Finite Group Databasebeta

← #35332148

Subgroups — #35332148

Order 21248.

1506 conjugacy classes of subgroups.

The subgroup lattice has 994 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127576C211yesmaximal, characteristic
2C2×#19127569C211yesmaximal, characteristic, complemented
3#24905731C211yesmaximal, characteristic, complemented
4#24905720C211yesmaximal, characteristic, complemented
5#24905720C211yesmaximal, characteristic, complemented
6#24905716C211yesmaximal, characteristic, complemented
7#24905712C211yesmaximal, characteristic
8#24905708C211yesmaximal, characteristic
9#24905700C211yesmaximal, characteristic
10#24905697C211yesmaximal, characteristic, complemented
11#24905693C211yesmaximal, characteristic, complemented
12#24905688C211yesmaximal, characteristic, complemented
13#24905685C211yesmaximal, characteristic
14#24905685C211yesmaximal, characteristic
15C2×#388×C83C211yesmaximal, characteristic
16C24×Dic83C2211yescharacteristic
17C22×C4⋊Dic83C2211yescharacteristic
18C22×C4⋊Dic83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×C22⋊Dic83C2211yescharacteristic
21C22×C22⋊Dic83C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C4×Dic83C2211yescharacteristic
24#19127576—24no—
25#19127569—24no—
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
45C2×C83⋊#95C2211yescharacteristic
46C22×C4⋊C4×C83C2211yescharacteristic
47C22×C22⋊C4×C83C2211yescharacteristic
48C22×C22⋊C4×C83C2211yescharacteristic
49C22×C22⋊C4×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51#388×C83C418yescomplemented
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C23×Dic83—22no—
55C23×Dic83—22no—
56C23×Dic83—22no—
57C23×Dic83—41no—
58C23×Dic83—41no—
59C23×Dic83—41no—
60C23×Dic83—41no—
61C23×Dic83C2311yescharacteristic
62C23×Dic83C2311yescharacteristic
63C23×Dic83C2311yescharacteristic
64C23×Dic83C2311yescharacteristic
65C23×Dic83C2311yescharacteristic
66C23×Dic83C2311yescharacteristic
67C23×Dic83C2311yescharacteristic
68C23×Dic83C2311yescharacteristic
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×C22⋊Dic83—22no—
79C2×C22⋊Dic83—22no—
80C2×C22⋊Dic83—22no—
81C2×C22⋊Dic83—22no—
82C2×C22⋊Dic83—22no—
83C2×C22⋊Dic83—41no—
84C2×C22⋊Dic83—41no—
85C2×C22⋊Dic83—41no—
86C2×C22⋊Dic83—41no—
87C2×C4×Dic83—22no—
88C2×C4×Dic83—41no—
89C2×C4×Dic83—41no—
90C83⋊#95—22no—
91C83⋊#95—22no—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
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⋊#95D414yes—
110C25×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83—41no—
118C2×C4⋊C4×C83—41no—
119C2×C4⋊C4×C83C2×C414yescomplemented
120C2×C22⋊C4×C83—22no—
121C2×C22⋊C4×C83—22no—
122C2×C22⋊C4×C83—22no—
123C2×C22⋊C4×C83—22no—
124C2×C22⋊C4×C83—41no—
125C2×C22⋊C4×C83—41no—
126C2×C22⋊C4×C83C2×C414yes—
127C2×C22⋊C4×C83C2×C414yes—
128C2×C22⋊C4×C83C2×C414yes—
129C2×C42×C83—22no—
130C2×C42×C83—22no—
131C2×C42×C83C2×C414yescomplemented
132#95×C83C2×C414yescomplemented
133#95×C83C2×C414yescomplemented
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×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—44no—
187C22×Dic83—44no—
188C22×Dic83—44no—
189C22×Dic83—44no—
190C22×Dic83—44no—
191C22×Dic83—44no—
192C22×Dic83—44no—
193C22×Dic83C2×D412yes—
194C22×Dic83C2×D412yes—
195C22×Dic83#4112yes—
196C22×Dic83#4112yes—
197C4⋊Dic83—44no—
198C4⋊Dic83—44no—
199C4⋊Dic83—44no—
200C22⋊Dic83—44no—
201C22⋊Dic83—44no—
202C22⋊Dic83—44no—
203C4×Dic83—44no—
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×C83—21no—
213C24×C83—21no—
214C24×C83—21no—
215C24×C83—21no—
216C24×C83C22×C412yes—
217C24×C83#4112yes—
218C24×C83#4112yes—
