Finite Group Databasebeta

← C2×#24921436 #36312509

Subgroups — C2×#24921436 #36312509

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#24921436C2132yesmaximal, direct product factor
2C2×#19128426C211yesmaximal, characteristic, complemented
3C2×#19128412C211yesmaximal, characteristic, complemented
4C2×#19128412C211yesmaximal, characteristic, complemented
5C2×#19128395C212yesmaximal, complemented
6C2×#19128392C214yesmaximal, complemented
7C2×#19128390C212yesmaximal, complemented
8C2×#19128385C212yesmaximal, complemented
9C2×#19128354C211yesmaximal, characteristic, complemented
10C2×#19128353C212yesmaximal, complemented
11C2×#19128309C212yesmaximal, complemented
12C2×#19128297C214yesmaximal, complemented
13C2×#19128236C212yesmaximal, complemented
14C2×#19128235C211yesmaximal, characteristic, complemented
15C2×#125×D83C212yesmaximal, complemented
16C2×#19128183C212yesmaximal, complemented
17C2×C4×#13050590C211yesmaximal, characteristic, complemented
18C2×#533×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×#13050590C2211yescharacteristic
21#19128426C22116yescomplemented
22#19128412C22116yescomplemented
23#19128412C22116yescomplemented
24#19128395C22132yescomplemented
25#19128392C22164yescomplemented
26#19128390C22132yescomplemented
27#19128385C22132yescomplemented
28#19128354C22116yescomplemented
29#19128353C22132yescomplemented
30#19128309C22132yescomplemented
31#19128297C22164yescomplemented
32C2×#14581790C2212yes—
33#19128236C22132yescomplemented
34#19128235C22116yescomplemented
35C2×#14581787C2214yes—
36C2×#14581786C2212yes—
37C2×#14581786C2214yes—
38C2×#14581785C2214yes—
39C2×#14581784C2211yescharacteristic
40C2×#14581784C2214yes—
41C2×#14581783C2212yes—
42C2×#14581783C2212yes—
43C2×#14581783C2212yes—
44C2×#14581782C2214yes—
45C2×#14581782C2214yes—
46C2×#14581782C2214yes—
47#125×D83C22132yescomplemented
48C2×#14581780C2211yescharacteristic
49C2×#14581777C2214yes—
50C2×#14581777C2214yes—
51C2×#14581775C2212yes—
52C2×#14581774C2214yes—
53C2×#14581774C2214yes—
54C2×#14581772C2212yes—
55C2×#14581772C2212yes—
56C2×#14581771C2211yescharacteristic
57C2×#14581768C2212yes—
58C2×#14581768C2214yes—
59C2×#14581768C2214yes—
60C2×#14581767C2212yes—
61C2×#14581766C2211yescharacteristic
62C2×#14581765C2214yes—
63#19128183C22132yescomplemented
64C4×#13050590C22116yescomplemented
65C2×Q8×Dic83C2212yes—
66C2×C4×Dic166C2211yescharacteristic
67C2×C4×Dic166C2211yescharacteristic
68C2×C4×Dic166C2211yescharacteristic
69C2×#14581757C2212yes—
70C2×C4×D332C2211yescharacteristic
71C2×C4×D332C2211yescharacteristic
72C2×C4×D332C2214yes—
73C2×C4×D332C2211yescharacteristic
74C2×#14581754C2212yes—
75C2×#14581754C2214yes—
76C2×#14581754C2212yes—
77C2×C4×C22⋊D83C2212yes—
78C2×C4×C22⋊D83C2212yes—
79C2×C4×C22⋊D83C2212yes—
80C2×#14581751C2211yescharacteristic
81C2×#14581750C2214yes—
82C2×#14581749C2212yes—
83C2×#14581749C2214yes—
