Finite Group Databasebeta

← C2×#24912731 #35574641

Subgroups — C2×#24912731 #35574641

Order 21248.

2334 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24912731C2116yesmaximal, direct product factor
2C2×#19127635C211yesmaximal, characteristic, complemented
3C2×#19127623C211yesmaximal, characteristic
4C2×#19127621C211yesmaximal, characteristic, complemented
5C2×#19127614C211yesmaximal, characteristic
6C2×#19127607C211yesmaximal, characteristic, complemented
7C2×#19127592C211yesmaximal, characteristic
8C2×#19127592C211yesmaximal, characteristic
9C2×#19127585C211yesmaximal, characteristic, complemented
10C2×#19127585C211yesmaximal, characteristic, complemented
11C2×#19127582C211yesmaximal, characteristic, complemented
12C2×#19127572C211yesmaximal, characteristic
13C2×#19127565C211yesmaximal, characteristic, complemented
14C2×#19127560C211yesmaximal, characteristic
15C2×C4×(C2×D83)⋊C4C211yesmaximal, characteristic
16C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C4×D83C2211yescharacteristic
19C22×C4⋊Dic83C2211yescharacteristic
20C22×Dic83⋊C4C2211yescharacteristic
21C22×Dic83⋊C4C2211yescharacteristic
22C22×Dic83⋊C4C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×(C2×D83)⋊C4C2211yescharacteristic
27C22×(C2×D83)⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×C4×Dic83C2211yescharacteristic
33#19127635C2218yescomplemented
34#19127623C2218yes—
35#19127621C2218yescomplemented
36#19127614C2218yes—
37#19127607C2218yescomplemented
38#19127592C2218yes—
39#19127592C2218yes—
40#19127585C2218yescomplemented
41#19127585C2218yescomplemented
42#19127582C2218yescomplemented
43#19127572C2218yes—
44#19127565C2218yescomplemented
45#19127560C2218yes—
46C4×(C2×D83)⋊C4C2218yes—
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
59C22×C4⋊C4×C83C2211yescharacteristic
60C22×C4⋊C4×C83C2211yescharacteristic
61C22×C42×C83C2211yescharacteristic
62C22×C42×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64C4×C4⋊C4×C83C2218yescomplemented
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C24×D83C2311yescharacteristic
68C22×Dic166—24no—
69C22×Dic166—42no—
70C22×Dic166—42no—
71C22×Dic166C2314yes—
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C22×C4×D83—24no—
80C22×C4×D83—24no—
81C22×C4×D83—42no—
82C22×C4×D83C2314yes—
83C2×C4⋊Dic83—42no—
84C2×C4⋊Dic83C2314yes—
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—24no—
87C2×Dic83⋊C4—24no—
88C2×Dic83⋊C4—42no—
89C2×Dic83⋊C4—42no—
90C2×Dic83⋊C4—42no—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—42no—
100C2×(C2×D83)⋊C4—42no—
101C2×(C2×D83)⋊C4—42no—
102C2×(C2×D83)⋊C4Q818yescomplemented
103C2×(C2×D83)⋊C4C2314yes—
104C2×(C2×D83)⋊C4C2314yes—
105C2×(C2×D83)⋊C4C2314yes—
106C2×(C2×D83)⋊C4C2314yes—
107C2×(C2×D83)⋊C4C2314yes—
108C2×(C2×D83)⋊C4C2314yes—
109C2×C4×Dic83—24no—
110C2×C4×Dic83C2314yes—
111C83⋊#95C2314yes—
112C83⋊#95C2314yes—
113C83⋊#95C2314yes—
114C83⋊#95C2314yes—
115C83⋊#95C2314yes—
116C83⋊#95C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C23×C4×C83C2311yescharacteristic
