Finite Group Databasebeta

← #35328813

Subgroups — #35328813

Order 21248.

1210 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127587C211yesmaximal, characteristic
2#24905732C211yesmaximal, characteristic
3#24905721C211yesmaximal, characteristic
4#24905719C211yesmaximal, characteristic
5#24905698C211yesmaximal, characteristic
6#24905697C211yesmaximal, characteristic
7#24905697C211yesmaximal, characteristic
8#24905694C211yesmaximal, characteristic
9#24905692C211yesmaximal, characteristic
10#24905687C211yesmaximal, characteristic
11#24905687C211yesmaximal, characteristic
12#24905687C211yesmaximal, characteristic
13#95×Dic83C211yesmaximal, characteristic
14#95×Dic83C211yesmaximal, characteristic
15C83×#1445C211yesmaximal, characteristic
16C22×C4⋊Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×C4×Dic83C2211yescharacteristic
20C22×C4×Dic83C2211yescharacteristic
21C22×C4×Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24#19127587C418yescomplemented
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
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
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⋊Dic83C2×C414yes—
66C2×Dic83⋊C4—22no—
67C2×Dic83⋊C4—22no—
68C2×Dic83⋊C4—41no—
69C2×C4×Dic83—22no—
70C2×C4×Dic83—22no—
71C2×C4×Dic83—22no—
72C2×C4×Dic83—22no—
73C2×C4×Dic83—22no—
74C2×C4×Dic83—41no—
75C2×C4×Dic83—41no—
76C2×C4×Dic83—41no—
77C2×C4×Dic83—41no—
78C2×C4×Dic83—41no—
79C2×C4×Dic83—41no—
80C2×C4×Dic83—41no—
81C2×C4×Dic83—41no—
82C2×C4×Dic83C2×C414yes—
83C2×C4×Dic83Q814yes—
84C83⋊#95—22no—
85C83⋊#95—22no—
86C83⋊#95—22no—
87C83⋊#95—22no—
88C83⋊#95—22no—
89C83⋊#95—22no—
90C83⋊#95—22no—
91C83⋊#95—22no—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—41no—
97C83⋊#95—41no—
98C83⋊#95—41no—
99C83⋊#95—41no—
100C83⋊#95C2×C414yes—
101C83⋊#95C2×C414yes—
102C83⋊#95C2×C414yes—
103C83⋊#95C2×C414yes—
104C23×C4×C83C2311yescharacteristic
105C23×C4×C83C2311yescharacteristic
106C23×C4×C83C2311yescharacteristic
107C23×C4×C83C2311yescharacteristic
108C23×C4×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C2×C4⋊C4×C83—22no—
112C2×C4⋊C4×C83—22no—
113C2×C4⋊C4×C83C2×C414yes—
114#95×C83—22no—
115#95×C83—22no—
116#95×C83—22no—
117#95×C83—22no—
118#95×C83—41no—
119#95×C83—41no—
120C22×Dic83—21no—
121C22×Dic83—21no—
122C22×Dic83—21no—
123C22×Dic83—21no—
124C22×Dic83—21no—
125C22×Dic83—21no—
126C22×Dic83—21no—
127C22×Dic83—21no—
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×Dic83C22×C412yes—
166C22×Dic83C22×C412yes—
167C22×Dic83C22×C412yes—
168C22×Dic83C22×C412yes—
169C22×Dic83C2×Q812yes—
170C22×Dic83C2×Q812yes—
171C22×Dic83#4112yes—
172C22×Dic83#4112yes—
173C22×Dic83#4112yes—
174C22×Dic83#4112yes—
175C22×Dic83#4112yes—
176C4⋊Dic83—44no—
177C4⋊Dic83—44no—
178Dic83⋊C4—44no—
179C4×Dic83—44no—
180C4×Dic83—44no—
181C4×Dic83—44no—
182C4×Dic83—44no—
183C4×Dic83—44no—
184C24×C83C2411yescharacteristic
185C22×C4×C83—21no—
186C22×C4×C83—21no—
187C22×C4×C83—21no—
188C22×C4×C83—21no—
189C22×C4×C83—21no—