219C24×C83C2411yescharacteristic
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×C83C22×C412yes—
258C22×C4×C83C22×C412yes—
259C22×C4×C83C22×C412yes—
260C22×C4×C83C2×D412yes—
261C22×C4×C83#4112yes—
262C4⋊C4×C83—44no—
263C22⋊C4×C83—28no—
264C22⋊C4×C83—28no—
265C22⋊C4×C83—44no—
266C42×C83—28no—
267C23×C83—22no—
268C23×C83—22no—
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—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×C83—41no—
295C23×C83—41no—
296C23×C83—41no—
297C23×C83—41no—
298C23×C83—41no—
299C23×C83—41no—
300C23×C83—41no—
301C23×C83#11714yes—
302C23×C83C23×C411yescharacteristic
303C23×C83C22×D411yescharacteristic
304C23×C83C2×#4111yescharacteristic
305C23×C83C2×#4111yescharacteristic
306C23×C83C2×#4111yescharacteristic
307C23×C83C2×#4111yescharacteristic
308C23×C83C2×#4111yescharacteristic
309C23×C83H(5,𝔽2)11yescharacteristic
310C23×C83H(5,𝔽2)11yescharacteristic
311C23×C83H(5,𝔽2)11yescharacteristic
312C23×C83H(5,𝔽2)11yescharacteristic
313C23×C83H(5,𝔽2)11yescharacteristic
314C23×C832−1+411yescharacteristic
315C23×C832−1+411yescharacteristic
316C23×C832−1+411yescharacteristic
317C2×C4×C83—22no—
318C2×C4×C83—22no—
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—22no—
335C2×C4×C83—22no—
336C2×C4×C83—22no—
337C2×C4×C83—22no—
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×C83C4×D414yes—
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—22no—
371C2×Dic83—416no—
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—
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—
416C22×C83—24no—
417C22×C83—24no—
418C22×C83—24no—
419C22×C83—42no—
420C22×C83—42no—
421C22×C83—42no—
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×C83C2×#11711yescharacteristic
432C22×C83C2×C4×D411yescharacteristic
433C22×C83C4×#4111yescharacteristic
434C22×C83#51811yescharacteristic
435C22×C83#52011yescharacteristic
436C22×C83#52011yescharacteristic
437C22×C83#52011yescharacteristic
438C22×C83#53511yescharacteristic
439C22×C83#53711yescharacteristic
440C22×C83#53811yescharacteristic
441C22×C83#53811yescharacteristic
442C22×C83#53811yescharacteristic
443C22×C83#53811yescharacteristic
444C22×C83#53911yescharacteristic
445C22×C83#53911yescharacteristic
446C22×C83#54011yescharacteristic
447C22×C83#54211yescharacteristic
448C22×C83#54211yescharacteristic
449C22×C83#54211yescharacteristic
450C22×C83#54611yescharacteristic
451C22×C83#54611yescharacteristic
452C22×C83#54711yescharacteristic
453C22×C83#54811yescharacteristic
454C22×C83#55111yescharacteristic
455C22×C83#55111yescharacteristic
456C22×C83#55111yescharacteristic
457C22×C83#55211yescharacteristic
458C22×C83#55211yescharacteristic
459C22×C83#55211yescharacteristic
460C22×C83#55211yescharacteristic
461C22×C83#55311yescharacteristic
462C22×C83#56011yescharacteristic
463C22×C83#56311yescharacteristic
464C22×C83#56311yescharacteristic
465C22×C83#56311yescharacteristic
466C4×C83—24no—
467C4×C83—42no—
468C4×C83—42no—
469C4×C83—42no—
470C4×C83—42no—
471C4×C83—42no—
472Dic83—42no—
473Dic83—42no—
474Dic83—42no—
475Dic83—42no—
476Dic83—81no—
477Dic83—81no—
478Dic83—81no—
479Dic83—81no—
480#14389—831nomaximal, Sylow
481C2×C83—44no—
482C2×C83#231811yescharacteristic
483C2×C83#232411yescharacteristic
484C2×C83#233711yescharacteristic
485C2×C83#234311yescharacteristic
486C2×C83#235211yescharacteristic
487C2×C83#235911yescharacteristic
488C2×C83#238311yescharacteristic
489C2×C83#268511yescharacteristic
490C2×C83#269511yescharacteristic
491C2×C83#270211yescharacteristic
492C2×C83#272311yescharacteristic
493C2×C83#273811yescharacteristic
