Finite Group Databasebeta

← C2×#24911606 #35572002

Subgroups — C2×#24911606 #35572002

Order 21248.

2942 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581782C211yesmaximal, characteristic, complemented
2C23×Dic83⋊C4C211yesmaximal, characteristic
3#24911606C2116yesmaximal, direct product factor
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127635C211yesmaximal, characteristic, complemented
6C2×#19127634C211yesmaximal, characteristic, complemented
7C2×#19127632C211yesmaximal, characteristic, complemented
8C2×#19127596C211yesmaximal, characteristic, complemented
9C2×#19127586C211yesmaximal, characteristic, complemented
10C2×#19127583C211yesmaximal, characteristic, complemented
11C2×#19127576C211yesmaximal, characteristic
12C2×#19127573C211yesmaximal, characteristic
13C2×#19127573C211yesmaximal, characteristic
14C2×#19127559C211yesmaximal, characteristic
15C2×C4×C22⋊Dic83C211yesmaximal, characteristic
16C2×#385×C83C211yesmaximal, characteristic
17C24×Dic83C2211yescharacteristic
18C24×Dic83C2211yescharacteristic
19C2×#14581782—28no—
20C2×#14581782C2218yescomplemented
21C22×C4⋊Dic83C2211yescharacteristic
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4—28no—
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2218yes—
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×C22⋊Dic83C2211yescharacteristic
36C22×C22⋊Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127642C2218yescomplemented
40#19127635C2218yescomplemented
41#19127634C2218yescomplemented
42#19127632C2218yescomplemented
43#19127596C2218yescomplemented
44#19127586C2218yescomplemented
45#19127583C2218yescomplemented
46#19127576C2218yes—
47#19127573C2218yes—
48#19127573C2218yes—
49#19127559C2218yes—
50C4×C22⋊Dic83C2218yes—
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
69C23×Dic83—24no—
70C23×Dic83—24no—
71C23×Dic83—24no—
72C23×Dic83—24no—
73C23×Dic83—24no—
74C23×Dic83—42no—
75C23×Dic83C2314yes—
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2314yes—
80C23×Dic83C2311yescharacteristic
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85#14581782—232no—
86C2×C4⋊Dic83—24no—
87C2×C4⋊Dic83—24no—
88C2×C4⋊Dic83C2314yes—
89C2×C4⋊Dic83C2314yes—
90C2×Dic83⋊C4—24no—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—24no—
96C2×Dic83⋊C4—232no—
97C2×Dic83⋊C4—24no—
98C2×Dic83⋊C4—42no—
99C2×Dic83⋊C4—42no—
100C2×Dic83⋊C4D418yes—
101C2×Dic83⋊C4C2314yes—
102C2×Dic83⋊C4C2314yes—
103C2×Dic83⋊C4C2314yes—
104C2×Dic83⋊C4C2314yes—
105C2×Dic83⋊C4C2314yes—
106C2×Dic83⋊C4C2314yes—
107C2×Dic83⋊C4C2314yes—
108C2×Dic83⋊C4C2314yes—
109C2×Dic83⋊C4C2314yes—
110C2×Dic83⋊C4C2314yes—
111C2×C22⋊Dic83—24no—
112C2×C22⋊Dic83Q818yes—
113C2×C22⋊Dic83C2314yes—
114C2×C22⋊Dic83C2314yes—
115C2×C4×Dic83—24no—
116C2×C4×Dic83—42no—
117C2×C4×Dic83C2314yes—
118C2×C4×Dic83C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C83⋊#95C2314yes—
128C83⋊#95C2314yes—
129C25×C83C2311yescharacteristic
130C23×C4×C83—24no—
131C23×C4×C83—24no—
132C23×C4×C83—42no—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2314yes—
