Finite Group Databasebeta

← C2×#24918868 #36277308

Subgroups — C2×#24918868 #36277308

Order 21248.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128322C211yesmaximal, characteristic, complemented
2#24918868C2116yesmaximal, direct product factor
3C2×#19128005C211yesmaximal, characteristic, complemented
4C2×#19127998C211yesmaximal, characteristic, complemented
5C2×#19127991C211yesmaximal, characteristic, complemented
6C2×#19127981C211yesmaximal, characteristic, complemented
7C2×#19127952C211yesmaximal, characteristic, complemented
8C2×#19127945C211yesmaximal, characteristic, complemented
9C2×#19127935C211yesmaximal, characteristic, complemented
10C2×#19127928C211yesmaximal, characteristic, complemented
11C2×#19127898C211yesmaximal, characteristic, complemented
12C2×#19127916C211yesmaximal, characteristic, complemented
13C2×#19127916C211yesmaximal, characteristic, complemented
14C2×#19127893C211yesmaximal, characteristic, complemented
15C2×#19127728C211yesmaximal, characteristic, complemented
16C2×#540×C83C211yesmaximal, characteristic, complemented
17C22×#13050578C2211yescharacteristic
18C22×#13050578C2211yescharacteristic
19C22×#13050575C2211yescharacteristic
20C22×#13050575C2211yescharacteristic
21C22×#13050574C2211yescharacteristic
22C23×C83⋊C8C2211yescharacteristic
23#19128322—24no—
24#19128322C2218yescomplemented
25C2×#14581792C2211yescharacteristic
26C2×#14581787—21no—
27C2×#14581780C2211yescharacteristic
28C2×#14581778—21no—
29C2×#14581774—21no—
30C2×#14581771C2211yescharacteristic
31C2×#14581770—21no—
32C2×#14581766C2211yescharacteristic
33C2×C4×Dic166C2211yescharacteristic
34C2×C4×D332C2211yescharacteristic
35#19128005C2218yescomplemented
36#19127998C2218yescomplemented
37#19127991C2218yescomplemented
38#19127981C2218yescomplemented
39#19127952C2218yescomplemented
40#19127945C2218yescomplemented
41#19127935C2218yescomplemented
42#19127928C2218yescomplemented
43#19127916C2218yescomplemented
44#19127916C2218yescomplemented
45#19127898C2218yescomplemented
46#19127893C2218yescomplemented
47C2×#14581725C2211yescharacteristic
48C2×#14581725C2211yescharacteristic
49C2×#14581723C2211yescharacteristic
50C2×#14581723C2211yescharacteristic
51#19127728C2218yescomplemented
52C2×C4⋊(C83⋊C8)C2211yescharacteristic
53C2×C4⋊(C83⋊C8)C2211yescharacteristic
54C2×C4⋊(C83⋊C8)C2211yescharacteristic
55C2×C4⋊(C83⋊C8)C2211yescharacteristic
56C2×#14581715C2211yescharacteristic
57C2×#14581715C2211yescharacteristic
58C2×#14581713C2211yescharacteristic
59C2×#14581713C2211yescharacteristic
60C2×#14581713C2211yescharacteristic
61C2×#14581713C2211yescharacteristic
62C2×#14581712C2211yescharacteristic
63C2×#14581712C2211yescharacteristic
64#540×C83—24no—
65#540×C83C2218yescomplemented
66C2×#127×C83C2211yescharacteristic
67C2×#125×C83C2211yescharacteristic
68C2×#123×C83—21no—
69C2×#123×C83—21no—
70C2×#121×C83—21no—
71C2×#121×C83—21no—
72C2×#121×C83C2211yescharacteristic
73C2×#121×C83C2211yescharacteristic
74C2×C4×D4×C83C2211yescharacteristic
