Finite Group Databasebeta

← #35566571

Subgroups — #35566571

Order 21248.

2548 conjugacy classes of subgroups.

The subgroup lattice has 742 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128354C211yesmaximal, characteristic
2#24910592C214yesmaximal, complemented
3#24910523C211yesmaximal, characteristic, complemented
4#24910500C212yesmaximal, complemented
5#24910486C212yesmaximal, complemented
6#24910414C211yesmaximal, characteristic, complemented
7#24910414C211yesmaximal, characteristic, complemented
8#24910339C212yesmaximal, complemented
9#24910301C212yesmaximal, complemented
10#24910256C214yesmaximal, complemented
11#24910157C212yesmaximal, complemented
12#24910001C212yesmaximal, complemented
13#24909952C212yesmaximal, complemented
14#24909927C211yesmaximal, characteristic, complemented
15#24909817C212yesmaximal, complemented
16C42×D332C211yesmaximal, characteristic, complemented
17C4×C4⋊Q8×C83C211yesmaximal, characteristic, complemented
18C22×#13050591C2212yes—
19#19128354C4116yescomplemented
20C2×#14581777C2214yes—
21C2×#14581768C2212yes—
22C2×#14581767C2212yes—
23C2×Q8×Dic83C2212yes—
24C2×C4×D332C2211yescharacteristic
25C2×C4×D332C2211yescharacteristic
26C2×C4×D332C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×#14581750C2212yes—
29C2×#14581750C2212yes—
30C2×#14581749C2212yes—
31C2×C4⋊C4×D83C2212yes—
32C2×C42×D83C2212yes—
33#19127608C2212yes—
34#19127603C2214yes—
35#19127603C2211yescharacteristic
36#19127603C2211yescharacteristic
37#19127602C2212yes—
38#19127602C2212yes—
39#19127602C2214yes—
40#19127600C2212yes—
41#19127599C2211yescharacteristic
42#19127599C2211yescharacteristic
43#19127592C2212yes—
44#19127592C2214yes—
45#19127592C2212yes—
46#19127591C2214yes—
47#19127591C2214yes—
48#19127591C2214yes—
49#19127588C2214yes—
50#19127587C2214yes—
51#19127582C2214yes—
52#19127579C2214yes—
53#19127579C2214yes—
54#19127575C2214yes—
55#19127558C2212yes—
56#19127558C2214yes—
57#19127558C2212yes—
58C4⋊C4×Dic83C2212yes—
59C4⋊C4×Dic83C2212yes—
60C4⋊C4×Dic83C2212yes—
61C4×Dic83⋊C4C2214yes—
62C4×C4⋊Dic83C2211yescharacteristic
63C4×C4⋊Dic83C2211yescharacteristic
64C4×C4⋊Dic83C2211yescharacteristic
65C4×C4⋊Dic83C2211yescharacteristic
66#19127552C2214yes—
67C4×(C2×D83)⋊C4C2212yes—
68C4×(C2×D83)⋊C4C2214yes—
69C4×(C2×D83)⋊C4C2212yes—
70C4×(C2×D83)⋊C4C2212yes—
71C4×(C2×D83)⋊C4C2212yes—
72#19127548C2214yes—
73#19127548C2214yes—
74#19127548C2214yes—
75C2×C4⋊Q8×C83C2211yescharacteristic
76C2×C4×Q8×C83C2212yes—
77#391×C83C2212yes—
78#389×C83C2212yes—
79#389×C83C2212yes—
80#384×C83C2211yescharacteristic
81C4×C4⋊C4×C83C2212yes—
82C4×C4⋊C4×C83C2212yes—
83C43×C83C2211yescharacteristic
84C2×#13050591—44no—
85C2×#13050591—44no—
86C2×#13050591C2×C4116yescomplemented
87C22×D332C2311yescharacteristic
88C22×D332C2311yescharacteristic
89C22×D332C2314yes—
90C22×C4×D83C2312yes—
91C22×C4×D83C2312yes—
92C22×C4×D83C2312yes—
93C22×C4×D83C2312yes—
94C22×C4×D83C2314yes—
95#14581777C2×C4132yescomplemented
96#14581768C2×C4116yescomplemented
97#14581767C2×C4116yes—
98Q8×Dic83—44no—
99C4×D332—24no—
100C4×D332—24no—
101C4×D332C2×C418yes—
102C4×D332C2×C418yescomplemented
103#14581750—28no—
104#14581750—44no—
105#14581749—28no—
106C2×C4⋊Dic83C2311yescharacteristic
