Finite Group Databasebeta

← #35325937

Subgroups — #35325937

Order 21248.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127594C211yesmaximal, characteristic
2C2×C22⋊C4×Dic83C211yesmaximal, characteristic
3C2×C22⋊C4×Dic83C211yesmaximal, characteristic
4C2×#19127547C211yesmaximal, characteristic, complemented
5#24905700C211yesmaximal, characteristic
6#24905700C211yesmaximal, characteristic
7#24905697C211yesmaximal, characteristic, complemented
8#24905695C211yesmaximal, characteristic, complemented
9#24905692C211yesmaximal, characteristic, complemented
10#24905688C211yesmaximal, characteristic, complemented
11#24905685C211yesmaximal, characteristic
12C4×C83⋊#95C211yesmaximal, characteristic, complemented
13#95×Dic83C211yesmaximal, characteristic, complemented
14#95×Dic83C211yesmaximal, characteristic, complemented
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127594C418yescomplemented
29C22⋊C4×Dic83—24no—
30C22⋊C4×Dic83C418yescomplemented
31#19127547—24no—
32C2×C83⋊#95C2211yescharacteristic
33C2×C83⋊#95C2211yescharacteristic
34C2×C83⋊#95C2211yescharacteristic
35C2×C83⋊#95C2211yescharacteristic
36C2×C83⋊#95C2211yescharacteristic
37C2×C83⋊#95C2211yescharacteristic
38C2×C83⋊#95C2211yescharacteristic
39C2×C83⋊#95C2211yescharacteristic
40C2×C83⋊#95C2211yescharacteristic
41C2×C83⋊#95C2211yescharacteristic
42C2×C83⋊#95C2211yescharacteristic
43C2×C83⋊#95C2211yescharacteristic
44C2×C83⋊#95C2211yescharacteristic
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C2×C83⋊#95C2211yescharacteristic
48C22×C4⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C22⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C42×C83C2211yescharacteristic
53#388×C83C418yescomplemented
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83—22no—
57C23×Dic83—22no—
58C23×Dic83—22no—
59C23×Dic83—22no—
60C23×Dic83—41no—
61C23×Dic83—41no—
62C23×Dic83C2×C414yes—
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C2×C4⋊Dic83—41no—
72C2×C4⋊Dic83—41no—
73C2×C4⋊Dic83C2×C414yescomplemented
74C2×C22⋊Dic83—22no—
75C2×C22⋊Dic83—22no—
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—22no—
78C2×C22⋊Dic83—41no—
79C2×C22⋊Dic83—41no—
80C2×C22⋊Dic83C2×C414yes—
81C2×C22⋊Dic83C2×C414yes—
82C2×C22⋊Dic83C2×C414yes—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—22no—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—22no—
89C2×C4×Dic83—22no—
90C2×C4×Dic83—22no—
91C2×C4×Dic83—22no—
92C2×C4×Dic83—22no—
93C2×C4×Dic83—22no—
94C2×C4×Dic83—22no—
95C2×C4×Dic83—41no—
96C2×C4×Dic83—41no—
97C2×C4×Dic83—41no—
98C2×C4×Dic83—41no—
99C2×C4×Dic83—41no—
100C2×C4×Dic83—41no—
101C2×C4×Dic83C2×C414yes—
102C2×C4×Dic83C2×C414yes—
103C2×C4×Dic83C2×C414yescomplemented
104C83⋊#95—22no—
105C83⋊#95—22no—
106C83⋊#95—22no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—22no—
112C83⋊#95—22no—
113C83⋊#95—41no—
114C83⋊#95—41no—
115C83⋊#95C2×C414yes—
116C83⋊#95C2×C414yes—