190C22×C4×C83—21no—
191C22×C4×C83—21no—
192C22×C4×C83—21no—
193C22×C4×C83—21no—
194C22×C4×C83—21no—
195C22×C4×C83—21no—
196C22×C4×C83—21no—
197C22×C4×C83—21no—
198C22×C4×C83—21no—
199C22×C4×C83—21no—
200C22×C4×C83—21no—
201C22×C4×C83—21no—
202C22×C4×C83—21no—
203C22×C4×C83—21no—
204C22×C4×C83—21no—
205C22×C4×C83—21no—
206C22×C4×C83—21no—
207C22×C4×C83—21no—
208C22×C4×C83—21no—
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×C83C22×C412yes—
227C22×C4×C83C22×C412yes—
228C22×C4×C83C22×C412yes—
229C22×C4×C83C2×Q812yes—
230C22×C4×C83#4112yes—
231C22×C4×C83#4112yes—
232C22×C4×C83#4112yes—
233C22×C4×C83#4112yes—
234C4⋊C4×C83—28no—
235C23×C83C23×C411yescharacteristic
236C23×C83C22×Q811yescharacteristic
237C23×C83C2×#4111yescharacteristic
238C23×C83C2×#4111yescharacteristic
239C23×C83C2×#4111yescharacteristic
240C23×C83C2×#4111yescharacteristic
241C23×C83C2×#4111yescharacteristic
242C23×C83C2×#4111yescharacteristic
243C23×C83C2×#4111yescharacteristic
244C23×C83C2×#4111yescharacteristic
245C23×C83C2×#4111yescharacteristic
246C23×C83H(5,𝔽2)11yescharacteristic
247C23×C83H(5,𝔽2)11yescharacteristic
248C23×C83H(5,𝔽2)11yescharacteristic
249C23×C832−1+411yescharacteristic
250C2×C4×C83—22no—
251C2×C4×C83—22no—
252C2×C4×C83—22no—
253C2×C4×C83—22no—
254C2×C4×C83—22no—
255C2×C4×C83—22no—
256C2×C4×C83—22no—
257C2×C4×C83—22no—
258C2×C4×C83—22no—
259C2×C4×C83—22no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—41no—
272C2×C4×C83—41no—
273C2×C4×C83—41no—
274C2×C4×C83—41no—
275C2×C4×C83—41no—
276C2×C4×C83—41no—
277C2×C4×C83—41no—
278C2×C4×C83—41no—
279C2×C4×C83—41no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—41no—
286C2×C4×C83—41no—
287C2×C4×C83—41no—
288C2×C4×C83—41no—
289C2×C4×C83—41no—
290C2×C4×C83—41no—
291C2×C4×C83—41no—
292C2×C4×C83—41no—
293C2×C4×C83—41no—
294C2×C4×C83—41no—
295C2×C4×C83—41no—
296C2×C4×C83—41no—
297C2×C4×C83—41no—
298C2×C4×C83#11714yes—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—41no—
327C2×Dic83—41no—
328C2×Dic83—41no—
329C2×Dic83—41no—
330C2×Dic83—41no—
331C2×Dic83—41no—
332C2×Dic83—41no—
333C2×Dic83—41no—
334C2×Dic83—41no—
335C2×Dic83—41no—
336C2×Dic83—41no—
337C2×Dic83—41no—
338C2×Dic83—41no—
339C2×Dic83—41no—
340C2×Dic83—41no—
341C2×Dic83—41no—
342C2×Dic83—41no—
343C2×Dic83—41no—
344C2×Dic83—41no—
345C2×Dic83—41no—
346C2×Dic83—41no—
347C2×Dic83—41no—
348C2×Dic83—41no—
349C2×Dic83—41no—
350C2×Dic83—41no—
351C2×Dic83—41no—
352C2×Dic83—41no—
353C2×Dic83C4×Q814yes—
354C2×Dic83#12514yes—
355C22×C83C2×#11711yescharacteristic
356C22×C83C2×C4×Q811yescharacteristic
357C22×C83C4×#4111yescharacteristic
358C22×C83C4×#4111yescharacteristic
359C22×C83C4×#4111yescharacteristic
360C22×C83#51811yescharacteristic
361C22×C83#52011yescharacteristic
362C22×C83C2×#12511yescharacteristic
363C22×C83#52911yescharacteristic
364C22×C83#52911yescharacteristic
365C22×C83#52911yescharacteristic
366C22×C83#52911yescharacteristic
367C22×C83#53311yescharacteristic
368C22×C83#53311yescharacteristic
369C22×C83#53311yescharacteristic
