Finite Group Databasebeta

← #35334767

Subgroups — #35334767

Order 21248.

1506 conjugacy classes of subgroups.

The subgroup lattice has 1000 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#24905724C211yesmaximal, characteristic, complemented
6#24905706C211yesmaximal, characteristic
7#24905700C211yesmaximal, characteristic
8#24905696C211yesmaximal, characteristic, complemented
9#24905694C211yesmaximal, characteristic, complemented
10#24905690C211yesmaximal, characteristic, complemented
11#24905689C211yesmaximal, characteristic, complemented
12#24905685C211yesmaximal, characteristic
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C83×#1437C211yesmaximal, characteristic
16C23×Dic166C2211yescharacteristic
17C24×Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×C22⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C4×Dic83C2211yescharacteristic
23#19127613C418yescomplemented
24C2×C83⋊#95C2211yescharacteristic
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
48C22×C42×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×C414yescomplemented
59C23×Dic83—22no—
60C23×Dic83—22no—
61C23×Dic83—22no—
62C23×Dic83—41no—
63C23×Dic83—41no—
64C23×Dic83—41no—
65C23×Dic83—41no—
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
69C23×Dic83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C2×Dic83⋊C4—22no—
75C2×Dic83⋊C4—22no—
76C2×Dic83⋊C4—41no—
77C2×C22⋊Dic83—22no—
78C2×C22⋊Dic83—22no—
79C2×C22⋊Dic83—41no—
80C2×C22⋊Dic83—41no—
81C2×C22⋊Dic83—41no—
82C2×C22⋊Dic83—41no—
83C2×C22⋊Dic83—41no—
84C2×C22⋊Dic83C2×C414yes—
85C2×C22⋊Dic83C2×C414yes—
86C2×C4×Dic83—22no—
87C2×C4×Dic83—41no—
88C2×C4×Dic83—41no—
89C83⋊#95—22no—
90C83⋊#95—22no—
91C83⋊#95—22no—
92C83⋊#95—22no—
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—
106C83⋊#95—41no—
107C83⋊#95C2×C414yescomplemented
108C83⋊#95C2×C414yescomplemented
109C83⋊#95C2×C414yescomplemented
110C25×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C2×C22⋊C4×C83—22no—
118C2×C22⋊C4×C83—22no—
119C2×C22⋊C4×C83—41no—
120C2×C22⋊C4×C83—41no—
121C2×C22⋊C4×C83—41no—
122C2×C22⋊C4×C83—41no—
123C2×C22⋊C4×C83—41no—
124C2×C22⋊C4×C83C2×C414yes—
125C2×C22⋊C4×C83Q814yescomplemented
126C2×C42×C83—22no—
127C2×C42×C83—41no—
128C2×C42×C83—41no—
129#95×C83—41no—
130#95×C83—41no—
131#95×C83—41no—
132C2×Dic166—44no—
133C2×Dic166—44no—
134C2×Dic166—44no—
135C2×Dic166—44no—
136C2×Dic166—44no—
137C2×Dic166—44no—
138C2×Dic166—44no—
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×Dic83—21no—
187C22×Dic83—21no—
188C22×Dic83—44no—
189C22×Dic83—44no—
190C22×Dic83—44no—
191C22×Dic83—44no—
192C22×Dic83—44no—
193C22×Dic83—44no—
194C22×Dic83—44no—
195C22×Dic83C22×C412yes—
196C22×Dic83C22×C412yes—
197C22×Dic83C22×C412yes—
198C22×Dic83C22×C412yes—
199C22×Dic83#4112yes—
200C22×Dic83#4112yes—
201C22×Dic83#4112yes—
202Dic83⋊C4—44no—
203C22⋊Dic83—44no—
204C22⋊Dic83—44no—
205C22⋊Dic83—44no—
206C4×Dic83—44no—
207C24×C83—21no—
208C24×C83—21no—
209C24×C83—21no—
210C24×C83—21no—
211C24×C83—21no—
212C24×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83—21no—
217C24×C83—21no—
218C24×C83—21no—
219C24×C83C22×C412yes—
220C24×C83C2×Q812yes—
221C24×C83#4112yes—
222C24×C83C2411yescharacteristic
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×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83C22×C412yes—
261C22×C4×C83C22×C412yes—
262C22×C4×C83C2×Q812yes—
263C22×C4×C83C2×Q812yes—
264C22×C4×C83#4112yes—
265C22⋊C4×C83—44no—
266C22⋊C4×C83—44no—
267C22⋊C4×C83—44no—
268C42×C83—44no—
269C23×C83—22no—
270C23×C83—22no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—22no—
278C23×C83—22no—
279C23×C83—22no—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—22no—
285C23×C83—22no—
286C23×C83—22no—