124C23×C4×C83C2311yescharacteristic
125C23×C4×C83C2311yescharacteristic
126C23×C4×C83C2311yescharacteristic
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C2×C4⋊C4×C83—24no—
131C2×C4⋊C4×C83—24no—
132C2×C4⋊C4×C83C2314yes—
133C2×C4⋊C4×C83C2314yes—
134C2×C42×C83—24no—
135C2×C42×C83—42no—
136C2×C42×C83—42no—
137C2×C42×C83C2314yes—
138C2×C42×C83C2314yes—
139C2×C42×C83C2314yes—
140#95×C83C2314yes—
141#95×C83C2314yes—
142C23×D83—22no—
143C23×D83—22no—
144C23×D83—22no—
145C23×D83—22no—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83C2×Q814yes—
149C23×D83C2412yes—
150C2×Dic166—28no—
151C2×Dic166—44no—
152C2×Dic166—44no—
153C2×Dic166—416no—
154C22×Dic83—22no—
155C22×Dic83—22no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
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×Dic83C2×Q814yes—
174C22×Dic83#4114yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C2×C4×D83—28no—
183C2×C4×D83—28no—
184C2×C4×D83—44no—
185C2×C4×D83—416no—
186C4⋊Dic83—44no—
187Dic83⋊C4—28no—
188Dic83⋊C4—28no—
189Dic83⋊C4—28no—
190Dic83⋊C4—44no—
191Dic83⋊C4—44no—
192Dic83⋊C4—44no—
193(C2×D83)⋊C4—28no—
194(C2×D83)⋊C4—28no—
195(C2×D83)⋊C4—44no—
196(C2×D83)⋊C4—44no—
197(C2×D83)⋊C4—44no—
198(C2×D83)⋊C4C2×Q8116yescomplemented
199C4×Dic83—28no—
200C24×C83C2411yescharacteristic
201C22×C4×C83—22no—
202C22×C4×C83—22no—
203C22×C4×C83—22no—
204C22×C4×C83—22no—
205C22×C4×C83—22no—
206C22×C4×C83—22no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—22no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—22no—
215C22×C4×C83—22no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
218C22×C4×C83C2×Q814yes—
219C22×C4×C83#4114yes—
220C22×C4×C83#4114yes—
221C22×C4×C83#4114yes—
222C22×C4×C83C2412yes—
223C22×C4×C83C2412yes—
224C22×C4×C83C2412yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C4⋊C4×C83—28no—
230C4⋊C4×C83—28no—
231C42×C83—28no—
232C42×C83—44no—
233C42×C83—44no—
234C23×C83C22×Q812yes—
235C23×C83C2×#4112yes—
236C23×C83C2×#4112yes—
237C23×C83C2×#4112yes—
238C23×C83C2×#4112yes—
239C23×C83H(5,𝔽2)12yes—
240C23×C83H(5,𝔽2)12yes—
241C23×C83C2511yescharacteristic
242C22×D83—28no—
243C22×D83—28no—
244C22×D83—28no—
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—44no—
252C22×D83—44no—
253C22×D83—44no—
254C22×D83—44no—
255C22×D83C22×Q814yes—
256C2×C4×C83—28no—
257C2×C4×C83—28no—
258C2×C4×C83—28no—
259C2×C4×C83—28no—
260C2×C4×C83—22no—
261C2×C4×C83—22no—
262C2×C4×C83—22no—
263C2×C4×C83—22no—
264C2×C4×C83—22no—
265C2×C4×C83—22no—
266C2×C4×C83—22no—
267C2×C4×C83—22no—
268C2×C4×C83—22no—
269C2×C4×C83—22no—
270C2×C4×C83—22no—
271C2×C4×C83—22no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—44no—
278C2×C4×C83—44no—
279C2×C4×C83—44no—
280C2×C4×C83C22×Q814yes—
281C2×C4×C83C2×#4114yes—
282C2×C4×C83C2×#4114yes—
283C2×C4×C83C2×#4114yes—
284C2×Dic83—28no—
285C2×Dic83—28no—
286C2×Dic83—22no—
287C2×Dic83—22no—
288C2×Dic83—22no—
289C2×Dic83—22no—
290C2×Dic83—22no—
291C2×Dic83—22no—
292C2×Dic83—22no—
293C2×Dic83—22no—
294C2×Dic83—22no—
