Finite Group Databasebeta

← #35577426

Subgroups — #35577426

Order 21248.

2930 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊Q8×D83C211yesmaximal, characteristic, complemented
2C2×C4×D4×D83C211yesmaximal, characteristic
3#24915798C212yesmaximal, complemented
4#24915749C212yesmaximal, complemented
5#24913277C211yesmaximal, characteristic, complemented
6#24913275C211yesmaximal, characteristic, complemented
7#24913269C211yesmaximal, characteristic, complemented
8#24913267C211yesmaximal, characteristic, complemented
9#24912814C212yesmaximal, complemented
10#24912808C212yesmaximal, complemented
11#24912645C211yesmaximal, characteristic, complemented
12#24912643C211yesmaximal, characteristic, complemented
13#24912639C211yesmaximal, characteristic, complemented
14#24911775C211yesmaximal, characteristic, complemented
15#24911773C211yesmaximal, characteristic, complemented
16#24910913C212yesmaximal, complemented
17#24910911C212yesmaximal, complemented
18#24910823C211yesmaximal, characteristic, complemented
19#24910821C211yesmaximal, characteristic, complemented
20#24910076C212yesmaximal, complemented
21#24910037C212yesmaximal
22C2×#19127560C211yesmaximal, characteristic, complemented
23C83×#2564C211yesmaximal, characteristic, complemented
24C22×Q8×D83C2211yescharacteristic, complemented
25C22×D4×D83C2211yescharacteristic
26C23×C4×D83C2211yescharacteristic
27C23×C4×D83C2211yescharacteristic
28C2×#14581772C2211yescharacteristic
29C2×#14581771C2211yescharacteristic, complemented
30C2×#14581770C2212yes—
31C2×#14581770C2212yescomplemented
32C2×#14581769C2212yescomplemented
33C2×#14581769C2212yescomplemented
34C2×#14581768C2211yescharacteristic
35C22⋊Q8×D83—28no—
36C2×C4×D332C2211yescharacteristic
37C2×D4×Dic83C2211yescharacteristic
38C2×#14581754C2211yescharacteristic
39C2×C4×C22⋊D83C2211yescharacteristic
40C2×C4×C22⋊D83C2211yescharacteristic
41C2×(C22⋊D83)⋊C4C2211yescharacteristic
42C2×(C22⋊D83)⋊C4C2211yescharacteristic
43C4×D4×D83—28no—
44C22×Dic83⋊C4C2212yescomplemented
45C2×C4⋊C4×D83C2211yescharacteristic
46C2×C4⋊C4×D83C2211yescharacteristic, complemented
47C2×C4⋊C4×D83C2212yescomplemented
48C22×(C2×D83)⋊C4C2212yes—
49C2×C22⋊C4×D83C2211yescharacteristic
50C2×C22⋊C4×D83C2211yescharacteristic
51C2×C22⋊C4×D83C2212yes—
52C2×C42×D83C2211yescharacteristic
53#19127641C2211yescharacteristic, complemented
54#19127640C2211yescharacteristic, complemented
55#19127639C2211yescharacteristic, complemented
56#19127638C2211yescharacteristic, complemented
57#19127637C2211yescharacteristic, complemented
58#19127636C2211yescharacteristic, complemented
59#19127635C2212yescomplemented
60#19127635C2212yescomplemented
61#19127633C2212yescomplemented
62#19127632C2212yescomplemented
63#19127625C2212yescomplemented
64#19127624C2212yescomplemented
65#19127624C2212yescomplemented
