Finite Group Databasebeta

← C2×#24911430 #35572263

Subgroups — C2×#24911430 #35572263

Order 21248.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581780C211yesmaximal, characteristic, complemented
2C22×#14581777C211yesmaximal, characteristic, complemented
3C22×#14581770C211yesmaximal, characteristic, complemented
4C22×C4×D332C211yesmaximal, characteristic, complemented
5#24911430C2116yesmaximal, direct product factor
6C2×#19127623C211yesmaximal, characteristic, complemented
7C2×#19127622C211yesmaximal, characteristic, complemented
8C2×#19127618C211yesmaximal, characteristic, complemented
9C2×#19127611C211yesmaximal, characteristic
10C2×#19127603C211yesmaximal, characteristic, complemented
11C2×#19127592C211yesmaximal, characteristic, complemented
12C2×#19127592C211yesmaximal, characteristic, complemented
13C2×#19127592C211yesmaximal, characteristic, complemented
14C2×#19127579C211yesmaximal, characteristic, complemented
15C2×#19127575C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×D332C2211yescharacteristic
19C23×D332C2211yescharacteristic
20C23×D332C2211yescharacteristic
21C23×C4×D83C2211yescharacteristic
22C23×C4×D83C2211yescharacteristic
23C2×#14581780—28no—
24C2×#14581780C2218yescomplemented
25C2×#14581777—28no—
26C2×#14581777C2218yescomplemented
27C2×#14581770—28no—
28C2×#14581770C2218yescomplemented
29C2×C4×D332—28no—
30C2×C4×D332C2218yescomplemented
31C22×C4⋊Dic83C2211yescharacteristic
32C22×C4⋊Dic83C2211yescharacteristic
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×(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#19127623C2218yescomplemented
50#19127622C2218yescomplemented
51#19127618C2218yescomplemented
52#19127611C2218yes—
53#19127603C2218yescomplemented
54#19127592C2218yescomplemented
55#19127592C2218yescomplemented
56#19127592C2218yescomplemented
57#19127579C2218yescomplemented
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
66C22×C42×C83C2211yescharacteristic
67C22×C42×C83C2211yescharacteristic
68C4×C4⋊C4×C83C2218yescomplemented
69C2×#95×C83C2211yescharacteristic
70C2×#95×C83C2211yescharacteristic
71C24×D83C2311yescharacteristic
72C24×D83C2311yescharacteristic
73C24×D83C2311yescharacteristic
74C22×Dic166—24no—
75C22×Dic166—24no—
76C22×Dic166—42no—
77C22×Dic166C2314yes—
78C22×D332—24no—
79C22×D332—24no—
80C22×D332—24no—
81C22×D332—24no—
82C22×D332—24no—
83C22×D332—24no—
84C22×D332—24no—
85C22×D332—42no—
86C22×D332—42no—
87C22×D332C2314yes—
88C22×D332C2314yes—
89C22×D332C2314yes—
90C23×Dic83C2311yescharacteristic
91C23×Dic83C2311yescharacteristic
92C23×Dic83C2311yescharacteristic
93C23×Dic83C2311yescharacteristic
94C23×Dic83C2311yescharacteristic
95C22×C4×D83—24no—
96C22×C4×D83—24no—
97C22×C4×D83—24no—
