Finite Group Databasebeta

← #35567423

Subgroups — #35567423

Order 21248.

2190 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128235C211yesmaximal, characteristic
2#24910607C214yesmaximal, complemented
3#24910557C212yesmaximal, complemented
4#24910532C212yesmaximal, complemented
5#24910418C211yesmaximal, characteristic, complemented
6#24910410C211yesmaximal, characteristic, complemented
7#24910407C212yesmaximal, complemented
8#24910385C212yesmaximal, complemented
9C4⋊C4×Dic166C211yesmaximal, characteristic, complemented
10C4⋊C4×D332C211yesmaximal, characteristic, complemented
11#24910234C214yesmaximal, complemented
12#24910156C212yesmaximal
13#24910145C212yesmaximal, complemented
14#24910084C212yesmaximal, complemented
15#24910071C212yesmaximal, complemented
16#24909870C211yesmaximal, characteristic, complemented
17C83×#2285C211yesmaximal, characteristic, complemented
18#19128235C4116yescomplemented
19C2×#14581786C2212yes—
20C2×#14581784C2211yescharacteristic
21C2×#14581780C2211yescharacteristic
22C2×#14581775C2212yes—
23C2×#14581771C2211yescharacteristic
24C2×#14581766C2211yescharacteristic
25C2×C4×Dic166C2212yes—
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×D332C2212yes—
28C2×C4×D332C2211yescharacteristic
29C2×C4×C22⋊D83C2212yes—
30C2×#14581751C2212yes—
31C2×#14581750C2212yes—
32C2×#14581749C2212yes—
33C2×C4⋊C4×D83C2212yes—
34#19127607C2212yes—
35#19127603C2212yes—
36#19127601C2214yes—
37#19127599C2212yes—
38#19127599C2212yes—
39#19127598C2214yes—
40#19127596C2214yes—
41#19127596C2214yes—
42#19127595C2214yes—
43#19127593C2214yes—
44#19127591C2214yes—
45#19127591C2214yes—
46#19127590C2214yes—
47#19127589C2214yes—
48#19127588C2214yes—
49#19127583C2214yes—
50#19127582C2214yes—
51#19127582C2214yes—
52#19127577C2214yes—
53#19127575C2214yes—
54#19127572C2214yes—
55#19127572C2214yes—
56#19127571C2211yescharacteristic
57#19127571C2211yescharacteristic
58#19127570C2212yes—
59#19127567C2212yes—
60#19127566C2212yes—
61#19127561C2212yes—
62#19127561C2212yes—
63#19127558C2212yes—
64#19127558C2212yes—
65C4⋊C4×Dic83C2212yes—
66C4⋊C4×Dic83C2212yes—
67C4×C4⋊Dic83C2212yes—
68C4×C4⋊Dic83C2212yes—
69C4×C4⋊Dic83C2212yes—
70C4×C4⋊Dic83C2212yes—
71#19127552C2214yes—
72#19127548C2214yes—
73C2×#117×C83C2212yes—
74C22×C42×C83C2211yescharacteristic
75#384×C83C2211yescharacteristic
76#384×C83C2211yescharacteristic
77#382×C83C2212yes—
78#380×C83C2212yes—
79#380×C83C2211yescharacteristic
80#380×C83C2211yescharacteristic
81C4×C4⋊C4×C83C2211yescharacteristic
82C4×C4⋊C4×C83C2211yescharacteristic
83C4×C4⋊C4×C83C2212yes—
84C22×Dic166C2311yescharacteristic
85C22×D332C2311yescharacteristic
86C22×C22⋊D83C2312yes—
87C22×C4×D83C2312yes—
88C22×C4×D83C2314yes—
89#14581786C2×C4116yescomplemented
90#14581784C2×C418yescomplemented
91#14581780C2×C418yes—
92#14581775C2×C4116yescomplemented
93#14581771C2×C418yescomplemented
94#14581766C2×C418yes—
95C4×Dic166—44no—
96C4×Dic166C2×C418yescomplemented
97C4×D332—44no—
98C4×D332C2×C418yes—
99C4×C22⋊D83C2×C4116yescomplemented
100#14581751—44no—
101#14581750—44no—
102#14581749C2×C4116yescomplemented
103C2×C4⋊Dic83C2312yes—
104C2×C4⋊Dic83C2312yes—
105C2×C4⋊Dic83C2312yes—
106C2×C4⋊Dic83C2312yes—