84C2×#14581749C2212yes—
85C2×C4⋊C4×D83C2214yes—
86C2×C4⋊C4×D83C2212yes—
87C2×C4⋊C4×D83C2214yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C42×D83C2212yes—
91#533×C83C22116yescomplemented
92C2×C4⋊Q8×C83C2211yescharacteristic
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#125×C83C2212yes—
95C2×C22⋊Q8×C83C2212yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2212yes—
98C2×C4×Q8×C83C2212yes—
99C2×#117×C83C2212yes—
100C22×C42×C83C2211yescharacteristic
101C2×#13050591—216no—
102C2×#13050591C23116yes—
103C2×#13050590—28no—
104C2×#13050590C2318yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2311yescharacteristic
107C22×D332C2311yescharacteristic
108C22×D332C2314yes—
109C22×D332C2311yescharacteristic
110C22×C22⋊D83C2312yes—
111C22×C22⋊D83C2312yes—
112C22×C4×D83C2312yes—
113C22×C4×D83C2312yes—
114C22×C4×D83C2314yes—
115C22×C4×D83C2312yes—
116C22×C4×D83C2312yes—
117C22×C4×D83C2314yes—
118C22×C4×D83C2314yes—
119#14581790C23116yes—
120#14581787C23132yes—
121#14581786C23116yes—
122#14581786C23132yes—
123#14581785C23132yes—
124#14581784C23132yes—
125#14581784C2318yes—
126#14581783C23116yes—
127#14581783C23116yes—
128#14581783C23116yes—
129#14581782C23132yes—
130#14581782C23132yes—
131#14581782C23132yes—
132#14581780C2318yes—
133#14581777C23132yes—
134#14581777C23132yes—
135#14581775C23116yes—
136#14581774C23132yes—
137#14581774C23132yes—
138#14581772C23116yes—
139#14581772C23116yes—
140#14581771C2318yes—
141#14581768C23116yes—
142#14581768C23132yes—
143#14581768C23132yes—
144#14581767C23116yes—
145#14581766C2318yes—
146#14581765C23132yes—
147Q8×Dic83C23116yes—
148C4×Dic166C2318yes—
149C4×Dic166C2318yes—
150C4×Dic166C2318yes—
151#14581757C23116yes—
152C4×D332C2318yes—
153C4×D332C2318yes—
154C4×D332C23132yes—
155C4×D332C2318yes—
156#14581754C23116yes—
157#14581754C23116yes—
158#14581754C23132yes—
159C4×C22⋊D83C23116yes—
160C4×C22⋊D83C23116yes—
161C4×C22⋊D83C23116yes—
162#14581751C2318yes—
163#14581750C23132yes—
164#14581749C23132yes—
165#14581749C23116yes—
166#14581749C23116yes—
167C2×C4⋊Dic83C2311yescharacteristic
168C2×C4⋊Dic83C2311yescharacteristic
169C2×C4⋊Dic83C2311yescharacteristic
170C2×C4⋊Dic83C2314yes—
171C2×C4⋊Dic83C2314yes—
172C2×C4⋊Dic83C2314yes—
173C2×C4⋊Dic83C2311yescharacteristic
174C2×Dic83⋊C4C2314yes—
175C2×Dic83⋊C4C2312yes—
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2314yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C4⋊C4×D83C23132yes—
186C4⋊C4×D83C23116yes—
187C4⋊C4×D83C23116yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C23132yes—
190C2×C22⋊Dic83C2312yes—
191C2×C22⋊Dic83C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×(C2×D83)⋊C4C2314yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2312yes—
203C2×C4×Dic83C2312yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2312yes—
206C42×D83C23116yes—
207C22×Q8×C83C2312yes—
208C22×Q8×C83C2312yes—
