Finite Group Databasebeta

← #35565254

Subgroups — #35565254

Order 21248.

2286 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128238C211yesmaximal, characteristic
2#24910586C214yesmaximal, complemented
3#24910500C212yesmaximal
4#24910486C212yesmaximal, complemented
5#24910420C211yesmaximal, characteristic, complemented
6#24910414C211yesmaximal, characteristic, complemented
7#24910414C212yesmaximal, complemented
8#24910395C212yesmaximal, complemented
9C4⋊C4×D332C211yesmaximal, characteristic, complemented
10#24910256C214yesmaximal, complemented
11#24910071C212yesmaximal, complemented
12#24910022C212yesmaximal, complemented
13C4×#14581781C212yesmaximal, complemented
14#24909868C211yesmaximal, characteristic, complemented
15#24909817C212yesmaximal, complemented
16C4×#14581750C211yesmaximal, characteristic, complemented
17Q8×C4⋊C4×C83C211yesmaximal, characteristic, complemented
18#19128238C4116yescomplemented
19C2×#14581787C2212yes—
20C2×#14581783C2211yescharacteristic
21C2×#14581781C2211yescharacteristic
22C2×#14581777C2212yes—
23C2×#14581768C2211yescharacteristic
24C2×#14581767C2211yescharacteristic
25C2×C4×D332C2212yes—
26C2×C4×D332C2211yescharacteristic
27C2×C4×D332C2212yes—
28C2×#14581750C2211yescharacteristic
29C2×#14581750C2211yescharacteristic
30C2×#14581750C2212yes—
31C2×#14581750C2212yes—
32C2×#14581749C2212yes—
33C2×C4⋊C4×D83C2212yes—
34C2×C42×D83C2211yescharacteristic
35#19127608C2212yes—
36#19127602C2214yes—
37#19127602C2212yes—
38#19127599C2212yes—
39#19127592C2214yes—
40#19127591C2214yes—
41#19127591C2214yes—
42#19127591C2214yes—
43#19127591C2214yes—
44#19127591C2214yes—
45#19127587C2214yes—
46#19127586C2214yes—
47#19127582C2214yes—
48#19127582C2214yes—
49#19127579C2214yes—
50#19127575C2214yes—
51#19127571C2211yescharacteristic
52#19127567C2212yes—
53#19127566C2212yes—
54#19127558C2212yes—
55#19127558C2212yes—
56#19127558C2212yes—
57#19127558C2212yes—
58C4⋊C4×Dic83C2212yes—
59C4⋊C4×Dic83C2212yes—
60C4⋊C4×Dic83C2212yes—
61C4⋊C4×Dic83C2214yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2211yescharacteristic
64C4⋊C4×Dic83C2211yescharacteristic
65C4×Dic83⋊C4C2214yes—
66C4×C4⋊Dic83C2211yescharacteristic
67C4×C4⋊Dic83C2212yes—
68#19127552C2214yes—
69C4×(C2×D83)⋊C4C2214yes—
70C4×(C2×D83)⋊C4C2212yes—
71C4×(C2×D83)⋊C4C2214yes—
72#19127548C2214yes—
73#19127548C2212yes—
74#19127546C2212yes—
75C42×Dic83C2212yes—
76C2×C4×Q8×C83C2212yes—
77C2×C4×Q8×C83C2211yescharacteristic
78#389×C83C2212yes—
79#389×C83C2214yes—
80#384×C83C2211yescharacteristic
81#384×C83C2212yes—
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×D332C2311yescharacteristic
85C22×D332C2312yes—
86C22×C4×D83C2311yescharacteristic
87C22×C4×D83C2312yes—
88C22×C4×D83C2311yescharacteristic
89C22×C4×D83C2314yes—
90C22×C4×D83C2311yescharacteristic
91#14581787C2×C4116yescomplemented
92#14581783C2×C418yescomplemented
93#14581781C2×C418yes—
94#14581777C2×C4116yescomplemented
95#14581768C2×C418yescomplemented
96#14581767C2×C418yes—
97C4×D332—44no—
98C4×D332C2×C418yes—
99C4×D332C2×C4116yescomplemented
100#14581750—24no—
101#14581750—28no—
102#14581750—24no—
103#14581750—44no—
104#14581749C2×C4116yescomplemented
105C2×C4⋊Dic83C2311yescharacteristic
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2312yes—
