Finite Group Databasebeta

← C2×#24911277 #35571889

Subgroups — C2×#24911277 #35571889

Order 21248.

3830 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581772C211yesmaximal, characteristic, complemented
2C22×#14581770C211yesmaximal, characteristic, complemented
3C22×C4×D332C211yesmaximal, characteristic
4C22×C4⋊C4×D83C211yesmaximal, characteristic, complemented
5#24911277C2116yesmaximal, direct product factor
6C2×#19127638C211yesmaximal, characteristic, complemented
7C2×#19127633C211yesmaximal, characteristic, complemented
8C2×#19127623C211yesmaximal, characteristic, complemented
9C2×#19127622C211yesmaximal, characteristic, complemented
10C2×#19127599C211yesmaximal, characteristic, complemented
11C2×#19127579C211yesmaximal, characteristic
12C2×#19127579C211yesmaximal, characteristic
13C2×#19127575C211yesmaximal, characteristic, complemented
14C2×#19127575C211yesmaximal, characteristic, complemented
15C2×#19127575C211yesmaximal, characteristic, complemented
16C2×#387×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C23×C4×D83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C23×C4×D83C2211yescharacteristic
23C2×#14581772—28no—
24C2×#14581772C2218yescomplemented
25C2×#14581770—28no—
26C2×#14581770C2218yescomplemented
27C2×C4×D332—28no—
28C2×C4×D332C2218yes—
29C22×C4⋊Dic83C2211yescharacteristic
30C22×C4⋊Dic83C2211yescharacteristic
31C22×C4⋊Dic83C2211yescharacteristic
32C22×C4⋊Dic83C2211yescharacteristic
33C22×C4⋊Dic83C2211yescharacteristic
34C22×C4⋊Dic83C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×Dic83⋊C4C2211yescharacteristic
37C22×Dic83⋊C4C2211yescharacteristic
38C22×Dic83⋊C4C2211yescharacteristic
39C2×C4⋊C4×D83—28no—
40C2×C4⋊C4×D83C2218yescomplemented
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×(C2×D83)⋊C4C2211yescharacteristic
45C22×(C2×D83)⋊C4C2211yescharacteristic
46C22×(C2×D83)⋊C4C2211yescharacteristic
47C22×(C2×D83)⋊C4C2211yescharacteristic
48C22×(C2×D83)⋊C4C2211yescharacteristic
49#19127638C2218yescomplemented
50#19127633C2218yescomplemented
51#19127623C2218yescomplemented
52#19127622C2218yescomplemented
53#19127599C2218yescomplemented
54#19127579C2218yes—
55#19127579C2218yes—
56#19127575C2218yescomplemented
57#19127575C2218yescomplemented
58#19127575C2218yescomplemented
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C2×C83⋊#95C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C4⋊C4×C83C2211yescharacteristic
65C22×C42×C83C2211yescharacteristic
66#387×C83C2218yescomplemented
67C2×#95×C83C2211yescharacteristic
68C2×#95×C83C2211yescharacteristic
69C2×#95×C83C2211yescharacteristic
70C2×#95×C83C2211yescharacteristic
71C24×D83C2311yescharacteristic
72C24×D83C2311yescharacteristic
73C22×Dic166—24no—
74C22×Dic166—24no—
75C22×Dic166—42no—
