Finite Group Databasebeta

← #35421147

Subgroups — #35421147

Order 21248.

1108 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128229C211yesmaximal, characteristic
2C2×#19127831C211yesmaximal, characteristic, complemented
3C2×#19127829C211yesmaximal, characteristic, complemented
4#24908261C211yesmaximal, characteristic, complemented
5#24908259C211yesmaximal, characteristic, complemented
6#24908259C211yesmaximal, characteristic, complemented
7#24908259C211yesmaximal, characteristic, complemented
8#24908257C211yesmaximal, characteristic, complemented
9#24908255C211yesmaximal, characteristic, complemented
10#24907447C211yesmaximal, characteristic, complemented
11#24907446C211yesmaximal, characteristic, complemented
12#24907442C211yesmaximal, characteristic, complemented
13#24907228C211yesmaximal, characteristic, complemented
14#24907224C211yesmaximal, characteristic, complemented
15C83×#1750C211yesmaximal, characteristic, complemented
16#19128229—24no—
17#19128229—24no—
18C2×#14581787C411yescharacteristic
19C2×#14581785C411yescharacteristic
20C2×#14581782C411yescharacteristic
21C2×#14581778C411yescharacteristic
22C2×#14581777C411yescharacteristic
23C2×#14581774C411yescharacteristic
24C2×#14581770C411yescharacteristic
25C2×#14581765C411yescharacteristic
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×C4×C22⋊D83C2211yescharacteristic
29C2×C4×C22⋊D83C2211yescharacteristic
30C2×#14581749C2211yescharacteristic
31C2×C42×D83C2211yescharacteristic
32#19127831—24no—
33#19127829—24no—
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×C4⋊(C83⋊C8)C2211yescharacteristic
36C2×Dic83⋊C8C2211yescharacteristic
37C2×Dic83⋊C8C2211yescharacteristic
38C2×Dic83⋊C8C2211yescharacteristic
39C2×Dic83⋊C8C2211yescharacteristic
40C2×C22⋊(C83⋊C8)C2211yescharacteristic
41C2×C22⋊(C83⋊C8)C2211yescharacteristic
42C2×(C2×D83)⋊C8C2211yescharacteristic
43C2×(C2×D83)⋊C8C2211yescharacteristic
44C2×(C2×D83)⋊C8C2211yescharacteristic
45C2×(C2×D83)⋊C8C2211yescharacteristic
46C2×(C2×D83)⋊C8C2211yescharacteristic
47C2×(C2×D83)⋊C8C2211yescharacteristic
48C2×(C2×D83)⋊C8C2211yescharacteristic
49C2×(C2×D83)⋊C8C2211yescharacteristic
50C2×#14581702C2211yescharacteristic
51C2×#14581702C2211yescharacteristic
52C2×#14581702C2211yescharacteristic
53C2×C8×Dic83C2211yescharacteristic
54#19127456C2211yescharacteristic
55#19127456C2211yescharacteristic
56C2×#117×C83C2211yescharacteristic
57C2×C22⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×#97×C83C2211yescharacteristic
60C2×C4×C8×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×D332C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C22×C22⋊D83C2×C411yescharacteristic
67C22×C4×D83C2×C411yescharacteristic
68C22×C4×D83C2×C411yescharacteristic
69C22×C4×D83C2311yescharacteristic
70C22×C4×D83C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75#14581787—24no—
76#14581785—24no—
77#14581782—24no—
78#14581778—24no—
79#14581777—24no—
80#14581774—24no—
81#14581770—24no—
82#14581765—24no—
83C4×Dic166D414yes—
84C4×Dic166D414yes—