117C83⋊#95C2×C414yescomplemented
118C83⋊#95C2×C414yescomplemented
119C83⋊#95D414yes—
120C25×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C2×C4⋊C4×C83—41no—
128C2×C4⋊C4×C83—41no—
129C2×C4⋊C4×C83C2×C414yescomplemented
130C2×C22⋊C4×C83—22no—
131C2×C22⋊C4×C83—22no—
132C2×C22⋊C4×C83—41no—
133C2×C22⋊C4×C83—41no—
134C2×C22⋊C4×C83C2×C414yes—
135C2×C22⋊C4×C83C2×C414yes—
136C2×C22⋊C4×C83C2×C414yes—
137C2×C22⋊C4×C83C2×C414yes—
138C2×C22⋊C4×C83C2×C414yes—
139C2×C42×C83—22no—
140C2×C42×C83—22no—
141C2×C42×C83C2×C414yescomplemented
142#95×C83C2×C414yescomplemented
143#95×C83C2×C414yescomplemented
144C22×Dic83—21no—
145C22×Dic83—21no—
146C22×Dic83—21no—
147C22×Dic83—21no—
148C22×Dic83—21no—
149C22×Dic83—21no—
150C22×Dic83—21no—
151C22×Dic83—21no—
152C22×Dic83—21no—
153C22×Dic83—21no—
154C22×Dic83—21no—
155C22×Dic83—21no—
156C22×Dic83—21no—
157C22×Dic83—21no—
158C22×Dic83—21no—
159C22×Dic83—21no—
160C22×Dic83—21no—
161C22×Dic83—21no—
162C22×Dic83—21no—
163C22×Dic83—21no—
164C22×Dic83—21no—
165C22×Dic83—21no—
166C22×Dic83—21no—
167C22×Dic83—21no—
168C22×Dic83—21no—
169C22×Dic83—21no—
170C22×Dic83—21no—
171C22×Dic83—21no—
172C22×Dic83—21no—
173C22×Dic83—21no—
174C22×Dic83—21no—
175C22×Dic83—21no—
176C22×Dic83—21no—
177C22×Dic83—21no—
178C22×Dic83—21no—
179C22×Dic83—21no—
180C22×Dic83—21no—
181C22×Dic83—21no—
182C22×Dic83—21no—
183C22×Dic83—21no—
184C22×Dic83—28no—
185C22×Dic83—28no—
186C22×Dic83—44no—
187C22×Dic83—44no—
188C22×Dic83—44no—
189C22×Dic83—44no—
190C22×Dic83—44no—
191C22×Dic83C22×C412yes—
192C22×Dic83C22×C412yes—
193C22×Dic83C22×C412yes—
194C22×Dic83C22×C412yes—
195C22×Dic83C22×C412yes—
196C22×Dic83C22×C412yes—
197C22×Dic83C22×C412yes—
198C22×Dic83C22×C412yes—
199C22×Dic83C2×D412yes—
200C22×Dic83C2×D412yes—
201C22×Dic83#4112yes—
202C22×Dic83#4112yes—
203C22×Dic83#4112yes—
204C22×Dic83#4112yes—
205C22×Dic83#4112yes—
206C22×Dic83#4112yes—
207C4⋊Dic83—44no—
208C22⋊Dic83—28no—
209C22⋊Dic83—28no—
210C22⋊Dic83—44no—
211C4×Dic83—28no—
212C4×Dic83—28no—
213C4×Dic83—44no—
214C4×Dic83—44no—
215C4×Dic83—44no—
216C4×Dic83—44no—
217C4×Dic83—44no—
218C24×C83—21no—
219C24×C83—21no—
220C24×C83—21no—
221C24×C83—21no—
222C24×C83—21no—
223C24×C83—21no—
224C24×C83—21no—
225C24×C83—21no—
226C24×C83—21no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83—21no—
230C24×C83C22×C412yes—
231C24×C83C22×C412yes—
232C24×C83C22×C412yes—
233C24×C83C2411yescharacteristic
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83—21no—
237C22×C4×C83—21no—
238C22×C4×C83—21no—
239C22×C4×C83—21no—
240C22×C4×C83—21no—
241C22×C4×C83—21no—
242C22×C4×C83—21no—
243C22×C4×C83—21no—
244C22×C4×C83—21no—
245C22×C4×C83—21no—
246C22×C4×C83—21no—
247C22×C4×C83—21no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—21no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83C22×C412yes—
265C22×C4×C83C22×C412yes—
266C22×C4×C83C22×C412yes—
267C22×C4×C83C22×C412yes—
