Finite Group Databasebeta

← #35565384

Subgroups — #35565384

Order 21248.

2442 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128181C211yesmaximal, characteristic
2#24910438C212yesmaximal, complemented
3#24910430C212yesmaximal, complemented
4#24910422C212yesmaximal, complemented
5#24910414C212yesmaximal, complemented
6#24910355C212yesmaximal, complemented
7#24910347C212yesmaximal, complemented
8#24910339C212yesmaximal, complemented
9#24910331C212yesmaximal, complemented
10#24910091C214yesmaximal, complemented
11#24910056C211yesmaximal, characteristic
12#24909951C211yesmaximal, characteristic
13#24909947C211yesmaximal, characteristic, complemented
14#24909899C214yesmaximal, complemented
15#24909819C211yesmaximal, characteristic, complemented
16C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
17C83×#2317C211yesmaximal, characteristic, complemented
18C22×#13050590C2211yescharacteristic
19#19128181C4116yescomplemented
20C2×C4×Dic166C2212yes—
21C2×C4×D332C2212yes—
22C2×(C22⋊D83)⋊C4C2214yes—
23C2×#14581751C2211yescharacteristic
24C2×#14581750C2214yes—
25C2×#14581750C2212yes—
26C22×C4⋊Dic83C2211yescharacteristic
27C2×C4⋊C4×D83C2212yes—
28C22×C4×Dic83C2211yescharacteristic
29C22×C4×Dic83C2212yes—
30#19127606C2211yescharacteristic
31#19127606C2212yes—
32#19127606C2211yescharacteristic
33#19127602C2211yescharacteristic
34#19127602C2212yes—
35#19127602C2211yescharacteristic
36#19127600C2211yescharacteristic
37#19127600C2211yescharacteristic
38#19127600C2211yescharacteristic
39#19127600C2211yescharacteristic
40#19127593C2214yes—
41#19127593C2214yes—
42#19127591C2214yes—
43#19127591C2214yes—
44#19127588C2214yes—
45#19127588C2214yes—
46#19127582C2214yes—
47#19127582C2214yes—
48#19127580C2214yes—
49#19127578C2212yes—
50#19127578C2212yes—
51#19127576C2212yes—
52#19127576C2212yes—
53#19127568C2214yes—
54#19127566C2214yes—
55#19127563C2214yes—
56#19127558C2214yes—
57#19127558C2212yes—
58#19127558C2212yes—
59C4⋊C4×Dic83C2212yes—
60C4⋊C4×Dic83C2212yes—
61C4⋊C4×Dic83C2214yes—
62C4⋊C4×Dic83C2212yes—
63C4⋊C4×Dic83C2212yes—
64C4⋊C4×Dic83C2212yes—
65C4⋊C4×Dic83C2212yes—
66C4×C4⋊Dic83C2212yes—
67C4×C4⋊Dic83C2212yes—
68C4×C4⋊Dic83C2212yes—
69C4×C4⋊Dic83C2212yes—
70C22⋊C4×Dic83C2214yes—
71C4×(C2×D83)⋊C4C2212yes—
72C4×(C2×D83)⋊C4C2212yes—
73#19127548C2214yes—
74#19127546C2214yes—
75C2×C83⋊#95C2212yes—
76C2×#117×C83C2211yescharacteristic
77C2×#117×C83C2211yescharacteristic
78C22×C4⋊C4×C83C2211yescharacteristic
79#389×C83C2212yes—
80#389×C83C2212yes—
81#385×C83C2214yes—
82#384×C83C2212yes—
83#382×C83C2212yes—
84C2×#13050590—24no—
85C2×#13050590—24no—
86C2×#13050590C2×C418yes—
87C22×Dic166C2311yescharacteristic
88C22×D332C2311yescharacteristic
89C22×C22⋊D83C2312yes—
90C23×Dic83C2311yescharacteristic
91C23×Dic83C2311yescharacteristic
92C23×Dic83C2312yes—
93C22×C4×D83C2312yes—
94C22×C4×D83C2314yes—
95C4×Dic166C2×C4116yescomplemented
96C4×D332C2×C4116yescomplemented
97(C22⋊D83)⋊C4C2×C4132yes—
98#14581751—24no—
99#14581750—48no—
100#14581750C2×C4116yescomplemented
101C2×C4⋊Dic83C2×C418yes—
102C2×C4⋊Dic83C2311yescharacteristic
103C2×C4⋊Dic83C2311yescharacteristic
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2312yes—
110C2×Dic83⋊C4C2314yes—
111C4⋊C4×D83C2×C4116yescomplemented
112C2×C22⋊Dic83C2312yes—
