Finite Group Databasebeta

← #35335349

Subgroups — #35335349

Order 21248.

1290 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127614C211yesmaximal, characteristic
2#24905733C211yesmaximal, characteristic, complemented
3#24905733C211yesmaximal, characteristic, complemented
4#24905724C211yesmaximal, characteristic, complemented
5#24905723C211yesmaximal, characteristic, complemented
6#24905720C211yesmaximal, characteristic, complemented
7#24905711C211yesmaximal, characteristic
8#24905711C211yesmaximal, characteristic
9#24905711C211yesmaximal, characteristic
10#24905709C211yesmaximal, characteristic
11#24905705C211yesmaximal, characteristic
12#24905699C211yesmaximal, characteristic
13#24905697C211yesmaximal, characteristic, complemented
14#24905695C211yesmaximal, characteristic, complemented
15C83×#1442C211yesmaximal, characteristic, complemented
16C23×Dic166C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×(C2×D83)⋊C4C2211yescharacteristic
19C22×(C2×D83)⋊C4C2211yescharacteristic
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×C4×Dic83C2211yescharacteristic
26#19127614C418yescomplemented
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
44C2×C83⋊#95C2211yescharacteristic
45C22×C4⋊C4×C83C2211yescharacteristic
46C2×#95×C83C2211yescharacteristic
47C2×#95×C83C2211yescharacteristic
48C2×#95×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C24×D83C2311yescharacteristic
53C22×Dic166—41no—
54C22×Dic166—41no—
55C22×Dic166—41no—
56C22×Dic166—41no—
57C22×Dic166—41no—
58C22×Dic166—41no—
59C22×Dic166C2×C414yes—
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C2×C4⋊Dic83—22no—
68C2×C4⋊Dic83—41no—
69C2×C4⋊Dic83—41no—
70C2×(C2×D83)⋊C4—22no—
71C2×(C2×D83)⋊C4—22no—
72C2×(C2×D83)⋊C4—41no—
73C2×(C2×D83)⋊C4—41no—
74C2×(C2×D83)⋊C4—41no—
75C2×(C2×D83)⋊C4—41no—
76C2×(C2×D83)⋊C4—41no—
77C2×(C2×D83)⋊C4—41no—
78C2×(C2×D83)⋊C4—41no—
79C2×(C2×D83)⋊C4—41no—
80C2×(C2×D83)⋊C4—41no—
81C2×(C2×D83)⋊C4—41no—
82C2×(C2×D83)⋊C4—41no—
83C2×(C2×D83)⋊C4—41no—
84C2×(C2×D83)⋊C4—41no—
85C2×(C2×D83)⋊C4—41no—
86C2×(C2×D83)⋊C4—41no—
87C2×(C2×D83)⋊C4—41no—
88C2×(C2×D83)⋊C4C2×C414yes—
89C2×(C2×D83)⋊C4C2×C414yes—
90C2×(C2×D83)⋊C4C2×C414yes—
91C2×C4×Dic83—41no—
92C2×C4×Dic83—41no—
93C2×C4×Dic83—41no—
94C83⋊#95—22no—
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—
106C83⋊#95—41no—
107C83⋊#95—41no—
108C83⋊#95—41no—
109C83⋊#95—41no—
110C83⋊#95C2×C414yes—
111C83⋊#95C2×C414yes—
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C23×C4×C83C2311yescharacteristic
118C23×C4×C83C2311yescharacteristic
119C2×C4⋊C4×C83—22no—
120C2×C4⋊C4×C83—41no—
121C2×C4⋊C4×C83—41no—
122#95×C83—22no—
123#95×C83—41no—
124#95×C83—41no—
125#95×C83—41no—
126#95×C83—41no—
127#95×C83C2×C414yes—
128C23×D83—21no—
129C23×D83—21no—
130C23×D83—21no—
131C23×D83—21no—
132C23×D83—21no—
133C23×D83—21no—
134C23×D83—21no—
135C23×D83—21no—
136C23×D83—21no—
137C23×D83—21no—
138C23×D83—21no—
139C23×D83—21no—
140C23×D83—21no—
141C23×D83—21no—
142C23×D83C22×C412yes—
143C2×Dic166—44no—
