Finite Group Databasebeta

← #35402201

Subgroups — #35402201

Order 21248.

1598 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128180C211yesmaximal, characteristic
2C2×#19127699C211yesmaximal, characteristic
3C2×#19127694C211yesmaximal, characteristic
4C2×#19127655C211yesmaximal, characteristic, complemented
5#24909817C211yesmaximal, characteristic, complemented
6#24907296C211yesmaximal, characteristic, complemented
7#24907292C211yesmaximal, characteristic, complemented
8#24907290C211yesmaximal, characteristic, complemented
9#24907288C211yesmaximal, characteristic, complemented
10C4×#14581717C211yesmaximal, characteristic, complemented
11#24907282C211yesmaximal, characteristic, complemented
12#102×Dic83C211yesmaximal, characteristic, complemented
13#24907181C211yesmaximal, characteristic, complemented
14#340×D83C211yesmaximal, characteristic, complemented
15C4×#102×C83C211yesmaximal, characteristic, complemented
16C22×#13050589C2211yescharacteristic
17C22×#13050573C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19#19128180—24no—
20#19128180C418yescomplemented
21C2×C4×Dic166C2211yescharacteristic
22C2×#14581757C2211yescharacteristic
23C2×D4×Dic83C2211yescharacteristic
24C2×C4×C22⋊D83—21no—
25C2×(C22⋊D83)⋊C4—21no—
26C2×#14581750C2211yescharacteristic
27C2×#14581749C2211yescharacteristic
28C2×#14581748—21no—
29C22×Dic83⋊C4—21no—
30C2×C4⋊C4×D83C2211yescharacteristic
31C2×C4⋊C4×D83C2211yescharacteristic
32#19127699C418yescomplemented
33#19127694C418yescomplemented
34C2×#14581717C2211yescharacteristic
35C2×#14581717C2211yescharacteristic
36C2×#14581715C2211yescharacteristic
37C2×#14581715C2211yescharacteristic
38C2×#14581713C2211yescharacteristic
39C2×#14581713C2211yescharacteristic
40#19127655—24no—
41C2×#14581703C2211yescharacteristic
42C2×#14581702C2211yescharacteristic
43C2×C8×Dic83C2211yescharacteristic
44C4⋊C4×Dic83C2211yescharacteristic
45C4⋊C4×Dic83C2211yescharacteristic
46C4×Dic83⋊C4—21no—
47C4×C4⋊Dic83C2211yescharacteristic
48#19127552—21no—
49C4×(C2×D83)⋊C4—21no—
50#19127548—21no—
51#19127464C2211yescharacteristic
52#19127464C2211yescharacteristic
53#19127463C2211yescharacteristic
54#19127463C2211yescharacteristic
55#19127463C2211yescharacteristic
56#19127463C2211yescharacteristic
57C2×C4×D4×C83C2211yescharacteristic
58C2×#102×C83C2211yescharacteristic
59C2×#102×C83C2211yescharacteristic
60C2×C4×C8×C83C2211yescharacteristic
61C4×C4⋊C4×C83C2211yescharacteristic
62#340×C83C2211yescharacteristic
63#340×C83C2211yescharacteristic
64C2×#13050589—22no—
65C2×#13050589—22no—
66C2×#13050589—22no—
67C2×#13050589C2×C414yes—
68C2×#13050589C2×C414yes—
