Finite Group Databasebeta

← #35331123

Subgroups — #35331123

Order 21248.

1566 conjugacy classes of subgroups.

The subgroup lattice has 1006 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127563C211yesmaximal, characteristic
2C2×#19127560C211yesmaximal, characteristic
3C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
4#24905727C211yesmaximal, characteristic, complemented
5#24905726C211yesmaximal, characteristic, complemented
6#24905721C211yesmaximal, characteristic, complemented
7#24905718C211yesmaximal, characteristic, complemented
8#24905709C211yesmaximal, characteristic
9#24905707C211yesmaximal, characteristic
10#24905707C211yesmaximal, characteristic
11#24905705C211yesmaximal, characteristic
12#24905697C211yesmaximal, characteristic, complemented
13#24905696C211yesmaximal, characteristic, complemented
14#24905694C211yesmaximal, characteristic, complemented
15C83×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×Dic83⋊C4C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×C4×Dic83C2211yescharacteristic
29#19127563C418yescomplemented
30#19127560—24no—
31C4×(C2×D83)⋊C4—24no—
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
45C2×C83⋊#95C2211yescharacteristic
46C2×C83⋊#95C2211yescharacteristic
47C22×C4⋊C4×C83C2211yescharacteristic
48C22×C42×C83C2211yescharacteristic
49C2×#95×C83C2211yescharacteristic
50C2×#95×C83C2211yescharacteristic
51C2×#95×C83C2211yescharacteristic
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C24×D83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C22×C4×D83—41no—
63C22×C4×D83—41no—
64C22×C4×D83—41no—
65C22×C4×D83—41no—
66C22×C4×D83C2×C414yes—
67C22×C4×D83D414yes—
68C22×C4×D83Q814yes—
69C2×C4⋊Dic83—22no—
70C2×C4⋊Dic83—41no—
71C2×C4⋊Dic83—41no—
72C2×Dic83⋊C4—22no—
73C2×Dic83⋊C4—22no—
74C2×Dic83⋊C4—22no—
75C2×Dic83⋊C4—22no—
76C2×Dic83⋊C4—41no—
77C2×Dic83⋊C4—41no—
78C2×Dic83⋊C4—41no—
79C2×Dic83⋊C4—41no—
80C2×Dic83⋊C4—41no—
81C2×Dic83⋊C4—41no—
82C2×Dic83⋊C4—41no—
83C2×Dic83⋊C4—41no—
84C2×(C2×D83)⋊C4—22no—
85C2×(C2×D83)⋊C4—22no—
86C2×(C2×D83)⋊C4—22no—
87C2×(C2×D83)⋊C4—22no—
88C2×(C2×D83)⋊C4—22no—
89C2×(C2×D83)⋊C4—22no—
90C2×(C2×D83)⋊C4—22no—
91C2×(C2×D83)⋊C4—22no—
92C2×(C2×D83)⋊C4—41no—
93C2×(C2×D83)⋊C4—41no—
94C2×(C2×D83)⋊C4—41no—
95C2×(C2×D83)⋊C4—41no—
96C2×(C2×D83)⋊C4—41no—
97C2×(C2×D83)⋊C4—41no—
98C2×(C2×D83)⋊C4—41no—
99C2×(C2×D83)⋊C4—41no—
100C2×(C2×D83)⋊C4C2×C414yes—
101C2×(C2×D83)⋊C4C2×C414yes—
102C2×C4×Dic83—22no—
103C2×C4×Dic83—41no—
104C2×C4×Dic83—41no—
105C83⋊#95—22no—
106C83⋊#95—22no—
107C83⋊#95—22no—
108C83⋊#95—22no—
109C83⋊#95—22no—
110C83⋊#95—22no—
111C83⋊#95—41no—
112C83⋊#95—41no—
113C83⋊#95—41no—
114C83⋊#95—41no—
115C83⋊#95—41no—
116C83⋊#95—41no—
117C83⋊#95C2×C414yes—
118C83⋊#95C2×C414yes—
119C83⋊#95C2×C414yes—
120C23×C4×C83C2311yescharacteristic
121C23×C4×C83C2311yescharacteristic
122C23×C4×C83C2311yescharacteristic
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C2×C4⋊C4×C83—22no—
128C2×C4⋊C4×C83—41no—
129C2×C4⋊C4×C83—41no—
130C2×C42×C83—22no—
131C2×C42×C83—41no—
132C2×C42×C83—41no—
133#95×C83—22no—
134#95×C83—22no—
135#95×C83—41no—
136#95×C83—41no—
137#95×C83C2×C414yes—
138C23×D83—21no—
139C23×D83—21no—
140C23×D83—21no—
141C23×D83—21no—
142C23×D83—21no—
143C23×D83—21no—
144C23×D83—21no—
145C23×D83—21no—
146C23×D83—21no—
147C23×D83—21no—
148C23×D83—21no—