115C4⋊C4×D83—28no—
116C2×(C2×D83)⋊C4C2312yes—
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×(C2×D83)⋊C4C2312yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2312yes—
129C2×C4×Dic83C2312yes—
130C2×C4×Dic83C2312yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2314yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2312yes—
135C2×C4×Dic83C2311yescharacteristic
136C2×C4×Dic83C2311yescharacteristic
137C2×C4×Dic83C2311yescharacteristic
138C42×D83C2×C418yescomplemented
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C83⋊#95C2312yes—
148C83⋊#95C2314yes—
149C22×Q8×C83C2311yescharacteristic
150C4×Q8×C83—44no—
151C4×Q8×C83C2×C418yescomplemented
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C4⋊C4×C83C2312yes—
160C2×C4⋊C4×C83C2311yescharacteristic
161C2×C42×C83C2312yes—
162C2×C42×C83C2314yes—
163C2×C42×C83C2312yes—
164C2×C42×C83C2311yescharacteristic
165#95×C83C2314yes—
166#95×C83C2312yes—
167C23×D83C2411yescharacteristic
168C23×D83C2412yes—
169C2×D332—22no—
170C2×D332—22no—
171C2×D332—42no—
172C2×D332—42no—
173C2×D332C22×C414yes—
174C2×D332C22×C418yes—
175C22×Dic83C2414yes—
176C22×Dic83C2412yes—
177C22×Dic83C2411yescharacteristic
178C22×Dic83C2411yescharacteristic
179C22×Dic83C2411yescharacteristic
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C2×C4×D83—24no—
183C2×C4×D83—22no—
184C2×C4×D83—24no—
185C2×C4×D83—22no—
186C2×C4×D83—22no—
187C2×C4×D83—22no—
188C2×C4×D83—28no—
189C2×C4×D83—41no—
190C2×C4×D83—41no—
191C2×C4×D83—44no—
192C2×C4×D83—44no—
193C2×C4×D83C22×C414yes—
194C2×C4×D83C22×C414yes—
195C2×C4×D83C22×C418yes—
196C2×C4×D83C22×C414yes—
197C4⋊Dic83—24no—
198C4⋊Dic83—22no—
199C4⋊Dic83—24no—
200C4⋊Dic83—42no—
201C4⋊Dic83C22×C414yes—
202C4⋊Dic83C22×C418yes—
203C4⋊Dic83#4114yes—
204Dic83⋊C4—28no—
205Dic83⋊C4C22×C418yes—
206Dic83⋊C4C22×C418yes—
207(C2×D83)⋊C4—24no—
208(C2×D83)⋊C4—24no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—44no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4—44no—
213(C2×D83)⋊C4C22×C418yes—
214(C2×D83)⋊C4C22×C418yes—
215(C2×D83)⋊C4C22×C418yes—
216(C2×D83)⋊C4C22×C418yes—
217(C2×D83)⋊C4C22×C418yes—
218C4×Dic83—24no—
219C4×Dic83—24no—
220C4×Dic83—28no—
221C4×Dic83—24no—
222C4×Dic83—42no—
223C4×Dic83—44no—
224C4×Dic83—42no—
225C4×Dic83—44no—
226C4×Dic83C22×C414yes—
227C4×Dic83C22×C414yes—
228C4×Dic83C22×C414yes—
229C2×Q8×C83—22no—
230C2×Q8×C83—22no—
231C2×Q8×C83C22×C414yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2414yes—
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—24no—
241C4⋊C4×C83—22no—
242C4⋊C4×C83—24no—
243C4⋊C4×C83—42no—
244C4⋊C4×C83—44no—
245C4⋊C4×C83—44no—
246C4⋊C4×C83C22×C414yes—
247C4⋊C4×C83C22×C418yes—
248C4⋊C4×C83#4114yes—
249C42×C83—24no—
250C42×C83—44no—
251C42×C83C22×C414yes—
252C42×C83C22×C418yes—
253C23×C83C2511yescharacteristic
254C22×D83—21no—
255C22×D83—22no—
256C22×D83—21no—
257C22×D83—22no—
258C22×D83—21no—
259C22×D83—22no—
260C22×D83—21no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—21no—
265C22×D83—21no—
266C22×D83C23×C414yes—
267C22×D83C23×C412yes—
268Q8×C83—28no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—21no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—21no—
277C2×C4×C83—22no—
278C2×C4×C83—24no—
279C2×C4×C83—22no—
280C2×C4×C83—24no—
281C2×C4×C83—22no—