494C2×C83#274911yescharacteristic
495C2×C83#276411yescharacteristic
496C2×C83#277011yescharacteristic
497C2×#388D8311yescharacteristic
498C2×#385—831no—
499C2×#383—831no—
500#1445—831no—
501#1442—831no—
502#1442—831no—
503#1441—831no—
504#1440—831no—
505#1439—831no—
506#1437—831no—
507#1436—831no—
508C4⋊#95—831no—
509#1434—831no—
510C22⋊#95—831no—
511C22⋊#95—831no—
512C83#1438911yescharacteristic, complemented, Sylow
513C24×C4—831no—
514C22×C4⋊C4—831no—
515C22×C4⋊C4—831no—
516C22×C4⋊C4—831no—
517C22×C4⋊C4C2×D8311yescharacteristic
518C22×C22⋊C4—831no—
519C22×C22⋊C4—831no—
520C22×C22⋊C4—831no—
521C22×C22⋊C4C2×D8311yescharacteristic
522C22×C22⋊C4C2×D8311yescharacteristic
523C22×C22⋊C4C2×D8311yescharacteristic
524C22×C42—831no—
525C22×C42C2×D8311yescharacteristic
526#388Dic8318yescomplemented
527#385—1664no—
528#383—1664no—
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
551C25C22×D8311yescharacteristic
552C23×C4—3321no—
553C23×C4—3321no—
554C23×C4—3321no—
555C23×C4—3321no—
556C23×C4—831no—
557C23×C4—831no—
558C23×C4—831no—
559C23×C4—831no—
560C23×C4—831no—
561C23×C4—831no—
562C23×C4—831no—
563C23×C4—831no—
564C23×C4—1662no—
565C23×C4—1662no—
566C23×C4—1662no—
567C23×C4C22×D8311yescharacteristic
568C23×C4C22×D8311yescharacteristic
569C23×C4C22×D8311yescharacteristic
570C23×C4C22×D8311yescharacteristic
571C23×C4C22×D8311yescharacteristic
572C23×C4C22×D8311yescharacteristic
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—3321no—
576C2×C4⋊C4—3321no—
577C2×C4⋊C4—3321no—
578C2×C4⋊C4—3321no—
579C2×C4⋊C4—1662no—
580C2×C4⋊C4—1662no—
581C2×C4⋊C4—1662no—
582C2×C4⋊C4—1662no—
583C2×C4⋊C4—1662no—
584C2×C4⋊C4C2×Dic8314yescomplemented
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
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—1662no—
596C2×C22⋊C4—1662no—
597C2×C22⋊C4—1662no—
598C2×C22⋊C4—1662no—
599C2×C22⋊C4—1662no—
600C2×C22⋊C4C2×Dic8314yes—
601C2×C22⋊C4C2×Dic8314yes—
602C2×C22⋊C4C2×Dic8314yes—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—3321no—
606C2×C42—3321no—
607C2×C42—1662no—
608C2×C42C2×Dic8314yescomplemented
609#95—3321no—
610#95—3321no—
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—834no—
622#95—1662no—
623#95—1662no—
624#95—1662no—
625#95—1662no—
626#95—1662no—
627#95—1662no—
628#95—1662no—
629#95C2×Dic8314yescomplemented
630#95C2×Dic8314yescomplemented
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24C22×Dic8312yes—
644C24#1305059012yes—
645C24#1305059012yes—
646C24C23×D8311yescharacteristic
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—3324no—
682C22×C4—3324no—
683C22×C4—3324no—
684C22×C4—3324no—
685C22×C4—3324no—
686C22×C4—3324no—
687C22×C4—3324no—
688C22×C4—832no—
689C22×C4—832no—
690C22×C4—832no—
691C22×C4—832no—
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×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×C4C22×Dic8312yes—
745C22×C4C22×Dic8312yes—
746C22×C4C22×Dic8312yes—
747C22×C4C22×Dic8312yes—
748C22×C4C22×Dic8312yes—
749C22×C4C22×Dic8312yes—
750C22×C4D4×D8312yes—
751C22×C4#1305058912yes—
752C4⋊C4—44no—
753C4⋊C4—3324no—
754C4⋊C4—3324no—
755C4⋊C4—3324no—
756C22⋊C4—28no—
757C22⋊C4—28no—
758C22⋊C4—44no—
759C22⋊C4—3324no—
760C22⋊C4—3324no—
761C22⋊C4—3324no—
762C42—28no—
763C42—3324no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
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—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23#1458175114yes—
799C23C23×Dic8311yescharacteristic
800C23C2×D4×D8311yescharacteristic
801C23#41×D8311yescharacteristic
802C23#41×D8311yescharacteristic
803C23C2×#1305058911yescharacteristic
