Finite Group Databasebeta

← #35420945

Subgroups — #35420945

Order 21248.

1036 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128255C211yesmaximal, characteristic
2C2×#19127831C211yesmaximal, characteristic, complemented
3C2×#19127830C211yesmaximal, characteristic, complemented
4#24908404C211yesmaximal, characteristic, complemented
5#24908401C211yesmaximal, characteristic, complemented
6#24908401C211yesmaximal, characteristic, complemented
7#24908401C211yesmaximal, characteristic, complemented
8#24908397C211yesmaximal, characteristic, complemented
9#24907446C211yesmaximal, characteristic
10#24907444C211yesmaximal, characteristic
11#24907442C211yesmaximal, characteristic
12#24907230C211yesmaximal, characteristic
13#24907228C211yesmaximal, characteristic
14#24907224C211yesmaximal, characteristic
15C83×#1984C211yesmaximal, characteristic, complemented
16#19128255—24no—
17#19128255—24no—
18C2×#14581791C411yescharacteristic
19C2×#14581790C411yescharacteristic
20C2×#14581782C411yescharacteristic
21C2×#14581782C411yescharacteristic
22C2×#14581772C411yescharacteristic
23C2×#14581770C411yescharacteristic
24C2×#14581770C411yescharacteristic
25C2×#14581768C411yescharacteristic
26C2×C4×Dic166C2211yescharacteristic
27C2×C4×Dic166C2211yescharacteristic
28C2×C4×Dic166C2211yescharacteristic
29C2×#14581749C2211yescharacteristic
30C2×#14581749C2211yescharacteristic
31C2×C42×D83C2211yescharacteristic
32#19127831—24no—
33#19127830—24no—
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×Dic83⋊C8C2211yescharacteristic
36C2×Dic83⋊C8C2211yescharacteristic
37C2×Dic83⋊C8C2211yescharacteristic
38C2×Dic83⋊C8C2211yescharacteristic
39C2×(C2×D83)⋊C8C2211yescharacteristic
40C2×(C2×D83)⋊C8C2211yescharacteristic
41C2×(C2×D83)⋊C8C2211yescharacteristic
42C2×(C2×D83)⋊C8C2211yescharacteristic
43C2×#14581703C2211yescharacteristic
44C2×#14581702C2211yescharacteristic
45C2×#14581702C2211yescharacteristic
46C2×#14581702C2211yescharacteristic
47C2×C8×Dic83C2211yescharacteristic
48#19127456C2211yescharacteristic
49#19127456C2211yescharacteristic
50#19127456C2211yescharacteristic
51#19127456C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55#19127455C2211yescharacteristic
56C2×C4×Q8×C83C2211yescharacteristic
57C2×C4⋊C8×C83C2211yescharacteristic
58C2×C4×C8×C83C2211yescharacteristic
59#336×C83C2211yescharacteristic
60#336×C83C2211yescharacteristic
61#336×C83C2211yescharacteristic
62#336×C83C2211yescharacteristic
63C22×Dic166C2×C411yescharacteristic
64C22×Dic166C2×C411yescharacteristic
65C22×Dic166C2×C411yescharacteristic
66C22×C4×D83C2×C411yescharacteristic
67C22×C4×D83C2×C411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C22×C83⋊C8C2311yescharacteristic
70C22×C83⋊C8C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73#14581791—24no—
