Finite Group Databasebeta

← #35564587

Subgroups — #35564587

Order 21248.

2470 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×C4×#13050591C211yesmaximal, characteristic
2#24910420C211yesmaximal, characteristic, complemented
3#24910395C212yesmaximal, complemented
4#24910389C212yesmaximal, complemented
5C4⋊C4×D332C211yesmaximal, characteristic, complemented
6#24910363C211yesmaximal, characteristic, complemented
7#24910344C212yesmaximal, complemented
8#24910318C214yesmaximal, complemented
9#24910292C212yesmaximal
10#24910108C212yesmaximal, complemented
11#24910095C214yesmaximal, complemented
12#24909868C211yesmaximal, characteristic, complemented
13#24909859C211yesmaximal, characteristic, complemented
14#24909859C212yesmaximal, complemented
15#382×D83C212yesmaximal, complemented
16#24909823C212yesmaximal, complemented
17C83×#2355C211yesmaximal, characteristic, complemented
18C22×#13050591C2211yescharacteristic
19C4×#13050591C4116yescomplemented
20C2×Q8×Dic83C2211yescharacteristic
21C2×C4×D332C2212yes—
22C2×C4×D332C2211yescharacteristic
23C2×C4×D332C2212yes—
24C2×#14581754C2212yes—
25C2×#14581754C2211yescharacteristic
26C2×#14581754C2212yes—
27C2×#14581750C2212yes—
28C2×#14581750C2211yescharacteristic
29C2×#14581750C2212yes—
30C2×C4⋊C4×D83C2212yes—
31C2×C4⋊C4×D83C2212yes—
32C2×C42×D83C2212yes—
33C2×C42×D83C2211yescharacteristic
34#19127608C2212yes—
35#19127599C2212yes—
36#19127597C2212yes—
37#19127592C2214yes—
38#19127590C2214yes—
39#19127587C2214yes—
40#19127586C2214yes—
41#19127584C2214yes—
42#19127579C2214yes—
43#19127579C2214yes—
44#19127575C2214yes—
45#19127572C2214yes—
46#19127571C2211yescharacteristic
47#19127568C2214yes—
48#19127568C2212yes—
49#19127567C2212yes—
50#19127566C2211yescharacteristic
51#19127566C2212yes—
52#19127566C2211yescharacteristic
53#19127565C2214yes—
54#19127565C2214yes—
55#19127563C2212yes—
56#19127563C2214yes—
57#19127558C2212yes—
58#19127558C2212yes—
59#19127558C2212yes—
60#19127558C2212yes—
61#19127558C2211yescharacteristic
62#19127558C2211yescharacteristic
63C4⋊C4×Dic83C2212yes—
64C4⋊C4×Dic83C2212yes—
65C4⋊C4×Dic83C2212yes—
66C4×C4⋊Dic83C2211yescharacteristic
67C4×C4⋊Dic83C2212yes—
68C4×(C2×D83)⋊C4C2212yes—
69C4×(C2×D83)⋊C4C2214yes—
70C4×(C2×D83)⋊C4C2214yes—
71#19127548C2214yes—
72#19127547C2214yes—
73#19127547C2212yes—
74#95×D83C2214yes—
75#95×D83C2214yes—
76C2×C4×Q8×C83C2211yescharacteristic
77#391×C83C2212yes—
78#387×C83C2214yes—
79#384×C83C2211yescharacteristic
80#382×C83C2212yes—
81C4×C4⋊C4×C83C2212yes—
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C2×#13050591—24no—
85C2×#13050591—24no—
86C2×#13050591C2×C418yes—
87C22×D332C2312yes—
88C22×D332C2311yescharacteristic
89C22×C4×D83C2312yes—
90C22×C4×D83C2311yescharacteristic
91C22×C4×D83C2311yescharacteristic
92C22×C4×D83C2312yes—
93C22×C4×D83C2314yes—
94C22×C4×D83C2314yes—
95C22×C4×D83C2311yescharacteristic
96C22×C4×D83C2312yes—
97Q8×Dic83C2×C418yescomplemented
98C4×D332—28no—
99C4×D332C2×C418yes—
100C4×D332C2×C4116yescomplemented
101#14581754—28no—
102#14581754C2×C418yes—
103#14581754C2×C4116yescomplemented
104#14581750—44no—
105#14581750C2×C418yescomplemented
106#14581750C2×C4116yescomplemented
107C2×C4⋊Dic83C2311yescharacteristic
108C2×C4⋊Dic83C2311yescharacteristic
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2312yes—
111C2×C4⋊Dic83C2312yes—
112C2×C4⋊Dic83C2312yes—