113C2×(C2×D83)⋊C4C2312yes—
114C2×(C2×D83)⋊C4C2312yes—
115C2×(C2×D83)⋊C4C2312yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×C4×Dic83—24no—
121C2×C4×Dic83—44no—
122C2×C4×Dic83C2311yescharacteristic
123C2×C4×Dic83C2311yescharacteristic
124C2×C4×Dic83C2312yes—
125C2×C4×Dic83C2314yes—
126C2×C4×Dic83C2311yescharacteristic
127C2×C4×Dic83C2311yescharacteristic
128C2×C4×Dic83C2314yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C83⋊#95C2312yes—
135C83⋊#95C2312yes—
136C83⋊#95C2312yes—
137C83⋊#95C2312yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2312yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C23×C4×C83C2312yes—
147C23×C4×C83C2311yescharacteristic
148#117×C83—24no—
149#117×C83C2×C418yes—
150C2×C4⋊C4×C83—24no—
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2314yes—
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2311yescharacteristic
158C2×C4⋊C4×C83C2311yescharacteristic
159C2×C22⋊C4×C83C2312yes—
160C2×C22⋊C4×C83C2312yes—
161C2×C42×C83C2312yes—
162C2×C42×C83C2312yes—
163#95×C83C2314yes—
164#95×C83C2314yes—
165C23×D83C2412yes—
166#13050590—232no—
167C2×Dic166—22no—
168C2×Dic166—22no—
169C2×Dic166C22×C414yes—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332C22×C414yes—
173C2×C22⋊D83—24no—
174C2×C22⋊D83—24no—
175C2×C22⋊D83C22×C418yes—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—42no—
181C22×Dic83—41no—
182C22×Dic83—41no—
183C22×Dic83—42no—
184C22×Dic83C22×C418yes—
185C22×Dic83C2411yescharacteristic
186C22×Dic83C2411yescharacteristic
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2414yes—
190C22×Dic83C2412yes—
191C22×Dic83C2411yescharacteristic
192C22×Dic83C2411yescharacteristic
193C2×C4×D83—24no—
194C2×C4×D83—24no—
195C2×C4×D83—44no—
196C2×C4×D83—44no—
197C2×C4×D83C22×C418yes—
198C2×C4×D83C22×C4116yes—
199C4⋊Dic83—22no—
200C4⋊Dic83—22no—
201C4⋊Dic83—24no—
202C4⋊Dic83—24no—
203C4⋊Dic83—42no—
204C4⋊Dic83—42no—
205C4⋊Dic83C22×C418yes—
206C4⋊Dic83C22×C418yes—
207Dic83⋊C4C22×C4116yes—
208C22⋊Dic83—24no—
209(C2×D83)⋊C4—24no—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4—42no—
213(C2×D83)⋊C4—42no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4C22×C4116yes—
216C4×Dic83—22no—
217C4×Dic83—22no—
218C4×Dic83—22no—
219C4×Dic83—22no—
220C4×Dic83—24no—
221C4×Dic83—28no—
222C4×Dic83—44no—
223C4×Dic83—44no—
224C4×Dic83—44no—
225C4×Dic83C22×C4116yes—
226C24×C83C2411yescharacteristic
227C22×C4×C83—24no—
228C22×C4×C83—42no—
229C22×C4×C83—42no—
230C22×C4×C83C22×C414yes—
231C22×C4×C83#4114yes—
232C22×C4×C83#4114yes—
233C22×C4×C83C2412yes—
234C22×C4×C83C2414yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2411yescharacteristic
239C22×C4×C83C2411yescharacteristic
240C4⋊C4×C83—24no—
241C4⋊C4×C83—24no—
242C4⋊C4×C83—22no—
243C4⋊C4×C83—22no—
244C4⋊C4×C83—44no—
245C4⋊C4×C83—44no—
246C4⋊C4×C83C22×C414yes—
247C4⋊C4×C83C22×C414yes—
248C22⋊C4×C83—24no—
249C22⋊C4×C83C22×C418yes—
250C42×C83—24no—
251C42×C83C22×C418yes—
252C23×C83—21no—
253C23×C83—21no—
254C23×C83—21no—
255C23×C83—21no—
256C23×C83C23×C412yes—
257C23×C83C2×#4112yes—
258C23×C83C2×#4112yes—
259C23×C83C2511yescharacteristic
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—22no—
266C22×D83C23×C414yes—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—24no—
274C2×C4×C83—22no—
