Finite Group Databasebeta

← #35421145

Subgroups — #35421145

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×#19128231C211yesmaximal, characteristic
2C2×#19127831C211yesmaximal, characteristic, complemented
3C2×#19127830C211yesmaximal, characteristic, complemented
4#24908262C211yesmaximal, characteristic, complemented
5#24908259C211yesmaximal, characteristic, complemented
6#24908259C211yesmaximal, characteristic, complemented
7#24908259C211yesmaximal, characteristic, complemented
8#24908255C211yesmaximal, characteristic, complemented
9#24907445C211yesmaximal, characteristic, complemented
10#24907444C211yesmaximal, characteristic, complemented
11#24907441C211yesmaximal, characteristic, complemented
12#24907231C211yesmaximal, characteristic, complemented
13#24907230C211yesmaximal, characteristic, complemented
14#24907227C211yesmaximal, characteristic, complemented
15C83×#1954C211yesmaximal, characteristic, complemented
16#19128231—24no—
17#19128231—24no—
18C2×#14581787C411yescharacteristic
19C2×#14581785C411yescharacteristic
20C2×#14581782C411yescharacteristic
21C2×#14581778C411yescharacteristic
22C2×#14581776C411yescharacteristic
23C2×#14581773C411yescharacteristic
24C2×#14581769C411yescharacteristic
25C2×#14581764C411yescharacteristic
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×C22⋊D83C2211yescharacteristic
28C2×C4×C22⋊D83C2211yescharacteristic
29C2×#14581751C2211yescharacteristic
30C2×#14581749C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32#19127831—24no—
33#19127830—24no—
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×Dic83⋊C8C2211yescharacteristic
36C2×Dic83⋊C8C2211yescharacteristic
37C2×Dic83⋊C8C2211yescharacteristic
38C2×Dic83⋊C8C2211yescharacteristic
39C2×C22⋊(C83⋊C8)C2211yescharacteristic
40C2×C22⋊(C83⋊C8)C2211yescharacteristic
41C2×C22⋊(C83⋊C8)C2211yescharacteristic
42C2×C22⋊(C83⋊C8)C2211yescharacteristic
43C2×(C2×D83)⋊C8C2211yescharacteristic
44C2×(C2×D83)⋊C8C2211yescharacteristic
45C2×(C2×D83)⋊C8C2211yescharacteristic
46C2×(C2×D83)⋊C8C2211yescharacteristic
47C2×#14581703C2211yescharacteristic
48C2×#14581702C2211yescharacteristic
49C2×#14581702C2211yescharacteristic
50C2×#14581702C2211yescharacteristic
51C2×C8×Dic83C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C2×C4×D4×C83C2211yescharacteristic
57C2×C4⋊C8×C83C2211yescharacteristic
58C2×C22⋊C8×C83C2211yescharacteristic
59C2×C22⋊C8×C83C2211yescharacteristic
60C2×C22⋊C8×C83C2211yescharacteristic
61C2×C22⋊C8×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×C22⋊D83C2×C411yescharacteristic
65C22×C22⋊D83C2×C411yescharacteristic
66C23×Dic83C2×C411yescharacteristic
67C23×Dic83C2×C411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73#14581787—24no—
74#14581785—24no—
75#14581782—24no—
76#14581778—24no—
77#14581776—24no—
78#14581773—24no—
79#14581769—24no—
80#14581764—24no—
81C4×Dic166D414yes—
82C4×Dic166D414yes—
83C4×C22⋊D83—22no—
84C4×C22⋊D83—22no—
85C4×C22⋊D83—22no—
86C4×C22⋊D83—22no—
87#14581751—22no—
88#14581751—22no—
89#14581749—22no—
90#14581749—22no—
91C2×C4⋊Dic83C2×C411yescharacteristic
92C2×C4⋊Dic83C2×C411yescharacteristic
93C2×C4⋊Dic83C2×C411yescharacteristic
94C2×Dic83⋊C4C2×C411yescharacteristic
95C2×Dic83⋊C4C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×Dic83⋊C4C2×C411yescharacteristic
100C2×C22⋊Dic83C2×C411yescharacteristic
101C2×C22⋊Dic83C2×C411yescharacteristic
102C2×C22⋊Dic83C2×C411yescharacteristic
103C2×C22⋊Dic83C2×C411yescharacteristic
104C2×(C2×D83)⋊C4C2×C411yescharacteristic
105C2×(C2×D83)⋊C4C2×C411yescharacteristic
106C2×(C2×D83)⋊C4C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×C4×Dic83—22no—
109C2×C4×Dic83—22no—
