Finite Group Databasebeta

← C2×#24921443 #36312519

Subgroups — C2×#24921443 #36312519

Order 21248.

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#24921443C2132yesmaximal, direct product factor
2C2×#19128430C211yesmaximal, characteristic, complemented
3C2×#19128411C211yesmaximal, characteristic, complemented
4C2×#19128408C211yesmaximal, characteristic, complemented
5C2×#19128398C212yesmaximal, complemented
6C2×#19128391C212yesmaximal, complemented
7C2×#19128387C214yesmaximal, complemented
8C2×#19128385C212yesmaximal, complemented
9C2×#19128356C212yesmaximal, complemented
10C2×#19128356C211yesmaximal, characteristic, complemented
11C2×#19128313C212yesmaximal, complemented
12C2×#19128294C214yesmaximal, complemented
13C2×#19128258C211yesmaximal, characteristic, complemented
14C2×#19128230C212yesmaximal, complemented
15C2×#125×D83C212yesmaximal, complemented
16C2×#19128181C212yesmaximal, complemented
17C2×C4×#13050590C211yesmaximal, characteristic, complemented
18C2×#529×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2211yescharacteristic
20C22×#13050590C2212yes—
21#19128430C22116yescomplemented
22#19128411C22116yescomplemented
23#19128408C22116yescomplemented
24#19128398C22132yescomplemented
25#19128391C22132yescomplemented
26#19128387C22164yescomplemented
27#19128385C22132yescomplemented
28#19128356C22116yescomplemented
29#19128356C22132yescomplemented
30#19128313C22132yescomplemented
31#19128294C22164yescomplemented
32#19128258C22116yescomplemented
33C2×#14581792C2211yescharacteristic
34C2×#14581792C2212yes—
35C2×#14581792C2211yescharacteristic
36#19128230C22132yescomplemented
37C2×#14581785C2214yes—
38C2×#14581785C2214yes—
39C2×#14581785C2214yes—
40C2×#14581784C2212yes—
41C2×#14581784C2212yes—
42C2×#14581783C2212yes—
43C2×#14581783C2212yes—
44C2×#14581783C2214yes—
45C2×#14581782C2214yes—
46C2×#14581782C2214yes—
47C2×#14581782C2214yes—
48#125×D83C22132yescomplemented
49C2×#14581774C2214yes—
50C2×#14581774C2214yes—
51C2×#14581774C2214yes—
52C2×#14581773C2214yes—
53C2×#14581771C2212yes—
54C2×#14581771C2212yes—
55C2×#14581771C2212yes—
56C2×#14581771C2212yes—
57C2×#14581770C2214yes—
58C2×#14581769C2214yes—
59C2×#14581768C2212yes—
60C2×#14581763C2212yes—
61C2×#14581763C2214yes—
62#19128181C22132yescomplemented
63C4×#13050590C22116yescomplemented
64C2×Q8×Dic83C2212yes—
65C2×C4×Dic166C2211yescharacteristic
66C2×C4×Dic166C2211yescharacteristic
67C2×C4×Dic166C2212yes—
68C2×C4×Dic166C2212yes—
69C2×C4×Dic166C2212yes—
70C2×C4×D332C2211yescharacteristic
71C2×C4×D332C2211yescharacteristic
72C2×C4×D332C2212yes—
73C2×D4×Dic83C2212yes—
74C2×C4×C22⋊D83C2212yes—
75C2×C4×C22⋊D83C2212yes—
76C2×(C22⋊D83)⋊C4C2214yes—
77C2×(C22⋊D83)⋊C4C2214yes—
78C2×#14581751C2211yescharacteristic
79C2×#14581751C2212yes—
80C2×#14581750C2214yes—
81C2×#14581749C2212yes—
82C2×#14581748C2214yes—
83C22×C4⋊Dic83C2212yes—
84C2×C4⋊C4×D83C2214yes—
85C2×C4⋊C4×D83C2212yes—
86C2×C4⋊C4×D83C2214yes—
