Finite Group Databasebeta

← #35335352

Subgroups — #35335352

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×#19127613C211yesmaximal, characteristic
2#24905733C211yesmaximal, characteristic, complemented
3#24905733C211yesmaximal, characteristic, complemented
4#24905724C211yesmaximal, characteristic, complemented
5#24905723C211yesmaximal, characteristic, complemented
6#24905721C211yesmaximal, characteristic, complemented
7#24905719C211yesmaximal, characteristic, complemented
8#24905710C211yesmaximal, characteristic
9#24905710C211yesmaximal, characteristic
10#24905708C211yesmaximal, characteristic
11#24905706C211yesmaximal, characteristic
12#24905700C211yesmaximal, characteristic
13#24905698C211yesmaximal, characteristic, complemented
14#24905697C211yesmaximal, characteristic, complemented
15C83×#1440C211yesmaximal, characteristic
16C23×Dic166C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24#19127613C418yescomplemented
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×C22⋊C4×C83C2211yescharacteristic
46C22×C22⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C2×#95×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C22×Dic166—41no—
53C22×Dic166—41no—
54C22×Dic166—41no—
55C22×Dic166—41no—
56C22×Dic166—41no—
57C22×Dic166—41no—
58C22×Dic166C2×C414yes—
59C23×Dic83C2311yescharacteristic
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×Dic83⋊C4—22no—
71C2×Dic83⋊C4—41no—
72C2×Dic83⋊C4—41no—
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⋊Dic83C2×C414yes—
84C2×C22⋊Dic83C2×C414yes—
85C2×C4×Dic83—41no—
86C2×C4×Dic83—41no—
87C2×C4×Dic83—41no—
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⋊#95C2×C414yes—
106C83⋊#95C2×C414yes—
107C83⋊#95C2×C414yes—
108C25×C83C2311yescharacteristic
109C23×C4×C83C2311yescharacteristic
110C23×C4×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C2×C22⋊C4×C83—22no—
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×C83—41no—
123C2×C22⋊C4×C83C2×C414yes—
124#95×C83—22no—
125#95×C83—41no—
126#95×C83—41no—
127#95×C83—41no—
128C2×Dic166—44no—
129C2×Dic166—44no—
130C2×Dic166—44no—
131C2×Dic166—44no—
132C2×Dic166—44no—
133C2×Dic166—44no—
134C2×Dic166—44no—
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—21no—
183C22×Dic83—21no—
184C22×Dic83—21no—
185C22×Dic83—21no—
186C22×Dic83C22×C412yes—
187C22×Dic83C22×C412yes—
188C22×Dic83C22×C412yes—
189C22×Dic83C22×C412yes—
190C22×Dic83#4112yes—
191C4⋊Dic83—44no—
192Dic83⋊C4—44no—
193C22⋊Dic83—44no—
194C22⋊Dic83—44no—
195C22⋊Dic83—44no—
196C22⋊Dic83—44no—
197C4×Dic83—44no—
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×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83C22×C412yes—
213C24×C83C2411yescharacteristic
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×C83C22×C412yes—
254C22×C4×C83C22×C412yes—
255C22×C4×C83#4112yes—
256C22⋊C4×C83—44no—
257C22⋊C4×C83—44no—
258C22⋊C4×C83—44no—
259C23×C83—22no—
260C23×C83—22no—
261C23×C83—22no—
262C23×C83—22no—
263C23×C83—22no—
264C23×C83—22no—
265C23×C83—22no—
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×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83C23×C411yescharacteristic
295C23×C83C2×#4111yescharacteristic
296C23×C83C2×#4111yescharacteristic
297C23×C83H(5,𝔽2)11yescharacteristic
298C23×C83H(5,𝔽2)11yescharacteristic
299C23×C83H(5,𝔽2)11yescharacteristic
300C23×C83H(5,𝔽2)11yescharacteristic
301C23×C83H(5,𝔽2)11yescharacteristic
302C23×C83H(5,𝔽2)11yescharacteristic
303C23×C83H(5,𝔽2)11yescharacteristic
304C23×C83H(5,𝔽2)11yescharacteristic
305C23×C832−1+411yescharacteristic
306C23×C832−1+411yescharacteristic
307C23×C832−1+411yescharacteristic
308C23×C832−1+411yescharacteristic
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—41no—
319C2×C4×C83—41no—
320C2×C4×C83—41no—
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×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
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—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—
403C2×Dic83—41no—
404C2×Dic83—41no—
405C2×Dic83—41no—
406C2×Dic83—41no—
407Dic166—416no—
408C22×C83—42no—