275C2×C4×C83—24no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—24no—
279C2×C4×C83—22no—
280C2×C4×C83—48no—
281C2×C4×C83#117116yescomplemented
282C2×C4×C83C23×C414yes—
283C2×C4×C83C23×C414yes—
284C2×C4×C83C23×C412yes—
285C2×C4×C83C23×C412yes—
286C2×C4×C83C2×#4112yes—
287C2×C4×C83C2×#4112yes—
288C2×C4×C83C2×#4112yes—
289C2×C4×C83C2×#4112yes—
290C22⋊D83—216no—
291C2×Dic83—28no—
292C2×Dic83—21no—
293C2×Dic83—21no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—24no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—24no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—21no—
311C2×Dic83—21no—
312C2×Dic83—48no—
313C2×Dic83—44no—
314C2×Dic83C23×C414yes—
315C2×Dic83C23×C418yes—
316C2×Dic83H(5,𝔽2)12yes—
317C2×Dic832−1+412yes—
318D332—28no—
319C4×D83—216no—
320C4×D83—416no—
321Dic166—28no—
322C22×C83—22no—
323C22×C83—22no—
324C22×C83—22no—
325C22×C83—22no—
326C22×C83—22no—
327C22×C83—22no—
328C22×C83C2×#11714yes—
329C22×C83C24×C411yescharacteristic
330C22×C83C22×#4111yescharacteristic
331C22×C83C22×#4111yescharacteristic
332C22×C83C2×H(5,𝔽2)11yescharacteristic
333C22×C83C2×2−1+411yescharacteristic
334C22×C83#58511yescharacteristic
335C22×C83#58511yescharacteristic
336C2×D83—24no—
337C2×D83—24no—
338C2×D83—24no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83—42no—
342C2×D83—42no—
343C4×C83—24no—
344C4×C83—24no—
345C4×C83—42no—
346C4×C83—44no—
347C4×C83—42no—
348C4×C83C2×#11714yes—
349C4×C83C2×#11714yes—
350Dic83—24no—
351Dic83—28no—
352Dic83—22no—
353Dic83—22no—
354Dic83—42no—
355Dic83—42no—
356Dic83—41no—
357Dic83—41no—
358#34252—831nomaximal, Sylow
359C2×C83—24no—
360C2×C83C22×#11711yescharacteristic
361C2×C83C4×H(5,𝔽2)11yescharacteristic
362C2×C83C4×2−1+411yescharacteristic
363C2×C83#349211yescharacteristic
364C2×C83#349311yescharacteristic
365C2×C83#350611yescharacteristic
366C2×C83#350711yescharacteristic
367D83—44no—
368C2×#520—831no—
369#2357—832no—
370#2356—832no—
371#2355—832no—
372#2354—832no—
373#2347—832no—
374#2346—832no—
375#2345—832no—
376#2344—832no—
377#2318—834no—
378#2317D8311yescharacteristic, complemented
379#2311—831no—
380#2297—831no—
381#2296—831no—
382#2290—834no—
383#2274—831no—
384C2×C4×C4⋊C4—831no—
385C83#3425211yescharacteristic, complemented, Sylow
386C22×#41—831no—
387#520—8316no—
388C2×C4×Q8—832no—
389C2×C4×D4—834no—
390C2×C4×D4—832no—
391C2×#117—831no—
392C2×#117—834no—
393C2×#117—832no—
394C2×#117C2×D8311yescharacteristic
395C2×#117C2×D8311yescharacteristic
396C22×C4⋊C4—831no—
397C22×C4⋊C4—832no—
398C22×C4⋊C4C2×D8311yescharacteristic
399C22×C42—832no—
400C22×C42—831no—
401#391—832no—
402#391—831no—
403#391—831no—
404#390—832no—
405#390—831no—
406#390—831no—
407#389—831no—
408#389—831no—
409#389—831no—
410#389—831no—
411#389C2×D8312yes—
412#389C2×D8312yes—
413#388—834no—
414#388—834no—
415#388—834no—
416#388—834no—
417#387—834no—
418#387—834no—
419#387—834no—
420#387—834no—
421#386—834no—
422#386—832no—
423#386—832no—
424#385—832no—
425#385—832no—
426#385C2×D8314yes—
427#384C2×D8312yes—
428#383—834no—
429#382—834no—
430#382C2×D8312yes—
431#381—834no—
432#380—832no—
433#380—832no—
434#380—834no—
435C4×C4⋊C4—832no—
436C4×C4⋊C4—832no—
437C4×C4⋊C4—834no—
438C4×C4⋊C4—832no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—832no—
