—
494C2×C22⋊Q8—712no—
495C2×C22⋊Q8—711no—
496C2×C22⋊Q8—712no—
497C2×C22⋊Q8—712no—
498C2×C22⋊Q8C2×D7112yes—
499C2×C22⋊Q8C2×D7112yes—
500C2×#121—711no—
501C2×#121—712no—
502C2×#121—714no—
503#520—7132no—
504C4×#41—7116no—
505C2×C4×Q8—712no—
506C2×C4×Q8—712no—
507C2×C4×Q8—711no—
508C2×C4×Q8—711no—
509C2×C4×Q8—711no—
510C2×C4×Q8C2×D7112yes—
511C2×C4×Q8C2×D7112yes—
512C2×C4×D4—712no—
513C2×C4×D4—712no—
514C2×C4×D4—712no—
515C2×C4×D4—714no—
516C2×C4×D4—712no—
517C2×C4×D4—712no—
518C2×C4×D4—711no—
519C2×C4×D4—711no—
520C2×C4×D4—714no—
521C2×C4×D4—711no—
522C2×#117—711no—
523C2×#117—714no—
524C2×#117—712no—
525C2×#117—712no—
526C2×#117—714no—
527C2×#117C2×D7112yes—
528C22×C4⋊C4—714no—
529C22×C4⋊C4—712no—
530C22×C4⋊C4—712no—
531C22×C4⋊C4—714no—
532C22×C4⋊C4—712no—
533C22×C42—712no—
534C22×C42C2×D7111yescharacteristic
535C2×#41—7116no—
536C2×#41—718no—
537C2×#41—1428no—
538C2×#41—14216no—
539C22×Q8—711no—
540C22×Q8—711no—
541C22×Q8C22×D7112yes—
542C22×Q8C22×D7112yes—
543C22×D4—712no—
544C22×D4—712no—
545C22×D4—711no—
546C22×D4—711no—
547C22×D4—714no—
548C23×C4—714no—
549C23×C4—712no—
550C23×C4—714no—
551C23×C4—714no—
552C23×C4—712no—
553C23×C4—712no—
554C23×C4—712no—
555C23×C4C22×D7111yescharacteristic
556C23×C4C22×D7111yescharacteristic
557C23×C4C22×D7111yescharacteristic
558C4⋊Q8—7116no—
559C4⋊Q8C22×D7118yes—
560C4⋊Q8C22×D7118yes—
561#126—7132no—
562#126—7132no—
563#126—7116no—
564#126—7132no—
565#125—7132no—
566#125—7132no—
567#125—7116no—
568#125—7116no—
569#125—7132no—
570#125—7116no—
571#125—718no—
572#125—7132no—
573#125C22×D71116yes—
574#124—718no—
575#123—7116no—
576#123—7132no—
577#123—7132no—
578#123—7132no—
579#123—7132no—
580C22⋊Q8—7132no—
581C22⋊Q8—7132no—
582C22⋊Q8—7116no—
583C22⋊Q8—718no—
584C22⋊Q8—7116no—
585C22⋊Q8—7116no—
586C22⋊Q8C22×D71116yes—
587C22⋊Q8C22×D71116yes—
588#121—718no—
589#121—7116no—
590#121—7132no—
591C4×Q8—7116no—
592C4×Q8—7116no—
593C4×Q8—718no—
594C4×Q8—718no—
595C4×Q8—718no—
596C4×Q8C22×D71116yes—
597C4×Q8C22×D71116yes—
598C4×D4—7116no—
599C4×D4—7116no—
600C4×D4—7116no—
601C4×D4—7132no—
602C4×D4—7116no—
603C4×D4—7116no—
604C4×D4—718no—
605C4×D4—718no—
606C4×D4—7132no—
607C4×D4—718no—
608#117—718no—
609#117—7132no—
610#117—7116no—
611#117—7116no—
612#117—7132no—
613#117C22×D71116yes—
614C2×C4⋊C4—711no—
615C2×C4⋊C4—714no—
616C2×C4⋊C4—712no—
617C2×C4⋊C4—711no—
618C2×C4⋊C4—712no—
619C2×C4⋊C4—711no—
620C2×C4⋊C4—714no—
621C2×C4⋊C4—714no—
622C2×C4⋊C4—714no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—712no—
626C2×C4⋊C4—712no—
627C2×C4⋊C4—711no—
628C2×C4⋊C4—712no—
629C2×C4⋊C4—714no—
630C2×C4⋊C4—712no—
631C2×C4⋊C4—714no—
632C2×C4⋊C4—7132no—
633C2×C4⋊C4—7116no—
634C2×C4⋊C4—7132no—
635C2×C4⋊C4—7116no—
636C2×C4⋊C4—7116no—
637C2×C4⋊C4C22×D7114yes—
638C2×C4⋊C4C22×D7112yes—
639C2×C4⋊C4C22×D7112yes—
640C2×C4⋊C4C22×D7112yes—
641C2×C4⋊C4C22×D7114yes—
