Finite Group Databasebeta

← #35566667

Subgroups — #35566667

Order 21248.

2452 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128417C211yesmaximal, characteristic
2#24910539C214yesmaximal, complemented
3#24910500C212yesmaximal, complemented
4#24910481C212yesmaximal, complemented
5#24910410C211yesmaximal, characteristic, complemented
6C4⋊C4×D332C211yesmaximal, characteristic, complemented
7#24910355C212yesmaximal, complemented
8#24910352C212yesmaximal, complemented
9#24910275C214yesmaximal, complemented
10#24910154C212yesmaximal, complemented
11C4⋊Q8×Dic83C211yesmaximal, characteristic, complemented
12C4×#14581767C212yesmaximal, complemented
13#24909944C212yesmaximal, complemented
14#24909924C211yesmaximal, characteristic, complemented
15#24909817C212yesmaximal, complemented
16C4×#14581754C211yesmaximal, characteristic, complemented
17C83×#2369C211yesmaximal, characteristic, complemented
18#19128417C4116yescomplemented
19C2×#14581781C2214yes—
20C2×#14581767C2212yes—
21C2×#14581767C2212yes—
22C2×Q8×Dic83C2212yes—
23C2×C4×D332C2212yes—
24C2×C4×D332C2214yes—
25C2×C4×D332C2211yescharacteristic
26C2×C4×D332C2211yescharacteristic
27C2×#14581754C2211yescharacteristic
28C2×#14581754C2211yescharacteristic
29C2×#14581750C2212yes—
30C2×#14581750C2212yes—
31C2×#14581750C2212yes—
32C2×#14581749C2212yes—
33C2×C4⋊C4×D83C2212yes—
34C2×C42×D83C2212yes—
35#19127608C2212yes—
36#19127603C2212yes—
37#19127602C2214yes—
38#19127602C2211yescharacteristic
39#19127602C2211yescharacteristic
40#19127600C2212yes—
41#19127600C2212yes—
42#19127599C2212yes—
43#19127597C2211yescharacteristic
44#19127597C2211yescharacteristic
45#19127593C2214yes—
46#19127593C2214yes—
47#19127592C2214yes—
48#19127591C2214yes—
49#19127590C2214yes—
50#19127590C2212yes—
51#19127590C2212yes—
52#19127579C2214yes—
53#19127579C2214yes—
54#19127575C2214yes—
55#19127575C2214yes—
56#19127572C2214yes—
57#19127571C2211yescharacteristic
58#19127568C2214yes—
59#19127558C2212yes—
60#19127558C2212yes—
61C4⋊C4×Dic83C2212yes—
62C4⋊C4×Dic83C2211yescharacteristic
63C4⋊C4×Dic83C2214yes—
64C4⋊C4×Dic83C2212yes—
65C4⋊C4×Dic83C2211yescharacteristic
66C4×Dic83⋊C4C2214yes—
67C4×C4⋊Dic83C2212yes—
68#19127552C2214yes—
69C4×(C2×D83)⋊C4C2212yes—
70C4×(C2×D83)⋊C4C2212yes—
71C4×(C2×D83)⋊C4C2214yes—
72#19127548C2214yes—
73#19127548C2212yes—
74#19127548C2212yes—
75C42×Dic83C2211yescharacteristic
76C2×C4⋊Q8×C83C2211yescharacteristic
77#391×C83C2214yes—
78#389×C83C2212yes—
79#389×C83C2212yes—
80C4×C4⋊C4×C83C2212yes—
81C4×C4⋊C4×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×D332C2311yescharacteristic
85C22×D332C2311yescharacteristic
86C22×D332C2314yes—
87C22×C4×D83C2312yes—
88C22×C4×D83C2312yes—
89C22×C4×D83C2312yes—
90C22×C4×D83C2312yes—
91C22×C4×D83C2314yes—