107C2×C4⋊Dic83C2312yes—
108C2×C4⋊Dic83C2312yes—
109C2×C4⋊Dic83C2311yescharacteristic
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2312yes—
115C2×Dic83⋊C4C2312yes—
116C2×Dic83⋊C4C2312yes—
117C2×Dic83⋊C4C2312yes—
118C4⋊C4×D83—44no—
119C2×C22⋊Dic83C2314yes—
120C2×C22⋊Dic83C2312yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×(C2×D83)⋊C4C2314yes—
124C2×(C2×D83)⋊C4C2312yes—
125C2×(C2×D83)⋊C4C2312yes—
126C2×(C2×D83)⋊C4C2312yes—
127C2×(C2×D83)⋊C4C2312yes—
128C2×C4×Dic83C2314yes—
129C2×C4×Dic83C2314yes—
130C2×C4×Dic83C2314yes—
131C2×C4×Dic83C2314yes—
132C2×C4×Dic83C2312yes—
133C83⋊#95C2314yes—
134C83⋊#95C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C23×C4×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144#117×C83—44no—
145C2×C4⋊C4×C83C2311yescharacteristic
146C2×C4⋊C4×C83C2311yescharacteristic
147C2×C4⋊C4×C83C2311yescharacteristic
148C2×C4⋊C4×C83C2311yescharacteristic
149C2×C4⋊C4×C83C2312yes—
150C2×C4⋊C4×C83C2312yes—
151C2×C4⋊C4×C83C2312yes—
152C2×C4⋊C4×C83C2312yes—
153C2×C22⋊C4×C83C2312yes—
154C2×C22⋊C4×C83C2312yes—
155C2×C42×C83C2×C418yescomplemented
156C2×C42×C83C2312yes—
157C2×C42×C83C2312yes—
158C2×C42×C83C2311yescharacteristic
159C2×C42×C83C2311yescharacteristic
160C2×C42×C83C2311yescharacteristic
161C2×C42×C83C2311yescharacteristic
162#95×C83C2312yes—
163#95×C83C2312yes—
164#95×C83C2312yes—
165#95×C83C2312yes—
166C23×D83C2412yes—
167C2×Dic166—22no—
168C2×Dic166—22no—
169C2×Dic166C22×C414yes—
170C2×D332—22no—
171C2×D332—22no—
172C2×D332C22×C414yes—
173C2×C22⋊D83—42no—
174C2×C22⋊D83—42no—
175C2×C22⋊D83C22×C418yes—
176C22×Dic83C2414yes—
177C22×Dic83C2414yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C2×C4×D83—24no—
182C2×C4×D83—24no—
183C2×C4×D83—44no—
184C2×C4×D83—44no—
185C2×C4×D83—44no—
186C2×C4×D83C22×C418yes—
187C4⋊Dic83—24no—
188C4⋊Dic83—24no—
189C4⋊Dic83—24no—
190C4⋊Dic83—24no—
191C4⋊Dic83—42no—
192C4⋊Dic83—42no—
193C4⋊Dic83C22×C414yes—
194C4⋊Dic83C22×C414yes—
195Dic83⋊C4—44no—
196Dic83⋊C4—44no—
197Dic83⋊C4—44no—
198Dic83⋊C4C22×C418yes—
199Dic83⋊C4C22×C418yes—
200Dic83⋊C4C22×C418yes—
201Dic83⋊C4C22×C418yes—
202C22⋊Dic83—44no—
203C22⋊Dic83C22×C418yes—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4—44no—
207(C2×D83)⋊C4C22×C418yes—
208(C2×D83)⋊C4C22×C418yes—
209(C2×D83)⋊C4C22×C418yes—
210(C2×D83)⋊C4C22×C418yes—
211C4×Dic83—44no—
212C4×Dic83—44no—
213C4×Dic83—44no—
214C4×Dic83—44no—
215C4×Dic83C22×C418yes—
216C24×C83C2411yescharacteristic
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—41no—
222C22×C4×C83—41no—
223C22×C4×C83C22×C414yes—
224C22×C4×C83C22×C414yes—
225C22×C4×C83C22×C414yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2411yescharacteristic
231C22×C4×C83C2411yescharacteristic
232C22×C4×C83C2411yescharacteristic
233C22×C4×C83C2411yescharacteristic
234C22×C4×C83C2411yescharacteristic
235C22×C4×C83C2411yescharacteristic
236C4⋊C4×C83—22no—
237C4⋊C4×C83—22no—
238C4⋊C4×C83—22no—
239C4⋊C4×C83—22no—
240C4⋊C4×C83—42no—
241C4⋊C4×C83—42no—
242C4⋊C4×C83—42no—
243C4⋊C4×C83—42no—
244C22⋊C4×C83—42no—
245C22⋊C4×C83—42no—
246C42×C83—24no—
247C42×C83—24no—
248C42×C83C22×C414yes—
249C42×C83C22×C414yes—
250C42×C83C22×C414yes—
251C42×C83C22×C414yes—
252C23×C83—21no—
253C23×C83—21no—
