Finite Group Databasebeta

← #35421141

Subgroups — #35421141

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×#19128238C211yesmaximal, characteristic
2C2×#19127832C211yesmaximal, characteristic, complemented
3#24908261C211yesmaximal, characteristic, complemented
4#24908261C211yesmaximal, characteristic, complemented
5#24908260C211yesmaximal, characteristic, complemented
6#24908260C211yesmaximal, characteristic, complemented
7#24908257C211yesmaximal, characteristic, complemented
8#24908256C211yesmaximal, characteristic, complemented
9#24907444C211yesmaximal, characteristic, complemented
10#24907444C211yesmaximal, characteristic, complemented
11#24907440C211yesmaximal, characteristic, complemented
12#24907232C211yesmaximal, characteristic, complemented
13#24907230C211yesmaximal, characteristic, complemented
14#24907226C211yesmaximal, characteristic, complemented
15C2×#446×C83C211yesmaximal, characteristic, complemented
16#19128238—24no—
17#19128238—24no—
18C2×#14581787C411yescharacteristic
19C2×#14581787C411yescharacteristic
20C2×#14581783C411yescharacteristic
21C2×#14581781C411yescharacteristic
22C2×#14581777C411yescharacteristic
23C2×#14581777C411yescharacteristic
24C2×#14581768C411yescharacteristic
25C2×#14581767C411yescharacteristic
26C2×C4×D332C2211yescharacteristic
27C2×C4×D332C2211yescharacteristic
28C2×C4×D332C2211yescharacteristic
29C2×#14581749C2211yescharacteristic
30C2×#14581749C2211yescharacteristic
31C2×C42×D83C2211yescharacteristic
32#19127832—24no—
33C2×C4⋊(C83⋊C8)C2211yescharacteristic
34C2×C4⋊(C83⋊C8)C2211yescharacteristic
35C2×C4⋊(C83⋊C8)C2211yescharacteristic
36C2×(C2×D83)⋊C8C2211yescharacteristic
37C2×(C2×D83)⋊C8C2211yescharacteristic
38C2×(C2×D83)⋊C8C2211yescharacteristic
39C2×(C2×D83)⋊C8C2211yescharacteristic
40C2×(C2×D83)⋊C8C2211yescharacteristic
41C2×(C2×D83)⋊C8C2211yescharacteristic
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×#14581703C2211yescharacteristic
49C2×#14581703C2211yescharacteristic
50C2×C4×C83⋊C8C2211yescharacteristic
51#19127455C2211yescharacteristic
52#19127455C2211yescharacteristic
53#19127455C2211yescharacteristic
54#19127455C2211yescharacteristic
55C2×C4×Q8×C83C2211yescharacteristic
56#446×C83—24no—
57C2×C4⋊C8×C83C2211yescharacteristic
58C2×C4⋊C8×C83C2211yescharacteristic
59C2×C4⋊C8×C83C2211yescharacteristic
60C2×#97×C83C2211yescharacteristic
61C2×#97×C83C2211yescharacteristic
62C2×C4×C8×C83C2211yescharacteristic
63C22×D332C2×C411yescharacteristic
64C22×D332C2×C411yescharacteristic
65C22×D332C2×C411yescharacteristic
66C22×C4×D83C2×C411yescharacteristic
67C22×C4×D83C2×C411yescharacteristic
68C22×C4×D83C2311yescharacteristic
69C22×C4×D83C2311yescharacteristic
70C22×C4×D83C2311yescharacteristic
71C22×C83⋊C8C2311yescharacteristic
72C22×C83⋊C8C2311yescharacteristic
73C22×C83⋊C8C2311yescharacteristic
74C22×C83⋊C8C2311yescharacteristic
75#14581787—24no—
76#14581787—24no—
