Finite Group Databasebeta

← C2×#24920231 #36284185

Subgroups — C2×#24920231 #36284185

Order 21248.

1874 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128436C211yesmaximal, characteristic
2#24920231C2116yesmaximal, direct product factor
3C2×#19128067C211yesmaximal, characteristic
4C2×#19128063C211yesmaximal, characteristic, complemented
5C2×#19128058C211yesmaximal, characteristic, complemented
6C2×#19128005C211yesmaximal, characteristic, complemented
7C2×#19127998C211yesmaximal, characteristic, complemented
8C2×#19127988C211yesmaximal, characteristic, complemented
9C2×#19127923C211yesmaximal, characteristic, complemented
10C2×#19127923C211yesmaximal, characteristic, complemented
11C2×#19127901C211yesmaximal, characteristic
12C2×#19127832C211yesmaximal, characteristic, complemented
13C2×#19127806C211yesmaximal, characteristic, complemented
14C2×#19127799C211yesmaximal, characteristic, complemented
15C2×C4×#13050577C211yesmaximal, characteristic, complemented
16C2×#557×C83C211yesmaximal, characteristic, complemented
17C22×#13050580C2211yescharacteristic
18C22×#13050577C2211yescharacteristic
19C22×#13050577C2211yescharacteristic
20#19128436—24no—
21#19128436C2218yes—
22C2×#14581789C2211yescharacteristic
23C2×#14581781—21no—
24C2×#14581780C2211yescharacteristic
25C2×#14581780C2211yescharacteristic
26C2×#14581777—21no—
27C2×#14581777—21no—
28C2×C4×Dic166C2211yescharacteristic
29C2×C4×D332C2211yescharacteristic
30C2×C4×D332C2211yescharacteristic
31C2×#14581754—21no—
32#19128067C2218yes—
33#19128063C2218yescomplemented
34#19128058C2218yescomplemented
35#19128005C2218yescomplemented
36#19127998C2218yescomplemented
37#19127988C2218yescomplemented
38#19127923C2218yescomplemented
39#19127923C2218yescomplemented
40#19127901C2218yes—
41#19127832C2218yescomplemented
42#19127806C2218yescomplemented
43#19127799C2218yescomplemented
44C4×#13050577C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581723C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×C4⋊(C83⋊C8)C2211yescharacteristic
51C2×#14581716C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581712C2211yescharacteristic
56C2×#14581712C2211yescharacteristic
57C2×#14581712C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×#14581703C2211yescharacteristic
62C2×#14581703C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#557×C83—24no—
65#557×C83C2218yescomplemented
66C2×C4⋊Q8×C83—21no—
67C2×C4⋊Q8×C83C2211yescharacteristic
68C2×#125×C83—21no—
69C2×#125×C83—21no—
70C2×#125×C83C2211yescharacteristic
71C2×#125×C83C2211yescharacteristic
72C2×C4×Q8×C83—21no—
73C2×C4×Q8×C83C2211yescharacteristic
74C2×C4×Q8×C83C2211yescharacteristic
75C2×C4×Q8×C83C2211yescharacteristic
76C2×C4×Q8×C83C2211yescharacteristic
77C22×Dic166C2311yescharacteristic
78C22×D332—21no—
79C22×D332—21no—