76C22×Dic166C2314yes—
77C22×D332—24no—
78C22×D332—24no—
79C22×D332Q818yescomplemented
80C22×D332C2314yes—
81C23×Dic83C2311yescharacteristic
82C23×Dic83C2311yescharacteristic
83C23×Dic83C2311yescharacteristic
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C22×C4×D83—24no—
88C22×C4×D83—24no—
89C22×C4×D83—24no—
90C22×C4×D83—24no—
91C22×C4×D83—24no—
92C22×C4×D83—24no—
93C22×C4×D83—24no—
94C22×C4×D83—24no—
95C22×C4×D83—24no—
96C22×C4×D83—42no—
97C22×C4×D83—42no—
98C22×C4×D83—42no—
99C22×C4×D83C2314yes—
100C22×C4×D83C2314yes—
101C22×C4×D83C2314yes—
102C22×C4×D83C2314yes—
103#14581772—232no—
104#14581770—232no—
105C4×D332—232no—
106C2×C4⋊Dic83—24no—
107C2×C4⋊Dic83—24no—
108C2×C4⋊Dic83—24no—
109C2×C4⋊Dic83—24no—
110C2×C4⋊Dic83—24no—
111C2×C4⋊Dic83—42no—
112C2×C4⋊Dic83C2314yes—
113C2×C4⋊Dic83C2314yes—
114C2×C4⋊Dic83C2314yes—
115C2×C4⋊Dic83C2314yes—
116C2×C4⋊Dic83C2314yes—
117C2×C4⋊Dic83C2314yes—
118C2×Dic83⋊C4—24no—
119C2×Dic83⋊C4—24no—
120C2×Dic83⋊C4—24no—
121C2×Dic83⋊C4—24no—
122C2×Dic83⋊C4C2314yes—
123C2×Dic83⋊C4C2314yes—
124C2×Dic83⋊C4C2314yes—
125C2×Dic83⋊C4C2314yes—
126C4⋊C4×D83—232no—
127C2×(C2×D83)⋊C4—24no—
128C2×(C2×D83)⋊C4—24no—
129C2×(C2×D83)⋊C4—24no—
130C2×(C2×D83)⋊C4—24no—
131C2×(C2×D83)⋊C4—24no—
132C2×(C2×D83)⋊C4—24no—
133C2×(C2×D83)⋊C4—42no—
134C2×(C2×D83)⋊C4D418yes—
135C2×(C2×D83)⋊C4C2314yes—
136C2×(C2×D83)⋊C4C2314yes—
137C2×(C2×D83)⋊C4C2314yes—
138C2×(C2×D83)⋊C4C2314yes—
139C2×(C2×D83)⋊C4C2314yes—
140C2×(C2×D83)⋊C4C2314yes—
141C2×(C2×D83)⋊C4C2314yes—
142C2×(C2×D83)⋊C4C2314yes—
143C83⋊#95C2314yes—
144C83⋊#95C2314yes—
145C83⋊#95C2314yes—
146C83⋊#95C2314yes—
147C23×C4×C83C2311yescharacteristic
148C23×C4×C83C2311yescharacteristic
149C23×C4×C83C2311yescharacteristic
150C23×C4×C83C2311yescharacteristic
151C23×C4×C83C2311yescharacteristic
152C23×C4×C83C2311yescharacteristic
153C23×C4×C83C2311yescharacteristic
154C2×C4⋊C4×C83—24no—
155C2×C4⋊C4×C83D418yescomplemented
156C2×C4⋊C4×C83C2314yes—
157C2×C4⋊C4×C83C2314yes—
158C2×C42×C83—24no—
159C2×C42×C83C2314yes—
160#95×C83C2314yes—
161#95×C83C2314yes—
162#95×C83C2314yes—
163#95×C83C2314yes—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83—22no—
167C23×D83—22no—
168C23×D83—22no—
169C23×D83—22no—
170C23×D83—22no—
171C23×D83—22no—
172C23×D83—22no—
173C23×D83—22no—
174C23×D83C2×D414yes—
175C23×D83C2×Q814yes—
176C23×D83C2×Q814yes—
177C23×D83#4114yes—
178C23×D83C2412yes—
179C23×D83C2412yes—
180C2×Dic166—28no—
181C2×Dic166—28no—
182C2×Dic166—44no—
183C2×Dic166—416no—
184C2×D332—232no—
185C2×D332—28no—
186C2×D332—28no—
187C2×D332C2×Q8116yescomplemented
188C22×Dic83—22no—
189C22×Dic83—22no—
190C22×Dic83—22no—
191C22×Dic83—22no—
192C22×Dic83—22no—
193C22×Dic83—22no—
194C22×Dic83—22no—
195C22×Dic83—22no—
196C22×Dic83—22no—
197C22×Dic83—22no—