282C2×C4×C83—24no—
283C2×C4×C83C23×C412yes—
284C2×C4×C83C23×C414yes—
285C2×C4×C83C23×C414yes—
286C2×C4×C83C23×C412yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C2×#4112yes—
289C2×C4×C83C2×#4114yes—
290C2×C4×C83C2×#4112yes—
291C2×C4×C83H(5,𝔽2)12yes—
292C2×C4×C832−1+412yes—
293C2×Dic83—21no—
294C2×Dic83—22no—
295C2×Dic83—21no—
296C2×Dic83—22no—
297C2×Dic83—21no—
298C2×Dic83—22no—
299C2×Dic83—21no—
300C2×Dic83—22no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—22no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—24no—
309C2×Dic83C23×C412yes—
310C2×Dic83C23×C412yes—
311C2×Dic83C23×C412yes—
312C2×Dic83C23×C414yes—
313C2×Dic83C2×#4114yes—
314D332—28no—
315D332—48no—
316C4×D83—216no—
317C4×D83—28no—
318C4×D83—28no—
319C4×D83—44no—
320C4×D83—88no—
321C22×C83C24×C411yescharacteristic
322C22×C83C22×#4111yescharacteristic
323C22×C83C22×#4111yescharacteristic
324C22×C83C2×H(5,𝔽2)11yescharacteristic
325C22×C83C2×2−1+411yescharacteristic
326C22×C83#58511yescharacteristic
327C22×C83#58511yescharacteristic
328C2×D83—22no—
329C2×D83—24no—
330C2×D83—22no—
331C2×D83—24no—
332C2×D83—22no—
333C2×D83—24no—
334C2×D83—42no—
335C2×D83—41no—
336C2×D83—41no—
337C2×D83—42no—
338C2×D83—41no—
339C2×D83—42no—
340C2×D83—41no—
341C2×D83—42no—
342C4×C83—24no—
343C4×C83—22no—
344C4×C83—24no—
345C4×C83—24no—
346C4×C83—42no—
347C4×C83—44no—
348C4×C83C4×#4114yes—
349C4×C83#52014yes—
350Dic83—22no—
351Dic83—24no—
352Dic83—22no—
353Dic83—22no—
354Dic83—24no—
355Dic83—44no—
356Dic83—42no—
357#34242—831nomaximal, Sylow
358C2×C83C2×C4×#4111yescharacteristic
359C2×C83C2×#52011yescharacteristic
360C2×C83#342811yescharacteristic
361C2×C83#351411yescharacteristic
362C2×C83#351511yescharacteristic
363C2×C83#351711yescharacteristic
364C2×C83#351811yescharacteristic
365D83—42no—
366D83—44no—
367C2×#529—831no—
368#2373—834no—
369#2363—832no—
370#2362—832no—
371#2355—831no—
372#2354—832no—
373#2354—831no—
374#2352—832no—
375Q8×C4⋊C4D8311yescharacteristic, complemented
376D4×C4⋊C4—831no—
377#2335—834no—
378#2314—832no—
379C4×#125—832no—
380C4×#124—832no—
381#2285—831no—
382#2274—832no—
383C4×#117—831no—
384C83#3424211yescharacteristic, complemented, Sylow
385#529—8316no—
386C2×#126—832no—
387C2×#125—831no—
388C2×#124—831no—
389C2×#123—832no—
390C2×C22⋊Q8—831no—
391C2×#121—831no—
392C2×C4×Q8C2×D8312yes—
393C2×C4×Q8C2×D8311yescharacteristic
394C2×C4×D4—832no—
395C2×C4×D4—831no—
396C2×C4×D4—832no—
397C2×#117—832no—
398C2×#117—831no—
399C2×#117—831no—
400C2×#117—832no—
401C2×#117—832no—
402C22×C4⋊C4—832no—
403C22×C42—831no—
404#391—832no—
405#390—834no—
406#390—832no—
407#389—832no—
408#389C2×D8312yes—
409#389C2×D8314yes—
410#388—834no—
411#388—834no—
412#388—834no—
413#388—834no—
414#388—834no—
415#388—834no—
416#387—834no—
417#387—834no—
418#387—834no—
419#387—834no—
420#386—834no—
421#385—834no—
422#384—831no—
423#384C2×D8312yes—
424#384C2×D8311yescharacteristic
425#382—832no—
426#382—832no—
427#380—832no—
428#380—832no—
429#380—832no—
430#380—832no—
431C4×C4⋊C4—832no—
432C4×C4⋊C4—834no—
433C4×C4⋊C4—832no—
434C4×C4⋊C4—831no—
435C4×C4⋊C4—832no—
436C4×C4⋊C4—832no—
437C4×C4⋊C4—831no—
438C4×C4⋊C4—831no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—834no—
441C4×C4⋊C4—834no—
442C4×C4⋊C4C2×D8311yescharacteristic
