Finite Group Databasebeta

← C2×#24913097 #35575164

Subgroups — C2×#24913097 #35575164

Order 21248.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581787C211yesmaximal, characteristic
2C22×#14581757C211yesmaximal, characteristic, complemented
3#24913097C2116yesmaximal, direct product factor
4C2×#19127642C211yesmaximal, characteristic, complemented
5C2×#19127636C211yesmaximal, characteristic
6C2×#19127621C211yesmaximal, characteristic, complemented
7C2×#19127614C211yesmaximal, characteristic
8C2×#19127596C211yesmaximal, characteristic, complemented
9C2×#19127592C211yesmaximal, characteristic
10C2×#19127591C211yesmaximal, characteristic
11C2×#19127591C211yesmaximal, characteristic
12C2×#19127590C211yesmaximal, characteristic
13C2×#19127588C211yesmaximal, characteristic, complemented
14C2×#19127587C211yesmaximal, characteristic, complemented
15C2×#19127547C211yesmaximal, characteristic, complemented
16C2×#389×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C2×#14581787—28no—
19C2×#14581787C2218yes—
20C2×#14581757—28no—
21C2×#14581757C2218yescomplemented
22C22×C4⋊Dic83C2211yescharacteristic
23C22×Dic83⋊C4C2211yescharacteristic
24C22×Dic83⋊C4C2211yescharacteristic
25C22×Dic83⋊C4C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×(C2×D83)⋊C4C2211yescharacteristic
29C22×(C2×D83)⋊C4C2211yescharacteristic
30C22×(C2×D83)⋊C4C2211yescharacteristic
31C22×(C2×D83)⋊C4C2211yescharacteristic
32C22×(C2×D83)⋊C4C2211yescharacteristic
33C22×(C2×D83)⋊C4C2211yescharacteristic
34C22×(C2×D83)⋊C4C2211yescharacteristic
35C22×C4×Dic83C2211yescharacteristic
36C22×C4×Dic83C2211yescharacteristic
37C22×C4×Dic83C2211yescharacteristic
38C22×C4×Dic83C2211yescharacteristic
39#19127642C2218yescomplemented
40#19127636C2218yes—
41#19127621C2218yescomplemented
42#19127614C2218yes—
43#19127596C2218yescomplemented
44#19127592C2218yes—
45#19127591C2218yes—
46#19127591C2218yes—
47#19127590C2218yes—
48#19127588C2218yescomplemented
49#19127587C2218yescomplemented
50#19127547C2218yescomplemented
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
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66#389×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C22×Dic166—24no—
71C22×Dic166—24no—
72C22×Dic166—24no—
73C22×Dic166C2314yes—
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C23×Dic83C2311yescharacteristic
78C23×Dic83C2311yescharacteristic
79C23×Dic83C2311yescharacteristic
80C23×Dic83C2311yescharacteristic
81#14581787—232no—
82#14581757—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83C2314yes—
85C2×Dic83⋊C4—24no—
86C2×Dic83⋊C4—24no—
87C2×Dic83⋊C4—24no—
88C2×Dic83⋊C4—24no—
89C2×Dic83⋊C4—24no—
90C2×Dic83⋊C4C2314yes—
91C2×Dic83⋊C4C2314yes—
92C2×Dic83⋊C4C2314yes—
93C2×Dic83⋊C4C2314yes—
94C2×Dic83⋊C4C2314yes—
95C2×(C2×D83)⋊C4—24no—
96C2×(C2×D83)⋊C4—24no—
97C2×(C2×D83)⋊C4—24no—
98C2×(C2×D83)⋊C4—24no—
