Finite Group Databasebeta

← C2×#24912709 #35574795

Subgroups — C2×#24912709 #35574795

Order 21248.

2614 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912709C2116yesmaximal, direct product factor
2C2×#19127641C211yesmaximal, characteristic, complemented
3C2×#19127616C211yesmaximal, characteristic
4C2×#19127614C211yesmaximal, characteristic, complemented
5C2×#19127613C211yesmaximal, characteristic, complemented
6C2×#19127605C211yesmaximal, characteristic, complemented
7C2×#19127594C211yesmaximal, characteristic, complemented
8C2×#19127593C211yesmaximal, characteristic, complemented
9C2×#19127580C211yesmaximal, characteristic
10C2×#19127577C211yesmaximal, characteristic
11C2×#19127568C211yesmaximal, characteristic, complemented
12C2×#19127568C211yesmaximal, characteristic, complemented
13C2×#19127563C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic83C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic, complemented
16C2×#381×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C22×C4⋊Dic83C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×C22⋊Dic83C2211yescharacteristic
23C22×C22⋊Dic83C2211yescharacteristic
24C22×C22⋊Dic83C2211yescharacteristic
25C22×(C2×D83)⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×C4×Dic83C2211yescharacteristic
31C22×C4×Dic83C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33#19127641C2218yescomplemented
34#19127616C2218yes—
35#19127614C2218yescomplemented
36#19127613C2218yescomplemented
37#19127605C2218yescomplemented
38#19127594C2218yescomplemented
39#19127593C2218yescomplemented
40#19127580C2218yes—
41#19127577C2218yes—
42#19127568C2218yescomplemented
43#19127568C2218yescomplemented
44#19127563C2218yescomplemented
45C4×C22⋊Dic83C2218yescomplemented
46#19127548C2218yescomplemented
47C2×C83⋊#95C2211yescharacteristic
48C2×C83⋊#95C2211yescharacteristic
49C2×C83⋊#95C2211yescharacteristic
50C2×C83⋊#95C2211yescharacteristic
51C2×C83⋊#95C2211yescharacteristic
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C24×C4×C83C2211yescharacteristic
60C22×C22⋊C4×C83C2211yescharacteristic
61C22×C22⋊C4×C83C2211yescharacteristic
62#381×C83C2218yescomplemented
63C2×#95×C83C2211yescharacteristic
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C22×Dic166—24no—
69C22×Dic166—42no—
70C22×Dic166—42no—
71C22×Dic166C2314yes—
72C22×C22⋊D83—24no—
73C22×C22⋊D83—24no—
74C22×C22⋊D83—42no—
75C22×C22⋊D83C2314yes—
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C22×C4×D83—24no—
84C22×C4×D83—24no—
85C22×C4×D83—42no—
86C22×C4×D83C2314yes—
87C2×C4⋊Dic83—42no—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—42no—
90C2×Dic83⋊C4C2314yes—
91C2×C22⋊Dic83—24no—
92C2×C22⋊Dic83—24no—
93C2×C22⋊Dic83—42no—
94C2×C22⋊Dic83C2314yes—
95C2×C22⋊Dic83C2314yes—
96C2×C22⋊Dic83C2314yes—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—42no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4C2314yes—
103C2×(C2×D83)⋊C4C2314yes—
104C2×(C2×D83)⋊C4C2314yes—
105C2×(C2×D83)⋊C4C2314yes—
106C2×(C2×D83)⋊C4C2314yes—
107C2×C4×Dic83—24no—
108C2×C4×Dic83—24no—
109C2×C4×Dic83—42no—
110C2×C4×Dic83C2314yes—
111C2×C4×Dic83C2314yes—
112C2×C4×Dic83C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C25×C83C2311yescharacteristic
126C23×C4×C83—24no—
127C23×C4×C83—24no—
128C23×C4×C83—42no—
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2314yes—
135C23×C4×C83C2311yescharacteristic
136C2×C22⋊C4×C83—24no—
137C2×C22⋊C4×C83—42no—
138C2×C22⋊C4×C83C2314yes—
139C2×C22⋊C4×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142#95×C83C2314yes—
143#95×C83C2314yes—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—22no—
150C23×D83#4114yes—
151C23×D83C2412yes—
152C2×Dic166—28no—