295C2×Dic83—22no—
296C2×Dic83—22no—
297C2×Dic83—22no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—44no—
306C2×Dic83—44no—
307C2×Dic83—44no—
308C2×Dic83—44no—
309C2×Dic83—44no—
310C2×Dic83C22×Q814yes—
311C2×Dic83C2×#4114yes—
312C4×D83—416no—
313Dic166—416no—
314C22×C83#52914yes—
315C22×C83#53314yes—
316C22×C83#53814yes—
317C22×C83#55114yes—
318C22×C83#55414yes—
319C22×C83#55414yes—
320C22×C83#55514yes—
321C22×C83C23×Q811yescharacteristic
322C22×C83C22×#4111yescharacteristic
323C22×C83C22×#4111yescharacteristic
324C22×C83C22×#4111yescharacteristic
325C22×C83C22×#4111yescharacteristic
326C22×C83C2×H(5,𝔽2)11yescharacteristic
327C22×C83C2×H(5,𝔽2)11yescharacteristic
328C2×D83—24no—
329C2×D83—24no—
330C2×D83—24no—
331C2×D83—416no—
332C2×D83—42no—
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C4×C83—24no—
337C4×C83—24no—
338C4×C83—24no—
339C4×C83—24no—
340C4×C83—42no—
341C4×C83—42no—
342C4×C83—42no—
343Dic83—24no—
344Dic83—24no—
345Dic83—42no—
346Dic83—42no—
347Dic83—42no—
348Dic83—42no—
349Dic83—42no—
350C2×#2574—831nomaximal, Sylow
351C2×C83#257418yescomplemented
352C2×C83C2×#52911yescharacteristic
353C2×C83C2×#53311yescharacteristic
354C2×C83C2×#53811yescharacteristic
355C2×C83C2×#55111yescharacteristic
356C2×C83C2×#55411yescharacteristic
357C2×C83C2×#55411yescharacteristic
358C2×C83C2×#55511yescharacteristic
359D83—44no—
360#2574—8316no—
361C2×#398—831no—
362C2×#396—831no—
363C2×#395—831no—
364C2×#393—831no—
365C2×#391—831no—
366C2×#388—831no—
367C2×#388—831no—
368C2×#387—831no—
369C2×#387—831no—
370C2×#387—831no—
371C2×#385—831no—
372C2×#382—831no—
373C2×#380—831no—
374C2×C4×C4⋊C4D8311yescharacteristic, complemented
375C2×C4×C22⋊C4—831no—
376C83C2×#257411yescharacteristic, complemented, Sylow
377C23×Q8—831no—
378C24×C4—831no—
379C22×C4⋊C4—831no—
380C22×C4⋊C4—831no—
381C22×C4⋊C4—831no—
382C22×C4⋊C4—831no—
383C22×C4⋊C4—831no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4C2×D8311yescharacteristic
387C22×C4⋊C4C2×D8311yescharacteristic
388C22×C22⋊C4—831no—
389C22×C22⋊C4—831no—
390C22×C22⋊C4—831no—
391C22×C22⋊C4—831no—
392C22×C22⋊C4—831no—
393C22×C22⋊C4—831no—
394C22×C42—831no—
395C22×C42C2×D8311yescharacteristic
396C22×C42C2×D8311yescharacteristic
397C22×C42C2×D8311yescharacteristic
398#398—838no—
399#396—838no—
400#395—838no—
401#393—838no—
402#391—838no—
403#388—838no—
404#388—838no—
405#387—838no—
406#387—838no—
407#387—838no—
408#385—838no—
409#382—838no—
410#380—838no—
411C4×C4⋊C4C2×D8318yescomplemented
412C4×C22⋊C4—838no—
413C2×#95—831no—
414C2×#95—831no—
415C2×#95—831no—
416C2×#95—831no—
417C2×#95—831no—
418C2×#95—831no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95C2×D8311yescharacteristic
426C2×#95C2×D8311yescharacteristic
427C25—831no—
428C22×Q8—3322no—
429C22×Q8—3322no—
430C22×Q8—834no—
431C22×Q8—1664no—
432C23×C4—3322no—
433C23×C4—834no—
434C23×C4—831no—
435C23×C4—831no—
436C23×C4—831no—
437C23×C4—831no—
438C23×C4—831no—
439C23×C4—831no—
440C23×C4—831no—
441C23×C4—1664no—
442C23×C4—1664no—