75C2×C4×D4×C83C2211yescharacteristic
76C2×#117×C83C2211yescharacteristic
77C22×Dic166—21no—
78C22×Dic166C2311yescharacteristic
79C22×D332C2311yescharacteristic
80C22×C22⋊D83—21no—
81C22×C4×D83—21no—
82C2×#13050578—42no—
83C2×#13050578—42no—
84C2×#13050578C2314yes—
85C2×#13050578C2314yes—
86C2×#13050575—42no—
87C2×#13050575—42no—
88C2×#13050575C2314yes—
89C2×#13050575C2314yes—
90C2×#13050574—42no—
91C2×#13050574C2314yes—
92C22×C83⋊C8—42no—
93C22×C83⋊C8C2311yescharacteristic
94C22×C83⋊C8C2311yescharacteristic
95C22×C83⋊C8C2311yescharacteristic
96C22×C83⋊C8C2311yescharacteristic
97C22×C83⋊C8C2314yes—
98#14581792—22no—
99#14581792C2314yes—
100#14581787—28no—
101#14581780—22no—
102#14581780C2314yes—
103#14581778—28no—
104#14581774—28no—
105#14581771—22no—
106#14581771C2314yes—
107#14581770—28no—
108#14581766—22no—
109#14581766C2314yes—
110C4×Dic166—22no—
111C4×Dic166C2314yes—
112C4×D332—22no—
113C4×D332C2314yes—
114C2×C4⋊Dic83—21no—
115C2×C4⋊Dic83C2311yescharacteristic
116C2×C4⋊Dic83C2311yescharacteristic
117C2×Dic83⋊C4—21no—
118C2×Dic83⋊C4—21no—
119C2×C22⋊Dic83—21no—
120C2×(C2×D83)⋊C4—21no—
121C2×(C2×D83)⋊C4—21no—
122C2×(C2×D83)⋊C4—21no—
123C2×(C2×D83)⋊C4—21no—
124C2×C4×Dic83—21no—
125#14581725C2314yes—
126#14581725C2314yes—
127#14581723C2314yes—
128#14581723C2314yes—
129C4⋊(C83⋊C8)C2314yes—
130C4⋊(C83⋊C8)C2314yes—
131C4⋊(C83⋊C8)C2314yes—
132C4⋊(C83⋊C8)C2314yes—
133#14581715C2314yes—
134#14581715C2314yes—
135#14581713C2314yes—
136#14581713C2314yes—
137#14581713C2314yes—
138#14581713C2314yes—
139#14581712C2314yes—
140#14581712C2314yes—
141C22×D4×C83—21no—
142C22×D4×C83—21no—
143C22×D4×C83—21no—
144C22×D4×C83—21no—
145C22×D4×C83C2311yescharacteristic
146C22×D4×C83C2311yescharacteristic
147C23×C4×C83—21no—
148C23×C4×C83—21no—
149C23×C4×C83C2311yescharacteristic
150#127×C83—22no—
151#127×C83C2314yes—
152#125×C83—22no—
153#125×C83C2314yes—
154#123×C83—28no—
155#123×C83—28no—
156#121×C83—22no—
157#121×C83—22no—
158#121×C83—28no—
159#121×C83—28no—
160#121×C83C2314yes—
161#121×C83C2314yes—
162C4×D4×C83—22no—
163C4×D4×C83—22no—
164C4×D4×C83C2314yes—
165C4×D4×C83C2314yes—
166#117×C83D414yes—
167#117×C83C2314yes—
168C2×C4⋊C4×C83—21no—
169C2×C4⋊C4×C83—21no—
170C2×C4⋊C4×C83D411yescharacteristic
171C2×C4⋊C4×C83D411yescharacteristic
172C2×C4⋊C4×C83C2311yescharacteristic
173C2×C4⋊C4×C83C2311yescharacteristic
174C2×C22⋊C4×C83—21no—
175C2×C22⋊C4×C83—21no—
176C2×C22⋊C4×C83—21no—
177C2×C22⋊C4×C83—21no—
178C2×C22⋊C4×C83D411yescharacteristic
179C2×C22⋊C4×C83D411yescharacteristic
180C2×C42×C83C2311yescharacteristic
181C2×C42×C83C2311yescharacteristic
182C23×D83—21no—
183C2×Dic166—22no—
184C2×Dic166—22no—
185C2×Dic166—21no—
186C2×Dic166—24no—
187C2×Dic166—82no—
188C2×Dic166C2412yes—
189C2×D332—22no—
190C2×D332—22no—
191C2×D332—21no—
192C2×D332C2412yes—
193C2×C22⋊D83—24no—
194C2×C22⋊D83—82no—
195C22×Dic83—21no—
196C22×Dic83—21no—
197C22×Dic83—21no—
198C2×C4×D83—24no—
199C2×C4×D83—82no—
200#13050578—44no—
201#13050578—44no—
202#13050575—44no—
203#13050575—44no—