268C22×C4×C83C22×C412yes—
269C22×C4×C83C22×C412yes—
270C22×C4×C83C22×C412yes—
271C22×C4×C83C22×C412yes—
272C22×C4×C83C22×C412yes—
273C22×C4×C83C22×C412yes—
274C22×C4×C83C2×D412yes—
275C22×C4×C83#4112yes—
276C4⋊C4×C83—44no—
277C22⋊C4×C83—28no—
278C22⋊C4×C83—44no—
279C22⋊C4×C83C42116yescomplemented
280C42×C83—28no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—22no—
285C23×C83—22no—
286C23×C83—22no—
287C23×C83—22no—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83—22no—
295C23×C83—22no—
296C23×C83—22no—
297C23×C83—22no—
298C23×C83—22no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83—41no—
302C23×C83—41no—
303C23×C83—41no—
304C23×C83—41no—
305C23×C83—41no—
306C23×C83—41no—
307C23×C83—41no—
308C23×C83—41no—
309C23×C83—41no—
310C23×C83—41no—
311C23×C83—41no—
312C23×C83—41no—
313C23×C83—41no—
314C23×C83—41no—
315C23×C83C2×C4214yes—
316C23×C83C23×C411yescharacteristic
317C23×C83C23×C411yescharacteristic
318C23×C83C23×C411yescharacteristic
319C23×C83C22×D411yescharacteristic
320C23×C83C2×#4111yescharacteristic
321C23×C83C2×#4111yescharacteristic
322C23×C83C2×#4111yescharacteristic
323C23×C83C2×#4111yescharacteristic
324C23×C83C2×#4111yescharacteristic
325C23×C83C2×#4111yescharacteristic
326C23×C83C2×#4111yescharacteristic
327C23×C83H(5,𝔽2)11yescharacteristic
328C23×C83H(5,𝔽2)11yescharacteristic
329C23×C83H(5,𝔽2)11yescharacteristic
330C23×C832−1+411yescharacteristic
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
341C2×C4×C83—22no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—22no—
358C2×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
361C2×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83C2×C4214yes—
371C2×C4×C83C2×C4214yes—
372C2×C4×C83C4×D414yes—
373C2×Dic83—22no—
374C2×Dic83—22no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—22no—
380C2×Dic83—22no—
381C2×Dic83—22no—
382C2×Dic83—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
390C2×Dic83—22no—
391C2×Dic83—22no—
392C2×Dic83—22no—
393C2×Dic83—22no—
394C2×Dic83—22no—
395C2×Dic83—22no—
396C2×Dic83—22no—
397C2×Dic83—22no—
398C2×Dic83—22no—
399C2×Dic83—22no—
400C2×Dic83—22no—
401C2×Dic83—22no—
402C2×Dic83—22no—
403C2×Dic83—22no—
404C2×Dic83—22no—
405C2×Dic83—22no—
406C2×Dic83—22no—
407C2×Dic83—22no—
408C2×Dic83—22no—
409C2×Dic83—416no—
410C2×Dic83—41no—
411C2×Dic83—41no—
412C2×Dic83—41no—
413C2×Dic83—41no—
414C2×Dic83—41no—
415C2×Dic83—41no—
416C2×Dic83—41no—
417C2×Dic83—41no—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83—41no—
421C2×Dic83—41no—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83#11714yes—
427C2×Dic83#11714yes—
428C2×Dic83C4×D414yes—
429C2×Dic83C4×D414yes—
430C22×C83—24no—
431C22×C83—24no—
432C22×C83—24no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—42no—
436C22×C83—42no—
437C22×C83—42no—
438C22×C83—42no—
439C22×C83—42no—
440C22×C83—42no—
441C22×C83—42no—
442C22×C83—42no—
443C22×C83—42no—
444C22×C83—42no—