74#14581790—24no—
75#14581782—24no—
76#14581782—24no—
77#14581772—24no—
78#14581770—24no—
79#14581770—24no—
80#14581768—24no—
81C4×Dic166—22no—
82C4×Dic166—22no—
83C4×Dic166—22no—
84C4×Dic166—22no—
85C4×Dic166D414yes—
86C4×Dic166D414yes—
87#14581749—22no—
88#14581749—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×Dic83⋊C4C2×C411yescharacteristic
101C2×Dic83⋊C4C2×C411yescharacteristic
102C2×Dic83⋊C4C2×C411yescharacteristic
103C2×Dic83⋊C4C2×C411yescharacteristic
104C2×(C2×D83)⋊C4C2×C411yescharacteristic
105C2×(C2×D83)⋊C4C2×C411yescharacteristic
106C2×(C2×D83)⋊C4C2×C411yescharacteristic
107C2×(C2×D83)⋊C4C2×C411yescharacteristic
108C2×C4×Dic83C2×C411yescharacteristic
109C2×C4×Dic83C2×C411yescharacteristic
110C2×C4×Dic83C2311yescharacteristic
111C2×C4×Dic83C2311yescharacteristic
112C2×C4×Dic83C2311yescharacteristic
113C42×D83—22no—
114C42×D83—22no—
115C4⋊(C83⋊C8)—22no—
116Dic83⋊C8—22no—
117Dic83⋊C8—22no—
118Dic83⋊C8—22no—
119Dic83⋊C8—22no—
120(C2×D83)⋊C8—22no—
121(C2×D83)⋊C8—22no—
122(C2×D83)⋊C8—22no—
123(C2×D83)⋊C8Q814yescomplemented
124#14581703—22no—
125#14581702—22no—
126#14581702—22no—
127#14581702—22no—
128C8×Dic83—22no—
129C22×Q8×C83C2×C411yescharacteristic
130C22×C8×C83C2311yescharacteristic
131C22×C8×C83C2311yescharacteristic
132C22×C8×C83C2311yescharacteristic
133C22×C8×C83C2311yescharacteristic
134C4×Q8×C83—22no—
135C4×Q8×C83—22no—
136C2×C4⋊C4×C83C2×C411yescharacteristic
137C2×C4⋊C4×C83C2×C411yescharacteristic
138C2×C4⋊C4×C83C2×C411yescharacteristic
139C2×C42×C83C2311yescharacteristic
140C2×C42×C83C2311yescharacteristic
141C2×C42×C83C2311yescharacteristic
142C4⋊C8×C83—22no—
143C4×C8×C83—22no—
144C23×D83C22×C411yescharacteristic
145C2×Dic166—22no—
146C2×Dic166—22no—
147C2×Dic166—22no—
148C2×Dic166—41no—
149C2×Dic166—41no—
150C2×Dic166—41no—
151C2×Dic166—41no—
152C2×Dic166—41no—
153C2×Dic166C22⋊C414yes—
154C22×Dic83C22×C411yescharacteristic
155C22×Dic83C22×C411yescharacteristic
156C22×Dic83C22×C411yescharacteristic
157C22×Dic83C22×C411yescharacteristic
158C22×Dic83C22×C411yescharacteristic
159C22×Dic83C22×C411yescharacteristic
160C22×Dic83C22×C411yescharacteristic
161C2×C4×D83—21no—
162C2×C4×D83—21no—
163C2×C4×D83—21no—
164C2×C4×D83—21no—
165C2×C4×D83—22no—
166C2×C4×D83—22no—
167C2×C4×D83—22no—
168C2×C4×D83—41no—
169C2×C4×D83—41no—
170C2×C4×D83—41no—
171C2×C4×D83C2×Q812yes—
172C2×C4×D83#4112yes—
173C2×C83⋊C8—21no—
174C2×C83⋊C8—21no—
175C2×C83⋊C8—21no—
176C2×C83⋊C8—21no—
177C2×C83⋊C8—21no—
178C2×C83⋊C8—21no—
179C2×C83⋊C8—21no—
180C2×C83⋊C8—21no—
181C2×C83⋊C8—21no—
182C2×C83⋊C8—21no—
183C2×C83⋊C8—21no—
184C2×C83⋊C8C2×Q812yes—
185C4⋊Dic83—22no—
186C4⋊Dic83—22no—
187C4⋊Dic83C22⋊C414yes—
188Dic83⋊C4—22no—
189Dic83⋊C4—22no—