77#14581783—24no—
78#14581781—24no—
79#14581777—24no—
80#14581777—24no—
81#14581768—24no—
82#14581767—24no—
83C4×D332—22no—
84C4×D332—22no—
85C4×D332—22no—
86C4×D332—22no—
87C4×D332—22no—
88C4×D332—22no—
89#14581749—22no—
90#14581749—22no—
91#14581749—22no—
92#14581749—22no—
93C2×C4⋊Dic83C2×C411yescharacteristic
94C2×C4⋊Dic83C2×C411yescharacteristic
95C2×C4⋊Dic83C2×C411yescharacteristic
96C2×Dic83⋊C4C2×C411yescharacteristic
97C2×Dic83⋊C4C2×C411yescharacteristic
98C2×Dic83⋊C4C2×C411yescharacteristic
99C2×Dic83⋊C4C2×C411yescharacteristic
100C2×(C2×D83)⋊C4C2×C411yescharacteristic
101C2×(C2×D83)⋊C4C2×C411yescharacteristic
102C2×(C2×D83)⋊C4C2×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×(C2×D83)⋊C4C2×C411yescharacteristic
110C2×C4×Dic83C2×C411yescharacteristic
111C2×C4×Dic83C2×C411yescharacteristic
112C2×C4×Dic83C2311yescharacteristic
113C42×D83—22no—
114C42×D83—22no—
115C4⋊(C83⋊C8)—22no—
116C4⋊(C83⋊C8)—22no—
117C4⋊(C83⋊C8)—22no—
118(C2×D83)⋊C8—22no—
119(C2×D83)⋊C8—22no—
120(C2×D83)⋊C8—22no—
121(C2×D83)⋊C8—22no—
122(C2×D83)⋊C8—22no—
123(C2×D83)⋊C8—22no—
124(C2×D83)⋊C8—41no—
125(C2×D83)⋊C8—41no—
126(C2×D83)⋊C8—41no—
127(C2×D83)⋊C8—41no—
128(C2×D83)⋊C8—41no—
129(C2×D83)⋊C8—41no—
130#14581703—22no—
131#14581703—22no—
132C4×C83⋊C8—22no—
133C22×Q8×C83C2×C411yescharacteristic
134C22×C8×C83C2311yescharacteristic
135C22×C8×C83C2311yescharacteristic
136C22×C8×C83C2311yescharacteristic
137C22×C8×C83C2311yescharacteristic
138C4×Q8×C83D414yes—
139C4×Q8×C83D414yes—
140C2×C4⋊C4×C83C2×C411yescharacteristic
141C2×C4⋊C4×C83C2×C411yescharacteristic
142C2×C4⋊C4×C83C2×C411yescharacteristic
143C2×C42×C83C2311yescharacteristic
144C2×C42×C83C2311yescharacteristic
145C2×C42×C83C2311yescharacteristic
146C4⋊C8×C83—22no—
147C4⋊C8×C83—22no—
148C4⋊C8×C83—22no—
149#97×C83—22no—
150#97×C83—22no—
151C4×C8×C83—22no—
152C23×D83C22×C411yescharacteristic
153C23×D83C22×C411yescharacteristic
154C23×D83C22×C411yescharacteristic
155C2×D332—22no—
156C2×D332—22no—
157C2×D332—22no—
158C2×D332—22no—
159C2×D332—22no—
160C2×D332—41no—
161C2×D332—41no—
162C2×D332—41no—
163C2×D332—41no—
164C22×Dic83C22×C411yescharacteristic
165C22×Dic83C22×C411yescharacteristic
166C22×Dic83C22×C411yescharacteristic
167C22×Dic83C22×C411yescharacteristic
168C22×Dic83C22×C411yescharacteristic
169C2×C4×D83—22no—
170C2×C4×D83—22no—
171C2×C4×D83—22no—
172C2×C4×D83—21no—
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—21no—
186C2×C4×D83—21no—
187C2×C4×D83—21no—
188C2×C4×D83—21no—
189C2×C4×D83—21no—
190C2×C4×D83—41no—
191C2×C4×D83—41no—
192C2×C4×D83—41no—
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—
202C2×C83⋊C8—21no—
203C2×C83⋊C8—21no—
204C2×C83⋊C8#4112yes—
205C4⋊Dic83—22no—
206C4⋊Dic83—22no—
207C4⋊Dic83—22no—
208Dic83⋊C4—22no—
209Dic83⋊C4—22no—
210Dic83⋊C4—22no—
211Dic83⋊C4—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—
218(C2×D83)⋊C4—22no—
219(C2×D83)⋊C4—22no—
