Finite Group Databasebeta

← C2×#24913036 #35575152

Subgroups — C2×#24913036 #35575152

Order 21248.

2766 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581757C211yesmaximal, characteristic, complemented
2C22×#14581751C211yesmaximal, characteristic
3#24913036C2116yesmaximal, direct product factor
4C2×#19127634C211yesmaximal, characteristic, complemented
5C2×#19127629C211yesmaximal, characteristic
6C2×#19127622C211yesmaximal, characteristic, complemented
7C2×#19127613C211yesmaximal, characteristic
8C2×#19127595C211yesmaximal, characteristic
9C2×#19127594C211yesmaximal, characteristic
10C2×#19127588C211yesmaximal, characteristic, complemented
11C2×#19127587C211yesmaximal, characteristic, complemented
12C2×#19127586C211yesmaximal, characteristic, complemented
13C2×#19127582C211yesmaximal, characteristic, complemented
14C2×#19127574C211yesmaximal, characteristic
15C2×#19127568C211yesmaximal, characteristic, complemented
16C2×#385×C83C211yesmaximal, characteristic
17C23×Dic166C2211yescharacteristic
18C2×#14581757—28no—
19C2×#14581757C2218yescomplemented
20C2×#14581751—28no—
21C2×#14581751C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×C22⋊Dic83C2211yescharacteristic
30C22×C22⋊Dic83C2211yescharacteristic
31C22×C22⋊Dic83C2211yescharacteristic
32C22×C22⋊Dic83C2211yescharacteristic
33C22×C4×Dic83C2211yescharacteristic
34C22×C4×Dic83C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37#19127634C2218yescomplemented
38#19127629C2218yes—
39#19127622C2218yescomplemented
40#19127613C2218yes—
41#19127595C2218yes—
42#19127594C2218yes—
43#19127588C2218yescomplemented
44#19127587C2218yescomplemented
45#19127586C2218yescomplemented
46#19127582C2218yescomplemented
47#19127574C2218yes—
48#19127568C2218yescomplemented
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
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C24×C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66#385×C83C2218yes—
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C22×Dic166—24no—
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166C2314yes—
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81#14581757—232no—
82#14581751—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83—24no—
85C2×C4⋊Dic83—24no—
86C2×C4⋊Dic83C2314yes—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×Dic83⋊C4C2314yes—
96C2×Dic83⋊C4C2314yes—
97C2×C22⋊Dic83—24no—
98C2×C22⋊Dic83—24no—
99C2×C22⋊Dic83—24no—
100C2×C22⋊Dic83—24no—
101C2×C22⋊Dic83C2314yes—
102C2×C22⋊Dic83C2314yes—
103C2×C22⋊Dic83C2314yes—
104C2×C22⋊Dic83C2314yes—
105C2×C4×Dic83—24no—
106C2×C4×Dic83—24no—
107C2×C4×Dic83—24no—
108C2×C4×Dic83D418yes—
109C2×C4×Dic83C2314yes—
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—24no—
129C23×C4×C83C2314yes—
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C2×C4⋊C4×C83—24no—
137C2×C4⋊C4×C83—24no—
138C2×C4⋊C4×C83C2314yes—
139C2×C4⋊C4×C83C2314yes—
140C2×C22⋊C4×C83—24no—
141C2×C22⋊C4×C83—24no—
142C2×C22⋊C4×C83C2314yes—
143C2×C22⋊C4×C83C2314yes—
144#95×C83C2314yes—
145#95×C83C2314yes—
146C2×Dic166—232no—
147C2×Dic166—28no—
148C2×Dic166—28no—
149C2×Dic166—28no—
150C22×Dic83—22no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
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×Dic83C2×D414yes—
172C22×Dic83C2×D414yes—
173C22×Dic83#4114yes—
174C22×Dic83C2412yes—
175C22×Dic83C2412yes—
176C22×Dic83C2412yes—
177C22×Dic83C2412yes—
178C22×Dic83C2412yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C4⋊Dic83—28no—