69C2×#13050589C2×C414yes—
70C22×Dic166C2311yescharacteristic
71C22×C22⋊D83—21no—
72C23×Dic83—21no—
73C23×Dic83—21no—
74C22×C4×D83—21no—
75C22×C4×D83—21no—
76C22×C4×D83C2311yescharacteristic
77C2×#13050573—22no—
78C2×#13050573—22no—
79C2×#13050573C2×C414yescomplemented
80C22×C83⋊C8C2311yescharacteristic
81C22×C83⋊C8C2311yescharacteristic
82C2×C8×D83—22no—
83C2×C8×D83—22no—
84C2×C8×D83C2×C414yescomplemented
85C4×Dic166—22no—
86C4×Dic166C2×C414yescomplemented
87#14581757—22no—
88#14581757C2×C414yescomplemented
89D4×Dic83—22no—
90D4×Dic83C2×C414yescomplemented
91C4×C22⋊D83—28no—
92(C22⋊D83)⋊C4—28no—
93#14581750—22no—
94#14581750C2×C414yescomplemented
95#14581749C2×C414yes—
96#14581749D414yes—
97#14581748—28no—
98C2×C4⋊Dic83C2311yescharacteristic
99C2×C4⋊Dic83C2311yescharacteristic
100C2×C4⋊Dic83C2311yescharacteristic
101C2×Dic83⋊C4—21no—
102C2×Dic83⋊C4—21no—
103C2×Dic83⋊C4—21no—
104C2×Dic83⋊C4—28no—
105C2×Dic83⋊C4—21no—
106C2×Dic83⋊C4D411yescharacteristic
107C2×Dic83⋊C4D411yescharacteristic
108C4⋊C4×D83—22no—
109C4⋊C4×D83—22no—
110C4⋊C4×D83C2×C414yes—
111C4⋊C4×D83C2×C414yescomplemented
112C2×C22⋊Dic83—21no—
113C2×(C2×D83)⋊C4—21no—
114C2×(C2×D83)⋊C4D411yescharacteristic
115C2×(C2×D83)⋊C4D411yescharacteristic
116C2×C4×Dic83—21no—
117C2×C4×Dic83—21no—
118C2×C4×Dic83—21no—
119C2×C4×Dic83—21no—
120C2×C4×Dic83—21no—
121C2×C4×Dic83—21no—
122C2×C4×Dic83C2311yescharacteristic
123#14581717C2×C414yescomplemented
124#14581717C2×C414yescomplemented
125#14581715C2×C414yescomplemented
126#14581715C2×C414yescomplemented
127#14581713C2×C414yescomplemented
128#14581713C2×C414yescomplemented
129#14581703—22no—
130#14581702—22no—
131C8×Dic83—22no—
132C83⋊#95—21no—
133C83⋊#95—21no—
134C83⋊#95—21no—
135C22×D4×C83C2311yescharacteristic
136C23×C4×C83—21no—
137C22×C8×C83C2311yescharacteristic
138C22×C8×C83C2311yescharacteristic
139C4×D4×C83—22no—
140C4×D4×C83C2×C414yescomplemented
141C2×C4⋊C4×C83C2311yescharacteristic
142C2×C4⋊C4×C83C2311yescharacteristic
143C2×C4⋊C4×C83C2311yescharacteristic
144C2×C22⋊C4×C83—21no—
145C2×C42×C83—21no—
146C2×C42×C83C2311yescharacteristic
147#102×C83C2×C414yescomplemented
148#102×C83C2×C414yescomplemented
149C4×C8×C83—22no—
150#95×C83—21no—
151C23×D83C2×D411yescharacteristic
152#13050589—28no—
153#13050589—28no—
154#13050589—28no—
155#13050589C42116yescomplemented
156C2×Dic166—21no—
157C2×Dic166—21no—
158C2×Dic166—21no—
159C2×Dic166C22×C412yes—
160C2×Dic166C22×C412yes—
161C2×Dic166C22×C412yes—
162C2×C22⋊D83—24no—
163C2×C22⋊D83—24no—
164C2×C22⋊D83—24no—
165C22×Dic83—21no—
166C22×Dic83—24no—
167C22×Dic83—24no—
168C22×Dic83—24no—
169C22×Dic83—21no—
170C22×Dic83—21no—
