Finite Group Databasebeta

← C2×#24919725 #36281267

Subgroups — C2×#24919725 #36281267

Order 21248.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128360C211yesmaximal, characteristic
2#24919725C2116yesmaximal, direct product factor
3C2×#19128058C211yesmaximal, characteristic, complemented
4C2×#19128036C211yesmaximal, characteristic, complemented
5C2×#19128025C211yesmaximal, characteristic, complemented
6C2×#19128005C211yesmaximal, characteristic, complemented
7C2×#19127957C211yesmaximal, characteristic, complemented
8C2×#19127949C211yesmaximal, characteristic, complemented
9C2×#19127923C211yesmaximal, characteristic, complemented
10C2×#19127861C211yesmaximal, characteristic, complemented
11C2×#19127856C211yesmaximal, characteristic, complemented
12C2×C4×#13050580C211yesmaximal, characteristic, complemented
13C2×#19127779C211yesmaximal, characteristic, complemented
14C2×#19127700C211yesmaximal, characteristic, complemented
15C2×#19127709C211yesmaximal, characteristic, complemented
16C2×#552×C83C211yesmaximal, characteristic, complemented
17C22×#13050590C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C22×#13050580C2211yescharacteristic
20C22×#13050580C2211yescharacteristic
21C22×#13050577C2211yescharacteristic
22C22×#13050574C2211yescharacteristic
23C22×#13050574C2211yescharacteristic
24#19128360—24no—
25#19128360C2218yes—
26C2×#14581780C2211yescharacteristic
27C2×#14581778—21no—
28C2×#14581771C2211yescharacteristic
29C2×#14581770—21no—
30C2×#14581766C2211yescharacteristic
31C2×#14581764—21no—
32C2×C4×Dic166C2211yescharacteristic
33C2×(C22⋊D83)⋊C4—21no—
34#19128058C2218yescomplemented
35#19128036C2218yescomplemented
36#19128025C2218yescomplemented
37#19128005C2218yescomplemented
38#19127957C2218yescomplemented
39#19127949C2218yescomplemented
40#19127923C2218yescomplemented
41#19127861C2218yescomplemented
42#19127856C2218yescomplemented
43C4×#13050580C2218yescomplemented
44#19127779C2218yescomplemented
45C2×#14581725C2211yescharacteristic
46C2×#14581725C2211yescharacteristic
47C2×#14581723C2211yescharacteristic
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49#19127709C2218yescomplemented
50#19127700C2218yescomplemented
51C2×#14581716C2211yescharacteristic
52C2×#14581715C2211yescharacteristic
53C2×#14581715C2211yescharacteristic
54C2×#14581715C2211yescharacteristic
55C2×#14581715C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581715C2211yescharacteristic
58C2×#14581712C2211yescharacteristic
59C2×#14581712C2211yescharacteristic
60C2×#14581712C2211yescharacteristic
61C2×C22⋊(C83⋊C8)C2211yescharacteristic
62C2×C22⋊(C83⋊C8)C2211yescharacteristic
63C2×C4×C83⋊C8C2211yescharacteristic
64#552×C83—24no—
65#552×C83C2218yescomplemented
66C2×#126×C83—21no—
67C2×#125×C83—21no—
68C2×#125×C83C2211yescharacteristic
69C2×#123×C83—21no—
70C2×C22⋊Q8×C83C2211yescharacteristic
71C2×C22⋊Q8×C83C2211yescharacteristic
72C2×C4×Q8×C83C2211yescharacteristic
73C2×C4×D4×C83C2211yescharacteristic
74C2×#117×C83—21no—
75C2×#117×C83C2211yescharacteristic
