Finite Group Databasebeta

← #35327416

Subgroups — #35327416

Order 21248.

1746 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×#19127587C211yesmaximal, characteristic, complemented
2C2×#19127561C211yesmaximal, characteristic
3C2×C4⋊C4×Dic83C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊Dic83C211yesmaximal, characteristic
5#24905728C211yesmaximal, characteristic, complemented
6#24905716C211yesmaximal, characteristic, complemented
7#24905708C211yesmaximal, characteristic
8#24905708C211yesmaximal, characteristic
9#24905700C211yesmaximal, characteristic
10#24905700C211yesmaximal, characteristic
11#24905697C211yesmaximal, characteristic, complemented
12#24905697C211yesmaximal, characteristic, complemented
13#24905695C211yesmaximal, characteristic, complemented
14#24905688C211yesmaximal, characteristic, complemented
15C2×#385×C83C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C4×Dic83C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26C22×C4×Dic83C2211yescharacteristic
27C22×C4×Dic83C2211yescharacteristic
28#19127587—24no—
29#19127561—24no—
30C4⋊C4×Dic83—24no—
31C4×C22⋊Dic83—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
48C24×C4×C83C2211yescharacteristic
49C22×C4⋊C4×C83C2211yescharacteristic
50C22×C4⋊C4×C83C2211yescharacteristic
51C22×C22⋊C4×C83C2211yescharacteristic
52C22×C22⋊C4×C83C2211yescharacteristic
53#385×C83C418yescomplemented
54C2×#95×C83C2211yescharacteristic
55C2×#95×C83C2211yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C2×C4⋊Dic83—22no—
65C2×C4⋊Dic83—22no—
66C2×C4⋊Dic83—22no—
67C2×C4⋊Dic83—22no—
68C2×C4⋊Dic83—22no—
69C2×C4⋊Dic83—22no—
70C2×C4⋊Dic83—22no—
71C2×C4⋊Dic83—22no—
72C2×C4⋊Dic83—41no—
73C2×C4⋊Dic83—41no—
74C2×C4⋊Dic83—41no—
75C2×C4⋊Dic83—41no—
76C2×C22⋊Dic83—22no—
77C2×C22⋊Dic83—22no—
78C2×C22⋊Dic83—22no—
79C2×C22⋊Dic83—22no—
80C2×C22⋊Dic83—22no—
81C2×C22⋊Dic83—22no—
82C2×C22⋊Dic83—22no—
83C2×C22⋊Dic83—22no—
84C2×C22⋊Dic83—22no—
85C2×C22⋊Dic83—41no—
86C2×C22⋊Dic83—41no—
87C2×C22⋊Dic83Q814yes—
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—22no—
96C2×C4×Dic83—22no—
97C2×C4×Dic83—41no—
98C2×C4×Dic83—41no—
99C2×C4×Dic83—41no—
100C83⋊#95—22no—
101C83⋊#95—22no—
102C83⋊#95—22no—
103C83⋊#95—22no—
104C83⋊#95—22no—
105C83⋊#95—22no—
106C83⋊#95—22no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C83⋊#95—41no—
110C83⋊#95—41no—
111C83⋊#95—41no—
112C83⋊#95—41no—
113C83⋊#95—41no—
114C83⋊#95D414yes—
115C83⋊#95D414yes—
116C25×C83C2311yescharacteristic
117C23×C4×C83—22no—
118C23×C4×C83—22no—
119C23×C4×C83—22no—
120C23×C4×C83—22no—
121C23×C4×C83—41no—
122C23×C4×C83—41no—
123C23×C4×C83C2×C414yes—
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83—22no—
131C2×C4⋊C4×C83—22no—
132C2×C4⋊C4×C83—22no—
133C2×C4⋊C4×C83—22no—
134C2×C4⋊C4×C83C2×C414yes—
135C2×C4⋊C4×C83C2×C414yes—
136C2×C22⋊C4×C83—22no—
137C2×C22⋊C4×C83—22no—
138C2×C22⋊C4×C83—41no—
139C2×C22⋊C4×C83—41no—
140C2×C22⋊C4×C83C2×C414yes—
141C2×C22⋊C4×C83C2×C414yes—
142#95×C83C2×C414yes—
143#95×C83C2×C414yes—
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×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—21no—
189C22×Dic83—21no—
190C22×Dic83—21no—
191C22×Dic83—21no—
192C22×Dic83C2×D412yes—
193C22×Dic83C2×D412yes—
194C22×Dic83C2×D412yes—
195C22×Dic83C2×D412yes—
196C22×Dic83C2×Q812yes—
197C22×Dic83C2×Q812yes—
198C22×Dic83#4112yes—
199C22×Dic83#4112yes—
200C4⋊Dic83—28no—
201C4⋊Dic83—44no—
202C4⋊Dic83—44no—
203C4⋊Dic83—44no—
204C22⋊Dic83—28no—
205C22⋊Dic83—28no—
