Finite Group Databasebeta

← #35335257

Subgroups — #35335257

Order 21248.

1226 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24905728C211yesmaximal, characteristic, complemented
2#24905725C211yesmaximal, characteristic, complemented
3#24905725C211yesmaximal, characteristic, complemented
4#24905720C211yesmaximal, characteristic, complemented
5#24905716C211yesmaximal, characteristic, complemented
6#24905716C211yesmaximal, characteristic, complemented
7#24905712C211yesmaximal, characteristic
8#24905708C211yesmaximal, characteristic
9#24905708C211yesmaximal, characteristic
10#24905708C211yesmaximal, characteristic
11#24905708C211yesmaximal, characteristic
12#24905700C211yesmaximal, characteristic
13#24905697C211yesmaximal, characteristic, complemented
14#24905697C211yesmaximal, characteristic, complemented
15C2×#397×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
25C2×C83⋊#95C2211yescharacteristic
26C2×C83⋊#95C2211yescharacteristic
27C2×C83⋊#95C2211yescharacteristic
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
44C22×C4⋊C4×C83C2211yescharacteristic
45C22×C22⋊C4×C83C2211yescharacteristic
46C22×C22⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48#397×C83C418yescomplemented
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C23×Dic83C2311yescharacteristic
53C23×Dic83C2311yescharacteristic
54C23×Dic83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C2×C4⋊Dic83—22no—
61C2×C4⋊Dic83—22no—
62C2×C4⋊Dic83—41no—
63C2×C4⋊Dic83—41no—
64C2×C4⋊Dic83—41no—
65C2×C4⋊Dic83—41no—
66C2×C4⋊Dic83—41no—
67C2×C4⋊Dic83—41no—
68C2×C4⋊Dic83—41no—
69C2×C4⋊Dic83—41no—
70C2×C4⋊Dic83—41no—
71C2×C4⋊Dic83—41no—
72C2×C22⋊Dic83—22no—
73C2×C22⋊Dic83—22no—
74C2×C22⋊Dic83—41no—
75C2×C22⋊Dic83—41no—
76C2×C22⋊Dic83—41no—
77C2×C22⋊Dic83—41no—
78C2×C22⋊Dic83—41no—
79C2×C22⋊Dic83—41no—
80C2×C22⋊Dic83—41no—
81C2×C22⋊Dic83—41no—
82C2×C22⋊Dic83—41no—
83C2×C22⋊Dic83—41no—
84C2×C4×Dic83—41no—
85C2×C4×Dic83—41no—
86C2×C4×Dic83—41no—
87C83⋊#95—22no—
88C83⋊#95—22no—
89C83⋊#95—41no—
90C83⋊#95—41no—
91C83⋊#95—41no—
92C83⋊#95—41no—
93C83⋊#95—41no—
94C83⋊#95—41no—
95C83⋊#95—41no—
96C83⋊#95—41no—
97C83⋊#95—41no—
98C83⋊#95—41no—
99C83⋊#95—41no—
100C83⋊#95—41no—
101C83⋊#95—41no—
102C83⋊#95—41no—
103C83⋊#95—41no—
104C83⋊#95—41no—
105C83⋊#95—41no—
106C25×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C2×C4⋊C4×C83—41no—
114C2×C4⋊C4×C83—41no—
115C2×C4⋊C4×C83C2×C414yes—
116C2×C22⋊C4×C83—41no—
117C2×C22⋊C4×C83—41no—
118C2×C22⋊C4×C83—41no—
119C2×C22⋊C4×C83—41no—
120C2×C22⋊C4×C83—41no—
121C2×C22⋊C4×C83—41no—
122C2×C22⋊C4×C83C2×C414yes—
123C2×C22⋊C4×C83C2×C414yes—
124C2×C22⋊C4×C83C2×C414yes—
125#95×C83C2×C414yes—
126#95×C83C2×C414yes—
127#95×C83C2×C414yes—
128C22×Dic83—21no—
129C22×Dic83—21no—
130C22×Dic83—21no—
131C22×Dic83—21no—