113C2×C4⋊Dic83C2311yescharacteristic
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C4⋊C4×D83—44no—
117C4⋊C4×D83—44no—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2312yes—
122C2×(C2×D83)⋊C4C2312yes—
123C2×(C2×D83)⋊C4C2312yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×C4×Dic83C2312yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2314yes—
129C2×C4×Dic83C2311yescharacteristic
130C2×C4×Dic83C2311yescharacteristic
131C2×C4×Dic83C2312yes—
132C2×C4×Dic83C2312yes—
133C2×C4×Dic83C2311yescharacteristic
134C42×D83C2×C418yescomplemented
135C42×D83C2×C4116yescomplemented
136C83⋊#95C2312yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2312yes—
146C83⋊#95C2312yes—
147C83⋊#95C2312yes—
148C83⋊#95C2312yes—
149C83⋊#95C2314yes—
150C22×Q8×C83C2311yescharacteristic
151C4×Q8×C83C2×C418yescomplemented
152C2×C4⋊C4×C83C2312yes—
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2311yescharacteristic
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2311yescharacteristic
158C2×C4⋊C4×C83C2312yes—
159C2×C42×C83C2312yes—
160C2×C42×C83C2314yes—
161C2×C42×C83C2312yes—
162C2×C42×C83C2311yescharacteristic
163#95×C83C2312yes—
164#95×C83C2314yes—
165#95×C83C2314yes—
166#95×C83C2314yes—
167C23×D83C2411yescharacteristic
168C23×D83C2412yes—
169#13050591—232no—
170C2×D332—24no—
171C2×D332—24no—
172C2×D332C22×C418yes—
173C2×D332C22×C414yes—
174C2×D332#4114yes—
175C2×D332#4114yes—
176C22×Dic83C2412yes—
177C22×Dic83C2414yes—
178C22×Dic83C2412yes—
179C22×Dic83C2411yescharacteristic
180C22×Dic83C2411yescharacteristic
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2412yes—
183C2×C4×D83—24no—
184C2×C4×D83—24no—
185C2×C4×D83—22no—
186C2×C4×D83—22no—
187C2×C4×D83—24no—
188C2×C4×D83—22no—
189C2×C4×D83—24no—
190C2×C4×D83—22no—
191C2×C4×D83—28no—
192C2×C4×D83—28no—
193C2×C4×D83—42no—
194C2×C4×D83—41no—
195C2×C4×D83—42no—
196C2×C4×D83—41no—
197C2×C4×D83—44no—
198C2×C4×D83—44no—
199C2×C4×D83—44no—
200C2×C4×D83—44no—
201C2×C4×D83C22×C418yes—
202C2×C4×D83C22×C414yes—
203C2×C4×D83C22×C418yes—
204C2×C4×D83C22×C414yes—
205C2×C4×D83C22×C418yes—
206C2×C4×D83C22×C414yes—
207C4⋊Dic83—24no—
208C4⋊Dic83—22no—
209C4⋊Dic83—24no—
210C4⋊Dic83—22no—
211C4⋊Dic83—42no—
212C4⋊Dic83C22×C414yes—
213C4⋊Dic83C22×C418yes—
214Dic83⋊C4—44no—
215Dic83⋊C4—44no—
216(C2×D83)⋊C4—28no—
217(C2×D83)⋊C4—28no—
218(C2×D83)⋊C4—42no—
219(C2×D83)⋊C4—42no—
220(C2×D83)⋊C4—44no—
221(C2×D83)⋊C4C22×C418yes—
222(C2×D83)⋊C4C22×C418yes—
223(C2×D83)⋊C4C22×C418yes—
224C4×Dic83—24no—
225C4×Dic83—44no—
226C4×Dic83—44no—
227C4×Dic83C22×C414yes—
228C4×Dic83C22×C414yes—
229C4×Dic83C22×C418yes—
230C4×Dic83C22×C414yes—
231C4×Dic83C22×C418yes—
232C2×Q8×C83—22no—
233C2×Q8×C83—22no—
234C2×Q8×C83C22×C414yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2414yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2411yescharacteristic
241C22×C4×C83C2411yescharacteristic
242C22×C4×C83C2411yescharacteristic
243C4⋊C4×C83—24no—
244C4⋊C4×C83—22no—
245C4⋊C4×C83—24no—
246C4⋊C4×C83—22no—
247C4⋊C4×C83—42no—
248C4⋊C4×C83C22×C414yes—
249C4⋊C4×C83C22×C418yes—
250C42×C83—24no—
251C42×C83—44no—
252C42×C83C22×C414yes—
253C42×C83C22×C418yes—
254C23×C83C2511yescharacteristic
255C22×D83—22no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83—21no—
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—21no—
265C22×D83C23×C412yes—