198C22×Dic83—22no—
199C22×Dic83—22no—
200C22×Dic83—22no—
201C22×Dic83—22no—
202C22×Dic83—22no—
203C22×Dic83—22no—
204C22×Dic83C2×D414yes—
205C22×Dic83#4114yes—
206C22×Dic83C2412yes—
207C22×Dic83C2412yes—
208C22×Dic83C2412yes—
209C22×Dic83C2412yes—
210C22×Dic83C2412yes—
211C22×Dic83C2412yes—
212C2×C4×D83—232no—
213C2×C4×D83—28no—
214C2×C4×D83—28no—
215C2×C4×D83—28no—
216C2×C4×D83—28no—
217C2×C4×D83—28no—
218C2×C4×D83—28no—
219C2×C4×D83—28no—
220C2×C4×D83—28no—
221C2×C4×D83—28no—
222C2×C4×D83—44no—
223C2×C4×D83—44no—
224C2×C4×D83—44no—
225C2×C4×D83—416no—
226C2×C4×D83—416no—
227C2×C4×D83—416no—
228C4⋊Dic83—28no—
229C4⋊Dic83—28no—
230C4⋊Dic83—28no—
231C4⋊Dic83—28no—
232C4⋊Dic83—28no—
233C4⋊Dic83—44no—
234Dic83⋊C4—28no—
235Dic83⋊C4—28no—
236Dic83⋊C4—28no—
237Dic83⋊C4—28no—
238(C2×D83)⋊C4—28no—
239(C2×D83)⋊C4—28no—
240(C2×D83)⋊C4—28no—
241(C2×D83)⋊C4—28no—
242(C2×D83)⋊C4—28no—
243(C2×D83)⋊C4—28no—
244(C2×D83)⋊C4—44no—
245(C2×D83)⋊C4C2×D4116yes—
246C24×C83C2411yescharacteristic
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—22no—
254C22×C4×C83—22no—
255C22×C4×C83—22no—
256C22×C4×C83—22no—
257C22×C4×C83—22no—
258C22×C4×C83—22no—
259C22×C4×C83—22no—
260C22×C4×C83—22no—
261C22×C4×C83—22no—
262C22×C4×C83—22no—
263C22×C4×C83C2×D414yes—
264C22×C4×C83C2×D414yes—
265C22×C4×C83C2×D414yes—
266C22×C4×C83C2×D414yes—
267C22×C4×C83C2×Q814yes—
268C22×C4×C83C2412yes—
269C22×C4×C83C2412yes—
270C22×C4×C83C2412yes—
271C22×C4×C83C2412yes—
272C22×C4×C83C2412yes—
273C22×C4×C83C2412yes—
274C22×C4×C83C2412yes—
275C4⋊C4×C83—28no—
276C4⋊C4×C83C2×D4116yescomplemented
277C42×C83—28no—
278C23×C83C22×D412yes—
279C23×C83C22×D412yes—
280C23×C83C22×Q812yes—
281C23×C83C2×#4112yes—
282C23×C83C2×#4112yes—
283C23×C83H(5,𝔽2)12yes—
284C23×C832−1+412yes—
285C23×C83C2511yescharacteristic
286C22×D83—28no—
287C22×D83—28no—
288C22×D83—28no—
289C22×D83—28no—
290C22×D83—28no—
291C22×D83—28no—
292C22×D83—22no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—28no—
297C22×D83—28no—
298C22×D83—28no—
299C22×D83—22no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—44no—
306C22×D83—44no—
307C22×D83—44no—
308C22×D83—44no—
309C22×D83C22⋊Q8116yescomplemented
310C22×D83C22×D414yes—
311C22×D83C22×Q814yes—
312C22×D83C22×Q814yes—
313C22×D83C2×#4114yes—
314C2×C4×C83—28no—
315C2×C4×C83—28no—
316C2×C4×C83—28no—
317C2×C4×C83—28no—
318C2×C4×C83—28no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—22no—
323C2×C4×C83—22no—
324C2×C4×C83—22no—
325C2×C4×C83—22no—
326C2×C4×C83—22no—
327C2×C4×C83—22no—
328C2×C4×C83—22no—
329C2×C4×C83—22no—
330C2×C4×C83—22no—
331C2×C4×C83—22no—
332C2×C4×C83—22no—
333C2×C4×C83—22no—
334C2×C4×C83—22no—
335C2×C4×C83—44no—
336C2×C4×C83—44no—
337C2×C4×C83C22×D414yes—
338C2×C4×C83C22×D414yes—
339C2×C4×C83C22×D414yes—