98C22×C4×D83—24no—
99C22×C4×D83—42no—
100C22×C4×D83—42no—
101C22×C4×D83C2314yes—
102C22×C4×D83C2314yes—
103#14581780—232no—
104#14581777—232no—
105#14581770—232no—
106C4×D332—232no—
107C2×C4⋊Dic83—24no—
108C2×C4⋊Dic83—42no—
109C2×C4⋊Dic83C2314yes—
110C2×C4⋊Dic83C2314yes—
111C2×Dic83⋊C4—24no—
112C2×Dic83⋊C4—24no—
113C2×Dic83⋊C4—24no—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C2×Dic83⋊C4C2314yes—
117C2×(C2×D83)⋊C4—24no—
118C2×(C2×D83)⋊C4—24no—
119C2×(C2×D83)⋊C4—24no—
120C2×(C2×D83)⋊C4—24no—
121C2×(C2×D83)⋊C4—24no—
122C2×(C2×D83)⋊C4—24no—
123C2×(C2×D83)⋊C4—24no—
124C2×(C2×D83)⋊C4—24no—
125C2×(C2×D83)⋊C4—24no—
126C2×(C2×D83)⋊C4—24no—
127C2×(C2×D83)⋊C4—24no—
128C2×(C2×D83)⋊C4—24no—
129C2×(C2×D83)⋊C4D418yescomplemented
130C2×(C2×D83)⋊C4C2314yes—
131C2×(C2×D83)⋊C4C2314yes—
132C2×(C2×D83)⋊C4C2314yes—
133C2×(C2×D83)⋊C4C2314yes—
134C2×(C2×D83)⋊C4C2314yes—
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×C83—24no—
160C2×C42×C83—24no—
161C2×C42×C83C2314yes—
162C2×C42×C83C2314yes—
163C2×C42×C83C2314yes—
164#95×C83C2314yes—
165#95×C83C2314yes—
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×D83—22no—
175C23×D83—22no—
176C23×D83—22no—
177C23×D83—22no—
178C23×D83—22no—
179C23×D83—22no—
180C23×D83—22no—
181C23×D83—22no—
182C23×D83—22no—
183C23×D83—22no—
184C23×D83—22no—
185C23×D83C2×D414yes—
186C23×D83#4114yes—
187C23×D83C2412yes—
188C23×D83C2412yes—
189C23×D83C2412yes—
190C2×Dic166—28no—
191C2×Dic166—28no—
192C2×Dic166—44no—
193C2×Dic166—416no—
194C2×D332—232no—
195C2×D332—28no—
196C2×D332—28no—
197C2×D332—28no—
198C2×D332—28no—
199C2×D332—28no—
200C2×D332—28no—
201C2×D332—28no—
202C2×D332—44no—
203C2×D332—44no—
204C2×D332—416no—
205C2×D332—416no—
206C22×Dic83—22no—
207C22×Dic83—22no—
208C22×Dic83—22no—
209C22×Dic83—22no—
210C22×Dic83—22no—
211C22×Dic83—22no—
212C22×Dic83—22no—
213C22×Dic83—22no—
214C22×Dic83—22no—
215C22×Dic83—22no—
216C22×Dic83—22no—
217C22×Dic83—22no—
218C22×Dic83—22no—
219C22×Dic83—22no—
220C22×Dic83C2×D414yes—
221C22×Dic83C2412yes—
222C22×Dic83C2412yes—
223C22×Dic83C2412yes—
224C22×Dic83C2412yes—
225C22×Dic83C2412yes—
226C2×C4×D83—28no—
227C2×C4×D83—28no—
228C2×C4×D83—28no—
229C2×C4×D83—28no—
230C2×C4×D83—44no—
231C2×C4×D83—44no—
232C2×C4×D83—416no—
233C2×C4×D83—416no—
234C4⋊Dic83—28no—
235C4⋊Dic83—44no—
236Dic83⋊C4—28no—
237Dic83⋊C4—28no—
238Dic83⋊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—28no—
245(C2×D83)⋊C4—28no—
246(C2×D83)⋊C4—28no—
247(C2×D83)⋊C4—28no—
248(C2×D83)⋊C4—28no—
249(C2×D83)⋊C4—28no—
250(C2×D83)⋊C4—28no—
251(C2×D83)⋊C4C2×D4116yescomplemented
252C24×C83C2411yescharacteristic
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×C83—22no—
264C22×C4×C83—22no—
265C22×C4×C83—22no—
266C22×C4×C83—22no—