66#19127623C2212yescomplemented
67#19127622C2211yescharacteristic, complemented
68#19127621C2211yescharacteristic, complemented
69#19127620C2211yescharacteristic, complemented
70#19127614C2211yescharacteristic, complemented
71#19127613C2211yescharacteristic, complemented
72#19127612C2211yescharacteristic, complemented
73#19127605C2212yescomplemented
74#19127605C2212yescomplemented
75#19127598C2212yescomplemented
76#19127596C2212yescomplemented
77#19127586C2212yescomplemented
78#19127585C2212yescomplemented
79#19127582C2212yescomplemented
80#19127581C2212yes—
81#19127580C2212yes—
82#19127579C2212yes—
83#19127579C2212yes—
84#19127578C2212yes—
85#19127577C2212yes—
86#19127577C2212yes—
87#19127575C2212yes—
88#19127575C2212yes—
89#19127575C2212yescomplemented
90#19127575C2212yescomplemented
91#19127575C2212yescomplemented
92#19127574C2212yescomplemented
93#19127572C2212yes—
94#19127572C2212yes—
95#19127572C2212yescomplemented
96#19127572C2212yescomplemented
97#19127572C2212yescomplemented
98#19127563C2212yes—
99#19127563C2212yes—
100#19127561C2212yescomplemented
101#19127560C2212yes—
102#19127560C2211yescharacteristic
103#19127560C2211yescharacteristic
104#19127560C2211yescharacteristic, complemented
105#19127560C2211yescharacteristic, complemented
106#19127560C2212yescomplemented
107#19127560C2212yescomplemented
108#19127559C2212yescomplemented
109#19127559C2212yescomplemented
110#19127559C2212yescomplemented
111#19127556C2212yes—
112#19127556C2212yes—
113C2×C83⋊#95C2211yescharacteristic, complemented
114C2×C22⋊Q8×C83C2211yescharacteristic, complemented
115C2×C4×D4×C83C2211yescharacteristic
116#400×C83C2211yescharacteristic, complemented
117#399×C83C2211yescharacteristic, complemented
118#395×C83C2211yescharacteristic, complemented
119#393×C83C2211yescharacteristic, complemented
120#387×C83C2212yescomplemented
121#386×C83C2212yes—
122#385×C83C2212yescomplemented
123#380×C83C2212yescomplemented
124C2×#95×C83C2211yescharacteristic, complemented
125C24×D83C2311yescharacteristic
126C24×D83C2311yescharacteristic
127C22×Dic166C2312yes—
128C22×Dic166C2311yescharacteristic
129C2×Q8×D83—24no—
130C2×Q8×D83—44no—
131C22×D332C2311yescharacteristic
132C22×C22⋊D83C2311yescharacteristic
133C22×C22⋊D83C2311yescharacteristic
134C2×D4×D83—24no—
135C2×D4×D83—24no—
136C2×D4×D83Q818yescomplemented
137C23×Dic83C2311yescharacteristic
138C23×Dic83C2311yescharacteristic
139C23×Dic83C2312yes—
140C22×C4×D83—24no—
141C22×C4×D83—44no—
142C22×C4×D83—44no—
143C22×C4×D83D418yes—
144C22×C4×D83C2311yescharacteristic
145C22×C4×D83C2311yescharacteristic
146C22×C4×D83C2311yescharacteristic
147C22×C4×D83C2311yescharacteristic
148C22×C4×D83C2311yescharacteristic
149C22×C4×D83C2311yescharacteristic
150C22×C4×D83C2311yescharacteristic
151C22×C4×D83C2312yes—
152C22×C4×D83C2312yes—
153C22×C4×D83C2311yescharacteristic