190Dic83⋊C4—22no—
191Dic83⋊C4—22no—
192Dic83⋊C4—22no—
193Dic83⋊C4—22no—
194Dic83⋊C4—22no—
195Dic83⋊C4—22no—
196Dic83⋊C4C22⋊C414yes—
197Dic83⋊C4C22⋊C414yes—
198(C2×D83)⋊C4—22no—
199(C2×D83)⋊C4—22no—
200(C2×D83)⋊C4—22no—
201(C2×D83)⋊C4—22no—
202C4×Dic83—21no—
203C4×Dic83—21no—
204C4×Dic83—22no—
205C4×Dic83—22no—
206C4×Dic83C2×D412yes—
207C4×Dic83C2×D412yes—
208C4×Dic83C2×D412yes—
209C4×Dic83C2×D412yes—
210C2×Q8×C83—22no—
211C2×Q8×C83—22no—
212C2×Q8×C83—41no—
213C22×C4×C83C22×C411yescharacteristic
214C22×C4×C83C22×C411yescharacteristic
215C22×C4×C83C22×C411yescharacteristic
216C22×C4×C83C22×C411yescharacteristic
217C22×C4×C83C22×C411yescharacteristic
218C22×C4×C83C22×C411yescharacteristic
219C22×C4×C83C2411yescharacteristic
220C2×C8×C83—21no—
221C2×C8×C83—21no—
222C2×C8×C83—21no—
223C2×C8×C83—21no—
224C2×C8×C83—21no—
225C2×C8×C83—21no—
226C2×C8×C83—21no—
227C2×C8×C83—21no—
228C2×C8×C83—21no—
229C2×C8×C83—21no—
230C2×C8×C83—21no—
231C2×C8×C83C2×Q812yes—
232C4⋊C4×C83—22no—
233C4⋊C4×C83—22no—
234C4⋊C4×C83—22no—
235C42×C83—21no—
236C42×C83—21no—
237C42×C83—21no—
238C42×C83—21no—
239C42×C83C2×D412yes—
240C42×C83C2×D412yes—
241C23×C83C23×C411yescharacteristic
242C22×D83—21no—
243C22×D83—21no—
244C22×D83—21no—
245C22×D83—21no—
246C22×D83—21no—
247C22×D83—21no—
248C22×D83C4×Q812yes—
249Q8×C83—44no—
250C2×C4×C83—21no—
251C2×C4×C83—21no—
252C2×C4×C83—21no—
253C2×C4×C83—21no—
254C2×C4×C83—21no—
255C2×C4×C83—21no—
256C2×C4×C83—21no—
257C2×C4×C83—21no—
258C2×C4×C83—21no—
259C2×C4×C83—21no—
260C2×C4×C83—21no—
261C2×C4×C83—21no—
262C2×C4×C83—21no—
263C2×C4×C83—21no—
264C2×C4×C83—21no—
265C2×C4×C83C2×C22⋊C412yes—
266C2×C4×C83C2×C22⋊C412yes—
267C2×C4×C83#13112yes—
268C2×C4×C83C22×D411yescharacteristic
269C2×C4×C83C22×D411yescharacteristic
270C2×C4×C83C22×Q811yescharacteristic
271C2×C4×C83C2×#4111yescharacteristic
272C2×C4×C832−1+411yescharacteristic
273C2×C4×C832−1+411yescharacteristic
274C2×Dic83—21no—
275C2×Dic83—21no—
276C2×Dic83—21no—
277C2×Dic83—21no—
278C2×Dic83—21no—
279C2×Dic83—21no—
280C2×Dic83—21no—
281C2×Dic83—21no—
282C2×Dic83—21no—
283C2×Dic83—21no—
284C2×Dic83—21no—
285C2×Dic83—21no—
286C2×Dic83—21no—
287C2×Dic83—21no—
288C2×Dic83—21no—
289C2×Dic83—21no—
290C2×Dic83C2×C22⋊C412yes—
291C2×Dic83C2×C22⋊C412yes—
292C2×Dic83C2×C22⋊C412yes—
293C2×Dic83C2×C22⋊C412yes—
294C2×Dic83C4×Q812yes—
295C4×D83—22no—
296C4×D83—22no—
297C4×D83—22no—
298C4×D83—22no—
299C4×D83—44no—
300C4×D83—44no—
301Dic166—44no—
302Dic166—44no—
303Dic166—44no—
304C8×C83—22no—
305C8×C83—41no—
306C8×C83—41no—
307C8×C83—41no—
308C83⋊C8—22no—
309C83⋊C8—41no—
310C83⋊C8—41no—
311C83⋊C8—41no—
312C22×C83C22×C22⋊C411yescharacteristic
313C22×C83C2×C4×Q811yescharacteristic
314C22×C83#51911yescharacteristic
315C22×C83C2×#13111yescharacteristic