149C23×D83—21no—
150C23×D83C22×C412yes—
151C23×D83C2×D412yes—
152C23×D83C2×Q812yes—
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×Dic83C2×D412yes—
199C22×Dic83C2×Q812yes—
200C22×Dic83#4112yes—
201C22×Dic83#4112yes—
202C2×C4×D83—44no—
203C2×C4×D83—44no—
204C2×C4×D83—44no—
205C2×C4×D83—44no—
206C2×C4×D83—44no—
207C2×C4×D83—44no—
208C2×C4×D83C4⋊C4116yescomplemented
209C4⋊Dic83—44no—
210Dic83⋊C4—44no—
211Dic83⋊C4—44no—
212Dic83⋊C4—44no—
213Dic83⋊C4—44no—
214(C2×D83)⋊C4—28no—
215(C2×D83)⋊C4—28no—
216(C2×D83)⋊C4—44no—
217(C2×D83)⋊C4—44no—
218(C2×D83)⋊C4—44no—
219(C2×D83)⋊C4—44no—
220C4×Dic83—44no—
221C24×C83C2411yescharacteristic
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×C83—21no—
255C22×C4×C83—21no—
256C22×C4×C83—21no—
257C22×C4×C83—21no—
258C22×C4×C83—21no—
259C22×C4×C83—21no—
260C22×C4×C83—21no—
261C22×C4×C83—21no—
262C22×C4×C83—21no—
263C22×C4×C83—21no—
264C22×C4×C83C22×C412yes—
265C22×C4×C83C22×C412yes—
266C22×C4×C83C22×C412yes—
267C22×C4×C83C2×D412yes—
268C22×C4×C83C2×Q812yes—
269C22×C4×C83#4112yes—
270C22×C4×C83#4112yes—
271C4⋊C4×C83—44no—
272C42×C83—44no—
273C23×C83C23×C411yescharacteristic
274C23×C83C22×D411yescharacteristic
275C23×C83C22×Q811yescharacteristic
276C23×C83C2×#4111yescharacteristic
277C23×C83C2×#4111yescharacteristic
278C23×C83C2×#4111yescharacteristic
279C23×C83C2×#4111yescharacteristic
280C23×C83H(5,𝔽2)11yescharacteristic
281C23×C83H(5,𝔽2)11yescharacteristic
282C23×C83H(5,𝔽2)11yescharacteristic
283C23×C83H(5,𝔽2)11yescharacteristic
284C23×C83H(5,𝔽2)11yescharacteristic
285C23×C83H(5,𝔽2)11yescharacteristic
286C23×C832−1+411yescharacteristic
287C23×C832−1+411yescharacteristic
288C22×D83—22no—
289C22×D83—22no—
290C22×D83—22no—
291C22×D83—22no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—41no—
307C22×D83—41no—
308C22×D83—41no—
309C22×D83—41no—
310C22×D83—41no—
311C22×D83—41no—
312C22×D83—41no—
313C22×D83—41no—
314C22×D83—41no—
315C22×D83—41no—
316C22×D83—41no—
317C22×D83—41no—
318C22×D83—41no—
319C22×D83—41no—
320C22×D83—41no—
321C22×D83—41no—
322C22×D83C2×C4⋊C414yes—
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—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
338C2×C4×C83—22no—
339C2×C4×C83—22no—
340C2×C4×C83—22no—
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×C4×C83—41no—
362C2×C4×C83—41no—
363C2×C4×C83—41no—
364C2×C4×C83—41no—
365C2×C4×C83—41no—
366C2×C4×C83—41no—
367C2×C4×C83—41no—
368C2×C4×C83—41no—
369C2×C4×C83—41no—
370C2×C4×C83—41no—
371C2×C4×C83C2×C4⋊C414yes—
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—22no—
383C2×Dic83—22no—
384C2×Dic83—22no—
385C2×Dic83—22no—
386C2×Dic83—22no—
387C2×Dic83—22no—
388C2×Dic83—22no—
389C2×Dic83—22no—
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—
418C2×Dic83—41no—
419C2×Dic83—41no—
420C2×Dic83C2×C4⋊C414yes—
421C4×D83—416no—
422C22×C83C22×C4⋊C411yescharacteristic
423C22×C83C4×#4111yescharacteristic
424C22×C83C4×#4111yescharacteristic
425C22×C83#51811yescharacteristic
426C22×C83#51811yescharacteristic
427C22×C83#52011yescharacteristic
428C22×C83#52011yescharacteristic
429C22×C83#52511yescharacteristic
430C22×C83#52511yescharacteristic
431C22×C83#53311yescharacteristic
432C22×C83#53311yescharacteristic
433C22×C83#53411yescharacteristic
434C22×C83#53411yescharacteristic
435C22×C83#53511yescharacteristic