204#13050574—44no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8—22no—
209C2×C83⋊C8—44no—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C2×C83⋊C8C2412yes—
213C2×C83⋊C8C2412yes—
214C4⋊Dic83—21no—
215C4⋊Dic83—21no—
216C4⋊Dic83—24no—
217C4⋊Dic83C2412yes—
218C4⋊Dic83C2412yes—
219Dic83⋊C4—24no—
220Dic83⋊C4—24no—
221C22⋊Dic83—24no—
222(C2×D83)⋊C4—24no—
223(C2×D83)⋊C4—24no—
224(C2×D83)⋊C4—24no—
225(C2×D83)⋊C4—24no—
226C4×Dic83—24no—
227C24×C83—21no—
228C24×C83—21no—
229C24×C83C2×D411yescharacteristic
230C2×D4×C83—24no—
231C2×D4×C83—24no—
232C2×D4×C83—21no—
233C2×D4×C83—21no—
234C2×D4×C83—24no—
235C2×D4×C83—24no—
236C2×D4×C83—22no—
237C2×D4×C83—22no—
238C2×D4×C83—22no—
239C2×D4×C83—22no—
240C2×D4×C83—82no—
241C2×D4×C83—82no—
242C2×D4×C83—82no—
243C2×D4×C83—82no—
244C2×D4×C83C2412yes—
245C2×D4×C83C2412yes—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—21no—
249C22×C4×C83—21no—
250C22×C4×C83—24no—
251C22×C4×C83—24no—
252C22×C4×C83—82no—
253C22×C4×C83—82no—
254C22×C4×C83C2×D412yes—
255C22×C4×C83C2×D411yescharacteristic
256C22×C4×C83C2×D411yescharacteristic
257C22×C4×C83C2×D411yescharacteristic
258C22×C4×C83C2×D411yescharacteristic
259C22×C4×C83C2×D411yescharacteristic
260C22×C4×C83C2412yes—
261C22×C4×C83C2411yescharacteristic
262C4⋊C4×C83—24no—
263C4⋊C4×C83—24no—
264C4⋊C4×C83—21no—
265C4⋊C4×C83—21no—
266C4⋊C4×C83C2×D414yes—
267C4⋊C4×C83C2×D414yes—
268C4⋊C4×C83C2412yes—
269C4⋊C4×C83C2412yes—
270C22⋊C4×C83—24no—
271C22⋊C4×C83—24no—
272C22⋊C4×C83—24no—
273C22⋊C4×C83—24no—
274C22⋊C4×C83C2×D414yes—
275C22⋊C4×C83C2×D414yes—
276C42×C83C2×D412yes—
277C42×C83C2×D412yes—
278C42×C83C2412yes—
279C42×C83C2412yes—
280C23×C83—22no—
281C23×C83—22no—
282C23×C83—22no—
283C23×C83—22no—
284C23×C83—22no—
285C23×C83—42no—
286C23×C83—42no—
287C23×C83—42no—
288C23×C83—42no—
289C23×C83—42no—
290C23×C83—42no—
291C23×C83C22×D412yes—
292C23×C83C22×D411yescharacteristic
293C22×D83—22no—
294C22×D83—42no—
295C22×D83—42no—
296C22×D83—42no—
297D4×C83—22no—
298D4×C83—22no—
299D4×C83—22no—
300D4×C83—22no—
301D4×C83—42no—
302D4×C83—42no—
303D4×C83—84no—
304D4×C83—84no—
305D4×C83—84no—
306D4×C83—84no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—24no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—42no—
318C2×C4×C83—42no—
319C2×C4×C83—84no—
320C2×C4×C83—84no—
321C2×C4×C83C22×D412yes—
322C2×C4×C83C22×D412yes—
323C2×C4×C83C22×D412yes—
324C2×C4×C83C22×D412yes—
325C2×C4×C83C22×D412yes—
326C2×C4×C83C22×D411yescharacteristic
327C2×C4×C83H(5,𝔽2)12yes—
328C2×C4×C832−1+412yes—
329C2×C4×C83C2511yescharacteristic
330C22⋊D83—84no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—42no—
335C2×Dic83—42no—
336C2×Dic83—42no—
337D332—22no—
338D332—22no—
339D332—42no—
340C4×D83—84no—
341Dic166—22no—
342Dic166—22no—
343Dic166—42no—
344Dic166—84no—
345C83⋊C8—22no—
346C83⋊C8—22no—
347C83⋊C8—22no—
348C83⋊C8—22no—
349C22×C83—22no—
350C22×C83—22no—
351C22×C83—22no—
352C22×C83—44no—
353C22×C83—42no—
354C22×C83—42no—
355C22×C83—42no—
356C22×C83—42no—
357C22×C83—42no—