220(C2×D83)⋊C4—22no—
221(C2×D83)⋊C4—22no—
222C4×Dic83—22no—
223C4×Dic83—22no—
224C4×Dic83—21no—
225C4×Dic83—21no—
226C2×Q8×C83—41no—
227C2×Q8×C83—41no—
228C2×Q8×C83C22⋊C414yes—
229C22×C4×C83C22×C411yescharacteristic
230C22×C4×C83C22×C411yescharacteristic
231C22×C4×C83C22×C411yescharacteristic
232C22×C4×C83C22×C411yescharacteristic
233C22×C4×C83C22×C411yescharacteristic
234C22×C4×C83C22×C411yescharacteristic
235C22×C4×C83C2411yescharacteristic
236C2×C8×C83—21no—
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—
248C4⋊C4×C83C22⋊C414yes—
249C4⋊C4×C83C22⋊C414yes—
250C4⋊C4×C83C22⋊C414yes—
251C42×C83C2×D412yes—
252C42×C83C2×D412yes—
253C42×C83C2×D412yes—
254C42×C83C2×D412yes—
255C42×C83C2×D412yes—
256C42×C83C2×D412yes—
257C23×C83C23×C411yescharacteristic
258C22×D83—21no—
259C22×D83—21no—
260C22×D83—21no—
261C22×D83—21no—
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—21no—
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—
279Q8×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—21no—
291C2×C4×C83—21no—
292C2×C4×C83C2×C22⋊C412yes—
293C2×C4×C83C2×C22⋊C412yes—
294C2×C4×C83C2×C22⋊C412yes—
295C2×C4×C83C2×C22⋊C412yes—
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
304C2×Dic83—21no—
305C2×Dic83—21no—
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—
319D332—44no—
320D332—44no—
321D332—44no—
322C4×D83—44no—
323C4×D83—44no—
324C4×D83—41no—
325C4×D83—41no—
326C4×D83—41no—
327C4×D83—41no—
328C4×D83—41no—
329C4×D83—41no—
330C4×D83—41no—
331C4×D83—41no—
332C4×D83—41no—
333C4×D83—41no—
334C4×D83—41no—
335C4×D83—41no—
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×C83C22×C22⋊C411yescharacteristic
345C22×C83C4×#4111yescharacteristic
346C22×C83#52011yescharacteristic
347C22×C83C2×#13111yescharacteristic
348C22×C83#56811yescharacteristic
349C22×C83#56811yescharacteristic
350C22×C83#56811yescharacteristic
351C2×D83—22no—
352C2×D83—22no—
353C2×D83—22no—
354C2×D83—41no—
355C2×D83—41no—
356C2×D83—41no—
357C2×D83—41no—
358C2×D83—41no—
359C2×D83—41no—
360C2×D83—41no—
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—22no—
375C4×C83—22no—
376C4×C83—22no—
377C4×C83—22no—
378C4×C83#54811yescharacteristic
379C4×C83#54811yescharacteristic
380C4×C83#55011yescharacteristic
381C4×C83#55011yescharacteristic
382Dic83—41no—
383Dic83—41no—
384Dic83—41no—
385Dic83—41no—
386Dic83—41no—
387#22533—831nomaximal, Sylow
388C2×C83#234111yescharacteristic
389C2×C83#287911yescharacteristic
390C2×C83#288011yescharacteristic
391C2×C83#296711yescharacteristic
392C2×C83#296811yescharacteristic
393C2×C83#299211yescharacteristic
394C2×C83#299511yescharacteristic
395D83—42no—
396D83—81no—
397D83—81no—
398C2×#529—831no—
399C2×#446—831no—
400C2×#446D8311yescharacteristic, complemented
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#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×Q8C2×D8311yescharacteristic