183C4⋊Dic83—28no—
184C4⋊Dic83—28no—
185Dic83⋊C4—28no—
186Dic83⋊C4—28no—
187Dic83⋊C4—28no—
188Dic83⋊C4—28no—
189C22⋊Dic83—28no—
190C22⋊Dic83—28no—
191C22⋊Dic83—28no—
192C22⋊Dic83—28no—
193C4×Dic83—28no—
194C4×Dic83—28no—
195C4×Dic83—28no—
196C4×Dic83C2×D4116yes—
197C24×C83—22no—
198C24×C83—22no—
199C24×C83—22no—
200C24×C83—22no—
201C24×C83—22no—
202C24×C83—22no—
203C24×C83#4114yes—
204C24×C83C2412yes—
205C24×C83C2411yescharacteristic
206C22×C4×C83—232no—
207C22×C4×C83—22no—
208C22×C4×C83—22no—
209C22×C4×C83—22no—
210C22×C4×C83—28no—
211C22×C4×C83—22no—
212C22×C4×C83—22no—
213C22×C4×C83—22no—
214C22×C4×C83—28no—
215C22×C4×C83—28no—
216C22×C4×C83—22no—
217C22×C4×C83—22no—
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×C83C2×D414yes—
226C22×C4×C83#4114yes—
227C22×C4×C83#4114yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2412yes—
232C22×C4×C83C2412yes—
233C22×C4×C83C2412yes—
234C4⋊C4×C83—28no—
235C4⋊C4×C83—28no—
236C22⋊C4×C83—28no—
237C22⋊C4×C83—28no—
238C23×C83—28no—
239C23×C83—28no—
240C23×C83—28no—
241C23×C83—22no—
242C23×C83—22no—
243C23×C83—22no—
244C23×C83—22no—
245C23×C83—22no—
246C23×C83—22no—
247C23×C83—44no—
248C23×C83—44no—
249C23×C83—44no—
250C23×C83—44no—
251C23×C83C22×D412yes—
252C23×C83C2×#4112yes—
253C23×C83C2×#4114yes—
254C23×C83C2×#4112yes—
255C23×C83C2×#4112yes—
256C23×C83C2×#4112yes—
257C23×C832−1+412yes—
258C23×C832−1+412yes—
259C23×C83C2511yescharacteristic
260C2×C4×C83—232no—
261C2×C4×C83—28no—
262C2×C4×C83—28no—
263C2×C4×C83—28no—
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—22no—
278C2×C4×C83—22no—
279C2×C4×C83—44no—
280C2×C4×C83—44no—
281C2×C4×C83—44no—
282C2×C4×C83C22×D414yes—
283C2×C4×C83C2×#4114yes—
284C2×C4×C83C2×#4114yes—
285C2×Dic83—28no—
286C2×Dic83—28no—
287C2×Dic83—28no—
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—22no—
306C2×Dic83—22no—
307C2×Dic83—22no—
308C2×Dic83—22no—
309C2×Dic83—44no—
310C2×Dic83—44no—
311C2×Dic83—44no—
312C2×Dic83—44no—
313C2×Dic83—44no—
314C2×Dic83C22×D414yes—
315C2×Dic83C22×D414yes—
316C2×Dic83C2×#4114yes—
317Dic166—232no—
318C22×C83—24no—
319C22×C83—24no—
320C22×C83—24no—
321C22×C83—416no—
322C22×C83—42no—
323C22×C83—42no—
324C22×C83—42no—
325C22×C83—42no—
326C22×C83#52514yes—
327C22×C83#52514yes—
328C22×C83#53614yes—
329C22×C83#55214yes—
330C22×C83#55214yes—
331C22×C83#55614yes—
332C22×C83#55614yes—
333C22×C83C23×D411yescharacteristic
334C22×C83C22×#4111yescharacteristic
335C22×C83C22×#4111yescharacteristic
336C22×C83C22×#4111yescharacteristic
337C22×C83C22×#4111yescharacteristic
338C22×C83C2×2−1+411yescharacteristic
339C22×C83C2×2−1+411yescharacteristic
340C4×C83—24no—
341C4×C83—24no—
342C4×C83—24no—
343C4×C83—42no—
344C4×C83—42no—
345C4×C83—42no—
346Dic83—24no—
347Dic83—24no—
348Dic83—24no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352Dic83—42no—
353Dic83—42no—
354C2×#2599—831nomaximal, Sylow
355C2×C83—44no—
356C2×C83#259918yescomplemented
357C2×C83C2×#52511yescharacteristic
358C2×C83C2×#52511yescharacteristic
359C2×C83C2×#53611yescharacteristic
360C2×C83C2×#55211yescharacteristic
361C2×C83C2×#55211yescharacteristic
362C2×C83C2×#55611yescharacteristic
363C2×C83C2×#55611yescharacteristic
364C22×C4×Q8—831no—
365C22×#117—831no—
366#2599—8316no—
367C2×#398—831no—
368C2×#397—831no—
369C2×#395—831no—
370C2×#393—831no—
371C2×#388—831no—
372C2×#388—831no—
373C2×#387—831no—
374C2×#387—831no—
375C2×#387—831no—
376C2×#387—831no—