132C22×Dic83—21no—
133C22×Dic83—21no—
134C22×Dic83—21no—
135C22×Dic83—21no—
136C22×Dic83—21no—
137C22×Dic83—21no—
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#4112yes—
183C22×Dic83#4112yes—
184C4⋊Dic83—44no—
185C4⋊Dic83—44no—
186C4⋊Dic83—44no—
187C4⋊Dic83—44no—
188C22⋊Dic83—44no—
189C22⋊Dic83—44no—
190C22⋊Dic83—44no—
191C22⋊Dic83—44no—
192C4×Dic83—44no—
193C24×C83—21no—
194C24×C83—21no—
195C24×C83—21no—
196C24×C83—21no—
197C24×C83—21no—
198C24×C83—21no—
199C24×C83—21no—
200C24×C83—21no—
201C24×C83—21no—
202C24×C83—21no—
203C24×C83—21no—
204C24×C83—21no—
205C24×C83—21no—
206C24×C83—21no—
207C24×C83C22×C412yes—
208C24×C83C2411yescharacteristic
209C22×C4×C83—21no—
210C22×C4×C83—21no—
211C22×C4×C83—21no—
212C22×C4×C83—21no—
213C22×C4×C83—21no—
214C22×C4×C83—21no—
215C22×C4×C83—21no—
216C22×C4×C83—21no—
217C22×C4×C83—21no—
218C22×C4×C83—21no—
219C22×C4×C83—21no—
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×C83C22×C412yes—
246C22×C4×C83C22×C412yes—
247C22×C4×C83C22×C412yes—
248C22×C4×C83C22×C412yes—
249C22×C4×C83C22×C412yes—
250C22×C4×C83C22×C412yes—
251C4⋊C4×C83—44no—
252C22⋊C4×C83—44no—
253C22⋊C4×C83—44no—
254C22⋊C4×C83—44no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—22no—
258C23×C83—22no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—41no—
263C23×C83—41no—
264C23×C83—41no—
265C23×C83—41no—
266C23×C83—41no—
267C23×C83—41no—
268C23×C83—41no—
269C23×C83—41no—
270C23×C83—41no—
271C23×C83—41no—
272C23×C83—41no—
273C23×C83—41no—
274C23×C83—41no—
275C23×C83—41no—
276C23×C83—41no—
277C23×C83—41no—
278C23×C83—41no—
279C23×C83—41no—
280C23×C83—41no—
281C23×C83—41no—
282C23×C83—41no—
283C23×C83—41no—
284C23×C83—41no—
285C23×C83—41no—
286C23×C83—41no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83C23×C411yescharacteristic
291C23×C83C2×#4111yescharacteristic
292C23×C83C2×#4111yescharacteristic
293C23×C83H(5,𝔽2)11yescharacteristic
294C23×C83H(5,𝔽2)11yescharacteristic
295C23×C83H(5,𝔽2)11yescharacteristic
296C23×C83H(5,𝔽2)11yescharacteristic
297C23×C83H(5,𝔽2)11yescharacteristic
298C23×C83H(5,𝔽2)11yescharacteristic
299C23×C83H(5,𝔽2)11yescharacteristic
300C23×C83H(5,𝔽2)11yescharacteristic
301C23×C832−1+411yescharacteristic
302C23×C832−1+411yescharacteristic
303C23×C832−1+411yescharacteristic
304C23×C832−1+411yescharacteristic
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—41no—
324C2×C4×C83—41no—
325C2×C4×C83—41no—
326C2×C4×C83—41no—
327C2×C4×C83—41no—
328C2×C4×C83—41no—
329C2×C4×C83—41no—
330C2×C4×C83—41no—
331C2×C4×C83—41no—
332C2×C4×C83—41no—
333C2×C4×C83—41no—
334C2×C4×C83—41no—
335C2×C4×C83—41no—
336C2×C4×C83—41no—
337C2×C4×C83—41no—
338C2×C4×C83—41no—
339C2×C4×C83—41no—
340C2×C4×C83—41no—
341C2×C4×C83—41no—
342C2×C4×C83—41no—
343C2×C4×C83—41no—
344C2×C4×C83—41no—