206C22⋊Dic83—44no—
207C22⋊Dic83—44no—
208C4×Dic83—28no—
209C4×Dic83—44no—
210C4×Dic83—44no—
211C4×Dic83—44no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83—21no—
217C24×C83—21no—
218C24×C83—21no—
219C24×C83—21no—
220C24×C83—21no—
221C24×C83—21no—
222C24×C83—21no—
223C24×C83—21no—
224C24×C83C22×C412yes—
225C24×C83C2×Q812yes—
226C24×C83#4112yes—
227C24×C83C2411yescharacteristic
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—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—28no—
259C22×C4×C83—28no—
260C22×C4×C83—44no—
261C22×C4×C83—44no—
262C22×C4×C83—44no—
263C22×C4×C83—44no—
264C22×C4×C83—44no—
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×C83C2×D412yes—
272C22×C4×C83C2×D412yes—
273C22×C4×C83#4112yes—
274C22×C4×C83#4112yes—
275C22×C4×C83#4112yes—
276C22×C4×C83#4112yes—
277C4⋊C4×C83—28no—
278C4⋊C4×C83—28no—
279C22⋊C4×C83—28no—
280C22⋊C4×C83—44no—
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×C83C4×Q814yes—
316C23×C83C23×C411yescharacteristic
317C23×C83C22×D411yescharacteristic
318C23×C83C22×D411yescharacteristic
319C23×C83C22×Q811yescharacteristic
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—416no—
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×C83—41no—
371C2×C4×C83#11714yes—
372C2×C4×C83C4×D414yes—
373C2×C4×C83C4×D414yes—
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—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×Dic83—41no—
422C2×Dic83—41no—
423C2×Dic83—41no—
424C2×Dic83—41no—
425C2×Dic83—41no—
426C2×Dic83—41no—
427C2×Dic83—41no—
428C2×Dic83—41no—
429C2×Dic83C22⋊Q814yes—
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×C83C2×#11711yescharacteristic
446C22×C83C2×C4×D411yescharacteristic
447C22×C83C2×C4×D411yescharacteristic
448C22×C83C2×C4×Q811yescharacteristic
449C22×C83C4×#4111yescharacteristic
450C22×C83#51811yescharacteristic
451C22×C83#52011yescharacteristic
452C22×C83C2×C22⋊Q811yescharacteristic
453C22×C83#52511yescharacteristic
454C22×C83#52511yescharacteristic
455C22×C83#52511yescharacteristic
456C22×C83#52911yescharacteristic
457C22×C83#52911yescharacteristic
458C22×C83#52911yescharacteristic
459C22×C83#53311yescharacteristic
460C22×C83#53811yescharacteristic
461C22×C83#53911yescharacteristic
462C22×C83#54011yescharacteristic
463C22×C83#54211yescharacteristic
464C22×C83D4211yescharacteristic
465C22×C83#54611yescharacteristic
466C22×C83#54611yescharacteristic
467C22×C83#54611yescharacteristic
468C22×C83#54711yescharacteristic
469C22×C83D4×Q811yescharacteristic
470C22×C83#55011yescharacteristic
471C22×C83#55111yescharacteristic
472C22×C83#55211yescharacteristic
473C22×C83#55311yescharacteristic
474C22×C83#55311yescharacteristic
475C22×C83#55411yescharacteristic
476C22×C83#55411yescharacteristic
477C22×C83#55411yescharacteristic
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—42no—
488Dic83—42no—
489Dic83—42no—
490Dic83—42no—
491Dic83—42no—
492Dic83—81no—
493Dic83—81no—
494#13987—831nomaximal, Sylow
495C2×C83—44no—
496C2×C83#229011yescharacteristic
497C2×C83C4×C22⋊Q811yescharacteristic
498C2×C83#233511yescharacteristic
499C2×C83#234511yescharacteristic
500C2×C83#235411yescharacteristic
501C2×C83#235811yescharacteristic
502C2×C83#236011yescharacteristic
503C2×C83#244911yescharacteristic
504C2×C83#245411yescharacteristic
505C2×C83#245611yescharacteristic
506C2×C83#246511yescharacteristic
507C2×C83#246811yescharacteristic
508C2×C83#247611yescharacteristic
509C2×C83#257411yescharacteristic
