Finite Group Databasebeta

← C2×#24916453 #36268873

Subgroups — C2×#24916453 #36268873

Order 21248.

2026 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128229C211yesmaximal, characteristic
2#24916453C2116yesmaximal, direct product factor
3C2×#19127831C211yesmaximal, characteristic, complemented
4C2×#19127829C211yesmaximal, characteristic, complemented
5C2×#19127774C211yesmaximal, characteristic, complemented
6C2×#19127772C211yesmaximal, characteristic, complemented
7C2×#19127770C211yesmaximal, characteristic, complemented
8C2×#19127770C211yesmaximal, characteristic, complemented
9C2×C8×D332C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D83C211yesmaximal, characteristic, complemented
11C2×#19127762C211yesmaximal, characteristic, complemented
12C2×#19127760C211yesmaximal, characteristic, complemented
13C2×#19127752C211yesmaximal, characteristic, complemented
14C2×#19127658C211yesmaximal, characteristic, complemented
15C2×#97×D83C211yesmaximal, characteristic, complemented
16C2×#405×C83C211yesmaximal, characteristic, complemented
17C22×#13050573C2211yescharacteristic
18C22×C8×D83C2211yescharacteristic
19C22×C8×D83C2211yescharacteristic
20C22×C8×D83C2211yescharacteristic
21#19128229C418yes—
22#19128229C2218yes—
23C2×#14581787C411yescharacteristic
24C2×#14581785C411yescharacteristic
25C2×#14581782C411yescharacteristic
26C2×#14581778C411yescharacteristic
27C2×#14581777C411yescharacteristic
28C2×#14581774C411yescharacteristic
29C2×#14581770C411yescharacteristic
30C2×#14581765C411yescharacteristic
31C2×C4×Dic166C2211yescharacteristic
32C2×C4×D332C2211yescharacteristic
33C2×C4×C22⋊D83C2211yescharacteristic
34C2×C4×C22⋊D83C2211yescharacteristic
35C2×#14581749C2211yescharacteristic
36C2×C42×D83C2211yescharacteristic
37#19127831C2218yescomplemented
38#19127829C2218yescomplemented
39#19127774C2218yescomplemented
40#19127772C2218yescomplemented
41#19127770C2218yescomplemented
42#19127770C2218yescomplemented
43C8×D332C2218yescomplemented
44C8×C22⋊D83C2218yescomplemented
45#19127762C2218yescomplemented
46#19127760C2218yescomplemented
47#19127752C2218yescomplemented
48C2×C4⋊(C83⋊C8)C2211yescharacteristic
49C2×C4⋊(C83⋊C8)C2211yescharacteristic
50C2×Dic83⋊C8C2211yescharacteristic
51C2×Dic83⋊C8C2211yescharacteristic
52C2×Dic83⋊C8C2211yescharacteristic
53C2×Dic83⋊C8C2211yescharacteristic
54C2×C22⋊(C83⋊C8)C2211yescharacteristic
55C2×C22⋊(C83⋊C8)C2211yescharacteristic
56C2×(C2×D83)⋊C8C2211yescharacteristic
57C2×(C2×D83)⋊C8C2211yescharacteristic
58C2×(C2×D83)⋊C8C2211yescharacteristic
59C2×(C2×D83)⋊C8C2211yescharacteristic
60#19127658C2218yescomplemented
61C2×#14581703C2211yescharacteristic
62C2×#14581702C2211yescharacteristic
