Finite Group Databasebeta

← #35330873

Subgroups — #35330873

Order 21248.

1414 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19127592C211yesmaximal, characteristic
2C2×#19127592C211yesmaximal, characteristic
3#24905729C211yesmaximal, characteristic, complemented
4#24905726C211yesmaximal, characteristic, complemented
5#24905722C211yesmaximal, characteristic, complemented
6#24905714C211yesmaximal, characteristic, complemented
7#24905711C211yesmaximal, characteristic
8#24905707C211yesmaximal, characteristic
9#24905705C211yesmaximal, characteristic
10#24905705C211yesmaximal, characteristic
11#24905701C211yesmaximal, characteristic
12#24905696C211yesmaximal, characteristic, complemented
13#24905690C211yesmaximal, characteristic, complemented
14#24905690C211yesmaximal, characteristic, complemented
15C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
16C22×Dic83⋊C4C2211yescharacteristic
17C22×Dic83⋊C4C2211yescharacteristic
18C22×Dic83⋊C4C2211yescharacteristic
19C22×(C2×D83)⋊C4C2211yescharacteristic
20C22×(C2×D83)⋊C4C2211yescharacteristic
21C22×(C2×D83)⋊C4C2211yescharacteristic
22C22×(C2×D83)⋊C4C2211yescharacteristic
23C22×(C2×D83)⋊C4C2211yescharacteristic
24C22×(C2×D83)⋊C4C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26#19127592—24no—
27#19127592C418yescomplemented
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×C4⋊C4×C83C2211yescharacteristic
48C22×C42×C83C2211yescharacteristic
49C22×C42×C83C2211yescharacteristic
50C22×C42×C83C2211yescharacteristic
51C4×C4⋊C4×C83—24no—
52C2×#95×C83C2211yescharacteristic
53C2×#95×C83C2211yescharacteristic
54C24×D83C2311yescharacteristic
55C23×Dic83C2311yescharacteristic
56C23×Dic83C2311yescharacteristic
57C23×Dic83C2311yescharacteristic
58C23×Dic83C2311yescharacteristic
59C23×Dic83C2311yescharacteristic
60C23×Dic83C2311yescharacteristic
61C23×Dic83C2311yescharacteristic
62C2×Dic83⋊C4—22no—
63C2×Dic83⋊C4—22no—
64C2×Dic83⋊C4—41no—
65C2×Dic83⋊C4—41no—
66C2×Dic83⋊C4—41no—
67C2×Dic83⋊C4—41no—
68C2×Dic83⋊C4—41no—
69C2×Dic83⋊C4—41no—
70C2×Dic83⋊C4C2×C414yes—
71C2×(C2×D83)⋊C4—22no—
72C2×(C2×D83)⋊C4—22no—
73C2×(C2×D83)⋊C4—22no—
74C2×(C2×D83)⋊C4—22no—
75C2×(C2×D83)⋊C4—22no—
76C2×(C2×D83)⋊C4—22no—
77C2×(C2×D83)⋊C4—22no—
78C2×(C2×D83)⋊C4—22no—
79C2×(C2×D83)⋊C4—41no—
80C2×(C2×D83)⋊C4—41no—
81C2×(C2×D83)⋊C4—41no—
82C2×(C2×D83)⋊C4—41no—
83C2×(C2×D83)⋊C4—41no—
84C2×(C2×D83)⋊C4—41no—
85C2×(C2×D83)⋊C4—41no—
86C2×(C2×D83)⋊C4—41no—
87C2×(C2×D83)⋊C4—41no—
88C2×(C2×D83)⋊C4—41no—
89C2×(C2×D83)⋊C4C2×C414yes—
90C2×(C2×D83)⋊C4C2×C414yes—
91C2×(C2×D83)⋊C4C2×C414yes—
92C83⋊#95—22no—
93C83⋊#95—22no—
94C83⋊#95—22no—
95C83⋊#95—22no—
96C83⋊#95—22no—
97C83⋊#95—22no—
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⋊#95C2×C414yes—
109C83⋊#95C2×C414yes—
110C23×C4×C83C2311yescharacteristic
111C23×C4×C83C2311yescharacteristic
112C23×C4×C83C2311yescharacteristic
113C23×C4×C83C2311yescharacteristic
114C23×C4×C83C2311yescharacteristic
115C23×C4×C83C2311yescharacteristic
116C23×C4×C83C2311yescharacteristic
117C2×C4⋊C4×C83—22no—
118C2×C4⋊C4×C83—22no—
119C2×C4⋊C4×C83—22no—
120C2×C4⋊C4×C83—22no—
121C2×C4⋊C4×C83—22no—
122C2×C4⋊C4×C83—22no—
