Finite Group Databasebeta

← C2×#24911175 #35572893

Subgroups — C2×#24911175 #35572893

Order 21248.

2726 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581782C211yesmaximal, characteristic, complemented
2C22×#14581749C211yesmaximal, characteristic
3#24911175C2116yesmaximal, direct product factor
4C2×#19127638C211yesmaximal, characteristic
5C2×#19127636C211yesmaximal, characteristic
6C2×#19127625C211yesmaximal, characteristic
7C2×#19127623C211yesmaximal, characteristic
8C2×#19127599C211yesmaximal, characteristic, complemented
9C2×#19127598C211yesmaximal, characteristic, complemented
10C2×#19127598C211yesmaximal, characteristic, complemented
11C2×#19127598C211yesmaximal, characteristic, complemented
12C2×#19127584C211yesmaximal, characteristic, complemented
13C2×#19127570C211yesmaximal, characteristic, complemented
14C2×#19127560C211yesmaximal, characteristic
15C2×#19127548C211yesmaximal, characteristic
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×C4×D83C2211yescharacteristic
18C2×#14581782—28no—
19C2×#14581782C2218yescomplemented
20C2×#14581749—28no—
21C2×#14581749C2218yes—
22C22×C4⋊Dic83C2211yescharacteristic
23C22×C4⋊Dic83C2211yescharacteristic
24C22×C4⋊Dic83C2211yescharacteristic
25C22×C4⋊Dic83C2211yescharacteristic
26C22×Dic83⋊C4C2211yescharacteristic
27C22×Dic83⋊C4C2211yescharacteristic
28C22×Dic83⋊C4C2211yescharacteristic
29C22×Dic83⋊C4C2211yescharacteristic
30C22×Dic83⋊C4C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×(C2×D83)⋊C4C2211yescharacteristic
37C22×(C2×D83)⋊C4C2211yescharacteristic
38C22×(C2×D83)⋊C4C2211yescharacteristic
39C22×(C2×D83)⋊C4C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×C4×Dic83C2211yescharacteristic
43C22×C4×Dic83C2211yescharacteristic
44C22×C4×Dic83C2211yescharacteristic
45#19127638C2218yes—
46#19127636C2218yes—
47#19127625C2218yes—
48#19127623C2218yes—
49#19127599C2218yescomplemented
50#19127598C2218yescomplemented
51#19127598C2218yescomplemented
52#19127598C2218yescomplemented
53#19127584C2218yescomplemented
54#19127570C2218yescomplemented
55#19127560C2218yes—
56#19127548C2218yes—
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C22×C4⋊C4×C83C2211yescharacteristic
62C22×C4⋊C4×C83C2211yescharacteristic
63C22×C42×C83C2211yescharacteristic
64#387×C83C2218yescomplemented
65C2×#95×C83C2211yescharacteristic
66C2×#95×C83C2211yescharacteristic
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C24×D83C2311yescharacteristic
70C23×Dic83C2311yescharacteristic
71C23×Dic83C2311yescharacteristic
72C23×Dic83C2311yescharacteristic
73C23×Dic83C2311yescharacteristic
74C23×Dic83C2311yescharacteristic
75C23×Dic83C2311yescharacteristic
76C23×Dic83C2311yescharacteristic
77C22×C4×D83—24no—
78C22×C4×D83—24no—
79C22×C4×D83Q818yes—
80C22×C4×D83C2314yes—
81#14581782—232no—
82#14581749—232no—
83C2×C4⋊Dic83—24no—
84C2×C4⋊Dic83—24no—
85C2×C4⋊Dic83—24no—
86C2×C4⋊Dic83—42no—
87C2×C4⋊Dic83C2314yes—
88C2×C4⋊Dic83C2314yes—