254C23×C83—21no—
255C23×C83—21no—
256C23×C83—21no—
257C23×C83—21no—
258C23×C83C23×C412yes—
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—21no—
268C2×C4×C83—21no—
269C2×C4×C83—21no—
270C2×C4×C83—21no—
271C2×C4×C83—21no—
272C2×C4×C83—21no—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—28no—
276C2×C4×C83—28no—
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×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—44no—
290C2×C4×C83C23×C412yes—
291C2×C4×C83C23×C412yes—
292C2×C4×C83C23×C412yes—
293C2×C4×C83C23×C412yes—
294C2×C4×C83C23×C412yes—
295C2×C4×C83C23×C412yes—
296C2×C4×C83H(5,𝔽2)12yes—
297C2×C4×C83H(5,𝔽2)12yes—
298C2×C4×C832−1+412yes—
299C2×C4×C832−1+412yes—
300C22⋊D83—48no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—24no—
308C2×Dic83—24no—
309C2×Dic83—24no—
310C2×Dic83—24no—
311C2×Dic83—24no—
312C2×Dic83—24no—
313C2×Dic83C23×C414yes—
314C2×Dic83C23×C414yes—
315C2×Dic83C23×C414yes—
316D332—28no—
317C4×D83—216no—
318C4×D83—88no—
319Dic166—28no—
320C22×C83—22no—
321C22×C83—22no—
322C22×C83—22no—
323C22×C83—41no—
324C22×C83—41no—
325C22×C83—41no—
326C22×C83—41no—
327C22×C83C24×C411yescharacteristic
328C22×C83C2×H(5,𝔽2)11yescharacteristic
329C22×C83C2×H(5,𝔽2)11yescharacteristic
330C22×C83C2×2−1+411yescharacteristic
331C22×C83C2×2−1+411yescharacteristic
332C22×C83#58511yescharacteristic
333C22×C83#58511yescharacteristic
334C2×D83—24no—
335C2×D83—24no—
336C2×D83—24no—
337C2×D83—42no—
338C2×D83—42no—
339C2×D83—42no—
340C2×D83—42no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—42no—
346C4×C83—42no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83#52014yes—
350C4×C83#52014yes—
351Dic83—24no—
352Dic83—24no—
353Dic83—24no—
354Dic83—44no—
355Dic83—44no—
356#34383—831nomaximal, Sylow
357C2×C83—42no—
358C2×C83C2×#52011yescharacteristic
359C2×C83C2×#52011yescharacteristic
360C2×C83#342811yescharacteristic
361C2×C83#354611yescharacteristic
362C2×C83#354711yescharacteristic
363C2×C83#355411yescharacteristic
364C2×C83#355511yescharacteristic
365D83—44no—
366C2×#529—831no—
367#2376—834no—
368#2370—832no—
369#2367—832no—
370#2355—831no—
371#2354—832no—
372#2354—831no—
373#2352—832no—
374Q8×C4⋊C4—831no—
375D4×C4⋊C4—831no—
376#2334—834no—
377#2324—832no—
378#2323—832no—
379#2317—832no—
380#2314—832no—
381#2285—831no—
382#2285D8311yescharacteristic, complemented
383C83#3438311yescharacteristic, complemented, Sylow
384#529—8316no—
385C2×#126—832no—
386C2×#125—831no—
387C2×#124—831no—
388C2×#123—832no—
389C2×C22⋊Q8—831no—
390C2×#121—831no—
391C2×C4×Q8—832no—
392C2×C4×Q8—831no—
393C2×C4×D4—832no—
394C2×C4×D4—832no—
395C2×C4×D4—831no—
396C2×#117—832no—
397C2×#117—832no—
398C2×#117—832no—
399C2×#117C2×D8312yes—
400C22×C4⋊C4—832no—
401C22×C42C2×D8311yescharacteristic
402#391—832no—
403#390—834no—
404#390—832no—
405#389—834no—
406#389—834no—
407#389—832no—
408#389—832no—
409#389—834no—
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#385—834no—
423#385—834no—
424#384—832no—
425#384—831no—
426#384—831no—
427#384C2×D8311yescharacteristic
428#384C2×D8311yescharacteristic
429#382—832no—
430#382—832no—
431#382C2×D8312yes—
432#380—832no—
433#380—832no—
434#380—832no—
435#380—832no—
436#380C2×D8311yescharacteristic