63C2×#14581702C2211yescharacteristic
64C2×#14581702C2211yescharacteristic
65#97×D83C2218yescomplemented
66C2×C4×C83⋊C8C2211yescharacteristic
67C2×C8×Dic83C2211yescharacteristic
68C22×M16×C83C2211yescharacteristic
69C23×C8×C83C2211yescharacteristic
70C2×#117×C83C2211yescharacteristic
71#405×C83C2218yescomplemented
72C2×#97×C83C2211yescharacteristic
73C2×#97×C83C2211yescharacteristic
74C2×C4×C8×C83C2211yescharacteristic
75C2×C4×C8×C83C2211yescharacteristic
76C22×Dic166C2×C411yescharacteristic
77C22×D332C2×C411yescharacteristic
78C22×C22⋊D83C2×C411yescharacteristic
79C22×C22⋊D83C2×C411yescharacteristic
80C22×C4×D83C2×C411yescharacteristic
81C22×C4×D83C2×C411yescharacteristic
82C22×C4×D83C2311yescharacteristic
83C22×C4×D83C2311yescharacteristic
84C2×#13050573—24no—
85C2×#13050573C2314yes—
86C22×C83⋊C8C2311yescharacteristic
87C22×C83⋊C8C2311yescharacteristic
88C22×C83⋊C8C2311yescharacteristic
89C22×C83⋊C8C2311yescharacteristic
90C2×C8×D83—24no—
91C2×C8×D83—24no—
92C2×C8×D83—24no—
93C2×C8×D83C2314yes—
94C2×C8×D83C2314yes—
95C2×C8×D83C2314yes—
96#14581787C2×C418yes—
97#14581785C2×C418yes—
98#14581782C2×C418yes—
99#14581778C2×C418yes—
100#14581777C2×C418yes—
101#14581774C2×C418yes—
102#14581770C2×C418yes—
103#14581765C2×C418yes—
104C4×Dic166C2×C414yes—
105C4×Dic166C2314yes—
106C4×D332C2×C414yes—
107C4×D332C2314yes—
108C4×C22⋊D83C2×C414yes—
109C4×C22⋊D83C2×C414yes—
110C4×C22⋊D83C2314yes—
111C4×C22⋊D83C2314yes—
112#14581749C2×C414yes—
113#14581749C2314yes—
114C2×C4⋊Dic83C2×C411yescharacteristic
115C2×C4⋊Dic83C2×C411yescharacteristic
116C2×Dic83⋊C4C2×C411yescharacteristic
117C2×Dic83⋊C4C2×C411yescharacteristic
118C2×Dic83⋊C4C2×C411yescharacteristic
119C2×Dic83⋊C4C2×C411yescharacteristic
120C2×Dic83⋊C4C2×C411yescharacteristic
121C2×Dic83⋊C4C2×C411yescharacteristic
122C2×C22⋊Dic83C2×C411yescharacteristic
123C2×C22⋊Dic83C2×C411yescharacteristic
124C2×(C2×D83)⋊C4C2×C411yescharacteristic
125C2×(C2×D83)⋊C4C2×C411yescharacteristic
126C2×(C2×D83)⋊C4C2×C411yescharacteristic
127C2×(C2×D83)⋊C4C2×C411yescharacteristic
128C2×(C2×D83)⋊C4C2×C411yescharacteristic
129C2×(C2×D83)⋊C4C2×C411yescharacteristic
130C2×C4×Dic83C2×C411yescharacteristic
131C2×C4×Dic83C2×C411yescharacteristic
132C2×C4×Dic83C2311yescharacteristic
133C2×C4×Dic83C2311yescharacteristic
134C42×D83C2×C414yes—
135C42×D83C2314yes—
136C4⋊(C83⋊C8)C2314yes—
137C4⋊(C83⋊C8)C2314yes—
138Dic83⋊C8C2314yes—
139Dic83⋊C8C2314yes—
140Dic83⋊C8C2314yes—
141Dic83⋊C8C2314yes—
142C22⋊(C83⋊C8)C2314yes—
143C22⋊(C83⋊C8)C2314yes—
144(C2×D83)⋊C8C2314yes—
145(C2×D83)⋊C8C2314yes—
146(C2×D83)⋊C8C2314yes—
147(C2×D83)⋊C8C2314yes—
148#14581703C2314yes—
149#14581702C2314yes—
150#14581702C2314yes—
151#14581702C2314yes—
152C4×C83⋊C8C2314yes—
