Finite Group Databasebeta

← #35328544

Subgroups — #35328544

Order 21248.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127587C211yesmaximal, characteristic, complemented
2C2×C4×C22⋊Dic83C211yesmaximal, characteristic
3#24905725C211yesmaximal, characteristic, complemented
4#24905716C211yesmaximal, characteristic, complemented
5#24905708C211yesmaximal, characteristic
6#24905708C211yesmaximal, characteristic
7#24905700C211yesmaximal, characteristic
8#24905700C211yesmaximal, characteristic
9#24905697C211yesmaximal, characteristic, complemented
10#24905695C211yesmaximal, characteristic, complemented
11#24905692C211yesmaximal, characteristic, complemented
12#24905688C211yesmaximal, characteristic, complemented
13#24905686C211yesmaximal, characteristic
14#95×Dic83C211yesmaximal, characteristic, complemented
15C2×#385×C83C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C22⋊Dic83C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127587—24no—
27C4×C22⋊Dic83—24no—
28C2×C83⋊#95C2211yescharacteristic
29C2×C83⋊#95C2211yescharacteristic
30C2×C83⋊#95C2211yescharacteristic
31C2×C83⋊#95C2211yescharacteristic
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
46C24×C4×C83C2211yescharacteristic
47C22×C4⋊C4×C83C2211yescharacteristic
48C22×C4⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C22⋊C4×C83C2211yescharacteristic
51#385×C83C418yescomplemented
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C2×C4⋊Dic83—22no—
63C2×C4⋊Dic83—22no—
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—41no—
66C2×C4⋊Dic83—41no—
67C2×C4⋊Dic83—41no—
68C2×C22⋊Dic83—22no—
69C2×C22⋊Dic83—22no—
70C2×C22⋊Dic83—22no—
71C2×C22⋊Dic83—22no—
72C2×C22⋊Dic83—22no—
73C2×C22⋊Dic83—22no—
74C2×C22⋊Dic83—22no—
75C2×C22⋊Dic83—22no—
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—41no—
78C2×C22⋊Dic83—41no—
79C2×C22⋊Dic83Q814yes—
80C2×C4×Dic83—22no—
81C2×C4×Dic83—22no—
82C2×C4×Dic83—22no—
83C2×C4×Dic83—22no—
84C2×C4×Dic83—22no—
85C2×C4×Dic83—41no—
86C2×C4×Dic83—41no—
87C2×C4×Dic83—41no—
88C2×C4×Dic83—41no—
89C2×C4×Dic83—41no—
90C2×C4×Dic83—41no—
91C2×C4×Dic83D414yes—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
97C83⋊#95—22no—
98C83⋊#95—22no—
99C83⋊#95—22no—
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—22no—
104C83⋊#95—22no—
105C83⋊#95—41no—
106C83⋊#95—41no—
107C83⋊#95—41no—
108C83⋊#95—41no—
109C83⋊#95—41no—
110C25×C83C2311yescharacteristic
111C23×C4×C83—22no—
112C23×C4×C83—22no—
113C23×C4×C83—41no—
114C23×C4×C83—41no—
115C23×C4×C83—41no—
116C23×C4×C83—41no—
117C23×C4×C83C2×C414yes—
118C23×C4×C83C2311yescharacteristic
119C23×C4×C83C2311yescharacteristic
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C2×C4⋊C4×C83—22no—
125C2×C4⋊C4×C83—22no—
126C2×C4⋊C4×C83—41no—
127C2×C4⋊C4×C83—41no—
128C2×C4⋊C4×C83C2×C414yes—
129C2×C4⋊C4×C83C2×C414yes—
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—
136#95×C83C2×C414yes—
137#95×C83C2×C414yes—
138C22×Dic83—21no—
139C22×Dic83—21no—
140C22×Dic83—21no—
141C22×Dic83—21no—
142C22×Dic83—21no—
143C22×Dic83—21no—
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—21no—
185C22×Dic83—21no—
186C22×Dic83C2×D412yes—
187C22×Dic83C2×D412yes—
188C22×Dic83C2×Q812yes—
189C22×Dic83C2×Q812yes—
190C22×Dic83#4112yes—
191C22×Dic83#4112yes—