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2314yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×C4⋊Dic83C2311yescharacteristic
113C2×Dic83⋊C4C2312yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2314yes—
116C4⋊C4×D83C2×C4116yescomplemented
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2312yes—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×(C2×D83)⋊C4C2312yes—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2312yes—
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2312yes—
136C2×C4×Dic83C2314yes—
137C42×D83—44no—
138C83⋊#95C2314yes—
139C83⋊#95C2312yes—
140C83⋊#95C2312yes—
141C83⋊#95C2312yes—
142C83⋊#95C2312yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2312yes—
147C83⋊#95C2312yes—
148C22×Q8×C83C2312yes—
149C4⋊Q8×C83C2×C418yescomplemented
150C4×Q8×C83—44no—
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2314yes—
154C2×C4⋊C4×C83C2312yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C42×C83C2311yescharacteristic
158C2×C42×C83C2311yescharacteristic
159C2×C42×C83C2311yescharacteristic
160C2×C42×C83C2311yescharacteristic
161C2×C42×C83C2314yes—
162C2×C42×C83C2311yescharacteristic
163C2×C42×C83C2311yescharacteristic
164C2×C42×C83C2311yescharacteristic
165#95×C83C2314yes—
166#95×C83C2314yes—
167C23×D83C2412yes—
168C23×D83C2412yes—
169#13050591—432no—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332—22no—
173C2×D332—22no—
174C2×D332—44no—
175C2×D332—44no—
176C2×D332C22×C414yes—
177C2×D332C22×C414yes—
178C2×D332C22×C4116yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C2×C4×D83—24no—
186C2×C4×D83—24no—
187C2×C4×D83—24no—
188C2×C4×D83—24no—
189C2×C4×D83—24no—
190C2×C4×D83—24no—
191C2×C4×D83—24no—
192C2×C4×D83—42no—
193C2×C4×D83—44no—
194C2×C4×D83—44no—
195C2×C4×D83—42no—
196C2×C4×D83—42no—
197C2×C4×D83C22×C418yes—
198C2×C4×D83C22×C418yes—
199C2×C4×D83C22×C4116yes—
200C4⋊Dic83—22no—
201C4⋊Dic83—22no—
202C4⋊Dic83—22no—
203C4⋊Dic83—44no—
204C4⋊Dic83C22×C414yes—
205C4⋊Dic83C22×C414yes—
206C4⋊Dic83#4114yescomplemented
207Dic83⋊C4—24no—
208Dic83⋊C4—24no—
209Dic83⋊C4C22×C4116yes—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—24no—
212(C2×D83)⋊C4—24no—
213(C2×D83)⋊C4—24no—
214(C2×D83)⋊C4—28no—
215(C2×D83)⋊C4—24no—
216(C2×D83)⋊C4—42no—
217(C2×D83)⋊C4—44no—
218(C2×D83)⋊C4—44no—
219(C2×D83)⋊C4—44no—
220(C2×D83)⋊C4C22×C4116yes—
221(C2×D83)⋊C4C22×C418yes—
222(C2×D83)⋊C4C22×C418yes—
223C4×Dic83—24no—
224C4×Dic83—24no—
225C4×Dic83—28no—
226C4×Dic83—42no—
227C4×Dic83—42no—
228C4×Dic83—44no—
229C4×Dic83—44no—
230C2×Q8×C83—24no—
231C2×Q8×C83—24no—
232C2×Q8×C83C22×C418yes—
233C22×C4×C83C2414yes—
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2414yes—
236C22×C4×C83C2411yescharacteristic
237C22×C4×C83C2411yescharacteristic
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2411yescharacteristic
242C4⋊C4×C83—24no—
243C4⋊C4×C83—24no—
244C4⋊C4×C83—42no—
245C4⋊C4×C83—44no—
246C4⋊C4×C83C22×C418yes—
247C4⋊C4×C83C22×C418yes—
248C42×C83—22no—
249C42×C83—22no—
250C42×C83—22no—
251C42×C83—22no—
252C42×C83—41no—
253C42×C83—44no—
254C42×C83C22×C414yes—
255C42×C83#4114yescomplemented
256C23×C83C2511yescharacteristic
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83—22no—
267C22×D83—22no—
268C22×D83—22no—
269C22×D83C23×C414yes—
270C22×D83C23×C414yes—
271Q8×C83—216no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—24no—