804C23C2×#1305059011yescharacteristic
805C23C2×#1305059011yescharacteristic
806C23#1458183711yescharacteristic
807C23#1458183711yescharacteristic
808C23#1458183811yescharacteristic
809C23#1458183811yescharacteristic
810C23#1458183811yescharacteristic
811C23#1458183911yescharacteristic
812C23#1458183911yescharacteristic
813C23#1458183911yescharacteristic
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
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—33216no—
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—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—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×C4D4×Dic8314yes—
913C22—24no—
914C22—24no—
915C22—24no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22C2×#1458175111yescharacteristic
929C22C2×D4×Dic8311yescharacteristic
930C22#41×Dic8311yescharacteristic
931C22#1912817611yescharacteristic
932C22#1912818411yescharacteristic
933C22#1912818411yescharacteristic
934C22#1912818411yescharacteristic
935C22#1912826711yescharacteristic
936C22#1912828011yescharacteristic
937C22#1912828411yescharacteristic
938C22#1912828411yescharacteristic
939C22#1912828511yescharacteristic
940C22#1912828511yescharacteristic
941C22#1912829311yescharacteristic
942C22#1912829311yescharacteristic
943C22#1912830411yescharacteristic
944C22#1912831511yescharacteristic
945C22#1912831511yescharacteristic
946C22#1912831811yescharacteristic
947C22#1912834311yescharacteristic
948C22#1912834711yescharacteristic
949C22#1912834911yescharacteristic
950C22#1912836011yescharacteristic
951C22#1912837411yescharacteristic
952C22#1912837511yescharacteristic
953C22#1912837511yescharacteristic
954C22#1912838411yescharacteristic
955C22#1912838411yescharacteristic
956C22#1912838811yescharacteristic
957C22#1912839111yescharacteristic
958C22#1912839711yescharacteristic
959C22#1912844211yescharacteristic
960C22#1912845311yescharacteristic
961C22#1912845311yescharacteristic
962C22#1912845311yescharacteristic
963C4—24no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—3322no—
970C4—3322no—
971C4—3322no—
972C4—3322no—
973C4—6641no—
974C4—6641no—
975C4—6641no—
976C4—6641no—
977C2—44no—
978C2#2491009611yescharacteristic
979C2#2491015811yescharacteristic
980C2#2491027811yescharacteristic
981C2#2491032311yescharacteristic
982C2#2491039211yescharacteristic
983C2#2491045911yescharacteristic
984C2#2491065511yescharacteristic
985C2#2491385711yescharacteristic
986C2#2491400111yescharacteristic
987C2#2491409211yescharacteristic
988C2#2491438611yescharacteristic
989C2#2491452711yescharacteristic
990C2#2491468111yescharacteristic
991C2#2491488811yescharacteristic
992C2#2491497111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×#388×C83C2
socle, cosocleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#388D83
hypocenterC83#14389
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#19127569C2semidirect
3. #24905731C2semidirect
4. #24905720C2semidirect
5. #24905720C2semidirect
6. #24905716C2semidirect
10. #24905697C2semidirect
11. #24905693C2semidirect
12. #24905688C2semidirect
51. #388×C83C4semidirect
119. C2×C4⋊C4×C83C2×C4semidirect
131. C2×C42×C83C2×C4semidirect
132. #95×C83C2×C4semidirect
133. #95×C83C2×C4semidirect
512. C83#14389semidirect
526. #388Dic83semidirect
584. C2×C4⋊C4C2×Dic83semidirect
608. C2×C42C2×Dic83semidirect
629. #95C2×Dic83semidirect
630. #95C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
C2×#191275762
C2×#191275692
#249057312
#249057202
#249057162
#249057122
#249057082
#249057002
#249056972
#249056932
#249056882
#249056852
C2×#388×C832
#1438983