80C22×D332C2311yescharacteristic
81C22×D332C2311yescharacteristic
82C22×C4×D83—21no—
83C22×C4×D83—21no—
84C2×#13050580—24no—
85C2×#13050580C2314yes—
86C2×#13050577—24no—
87C2×#13050577—24no—
88C2×#13050577C2314yes—
89C2×#13050577C2314yes—
90C22×C83⋊C8C2311yescharacteristic
91C22×C83⋊C8C2311yescharacteristic
92C22×C83⋊C8C2311yescharacteristic
93C22×C83⋊C8C2311yescharacteristic
94#14581789—22no—
95#14581789C2314yes—
96#14581781—28no—
97#14581780—22no—
98#14581780—22no—
99#14581780C2314yes—
100#14581780C2314yes—
101#14581777—28no—
102#14581777—28no—
103C4×Dic166—22no—
104C4×Dic166C2314yes—
105C4×D332—22no—
106C4×D332—22no—
107C4×D332C2314yes—
108C4×D332C2314yes—
109#14581754—28no—
110C2×C4⋊Dic83C2311yescharacteristic
111C2×Dic83⋊C4—21no—
112C2×(C2×D83)⋊C4—21no—
113C2×(C2×D83)⋊C4—21no—
114C2×(C2×D83)⋊C4—21no—
115C2×(C2×D83)⋊C4—21no—
116C2×(C2×D83)⋊C4—21no—
117C2×(C2×D83)⋊C4—21no—
118C2×C4×Dic83—21no—
119#14581725C2314yes—
120#14581723C2314yes—
121#14581723C2314yes—
122C4⋊(C83⋊C8)C2314yes—
123C4⋊(C83⋊C8)C2314yes—
124C4⋊(C83⋊C8)C2314yes—
125#14581716C2314yes—
126#14581715C2314yes—
127#14581715C2314yes—
128#14581715C2314yes—
129#14581712C2314yes—
130#14581712C2314yes—
131#14581712C2314yes—
132#14581712C2314yes—
133#14581712C2314yes—
134#14581712C2314yes—
135#14581703C2314yes—
136#14581703C2314yes—
137C4×C83⋊C8C2314yes—
138C22×Q8×C83—21no—
139C22×Q8×C83D411yescharacteristic
140C22×Q8×C83C2311yescharacteristic
141C4⋊Q8×C83—28no—
142C4⋊Q8×C83—22no—
143C4⋊Q8×C83C2314yes—
144#125×C83—28no—
145#125×C83—28no—
146#125×C83—22no—
147#125×C83—22no—
148#125×C83C2314yes—
149#125×C83C2314yes—
150C4×Q8×C83—28no—
151C4×Q8×C83—22no—
152C4×Q8×C83—22no—
153C4×Q8×C83—22no—
154C4×Q8×C83D414yes—
155C4×Q8×C83C2314yes—
156C4×Q8×C83C2314yes—
157C4×Q8×C83C2314yes—
158C4×Q8×C83C2314yes—
159C2×C4⋊C4×C83—21no—
160C2×C4⋊C4×C83—21no—
161C2×C4⋊C4×C83—21no—
162C2×C4⋊C4×C83—21no—
163C2×C4⋊C4×C83—21no—
164C2×C4⋊C4×C83—21no—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—21no—
167C2×C4⋊C4×C83D411yescharacteristic
168C2×C4⋊C4×C83D411yescharacteristic
169C2×C4⋊C4×C83D411yescharacteristic
170C2×C4⋊C4×C83C2311yescharacteristic
171C2×C4⋊C4×C83C2311yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C42×C83—21no—
174C2×C42×C83—21no—
175C2×C42×C83—21no—
176C2×C42×C83C2311yescharacteristic
177C2×C42×C83C2311yescharacteristic
178C2×C42×C83C2311yescharacteristic
179C23×D83—21no—
180C23×D83—21no—
181C2×Dic166—22no—
182C2×Dic166—22no—
183C2×Dic166—21no—
184C2×Dic166C2412yes—
185C2×D332—22no—
186C2×D332—22no—
187C2×D332—22no—
188C2×D332—22no—
189C2×D332—21no—
190C2×D332—21no—
191C2×D332—24no—
192C2×D332—24no—
193C2×D332—44no—
194C2×D332—82no—
195C2×D332C2412yes—
196C2×D332C2412yes—
197C22×Dic83—21no—
198C22×Dic83—21no—
199C2×C4×D83—24no—
200C2×C4×D83—24no—
201C2×C4×D83—82no—
202C2×C4×D83—82no—