316C22×C83#56811yescharacteristic
317C22×C83#56811yescharacteristic
318C22×C83#56811yescharacteristic
319C2×D83—22no—
320C2×D83—22no—
321C2×D83—22no—
322C2×D83—41no—
323C2×D83—41no—
324C2×D83—41no—
325C2×D83—41no—
326C4×C83—22no—
327C4×C83—22no—
328C4×C83—22no—
329C4×C83—41no—
330C4×C83—41no—
331C4×C83—41no—
332C4×C83#54811yescharacteristic
333C4×C83#54811yescharacteristic
334C4×C83D4×Q811yescharacteristic
335C4×C83D4×Q811yescharacteristic
336Dic83—22no—
337Dic83—22no—
338Dic83—22no—
339Dic83—22no—
340Dic83—22no—
341Dic83—41no—
342Dic83—41no—
343#22511—831nomaximal, Sylow
344C2×C83Q8×C22⋊C411yescharacteristic
345C2×C83#287911yescharacteristic
346C2×C83#288011yescharacteristic
347C2×C83#296111yescharacteristic
348C2×C83#296211yescharacteristic
349C2×C83#298511yescharacteristic
350C2×C83#298711yescharacteristic
351D83—42no—
352C2×#533—831no—
353C2×#446—831no—
354C2×#446—831no—
355#1985—831no—
356#1985—831no—
357#1985—831no—
358#1985—831no—
359#1984—831no—
360#1984D8311yescharacteristic, complemented
361#1798—831no—
362#1798—831no—
363#1797—831no—
364#1750—831no—
365#1750—831no—
366#1749—831no—
367C83#2251111yescharacteristic, complemented, Sylow
368#533—1664no—
369#533—1664no—
370C2×C4⋊Q8—831no—
371C2×C4⋊Q8—831no—
372C2×#125—831no—
373C2×#125—831no—
374C2×C22⋊Q8—831no—
375C2×C22⋊Q8—831no—
376C2×C22⋊Q8—831no—
377C2×C22⋊Q8—831no—
378C2×C4×Q8—831no—
379C2×C4×Q8—831no—
380C2×C4×Q8—831no—
381C2×C4×Q8C2×D8311yescharacteristic
382C2×#117—831no—
383C2×#117—831no—
384C22×C42—831no—
385#446—1664no—
386#446—1664no—
387C2×C4⋊C8—831no—
388C2×C4⋊C8—831no—
389C2×C4⋊C8—831no—
390C2×C4⋊C8—831no—
391C2×C4⋊C8—831no—
392C2×C4⋊C8C2×D8311yescharacteristic
393C2×C22⋊C8—831no—
394C2×C22⋊C8—831no—
395C2×C22⋊C8—831no—
396C2×C22⋊C8—831no—
397C2×#97—831no—
398C2×#97—831no—
399C2×#97—831no—
400C2×#97—831no—
401C2×C4×C8—831no—
402C2×C4×C8C2×D8311yescharacteristic
403#336—831no—
404#336—831no—
405#336—831no—
406#336—831no—
407#336—831no—
408#336—831no—
409#336—831no—
410#336—831no—
411#336C2×D8311yescharacteristic
412#336C2×D8311yescharacteristic
413#336C2×D8311yescharacteristic
414#336C2×D8311yescharacteristic
415C22×Q8—831no—
416C22×Q8—831no—
417C22×Q8—831no—
418C22×Q8C4×D8311yescharacteristic
419C23×C4—831no—
420C23×C4—831no—
421C23×C4—831no—
422C22×C8—831no—
423C22×C8—831no—
424C22×C8—831no—
425C22×C8—831no—
426C22×C8C22×D8311yescharacteristic
427C22×C8C22×D8311yescharacteristic
428C22×C8C22×D8311yescharacteristic
429C22×C8C22×D8311yescharacteristic
430C4⋊Q8—1664no—
431C4⋊Q8—1664no—
432#125—1664no—
433#125—1664no—
434C22⋊Q8—1664no—
435C22⋊Q8—1664no—
436C22⋊Q8—1664no—
437C22⋊Q8—1664no—
438C4×Q8—22no—
439C4×Q8—22no—
440C4×Q8—834no—
441C4×Q8—834no—
442C4×Q8—1662no—
443C4×Q8—1662no—
444C4×Q8—1662no—