287C23×C83—41no—
288C23×C83—41no—
289C23×C83—41no—
290C23×C83—41no—
291C23×C83—41no—
292C23×C83—41no—
293C23×C83—41no—
294C23×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83—41no—
302C23×C83—41no—
303C23×C83C4×Q814yes—
304C23×C83C23×C411yescharacteristic
305C23×C83C22×Q811yescharacteristic
306C23×C83C2×#4111yescharacteristic
307C23×C83C2×#4111yescharacteristic
308C23×C83C2×#4111yescharacteristic
309C23×C83C2×#4111yescharacteristic
310C23×C83C2×#4111yescharacteristic
311C23×C83H(5,𝔽2)11yescharacteristic
312C23×C83H(5,𝔽2)11yescharacteristic
313C23×C83H(5,𝔽2)11yescharacteristic
314C23×C83H(5,𝔽2)11yescharacteristic
315C23×C83H(5,𝔽2)11yescharacteristic
316C23×C83H(5,𝔽2)11yescharacteristic
317C23×C83H(5,𝔽2)11yescharacteristic
318C23×C832−1+411yescharacteristic
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
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×C4×C83—41no—
359C2×C4×C83—41no—
360C2×C4×C83—41no—
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—22no—
371C2×Dic83—22no—
372C2×Dic83—22no—
373C2×Dic83—22no—
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—416no—
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—
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—
418Dic166—416no—
419C22×C83—24no—
420C22×C83—24no—
421C22×C83—24no—
422C22×C83—42no—
423C22×C83—42no—
424C22×C83—42no—
425C22×C83—42no—
426C22×C83—42no—
427C22×C83—42no—
428C22×C83—42no—
429C22×C83—42no—
430C22×C83—42no—
431C22×C83—42no—
432C22×C83—42no—
433C22×C83—42no—
434C22×C83C2×C4×Q811yescharacteristic
435C22×C83C4×#4111yescharacteristic
436C22×C83C4×#4111yescharacteristic
437C22×C83#51811yescharacteristic
438C22×C83#51811yescharacteristic
439C22×C83#51811yescharacteristic
440C22×C83#52011yescharacteristic
441C22×C83#53811yescharacteristic
442C22×C83#53811yescharacteristic
443C22×C83#53811yescharacteristic
444C22×C83#53811yescharacteristic
445C22×C83#53811yescharacteristic
446C22×C83#53911yescharacteristic
447C22×C83#54211yescharacteristic
448C22×C83#54211yescharacteristic
449C22×C83#54211yescharacteristic
450C22×C83#54211yescharacteristic
451C22×C83#54311yescharacteristic
452C22×C83#54411yescharacteristic
453C22×C83#55111yescharacteristic
454C22×C83#55111yescharacteristic
455C22×C83#55111yescharacteristic
456C22×C83#55111yescharacteristic
457C22×C83#55111yescharacteristic
458C22×C83#55111yescharacteristic
459C22×C83#55411yescharacteristic
460C22×C83#55411yescharacteristic
461C22×C83#55411yescharacteristic
462C22×C83#55411yescharacteristic
463C22×C83#55511yescharacteristic
464C22×C83#55511yescharacteristic
465C22×C83#56011yescharacteristic
466C22×C83#56011yescharacteristic
467C22×C83#56011yescharacteristic
468C22×C83H(3,𝔽4)11yescharacteristic
469C4×C83—42no—
470C4×C83—42no—
471C4×C83—42no—
472C4×C83—42no—
473C4×C83—42no—
474C4×C83—81no—
475Dic83—42no—
476Dic83—42no—
477Dic83—42no—
478Dic83—42no—
479Dic83—42no—
480Dic83—42no—
481Dic83—42no—
482Dic83—81no—
483#14596—831nomaximal, Sylow
484C2×C83—44no—
485C2×C83#232911yescharacteristic
486C2×C83#233711yescharacteristic
487C2×C83#233711yescharacteristic
488C2×C83#236811yescharacteristic
489C2×C83#236811yescharacteristic
490C2×C83#237211yescharacteristic
491C2×C83#237511yescharacteristic
492C2×C83#273611yescharacteristic
493C2×C83#273711yescharacteristic
494C2×C83#273711yescharacteristic
495C2×C83#274211yescharacteristic
496C2×C83#276011yescharacteristic
497C2×C83#276311yescharacteristic
498C2×C83#278411yescharacteristic
499C2×C83#278411yescharacteristic
500C2×#393—831no—
501#1446—831no—
502#1446—831no—
503#1443—831no—
504#1443—831no—
505#1439—831no—
506#1437—831no—
507#1437D8311yescharacteristic
508#1436—831no—
509#1436—831no—
510#1434—831no—
511#1434—831no—