76C22×C4⋊C4×C83C2211yescharacteristic
77C2×#13050590—24no—
78C2×#13050590—22no—
79C2×#13050590—42no—
80C2×#13050590C2314yes—
81C22×Dic166—24no—
82C22×Dic166—22no—
83C22×Dic166—21no—
84C22×Dic166—42no—
85C22×Dic166C2311yescharacteristic
86C22×Dic166C2314yes—
87C22×Dic166C2311yescharacteristic
88C22×D332C2311yescharacteristic
89C22×C22⋊D83—21no—
90C22×C22⋊D83—21no—
91C23×Dic83—21no—
92C22×C4×D83—21no—
93C2×#13050580—24no—
94C2×#13050580—42no—
95C2×#13050580C2314yes—
96C2×#13050580C2314yes—
97C2×#13050577—42no—
98C2×#13050577C2314yes—
99C2×#13050574—42no—
100C2×#13050574—42no—
101C2×#13050574C2314yes—
102C2×#13050574C2314yes—
103C22×C83⋊C8C2311yescharacteristic
104C22×C83⋊C8C2311yescharacteristic
105C22×C83⋊C8C2311yescharacteristic
106C22×C83⋊C8C2311yescharacteristic
107#14581780—22no—
108#14581780C2314yes—
109#14581778—28no—
110#14581771—22no—
111#14581771C2314yes—
112#14581770—28no—
113#14581766—22no—
114#14581766C2314yes—
115#14581764—28no—
116C4×Dic166—22no—
117C4×Dic166C2314yes—
118(C22⋊D83)⋊C4—28no—
119C2×C4⋊Dic83C2311yescharacteristic
120C2×Dic83⋊C4—21no—
121C2×Dic83⋊C4—21no—
122C2×C22⋊Dic83—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×(C2×D83)⋊C4—21no—
125C2×(C2×D83)⋊C4—21no—
126C2×C4×Dic83—21no—
127#14581725C2314yes—
128#14581725C2314yes—
129#14581723C2314yes—
130C4⋊(C83⋊C8)C2314yes—
131#14581716C2314yes—
132#14581715C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135#14581715C2314yes—
136#14581715C2314yes—
137#14581715C2314yes—
138#14581712C2314yes—
139#14581712C2314yes—
140#14581712C2314yes—
141C22⋊(C83⋊C8)C2314yes—
142C22⋊(C83⋊C8)C2314yes—
143C4×C83⋊C8C2314yes—
144C22×Q8×C83C2311yescharacteristic
145C22×D4×C83D411yescharacteristic
146C23×C4×C83—21no—
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149#126×C83—28no—
150#125×C83—28no—
151#125×C83—22no—
152#125×C83C2314yes—
153#123×C83—28no—
154C22⋊Q8×C83—22no—
155C22⋊Q8×C83—22no—
156C22⋊Q8×C83C2314yes—
157C22⋊Q8×C83C2314yes—
158C4×Q8×C83—22no—
159C4×Q8×C83C2314yes—
160C4×D4×C83D414yes—
161C4×D4×C83C2314yes—
162#117×C83—22no—
163#117×C83—28no—
164#117×C83C2314yes—
165C2×C4⋊C4×C83—21no—
166C2×C4⋊C4×C83—22no—
167C2×C4⋊C4×C83—21no—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83—21no—
171C2×C4⋊C4×C83—21no—
172C2×C4⋊C4×C83D411yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C4⋊C4×C83C2311yescharacteristic
175C2×C4⋊C4×C83C2314yes—
176C2×C4⋊C4×C83C2311yescharacteristic
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83—21no—
179C2×C22⋊C4×C83—21no—
180C2×C22⋊C4×C83D411yescharacteristic
181C2×C22⋊C4×C83D411yescharacteristic
182C2×C42×C83—21no—
183C2×C42×C83—21no—
184C2×C42×C83C2311yescharacteristic
185C23×D83—21no—
186#13050590—28no—
187#13050590—44no—
188#13050590—48no—
189C2×Dic166—21no—
190C2×Dic166—22no—
191C2×Dic166—22no—
192C2×Dic166—22no—
193C2×Dic166—28no—
194C2×Dic166—24no—
195C2×Dic166—21no—
196C2×Dic166—44no—
197C2×Dic166—48no—
198C2×Dic166—44no—
199C2×Dic166#4114yes—
200C2×Dic166C2412yes—
201C2×Dic166C2412yes—
202C2×D332—22no—
203C2×D332—22no—
204C2×D332—21no—
205C2×D332C2412yes—