437#380C2×D8311yescharacteristic
438#380C2×D8312yes—
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—834no—
446C4×C4⋊C4C2×D8311yescharacteristic
447C4×C4⋊C4C2×D8311yescharacteristic
448C4×C4⋊C4C2×D8312yes—
449C4×C22⋊C4—834no—
450C22×Q8—831no—
451C22×D4—832no—
452C22×D4—831no—
453C23×C4—834no—
454C23×C4—832no—
455C23×C4C22×D8311yescharacteristic
456C23×C4C22×D8311yescharacteristic
457C23×C4C22×D8311yescharacteristic
458#126—8316no—
459#125—838no—
460#124—838no—
461#123—8316no—
462C22⋊Q8—838no—
463#121—838no—
464C4×Q8—3324no—
465C4×Q8—838no—
466C4×D4—3324no—
467C4×D4—8316no—
468C4×D4—838no—
469#117—44no—
470#117—3324no—
471#117—3324no—
472#117—8316no—
473C2×C4⋊C4—3324no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—832no—
477C2×C4⋊C4—832no—
478C2×C4⋊C4—834no—
479C2×C4⋊C4—832no—
480C2×C4⋊C4—832no—
481C2×C4⋊C4—831no—
482C2×C4⋊C4—832no—
483C2×C4⋊C4—831no—
484C2×C4⋊C4—832no—
485C2×C4⋊C4—832no—
486C2×C4⋊C4—832no—
487C2×C4⋊C4—832no—
488C2×C4⋊C4—832no—
489C2×C4⋊C4C22×D8311yescharacteristic
490C2×C4⋊C4C22×D8311yescharacteristic
491C2×C4⋊C4C22×D8311yescharacteristic
492C2×C4⋊C4C22×D8311yescharacteristic
493C2×C4⋊C4C22×D8312yes—
494C2×C4⋊C4C22×D8312yes—
495C2×C4⋊C4C22×D8312yes—
496C2×C4⋊C4C22×D8312yes—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—832no—
502C2×C22⋊C4—832no—
503C2×C22⋊C4—832no—
504C2×C22⋊C4—832no—
505C2×C22⋊C4—832no—
506C2×C22⋊C4C22×D8312yes—
507C2×C22⋊C4C22×D8312yes—
508C2×C42—834no—
509C2×C42—834no—
510C2×C42—834no—
511C2×C42—834no—
512C2×C42—832no—
513C2×C42C4×D8318yescomplemented
514C2×C42C22×D8312yes—
515C2×C42C22×D8312yes—
516C2×C42C22×D8311yescharacteristic
517C2×C42C22×D8311yescharacteristic
518C2×C42C22×D8311yescharacteristic
519C2×C42C22×D8311yescharacteristic
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95C22×D8312yes—
529#95C22×D8312yes—
530#95C22×D8312yes—
531#95C22×D8312yes—
532C24—832no—
533C24C23×D8311yescharacteristic
534C2×Q8—834no—
535C2×Q8—1662no—
536C2×Q8—1662no—
537C2×D4—3322no—
538C2×D4—3322no—
539C2×D4—838no—
540C2×D4—834no—
541C2×D4—1662no—
542C2×D4—1662no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—41no—
548C22×C4—41no—
549C22×C4—3324no—
550C22×C4—3324no—
551C22×C4—3324no—
552C22×C4—832no—
553C22×C4—832no—
554C22×C4—832no—
555C22×C4—838no—
556C22×C4—834no—
557C22×C4—834no—
558C22×C4—1664no—
559C22×C4—1664no—
560C22×C4C2×C4×D8314yes—
561C22×C4C2×C4×D8314yes—
562C22×C4C2×C4×D8314yes—
563C22×C4C23×D8312yes—
564C22×C4C23×D8312yes—
565C22×C4C23×D8312yes—
566C22×C4C23×D8312yes—
567C22×C4C23×D8311yescharacteristic
568C22×C4C23×D8311yescharacteristic
569C22×C4C23×D8311yescharacteristic
570C22×C4C23×D8311yescharacteristic
571C22×C4C23×D8311yescharacteristic
572C22×C4C23×D8311yescharacteristic
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—22no—
576C4⋊C4—22no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—3324no—
582C4⋊C4—3324no—
583C4⋊C4—3324no—
584C4⋊C4—3322no—
585C4⋊C4—3322no—
586C4⋊C4—838no—
587C4⋊C4—838no—
588C4⋊C4—834no—
589C4⋊C4—838no—
590C4⋊C4—834no—
591C4⋊C4—838no—
592C4⋊C4—1664no—
593C4⋊C4—1664no—
594C4⋊C4—1664no—
595C4⋊C4—1664no—
596C22⋊C4—42no—
597C22⋊C4—42no—
598C22⋊C4—3324no—
599C22⋊C4—3324no—
600C22⋊C4—3324no—