171C22×Dic83—21no—
172C22×Dic83—24no—
173C22×Dic83—81no—
174C22×Dic83—81no—
175C22×Dic83C2×D411yescharacteristic
176C22×Dic83C2×D411yescharacteristic
177C22×Dic83C2×D411yescharacteristic
178C2×C4×D83—24no—
179C2×C4×D83—24no—
180C2×C4×D83—81no—
181C2×C4×D83—81no—
182C2×C4×D83—81no—
183C2×C4×D83—81no—
184C2×C4×D83C22×C412yes—
185C2×C4×D83C22×C412yes—
186C2×C4×D83C22×C412yes—
187C2×C4×D83C2×D412yes—
188C2×C4×D83#4112yes—
189C2×C4×D83#4112yes—
190#13050573—28no—
191C2×C83⋊C8—21no—
192C2×C83⋊C8—21no—
193C2×C83⋊C8—21no—
194C2×C83⋊C8—21no—
195C2×C83⋊C8C22×C412yes—
196C2×C83⋊C8C22×C412yes—
197C8×D83—28no—
198C4⋊Dic83—21no—
199C4⋊Dic83—21no—
200C4⋊Dic83—21no—
201C4⋊Dic83C22×C412yes—
202C4⋊Dic83C22×C412yes—
203C4⋊Dic83C22×C412yes—
204Dic83⋊C4—24no—
205Dic83⋊C4—24no—
206Dic83⋊C4—24no—
207Dic83⋊C4—24no—
208Dic83⋊C4C22⋊C414yes—
209Dic83⋊C4C22⋊C414yes—
210C22⋊Dic83—24no—
211(C2×D83)⋊C4—24no—
212(C2×D83)⋊C4C22⋊C414yes—
213(C2×D83)⋊C4C22⋊C414yes—
214C4×Dic83—24no—
215C4×Dic83—24no—
216C4×Dic83—24no—
217C4×Dic83—81no—
218C4×Dic83—81no—
219C4×Dic83—81no—
220C4×Dic83C22×C412yes—
221C4×Dic83C2×D412yes—
222C24×C83—21no—
223C2×D4×C83—21no—
224C2×D4×C83—21no—
225C2×D4×C83—21no—
226C2×D4×C83C22×C412yes—
227C2×D4×C83C22×C412yes—
228C2×D4×C83C22×C412yes—
229C22×C4×C83—21no—
230C22×C4×C83—21no—
231C22×C4×C83—21no—
232C22×C4×C83—24no—
233C22×C4×C83—81no—
234C22×C4×C83—81no—
235C22×C4×C83C2×D411yescharacteristic
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2411yescharacteristic
238C2×C8×C83—21no—
239C2×C8×C83—21no—
240C2×C8×C83—21no—
241C2×C8×C83—21no—
242C2×C8×C83C22×C412yes—
243C2×C8×C83C22×C412yes—
244C4⋊C4×C83—21no—
245C4⋊C4×C83—21no—
246C4⋊C4×C83—21no—
247C4⋊C4×C83C22×C412yes—
248C4⋊C4×C83C22×C412yes—
249C4⋊C4×C83C22×C412yes—
250C22⋊C4×C83—24no—
251C42×C83—81no—
252C42×C83C22×C412yes—
253C42×C83C2×D412yes—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83—41no—
258C23×C83—41no—
259C23×C83—41no—
260C23×C83—41no—
261C23×C83C22×D411yescharacteristic
262C22×D83—21no—
263C22×D83—21no—
264C22×D83—21no—
265C22×D83—21no—
266C22×D83C2×C22⋊C412yes—
267C22×D83C4×D412yes—
268C22×D83C4×D412yes—
269D4×C83—22no—
270D4×C83—22no—
271D4×C83—22no—
272D4×C83C2×C4214yes—
273C2×C4×C83—21no—
274C2×C4×C83—21no—
275C2×C4×C83—21no—
276C2×C4×C83—21no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—41no—
281C2×C4×C83—41no—
282C2×C4×C83—41no—
283C2×C4×C83—41no—
284C2×C4×C83—41no—
285C2×C4×C83—41no—
286C2×C4×C83—84no—
287C2×C4×C83C2×C22⋊C412yes—
288C2×C4×C83C2×C22⋊C412yes—
289C2×C4×C83C23×C411yescharacteristic
290C2×C4×C83C23×C411yescharacteristic
291C2×C4×C83C23×C411yescharacteristic