266C22×D83C23×C414yes—
267C22×D83C2×#4114yes—
268C22×D83C2×#4114yes—
269Q8×C83—28no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—21no—
274C2×C4×C83—22no—
275C2×C4×C83—21no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—24no—
279C2×C4×C83—24no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—24no—
284C2×C4×C83—22no—
285C2×C4×C83C23×C412yes—
286C2×C4×C83C23×C414yes—
287C2×C4×C83C23×C414yes—
288C2×C4×C83C23×C412yes—
289C2×C4×C83C23×C412yes—
290C2×C4×C83C2×#4112yes—
291C2×C4×C83C2×#4112yes—
292C2×C4×C83H(5,𝔽2)12yes—
293C2×C4×C832−1+412yes—
294C2×Dic83—21no—
295C2×Dic83—21no—
296C2×Dic83—21no—
297C2×Dic83—22no—
298C2×Dic83—21no—
299C2×Dic83—22no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—24no—
305C2×Dic83—24no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—24no—
310C2×Dic83—22no—
311C2×Dic83C23×C412yes—
312C2×Dic83C23×C412yes—
313C2×Dic83C23×C412yes—
314C2×Dic83C23×C414yes—
315D332—216no—
316D332#117116yescomplemented
317C4×D83—216no—
318C4×D83—28no—
319C4×D83—216no—
320C4×D83—28no—
321C4×D83—48no—
322C4×D83—44no—
323C4×D83—88no—
324C4×D83—88no—
325C22×C83C24×C411yescharacteristic
326C22×C83C22×#4111yescharacteristic
327C22×C83C22×#4111yescharacteristic
328C22×C83C2×H(5,𝔽2)11yescharacteristic
329C22×C83C2×2−1+411yescharacteristic
330C22×C83#58511yescharacteristic
331C22×C83#58511yescharacteristic
332C2×D83—24no—
333C2×D83—24no—
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—24no—
337C2×D83—24no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—41no—
342C2×D83—41no—
343C2×D83—41no—
344C2×D83—41no—
345C2×D83C2×#11718yes—
346C4×C83—24no—
347C4×C83—24no—
348C4×C83—22no—
349C4×C83—42no—
350C4×C83—44no—
351C4×C83—42no—
352C4×C83C2×#11714yes—
353C4×C83#52014yes—
354Dic83—22no—
355Dic83—22no—
356Dic83—24no—
357Dic83—22no—
358Dic83—42no—
359Dic83—44no—
360Dic83—42no—
361#34191—831nomaximal, Sylow
362C2×C83C22×#11711yescharacteristic
363C2×C83C2×#52011yescharacteristic
364C2×C83#342811yescharacteristic
365C2×C83#351411yescharacteristic
366C2×C83#351411yescharacteristic
367C2×C83#351511yescharacteristic
368C2×C83#351511yescharacteristic
369D83—28no—
370D83—42no—
371C2×C4×#41—831no—
372#2355—831no—
373#2355D8311yescharacteristic, complemented
374#2352—832no—
375#2352—832no—
376D4×C4⋊C4—831no—
377D4×C4⋊C4—831no—
378#2346—832no—
379#2343—834no—
380#2339—832no—
381#2320—832no—
382#2318—834no—
383#2285—831no—
384#2283—831no—
385#2283—832no—
386C2×#382—832no—
387#2275—832no—
388C83#3419111yescharacteristic, complemented, Sylow
389C22×#41—831no—
390C4×#41—8316no—
391C2×C4×Q8—831no—
392C2×C4×Q8C2×D8311yescharacteristic
393C2×C4×D4—832no—
394C2×C4×D4—831no—
395C2×C4×D4—832no—
396C2×C4×D4—831no—
397C2×C4×D4—832no—
398C2×C4×D4—832no—
399C2×#117—832no—
400C2×#117—832no—
401C2×#117—831no—
402C22×C4⋊C4—832no—
403C22×C4⋊C4—832no—
404C22×C42—832no—
405C22×C42—831no—
406#391—832no—
407#391C2×D8312yes—
408#389—832no—
409#389—832no—
410#388—834no—
411#388—834no—
412#387—834no—
413#387—834no—
414#387—834no—
415#387C2×D8314yes—
416#386—834no—
417#386—834no—
418#385—834no—
419#385—834no—
420#384—831no—
421#384C2×D8311yescharacteristic
422#383—834no—
423#383—832no—
424#382—831no—
425#382—832no—
426#382—831no—
427#382—832no—
428#382—834no—
429#382—834no—
430#382C2×D8312yes—
431#381—832no—
432#381—834no—
433#380—832no—
434#380—832no—
435#380—832no—
436#380—832no—