192C22×Dic83#4112yes—
193C22×Dic83#4112yes—
194C4⋊Dic83—44no—
195C4⋊Dic83—44no—
196C22⋊Dic83—28no—
197C22⋊Dic83—28no—
198C22⋊Dic83—44no—
199C22⋊Dic83—44no—
200C4×Dic83—44no—
201C4×Dic83—44no—
202C4×Dic83—44no—
203C4×Dic83—44no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83C22×C412yes—
217C24×C83C2×Q812yes—
218C24×C83#4112yes—
219C24×C83C2411yescharacteristic
220C22×C4×C83—21no—
221C22×C4×C83—21no—
222C22×C4×C83—21no—
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×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—28no—
253C22×C4×C83—44no—
254C22×C4×C83—44no—
255C22×C4×C83—44no—
256C22×C4×C83—44no—
257C22×C4×C83—44no—
258C22×C4×C83—44no—
259C22×C4×C83C22×C412yes—
260C22×C4×C83C22×C412yes—
261C22×C4×C83C22×C412yes—
262C22×C4×C83C22×C412yes—
263C22×C4×C83C22×C412yes—
264C22×C4×C83C22×C412yes—
265C22×C4×C83C2×D412yes—
266C22×C4×C83#4112yes—
267C22×C4×C83#4112yes—
268C22×C4×C83#4112yes—
269C4⋊C4×C83—28no—
270C4⋊C4×C83—44no—
271C22⋊C4×C83—28no—
272C22⋊C4×C83—44no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
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—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
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×C83C4×Q814yes—
308C23×C83C23×C411yescharacteristic
309C23×C83C22×D411yescharacteristic
310C23×C83C22×Q811yescharacteristic
311C23×C83C2×#4111yescharacteristic
312C23×C83C2×#4111yescharacteristic
313C23×C83C2×#4111yescharacteristic
314C23×C83C2×#4111yescharacteristic
315C23×C83C2×#4111yescharacteristic
316C23×C83C2×#4111yescharacteristic
317C23×C83C2×#4111yescharacteristic
318C23×C83C2×#4111yescharacteristic
319C23×C83H(5,𝔽2)11yescharacteristic
320C23×C83H(5,𝔽2)11yescharacteristic
321C23×C83H(5,𝔽2)11yescharacteristic
322C23×C83H(5,𝔽2)11yescharacteristic
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
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—416no—
348C2×C4×C83—41no—
349C2×C4×C83—41no—
350C2×C4×C83—41no—
351C2×C4×C83—41no—
352C2×C4×C83—41no—
353C2×C4×C83—41no—
354C2×C4×C83—41no—
355C2×C4×C83—41no—
356C2×C4×C83—41no—
357C2×C4×C83—41no—
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#11714yes—
365C2×C4×C83C4×D414yes—
366C2×Dic83—22no—
367C2×Dic83—22no—
368C2×Dic83—22no—
369C2×Dic83—22no—
370C2×Dic83—22no—
371C2×Dic83—22no—
372C2×Dic83—22no—
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—41no—
388C2×Dic83—41no—
389C2×Dic83—41no—
390C2×Dic83—41no—
391C2×Dic83—41no—
392C2×Dic83—41no—
393C2×Dic83—41no—
394C2×Dic83—41no—
395C2×Dic83—41no—
396C2×Dic83—41no—
397C2×Dic83—41no—
398C2×Dic83—41no—
399C2×Dic83—41no—
400C2×Dic83—41no—
401C2×Dic83—41no—
402C2×Dic83—41no—
403C2×Dic83—41no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407C2×Dic83—41no—
408C2×Dic83—41no—
409C2×Dic83—41no—
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×Dic83C22⋊Q814yes—
422C22×C83—24no—
423C22×C83—24no—
424C22×C83—24no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—42no—
430C22×C83—42no—
431C22×C83—42no—
432C22×C83—42no—
433C22×C83—42no—
434C22×C83—42no—
435C22×C83—42no—
436C22×C83—42no—
437C22×C83C2×#11711yescharacteristic
438C22×C83C2×C4×D411yescharacteristic
439C22×C83C2×C4×Q811yescharacteristic
440C22×C83C4×#4111yescharacteristic
441C22×C83C4×#4111yescharacteristic