292C2×C4×C83C22×D411yescharacteristic
293C2×C4×C83C2×#4111yescharacteristic
294C2×C4×C83C2×#4111yescharacteristic
295C22⋊D83—216no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—21no—
300C2×Dic83—21no—
301C2×Dic83—21no—
302C2×Dic83—21no—
303C2×Dic83—216no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—41no—
308C2×Dic83—41no—
309C2×Dic83—41no—
310C2×Dic83—41no—
311C2×Dic83—41no—
312C2×Dic83—41no—
313C2×Dic83—84no—
314C2×Dic83C2×C22⋊C412yes—
315C2×Dic83C2×C22⋊C412yes—
316C2×Dic83C2×C22⋊C412yes—
317C2×Dic83C4×D412yes—
318C2×Dic83C4×D412yes—
319C4×D83—84no—
320C4×D83—84no—
321C4×D83C2×C4214yes—
322C4×D83#11714yes—
323C4×D83C4×D414yes—
324C4×D83C4×D414yes—
325Dic166—22no—
326Dic166—22no—
327Dic166—22no—
328Dic166C2×C4214yes—
329C8×C83—22no—
330C8×C83—22no—
331C83⋊C8—22no—
332C83⋊C8—22no—
333C22×C83—24no—
334C22×C83—42no—
335C22×C83—42no—
336C22×C83—42no—
337C22×C83—42no—
338C22×C83—42no—
339C22×C83—42no—
340C22×C83C22×C22⋊C411yescharacteristic
341C22×C83C2×C4×D411yescharacteristic
342C22×C83C2×C4×D411yescharacteristic
343C22×C83#57611yescharacteristic
344C22×C83#57711yescharacteristic
345C22×C83#57711yescharacteristic
346C22×C83#57811yescharacteristic
347C2×D83—22no—
348C2×D83—22no—
349C2×D83—22no—
350C2×D83—22no—
351C2×D83—22no—
352C2×D83—22no—
353C2×D83C4×C22⋊C414yes—
354C4×C83—22no—
355C4×C83—22no—
356C4×C83—42no—
357C4×C83—42no—
358C4×C83—42no—
359C4×C83C22×C4211yescharacteristic
360C4×C83C2×#11711yescharacteristic
361C4×C83C2×C4×D411yescharacteristic
362C4×C83C2×C4×D411yescharacteristic
363Dic83—22no—
364Dic83—22no—
365Dic83—24no—
366Dic83—42no—
367Dic83—42no—
368Dic83—42no—
369Dic83C4×C22⋊C414yes—
370#20415—831nomaximal, Sylow
371C2×C83—44no—
372C2×C83C2×C4×C22⋊C411yescharacteristic
373C2×C83#289711yescharacteristic
374C2×C83#289811yescharacteristic
375C2×C83#294611yescharacteristic
376C2×C83#294711yescharacteristic
377C2×C83#295111yescharacteristic
378C2×C83#295211yescharacteristic
379D83—24no—
380C2×#520—831no—
381C2×#417—831no—
382C2×#416—831no—
383C2×#405—831no—
384#2274—831no—
385#1763—831no—
386#1763—831no—
387#1762—831no—
388#1762—831no—
389C4×#103—831no—
390C4×#103—831no—
391C4×#102—831no—
392C4×#102D8311yescharacteristic, complemented
393#1736—831no—
394C2×#340—831no—
395C83#2041511yescharacteristic, complemented, Sylow
396C22×#41—831no—
397C22×M16—831no—
398C23×C8—831no—
399#520—838no—
400#520—1664no—
401C2×C4×Q8—831no—
402C2×C4×Q8—831no—
403C2×C4×D4—831no—
404C2×C4×D4—1661no—
405C2×C4×D4—1661no—
406C2×C4×D4C2×D8311yescharacteristic
407C2×#117—831no—
408C2×#117—831no—
409C2×#117—1661no—
410C22×C4⋊C4—831no—
411C22×C4⋊C4—831no—