144C2×Dic166—44no—
145C2×Dic166—44no—
146C2×Dic166—44no—
147C2×Dic166—44no—
148C2×Dic166—44no—
149C2×Dic166—44no—
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×Dic83—21no—
193C22×Dic83—21no—
194C22×Dic83—21no—
195C22×Dic83C22×C412yes—
196C22×Dic83C22×C412yes—
197C22×Dic83C22×C412yes—
198C22×Dic83#4112yes—
199C4⋊Dic83—44no—
200(C2×D83)⋊C4—44no—
201(C2×D83)⋊C4—44no—
202(C2×D83)⋊C4—44no—
203(C2×D83)⋊C4—44no—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4—44no—
207C4×Dic83—44no—
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×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×C83C22×C412yes—
255C22×C4×C83C22×C412yes—
256C22×C4×C83C22×C412yes—
257C22×C4×C83#4112yes—
258C4⋊C4×C83—44no—
259C23×C83C23×C411yescharacteristic
260C23×C83C2×#4111yescharacteristic
261C23×C83C2×#4111yescharacteristic
262C23×C83H(5,𝔽2)11yescharacteristic
263C23×C83H(5,𝔽2)11yescharacteristic
264C23×C83H(5,𝔽2)11yescharacteristic
265C23×C83H(5,𝔽2)11yescharacteristic
266C23×C83H(5,𝔽2)11yescharacteristic
267C23×C83H(5,𝔽2)11yescharacteristic
268C23×C83H(5,𝔽2)11yescharacteristic
269C23×C83H(5,𝔽2)11yescharacteristic
270C23×C832−1+411yescharacteristic
271C23×C832−1+411yescharacteristic
272C23×C832−1+411yescharacteristic
273C23×C832−1+411yescharacteristic
274C22×D83—22no—
275C22×D83—22no—
276C22×D83—22no—
277C22×D83—22no—
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—41no—
282C22×D83—41no—
283C22×D83—41no—
284C22×D83—41no—
285C22×D83—41no—
286C22×D83—41no—
287C22×D83—41no—
288C22×D83—41no—
289C22×D83—41no—
290C22×D83—41no—
291C22×D83—41no—
292C22×D83—41no—
293C22×D83—41no—
294C22×D83—41no—
295C22×D83—41no—
296C22×D83—41no—
297C22×D83—41no—
298C22×D83—41no—
299C22×D83—41no—
300C22×D83—41no—
301C22×D83—41no—
302C22×D83—41no—
303C22×D83—41no—
304C22×D83—41no—
305C22×D83—41no—
306C22×D83—41no—
307C22×D83—41no—
308C22×D83—41no—
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—41no—
322C2×C4×C83—41no—
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×C4×C83—41no—
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×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—22no—
361C2×Dic83—22no—
362C2×Dic83—22no—
363C2×Dic83—22no—
364C2×Dic83—22no—
365C2×Dic83—22no—
366C2×Dic83—22no—
367C2×Dic83—22no—
368C2×Dic83—22no—
369C2×Dic83—22no—
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—
403C2×Dic83—41no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407Dic166—416no—
408C22×C83C4×#4111yescharacteristic
409C22×C83#51811yescharacteristic
410C22×C83#51811yescharacteristic
411C22×C83#51811yescharacteristic
412C22×C83#51911yescharacteristic
413C22×C83#52011yescharacteristic
414C22×C83#52011yescharacteristic
415C22×C83#53811yescharacteristic
416C22×C83#53811yescharacteristic
417C22×C83#53811yescharacteristic
418C22×C83#53811yescharacteristic
419C22×C83#53911yescharacteristic
420C22×C83#53911yescharacteristic
421C22×C83#54211yescharacteristic
422C22×C83#54211yescharacteristic
423C22×C83#54211yescharacteristic
424C22×C83#54211yescharacteristic