87C2×C4⋊C4×D83C2212yes—
88C2×C42×D83C2212yes—
89#529×C83C22116yescomplemented
90C2×#126×C83C2212yes—
91C2×#125×C83C2211yescharacteristic
92C2×#124×C83C2211yescharacteristic
93C2×#123×C83C2212yes—
94C2×C22⋊Q8×C83C2211yescharacteristic
95C2×#121×C83C2211yescharacteristic
96C2×C4×Q8×C83C2211yescharacteristic
97C2×C4×D4×C83C2212yes—
98C2×C4×D4×C83C2211yescharacteristic
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050590—28no—
102C2×#13050590—216no—
103C2×#13050590C2318yes—
104C2×#13050590C23116yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2312yes—
107C22×Dic166C2312yes—
108C22×D332C2311yescharacteristic
109C22×C22⋊D83C2314yes—
110C22×C22⋊D83C2312yes—
111C23×Dic83C2314yes—
112C22×C4×D83C2312yes—
113C22×C4×D83C2312yes—
114C22×C4×D83C2314yes—
115C22×C4×D83C2312yes—
116C22×C4×D83C2314yes—
117#14581792C2318yes—
118#14581792C23116yes—
119#14581792C2318yes—
120#14581785C23132yes—
121#14581785C23132yes—
122#14581785C23132yes—
123#14581784C23116yes—
124#14581784C23116yes—
125#14581783C23116yes—
126#14581783C23132yes—
127#14581783C23116yes—
128#14581782C23132yes—
129#14581782C23132yes—
130#14581782C23132yes—
131#14581774C23132yes—
132#14581774C23132yes—
133#14581774C23132yes—
134#14581773C23132yes—
135#14581771C23116yes—
136#14581771C23116yes—
137#14581771C23116yes—
138#14581771C23116yes—
139#14581770C23132yes—
140#14581769C23132yes—
141#14581768C23116yes—
142#14581763C23116yes—
143#14581763C23132yes—
144Q8×Dic83C23116yes—
145C4×Dic166C23116yes—
146C4×Dic166C23116yes—
147C4×Dic166C2318yes—
148C4×Dic166C2318yes—
149C4×Dic166C23116yes—
150C4×D332C2318yes—
151C4×D332C23116yes—
152C4×D332C2318yes—
153D4×Dic83C23116yes—
154C4×C22⋊D83C23116yes—
155C4×C22⋊D83C23116yes—
156(C22⋊D83)⋊C4C23132yes—
157(C22⋊D83)⋊C4C23132yes—
158#14581751C23116yes—
159#14581751C2318yes—
160#14581750C23132yes—
161#14581749C23116yes—
162#14581748C23132yes—
163C2×C4⋊Dic83C23116yes—
164C2×C4⋊Dic83C2314yes—
165C2×C4⋊Dic83C2312yes—
166C2×C4⋊Dic83C2312yes—
167C2×C4⋊Dic83C2314yes—
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2314yes—
173C2×Dic83⋊C4C2314yes—
174C2×Dic83⋊C4C2314yes—
175C2×Dic83⋊C4C2314yes—
176C2×Dic83⋊C4C2314yes—
177C2×Dic83⋊C4C2314yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C4⋊C4×D83C23116yes—
183C4⋊C4×D83C23132yes—
184C4⋊C4×D83C23116yes—
185C4⋊C4×D83C23132yes—
186C2×C22⋊Dic83C2314yes—
187C2×C22⋊Dic83C2312yes—
188C2×C22⋊Dic83C2314yes—
189C2×C22⋊Dic83C2314yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2314yes—
193C2×C4×Dic83C2312yes—
194C2×C4×Dic83C2312yes—
195C2×C4×Dic83C2312yes—
196C2×C4×Dic83C2314yes—
197C2×C4×Dic83C2314yes—
198C42×D83C23116yes—
199C22×Q8×C83C2311yescharacteristic
200C22×D4×C83C2311yescharacteristic
201C22×D4×C83C2312yes—
202C23×C4×C83C2311yescharacteristic
203C23×C4×C83C2311yescharacteristic
204C23×C4×C83C2312yes—
205C23×C4×C83C2311yescharacteristic
206#126×C83C23116yes—
207#125×C83C2318yes—
208#124×C83C2318yes—
209#123×C83C23116yes—