153C2×Dic166—44no—
154C2×Dic166—44no—
155C2×Dic166—416no—
156C2×C22⋊D83—28no—
157C2×C22⋊D83—28no—
158C2×C22⋊D83—44no—
159C2×C22⋊D83—416no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—22no—
163C22×Dic83—22no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—22no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83—22no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83#4114yes—
180C22×Dic83#4114yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C2×C4×D83—28no—
189C2×C4×D83—28no—
190C2×C4×D83—44no—
191C2×C4×D83—416no—
192C4⋊Dic83—44no—
193Dic83⋊C4—44no—
194C22⋊Dic83—28no—
195C22⋊Dic83—28no—
196C22⋊Dic83—44no—
197(C2×D83)⋊C4—28no—
198(C2×D83)⋊C4—28no—
199(C2×D83)⋊C4—28no—
200(C2×D83)⋊C4—44no—
201(C2×D83)⋊C4—44no—
202C4×Dic83—28no—
203C4×Dic83—28no—
204C4×Dic83—44no—
205C24×C83—22no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83—22no—
211C24×C83#4114yes—
212C24×C83C2412yes—
213C24×C83C2411yescharacteristic
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—28no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—22no—
225C22×C4×C83—22no—
226C22×C4×C83—22no—
227C22×C4×C83—22no—
228C22×C4×C83—22no—
229C22×C4×C83—22no—
230C22×C4×C83—22no—
231C22×C4×C83—22no—
232C22×C4×C83—28no—
233C22×C4×C83—44no—
234C22×C4×C83—416no—
235C22×C4×C83#4114yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C22×C4×C83C2412yes—
242C22⋊C4×C83—28no—
243C22⋊C4×C83—44no—
244C23×C83—28no—
245C23×C83—28no—
246C23×C83—28no—
247C23×C83—22no—
248C23×C83—22no—
249C23×C83—22no—
250C23×C83—22no—
251C23×C83—22no—
252C23×C83—22no—
253C23×C83—44no—
254C23×C83—44no—
255C23×C83—44no—
256C23×C83—44no—
257C23×C83C2×#4112yes—
258C23×C83C2×#4112yes—
259C23×C83C2×#4112yes—
260C23×C83C2×#4114yes—
261C23×C83C2×#4112yes—
262C23×C83C2×#4112yes—
263C23×C83H(5,𝔽2)12yes—
264C23×C83H(5,𝔽2)12yes—
265C23×C83C2511yescharacteristic
266C22×D83—28no—
267C22×D83—28no—
268C22×D83—28no—
269C22×D83—22no—
270C22×D83—22no—
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—44no—
276C22×D83—44no—
277C22×D83—44no—
278C22×D83—44no—
279C22×D83C2×#4114yes—
280C2×C4×C83—28no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
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—22no—
295C2×C4×C83—22no—
296C2×C4×C83—22no—
297C2×C4×C83—22no—
298C2×C4×C83—416no—
299C2×C4×C83—44no—
300C2×C4×C83—44no—
301C2×C4×C83—44no—
302C2×C4×C83—44no—
303C2×C4×C83—44no—
304C2×C4×C83C2×#4114yes—
305C22⋊D83—416no—
306C2×Dic83—28no—
307C2×Dic83—28no—
308C2×Dic83—22no—
309C2×Dic83—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—22no—
314C2×Dic83—22no—
315C2×Dic83—22no—
316C2×Dic83—22no—
317C2×Dic83—22no—
318C2×Dic83—22no—
319C2×Dic83—22no—
320C2×Dic83—22no—
321C2×Dic83—22no—
322C2×Dic83—22no—
323C2×Dic83—22no—
324C2×Dic83—22no—
325C2×Dic83—22no—
326C2×Dic83—22no—
327C2×Dic83—44no—
328C2×Dic83—44no—
329C2×Dic83—44no—
330C2×Dic83—44no—
331C2×Dic83—44no—
332C2×Dic83C2×#4114yes—
333C2×Dic83C2×#4114yes—
334C4×D83—416no—
335Dic166—416no—
336C22×C83—24no—
337C22×C83—24no—
338C22×C83—24no—
339C22×C83—416no—
340C22×C83—42no—
341C22×C83—42no—
342C22×C83—42no—
343C22×C83—42no—
344C22×C83#52914yes—
345C22×C83#52914yes—
346C22×C83#53814yes—
347C22×C83#55114yes—
348C22×C83#55114yes—
349C22×C83#55114yes—
350C22×C83#55514yes—
351C22×C83C22×#4111yescharacteristic
352C22×C83C22×#4111yescharacteristic
353C22×C83C22×#4111yescharacteristic
354C22×C83C22×#4111yescharacteristic
355C22×C83C22×#4111yescharacteristic
356C22×C83C2×H(5,𝔽2)11yescharacteristic
357C22×C83C2×H(5,𝔽2)11yescharacteristic
358C2×D83—24no—
359C2×D83—24no—
360C2×D83—24no—
361C2×D83—416no—
362C2×D83—42no—
363C2×D83—42no—
364C2×D83—42no—
365C2×D83—42no—
366C4×C83—24no—
367C4×C83—42no—
368C4×C83—42no—