267C22×C4×C83—22no—
268C22×C4×C83C2×D414yes—
269C22×C4×C83C2×D414yes—
270C22×C4×C83C2×D414yes—
271C22×C4×C83C2×D414yes—
272C22×C4×C83#4114yes—
273C22×C4×C83#4114yes—
274C22×C4×C83C2412yes—
275C22×C4×C83C2412yes—
276C22×C4×C83C2412yes—
277C22×C4×C83C2412yes—
278C22×C4×C83C2412yes—
279C22×C4×C83C2412yes—
280C22×C4×C83C2412yes—
281C4⋊C4×C83—28no—
282C4⋊C4×C83C2×D4116yescomplemented
283C42×C83—28no—
284C42×C83—28no—
285C42×C83—28no—
286C23×C83C22×D412yes—
287C23×C83C22×D412yes—
288C23×C83C2×#4112yes—
289C23×C83C2×#4112yes—
290C23×C83C2×#4112yes—
291C23×C83H(5,𝔽2)12yes—
292C23×C832−1+412yes—
293C23×C83C2511yescharacteristic
294C22×D83—28no—
295C22×D83—28no—
296C22×D83—28no—
297C22×D83—28no—
298C22×D83—28no—
299C22×D83—28no—
300C22×D83—22no—
301C22×D83—22no—
302C22×D83—22no—
303C22×D83—22no—
304C22×D83—22no—
305C22×D83—22no—
306C22×D83—22no—
307C22×D83—22no—
308C22×D83—22no—
309C22×D83—22no—
310C22×D83—22no—
311C22×D83—22no—
312C22×D83—22no—
313C22×D83—22no—
314C22×D83—22no—
315C22×D83—22no—
316C22×D83—22no—
317C22×D83—22no—
318C22×D83—22no—
319C22×D83—44no—
320C22×D83—44no—
321C22×D83—44no—
322C22×D83—44no—
323C22×D83—44no—
324C22×D83—44no—
325C22×D83—44no—
326C22×D83—44no—
327C22×D83—44no—
328C22×D83—44no—
329C22×D83—44no—
330C22×D83—44no—
331C22×D83—44no—
332C22×D83—44no—
333C22×D83—44no—
334C22×D83C22×D414yes—
335C22×D83C2×#4114yes—
336C2×C4×C83—28no—
337C2×C4×C83—28no—
338C2×C4×C83—28no—
339C2×C4×C83—28no—
340C2×C4×C83—28no—
341C2×C4×C83—28no—
342C2×C4×C83—22no—
343C2×C4×C83—22no—
344C2×C4×C83—22no—
345C2×C4×C83—22no—
346C2×C4×C83—22no—
347C2×C4×C83—22no—
348C2×C4×C83—22no—
349C2×C4×C83—22no—
350C2×C4×C83—22no—
351C2×C4×C83—22no—
352C2×C4×C83—22no—
353C2×C4×C83—22no—
354C2×C4×C83—22no—
355C2×C4×C83—22no—
356C2×C4×C83—22no—
357C2×C4×C83—44no—
358C2×C4×C83C22×D414yes—
359C2×C4×C83C22×D414yes—
360C2×C4×C83C22×D414yes—
361C2×C4×C83C22×D414yes—
362C2×C4×C83C2×#4114yes—
363C2×C4×C83C2×#4114yes—
364C2×Dic83—28no—
365C2×Dic83—22no—
366C2×Dic83—22no—
367C2×Dic83—22no—
368C2×Dic83—22no—
369C2×Dic83—22no—
370C2×Dic83—22no—
371C2×Dic83—22no—
372C2×Dic83—22no—
373C2×Dic83—22no—
374C2×Dic83—22no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—22no—
378C2×Dic83—22no—
379C2×Dic83—44no—
380C2×Dic83—44no—
381C2×Dic83—44no—
382C2×Dic83—44no—
383C2×Dic83C22×D414yes—
384D332—232no—
385D332—416no—
386D332—416no—
387C4×D83—416no—
388C4×D83—416no—
389Dic166—416no—
390C22×C83#52514yes—
391C22×C83#53214yes—
392C22×C83#54214yes—
393C22×C83D4214yes—
394C22×C83#54714yes—
395C22×C83#54814yes—
396C22×C83#55114yes—
397C22×C83C23×D411yescharacteristic
398C22×C83C23×D411yescharacteristic
399C22×C83C22×#4111yescharacteristic
400C22×C83C22×#4111yescharacteristic
401C22×C83C22×#4111yescharacteristic