370C22×C83#53811yescharacteristic
371C22×C83#53911yescharacteristic
372C22×C83#54311yescharacteristic
373C22×C83#54411yescharacteristic
374C22×C83#55111yescharacteristic
375C22×C83#55111yescharacteristic
376C22×C83#55111yescharacteristic
377C22×C83#55111yescharacteristic
378C22×C83#55211yescharacteristic
379C22×C83#55211yescharacteristic
380C22×C83#55211yescharacteristic
381C22×C83#55311yescharacteristic
382C22×C83#55311yescharacteristic
383C22×C83#55311yescharacteristic
384C22×C83#55311yescharacteristic
385C22×C83#55311yescharacteristic
386C22×C83#55611yescharacteristic
387C22×C83#55911yescharacteristic
388C22×C83#55911yescharacteristic
389C22×C83#55911yescharacteristic
390C4×C83—24no—
391C4×C83—42no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396C4×C83—81no—
397Dic83—24no—
398Dic83—24no—
399Dic83—42no—
400Dic83—42no—
401Dic83—42no—
402Dic83—42no—
403Dic83—42no—
404Dic83—81no—
405#14093—831nomaximal, Sylow
406C2×C83#229511yescharacteristic
407C2×C83C4×#12511yescharacteristic
408C2×C83#232911yescharacteristic
409C2×C83#234311yescharacteristic
410C2×C83#235711yescharacteristic
411C2×C83#237311yescharacteristic
412C2×C83#237411yescharacteristic
413C2×C83#256911yescharacteristic
414C2×C83#257011yescharacteristic
415C2×C83#257511yescharacteristic
416C2×C83#257811yescharacteristic
417C2×C83#259511yescharacteristic
418C2×C83#259611yescharacteristic
419C2×C83#260611yescharacteristic
420C2×C83#260711yescharacteristic
421C2×#387—831no—
422#1445—831no—
423#1445D8311yescharacteristic
424#1442—831no—
425#1442—831no—
426#1436—831no—
427#1436—831no—
428#1436—831no—
429#1436—831no—
430C4⋊#95—831no—
431#1434—831no—
432#1434—831no—
433#1434—831no—
434C4×#95—831no—
435C4×#95—831no—
436C83#1409311yescharacteristic, complemented, Sylow
437C22×C4⋊C4—831no—
438C22×C4⋊C4—831no—
439C22×C4⋊C4—831no—
440C22×C4⋊C4C2×D8311yescharacteristic
441C22×C42—831no—
442C22×C42—831no—
443C22×C42—831no—
444C22×C42—831no—
445C22×C42—831no—
446#387—838no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—831no—
452C2×#95—831no—
453C2×#95—831no—
454C2×#95—831no—
455C2×#95—831no—
456C2×#95—831no—
457C2×#95—831no—
458C2×#95—831no—
459C2×#95—831no—
460C2×#95—831no—
461C2×#95—831no—
462C2×#95—831no—
463C2×#95—831no—
464C2×#95—831no—
465C2×#95—831no—
466C2×#95—831no—
467C2×#95C2×D8311yescharacteristic
468C2×#95C2×D8311yescharacteristic
469C2×#95C2×D8311yescharacteristic
470C2×#95C2×D8311yescharacteristic
471C2×#95C2×D8311yescharacteristic
472C2×#95C2×D8311yescharacteristic
473C23×C4—831no—
474C23×C4—831no—
475C23×C4—831no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—831no—
480C23×C4—831no—
481C23×C4C22×D8311yescharacteristic
482C23×C4C22×D8311yescharacteristic
483C23×C4C22×D8311yescharacteristic
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8311yescharacteristic
486C23×C4C22×D8311yescharacteristic
487C23×C4C22×D8311yescharacteristic
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—3321no—
491C2×C4⋊C4—3321no—