153C8×Dic83C2314yes—
154C23×C4×C83C2311yescharacteristic
155C2×M16×C83—24no—
156C2×M16×C83C2314yes—
157C22×C8×C83—24no—
158C22×C8×C83C2311yescharacteristic
159C22×C8×C83C2314yes—
160C22×C8×C83C2311yescharacteristic
161C22×C8×C83C2311yescharacteristic
162C22×C8×C83C2311yescharacteristic
163#117×C83C2×C414yes—
164#117×C83C2314yes—
165C2×C4⋊C4×C83C2×C411yescharacteristic
166C2×C4⋊C4×C83C2×C411yescharacteristic
167C2×C22⋊C4×C83C2×C411yescharacteristic
168C2×C22⋊C4×C83C2×C411yescharacteristic
169C2×C42×C83C2311yescharacteristic
170C2×C42×C83C2311yescharacteristic
171#97×C83C2314yes—
172#97×C83C2314yes—
173C4×C8×C83C2314yes—
174C4×C8×C83C2314yes—
175C23×D83C22×C411yescharacteristic
176C23×D83C22×C411yescharacteristic
177C2×Dic166—42no—
178C2×Dic166C22×C414yes—
179C2×D332—24no—
180C2×D332C22×C414yes—
181C2×C22⋊D83—24no—
182C2×C22⋊D83—42no—
183C2×C22⋊D83C22×C414yes—
184C2×C22⋊D83C22×C414yes—
185C22×Dic83C22×C411yescharacteristic
186C22×Dic83C22×C411yescharacteristic
187C22×Dic83C22×C411yescharacteristic
188C22×Dic83C22×C411yescharacteristic
189C22×Dic83C22×C411yescharacteristic
190C22×Dic83C22×C411yescharacteristic
191C2×C4×D83—24no—
192C2×C4×D83—22no—
193C2×C4×D83—22no—
194C2×C4×D83—22no—
195C2×C4×D83—22no—
196C2×C4×D83—42no—
197C2×C4×D83C22×C414yes—
198C2×C4×D83C22×C412yes—
199C2×C4×D83C22×C412yes—
200C2×C4×D83C22×C414yes—
201C2×C4×D83C2412yes—
202C2×C4×D83C2412yes—
203#13050573—28no—
204C2×C83⋊C8—22no—
205C2×C83⋊C8—22no—
206C2×C83⋊C8—22no—
207C2×C83⋊C8—22no—
208C2×C83⋊C8C2412yes—
209C2×C83⋊C8C2412yes—
210C2×C83⋊C8C2412yes—
211C2×C83⋊C8C2412yes—
212C8×D83—28no—
213C8×D83—28no—
214C8×D83—28no—
215C4⋊Dic83C22×C414yes—
216C4⋊Dic83C22×C414yes—
217Dic83⋊C4C22×C414yes—
218Dic83⋊C4C22×C414yes—
219Dic83⋊C4C22×C414yes—
220Dic83⋊C4C22×C414yes—
221Dic83⋊C4C22×C414yes—
222Dic83⋊C4C22×C414yes—
223C22⋊Dic83C22×C414yes—
224C22⋊Dic83C22×C414yes—
225(C2×D83)⋊C4C22×C414yes—
226(C2×D83)⋊C4C22×C414yes—
227(C2×D83)⋊C4C22×C414yes—
228(C2×D83)⋊C4C22×C414yes—
229(C2×D83)⋊C4C22×C414yes—
230(C2×D83)⋊C4C22×C414yes—
231C4×Dic83C22×C414yes—
232C4×Dic83C22×C414yes—
233C4×Dic83C22×C412yes—
234C4×Dic83C22×C412yes—
235C4×Dic83C2412yes—
236C4×Dic83C2412yes—
237C24×C83C22×C411yescharacteristic
238C22×C4×C83—22no—
239C22×C4×C83—22no—
240C22×C4×C83C22×C411yescharacteristic
241C22×C4×C83C22×C411yescharacteristic
242C22×C4×C83C22×C411yescharacteristic
243C22×C4×C83C22×C411yescharacteristic
244C22×C4×C83C22×C411yescharacteristic
245C22×C4×C83C22×C412yes—
246C22×C4×C83C2412yes—
247C22×C4×C83C2411yescharacteristic
248M16×C83—28no—
249C2×C8×C83—22no—
250C2×C8×C83—22no—
251C2×C8×C83—28no—
252C2×C8×C83#4114yes—
253C2×C8×C83#4114yes—
254C2×C8×C83C2412yes—
255C2×C8×C83C2412yes—