210C22⋊Q8×C83C2318yes—
211#121×C83C2318yes—
212C4×Q8×C83C2318yes—
213C4×D4×C83C23116yes—
214C4×D4×C83C2318yes—
215#117×C83C23116yes—
216C2×C4⋊C4×C83C2312yes—
217C2×C4⋊C4×C83C2312yes—
218C2×C4⋊C4×C83C2311yescharacteristic
219C2×C4⋊C4×C83C2312yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2312yes—
222C2×C22⋊C4×C83C2312yes—
223C2×C22⋊C4×C83C2312yes—
224C2×C22⋊C4×C83C2312yes—
225C2×C22⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2312yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2318yes—
232C2×C42×C83C2312yes—
233C23×D83C2412yes—
234#13050590—232no—
235#13050590—264no—
236C2×Dic166—24no—
237C2×Dic166—28no—
238C2×Dic166—44no—
239C2×Dic166C2418yes—
240C2×Dic166C2414yes—
241C2×Dic166C2418yes—
242C2×D332#4118yes—
243C2×D332C2414yes—
244C2×C22⋊D83—216no—
245C2×C22⋊D83—28no—
246C2×C22⋊D83C24116yes—
247C2×C22⋊D83C2418yes—
248C22×Dic83—48no—
249C22×Dic83C2412yes—
250C22×Dic83C2414yes—
251C22×Dic83C2412yes—
252C22×Dic83C2414yes—
253C22×Dic83C2412yes—
254C22×Dic83C24116yes—
255C2×C4×D83—28no—
256C2×C4×D83—216no—
257C2×C4×D83—28no—
258C2×C4×D83—44no—
259C2×C4×D83—48no—
260C2×C4×D83C2418yes—
261C2×C4×D83C2418yes—
262C2×C4×D83C24116yes—
263C2×C4×D83C24116yes—
264C2×C4×D83C2418yes—
265C4⋊Dic83C24116yes—
266C4⋊Dic83C2418yes—
267C4⋊Dic83C2418yes—
268C4⋊Dic83C24116yes—
269C4⋊Dic83C2414yes—
270C4⋊Dic83C2418yes—
271C4⋊Dic83C2418yes—
272C4⋊Dic83C24116yes—
273C4⋊Dic83C2414yes—
274Dic83⋊C4C24116yes—
275Dic83⋊C4C2418yes—
276Dic83⋊C4C24116yes—
277Dic83⋊C4C24116yes—
278Dic83⋊C4C24116yes—
279Dic83⋊C4C24116yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C2418yes—
283C22⋊Dic83C24116yes—
284C22⋊Dic83C24116yes—
285C22⋊Dic83C24116yes—
286C22⋊Dic83C2418yes—
287(C2×D83)⋊C4C24116yes—
288(C2×D83)⋊C4C2418yes—
289(C2×D83)⋊C4C2418yes—
290C4×Dic83C2418yes—
291C4×Dic83C2418yes—
292C4×Dic83C24116yes—
293C4×Dic83C2418yes—
294C4×Dic83C24116yes—
295C24×C83C2412yes—
296C24×C83C2411yescharacteristic
297C2×Q8×C83—24no—
298C2×Q8×C83C2414yes—
299C2×D4×C83—24no—
300C2×D4×C83—44no—
301C2×D4×C83C2414yes—
302C2×D4×C83C2418yes—
303C22×C4×C83—24no—
304C22×C4×C83—28no—
305C22×C4×C83—24no—
306C22×C4×C83—42no—
307C22×C4×C83C2414yes—
308C22×C4×C83C2418yes—
309C22×C4×C83C2411yescharacteristic
310C22×C4×C83C2411yescharacteristic
311C22×C4×C83C2412yes—
312C22×C4×C83C2412yes—
313C22×C4×C83C2411yescharacteristic
314C22×C4×C83C2411yescharacteristic
315C22×C4×C83C2414yes—
316C22×C4×C83C2412yes—
317C22×C4×C83C2414yes—
318C22×C4×C83C2411yescharacteristic
319C22×C4×C83C2411yescharacteristic
320C4⋊C4×C83C2418yes—
321C4⋊C4×C83C2418yes—
322C4⋊C4×C83C2418yes—
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2414yes—
325C4⋊C4×C83C2414yes—
326C22⋊C4×C83C2418yes—
327C22⋊C4×C83C2418yes—
328C22⋊C4×C83C2418yes—
329C22⋊C4×C83C2418yes—
330C22⋊C4×C83C2418yes—
331C42×C83C2414yes—
332C42×C83C2418yes—
333C42×C83C2414yes—
334C42×C83C2414yes—
335C42×C83C2414yes—
336C23×C83—24no—
337C23×C83—22no—
338C23×C83—22no—