492C2×C4⋊C4—3321no—
493C2×C4⋊C4—3321no—
494C2×C4⋊C4—834no—
495C2×C4⋊C4—1662no—
496C2×C4⋊C4—1662no—
497C2×C4⋊C4—1662no—
498C2×C4⋊C4—1662no—
499C2×C4⋊C4C4×D8314yes—
500C2×C42—3321no—
501C2×C42—3321no—
502C2×C42—3321no—
503C2×C42—3321no—
504C2×C42—3321no—
505C2×C42—3321no—
506C2×C42—3321no—
507C2×C42—3321no—
508C2×C42—834no—
509C2×C42—834no—
510C2×C42—1662no—
511C2×C42—1662no—
512C2×C42—1662no—
513C2×C42—1662no—
514C2×C42—1662no—
515#95—22no—
516#95—22no—
517#95—22no—
518#95—22no—
519#95—41no—
520#95—41no—
521#95—3321no—
522#95—3321no—
523#95—3321no—
524#95—3321no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—1662no—
530#95—1662no—
531#95—1662no—
532#95—1662no—
533#95—1662no—
534#95—1662no—
535#95—1662no—
536#95—1662no—
537#95—1662no—
538#95—1662no—
539#95—1662no—
540#95—1662no—
541C24C23×D8311yescharacteristic
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—832no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—832no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—832no—
592C22×C4—832no—
593C22×C4—832no—
594C22×C4—1661no—
595C22×C4—1661no—
596C22×C4—1661no—
597C22×C4—1661no—
598C22×C4—1661no—
599C22×C4—1661no—
600C22×C4—1661no—
601C22×C4—1661no—
602C22×C4—1661no—
603C22×C4—1661no—
604C22×C4—1661no—
605C22×C4—1661no—
606C22×C4—1661no—
607C22×C4—1661no—
608C22×C4—1661no—
609C22×C4—1661no—
610C22×C4—1661no—
611C22×C4—1661no—
612C22×C4—1661no—
613C22×C4—1661no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1661no—
617C22×C4—1661no—
618C22×C4—1661no—
619C22×C4—1661no—
620C22×C4—1661no—
621C22×C4—1661no—
622C22×C4—1661no—
623C22×C4—1661no—
624C22×C4—1661no—
625C22×C4—1661no—
626C22×C4—1661no—
627C22×C4—1661no—
628C22×C4—1661no—
629C22×C4—1661no—
630C22×C4—1661no—
631C22×C4—1661no—
632C22×C4—1661no—
633C22×C4—1661no—
634C22×C4—1661no—
635C22×C4—1661no—
636C22×C4—1661no—
637C22×C4—1661no—
638C22×C4—1661no—
639C22×C4C2×C4×D8312yes—
640C22×C4C2×C4×D8312yes—
641C22×C4C2×C4×D8312yes—
642C22×C4Q8×D8312yes—
643C22×C4#1305058912yes—
644C22×C4#1305058912yes—
645C22×C4#1305058912yes—
646C22×C4#1305059112yes—
647C4⋊C4—28no—
648C4⋊C4—3324no—
649C4⋊C4—3324no—
650C4⋊C4—3324no—
651C42—3324no—
652C42—3324no—
653C42—3324no—
654C42—3324no—
655C42—3324no—
656C23C22×C4×D8311yescharacteristic
657C23C2×Q8×D8311yescharacteristic
658C23#41×D8311yescharacteristic
659C23#41×D8311yescharacteristic
660C23#41×D8311yescharacteristic
661C23#41×D8311yescharacteristic
662C23#41×D8311yescharacteristic
663C23C2×#1305058911yescharacteristic
664C23C2×#1305058911yescharacteristic
665C23C2×#1305058911yescharacteristic
666C23C2×#1305059111yescharacteristic
667C23#1458183711yescharacteristic
668C23#1458183811yescharacteristic
669C23#1458183811yescharacteristic
670C23#1458183911yescharacteristic
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—3321no—
720C2×C4—3321no—
721C2×C4—3321no—
722C2×C4—3321no—
723C2×C4—3321no—
724C2×C4—3321no—
725C2×C4—3321no—
726C2×C4—3321no—
727C2×C4—3321no—
728C2×C4—3321no—
729C2×C4—3321no—
730C2×C4—3321no—