345C2×C4×C83—41no—
346C2×C4×C83—41no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—41no—
354C2×Dic83—41no—
355C2×Dic83—41no—
356C2×Dic83—41no—
357C2×Dic83—41no—
358C2×Dic83—41no—
359C2×Dic83—41no—
360C2×Dic83—41no—
361C2×Dic83—41no—
362C2×Dic83—41no—
363C2×Dic83—41no—
364C2×Dic83—41no—
365C2×Dic83—41no—
366C2×Dic83—41no—
367C2×Dic83—41no—
368C2×Dic83—41no—
369C2×Dic83—41no—
370C2×Dic83—41no—
371C2×Dic83—41no—
372C2×Dic83—41no—
373C2×Dic83—41no—
374C2×Dic83—41no—
375C2×Dic83—41no—
376C2×Dic83—41no—
377C2×Dic83—41no—
378C2×Dic83—41no—
379C2×Dic83—41no—
380C2×Dic83—41no—
381C2×Dic83—41no—
382C2×Dic83—41no—
383C2×Dic83—41no—
384C2×Dic83—41no—
385C2×Dic83—41no—
386C2×Dic83—41no—
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—
403C22×C83—42no—
404C22×C83—42no—
405C22×C83—42no—
406C22×C83—42no—
407C22×C83—42no—
408C22×C83—42no—
409C22×C83—42no—
410C22×C83—81no—
411C22×C83—81no—
412C22×C83—81no—
413C22×C83—81no—
414C22×C83—81no—
415C22×C83—81no—
416C22×C83—81no—
417C22×C83—81no—
418C22×C83C4×#4111yescharacteristic
419C22×C83#51811yescharacteristic
420C22×C83#51811yescharacteristic
421C22×C83#52011yescharacteristic
422C22×C83#52011yescharacteristic
423C22×C83#52011yescharacteristic
424C22×C83#52011yescharacteristic
425C22×C83#53811yescharacteristic
426C22×C83#53811yescharacteristic
427C22×C83#53811yescharacteristic
428C22×C83#53811yescharacteristic
429C22×C83#53911yescharacteristic
430C22×C83#53911yescharacteristic
431C22×C83#54011yescharacteristic
432C22×C83#54111yescharacteristic
433C22×C83#54211yescharacteristic
434C22×C83#54211yescharacteristic
435C22×C83#54211yescharacteristic
436C22×C83#54211yescharacteristic
437C22×C83#56011yescharacteristic
438C22×C83#56011yescharacteristic
439C22×C83#56011yescharacteristic
440C22×C83#56011yescharacteristic
441C22×C83#56011yescharacteristic
442C22×C83#56211yescharacteristic
443C22×C83#56211yescharacteristic
444C22×C83#56211yescharacteristic
445C22×C83#56211yescharacteristic
446C22×C83#56211yescharacteristic
447C22×C83#56211yescharacteristic
448C22×C83#56311yescharacteristic
449C22×C83#56311yescharacteristic
450C22×C83#56311yescharacteristic
451C22×C83#56311yescharacteristic
452C22×C83#56311yescharacteristic
453C4×C83—42no—
454C4×C83—42no—
455C4×C83—42no—
456C4×C83—42no—
457C4×C83—42no—
458C4×C83—42no—
459Dic83—42no—
460Dic83—42no—
461Dic83—81no—
462Dic83—81no—
463Dic83—81no—
464Dic83—81no—
465Dic83—81no—
466Dic83—81no—
467#14642—831nomaximal, Sylow
468C2×C83—82no—
469C2×C83#233411yescharacteristic
470C2×C83#233511yescharacteristic
471C2×C83#233711yescharacteristic
472C2×C83#237611yescharacteristic
473C2×C83#237611yescharacteristic
474C2×C83#237711yescharacteristic
475C2×C83#238311yescharacteristic
476C2×C83#282511yescharacteristic
477C2×C83#282711yescharacteristic