99C2×(C2×D83)⋊C4—24no—
100C2×(C2×D83)⋊C4—24no—
101C2×(C2×D83)⋊C4—24no—
102C2×(C2×D83)⋊C4C2314yes—
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×Dic83—24no—
111C2×C4×Dic83—24no—
112C2×C4×Dic83D418yes—
113C2×C4×Dic83C2314yes—
114C2×C4×Dic83C2314yes—
115C2×C4×Dic83C2314yes—
116C2×C4×Dic83C2314yes—
117C83⋊#95C2314yes—
118C83⋊#95C2314yes—
119C83⋊#95C2314yes—
120C83⋊#95C2314yes—
121C83⋊#95C2314yes—
122C83⋊#95C2314yes—
123C83⋊#95C2314yes—
124C83⋊#95C2314yes—
125C83⋊#95C2314yes—
126C83⋊#95C2314yes—
127C23×C4×C83C2311yescharacteristic
128C23×C4×C83C2311yescharacteristic
129C23×C4×C83C2311yescharacteristic
130C23×C4×C83C2311yescharacteristic
131C23×C4×C83C2311yescharacteristic
132C23×C4×C83C2311yescharacteristic
133C23×C4×C83C2311yescharacteristic
134C2×C4⋊C4×C83—24no—
135C2×C4⋊C4×C83—24no—
136C2×C4⋊C4×C83—24no—
137C2×C4⋊C4×C83—24no—
138C2×C4⋊C4×C83C2314yes—
139C2×C4⋊C4×C83C2314yes—
140C2×C4⋊C4×C83C2314yes—
141C2×C4⋊C4×C83C2314yes—
142C2×C42×C83—24no—
143C2×C42×C83C2314yes—
144#95×C83C2314yes—
145#95×C83C2314yes—
146C23×D83—22no—
147C23×D83—22no—
148C23×D83—22no—
149C23×D83—22no—
150C23×D83—22no—
151C23×D83—22no—
152C23×D83—22no—
153C23×D83C2412yes—
154C2×Dic166—232no—
155C2×Dic166—28no—
156C2×Dic166—28no—
157C2×Dic166—28no—
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×Dic83—22no—
174C22×Dic83—22no—
175C22×Dic83C2×D414yes—
176C22×Dic83C2×D414yes—
177C22×Dic83#4114yes—
178C22×Dic83#4114yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C4⋊Dic83—28no—
187Dic83⋊C4—28no—
188Dic83⋊C4—28no—
189Dic83⋊C4—28no—
190Dic83⋊C4—28no—
191Dic83⋊C4—28no—
192(C2×D83)⋊C4—28no—
193(C2×D83)⋊C4—28no—
194(C2×D83)⋊C4—28no—
195(C2×D83)⋊C4—28no—
196(C2×D83)⋊C4—28no—
197(C2×D83)⋊C4—28no—
198(C2×D83)⋊C4—28no—
199C4×Dic83—28no—
200C4×Dic83—28no—
201C4×Dic83—28no—
202C4×Dic83C2×D4116yes—
203C24×C83C2411yescharacteristic
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×C83—22no—
219C22×C4×C83—22no—
220C22×C4×C83—22no—
221C22×C4×C83—22no—
222C22×C4×C83C2×D414yes—
223C22×C4×C83#4114yes—
224C22×C4×C83#4114yes—
225C22×C4×C83C2412yes—
226C22×C4×C83C2412yes—
227C22×C4×C83C2412yes—
228C22×C4×C83C2412yes—
229C22×C4×C83C2412yes—
230C22×C4×C83C2412yes—
231C22×C4×C83C2412yes—
232C4⋊C4×C83—28no—
233C4⋊C4×C83—28no—
234C4⋊C4×C83—28no—
235C4⋊C4×C83—28no—
236C42×C83—28no—
237C23×C83C22×D412yes—
238C23×C83C2×#4112yes—
239C23×C83C2×#4112yes—
240C23×C83C2×#4112yes—
241C23×C83C2×#4112yes—
242C23×C832−1+412yes—
243C23×C832−1+412yes—
244C23×C83C2511yescharacteristic
245C22×D83—22no—
246C22×D83—22no—
247C22×D83—22no—
248C22×D83—22no—
249C22×D83—22no—
250C22×D83—22no—
251C22×D83—22no—
252C22×D83—44no—
253C22×D83—44no—
254C22×D83—44no—
255C22×D83—44no—
256C22×D83—44no—
257C22×D83—44no—
258C22×D83—44no—
259C2×C4×C83—28no—
260C2×C4×C83—28no—
261C2×C4×C83—28no—
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—22no—
278C2×C4×C83—22no—