512C22⋊#95—831no—
513C22⋊#95—831no—
514C22⋊#95—831no—
515C83#1459611yescharacteristic, complemented, Sylow
516C23×Q8—831no—
517C24×C4—831no—
518C22×C4⋊C4—831no—
519C22×C22⋊C4—831no—
520C22×C22⋊C4—831no—
521C22×C22⋊C4—831no—
522C22×C22⋊C4C2×D8311yescharacteristic
523C22×C22⋊C4C2×D8311yescharacteristic
524C22×C22⋊C4C2×D8311yescharacteristic
525C22×C42—831no—
526C22×C42C2×D8311yescharacteristic
527#393—838no—
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×#95—831no—
538C2×#95—831no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95—831no—
544C2×#95—831no—
545C2×#95—831no—
546C2×#95—831no—
547C2×#95—831no—
548C2×#95—831no—
549C2×#95C2×D8311yescharacteristic
550C2×#95C2×D8311yescharacteristic
551C2×#95C2×D8311yescharacteristic
552C25C22×D8311yescharacteristic
553C22×Q8—3321no—
554C22×Q8—3321no—
555C22×Q8—3321no—
556C22×Q8—3321no—
557C22×Q8—3321no—
558C22×Q8—3321no—
559C22×Q8—834no—
560C23×C4—3321no—
561C23×C4—3321no—
562C23×C4—3321no—
563C23×C4—3321no—
564C23×C4—831no—
565C23×C4—831no—
566C23×C4—831no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—831no—
570C23×C4—831no—
571C23×C4—831no—
572C23×C4—1662no—
573C23×C4—1662no—
574C23×C4—1662no—
575C23×C4C22×D8311yescharacteristic
576C23×C4C22×D8311yescharacteristic
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8311yescharacteristic
579C23×C4C22×D8311yescharacteristic
580C23×C4C22×D8311yescharacteristic
581C2×C4⋊C4—3321no—
582C2×C4⋊C4—1662no—
583C2×C4⋊C4—1662no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—41no—
587C2×C22⋊C4—41no—
588C2×C22⋊C4—41no—
589C2×C22⋊C4—41no—
590C2×C22⋊C4—41no—
591C2×C22⋊C4—3321no—
592C2×C22⋊C4—3321no—
593C2×C22⋊C4—3321no—
594C2×C22⋊C4—3321no—
595C2×C22⋊C4—3321no—
596C2×C22⋊C4—834no—
597C2×C22⋊C4—834no—
598C2×C22⋊C4—1662no—
599C2×C22⋊C4—1662no—
600C2×C22⋊C4Dic16614yescomplemented
601C2×C22⋊C4C4×D8314yes—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—3321no—
606C2×C42—3321no—
607C2×C42—1662no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95—3321no—
612#95—3321no—
613#95—3321no—
614#95—3321no—
615#95—3321no—
616#95—3321no—
617#95—3321no—
618#95—3321no—
619#95—3321no—
620#95—3321no—
621#95—3321no—
622#95—3321no—
623#95—3321no—
624#95—3321no—
625#95—834no—
626#95—834no—
627#95—834no—
628#95—1662no—
629#95—1662no—
630#95—1662no—
631#95—1662no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×C4×D8312yes—
645C24C2×Dic16612yes—
646C24#1305059012yes—
647C24C23×D8311yescharacteristic
648C2×Q8—3324no—
649C2×Q8—3324no—
650C2×Q8—3324no—
651C2×Q8—3324no—
652C2×Q8—3324no—
653C2×Q8—3324no—
654C2×Q8—3324no—
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—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—3324no—
693C22×C4—3324no—
694C22×C4—3324no—
695C22×C4—3324no—
696C22×C4—3324no—
697C22×C4—3324no—
698C22×C4—3324no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—832no—
703C22×C4—832no—
704C22×C4—832no—
705C22×C4—832no—
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×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×C4C2×C4×D8312yes—
756C22×C4C2×C4×D8312yes—
757C22×C4C2×Dic16612yes—
758C22×C4C2×Dic16612yes—
759C22×C4#1305058912yes—
760C4⋊C4—3324no—
761C22⋊C4—44no—
762C22⋊C4—44no—
763C22⋊C4—44no—
764C22⋊C4—3324no—
765C22⋊C4—3324no—
766C22⋊C4—3324no—
767C42—44no—
768C42—3324no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23C4×Dic16614yes—
804C23C22×C4×D8311yescharacteristic
805C23C22×Dic16611yescharacteristic
806C23#41×D8311yescharacteristic
807C23#41×D8311yescharacteristic
808C23#41×D8311yescharacteristic
809C23C2×#1305058911yescharacteristic
810C23C2×#1305059011yescharacteristic
811C23#1458183711yescharacteristic
812C23#1458183711yescharacteristic
813C23#1458183711yescharacteristic