445C22×C83C22×C4211yescharacteristic
446C22×C83C2×#11711yescharacteristic
447C22×C83C2×#11711yescharacteristic
448C22×C83C2×C4×D411yescharacteristic
449C22×C83C2×C4×D411yescharacteristic
450C22×C83C2×C4×D411yescharacteristic
451C22×C83C4×#4111yescharacteristic
452C22×C83C4×#4111yescharacteristic
453C22×C83C4×#4111yescharacteristic
454C22×C83C4×#4111yescharacteristic
455C22×C83C4×#4111yescharacteristic
456C22×C83C4×#4111yescharacteristic
457C22×C83C4×#4111yescharacteristic
458C22×C83#51811yescharacteristic
459C22×C83#51811yescharacteristic
460C22×C83#51811yescharacteristic
461C22×C83#52011yescharacteristic
462C22×C83#52011yescharacteristic
463C22×C83#52011yescharacteristic
464C22×C83#54611yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54711yescharacteristic
467C22×C83#55011yescharacteristic
468C22×C83#55111yescharacteristic
469C22×C83#55111yescharacteristic
470C22×C83#55111yescharacteristic
471C22×C83#55111yescharacteristic
472C22×C83#55211yescharacteristic
473C22×C83#55211yescharacteristic
474C22×C83#55311yescharacteristic
475C22×C83#55311yescharacteristic
476C22×C83#55511yescharacteristic
477C22×C83#55511yescharacteristic
478C22×C83#55511yescharacteristic
479C22×C83#55611yescharacteristic
480C4×C83—24no—
481C4×C83—24no—
482C4×C83—24no—
483C4×C83—42no—
484C4×C83—42no—
485C4×C83—42no—
486Dic83—24no—
487Dic83—24no—
488Dic83—24no—
489Dic83—24no—
490Dic83—42no—
491Dic83—42no—
492Dic83—42no—
493Dic83—42no—
494#13816—831nomaximal, Sylow
495C2×C83—44no—
496C2×C83C4×#11711yescharacteristic
497C2×C83C42×D411yescharacteristic
498C2×C83#227511yescharacteristic
499C2×C83#234211yescharacteristic
500C2×C83#234611yescharacteristic
501C2×C83#235311yescharacteristic
502C2×C83#235411yescharacteristic
503C2×C83#235911yescharacteristic
504C2×C83#235911yescharacteristic
505C2×C83#236311yescharacteristic
506C2×C83#236311yescharacteristic
507C2×C83#237211yescharacteristic
508C2×C83#237211yescharacteristic
509C2×C83#237311yescharacteristic
510C2×C83#237311yescharacteristic
511C2×#388—831no—
512C2×#388D8311yescharacteristic
513C2×C4×C22⋊C4—831no—
514C2×C4×C22⋊C4—831no—
515C2×#376—831no—
516#1437—831no—
517#1437—831no—
518#1436—831no—
519#1436—831no—
520C4⋊#95—831no—
521#1434—831no—
522C22⋊#95—831no—
523C4×#95—831no—
524C4×#95—831no—
525C4×#95—831no—
526C83#1381611yescharacteristic, complemented, Sylow
527C24×C4—831no—
528C22×C4⋊C4—831no—
529C22×C4⋊C4C2×D8311yescharacteristic
530C22×C22⋊C4—831no—
531C22×C22⋊C4—831no—
532C22×C22⋊C4—831no—
533C22×C22⋊C4C2×D8311yescharacteristic
534C22×C22⋊C4C2×D8311yescharacteristic
535C22×C22⋊C4C2×D8311yescharacteristic
536C22×C42—831no—
537C22×C42—831no—
538C22×C42—831no—
539C22×C42—831no—
540C22×C42—831no—
541C22×C42—831no—
542C22×C42—831no—
543C22×C42C2×D8311yescharacteristic
544#388—838no—
545#388Dic8318yescomplemented
546C4×C22⋊C4—838no—
547C4×C22⋊C4—1664no—
548#376—1664no—
549C2×#95—831no—
550C2×#95—831no—
551C2×#95—831no—