377C2×#385—831no—
378C2×#385D8311yescharacteristic
379C2×#383—831no—
380C83C2×#259911yescharacteristic, complemented, Sylow
381C23×Q8—831no—
382C24×C4C2×D8311yescharacteristic
383C2×C4×Q8—838no—
384C2×C4×Q8—1668no—
385C2×#117—838no—
386C2×#117—1668no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4—831no—
391C22×C4⋊C4—831no—
392C22×C4⋊C4—831no—
393C22×C4⋊C4—831no—
394C22×C4⋊C4C2×D8311yescharacteristic
395C22×C4⋊C4C2×D8311yescharacteristic
396C22×C22⋊C4—831no—
397C22×C22⋊C4—831no—
398C22×C22⋊C4—831no—
399C22×C22⋊C4—831no—
400C22×C22⋊C4C2×D8311yescharacteristic
401C22×C22⋊C4C2×D8311yescharacteristic
402C22×C42—831no—
403C22×C42—831no—
404C22×C42—831no—
405C22×C42—831no—
406#398—838no—
407#397—838no—
408#395—838no—
409#393—838no—
410#388—838no—
411#388—838no—
412#387—838no—
413#387—838no—
414#387—838no—
415#387—838no—
416#385—838no—
417#385C2×D8318yes—
418#383—838no—
419C2×#95—831no—
420C2×#95—831no—
421C2×#95—831no—
422C2×#95—831no—
423C2×#95—831no—
424C2×#95—831no—
425C2×#95—831no—
426C2×#95—831no—
427C2×#95—831no—
428C2×#95—831no—
429C2×#95—831no—
430C2×#95—831no—
431C2×#95C2×D8311yescharacteristic
432C2×#95C2×D8311yescharacteristic
433C25C22×D8311yescharacteristic
434C22×Q8—834no—
435C22×Q8—1664no—
436C22×Q8—1664no—
437C22×Q8—1664no—
438C23×C4—24no—
439C23×C4—24no—
440C23×C4—24no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—831no—
444C23×C4—831no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—831no—
449C23×C4C22×D8314yes—
450C23×C4C22×D8311yescharacteristic
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C23×C4C22×D8311yescharacteristic
456C4×Q8—16632no—
457#117—16632no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—834no—
461C2×C4⋊C4—834no—
462C2×C4⋊C4—834no—
463C2×C4⋊C4—834no—
464C2×C4⋊C4—834no—
465C2×C4⋊C4—834no—
466C2×C4⋊C4—834no—
467C2×C4⋊C4—1664no—
468C2×C4⋊C4—1664no—
469C2×C4⋊C4—1664no—
470C2×C4⋊C4—1664no—
471C2×C4⋊C4—1664no—
472C2×C4⋊C4—1664no—
473C2×C4⋊C4—1664no—
474C2×C4⋊C4C22×D8314yes—
475C2×C4⋊C4C22×D8314yes—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—834no—
479C2×C22⋊C4—834no—
480C2×C22⋊C4—834no—
481C2×C22⋊C4—834no—
482C2×C22⋊C4—1664no—
483C2×C22⋊C4—1664no—
484C2×C22⋊C4—1664no—
485C2×C22⋊C4—1664no—
486C2×C22⋊C4C22×D8314yes—
487C2×C22⋊C4C22×D8314yes—
488C2×C42—838no—
489C2×C42—834no—
490C2×C42—834no—
491C2×C42—834no—
492C2×C42—834no—
493C2×C42—1664no—
494C2×C42—1664no—
495C2×C42—1664no—
496#95—834no—
497#95—834no—
498#95—834no—
499#95—834no—
500#95—834no—
501#95—834no—
502#95—834no—
503#95—834no—
504#95—834no—
505#95—834no—
506#95—834no—
507#95—834no—
508#95C22×D8314yes—
509#95C22×D8314yes—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24#1305058914yes—
517C24C23×D8312yes—
518C24C23×D8311yescharacteristic
519C2×Q8—1668no—
520C2×Q8—1668no—
521C2×Q8—16632no—
522C2×Q8—1668no—
523C22×C4—232no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—28no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—28no—
532C22×C4—28no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—834no—
543C22×C4—834no—
544C22×C4—834no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—832no—
550C22×C4—832no—
551C22×C4—832no—
552C22×C4—832no—
553C22×C4—1662no—
554C22×C4—1662no—
555C22×C4—1662no—
556C22×C4—1662no—
557C22×C4—1662no—
558C22×C4—1662no—
559C22×C4—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4—1662no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4D4×D8314yes—
575C22×C4#1305058914yes—
576C22×C4#1305059014yes—