203#13050580—28no—
204#13050577—28no—
205#13050577—28no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8—22no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83C2412yes—
216Dic83⋊C4—24no—
217(C2×D83)⋊C4—24no—
218(C2×D83)⋊C4—24no—
219(C2×D83)⋊C4—24no—
220(C2×D83)⋊C4—24no—
221(C2×D83)⋊C4—24no—
222(C2×D83)⋊C4—24no—
223C4×Dic83—24no—
224C2×Q8×C83—21no—
225C2×Q8×C83—24no—
226C2×Q8×C83—22no—
227C2×Q8×C83—42no—
228C2×Q8×C83—44no—
229C2×Q8×C83C2×D414yes—
230C2×Q8×C83#4114yes—
231C2×Q8×C83C2412yes—
232C22×C4×C83—21no—
233C22×C4×C83—21no—
234C22×C4×C83—21no—
235C22×C4×C83—21no—
236C22×C4×C83C2×D411yescharacteristic
237C22×C4×C83C2×D411yescharacteristic
238C22×C4×C83C2×D411yescharacteristic
239C22×C4×C83C2×D411yescharacteristic
240C22×C4×C83C2×D411yescharacteristic
241C22×C4×C83C2×D411yescharacteristic
242C22×C4×C83C2411yescharacteristic
243C4⋊C4×C83—24no—
244C4⋊C4×C83—24no—
245C4⋊C4×C83—24no—
246C4⋊C4×C83—24no—
247C4⋊C4×C83—24no—
248C4⋊C4×C83—24no—
249C4⋊C4×C83—24no—
250C4⋊C4×C83—24no—
251C4⋊C4×C83—21no—
252C4⋊C4×C83—21no—
253C4⋊C4×C83—21no—
254C4⋊C4×C83C2×D414yes—
255C4⋊C4×C83C2×D414yes—
256C4⋊C4×C83C2×D414yes—
257C4⋊C4×C83C2412yes—
258C4⋊C4×C83C2412yes—
259C4⋊C4×C83C2412yes—
260C42×C83—24no—
261C42×C83—24no—
262C42×C83—24no—
263C42×C83C2×D412yes—
264C42×C83C2×D412yes—
265C42×C83C2×D412yes—
266C42×C83C2412yes—
267C42×C83C2412yes—
268C42×C83C2412yes—
269C23×C83C22×D411yescharacteristic
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—42no—
273C22×D83—42no—
274C22×D83—42no—
275C22×D83—42no—
276C22×D83—42no—
277C22×D83—42no—
278Q8×C83—24no—
279Q8×C83—22no—
280Q8×C83—44no—
281Q8×C83—48no—
282Q8×C83C2×#4114yes—
283C2×C4×C83—24no—
284C2×C4×C83—22no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83—22no—
288C2×C4×C83—22no—
289C2×C4×C83—22no—
290C2×C4×C83—22no—
291C2×C4×C83—22no—
292C2×C4×C83—22no—
293C2×C4×C83—22no—
294C2×C4×C83—42no—
295C2×C4×C83—42no—
296C2×C4×C83—42no—
297C2×C4×C83C22×D412yes—
298C2×C4×C83C22×D412yes—
299C2×C4×C83C22×D412yes—
300C2×C4×C83C22×D412yes—
301C2×C4×C83C22×D412yes—
302C2×C4×C83C22×D412yes—
303C2×C4×C83C22×D411yescharacteristic
304C2×C4×C83C2×#4112yes—
305C2×C4×C832−1+412yes—
306C2×C4×C83C2511yescharacteristic
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—42no—
310C2×Dic83—42no—
311D332—22no—
312D332—22no—
313D332—22no—
314D332—22no—
315D332—48no—
316D332—42no—
317D332—42no—
318D332—84no—
319C4×D83—84no—
320C4×D83—84no—
321Dic166—22no—
322Dic166—22no—
323Dic166—42no—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C83⋊C8—22no—
327C83⋊C8—22no—
328C22×C83#54812yes—
329C22×C83#57512yes—
330C22×C83#57712yes—
331C22×C83C23×D411yescharacteristic
332C2×D83—42no—
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—42no—
338C2×D83—84no—
339C2×D83—84no—
340C4×C83—24no—
341C4×C83—22no—
342C4×C83—22no—