478C2×C83#282911yescharacteristic
479C2×C83#283011yescharacteristic
480C2×C83#283111yescharacteristic
481C2×C83#283111yescharacteristic
482C2×C83#283711yescharacteristic
483C2×C83#283811yescharacteristic
484C2×#397D8311yescharacteristic
485#1444—831no—
486#1443—831no—
487#1443—831no—
488#1442—831no—
489#1441—831no—
490#1441—831no—
491#1440—831no—
492#1439—831no—
493#1439—831no—
494#1439—831no—
495#1439—831no—
496#1437—831no—
497#1436—831no—
498#1436—831no—
499C83#1464211yescharacteristic, complemented, Sylow
500C22×C4⋊C4—831no—
501C22×C4⋊C4—831no—
502C22×C4⋊C4—831no—
503C22×C4⋊C4—831no—
504C22×C4⋊C4C2×D8311yescharacteristic
505C22×C22⋊C4—831no—
506C22×C22⋊C4—831no—
507C22×C22⋊C4—831no—
508C22×C22⋊C4—831no—
509C22×C22⋊C4C2×D8311yescharacteristic
510C22×C22⋊C4C2×D8311yescharacteristic
511C22×C22⋊C4C2×D8311yescharacteristic
512C22×C42—831no—
513#397Dic8318yescomplemented
514C2×#95—831no—
515C2×#95—831no—
516C2×#95—831no—
517C2×#95—831no—
518C2×#95—831no—
519C2×#95—831no—
520C2×#95—831no—
521C2×#95—831no—
522C2×#95—831no—
523C2×#95—831no—
524C2×#95—831no—
525C2×#95—831no—
526C2×#95—831no—
527C2×#95—831no—
528C2×#95—831no—
529C2×#95—831no—
530C2×#95—831no—
531C2×#95—831no—
532C2×#95—831no—
533C2×#95C2×D8311yescharacteristic
534C2×#95C2×D8311yescharacteristic
535C2×#95C2×D8311yescharacteristic
536C25C22×D8311yescharacteristic
537C23×C4—831no—
538C23×C4—831no—
539C23×C4—831no—
540C23×C4—831no—
541C23×C4—831no—
542C23×C4—831no—
543C23×C4—831no—
544C23×C4—831no—
545C23×C4C22×D8311yescharacteristic
546C23×C4C22×D8311yescharacteristic
547C23×C4C22×D8311yescharacteristic
548C23×C4C22×D8311yescharacteristic
549C23×C4C22×D8311yescharacteristic
550C23×C4C22×D8311yescharacteristic
551C2×C4⋊C4—41no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4—3321no—
554C2×C4⋊C4—3321no—
555C2×C4⋊C4—3321no—
556C2×C4⋊C4—3321no—
557C2×C4⋊C4—3321no—
558C2×C4⋊C4—3321no—
559C2×C4⋊C4—3321no—
560C2×C4⋊C4—3321no—
561C2×C4⋊C4—3321no—
562C2×C4⋊C4—3321no—
563C2×C4⋊C4—1662no—
564C2×C4⋊C4—1662no—
565C2×C4⋊C4C2×Dic8314yes—
566C2×C22⋊C4—41no—
567C2×C22⋊C4—41no—
568C2×C22⋊C4—41no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—3321no—
573C2×C22⋊C4—3321no—
574C2×C22⋊C4—3321no—
575C2×C22⋊C4—3321no—
576C2×C22⋊C4—3321no—
577C2×C22⋊C4—3321no—
578C2×C22⋊C4—3321no—
579C2×C22⋊C4—3321no—
580C2×C22⋊C4—3321no—
581C2×C22⋊C4—3321no—
582C2×C22⋊C4—1662no—
583C2×C22⋊C4—1662no—
584C2×C22⋊C4C2×Dic8314yes—
585C2×C22⋊C4C2×Dic8314yes—
586C2×C22⋊C4C2×Dic8314yes—
587C2×C42—3321no—
588C2×C42—3321no—
589C2×C42—3321no—
590#95—3321no—
591#95—3321no—
592#95—3321no—
593#95—3321no—
594#95—3321no—
595#95—3321no—
596#95—3321no—
597#95—3321no—
598#95—3321no—
599#95—3321no—
600#95—3321no—
601#95—3321no—
602#95—3321no—
603#95—3321no—
604#95—3321no—
605#95—3321no—