358C22×C83—42no—
359C22×C83—84no—
360C22×C83—84no—
361C22×C83#53712yes—
362C22×C83#57612yes—
363C22×C83#57712yes—
364C22×C83C23×D411yescharacteristic
365C2×D83—42no—
366C2×D83—42no—
367C2×D83—42no—
368C2×D83—84no—
369C4×C83—22no—
370C4×C83—22no—
371C4×C83—22no—
372C4×C83—22no—
373C4×C83—22no—
374C4×C83—42no—
375C4×C83—42no—
376C4×C83#53712yes—
377C4×C83C2×H(5,𝔽2)11yescharacteristic
378C4×C83C2×2−1+411yescharacteristic
379Dic83—42no—
380Dic83—42no—
381Dic83—42no—
382C2×#3257—831nomaximal, Sylow
383C2×C83—42no—
384C2×C83—82no—
385C2×C83—82no—
386C2×C83#325714yescomplemented
387C2×C83C2×#53711yescharacteristic
388C2×C83C2×#57611yescharacteristic
389C2×C83C2×#57711yescharacteristic
390D83—82no—
391C2×#542—831no—
392C2×#540D8311yescharacteristic, complemented
393#3257—8316no—
394C2×#479—831no—
395C2×#478—831no—
396C2×#476—831no—
397C2×#474—831no—
398C2×#469—831no—
399C2×#468—831no—
400C2×#466—831no—
401C2×#465—831no—
402C2×#460—831no—
403C2×#463—831no—
404C2×#463—831no—
405C2×#459—831no—
406C2×#424—831no—
407C83C2×#325711yescharacteristic, complemented, Sylow
408C22×SD16—831no—
409C22×SD16—831no—
410C22×D8—831no—
411C22×D8—831no—
412C22×M16—831no—
413C23×C8—831no—
414#542—838no—
415#542—1664no—
416#540—24no—
417#540C2×D8318yescomplemented
418C2×C4⋊Q8—831no—
419C2×#127C2×D8311yescharacteristic
420C2×#126—1661no—
421C2×#125C2×D8311yescharacteristic
422C2×#124—831no—
423C2×#124—1661no—
424C2×#123—21no—
425C2×#123—21no—
426C2×#123—1661no—
427C2×C22⋊Q8—831no—
428C2×C22⋊Q8—1661no—
429C2×#121—21no—
430C2×#121—21no—
431C2×#121—831no—
432C2×#121C2×D8311yescharacteristic
433C2×#121C2×D8311yescharacteristic
434C2×C4×Q8—831no—
435C2×C4×D4—831no—
436C2×C4×D4C2×D8311yescharacteristic
437C2×C4×D4C2×D8311yescharacteristic
438C2×#117C2×D8311yescharacteristic
439#479—838no—
440#478—838no—
441#476—838no—
442#474—838no—
443#469—838no—
444#468—838no—
445#466—838no—
446#465—838no—
447#463—838no—
448#463—838no—
449#460—838no—
450#459—838no—
451C2×#107—831no—
452C2×#107—831no—
453C2×#106—831no—
454C2×#106—831no—
455#424—838no—
456C2×C4⋊C8—831no—
457C2×C4⋊C8—831no—
458C2×C4⋊C8—831no—
459C2×C4⋊C8—831no—
460C2×#103—831no—
461C2×#103—831no—
462C2×#102—831no—
463C2×#102—831no—
464C2×#102—831no—
465C2×#102—831no—
466C2×#102—831no—
467C2×#102—831no—
468C22×Q8—831no—
469C22×Q8—1661no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4—21no—
474C22×D4—831no—
475C22×D4—1661no—
476C22×D4C22×D8311yescharacteristic
477C22×D4C22×D8311yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—1661no—
481C23×C4C22×D8311yescharacteristic
482C2×SD16—3322no—
483C2×SD16—3322no—
484C2×SD16—834no—
485C2×SD16—834no—
486C2×D8—3322no—
487C2×D8—3322no—
488C2×D8—834no—
489C2×D8—834no—
490C2×M16—3322no—
491C2×M16—834no—
492C22×C8—3322no—
493C22×C8—834no—
494C22×C8—831no—
495C22×C8—831no—
496C22×C8—831no—
497C22×C8—831no—
498C4⋊Q8—834no—
499C4⋊Q8—1662no—
500#127—22no—
501#127C22×D8314yes—
502#126—1668no—
503#125—22no—
504#125C22×D8314yes—
505#124—834no—
506#124—1668no—
507#124—1662no—