445C4×Q8—1662no—
446#117—1662no—
447#117—1662no—
448#117—1662no—
449#117—1662no—
450C2×C4⋊C4—831no—
451C2×C4⋊C4—831no—
452C2×C4⋊C4—831no—
453C2×C4⋊C4—831no—
454C2×C4⋊C4—831no—
455C2×C4⋊C4—831no—
456C2×C4⋊C4—831no—
457C2×C4⋊C4—831no—
458C2×C4⋊C4—831no—
459C2×C4⋊C4—831no—
460C2×C4⋊C4—831no—
461C2×C4⋊C4—831no—
462C2×C4⋊C4—831no—
463C2×C4⋊C4C4×D8311yescharacteristic
464C2×C4⋊C4C4×D8311yescharacteristic
465C2×C4⋊C4C4×D8311yescharacteristic
466C2×C22⋊C4—831no—
467C2×C22⋊C4—831no—
468C2×C22⋊C4—831no—
469C2×C22⋊C4—831no—
470C2×C42—831no—
471C2×C42—831no—
472C2×C42—831no—
473C2×C42—831no—
474C2×C42—831no—
475C2×C42—1662no—
476C2×C42—1662no—
477C2×C42C22×D8311yescharacteristic
478C2×C42C22×D8311yescharacteristic
479C2×C42C22×D8311yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—1662no—
482C4⋊C8—1662no—
483C4⋊C8—1662no—
484C4⋊C8—1662no—
485C4⋊C8—1662no—
486C22⋊C8—834no—
487C22⋊C8—1662no—
488C22⋊C8—1662no—
489C22⋊C8—1662no—
490#97—1662no—
491#97—1662no—
492#97—1662no—
493#97—1662no—
494C4×C8—22no—
495C4×C8—1662no—
496C24—831no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—41no—
500C2×Q8—3321no—
501C2×Q8—3321no—
502C2×Q8—3321no—
503C2×Q8—3321no—
504C2×Q8—3321no—
505C2×Q8—834no—
506C2×Q8—1662no—
507C2×Q8—1662no—
508C2×Q8—1662no—
509C22×C4—3321no—
510C22×C4—3321no—
511C22×C4—3321no—
512C22×C4—831no—
513C22×C4—831no—
514C22×C4—831no—
515C22×C4—831no—
516C22×C4—831no—
517C22×C4—832no—
518C22×C4—832no—
519C22×C4—831no—
520C22×C4—831no—
521C22×C4—1662no—
522C22×C4—1662no—
523C22×C4—1662no—
524C22×C4—1661no—
525C22×C4—1661no—
526C22×C4—1661no—
527C22×C4—1661no—
528C22×C4C2×C4×D8311yescharacteristic
529C22×C4C2×C4×D8311yescharacteristic
530C22×C4C2×C4×D8311yescharacteristic
531C22×C4C2×C4×D8311yescharacteristic
532C22×C4C2×C4×D8311yescharacteristic
533C22×C4C2×C4×D8311yescharacteristic
534C22×C4C23×D8311yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—832no—
547C2×C8—1661no—
548C2×C8—1661no—
549C2×C8—1661no—
550C2×C8—1661no—
551C2×C8—1661no—
552C2×C8—1661no—
553C2×C8—1661no—
554C2×C8—1661no—
555C2×C8—1661no—
556C2×C8—1661no—
557C2×C8—1661no—
558C2×C8Q8×D8312yes—
559C4⋊C4—22no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—834no—
563C4⋊C4—834no—
564C4⋊C4—834no—
565C4⋊C4—1662no—
566C4⋊C4—1662no—
567C4⋊C4—1662no—
568C4⋊C4—1662no—
569C4⋊C4—1662no—
570C4⋊C4—1662no—
571C4⋊C4—1662no—
572C4⋊C4—1662no—
573C4⋊C4—1662no—
574C4⋊C4—1662no—
575C22⋊C4—1662no—
576C22⋊C4—1662no—
577C22⋊C4—1662no—
578C22⋊C4—1662no—
579C42—21no—
580C42—21no—
581C42—21no—
582C42—21no—
583C42—832no—
584C42—832no—
585C42—832no—
586C42—832no—
587C42—1662no—
588C42—1662no—
589C42—1661no—
590C42—1661no—
591C42D4×D8312yes—
592C42D4×D8312yes—
593C23—832no—
594C23—1661no—
595C23—1661no—
596C23—1661no—
597C23—1661no—