85C4×D332—22no—
86C4×D332—22no—
87C4×C22⋊D83—22no—
88C4×C22⋊D83—22no—
89C4×C22⋊D83—22no—
90C4×C22⋊D83—22no—
91#14581749—22no—
92#14581749—22no—
93C2×C4⋊Dic83C2×C411yescharacteristic
94C2×C4⋊Dic83C2×C411yescharacteristic
95C2×Dic83⋊C4C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×Dic83⋊C4C2×C411yescharacteristic
100C2×Dic83⋊C4C2×C411yescharacteristic
101C2×C22⋊Dic83C2×C411yescharacteristic
102C2×C22⋊Dic83C2×C411yescharacteristic
103C2×(C2×D83)⋊C4C2×C411yescharacteristic
104C2×(C2×D83)⋊C4C2×C411yescharacteristic
105C2×(C2×D83)⋊C4C2×C411yescharacteristic
106C2×(C2×D83)⋊C4C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×(C2×D83)⋊C4C2×C411yescharacteristic
109C2×C4×Dic83C2×C411yescharacteristic
110C2×C4×Dic83C2×C411yescharacteristic
111C2×C4×Dic83C2311yescharacteristic
112C2×C4×Dic83C2311yescharacteristic
113C42×D83—22no—
114C42×D83—22no—
115C4⋊(C83⋊C8)—22no—
116C4⋊(C83⋊C8)—22no—
117Dic83⋊C8—22no—
118Dic83⋊C8—22no—
119Dic83⋊C8—22no—
120Dic83⋊C8—22no—
121C22⋊(C83⋊C8)—41no—
122C22⋊(C83⋊C8)—41no—
123(C2×D83)⋊C8—22no—
124(C2×D83)⋊C8—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—22no—
127(C2×D83)⋊C8—41no—
128(C2×D83)⋊C8—41no—
129(C2×D83)⋊C8—41no—
130(C2×D83)⋊C8—41no—
131#14581702—22no—
132#14581702—22no—
133#14581702—22no—
134C8×Dic83—22no—
135C23×C4×C83C2311yescharacteristic
136C22×C8×C83C2311yescharacteristic
137C22×C8×C83C2311yescharacteristic
138C22×C8×C83C2311yescharacteristic
139C22×C8×C83C2311yescharacteristic
140#117×C83—22no—
141#117×C83—22no—
142C2×C4⋊C4×C83C2×C411yescharacteristic
143C2×C4⋊C4×C83C2×C411yescharacteristic
144C2×C22⋊C4×C83C2×C411yescharacteristic
145C2×C22⋊C4×C83C2×C411yescharacteristic
146C2×C42×C83C2311yescharacteristic
147C2×C42×C83C2311yescharacteristic
148C22⋊C8×C83—22no—
149C22⋊C8×C83—22no—
150#97×C83—22no—
151C4×C8×C83—22no—
152C23×D83C22×C411yescharacteristic
153C23×D83C22×C411yescharacteristic
154C2×Dic166—41no—
155C2×Dic166—41no—
156C2×Dic166C22⋊C414yes—
157C2×D332—22no—
158C2×D332—22no—
159C2×D332—41no—
160C2×C22⋊D83—22no—
161C2×C22⋊D83—22no—
162C2×C22⋊D83—22no—
163C2×C22⋊D83—41no—
164C2×C22⋊D83—41no—
165C2×C22⋊D83—41no—
166C22×Dic83C22×C411yescharacteristic
167C22×Dic83C22×C411yescharacteristic
168C22×Dic83C22×C411yescharacteristic
169C22×Dic83C22×C411yescharacteristic
170C22×Dic83C22×C411yescharacteristic
171C22×Dic83C22×C411yescharacteristic
172C2×C4×D83—22no—
173C2×C4×D83—21no—
174C2×C4×D83—21no—
175C2×C4×D83—21no—
176C2×C4×D83—21no—
177C2×C4×D83—21no—
178C2×C4×D83—21no—
179C2×C4×D83—21no—
180C2×C4×D83—21no—
181C2×C4×D83—21no—
182C2×C4×D83—21no—
183C2×C4×D83—21no—
184C2×C4×D83—21no—
185C2×C4×D83—22no—
186C2×C4×D83—22no—
187C2×C4×D83—41no—
188C2×C4×D83—41no—
189C2×C4×D83—41no—
190C2×C83⋊C8—21no—
191C2×C83⋊C8—21no—
192C2×C83⋊C8—21no—
193C2×C83⋊C8—21no—
194C2×C83⋊C8—21no—
195C2×C83⋊C8—21no—
196C2×C83⋊C8—21no—
197C2×C83⋊C8—21no—
198C2×C83⋊C8—21no—
199C2×C83⋊C8—21no—
200C2×C83⋊C8—21no—
201C2×C83⋊C8—21no—
202C4⋊Dic83—22no—
203C4⋊Dic83C22⋊C414yes—
204Dic83⋊C4—22no—
205Dic83⋊C4—22no—
206Dic83⋊C4—22no—