277C2×C4×C83—24no—
278C2×C4×C83—21no—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—24no—
284C2×C4×C83—21no—
285C2×C4×C83—24no—
286C2×C4×C83—21no—
287C2×C4×C83—24no—
288C2×C4×C83C23×C412yes—
289C2×C4×C83C23×C418yes—
290C2×C4×C83C23×C412yes—
291C2×C4×C83C23×C412yes—
292C2×C4×C83C2×#4112yes—
293C2×C4×C83C2×#4112yes—
294C2×C4×C83C2×#4112yes—
295C2×C4×C83C2×#4112yes—
296C2×C4×C83H(5,𝔽2)12yes—
297C2×C4×C83H(5,𝔽2)12yes—
298C2×C4×C832−1+412yes—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83C23×C414yes—
315C2×Dic83C23×C414yes—
316C2×Dic83C2×#4114yes—
317D332—28no—
318D332—28no—
319D332—416no—
320C4×D83—216no—
321C4×D83—216no—
322C4×D83—416no—
323C4×D83—48no—
324C4×D83—48no—
325C22×C83C24×C411yescharacteristic
326C22×C83C22×#4111yescharacteristic
327C22×C83C22×#4111yescharacteristic
328C22×C83C2×H(5,𝔽2)11yescharacteristic
329C22×C83C2×H(5,𝔽2)11yescharacteristic
330C22×C83C2×2−1+411yescharacteristic
331C22×C83#58511yescharacteristic
332C2×D83—24no—
333C2×D83—24no—
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—24no—
337C2×D83—24no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83—42no—
342C2×D83—42no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—42no—
346C4×C83—28no—
347C4×C83—22no—
348C4×C83—22no—
349C4×C83—22no—
350C4×C83—22no—
351C4×C83—41no—
352C4×C83—44no—
353C4×C83C4×#4114yes—
354C4×C83#51814yes—
355Dic83—24no—
356Dic83—24no—
357Dic83—24no—
358Dic83—42no—
359Dic83—42no—
360Dic83—42no—
361#34316—831nomaximal, Sylow
362C2×C83C2×C4×#4111yescharacteristic
363C2×C83C2×#51811yescharacteristic
364C2×C83C4×2−1+411yescharacteristic
365C2×C83#350611yescharacteristic
366C2×C83#351111yescharacteristic
367C2×C83#351711yescharacteristic
368C2×C83#352011yescharacteristic
369D83—44no—
370D83—44no—
371C2×#547—831no—
372#2374—834no—
373#2365—831no—
374#2363—832no—
375#2362—832no—
376#2354—831no—
377#2354—831no—
378#2345—832no—
379#2341—832no—
380#2335—834no—
381#2324—832no—
382C4×C4⋊Q8D8311yescharacteristic, complemented
383C4×C22⋊Q8—832no—
384#2297—832no—
385#2293—831no—
386#2274—832no—
387C42×D4—831no—
388C83#3431611yescharacteristic, complemented, Sylow
389C22×#41—832no—
390#547—8316no—
391C2×C4⋊Q8C2×D8311yescharacteristic
392C2×#123—834no—
393C2×C22⋊Q8—832no—
394C2×#121—832no—
395C2×C4×Q8—832no—
396C2×C4×Q8C2×D8312yes—
397C2×C4×D4—831no—
398C2×C4×D4—831no—
399C2×C4×D4—831no—
400C2×C4×D4—831no—
401C2×#117—832no—
402C2×#117—832no—
403C2×#117—832no—
404C22×C4⋊C4—832no—
405C22×C42—832no—
406#391—832no—
407#391C2×D8312yes—
408#390—832no—
409#390—834no—
410#390—832no—
411#390—834no—
412#390—831no—
413#390—831no—
414#389—832no—
415#389—831no—
416#389—831no—
417#389C2×D8312yes—
418#389C2×D8312yes—
419#388—834no—
420#388—834no—
421#388—834no—
422#388—834no—
423#388—832no—
424#388—832no—
425#387—834no—
426#387—834no—
427#387—834no—
428#386—834no—
429#386—834no—
430#385—834no—
431#384C2×D8311yescharacteristic
432#380—832no—
433#380—834no—
434#380—832no—
435C4×C4⋊C4—832no—
436C4×C4⋊C4—832no—
437C4×C4⋊C4—832no—
438C4×C4⋊C4—831no—
439C4×C4⋊C4—831no—
440C4×C4⋊C4—831no—
441C4×C4⋊C4—831no—
442C4×C4⋊C4—834no—
443C4×C4⋊C4—834no—
444C4×C4⋊C4C2×D8312yes—
445C4×C4⋊C4C2×D8312yes—
446C4×C22⋊C4—832no—
447C4×C22⋊C4—832no—
448C4×C22⋊C4—834no—
449C4×C22⋊C4—832no—
450C4×C22⋊C4—832no—