256C2×C8×C83C2412yes—
257C2×C8×C83C2412yes—
258C4⋊C4×C83C22×C414yes—
259C4⋊C4×C83C22×C414yes—
260C22⋊C4×C83C22×C414yes—
261C22⋊C4×C83C22×C414yes—
262C42×C83C22×C412yes—
263C42×C83C22×C412yes—
264C42×C83C2412yes—
265C42×C83C2412yes—
266C23×C83—22no—
267C23×C83—22no—
268C23×C83—22no—
269C23×C83C23×C412yes—
270C23×C83C23×C411yescharacteristic
271C22×D83—22no—
272C22×D83—22no—
273C22×D83—22no—
274C22×D83—22no—
275C22×D83—22no—
276C22×D83#13114yes—
277C22×D83C23×C412yes—
278C22×D83C23×C412yes—
279C2×C4×C83—22no—
280C2×C4×C83—22no—
281C2×C4×C83—22no—
282C2×C4×C83—22no—
283C2×C4×C83—22no—
284C2×C4×C83—24no—
285C2×C4×C83—22no—
286C2×C4×C83—22no—
287C2×C4×C83C23×C412yes—
288C2×C4×C83C23×C412yes—
289C2×C4×C83C23×C412yes—
290C2×C4×C83C23×C412yes—
291C2×C4×C83C23×C412yes—
292C2×C4×C83C23×C411yescharacteristic
293C2×C4×C83C2×#4112yes—
294C2×C4×C83C2×#4112yes—
295C2×C4×C83C2511yescharacteristic
296C22⋊D83—28no—
297C22⋊D83—44no—
298C2×Dic83—22no—
299C2×Dic83—22no—
300C2×Dic83—22no—
301C2×Dic83—22no—
302C2×Dic83—22no—
303C2×Dic83—22no—
304C2×Dic83C23×C412yes—
305C2×Dic83C23×C412yes—
306C2×Dic83C23×C412yes—
307C2×Dic83C23×C412yes—
308C2×Dic83C23×C412yes—
309C2×Dic83C23×C412yes—
310D332—28no—
311C4×D83—28no—
312C4×D83—24no—
313C4×D83—24no—
314C4×D83—22no—
315C4×D83—22no—
316C4×D83—22no—
317C4×D83—22no—
318C4×D83—44no—
319Dic166—44no—
320C8×C83—22no—
321C8×C83—22no—
322C8×C83C2×#4114yes—
323C8×C83C2×#4114yes—
324C83⋊C8—22no—
325C83⋊C8—22no—
326C83⋊C8—22no—
327C83⋊C8—22no—
328C22×C83—22no—
329C22×C83—22no—
330C22×C83—22no—
331C22×C83—44no—
332C22×C83C4×#4112yes—
333C22×C83C2×#13112yes—
334C22×C83#56812yes—
335C22×C83C24×C411yescharacteristic
336C2×D83—22no—
337C2×D83—28no—
338C2×D83—22no—
339C2×D83—22no—
340C2×D83—22no—
341C2×D83—22no—
342C2×D83—44no—
343C2×D83C2×#13114yes—
344C4×C83—22no—
345C4×C83—22no—
346C4×C83—22no—
347C4×C83—22no—
348C4×C83—22no—
349C4×C83C4×#4112yes—
350C4×C83C22×#4111yescharacteristic
351C4×C83C22×#4111yescharacteristic
352Dic83—22no—
353Dic83—22no—
354Dic83—22no—
355Dic83—22no—
356Dic83—22no—
357Dic83—22no—
358C2×#2968—831nomaximal, Sylow
359C2×C83—42no—
360C2×C83#296814yescomplemented
361C2×C83C2×C4×#4111yescharacteristic
362C2×C83C22×#13111yescharacteristic
363C2×C83C2×#56811yescharacteristic
364D83—24no—
365D83—42no—
366C2×#529—831no—
367#2968—8316no—
368C2×#446—831no—
369C2×#446—831no—
370C2×#435—831no—
371C2×#435—831no—
372C2×#435—831no—
373C2×#435—831no—
374C2×C8×D4—831no—
375C2×C8×D4—831no—
376C2×#433—831no—
377C2×#433—831no—
378C2×#431—831no—
379C2×#405—831no—
380C2×#405D8311yescharacteristic, complemented
381C22×#97—831no—
382C83C2×#296811yescharacteristic, complemented, Sylow
383C22×M16—831no—
384C22×M16C2×D8311yescharacteristic