209C23×C4×C83C2311yescharacteristic
210C23×C4×C83C2311yescharacteristic
211C23×C4×C83C2311yescharacteristic
212C4⋊Q8×C83C2318yes—
213C4⋊Q8×C83C2318yes—
214#125×C83C23116yes—
215C22⋊Q8×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C4×Q8×C83C23116yes—
218C4×Q8×C83C23116yes—
219#117×C83C23116yes—
220C2×C4⋊C4×C83C2312yes—
221C2×C4⋊C4×C83C2312yes—
222C2×C4⋊C4×C83C2314yes—
223C2×C4⋊C4×C83C2314yes—
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C22⋊C4×C83C2314yes—
227C2×C42×C83C2311yescharacteristic
228C2×C42×C83C2311yescharacteristic
229C2×C42×C83C2311yescharacteristic
230C2×C42×C83C2311yescharacteristic
231C2×C42×C83C2318yes—
232C2×C42×C83C2314yes—
233C23×D83C2412yes—
234C23×D83C2412yes—
235#13050591—264no—
236#13050590—232no—
237C2×Dic166—24no—
238C2×Dic166—24no—
239C2×Dic166C2414yes—
240C2×Dic166C2414yes—
241C2×D332—216no—
242C2×D332—24no—
243C2×D332#4118yes—
244C2×D332C24116yes—
245C2×D332C2414yes—
246C2×D332C2414yes—
247C2×C22⋊D83—28no—
248C2×C22⋊D83—44no—
249C2×C22⋊D83C2418yes—
250C2×C22⋊D83C2418yes—
251C22×Dic83C2412yes—
252C22×Dic83C2412yes—
253C22×Dic83C2412yes—
254C22×Dic83C2412yes—
255C22×Dic83C2412yes—
256C22×Dic83C2412yes—
257C2×C4×D83—28no—
258C2×C4×D83—216no—
259C2×C4×D83—28no—
260C2×C4×D83—28no—
261C2×C4×D83—44no—
262C2×C4×D83—48no—
263C2×C4×D83—48no—
264C2×C4×D83C2418yes—
265C2×C4×D83C2418yes—
266C2×C4×D83C24116yes—
267C2×C4×D83C2418yes—
268C2×C4×D83C24116yes—
269C2×C4×D83C24116yes—
270C2×C4×D83C2418yes—
271C4⋊Dic83C2414yes—
272C4⋊Dic83C2414yes—
273C4⋊Dic83C24116yes—
274C4⋊Dic83C24116yes—
275C4⋊Dic83C2414yes—
276C4⋊Dic83C24116yes—
277C4⋊Dic83C2414yes—
278Dic83⋊C4C24116yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C2418yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289C22⋊Dic83C2418yes—
290C22⋊Dic83C2418yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C2418yes—
296(C2×D83)⋊C4C24116yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C2418yes—
300C4×Dic83C2418yes—
301C4×Dic83C2418yes—
302C4×Dic83C24116yes—
303C4×Dic83C2418yes—
304C4×Dic83C2418yes—
305C24×C83C2411yescharacteristic
306C2×Q8×C83—28no—
307C2×Q8×C83—44no—
308C2×Q8×C83C2418yes—
309C2×Q8×C83C2418yes—
310C22×C4×C83—24no—
311C22×C4×C83—24no—
312C22×C4×C83—42no—
313C22×C4×C83C2414yes—
314C22×C4×C83C2411yescharacteristic
315C22×C4×C83C2411yescharacteristic
316C22×C4×C83C2414yes—
317C22×C4×C83C2414yes—
318C22×C4×C83C2414yes—
319C22×C4×C83C2411yescharacteristic
320C22×C4×C83C2411yescharacteristic
321C22×C4×C83C2414yes—
322C22×C4×C83C2411yescharacteristic
323C22×C4×C83C2411yescharacteristic
324C4⋊C4×C83C2418yes—
325C4⋊C4×C83C2418yes—
326C4⋊C4×C83C2418yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C24116yes—
329C4⋊C4×C83C24116yes—
330C22⋊C4×C83C24116yes—
331C42×C83C2414yes—
332C42×C83C24116yes—
333C42×C83C2414yes—
334C42×C83C2414yes—
335C42×C83C2414yes—
336C23×C83—22no—
337C23×C83—22no—
338C23×C83—22no—
339C23×C83C2512yes—