340C2×C4×C83C22×D414yes—
341C2×C4×C83C22×Q814yes—
342C2×Dic83—28no—
343C2×Dic83—28no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—22no—
348C2×Dic83—22no—
349C2×Dic83—22no—
350C2×Dic83—22no—
351C2×Dic83—22no—
352C2×Dic83—22no—
353C2×Dic83—22no—
354C2×Dic83—22no—
355C2×Dic83—22no—
356C2×Dic83—22no—
357C2×Dic83—22no—
358C2×Dic83—22no—
359C2×Dic83—22no—
360C2×Dic83—44no—
361C2×Dic83—44no—
362C2×Dic83—44no—
363C2×Dic83—44no—
364C2×Dic83C22×D414yes—
365C2×Dic83C2×#4114yes—
366D332—232no—
367C4×D83—232no—
368C4×D83—416no—
369C4×D83—416no—
370C4×D83—416no—
371Dic166—416no—
372C22×C83C2×C22⋊Q814yes—
373C22×C83#52514yes—
374C22×C83#53914yes—
375C22×C83D4214yes—
376C22×C83#54714yes—
377C22×C83D4×Q814yes—
378C22×C83#55414yes—
379C22×C83C23×D411yescharacteristic
380C22×C83C23×D411yescharacteristic
381C22×C83C23×Q811yescharacteristic
382C22×C83C22×#4111yescharacteristic
383C22×C83C22×#4111yescharacteristic
384C22×C83C2×H(5,𝔽2)11yescharacteristic
385C22×C83C2×2−1+411yescharacteristic
386C2×D83—24no—
387C2×D83—24no—
388C2×D83—24no—
389C2×D83—24no—
390C2×D83—24no—
391C2×D83—24no—
392C2×D83—232no—
393C2×D83—24no—
394C2×D83—24no—
395C2×D83—24no—
396C2×D83—42no—
397C2×D83—42no—
398C2×D83—42no—
399C2×D83—42no—
400C2×D83—416no—
401C2×D83C2×C22⋊Q818yescomplemented
402C4×C83—24no—
403C4×C83—24no—
404C4×C83—24no—
405C4×C83—24no—
406C4×C83—24no—
407C4×C83—42no—
408C4×C83—42no—
409Dic83—24no—
410Dic83—24no—
411Dic83—42no—
412Dic83—42no—
413Dic83—42no—
414Dic83—42no—
415C2×#2449—831nomaximal, Sylow
416C2×C83#244918yescomplemented
417C2×C83C22×C22⋊Q811yescharacteristic
418C2×C83C2×#52511yescharacteristic
419C2×C83C2×#53911yescharacteristic
420C2×C83C2×D4211yescharacteristic
421C2×C83C2×#54711yescharacteristic
422C2×C83C2×D4×Q811yescharacteristic
423C2×C83C2×#55411yescharacteristic
424D83—28no—
425D83—44no—
426C22×C22⋊Q8—831no—
427C22×C22⋊Q8—831no—
428C22×C4×D4—831no—
429C23×C4⋊C4—831no—
430#2449—8316no—
431C2×#399—831no—
432C2×#398—831no—
433C2×#396—831no—
434C2×#395—831no—
435C2×#389—831no—
436C2×#387D8311yescharacteristic, complemented
437C2×#386—831no—
438C2×#386—831no—
439C2×#385—831no—
440C2×#385—831no—
441C2×#385—831no—
442C83C2×#244911yescharacteristic, complemented, Sylow
443C23×Q8—831no—
444C23×D4—831no—
445C24×C4—831no—
446C24×C4—831no—
447C24×C4—831no—
448C24×C4—831no—
449C2×C22⋊Q8—838no—
450C2×C22⋊Q8—838no—
451C2×C22⋊Q8—1668no—
452C2×C22⋊Q8—1668no—
453C2×C4×D4—838no—
454C2×C4×D4—1668no—
455C22×C4⋊C4—831no—
456C22×C4⋊C4—831no—
457C22×C4⋊C4—831no—
458C22×C4⋊C4—831no—
459C22×C4⋊C4—831no—
460C22×C4⋊C4—831no—
461C22×C4⋊C4—831no—
462C22×C4⋊C4—831no—
463C22×C4⋊C4—831no—
464C22×C4⋊C4—831no—
465C22×C4⋊C4—838no—
466C22×C4⋊C4—1668no—
467C22×C4⋊C4C2×D8311yescharacteristic
468C22×C4⋊C4C2×D8311yescharacteristic