385C23×C8—831no—
386C23×C8—831no—
387C23×C8—831no—
388C23×C8C2×D8311yescharacteristic
389#529—838no—
390#529—838no—
391C2×#126—831no—
392C2×#126—831no—
393C2×#125—831no—
394C2×#124—831no—
395C2×#123—831no—
396C2×#123—831no—
397C2×C22⋊Q8—831no—
398C2×#121—831no—
399C2×C4×Q8—831no—
400C2×C4×D4—831no—
401C2×C4×D4—831no—
402C2×C4×D4—831no—
403C2×#117—831no—
404C2×#117C2×D8311yescharacteristic
405C22×C42—831no—
406#446—838no—
407#446—838no—
408#435—838no—
409#435—838no—
410#435—838no—
411#435—838no—
412C8×D4—838no—
413C8×D4—838no—
414#433—838no—
415#433—838no—
416#431—838no—
417C2×C4⋊C8—831no—
418C2×C4⋊C8—831no—
419C2×C4⋊C8—831no—
420C2×C4⋊C8—831no—
421C2×C4⋊C8—831no—
422C2×C4⋊C8—831no—
423C2×C22⋊C8—831no—
424C2×C22⋊C8—831no—
425C2×C22⋊C8—831no—
426C2×C22⋊C8—831no—
427C2×C22⋊C8—831no—
428C2×C22⋊C8—831no—
429#405—838no—
430#405C2×D8318yescomplemented
431C2×#97—831no—
432C2×#97—831no—
433C2×#97—831no—
434C2×#97—831no—
435C2×#97—838no—
436C2×#97C2×D8311yescharacteristic
437C2×#97C2×D8311yescharacteristic
438C2×C4×C8—831no—
439C2×C4×C8—831no—
440C2×C4×C8C2×D8311yescharacteristic
441C2×C4×C8C2×D8311yescharacteristic
442C22×Q8—831no—
443C22×D4—831no—
444C22×D4—831no—
445C22×D4—831no—
446C23×C4—831no—
447C23×C4—831no—
448C23×C4—831no—
449C23×C4—831no—
450C23×C4C22×D8311yescharacteristic
451C2×M16—24no—
452C2×M16—834no—
453C2×M16—1664no—
454C2×M16C22×D8314yes—
455C22×C8—24no—
456C22×C8—831no—
457C22×C8—831no—
458C22×C8—831no—
459C22×C8—831no—
460C22×C8—834no—
461C22×C8—834no—
462C22×C8—834no—
463C22×C8—1664no—
464C22×C8—1664no—
465C22×C8—1664no—
466C22×C8C22×D8314yes—
467C22×C8C22×D8311yescharacteristic
468C22×C8C22×D8311yescharacteristic
469C22×C8C22×D8311yescharacteristic
470C22×C8C22×D8311yescharacteristic
471#126—838no—
472#126—838no—
473#125—838no—
474#124—838no—
475#123—838no—
476#123—838no—
477C22⋊Q8—838no—
478#121—838no—
479C4×Q8—834no—
480C4×Q8—834no—
481C4×D4—834no—
482C4×D4—834no—
483C4×D4—834no—
484C4×D4—834no—
485C4×D4—834no—
486C4×D4—834no—
487#117—834no—
488#117—834no—
489#117C4×D8314yes—
490#117C22×D8314yes—
491C2×C4⋊C4—831no—
492C2×C4⋊C4—831no—
493C2×C4⋊C4—831no—
494C2×C4⋊C4—831no—
495C2×C4⋊C4—831no—
496C2×C4⋊C4—831no—
497C2×C4⋊C4—831no—
498C2×C4⋊C4—831no—
499C2×C4⋊C4C4×D8311yescharacteristic
500C2×C4⋊C4C4×D8311yescharacteristic
501C2×C22⋊C4—831no—
502C2×C22⋊C4—831no—
503C2×C22⋊C4—831no—
504C2×C22⋊C4—831no—
505C2×C22⋊C4—831no—
506C2×C22⋊C4—831no—
507C2×C22⋊C4—831no—
508C2×C22⋊C4—831no—
509C2×C22⋊C4C4×D8311yescharacteristic
510C2×C22⋊C4C4×D8311yescharacteristic
511C2×C42—831no—
512C2×C42—831no—
513C2×C42—831no—
514C2×C42—831no—
515C2×C42—834no—
516C2×C42—834no—
517C2×C42C22×D8311yescharacteristic
518C2×C42C22×D8311yescharacteristic