606#95—3321no—
607#95—1662no—
608#95—1662no—
609#95C2×Dic8314yes—
610#95C2×Dic8314yes—
611#95C2×Dic8314yes—
612C24—21no—
613C24—21no—
614C24—21no—
615C24—21no—
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24C22×Dic8312yes—
627C24C23×D8311yescharacteristic
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—832no—
665C22×C4—832no—
666C22×C4—1661no—
667C22×C4—1661no—
668C22×C4—1661no—
669C22×C4—1661no—
670C22×C4—1661no—
671C22×C4—1661no—
672C22×C4—1661no—
673C22×C4—1661no—
674C22×C4—1661no—
675C22×C4—1661no—
676C22×C4—1661no—
677C22×C4—1661no—
678C22×C4—1661no—
679C22×C4—1661no—
680C22×C4—1661no—
681C22×C4—1661no—
682C22×C4—1661no—
683C22×C4—1661no—
684C22×C4—1661no—
685C22×C4—1661no—
686C22×C4—1661no—
687C22×C4—1661no—
688C22×C4—1661no—
689C22×C4—1661no—
690C22×C4—1661no—
691C22×C4—1661no—
692C22×C4—1661no—
693C22×C4—1661no—
694C22×C4—1661no—
695C22×C4—1661no—
696C22×C4—1661no—
697C22×C4—1661no—
698C22×C4—1661no—
699C22×C4—1661no—
700C22×C4—1661no—
701C22×C4—1661no—
702C22×C4—1661no—
703C22×C4—1661no—
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×C4C22×Dic8312yes—
721C22×C4C22×Dic8312yes—
722C22×C4C22×Dic8312yes—
723C22×C4C22×Dic8312yes—
724C22×C4C22×Dic8312yes—
725C22×C4C22×Dic8312yes—
726C4⋊C4—44no—
727C4⋊C4—3324no—
728C4⋊C4—3324no—
729C4⋊C4—3324no—
730C4⋊C4—3324no—
731C22⋊C4—44no—
732C22⋊C4—44no—
733C22⋊C4—44no—
734C22⋊C4—3324no—
735C22⋊C4—3324no—
736C22⋊C4—3324no—
737C22⋊C4—3324no—
738C42—3324no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23C23×Dic8311yescharacteristic
775C23#41×D8311yescharacteristic
776C23#41×D8311yescharacteristic
777C23#1458183711yescharacteristic
778C23#1458183711yescharacteristic
779C23#1458183711yescharacteristic
780C23#1458183711yescharacteristic
781C23#1458183811yescharacteristic
782C23#1458183811yescharacteristic
783C23#1458183811yescharacteristic
784C23#1458183811yescharacteristic
785C23#1458183911yescharacteristic
786C23#1458183911yescharacteristic
787C23#1458183911yescharacteristic
788C23#1458183911yescharacteristic
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—3321no—
832C2×C4—3321no—
833C2×C4—3321no—
834C2×C4—3321no—
835C2×C4—3321no—
836C2×C4—3321no—
837C2×C4—3321no—
838C2×C4—3321no—
839C2×C4—3321no—
840C2×C4—3321no—
841C2×C4—3321no—
842C2×C4—3321no—
843C2×C4—3321no—
844C2×C4—3321no—
845C2×C4—3321no—
846C2×C4—3321no—
847C2×C4—3321no—
848C2×C4—3321no—
849C2×C4—3321no—
850C2×C4—3321no—
851C2×C4—3321no—
852C2×C4—3321no—
853C2×C4—3321no—
854C2×C4—3321no—
855C2×C4—3321no—
856C2×C4—3321no—
857C2×C4—3321no—
858C2×C4—3321no—
859C2×C4—3321no—
860C2×C4—3321no—
861C2×C4—3321no—
862C2×C4—3321no—
863C2×C4—3321no—
864C2×C4—3321no—
865C2×C4—3321no—
866C2×C4—3321no—
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—1662no—
882C2×C4—1662no—
883C2×C4—1662no—