123C2×C42×C83—22no—
124C2×C42×C83—22no—
125C2×C42×C83—22no—
126C2×C42×C83—41no—
127C2×C42×C83—41no—
128C2×C42×C83—41no—
129C2×C42×C83—41no—
130C2×C42×C83C2×C414yes—
131C2×C42×C83D414yes—
132#95×C83—22no—
133#95×C83—22no—
134C23×D83—21no—
135C23×D83—21no—
136C23×D83—21no—
137C23×D83—21no—
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×D83C22×C412yes—
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—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—
198Dic83⋊C4—44no—
199Dic83⋊C4—44no—
200Dic83⋊C4—44no—
201(C2×D83)⋊C4—28no—
202(C2×D83)⋊C4—28no—
203(C2×D83)⋊C4—44no—
204(C2×D83)⋊C4—44no—
205(C2×D83)⋊C4—44no—
206(C2×D83)⋊C4—44no—
207(C2×D83)⋊C4—44no—
208C24×C83C2411yescharacteristic
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×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×C83C22×C412yes—
248C22×C4×C83C22×C412yes—
249C22×C4×C83C22×C412yes—
250C22×C4×C83C2×D412yes—
251C22×C4×C83C2×D412yes—
252C22×C4×C83C2×D412yes—
253C22×C4×C83#4112yes—
254C22×C4×C83#4112yes—
255C22×C4×C83#4112yes—
256C22×C4×C83#4112yes—
257C22×C4×C83#4112yes—
258C4⋊C4×C83—28no—
259C4⋊C4×C83—28no—
260C42×C83—28no—
261C42×C83—44no—
262C42×C83—44no—
263C23×C83C23×C411yescharacteristic
264C23×C83C22×D411yescharacteristic
265C23×C83C2×#4111yescharacteristic
266C23×C83C2×#4111yescharacteristic
267C23×C83C2×#4111yescharacteristic
268C23×C83C2×#4111yescharacteristic
269C23×C83C2×#4111yescharacteristic
270C23×C83H(5,𝔽2)11yescharacteristic
271C23×C83H(5,𝔽2)11yescharacteristic
272C23×C83H(5,𝔽2)11yescharacteristic
273C23×C83H(5,𝔽2)11yescharacteristic
274C23×C83H(5,𝔽2)11yescharacteristic
275C23×C832−1+411yescharacteristic
276C23×C832−1+411yescharacteristic
277C23×C832−1+411yescharacteristic
278C22×D83—22no—
279C22×D83—22no—
280C22×D83—22no—
281C22×D83—22no—
282C22×D83—22no—
283C22×D83—22no—
284C22×D83—22no—
285C22×D83—41no—
286C22×D83—41no—
287C22×D83—41no—
288C22×D83—41no—
289C22×D83—41no—
290C22×D83—41no—
291C22×D83—41no—
292C22×D83—41no—
293C22×D83—41no—
294C22×D83—41no—
295C22×D83—41no—
296C22×D83—41no—
297C22×D83—41no—
298C22×D83—41no—
299C22×D83—41no—
300C22×D83—41no—
301C22×D83—41no—
302C22×D83—41no—
303C22×D83—41no—
304C22×D83—41no—
305C22×D83—41no—
306C22×D83—41no—
307C22×D83—41no—
308C22×D83—41no—
309C22×D83—41no—
310C22×D83—41no—
311C22×D83—41no—
312C22×D83—41no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
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—22no—
339C2×C4×C83—22no—
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#11714yes—
361C2×C4×C83C4×D414yes—
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—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—
407C2×Dic83—41no—
408C2×Dic83—41no—
409C2×Dic83—41no—
410C2×Dic83—41no—
411C22×C83C2×#11711yescharacteristic
412C22×C83C2×C4×D411yescharacteristic
413C22×C83C4×#4111yescharacteristic
414C22×C83#51811yescharacteristic
415C22×C83#52011yescharacteristic
416C22×C83#52011yescharacteristic
417C22×C83#52011yescharacteristic
418C22×C83#52511yescharacteristic
419C22×C83#52511yescharacteristic
420C22×C83#52911yescharacteristic
421C22×C83#52911yescharacteristic
422C22×C83#53411yescharacteristic