519C4⋊C8—834no—
520C4⋊C8—834no—
521C4⋊C8—834no—
522C4⋊C8—834no—
523C4⋊C8—834no—
524C4⋊C8—834no—
525C22⋊C8—834no—
526C22⋊C8—834no—
527C22⋊C8—834no—
528C22⋊C8—834no—
529C22⋊C8—834no—
530C22⋊C8—834no—
531#97—834no—
532#97—834no—
533#97—834no—
534#97—834no—
535#97C22×D8314yes—
536#97C22×D8314yes—
537C4×C8—834no—
538C4×C8—834no—
539C4×C8C22×D8314yes—
540C4×C8C22×D8314yes—
541C24—831no—
542C24—831no—
543C24C2×C4×D8311yescharacteristic
544C2×Q8—3322no—
545C2×Q8—834no—
546C2×D4—3322no—
547C2×D4—834no—
548C2×D4—834no—
549C2×D4—834no—
550C2×D4—1664no—
551C2×D4—1664no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—3322no—
555C22×C4—834no—
556C22×C4—831no—
557C22×C4—831no—
558C22×C4—831no—
559C22×C4—831no—
560C22×C4—831no—
561C22×C4—831no—
562C22×C4—832no—
563C22×C4—834no—
564C22×C4—832no—
565C22×C4—832no—
566C22×C4—832no—
567C22×C4—1664no—
568C22×C4—1662no—
569C22×C4—1662no—
570C22×C4—1662no—
571C22×C4—1662no—
572C22×C4C2×C4×D8311yescharacteristic
573C22×C4C2×C4×D8311yescharacteristic
574C22×C4C2×C4×D8311yescharacteristic
575C22×C4C2×C4×D8311yescharacteristic
576C22×C4C2×C4×D8311yescharacteristic
577C22×C4C2×C4×D8312yes—
578C22×C4C23×D8312yes—
579C22×C4C23×D8311yescharacteristic
580M16—28no—
581M16—1668no—
582C2×C8—22no—
583C2×C8—22no—
584C2×C8—28no—
585C2×C8—832no—
586C2×C8—832no—
587C2×C8—832no—
588C2×C8—832no—
589C2×C8—1662no—
590C2×C8—1662no—
591C2×C8—1662no—
592C2×C8—1662no—
593C2×C8—1668no—
594C2×C8—1668no—
595C2×C8—1668no—
596C2×C8#1305059014yes—
597C2×C8#1305059014yes—
598C2×C8C23×D8312yes—
599C2×C8C23×D8312yes—
600C2×C8C23×D8312yes—
601C2×C8C23×D8312yes—
602C4⋊C4—834no—
603C4⋊C4—834no—
604C4⋊C4—834no—
605C4⋊C4—834no—
606C4⋊C4—834no—
607C4⋊C4—834no—
608C4⋊C4—834no—
609C4⋊C4—834no—
610C4⋊C4C2×C4×D8314yes—
611C4⋊C4C2×C4×D8314yes—
612C22⋊C4—834no—
613C22⋊C4—834no—
614C22⋊C4—834no—
615C22⋊C4—834no—
616C22⋊C4—834no—
617C22⋊C4—834no—
618C22⋊C4—834no—
619C22⋊C4—834no—
620C22⋊C4C2×C4×D8314yes—
621C22⋊C4C2×C4×D8314yes—
622C42—832no—
623C42—834no—
624C42—834no—
625C42—832no—
626C42—832no—
627C42—832no—
628C42C2×C4×D8312yes—
629C42C2×C4×D8312yes—
630C42C23×D8312yes—
631C42C23×D8312yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—834no—
636C23—832no—
637C23—832no—
638C23—1662no—
639C23—1662no—
640C23—1662no—
641C23—1662no—
642C23—1662no—
643C23C22×C4×D8312yes—
644C23C22×C4×D8311yescharacteristic
645Q8—3324no—
646D4—3324no—
647D4—1668no—
648D4—1668no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—3324no—
658C2×C4—832no—
659C2×C4—832no—
660C2×C4—832no—
661C2×C4—832no—
662C2×C4—832no—
663C2×C4—832no—
664C2×C4—1668no—
665C2×C4—1662no—
666C2×C4—1662no—
667C2×C4—1662no—
668C2×C4—1662no—
669C2×C4—1662no—
670C2×C4—1662no—
671C2×C4—1664no—
