Finite Group Databasebeta

← C2×#24911832 #35573625

Subgroups — C2×#24911832 #35573625

Order 21248.

2854 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581791C211yesmaximal, characteristic, complemented
2C22×#14581770C211yesmaximal, characteristic
3#24911832C2116yesmaximal, direct product factor
4C2×#19127643C211yesmaximal, characteristic, complemented
5C2×#19127614C211yesmaximal, characteristic
6C2×#19127614C211yesmaximal, characteristic
7C2×#19127606C211yesmaximal, characteristic, complemented
8C2×#19127605C211yesmaximal, characteristic, complemented
9C2×#19127605C211yesmaximal, characteristic, complemented
10C2×#19127605C211yesmaximal, characteristic, complemented
11C2×#19127593C211yesmaximal, characteristic
12C2×#19127591C211yesmaximal, characteristic
13C2×#19127560C211yesmaximal, characteristic
14C2×#19127552C211yesmaximal, characteristic, complemented
15C2×#19127548C211yesmaximal, characteristic
16C2×#400×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×Dic166C2211yescharacteristic
19C23×Dic166C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C2×#14581791—28no—
22C2×#14581791C2218yescomplemented
23C2×#14581770—28no—
24C2×#14581770C2218yes—
25C22×C4⋊Dic83C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×(C2×D83)⋊C4C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39C22×C4×Dic83C2211yescharacteristic
40#19127643C2218yescomplemented
41#19127614C2218yes—
42#19127614C2218yes—
43#19127606C2218yescomplemented
44#19127605C2218yescomplemented
45#19127605C2218yescomplemented
46#19127605C2218yescomplemented
47#19127593C2218yes—
48#19127591C2218yes—
49#19127560C2218yes—
50#19127552C2218yescomplemented
51#19127548C2218yes—
52C2×C83⋊#95C2211yescharacteristic
53C2×C83⋊#95C2211yescharacteristic
54C2×C83⋊#95C2211yescharacteristic
55C2×C83⋊#95C2211yescharacteristic
56C2×C83⋊#95C2211yescharacteristic
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63#400×C83C2218yescomplemented
64C2×#95×C83C2211yescharacteristic
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166—24no—
75C22×Dic166—24no—
76C22×Dic166—24no—
77C22×Dic166—42no—
78C22×Dic166—42no—
79C22×Dic166C2314yes—
80C22×Dic166C2314yes—
81C22×Dic166C2314yes—
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C22×C4×D83—24no—
90C22×C4×D83—24no—
91C22×C4×D83—24no—
92C22×C4×D83C2314yes—
93#14581791—232no—
94#14581770—232no—
95C2×C4⋊Dic83—24no—
96C2×C4⋊Dic83C2314yes—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—24no—
99C2×Dic83⋊C4—24no—
100C2×Dic83⋊C4D418yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×(C2×D83)⋊C4—24no—
106C2×(C2×D83)⋊C4—24no—
107C2×(C2×D83)⋊C4—24no—
108C2×(C2×D83)⋊C4—42no—
109C2×(C2×D83)⋊C4—42no—
110C2×(C2×D83)⋊C4Q818yescomplemented
111C2×(C2×D83)⋊C4C2314yes—
112C2×(C2×D83)⋊C4C2314yes—
113C2×(C2×D83)⋊C4C2314yes—
114C2×(C2×D83)⋊C4C2314yes—
115C2×(C2×D83)⋊C4C2314yes—
116C2×(C2×D83)⋊C4C2314yes—
117C2×C4×Dic83—24no—
118C2×C4×Dic83—24no—
119C2×C4×Dic83—42no—
120C2×C4×Dic83—42no—
121C2×C4×Dic83C2314yes—
122C2×C4×Dic83C2314yes—
123C2×C4×Dic83C2314yes—