409C22×C83—42no—
410C22×C83—42no—
411C22×C83—42no—
412C22×C83—42no—
413C22×C83—42no—
414C22×C83—42no—
415C22×C83—81no—
416C22×C83—81no—
417C22×C83—81no—
418C22×C83—81no—
419C22×C83—81no—
420C22×C83—81no—
421C22×C83—81no—
422C22×C83—81no—
423C22×C83C4×#4111yescharacteristic
424C22×C83#51811yescharacteristic
425C22×C83#51811yescharacteristic
426C22×C83#51811yescharacteristic
427C22×C83#51911yescharacteristic
428C22×C83#52011yescharacteristic
429C22×C83#52011yescharacteristic
430C22×C83#53811yescharacteristic
431C22×C83#53811yescharacteristic
432C22×C83#53811yescharacteristic
433C22×C83#53811yescharacteristic
434C22×C83#53911yescharacteristic
435C22×C83#53911yescharacteristic
436C22×C83#54211yescharacteristic
437C22×C83#54211yescharacteristic
438C22×C83#54211yescharacteristic
439C22×C83#54211yescharacteristic
440C22×C83#54211yescharacteristic
441C22×C83#54211yescharacteristic
442C22×C83#56011yescharacteristic
443C22×C83#56011yescharacteristic
444C22×C83#56011yescharacteristic
445C22×C83H(3,𝔽4)11yescharacteristic
446C22×C83H(3,𝔽4)11yescharacteristic
447C22×C83#56211yescharacteristic
448C22×C83#56211yescharacteristic
449C22×C83#56211yescharacteristic
450C22×C83#56211yescharacteristic
451C22×C83#56211yescharacteristic
452C22×C83#56211yescharacteristic
453C22×C83#56311yescharacteristic
454C22×C83#56311yescharacteristic
455C22×C83#56311yescharacteristic
456C22×C83#56311yescharacteristic
457C22×C83#56311yescharacteristic
458C4×C83—42no—
459C4×C83—42no—
460C4×C83—42no—
461C4×C83—81no—
462C4×C83—81no—
463C4×C83—81no—
464Dic83—42no—
465Dic83—42no—
466Dic83—42no—
467Dic83—42no—
468Dic83—42no—
469Dic83—81no—
470Dic83—81no—
471Dic83—81no—
472#14649—831nomaximal, Sylow
473C2×C83—82no—
474C2×C83#233211yescharacteristic
475C2×C83#233711yescharacteristic
476C2×C83#233711yescharacteristic
477C2×C83#237511yescharacteristic
478C2×C83#237811yescharacteristic
479C2×C83#237811yescharacteristic
480C2×C83#237911yescharacteristic
481C2×C83#282411yescharacteristic
482C2×C83#282411yescharacteristic
483C2×C83#283011yescharacteristic
484C2×C83#283011yescharacteristic
485C2×C83#283211yescharacteristic
486C2×C83#283211yescharacteristic
487C2×C83#283811yescharacteristic
488C2×C83#283811yescharacteristic
489C2×#393—831no—
490#1446—831no—
491#1446—831no—
492#1443—831no—
493#1443—831no—
494#1442—831no—
495#1442—831no—
496#1440—831no—
497#1440—831no—
498#1440D8311yescharacteristic
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⋊C4—831no—
508C22×C22⋊C4—831no—
509C22×C22⋊C4—831no—
510C22×C22⋊C4—831no—
511C22×C22⋊C4—831no—
512C22×C22⋊C4C2×D8311yescharacteristic
513C22×C22⋊C4C2×D8311yescharacteristic
514C22×C22⋊C4C2×D8311yescharacteristic
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×#95—831no—
536C2×#95—831no—
537C2×#95C2×D8311yescharacteristic
538C2×#95C2×D8311yescharacteristic
539C2×#95C2×D8311yescharacteristic
540C2×#95C2×D8311yescharacteristic
541C25C22×D8311yescharacteristic
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×C4—831no—
557C23×C4C22×D8311yescharacteristic
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8311yescharacteristic
561C23×C4C22×D8311yescharacteristic
562C23×C4C22×D8311yescharacteristic
563C2×C4⋊C4—3321no—
564C2×C4⋊C4—3321no—
565C2×C4⋊C4—3321no—
566C2×C4⋊C4—3321no—
567C2×C4⋊C4—1662no—
568C2×C4⋊C4—1662no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C22⋊C4—41no—
576C2×C22⋊C4—41no—
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—3321no—
586C2×C22⋊C4—834no—
587C2×C22⋊C4—834no—
588C2×C22⋊C4—1662no—
589C2×C22⋊C4C4×D8314yes—
590C2×C42—3321no—
591C2×C42—3321no—
592C2×C42—3321no—
593#95—22no—
594#95—41no—
595#95—41no—
596#95—41no—
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—3321no—
608#95—3321no—
609#95—3321no—
610#95—3321no—
611#95—3321no—
612#95—3321no—
613#95—834no—
614#95—834no—
615#95—834no—
616#95—1662no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24—21no—
631C24C2×C4×D8312yes—
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—832no—
680C22×C4—832no—
681C22×C4—832no—
682C22×C4—832no—
683C22×C4—832no—