339C23×C83—24no—
340C23×C83—22no—
341C23×C83—24no—
342C23×C83C2514yes—
343C23×C83C2512yes—
344C23×C83C2511yescharacteristic
345C22×D83—24no—
346C22×D83—24no—
347C22×D83C2×#4118yes—
348C22×D83C2514yes—
349Q8×C83—28no—
350D4×C83—28no—
351D4×C83—48no—
352C2×C4×C83—22no—
353C2×C4×C83—24no—
354C2×C4×C83—22no—
355C2×C4×C83—24no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—24no—
359C2×C4×C83—28no—
360C2×C4×C83—216no—
361C2×C4×C83—28no—
362C2×C4×C83—44no—
363C2×C4×C83C2×#4114yes—
364C2×C4×C832−1+414yes—
365C2×C4×C83C2512yes—
366C2×C4×C83C2512yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2512yes—
369C2×C4×C83C2514yes—
370C2×C4×C83C2514yes—
371C2×C4×C83C2514yes—
372C2×C4×C83C2512yes—
373C2×C4×C83C2512yes—
374C22⋊D83—232no—
375C22⋊D83—216no—
376C2×Dic83—24no—
377C2×Dic83—28no—
378C2×Dic83—24no—
379C2×Dic83—24no—
380C2×Dic83—28no—
381C2×Dic83—416no—
382C2×Dic83C2514yes—
383C2×Dic83C2514yes—
384C2×Dic83C2514yes—
385C2×Dic83C2518yes—
386C2×Dic83C2518yes—
387D332C2×#41116yes—
388C4×D83—216no—
389C4×D83—232no—
390C4×D83—216no—
391C4×D83—416no—
392C4×D83—48no—
393Dic166—216no—
394Dic166—28no—
395Dic166—48no—
396C22×C83—24no—
397C22×C83—22no—
398C22×C83—22no—
399C22×C83—24no—
400C22×C83—24no—
401C22×C83—22no—
402C22×C83—44no—
403C22×C83—48no—
404C22×C83C22×#4112yes—
405C22×C83C2×2−1+412yes—
406C22×C83#58512yes—
407C22×C83C2611yescharacteristic
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—216no—
411C2×D83C22×#4118yes—
412C4×C83—22no—
413C4×C83—24no—
414C4×C83—22no—
415C4×C83—24no—
416C4×C83—22no—
417C4×C83—22no—
418C4×C83—24no—
419C4×C83C22×#4114yes—
420C4×C83C2×2−1+414yes—
421Dic83—24no—
422Dic83—28no—
423Dic83—24no—
424Dic83—28no—
425Dic83—24no—
426C2×#3515—831nomaximal, Sylow
427C2×C83—42no—
428C2×C83—44no—
429C2×C83#351514yescomplemented
430C2×C83C23×#4111yescharacteristic
431C2×C83C22×2−1+411yescharacteristic
432C2×C83C2×#58511yescharacteristic
433D83—28no—
434#3515—8332no—
435C2×#557—831no—
436C2×#554—831no—
437C2×#554—831no—
438C2×#553—832no—
439C2×#552—834no—
440C2×#552—832no—
441C2×#552—832no—
442C2×#547—831no—
443C2×#547—832no—
444C2×#541—832no—
445C2×#539—834no—
446C2×#533—831no—
447C2×#529—832no—
448C2×#529D8311yescharacteristic, complemented
449C22×#125—832no—
450C2×#520—832no—
451C2×C4×#41—831no—
452C83C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—831no—
454C22×#41—832no—
455#557—8316no—
456#554—8316no—
457#554—8316no—
458#553—8332no—
459#552—8364no—
460#552—8332no—
461#552—8332no—
462#547—8316no—
463#547—8332no—
464#541—8332no—
465#539—8364no—
466#533—8316no—
467C2×C4⋊Q8—831no—
468C2×C4⋊Q8—831no—
469C2×C4⋊Q8—832no—
470#529—8332no—
471#529C2×D83116yescomplemented
472C2×#126—834no—
473C2×#126—834no—
474C2×#126—834no—
475C2×#126C2×D8312yes—
476C2×#125—8332no—
477C2×#125—834no—
478C2×#125—834no—
479C2×#125—832no—
480C2×#125—832no—
481C2×#125—834no—
482C2×#125—834no—
483C2×#125—832no—
484C2×#125—832no—
485C2×#125C2×D8311yescharacteristic