443C23×C4C22×D8311yescharacteristic
444C23×C4C22×D8311yescharacteristic
445C23×C4C22×D8311yescharacteristic
446C23×C4C22×D8311yescharacteristic
447C23×C4C22×D8311yescharacteristic
448C23×C4C22×D8311yescharacteristic
449C23×C4C22×D8311yescharacteristic
450C2×C4⋊C4—24no—
451C2×C4⋊C4—24no—
452C2×C4⋊C4—3322no—
453C2×C4⋊C4—3322no—
454C2×C4⋊C4—3322no—
455C2×C4⋊C4—3322no—
456C2×C4⋊C4—834no—
457C2×C4⋊C4—834no—
458C2×C4⋊C4—834no—
459C2×C4⋊C4—834no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—834no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—1664no—
464C2×C4⋊C4—1664no—
465C2×C4⋊C4—1664no—
466C2×C4⋊C4C22×D8314yes—
467C2×C4⋊C4C22×D8314yes—
468C2×C22⋊C4—3322no—
469C2×C22⋊C4—3322no—
470C2×C22⋊C4—3322no—
471C2×C22⋊C4—834no—
472C2×C22⋊C4—834no—
473C2×C22⋊C4—834no—
474C2×C22⋊C4—838no—
475C2×C22⋊C4—834no—
476C2×C22⋊C4—834no—
477C2×C22⋊C4—834no—
478C2×C22⋊C4—1664no—
479C2×C22⋊C4—1664no—
480C2×C42—24no—
481C2×C42—42no—
482C2×C42—42no—
483C2×C42—834no—
484C2×C42—1664no—
485C2×C42C22×D8314yes—
486C2×C42C22×D8314yes—
487C2×C42C22×D8314yes—
488#95—834no—
489#95—834no—
490#95—834no—
491#95—834no—
492#95—834no—
493#95—834no—
494#95—834no—
495#95—834no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95C22×D8314yes—
501#95C22×D8314yes—
502C24—834no—
503C24—832no—
504C24—1662no—
505C24—1662no—
506C24—1662no—
507C24—1662no—
508C24—1662no—
509C24—1662no—
510C24C23×D8311yescharacteristic
511C2×Q8—33216no—
512C2×Q8—3324no—
513C2×Q8—3324no—
514C2×Q8—1668no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—33216no—
533C22×C4—3324no—
534C22×C4—834no—
535C22×C4—834no—
536C22×C4—832no—
537C22×C4—832no—
538C22×C4—832no—
539C22×C4—832no—
540C22×C4—832no—
541C22×C4—832no—
542C22×C4—832no—
543C22×C4—1668no—
544C22×C4—1662no—
545C22×C4—1662no—
546C22×C4—1662no—
547C22×C4—1662no—
548C22×C4—1662no—
549C22×C4—1662no—
550C22×C4—1662no—
551C22×C4—1662no—
552C22×C4—1662no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1662no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1668no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4Q8×D8314yes—
565C22×C4#1305059014yes—
566C22×C4#1305059014yes—
567C22×C4#1305059014yes—
568C22×C4C23×D8312yes—
569C22×C4C23×D8312yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8312yes—
572C22×C4C23×D8312yes—
573C22×C4C23×D8312yes—
574C22×C4C23×D8312yes—
575C4⋊C4—28no—
576C4⋊C4—28no—
577C4⋊C4—3324no—
578C4⋊C4—3324no—
579C4⋊C4—3324no—
580C4⋊C4—3324no—
581C4⋊C4—1668no—
582C4⋊C4—1668no—
583C4⋊C4—1668no—
584C22⋊C4—3324no—
585C22⋊C4—3324no—
586C22⋊C4—3324no—
587C22⋊C4—8316no—
588C22⋊C4—1668no—
589C22⋊C4—1668no—
590C42—28no—
591C42—44no—
592C42—44no—
593C42—1668no—
594C23—3324no—
595C23—3324no—
596C23—3324no—
597C23—3324no—
598C23—834no—
599C23—1668no—
600C23—1668no—
601C23—1668no—
602C23—1662no—
603C23—1662no—
604C23—1662no—
605C23—1662no—
606C23—1662no—
607C23—1662no—
608C23C2×Q8×D8312yes—
609C23#41×D8312yes—
610C23C2×#1305059012yes—
611C23C2×#1305059012yes—
612C23C2×#1305059012yes—
613C23#1458183712yes—