642C2×C4⋊C4C22×D7112yes—
643C2×C22⋊C4—712no—
644C2×C22⋊C4—712no—
645C2×C22⋊C4—712no—
646C2×C22⋊C4—712no—
647C2×C22⋊C4—712no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4—712no—
650C2×C22⋊C4—712no—
651C2×C22⋊C4—714no—
652C2×C22⋊C4—714no—
653C2×C22⋊C4—712no—
654C2×C22⋊C4C22×D7114yes—
655C2×C42—712no—
656C2×C42—714no—
657C2×C42—712no—
658C2×C42—712no—
659C2×C42—712no—
660C2×C42—7116no—
661C2×C42C22×D7111yescharacteristic
662C2×C42C22×D7111yescharacteristic
663C2×C42C22×D7114yes—
664C2×C42C22×D7111yescharacteristic
665C2×C42C22×D7118yes—
666C2×C42C22×D7111yescharacteristic
667C24—712no—
668C24—712no—
669C24C23×D7111yescharacteristic
670#41—14232no—
671#41—14264no—
672C2×Q8—28no—
673C2×Q8—44no—
674C2×Q8—714no—
675C2×Q8—714no—
676C2×Q8—1424no—
677C2×Q8—1424no—
678C2×Q8C23×D7118yes—
679C2×Q8C23×D7118yes—
680C2×D4—2844no—
681C2×D4—718no—
682C2×D4—718no—
683C2×D4—718no—
684C2×D4—714no—
685C2×D4—714no—
686C2×D4—7116no—
687C2×D4—14216no—
688C2×D4—1428no—
689C2×D4—1424no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—42no—
693C22×C4—2844no—
694C22×C4—2848no—
695C22×C4—2848no—
696C22×C4—718no—
697C22×C4—7116no—
698C22×C4—7116no—
699C22×C4—712no—
700C22×C4—712no—
701C22×C4—712no—
702C22×C4—712no—
703C22×C4—712no—
704C22×C4—712no—
705C22×C4—718no—
706C22×C4—718no—
707C22×C4—7116no—
708C22×C4—718no—
709C22×C4—1428no—
710C22×C4—14216no—
711C22×C4—1428no—
712C22×C4—1428no—
713C22×C4C23×D7114yes—
714C22×C4C23×D7114yes—
715C22×C4C23×D7111yescharacteristic
716C22×C4C23×D7111yescharacteristic
717C22×C4C23×D7114yes—
718C22×C4C23×D7111yescharacteristic
719C22×C4C23×D7111yescharacteristic
720C22×C4C23×D7114yes—
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—718no—
731C4⋊C4—718no—
732C4⋊C4—718no—
733C4⋊C4—718no—
734C4⋊C4—7116no—
735C4⋊C4—714no—
736C4⋊C4—714no—
737C4⋊C4—714no—
738C4⋊C4—7116no—
739C4⋊C4—7116no—
740C4⋊C4—714no—
741C4⋊C4—7116no—
742C4⋊C4C23×D71116yes—
743C4⋊C4C23×D7118yes—
744C4⋊C4C23×D7118yes—
745C4⋊C4C23×D7118yes—
746C4⋊C4C23×D71116yes—
747C4⋊C4C23×D7118yes—
748C22⋊C4—718no—
749C22⋊C4—718no—
750C22⋊C4—718no—
751C22⋊C4—718no—
752C22⋊C4—718no—
753C22⋊C4—7116no—
754C22⋊C4—718no—
755C22⋊C4—718no—
756C22⋊C4—7116no—
757C22⋊C4—7116no—
758C22⋊C4—718no—
759C22⋊C4C23×D71116yes—
760C42—718no—
761C42—718no—
762C42—718no—
763C42—7116no—
764C42—718no—
765C42C23×D7114yes—
766C42C23×D7114yes—
767C42C23×D7114yes—
768C42C23×D7114yes—
769C42C23×D71116yes—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—718no—
774C23—714no—
775C23—714no—
776C23—1424no—
777C23—1424no—
778C23—1424no—
779C23—1424no—
780C23—1424no—
781C23C24×D7112yes—
782C23C24×D7111yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—1428no—
786Q8—1428no—
787D4—2848no—
788D4—7116no—
789D4—14232no—
790D4—14216no—
791D4—1428no—
792C2×C4—22no—
793C2×C4—28no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—28no—