469C22×C22⋊C4—831no—
470C22×C22⋊C4—831no—
471C22×C22⋊C4—831no—
472C22×C22⋊C4—831no—
473C22×C22⋊C4—831no—
474C22×C22⋊C4—831no—
475C22×C22⋊C4—831no—
476C22×C22⋊C4—831no—
477C22×C42C2×D8311yescharacteristic
478#399—838no—
479#398—838no—
480#396—838no—
481#395—838no—
482#389—838no—
483#387C2×D8318yescomplemented
484#386—838no—
485#386—838no—
486#385—838no—
487#385—838no—
488#385—838no—
489C2×#95—831no—
490C2×#95—831no—
491C2×#95—831no—
492C2×#95—831no—
493C2×#95C2×D8311yescharacteristic
494C2×#95C2×D8311yescharacteristic
495C2×#95C2×D8311yescharacteristic
496C2×#95C2×D8311yescharacteristic
497C25—831no—
498C25—831no—
499C22×Q8—3322no—
500C22×Q8—834no—
501C22×Q8—1664no—
502C22×Q8—1664no—
503C22×D4—838no—
504C22×D4—834no—
505C22×D4—1664no—
506C22×D4—1664no—
507C23×C4—3322no—
508C23×C4—3322no—
509C23×C4—3322no—
510C23×C4—834no—
511C23×C4—834no—
512C23×C4—834no—
513C23×C4—831no—
514C23×C4—831no—
515C23×C4—831no—
516C23×C4—831no—
517C23×C4—831no—
518C23×C4—831no—
519C23×C4—834no—
520C23×C4—1664no—
521C23×C4—1664no—
522C23×C4—1664no—
523C23×C4—1664no—
524C23×C4—1664no—
525C23×C4—1664no—
526C23×C4—1664no—
527C23×C4—1664no—
528C23×C4—1664no—
529C23×C4C22×D8311yescharacteristic
530C23×C4C22×D8311yescharacteristic
531C23×C4C22×D8311yescharacteristic
532C23×C4C22×D8311yescharacteristic
533C23×C4C22×D8311yescharacteristic
534C23×C4C22×D8311yescharacteristic
535C23×C4C22×D8311yescharacteristic
536C22⋊Q8—16632no—
537C22⋊Q8—16632no—
538C4×D4—16632no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—3322no—
541C2×C4⋊C4—834no—
542C2×C4⋊C4—834no—
543C2×C4⋊C4—834no—
544C2×C4⋊C4—834no—
545C2×C4⋊C4—834no—
546C2×C4⋊C4—834no—
547C2×C4⋊C4—834no—
548C2×C4⋊C4—834no—
549C2×C4⋊C4—834no—
550C2×C4⋊C4—834no—
551C2×C4⋊C4—1664no—
552C2×C4⋊C4—1664no—
553C2×C4⋊C4—1664no—
554C2×C4⋊C4—1664no—
555C2×C4⋊C4—1664no—
556C2×C4⋊C4—1664no—
557C2×C4⋊C4—1664no—
558C2×C4⋊C4—1664no—
559C2×C4⋊C4—1664no—
560C2×C4⋊C4—16632no—
561C2×C4⋊C4D33218yescomplemented
562C2×C4⋊C4C22×D8314yes—
563C2×C4⋊C4C22×D8314yes—
564C2×C22⋊C4—3322no—
565C2×C22⋊C4—834no—
566C2×C22⋊C4—838no—
567C2×C22⋊C4—834no—
568C2×C22⋊C4—834no—
569C2×C22⋊C4—834no—
570C2×C22⋊C4—834no—
571C2×C22⋊C4—834no—
572C2×C22⋊C4—834no—
573C2×C22⋊C4—834no—
574C2×C22⋊C4—1664no—
575C2×C22⋊C4—1664no—
576C2×C22⋊C4—1664no—
577C2×C22⋊C4—1664no—
578C2×C22⋊C4—1664no—
579C2×C22⋊C4—1664no—
580C2×C42—24no—
581C2×C42C22×D8314yes—
582#95—834no—
583#95—834no—
584#95—834no—
585#95—834no—
586#95C22×D8314yes—
587#95C22×D8314yes—
588#95C22×D8314yes—
589#95C22×D8314yes—
590C24—834no—
591C24—834no—
592C24—834no—
593C24—832no—
594C24—834no—
595C24—832no—
596C24—1662no—
597C24—1662no—
598C24—1662no—
599C24—1662no—
600C24—1662no—
601C24—1662no—
602C24—1662no—
603C24—1662no—
604C24—1662no—
605C24—1662no—