110C2×C4×Dic83C2×C411yescharacteristic
111C2×C4×Dic83C2×C411yescharacteristic
112C2×C4×Dic83C2311yescharacteristic
113C2×C4×Dic83C2311yescharacteristic
114C2×C4×Dic83C2311yescharacteristic
115C4⋊(C83⋊C8)—22no—
116Dic83⋊C8—22no—
117Dic83⋊C8—22no—
118Dic83⋊C8—22no—
119Dic83⋊C8—22no—
120C22⋊(C83⋊C8)—22no—
121C22⋊(C83⋊C8)—22no—
122C22⋊(C83⋊C8)—41no—
123C22⋊(C83⋊C8)—41no—
124(C2×D83)⋊C8—22no—
125(C2×D83)⋊C8—22no—
126(C2×D83)⋊C8—41no—
127(C2×D83)⋊C8—41no—
128#14581703—22no—
129#14581702—22no—
130#14581702—22no—
131#14581702—22no—
132C8×Dic83—22no—
133C22×D4×C83C2×C411yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C22×C8×C83C2311yescharacteristic
137C22×C8×C83C2311yescharacteristic
138C22×C8×C83C2311yescharacteristic
139C22×C8×C83C2311yescharacteristic
140C4×D4×C83—22no—
141C4×D4×C83—22no—
142C2×C4⋊C4×C83C2×C411yescharacteristic
143C2×C22⋊C4×C83C2×C411yescharacteristic
144C2×C22⋊C4×C83C2×C411yescharacteristic
145C2×C42×C83C2311yescharacteristic
146C4⋊C8×C83—22no—
147C22⋊C8×C83—22no—
148C22⋊C8×C83—22no—
149C22⋊C8×C83—41no—
150C22⋊C8×C83—41no—
151C4×C8×C83—22no—
152C23×D83C22×C411yescharacteristic
153C2×Dic166—41no—
154C2×Dic166—41no—
155C2×Dic166C22⋊C414yes—
156C2×C22⋊D83—22no—
157C2×C22⋊D83—22no—
158C2×C22⋊D83—22no—
159C2×C22⋊D83—41no—
160C2×C22⋊D83—41no—
161C2×C22⋊D83—41no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—41no—
166C22×Dic83—41no—
167C22×Dic83—41no—
168C22×Dic83C22×C411yescharacteristic
169C22×Dic83C22×C411yescharacteristic
170C22×Dic83C22×C411yescharacteristic
171C22×Dic83C22×C411yescharacteristic
172C22×Dic83C22×C411yescharacteristic
173C22×Dic83C22×C411yescharacteristic
174C22×Dic83C22×C411yescharacteristic
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×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8—21no—
185C2×C83⋊C8—21no—
186C2×C83⋊C8—21no—
187C2×C83⋊C8—21no—
188C2×C83⋊C8—21no—
189C2×C83⋊C8—21no—
190C2×C83⋊C8—21no—
191C2×C83⋊C8—21no—
192C2×C83⋊C8#4112yes—
193C4⋊Dic83—22no—
194C4⋊Dic83—22no—
195C4⋊Dic83C22⋊C414yes—
196Dic83⋊C4—22no—
197Dic83⋊C4—22no—
198Dic83⋊C4—22no—
199Dic83⋊C4—22no—
200Dic83⋊C4C22⋊C414yes—
201Dic83⋊C4C22⋊C414yes—
202C22⋊Dic83—22no—
203C22⋊Dic83—22no—
204C22⋊Dic83—22no—
205C22⋊Dic83—22no—
206(C2×D83)⋊C4—22no—
207(C2×D83)⋊C4—22no—
208(C2×D83)⋊C4—22no—
209(C2×D83)⋊C4—22no—
210C4×Dic83—21no—
211C4×Dic83—21no—
212C4×Dic83—22no—
213C4×Dic83—22no—
214C4×Dic83C2×D412yes—
215C4×Dic83C2×D412yes—
216C4×Dic83C2×D412yes—
217C4×Dic83C2×D412yes—
218C24×C83C22×C411yescharacteristic
219C24×C83C22×C411yescharacteristic
220C2×D4×C83—22no—
221C2×D4×C83—22no—
222C2×D4×C83—41no—
223C22×C4×C83—21no—
224C22×C4×C83—21no—
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×C83—21no—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83C22×C411yescharacteristic
236C22×C4×C83C22×C411yescharacteristic
237C22×C4×C83C22×C411yescharacteristic
238C22×C4×C83C22×C411yescharacteristic
239C22×C4×C83C2411yescharacteristic
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—21no—
248C2×C8×C83—21no—
249C2×C8×C83—21no—
250C2×C8×C83—21no—
251C2×C8×C83#4112yes—
252C4⋊C4×C83—22no—
253C22⋊C4×C83—22no—
254C22⋊C4×C83—22no—
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×C83—21no—
265C23×C83—21no—
266C23×C83—21no—
267C23×C83—21no—
268C23×C83—21no—
269C23×C83—21no—
270C23×C83#13112yes—
271C23×C83C23×C411yescharacteristic
272C22×D83—21no—
273C22×D83—21no—
274C22×D83—21no—
275C22×D83—21no—
276C22×D83—21no—
277C22×D83—21no—
278C22×D83—21no—
279D4×C83—44no—
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—41no—
291C2×C4×C83—41no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83C2×C22⋊C412yes—
299C2×C4×C83C2×C22⋊C412yes—