139C23×C4×C83C2311yescharacteristic
140C2×C4⋊C4×C83—24no—
141C2×C4⋊C4×C83—42no—
142C2×C4⋊C4×C83C2314yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C22⋊C4×C83—24no—
145C2×C22⋊C4×C83—24no—
146C2×C22⋊C4×C83C2314yes—
147C2×C22⋊C4×C83C2314yes—
148#95×C83C2314yes—
149#95×C83C2314yes—
150C22×Dic83—232no—
151C22×Dic83—22no—
152C22×Dic83—22no—
153C22×Dic83—22no—
154C22×Dic83—22no—
155C22×Dic83—28no—
156C22×Dic83—22no—
157C22×Dic83—22no—
158C22×Dic83—22no—
159C22×Dic83—22no—
160C22×Dic83—22no—
161C22×Dic83—22no—
162C22×Dic83—28no—
163C22×Dic83—28no—
164C22×Dic83—22no—
165C22×Dic83—22no—
166C22×Dic83—28no—
167C22×Dic83—22no—
168C22×Dic83—22no—
169C22×Dic83—22no—
170C22×Dic83—22no—
171C22×Dic83—22no—
172C22×Dic83—22no—
173C22×Dic83—22no—
174C22×Dic83—28no—
175C22×Dic83—44no—
176C22×Dic83—416no—
177C22×Dic83C2×D414yes—
178C22×Dic83C2×D414yes—
179C22×Dic83C2×Q814yes—
180C22×Dic83C2×Q814yes—
181C22×Dic83#4114yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C22×Dic83C2412yes—
187C22×Dic83C2412yes—
188C22×Dic83C2412yes—
189C22×Dic83C2412yes—
190C4⋊Dic83—28no—
191C4⋊Dic83—28no—
192Dic83⋊C4—28no—
193Dic83⋊C4—28no—
194Dic83⋊C4—28no—
195Dic83⋊C4—28no—
196Dic83⋊C4—28no—
197Dic83⋊C4—28no—
198Dic83⋊C4—28no—
199Dic83⋊C4—44no—
200Dic83⋊C4—44no—
201Dic83⋊C4C2×D4116yes—
202C22⋊Dic83—28no—
203C22⋊Dic83C2×Q8116yes—
204C4×Dic83—28no—
205C4×Dic83—44no—
206C24×C83—22no—
207C24×C83—22no—
208C24×C83—22no—
209C24×C83—22no—
210C24×C83C2×Q814yes—
211C24×C83#4114yes—
212C24×C83#4114yes—
213C24×C83C2412yes—
214C24×C83C2411yescharacteristic
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—22no—
222C22×C4×C83—22no—
223C22×C4×C83—22no—
224C22×C4×C83—28no—
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—28no—
234C22×C4×C83—44no—
235C22×C4×C83—416no—
236C22×C4×C83C2×D414yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C22×C4×C83C2412yes—
242C22×C4×C83C2412yes—
243C4⋊C4×C83—28no—
244C4⋊C4×C83—44no—
245C22⋊C4×C83—28no—
246C22⋊C4×C83—28no—
247C23×C83—28no—
248C23×C83—28no—
249C23×C83—28no—
250C23×C83—28no—
251C23×C83—28no—
252C23×C83—28no—
253C23×C83—22no—
254C23×C83—22no—
255C23×C83—22no—
256C23×C83—22no—
257C23×C83#125116yescomplemented
258C23×C83C22×D412yes—
259C23×C83C22×Q814yes—
260C23×C83C22×Q812yes—
261C23×C83C2×#4112yes—
262C23×C83C2×#4114yes—
263C23×C83C2×#4112yes—
264C23×C83C2×#4114yes—
265C23×C83C2×#4112yes—
266C23×C83H(5,𝔽2)12yes—
267C23×C832−1+412yes—
268C23×C83C2511yescharacteristic
269C2×C4×C83—28no—
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—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—416no—
288C2×C4×C83—44no—
289C2×C4×C83—44no—
290C2×C4×C83—44no—
291C2×C4×C83—44no—
292C2×C4×C83—44no—
293C2×C4×C83C22×D414yes—
294C2×Dic83—232no—
295C2×Dic83—28no—
296C2×Dic83—28no—
297C2×Dic83—28no—
298C2×Dic83—28no—
299C2×Dic83—28no—
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—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—416no—
320C2×Dic83—44no—
321C2×Dic83—44no—
322C2×Dic83—44no—