442C22×C83#51811yescharacteristic
443C22×C83#51811yescharacteristic
444C22×C83C2×C22⋊Q811yescharacteristic
445C22×C83#52511yescharacteristic
446C22×C83#52911yescharacteristic
447C22×C83#52911yescharacteristic
448C22×C83#52911yescharacteristic
449C22×C83#53211yescharacteristic
450C22×C83#53211yescharacteristic
451C22×C83#53311yescharacteristic
452C22×C83#53411yescharacteristic
453C22×C83#53511yescharacteristic
454C22×C83#53811yescharacteristic
455C22×C83#53811yescharacteristic
456C22×C83#55111yescharacteristic
457C22×C83#55111yescharacteristic
458C22×C83#55111yescharacteristic
459C22×C83#55111yescharacteristic
460C22×C83#55111yescharacteristic
461C22×C83#55311yescharacteristic
462C22×C83#55311yescharacteristic
463C22×C83#55311yescharacteristic
464C22×C83#55311yescharacteristic
465C22×C83#55311yescharacteristic
466C22×C83#55311yescharacteristic
467C22×C83#55411yescharacteristic
468C22×C83#55411yescharacteristic
469C22×C83#55411yescharacteristic
470C22×C83#55411yescharacteristic
471C22×C83#55911yescharacteristic
472C4×C83—24no—
473C4×C83—24no—
474C4×C83—42no—
475C4×C83—42no—
476C4×C83—42no—
477C4×C83—42no—
478Dic83—24no—
479Dic83—42no—
480Dic83—42no—
481Dic83—42no—
482Dic83—42no—
483Dic83—42no—
484Dic83—81no—
485Dic83—81no—
486#14075—831nomaximal, Sylow
487C2×C83—44no—
488C2×C83#229311yescharacteristic
489C2×C83C4×C22⋊Q811yescharacteristic
490C2×C83#232111yescharacteristic
491C2×C83#234511yescharacteristic
492C2×C83#235311yescharacteristic
493C2×C83#236811yescharacteristic
494C2×C83#237411yescharacteristic
495C2×C83#256411yescharacteristic
496C2×C83#256611yescharacteristic
497C2×C83#257611yescharacteristic
498C2×C83#257811yescharacteristic
499C2×C83#258711yescharacteristic
500C2×C83#258911yescharacteristic
501C2×C83#260211yescharacteristic
502C2×C83#260311yescharacteristic
503C2×#387—831no—
504C2×#385D8311yescharacteristic
505C2×C4×C22⋊C4—831no—
506#1443—831no—
507#1441—831no—
508#1439—831no—
509#1439—831no—
510#1437—831no—
511#1437—831no—
512#1436—831no—
513#1436—831no—
514C4⋊#95—831no—
515#1434—831no—
516C22⋊#95—831no—
517C4×#95—831no—
518C83#1407511yescharacteristic, complemented, Sylow
519C24×C4C2×D8311yescharacteristic
520C22×C4⋊C4—831no—
521C22×C4⋊C4—831no—
522C22×C4⋊C4C2×D8311yescharacteristic
523C22×C4⋊C4C2×D8311yescharacteristic
524C22×C22⋊C4—831no—
525C22×C22⋊C4—831no—
526C22×C22⋊C4—831no—
527C22×C22⋊C4—831no—
528C22×C22⋊C4C2×D8311yescharacteristic
529C22×C22⋊C4C2×D8311yescharacteristic
530C22×C42—831no—
531C22×C42—831no—
532C22×C42—831no—
533C22×C42—831no—
534#387—1664no—
535#385Dic8318yescomplemented
536C4×C22⋊C4—1664no—
537C2×#95—831no—
538C2×#95—831no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95—831no—
544C2×#95—831no—
545C2×#95—831no—
546C2×#95—831no—
547C2×#95—831no—
548C2×#95—831no—
549C2×#95—831no—
550C2×#95—831no—
551C2×#95—831no—
552C2×#95—831no—
553C2×#95—831no—
554C2×#95—831no—
555C2×#95C2×D8311yescharacteristic
556C2×#95C2×D8311yescharacteristic
557C25C22×D8311yescharacteristic
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4—831no—
565C23×C4—831no—
566C23×C4—831no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—831no—
570C23×C4—831no—
571C23×C4—831no—
572C23×C4C2×Dic8314yes—
573C23×C4C22×D8311yescharacteristic