124C2×C4×Dic83C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C83⋊#95C2314yes—
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C23×C4×C83C2311yescharacteristic
141C2×C4⋊C4×C83—24no—
142C2×C4⋊C4×C83—24no—
143C2×C4⋊C4×C83C2314yes—
144C2×C4⋊C4×C83C2314yes—
145#95×C83C2314yes—
146#95×C83C2314yes—
147#95×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83—22no—
154C23×D83—22no—
155C23×D83—22no—
156C23×D83C2×Q814yes—
157C23×D83C2412yes—
158C2×Dic166—28no—
159C2×Dic166—28no—
160C2×Dic166—28no—
161C2×Dic166—28no—
162C2×Dic166—28no—
163C2×Dic166—28no—
164C2×Dic166—28no—
165C2×Dic166—44no—
166C2×Dic166—44no—
167C2×Dic166—416no—
168C2×Dic166—416no—
169C2×Dic166—416no—
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—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83C2×D414yes—
186C22×Dic83C2×D414yes—
187C22×Dic83C2×Q814yes—
188C22×Dic83#4114yes—
189C22×Dic83#4114yes—
190C22×Dic83#4114yes—
191C22×Dic83C2412yes—
192C22×Dic83C2412yes—
193C22×Dic83C2412yes—
194C22×Dic83C2412yes—
195C22×Dic83C2412yes—
196C22×Dic83C2412yes—
197C22×Dic83C2412yes—
198C2×C4×D83—28no—
199C2×C4×D83—28no—
200C2×C4×D83—28no—
201C2×C4×D83—416no—
202C4⋊Dic83—28no—
203Dic83⋊C4—28no—
204Dic83⋊C4—28no—
205Dic83⋊C4—28no—
206Dic83⋊C4C2×D4116yes—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—28no—
209(C2×D83)⋊C4—28no—
210(C2×D83)⋊C4—44no—
211(C2×D83)⋊C4—44no—
212(C2×D83)⋊C4C2×Q8116yescomplemented
213C4×Dic83—28no—
214C4×Dic83—28no—
215C4×Dic83—44no—
216C4×Dic83—44no—
217C24×C83C2411yescharacteristic
218C22×C4×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
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—22no—
233C22×C4×C83—22no—
234C22×C4×C83—22no—
235C22×C4×C83—22no—
236C22×C4×C83—22no—
237C22×C4×C83C2×D414yes—
238C22×C4×C83C2×Q814yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C22×C4×C83C2412yes—
242C22×C4×C83C2412yes—
243C22×C4×C83C2412yes—
244C22×C4×C83C2412yes—
245C22×C4×C83C2412yes—
246C4⋊C4×C83—28no—
247C4⋊C4×C83—28no—
248C23×C83C22×D412yes—
249C23×C83C22×Q812yes—
250C23×C83C2×#4112yes—
251C23×C83C2×#4112yes—
252C23×C83C2×#4112yes—
253C23×C83H(5,𝔽2)12yes—
254C23×C832−1+412yes—
255C23×C83C2511yescharacteristic
256C22×D83—28no—
257C22×D83—28no—
258C22×D83—28no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—22no—
263C22×D83—22no—
264C22×D83—22no—
265C22×D83—44no—
266C22×D83—44no—
267C22×D83—44no—
268C22×D83—44no—
269C22×D83C22×Q814yes—
270C2×C4×C83—28no—
271C2×C4×C83—28no—
272C2×C4×C83—22no—
273C2×C4×C83—22no—
274C2×C4×C83—22no—
275C2×C4×C83—22no—
276C2×C4×C83—22no—
277C2×C4×C83—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
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—44no—
292C2×C4×C83—44no—
293C2×C4×C83—44no—
294C2×C4×C83—44no—
295C2×C4×C83—44no—
296C2×C4×C83C22×D414yes—
297C2×C4×C83C22×Q814yes—
298C2×Dic83—28no—
299C2×Dic83—28no—
300C2×Dic83—28no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83—22no—
305C2×Dic83—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
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—44no—