154C22×C4×D83C2311yescharacteristic
155#14581772—24no—
156#14581771—24no—
157#14581770—28no—
158#14581770—44no—
159#14581769—28no—
160#14581769—44no—
161#14581768—24no—
162C4×D332—24no—
163D4×Dic83—24no—
164#14581754—24no—
165C4×C22⋊D83—24no—
166C4×C22⋊D83—24no—
167(C22⋊D83)⋊C4—24no—
168(C22⋊D83)⋊C4—24no—
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2312yes—
174C2×Dic83⋊C4—44no—
175C2×Dic83⋊C4C2312yes—
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2311yescharacteristic
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2311yescharacteristic
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2312yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83—24no—
189C4⋊C4×D83—28no—
190C4⋊C4×D83—24no—
191C2×C22⋊Dic83C2311yescharacteristic
192C2×C22⋊Dic83C2312yes—
193C2×C22⋊Dic83C2311yescharacteristic
194C2×C22⋊Dic83C2312yes—
195C2×C22⋊Dic83C2312yes—
196C2×(C2×D83)⋊C4—28no—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2312yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×(C2×D83)⋊C4C2312yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×(C2×D83)⋊C4C2311yescharacteristic
204C2×(C2×D83)⋊C4C2311yescharacteristic
205C2×(C2×D83)⋊C4C2311yescharacteristic
206C2×(C2×D83)⋊C4C2311yescharacteristic
207C2×(C2×D83)⋊C4C2312yes—
208C2×(C2×D83)⋊C4C2312yes—
209C2×(C2×D83)⋊C4C2312yes—
210C2×(C2×D83)⋊C4C2312yes—
211C22⋊C4×D83—24no—
212C22⋊C4×D83—28no—
213C22⋊C4×D83—24no—
214C2×C4×Dic83C2311yescharacteristic
215C2×C4×Dic83C2311yescharacteristic
216C2×C4×Dic83C2311yescharacteristic
217C42×D83—24no—
218C83⋊#95C2312yes—
219C83⋊#95C2312yes—
220C83⋊#95C2312yes—
221C83⋊#95C2312yes—
222C83⋊#95C2312yes—
223C83⋊#95C2312yes—
224C83⋊#95C2311yescharacteristic
225C83⋊#95C2311yescharacteristic
226C83⋊#95C2312yes—
227C83⋊#95C2312yes—
228C83⋊#95C2312yes—
229C83⋊#95C2312yes—
230C83⋊#95C2312yes—
231C83⋊#95C2312yes—
232C83⋊#95C2312yes—
233C22×Q8×C83C2311yescharacteristic
234C22×D4×C83C2311yescharacteristic
235C23×C4×C83C2312yes—
236C23×C4×C83C2311yescharacteristic
237C23×C4×C83C2311yescharacteristic
238C22⋊Q8×C83—24no—
239C4×D4×C83—24no—
240C2×C4⋊C4×C83C2312yes—
241C2×C4⋊C4×C83C2311yescharacteristic
242C2×C4⋊C4×C83C2311yescharacteristic
243C2×C4⋊C4×C83C2312yes—
244C2×C4⋊C4×C83C2312yes—
245C2×C22⋊C4×C83C2311yescharacteristic
246C2×C22⋊C4×C83C2312yes—
247C2×C22⋊C4×C83C2311yescharacteristic
248C2×C22⋊C4×C83C2312yes—
249C2×C22⋊C4×C83C2312yes—
250C2×C42×C83C2311yescharacteristic
251#95×C83C2312yes—
252#95×C83C2311yescharacteristic
253#95×C83C2311yescharacteristic
254#95×C83C2312yes—
255#95×C83C2312yes—
256#95×C83C2312yes—
257#95×C83C2312yes—
258C23×D83—22no—
259C23×D83—22no—
260C23×D83—42no—
261C23×D83—42no—
262C23×D83—42no—
263C23×D83—42no—
264C23×D83C2×D414yes—
265C23×D83C2×Q814yes—
266C23×D83C2×Q814yescomplemented
267C23×D83#4114yes—
268C23×D83C2411yescharacteristic
269C23×D83C2411yescharacteristic