92#14581781C2×C4132yescomplemented
93#14581767C2×C4116yescomplemented
94#14581767C2×C4116yescomplemented
95Q8×Dic83—44no—
96C4×D332—44no—
97C4×D332—48no—
98C4×D332C2×C418yescomplemented
99C4×D332C2×C418yescomplemented
100#14581754—24no—
101#14581754—24no—
102#14581750—44no—
103#14581750C2×C4116yescomplemented
104#14581750C2×C4116yescomplemented
105#14581749—28no—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2314yes—
109C2×C4⋊Dic83C2312yes—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×C4⋊Dic83C2311yescharacteristic
112C2×Dic83⋊C4C2312yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2312yes—
115C4⋊C4×D83—28no—
116C2×(C2×D83)⋊C4C2312yes—
117C2×(C2×D83)⋊C4C2312yes—
118C2×(C2×D83)⋊C4C2312yes—
119C2×(C2×D83)⋊C4C2312yes—
120C2×(C2×D83)⋊C4C2312yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2314yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2312yes—
129C2×C4×Dic83C2311yescharacteristic
130C2×C4×Dic83C2311yescharacteristic
131C2×C4×Dic83C2311yescharacteristic
132C2×C4×Dic83C2311yescharacteristic
133C2×C4×Dic83C2312yes—
134C2×C4×Dic83C2314yes—
135C2×C4×Dic83C2314yes—
136C2×C4×Dic83C2312yes—
137C2×C4×Dic83C2311yescharacteristic
138C2×C4×Dic83C2314yes—
139C2×C4×Dic83C2311yescharacteristic
140C42×D83—44no—
141C83⋊#95C2314yes—
142C83⋊#95C2314yes—
143C83⋊#95C2312yes—
144C83⋊#95C2312yes—
145C83⋊#95C2314yes—
146C83⋊#95C2312yes—
147C83⋊#95C2314yes—
148C83⋊#95C2312yes—
149C22×Q8×C83C2312yes—
150C4⋊Q8×C83C2×C418yescomplemented
151C2×C4⋊C4×C83C2311yescharacteristic
152C2×C4⋊C4×C83C2311yescharacteristic
153C2×C4⋊C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83C2314yes—
155C2×C4⋊C4×C83C2312yes—
156C2×C4⋊C4×C83C2312yes—
157C2×C4⋊C4×C83C2311yescharacteristic
158C2×C42×C83C2312yes—
159C2×C42×C83C2312yes—
160C2×C42×C83C2314yes—
161C2×C42×C83C2311yescharacteristic
162#95×C83C2314yes—
163#95×C83C2314yes—
164#95×C83C2312yes—
165#95×C83C2312yes—
166C23×D83C2412yes—
167C23×D83C2412yes—
168C2×D332—22no—
169C2×D332—22no—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332—44no—
173C2×D332—44no—
174C2×D332C22×C414yes—
175C2×D332C22×C414yes—
176C2×D332C22×C4116yes—
177C22×Dic83C2414yes—
178C22×Dic83C2411yescharacteristic
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2411yescharacteristic
182C22×Dic83C2411yescharacteristic
183C22×Dic83C2411yescharacteristic
184C2×C4×D83—24no—
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—28no—
192C2×C4×D83—42no—
193C2×C4×D83—42no—
194C2×C4×D83—42no—
195C2×C4×D83—44no—
196C2×C4×D83—44no—
197C2×C4×D83C22×C418yes—
198C2×C4×D83C22×C418yes—
199C4⋊Dic83—24no—
200C4⋊Dic83—24no—
201C4⋊Dic83—28no—
202C4⋊Dic83—42no—
203C4⋊Dic83C22×C414yes—
204C4⋊Dic83C22×C414yes—
205Dic83⋊C4—28no—
206Dic83⋊C4—24no—
207Dic83⋊C4—24no—
208(C2×D83)⋊C4—24no—
209(C2×D83)⋊C4—24no—
210(C2×D83)⋊C4—24no—