89C2×C4⋊Dic83C2314yes—
90C2×C4⋊Dic83C2314yes—
91C2×Dic83⋊C4—24no—
92C2×Dic83⋊C4—24no—
93C2×Dic83⋊C4—24no—
94C2×Dic83⋊C4—24no—
95C2×Dic83⋊C4—24no—
96C2×Dic83⋊C4—24no—
97C2×Dic83⋊C4—42no—
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×(C2×D83)⋊C4—24no—
112C2×(C2×D83)⋊C4—24no—
113C2×(C2×D83)⋊C4—24no—
114C2×(C2×D83)⋊C4—24no—
115C2×(C2×D83)⋊C4—42no—
116C2×(C2×D83)⋊C4—42no—
117C2×(C2×D83)⋊C4C2314yes—
118C2×(C2×D83)⋊C4C2314yes—
119C2×(C2×D83)⋊C4C2314yes—
120C2×(C2×D83)⋊C4C2314yes—
121C2×(C2×D83)⋊C4C2314yes—
122C2×(C2×D83)⋊C4C2314yes—
123C2×C4×Dic83—24no—
124C2×C4×Dic83—24no—
125C2×C4×Dic83—24no—
126C2×C4×Dic83C2314yes—
127C2×C4×Dic83C2314yes—
128C2×C4×Dic83C2314yes—
129C83⋊#95C2314yes—
130C83⋊#95C2314yes—
131C83⋊#95C2314yes—
132C83⋊#95C2314yes—
133C23×C4×C83C2311yescharacteristic
134C23×C4×C83C2311yescharacteristic
135C23×C4×C83C2311yescharacteristic
136C23×C4×C83C2311yescharacteristic
137C23×C4×C83C2311yescharacteristic
138C23×C4×C83C2311yescharacteristic
139C23×C4×C83C2311yescharacteristic
140C2×C4⋊C4×C83—24no—
141C2×C4⋊C4×C83—24no—
142C2×C4⋊C4×C83C2314yes—
143C2×C4⋊C4×C83C2314yes—
144C2×C42×C83—24no—
145C2×C42×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—
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×Dic83C2×D414yes—
175C22×Dic83C2×D414yes—
176C22×Dic83C2×Q814yes—
177C22×Dic83#4114yes—
178C22×Dic83#4114yes—
179C22×Dic83C2412yes—
180C22×Dic83C2412yes—
181C22×Dic83C2412yes—
182C22×Dic83C2412yes—
183C22×Dic83C2412yes—
184C22×Dic83C2412yes—
185C22×Dic83C2412yes—
186C2×C4×D83—232no—
187C2×C4×D83—28no—
188C2×C4×D83—28no—
189C2×C4×D83C2×Q8116yes—
190C4⋊Dic83—28no—
191C4⋊Dic83—28no—
192C4⋊Dic83—28no—
193C4⋊Dic83—44no—
194Dic83⋊C4—28no—
195Dic83⋊C4—28no—
196Dic83⋊C4—28no—
197Dic83⋊C4—28no—
198Dic83⋊C4—28no—
199Dic83⋊C4—28no—
200Dic83⋊C4—44no—
201Dic83⋊C4—44no—
202Dic83⋊C4—44no—
203Dic83⋊C4C2×D4116yes—
204(C2×D83)⋊C4—28no—
205(C2×D83)⋊C4—28no—
206(C2×D83)⋊C4—28no—
207(C2×D83)⋊C4—28no—
208(C2×D83)⋊C4—44no—
209(C2×D83)⋊C4—44no—
210C4×Dic83—28no—
211C4×Dic83—28no—
212C4×Dic83—28no—
213C24×C83C2411yescharacteristic
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×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×C83C2×D414yes—
233C22×C4×C83C2×Q814yes—
234C22×C4×C83#4114yes—
235C22×C4×C83C2412yes—
236C22×C4×C83C2412yes—
237C22×C4×C83C2412yes—
238C22×C4×C83C2412yes—
239C22×C4×C83C2412yes—
240C22×C4×C83C2412yes—
241C22×C4×C83C2412yes—
242C4⋊C4×C83—28no—
243C4⋊C4×C83—28no—
244C42×C83—28no—
245C23×C83C22×D412yes—
246C23×C83C22×Q812yes—
247C23×C83C2×#4112yes—
248C23×C83C2×#4112yes—
249C23×C83C2×#4112yes—
250C23×C83H(5,𝔽2)12yes—
251C23×C832−1+412yes—
252C23×C83C2511yescharacteristic
253C22×D83—28no—
254C22×D83—28no—
255C22×D83—28no—
256C22×D83—22no—
257C22×D83—22no—
258C22×D83—22no—
259C22×D83—22no—
260C22×D83—22no—
261C22×D83—22no—
262C22×D83—44no—
263C22×D83—44no—
264C22×D83—44no—
265C22×D83—44no—
266C22×D83C22×Q814yes—
267C2×C4×C83—28no—
268C2×C4×C83—28no—