343C4×C83—22no—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—22no—
347C4×C83—42no—
348C4×C83—42no—
349C4×C83—42no—
350C4×C83#54812yes—
351C4×C83C22×#4111yescharacteristic
352C4×C83C2×2−1+411yescharacteristic
353Dic83—42no—
354Dic83—42no—
355C2×#3371—831nomaximal, Sylow
356C2×C83#337114yescomplemented
357C2×C83C2×#54811yescharacteristic
358C2×C83C2×#57511yescharacteristic
359C2×C83C2×#57711yescharacteristic
360D83—82no—
361D83—82no—
362C2×#559—831no—
363C2×#557D8311yescharacteristic, complemented
364#3371—8316no—
365C2×#490—831no—
366C2×#489—831no—
367C2×#488—831no—
368C2×#479—831no—
369C2×#478—831no—
370C2×#476—831no—
371C2×#464—831no—
372C2×#464—831no—
373C2×#460—831no—
374C2×#446—831no—
375C2×#441—831no—
376C2×#440—831no—
377C2×C4×SD16—831no—
378C83C2×#337111yescharacteristic, complemented, Sylow
379C22×Q16—831no—
380C22×SD16—831no—
381C22×SD16—831no—
382#559—838no—
383#559—1664no—
384#557—24no—
385#557C2×D8318yescomplemented
386C2×C4⋊Q8—21no—
387C2×C4⋊Q8C2×D8311yescharacteristic
388C2×#127—831no—
389C2×#125—21no—
390C2×#125—21no—
391C2×#125C2×D8311yescharacteristic
392C2×#125C2×D8311yescharacteristic
393C2×#124—831no—
394C2×#124—831no—
395C2×#124—1661no—
396C2×#123—1661no—
397C2×#123—1661no—
398C2×C4×Q8—21no—
399C2×C4×Q8—831no—
400C2×C4×Q8C2×D8311yescharacteristic
401C2×C4×Q8C2×D8311yescharacteristic
402C2×C4×Q8C2×D8311yescharacteristic
403C2×C4×Q8C2×D8311yescharacteristic
404C2×C4×D4—831no—
405C2×C4×D4—831no—
406C2×C4×D4—1661no—
407#490—838no—
408#489—838no—
409#488—838no—
410#479—838no—
411#478—838no—
412#476—838no—
413#464—838no—
414#464—838no—
415#460—838no—
416#446—838no—
417#441—838no—
418#440—838no—
419C4×SD16—838no—
420C2×#107—831no—
421C2×#106—831no—
422C2×#106—831no—
423C2×C4⋊C8—831no—
424C2×C4⋊C8—831no—
425C2×C4⋊C8—831no—
426C2×#103—831no—
427C2×#103—831no—
428C2×#103—831no—
429C2×#103—831no—
430C2×#102—831no—
431C2×#102—831no—
432C2×#102—831no—
433C2×#102—831no—
434C2×#102—831no—
435C2×#102—831no—
436C2×#97—831no—
437C2×#97—831no—
438C2×C4×C8—831no—
439C22×Q8—21no—
440C22×Q8—831no—
441C22×Q8C22⋊D8311yescharacteristic
442C22×Q8C22×D8311yescharacteristic
443C22×D4—831no—
444C22×D4—831no—
445C22×D4—1661no—
446C22×D4—1661no—
447C23×C4—1661no—
448C23×C4—1661no—
449C2×Q16—834no—
450C2×Q16—1664no—
451C2×SD16—834no—
452C2×SD16—834no—
453C2×SD16—1664no—
454C2×SD16—1664no—
455C22×C8—831no—
456C22×C8—831no—
457C22×C8—831no—
458C22×C8—831no—
459C4⋊Q8—28no—
460C4⋊Q8—22no—
461C4⋊Q8C22×D8314yes—
462#127—834no—
463#127—1662no—
464#125—28no—
465#125—28no—
466#125—22no—
467#125—22no—
468#125C22×D8314yes—
469#125C22×D8314yes—
470#124—834no—
471#124—834no—
472#124—1668no—
473#124—1662no—
474#124—1662no—
475#123—1668no—
476#123—1668no—
477C4×Q8—28no—
478C4×Q8—22no—
479C4×Q8—22no—
480C4×Q8—22no—
481C4×Q8—834no—
482C4×Q8—1662no—
483C4×Q8C22⋊D8314yes—