442C4×C4⋊C4—832no—
443C4×C4⋊C4—832no—
444C4×C4⋊C4—832no—
445C4×C4⋊C4—832no—
446C4×C22⋊C4—834no—
447C4×C22⋊C4—832no—
448C4×C22⋊C4—832no—
449C4×C22⋊C4—834no—
450#376—834no—
451C2×#95—832no—
452C2×#41—838no—
453C2×#41—1664no—
454C2×#41—1664no—
455C22×Q8—831no—
456C22×D4—832no—
457C22×D4—831no—
458C23×C4—832no—
459C23×C4—834no—
460C23×C4—831no—
461C23×C4—832no—
462C23×C4—831no—
463C23×C4C22×D8312yes—
464C23×C4C22×D8311yescharacteristic
465C4×Q8—8316no—
466C4×D4—8332no—
467C4×D4—8316no—
468#117—24no—
469#117—3328no—
470#117—8316no—
471#117—1664no—
472#117C4×D8318yes—
473C2×C4⋊C4—24no—
474C2×C4⋊C4—832no—
475C2×C4⋊C4—832no—
476C2×C4⋊C4—838no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—832no—
479C2×C4⋊C4—834no—
480C2×C4⋊C4—8316no—
481C2×C4⋊C4—832no—
482C2×C4⋊C4—831no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—832no—
485C2×C4⋊C4C22×D8312yes—
486C2×C4⋊C4C22×D8312yes—
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8314yes—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C22⋊C4—834no—
494C2×C22⋊C4—832no—
495C2×C22⋊C4—834no—
496C2×C22⋊C4—832no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—832no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—832no—
501C2×C22⋊C4C22×D8312yes—
502C2×C22⋊C4C22×D8312yes—
503C2×C42—3324no—
504C2×C42—834no—
505C2×C42—834no—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—834no—
509C2×C42—832no—
510C2×C42—831no—
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—1664no—
515C2×C42C22×D8312yes—
516C2×C42C22×D8312yes—
517#95—834no—
518#95—834no—
519#95—832no—
520#95—832no—
521#95—834no—
522#95—832no—
523#95—834no—
524#95—834no—
525#95—832no—
526#95—832no—
527#95—832no—
528#95—834no—
529#95—832no—
530#95—832no—
531#95C22×D8314yes—
532#95C22×D8314yes—
533C24—832no—
534C24C23×D8311yescharacteristic
535#41—16632no—
536C2×Q8—834no—
537C2×Q8—1662no—
538C2×Q8—1662no—
539C2×D4—838no—
540C2×D4—834no—
541C2×D4—1664no—
542C2×D4—1664no—
543C2×D4—1662no—
544C2×D4—1662no—
545C22×C4—24no—
546C22×C4—42no—
547C22×C4—42no—
548C22×C4—3324no—
549C22×C4—3324no—
550C22×C4—3322no—
551C22×C4—3321no—
552C22×C4—3321no—
553C22×C4—3322no—
554C22×C4—838no—
555C22×C4—8316no—
556C22×C4—832no—
557C22×C4—831no—
558C22×C4—831no—
559C22×C4—834no—
560C22×C4—838no—
561C22×C4—831no—
562C22×C4—831no—
563C22×C4—832no—
564C22×C4—832no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1664no—
570C22×C4—1664no—
571C22×C4C2×C4×D8314yes—
572C22×C4#1305058914yes—
573C22×C4#1305059114yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8314yes—
576C22×C4C23×D8312yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8311yescharacteristic
580C22×C4C23×D8311yescharacteristic
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—22no—
584C4⋊C4—22no—
585C4⋊C4—44no—
586C4⋊C4—44no—
587C4⋊C4—3322no—
588C4⋊C4—3322no—
589C4⋊C4—838no—
590C4⋊C4—8316no—
591C4⋊C4—838no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1662no—
595C4⋊C4—1662no—
596C4⋊C4C2×C4×D8314yes—
597C4⋊C4C2×C4×D8314yes—
598C22⋊C4—24no—
599C22⋊C4—3324no—
600C22⋊C4—3322no—
601C22⋊C4—3324no—
602C22⋊C4—3322no—
603C22⋊C4—8316no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C22⋊C4—1664no—
607C22⋊C4C2×C4×D8318yes—
608C42—24no—
609C42—3324no—
610C42—3324no—
611C42—3324no—
612C42—8316no—
613C42—1668no—
614C42—1662no—