510C2×C83#257711yescharacteristic
511C2×#387—831no—
512C2×#385D8311yescharacteristic
513C2×#380—831no—
514C2×C4×C4⋊C4—831no—
515C2×C4×C22⋊C4—831no—
516#1444—831no—
517#1441—831no—
518#1439—831no—
519#1439—831no—
520#1437—831no—
521#1437—831no—
522#1436—831no—
523#1436—831no—
524#1436—831no—
525#1434—831no—
526C83#1398711yescharacteristic, complemented, Sylow
527C24×C4C2×D8311yescharacteristic
528C22×C4⋊C4—831no—
529C22×C4⋊C4—831no—
530C22×C4⋊C4—831no—
531C22×C4⋊C4—831no—
532C22×C4⋊C4C2×D8311yescharacteristic
533C22×C4⋊C4C2×D8311yescharacteristic
534C22×C22⋊C4—831no—
535C22×C22⋊C4—831no—
536C22×C22⋊C4—831no—
537C22×C22⋊C4—831no—
538C22×C22⋊C4C2×D8311yescharacteristic
539C22×C22⋊C4C2×D8311yescharacteristic
540C22×C42—831no—
541C22×C42—831no—
542C22×C42—831no—
543C22×C42—831no—
544#387—1664no—
545#385Dic8318yescomplemented
546#380—1664no—
547C4×C4⋊C4—1664no—
548C4×C22⋊C4—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—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4—831no—
575C23×C4—831no—
576C23×C4—831no—
577C23×C4—831no—
578C23×C4—831no—
579C23×C4—831no—
580C23×C4—831no—
581C23×C4—831no—
582C23×C4C2×Dic8314yes—
583C23×C4C22×D8311yescharacteristic
584C23×C4C22×D8311yescharacteristic
585C23×C4C22×D8311yescharacteristic
586C23×C4C22×D8311yescharacteristic
587C23×C4C22×D8311yescharacteristic
588C23×C4C22×D8311yescharacteristic
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—3321no—
594C2×C4⋊C4—3321no—
595C2×C4⋊C4—3321no—
596C2×C4⋊C4—3321no—
597C2×C4⋊C4—1662no—
598C2×C4⋊C4—1662no—
599C2×C4⋊C4—1662no—
600C2×C4⋊C4—1662no—
601C2×C4⋊C4—1662no—
602C2×C4⋊C4—1662no—
603C2×C4⋊C4—1662no—
604C2×C4⋊C4—1662no—
605C2×C4⋊C4C2×Dic8314yes—
606C2×C4⋊C4C2×Dic8314yes—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4—3321no—
612C2×C22⋊C4—3321no—
613C2×C22⋊C4—834no—
614C2×C22⋊C4—1662no—
615C2×C22⋊C4—1662no—
616C2×C22⋊C4—1662no—
617C2×C22⋊C4—1662no—
618C2×C22⋊C4—1662no—
619C2×C22⋊C4—1662no—
620C2×C22⋊C4—1662no—
621C2×C22⋊C4—1662no—
622C2×C22⋊C4—1662no—
623C2×C22⋊C4C2×Dic8314yes—
624C2×C22⋊C4C2×Dic8314yes—
625C2×C42—3321no—
626C2×C42—3321no—
627C2×C42—3321no—
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×C42—1662no—
637#95—3321no—
638#95—3321no—
639#95—3321no—
640#95—3321no—
641#95—3321no—
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×Dic8314yes—
654#95C2×Dic8314yes—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24C22×Dic8312yes—
668C24Q8×D8312yes—
669C24#1305059112yes—
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—28no—
702C22×C4—28no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—44no—
707C22×C4—44no—
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—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×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×C4C22×Dic8312yes—
765C22×C4C22×Dic8312yes—
766C22×C4C22×Dic8312yes—
767C22×C4C22×Dic8312yes—
768C22×C4C22×Dic8312yes—
769C22×C4C22×Dic8312yes—
770C22×C4D4×D8312yes—
771C22×C4D4×D8312yes—
772C22×C4#1305058912yes—
773C22×C4#1305058912yes—
774C22×C4#1305059012yes—
775C22×C4#1305059012yes—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—3324no—
779C4⋊C4—3324no—
780C4⋊C4—3324no—
781C4⋊C4—1668no—
782C22⋊C4—28no—
783C22⋊C4—44no—
784C22⋊C4—3324no—
785C22⋊C4—3324no—
786C22⋊C4—1668no—
787C22⋊C4—1668no—
788C42—3324no—
789C42—3324no—
790C42—3324no—
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—
826C23Q8×Dic8314yes—
827C23C23×Dic8311yescharacteristic
828C23C2×D4×D8311yescharacteristic