577C22×C4C23×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8312yes—
580C22×C4C23×D8312yes—
581C22×C4C23×D8312yes—
582C22×C4C23×D8312yes—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—1668no—
586C4⋊C4—1668no—
587C4⋊C4—1668no—
588C4⋊C4—1668no—
589C4⋊C4—1668no—
590C4⋊C4—1668no—
591C4⋊C4—1668no—
592C22⋊C4—28no—
593C22⋊C4—28no—
594C22⋊C4—1668no—
595C22⋊C4—1668no—
596C22⋊C4—1668no—
597C22⋊C4—1668no—
598C42—8316no—
599C42—1668no—
600C42—1668no—
601C42—1668no—
602C23—28no—
603C23—28no—
604C23—28no—
605C23—22no—
606C23—22no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—44no—
612C23—44no—
613C23—44no—
614C23—44no—
615C23C2×D4×D8312yes—
616C23#41×D8312yes—
617C23C2×#1305058914yes—
618C23C2×#1305058912yes—
619C23C2×#1305058912yes—
620C23C2×#1305059012yes—
621C23#1458183912yes—
622C23#1458184012yes—
623C23C24×D8311yescharacteristic
624Q8—16632no—
625C2×C4—232no—
626C2×C4—28no—
627C2×C4—28no—
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—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—3324no—
648C2×C4—3324no—
649C2×C4—3324no—
650C2×C4—3324no—
651C2×C4—3324no—
652C2×C4—834no—
653C2×C4—834no—
654C2×C4—834no—
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—1662no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1668no—
671C2×C4—1668no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1668no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4C2×D4×D8314yes—
680C2×C4C2×#1305058914yes—
681C2×C4C2×#1305059014yes—
682C22—24no—
683C22—24no—
684C22—24no—
685C22—42no—
686C22—416no—
687C22—42no—
688C22—42no—
689C22—42no—
690C22#1912820714yes—
691C22#1912821014yes—
692C22#1912827414yes—
693C22#1912838614yes—
694C22#1912838814yes—
695C22#1912842114yes—
696C22#1912842214yes—
697C22C22×D4×D8311yescharacteristic
698C22C2×#41×D8311yescharacteristic
699C22C22×#1305058911yescharacteristic
700C22C22×#1305058911yescharacteristic
701C22C22×#1305059011yescharacteristic
702C22C2×#1458183911yescharacteristic
703C22C2×#1458184011yescharacteristic
704C4—24no—
705C4—24no—
706C4—24no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—3322no—
711C4—3322no—
712C4—3322no—
713C4—3322no—
714C4—3322no—
715C4—1664no—
716C4—1664no—
717C4—1664no—
718C2—44no—
719C2#2491303618yesdirect product factor
720C2C2×#1912820711yescharacteristic
721C2C2×#1912821011yescharacteristic
722C2C2×#1912827411yescharacteristic
723C2C2×#1912838611yescharacteristic
724C2C2×#1912838811yescharacteristic
725C2C2×#1912842111yescharacteristic
726C2C2×#1912842211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83C2×#2599
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14581757C2semidirect
3. #24913036C2direct (N × H)
4. C2×#19127634C2semidirect
6. C2×#19127622C2semidirect
10. C2×#19127588C2semidirect
11. C2×#19127587C2semidirect
12. C2×#19127586C2semidirect
13. C2×#19127582C2semidirect
15. C2×#19127568C2semidirect
19. C2×#14581757C22semidirect
37. #19127634C22semidirect
39. #19127622C22semidirect
43. #19127588C22semidirect
44. #19127587C22semidirect
45. #19127586C22semidirect
46. #19127582C22semidirect
48. #19127568C22semidirect
356. C2×C83#2599semidirect
380. C83C2×#2599semidirect
719. C2#24913036direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817572
C22×#145817512
#249130362
C2×#191276342
C2×#191276292
C2×#191276222
C2×#191276132
C2×#191275952
C2×#191275942
C2×#191275882
C2×#191275872
C2×#191275862
C2×#191275822
C2×#191275742
C2×#191275682
C2×#385×C832
C2×#259983