300C2×C4×C83C22×D411yescharacteristic
301C2×C4×C83C22×D411yescharacteristic
302C2×C4×C83C2×#4111yescharacteristic
303C2×C4×C83C2×#4111yescharacteristic
304C2×C4×C83H(5,𝔽2)11yescharacteristic
305C2×C4×C832−1+411yescharacteristic
306C22⋊D83—44no—
307C22⋊D83—44no—
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×Dic83—21no—
321C2×Dic83—21no—
322C2×Dic83—21no—
323C2×Dic83—21no—
324C2×Dic83—21no—
325C2×Dic83—44no—
326C2×Dic83—44no—
327C2×Dic83C2×C22⋊C412yes—
328C2×Dic83C2×C22⋊C412yes—
329C2×Dic83C2×C22⋊C412yes—
330C2×Dic83C2×C22⋊C412yes—
331C4×D83—41no—
332C4×D83—41no—
333C4×D83—41no—
334C4×D83—41no—
335Dic166—44no—
336C8×C83—22no—
337C8×C83—41no—
338C8×C83—41no—
339C8×C83—41no—
340C83⋊C8—22no—
341C83⋊C8—41no—
342C83⋊C8—41no—
343C83⋊C8—41no—
344C22×C83—22no—
345C22×C83—22no—
346C22×C83—22no—
347C22×C83—41no—
348C22×C83—41no—
349C22×C83—41no—
350C22×C83—41no—
351C22×C83—41no—
352C22×C83—41no—
353C22×C83—41no—
354C22×C83—41no—
355C22×C83—41no—
356C22×C83—41no—
357C22×C83—41no—
358C22×C83C22×C22⋊C411yescharacteristic
359C22×C83C4×#4111yescharacteristic
360C22×C83#52011yescharacteristic
361C22×C83C2×#13111yescharacteristic
362C22×C83#56811yescharacteristic
363C22×C83#56811yescharacteristic
364C22×C83#56811yescharacteristic
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#54811yescharacteristic
377C4×C83#54811yescharacteristic
378C4×C83#55011yescharacteristic
379C4×C83#55011yescharacteristic
380Dic83—22no—
381Dic83—22no—
382Dic83—22no—
383Dic83—22no—
384Dic83—41no—
385Dic83—41no—
386Dic83—41no—
387#22533—831nomaximal, Sylow
388C2×C83—42no—
389C2×C83—81no—
390C2×C83#234111yescharacteristic
391C2×C83#287911yescharacteristic
392C2×C83#288011yescharacteristic
393C2×C83#296711yescharacteristic
394C2×C83#296811yescharacteristic
395C2×C83#299211yescharacteristic
396C2×C83#299511yescharacteristic
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#1954D8311yescharacteristic, complemented
407#1798—831no—
408#1798—831no—
409#1797—831no—
410#1750—831no—
411#1750—831no—
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×D4C2×D8311yescharacteristic
428C2×#117—831no—
429C2×#117—831no—
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⋊C8C2×D8311yescharacteristic
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⋊C8C2×D8311yescharacteristic
448C2×C22⋊C8C2×D8311yescharacteristic
449C2×C22⋊C8C2×D8311yescharacteristic
450C2×C22⋊C8C2×D8311yescharacteristic
451C2×#97—831no—
452C2×#97—831no—
453C2×#97—831no—
454C2×#97—831no—
455C2×C4×C8—831no—
456C2×C4×C8C2×D8311yescharacteristic
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461C22×Q8—831no—
462C22×D4—831no—
463C22×D4—831no—
464C22×D4C4×D8311yescharacteristic
465C23×C4—831no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4C22×D8311yescharacteristic
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—22no—
489C4×D4—22no—
490C4×D4—1662no—
491C4×D4—1662no—
492C4×D4—1662no—
493C4×D4—1662no—
494#117—1662no—
495#117—1662no—
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⋊C4—831no—
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—831no—
523C2×C42—1662no—
524C2×C42—1662no—
525C2×C42C22×D8311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—1662no—
528C4⋊C8—1662no—
529C4⋊C8—1662no—
530C4⋊C8—1662no—
531C4⋊C8—1662no—
532C22⋊C8—22no—
533C22⋊C8—22no—
534C22⋊C8—41no—
535C22⋊C8—41no—
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—1662no—
545#97—1662no—
546#97—1662no—
547#97—1662no—
548C4×C8—22no—
549C4×C8—1662no—
550C24—831no—
551C24C2×C4×D8311yescharacteristic
552C24C2×C4×D8311yescharacteristic
553C2×Q8—3321no—
554C2×Q8—3321no—
555C2×Q8—834no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—41no—