425C2×C4×D4—831no—
426C2×C4×D4—831no—
427C2×C4×D4—831no—
428C2×#117—831no—
429C2×#117—831no—
430C22×C42—831no—
431#446—24no—
432#446—1664no—
433C2×C4⋊C8—831no—
434C2×C4⋊C8—831no—
435C2×C4⋊C8—831no—
436C2×C4⋊C8C2×D8311yescharacteristic
437C2×C4⋊C8C2×D8311yescharacteristic
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⋊C8—831no—
448C2×C22⋊C8—831no—
449C2×C22⋊C8—831no—
450C2×C22⋊C8—831no—
451C2×#97—831no—
452C2×#97—831no—
453C2×#97C2×D8311yescharacteristic
454C2×#97C2×D8311yescharacteristic
455C2×C4×C8—831no—
456C2×C4×C8C2×D8311yescharacteristic
457#336—831no—
458#336—831no—
459#336—831no—
460#336—831no—
461C22×Q8C4×D8311yescharacteristic
462C22×D4—831no—
463C22×D4—831no—
464C22×D4—831no—
465C23×C4—831no—
466C23×C4—831no—
467C23×C4—831no—
468C23×C4—831no—
469C23×C4—831no—
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×Q8D33214yes—
487C4×Q8C22⋊D8314yes—
488C4×D4—1662no—
489C4×D4—1662no—
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⋊C4C4×D8311yescharacteristic
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⋊C4—831no—
517C2×C22⋊C4—831no—
518C2×C42—831no—
519C2×C42—831no—
520C2×C42—831no—
521C2×C42—1662no—
522C2×C42—1662no—
523C2×C42C22×D8311yescharacteristic
524C2×C42C22×D8311yescharacteristic
525C2×C42C22×D8311yescharacteristic
526C4⋊C8—22no—
527C4⋊C8—22no—
528C4⋊C8—22no—
529C4⋊C8—1662no—
530C4⋊C8—1662no—
531C4⋊C8—1662no—
532C22⋊C8—3321no—
533C22⋊C8—3321no—
534C22⋊C8—3321no—
535C22⋊C8—3321no—
536C22⋊C8—3321no—
537C22⋊C8—3321no—
538C22⋊C8—1662no—
539C22⋊C8—1662no—
540C22⋊C8—1662no—
541C22⋊C8—1662no—
542C22⋊C8—1662no—
543C22⋊C8—1662no—
544#97—22no—
545#97—22no—
546#97—1662no—
547#97—1662no—
548C4×C8—22no—
549C4×C8—1662no—
550C24—831no—
551C24—831no—
552C24—831no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8(C2×D83)⋊C414yes—
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—3321no—
566C22×C4—3321no—
567C22×C4—3321no—
568C22×C4—831no—
569C22×C4—831no—
570C22×C4—831no—
571C22×C4—831no—
572C22×C4—831no—
573C22×C4—1662no—
574C22×C4—1661no—
575C22×C4—1661no—
576C22×C4—1661no—
577C22×C4—1661no—
578C22×C4—1661no—
579C22×C4—1661no—
580C22×C4—1661no—
581C22×C4—1661no—
582C22×C4—1661no—
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—1662no—
593C22×C4—1662no—
594C22×C4C2×C4×D8311yescharacteristic
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—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#1305059112yes—
625C4⋊C4—1662no—
626C4⋊C4—1662no—
627C4⋊C4—1662no—
628C4⋊C4—1662no—
629C4⋊C4—1662no—
630C4⋊C4—1662no—
631C4⋊C4—1662no—
632C4⋊C4(C2×D83)⋊C414yes—
633C4⋊C4(C2×D83)⋊C414yes—
634C4⋊C4(C2×D83)⋊C414yes—
635C22⋊C4—1662no—
636C22⋊C4—1662no—
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—1661no—
646C42—1661no—
647C42—1662no—
648C42—1662no—
649C42C2×C22⋊D8312yes—
650C42C2×C22⋊D8312yes—
651C42C2×C22⋊D8312yes—
652C42C2×D33212yes—
653C42C2×D33212yes—
654C42C2×D33212yes—
655C23—832no—
656C23—1661no—