552C2×#95—831no—
553C2×#95—831no—
554C2×#95—831no—
555C2×#95—831no—
556C2×#95—831no—
557C2×#95—831no—
558C2×#95—831no—
559C2×#95—831no—
560C2×#95—831no—
561C2×#95—831no—
562C2×#95—831no—
563C2×#95—831no—
564C2×#95—831no—
565C2×#95C2×D8311yescharacteristic
566C2×#95C2×D8311yescharacteristic
567C25C22×D8311yescharacteristic
568C23×C4—3321no—
569C23×C4—3321no—
570C23×C4—834no—
571C23×C4—831no—
572C23×C4—831no—
573C23×C4—831no—
574C23×C4—831no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4—1662no—
580C23×C4—1662no—
581C23×C4—1662no—
582C23×C4—1662no—
583C23×C4C22×D8311yescharacteristic
584C23×C4C22×D8311yescharacteristic
585C23×C4C22×D8311yescharacteristic
586C23×C4C22×D8311yescharacteristic
587C23×C4C22×D8311yescharacteristic
588C23×C4C22×D8311yescharacteristic
589C2×C4⋊C4—41no—
590C2×C4⋊C4—41no—
591C2×C4⋊C4—3321no—
592C2×C4⋊C4—3321no—
593C2×C4⋊C4—834no—
594C2×C4⋊C4C2×Dic8314yescomplemented
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—3321no—
600C2×C22⋊C4—3321no—
601C2×C22⋊C4—834no—
602C2×C22⋊C4—834no—
603C2×C22⋊C4—834no—
604C2×C22⋊C4—1662no—
605C2×C22⋊C4—1662no—
606C2×C22⋊C4—1662no—
607C2×C22⋊C4—1662no—
608C2×C22⋊C4C4×D8314yes—
609C2×C22⋊C4C4×D8314yes—
610C2×C22⋊C4C2×Dic8314yes—
611C2×C22⋊C4C2×Dic8314yes—
612C2×C22⋊C4C2×Dic8314yes—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—3321no—
616C2×C42—3321no—
617C2×C42—3321no—
618C2×C42—3321no—
619C2×C42—3321no—
620C2×C42—3321no—
621C2×C42—834no—
622C2×C42—834no—
623C2×C42—834no—
624C2×C42—1662no—
625C2×C42—1662no—
626C2×C42—1662no—
627C2×C42—1662no—
628C2×C42—1662no—
629C2×C42—1662no—
630C2×C42—1662no—
631C2×C42—1662no—
632C2×C42—1662no—
633C2×C42—1662no—
634C2×C42—1662no—
635C2×C42—1662no—
636C2×C42C2×Dic8314yescomplemented
637#95—3321no—
638#95—3321no—
639#95—834no—
640#95—834no—
641#95—834no—
642#95—834no—
643#95—834no—
644#95—1662no—
645#95—1662no—
646#95—1662no—
647#95—1662no—
648#95—1662no—
649#95—1662no—
650#95—1662no—
651#95—1662no—
652#95—1662no—
653#95C2×Dic8314yescomplemented
654#95C2×Dic8314yescomplemented
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C2×C4×D8312yes—
668C24C2×C4×D8312yes—
669C24C22×Dic8312yes—
670C24C23×D8311yescharacteristic
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—3324no—
702C22×C4—3324no—
703C22×C4—3324no—
704C22×C4—3324no—
705C22×C4—3324no—
706C22×C4—832no—
707C22×C4—832no—
708C22×C4—832no—
709C22×C4—832no—
710C22×C4—832no—
711C22×C4—832no—
712C22×C4—832no—
713C22×C4—832no—
714C22×C4—832no—
715C22×C4—832no—
716C22×C4—832no—
717C22×C4—832no—
718C22×C4—832no—
719C22×C4—832no—
720C22×C4—832no—
721C22×C4—832no—
722C22×C4—1668no—
723C22×C4—1668no—
724C22×C4—1661no—
725C22×C4—1661no—
726C22×C4—1661no—
727C22×C4—1661no—
728C22×C4—1661no—
729C22×C4—1661no—
730C22×C4—1661no—
731C22×C4—1661no—
732C22×C4—1661no—
733C22×C4—1661no—
734C22×C4—1661no—
735C22×C4—1661no—
736C22×C4—1661no—
737C22×C4—1661no—
738C22×C4—1661no—