412C22×C4⋊C4—1661no—
413#417—838no—
414#416—838no—
415C2×#103—831no—
416C2×#103—831no—
417C2×#103—831no—
418C2×#103—831no—
419C2×#102—831no—
420C2×#102—831no—
421C2×#102C2×D8311yescharacteristic
422C2×#102C2×D8311yescharacteristic
423#405—1664no—
424C2×#97—831no—
425C2×#97—831no—
426C2×C4×C8—831no—
427C2×C4×C8C2×D8311yescharacteristic
428C4×C4⋊C4—831no—
429C4×C4⋊C4—831no—
430C4×C4⋊C4—831no—
431C4×C4⋊C4—1661no—
432C4×C4⋊C4—1661no—
433C4×C4⋊C4C2×D8311yescharacteristic
434C4×C22⋊C4—1661no—
435C4×C22⋊C4—1661no—
436#340—831no—
437#340—831no—
438#340—831no—
439#340—831no—
440#340—831no—
441#340—831no—
442#340C2×D8311yescharacteristic
443#340C2×D8311yescharacteristic
444C2×#41—834no—
445C2×#41—834no—
446C2×#41—834no—
447C2×#41—1662no—
448C2×#41—1662no—
449C2×#41—1662no—
450C22×Q8—831no—
451C22×D4—1661no—
452C22×D4C22×D8311yescharacteristic
453C23×C4—21no—
454C23×C4—831no—
455C23×C4—1661no—
456C23×C4—1661no—
457C23×C4—1661no—
458C23×C4—1661no—
459C2×M16—834no—
460C2×M16—1662no—
461C2×M16—1662no—
462C22×C8—831no—
463C22×C8—831no—
464C22×C8—834no—
465C22×C8—1662no—
466C22×C8—1662no—
467C22×C8C22×D8311yescharacteristic
468C22×C8C22×D8311yescharacteristic
469C4×Q8—834no—
470C4×Q8—834no—
471C4×Q8—1662no—
472C4×Q8—1662no—
473C4×D4—22no—
474C4×D4—834no—
475C4×D4—1662no—
476C4×D4—1668no—
477C4×D4—1668no—
478C4×D4C4×D8314yescomplemented
479#117—834no—
480#117—834no—
481#117—834no—
482#117—1668no—
483#117—1662no—
484C2×C4⋊C4—831no—
485C2×C4⋊C4—831no—
486C2×C4⋊C4—831no—
487C2×C4⋊C4—831no—
488C2×C4⋊C4—831no—
489C2×C4⋊C4—834no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—1662no—
492C2×C4⋊C4—1662no—
493C2×C4⋊C4—1668no—
494C2×C4⋊C4—1661no—
495C2×C4⋊C4—1661no—
496C2×C4⋊C4—1661no—
497C2×C4⋊C4—1661no—
498C2×C4⋊C4C22×D8311yescharacteristic
499C2×C4⋊C4C22×D8311yescharacteristic
500C2×C4⋊C4C22×D8311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—831no—
503C2×C22⋊C4—831no—
504C2×C22⋊C4—1661no—
505C2×C22⋊C4—1661no—
506C2×C42—21no—
507C2×C42—831no—
508C2×C42—1661no—
509C2×C42—1661no—
510C2×C42—1661no—
511C2×C42—1661no—
512C2×C42—1661no—
513C2×C42—1661no—
514C2×C42C22×D8311yescharacteristic
515#103—834no—
516#103—834no—
517#103—834no—
518#103—834no—
519#102—834no—
520#102—834no—
521#102C4×D8314yescomplemented
522#102C4×D8314yescomplemented
523#97—1662no—
524#97—1662no—
525C4×C8—22no—
526C4×C8—1662no—
527#95—21no—
528#95—1661no—
529#95—1661no—
530#95—1661no—
531C24—21no—
532C24—831no—
533#41—8316no—
534#41—1668no—
535#41—1668no—
536#41—1668no—
537C2×Q8—832no—
538C2×Q8—832no—
539C2×Q8—832no—
540C2×Q8—1661no—
541C2×Q8—1661no—
542C2×Q8—1661no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—1664no—