206C2×C22⋊D83—24no—
207C2×C22⋊D83—24no—
208C2×C22⋊D83—44no—
209C2×C22⋊D83—44no—
210C22×Dic83—21no—
211C22×Dic83—24no—
212C22×Dic83—21no—
213C22×Dic83—21no—
214C22×Dic83—44no—
215C2×C4×D83—24no—
216C2×C4×D83—44no—
217#13050580—28no—
218#13050580—44no—
219#13050577—44no—
220#13050574—44no—
221#13050574—44no—
222C2×C83⋊C8—22no—
223C2×C83⋊C8—22no—
224C2×C83⋊C8—22no—
225C2×C83⋊C8—22no—
226C2×C83⋊C8C2412yes—
227C2×C83⋊C8C2412yes—
228C2×C83⋊C8C2412yes—
229C2×C83⋊C8C2412yes—
230C4⋊Dic83—21no—
231C4⋊Dic83C2412yes—
232Dic83⋊C4—24no—
233Dic83⋊C4—24no—
234C22⋊Dic83—24no—
235(C2×D83)⋊C4—24no—
236(C2×D83)⋊C4—24no—
237(C2×D83)⋊C4—24no—
238C4×Dic83—24no—
239C24×C83C2×D411yescharacteristic
240C24×C83C2×D411yescharacteristic
241C2×Q8×C83—21no—
242C2×Q8×C83—22no—
243C2×Q8×C83—22no—
244C2×Q8×C83C2412yes—
245C2×D4×C83—42no—
246C2×D4×C83C2×D414yes—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—21no—
252C22×C4×C83—21no—
253C22×C4×C83—21no—
254C22×C4×C83—21no—
255C22×C4×C83—24no—
256C22×C4×C83—44no—
257C22×C4×C83C2×D412yes—
258C22×C4×C83C2×D412yes—
259C22×C4×C83C2×D411yescharacteristic
260C22×C4×C83C2×D411yescharacteristic
261C22×C4×C83C2×D411yescharacteristic
262C22×C4×C83C2×D411yescharacteristic
263C22×C4×C83C2412yes—
264C22×C4×C83C2412yes—
265C22×C4×C83C2411yescharacteristic
266C4⋊C4×C83—21no—
267C4⋊C4×C83—21no—
268C4⋊C4×C83—24no—
269C4⋊C4×C83—24no—
270C4⋊C4×C83—24no—
271C4⋊C4×C83—24no—
272C4⋊C4×C83—24no—
273C4⋊C4×C83—24no—
274C4⋊C4×C83—21no—
275C4⋊C4×C83C2×D414yes—
276C4⋊C4×C83C2412yes—
277C4⋊C4×C83C2412yes—
278C4⋊C4×C83C2412yes—
279C22⋊C4×C83—24no—
280C22⋊C4×C83—24no—
281C22⋊C4×C83—24no—
282C22⋊C4×C83C2×D414yes—
283C22⋊C4×C83C2×D414yes—
284C42×C83—24no—
285C42×C83—24no—
286C42×C83C2×D412yes—
287C42×C83C2412yes—
288C23×C83—22no—
289C23×C83—22no—
290C23×C83—22no—
291C23×C83—22no—
292C23×C83—22no—
293C23×C83—22no—
294C23×C83C22×D412yes—
295C23×C83C22×D412yes—
296C23×C83C22×D411yescharacteristic
297C22×D83—22no—
298C22×D83—42no—
299C22×D83—42no—
300C22×D83—42no—
301Q8×C83—22no—
302Q8×C83—22no—
303Q8×C83—42no—
304D4×C83—44no—
305C2×C4×C83—22no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—24no—
310C2×C4×C83—24no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
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—48no—
320C2×C4×C83—42no—
321C2×C4×C83—42no—
322C2×C4×C83—42no—
323C2×C4×C83—42no—
324C2×C4×C83C22×D412yes—
325C2×C4×C83C22×D412yes—
326C2×C4×C83C22×D412yes—
327C2×C4×C83C22×D412yes—
328C2×C4×C83C22×D411yescharacteristic
329C2×C4×C83C2×#4112yes—
330C2×C4×C83H(5,𝔽2)12yes—
331C2×C4×C83C2511yescharacteristic
332C22⋊D83—48no—
333C22⋊D83—48no—
334C2×Dic83—24no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—48no—
339C2×Dic83—42no—
340C2×Dic83—42no—
341D332—22no—
342D332—22no—
343D332—42no—
344C4×D83—48no—
345Dic166—24no—
346Dic166—22no—
347Dic166—22no—
348Dic166—22no—
349Dic166—48no—
350Dic166—42no—
351Dic166C2×#4114yes—
352C83⋊C8—22no—
353C83⋊C8—22no—
354C83⋊C8—22no—
355C83⋊C8—22no—
356C22×C83—22no—
357C22×C83—22no—
358C22×C83—22no—
359C22×C83—22no—