270C23×D83C2411yescharacteristic
271C2×Dic166—22no—
272C2×Dic166—24no—
273C2×Dic166—24no—
274C2×Dic166—24no—
275C2×Dic166—42no—
276Q8×D83—416no—
277C2×D332—22no—
278C2×D332—22no—
279C2×D332C2×Q814yes—
280C2×C22⋊D83—22no—
281C2×C22⋊D83—22no—
282C2×C22⋊D83—22no—
283C2×C22⋊D83—22no—
284C2×C22⋊D83C2×Q814yes—
285C2×C22⋊D83C2×Q814yescomplemented
286D4×D83—232no—
287C22×Dic83—24no—
288C22×Dic83—24no—
289C22×Dic83—22no—
290C22×Dic83—24no—
291C22×Dic83—42no—
292C22×Dic83—42no—
293C22×Dic83C2×D414yes—
294C22×Dic83C2411yescharacteristic
295C22×Dic83C2412yes—
296C22×Dic83C2411yescharacteristic
297C22×Dic83C2412yes—
298C22×Dic83C2412yes—
299C22×Dic83C2412yes—
300C22×Dic83C2411yescharacteristic
301C22×Dic83C2411yescharacteristic
302C22×Dic83C2411yescharacteristic
303C2×C4×D83—22no—
304C2×C4×D83—22no—
305C2×C4×D83—24no—
306C2×C4×D83—24no—
307C2×C4×D83—22no—
308C2×C4×D83—24no—
309C2×C4×D83—22no—
310C2×C4×D83—24no—
311C2×C4×D83—22no—
312C2×C4×D83—22no—
313C2×C4×D83—24no—
314C2×C4×D83—416no—
315C2×C4×D83—416no—
316C2×C4×D83—42no—
317C2×C4×D83—42no—
318C2×C4×D83—42no—
319C2×C4×D83—42no—
320C2×C4×D83—42no—
321C2×C4×D83—42no—
322C2×C4×D83—42no—
323C2×C4×D83—42no—
324C2×C4×D83—42no—
325C2×C4×D83C2×D414yes—
326C2×C4×D83C2×D414yes—
327C2×C4×D83C2×D414yes—
328C2×C4×D83C2×D414yes—
329C2×C4×D83C2×Q814yescomplemented
330C4⋊Dic83—22no—
331C4⋊Dic83—24no—
332C4⋊Dic83—22no—
333C4⋊Dic83—42no—
334C4⋊Dic83—42no—
335Dic83⋊C4—24no—
336Dic83⋊C4—22no—
337Dic83⋊C4—24no—
338Dic83⋊C4—24no—
339Dic83⋊C4—22no—
340Dic83⋊C4—24no—
341Dic83⋊C4—24no—
342Dic83⋊C4—42no—
343Dic83⋊C4—42no—
344Dic83⋊C4—42no—
345Dic83⋊C4—42no—
346Dic83⋊C4—42no—
347Dic83⋊C4—42no—
348C22⋊Dic83—24no—
349C22⋊Dic83—22no—
350C22⋊Dic83—22no—
351C22⋊Dic83—42no—
352C22⋊Dic83—42no—
353(C2×D83)⋊C4—24no—
354(C2×D83)⋊C4—24no—
355(C2×D83)⋊C4—22no—
356(C2×D83)⋊C4—22no—
357(C2×D83)⋊C4—24no—
358(C2×D83)⋊C4—24no—
359(C2×D83)⋊C4—24no—
360(C2×D83)⋊C4—24no—
361(C2×D83)⋊C4—22no—
362(C2×D83)⋊C4—22no—
363(C2×D83)⋊C4—42no—
364(C2×D83)⋊C4—42no—
365(C2×D83)⋊C4—42no—
366(C2×D83)⋊C4—42no—
367C4×Dic83—22no—
368C4×Dic83—22no—
369C4×Dic83—22no—
370C24×C83C2411yescharacteristic
371C24×C83C2411yescharacteristic
372C2×Q8×C83—22no—
373C2×Q8×C83—42no—
374C2×D4×C83—22no—
375C2×D4×C83—22no—
376C2×D4×C83C2×Q814yescomplemented
377C22×C4×C83—24no—
378C22×C4×C83—22no—
379C22×C4×C83—42no—
380C22×C4×C83—42no—
381C22×C4×C83—42no—
382C22×C4×C83—42no—
383C22×C4×C83C2×D414yes—
384C22×C4×C83C2411yescharacteristic
385C22×C4×C83C2412yes—
386C22×C4×C83C2411yescharacteristic
387C22×C4×C83C2412yes—
388C22×C4×C83C2412yes—
389C22×C4×C83C2412yes—
390C22×C4×C83C2411yescharacteristic
391C22×C4×C83C2411yescharacteristic
392C22×C4×C83C2411yescharacteristic
393C4⋊C4×C83—24no—
394C4⋊C4×C83—22no—
395C4⋊C4×C83—22no—
396C4⋊C4×C83—42no—
397C4⋊C4×C83—42no—
398C22⋊C4×C83—24no—
399C22⋊C4×C83—22no—