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—22no—
288C2×C4×C83—44no—
289C2×C4×C83—44no—
290C2×C4×C83—44no—
291C2×C4×C83—44no—
292C2×C4×C83C22×D414yes—
293C2×C4×C83C22×Q814yes—
294C2×C4×C83C2×#4114yes—
295C2×Dic83—28no—
296C2×Dic83—28no—
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—22no—
310C2×Dic83—22no—
311C2×Dic83—22no—
312C2×Dic83—22no—
313C2×Dic83—44no—
314C2×Dic83—44no—
315C2×Dic83—44no—
316C2×Dic83—44no—
317C2×Dic83C22⋊Q8116yes—
318C2×Dic83C22×D414yes—
319C2×Dic83C22×D414yes—
320C2×Dic83C22×Q814yes—
321C2×Dic83C2×#4114yes—
322C2×Dic83C2×#4114yes—
323C4×D83—232no—
324C22×C83C2×C22⋊Q814yes—
325C22×C83#53314yes—
326C22×C83#54414yes—
327C22×C83#54714yes—
328C22×C83#55014yes—
329C22×C83#55214yes—
330C22×C83#55314yes—
331C22×C83C23×D411yescharacteristic
332C22×C83C23×Q811yescharacteristic
333C22×C83C22×#4111yescharacteristic
334C22×C83C22×#4111yescharacteristic
335C22×C83C22×#4111yescharacteristic
336C22×C83C2×H(5,𝔽2)11yescharacteristic
337C22×C83C2×2−1+411yescharacteristic
338C2×D83—24no—
339C2×D83—24no—
340C2×D83—24no—
341C2×D83—42no—
342C2×D83—416no—
343C2×D83—42no—
344C2×D83—42no—
345C2×D83—42no—
346C4×C83—24no—
347C4×C83—24no—
348C4×C83—24no—
349C4×C83—42no—
350C4×C83—42no—
351C4×C83—42no—
352C4×C83—42no—
353Dic83—24no—
354Dic83—24no—
355Dic83—42no—
356Dic83—42no—
357Dic83—42no—
358Dic83—42no—
359Dic83C2×C22⋊Q818yes—
360C2×#2441—831nomaximal, Sylow
361C2×C83#244118yescomplemented
362C2×C83C22×C22⋊Q811yescharacteristic
363C2×C83C2×#53311yescharacteristic
364C2×C83C2×#54411yescharacteristic
365C2×C83C2×#54711yescharacteristic
366C2×C83C2×#55011yescharacteristic
367C2×C83C2×#55211yescharacteristic
368C2×C83C2×#55311yescharacteristic
369D83—44no—
370C22×#125—831no—
371C22×#117—831no—
372#2441—8316no—
373C2×#399—831no—
374C2×#399—831no—
375C2×#396—831no—
376C2×#396—831no—
377C2×#389—831no—
378C2×#389—831no—
379C2×#389—831no—
380C2×#389—831no—
381C2×#387—831no—
382C2×#387D8311yescharacteristic, complemented
383C2×#384—831no—
384C2×#380—831no—
385C2×C4×C22⋊C4—831no—
386C83C2×#244111yescharacteristic, complemented, Sylow
387C24×C4—831no—
388C2×#125—838no—
389C2×#125—1668no—
390C2×#117—838no—
391C2×#117—1668no—
392C22×C4⋊C4—831no—
393C22×C4⋊C4—831no—
394C22×C4⋊C4—831no—
395C22×C4⋊C4—831no—
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⋊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×C42C2×D8311yescharacteristic
418#399—838no—
419#399—838no—
420#396—838no—
421#396—838no—
422#389—838no—
423#389—838no—
424#389—838no—
425#389—838no—
426#387—838no—
427#387C2×D8318yescomplemented
428#384—838no—
429#380—838no—
430C4×C22⋊C4—838no—
431C2×#95—831no—
432C2×#95—831no—
433C2×#95—831no—
434C2×#95—831no—
435C2×#95C2×D8311yescharacteristic
436C2×#95C2×D8311yescharacteristic
437C2×#95C2×D8311yescharacteristic
438C2×#95C2×D8311yescharacteristic
439C25—831no—
440C23×C4—831no—
441C23×C4—831no—
442C23×C4—831no—
443C23×C4—838no—
444C23×C4—834no—