657C23—1661no—
658C23—1661no—
659C23—1661no—
660C23—1661no—
661C23—1661no—
662C23—1661no—
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—44no—
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—3324no—
694C2×C4—3324no—
695C2×C4—3321no—
696C2×C4—3321no—
697C2×C4—3321no—
698C2×C4—3321no—
699C2×C4—3321no—
700C2×C4—3321no—
701C2×C4—3321no—
702C2×C4—3321no—
703C2×C4—3321no—
704C2×C4—3321no—
705C2×C4—3321no—
706C2×C4—3321no—
707C2×C4—1661no—
708C2×C4—1661no—
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×C4C2×(C2×D83)⋊C412yes—
723C2×C4C2×(C2×D83)⋊C412yes—
724C2×C4C2×(C2×D83)⋊C412yes—
725C2×C4C2×(C2×D83)⋊C412yes—
726C2×C4C2×(C2×D83)⋊C412yes—
727C2×C4C2×(C2×D83)⋊C412yes—
728C2×C4C22×C22⋊D8311yescharacteristic
729C2×C4C22×D33211yescharacteristic
730C2×C4#41×D8311yescharacteristic
731C2×C4C2×#1305059111yescharacteristic
732C2×C4#1458183811yescharacteristic
733C2×C4#1458184011yescharacteristic
734C8—22no—
735C8—41no—
736C8—41no—
737C8—41no—
738C8—3321no—
739C8—3321no—
740C8—3321no—
741C8—1662no—
742C22—3321no—
743C22—3321no—
744C22—3321no—
745C22—3321no—
746C22—3321no—
747C22—3321no—
748C22—3321no—
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—
763C22C22×(C2×D83)⋊C411yescharacteristic
764C22C4×#1305059111yescharacteristic
765C22#1912818311yescharacteristic
766C22#131×D8311yescharacteristic
767C22#1912846611yescharacteristic
768C22#1912846711yescharacteristic
769C22#1912846711yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—22no—
774C4—22no—
775C4—22no—
776C4—3321no—
777C4—3321no—
778C4—3321no—
779C4—3321no—
780C4—3321no—
781C4#1912836211yescharacteristic
782C4#1912836311yescharacteristic
783C4#1912837011yescharacteristic
784C4#1912837311yescharacteristic
785C2—3322no—
786C2—6641no—
787C2—6641no—
788C2#2491030111yescharacteristic
789C2#2491590711yescharacteristic
790C2#2491591011yescharacteristic
791C2#2491644711yescharacteristic
792C2#2491645611yescharacteristic
793C2#2491660111yescharacteristic
794C2#2491663211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D83
commutator, socleC23×C83C23×C4
FittingC2×#446×C83C2
prime radicalC2×#14581767C4
cosocleC22×C4×C83C24
hypercenterC2×#446D83
hypocenterC83#22533
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#19127832C2semidirect
3. #24908261C2semidirect
4. #24908261C2semidirect
5. #24908260C2semidirect
6. #24908260C2semidirect
7. #24908257C2semidirect
8. #24908256C2semidirect
9. #24907444C2semidirect
10. #24907444C2semidirect
11. #24907440C2semidirect
12. #24907232C2semidirect
13. #24907230C2semidirect
14. #24907226C2semidirect
15. C2×#446×C83C2semidirect
400. C2×#446D83semidirect
413. C83#22533semidirect

Maximal subgroups

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

subgroupindex
C2×#191282382
C2×#191278322
#249082612
#249082602
#249082572
#249082562
#249074442
#249074402
#249072322
#249072302
#249072262
C2×#446×C832
#2253383