340C23×C83C2511yescharacteristic
341C22×D83—24no—
342C22×D83—24no—
343C22×D83—24no—
344C22×D83—24no—
345C22×D83—24no—
346C22×D83C2×#4118yes—
347C22×D83C2514yes—
348C22×D83C2514yes—
349Q8×C83—216no—
350Q8×C83—48no—
351C2×C4×C83—22no—
352C2×C4×C83—28no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—28no—
357C2×C4×C83—28no—
358C2×C4×C83—28no—
359C2×C4×C83—44no—
360C2×C4×C83C2×#4114yes—
361C2×C4×C832−1+414yes—
362C2×C4×C83C2512yes—
363C2×C4×C83C2512yes—
364C2×C4×C83C2512yes—
365C2×C4×C83C2512yes—
366C2×C4×C83C2518yes—
367C2×C4×C83C2518yes—
368C2×C4×C83C2512yes—
369C2×C4×C83C2512yes—
370C22⋊D83—216no—
371C22⋊D83—48no—
372C2×Dic83—24no—
373C2×Dic83—24no—
374C2×Dic83—24no—
375C2×Dic83—24no—
376C2×Dic83—24no—
377C2×Dic83—24no—
378C2×Dic83C2514yes—
379C2×Dic83C2514yes—
380C2×Dic83C2514yes—
381C2×Dic83C2514yes—
382C2×Dic83C2514yes—
383C2×Dic83C2514yes—
384D332—232no—
385D332—28no—
386D332C2×#41116yes—
387C4×D83—216no—
388C4×D83—232no—
389C4×D83—216no—
390C4×D83—216no—
391C4×D83—48no—
392C4×D83—416no—
393C4×D83—416no—
394Dic166—28no—
395Dic166—28no—
396C22×C83—22no—
397C22×C83—22no—
398C22×C83—22no—
399C22×C83—44no—
400C22×C83C22×#4112yes—
401C22×C83C2×2−1+412yes—
402C22×C83#58512yes—
403C22×C83C2611yescharacteristic
404C2×D83—24no—
405C2×D83—24no—
406C2×D83—216no—
407C2×D83—24no—
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—48no—
411C2×D83C22×#4118yes—
412C4×C83—22no—
413C4×C83—28no—
414C4×C83—22no—
415C4×C83—22no—
416C4×C83—28no—
417C4×C83—22no—
418C4×C83C22×#4114yes—
419C4×C83C2×2−1+414yes—
420Dic83—24no—
421Dic83—24no—
422Dic83—24no—
423Dic83—24no—
424Dic83—24no—
425Dic83—24no—
426C2×#3515—831nomaximal, Sylow
427C2×C83—42no—
428C2×C83#351514yescomplemented
429C2×C83C23×#4111yescharacteristic
430C2×C83C22×2−1+411yescharacteristic
431C2×C83C2×#58511yescharacteristic
432D83—28no—
433D83—44no—
434#3515—8332no—
435C2×#557—831no—
436C2×#554—831no—
437C2×#554—831no—
438C2×#553—832no—
439C2×#552—832no—
440C2×#552—834no—
441C2×#552—832no—
442C2×#547—831no—
443C2×#547—832no—
444C2×#541—832no—
445C2×#539—834no—
446C2×#533D8311yescharacteristic, complemented
447C2×#529—831no—
448C2×#529—832no—
449C22×#125—832no—
450C2×#520—832no—
451C2×C4×#41—831no—
452C83C2×#351511yescharacteristic, complemented, Sylow
453C22×#41—832no—
454C22×#41—831no—
455#557—8316no—
456#554—8316no—
457#554—8316no—
458#553—8332no—
459#552—8332no—
460#552—8364no—
461#552—8332no—
462#547—8316no—
463#547—8332no—
464#541—8332no—
465#539—8364no—
466#533C2×D83116yescomplemented
467C2×C4⋊Q8—832no—
468C2×C4⋊Q8C2×D8311yescharacteristic
469C2×C4⋊Q8C2×D8311yescharacteristic
470#529—8332no—
471#529—8316no—
472C2×#126—834no—
473C2×#126—834no—
474C2×#126—832no—
475C2×#126—834no—
476C2×#125—8332no—
477C2×#125—834no—
478C2×#125—834no—
479C2×#125—832no—
480C2×#125—832no—
481C2×#125—834no—
482C2×#125—832no—
483C2×#125—831no—
484C2×#125—834no—
485C2×#125C2×D8312yes—