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×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×C4C2×C4×D8312yes—
736C22×C4C2×C4×D8312yes—
737C22×C4#1305058912yes—
738C4⋊C4—3324no—
739C4⋊C4—3324no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—3324no—
744C22⋊C4—3324no—
745C22⋊C4—3324no—
746C22⋊C4—3324no—
747C42—3324no—
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
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—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23C22×C4×D8311yescharacteristic
784C23#41×D8311yescharacteristic
785C23C2×#1305058911yescharacteristic
786C23#1458183711yescharacteristic
787C23#1458183711yescharacteristic
788C23#1458183711yescharacteristic
789C23#1458183711yescharacteristic
790C23#1458183711yescharacteristic
791C23#1458183811yescharacteristic
792C23#1458183811yescharacteristic
793C23#1458183811yescharacteristic
794C23#1458183911yescharacteristic
795C23#1458183911yescharacteristic
796C23#1458183911yescharacteristic
797C23#1458183911yescharacteristic
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—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—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—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—3321no—
882C2×C4—1662no—
883C2×C4—1662no—
884C2×C4—1662no—
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—42no—
898C22—42no—
899C22—42no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22C4×#1305058911yescharacteristic
913C22#1912817311yescharacteristic
914C22#1912817311yescharacteristic
915C22#1912817411yescharacteristic
916C22#1912817811yescharacteristic
917C22#1912818011yescharacteristic
918C22#1912818111yescharacteristic
919C22#1912828311yescharacteristic
920C22#1912828611yescharacteristic
921C22#1912828811yescharacteristic
922C22#1912829011yescharacteristic
923C22#1912829211yescharacteristic
924C22#1912829511yescharacteristic
925C22#1912831511yescharacteristic
926C22#1912831811yescharacteristic
927C22#1912831811yescharacteristic
928C22#1912831911yescharacteristic
929C22#1912831911yescharacteristic
930C22#1912832011yescharacteristic
931C22#1912843911yescharacteristic
932C22#1912843911yescharacteristic
933C22#1912844111yescharacteristic
934C22#1912844311yescharacteristic
935C22#1912844411yescharacteristic
936C22#1912844611yescharacteristic
937C22#1912844611yescharacteristic
938C22#1912844811yescharacteristic
939C22#1912844811yescharacteristic
940C22#1912844811yescharacteristic
941C22#1912844811yescharacteristic
942C22#1912845111yescharacteristic
943C22#1912845311yescharacteristic
944C22#1912845311yescharacteristic
945C22#1912845411yescharacteristic
946C22#1912845411yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—81no—
951C4—81no—
952C4—81no—
953C4—3322no—
954C4—3322no—
955C4—3322no—
956C4—3322no—
957C4—3322no—
958C4—6641no—
959C4—6641no—
960C4—6641no—
961C2—82no—
962C2#2491022011yescharacteristic
963C2#2491027011yescharacteristic
964C2#2491027211yescharacteristic
965C2#2491060111yescharacteristic
966C2#2491062311yescharacteristic
967C2#2491063111yescharacteristic
968C2#2491063211yescharacteristic
969C2#2491554111yescharacteristic
970C2#2491554611yescharacteristic
971C2#2491560811yescharacteristic
972C2#2491560911yescharacteristic
973C2#2491562911yescharacteristic
974C2#2491563411yescharacteristic
975C2#2491569111yescharacteristic
976C2#2491569611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1440C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenter#1440D83
hypocenterC83#14649
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. #24905733C2semidirect
3. #24905733C2semidirect
4. #24905724C2semidirect
5. #24905723C2semidirect
6. #24905721C2semidirect
7. #24905719C2semidirect
13. #24905698C2semidirect
14. #24905697C2semidirect
24. #19127613C4semidirect
504. C83#14649semidirect

Maximal subgroups

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

subgroupindex
C2×#191276132
#249057332
#249057242
#249057232
#249057212
#249057192
#249057102
#249057082
#249057062
#249057002
#249056982
#249056972
C83×#14402
#1464983