211(C2×D83)⋊C4—24no—
212(C2×D83)⋊C4—24no—
213(C2×D83)⋊C4—42no—
214(C2×D83)⋊C4—44no—
215(C2×D83)⋊C4—44no—
216(C2×D83)⋊C4—44no—
217(C2×D83)⋊C4C22×C4116yes—
218(C2×D83)⋊C4C22×C4116yes—
219(C2×D83)⋊C4C22×C418yes—
220(C2×D83)⋊C4C22×C418yes—
221C4×Dic83—22no—
222C4×Dic83—22no—
223C4×Dic83—22no—
224C4×Dic83—22no—
225C4×Dic83—42no—
226C4×Dic83—42no—
227C4×Dic83—41no—
228C4×Dic83—44no—
229C4×Dic83—44no—
230C4×Dic83C22×C4116yes—
231C4×Dic83#4114yes—
232C2×Q8×C83—42no—
233C2×Q8×C83—42no—
234C2×Q8×C83C22×C418yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2414yes—
239C22×C4×C83C2411yescharacteristic
240C22×C4×C83C2412yes—
241C22×C4×C83C2411yescharacteristic
242C22×C4×C83C2411yescharacteristic
243C4⋊C4×C83—22no—
244C4⋊C4×C83—22no—
245C4⋊C4×C83—22no—
246C4⋊C4×C83—44no—
247C4⋊C4×C83C22×C418yes—
248C4⋊C4×C83C22×C418yes—
249C4⋊C4×C83#4114yes—
250C42×C83—24no—
251C42×C83—24no—
252C42×C83—44no—
253C42×C83C22×C414yes—
254C23×C83C2511yescharacteristic
255C22×D83—22no—
256C22×D83—22no—
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×D83C23×C414yes—
268C22×D83C23×C414yes—
269Q8×C83—48no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—24no—
273C2×C4×C83—21no—
274C2×C4×C83—24no—
275C2×C4×C83—21no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—22no—
285C2×C4×C83C23×C412yes—
286C2×C4×C83C23×C418yes—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C23×C412yes—
289C2×C4×C83C2×#4112yes—
290C2×C4×C83C2×#4114yes—
291C2×C4×C83C2×#4112yes—
292C2×C4×C83H(5,𝔽2)12yes—
293C2×C4×C832−1+412yes—
294C2×Dic83—21no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—21no—
298C2×Dic83—21no—
299C2×Dic83—21no—
300C2×Dic83—22no—
301C2×Dic83—21no—
302C2×Dic83—22no—
303C2×Dic83—21no—
304C2×Dic83—21no—
305C2×Dic83—24no—
306C2×Dic83—24no—
307C2×Dic83—24no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83C23×C414yes—
311C2×Dic83C23×C414yes—
312C2×Dic83C2×#4112yes—
313C2×Dic83C2×#4112yes—
314C2×Dic83H(5,𝔽2)12yes—
315D332—28no—
316D332—28no—
317D332—416no—
318C4×D83—216no—
319C4×D83—216no—
320C4×D83—48no—
321C4×D83—48no—
322C4×D83—88no—
323C22×C83C24×C411yescharacteristic
324C22×C83C22×#4111yescharacteristic
325C22×C83C22×#4111yescharacteristic
326C22×C83C2×H(5,𝔽2)11yescharacteristic
327C22×C83C2×H(5,𝔽2)11yescharacteristic
328C22×C83C2×2−1+411yescharacteristic
329C22×C83#58511yescharacteristic
330C2×D83—24no—
331C2×D83—24no—
332C2×D83—24no—
333C2×D83—24no—
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—42no—
341C2×D83—42no—
342C2×D83—42no—
343C2×D83—42no—
344C4×C83—28no—
345C4×C83—22no—
346C4×C83—24no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83C4×#4114yes—
351C4×C83#52014yes—
352Dic83—24no—
353Dic83—24no—
354Dic83—22no—
355Dic83—22no—
356Dic83—22no—
357Dic83—41no—
358Dic83—44no—
359#34321—831nomaximal, Sylow