207Dic83⋊C4—22no—
208Dic83⋊C4C22⋊C414yes—
209Dic83⋊C4C22⋊C414yes—
210C22⋊Dic83—22no—
211C22⋊Dic83—22no—
212(C2×D83)⋊C4—22no—
213(C2×D83)⋊C4—22no—
214(C2×D83)⋊C4—22no—
215(C2×D83)⋊C4—22no—
216(C2×D83)⋊C4—22no—
217(C2×D83)⋊C4—22no—
218C4×Dic83—22no—
219C4×Dic83—22no—
220C4×Dic83C2×D412yes—
221C4×Dic83C2×D412yes—
222C4×Dic83C2×D412yes—
223C4×Dic83C2×D412yes—
224C24×C83C22×C411yescharacteristic
225C22×C4×C83—21no—
226C22×C4×C83—21no—
227C22×C4×C83—21no—
228C22×C4×C83—21no—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83C22×C411yescharacteristic
232C22×C4×C83C22×C411yescharacteristic
233C22×C4×C83C22×C411yescharacteristic
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C2411yescharacteristic
237C2×C8×C83—21no—
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83—21no—
243C2×C8×C83—21no—
244C2×C8×C83—21no—
245C2×C8×C83—21no—
246C2×C8×C83—21no—
247C2×C8×C83#4112yes—
248C2×C8×C83#4112yes—
249C4⋊C4×C83—22no—
250C4⋊C4×C83—22no—
251C22⋊C4×C83—22no—
252C22⋊C4×C83—22no—
253C42×C83—21no—
254C42×C83—21no—
255C42×C83C2×D412yes—
256C42×C83C2×D412yes—
257C23×C83—21no—
258C23×C83—21no—
259C23×C83—21no—
260C23×C83—21no—
261C23×C83—21no—
262C23×C83—21no—
263C23×C83—21no—
264C23×C83C23×C411yescharacteristic
265C22×D83—21no—
266C22×D83—21no—
267C22×D83—21no—
268C22×D83—21no—
269C22×D83—21no—
270C22×D83—21no—
271C22×D83—21no—
272C22×D83—21no—
273C22×D83—21no—
274C22×D83—21no—
275C22×D83—21no—
276C22×D83—21no—
277C22×D83—21no—
278C22×D83#13112yes—
279C2×C4×C83—21no—
280C2×C4×C83—21no—
281C2×C4×C83—21no—
282C2×C4×C83—21no—
283C2×C4×C83—21no—
284C2×C4×C83—21no—
285C2×C4×C83—21no—
286C2×C4×C83—21no—
287C2×C4×C83—21no—
288C2×C4×C83—21no—
289C2×C4×C83—21no—
290C2×C4×C83—21no—
291C2×C4×C83—21no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83C2×C22⋊C412yes—
297C2×C4×C83C2×C22⋊C412yes—
298C2×C4×C83C22×D411yescharacteristic
299C2×C4×C83C22×D411yescharacteristic
300C2×C4×C83C2×#4111yescharacteristic
301C2×C4×C83C2×#4111yescharacteristic
302C2×C4×C83H(5,𝔽2)11yescharacteristic
303C2×C4×C832−1+411yescharacteristic
304C22⋊D83—44no—
305C22⋊D83—44no—
306C2×Dic83—21no—
307C2×Dic83—21no—
308C2×Dic83—21no—
309C2×Dic83—21no—
310C2×Dic83—21no—
311C2×Dic83—21no—
312C2×Dic83—21no—
313C2×Dic83—21no—
314C2×Dic83—21no—
315C2×Dic83—21no—
316C2×Dic83—21no—
317C2×Dic83—21no—
318C2×Dic83—21no—
319C2×Dic83—21no—
320C2×Dic83C2×C22⋊C412yes—
321C2×Dic83C2×C22⋊C412yes—
322C2×Dic83C2×C22⋊C412yes—
323C2×Dic83C2×C22⋊C412yes—
324D332—44no—
325C4×D83—44no—
326C4×D83—44no—
327C4×D83—41no—
328C4×D83—41no—
329C4×D83—41no—
330C4×D83—41no—
331C4×D83—41no—
332C4×D83—41no—
333C4×D83—41no—
334C4×D83—41no—
335Dic166—44no—
336C8×C83—22no—
337C8×C83—22no—
338C8×C83—41no—
339C8×C83—41no—
340C83⋊C8—41no—
341C83⋊C8—41no—
342C83⋊C8—41no—
343C83⋊C8—41no—
344C22×C83—41no—
345C22×C83—41no—
346C22×C83—41no—
347C22×C83—41no—
348C22×C83—41no—
349C22×C83—41no—
350C22×C83—41no—
351C22×C83C22×C22⋊C411yescharacteristic
352C22×C83C4×#4111yescharacteristic
353C22×C83#52011yescharacteristic
354C22×C83C2×#13111yescharacteristic