436C22×C83#53611yescharacteristic
437C22×C83#53811yescharacteristic
438C22×C83#53811yescharacteristic
439C22×C83#53811yescharacteristic
440C22×C83#53811yescharacteristic
441C22×C83#53911yescharacteristic
442C22×C83#53911yescharacteristic
443C22×C83#53911yescharacteristic
444C22×C83#53911yescharacteristic
445C22×C83#54011yescharacteristic
446C22×C83#54011yescharacteristic
447C22×C83#54011yescharacteristic
448C22×C83#54011yescharacteristic
449C22×C83#54211yescharacteristic
450C22×C83#54211yescharacteristic
451C22×C83#54211yescharacteristic
452C22×C83#54211yescharacteristic
453C22×C83#54311yescharacteristic
454C22×C83#54311yescharacteristic
455C22×C83#54411yescharacteristic
456C22×C83#54411yescharacteristic
457C2×D83—24no—
458C2×D83—24no—
459C2×D83—24no—
460C2×D83—42no—
461C2×D83—42no—
462C2×D83—42no—
463C2×D83—42no—
464C2×D83—42no—
465C2×D83—42no—
466C2×D83—42no—
467C2×D83—42no—
468C2×D83—42no—
469C2×D83—42no—
470C2×D83—42no—
471C2×D83—42no—
472C4×C83—24no—
473C4×C83—42no—
474C4×C83—42no—
475C4×C83—42no—
476C4×C83—42no—
477C4×C83—81no—
478C4×C83—81no—
479Dic83—24no—
480Dic83—42no—
481Dic83—42no—
482Dic83—42no—
483Dic83—42no—
484Dic83—81no—
485Dic83—81no—
486#14295—831nomaximal, Sylow
487C2×C83#229611yescharacteristic
488C2×C83#231511yescharacteristic
489C2×C83#231711yescharacteristic
490C2×C83#233511yescharacteristic
491C2×C83#233511yescharacteristic
492C2×C83#233511yescharacteristic
493C2×C83#233511yescharacteristic
494C2×C83#263511yescharacteristic
495C2×C83#263511yescharacteristic
496C2×C83#263811yescharacteristic
497C2×C83#263811yescharacteristic
498C2×C83#266511yescharacteristic
499C2×C83#266511yescharacteristic
500C2×C83#266711yescharacteristic
501C2×C83#266711yescharacteristic
502D83—44no—
503C2×#381—831no—
504C2×#380—831no—
505C2×C4×C22⋊C4—831no—
506#1444—831no—
507#1444—831no—
508#1442—831no—
509#1442—831no—
510#1439—831no—
511#1439—831no—
512#1439—831no—
513#1439—831no—
514#1436—831no—
515#1436—831no—
516#1436—831no—
517#1436D8311yescharacteristic, complemented
518C83#1429511yescharacteristic, complemented, Sylow
519C24×C4—831no—
520C22×C4⋊C4—831no—
521C22×C4⋊C4—831no—
522C22×C4⋊C4—831no—
523C22×C4⋊C4—831no—
524C22×C4⋊C4—831no—
525C22×C4⋊C4C2×D8311yescharacteristic
526C22×C22⋊C4—831no—
527C22×C22⋊C4—831no—
528C22×C22⋊C4—831no—
529C22×C22⋊C4—831no—
530C22×C22⋊C4—831no—
531C22×C22⋊C4—831no—
532C22×C42—831no—
533C22×C42C2×D8311yescharacteristic
534#381—838no—
535#380—1664no—
536C4×C22⋊C4—1664no—
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×#95—831no—
550C2×#95—831no—
551C2×#95—831no—
552C2×#95C2×D8311yescharacteristic
553C2×#95C2×D8311yescharacteristic
554C2×#95C2×D8311yescharacteristic
555C2×#95C2×D8311yescharacteristic
556C2×#95C2×D8311yescharacteristic
557C25—831no—
558C23×C4—3321no—
559C23×C4—3321no—
560C23×C4—3321no—
561C23×C4—3321no—
562C23×C4—834no—
563C23×C4—834no—
564C23×C4—834no—
565C23×C4—831no—
566C23×C4—831no—
567C23×C4—831no—
568C23×C4—831no—
569C23×C4—831no—
570C23×C4—831no—
571C23×C4—831no—
572C23×C4C22×D8311yescharacteristic
573C23×C4C22×D8311yescharacteristic
574C23×C4C22×D8311yescharacteristic
575C23×C4C22×D8311yescharacteristic
576C23×C4C22×D8311yescharacteristic
577C23×C4C22×D8311yescharacteristic
578C23×C4C22×D8311yescharacteristic
579C2×C4⋊C4—22no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—3321no—