360C2×C83C2×C4×#4111yescharacteristic
361C2×C83C2×#52011yescharacteristic
362C2×C83C4×H(5,𝔽2)11yescharacteristic
363C2×C83#350611yescharacteristic
364C2×C83#351111yescharacteristic
365C2×C83#351811yescharacteristic
366C2×C83#351911yescharacteristic
367D83—44no—
368D83—44no—
369C2×#555—831no—
370#2369D8311yescharacteristic, complemented
371#2367—834no—
372#2363—832no—
373#2361—832no—
374#2354—831no—
375D4×C4⋊C4—831no—
376#2347—832no—
377#2347—832no—
378#2337—834no—
379#2324—832no—
380C4×C4⋊Q8—831no—
381C4×#121—832no—
382#2296—832no—
383#2293—831no—
384#2274—832no—
385C42×D4—831no—
386C83#3432111yescharacteristic, complemented, Sylow
387#555—8316no—
388C2×C4⋊Q8C2×D8311yescharacteristic
389C2×#124—834no—
390C2×#121—832no—
391C2×#121—832no—
392C2×C4×Q8—832no—
393C2×C4×D4—831no—
394C2×C4×D4—831no—
395C2×C4×D4—832no—
396C2×C4×D4—834no—
397C2×C4×D4—831no—
398C2×C4×D4—831no—
399C2×#117—832no—
400C2×#117—832no—
401C2×#117—832no—
402C2×#117—832no—
403C22×C4⋊C4—832no—
404C22×C42—832no—
405#391—832no—
406#391C2×D8314yes—
407#390—834no—
408#390—831no—
409#390—831no—
410#390—832no—
411#389—832no—
412#389—832no—
413#389—831no—
414#389—831no—
415#389—832no—
416#389C2×D8312yes—
417#389C2×D8312yes—
418#388—834no—
419#388—834no—
420#388—834no—
421#388—832no—
422#388—834no—
423#388—832no—
424#388—834no—
425#386—834no—
426#386—834no—
427#385—834no—
428#385—834no—
429#385—834no—
430#384—831no—
431#383—834no—
432#380—832no—
433#380—832no—
434C4×C4⋊C4—832no—
435C4×C4⋊C4—832no—
436C4×C4⋊C4—831no—
437C4×C4⋊C4—834no—
438C4×C4⋊C4—831no—
439C4×C4⋊C4—832no—
440C4×C4⋊C4—834no—
441C4×C4⋊C4—834no—
442C4×C4⋊C4C2×D8312yes—
443C4×C4⋊C4C2×D8311yescharacteristic
444C4×C4⋊C4C2×D8311yescharacteristic
445C4×C4⋊C4C2×D8312yes—
446C4×C22⋊C4—834no—
447C4×C22⋊C4—832no—
448C4×C22⋊C4—832no—
449C4×C22⋊C4—832no—
450C4×C22⋊C4—834no—
451C4×C22⋊C4—832no—
452C43—831no—
453C22×Q8C22×D8312yes—
454C22×D4—834no—
455C22×D4—831no—
456C22×D4—831no—
457C23×C4—834no—
458C23×C4—832no—
459C23×C4—832no—
460C23×C4—832no—
461C23×C4—832no—
462C4⋊Q8C4×D8318yescomplemented
463#124—8332no—
464#121—8316no—
465#121—8316no—
466C4×Q8—3324no—
467C4×D4—3324no—
468C4×D4—3328no—
469C4×D4—838no—
470C4×D4—838no—
471C4×D4—1664no—
472C4×D4—1664no—
473#117—3324no—
474#117—8316no—
475#117—8316no—
476#117—1668no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—831no—
479C2×C4⋊C4—831no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—834no—
482C2×C4⋊C4—832no—
483C2×C4⋊C4—832no—
484C2×C4⋊C4—832no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—1668no—
487C2×C4⋊C4C22×D8311yescharacteristic
488C2×C4⋊C4C22×D8311yescharacteristic
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8312yes—
492C2×C4⋊C4C22×D8312yes—
493C2×C4⋊C4C22×D8311yescharacteristic
494C2×C22⋊C4—834no—