279C2×C4×C83—22no—
280C2×C4×C83—44no—
281C2×C4×C83—44no—
282C2×C4×C83—44no—
283C2×C4×C83—44no—
284C2×C4×C83C22×D414yes—
285C2×C4×C83C2×#4114yes—
286C2×C4×C83C2×#4114yes—
287C2×Dic83—28no—
288C2×Dic83—28no—
289C2×Dic83—28no—
290C2×Dic83—28no—
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—44no—
309C2×Dic83—44no—
310C2×Dic83—44no—
311C2×Dic83C22×D414yes—
312C2×Dic83C22×D414yes—
313C2×Dic83C2×#4114yes—
314C2×Dic83C2×#4114yes—
315Dic166—232no—
316C22×C83#52514yes—
317C22×C83#53214yes—
318C22×C83#53614yes—
319C22×C83#55214yes—
320C22×C83#55214yes—
321C22×C83#55614yes—
322C22×C83#55614yes—
323C22×C83C23×D411yescharacteristic
324C22×C83C22×#4111yescharacteristic
325C22×C83C22×#4111yescharacteristic
326C22×C83C22×#4111yescharacteristic
327C22×C83C22×#4111yescharacteristic
328C22×C83C2×2−1+411yescharacteristic
329C22×C83C2×2−1+411yescharacteristic
330C2×D83—42no—
331C2×D83—42no—
332C2×D83—42no—
333C2×D83—42no—
334C2×D83—42no—
335C2×D83—42no—
336C2×D83—42no—
337C2×D83—88no—
338C4×C83—24no—
339C4×C83—24no—
340C4×C83—24no—
341C4×C83—42no—
342C4×C83—42no—
343C4×C83—42no—
344C4×C83—42no—
345Dic83—24no—
346Dic83—24no—
347Dic83—24no—
348Dic83—24no—
349Dic83—42no—
350Dic83—42no—
351Dic83—42no—
352C2×#2604—831nomaximal, Sylow
353C2×C83#260418yescomplemented
354C2×C83C2×#52511yescharacteristic
355C2×C83C2×#53211yescharacteristic
356C2×C83C2×#53611yescharacteristic
357C2×C83C2×#55211yescharacteristic
358C2×C83C2×#55211yescharacteristic
359C2×C83C2×#55611yescharacteristic
360C2×C83C2×#55611yescharacteristic
361D83—82no—
362C22×#126—831no—
363C22×C4×Q8—831no—
364#2604—8316no—
365C2×#400—831no—
366C2×#399—831no—
367C2×#395—831no—
368C2×#393—831no—
369C2×#389—831no—
370C2×#389D8311yescharacteristic, complemented
371C2×#388—831no—
372C2×#388—831no—
373C2×#388—831no—
374C2×#388—831no—
375C2×#387—831no—
376C2×#387—831no—
377C2×#376—831no—
378C83C2×#260411yescharacteristic, complemented, Sylow
379C23×Q8—831no—
380C2×#126—838no—
381C2×#126—1668no—
382C2×C4×Q8—838no—
383C2×C4×Q8—1668no—
384C22×C4⋊C4—831no—
385C22×C4⋊C4—831no—
386C22×C4⋊C4—831no—
387C22×C4⋊C4—831no—
388C22×C4⋊C4—831no—
389C22×C4⋊C4—831no—
390C22×C4⋊C4C2×D8311yescharacteristic
391C22×C4⋊C4C2×D8311yescharacteristic
392C22×C4⋊C4C2×D8311yescharacteristic
393C22×C4⋊C4C2×D8311yescharacteristic
394C22×C22⋊C4—831no—
395C22×C22⋊C4—831no—
396C22×C22⋊C4—831no—
397C22×C22⋊C4—831no—
398C22×C22⋊C4—831no—
399C22×C22⋊C4—831no—
400C22×C22⋊C4—831no—
401C22×C42—831no—
402C22×C42—831no—
403C22×C42—831no—
404C22×C42—831no—
405C22×C42C2×D8311yescharacteristic
406#400—838no—
407#399—838no—
408#395—838no—
409#393—838no—
410#389—838no—
411#389C2×D8318yescomplemented
412#388—838no—
413#388—838no—
414#388—838no—
415#388—838no—
416#387—838no—
417#387—838no—
418#376—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×#95C2×D8311yescharacteristic
430C2×#95C2×D8311yescharacteristic