884C2×C4—1662no—
885C2×C4—1662no—
886C2×C4—1662no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—81no—
895C22—81no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22#41×Dic8311yescharacteristic
903C22#1912817611yescharacteristic
904C22#1912817611yescharacteristic
905C22#1912818411yescharacteristic
906C22#1912818411yescharacteristic
907C22#1912818411yescharacteristic
908C22#1912818411yescharacteristic
909C22#1912828511yescharacteristic
910C22#1912828511yescharacteristic
911C22#1912828711yescharacteristic
912C22#1912829011yescharacteristic
913C22#1912829211yescharacteristic
914C22#1912829411yescharacteristic
915C22#1912830311yescharacteristic
916C22#1912830811yescharacteristic
917C22#1912831511yescharacteristic
918C22#1912831511yescharacteristic
919C22#1912831711yescharacteristic
920C22#1912831911yescharacteristic
921C22#1912843911yescharacteristic
922C22#1912843911yescharacteristic
923C22#1912844111yescharacteristic
924C22#1912844111yescharacteristic
925C22#1912844211yescharacteristic
926C22#1912844611yescharacteristic
927C22#1912844611yescharacteristic
928C22#1912844811yescharacteristic
929C22#1912844811yescharacteristic
930C22#1912844811yescharacteristic
931C22#1912844811yescharacteristic
932C22#1912845311yescharacteristic
933C22#1912845311yescharacteristic
934C22#1912845311yescharacteristic
935C22#1912845411yescharacteristic
936C22#1912845411yescharacteristic
937C4—42no—
938C4—42no—
939C4—42no—
940C4—42no—
941C4—42no—
942C4—42no—
943C4—3322no—
944C4—3322no—
945C4—6641no—
946C4—6641no—
947C4—6641no—
948C4—6641no—
949C4—6641no—
950C4—6641no—
951C2—82no—
952C2#2491024211yescharacteristic
953C2#2491025711yescharacteristic
954C2#2491027811yescharacteristic
955C2#2491061111yescharacteristic
956C2#2491061111yescharacteristic
957C2#2491062011yescharacteristic
958C2#2491065511yescharacteristic
959C2#2491555311yescharacteristic
960C2#2491556811yescharacteristic
961C2#2491559211yescharacteristic
962C2#2491560811yescharacteristic
963C2#2491561211yescharacteristic
964C2#2491562211yescharacteristic
965C2#2491567811yescharacteristic
966C2#2491569511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#397×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#397D83
hypocenterC83#14642
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. #24905728C2semidirect
2. #24905725C2semidirect
3. #24905725C2semidirect
4. #24905720C2semidirect
5. #24905716C2semidirect
6. #24905716C2semidirect
13. #24905697C2semidirect
14. #24905697C2semidirect
48. #397×C83C4semidirect
499. C83#14642semidirect
513. #397Dic83semidirect

Maximal subgroups

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

subgroupindex
#249057282
#249057252
#249057202
#249057162
#249057122
#249057082
#249057002
#249056972
C2×#397×C832
#1464283