583C2×C4⋊C4—3321no—
584C2×C4⋊C4—3321no—
585C2×C4⋊C4—3321no—
586C2×C4⋊C4—3321no—
587C2×C4⋊C4—3321no—
588C2×C4⋊C4—3321no—
589C2×C4⋊C4—3321no—
590C2×C4⋊C4—3321no—
591C2×C4⋊C4—3321no—
592C2×C4⋊C4—1662no—
593C2×C4⋊C4—1662no—
594C2×C4⋊C4—1662no—
595C2×C4⋊C4—1662no—
596C2×C4⋊C4—1662no—
597C2×C22⋊C4—3321no—
598C2×C22⋊C4—3321no—
599C2×C22⋊C4—3321no—
600C2×C22⋊C4—3321no—
601C2×C22⋊C4—3321no—
602C2×C22⋊C4—3321no—
603C2×C22⋊C4—3321no—
604C2×C22⋊C4—3321no—
605C2×C22⋊C4—834no—
606C2×C22⋊C4—834no—
607C2×C22⋊C4—1662no—
608C2×C22⋊C4—1662no—
609C2×C22⋊C4—1662no—
610C2×C22⋊C4—1662no—
611C2×C22⋊C4—1662no—
612C2×C22⋊C4—1662no—
613C2×C22⋊C4—1662no—
614C2×C22⋊C4—1662no—
615C2×C42—22no—
616C2×C42—41no—
617C2×C42—41no—
618C2×C42—3321no—
619C2×C42—3321no—
620C2×C42—1662no—
621#95—22no—
622#95—22no—
623#95—41no—
624#95—41no—
625#95—3321no—
626#95—3321no—
627#95—3321no—
628#95—3321no—
629#95—3321no—
630#95—3321no—
631#95—834no—
632#95—834no—
633#95—834no—
634#95—1662no—
635#95—1662no—
636#95—1662no—
637#95—1662no—
638#95—1662no—
639#95—1662no—
640#95C4×D8314yes—
641C24—832no—
642C24—832no—
643C24—832no—
644C24—1661no—
645C24—1661no—
646C24—1661no—
647C24—1661no—
648C24—1661no—
649C24—1661no—
650C24—1661no—
651C24—1661no—
652C24—1661no—
653C24—1661no—
654C24—1661no—
655C24—1661no—
656C24C23×D8311yescharacteristic
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—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—3324no—
700C22×C4—3324no—
701C22×C4—3324no—
702C22×C4—3324no—
703C22×C4—3324no—
704C22×C4—3324no—
705C22×C4—8316no—
706C22×C4—832no—
707C22×C4—832no—
708C22×C4—832no—
709C22×C4—832no—
710C22×C4—832no—
711C22×C4—832no—
712C22×C4—832no—
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×C4×D8312yes—
758C22×C4D4×D8312yes—
759C22×C4Q8×D8312yes—
760C22×C4#1305059012yes—
761C22×C4#1305059012yes—
762C4⋊C4—44no—
763C4⋊C4—3324no—
764C4⋊C4—3324no—
765C4⋊C4—3324no—
766C4⋊C4—3324no—
767C4⋊C4—3324no—
768C22⋊C4—3324no—
769C22⋊C4—3324no—
770C22⋊C4—3324no—
771C22⋊C4—3324no—
772C22⋊C4—1668no—
773C22⋊C4—1668no—
774C42—44no—
775C42—3324no—
776C23—3321no—
777C23—3321no—
778C23—3321no—
779C23—3321no—
780C23—3321no—
781C23—3321no—
782C23—3321no—
783C23—3321no—
784C23—3321no—
785C23—3321no—
786C23—3321no—
787C23—3321no—
788C23—3321no—
789C23—3321no—
790C23—3321no—
791C23—3321no—
792C23—834no—
793C23—1662no—
794C23—1662no—
795C23—1662no—
796C23—1662no—
797C23—1662no—
798C23—1662no—
799C23—1662no—
800C23—1662no—
801C23—1662no—
802C23—1662no—
803C23—1662no—
804C23—1662no—
805C23—1662no—
806C23—1662no—
807C23—1662no—
808C23—1662no—
809C23—1662no—
810C23—1662no—
811C23C22×C4×D8311yescharacteristic
812C23C2×D4×D8311yescharacteristic
813C23C2×Q8×D8311yescharacteristic
814C23#41×D8311yescharacteristic
815C23#41×D8311yescharacteristic
816C23C2×#1305059011yescharacteristic
817C23C2×#1305059011yescharacteristic
818C23#1458183711yescharacteristic
819C23#1458183711yescharacteristic
820C23#1458183711yescharacteristic
821C23#1458183811yescharacteristic
822C23#1458183811yescharacteristic
823C23#1458183811yescharacteristic
824C23#1458183911yescharacteristic
825C23#1458184011yescharacteristic
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—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
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—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—33216no—