829C23C2×D4×D8311yescharacteristic
830C23C2×Q8×D8311yescharacteristic
831C23#41×D8311yescharacteristic
832C23#41×D8311yescharacteristic
833C23C2×#1305058911yescharacteristic
834C23C2×#1305058911yescharacteristic
835C23C2×#1305059011yescharacteristic
836C23C2×#1305059011yescharacteristic
837C23C2×#1305059111yescharacteristic
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—416no—
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—41no—
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—3321no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
905C2×C4—3321no—
906C2×C4—3321no—
907C2×C4—3321no—
908C2×C4—3321no—
909C2×C4—3321no—
910C2×C4—3321no—
911C2×C4—3321no—
912C2×C4—3321no—
913C2×C4—3321no—
914C2×C4—3321no—
915C2×C4—3321no—
916C2×C4—834no—
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×C4#1458175114yes—
939C2×C4D4×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—
956C22C2×#1458175111yescharacteristic
957C22C2×D4×Dic8311yescharacteristic
958C22C2×D4×Dic8311yescharacteristic
959C22C2×Q8×Dic8311yescharacteristic
960C22#41×Dic8311yescharacteristic
961C22#1912817611yescharacteristic
962C22#1912818411yescharacteristic
963C22C22⋊Q8×D8311yescharacteristic
964C22#1912821011yescharacteristic
965C22#1912821011yescharacteristic
966C22#1912821411yescharacteristic
967C22#1912823111yescharacteristic
968C22#1912823111yescharacteristic
969C22#1912823711yescharacteristic
970C22#1912825311yescharacteristic
971C22#1912828711yescharacteristic
972C22#1912829411yescharacteristic
973C22#1912830311yescharacteristic
974C22#1912831911yescharacteristic
975C22#1912833311yescharacteristic
976C22#1912833811yescharacteristic
977C22#1912833811yescharacteristic
978C22#1912834211yescharacteristic
979C22#1912835611yescharacteristic
980C22#1912836411yescharacteristic
981C22#1912837211yescharacteristic
982C22#1912838211yescharacteristic
983C22#1912839311yescharacteristic
984C22#1912839911yescharacteristic
985C22#1912839911yescharacteristic
986C22#1912840611yescharacteristic
987C22#1912840611yescharacteristic
988C22#1912840911yescharacteristic
989C22#1912841611yescharacteristic
990C22#1912842111yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—3322no—
998C4—3322no—
999C4—3322no—
1000C4—3322no—
1001C4—3322no—
1002C4—6641no—
1003C4—6641no—
1004C4—1664no—
1005C2—44no—
1006C2#2490990811yescharacteristic
1007C2C22⋊Q8×Dic8311yescharacteristic
1008C2#2491025711yescharacteristic
1009C2#2491034011yescharacteristic
1010C2#2491041211yescharacteristic
1011C2#2491044711yescharacteristic
1012C2#2491047211yescharacteristic
1013C2#2491127111yescharacteristic
1014C2#2491133211yescharacteristic
1015C2#2491136211yescharacteristic
1016C2#2491148811yescharacteristic
1017C2#2491153611yescharacteristic
1018C2#2491165311yescharacteristic
1019C2#2491274311yescharacteristic
1020C2#2491278611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#385×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83#13987
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. C2×C4⋊C4×Dic83C2semidirect
5. #24905728C2semidirect
6. #24905716C2semidirect
11. #24905697C2semidirect
12. #24905697C2semidirect
13. #24905695C2semidirect
14. #24905688C2semidirect
53. #385×C83C4semidirect
526. C83#13987semidirect
545. #385Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275872
C2×#191275612
C2×C4⋊C4×Dic832
C2×C4×C22⋊Dic832
#249057282
#249057162
#249057082
#249057002
#249056972
#249056952
#249056882
C2×#385×C832
#1398783