400C22⋊C4×C83—22no—
401C22⋊C4×C83—42no—
402C22⋊C4×C83—42no—
403C42×C83—22no—
404C23×C83—22no—
405C23×C83—22no—
406C23×C83—21no—
407C23×C83—21no—
408C23×C83—22no—
409C23×C83—22no—
410C23×C83C22×D412yes—
411C23×C83C22×Q812yes—
412C23×C83C22×Q812yes—
413C23×C83C2×#4112yes—
414C23×C83C2511yescharacteristic
415C22×D83—22no—
416C22×D83—22no—
417C22×D83—22no—
418C22×D83—22no—
419C22×D83—21no—
420C22×D83—21no—
421C22×D83—22no—
422C22×D83—22no—
423C22×D83—28no—
424C22×D83—44no—
425C22×D83—44no—
426C22×D83—48no—
427C22×D83—48no—
428C22×D83—48no—
429C22×D83—44no—
430C22×D83—44no—
431C22×D83—48no—
432C22×D83C22⋊Q8116yescomplemented
433C22×D83C22×D412yes—
434C22×D83C22×D412yes—
435C22×D83C22×Q812yes—
436C22×D83C22×Q812yes—
437C22×D83C22×Q812yes—
438C22×D83C2×#4112yes—
439C22×D83C2×#4112yes—
440Q8×C83—44no—
441D4×C83—28no—
442C2×C4×C83—21no—
443C2×C4×C83—21no—
444C2×C4×C83—22no—
445C2×C4×C83—22no—
446C2×C4×C83—21no—
447C2×C4×C83—22no—
448C2×C4×C83—21no—
449C2×C4×C83—22no—
450C2×C4×C83—22no—
451C2×C4×C83—22no—
452C2×C4×C83—22no—
453C2×C4×C83—22no—
454C2×C4×C83—22no—
455C2×C4×C83—22no—
456C2×C4×C83—22no—
457C2×C4×C83—22no—
458C2×C4×C83—22no—
459C2×C4×C83—22no—
460C2×C4×C83—22no—
461C2×C4×C83—22no—
462C2×C4×C83—44no—
463C2×C4×C83—44no—
464C2×C4×C83—84no—
465C2×C4×C83C22×D412yes—
466C2×C4×C83C22×D412yes—
467C2×C4×C83C22×Q812yes—
468C22⋊D83—28no—
469C22⋊D83—28no—
470C2×Dic83—21no—
471C2×Dic83—21no—
472C2×Dic83—22no—
473C2×Dic83—28no—
474C2×Dic83—21no—
475C2×Dic83—22no—
476C2×Dic83—21no—
477C2×Dic83—22no—
478C2×Dic83—22no—
479C2×Dic83—22no—
480C2×Dic83—22no—
481C2×Dic83—22no—
482C2×Dic83—22no—
483C2×Dic83—22no—
484C2×Dic83—22no—
485C2×Dic83—22no—
486C2×Dic83—22no—
487C2×Dic83—22no—
488C2×Dic83—22no—
489C2×Dic83—22no—
490C2×Dic83—44no—
491C2×Dic83—84no—
492C2×Dic83C22×D412yes—
493C2×Dic83C22×D412yes—
494C2×Dic83C22×Q812yes—
495C2×Dic83H(5,𝔽2)14yes—
496D332—28no—
497C4×D83—28no—
498C4×D83—28no—
499C4×D83—28no—
500C4×D83—44no—
501C4×D83—44no—
502C4×D83—44no—
503C4×D83—48no—
504C4×D83—44no—
505C4×D83—44no—
506C4×D83—48no—
507C4×D83—44no—
508Dic166—44no—
509Dic166—48no—
510C22×C83—22no—
511C22×C83—22no—
512C22×C83—24no—
513C22×C83—24no—
514C22×C83—22no—
515C22×C83—24no—
516C22×C83—41no—
517C22×C83—41no—
518C22×C83—42no—
519C22×C83C2×C22⋊Q814yes—
520C22×C83C23×D411yescharacteristic
521C22×C83C23×Q811yescharacteristic
522C22×C83C22×#4111yescharacteristic
523C22×C83C2×H(5,𝔽2)12yes—
524C22×C83#58512yes—
525C2×D83—22no—
526C2×D83—22no—
527C2×D83—22no—
528C2×D83—22no—
529C2×D83—24no—
530C2×D83—24no—
531C2×D83—24no—
532C2×D83—24no—
533C2×D83—22no—
534C2×D83—24no—
535C2×D83—416no—
536C2×D83—416no—
537C2×D83—41no—
538C2×D83—41no—
539C2×D83—42no—
540C2×D83C2×C22⋊Q814yes—
541C2×D83C2×C22⋊Q814yes—
542C4×C83—22no—
543C4×C83—22no—
544C4×C83—22no—
545C4×C83—42no—
546C4×C83—41no—
547C4×C83—41no—