437#380—831no—
438#380—831no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—832no—
441C4×C4⋊C4—832no—
442C4×C4⋊C4—831no—
443C4×C4⋊C4—832no—
444C4×C4⋊C4C2×D8312yes—
445C4×C4⋊C4C2×D8311yescharacteristic
446C4×C4⋊C4C2×D8312yes—
447C4×C22⋊C4—834no—
448C4×C22⋊C4—832no—
449C4×C22⋊C4—834no—
450C4×C22⋊C4—834no—
451#376—832no—
452#376—834no—
453C2×#95—834no—
454C2×#95—834no—
455C2×#41—838no—
456C2×#41—1664no—
457C2×#41—1664no—
458C22×Q8C22×D8311yescharacteristic
459C22×D4—831no—
460C22×D4—832no—
461C23×C4—832no—
462C23×C4—831no—
463C23×C4—834no—
464C23×C4—834no—
465C23×C4—832no—
466C23×C4—831no—
467C23×C4—832no—
468C23×C4—831no—
469C4×Q8—838no—
470C4×Q8C4×D8318yescomplemented
471C4×D4—838no—
472C4×D4—8316no—
473C4×D4—838no—
474C4×D4—8316no—
475C4×D4—1668no—
476C4×D4—1668no—
477#117—3324no—
478#117—8316no—
479#117—838no—
480C2×C4⋊C4—3324no—
481C2×C4⋊C4—3324no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—832no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4—832no—
490C2×C4⋊C4—831no—
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8312yes—
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8311yescharacteristic
495C2×C4⋊C4C22×D8312yes—
496C2×C4⋊C4C22×D8311yescharacteristic
497C2×C4⋊C4C22×D8312yes—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—832no—
500C2×C22⋊C4—832no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—834no—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—832no—
509C2×C42—831no—
510C2×C42—831no—
511C2×C42—832no—
512C2×C42—831no—
513C2×C42—8316no—
514C2×C42—838no—
515C2×C42—832no—
516C2×C42C22×D8312yes—
517C2×C42C22×D8314yes—
518C2×C42C22×D8312yes—
519C2×C42C22×D8311yescharacteristic
520#95—832no—
521#95—832no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—832no—
527#95—832no—
528#95—832no—
529#95—832no—
530#95—834no—
531#95—834no—
532#95—832no—
533#95—834no—
534#95C22×D8314yes—
535#95C22×D8314yes—
536#95C22×D8312yes—
537#95C22×D8314yes—
538C24—832no—
539C24—831no—
540#41—16632no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8C2×C4×D8314yes—
544C2×D4—834no—
545C2×D4—838no—
546C2×D4—834no—
547C2×D4—834no—
548C2×D4—1664no—
549C2×D4—1664no—
550C22×C4—3322no—
551C22×C4—3321no—
552C22×C4—3322no—
553C22×C4—3321no—
554C22×C4—3324no—
555C22×C4—3324no—
556C22×C4—3324no—
557C22×C4—3324no—
558C22×C4—838no—
559C22×C4—834no—
560C22×C4—831no—
561C22×C4—831no—
562C22×C4—831no—
563C22×C4—832no—
564C22×C4—838no—
565C22×C4—834no—
566C22×C4—838no—
567C22×C4—834no—
568C22×C4—832no—
569C22×C4—832no—
570C22×C4—834no—
571C22×C4—1668no—
572C22×C4—1668no—
573C22×C4—1664no—
574C22×C4—1664no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1664no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1664no—
581C22×C4C23×D8312yes—
582C22×C4C23×D8312yes—
583C22×C4C23×D8314yes—
584C22×C4C23×D8312yes—
585C22×C4C23×D8312yes—
586C22×C4C23×D8311yescharacteristic
587C22×C4C23×D8311yescharacteristic
588C22×C4C23×D8311yescharacteristic
589C4⋊C4—24no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C4⋊C4—22no—
593C4⋊C4—42no—
594C4⋊C4—3324no—
595C4⋊C4—3324no—
596C4⋊C4—3322no—
597C4⋊C4—838no—
598C4⋊C4—834no—
599C4⋊C4—1664no—
600C4⋊C4—1662no—
601C4⋊C4—1664no—
602C4⋊C4—1662no—
603C4⋊C4C2×C4×D8318yes—
604C4⋊C4C2×C4×D8314yes—
605C22⋊C4—3324no—
606C22⋊C4—3322no—
607C22⋊C4—3322no—
608C22⋊C4—838no—
609C22⋊C4—838no—
610C22⋊C4—838no—
611C22⋊C4—1668no—