614C23#1458183812yes—
615C23C24×D8311yescharacteristic
616Q8—33216no—
617C2×C4—28no—
618C2×C4—28no—
619C2×C4—28no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—28no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4—44no—
641C2×C4—33216no—
642C2×C4—3324no—
643C2×C4—3324no—
644C2×C4—3324no—
645C2×C4—3324no—
646C2×C4—3324no—
647C2×C4—834no—
648C2×C4—834no—
649C2×C4—1662no—
650C2×C4—1662no—
651C2×C4—1662no—
652C2×C4—1662no—
653C2×C4—1662no—
654C2×C4—1662no—
655C2×C4—1662no—
656C2×C4—1662no—
657C2×C4—1662no—
658C2×C4—1662no—
659C2×C4—1662no—
660C2×C4—1662no—
661C2×C4—1662no—
662C2×C4—1662no—
663C2×C4—1662no—
664C2×C4—1668no—
665C2×C4—1668no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4C2×Q8×D8314yes—
671C2×C4C2×#1305059014yes—
672C2×C4C2×#1305059014yes—
673C2×C4C2×#1305059014yes—
674C22—33216no—
675C22—3322no—
676C22—3322no—
677C22—3322no—
678C22—3322no—
679C22—1664no—
680C22—1664no—
681C22—1664no—
682C22#1912823514yes—
683C22#1912825514yes—
684C22#1912828414yes—
685C22#1912838014yes—
686C22#1912840614yes—
687C22#1912841114yes—
688C22#1912841414yes—
689C22C22×Q8×D8311yescharacteristic
690C22C2×#41×D8311yescharacteristic
691C22C22×#1305059011yescharacteristic
692C22C22×#1305059011yescharacteristic
693C22C22×#1305059011yescharacteristic
694C22C2×#1458183711yescharacteristic
695C22C2×#1458183811yescharacteristic
696C4—24no—
697C4—24no—
698C4—24no—
699C4—24no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—3322no—
704C4—3322no—
705C4—3322no—
706C4—3322no—
707C4—3322no—
708C4—1664no—
709C4—1664no—
710C2—3324no—
711C2#2491273118yesdirect product factor
712C2C2×#1912823511yescharacteristic
713C2C2×#1912825511yescharacteristic
714C2C2×#1912828411yescharacteristic
715C2C2×#1912838011yescharacteristic
716C2C2×#1912840611yescharacteristic
717C2C2×#1912841111yescharacteristic
718C2C2×#1912841411yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×C4×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#2574
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #24912731C2direct (N × H)
2. C2×#19127635C2semidirect
4. C2×#19127621C2semidirect
6. C2×#19127607C2semidirect
9. C2×#19127585C2semidirect
10. C2×#19127585C2semidirect
11. C2×#19127582C2semidirect
13. C2×#19127565C2semidirect
16. C2×C4×C4⋊C4×C83C2semidirect
33. #19127635C22semidirect
35. #19127621C22semidirect
37. #19127607C22semidirect
40. #19127585C22semidirect
41. #19127585C22semidirect
42. #19127582C22semidirect
44. #19127565C22semidirect
64. C4×C4⋊C4×C83C22semidirect
102. C2×(C2×D83)⋊C4Q8semidirect
198. (C2×D83)⋊C4C2×Q8semidirect
351. C2×C83#2574semidirect
374. C2×C4×C4⋊C4D83semidirect
376. C83C2×#2574semidirect
411. C4×C4⋊C4C2×D83semidirect
711. C2#24912731direct (N × H)

Maximal subgroups

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

subgroupindex
#249127312
C2×#191276352
C2×#191276232
C2×#191276212
C2×#191276142
C2×#191276072
C2×#191275922
C2×#191275852
C2×#191275822
C2×#191275722
C2×#191275652
C2×#191275602
C2×C4×(C2×D83)⋊C42
C2×C4×C4⋊C4×C832
C2×#257483