547C2×D4—1664no—
548C2×D4—1664no—
549C2×D4C2×C4×D8312yes—
550C2×D4C2×C4×D8312yes—
551C2×D4C2×C4×D8312yes—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—24no—
556C22×C4—81no—
557C22×C4—81no—
558C22×C4—831no—
559C22×C4—832no—
560C22×C4—832no—
561C22×C4—832no—
562C22×C4—832no—
563C22×C4—832no—
564C22×C4—832no—
565C22×C4—831no—
566C22×C4—831no—
567C22×C4—6641no—
568C22×C4—6641no—
569C22×C4—6641no—
570C22×C4—6641no—
571C22×C4—6641no—
572C22×C4—6641no—
573C22×C4—1664no—
574C22×C4—1664no—
575C22×C4—1661no—
576C22×C4—1661no—
577C22×C4—1661no—
578C22×C4—1664no—
579C22×C4—1664no—
580C22×C4—1664no—
581C22×C4—1664no—
582C22×C4—1661no—
583C22×C4D4×D8311yescharacteristic
584C22×C4D4×D8311yescharacteristic
585C22×C4C23×D8311yescharacteristic
586M16—1668no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—832no—
592C2×C8—832no—
593C2×C8—1668no—
594C2×C8—1661no—
595C2×C8—1661no—
596C2×C8—1661no—
597C2×C8—1661no—
598C2×C8C2×C4×D8312yes—
599C2×C8C2×C4×D8312yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—834no—
604C4⋊C4—834no—
605C4⋊C4—832no—
606C4⋊C4—832no—
607C4⋊C4—832no—
608C4⋊C4—1664no—
609C4⋊C4—1664no—
610C4⋊C4—1664no—
611C4⋊C4—1661no—
612C4⋊C4—1661no—
613C4⋊C4—1661no—
614C4⋊C4—1664no—
615C4⋊C4C2×C4×D8312yes—
616C4⋊C4C2×C4×D8312yes—
617C4⋊C4C2×C4×D8312yes—
618C22⋊C4—24no—
619C22⋊C4—834no—
620C22⋊C4—834no—
621C22⋊C4—1664no—
622C22⋊C4—1664no—
623C42—81no—
624C42—832no—
625C42—832no—
626C42—6641no—
627C42—6641no—
628C42—6641no—
629C42—1664no—
630C42—1664no—
631C42—1664no—
632C42C2×C4×D8312yes—
633C42D4×D8312yes—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—832no—
642C23—832no—
643C23—832no—
644C23—1661no—
645C23—1661no—
646C23—1661no—
647C23—1661no—
648C23C2×D4×D8311yescharacteristic
649Q8—834no—
650Q8—1662no—
651Q8—1662no—
652Q8—1662no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—16616no—
657D4C42×D8314yes—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—84no—
672C2×C4—3321no—
673C2×C4—3321no—
674C2×C4—3321no—
675C2×C4—3321no—
676C2×C4—3321no—
677C2×C4—3321no—
678C2×C4—832no—
679C2×C4—832no—
680C2×C4—832no—
681C2×C4—834no—
682C2×C4—834no—
683C2×C4—834no—
684C2×C4—834no—
685C2×C4—832no—
686C2×C4—832no—
687C2×C4—6644no—
688C2×C4—6644no—
689C2×C4—6644no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—16616no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1661no—
698C2×C4—1661no—
699C2×C4—1661no—
700C2×C4—1661no—
701C2×C4C22⋊C4×D8312yes—
702C2×C4C22⋊C4×D8312yes—
703C2×C4C22×C4×D8311yescharacteristic
704C2×C4C22×C4×D8311yescharacteristic
705C2×C4C22×C4×D8311yescharacteristic
706C2×C4C2×D4×D8311yescharacteristic