369C4×C83—42no—
370C4×C83—42no—
371C4×C83—42no—
372Dic83—24no—
373Dic83—24no—
374Dic83—42no—
375Dic83—42no—
376Dic83—42no—
377Dic83—42no—
378Dic83—42no—
379C2×#2572—831nomaximal, Sylow
380C2×C83—44no—
381C2×C83#257218yescomplemented
382C2×C83C2×#52911yescharacteristic
383C2×C83C2×#52911yescharacteristic
384C2×C83C2×#53811yescharacteristic
385C2×C83C2×#55111yescharacteristic
386C2×C83C2×#55111yescharacteristic
387C2×C83C2×#55111yescharacteristic
388C2×C83C2×#55511yescharacteristic
389D83—44no—
390#2572—8316no—
391C2×#400—831no—
392C2×#394—831no—
393C2×#393—831no—
394C2×#393—831no—
395C2×#391—831no—
396C2×#388—831no—
397C2×#388—831no—
398C2×#386—831no—
399C2×#386—831no—
400C2×#383—831no—
401C2×#383—831no—
402C2×#381—831no—
403C2×#381D8311yescharacteristic, complemented
404C2×C4×C22⋊C4—831no—
405C2×C4×C22⋊C4—831no—
406C83C2×#257211yescharacteristic, complemented, Sylow
407C23×Q8—831no—
408C23×D4—831no—
409C24×C4—831no—
410C24×C4C2×D8311yescharacteristic
411C22×C4⋊C4—831no—
412C22×C4⋊C4—831no—
413C22×C22⋊C4—831no—
414C22×C22⋊C4—831no—
415C22×C22⋊C4—831no—
416C22×C22⋊C4—831no—
417C22×C22⋊C4—831no—
418C22×C22⋊C4—831no—
419C22×C22⋊C4—831no—
420C22×C22⋊C4—831no—
421C22×C22⋊C4C2×D8311yescharacteristic
422C22×C22⋊C4C2×D8311yescharacteristic
423C22×C42—831no—
424C22×C42—831no—
425C22×C42—831no—
426#400—838no—
427#394—838no—
428#393—838no—
429#393—838no—
430#391—838no—
431#388—838no—
432#388—838no—
433#386—838no—
434#386—838no—
435#383—838no—
436#383—838no—
437#381—838no—
438#381C2×D8318yescomplemented
439C4×C22⋊C4—838no—
440C4×C22⋊C4—838no—
441C2×#95—831no—
442C2×#95—831no—
443C2×#95—831no—
444C2×#95—831no—
445C2×#95—831no—
446C2×#95—831no—
447C2×#95—831no—
448C2×#95—831no—
449C2×#95—831no—
450C2×#95—831no—
451C2×#95—831no—
452C2×#95—831no—
453C2×#95C2×D8311yescharacteristic
454C2×#95C2×D8311yescharacteristic
455C2×#95C2×D8311yescharacteristic
456C2×#95C2×D8311yescharacteristic
457C25—831no—
458C25C22×D8311yescharacteristic
459C22×Q8—3322no—
460C22×Q8—3322no—
461C22×Q8—834no—
462C22×Q8—1664no—
463C22×D4—3322no—
464C22×D4—834no—
465C22×D4—1664no—
466C22×D4—1664no—
467C23×C4—24no—
468C23×C4—24no—
469C23×C4—42no—
470C23×C4—3322no—
471C23×C4—834no—
472C23×C4—831no—
473C23×C4—831no—
474C23×C4—831no—
475C23×C4—831no—
476C23×C4—831no—
477C23×C4—831no—
478C23×C4—831no—
479C23×C4—1664no—
480C23×C4—1664no—
481C23×C4C22×D8311yescharacteristic
482C23×C4C22×D8311yescharacteristic
483C23×C4C22×D8311yescharacteristic
484C23×C4C22×D8311yescharacteristic
485C23×C4C22×D8311yescharacteristic
486C23×C4C22×D8314yes—
487C23×C4C22×D8311yescharacteristic
488C2×C4⋊C4—3322no—
489C2×C4⋊C4—3322no—
490C2×C4⋊C4—834no—
491C2×C4⋊C4—834no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—3322no—
495C2×C22⋊C4—3322no—
496C2×C22⋊C4—3322no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—834no—
502C2×C22⋊C4—834no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—1664no—
506C2×C22⋊C4—1664no—
507C2×C22⋊C4—1664no—
508C2×C22⋊C4—1664no—
509C2×C22⋊C4—1664no—
510C2×C22⋊C4C22×D8314yes—
511C2×C22⋊C4C22×D8314yes—
512C2×C42—3322no—
513C2×C42—834no—
514C2×C42—834no—
515C2×C42—834no—
516C2×C42—1664no—
517C2×C42—1664no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95—834no—
522#95—834no—
523#95—834no—
524#95—834no—
525#95—834no—
526#95—834no—
527#95—834no—
528#95—834no—
529#95—834no—
530#95C22×D8314yes—
531#95C22×D8314yes—
532#95C22×D8314yes—
533#95C22×D8314yes—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—834no—
541C24—832no—
542C24—1662no—
543C24—1662no—
544C24—1662no—
545C24—1662no—
546C24—1662no—
547C24—1662no—
548C24#1305058914yes—
549C24C23×D8312yes—
550C24C23×D8311yescharacteristic
551C2×Q8—3324no—
552C2×Q8—3324no—