317C2×Dic83—44no—
318C2×Dic83—44no—
319C2×Dic83#124116yes—
320C2×Dic83C22×D414yes—
321C2×Dic83C22×D414yes—
322C2×Dic83C22×Q814yes—
323C2×Dic83C2×#4114yes—
324C2×Dic83C2×#4114yes—
325C2×Dic83C2×#4114yes—
326C4×D83—416no—
327Dic166—416no—
328Dic166—416no—
329Dic166—416no—
330C22×C83C2×#12414yes—
331C22×C83#53314yes—
332C22×C83#54214yes—
333C22×C83#54614yes—
334C22×C83D4×Q814yes—
335C22×C83#55414yes—
336C22×C83#55614yes—
337C22×C83C23×D411yescharacteristic
338C22×C83C23×Q811yescharacteristic
339C22×C83C22×#4111yescharacteristic
340C22×C83C22×#4111yescharacteristic
341C22×C83C22×#4111yescharacteristic
342C22×C83C2×H(5,𝔽2)11yescharacteristic
343C22×C83C2×2−1+411yescharacteristic
344C2×D83—24no—
345C2×D83—24no—
346C2×D83—24no—
347C2×D83—42no—
348C2×D83—42no—
349C2×D83—42no—
350C2×D83—42no—
351C2×D83—416no—
352C4×C83—24no—
353C4×C83—24no—
354C4×C83—42no—
355C4×C83—42no—
356C4×C83—42no—
357C4×C83—42no—
358C4×C83—42no—
359Dic83—24no—
360Dic83—24no—
361Dic83—24no—
362Dic83—42no—
363Dic83—42no—
364Dic83—42no—
365Dic83C2×#12418yes—
366C2×#2492—831nomaximal, Sylow
367C2×C83#249218yescomplemented
368C2×C83C22×#12411yescharacteristic
369C2×C83C2×#53311yescharacteristic
370C2×C83C2×#54211yescharacteristic
371C2×C83C2×#54611yescharacteristic
372C2×C83C2×D4×Q811yescharacteristic
373C2×C83C2×#55411yescharacteristic
374C2×C83C2×#55611yescharacteristic
375D83—44no—
376C22×C4⋊Q8—831no—
377C22×C22⋊Q8—831no—
378#2492—8316no—
379C2×#400—831no—
380C2×#400D8311yescharacteristic, complemented
381C2×#393—831no—
382C2×#393—831no—
383C2×#391—831no—
384C2×#391—831no—
385C2×#391—831no—
386C2×#391—831no—
387C2×#388—831no—
388C2×#388—831no—
389C2×#380—831no—
390C2×C4×C4⋊C4—831no—
391C2×C4×C22⋊C4—831no—
392C83C2×#249211yescharacteristic, complemented, Sylow
393C23×Q8—831no—
394C23×Q8—831no—
395C23×Q8—831no—
396C24×C4—831no—
397C2×C4⋊Q8—838no—
398C2×C4⋊Q8—1668no—
399C2×C22⋊Q8—838no—
400C2×C22⋊Q8—1668no—
401C22×C4⋊C4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—831no—
404C22×C4⋊C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4C2×D8311yescharacteristic
407C22×C4⋊C4C2×D8311yescharacteristic
408C22×C22⋊C4—831no—
409C22×C22⋊C4—831no—
410C22×C22⋊C4—831no—
411C22×C22⋊C4—831no—
412C22×C22⋊C4—831no—
413C22×C22⋊C4—831no—
414C22×C42—831no—
415C22×C42—831no—
416C22×C42—831no—
417C22×C42—831no—
418#400—838no—
419#400C2×D8318yescomplemented
420#393—838no—
421#393—838no—
422#391—838no—
423#391—838no—
424#391—838no—
425#391—838no—
426#388—838no—
427#388—838no—
428#380—838no—
429C4×C4⋊C4—838no—
430C4×C22⋊C4—838no—
431C2×#95—831no—
432C2×#95—831no—
433C2×#95—831no—
434C2×#95—831no—
435C2×#95—831no—
436C2×#95—831no—
437C2×#95—831no—
438C2×#95—831no—
439C2×#95—831no—
440C2×#95C2×D8311yescharacteristic
441C2×#95C2×D8311yescharacteristic
442C2×#95C2×D8311yescharacteristic
443C2×#95C2×D8311yescharacteristic
444C2×#95C2×D8311yescharacteristic
445C25—831no—
446C22×Q8—3322no—
447C22×Q8—3322no—
448C22×Q8—834no—
449C22×Q8—834no—
450C22×Q8—834no—
451C22×Q8—1664no—
452C22×Q8—1664no—