355C22×C83#56811yescharacteristic
356C22×C83#56811yescharacteristic
357C22×C83#56811yescharacteristic
358C2×D83—22no—
359C2×D83—22no—
360C2×D83—22no—
361C2×D83—41no—
362C2×D83—41no—
363C2×D83—41no—
364C2×D83—41no—
365C2×D83—41no—
366C2×D83—41no—
367C2×D83—41no—
368C2×D83—41no—
369C2×D83—41no—
370C2×D83—41no—
371C2×D83—41no—
372C4×C83—22no—
373C4×C83—22no—
374C4×C83—41no—
375C4×C83—41no—
376C4×C83—41no—
377C4×C83#54811yescharacteristic
378C4×C83#54811yescharacteristic
379C4×C83#55011yescharacteristic
380C4×C83#55011yescharacteristic
381Dic83—22no—
382Dic83—22no—
383Dic83—22no—
384Dic83—22no—
385Dic83—41no—
386Dic83—41no—
387#22533—831nomaximal, Sylow
388C2×C83—81no—
389C2×C83#234111yescharacteristic
390C2×C83#287911yescharacteristic
391C2×C83#288011yescharacteristic
392C2×C83#296711yescharacteristic
393C2×C83#296811yescharacteristic
394C2×C83#299211yescharacteristic
395C2×C83#299511yescharacteristic
396D83—42no—
397D83—81no—
398C2×#529—831no—
399C2×#446—831no—
400C2×#446—831no—
401#1955—831no—
402#1955—831no—
403#1955—831no—
404#1955—831no—
405#1954—831no—
406#1954—831no—
407#1798—831no—
408#1798—831no—
409#1797—831no—
410#1750—831no—
411#1750D8311yescharacteristic, complemented
412#1749—831no—
413C83#2253311yescharacteristic, complemented, Sylow
414#529—1664no—
415#529—1664no—
416C2×#126—831no—
417C2×#126—831no—
418C2×#125—831no—
419C2×#124—831no—
420C2×#123—831no—
421C2×#123—831no—
422C2×C22⋊Q8—831no—
423C2×#121—831no—
424C2×C4×Q8—831no—
425C2×C4×D4—831no—
426C2×C4×D4—831no—
427C2×C4×D4—831no—
428C2×#117—831no—
429C2×#117C2×D8311yescharacteristic
430C22×C42—831no—
431#446—1664no—
432#446—1664no—
433C2×C4⋊C8—831no—
434C2×C4⋊C8—831no—
435C2×C4⋊C8—831no—
436C2×C4⋊C8—831no—
437C2×C4⋊C8—831no—
438C2×C4⋊C8—831no—
439C2×C22⋊C8—831no—
440C2×C22⋊C8—831no—
441C2×C22⋊C8—831no—
442C2×C22⋊C8—831no—
443C2×C22⋊C8—831no—
444C2×C22⋊C8—831no—
445C2×C22⋊C8—831no—
446C2×C22⋊C8—831no—
447C2×C22⋊C8—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8C2×D8311yescharacteristic
450C2×C22⋊C8C2×D8311yescharacteristic
451C2×#97—831no—
452C2×#97—831no—
453C2×#97—831no—
454C2×#97C2×D8311yescharacteristic
455C2×C4×C8—831no—
456C2×C4×C8C2×D8311yescharacteristic
457#336—831no—
458#336—831no—
459#336C2×D8311yescharacteristic
460#336C2×D8311yescharacteristic
461C22×Q8—831no—
462C22×D4—831no—
463C22×D4—831no—
464C22×D4—831no—
465C23×C4—831no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4C22×D8311yescharacteristic
470C22×C8—831no—
471C22×C8—831no—
472C22×C8—831no—
473C22×C8—831no—
474C22×C8C22×D8311yescharacteristic
475C22×C8C22×D8311yescharacteristic
476C22×C8C22×D8311yescharacteristic
477C22×C8C22×D8311yescharacteristic
478#126—1664no—
479#126—1664no—
480#125—1664no—
481#124—1664no—
482#123—1664no—
483#123—1664no—
484C22⋊Q8—1664no—
485#121—1664no—
486C4×Q8—834no—
487C4×Q8—834no—
488C4×D4—1662no—
489C4×D4—1662no—
490C4×D4—1662no—
491C4×D4—1662no—
492C4×D4—1662no—
493C4×D4—1662no—
494#117—22no—
495#117—22no—
496#117—1662no—