451C4×C22⋊C4—834no—
452C4×C22⋊C4—834no—
453C4×C22⋊C4—834no—
454C43C2×D8311yescharacteristic
455C2×#41—3324no—
456C2×#41—3324no—
457C2×#41—8316no—
458C22×Q8C22×D8312yes—
459C22×D4—834no—
460C22×D4—831no—
461C22×D4—831no—
462C23×C4—834no—
463C23×C4—832no—
464C23×C4—832no—
465C23×C4—832no—
466C23×C4—832no—
467C4⋊Q8C4×D8318yescomplemented
468#123—8332no—
469C22⋊Q8—8316no—
470#121—8316no—
471C4×Q8—44no—
472C4×Q8—3324no—
473C4×D4—838no—
474C4×D4—838no—
475C4×D4—1664no—
476C4×D4—1664no—
477#117—3324no—
478#117—1668no—
479#117—1668no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—8316no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4—831no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4C22×D8312yes—
492C2×C4⋊C4C22×D8312yes—
493C2×C4⋊C4C22×D8314yes—
494C2×C4⋊C4C22×D8312yes—
495C2×C4⋊C4C22×D8312yes—
496C2×C4⋊C4C22×D8312yes—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—834no—
506C2×C22⋊C4—832no—
507C2×C22⋊C4—832no—
508C2×C22⋊C4—832no—
509C2×C22⋊C4—832no—
510C2×C42—3324no—
511C2×C42—834no—
512C2×C42—834no—
513C2×C42—832no—
514C2×C42—832no—
515C2×C42—834no—
516C2×C42—832no—
517C2×C42—832no—
518C2×C42C22×D8311yescharacteristic
519C2×C42C22×D8311yescharacteristic
520C2×C42C22×D8311yescharacteristic
521C2×C42C22×D8311yescharacteristic
522C2×C42C22×D8314yes—
523C2×C42C22×D8311yescharacteristic
524C2×C42C22×D8311yescharacteristic
525C2×C42C22×D8311yescharacteristic
526#95—832no—
527#95—832no—
528#95—832no—
529#95—832no—
530#95—834no—
531#95—834no—
532#95—834no—
533#95—832no—
534#95—834no—
535#95—832no—
536#95C22×D8314yes—
537#95C22×D8314yes—
538C24—832no—
539C24—832no—
540#41—33232no—
541C2×Q8—24no—
542C2×Q8—24no—
543C2×Q8C2×C4×D8318yes—
544C2×D4—3324no—
545C2×D4—3324no—
546C2×D4—8316no—
547C2×D4—834no—
548C2×D4—834no—
549C2×D4—1662no—
550C2×D4—1662no—
551C2×D4—1662no—
552C2×D4—1662no—
553C22×C4—3322no—
554C22×C4—3322no—
555C22×C4—3324no—
556C22×C4—3324no—
557C22×C4—3322no—
558C22×C4—8316no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—838no—
563C22×C4—838no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—832no—
567C22×C4—1664no—
568C22×C4—1664no—
569C22×C4—1664no—
570C22×C4—1664no—
571C22×C4—1664no—
572C22×C4—1664no—
573C22×C4—1664no—
574C22×C4C23×D8311yescharacteristic
575C22×C4C23×D8314yes—
576C22×C4C23×D8311yescharacteristic
577C22×C4C23×D8314yes—
578C22×C4C23×D8311yescharacteristic
579C22×C4C23×D8311yescharacteristic
580C22×C4C23×D8311yescharacteristic
581C22×C4C23×D8311yescharacteristic
582C22×C4C23×D8311yescharacteristic
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—44no—
586C4⋊C4—42no—
587C4⋊C4—3324no—
588C4⋊C4—834no—
589C4⋊C4—8316no—
590C4⋊C4—834no—
591C4⋊C4—834no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C4⋊C4—1662no—
597C4⋊C4C2×C4×D8318yes—
598C4⋊C4C2×C4×D8318yes—
599C22⋊C4—3324no—
600C22⋊C4—3322no—
601C22⋊C4—3324no—
602C22⋊C4—3324no—
603C22⋊C4—838no—
604C22⋊C4—838no—
605C22⋊C4—8316no—
606C22⋊C4—1668no—
607C22⋊C4—1664no—
608C22⋊C4—1664no—
609C22⋊C4—1664no—
610C22⋊C4—1664no—
611C22⋊C4—1664no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—22no—
616C42—44no—
617C42—41no—
618C42—3322no—
619C42—3322no—
620C42—3324no—
621C42—3324no—
622C42—1668no—
623C42—1664no—
624C42—1664no—
625C42C2×C4×D8314yes—
626C42#1305059114yescomplemented