486C2×#124—831no—
487C2×#123—832no—
488C2×#123—834no—
489C2×#123—834no—
490C2×#123—834no—
491C2×#123—834no—
492C2×C22⋊Q8—834no—
493C2×C22⋊Q8—834no—
494C2×C22⋊Q8—832no—
495C2×C22⋊Q8—831no—
496C2×C22⋊Q8—832no—
497C2×C22⋊Q8—832no—
498C2×C22⋊Q8C2×D8312yes—
499C2×C22⋊Q8C2×D8312yes—
500C2×#121—831no—
501C2×#121—832no—
502C2×#121—834no—
503#520—8332no—
504C4×#41—8316no—
505C2×C4×Q8—832no—
506C2×C4×Q8—832no—
507C2×C4×Q8—831no—
508C2×C4×Q8—831no—
509C2×C4×Q8—831no—
510C2×C4×Q8C2×D8312yes—
511C2×C4×Q8C2×D8312yes—
512C2×C4×D4—832no—
513C2×C4×D4—832no—
514C2×C4×D4—832no—
515C2×C4×D4—834no—
516C2×C4×D4—832no—
517C2×C4×D4—832no—
518C2×C4×D4—831no—
519C2×C4×D4—831no—
520C2×C4×D4—834no—
521C2×C4×D4—831no—
522C2×#117—831no—
523C2×#117—834no—
524C2×#117—832no—
525C2×#117—832no—
526C2×#117—834no—
527C2×#117C2×D8312yes—
528C22×C4⋊C4—834no—
529C22×C4⋊C4—832no—
530C22×C4⋊C4—832no—
531C22×C4⋊C4—834no—
532C22×C4⋊C4—832no—
533C22×C42—832no—
534C22×C42C2×D8311yescharacteristic
535C2×#41—8316no—
536C2×#41—838no—
537C2×#41—1668no—
538C2×#41—16616no—
539C22×Q8—831no—
540C22×Q8—831no—
541C22×Q8C22×D8312yes—
542C22×Q8C22×D8312yes—
543C22×D4—832no—
544C22×D4—832no—
545C22×D4—831no—
546C22×D4—831no—
547C22×D4—834no—
548C23×C4—834no—
549C23×C4—832no—
550C23×C4—834no—
551C23×C4—834no—
552C23×C4—832no—
553C23×C4—832no—
554C23×C4—832no—
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C4⋊Q8—8316no—
559C4⋊Q8C22×D8318yes—
560C4⋊Q8C22×D8318yes—
561#126—8332no—
562#126—8332no—
563#126—8316no—
564#126—8332no—
565#125—8332no—
566#125—8332no—
567#125—8316no—
568#125—8316no—
569#125—8332no—
570#125—8316no—
571#125—838no—
572#125—8332no—
573#125C22×D83116yes—
574#124—838no—
575#123—8316no—
576#123—8332no—
577#123—8332no—
578#123—8332no—
579#123—8332no—
580C22⋊Q8—8332no—
581C22⋊Q8—8332no—
582C22⋊Q8—8316no—
583C22⋊Q8—838no—
584C22⋊Q8—8316no—
585C22⋊Q8—8316no—
586C22⋊Q8C22×D83116yes—
587C22⋊Q8C22×D83116yes—
588#121—838no—
589#121—8316no—
590#121—8332no—
591C4×Q8—8316no—
592C4×Q8—8316no—
593C4×Q8—838no—
594C4×Q8—838no—
595C4×Q8—838no—
596C4×Q8C22×D83116yes—
597C4×Q8C22×D83116yes—
598C4×D4—8316no—
599C4×D4—8316no—
600C4×D4—8316no—
601C4×D4—8332no—
602C4×D4—8316no—
603C4×D4—8316no—
604C4×D4—838no—
605C4×D4—838no—
606C4×D4—8332no—
607C4×D4—838no—
608#117—838no—
609#117—8332no—
610#117—8316no—
611#117—8316no—
612#117—8332no—
613#117C22×D83116yes—
614C2×C4⋊C4—831no—
615C2×C4⋊C4—834no—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—831no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—831no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—832no—
626C2×C4⋊C4—832no—
627C2×C4⋊C4—831no—
628C2×C4⋊C4—832no—
629C2×C4⋊C4—834no—
630C2×C4⋊C4—832no—
631C2×C4⋊C4—834no—
632C2×C4⋊C4—8332no—
633C2×C4⋊C4—8316no—
634C2×C4⋊C4—8316no—
635C2×C4⋊C4—8332no—
636C2×C4⋊C4—8316no—
637C2×C4⋊C4C22×D8314yes—
638C2×C4⋊C4C22×D8312yes—
639C2×C4⋊C4C22×D8312yes—
640C2×C4⋊C4C22×D8312yes—