814C23#1458183711yescharacteristic
815C23#1458183711yescharacteristic
816C23#1458183811yescharacteristic
817C23#1458183811yescharacteristic
818C23#1458183911yescharacteristic
819Q8—33216no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
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—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—33216no—
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—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—1662no—
899C2×C4—1662no—
900C2×C4—1662no—
901C2×C4—1662no—
902C2×C4—1662no—
903C2×C4—1662no—
904C2×C4—1662no—
905C2×C4—1662no—
906C2×C4—1662no—
907C2×C4—1662no—
908C2×C4—1662no—
909C2×C4—1662no—
910C2×C4—1662no—
911C2×C4—1662no—
912C2×C4—1662no—
913C2×C4—1662no—
914C2×C4—1662no—
915C2×C4—1662no—
916C2×C4—1662no—
917C2×C4—1662no—
918C2×C4—1662no—
919C22—24no—
920C22—24no—
921C22—24no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22C2×C4×Dic16611yescharacteristic
935C22C4×#1305058911yescharacteristic
936C22#1912816911yescharacteristic
937C22#1912817311yescharacteristic
938C22#1912817311yescharacteristic
939C22#1912817411yescharacteristic
940C22#1912818011yescharacteristic
941C22#1912828311yescharacteristic
942C22#1912828311yescharacteristic
943C22#1912828411yescharacteristic
944C22#1912828611yescharacteristic
945C22#1912828711yescharacteristic
946C22#1912829311yescharacteristic
947C22#1912831511yescharacteristic
948C22#1912831711yescharacteristic
949C22#1912831811yescharacteristic
950C22#1912831911yescharacteristic
951C22#1912832711yescharacteristic
952C22#1912832911yescharacteristic
953C22#1912837411yescharacteristic
954C22#1912837511yescharacteristic
955C22#1912837611yescharacteristic
956C22#1912837711yescharacteristic
957C22#1912838011yescharacteristic
958C22#1912838011yescharacteristic
959C22#1912840811yescharacteristic
960C22#1912841011yescharacteristic
961C22#1912841011yescharacteristic
962C22#1912841011yescharacteristic
963C22#1912841311yescharacteristic
964C22#1912841511yescharacteristic
965C22#1912843811yescharacteristic
966C22#1912843911yescharacteristic
967C22#1912843911yescharacteristic
968C22#1912844311yescharacteristic
969C4—42no—
970C4—42no—
971C4—42no—
972C4—42no—
973C4—42no—
974C4—81no—
975C4—3322no—
976C4—3322no—
977C4—3322no—
978C4—3322no—
979C4—3322no—
980C4—3322no—
981C4—3322no—
982C4—6641no—
983C2—44no—
984C2#2491019111yescharacteristic
985C2#2491027211yescharacteristic
986C2#2491027411yescharacteristic
987C2#2491054111yescharacteristic
988C2#2491054611yescharacteristic
989C2#2491057011yescharacteristic
990C2#2491060011yescharacteristic
991C2#2491450811yescharacteristic
992C2#2491451211yescharacteristic
993C2#2491451611yescharacteristic
994C2#2491458911yescharacteristic
995C2#2491483911yescharacteristic
996C2#2491487911yescharacteristic
997C2#2491516111yescharacteristic
998C2#2491516411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1437C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenter#1437D83
hypocenterC83#14596
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. #24905733C2semidirect
3. #24905733C2semidirect
4. #24905724C2semidirect
5. #24905724C2semidirect
8. #24905696C2semidirect
9. #24905694C2semidirect
10. #24905690C2semidirect
11. #24905689C2semidirect
23. #19127613C4semidirect
58. C22×Dic166C2×C4semidirect
107. C83⋊#95C2×C4semidirect
108. C83⋊#95C2×C4semidirect
109. C83⋊#95C2×C4semidirect
125. C2×C22⋊C4×C83Q8semidirect
515. C83#14596semidirect
600. C2×C22⋊C4Dic166semidirect

Maximal subgroups

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

subgroupindex
C2×#191276132
#249057332
#249057242
#249057062
#249057002
#249056962
#249056942
#249056902
#249056892
#249056852
C83×#14372
#1459683