497#117—1662no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4—831no—
500C2×C4⋊C4—831no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—831no—
503C2×C4⋊C4—831no—
504C2×C4⋊C4—831no—
505C2×C4⋊C4—831no—
506C2×C4⋊C4C4×D8311yescharacteristic
507C2×C4⋊C4C4×D8311yescharacteristic
508C2×C22⋊C4—831no—
509C2×C22⋊C4—831no—
510C2×C22⋊C4—831no—
511C2×C22⋊C4—831no—
512C2×C22⋊C4—831no—
513C2×C22⋊C4—831no—
514C2×C22⋊C4—831no—
515C2×C22⋊C4—831no—
516C2×C22⋊C4C4×D8311yescharacteristic
517C2×C22⋊C4C4×D8311yescharacteristic
518C2×C42—831no—
519C2×C42—831no—
520C2×C42—831no—
521C2×C42—831no—
522C2×C42—1662no—
523C2×C42—1662no—
524C2×C42C22×D8311yescharacteristic
525C2×C42C22×D8311yescharacteristic
526C4⋊C8—1662no—
527C4⋊C8—1662no—
528C4⋊C8—1662no—
529C4⋊C8—1662no—
530C4⋊C8—1662no—
531C4⋊C8—1662no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—3321no—
535C22⋊C8—3321no—
536C22⋊C8—3321no—
537C22⋊C8—3321no—
538C22⋊C8—3321no—
539C22⋊C8—3321no—
540C22⋊C8—1662no—
541C22⋊C8—1662no—
542C22⋊C8—1662no—
543C22⋊C8—1662no—
544#97—22no—
545#97—1662no—
546#97—1662no—
547#97—1662no—
548C4×C8—22no—
549C4×C8—1662no—
550C24—831no—
551C24—831no—
552C24C2×C4×D8311yescharacteristic
553C2×Q8—3321no—
554C2×Q8—3321no—
555C2×Q8—834no—
556C2×D4—3321no—
557C2×D4—3321no—
558C2×D4—3321no—
559C2×D4—3321no—
560C2×D4—1662no—
561C2×D4—1662no—
562C2×D4—1662no—
563C2×D4—1662no—
564C2×D4—1662no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—3321no—
572C22×C4—3321no—
573C22×C4—3321no—
574C22×C4—831no—
575C22×C4—831no—
576C22×C4—831no—
577C22×C4—831no—
578C22×C4—831no—
579C22×C4—831no—
580C22×C4—1662no—
581C22×C4—1662no—
582C22×C4—1662no—
583C22×C4—1661no—
584C22×C4—1661no—
585C22×C4—1661no—
586C22×C4—1661no—
587C22×C4—1661no—
588C22×C4—1661no—
589C22×C4—1661no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4C2×C4×D8311yescharacteristic
596C22×C4C2×C4×D8311yescharacteristic
597C22×C4C2×C4×D8311yescharacteristic
598C22×C4C2×C4×D8311yescharacteristic
599C22×C4C2×C4×D8311yescharacteristic
600C22×C4C23×D8311yescharacteristic
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—1661no—
612C2×C8—1661no—
613C2×C8—1661no—
614C2×C8—1661no—
615C2×C8—1661no—
616C2×C8—1661no—
617C2×C8—1661no—
618C2×C8—1661no—
619C2×C8—1661no—
620C2×C8—1661no—
621C2×C8—1661no—
622C2×C8—1661no—
623C2×C8#1305059012yes—
624C2×C8#1305059012yes—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—834no—
628C4⋊C4—834no—
629C4⋊C4—834no—
630C4⋊C4—1662no—
631C4⋊C4—1662no—
632C4⋊C4—1662no—
633C4⋊C4—1662no—
634C4⋊C4—1662no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—1662no—
638C22⋊C4—1662no—
639C22⋊C4—1662no—
640C22⋊C4—1662no—
641C22⋊C4—1662no—
642C22⋊C4—1662no—
643C22⋊C4—1662no—
644C22⋊C4—1662no—
645C42—21no—
646C42—21no—
647C42—832no—
648C42—832no—
649C42—832no—
650C42—832no—
651C42—1662no—
652C42—1662no—
653C42D4×D8312yes—
654C42D4×D8312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—832no—
663C23—1661no—
664C23—1661no—
665C23—1661no—
666C23—1661no—
667C23—1661no—
668C23—1661no—
669C23—1661no—
670C23—1661no—
671C23—1661no—