453C22×Q8—1664no—
454C22×Q8—1664no—
455C22×Q8—1664no—
456C22×Q8—1664no—
457C22×Q8—1664no—
458C23×C4—831no—
459C23×C4—831no—
460C23×C4—831no—
461C23×C4—831no—
462C23×C4—831no—
463C23×C4—831no—
464C23×C4—831no—
465C23×C4—834no—
466C23×C4—1664no—
467C23×C4—1664no—
468C23×C4—1664no—
469C23×C4C22×D8311yescharacteristic
470C23×C4C22×D8311yescharacteristic
471C23×C4C22×D8311yescharacteristic
472C23×C4C22×D8311yescharacteristic
473C23×C4C22×D8311yescharacteristic
474C23×C4C22×D8311yescharacteristic
475C23×C4C22×D8311yescharacteristic
476C4⋊Q8—16632no—
477C22⋊Q8—16632no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—838no—
481C2×C4⋊C4—834no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—1664no—
487C2×C4⋊C4—1664no—
488C2×C4⋊C4—1664no—
489C2×C4⋊C4—1664no—
490C2×C4⋊C4C22×D8314yes—
491C2×C4⋊C4C22×D8314yes—
492C2×C22⋊C4—3322no—
493C2×C22⋊C4—3322no—
494C2×C22⋊C4—834no—
495C2×C22⋊C4—834no—
496C2×C22⋊C4—838no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—834no—
501C2×C22⋊C4—1664no—
502C2×C22⋊C4—1664no—
503C2×C22⋊C4—1664no—
504C2×C42—3322no—
505C2×C42—3322no—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—834no—
509C2×C42—834no—
510C2×C42—1664no—
511C2×C42—1664no—
512#95—834no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95—834no—
517#95—834no—
518#95—834no—
519#95—834no—
520#95—834no—
521#95C22×D8314yes—
522#95C22×D8314yes—
523#95C22×D8314yes—
524#95C22×D8314yes—
525#95C22×D8314yes—
526C24—834no—
527C24—832no—
528C24—1662no—
529C24—1662no—
530C24—1662no—
531C24—1662no—
532C24—1662no—
533C24—1662no—
534C24C23×D8311yescharacteristic
535C2×Q8—33216no—
536C2×Q8—3324no—
537C2×Q8—3324no—
538C2×Q8—33216no—
539C2×Q8—33216no—
540C2×Q8—1668no—
541C2×Q8—1668no—
542C2×Q8—1668no—
543C2×Q8—1668no—
544C2×Q8—1668no—
545C2×Q8—1668no—
546C2×Q8—1668no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—33216no—
567C22×C4—834no—
568C22×C4—834no—
569C22×C4—834no—
570C22×C4—832no—
571C22×C4—834no—
572C22×C4—834no—
573C22×C4—834no—
574C22×C4—832no—
575C22×C4—832no—
576C22×C4—832no—
577C22×C4—832no—
578C22×C4—832no—
579C22×C4—832no—
580C22×C4—1668no—
581C22×C4—1668no—
582C22×C4—1668no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1662no—
589C22×C4—1662no—
590C22×C4—1662no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4—1662no—
595C22×C4—1662no—
596C22×C4—1662no—
597C22×C4—1662no—
598C22×C4D4×D8314yes—
599C22×C4Q8×D8314yes—
600C22×C4C23×D8312yes—
601C22×C4C23×D8312yes—
602C22×C4C23×D8312yes—
603C22×C4C23×D8312yes—
604C22×C4C23×D8312yes—
605C22×C4C23×D8312yes—
606C22×C4C23×D8312yes—
607C4⋊C4—28no—
608C4⋊C4—28no—
609C4⋊C4—8316no—
610C4⋊C4—1668no—
611C4⋊C4—1668no—
612C4⋊C4—1668no—
613C4⋊C4—1668no—
614C22⋊C4—3324no—
615C22⋊C4—3324no—
616C22⋊C4—8316no—
617C22⋊C4—1668no—
618C22⋊C4—1668no—
619C22⋊C4—1668no—
620C42—3324no—
621C42—3324no—
622C42—1668no—
623C42—1668no—
624C23—3324no—
625C23—3324no—
626C23—3324no—
627C23—3324no—
628C23—834no—
629C23—1668no—
630C23—1668no—
631C23—1668no—
632C23—1662no—
633C23—1662no—
634C23—1662no—
635C23—1662no—
636C23—1662no—