553C2×Q8—33216no—
554C2×Q8—1668no—
555C2×D4—33216no—
556C2×D4—3324no—
557C2×D4—1668no—
558C2×D4—1668no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—28no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—28no—
578C22×C4—44no—
579C22×C4—416no—
580C22×C4—3324no—
581C22×C4—33216no—
582C22×C4—834no—
583C22×C4—834no—
584C22×C4—832no—
585C22×C4—832no—
586C22×C4—832no—
587C22×C4—832no—
588C22×C4—832no—
589C22×C4—832no—
590C22×C4—832no—
591C22×C4—1668no—
592C22×C4—1668no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4—1662no—
599C22×C4—1662no—
600C22×C4—1662no—
601C22×C4—1662no—
602C22×C4—1662no—
603C22×C4—1662no—
604C22×C4—1662no—
605C22×C4—1662no—
606C22×C4—1662no—
607C22×C4—1662no—
608C22×C4—1662no—
609C22×C4—1662no—
610C22×C4—1662no—
611C22×C4—1662no—
612C22×C4#1305059014yes—
613C22×C4C23×D8312yes—
614C22×C4C23×D8312yes—
615C22×C4C23×D8312yes—
616C22×C4C23×D8312yes—
617C22×C4C23×D8312yes—
618C22×C4C23×D8312yes—
619C4⋊C4—3324no—
620C4⋊C4—3324no—
621C22⋊C4—28no—
622C22⋊C4—44no—
623C22⋊C4—3324no—
624C22⋊C4—3324no—
625C22⋊C4—3324no—
626C22⋊C4—1668no—
627C22⋊C4—1668no—
628C22⋊C4—1668no—
629C22⋊C4—1668no—
630C22⋊C4—1668no—
631C42—3324no—
632C42—1668no—
633C42—1668no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—3324no—
648C23—3324no—
649C23—3324no—
650C23—3324no—
651C23—834no—
652C23—1668no—
653C23—1668no—
654C23—1668no—
655C23—1662no—
656C23—1662no—
657C23—1662no—
658C23—1662no—
659C23—1662no—
660C23—1662no—
661C23#41×D8312yes—
662C23#41×D8312yes—
663C23#41×D8312yes—
664C23C2×#1305058914yes—
665C23C2×#1305058912yes—
666C23C2×#1305059012yes—
667C23#1458183712yes—
668C23#1458183812yes—
669C23C24×D8311yescharacteristic
670Q8—33216no—
671D4—33216no—
672C2×C4—28no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—416no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—33216no—
697C2×C4—3324no—
698C2×C4—3324no—
699C2×C4—3324no—
700C2×C4—3324no—
701C2×C4—3324no—
702C2×C4—834no—
703C2×C4—834no—
704C2×C4—1662no—
705C2×C4—1662no—
706C2×C4—1662no—
707C2×C4—1662no—
708C2×C4—1662no—
709C2×C4—1662no—
710C2×C4—1662no—
711C2×C4—1662no—
712C2×C4—1662no—
713C2×C4—1662no—
714C2×C4—1662no—
715C2×C4—1662no—
716C2×C4—1662no—
717C2×C4—1662no—
718C2×C4—1662no—
719C2×C4—1668no—
720C2×C4—1662no—
721C2×C4—1662no—
722C2×C4—1662no—
723C2×C4—1662no—
724C2×C4—1668no—
725C2×C4C2×#1305059014yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—416no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—33216no—
735C22—3322no—
736C22—3322no—
737C22—3322no—
738C22—3322no—
739C22—1664no—
740C22—1664no—
741C22—1664no—
742C22#1912822814yes—
743C22#1912822914yes—
744C22#1912828714yes—
745C22#1912837414yes—
746C22#1912837714yes—
747C22#1912837914yes—
748C22#1912841414yes—
749C22C2×#41×D8311yescharacteristic
750C22C2×#41×D8311yescharacteristic
751C22C2×#41×D8311yescharacteristic
752C22C22×#1305058911yescharacteristic
753C22C22×#1305059011yescharacteristic
754C22C2×#1458183711yescharacteristic
755C22C2×#1458183811yescharacteristic
756C4—24no—
757C4—42no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—42no—
762C4—3322no—
763C4—3322no—
764C4—3322no—
765C4—3322no—
766C4—3322no—
767C4—1664no—
768C4—1664no—
769C2—44no—
770C2—3324no—
771C2#2491270918yesdirect product factor
772C2C2×#1912822811yescharacteristic
773C2C2×#1912822911yescharacteristic
774C2C2×#1912828711yescharacteristic
775C2C2×#1912837411yescharacteristic
776C2C2×#1912837711yescharacteristic
777C2C2×#1912837911yescharacteristic
778C2C2×#1912841411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#381×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#381D83
hypocenterC83C2×#2572
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#381