425C22×C83#54211yescharacteristic
426C22×C83#54211yescharacteristic
427C22×C83#56011yescharacteristic
428C22×C83#56011yescharacteristic
429C22×C83#56011yescharacteristic
430C22×C83H(3,𝔽4)11yescharacteristic
431C22×C83H(3,𝔽4)11yescharacteristic
432C22×C83#56211yescharacteristic
433C22×C83#56211yescharacteristic
434C22×C83#56211yescharacteristic
435C22×C83#56211yescharacteristic
436C22×C83#56211yescharacteristic
437C22×C83#56211yescharacteristic
438C22×C83#56311yescharacteristic
439C22×C83#56311yescharacteristic
440C22×C83#56311yescharacteristic
441C22×C83#56311yescharacteristic
442C22×C83#56311yescharacteristic
443C2×D83—42no—
444C2×D83—42no—
445C2×D83—42no—
446C2×D83—42no—
447C2×D83—42no—
448C2×D83—42no—
449C2×D83—42no—
450C2×D83—81no—
451C2×D83—81no—
452C2×D83—81no—
453C2×D83—81no—
454C2×D83—81no—
455C2×D83—81no—
456C2×D83—81no—
457C2×D83—81no—
458C4×C83—42no—
459C4×C83—42no—
460C4×C83—42no—
461C4×C83—42no—
462C4×C83—81no—
463C4×C83—81no—
464C4×C83—81no—
465Dic83—42no—
466Dic83—42no—
467Dic83—42no—
468Dic83—42no—
469Dic83—81no—
470Dic83—81no—
471Dic83—81no—
472#14649—831nomaximal, Sylow
473C2×C83#233211yescharacteristic
474C2×C83#233711yescharacteristic
475C2×C83#233711yescharacteristic
476C2×C83#237511yescharacteristic
477C2×C83#237811yescharacteristic
478C2×C83#237811yescharacteristic
479C2×C83#237911yescharacteristic
480C2×C83#282411yescharacteristic
481C2×C83#282411yescharacteristic
482C2×C83#283011yescharacteristic
483C2×C83#283011yescharacteristic
484C2×C83#283211yescharacteristic
485C2×C83#283211yescharacteristic
486C2×C83#283811yescharacteristic
487C2×C83#283811yescharacteristic
488D83—82no—
489C2×#393—831no—
490#1446—831no—
491#1446—831no—
492#1443—831no—
493#1443—831no—
494#1442—831no—
495#1442D8311yescharacteristic, complemented
496#1440—831no—
497#1440—831no—
498#1440—831no—
499#1439—831no—
500#1439—831no—
501#1437—831no—
502#1436—831no—
503#1436—831no—
504C83#1464911yescharacteristic, complemented, Sylow
505C23×Q8—831no—
506C22×C4⋊C4—831no—
507C22×C4⋊C4C2×D8311yescharacteristic
508C22×C22⋊C4—831no—
509C22×C22⋊C4—831no—
510C22×C22⋊C4—831no—
511C22×C22⋊C4—831no—
512C22×C22⋊C4—831no—
513C22×C22⋊C4—831no—
514C22×C22⋊C4—831no—
515C22×C42—831no—
516#393—838no—
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×#95—831no—
534C2×#95—831no—
535C2×#95C2×D8311yescharacteristic
536C2×#95C2×D8311yescharacteristic
537C2×#95C2×D8311yescharacteristic
538C2×#95C2×D8311yescharacteristic
539C2×#95C2×D8311yescharacteristic
540C2×#95C2×D8311yescharacteristic
541C25—831no—
542C22×Q8—3321no—
543C22×Q8—3321no—
544C22×Q8—3321no—
545C22×Q8—3321no—
546C22×Q8—3321no—
547C22×Q8—3321no—
548C22×Q8—834no—
549C23×C4—831no—
550C23×C4—831no—
551C23×C4—831no—
552C23×C4—831no—
553C23×C4—831no—
554C23×C4—831no—
555C23×C4—831no—
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8311yescharacteristic
561C23×C4C22×D8311yescharacteristic
562C23×C4C22×D8311yescharacteristic
563C2×C4⋊C4—22no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—3321no—