627C23—834no—
628C23—834no—
629C23—1662no—
630C23—1662no—
631C23—1662no—
632C23—1662no—
633C23—1662no—
634C23—1662no—
635C23—1662no—
636C23—1662no—
637C23—1662no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23C24×D8311yescharacteristic
642Q8—216no—
643D4—33216no—
644D4—1668no—
645D4—1668no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—24no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—24no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—24no—
658C2×C4—21no—
659C2×C4—24no—
660C2×C4—21no—
661C2×C4—24no—
662C2×C4—3328no—
663C2×C4—3328no—
664C2×C4—33216no—
665C2×C4—834no—
666C2×C4—834no—
667C2×C4—834no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—16616no—
684C2×C4—16616no—
685C2×C4C22×C4×D8312yes—
686C2×C4C22×C4×D8318yes—
687C2×C4C22×C4×D8312yes—
688C2×C4C22×C4×D8312yes—
689C2×C4#41×D8312yes—
690C2×C4C2×#1305059112yes—
691C2×C4C2×#1305059112yes—
692C2×C4C2×#1305059112yes—
693C2×C4#1458183712yes—
694C2×C4#1458183812yes—
695C2×C4#1458184012yes—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—3322no—
700C22—3322no—
701C22—3322no—
702C22—3322no—
703C22—3322no—
704C22—1664no—
705C22—1664no—
706C22—1664no—
707C22—1664no—
708C22—1664no—
709C22—1664no—
710C22C23×C4×D8311yescharacteristic
711C22C2×#41×D8311yescharacteristic
712C22C22×#1305059111yescharacteristic
713C22C2×#1458183711yescharacteristic
714C22C2×#1458183811yescharacteristic
715C22C2×#1458184011yescharacteristic
716C22#1912853711yescharacteristic
717C4—22no—
718C4—28no—
719C4—22no—
720C4—22no—
721C4—22no—
722C4—41no—
723C4—44no—
724C4—3322no—
725C4—3322no—
726C4—3322no—
727C4—1664no—
728C4—1664no—
729C4—1664no—
730C4C4×#1305059114yes—
731C4#1912817314yes—
732C2—3324no—
733C2—3324no—
734C2C2×C4×#1305059111yescharacteristic
735C2C2×#1912817311yescharacteristic
736C2C4×#1458184011yescharacteristic
737C2#2492131711yescharacteristic
738C2#2492137611yescharacteristic
739C2#2492146111yescharacteristic
740C2#2492150711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC4×C4⋊Q8×C83C2
socle, cosocleC23×C83C25
prime radicalC2×#19128354C2
hypercenterC4×C4⋊Q8D83
hypocenterC83#34316
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C4×C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #24910592C2semidirect
3. #24910523C2semidirect
4. #24910500C2semidirect
5. #24910486C2semidirect
6. #24910414C2semidirect
7. #24910414C2semidirect
8. #24910339C2semidirect
9. #24910301C2semidirect
10. #24910256C2semidirect
11. #24910157C2semidirect
12. #24910001C2semidirect
13. #24909952C2semidirect
14. #24909927C2semidirect
15. #24909817C2semidirect
16. C42×D332C2semidirect
17. C4×C4⋊Q8×C83C2semidirect
19. #19128354C4semidirect
86. C2×#13050591C2×C4semidirect
95. #14581777C2×C4semidirect
96. #14581768C2×C4semidirect
102. C4×D332C2×C4semidirect
116. C4⋊C4×D83C2×C4semidirect
149. C4⋊Q8×C83C2×C4semidirect
206. C4⋊Dic83#41semidirect
255. C42×C83#41semidirect
382. C4×C4⋊Q8D83semidirect
388. C83#34316semidirect
467. C4⋊Q8C4×D83semidirect
626. C42#13050591semidirect

Maximal subgroups

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

subgroupindex
C2×#191283542
#249105922
#249105232
#249105002
#249104862
#249104142
#249103392
#249103012
#249102562
#249101572
#249100012
#249099522
#249099272
#249098172
C42×D3322
C4×C4⋊Q8×C832
#3431683