486C2×#124C2×D8311yescharacteristic
487C2×#123—834no—
488C2×#123—834no—
489C2×#123—834no—
490C2×#123—834no—
491C2×#123C2×D8312yes—
492C2×C22⋊Q8—832no—
493C2×C22⋊Q8—832no—
494C2×C22⋊Q8—832no—
495C2×C22⋊Q8—832no—
496C2×C22⋊Q8—832no—
497C2×C22⋊Q8—834no—
498C2×C22⋊Q8—834no—
499C2×C22⋊Q8C2×D8311yescharacteristic
500C2×#121—832no—
501C2×#121—834no—
502C2×#121C2×D8311yescharacteristic
503#520—8332no—
504C4×#41—8316no—
505C2×C4×Q8—832no—
506C2×C4×Q8—831no—
507C2×C4×Q8—831no—
508C2×C4×Q8—832no—
509C2×C4×Q8—832no—
510C2×C4×Q8—832no—
511C2×C4×Q8C2×D8311yescharacteristic
512C2×C4×D4—832no—
513C2×C4×D4—832no—
514C2×C4×D4—832no—
515C2×C4×D4—834no—
516C2×C4×D4—834no—
517C2×C4×D4—831no—
518C2×C4×D4—831no—
519C2×C4×D4—832no—
520C2×C4×D4C2×D8312yes—
521C2×C4×D4C2×D8311yescharacteristic
522C2×#117—831no—
523C2×#117—832no—
524C2×#117—834no—
525C2×#117—834no—
526C2×#117—832no—
527C2×#117C2×D8312yes—
528C22×C4⋊C4—832no—
529C22×C4⋊C4—834no—
530C22×C4⋊C4—832no—
531C22×C4⋊C4—834no—
532C22×C4⋊C4—832no—
533C22×C42—832no—
534C22×C42C2×D8311yescharacteristic
535C2×#41—838no—
536C2×#41—8316no—
537C2×#41—1668no—
538C2×#41—16616no—
539C22×Q8—832no—
540C22×Q8—831no—
541C22×Q8—832no—
542C22×Q8C22×D8311yescharacteristic
543C22×D4—832no—
544C22×D4—834no—
545C22×D4—831no—
546C22×D4C22×D8311yescharacteristic
547C22×D4C22×D8312yes—
548C23×C4—834no—
549C23×C4—834no—
550C23×C4—832no—
551C23×C4—834no—
552C23×C4—832no—
553C23×C4—832no—
554C23×C4C22×D8312yes—
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C4⋊Q8—838no—
559C4⋊Q8—838no—
560C4⋊Q8—8316no—
561#126—8332no—
562#126—8332no—
563#126—8332no—
564#126C22×D83116yes—
565#125—8332no—
566#125—8332no—
567#125—8316no—
568#125—8316no—
569#125—8332no—
570#125—8332no—
571#125—8316no—
572#125—8316no—
573#125C22×D8318yes—
574#124C22×D8318yes—
575#123—8332no—
576#123—8332no—
577#123—8332no—
578#123—8332no—
579#123C22×D83116yes—
580C22⋊Q8—8316no—
581C22⋊Q8—8316no—
582C22⋊Q8—8316no—
583C22⋊Q8—8316no—
584C22⋊Q8—8316no—
585C22⋊Q8—8332no—
586C22⋊Q8—8332no—
587C22⋊Q8C22×D8318yes—
588#121—8316no—
589#121—8332no—
590#121C22×D8318yes—
591C4×Q8—8316no—
592C4×Q8—838no—
593C4×Q8—838no—
594C4×Q8—8316no—
595C4×Q8—8316no—
596C4×Q8—8316no—
597C4×Q8C22×D8318yes—
598C4×D4—8316no—
599C4×D4—8316no—
600C4×D4—8316no—
601C4×D4—8332no—
602C4×D4—8332no—
603C4×D4—838no—
604C4×D4—838no—
605C4×D4—8316no—
606C4×D4C22×D83116yes—
607C4×D4C22×D8318yes—
608#117—838no—
609#117—8316no—
610#117—8332no—
611#117—8332no—
612#117—8316no—
613#117C22×D83116yes—
614C2×C4⋊C4—831no—
615C2×C4⋊C4—834no—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—834no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—8316no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—834no—
626C2×C4⋊C4—834no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—831no—
629C2×C4⋊C4—832no—
630C2×C4⋊C4—834no—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—834no—
633C2×C4⋊C4—8332no—
634C2×C4⋊C4—8316no—