739C22×C4—1661no—
740C22×C4—1661no—
741C22×C4—1661no—
742C22×C4—1661no—
743C22×C4—1661no—
744C22×C4—1661no—
745C22×C4—1661no—
746C22×C4—1661no—
747C22×C4—1661no—
748C22×C4—1661no—
749C22×C4—1661no—
750C22×C4—1661no—
751C22×C4—1661no—
752C22×C4—1661no—
753C22×C4—1661no—
754C22×C4—1661no—
755C22×C4—1661no—
756C22×C4—1661no—
757C22×C4—1661no—
758C22×C4—1661no—
759C22×C4—1661no—
760C22×C4—1661no—
761C22×C4—1661no—
762C22×C4—1661no—
763C22×C4—1661no—
764C22×C4C2×C4×D8312yes—
765C22×C4C2×C4×D8312yes—
766C22×C4C2×C4×D8312yes—
767C22×C4C2×C4×D8312yes—
768C22×C4C22×Dic8312yes—
769C22×C4C22×Dic8312yes—
770C22×C4C22×Dic8312yes—
771C22×C4C22×Dic8312yes—
772C22×C4C22×Dic8312yes—
773C22×C4C22×Dic8312yes—
774C22×C4D4×D8312yes—
775C22×C4#1305058912yes—
776C4⋊C4—44no—
777C4⋊C4—3324no—
778C22⋊C4—28no—
779C22⋊C4—44no—
780C22⋊C4—3324no—
781C22⋊C4—1668no—
782C22⋊C4—1668no—
783C22⋊C4C4×Dic83116yescomplemented
784C42—28no—
785C42—3324no—
786C42—3324no—
787C42—3324no—
788C42—3324no—
789C42—3324no—
790C42—1668no—
791C42—1668no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C2×C4×Dic8314yes—
827C23C22×C4×D8311yescharacteristic
828C23C22×C4×D8311yescharacteristic
829C23C23×Dic8311yescharacteristic
830C23C2×D4×D8311yescharacteristic
831C23#41×D8311yescharacteristic
832C23#41×D8311yescharacteristic
833C23#41×D8311yescharacteristic
834C23#41×D8311yescharacteristic
835C23#41×D8311yescharacteristic
836C23#41×D8311yescharacteristic
837C23C2×#1305058911yescharacteristic
838C23#1458183711yescharacteristic
839C23#1458183711yescharacteristic
840C23#1458183811yescharacteristic
841C23#1458183911yescharacteristic
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—3321no—
882C2×C4—3321no—
883C2×C4—3321no—
884C2×C4—3321no—
885C2×C4—3321no—
886C2×C4—3321no—
887C2×C4—3321no—
888C2×C4—3321no—
889C2×C4—3321no—
890C2×C4—3321no—
891C2×C4—3321no—
892C2×C4—3321no—
893C2×C4—3321no—
894C2×C4—3321no—
895C2×C4—3321no—
896C2×C4—3321no—
897C2×C4—33216no—
898C2×C4—834no—
899C2×C4—834no—
900C2×C4—834no—
901C2×C4—834no—
902C2×C4—1662no—
903C2×C4—1662no—
904C2×C4—1662no—
905C2×C4—1662no—
906C2×C4—1662no—
907C2×C4—1662no—
908C2×C4—1662no—
909C2×C4—1662no—
910C2×C4—1662no—
911C2×C4—1662no—
912C2×C4—1662no—
913C2×C4—1662no—
914C2×C4—1662no—
915C2×C4—1662no—
916C2×C4—1662no—
917C2×C4—1662no—
918C2×C4—1662no—
919C2×C4—1662no—
920C2×C4—1662no—
921C2×C4—1662no—
922C2×C4—1662no—
923C2×C4—1662no—
924C2×C4—1662no—
925C2×C4—1662no—
926C2×C4—1662no—
927C2×C4—1662no—
928C2×C4—1662no—
929C2×C4—1662no—
930C2×C4—1662no—
931C2×C4—1662no—
932C2×C4—1662no—
933C2×C4—1662no—
934C2×C4—1662no—
935C2×C4—1662no—
936C2×C4—1662no—
937C2×C4—1662no—
938C2×C4C2×C4×Dic8314yes—
939C2×C4C2×C4×Dic8314yes—
940C2×C4D4×Dic8314yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C22×C4×Dic8311yescharacteristic
957C22#117×D8311yescharacteristic
958C22#117×D8311yescharacteristic
959C22C4×D4×D8311yescharacteristic