606C24C23×D8311yescharacteristic
607C2×Q8—33216no—
608C2×Q8—3324no—
609C2×Q8—1668no—
610C2×Q8—1668no—
611C2×D4—8316no—
612C2×D4—1668no—
613C2×D4—16632no—
614C2×D4—1668no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—33216no—
632C22×C4—33216no—
633C22×C4—33216no—
634C22×C4—3324no—
635C22×C4—3324no—
636C22×C4—3324no—
637C22×C4—834no—
638C22×C4—834no—
639C22×C4—832no—
640C22×C4—832no—
641C22×C4—832no—
642C22×C4—832no—
643C22×C4—832no—
644C22×C4—832no—
645C22×C4—1668no—
646C22×C4—1668no—
647C22×C4—1668no—
648C22×C4—1668no—
649C22×C4—1668no—
650C22×C4—16632no—
651C22×C4—1662no—
652C22×C4—1662no—
653C22×C4—1662no—
654C22×C4—1662no—
655C22×C4—1662no—
656C22×C4—1662no—
657C22×C4—1662no—
658C22×C4—1662no—
659C22×C4—1662no—
660C22×C4—1662no—
661C22×C4—1662no—
662C22×C4—1662no—
663C22×C4—1668no—
664C22×C4—1668no—
665C22×C4—1668no—
666C22×C4—1662no—
667C22×C4—1662no—
668C22×C4—1662no—
669C22×C4—1662no—
670C22×C4—1668no—
671C22×C4D4×D8314yes—
672C22×C4C2×D33214yes—
673C22×C4C2×D33214yes—
674C22×C4C2×D33214yes—
675C22×C4Q8×D8314yes—
676C22×C4C23×D8312yes—
677C22×C4C23×D8312yes—
678C22×C4C23×D8312yes—
679C22×C4C23×D8312yes—
680C22×C4C23×D8312yes—
681C22×C4C23×D8312yes—
682C22×C4C23×D8312yes—
683C4⋊C4—28no—
684C4⋊C4—3324no—
685C4⋊C4—1668no—
686C4⋊C4—1668no—
687C4⋊C4—1668no—
688C4⋊C4—1668no—
689C4⋊C4—1668no—
690C4⋊C4—1668no—
691C4⋊C4—1668no—
692C4⋊C4—1668no—
693C4⋊C4—1668no—
694C4⋊C4C2×D332116yescomplemented
695C22⋊C4—3324no—
696C22⋊C4—8316no—
697C22⋊C4—1668no—
698C22⋊C4—1668no—
699C22⋊C4—1668no—
700C22⋊C4—1668no—
701C22⋊C4—1668no—
702C22⋊C4—1668no—
703C42—28no—
704C23—3324no—
705C23—3324no—
706C23—3324no—
707C23—3324no—
708C23—8316no—
709C23—834no—
710C23—834no—
711C23—834no—
712C23—834no—
713C23—1668no—
714C23—1668no—
715C23—1668no—
716C23—1662no—
717C23—1662no—
718C23—1662no—
719C23—1662no—
720C23—1662no—
721C23—1662no—
722C23—1668no—
723C23—1668no—
724C23—1668no—
725C23—1668no—
726C23—1668no—
727C23—1662no—
728C23—1662no—
729C23—1662no—
730C23—1662no—
731C23—1668no—
732C23C2×D4×D8312yes—
733C23C22×D33212yes—
734C23C2×Q8×D8312yes—
735C23#41×D8312yes—
736C23#41×D8312yes—
737C23#1458183812yes—
738C23#1458183912yes—
739C23C24×D8311yescharacteristic
740Q8—33216no—
741D4—16632no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—28no—
745C2×C4—28no—
746C2×C4—28no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—33216no—
766C2×C4—33216no—
767C2×C4—33216no—
768C2×C4—3324no—
769C2×C4—3324no—
770C2×C4—3324no—
771C2×C4—3324no—
772C2×C4—834no—
773C2×C4—834no—
774C2×C4—16632no—
775C2×C4—1662no—
776C2×C4—1662no—
777C2×C4—1662no—
778C2×C4—1662no—
779C2×C4—1662no—
780C2×C4—1662no—
781C2×C4—1662no—
782C2×C4—1662no—
783C2×C4—1662no—
784C2×C4—1662no—
785C2×C4—1662no—
786C2×C4—1662no—
787C2×C4—1668no—
788C2×C4—1668no—