443C4×C4⋊C4C2×D8312yes—
444C4×C22⋊C4—834no—
445C4×C22⋊C4—834no—
446C4×C22⋊C4—832no—
447C4×C22⋊C4—832no—
448C4×C22⋊C4—834no—
449#376—832no—
450C43—832no—
451C22×Q8C22×D8311yescharacteristic
452C22×D4—832no—
453C22×D4—831no—
454C23×C4—831no—
455C23×C4—834no—
456C23×C4—832no—
457C23×C4—831no—
458C23×C4—831no—
459#126—8316no—
460#125—838no—
461#124—838no—
462#123—8316no—
463C22⋊Q8—838no—
464#121—838no—
465C4×Q8—44no—
466C4×Q8C4×D8318yescomplemented
467C4×D4—3324no—
468C4×D4—838no—
469C4×D4—8316no—
470#117—3324no—
471#117—8316no—
472#117—1664no—
473#117—1668no—
474#117—1664no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—831no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—832no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—1668no—
486C2×C4⋊C4C22×D8312yes—
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8312yes—
489C2×C4⋊C4C22×D8314yes—
490C2×C4⋊C4C22×D8312yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8311yescharacteristic
495C2×C22⋊C4—834no—
496C2×C22⋊C4—834no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—832no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—832no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—834no—
506C2×C42—834no—
507C2×C42—832no—
508C2×C42—832no—
509C2×C42—834no—
510C2×C42—831no—
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—838no—
514C2×C42—832no—
515C2×C42—832no—
516C2×C42—834no—
517C2×C42—832no—
518C2×C42C22×D8312yes—
519C2×C42C22×D8314yes—
520C2×C42C22×D8312yes—
521C2×C42C22×D8311yescharacteristic
522#95—832no—
523#95—832no—
524#95—832no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95—834no—
531#95—834no—
532#95C22×D8312yes—
533#95C22×D8314yes—
534C24—832no—
535C24—831no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8C2×C4×D8314yes—
539C2×D4—3322no—
540C2×D4—3322no—
541C2×D4—838no—
542C2×D4—834no—
543C2×D4—1662no—
544C2×D4—1662no—
545C22×C4—3321no—
546C22×C4—3321no—
547C22×C4—3324no—
548C22×C4—3324no—
549C22×C4—834no—
550C22×C4—832no—
551C22×C4—831no—
552C22×C4—831no—
553C22×C4—831no—
554C22×C4—832no—
555C22×C4—834no—
556C22×C4—834no—
557C22×C4—838no—
558C22×C4—832no—
559C22×C4—834no—
560C22×C4—1668no—
561C22×C4—1664no—
562C22×C4—1662no—
563C22×C4—1664no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4C23×D8312yes—
568C22×C4C23×D8314yes—
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8311yescharacteristic
572C22×C4C23×D8312yes—
573C22×C4C23×D8311yescharacteristic
574C22×C4C23×D8311yescharacteristic
575C4⋊C4—22no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—44no—
579C4⋊C4—42no—
580C4⋊C4—44no—
581C4⋊C4—3322no—
582C4⋊C4—838no—
583C4⋊C4—838no—
584C4⋊C4—834no—
585C4⋊C4—838no—
586C4⋊C4—834no—
587C4⋊C4—1668no—
588C4⋊C4—1664no—
589C4⋊C4—1662no—
590C4⋊C4—1664no—
591C4⋊C4C2×C4×D8314yes—
592C4⋊C4C2×C4×D8318yes—
593C4⋊C4#1305059114yes—
594C22⋊C4—3324no—
595C22⋊C4—3324no—
596C22⋊C4—3324no—
597C22⋊C4—838no—
598C22⋊C4—838no—
599C22⋊C4—838no—
600C22⋊C4—838no—
601C22⋊C4—838no—
602C22⋊C4—1664no—
603C22⋊C4—1668no—
604C22⋊C4—1664no—
605C42—24no—
606C42—44no—
607C42—3324no—
608C42—3324no—
609C42—3322no—
610C42—3322no—
611C42—834no—
612C42—834no—
613C42—834no—
614C42—1664no—
615C42—1668no—
616C42—1664no—
617C42—1664no—
618C42C2×C4×D8314yes—
619C42C2×C4×D8318yes—
620C23—834no—