402C22×C83C2×H(5,𝔽2)11yescharacteristic
403C22×C83C2×2−1+411yescharacteristic
404C2×D83—24no—
405C2×D83—24no—
406C2×D83—24no—
407C2×D83—24no—
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—42no—
411C2×D83—42no—
412C2×D83—42no—
413C2×D83—42no—
414C2×D83—42no—
415C2×D83—42no—
416C2×D83—42no—
417C2×D83—42no—
418C2×D83—416no—
419C2×D83—416no—
420C2×D83—42no—
421C2×D83—42no—
422C2×D83—42no—
423C2×D83—42no—
424C2×D83—42no—
425C2×D83—42no—
426C2×D83—42no—
427C2×D83—88no—
428C4×C83—24no—
429C4×C83—24no—
430C4×C83—24no—
431C4×C83—24no—
432C4×C83—24no—
433C4×C83—24no—
434C4×C83—42no—
435Dic83—24no—
436Dic83—42no—
437Dic83—42no—
438Dic83—42no—
439Dic83—42no—
440C2×#2461—831nomaximal, Sylow
441C2×C83#246118yescomplemented
442C2×C83C2×#52511yescharacteristic
443C2×C83C2×#53211yescharacteristic
444C2×C83C2×#54211yescharacteristic
445C2×C83C2×D4211yescharacteristic
446C2×C83C2×#54711yescharacteristic
447C2×C83C2×#54811yescharacteristic
448C2×C83C2×#55111yescharacteristic
449D83—44no—
450D83—44no—
451D83—82no—
452C22×#124—831no—
453C22×#123—831no—
454C22×C22⋊Q8—831no—
455C22×C4×D4—831no—
456#2461—8316no—
457C2×#396—831no—
458C2×#395—831no—
459C2×#394—831no—
460C2×#392—831no—
461C2×#390—831no—
462C2×#388—831no—
463C2×#388—831no—
464C2×#388—831no—
465C2×#386—831no—
466C2×#385—831no—
467C2×C4×C4⋊C4D8311yescharacteristic, complemented
468C83C2×#246111yescharacteristic, complemented, Sylow
469C23×Q8—831no—
470C23×D4—831no—
471C23×D4—831no—
472C23×D4—831no—
473C24×C4—831no—
474C24×C4—831no—
475C2×#124—838no—
476C2×#124—1668no—
477C2×#123—838no—
478C2×#123—1668no—
479C2×C22⋊Q8—838no—
480C2×C22⋊Q8—1668no—
481C2×C4×D4—838no—
482C2×C4×D4—1668no—
483C22×C4⋊C4—831no—
484C22×C4⋊C4—831no—
485C22×C4⋊C4—831no—
486C22×C4⋊C4—831no—
487C22×C4⋊C4—831no—
488C22×C4⋊C4C2×D8311yescharacteristic
489C22×C4⋊C4C2×D8311yescharacteristic
490C22×C22⋊C4—831no—
491C22×C22⋊C4—831no—
492C22×C22⋊C4—831no—
493C22×C22⋊C4—831no—
494C22×C22⋊C4—831no—
495C22×C22⋊C4—831no—
496C22×C22⋊C4—831no—
497C22×C22⋊C4—831no—
498C22×C22⋊C4—831no—
499C22×C22⋊C4—831no—
500C22×C22⋊C4—831no—
501C22×C22⋊C4—831no—
502C22×C22⋊C4—831no—
503C22×C42C2×D8311yescharacteristic
504C22×C42C2×D8311yescharacteristic
505C22×C42C2×D8311yescharacteristic
506#396—838no—
507#395—838no—
508#394—838no—
509#392—838no—
510#390—838no—
511#388—838no—
512#388—838no—
513#388—838no—
514#386—838no—
515#385—838no—
516C4×C4⋊C4C2×D8318yescomplemented
517C2×#95—831no—
518C2×#95—831no—
519C2×#95—831no—
520C2×#95—831no—
521C2×#95C2×D8311yescharacteristic
522C2×#95C2×D8311yescharacteristic
523C25—831no—
524C25—831no—
525C25—831no—
526C22×Q8—3322no—
527C22×Q8—834no—
528C22×Q8—1664no—
529C22×Q8—1664no—
530C22×D4—3322no—
531C22×D4—3322no—