445C23×C4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—831no—
449C23×C4—1664no—
450C23×C4—1664no—
451C23×C4C22×D8311yescharacteristic
452C23×C4C22×D8311yescharacteristic
453C23×C4C22×D8311yescharacteristic
454C23×C4C22×D8311yescharacteristic
455C23×C4C22×D8311yescharacteristic
456C23×C4C22×D8311yescharacteristic
457C23×C4C22×D8311yescharacteristic
458#125—16632no—
459#117—16632no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—24no—
462C2×C4⋊C4—3322no—
463C2×C4⋊C4—3322no—
464C2×C4⋊C4—3322no—
465C2×C4⋊C4—3322no—
466C2×C4⋊C4—834no—
467C2×C4⋊C4—834no—
468C2×C4⋊C4—834no—
469C2×C4⋊C4—834no—
470C2×C4⋊C4—838no—
471C2×C4⋊C4—834no—
472C2×C4⋊C4—834no—
473C2×C4⋊C4—834no—
474C2×C4⋊C4—834no—
475C2×C4⋊C4—834no—
476C2×C4⋊C4—834no—
477C2×C4⋊C4—834no—
478C2×C4⋊C4—834no—
479C2×C4⋊C4—834no—
480C2×C4⋊C4—834no—
481C2×C4⋊C4—1664no—
482C2×C4⋊C4—1664no—
483C2×C4⋊C4—1664no—
484C2×C4⋊C4—1664no—
485C2×C4⋊C4—1664no—
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—834no—
497C2×C22⋊C4—834no—
498C2×C22⋊C4—834no—
499C2×C22⋊C4—834no—
500C2×C22⋊C4—1664no—
501C2×C22⋊C4—1664no—
502C2×C22⋊C4—1664no—
503C2×C22⋊C4—1664no—
504C2×C42—24no—
505C2×C42—834no—
506C2×C42—834no—
507C2×C42—834no—
508C2×C42—1664no—
509C2×C42—1664no—
510C2×C42—1664no—
511C2×C42C22×D8314yes—
512#95—834no—
513#95—834no—
514#95—834no—
515#95—834no—
516#95C22×D8314yes—
517#95C22×D8314yes—
518#95C22×D8314yes—
519#95C22×D8314yes—
520C24—834no—
521C24—832no—
522C24—1662no—
523C24—1662no—
524C24—1662no—
525C24—1662no—
526C24—1662no—
527C24—1662no—
528C24C23×D8311yescharacteristic
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—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—834no—
548C22×C4—834no—
549C22×C4—834no—
550C22×C4—832no—
551C22×C4—834no—
552C22×C4—834no—
553C22×C4—832no—
554C22×C4—832no—
555C22×C4—8316no—
556C22×C4—832no—
557C22×C4—832no—
558C22×C4—832no—
559C22×C4—832no—
560C22×C4—1668no—
561C22×C4—16632no—
562C22×C4—1668no—
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×C4—1662no—
575C22×C4—1662no—
576C22×C4—1662no—
577C22×C4—1662no—
578C22×C4—1662no—
579C22×C4D4×D8314yes—
580C22×C4Q8×D8314yes—
581C22×C4#1305059014yes—
582C22×C4C23×D8312yes—
583C22×C4C23×D8312yes—
584C22×C4C23×D8312yes—
585C22×C4C23×D8312yes—
586C22×C4C23×D8312yes—
587C22×C4C23×D8312yes—
588C22×C4C23×D8312yes—
589C4⋊C4—28no—
590C4⋊C4—28no—
591C4⋊C4—3324no—
592C4⋊C4—3324no—
593C4⋊C4—3324no—
594C4⋊C4—3324no—
595C4⋊C4—8316no—
596C4⋊C4—1668no—
597C4⋊C4—1668no—
598C4⋊C4—1668no—
599C4⋊C4—1668no—
600C4⋊C4—1668no—
601C4⋊C4—1668no—
602C4⋊C4—1668no—
603C4⋊C4—1668no—
604C4⋊C4—1668no—
605C22⋊C4—3324no—
606C22⋊C4—3324no—
607C22⋊C4—1668no—
608C22⋊C4—1668no—
609C22⋊C4—1668no—
610C22⋊C4—1668no—
611C42—28no—
612C42—1668no—
613C42—1668no—
614C42—1668no—
615C23—3324no—
616C23—3324no—
617C23—3324no—
618C23—3324no—
619C23—834no—
620C23—1668no—
621C23—1668no—
622C23—1668no—
623C23—1662no—
624C23—1662no—
625C23—1662no—
626C23—1662no—