495C2×C22⋊C4—834no—
496C2×C22⋊C4—834no—
497C2×C22⋊C4—832no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—832no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4—832no—
507C2×C42—3324no—
508C2×C42—834no—
509C2×C42—834no—
510C2×C42—831no—
511C2×C42—832no—
512C2×C42—832no—
513C2×C42—831no—
514C2×C42—834no—
515C2×C42—831no—
516C2×C42—831no—
517C2×C42—831no—
518C2×C42—831no—
519C2×C42C22×D8312yes—
520C2×C42C22×D8312yes—
521C2×C42C22×D8314yes—
522C2×C42C22×D8311yescharacteristic
523#95—832no—
524#95—832no—
525#95—834no—
526#95—832no—
527#95—834no—
528#95—832no—
529#95—834no—
530#95—834no—
531#95C22×D8312yes—
532#95C22×D8314yes—
533#95C22×D8314yes—
534#95C22×D8312yes—
535C24—832no—
536C24—832no—
537C2×Q8—42no—
538C2×Q8—42no—
539C2×Q8C2×C4×D8318yes—
540C2×D4—3324no—
541C2×D4—3324no—
542C2×D4—8316no—
543C2×D4—834no—
544C2×D4—834no—
545C2×D4—1662no—
546C2×D4—1662no—
547C2×D4—1662no—
548C2×D4—1662no—
549C22×C4—3322no—
550C22×C4—3322no—
551C22×C4—3322no—
552C22×C4—3324no—
553C22×C4—3324no—
554C22×C4—832no—
555C22×C4—831no—
556C22×C4—832no—
557C22×C4—831no—
558C22×C4—831no—
559C22×C4—838no—
560C22×C4—838no—
561C22×C4—831no—
562C22×C4—834no—
563C22×C4—1664no—
564C22×C4—1664no—
565C22×C4—1664no—
566C22×C4—1668no—
567C22×C4—1664no—
568C22×C4—1664no—
569C22×C4—1664no—
570C22×C4—1664no—
571C22×C4C23×D8312yes—
572C22×C4C23×D8312yes—
573C22×C4C23×D8312yes—
574C22×C4C23×D8314yes—
575C22×C4C23×D8311yescharacteristic
576C22×C4C23×D8312yes—
577C22×C4C23×D8311yescharacteristic
578C22×C4C23×D8311yescharacteristic
579C4⋊C4—22no—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—44no—
583C4⋊C4—3322no—
584C4⋊C4—834no—
585C4⋊C4—834no—
586C4⋊C4—1664no—
587C4⋊C4—1664no—
588C4⋊C4—1668no—
589C4⋊C4—1668no—
590C4⋊C4—1664no—
591C4⋊C4—1664no—
592C4⋊C4C2×C4×D8318yes—
593C4⋊C4C2×C4×D8318yes—
594C4⋊C4#1305059114yes—
595C22⋊C4—3324no—
596C22⋊C4—3324no—
597C22⋊C4—3324no—
598C22⋊C4—3322no—
599C22⋊C4—8316no—
600C22⋊C4—8316no—
601C22⋊C4—838no—
602C22⋊C4—838no—
603C22⋊C4—1664no—
604C22⋊C4—1664no—
605C22⋊C4—1664no—
606C22⋊C4—1664no—
607C22⋊C4—1664no—
608C42—24no—
609C42—24no—
610C42—44no—
611C42—3322no—
612C42—3322no—
613C42—3324no—
614C42—3324no—
615C42—3321no—
616C42—8316no—
617C42—834no—
618C42—1662no—
619C42—1662no—
620C42—1662no—
621C42—1662no—
622C42C2×C4×D8314yes—
623C23—834no—
624C23—834no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23—1662no—
630C23—1662no—
631C23—1662no—
632C23—1662no—
633C23—1662no—
634C23—1662no—
635C23—1662no—
636C23—1662no—
637C23C24×D8311yescharacteristic
638Q8—48no—
639D4—33216no—
640D4—1668no—
641D4—1668no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—21no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—3328no—
658C2×C4—3328no—
659C2×C4—834no—
660C2×C4—834no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—832no—