532C22×D4—834no—
533C22×D4—834no—
534C22×D4—834no—
535C22×D4—1664no—
536C22×D4—1664no—
537C22×D4—1664no—
538C22×D4—1664no—
539C22×D4—1664no—
540C22×D4—1664no—
541C22×D4—1664no—
542C23×C4—3322no—
543C23×C4—3322no—
544C23×C4—834no—
545C23×C4—834no—
546C23×C4—831no—
547C23×C4—831no—
548C23×C4—831no—
549C23×C4—831no—
550C23×C4—831no—
551C23×C4—1664no—
552C23×C4—1664no—
553C23×C4—1664no—
554C23×C4—1664no—
555C23×C4C22×D8311yescharacteristic
556C23×C4C22×D8311yescharacteristic
557C23×C4C22×D8311yescharacteristic
558C23×C4C22×D8311yescharacteristic
559C23×C4C22×D8311yescharacteristic
560C23×C4C22×D8311yescharacteristic
561C23×C4C22×D8311yescharacteristic
562#124—16632no—
563#123—16632no—
564C22⋊Q8—16632no—
565C4×D4—16632no—
566C2×C4⋊C4—24no—
567C2×C4⋊C4—3322no—
568C2×C4⋊C4—834no—
569C2×C4⋊C4—834no—
570C2×C4⋊C4—834no—
571C2×C4⋊C4—834no—
572C2×C4⋊C4—834no—
573C2×C4⋊C4—1664no—
574C2×C4⋊C4—1664no—
575C2×C4⋊C4—1664no—
576C2×C4⋊C4—1664no—
577C2×C4⋊C4D33218yescomplemented
578C2×C4⋊C4C22×D8314yes—
579C2×C4⋊C4C22×D8314yes—
580C2×C22⋊C4—838no—
581C2×C22⋊C4—834no—
582C2×C22⋊C4—834no—
583C2×C22⋊C4—834no—
584C2×C22⋊C4—834no—
585C2×C22⋊C4—834no—
586C2×C22⋊C4—834no—
587C2×C22⋊C4—834no—
588C2×C22⋊C4—834no—
589C2×C22⋊C4—834no—
590C2×C22⋊C4—834no—
591C2×C22⋊C4—834no—
592C2×C22⋊C4—834no—
593C2×C22⋊C4—834no—
594C2×C22⋊C4—1664no—
595C2×C22⋊C4—1664no—
596C2×C22⋊C4—1664no—
597C2×C22⋊C4—1664no—
598C2×C22⋊C4—1664no—
599C2×C22⋊C4—1664no—
600C2×C22⋊C4—1664no—
601C2×C22⋊C4—1664no—
602C2×C22⋊C4—1664no—
603C2×C22⋊C4—1664no—
604C2×C22⋊C4—1664no—
605C2×C22⋊C4—1664no—
606C2×C42—24no—
607C2×C42—24no—
608C2×C42—24no—
609C2×C42C22×D8314yes—
610C2×C42C22×D8314yes—
611C2×C42C22×D8314yes—
612#95—834no—
613#95—834no—
614#95—834no—
615#95—834no—
616#95C22×D8314yes—
617#95C22×D8314yes—
618C24—834no—
619C24—834no—
620C24—832no—
621C24—832no—
622C24—832no—
623C24—1662no—
624C24—1662no—
625C24—1662no—
626C24—1662no—
627C24—1662no—
628C24—1662no—
629C24—1662no—
630C24—1662no—
631C24—1662no—
632C24—1662no—
633C24—1662no—
634C24—1662no—
635C24—1662no—
636C24—1662no—
637C24—1662no—
638C24—1662no—
639C24—1662no—
640C24—1662no—
641C24—1662no—
642C24C23×D8311yescharacteristic
643C2×Q8—33216no—
644C2×Q8—3324no—
645C2×Q8—1668no—
646C2×Q8—1668no—
647C2×D4—33216no—
648C2×D4—33216no—
649C2×D4—3324no—
650C2×D4—3324no—
651C2×D4—1668no—
652C2×D4—1668no—
653C2×D4—1668no—
654C2×D4—1668no—
655C2×D4—16632no—
656C2×D4—1668no—
657C2×D4—1668no—
658C2×D4—1668no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—22no—
674C22×C4—33216no—
675C22×C4—33216no—
676C22×C4—3324no—
677C22×C4—3324no—
678C22×C4—834no—
679C22×C4—832no—
680C22×C4—832no—
681C22×C4—832no—
682C22×C4—832no—
683C22×C4—832no—
684C22×C4—1668no—
685C22×C4—1668no—