731C2×C4—3321no—
732C2×C4—3321no—
733C2×C4—3321no—
734C2×C4—3321no—
735C2×C4—3321no—
736C2×C4—3321no—
737C2×C4—3321no—
738C2×C4—3321no—
739C2×C4—3321no—
740C2×C4—3321no—
741C2×C4—3321no—
742C2×C4—3321no—
743C2×C4—3321no—
744C2×C4—3321no—
745C2×C4—3321no—
746C2×C4—834no—
747C2×C4—834no—
748C2×C4—1662no—
749C2×C4—1662no—
750C2×C4—1662no—
751C2×C4—1662no—
752C2×C4—1662no—
753C2×C4—1662no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1662no—
767C2×C4—1662no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4—1662no—
773C2×C4—1662no—
774C2×C4—1662no—
775C2×C4#1458174814yes—
776C22C2×#1458174811yescharacteristic
777C22C4×Q8×D8311yescharacteristic
778C22C4×#1305058911yescharacteristic
779C22#1912816911yescharacteristic
780C22C4×#1305059111yescharacteristic
781C22#1912817311yescharacteristic
782C22#1912818111yescharacteristic
783C22#125×D8311yescharacteristic
784C22#1912822811yescharacteristic
785C22#1912823011yescharacteristic
786C22#1912823411yescharacteristic
787C22#1912823711yescharacteristic
788C22#1912825311yescharacteristic
789C22#1912825311yescharacteristic
790C22#1912825611yescharacteristic
791C22#1912829011yescharacteristic
792C22#1912829411yescharacteristic
793C22#1912832611yescharacteristic
794C22#1912833111yescharacteristic
795C22#1912837411yescharacteristic
796C22#1912837411yescharacteristic
797C22#1912837411yescharacteristic
798C22#1912837811yescharacteristic
799C22#1912838811yescharacteristic
800C22#1912838811yescharacteristic
801C22#1912839311yescharacteristic
802C22#1912839811yescharacteristic
803C22#1912840211yescharacteristic
804C22#1912840311yescharacteristic
805C22#1912840411yescharacteristic
806C22#1912840411yescharacteristic
807C22#1912841811yescharacteristic
808C22#1912843311yescharacteristic
809C22#1912843511yescharacteristic
810C22#1912843711yescharacteristic
811C4—24no—
812C4—42no—
813C4—42no—
814C4—42no—
815C4—42no—
816C4—42no—
817C4—81no—
818C4—3322no—
819C4—3322no—
820C4—3322no—
821C4—3322no—
822C4—3322no—
823C4—6641no—
824C4—1664no—
825C4—1664no—
826C2#2490993811yescharacteristic
827C2#2491002011yescharacteristic
828C2#2491019011yescharacteristic
829C2#2491032511yescharacteristic
830C2#2491043511yescharacteristic
831C2#2491058211yescharacteristic
832C2#2491059511yescharacteristic
833C2#2491268111yescharacteristic
834C2#2491269011yescharacteristic
835C2#2491275311yescharacteristic
836C2#2491280011yescharacteristic
837C2#2491297711yescharacteristic
838C2#2491299411yescharacteristic
839C2#2491311411yescharacteristic
840C2#2491312511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1445C2
socle, prime radical, cosocleC24×C83C24
hypercenter#1445D83
hypocenterC83#14093
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
24. #19127587C4semidirect
436. C83#14093semidirect

Maximal subgroups

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

subgroupindex
C2×#191275872
#249057322
#249057212
#249057192
#249056982
#249056972
#249056942
#249056922
#249056872
#95×Dic832
C83×#14452
#1409383