707C2×C4#41×D8311yescharacteristic
708C2×C4#41×D8311yescharacteristic
709C8—22no—
710C8—22no—
711C8—1662no—
712C8—1662no—
713C22—24no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—834no—
721C22—1662no—
722C22—1662no—
723C22—1662no—
724C22—1662no—
725C22—1662no—
726C22—1662no—
727C22C2×C22⋊C4×D8311yescharacteristic
728C22C4×D4×D8311yescharacteristic
729C22C4×D4×D8311yescharacteristic
730C22#1912850211yescharacteristic
731C22#1912850711yescharacteristic
732C22#1912850811yescharacteristic
733C22#1912851511yescharacteristic
734C4—22no—
735C4—22no—
736C4—42no—
737C4—42no—
738C4—42no—
739C4—3322no—
740C4—3322no—
741C4—3322no—
742C4—834no—
743C4—1662no—
744C4—1662no—
745C4—1664no—
746C4C2×C42×D8311yescharacteristic
747C4#117×D8311yescharacteristic
748C4C4×D4×D8311yescharacteristic
749C4C4×D4×D8311yescharacteristic
750C2—44no—
751C2—1664no—
752C2C4×C22⋊C4×D8311yescharacteristic
753C2#2491598411yescharacteristic
754C2#2491599211yescharacteristic
755C2#2491628811yescharacteristic
756C2#2491629911yescharacteristic
757C2#2491633311yescharacteristic
758C2#2491634111yescharacteristic
subgroupG/H
centerC23C2×D4×D83
commutatorC4×C83C22×C42
FrattiniC22×C4C23×D83
FittingC4×#102×C83C2
socleC23×C83C22×D4
prime radicalC22×#13050589C22
cosocleC22×C4×C83C24
hypercenterC4×#102D83
hypocenterC83#20415
LCSG ▷ C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
4. C2×#19127655C2semidirect
5. #24909817C2semidirect
6. #24907296C2semidirect
7. #24907292C2semidirect
8. #24907290C2semidirect
9. #24907288C2semidirect
10. C4×#14581717C2semidirect
11. #24907282C2semidirect
12. #102×Dic83C2semidirect
13. #24907181C2semidirect
14. #340×D83C2semidirect
15. C4×#102×C83C2semidirect
20. #19128180C4semidirect
32. #19127699C4semidirect
33. #19127694C4semidirect
79. C2×#13050573C2×C4semidirect
84. C2×C8×D83C2×C4semidirect
86. C4×Dic166C2×C4semidirect
88. #14581757C2×C4semidirect
90. D4×Dic83C2×C4semidirect
94. #14581750C2×C4semidirect
111. C4⋊C4×D83C2×C4semidirect
123. #14581717C2×C4semidirect
124. #14581717C2×C4semidirect
125. #14581715C2×C4semidirect
126. #14581715C2×C4semidirect
127. #14581713C2×C4semidirect
128. #14581713C2×C4semidirect
140. C4×D4×C83C2×C4semidirect
147. #102×C83C2×C4semidirect
148. #102×C83C2×C4semidirect
155. #13050589C42semidirect
392. C4×#102D83semidirect
395. C83#20415semidirect
478. C4×D4C4×D83semidirect
521. #102C4×D83semidirect
522. #102C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191281802
C2×#191276992
C2×#191276942
C2×#191276552
#249098172
#249072962
#249072922
#249072902
#249072882
C4×#145817172
#249072822
#102×Dic832
#249071812
#340×D832
C4×#102×C832
#2041583