686C22×C4—1662no—
687C22×C4—1662no—
688C22×C4—1662no—
689C22×C4—1662no—
690C22×C4—1662no—
691C22×C4—1662no—
692C22×C4—1662no—
693C22×C4—1662no—
694C22×C4—1662no—
695C22×C4—1662no—
696C22×C4—1662no—
697C22×C4—1662no—
698C22×C4—1668no—
699C22×C4—1668no—
700C22×C4—1662no—
701C22×C4—1662no—
702C22×C4D4×D8314yes—
703C22×C4C2×D33214yes—
704C22×C4C2×D33214yes—
705C22×C4C2×D33214yes—
706C22×C4#1305059014yes—
707C22×C4#1305059014yes—
708C22×C4C23×D8312yes—
709C22×C4C23×D8312yes—
710C22×C4C23×D8312yes—
711C22×C4C23×D8312yes—
712C22×C4C23×D8312yes—
713C22×C4C23×D8312yes—
714C22×C4C23×D8312yes—
715C4⋊C4—28no—
716C4⋊C4—3324no—
717C4⋊C4—1668no—
718C4⋊C4—1668no—
719C4⋊C4—1668no—
720C4⋊C4—1668no—
721C4⋊C4C2×D332116yescomplemented
722C22⋊C4—8316no—
723C22⋊C4—1668no—
724C22⋊C4—1668no—
725C22⋊C4—1668no—
726C22⋊C4—1668no—
727C22⋊C4—1668no—
728C22⋊C4—1668no—
729C22⋊C4—1668no—
730C22⋊C4—1668no—
731C22⋊C4—1668no—
732C22⋊C4—1668no—
733C22⋊C4—1668no—
734C22⋊C4—1668no—
735C42—28no—
736C42—28no—
737C42—28no—
738C23—3324no—
739C23—3324no—
740C23—3324no—
741C23—3324no—
742C23—3324no—
743C23—3324no—
744C23—3324no—
745C23—3324no—
746C23—3324no—
747C23—3324no—
748C23—3324no—
749C23—3324no—
750C23—3324no—
751C23—3324no—
752C23—3324no—
753C23—834no—
754C23—834no—
755C23—1662no—
756C23—1662no—
757C23—1662no—
758C23—1662no—
759C23—1662no—
760C23—1662no—
761C23—1662no—
762C23—1668no—
763C23—1668no—
764C23—1668no—
765C23—1668no—
766C23—1668no—
767C23—1668no—
768C23—1662no—
769C23—1662no—
770C23—1662no—
771C23—1662no—
772C23—1662no—
773C23—1662no—
774C23—1662no—
775C23—1662no—
776C23—1662no—
777C23—1662no—
778C23—1662no—
779C23—1662no—
780C23C2×D4×D8312yes—
781C23C22×D33212yes—
782C23#41×D8312yes—
783C23C2×#1305059012yes—
784C23C2×#1305059012yes—
785C23#1458183812yes—
786C23#1458184012yes—
787C23C24×D8311yescharacteristic
788Q8—33216no—
789D4—33216no—
790D4—33216no—
791D4—16632no—
792C2×C4—28no—
793C2×C4—28no—
794C2×C4—28no—
795C2×C4—28no—
796C2×C4—28no—
797C2×C4—28no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—44no—
814C2×C4—33216no—
815C2×C4—33216no—
816C2×C4—3324no—
817C2×C4—3324no—
818C2×C4—3324no—
819C2×C4—3324no—
820C2×C4—834no—
821C2×C4—1662no—
822C2×C4—1662no—
823C2×C4—1662no—
824C2×C4—1662no—
825C2×C4—1662no—
826C2×C4—1662no—
827C2×C4—1662no—
828C2×C4—1662no—
829C2×C4—1662no—
830C2×C4—1662no—
831C2×C4—1662no—
832C2×C4—1662no—
833C2×C4—1668no—
834C2×C4—1662no—
835C2×C4—1662no—
836C2×C4C2×D4×D8314yes—
837C2×C4C22×D33214yes—
838C2×C4C22×D33214yes—
839C2×C4C22×D33214yes—
840C2×C4C2×#1305059014yes—
841C2×C4C2×#1305059014yes—
842C22—3322no—
843C22—3322no—
844C22—33216no—
845C22—33216no—
846C22—3322no—
847C22—3322no—
848C22—3322no—
849C22—3322no—
850C22—3322no—
851C22—3322no—