Complements

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

NH ≅ G/Ntype
1. #24912709C2direct (N × H)
2. C2×#19127641C2semidirect
4. C2×#19127614C2semidirect
5. C2×#19127613C2semidirect
6. C2×#19127605C2semidirect
7. C2×#19127594C2semidirect
8. C2×#19127593C2semidirect
11. C2×#19127568C2semidirect
12. C2×#19127568C2semidirect
13. C2×#19127563C2semidirect
14. C2×C4×C22⋊Dic83C2semidirect
15. C2×#19127548C2semidirect
16. C2×#381×C83C2semidirect
33. #19127641C22semidirect
35. #19127614C22semidirect
36. #19127613C22semidirect
37. #19127605C22semidirect
38. #19127594C22semidirect
39. #19127593C22semidirect
42. #19127568C22semidirect
43. #19127568C22semidirect
44. #19127563C22semidirect
45. C4×C22⋊Dic83C22semidirect
46. #19127548C22semidirect
62. #381×C83C22semidirect
381. C2×C83#2572semidirect
403. C2×#381D83semidirect
406. C83C2×#2572semidirect
438. #381C2×D83semidirect
771. C2#24912709direct (N × H)

Maximal subgroups

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

subgroupindex
#249127092
C2×#191276412
C2×#191276162
C2×#191276142
C2×#191276132
C2×#191276052
C2×#191275942
C2×#191275932
C2×#191275802
C2×#191275772
C2×#191275682
C2×#191275632
C2×C4×C22⋊Dic832
C2×#191275482
C2×#381×C832
C2×#257283