641C2×C4⋊C4C22×D8314yes—
642C2×C4⋊C4C22×D8312yes—
643C2×C22⋊C4—832no—
644C2×C22⋊C4—832no—
645C2×C22⋊C4—832no—
646C2×C22⋊C4—832no—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—834no—
649C2×C22⋊C4—832no—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—834no—
652C2×C22⋊C4—834no—
653C2×C22⋊C4—832no—
654C2×C22⋊C4C22×D8314yes—
655C2×C42—832no—
656C2×C42—834no—
657C2×C42—832no—
658C2×C42—832no—
659C2×C42—832no—
660C2×C42—8316no—
661C2×C42C22×D8311yescharacteristic
662C2×C42C22×D8311yescharacteristic
663C2×C42C22×D8314yes—
664C2×C42C22×D8311yescharacteristic
665C2×C42C22×D8318yes—
666C2×C42C22×D8311yescharacteristic
667C24—832no—
668C24—832no—
669C24C23×D8311yescharacteristic
670#41—16632no—
671#41—16664no—
672C2×Q8—28no—
673C2×Q8—44no—
674C2×Q8—834no—
675C2×Q8—834no—
676C2×Q8—1664no—
677C2×Q8—1664no—
678C2×Q8C23×D8318yes—
679C2×Q8C23×D8318yes—
680C2×D4—3324no—
681C2×D4—838no—
682C2×D4—838no—
683C2×D4—838no—
684C2×D4—834no—
685C2×D4—834no—
686C2×D4—8316no—
687C2×D4—16616no—
688C2×D4—1668no—
689C2×D4—1664no—
690C22×C4—24no—
691C22×C4—24no—
692C22×C4—42no—
693C22×C4—3324no—
694C22×C4—3328no—
695C22×C4—3328no—
696C22×C4—838no—
697C22×C4—8316no—
698C22×C4—8316no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—832no—
703C22×C4—832no—
704C22×C4—832no—
705C22×C4—838no—
706C22×C4—838no—
707C22×C4—8316no—
708C22×C4—838no—
709C22×C4—1668no—
710C22×C4—16616no—
711C22×C4—1668no—
712C22×C4—1668no—
713C22×C4C23×D8314yes—
714C22×C4C23×D8314yes—
715C22×C4C23×D8311yescharacteristic
716C22×C4C23×D8311yescharacteristic
717C22×C4C23×D8314yes—
718C22×C4C23×D8311yescharacteristic
719C22×C4C23×D8311yescharacteristic
720C22×C4C23×D8314yes—
721C22×C4C23×D8314yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C4⋊C4—834no—
725C4⋊C4—8316no—
726C4⋊C4—838no—
727C4⋊C4—834no—
728C4⋊C4—838no—
729C4⋊C4—834no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—8316no—
733C4⋊C4—8316no—
734C4⋊C4—8316no—
735C4⋊C4—838no—
736C4⋊C4—838no—
737C4⋊C4—834no—
738C4⋊C4—838no—
739C4⋊C4—8316no—
740C4⋊C4—838no—
741C4⋊C4—8316no—
742C4⋊C4C23×D83116yes—
743C4⋊C4C23×D8318yes—
744C4⋊C4C23×D8318yes—
745C4⋊C4C23×D8318yes—
746C4⋊C4C23×D83116yes—
747C4⋊C4C23×D8318yes—
748C22⋊C4—838no—
749C22⋊C4—838no—
750C22⋊C4—838no—
751C22⋊C4—838no—
752C22⋊C4—838no—
753C22⋊C4—8316no—
754C22⋊C4—838no—
755C22⋊C4—838no—
756C22⋊C4—8316no—
757C22⋊C4—8316no—
758C22⋊C4—838no—
759C22⋊C4C23×D83116yes—
760C42—838no—
761C42—838no—
762C42—838no—
763C42—8316no—
764C42—838no—
765C42C23×D8314yes—
766C42C23×D8314yes—
767C42C23×D8314yes—
768C42C23×D8314yes—
769C42C23×D83116yes—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—838no—
774C23—834no—
775C23—834no—
776C23—1664no—
777C23—1664no—
778C23—1664no—
779C23—1664no—
780C23—1664no—
781C23C24×D8312yes—
782C23C24×D8311yescharacteristic
783Q8—216no—
784Q8—48no—
785Q8—1668no—
786Q8—1668no—
787D4—3328no—
788D4—8316no—