852C22—3322no—
853C22—3322no—
854C22—3322no—
855C22—3322no—
856C22—3322no—
857C22—3322no—
858C22—3322no—
859C22—6648no—
860C22—1664no—
861C22—1664no—
862C22—1664no—
863C22—1664no—
864C22—1664no—
865C22—1664no—
866C22#1912821014yes—
867C22#1912825114yes—
868C22#1912832314yes—
869C22D4×D33214yes—
870C22#1912835214yes—
871C22#1912836314yes—
872C22#1912837514yes—
873C22C22×D4×D8311yescharacteristic
874C22C23×D33211yescharacteristic
875C22C2×#41×D8311yescharacteristic
876C22C22×#1305059011yescharacteristic
877C22C22×#1305059011yescharacteristic
878C22C2×#1458183811yescharacteristic
879C22C2×#1458184011yescharacteristic
880C4—24no—
881C4—24no—
882C4—24no—
883C4—24no—
884C4—24no—
885C4—24no—
886C4—42no—
887C4—3322no—
888C4—3322no—
889C4—3322no—
890C4—3322no—
891C4—1664no—
892C2—3324no—
893C2—3324no—
894C2—6642no—
895C2#2491143018yesdirect product factor
896C2C2×#1912821011yescharacteristic
897C2C2×#1912825111yescharacteristic
898C2C2×#1912832311yescharacteristic
899C2C2×D4×D33211yescharacteristic
900C2C2×#1912835211yescharacteristic
901C2C2×#1912836311yescharacteristic
902C2C2×#1912837511yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×C4×C4⋊C4×C83C2
socleC24×C83C24
prime radicalC2×#19127611C2
hypercenterC2×C4×C4⋊C4D83
hypocenterC83C2×#2461
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#14581780C2semidirect
2. C22×#14581777C2semidirect
3. C22×#14581770C2semidirect
4. C22×C4×D332C2semidirect
5. #24911430C2direct (N × H)
6. C2×#19127623C2semidirect
7. C2×#19127622C2semidirect
8. C2×#19127618C2semidirect
10. C2×#19127603C2semidirect
11. C2×#19127592C2semidirect
12. C2×#19127592C2semidirect
13. C2×#19127592C2semidirect
14. C2×#19127579C2semidirect
15. C2×#19127575C2semidirect
16. C2×C4×C4⋊C4×C83C2semidirect
24. C2×#14581780C22semidirect
26. C2×#14581777C22semidirect
28. C2×#14581770C22semidirect
30. C2×C4×D332C22semidirect
49. #19127623C22semidirect
50. #19127622C22semidirect
51. #19127618C22semidirect
53. #19127603C22semidirect
54. #19127592C22semidirect
55. #19127592C22semidirect
56. #19127592C22semidirect
57. #19127579C22semidirect
58. #19127575C22semidirect
68. C4×C4⋊C4×C83C22semidirect
129. C2×(C2×D83)⋊C4D4semidirect
155. C2×C4⋊C4×C83D4semidirect
251. (C2×D83)⋊C4C2×D4semidirect
282. C4⋊C4×C83C2×D4semidirect
441. C2×C83#2461semidirect
467. C2×C4×C4⋊C4D83semidirect
468. C83C2×#2461semidirect
516. C4×C4⋊C4C2×D83semidirect
577. C2×C4⋊C4D332semidirect
721. C4⋊C4C2×D332semidirect
895. C2#24911430direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145817802
C22×#145817772
C22×#145817702
C22×C4×D3322
#249114302
C2×#191276232
C2×#191276222
C2×#191276182
C2×#191276112
C2×#191276032
C2×#191275922
C2×#191275792
C2×#191275752
C2×C4×C4⋊C4×C832
C2×#246183