559C2×D4—3321no—
560C2×D4—3321no—
561C2×D4—3321no—
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—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—3321no—
578C22×C4—3321no—
579C22×C4—3321no—
580C22×C4—831no—
581C22×C4—831no—
582C22×C4—831no—
583C22×C4—831no—
584C22×C4—831no—
585C22×C4—831no—
586C22×C4—831no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
590C22×C4—1661no—
591C22×C4—1661no—
592C22×C4—1661no—
593C22×C4—1661no—
594C22×C4—1661no—
595C22×C4—1661no—
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—21no—
612C2×C8—832no—
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—1661no—
624C2×C8#1305058912yes—
625C4⋊C4—22no—
626C4⋊C4—834no—
627C4⋊C4—834no—
628C4⋊C4—834no—
629C4⋊C4—1662no—
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—832no—
646C42—832no—
647C42—832no—
648C42—832no—
649C42—1662no—
650C42—1662no—
651C42—1661no—
652C42—1661no—
653C42D4×D8312yes—
654C42D4×D8312yes—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—1661no—
669C23—1661no—
670C23—1661no—
671C23—1661no—
672C23—1661no—
673C23—1661no—
674C23—1661no—
675C23#1458179812yes—
676C23C22×C4×D8311yescharacteristic
677Q8—3324no—
678D4—44no—
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—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—3324no—
700C2×C4—3324no—
701C2×C4—3321no—
702C2×C4—3321no—
703C2×C4—3321no—
704C2×C4—3321no—
705C2×C4—832no—
706C2×C4—832no—
707C2×C4—832no—
708C2×C4—832no—
709C2×C4—1661no—
710C2×C4—1661no—
711C2×C4—1661no—
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×C4#41×D8311yescharacteristic
731C2×C4C2×#1305058911yescharacteristic
732C2×C4#1458183711yescharacteristic
733C2×C4#1458183911yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—3321no—
739C8—3321no—
740C8—3321no—
741C8—1662no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—3321no—
757C22—3321no—
758C22—3321no—
759C22—3321no—
760C22—3321no—
761C22—3321no—
762C22—3321no—
763C22C2×C22⋊C4×D8311yescharacteristic
764C22C4×#1305058911yescharacteristic
765C22#1912818011yescharacteristic
766C22C2×#1458179811yescharacteristic
767C22#1912846611yescharacteristic
768C22#1912846611yescharacteristic
769C22#1912846711yescharacteristic
770C4—22no—
771C4—22no—
772C4—41no—
773C4—41no—
774C4—3321no—
775C4—3321no—
776C4—3321no—
777C4—1662no—
778C4—1662no—
779C4—1662no—
780C4—1662no—
781C4#1912835711yescharacteristic
782C4#1912835911yescharacteristic
783C4#1912836911yescharacteristic
784C4#1912837111yescharacteristic
785C2—42no—
786C2—81no—
787C2—6641no—
788C2#2491030211yescharacteristic
789C2#2491590511yescharacteristic
790C2#2491590911yescharacteristic
791C2#2491644911yescharacteristic
792C2#2491645111yescharacteristic
793C2#2491659611yescharacteristic
794C2#2491662711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1954C2
prime radicalC2×#14581764C4
cosocleC22×C4×C83C24
hypercenter#1954D83
hypocenterC83#22533
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1954

Complements

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

NH ≅ G/Ntype
2. C2×#19127831C2semidirect
3. C2×#19127830C2semidirect
4. #24908262C2semidirect
5. #24908259C2semidirect
6. #24908259C2semidirect
7. #24908259C2semidirect
8. #24908255C2semidirect
9. #24907445C2semidirect
10. #24907444C2semidirect
11. #24907441C2semidirect
12. #24907231C2semidirect
13. #24907230C2semidirect
14. #24907227C2semidirect
15. C83×#1954C2semidirect
406. #1954D83semidirect
413. C83#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#191282312
C2×#191278312
C2×#191278302
#249082622
#249082592
#249082552
#249074452
#249074442
#249074412
#249072312
#249072302
#249072272
C83×#19542
#2253383