323C2×Dic83C22×D414yes—
324C2×Dic83C22×D414yes—
325C2×Dic83C22×Q814yes—
326C2×Dic83C22×Q814yes—
327C2×Dic83C2×#4114yes—
328C22×C83—24no—
329C22×C83—24no—
330C22×C83—24no—
331C22×C83—24no—
332C22×C83—24no—
333C22×C83—24no—
334C22×C83—232no—
335C22×C83#52514yes—
336C22×C83C2×#12514yes—
337C22×C83C2×#12518yescomplemented
338C22×C83#53914yes—
339C22×C83#54614yes—
340C22×C83D4×Q814yes—
341C22×C83#55214yes—
342C22×C83#55414yes—
343C22×C83C23×D411yescharacteristic
344C22×C83C23×Q811yescharacteristic
345C22×C83C22×#4111yescharacteristic
346C22×C83C22×#4111yescharacteristic
347C22×C83C22×#4111yescharacteristic
348C22×C83C2×H(5,𝔽2)11yescharacteristic
349C22×C83C2×2−1+411yescharacteristic
350C4×C83—24no—
351C4×C83—42no—
352C4×C83—42no—
353C4×C83—42no—
354C4×C83—42no—
355C4×C83—42no—
356Dic83—24no—
357Dic83—24no—
358Dic83—24no—
359Dic83—24no—
360Dic83—24no—
361Dic83—42no—
362Dic83—42no—
363Dic83—42no—
364C2×#2473—831nomaximal, Sylow
365C2×C83—28no—
366C2×C83#247318yescomplemented
367C2×C83C2×#52511yescharacteristic
368C2×C83C22×#12511yescharacteristic
369C2×C83C2×#53911yescharacteristic
370C2×C83C2×#54611yescharacteristic
371C2×C83C2×D4×Q811yescharacteristic
372C2×C83C2×#55211yescharacteristic
373C2×C83C2×#55411yescharacteristic
374C22×#125—831no—
375C23×C4⋊C4—831no—
376#2473—8316no—
377C2×#400—831no—
378C2×#398—831no—
379C2×#398—831no—
380C2×#398—831no—
381C2×#389—831no—
382C2×#387—831no—
383C2×#387—831no—
384C2×#385—831no—
385C2×#385—831no—
386C2×#385—831no—
387C2×#385D8311yescharacteristic
388C2×#380—831no—
389C2×C4×C22⋊C4—831no—
390C83C2×#247311yescharacteristic, complemented, Sylow
391C24×C4—831no—
392C24×C4—831no—
393C24×C4C2×D8311yescharacteristic
394C2×#125—838no—
395C2×#125—1668no—
396C22×C4⋊C4—831no—
397C22×C4⋊C4—831no—
398C22×C4⋊C4—831no—
399C22×C4⋊C4—831no—
400C22×C4⋊C4—831no—
401C22×C4⋊C4—831no—
402C22×C4⋊C4—831no—
403C22×C4⋊C4—831no—
404C22×C4⋊C4—831no—
405C22×C4⋊C4—831no—
406C22×C4⋊C4—831no—
407C22×C4⋊C4—838no—
408C22×C4⋊C4—831no—
409C22×C4⋊C4—1668no—
410C22×C4⋊C4C2×D8311yescharacteristic
411C22×C4⋊C4C2×D8311yescharacteristic
412C22×C22⋊C4—831no—
413C22×C22⋊C4—831no—
414C22×C22⋊C4C2×D8311yescharacteristic
415C22×C22⋊C4C2×D8311yescharacteristic
416C22×C42—831no—
417C22×C42—831no—
418#400—838no—
419#398—838no—
420#398—838no—
421#398—838no—
422#389—838no—
423#387—838no—
424#387—838no—
425#385—838no—
426#385—838no—
427#385—838no—
428#385C2×D8318yes—
429#380—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×#95—831no—
441C2×#95C2×D8311yescharacteristic
442C2×#95C2×D8311yescharacteristic
443C25C22×D8311yescharacteristic
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—42no—
447C23×C4—3322no—
448C23×C4—834no—
449C23×C4—831no—
450C23×C4—831no—
451C23×C4—831no—
452C23×C4—831no—
453C23×C4—831no—
454C23×C4—834no—
455C23×C4—831no—
456C23×C4—831no—
457C23×C4—831no—
458C23×C4—1664no—
459C23×C4—1664no—
460C23×C4—1664no—
461C23×C4—1664no—
462C23×C4—1664no—
463C23×C4C22×D8311yescharacteristic
464C23×C4C22×D8311yescharacteristic