423C22×C83#53511yescharacteristic
424C22×C83#53611yescharacteristic
425C22×C83#53711yescharacteristic
426C22×C83#53811yescharacteristic
427C22×C83#53811yescharacteristic
428C22×C83#53811yescharacteristic
429C22×C83#53911yescharacteristic
430C22×C83#53911yescharacteristic
431C22×C83#53911yescharacteristic
432C22×C83#54011yescharacteristic
433C22×C83#54011yescharacteristic
434C22×C83#54011yescharacteristic
435C22×C83#54011yescharacteristic
436C22×C83#54111yescharacteristic
437C22×C83#54111yescharacteristic
438C22×C83#54211yescharacteristic
439C22×C83#54211yescharacteristic
440C22×C83#54211yescharacteristic
441C22×C83#54211yescharacteristic
442C22×C83#54211yescharacteristic
443C22×C83#54211yescharacteristic
444C22×C83#54211yescharacteristic
445C22×C83#54211yescharacteristic
446C2×D83—42no—
447C2×D83—42no—
448C2×D83—42no—
449C2×D83—42no—
450C2×D83—42no—
451C2×D83—42no—
452C2×D83—42no—
453C2×D83—81no—
454C2×D83—81no—
455C2×D83—81no—
456C2×D83—81no—
457C2×D83—81no—
458C2×D83—81no—
459C2×D83—81no—
460C2×D83—81no—
461C4×C83—24no—
462C4×C83—24no—
463C4×C83—42no—
464C4×C83—42no—
465C4×C83—42no—
466C4×C83—42no—
467C4×C83—42no—
468Dic83—42no—
469Dic83—42no—
470Dic83—42no—
471Dic83—81no—
472Dic83—81no—
473Dic83—81no—
474Dic83—81no—
475#14268—831nomaximal, Sylow
476C2×C83#229011yescharacteristic
477C2×C83#231411yescharacteristic
478C2×C83#231911yescharacteristic
479C2×C83#232211yescharacteristic
480C2×C83#232411yescharacteristic
481C2×C83#233411yescharacteristic
482C2×C83#233711yescharacteristic
483C2×C83#263011yescharacteristic
484C2×C83#263211yescharacteristic
485C2×C83#263511yescharacteristic
486C2×C83#263711yescharacteristic
487C2×C83#265011yescharacteristic
488C2×C83#265111yescharacteristic
489C2×C83#265111yescharacteristic
490C2×C83#265411yescharacteristic
491D83—82no—
492C2×#388—831no—
493C2×#388—831no—
494C2×C4×C4⋊C4D8311yescharacteristic, complemented
495#1445—831no—
496#1444—831no—
497#1442—831no—
498#1441—831no—
499#1440—831no—
500#1439—831no—
501#1439—831no—
502#1439—831no—
503#1437—831no—
504#1436—831no—
505#1434—831no—
506#1434—831no—
507C83#1426811yescharacteristic, complemented, Sylow
508C22×C4⋊C4—831no—
509C22×C4⋊C4—831no—
510C22×C4⋊C4—831no—
511C22×C4⋊C4C2×D8311yescharacteristic
512C22×C4⋊C4C2×D8311yescharacteristic
513C22×C22⋊C4—831no—
514C22×C22⋊C4—831no—
515C22×C22⋊C4—831no—
516C22×C22⋊C4—831no—
517C22×C22⋊C4—831no—
518C22×C22⋊C4—831no—
519C22×C22⋊C4—831no—
520C22×C42C2×D8311yescharacteristic
521C22×C42C2×D8311yescharacteristic
522C22×C42C2×D8311yescharacteristic
523#388—838no—
524#388—1664no—
525C4×C4⋊C4—24no—
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×#95—831no—
538C2×#95—831no—
539C2×#95—831no—
540C2×#95—831no—
541C2×#95—831no—
542C2×#95—831no—
543C2×#95—831no—
544C2×#95C2×D8311yescharacteristic
545C2×#95C2×D8311yescharacteristic
546C25—831no—
547C23×C4—831no—
548C23×C4—831no—
549C23×C4—831no—
550C23×C4—831no—
551C23×C4—831no—
552C23×C4—831no—
553C23×C4—831no—
554C23×C4C22×D8311yescharacteristic
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8311yescharacteristic
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—3321no—