612C22⋊C4—1668no—
613C42—24no—
614C42—44no—
615C42—3324no—
616C42—3324no—
617C42—834no—
618C42—838no—
619C42—834no—
620C42—838no—
621C42—834no—
622C42—1664no—
623C42C2×C4×D8318yes—
624C42C2×C4×D8314yes—
625C23—834no—
626C23—834no—
627C23—834no—
628C23—832no—
629C23—1661no—
630C23—1661no—
631C23—1661no—
632C23—1661no—
633C23—1661no—
634C23—1661no—
635C23—1662no—
636C23—1662no—
637C23—1662no—
638C23—1662no—
639C23C24×D8311yescharacteristic
640Q8—28no—
641D4—8316no—
642D4—16616no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—3324no—
659C2×C4—3328no—
660C2×C4—832no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—834no—
664C2×C4—6648no—
665C2×C4—6648no—
666C2×C4—16616no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1664no—
670C2×C4—1664no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1664no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1661no—
679C2×C4—1662no—
680C2×C4—1661no—
681C2×C4—1662no—
682C2×C4—1661no—
683C2×C4—1661no—
684C2×C4—1668no—
685C2×C4—1668no—
686C2×C4—16616no—
687C2×C4C22×C4×D8314yes—
688C2×C4C22×C4×D8312yes—
689C2×C4C22×C4×D8314yes—
690C2×C4C22×C4×D8312yes—
691C2×C4C22×C4×D8312yes—
692C2×C4#41×D8312yes—
693C2×C4#41×D8312yes—
694C2×C4#1458183812yes—
695C2×C4#1458184012yes—
696C22—3321no—
697C22—3321no—
698C22—3321no—
699C22—3321no—
700C22—838no—
701C22—1662no—
702C22—1662no—
703C22—1662no—
704C22—1664no—
705C22—1664no—
706C22—1664no—
707C22—1664no—
708C22—1664no—
709C22—1664no—
710C22C23×C4×D8311yescharacteristic
711C22C2×#41×D8311yescharacteristic
712C22C2×#41×D8311yescharacteristic
713C22C2×#1458183811yescharacteristic
714C22C2×#1458184011yescharacteristic
715C22#1912853611yescharacteristic
716C22#1912853811yescharacteristic
717C4—24no—
718C4—24no—
719C4—22no—
720C4—44no—
721C4—42no—
722C4—42no—
723C4—3322no—
724C4—3324no—
725C4—3322no—
726C4—1662no—
727C4—1662no—
728C4—1664no—
729C4—1662no—
730C4#117×D8314yes—
731C4#1912818314yes—
732C2—3322no—
733C2—1668no—
734C2C2×#117×D8311yescharacteristic
735C2C2×#1912818311yescharacteristic
736C2#2492066311yescharacteristic
737C2#2492142311yescharacteristic
738C2#2492142711yescharacteristic
739C2#2492144011yescharacteristic
740C2#2492144411yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2355C2
socle, cosocleC23×C83C25
prime radicalC22×#13050591C22
hypercenter#2355D83
hypocenterC83#34191
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. #24910420C2semidirect
3. #24910395C2semidirect
4. #24910389C2semidirect
5. C4⋊C4×D332C2semidirect
6. #24910363C2semidirect
7. #24910344C2semidirect
8. #24910318C2semidirect
10. #24910108C2semidirect
11. #24910095C2semidirect
12. #24909868C2semidirect
13. #24909859C2semidirect
14. #24909859C2semidirect
15. #382×D83C2semidirect
16. #24909823C2semidirect
17. C83×#2355C2semidirect
19. C4×#13050591C4semidirect
97. Q8×Dic83C2×C4semidirect
100. C4×D332C2×C4semidirect
103. #14581754C2×C4semidirect
105. #14581750C2×C4semidirect
106. #14581750C2×C4semidirect
134. C42×D83C2×C4semidirect
135. C42×D83C2×C4semidirect
151. C4×Q8×C83C2×C4semidirect
316. D332#117semidirect
373. #2355D83semidirect
388. C83#34191semidirect
470. C4×Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#130505912
#249104202
#249103952
#249103892
C4⋊C4×D3322
#249103632
#249103442
#249103182
#249102922
#249101082
#249100952
#249098682
#249098592
#382×D832
#249098232
C83×#23552
#3419183