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—3321no—
899C2×C4—3321no—
900C2×C4—3321no—
901C2×C4—3321no—
902C2×C4—3321no—
903C2×C4—3321no—
904C2×C4—3321no—
905C2×C4—834no—
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—
919C2×C4—1662no—
920C2×C4—1662no—
921C2×C4—1662no—
922C2×C4—1662no—
923C2×C4—1662no—
924C2×C4C4⋊C4×D8314yes—
925C22—3322no—
926C22—3322no—
927C22—3322no—
928C22—3322no—
929C22—3322no—
930C22—3322no—
931C22—3322no—
932C22—3322no—
933C22—3322no—
934C22—3322no—
935C22—3322no—
936C22—3322no—
937C22—1664no—
938C22—1664no—
939C22—1664no—
940C22C2×C4⋊C4×D8311yescharacteristic
941C22#1912816911yescharacteristic
942C22C4×#1305059011yescharacteristic
943C22#1912817311yescharacteristic
944C22#1912817311yescharacteristic
945C22#1912818011yescharacteristic
946C22#1912818311yescharacteristic
947C22#1912821011yescharacteristic
948C22#1912821011yescharacteristic
949C22#1912825511yescharacteristic
950C22#1912825511yescharacteristic
951C22#1912826111yescharacteristic
952C22#1912826211yescharacteristic
953C22#1912826711yescharacteristic
954C22#1912827411yescharacteristic
955C22#1912828411yescharacteristic
956C22#1912828511yescharacteristic
957C22#1912828911yescharacteristic
958C22#1912829011yescharacteristic
959C22#1912829211yescharacteristic
960C22#1912829311yescharacteristic
961C22#1912829811yescharacteristic
962C22#1912829911yescharacteristic
963C22#1912830111yescharacteristic
964C22#1912830211yescharacteristic
965C22#1912830311yescharacteristic
966C22#1912830611yescharacteristic
967C22#1912831911yescharacteristic
968C22#1912832111yescharacteristic
969C22#1912832211yescharacteristic
970C22#1912832311yescharacteristic
971C22#1912832611yescharacteristic
972C22#1912832611yescharacteristic
973C22#1912832811yescharacteristic
974C22#1912833111yescharacteristic
975C4—24no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—81no—
981C4—81no—
982C4—3322no—
983C4—3322no—
984C4—3322no—
985C4—3322no—
986C4—6641no—
987C4—6641no—
988C4—1664no—
989C2—3324no—
990C2#2490994311yescharacteristic
991C2#2491007411yescharacteristic
992C2#2491008511yescharacteristic
993C2#2491024711yescharacteristic
994C2#2491025111yescharacteristic
995C2#2491025511yescharacteristic
996C2#2491025911yescharacteristic
997C2#2491335111yescharacteristic
998C2#2491335411yescharacteristic
999C2#2491338411yescharacteristic
1000C2#2491338711yescharacteristic
1001C2#2491363711yescharacteristic
1002C2#2491363911yescharacteristic
1003C2#2491366111yescharacteristic
1004C2#2491366311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC83×#1436C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenter#1436D83
hypocenterC83#14295
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
4. #24905727C2semidirect
5. #24905726C2semidirect
6. #24905721C2semidirect
7. #24905718C2semidirect
12. #24905697C2semidirect
13. #24905696C2semidirect
14. #24905694C2semidirect
15. C83×#1436C2semidirect
29. #19127563C4semidirect
208. C2×C4×D83C4⋊C4semidirect
517. #1436D83semidirect
518. C83#14295semidirect

Maximal subgroups

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

subgroupindex
C2×#191275632
C2×#191275602
C2×C4×(C2×D83)⋊C42
#249057272
#249057262
#249057212
#249057182
#249057092
#249057072
#249057052
#249056972
#249056962
#249056942
C83×#14362
#1429583