568C2×C4⋊C4—3321no—
569C2×C4⋊C4—3321no—
570C2×C4⋊C4—3321no—
571C2×C4⋊C4—3321no—
572C2×C4⋊C4—3321no—
573C2×C4⋊C4—834no—
574C2×C4⋊C4—1662no—
575C2×C4⋊C4—1662no—
576C2×C22⋊C4—3321no—
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—834no—
589C2×C22⋊C4—1662no—
590C2×C22⋊C4—1662no—
591C2×C22⋊C4—1662no—
592C2×C22⋊C4—1662no—
593C2×C22⋊C4—1662no—
594C2×C22⋊C4—1662no—
595C2×C22⋊C4—1662no—
596C2×C22⋊C4—1662no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—41no—
601C2×C42—41no—
602C2×C42—41no—
603C2×C42—41no—
604C2×C42C4×D8314yes—
605C2×C42C22⋊D8314yes—
606#95—22no—
607#95—22no—
608#95—3321no—
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—834no—
619#95—834no—
620#95—1662no—
621#95—1662no—
622#95—1662no—
623#95—1662no—
624#95—1662no—
625#95—1662no—
626C24—832no—
627C24—1661no—
628C24—1661no—
629C24—1661no—
630C24—1661no—
631C24—1661no—
632C24—1661no—
633C24—1661no—
634C24—1661no—
635C24—1661no—
636C24—1661no—
637C24—1661no—
638C24—1661no—
639C24—1661no—
640C24—1661no—
641C24C23×D8311yescharacteristic
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—21no—
680C22×C4—832no—
681C22×C4—832no—
682C22×C4—832no—
683C22×C4—1661no—
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×C4C2×C4×D8312yes—
730C22×C4C2×C4×D8312yes—
731C22×C4C2×C4×D8312yes—
732C22×C4C2×C22⋊D8312yes—
733C22×C4C2×C22⋊D8312yes—
734C22×C4C2×C22⋊D8312yes—
735C22×C4#1305059012yes—
736C22×C4#1305059012yes—
737C22×C4#1305059012yes—
738C22×C4#1305059012yes—
739C22×C4#1305059012yes—
740C4⋊C4—28no—
741C4⋊C4—28no—
742C4⋊C4—3324no—
743C4⋊C4—3324no—
744C4⋊C4—3324no—
745C22⋊C4—3324no—
746C22⋊C4—3324no—
747C22⋊C4—3324no—
748C22⋊C4—3324no—
749C22⋊C4—3324no—
750C22⋊C4—1668no—
751C22⋊C4—1668no—
752C42—28no—
753C42—44no—
754C42—44no—
755C23—3321no—
756C23—3321no—
757C23—3321no—
758C23—3321no—
759C23—3321no—
760C23—3321no—
761C23—3321no—
762C23—3321no—
763C23—3321no—
764C23—3321no—
765C23—3321no—
766C23—3321no—
767C23—3321no—
768C23—3321no—
769C23—3321no—
770C23—3321no—
771C23—3321no—
772C23—3321no—
773C23—3321no—
774C23—3321no—
775C23—3321no—
776C23—3321no—
777C23—3321no—
778C23—3321no—
779C23—3321no—
780C23—3321no—
781C23—3321no—
782C23—3321no—
783C23—1662no—
784C23—1662no—
785C23—1662no—
786C23—1662no—
787C23—1662no—
788C23—1662no—
789C23—1662no—
790C23C22×C4×D8311yescharacteristic
791C23C22×C22⋊D8311yescharacteristic
792C23C2×#1305059011yescharacteristic
793C23C2×#1305059011yescharacteristic
794C23C2×#1305059011yescharacteristic
795C23C2×#1305059011yescharacteristic
796C23C2×#1305059011yescharacteristic
797C23#1458183711yescharacteristic
798C23#1458183711yescharacteristic
799C23#1458183811yescharacteristic
800C23#1458183811yescharacteristic
801C23#1458183811yescharacteristic
802C23#1458183911yescharacteristic
803C23#1458184011yescharacteristic
804C23#1458184011yescharacteristic
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
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—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—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—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—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—1662no—