360C22×C83—22no—
361C22×C83—22no—
362C22×C83—44no—
363C22×C83—44no—
364C22×C83#54612yes—
365C22×C83#57512yes—
366C22×C83#57812yes—
367C22×C83C23×D411yescharacteristic
368C2×D83—42no—
369C2×D83—42no—
370C2×D83—42no—
371C2×D83—84no—
372C4×C83—22no—
373C4×C83—22no—
374C4×C83—22no—
375C4×C83—22no—
376C4×C83—42no—
377C4×C83—42no—
378C4×C83—42no—
379C4×C83—42no—
380C4×C83#54612yes—
381C4×C83C22×#4111yescharacteristic
382C4×C83C2×H(5,𝔽2)11yescharacteristic
383Dic83—24no—
384Dic83—42no—
385Dic83—42no—
386C2×#3327—831nomaximal, Sylow
387C2×C83—42no—
388C2×C83—42no—
389C2×C83#332714yescomplemented
390C2×C83C2×#54611yescharacteristic
391C2×C83C2×#57511yescharacteristic
392C2×C83C2×#57811yescharacteristic
393D83—82no—
394C2×#552D8311yescharacteristic, complemented
395C2×#548—831no—
396#3327—8316no—
397C2×#488—831no—
398C2×#484—831no—
399C2×#482—831no—
400C2×#479—831no—
401C2×#470—831no—
402C2×#468—831no—
403C2×#464—831no—
404C2×#452—831no—
405C2×#451—831no—
406C2×C4×Q16—831no—
407C2×#436—831no—
408C2×#417—831no—
409C2×#419—831no—
410C83C2×#332711yescharacteristic, complemented, Sylow
411C22×#41—831no—
412C23×Q8—831no—
413C22×Q16—831no—
414C22×Q16—831no—
415C22×SD16—831no—
416C22×M16—831no—
417C22×M16—831no—
418#552—24no—
419#552C2×D8318yescomplemented
420#548—838no—
421#548—1664no—
422C2×#126—21no—
423C2×#125—21no—
424C2×#125C2×D8311yescharacteristic
425C2×#124—831no—
426C2×#124—1661no—
427C2×#123—21no—
428C2×C22⋊Q8—831no—
429C2×C22⋊Q8—1661no—
430C2×C22⋊Q8C2×D8311yescharacteristic
431C2×C22⋊Q8C2×D8311yescharacteristic
432C2×#121—831no—
433C2×#121—1661no—
434C2×C4×Q8—831no—
435C2×C4×Q8C2×D8311yescharacteristic
436C2×C4×D4—1661no—
437C2×C4×D4C2×D8311yescharacteristic
438C2×#117—21no—
439C2×#117C2×D8311yescharacteristic
440C22×C4⋊C4C2×D8311yescharacteristic
441#488—838no—
442#484—838no—
443#482—838no—
444#479—838no—
445#470—838no—
446#468—838no—
447#464—838no—
448#452—838no—
449#451—838no—
450C4×Q16—838no—
451#436—838no—
452C2×#107—831no—
453C2×#107—831no—
454C2×#106—831no—
455C2×C4⋊C8—831no—
456#419—838no—
457#417—838no—
458C2×#103—831no—
459C2×#103—831no—
460C2×#103—831no—
461C2×#103—831no—
462C2×#103—831no—
463C2×#103—831no—
464C2×#103—831no—
465C2×#102—831no—
466C2×#102—831no—
467C2×#102—831no—
468C2×C22⋊C8—831no—
469C2×C22⋊C8—831no—
470C2×C4×C8—831no—
471C2×#41—3322no—
472C2×#41—834no—
473C2×#41—1664no—
474C2×#41—1662no—
475C22×Q8—3322no—
476C22×Q8—834no—
477C22×Q8—831no—
478C22×Q8—831no—
479C22×Q8—1664no—
480C22×Q8—1661no—
481C22×Q8—1662no—
482C22×Q8C22×D8311yescharacteristic
483C22×D4—831no—
484C22×D4—1661no—
485C22×D4—1661no—
486C22×D4C22⋊D8311yescharacteristic
487C23×C4—21no—
488C23×C4—1661no—
489C23×C4—1661no—
490C23×C4C22×D8311yescharacteristic
491C23×C4C22×D8311yescharacteristic
492C2×Q16—3322no—
493C2×Q16—834no—
494C2×Q16—834no—
495C2×Q16—1664no—
496C2×SD16—3322no—
497C2×SD16—834no—
498C2×M16—3322no—
499C2×M16—3322no—
500C2×M16—834no—
501C2×M16—834no—
502C22×C8—831no—
503C22×C8—831no—
504C22×C8—831no—
505C22×C8—831no—
506#126—28no—
507#125—28no—
508#125—22no—