672C2×C4—1664no—
673C2×C4—1662no—
674C2×C4—1662no—
675C2×C4—1662no—
676C2×C4—1662no—
677C2×C4C22×C4×D8312yes—
678C2×C4C22×C4×D8312yes—
679C2×C4C22×C4×D8312yes—
680C2×C4C22×C4×D8312yes—
681C2×C4C22×C4×D8312yes—
682C2×C4C22×C4×D8311yescharacteristic
683C2×C4C2×#1305059012yes—
684C2×C4C2×#1305059012yes—
685C2×C4C24×D8311yescharacteristic
686C8—22no—
687C8—22no—
688C8—1662no—
689C8—1662no—
690C8—1662no—
691C8—1662no—
692C8C2×#1305059014yes—
693C8C2×#1305059014yes—
694C22—22no—
695C22—22no—
696C22—22no—
697C22—44no—
698C22—3324no—
699C22—834no—
700C22—1662no—
701C22—1662no—
702C22—1662no—
703C22—1662no—
704C22—1662no—
705C22—1668no—
706C22C4×#1305059012yes—
707C22#131×D8312yes—
708C22#1912846612yes—
709C22C23×C4×D8311yescharacteristic
710C4—22no—
711C4—22no—
712C4—22no—
713C4—22no—
714C4—22no—
715C4—1662no—
716C4—1662no—
717C4—1662no—
718C4—1662no—
719C4—1662no—
720C4—1662no—
721C4C4×#1305059012yes—
722C4C22×#1305059011yescharacteristic
723C4C22×#1305059011yescharacteristic
724C2—42no—
725C2—3322no—
726C2—1664no—
727C2#2491645314yesdirect product factor
728C2C2×C4×#1305059011yescharacteristic
729C2C2×#131×D8311yescharacteristic
730C2C2×#1912846611yescharacteristic
subgroupG/H
centerC22×C4C23×D83
commutatorC22×C83C24×C4
FrattiniC2×C4C24×D83
FittingC2×#405×C83C2
socleC23×C83C23×C4
prime radicalC2×#14581765C4
cosocleC2×C4×C83C25
hypercenterC2×#405D83
hypocenterC83C2×#2968
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22×C4 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #24916453C2direct (N × H)
3. C2×#19127831C2semidirect
4. C2×#19127829C2semidirect
5. C2×#19127774C2semidirect
6. C2×#19127772C2semidirect
7. C2×#19127770C2semidirect
8. C2×#19127770C2semidirect
9. C2×C8×D332C2semidirect
10. C2×C8×C22⋊D83C2semidirect
11. C2×#19127762C2semidirect
12. C2×#19127760C2semidirect
13. C2×#19127752C2semidirect
14. C2×#19127658C2semidirect
15. C2×#97×D83C2semidirect
16. C2×#405×C83C2semidirect
37. #19127831C22semidirect
38. #19127829C22semidirect
39. #19127774C22semidirect
40. #19127772C22semidirect
41. #19127770C22semidirect
42. #19127770C22semidirect
43. C8×D332C22semidirect
44. C8×C22⋊D83C22semidirect
45. #19127762C22semidirect
46. #19127760C22semidirect
47. #19127752C22semidirect
60. #19127658C22semidirect
65. #97×D83C22semidirect
71. #405×C83C22semidirect
360. C2×C83#2968semidirect
380. C2×#405D83semidirect
382. C83C2×#2968semidirect
430. #405C2×D83semidirect
727. C2#24916453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#191282292
#249164532
C2×#191278312
C2×#191278292
C2×#191277742
C2×#191277722
C2×#191277702
C2×C8×D3322
C2×C8×C22⋊D832
C2×#191277622
C2×#191277602
C2×#191277522
C2×#191276582
C2×#97×D832
C2×#405×C832
C2×#296883