615C42—1662no—
616C42—1662no—
617C42—1662no—
618C42—1664no—
619C42C2×C4×D8318yes—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—834no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23C22×C4×D8312yes—
632C23C2×#1305058912yes—
633C23C2×#1305059112yes—
634C23C24×D8311yescharacteristic
635Q8—1668no—
636D4—16616no—
637D4—1668no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—24no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—48no—
652C2×C4—33216no—
653C2×C4—3324no—
654C2×C4—3328no—
655C2×C4—834no—
656C2×C4—838no—
657C2×C4—832no—
658C2×C4—832no—
659C2×C4—1661no—
660C2×C4—1661no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1662no—
665C2×C4—1662no—
666C2×C4—1661no—
667C2×C4—1661no—
668C2×C4—1662no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1668no—
672C2×C4—1662no—
673C2×C4—1661no—
674C2×C4—1661no—
675C2×C4—1662no—
676C2×C4—1661no—
677C2×C4—1664no—
678C2×C4—1661no—
679C2×C4—1664no—
680C2×C4—16616no—
681C2×C4#14581750116yescomplemented
682C2×C4C22×C4×D8314yes—
683C2×C4C22×C4×D8314yes—
684C2×C4C22×C4×D8312yes—
685C2×C4C22×C4×D8312yes—
686C2×C4C2×#1305058912yes—
687C2×C4C2×#1305058912yes—
688C2×C4C2×#1305059112yes—
689C2×C4C2×#1305059112yes—
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—3322no—
700C22—1664no—
701C22—1664no—
702C22—1664no—
703C22C2×#1458175014yes—
704C22C23×C4×D8311yescharacteristic
705C22C22×#1305058911yescharacteristic
706C22C22×#1305059111yescharacteristic
707C22H(5,𝔽2)×D8311yescharacteristic
708C222−1+4×D8311yescharacteristic
709C22#1912853611yescharacteristic
710C22#1912853811yescharacteristic
711C4—24no—
712C4—24no—
713C4—44no—
714C4—42no—
715C4—42no—
716C4—3322no—
717C4—3321no—
718C4—3321no—
719C4—3322no—
720C4—1664no—
721C4—1662no—
722C4—1662no—
723C4—1668no—
724C4C2×#1458175014yes—
725C4C2×#1458175014yes—
726C2—24no—
727C2—3324no—
728C2C22×#1458175011yescharacteristic
729C2#2492066911yescharacteristic
730C2#2492067411yescharacteristic
731C2#2492117311yescharacteristic
732C2#2492118411yescharacteristic
733C2#2492131411yescharacteristic
734C2#2492132711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2317C2
socle, cosocleC23×C83C25
prime radicalC22×#13050590C22
hypercenter#2317D83
hypocenterC83#34252
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2317

Complements

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

NH ≅ G/Ntype
2. #24910438C2semidirect
3. #24910430C2semidirect
4. #24910422C2semidirect
5. #24910414C2semidirect
6. #24910355C2semidirect
7. #24910347C2semidirect
8. #24910339C2semidirect
9. #24910331C2semidirect
10. #24910091C2semidirect
13. #24909947C2semidirect
14. #24909899C2semidirect
15. #24909819C2semidirect
16. C2×C4⋊C4×Dic83C2semidirect
17. C83×#2317C2semidirect
19. #19128181C4semidirect
95. C4×Dic166C2×C4semidirect
96. C4×D332C2×C4semidirect
100. #14581750C2×C4semidirect
111. C4⋊C4×D83C2×C4semidirect
281. C2×C4×C83#117semidirect
378. #2317D83semidirect
385. C83#34252semidirect
681. C2×C4#14581750semidirect

Maximal subgroups

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

subgroupindex
C2×#191281812
#249104382
#249104302
#249104222
#249104142
#249103552
#249103472
#249103392
#249103312
#249100912
#249100562
#249099512
#249099472
#249098992
#249098192
C2×C4⋊C4×Dic832
C83×#23172
#3425283