664C2×C4—6648no—
665C2×C4—1661no—
666C2×C4—1664no—
667C2×C4—1664no—
668C2×C4—1664no—
669C2×C4—1661no—
670C2×C4—1661no—
671C2×C4—1662no—
672C2×C4—1661no—
673C2×C4—1662no—
674C2×C4—1661no—
675C2×C4—1662no—
676C2×C4—1661no—
677C2×C4—1661no—
678C2×C4—1661no—
679C2×C4—1662no—
680C2×C4—1661no—
681C2×C4—16616no—
682C2×C4—16616no—
683C2×C4C22×C4×D8318yes—
684C2×C4C22×C4×D8312yes—
685C2×C4C22×C4×D8312yes—
686C2×C4C22×C4×D8312yes—
687C2×C4#41×D8312yes—
688C2×C4C2×#1305059114yes—
689C2×C4C2×#1305059112yes—
690C2×C4#1458183812yes—
691C2×C4#1458184012yes—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—3322no—
700C22—1664no—
701C22—1664no—
702C22—1664no—
703C22—1664no—
704C22—1664no—
705C22—1664no—
706C22C23×C4×D8311yescharacteristic
707C22C2×#41×D8311yescharacteristic
708C22C22×#1305059111yescharacteristic
709C22H(5,𝔽2)×D8311yescharacteristic
710C22C2×#1458183811yescharacteristic
711C22C2×#1458184011yescharacteristic
712C22#1912853611yescharacteristic
713C4—28no—
714C4—22no—
715C4—24no—
716C4—42no—
717C4—42no—
718C4—42no—
719C4—3321no—
720C4—3324no—
721C4—1662no—
722C4—1664no—
723C4—1664no—
724C4—1662no—
725C4—1662no—
726C4C4×#1305059114yes—
727C4#1912818314yes—
728C2—3324no—
729C2—3324no—
730C2C2×C4×#1305059111yescharacteristic
731C2C2×#1912818311yescharacteristic
732C2#2492066711yescharacteristic
733C2#2492130511yescharacteristic
734C2#2492137111yescharacteristic
735C2#2492148111yescharacteristic
736C2#2492149611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2369C2
socle, cosocleC23×C83C25
prime radicalC2×#19128417C2
hypercenter#2369D83
hypocenterC83#34321
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2369

Complements

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

NH ≅ G/Ntype
2. #24910539C2semidirect
3. #24910500C2semidirect
4. #24910481C2semidirect
5. #24910410C2semidirect
6. C4⋊C4×D332C2semidirect
7. #24910355C2semidirect
8. #24910352C2semidirect
9. #24910275C2semidirect
10. #24910154C2semidirect
11. C4⋊Q8×Dic83C2semidirect
12. C4×#14581767C2semidirect
13. #24909944C2semidirect
14. #24909924C2semidirect
15. #24909817C2semidirect
16. C4×#14581754C2semidirect
17. C83×#2369C2semidirect
18. #19128417C4semidirect
92. #14581781C2×C4semidirect
93. #14581767C2×C4semidirect
94. #14581767C2×C4semidirect
98. C4×D332C2×C4semidirect
99. C4×D332C2×C4semidirect
103. #14581750C2×C4semidirect
104. #14581750C2×C4semidirect
150. C4⋊Q8×C83C2×C4semidirect
370. #2369D83semidirect
386. C83#34321semidirect
462. C4⋊Q8C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191284172
#249105392
#249105002
#249104812
#249104102
C4⋊C4×D3322
#249103552
#249103522
#249102752
#249101542
C4⋊Q8×Dic832
C4×#145817672
#249099442
#249099242
#249098172
C4×#145817542
C83×#23692
#3432183