601C22⋊C4—3324no—
602C22⋊C4—838no—
603C22⋊C4—838no—
604C22⋊C4—838no—
605C22⋊C4—838no—
606C22⋊C4—838no—
607C42—24no—
608C42—24no—
609C42—3324no—
610C42—3324no—
611C42—3324no—
612C42—3324no—
613C42—838no—
614C42C2×C4×D8314yes—
615C42C2×C4×D8314yes—
616C42C2×C4×D8314yes—
617C42C2×C4×D8314yes—
618C23—21no—
619C23—21no—
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—
632C23C24×D8311yescharacteristic
633Q8—1668no—
634D4—3328no—
635D4—1668no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
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—22no—
658C2×C4—44no—
659C2×C4—834no—
660C2×C4—834no—
661C2×C4—834no—
662C2×C4—6648no—
663C2×C4—1664no—
664C2×C4—1664no—
665C2×C4—1664no—
666C2×C4—1664no—
667C2×C4—1664no—
668C2×C4—1664no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1662no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—16616no—
676C2×C4C22×C4×D8312yes—
677C2×C4C22×C4×D8312yes—
678C2×C4C22×C4×D8312yes—
679C2×C4C22×C4×D8312yes—
680C2×C4C22×C4×D8312yes—
681C2×C4C22×C4×D8312yes—
682C2×C4#1458183712yes—
683C2×C4#1458183812yes—
684C2×C4#1458183912yes—
685C2×C4#1458184012yes—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—3322no—
697C22—1664no—
698C22—1664no—
699C22—1664no—
700C22C23×C4×D8311yescharacteristic
701C22C2×#1458183711yescharacteristic
702C22C2×#1458183811yescharacteristic
703C22C2×#1458183911yescharacteristic
704C22C2×#1458184011yescharacteristic
705C22#1912853711yescharacteristic
706C22#1912853711yescharacteristic
707C4—22no—
708C4—22no—
709C4—22no—
710C4—22no—
711C4—42no—
712C4—42no—
713C4—42no—
714C4—42no—
715C4—3324no—
716C4—3324no—
717C4—1664no—
718C4—1664no—
719C4—1664no—
720C4#1912818114yes—
721C4#1912818214yes—
722C2—42no—
723C2—3324no—
724C2C2×#1912818111yescharacteristic
725C2C2×#1912818211yescharacteristic
726C2#2492066411yescharacteristic
727C2#2492183511yescharacteristic
728C2#2492185211yescharacteristic
729C2#2492193411yescharacteristic
730C2#2492195111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2285C2
socle, cosocleC23×C83C25
prime radicalC2×#14581766C22
hypercenter#2285D83
hypocenterC83#34383
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2285

Complements

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

NH ≅ G/Ntype
2. #24910607C2semidirect
3. #24910557C2semidirect
4. #24910532C2semidirect
5. #24910418C2semidirect
6. #24910410C2semidirect
7. #24910407C2semidirect
8. #24910385C2semidirect
9. C4⋊C4×Dic166C2semidirect
10. C4⋊C4×D332C2semidirect
11. #24910234C2semidirect
13. #24910145C2semidirect
14. #24910084C2semidirect
15. #24910071C2semidirect
16. #24909870C2semidirect
17. C83×#2285C2semidirect
18. #19128235C4semidirect
89. #14581786C2×C4semidirect
90. #14581784C2×C4semidirect
92. #14581775C2×C4semidirect
93. #14581771C2×C4semidirect
96. C4×Dic166C2×C4semidirect
99. C4×C22⋊D83C2×C4semidirect
102. #14581749C2×C4semidirect
155. C2×C42×C83C2×C4semidirect
382. #2285D83semidirect
383. C83#34383semidirect
513. C2×C42C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282352
#249106072
#249105572
#249105322
#249104182
#249104102
#249104072
#249103852
C4⋊C4×Dic1662
C4⋊C4×D3322
#249102342
#249101562
#249101452
#249100842
#249100712
#249098702
C83×#22852
#3438383