635C2×C4⋊C4—8332no—
636C2×C4⋊C4—8316no—
637C2×C4⋊C4C22×D8312yes—
638C2×C4⋊C4C22×D8311yescharacteristic
639C2×C4⋊C4C22×D8312yes—
640C2×C4⋊C4C22×D8311yescharacteristic
641C2×C4⋊C4C22×D8312yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C22⋊C4—832no—
644C2×C22⋊C4—834no—
645C2×C22⋊C4—834no—
646C2×C22⋊C4—834no—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—832no—
649C2×C22⋊C4—834no—
650C2×C22⋊C4C22×D8312yes—
651C2×C22⋊C4C22×D8312yes—
652C2×C22⋊C4C22×D8312yes—
653C2×C22⋊C4C22×D8312yes—
654C2×C22⋊C4C22×D8312yes—
655C2×C42—832no—
656C2×C42—834no—
657C2×C42—834no—
658C2×C42—832no—
659C2×C42—832no—
660C2×C42—8316no—
661C2×C42C22×D8311yescharacteristic
662C2×C42C22×D8311yescharacteristic
663C2×C42C22×D8312yes—
664C2×C42C22×D8311yescharacteristic
665C2×C42C22×D8318yes—
666C2×C42C22×D8311yescharacteristic
667C24—832no—
668C24C23×D8311yescharacteristic
669C24C23×D8312yes—
670#41—16632no—
671#41—16664no—
672C2×Q8—24no—
673C2×Q8—3324no—
674C2×Q8—838no—
675C2×Q8—834no—
676C2×Q8—838no—
677C2×Q8—1664no—
678C2×Q8—1668no—
679C2×Q8C23×D8314yes—
680C2×D4—24no—
681C2×D4—44no—
682C2×D4—838no—
683C2×D4—8316no—
684C2×D4—838no—
685C2×D4—834no—
686C2×D4—1668no—
687C2×D4—16616no—
688C2×D4C23×D8314yes—
689C2×D4C23×D8318yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—3324no—
695C22×C4—3328no—
696C22×C4—3328no—
697C22×C4—8316no—
698C22×C4—838no—
699C22×C4—8316no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—834no—
703C22×C4—832no—
704C22×C4—834no—
705C22×C4—838no—
706C22×C4—838no—
707C22×C4—8316no—
708C22×C4—16616no—
709C22×C4—1668no—
710C22×C4—1668no—
711C22×C4C23×D8314yes—
712C22×C4C23×D8314yes—
713C22×C4C23×D8318yes—
714C22×C4C23×D8311yescharacteristic
715C22×C4C23×D8311yescharacteristic
716C22×C4C23×D8311yescharacteristic
717C22×C4C23×D8312yes—
718C22×C4C23×D8311yescharacteristic
719C22×C4C23×D8312yes—
720C22×C4C23×D8312yes—
721C22×C4C23×D8314yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C4⋊C4—834no—
725C4⋊C4—8316no—
726C4⋊C4—838no—
727C4⋊C4—838no—
728C4⋊C4—8316no—
729C4⋊C4—838no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—8316no—
733C4⋊C4—8316no—
734C4⋊C4—8316no—
735C4⋊C4—8316no—
736C4⋊C4—838no—
737C4⋊C4—834no—
738C4⋊C4—838no—
739C4⋊C4—8316no—
740C4⋊C4—838no—
741C4⋊C4—8316no—
742C4⋊C4C23×D8318yes—
743C4⋊C4C23×D8314yes—
744C4⋊C4C23×D8318yes—
745C4⋊C4C23×D8314yes—
746C4⋊C4C23×D8318yes—
747C4⋊C4C23×D8318yes—
748C22⋊C4—838no—
749C22⋊C4—8316no—
750C22⋊C4—8316no—
751C22⋊C4—8316no—
752C22⋊C4—838no—
753C22⋊C4—838no—
754C22⋊C4—8316no—
755C22⋊C4C23×D8318yes—
756C22⋊C4C23×D8318yes—
757C22⋊C4C23×D8318yes—
758C22⋊C4C23×D8318yes—
759C22⋊C4C23×D8318yes—
760C42—838no—
761C42—838no—
762C42—838no—
763C42—8316no—
764C42—8316no—
765C42C23×D8314yes—
766C42C23×D8314yes—
767C42C23×D8314yes—
768C42C23×D8314yes—
769C42C23×D8318yes—
770C23—22no—
771C23—24no—
772C23—22no—
773C23—24no—
774C23—22no—
775C23—24no—
776C23—838no—
777C23—834no—
778C23—1664no—
779C23—1664no—