627C23—1662no—
628C23—1662no—
629C23C2×D4×D8312yes—
630C23C2×Q8×D8312yes—
631C23#41×D8312yes—
632C23#41×D8312yes—
633C23C2×#1305059012yes—
634C23#1458183812yes—
635C23#1458183912yes—
636C23C24×D8311yescharacteristic
637C2×C4—28no—
638C2×C4—28no—
639C2×C4—28no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
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—44no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—44no—
662C2×C4—3324no—
663C2×C4—3324no—
664C2×C4—3324no—
665C2×C4—3324no—
666C2×C4—8316no—
667C2×C4—834no—
668C2×C4—834no—
669C2×C4—834no—
670C2×C4—834no—
671C2×C4—834no—
672C2×C4—16632no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
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—1668no—
686C2×C4—1668no—
687C2×C4—1662no—
688C2×C4—1662no—
689C2×C4—1662no—
690C2×C4—1662no—
691C2×C4C2×D4×D8314yes—
692C2×C4C2×Q8×D8314yes—
693C2×C4C2×#1305059014yes—
694C22—33216no—
695C22—3322no—
696C22—3322no—
697C22—3322no—
698C22—3322no—
699C22—1664no—
700C22—1664no—
701C22—1664no—
702C22C22⋊Q8×D8314yes—
703C22#1912825514yes—
704C22#1912833114yes—
705C22#1912834914yes—
706C22#1912837214yes—
707C22#1912838414yes—
708C22#1912840214yes—
709C22C22×D4×D8311yescharacteristic
710C22C22×Q8×D8311yescharacteristic
711C22C2×#41×D8311yescharacteristic
712C22C2×#41×D8311yescharacteristic
713C22C22×#1305059011yescharacteristic
714C22C2×#1458183811yescharacteristic
715C22C2×#1458183911yescharacteristic
716C4—24no—
717C4—24no—
718C4—24no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—42no—
723C4—3322no—
724C4—3322no—
725C4—3322no—
726C4—3322no—
727C4—838no—
728C4—1664no—
729C4—1664no—
730C2—3324no—
731C2#2491117518yesdirect product factor
732C2C2×C22⋊Q8×D8311yescharacteristic
733C2C2×#1912825511yescharacteristic
734C2C2×#1912833111yescharacteristic
735C2C2×#1912834911yescharacteristic
736C2C2×#1912837211yescharacteristic
737C2C2×#1912838411yescharacteristic
738C2C2×#1912840211yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC24×D83C23
hypercenterC2×#387D83
hypocenterC83C2×#2441
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14581782C2semidirect
3. #24911175C2direct (N × H)
8. C2×#19127599C2semidirect
9. C2×#19127598C2semidirect
10. C2×#19127598C2semidirect
11. C2×#19127598C2semidirect
12. C2×#19127584C2semidirect
13. C2×#19127570C2semidirect
16. C2×#387×C83C2semidirect
19. C2×#14581782C22semidirect
49. #19127599C22semidirect
50. #19127598C22semidirect
51. #19127598C22semidirect
52. #19127598C22semidirect
53. #19127584C22semidirect
54. #19127570C22semidirect
64. #387×C83C22semidirect
361. C2×C83#2441semidirect
382. C2×#387D83semidirect
386. C83C2×#2441semidirect
427. #387C2×D83semidirect
731. C2#24911175direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817822
C22×#145817492
#249111752
C2×#191276382
C2×#191276362
C2×#191276252
C2×#191276232
C2×#191275992
C2×#191275982
C2×#191275842
C2×#191275702
C2×#191275602
C2×#191275482
C2×#387×C832
C2×#244183