508#123—28no—
509#123—28no—
510#123—1668no—
511C22⋊Q8—834no—
512C22⋊Q8—1662no—
513C22⋊Q8—1668no—
514#121—22no—
515#121—22no—
516#121—28no—
517#121—28no—
518#121—834no—
519#121—1662no—
520#121C22×D8314yes—
521#121C22×D8314yes—
522C4×Q8—834no—
523C4×Q8—1662no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—834no—
527C4×D4—1662no—
528C4×D4C22×D8314yes—
529C4×D4C22×D8314yes—
530#117C22⋊D8314yes—
531#117C22×D8314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—831no—
535C2×C4⋊C4—831no—
536C2×C4⋊C4—1661no—
537C2×C4⋊C4—1661no—
538C2×C4⋊C4—1661no—
539C2×C4⋊C4C22⋊D8311yescharacteristic
540C2×C4⋊C4C22⋊D8311yescharacteristic
541C2×C4⋊C4C22×D8311yescharacteristic
542C2×C4⋊C4C22×D8311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—1661no—
548C2×C22⋊C4—1661no—
549C2×C22⋊C4—1661no—
550C2×C22⋊C4—1661no—
551C2×C22⋊C4—1661no—
552C2×C22⋊C4C22⋊D8311yescharacteristic
553C2×C22⋊C4C22⋊D8311yescharacteristic
554C2×C42—1661no—
555C2×C42C22×D8311yescharacteristic
556C2×C42C22×D8311yescharacteristic
557#107—834no—
558#107—834no—
559#106—834no—
560#106—834no—
561C4⋊C8—834no—
562C4⋊C8—834no—
563C4⋊C8—834no—
564C4⋊C8—834no—
565#103—834no—
566#103—834no—
567#102—834no—
568#102—834no—
569#102—834no—
570#102—834no—
571#102—834no—
572#102—834no—
573C24—21no—
574C24—21no—
575C24—1661no—
576C24C2×C22⋊D8311yescharacteristic
577C2×Q8—832no—
578C2×Q8—6642no—
579C2×Q8—1662no—
580C2×Q8—1662no—
581C2×Q8—1661no—
582C2×Q8—1664no—
583C2×D4—24no—
584C2×D4—24no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—24no—
588C2×D4—24no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—22no—
592C2×D4—22no—
593C2×D4—82no—
594C2×D4—82no—
595C2×D4—82no—
596C2×D4—82no—
597C2×D4—832no—
598C2×D4—6642no—
599C2×D4—1664no—
600C2×D4—1661no—
601C2×D4—1662no—
602C2×D4—1662no—
603C2×D4C23×D8312yes—
604C2×D4C23×D8312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—82no—
613C22×C4—6642no—
614C22×C4—1661no—
615C22×C4—1661no—
616C22×C4—1661no—
617C22×C4—1664no—
618C22×C4C2×C22⋊D8312yes—
619C22×C4C2×C22⋊D8311yescharacteristic
620C22×C4C2×C22⋊D8311yescharacteristic
621C22×C4C2×C22⋊D8311yescharacteristic
622C22×C4C2×C22⋊D8311yescharacteristic
623C22×C4C2×C22⋊D8311yescharacteristic
624C22×C4C23×D8312yes—
625C22×C4C23×D8311yescharacteristic
626SD16—3324no—
627SD16—3324no—
628D8—3324no—
629D8—3324no—
630M16—3324no—
631C2×C8—3324no—
632C2×C8—832no—
633C2×C8—832no—
634C2×C8—832no—
635C2×C8—832no—
636C2×C8—1662no—
637C2×C8—1662no—
638C2×C8—1662no—
639C2×C8—1662no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—832no—
645C4⋊C4—832no—
646C4⋊C4—1661no—
647C4⋊C4—1661no—
648C4⋊C4—1664no—
649C4⋊C4—1664no—
650C4⋊C4—1664no—
651C4⋊C4C2×C22⋊D8314yes—
652C4⋊C4C2×C22⋊D8314yes—
653C4⋊C4C23×D8312yes—
654C4⋊C4C23×D8312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—1664no—
660C22⋊C4—1664no—
661C22⋊C4—1664no—
662C22⋊C4—1664no—
663C22⋊C4—1664no—
664C22⋊C4C2×C22⋊D8314yes—
665C22⋊C4C2×C22⋊D8314yes—
666C42—1664no—
667C42C2×C22⋊D8312yes—
668C42C2×C22⋊D8312yes—
669C42C23×D8312yes—