567C2×C4⋊C4—3321no—
568C2×C4⋊C4—1662no—
569C2×C22⋊C4—3321no—
570C2×C22⋊C4—3321no—
571C2×C22⋊C4—3321no—
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—3321no—
583C2×C22⋊C4—3321no—
584C2×C22⋊C4—3321no—
585C2×C22⋊C4—834no—
586C2×C22⋊C4—834no—
587C2×C22⋊C4—834no—
588C2×C22⋊C4—1662no—
589C2×C22⋊C4—1662no—
590C2×C42—3321no—
591C2×C42—3321no—
592C2×C42—3321no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
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—3321no—
608#95—3321no—
609#95—3321no—
610#95—3321no—
611#95—3321no—
612#95—3321no—
613#95—834no—
614#95—834no—
615#95—1662no—
616#95C4×D8314yes—
617C24—832no—
618C24—1661no—
619C24—1661no—
620C24—1661no—
621C24—1661no—
622C24—1661no—
623C24—1661no—
624C24—1661no—
625C24—1661no—
626C24—1661no—
627C24—1661no—
628C24—1661no—
629C24—1661no—
630C24—1661no—
631C24—1661no—
632C24C23×D8311yescharacteristic
633C2×Q8—3324no—
634C2×Q8—3324no—
635C2×Q8—3324no—
636C2×Q8—3324no—
637C2×Q8—3324no—
638C2×Q8—3324no—
639C2×Q8—3324no—
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—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—832no—
686C22×C4—832no—
687C22×C4—832no—
688C22×C4—832no—
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×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×C4C2×C4×D8312yes—
735C22×C4C2×C4×D8312yes—
736C22×C4C2×C4×D8312yes—
737C22×C4#1305058912yes—
738C4⋊C4—44no—
739C4⋊C4—3324no—
740C22⋊C4—3324no—
741C22⋊C4—3324no—
742C22⋊C4—3324no—
743C22⋊C4—3324no—
744C22⋊C4—3324no—
745C22⋊C4—3324no—
746C22⋊C4—3324no—
747C42—3324no—
748C23—3321no—
749C23—3321no—
750C23—3321no—
751C23—3321no—
752C23—3321no—
753C23—3321no—
754C23—3321no—
755C23—3321no—
756C23—3321no—
757C23—3321no—
758C23—3321no—
759C23—3321no—
760C23—3321no—
761C23—3321no—
762C23—3321no—
763C23—3321no—
764C23—3321no—
765C23—3321no—
766C23—3321no—
767C23—3321no—
768C23—3321no—
769C23—3321no—
770C23—3321no—
771C23—3321no—
772C23—3321no—
773C23—3321no—
774C23—3321no—
775C23—3321no—
776C23—1662no—
777C23—1662no—
778C23—1662no—
779C23—1662no—
780C23—1662no—
781C23—1662no—
782C23—1662no—
783C23C22×C4×D8311yescharacteristic
784C23#41×D8311yescharacteristic
785C23C2×#1305058911yescharacteristic
786C23#1458183711yescharacteristic
787C23#1458183711yescharacteristic
788C23#1458183711yescharacteristic
789C23#1458183811yescharacteristic
790C23#1458183811yescharacteristic
791C23#1458183811yescharacteristic
792C23#1458183811yescharacteristic
793C23#1458183811yescharacteristic
794C23#1458183911yescharacteristic
795C23#1458183911yescharacteristic
796C23#1458184011yescharacteristic
797C23#1458184011yescharacteristic
798Q8—33216no—
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—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
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—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
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—3321no—
882C2×C4—3321no—
883C2×C4—3321no—
884C2×C4—3321no—
885C2×C4—1662no—
886C2×C4—1662no—
887C2×C4—1662no—