789D4—16632no—
790D4—16616no—
791D4—1668no—
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—3328no—
802C2×C4—33216no—
803C2×C4—33216no—
804C2×C4—834no—
805C2×C4—834no—
806C2×C4—834no—
807C2×C4—834no—
808C2×C4—834no—
809C2×C4—834no—
810C2×C4—16616no—
811C2×C4—16632no—
812C2×C4—1664no—
813C2×C4—1664no—
814C2×C4—1664no—
815C2×C4—1664no—
816C2×C4—1664no—
817C2×C4—1664no—
818C2×C4—16616no—
819C2×C4—16616no—
820C2×C4#41×D8314yes—
821C2×C4#1458184014yes—
822C2×C4C24×D8312yes—
823C2×C4C24×D8312yes—
824C2×C4C24×D8318yes—
825C2×C4C24×D8312yes—
826C2×C4C24×D8312yes—
827C2×C4C24×D8318yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—44no—
834C22—3328no—
835C22—838no—
836C22—1664no—
837C22—1664no—
838C22—1664no—
839C22—16616no—
840C22—1664no—
841C22—1664no—
842C22C2×#41×D8312yes—
843C22C2×#1458184012yes—
844C22#1912853712yes—
845C22C25×D8311yescharacteristic
846C4—22no—
847C4—28no—
848C4—22no—
849C4—22no—
850C4—22no—
851C4—28no—
852C4—1664no—
853C4—1664no—
854C4—1664no—
855C4—1664no—
856C4—1664no—
857C4—1664no—
858C4C2×#41×D8314yes—
859C4C2×#1458184014yes—
860C2—42no—
861C2—3324no—
862C2—1668no—
863C2#2492143614yesdirect product factor
864C2C22×#41×D8311yescharacteristic
865C2C22×#1458184011yescharacteristic
866C2C2×#1912853711yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#533×C83C2
socleC23×C83C25
hypercenterC2×#533D83
hypocenterC83C2×#3515
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #24921436C2direct (N × H)
2. C2×#19128426C2semidirect
3. C2×#19128412C2semidirect
4. C2×#19128412C2semidirect
5. C2×#19128395C2semidirect
6. C2×#19128392C2semidirect
7. C2×#19128390C2semidirect
8. C2×#19128385C2semidirect
9. C2×#19128354C2semidirect
10. C2×#19128353C2semidirect
11. C2×#19128309C2semidirect
12. C2×#19128297C2semidirect
13. C2×#19128236C2semidirect
14. C2×#19128235C2semidirect
15. C2×#125×D83C2semidirect
16. C2×#19128183C2semidirect
17. C2×C4×#13050590C2semidirect
18. C2×#533×C83C2semidirect
21. #19128426C22semidirect
22. #19128412C22semidirect
23. #19128412C22semidirect
24. #19128395C22semidirect
25. #19128392C22semidirect
26. #19128390C22semidirect
27. #19128385C22semidirect
28. #19128354C22semidirect
29. #19128353C22semidirect
30. #19128309C22semidirect
31. #19128297C22semidirect
33. #19128236C22semidirect
34. #19128235C22semidirect
47. #125×D83C22semidirect
63. #19128183C22semidirect
64. C4×#13050590C22semidirect
91. #533×C83C22semidirect
428. C2×C83#3515semidirect
446. C2×#533D83semidirect
452. C83C2×#3515semidirect
466. #533C2×D83semidirect
863. C2#24921436direct (N × H)

Maximal subgroups

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

subgroupindex
#249214362
C2×#191284262
C2×#191284122
C2×#191283952
C2×#191283922
C2×#191283902
C2×#191283852
C2×#191283542
C2×#191283532
C2×#191283092
C2×#191282972
C2×#191282362
C2×#191282352
C2×#125×D832
C2×#191281832
C2×C4×#130505902
C2×#533×C832
C2×#351583