431C25—831no—
432C22×Q8—834no—
433C22×Q8—1664no—
434C22×Q8—1664no—
435C22×Q8—1664no—
436C23×C4—831no—
437C23×C4—831no—
438C23×C4—831no—
439C23×C4—831no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4C22×D8311yescharacteristic
444C23×C4C22×D8311yescharacteristic
445C23×C4C22×D8311yescharacteristic
446C23×C4C22×D8311yescharacteristic
447C23×C4C22×D8311yescharacteristic
448C23×C4C22×D8311yescharacteristic
449C23×C4C22×D8311yescharacteristic
450#126—16632no—
451C4×Q8—16632no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—24no—
455C2×C4⋊C4—24no—
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—1664no—
463C2×C4⋊C4—1664no—
464C2×C4⋊C4—1664no—
465C2×C4⋊C4—1664no—
466C2×C4⋊C4—1664no—
467C2×C4⋊C4—1664no—
468C2×C4⋊C4C22×D8314yes—
469C2×C4⋊C4C22×D8314yes—
470C2×C4⋊C4C22×D8314yes—
471C2×C4⋊C4C22×D8314yes—
472C2×C22⋊C4—834no—
473C2×C22⋊C4—834no—
474C2×C22⋊C4—834no—
475C2×C22⋊C4—834no—
476C2×C22⋊C4—834no—
477C2×C22⋊C4—834no—
478C2×C22⋊C4—834no—
479C2×C22⋊C4—1664no—
480C2×C22⋊C4—1664no—
481C2×C22⋊C4—1664no—
482C2×C22⋊C4—1664no—
483C2×C22⋊C4—1664no—
484C2×C22⋊C4—1664no—
485C2×C22⋊C4—1664no—
486C2×C42—24no—
487C2×C42—838no—
488C2×C42—834no—
489C2×C42—834no—
490C2×C42—834no—
491C2×C42—834no—
492C2×C42—1664no—
493C2×C42—1664no—
494C2×C42—1664no—
495C2×C42C22×D8314yes—
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#95C22×D8314yes—
507#95C22×D8314yes—
508C24—832no—
509C24—1662no—
510C24—1662no—
511C24—1662no—
512C24—1662no—
513C24—1662no—
514C24—1662no—
515C24—1662no—
516C24C23×D8311yescharacteristic
517C2×Q8—1668no—
518C2×Q8—1668no—
519C2×Q8—16632no—
520C2×Q8—1668no—
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—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—834no—
540C22×C4—834no—
541C22×C4—834no—
542C22×C4—834no—
543C22×C4—832no—
544C22×C4—832no—
545C22×C4—832no—
546C22×C4—832no—
547C22×C4—832no—
548C22×C4—832no—
549C22×C4—832no—
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—1662no—
560C22×C4—1662no—
561C22×C4—1662no—
562C22×C4—1662no—
563C22×C4—1662no—
564C22×C4—1662no—
565C22×C4—1662no—
566C22×C4—1662no—
567C22×C4D4×D8314yes—
568C22×C4#1305058914yes—
569C22×C4#1305059014yes—
570C22×C4C23×D8312yes—
571C22×C4C23×D8312yes—
572C22×C4C23×D8312yes—
573C22×C4C23×D8312yes—
574C22×C4C23×D8312yes—
575C22×C4C23×D8312yes—
576C22×C4C23×D8312yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—28no—
580C4⋊C4—28no—
581C4⋊C4—1668no—
582C4⋊C4—1668no—
583C4⋊C4—1668no—
584C4⋊C4—1668no—
585C4⋊C4—1668no—
586C4⋊C4—1668no—
587C22⋊C4—1668no—
588C22⋊C4—1668no—
589C22⋊C4—1668no—
590C22⋊C4—1668no—
591C22⋊C4—1668no—
592C22⋊C4—1668no—
593C22⋊C4—1668no—
594C42—28no—
595C42—8316no—
596C42—1668no—
597C42—1668no—
598C42—1668no—
599C23—3324no—
600C23—3324no—
601C23—3324no—
602C23—3324no—
603C23—3324no—
604C23—3324no—
605C23—3324no—
606C23—1662no—
607C23—1662no—
608C23—1662no—