888C2×C4—1662no—
889C2×C4—1662no—
890C2×C4—1662no—
891C2×C4—1662no—
892C2×C4—1662no—
893C2×C4—1662no—
894C2×C4—1662no—
895C2×C4—1662no—
896C2×C4—1662no—
897C22—3322no—
898C22—3322no—
899C22—3322no—
900C22—3322no—
901C22—3322no—
902C22—3322no—
903C22—3322no—
904C22—6641no—
905C22—6641no—
906C22—6641no—
907C22—6641no—
908C22—6641no—
909C22—6641no—
910C22—6641no—
911C22—6641no—
912C22C4×#1305058911yescharacteristic
913C22#1912817311yescharacteristic
914C22#1912817311yescharacteristic
915C22#1912817511yescharacteristic
916C22#1912817711yescharacteristic
917C22#1912818111yescharacteristic
918C22#1912818211yescharacteristic
919C22#1912828611yescharacteristic
920C22#1912828711yescharacteristic
921C22#1912828811yescharacteristic
922C22#1912829011yescharacteristic
923C22#1912829511yescharacteristic
924C22#1912829911yescharacteristic
925C22#1912831711yescharacteristic
926C22#1912831911yescharacteristic
927C22#1912832011yescharacteristic
928C22#1912832111yescharacteristic
929C22#1912832411yescharacteristic
930C22#1912832411yescharacteristic
931C22#1912843911yescharacteristic
932C22#1912844111yescharacteristic
933C22#1912844211yescharacteristic
934C22#1912844311yescharacteristic
935C22#1912844311yescharacteristic
936C22#1912844511yescharacteristic
937C22#1912844611yescharacteristic
938C22#1912844711yescharacteristic
939C22#1912844811yescharacteristic
940C22#1912844911yescharacteristic
941C22#1912844911yescharacteristic
942C22#1912845011yescharacteristic
943C22#1912845211yescharacteristic
944C22#1912845311yescharacteristic
945C22#1912845511yescharacteristic
946C22#1912845511yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—81no—
952C4—81no—
953C4—81no—
954C4—3322no—
955C4—3322no—
956C4—3322no—
957C4—3322no—
958C4—6641no—
959C4—6641no—
960C4—6641no—
961C2—6642no—
962C2#2491021511yescharacteristic
963C2#2491027011yescharacteristic
964C2#2491027711yescharacteristic
965C2#2491060311yescharacteristic
966C2#2491062511yescharacteristic
967C2#2491062811yescharacteristic
968C2#2491063411yescharacteristic
969C2#2491554411yescharacteristic
970C2#2491554611yescharacteristic
971C2#2491560311yescharacteristic
972C2#2491561011yescharacteristic
973C2#2491563211yescharacteristic
974C2#2491563311yescharacteristic
975C2#2491568911yescharacteristic
976C2#2491569211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1442C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenter#1442D83
hypocenterC83#14649
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
2. #24905733C2semidirect
3. #24905733C2semidirect
4. #24905724C2semidirect
5. #24905723C2semidirect
6. #24905720C2semidirect
13. #24905697C2semidirect
14. #24905695C2semidirect
15. C83×#1442C2semidirect
26. #19127614C4semidirect
495. #1442D83semidirect
504. C83#14649semidirect

Maximal subgroups

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

subgroupindex
C2×#191276142
#249057332
#249057242
#249057232
#249057202
#249057112
#249057092
#249057052
#249056992
#249056972
#249056952
C83×#14422
#1464983