789C2×C4—1662no—
790C2×C4—1662no—
791C2×C4—1662no—
792C2×C4—1662no—
793C2×C4C2×D4×D8314yes—
794C2×C4C22×D33214yes—
795C2×C4C22×D33214yes—
796C2×C4C22×D33214yes—
797C2×C4C2×Q8×D8314yes—
798C22—3322no—
799C22—3322no—
800C22—3322no—
801C22—33216no—
802C22—3322no—
803C22—838no—
804C22—1664no—
805C22—1664no—
806C22—1664no—
807C22—1664no—
808C22—1664no—
809C22—1664no—
810C22—1664no—
811C22—1664no—
812C22—16632no—
813C22—1664no—
814C22C22⋊Q8×D8314yes—
815C22#1912821314yes—
816C22#1912829214yes—
817C22D4×D33214yes—
818C22#1912834914yes—
819C22Q8×D33214yes—
820C22#1912840714yes—
821C22C22×D4×D8311yescharacteristic
822C22C23×D33211yescharacteristic
823C22C22×Q8×D8311yescharacteristic
824C22C2×#41×D8311yescharacteristic
825C22C2×#41×D8311yescharacteristic
826C22C2×#1458183811yescharacteristic
827C22C2×#1458183911yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—3322no—
836C4—3322no—
837C4—3322no—
838C4—3322no—
839C4—1664no—
840C4—1664no—
841C2—3324no—
842C2—1668no—
843C2#2491127718yesdirect product factor
844C2C2×C22⋊Q8×D8311yescharacteristic
845C2C2×#1912821311yescharacteristic
846C2C2×#1912829211yescharacteristic
847C2C2×D4×D33211yescharacteristic
848C2C2×#1912834911yescharacteristic
849C2C2×Q8×D33211yescharacteristic
850C2C2×#1912840711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#387×C83C2
socleC24×C83C24
prime radicalC23×D332C22
hypercenterC2×#387D83
hypocenterC83C2×#2449
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#14581772C2semidirect
2. C22×#14581770C2semidirect
4. C22×C4⋊C4×D83C2semidirect
5. #24911277C2direct (N × H)
6. C2×#19127638C2semidirect
7. C2×#19127633C2semidirect
8. C2×#19127623C2semidirect
9. C2×#19127622C2semidirect
10. C2×#19127599C2semidirect
13. C2×#19127575C2semidirect
14. C2×#19127575C2semidirect
15. C2×#19127575C2semidirect
16. C2×#387×C83C2semidirect
24. C2×#14581772C22semidirect
26. C2×#14581770C22semidirect
40. C2×C4⋊C4×D83C22semidirect
49. #19127638C22semidirect
50. #19127633C22semidirect
51. #19127623C22semidirect
52. #19127622C22semidirect
53. #19127599C22semidirect
56. #19127575C22semidirect
57. #19127575C22semidirect
58. #19127575C22semidirect
66. #387×C83C22semidirect
79. C22×D332Q8semidirect
155. C2×C4⋊C4×C83D4semidirect
187. C2×D332C2×Q8semidirect
276. C4⋊C4×C83C2×D4semidirect
309. C22×D83C22⋊Q8semidirect
401. C2×D83C2×C22⋊Q8semidirect
416. C2×C83#2449semidirect
436. C2×#387D83semidirect
442. C83C2×#2449semidirect
483. #387C2×D83semidirect
561. C2×C4⋊C4D332semidirect
694. C4⋊C4C2×D332semidirect
843. C2#24911277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817722
C22×#145817702
C22×C4×D3322
C22×C4⋊C4×D832
#249112772
C2×#191276382
C2×#191276332
C2×#191276232
C2×#191276222
C2×#191275992
C2×#191275792
C2×#191275752
C2×#387×C832
C2×#244983