670C42C23×D8312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—3322no—
683C23—3322no—
684C23—3322no—
685C23—1662no—
686C23C22×C22⋊D8312yes—
687C23C22×C22⋊D8311yescharacteristic
688Q8—3322no—
689Q8—6644no—
690Q8—1662no—
691Q8—1662no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—84no—
699D4—84no—
700D4—84no—
701D4—84no—
702D4—3322no—
703D4—6644no—
704D4—1662no—
705D4—1662no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—84no—
719C2×C4—84no—
720C2×C4—3322no—
721C2×C4—3322no—
722C2×C4—3322no—
723C2×C4—6644no—
724C2×C4—1662no—
725C2×C4—1662no—
726C2×C4—1662no—
727C2×C4C22×C22⋊D8312yes—
728C2×C4C22×C22⋊D8312yes—
729C2×C4C22×C22⋊D8312yes—
730C2×C4C22×C22⋊D8312yes—
731C2×C4C22×C22⋊D8312yes—
732C2×C4C22×C22⋊D8311yescharacteristic
733C2×C4#1458183812yes—
734C2×C4#1458183912yes—
735C2×C4C24×D8311yescharacteristic
736C8—1662no—
737C8—1662no—
738C8—1662no—
739C8—1662no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—84no—
751C22—84no—
752C22—3322no—
753C22—3322no—
754C22—3322no—
755C22—6644no—
756C22#1912827912yes—
757C22#1912850412yes—
758C22#1912851212yes—
759C22C23×C22⋊D8311yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—3322no—
768C4—3322no—
769C4—3322no—
770C4#1912827912yes—
771C4C2×#1458183811yescharacteristic
772C4C2×#1458183911yescharacteristic
773C2—42no—
774C2—82no—
775C2—82no—
776C2—6642no—
777C2#2491886814yesdirect product factor
778C2C2×#1912827911yescharacteristic
779C2C2×#1912850411yescharacteristic
780C2C2×#1912851211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC2×#540×C83C2
socleC23×C83C22×D4
hypercenterC2×#540D83
hypocenterC83C2×#3257
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#540

Complements

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

NH ≅ G/Ntype
1. C2×#19128322C2semidirect
2. #24918868C2direct (N × H)
3. C2×#19128005C2semidirect
4. C2×#19127998C2semidirect
5. C2×#19127991C2semidirect
6. C2×#19127981C2semidirect
7. C2×#19127952C2semidirect
8. C2×#19127945C2semidirect
9. C2×#19127935C2semidirect
10. C2×#19127928C2semidirect
11. C2×#19127898C2semidirect
12. C2×#19127916C2semidirect
13. C2×#19127916C2semidirect
14. C2×#19127893C2semidirect
15. C2×#19127728C2semidirect
16. C2×#540×C83C2semidirect
24. #19128322C22semidirect
35. #19128005C22semidirect
36. #19127998C22semidirect
37. #19127991C22semidirect
38. #19127981C22semidirect
39. #19127952C22semidirect
40. #19127945C22semidirect
41. #19127935C22semidirect
42. #19127928C22semidirect
43. #19127916C22semidirect
44. #19127916C22semidirect
45. #19127898C22semidirect
46. #19127893C22semidirect
51. #19127728C22semidirect
65. #540×C83C22semidirect
386. C2×C83#3257semidirect
392. C2×#540D83semidirect
407. C83C2×#3257semidirect
417. #540C2×D83semidirect
777. C2#24918868direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191283222
#249188682
C2×#191280052
C2×#191279982
C2×#191279912
C2×#191279812
C2×#191279522
C2×#191279452
C2×#191279352
C2×#191279282
C2×#191278982
C2×#191279162
C2×#191278932
C2×#191277282
C2×#540×C832
C2×#325783