893C2×C4—1662no—
894C2×C4—1662no—
895C2×C4—1662no—
896C2×C4—1662no—
897C2×C4—1662no—
898C2×C4—1662no—
899C2×C4—1662no—
900C2×C4—1662no—
901C2×C4#1458174914yes—
902C2×C4C4×C22⋊D8314yes—
903C22—3322no—
904C22—3322no—
905C22—3322no—
906C22—3322no—
907C22—3322no—
908C22—3322no—
909C22—3322no—
910C22—6641no—
911C22—6641no—
912C22—6641no—
913C22—6641no—
914C22—6641no—
915C22—6641no—
916C22—6641no—
917C22—6641no—
918C22C2×#1458174911yescharacteristic
919C22C2×C4×C22⋊D8311yescharacteristic
920C22C4×#1305059011yescharacteristic
921C22#1912817511yescharacteristic
922C22#1912818111yescharacteristic
923C22#1912818211yescharacteristic
924C22#1912818211yescharacteristic
925C22#1912821211yescharacteristic
926C22#1912821211yescharacteristic
927C22#1912823511yescharacteristic
928C22#1912823511yescharacteristic
929C22#1912826011yescharacteristic
930C22#1912826511yescharacteristic
931C22#1912827511yescharacteristic
932C22#1912827911yescharacteristic
933C22#1912828411yescharacteristic
934C22#1912828411yescharacteristic
935C22#1912828411yescharacteristic
936C22#1912829311yescharacteristic
937C22#1912829811yescharacteristic
938C22#1912829811yescharacteristic
939C22#1912830211yescharacteristic
940C22#1912830211yescharacteristic
941C22#1912830211yescharacteristic
942C22#1912830611yescharacteristic
943C22#1912830911yescharacteristic
944C22#1912830911yescharacteristic
945C22#1912831611yescharacteristic
946C22#1912832211yescharacteristic
947C22#1912832311yescharacteristic
948C22#1912832311yescharacteristic
949C22#1912832311yescharacteristic
950C22#1912832311yescharacteristic
951C22#1912832311yescharacteristic
952C22#1912832311yescharacteristic
953C4—24no—
954C4—24no—
955C4—42no—
956C4—42no—
957C4—42no—
958C4—42no—
959C4—42no—
960C4—3322no—
961C4—3322no—
962C4—3322no—
963C4—6641no—
964C4—6641no—
965C4—6641no—
966C4—6641no—
967C2—6642no—
968C2#2490990611yescharacteristic
969C2#2491006811yescharacteristic
970C2#2491010111yescharacteristic
971C2#2491013211yescharacteristic
972C2#2491015611yescharacteristic
973C2#2491023811yescharacteristic
974C2#2491027611yescharacteristic
975C2#2491330011yescharacteristic
976C2#2491332311yescharacteristic
977C2#2491334711yescharacteristic
978C2#2491336911yescharacteristic
979C2#2491347511yescharacteristic
980C2#2491349011yescharacteristic
981C2#2491349011yescharacteristic
982C2#2491353511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D83
commutatorC23×C83C23×C4
FittingC2×C4×C4⋊C4×C83C2
socle, cosocleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83#14268
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #24905729C2semidirect
4. #24905726C2semidirect
5. #24905722C2semidirect
6. #24905714C2semidirect
12. #24905696C2semidirect
13. #24905690C2semidirect
14. #24905690C2semidirect
15. C2×C4×C4⋊C4×C83C2semidirect
27. #19127592C4semidirect
494. C2×C4×C4⋊C4D83semidirect
507. C83#14268semidirect

Maximal subgroups

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

subgroupindex
C2×#191275922
#249057292
#249057262
#249057222
#249057142
#249057112
#249057072
#249057052
#249057012
#249056962
#249056902
C2×C4×C4⋊C4×C832
#1426883