798C2×C4—28no—
799C2×C4—28no—
800C2×C4—44no—
801C2×C4—2848no—
802C2×C4—28416no—
803C2×C4—28416no—
804C2×C4—714no—
805C2×C4—714no—
806C2×C4—714no—
807C2×C4—714no—
808C2×C4—714no—
809C2×C4—714no—
810C2×C4—14216no—
811C2×C4—14232no—
812C2×C4—1424no—
813C2×C4—1424no—
814C2×C4—1424no—
815C2×C4—1424no—
816C2×C4—1424no—
817C2×C4—1424no—
818C2×C4—14216no—
819C2×C4—14216no—
820C2×C4#41×D7114yes—
821C2×C4#1455617614yes—
822C2×C4C24×D7112yes—
823C2×C4C24×D7112yes—
824C2×C4C24×D7118yes—
825C2×C4C24×D7112yes—
826C2×C4C24×D7112yes—
827C2×C4C24×D7118yes—
828C2×C4C24×D7112yes—
829C2×C4C24×D7112yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—2848no—
835C22—718no—
836C22—1424no—
837C22—1424no—
838C22—1424no—
839C22—14216no—
840C22—1424no—
841C22—1424no—
842C22C2×#41×D7112yes—
843C22C2×#1455617612yes—
844C22#1798683512yes—
845C22C25×D7111yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—1424no—
853C4—1424no—
854C4—1424no—
855C4—1424no—
856C4—1424no—
857C4—1424no—
858C4C2×#41×D7114yes—
859C4C2×#1455617614yes—
860C2—42no—
861C2—2844no—
862C2—1428no—
863C2#2260231314yesdirect product factor
864C2C22×#41×D7111yescharacteristic
865C2C22×#1455617611yescharacteristic
866C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#533×C71C2
socleC23×C71C25
hypercenterC2×#533D71
hypocenterC71C2×#3515
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22602313C2direct (N × H)
2. C2×#17986724C2semidirect
3. C2×#17986710C2semidirect
4. C2×#17986710C2semidirect
5. C2×#17986693C2semidirect
6. C2×#17986690C2semidirect
7. C2×#17986688C2semidirect
8. C2×#17986683C2semidirect
9. C2×#17986652C2semidirect
10. C2×#17986651C2semidirect
11. C2×#17986607C2semidirect
12. C2×#17986595C2semidirect
13. C2×#17986534C2semidirect
14. C2×#17986533C2semidirect
15. C2×#125×D71C2semidirect
16. C2×#17986481C2semidirect
17. C2×C4×#11765865C2semidirect
18. C2×#533×C71C2semidirect
21. #17986724C22semidirect
22. #17986710C22semidirect
23. #17986710C22semidirect
24. #17986693C22semidirect
25. #17986690C22semidirect
26. #17986688C22semidirect
27. #17986683C22semidirect
28. #17986652C22semidirect
29. #17986651C22semidirect
30. #17986607C22semidirect
31. #17986595C22semidirect
33. #17986534C22semidirect
34. #17986533C22semidirect
47. #125×D71C22semidirect
63. #17986481C22semidirect
64. C4×#11765865C22semidirect
91. #533×C71C22semidirect
428. C2×C71#3515semidirect
446. C2×#533D71semidirect
452. C71C2×#3515semidirect
466. #533C2×D71semidirect
863. C2#22602313direct (N × H)

Maximal subgroups

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

subgroupindex
#226023132
C2×#179867242
C2×#179867102
C2×#179866932
C2×#179866902
C2×#179866882
C2×#179866832
C2×#179866522
C2×#179866512
C2×#179866072
C2×#179865952
C2×#179865342
C2×#179865332
C2×#125×D712
C2×#179864812
C2×C4×#117658652
C2×#533×C712
C2×#351571