574C23×C4C22×D8311yescharacteristic
575C23×C4C22×D8311yescharacteristic
576C23×C4C22×D8311yescharacteristic
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—3321no—
584C2×C4⋊C4—3321no—
585C2×C4⋊C4—3321no—
586C2×C4⋊C4—1662no—
587C2×C4⋊C4—1662no—
588C2×C4⋊C4—1662no—
589C2×C4⋊C4C2×Dic8314yes—
590C2×C4⋊C4C2×Dic8314yes—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—3321no—
596C2×C22⋊C4—3321no—
597C2×C22⋊C4—834no—
598C2×C22⋊C4—1662no—
599C2×C22⋊C4—1662no—
600C2×C22⋊C4—1662no—
601C2×C22⋊C4—1662no—
602C2×C22⋊C4—1662no—
603C2×C22⋊C4—1662no—
604C2×C22⋊C4—1662no—
605C2×C22⋊C4—1662no—
606C2×C22⋊C4—1662no—
607C2×C22⋊C4C2×Dic8314yes—
608C2×C22⋊C4C2×Dic8314yes—
609C2×C42—3321no—
610C2×C42—3321no—
611C2×C42—3321no—
612C2×C42—3321no—
613C2×C42—3321no—
614C2×C42—3321no—
615C2×C42—834no—
616C2×C42—1662no—
617C2×C42—1662no—
618C2×C42—1662no—
619C2×C42—1662no—
620C2×C42—1662no—
621#95—3321no—
622#95—3321no—
623#95—3321no—
624#95—3321no—
625#95—3321no—
626#95—1662no—
627#95—1662no—
628#95—1662no—
629#95—1662no—
630#95—1662no—
631#95—1662no—
632#95—1662no—
633#95—1662no—
634#95—1662no—
635#95—1662no—
636#95—1662no—
637#95—1662no—
638#95—1662no—
639#95C2×Dic8314yes—
640#95C2×Dic8314yes—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24C22×Dic8312yes—
654C24Q8×D8312yes—
655C24#1305059112yes—
656C24C23×D8311yescharacteristic
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
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—28no—
690C22×C4—44no—
691C22×C4—44no—
692C22×C4—44no—
693C22×C4—44no—
694C22×C4—44no—
695C22×C4—44no—
696C22×C4—832no—
697C22×C4—832no—
698C22×C4—832no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—832no—
703C22×C4—832no—
704C22×C4—1661no—
705C22×C4—1661no—
706C22×C4—1661no—
707C22×C4—1661no—
708C22×C4—1661no—
709C22×C4—1661no—
710C22×C4—1661no—
711C22×C4—1661no—
712C22×C4—1661no—
713C22×C4—1661no—
714C22×C4—1661no—
715C22×C4—1661no—
716C22×C4—1661no—
717C22×C4—1661no—
718C22×C4—1661no—
719C22×C4—1661no—
720C22×C4—1661no—
721C22×C4—1661no—
722C22×C4—1661no—
723C22×C4—1661no—
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×C4C22×Dic8312yes—
753C22×C4C22×Dic8312yes—
754C22×C4C22×Dic8312yes—
755C22×C4C22×Dic8312yes—
756C22×C4C22×Dic8312yes—
757C22×C4C22×Dic8312yes—
758C22×C4D4×D8312yes—
759C22×C4#1305058912yes—
760C22×C4#1305059012yes—
761C22×C4#1305059012yes—
762C4⋊C4—28no—
763C4⋊C4—44no—
764C4⋊C4—3324no—
765C4⋊C4—3324no—
766C22⋊C4—28no—
767C22⋊C4—44no—
768C22⋊C4—3324no—
769C22⋊C4—3324no—
770C22⋊C4—1668no—
771C22⋊C4—1668no—
772C42—3324no—
773C42—3324no—
774C42—3324no—
775C42—3324no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23Q8×Dic8314yes—
811C23C23×Dic8311yescharacteristic
812C23C2×D4×D8311yescharacteristic
813C23C2×Q8×D8311yescharacteristic
814C23#41×D8311yescharacteristic
815C23#41×D8311yescharacteristic
816C23#41×D8311yescharacteristic
817C23#41×D8311yescharacteristic
818C23C2×#1305058911yescharacteristic
819C23C2×#1305059011yescharacteristic
820C23C2×#1305059011yescharacteristic
821C23C2×#1305059111yescharacteristic
822C23#1458183711yescharacteristic
823C23#1458183711yescharacteristic
824C23#1458183711yescharacteristic
825C23#1458183711yescharacteristic
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