509#125C22×D8314yes—
510#124—834no—
511#124—1668no—
512#124—1662no—
513#123—28no—
514C22⋊Q8—22no—
515C22⋊Q8—22no—
516C22⋊Q8—834no—
517C22⋊Q8—1662no—
518C22⋊Q8—1668no—
519C22⋊Q8C22×D8314yes—
520C22⋊Q8C22×D8314yes—
521#121—834no—
522#121—1668no—
523#121—1662no—
524C4×Q8—22no—
525C4×Q8—834no—
526C4×Q8—1662no—
527C4×Q8C22×D8314yes—
528C4×D4—1668no—
529C4×D4C22⋊D8314yes—
530C4×D4C22×D8314yes—
531#117—22no—
532#117—28no—
533#117C22×D8314yes—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—22no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—831no—
542C2×C4⋊C4—1661no—
543C2×C4⋊C4—1661no—
544C2×C4⋊C4C22⋊D8311yescharacteristic
545C2×C4⋊C4C22×D8311yescharacteristic
546C2×C4⋊C4C22×D8311yescharacteristic
547C2×C4⋊C4C22×D8314yes—
548C2×C4⋊C4C22×D8311yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—1661no—
553C2×C22⋊C4—1661no—
554C2×C22⋊C4—1661no—
555C2×C22⋊C4—1661no—
556C2×C22⋊C4C22⋊D8311yescharacteristic
557C2×C22⋊C4C22⋊D8311yescharacteristic
558C2×C42—21no—
559C2×C42—21no—
560C2×C42—1661no—
561C2×C42C22×D8311yescharacteristic
562#107—834no—
563#107—834no—
564#106—834no—
565C4⋊C8—834no—
566#103—834no—
567#103—834no—
568#103—834no—
569#103—834no—
570#103—834no—
571#103—834no—
572#103—834no—
573#102—834no—
574#102—834no—
575#102—834no—
576C22⋊C8—834no—
577C22⋊C8—834no—
578C4×C8—834no—
579C24—1661no—
580C24C2×C22⋊D8311yescharacteristic
581C24C2×C22⋊D8311yescharacteristic
582#41—3328no—
583#41—3324no—
584#41—1668no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—3328no—
589C2×Q8—3324no—
590C2×Q8—3324no—
591C2×Q8—834no—
592C2×Q8—832no—
593C2×Q8—832no—
594C2×Q8—1668no—
595C2×Q8—1662no—
596C2×Q8—1662no—
597C2×Q8—1661no—
598C2×Q8—1664no—
599C2×Q8—1661no—
600C2×Q8—1662no—
601C2×Q8C23×D8312yes—
602C2×D4—42no—
603C2×D4—3324no—
604C2×D4—3324no—
605C2×D4—832no—
606C2×D4—1664no—
607C2×D4—1664no—
608C2×D4—1661no—
609C2×D4—1662no—
610C2×D4—1662no—
611C2×D4C2×C22⋊D8314yes—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—24no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—44no—
622C22×C4—3324no—
623C22×C4—3324no—
624C22×C4—1664no—
625C22×C4—1661no—
626C22×C4—1661no—
627C22×C4—1664no—
628C22×C4—1661no—
629C22×C4C2×C22⋊D8312yes—
630C22×C4C2×C22⋊D8312yes—
631C22×C4C2×C22⋊D8311yescharacteristic
632C22×C4C2×C22⋊D8311yescharacteristic
633C22×C4C2×C22⋊D8311yescharacteristic
634C22×C4C2×C22⋊D8311yescharacteristic
635C22×C4C23×D8312yes—
636C22×C4C23×D8312yes—
637C22×C4C23×D8311yescharacteristic
638Q16—3324no—
639Q16—1668no—
640SD16—3324no—
641M16—3324no—
642M16—3324no—
643C2×C8—832no—
644C2×C8—832no—
645C2×C8—832no—
646C2×C8—832no—
647C2×C8—1662no—
648C2×C8—1662no—
649C2×C8—1662no—
650C2×C8—1662no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—24no—
656C4⋊C4—24no—
657C4⋊C4—24no—
658C4⋊C4—24no—
659C4⋊C4—21no—
660C4⋊C4—832no—
661C4⋊C4—1661no—
662C4⋊C4—1664no—
663C4⋊C4—1664no—
664C4⋊C4C2×C22⋊D8314yes—
665C4⋊C4C23×D8312yes—
666C4⋊C4C23×D8312yes—
667C4⋊C4C23×D8312yes—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—24no—
671C22⋊C4—1664no—
672C22⋊C4—1664no—