465C23×C4C22×D8311yescharacteristic
466C23×C4C22×D8311yescharacteristic
467C23×C4C22×D8311yescharacteristic
468C23×C4C22×D8314yes—
469C23×C4C22×D8311yescharacteristic
470#125—16632no—
471C2×C4⋊C4—24no—
472C2×C4⋊C4—42no—
473C2×C4⋊C4—3322no—
474C2×C4⋊C4—3322no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—838no—
478C2×C4⋊C4—834no—
479C2×C4⋊C4—834no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—834no—
482C2×C4⋊C4—834no—
483C2×C4⋊C4—834no—
484C2×C4⋊C4—834no—
485C2×C4⋊C4—834no—
486C2×C4⋊C4—834no—
487C2×C4⋊C4—834no—
488C2×C4⋊C4—16632no—
489C2×C4⋊C4—1664no—
490C2×C4⋊C4—1664no—
491C2×C4⋊C4—1664no—
492C2×C4⋊C4—1664no—
493C2×C4⋊C4—1664no—
494C2×C4⋊C4—1664no—
495C2×C4⋊C4—1664no—
496C2×C4⋊C4—1664no—
497C2×C4⋊C4—1664no—
498C2×C4⋊C4C22×D8314yes—
499C2×C4⋊C4C22×D8314yes—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—838no—
503C2×C22⋊C4—834no—
504C2×C22⋊C4—834no—
505C2×C22⋊C4—1664no—
506C2×C22⋊C4C22×D8314yes—
507C2×C22⋊C4C22×D8314yes—
508C2×C42—3322no—
509C2×C42—834no—
510C2×C42—834no—
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#95—834no—
522#95C22×D8314yes—
523#95C22×D8314yes—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24Q8×D8314yes—
529C24#1305058914yes—
530C24#1305059014yes—
531C24C23×D8312yes—
532C24C23×D8311yescharacteristic
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—28no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
552C22×C4—44no—
553C22×C4—416no—
554C22×C4—33216no—
555C22×C4—3324no—
556C22×C4—834no—
557C22×C4—834no—
558C22×C4—834no—
559C22×C4—834no—
560C22×C4—834no—
561C22×C4—832no—
562C22×C4—832no—
563C22×C4—832no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—832no—
567C22×C4—832no—
568C22×C4—832no—
569C22×C4—1668no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4—1662no—
573C22×C4—1662no—
574C22×C4—1668no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4—1662no—
580C22×C4—1668no—
581C22×C4—1668no—
582C22×C4—16632no—
583C22×C4—1662no—
584C22×C4—1662no—
585C22×C4—1662no—
586C22×C4—1662no—
587C22×C4—1662no—
588C22×C4—1668no—
589C22×C4—1662no—
590C22×C4—1662no—
591C22×C4—1662no—
592C22×C4—1662no—
593C22×C4—1662no—
594C22×C4D4×D8314yes—
595C22×C4C23×D8312yes—
596C22×C4C23×D8312yes—
597C22×C4C23×D8312yes—
598C22×C4C23×D8312yes—
599C22×C4C23×D8312yes—
600C22×C4C23×D8312yes—
601C4⋊C4—28no—
602C4⋊C4—44no—
603C4⋊C4—3324no—
604C4⋊C4—3324no—
605C4⋊C4—8316no—
606C4⋊C4—1668no—
607C4⋊C4—1668no—
608C4⋊C4—1668no—
609C4⋊C4—1668no—
610C4⋊C4—1668no—
611C4⋊C4—1668no—
612C4⋊C4—1668no—
613C4⋊C4—1668no—
614C4⋊C4—1668no—
615C22⋊C4—28no—
616C22⋊C4—28no—
617C22⋊C4—8316no—
618C22⋊C4—1668no—
619C42—3324no—
620C42—1668no—
621C23—28no—
622C23—28no—
623C23—28no—
624C23—28no—
625C23—28no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—28no—
631C23#14581782116yescomplemented
632C23C2×D4×D8312yes—
633C23C2×Q8×D8314yes—
634C23C2×Q8×D8312yes—
635C23#41×D8312yes—
636C23C2×#1305058914yes—
637C23C2×#1305058912yes—
638C23C2×#1305059014yes—
639C23C2×#1305059012yes—
640C23#1458183712yes—