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—416no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—3321no—
868C2×C4—3321no—
869C2×C4—3321no—
870C2×C4—3321no—
871C2×C4—3321no—
872C2×C4—3321no—
873C2×C4—3321no—
874C2×C4—3321no—
875C2×C4—3321no—
876C2×C4—3321no—
877C2×C4—3321no—
878C2×C4—3321no—
879C2×C4—3321no—
880C2×C4—3321no—
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—3321no—
898C2×C4—3321no—
899C2×C4—3321no—
900C2×C4—3321no—
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#1458175114yes—
924C2×C4D4×Dic8314yes—
925C22—24no—
926C22—24no—
927C22—24no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22C2×#1458175111yescharacteristic
941C22C2×D4×Dic8311yescharacteristic
942C22C2×Q8×Dic8311yescharacteristic
943C22#41×Dic8311yescharacteristic
944C22#41×Dic8311yescharacteristic
945C22#1912817611yescharacteristic
946C22#1912817611yescharacteristic
947C22C22⋊Q8×D8311yescharacteristic
948C22#1912821411yescharacteristic
949C22#1912823311yescharacteristic
950C22#1912823311yescharacteristic
951C22#1912823711yescharacteristic
952C22#1912824811yescharacteristic
953C22#1912824811yescharacteristic
954C22#1912825311yescharacteristic
955C22#1912826111yescharacteristic
956C22#1912826611yescharacteristic
957C22#1912828611yescharacteristic
958C22#1912828611yescharacteristic
959C22#1912837811yescharacteristic
960C22#1912837811yescharacteristic
961C22#1912837911yescharacteristic
962C22#1912838011yescharacteristic
963C22#1912838011yescharacteristic
964C22#1912839611yescharacteristic
965C22#1912839611yescharacteristic
966C22#1912839911yescharacteristic
967C22#1912839911yescharacteristic
968C22#1912840011yescharacteristic
969C22#1912840011yescharacteristic
970C22#1912840511yescharacteristic
971C22#1912840511yescharacteristic
972C22#1912840611yescharacteristic
973C22#1912840611yescharacteristic
974C22#1912843511yescharacteristic
975C4—24no—
976C4—24no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—3322no—
982C4—3322no—
983C4—3322no—
984C4—3322no—
985C4—3322no—
986C4—6641no—
987C4—6641no—
988C4—1664no—
989C2—44no—
990C2#2490992811yescharacteristic
991C2C22⋊Q8×Dic8311yescharacteristic
992C2#2491012411yescharacteristic
993C2#2491034011yescharacteristic
994C2#2491040311yescharacteristic
995C2#2491054811yescharacteristic
996C2#2491059911yescharacteristic
997C2#2491264811yescharacteristic
998C2#2491266111yescharacteristic
999C2#2491276611yescharacteristic
1000C2#2491279611yescharacteristic
1001C2#2491288311yescharacteristic
1002C2#2491291311yescharacteristic
1003C2#2491307911yescharacteristic
1004C2#2491308911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#385×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83#14075
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#19127587C2semidirect
3. #24905725C2semidirect
4. #24905716C2semidirect
9. #24905697C2semidirect
10. #24905695C2semidirect
11. #24905692C2semidirect
12. #24905688C2semidirect
14. #95×Dic83C2semidirect
51. #385×C83C4semidirect
518. C83#14075semidirect
535. #385Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275872
C2×C4×C22⋊Dic832
#249057252
#249057162
#249057082
#249057002
#249056972
#249056952
#249056922
#249056882
#249056862
#95×Dic832
C2×#385×C832
#1407583