484C4×Q8C22×D8314yes—
485C4×Q8C22×D8314yes—
486C4×Q8C22×D8314yes—
487C4×Q8C22×D8314yes—
488C4×D4—834no—
489C4×D4—834no—
490C4×D4—1668no—
491C4×D4—1662no—
492C4×D4—1662no—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—831no—
502C2×C4⋊C4—1661no—
503C2×C4⋊C4C22⋊D8311yescharacteristic
504C2×C4⋊C4C22⋊D8311yescharacteristic
505C2×C4⋊C4C22⋊D8311yescharacteristic
506C2×C4⋊C4C22×D8311yescharacteristic
507C2×C4⋊C4C22×D8311yescharacteristic
508C2×C4⋊C4C22×D8311yescharacteristic
509C2×C22⋊C4—1661no—
510C2×C22⋊C4—1661no—
511C2×C22⋊C4—1661no—
512C2×C22⋊C4—1661no—
513C2×C22⋊C4—1661no—
514C2×C22⋊C4—1661no—
515C2×C42—21no—
516C2×C42—21no—
517C2×C42—21no—
518C2×C42—1661no—
519C2×C42C22×D8311yescharacteristic
520C2×C42C22×D8311yescharacteristic
521C2×C42C22×D8311yescharacteristic
522#107—834no—
523#106—834no—
524#106—834no—
525C4⋊C8—834no—
526C4⋊C8—834no—
527C4⋊C8—834no—
528#103—834no—
529#103—834no—
530#103—834no—
531#103—834no—
532#102—834no—
533#102—834no—
534#102—834no—
535#102—834no—
536#102—834no—
537#102—834no—
538#97—834no—
539#97—834no—
540C4×C8—834no—
541C24—1661no—
542C24—1661no—
543C2×Q8—21no—
544C2×Q8—24no—
545C2×Q8—22no—
546C2×Q8—42no—
547C2×Q8—44no—
548C2×Q8—832no—
549C2×Q8—1662no—
550C2×Q8—1662no—
551C2×Q8—1661no—
552C2×Q8C2×C22⋊D8314yes—
553C2×Q8#1305059114yes—
554C2×Q8C23×D8312yes—
555C2×D4—3324no—
556C2×D4—832no—
557C2×D4—832no—
558C2×D4—6642no—
559C2×D4—1664no—
560C2×D4—1661no—
561C2×D4—1661no—
562C2×D4—1664no—
563C2×D4—1662no—
564C2×D4—1662no—
565C2×D4—1662no—
566C2×D4—1662no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—6642no—
572C22×C4—6642no—
573C22×C4—1661no—
574C22×C4—1661no—
575C22×C4—1664no—
576C22×C4—1664no—
577C22×C4C2×C22⋊D8311yescharacteristic
578C22×C4C2×C22⋊D8311yescharacteristic
579C22×C4C2×C22⋊D8311yescharacteristic
580C22×C4C2×C22⋊D8311yescharacteristic
581C22×C4C2×C22⋊D8311yescharacteristic
582C22×C4C2×C22⋊D8311yescharacteristic
583C22×C4C23×D8311yescharacteristic
584Q16—1668no—
585SD16—1668no—
586SD16—1668no—
587C2×C8—832no—
588C2×C8—832no—
589C2×C8—832no—
590C2×C8—832no—
591C2×C8—1662no—
592C2×C8—1662no—
593C2×C8—1662no—
594C2×C8—1662no—
595C4⋊C4—24no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—24no—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—832no—
607C4⋊C4—1661no—
608C4⋊C4—1664no—
609C4⋊C4C2×C22⋊D8314yes—
610C4⋊C4C2×C22⋊D8314yes—
611C4⋊C4C2×C22⋊D8314yes—
612C4⋊C4C23×D8312yes—
613C4⋊C4C23×D8312yes—
614C4⋊C4C23×D8312yes—
615C22⋊C4—1664no—
616C22⋊C4—1664no—
617C22⋊C4—1664no—
618C22⋊C4—1664no—
619C22⋊C4—1664no—
620C22⋊C4—1664no—
621C42—24no—
622C42—24no—
623C42—24no—
624C42—1664no—
625C42C2×C22⋊D8312yes—
626C42C2×C22⋊D8312yes—
627C42C2×C22⋊D8312yes—
628C42C23×D8312yes—
629C42C23×D8312yes—
630C42C23×D8312yes—
631C23—3322no—
632C23—3322no—
633C23—3322no—
634C23—3322no—
635C23—3322no—