609C23—1662no—
610C23—1662no—
611C23—1662no—
612C23—1662no—
613C23C2×D4×D8312yes—
614C23#41×D8312yes—
615C23#41×D8312yes—
616C23C2×#1305058912yes—
617C23C2×#1305059012yes—
618C23#1458184012yes—
619C23#1458184012yes—
620C23C24×D8311yescharacteristic
621Q8—16632no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
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—44no—
644C2×C4—44no—
645C2×C4—44no—
646C2×C4—44no—
647C2×C4—3324no—
648C2×C4—3324no—
649C2×C4—3324no—
650C2×C4—834no—
651C2×C4—834no—
652C2×C4—834no—
653C2×C4—834no—
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—1668no—
664C2×C4—1668no—
665C2×C4—1668no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1668no—
672C2×C4—1662no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4C2×D4×D8314yes—
676C2×C4C2×#1305058914yes—
677C2×C4C2×#1305059014yes—
678C22—3322no—
679C22—3322no—
680C22—3322no—
681C22—3322no—
682C22—3322no—
683C22—3322no—
684C22—3322no—
685C22—6648no—
686C22#1912821014yes—
687C22#1912824614yes—
688C22#1912827614yes—
689C22#1912838314yes—
690C22#1912838614yes—
691C22#1912842214yes—
692C22#1912842314yes—
693C22C22×D4×D8311yescharacteristic
694C22C2×#41×D8311yescharacteristic
695C22C2×#41×D8311yescharacteristic
696C22C22×#1305058911yescharacteristic
697C22C22×#1305059011yescharacteristic
698C22C2×#1458184011yescharacteristic
699C22C2×#1458184011yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—3322no—
708C4—3322no—
709C4—3322no—
710C4—1664no—
711C4—1664no—
712C4—1664no—
713C4—1664no—
714C2—6642no—
715C2#2491309718yesdirect product factor
716C2C2×#1912821011yescharacteristic
717C2C2×#1912824611yescharacteristic
718C2C2×#1912827611yescharacteristic
719C2C2×#1912838311yescharacteristic
720C2C2×#1912838611yescharacteristic
721C2C2×#1912842211yescharacteristic
722C2C2×#1912842311yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#389×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#389D83
hypocenterC83C2×#2604
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#14581757C2semidirect
3. #24913097C2direct (N × H)
4. C2×#19127642C2semidirect
6. C2×#19127621C2semidirect
8. C2×#19127596C2semidirect
13. C2×#19127588C2semidirect
14. C2×#19127587C2semidirect
15. C2×#19127547C2semidirect
16. C2×#389×C83C2semidirect
21. C2×#14581757C22semidirect
39. #19127642C22semidirect
41. #19127621C22semidirect
43. #19127596C22semidirect
48. #19127588C22semidirect
49. #19127587C22semidirect
50. #19127547C22semidirect
66. #389×C83C22semidirect
353. C2×C83#2604semidirect
370. C2×#389D83semidirect
378. C83C2×#2604semidirect
411. #389C2×D83semidirect
715. C2#24913097direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817872
C22×#145817572
#249130972
C2×#191276422
C2×#191276362
C2×#191276212
C2×#191276142
C2×#191275962
C2×#191275922
C2×#191275912
C2×#191275902
C2×#191275882
C2×#191275872
C2×#191275472
C2×#389×C832
C2×#260483