672C23—1661no—
673C23—1661no—
674C23—1661no—
675C23—1661no—
676C23C22×C4×D8311yescharacteristic
677Q8—3324no—
678D4—3324no—
679D4—3324no—
680D4—3324no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—3324no—
699C2×C4—3324no—
700C2×C4—3321no—
701C2×C4—3321no—
702C2×C4—3321no—
703C2×C4—3321no—
704C2×C4—3321no—
705C2×C4—3321no—
706C2×C4—3321no—
707C2×C4—3321no—
708C2×C4—832no—
709C2×C4—832no—
710C2×C4—832no—
711C2×C4—832no—
712C2×C4—1661no—
713C2×C4—1661no—
714C2×C4—1661no—
715C2×C4—1661no—
716C2×C4—1661no—
717C2×C4—1661no—
718C2×C4—1661no—
719C2×C4—1661no—
720C2×C4—1661no—
721C2×C4—1661no—
722C2×C4—1661no—
723C2×C4—1661no—
724C2×C4—1661no—
725C2×C4—1661no—
726C2×C4C22⋊C4×D8312yes—
727C2×C4C22⋊C4×D8312yes—
728C2×C4C2×D4×D8311yescharacteristic
729C2×C4C2×D4×D8311yescharacteristic
730C2×C4C2×#1305059011yescharacteristic
731C2×C4C2×#1305059011yescharacteristic
732C2×C4#1458183811yescharacteristic
733C2×C4#1458183911yescharacteristic
734C8—22no—
735C8—22no—
736C8—41no—
737C8—41no—
738C8—3321no—
739C8—3321no—
740C8—3321no—
741C8—3321no—
742C22—41no—
743C22—41no—
744C22—41no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—3321no—
750C22—3321no—
751C22—3321no—
752C22—3321no—
753C22—3321no—
754C22—3321no—
755C22—3321no—
756C22—3321no—
757C22—3321no—
758C22—3321no—
759C22—3321no—
760C22—1662no—
761C22—1662no—
762C22—1662no—
763C22C2×C22⋊C4×D8311yescharacteristic
764C22C4×#1305059011yescharacteristic
765C22#1912818111yescharacteristic
766C22#131×D8311yescharacteristic
767C22#1912846611yescharacteristic
768C22#1912846611yescharacteristic
769C22#1912846611yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—3321no—
776C4—3321no—
777C4—1662no—
778C4—1662no—
779C4—1662no—
780C4—1662no—
781C4#1912836011yescharacteristic
782C4#1912836011yescharacteristic
783C4#1912837211yescharacteristic
784C4#1912837211yescharacteristic
785C2—81no—
786C2—3322no—
787C2—6641no—
788C2#2491030311yescharacteristic
789C2#2491590511yescharacteristic
790C2#2491591111yescharacteristic
791C2#2491644411yescharacteristic
792C2#2491645311yescharacteristic
793C2#2491659711yescharacteristic
794C2#2491662811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1750C2
prime radicalC2×#14581765C4
cosocleC22×C4×C83C24
hypercenter#1750D83
hypocenterC83#22533
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1750

Complements

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

NH ≅ G/Ntype
2. C2×#19127831C2semidirect
3. C2×#19127829C2semidirect
4. #24908261C2semidirect
5. #24908259C2semidirect
6. #24908259C2semidirect
7. #24908259C2semidirect
8. #24908257C2semidirect
9. #24908255C2semidirect
10. #24907447C2semidirect
11. #24907446C2semidirect
12. #24907442C2semidirect
13. #24907228C2semidirect
14. #24907224C2semidirect
15. C83×#1750C2semidirect
411. #1750D83semidirect
413. C83#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#191282292
C2×#191278312
C2×#191278292
#249082612
#249082592
#249082572
#249082552
#249074472
#249074462
#249074422
#249072282
#249072242
C83×#17502
#2253383