598C23—1661no—
599C23—1661no—
600C23C22×C4×D8311yescharacteristic
601Q8—44no—
602Q8—3324no—
603Q8—3324no—
604Q8—3324no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—3324no—
621C2×C4—3324no—
622C2×C4—832no—
623C2×C4—832no—
624C2×C4—832no—
625C2×C4—832no—
626C2×C4—832no—
627C2×C4—1661no—
628C2×C4—1661no—
629C2×C4—1661no—
630C2×C4—1661no—
631C2×C4—1661no—
632C2×C4—1661no—
633C2×C4—1661no—
634C2×C4—1661no—
635C2×C4—1661no—
636C2×C4—1661no—
637C2×C4—1661no—
638C2×C4—1661no—
639C2×C4—1661no—
640C2×C4—1661no—
641C2×C4—1661no—
642C2×C4—1661no—
643C2×C4—1662no—
644C2×C4—1662no—
645C2×C4—1662no—
646C2×C4—1662no—
647C2×C4C22⋊C4×D8312yes—
648C2×C4C22⋊C4×D8312yes—
649C2×C4#1458179812yes—
650C2×C4C2×D4×D8311yescharacteristic
651C2×C4C2×D4×D8311yescharacteristic
652C2×C4C2×Q8×D8311yescharacteristic
653C2×C4#41×D8311yescharacteristic
654C2×C4#1458183911yescharacteristic
655C2×C4#1458184011yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C8—3321no—
661C8—3321no—
662C8—3321no—
663C8—1662no—
664C22—3321no—
665C22—3321no—
666C22—3321no—
667C22—3321no—
668C22—1662no—
669C22—1662no—
670C22—1662no—
671C22C2×C22⋊C4×D8311yescharacteristic
672C22C4×Q8×D8311yescharacteristic
673C22#1912817711yescharacteristic
674C22C2×#1458179811yescharacteristic
675C22#1912846611yescharacteristic
676C22#1912846611yescharacteristic
677C22#1912846711yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—41no—
682C4—41no—
683C4—41no—
684C4—3321no—
685C4—3321no—
686C4—1662no—
687C4—1662no—
688C4—1662no—
689C4—1662no—
690C4—1662no—
691C4#1912835911yescharacteristic
692C4#1912836111yescharacteristic
693C4#1912836411yescharacteristic
694C4#1912836611yescharacteristic
695C2—3322no—
696C2#2491029711yescharacteristic
697C2#2491590511yescharacteristic
698C2#2491590911yescharacteristic
699C2#2491639911yescharacteristic
700C2#2491640511yescharacteristic
701C2#2491655411yescharacteristic
702C2#2491656611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC83×#1984C2
prime radicalC23×D83C22×C4
cosocleC22×C4×C83C24
hypercenter#1984D83
hypocenterC83#22511
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ #1984

Complements

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

NH ≅ G/Ntype
2. C2×#19127831C2semidirect
3. C2×#19127830C2semidirect
4. #24908404C2semidirect
5. #24908401C2semidirect
6. #24908401C2semidirect
7. #24908401C2semidirect
8. #24908397C2semidirect
15. C83×#1984C2semidirect
123. (C2×D83)⋊C8Q8semidirect
360. #1984D83semidirect
367. C83#22511semidirect

Maximal subgroups

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

subgroupindex
C2×#191282552
C2×#191278312
C2×#191278302
#249084042
#249084012
#249083972
#249074462
#249074442
#249074422
#249072302
#249072282
#249072242
C83×#19842
#2251183