673C22⋊C4—1664no—
674C22⋊C4—1664no—
675C22⋊C4C2×C22⋊D8314yes—
676C22⋊C4C2×C22⋊D8314yes—
677C42—24no—
678C42—24no—
679C42—1664no—
680C42C2×C22⋊D8312yes—
681C42C23×D8312yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—3322no—
689C23—3322no—
690C23—3322no—
691C23—1662no—
692C23C22×C22⋊D8312yes—
693C23C22×C22⋊D8312yes—
694C23C22×C22⋊D8311yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—42no—
698Q8—3328no—
699Q8—3322no—
700Q8—834no—
701Q8—1662no—
702Q8—1662no—
703Q8—1664no—
704Q8—1662no—
705D4—44no—
706D4—3328no—
707D4—3328no—
708D4—3322no—
709D4—1662no—
710D4—1662no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—3328no—
731C2×C4—3322no—
732C2×C4—3322no—
733C2×C4—3328no—
734C2×C4—1662no—
735C2×C4—1662no—
736C2×C4—1664no—
737C2×C4—1662no—
738C2×C4C22×C22⋊D8312yes—
739C2×C4C22×C22⋊D8312yes—
740C2×C4C22×C22⋊D8312yes—
741C2×C4C22×C22⋊D8312yes—
742C2×C4C22×C22⋊D8311yescharacteristic
743C2×C4#41×D8312yes—
744C2×C4#1458183812yes—
745C2×C4C24×D8311yescharacteristic
746C8—1662no—
747C8—1662no—
748C8—1662no—
749C8—1662no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—3322no—
759C22—3322no—
760C22—3322no—
761C22—6644no—
762C22#1912833912yes—
763C22#1912849912yes—
764C22#1912851612yes—
765C22C23×C22⋊D8311yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—42no—
774C4—3322no—
775C4—3322no—
776C4—1664no—
777C4#1912833912yes—
778C4C2×#41×D8311yescharacteristic
779C4C2×#1458183811yescharacteristic
780C2—42no—
781C2—42no—
782C2—6642no—
783C2#2491972514yesdirect product factor
784C2C2×#1912833911yescharacteristic
785C2C2×#1912849911yescharacteristic
786C2C2×#1912851611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#552×C83C2
socleC23×C83C22×D4
prime radicalC2×#19128360C2
hypercenterC2×#552D83
hypocenterC83C2×#3327
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #24919725C2direct (N × H)
3. C2×#19128058C2semidirect
4. C2×#19128036C2semidirect
5. C2×#19128025C2semidirect
6. C2×#19128005C2semidirect
7. C2×#19127957C2semidirect
8. C2×#19127949C2semidirect
9. C2×#19127923C2semidirect
10. C2×#19127861C2semidirect
11. C2×#19127856C2semidirect
12. C2×C4×#13050580C2semidirect
13. C2×#19127779C2semidirect
14. C2×#19127700C2semidirect
15. C2×#19127709C2semidirect
16. C2×#552×C83C2semidirect
34. #19128058C22semidirect
35. #19128036C22semidirect
36. #19128025C22semidirect
37. #19128005C22semidirect
38. #19127957C22semidirect
39. #19127949C22semidirect
40. #19127923C22semidirect
41. #19127861C22semidirect
42. #19127856C22semidirect
43. C4×#13050580C22semidirect
44. #19127779C22semidirect
49. #19127709C22semidirect
50. #19127700C22semidirect
65. #552×C83C22semidirect
389. C2×C83#3327semidirect
394. C2×#552D83semidirect
410. C83C2×#3327semidirect
419. #552C2×D83semidirect
783. C2#24919725direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283602
#249197252
C2×#191280582
C2×#191280362
C2×#191280252
C2×#191280052
C2×#191279572
C2×#191279492
C2×#191279232
C2×#191278612
C2×#191278562
C2×C4×#130505802
C2×#191277792
C2×#191277002
C2×#191277092
C2×#552×C832
C2×#332783