621C23—832no—
622C23—1661no—
623C23—1662no—
624C23—1661no—
625C23—1662no—
626C23—1661no—
627C23—1662no—
628C23—1661no—
629C23—1662no—
630C23—1662no—
631C23—1661no—
632C23—1662no—
633C23—1661no—
634C23C24×D8311yescharacteristic
635Q8—28no—
636D4—3328no—
637D4—1668no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—21no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—3324no—
653C2×C4—832no—
654C2×C4—832no—
655C2×C4—832no—
656C2×C4—834no—
657C2×C4—834no—
658C2×C4—6648no—
659C2×C4—1662no—
660C2×C4—1664no—
661C2×C4—1664no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1664no—
665C2×C4—1661no—
666C2×C4—1662no—
667C2×C4—1661no—
668C2×C4—1662no—
669C2×C4—1661no—
670C2×C4—1662no—
671C2×C4—1661no—
672C2×C4—1661no—
673C2×C4—1662no—
674C2×C4—1661no—
675C2×C4—1668no—
676C2×C4—16616no—
677C2×C4—1668no—
678C2×C4C22×C4×D8312yes—
679C2×C4C22×C4×D8314yes—
680C2×C4C22×C4×D8314yes—
681C2×C4C22×C4×D8312yes—
682C2×C4C22×C4×D8312yes—
683C2×C4#41×D8312yes—
684C2×C4C2×#1305059114yes—
685C2×C4C2×#1305059112yes—
686C2×C4#1458183712yes—
687C2×C4#1458184012yes—
688C22—3322no—
689C22—3321no—
690C22—3321no—
691C22—3322no—
692C22—3321no—
693C22—3322no—
694C22—3321no—
695C22—3322no—
696C22—1664no—
697C22—1662no—
698C22—1662no—
699C22—1664no—
700C22—1662no—
701C22—1664no—
702C22C23×C4×D8311yescharacteristic
703C22C2×#41×D8311yescharacteristic
704C22C22×#1305059111yescharacteristic
705C22C2×#1458183711yescharacteristic
706C22C2×#1458184011yescharacteristic
707C22#1912853611yescharacteristic
708C22#1912853811yescharacteristic
709C4—24no—
710C4—24no—
711C4—22no—
712C4—24no—
713C4—42no—
714C4—44no—
715C4—3324no—
716C4—3322no—
717C4—1662no—
718C4—1664no—
719C4—1662no—
720C4—1662no—
721C4—1664no—
722C4C4×#1305059114yes—
723C4#1912818214yes—
724C2—3324no—
725C2—3322no—
726C2C2×C4×#1305059111yescharacteristic
727C2C2×#1912818211yescharacteristic
728C2#2492066311yescharacteristic
729C2#2492142511yescharacteristic
730C2#2492144011yescharacteristic
731C2#2492146611yescharacteristic
732C2#2492148111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingQ8×C4⋊C4×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#14581767C22
hypercenterQ8×C4⋊C4D83
hypocenterC83#34242
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ Q8×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #24910586C2semidirect
4. #24910486C2semidirect
5. #24910420C2semidirect
6. #24910414C2semidirect
7. #24910414C2semidirect
8. #24910395C2semidirect
9. C4⋊C4×D332C2semidirect
10. #24910256C2semidirect
11. #24910071C2semidirect
12. #24910022C2semidirect
13. C4×#14581781C2semidirect
14. #24909868C2semidirect
15. #24909817C2semidirect
16. C4×#14581750C2semidirect
17. Q8×C4⋊C4×C83C2semidirect
18. #19128238C4semidirect
91. #14581787C2×C4semidirect
92. #14581783C2×C4semidirect
94. #14581777C2×C4semidirect
95. #14581768C2×C4semidirect
99. C4×D332C2×C4semidirect
104. #14581749C2×C4semidirect
138. C42×D83C2×C4semidirect
151. C4×Q8×C83C2×C4semidirect
375. Q8×C4⋊C4D83semidirect
384. C83#34242semidirect
466. C4×Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282382
#249105862
#249105002
#249104862
#249104202
#249104142
#249103952
C4⋊C4×D3322
#249102562
#249100712
#249100222
C4×#145817812
#249098682
#249098172
C4×#145817502
Q8×C4⋊C4×C832
#3424283