636C23—3322no—
637C23—1662no—
638C23—1662no—
639C23C22×C22⋊D8311yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—44no—
643Q8—48no—
644Q8—3322no—
645Q8—1662no—
646Q8—1662no—
647Q8C2×#1305059114yes—
648D4—3328no—
649D4—3322no—
650D4—3322no—
651D4—6644no—
652D4—1662no—
653D4—1662no—
654D4—1662no—
655D4—1662no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—42no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—3322no—
671C2×C4—3322no—
672C2×C4—6644no—
673C2×C4—6644no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4C22×C22⋊D8312yes—
677C2×C4C22×C22⋊D8312yes—
678C2×C4C22×C22⋊D8312yes—
679C2×C4C22×C22⋊D8312yes—
680C2×C4C22×C22⋊D8312yes—
681C2×C4C22×C22⋊D8312yes—
682C2×C4C22×C22⋊D8311yescharacteristic
683C2×C4C2×#1305059112yes—
684C2×C4#1458184012yes—
685C2×C4C24×D8311yescharacteristic
686C8—1662no—
687C8—1662no—
688C8—1662no—
689C8—1662no—
690C22—3322no—
691C22—3322no—
692C22—3322no—
693C22—3322no—
694C22—3322no—
695C22—3322no—
696C22—6644no—
697C22—6644no—
698C22#1912836212yes—
699C22#1912849912yes—
700C22#1912850912yes—
701C22C23×C22⋊D8311yescharacteristic
702C4—22no—
703C4—22no—
704C4—22no—
705C4—24no—
706C4—22no—
707C4—22no—
708C4—22no—
709C4—42no—
710C4—42no—
711C4—42no—
712C4—3322no—
713C4—3322no—
714C4#1912836212yes—
715C4C22×#1305059111yescharacteristic
716C4C2×#1458184011yescharacteristic
717C2—6642no—
718C2—6642no—
719C2#2492023114yesdirect product factor
720C2C2×#1912836211yescharacteristic
721C2C2×#1912849911yescharacteristic
722C2C2×#1912850911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#557×C83C2
socleC23×C83C22×D4
prime radicalC2×#14581789C22
hypercenterC2×#557D83
hypocenterC83C2×#3371
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #24920231C2direct (N × H)
4. C2×#19128063C2semidirect
5. C2×#19128058C2semidirect
6. C2×#19128005C2semidirect
7. C2×#19127998C2semidirect
8. C2×#19127988C2semidirect
9. C2×#19127923C2semidirect
10. C2×#19127923C2semidirect
12. C2×#19127832C2semidirect
13. C2×#19127806C2semidirect
14. C2×#19127799C2semidirect
15. C2×C4×#13050577C2semidirect
16. C2×#557×C83C2semidirect
33. #19128063C22semidirect
34. #19128058C22semidirect
35. #19128005C22semidirect
36. #19127998C22semidirect
37. #19127988C22semidirect
38. #19127923C22semidirect
39. #19127923C22semidirect
41. #19127832C22semidirect
42. #19127806C22semidirect
43. #19127799C22semidirect
44. C4×#13050577C22semidirect
65. #557×C83C22semidirect
356. C2×C83#3371semidirect
363. C2×#557D83semidirect
378. C83C2×#3371semidirect
385. #557C2×D83semidirect
719. C2#24920231direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191284362
#249202312
C2×#191280672
C2×#191280632
C2×#191280582
C2×#191280052
C2×#191279982
C2×#191279882
C2×#191279232
C2×#191279012
C2×#191278322
C2×#191278062
C2×#191277992
C2×C4×#130505772
C2×#557×C832
C2×#337183