637C23—1662no—
638C23C2×D4×D8312yes—
639C23C2×Q8×D8312yes—
640C23#41×D8312yes—
641C23#41×D8312yes—
642C23#41×D8312yes—
643C23#1458183812yes—
644C23#1458183912yes—
645C23C24×D8311yescharacteristic
646Q8—33216no—
647Q8—33216no—
648Q8—33216no—
649C2×C4—28no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
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—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—44no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—33216no—
676C2×C4—3324no—
677C2×C4—3324no—
678C2×C4—3324no—
679C2×C4—8316no—
680C2×C4—834no—
681C2×C4—834no—
682C2×C4—834no—
683C2×C4—834no—
684C2×C4—834no—
685C2×C4—834no—
686C2×C4—1662no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1668no—
696C2×C4—1668no—
697C2×C4—1668no—
698C2×C4—1662no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4—1662no—
702C2×C4—1662no—
703C2×C4—1662no—
704C2×C4C2×D4×D8314yes—
705C2×C4C2×Q8×D8314yes—
706C22—3322no—
707C22—3322no—
708C22—3322no—
709C22—3322no—
710C22—33216no—
711C22—1664no—
712C22—1664no—
713C22—1664no—
714C22#124×D8314yes—
715C22#1912825714yes—
716C22#1912831714yes—
717C22#1912834314yes—
718C22#1912836414yes—
719C22#1912840714yes—
720C22#1912841814yes—
721C22C22×D4×D8311yescharacteristic
722C22C22×Q8×D8311yescharacteristic
723C22C2×#41×D8311yescharacteristic
724C22C2×#41×D8311yescharacteristic
725C22C2×#41×D8311yescharacteristic
726C22C2×#1458183811yescharacteristic
727C22C2×#1458183911yescharacteristic
728C4—24no—
729C4—24no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—3322no—
736C4—3322no—
737C4—3322no—
738C4—838no—
739C4—1664no—
740C4—1664no—
741C4—1664no—
742C2—3324no—
743C2#2491183218yesdirect product factor
744C2C2×#124×D8311yescharacteristic
745C2C2×#1912825711yescharacteristic
746C2C2×#1912831711yescharacteristic
747C2C2×#1912834311yescharacteristic
748C2C2×#1912836411yescharacteristic
749C2C2×#1912840711yescharacteristic
750C2C2×#1912841811yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#400×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#400D83
hypocenterC83C2×#2492
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#14581791C2semidirect
3. #24911832C2direct (N × H)
4. C2×#19127643C2semidirect
7. C2×#19127606C2semidirect
8. C2×#19127605C2semidirect
9. C2×#19127605C2semidirect
10. C2×#19127605C2semidirect
14. C2×#19127552C2semidirect
16. C2×#400×C83C2semidirect
22. C2×#14581791C22semidirect
40. #19127643C22semidirect
43. #19127606C22semidirect
44. #19127605C22semidirect
45. #19127605C22semidirect
46. #19127605C22semidirect
50. #19127552C22semidirect
63. #400×C83C22semidirect
110. C2×(C2×D83)⋊C4Q8semidirect
212. (C2×D83)⋊C4C2×Q8semidirect
367. C2×C83#2492semidirect
380. C2×#400D83semidirect
392. C83C2×#2492semidirect
419. #400C2×D83semidirect
743. C2#24911832direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817912
C22×#145817702
#249118322
C2×#191276432
C2×#191276142
C2×#191276062
C2×#191276052
C2×#191275932
C2×#191275912
C2×#191275602
C2×#191275522
C2×#191275482
C2×#400×C832
C2×#249283