780C23C24×D8312yes—
781C23C24×D8314yes—
782C23C24×D8311yescharacteristic
783Q8—28no—
784Q8—3328no—
785Q8—1668no—
786Q8—16616no—
787D4—28no—
788D4—48no—
789D4—8316no—
790D4—16616no—
791D4—16632no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—216no—
801C2×C4—28no—
802C2×C4—44no—
803C2×C4—3328no—
804C2×C4—33216no—
805C2×C4—33216no—
806C2×C4—834no—
807C2×C4—834no—
808C2×C4—834no—
809C2×C4—838no—
810C2×C4—838no—
811C2×C4—16616no—
812C2×C4—16632no—
813C2×C4—1668no—
814C2×C4—1664no—
815C2×C4—1664no—
816C2×C4—1664no—
817C2×C4—1668no—
818C2×C4—16616no—
819C2×C4#41×D8314yes—
820C2×C4#1458183914yes—
821C2×C4C24×D8312yes—
822C2×C4C24×D8312yes—
823C2×C4C24×D8312yes—
824C2×C4C24×D8314yes—
825C2×C4C24×D8312yes—
826C2×C4C24×D8314yes—
827C2×C4C24×D8314yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—44no—
837C22—48no—
838C22—838no—
839C22—16616no—
840C22—1664no—
841C22—1664no—
842C22C2×#41×D8312yes—
843C22C2×#1458183912yes—
844C22#1912853712yes—
845C22C25×D8311yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—1664no—
854C4—1668no—
855C4—1664no—
856C4—1664no—
857C4—1668no—
858C4C2×#41×D8314yes—
859C4C2×#1458183914yes—
860C2—42no—
861C2—44no—
862C2—1668no—
863C2#2492144314yesdirect product factor
864C2C22×#41×D8311yescharacteristic
865C2C22×#1458183911yescharacteristic
866C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#529×C83C2
socleC23×C83C25
hypercenterC2×#529D83
hypocenterC83C2×#3515
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #24921443C2direct (N × H)
2. C2×#19128430C2semidirect
3. C2×#19128411C2semidirect
4. C2×#19128408C2semidirect
5. C2×#19128398C2semidirect
6. C2×#19128391C2semidirect
7. C2×#19128387C2semidirect
8. C2×#19128385C2semidirect
9. C2×#19128356C2semidirect
10. C2×#19128356C2semidirect
11. C2×#19128313C2semidirect
12. C2×#19128294C2semidirect
13. C2×#19128258C2semidirect
14. C2×#19128230C2semidirect
15. C2×#125×D83C2semidirect
16. C2×#19128181C2semidirect
17. C2×C4×#13050590C2semidirect
18. C2×#529×C83C2semidirect
21. #19128430C22semidirect
22. #19128411C22semidirect
23. #19128408C22semidirect
24. #19128398C22semidirect
25. #19128391C22semidirect
26. #19128387C22semidirect
27. #19128385C22semidirect
28. #19128356C22semidirect
29. #19128356C22semidirect
30. #19128313C22semidirect
31. #19128294C22semidirect
32. #19128258C22semidirect
36. #19128230C22semidirect
48. #125×D83C22semidirect
62. #19128181C22semidirect
63. C4×#13050590C22semidirect
89. #529×C83C22semidirect
429. C2×C83#3515semidirect
448. C2×#529D83semidirect
452. C83C2×#3515semidirect
471. #529C2×D83semidirect
863. C2#24921443direct (N × H)

Maximal subgroups

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

subgroupindex
#249214432
C2×#191284302
C2×#191284112
C2×#191284082
C2×#191283982
C2×#191283912
C2×#191283872
C2×#191283852
C2×#191283562
C2×#191283132
C2×#191282942
C2×#191282582
C2×#191282302
C2×#125×D832
C2×#191281812
C2×C4×#130505902
C2×#529×C832
C2×#351583