960C22C4×D4×D8311yescharacteristic
961C22C2×D4×Dic8311yescharacteristic
962C22C4×#1305058911yescharacteristic
963C22C4×#1305058911yescharacteristic
964C22#1912816911yescharacteristic
965C22#1912816911yescharacteristic
966C22#41×Dic8311yescharacteristic
967C22#41×Dic8311yescharacteristic
968C22#41×Dic8311yescharacteristic
969C22#1912817311yescharacteristic
970C22#1912817311yescharacteristic
971C22#1912817611yescharacteristic
972C22#1912818011yescharacteristic
973C22#1912818011yescharacteristic
974C22#1912818411yescharacteristic
975C22#1912834311yescharacteristic
976C22#1912834811yescharacteristic
977C22#1912834911yescharacteristic
978C22#1912836911yescharacteristic
979C22#1912837411yescharacteristic
980C22#1912837611yescharacteristic
981C22#1912838111yescharacteristic
982C22#1912838111yescharacteristic
983C22#1912838711yescharacteristic
984C22#1912838811yescharacteristic
985C22#1912839811yescharacteristic
986C22#1912840211yescharacteristic
987C22#1912841311yescharacteristic
988C22#1912841311yescharacteristic
989C22#1912841511yescharacteristic
990C22#1912841811yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—3322no—
998C4—3322no—
999C4—3322no—
1000C4—3322no—
1001C4—1664no—
1002C4—1664no—
1003C4—1664no—
1004C4—1664no—
1005C2—44no—
1006C2#117×Dic8311yescharacteristic
1007C2C4×D4×Dic8311yescharacteristic
1008C2#2490982411yescharacteristic
1009C2#2491030711yescharacteristic
1010C2#2491034511yescharacteristic
1011C2#2491039811yescharacteristic
1012C2#2491040911yescharacteristic
1013C2#2491045211yescharacteristic
1014C2#2491045911yescharacteristic
1015C2#2491049611yescharacteristic
1016C2#2491050511yescharacteristic
1017C2#2491057011yescharacteristic
1018C2#2491057511yescharacteristic
1019C2#2491058011yescharacteristic
1020C2#2491058711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC22×C83C22×C42
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#13816
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
4. C2×#19127547C2semidirect
7. #24905697C2semidirect
8. #24905695C2semidirect
9. #24905692C2semidirect
10. #24905688C2semidirect
12. C4×C83⋊#95C2semidirect
13. #95×Dic83C2semidirect
14. #95×Dic83C2semidirect
28. #19127594C4semidirect
30. C22⋊C4×Dic83C4semidirect
53. #388×C83C4semidirect
73. C2×C4⋊Dic83C2×C4semidirect
103. C2×C4×Dic83C2×C4semidirect
117. C83⋊#95C2×C4semidirect
118. C83⋊#95C2×C4semidirect
129. C2×C4⋊C4×C83C2×C4semidirect
141. C2×C42×C83C2×C4semidirect
142. #95×C83C2×C4semidirect
143. #95×C83C2×C4semidirect
279. C22⋊C4×C83C42semidirect
526. C83#13816semidirect
545. #388Dic83semidirect
594. C2×C4⋊C4C2×Dic83semidirect
636. C2×C42C2×Dic83semidirect
653. #95C2×Dic83semidirect
654. #95C2×Dic83semidirect
783. C22⋊C4C4×Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275942
C2×C22⋊C4×Dic832
C2×#191275472
#249057002
#249056972
#249056952
#249056922
#249056882
#249056852
C4×C83⋊#952
#95×Dic832
C2×#388×C832
#1381683