641C23#1458183912yes—
642C23C24×D8311yescharacteristic
643C2×C4—28no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
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—416no—
662C2×C4—44no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—3324no—
668C2×C4—3324no—
669C2×C4—3324no—
670C2×C4—33216no—
671C2×C4—834no—
672C2×C4—834no—
673C2×C4—834no—
674C2×C4—834no—
675C2×C4—834no—
676C2×C4—1662no—
677C2×C4—1662no—
678C2×C4—1662no—
679C2×C4—1662no—
680C2×C4—1662no—
681C2×C4—1662no—
682C2×C4—1662no—
683C2×C4—1662no—
684C2×C4—1662no—
685C2×C4—16632no—
686C2×C4—1668no—
687C2×C4—1668no—
688C2×C4—1668no—
689C2×C4—1668no—
690C2×C4—1668no—
691C2×C4—1662no—
692C2×C4—1662no—
693C2×C4—1662no—
694C2×C4—1662no—
695C2×C4—1662no—
696C2×C4—1662no—
697C2×C4—1662no—
698C2×C4—1662no—
699C2×C4—1662no—
700C2×C4—1662no—
701C2×C4C2×D4×D8314yes—
702C22—24no—
703C22—24no—
704C22—24no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—232no—
709C22#1912821014yes—
710C22C2×#1458178214yes—
711C22C2×#1458178218yescomplemented
712C22#1912829314yes—
713C22#1912833814yes—
714C22#1912836414yes—
715C22#1912838814yes—
716C22#1912840514yes—
717C22C22×D4×D8311yescharacteristic
718C22C22×Q8×D8311yescharacteristic
719C22C2×#41×D8311yescharacteristic
720C22C22×#1305058911yescharacteristic
721C22C22×#1305059011yescharacteristic
722C22C2×#1458183711yescharacteristic
723C22C2×#1458183911yescharacteristic
724C4—24no—
725C4—42no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—3322no—
731C4—3322no—
732C4—3322no—
733C4—1664no—
734C4—1664no—
735C4—1664no—
736C4—1664no—
737C4—1664no—
738C2—28no—
739C2#2491160618yesdirect product factor
740C2C2×#1912821011yescharacteristic
741C2C22×#1458178211yescharacteristic
742C2C2×#1912829311yescharacteristic
743C2C2×#1912833811yescharacteristic
744C2C2×#1912836411yescharacteristic
745C2C2×#1912838811yescharacteristic
746C2C2×#1912840511yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#385×C83C2
socleC24×C83C24
prime radicalC25×C83C23
hypercenterC2×#385D83
hypocenterC83C2×#2473
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14581782C2semidirect
3. #24911606C2direct (N × H)
4. C2×#19127642C2semidirect
5. C2×#19127635C2semidirect
6. C2×#19127634C2semidirect
7. C2×#19127632C2semidirect
8. C2×#19127596C2semidirect
9. C2×#19127586C2semidirect
10. C2×#19127583C2semidirect
20. C2×#14581782C22semidirect
39. #19127642C22semidirect
40. #19127635C22semidirect
41. #19127634C22semidirect
42. #19127632C22semidirect
43. #19127596C22semidirect
44. #19127586C22semidirect
45. #19127583C22semidirect
257. C23×C83#125semidirect
337. C22×C83C2×#125semidirect
366. C2×C83#2473semidirect
390. C83C2×#2473semidirect
631. C23#14581782semidirect
711. C22C2×#14581782semidirect
739. C2#24911606direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C23×Dic83⋊C42
#249116062
C2×#191276422
C2×#191276352
C2×#191276342
C2×#191276322
C2×#191275962
C2×#191275862
C2×#191275832
C2×#191275762
C2×#191275732
C2×#191275592
C2×C4×C22⋊Dic832
C2×#385×C832
C2×#247383