548C4×C83—42no—
549C4×C83—42no—
550C4×C83—42no—
551Dic83—22no—
552Dic83—22no—
553Dic83—42no—
554Dic83—41no—
555Dic83—41no—
556Dic83—42no—
557Dic83—42no—
558Dic83—42no—
559Dic83#53414yes—
560#35010—831nomaximal, Sylow
561C2×C83—24no—
562C2×C83—42no—
563C2×C83C22×C22⋊Q811yescharacteristic
564C2×C83C2×#53411yescharacteristic
565C2×C83#344911yescharacteristic
566C2×C83#350112yes—
567C2×C83#350512yes—
568D83—24no—
569D83—24no—
570D83—42no—
571C22×C22⋊Q8—831no—
572C22×C4×D4—831no—
573#2855—832no—
574#2848—832no—
575#2627—831no—
576#2627—831no—
577#2626—831no—
578#2626—831no—
579#2579—832no—
580#2579—832no—
581#2564—831no—
582#2564—831no—
583#2564—831no—
584#2564D8311yescharacteristic, complemented
585#2487—831no—
586#2487—831no—
587#2417—832no—
588#2417—832no—
589#2409—831no—
590#2409—831no—
591#2315—832no—
592#2308—832no—
593C2×#380—831no—
594C83#3501011yescharacteristic, complemented, Sylow
595C23×Q8—831no—
596C23×D4—831no—
597C24×C4—831no—
598C24×C4—831no—
599C2×C22⋊Q8—831no—
600C2×C22⋊Q8—831no—
601C2×C22⋊Q8—832no—
602C2×C22⋊Q8—832no—
603C2×C22⋊Q8—831no—
604C2×C22⋊Q8—832no—
605C2×C22⋊Q8—832no—
606C2×C22⋊Q8—1668no—
607C2×C22⋊Q8C2×D8311yescharacteristic, complemented
608C2×C4×D4—831no—
609C2×C4×D4—831no—
610C2×C4×D4—831no—
611C2×C4×D4—831no—
612C2×C4×D4—831no—
613C2×C4×D4—831no—
614C2×C4×D4—831no—
615C2×C4×D4—1668no—
616C2×C4×D4C2×D8311yescharacteristic
617C22×C4⋊C4—832no—
618C22×C4⋊C4—832no—
619C22×C4⋊C4—831no—
620C22×C4⋊C4—831no—
621C22×C22⋊C4—832no—
622C22×C22⋊C4—832no—
623C22×C22⋊C4—831no—
624C22×C22⋊C4—831no—
625C22×C42—831no—
626#400—831no—
627#400—831no—
628#400—831no—
629#400C2×D8311yescharacteristic, complemented
630#399—831no—
631#399—831no—
632#399—831no—
633#399C2×D8311yescharacteristic, complemented
634#398—832no—
635#398—832no—
636#398—832no—
637#398—832no—
638#396—832no—
639#396—832no—
640#396—832no—
641#396—832no—
642#395—831no—
643#395—831no—
644#395—831no—
645#395C2×D8311yescharacteristic, complemented
646#393—831no—
647#393—831no—
648#393—831no—
649#393C2×D8311yescharacteristic, complemented
650#391—832no—
651#391—832no—
652#389—832no—
653#389—832no—
654#387—832no—
655#387—832no—
656#387—832no—
657#387C2×D8312yescomplemented
658#386—832no—
659#386—832no—
660#386—832no—
661#386—832no—
662#386—832no—
663#386—832no—
664#386—832no—
665#386C2×D8312yes—
666#385—832no—
667#385—832no—
668#385—832no—
669#385—832no—
670#385—832no—
671#385—832no—
672#385—832no—
673#385—832no—
674#385—832no—
675#385—832no—
676#385—832no—
677#385C2×D8312yescomplemented
678#381—832no—
679#381—832no—
680#380—832no—
681#380—832no—
682#380—832no—
683#380—832no—
684#380—832no—
685#380—831no—
686#380—831no—
687#380—832no—
688#380—832no—
689#380—831no—
690#380—831no—
691#380C2×D8312yescomplemented
692#379—832no—
693#379—832no—
694C2×#95—831no—
695C2×#95C2×D8311yescharacteristic, complemented
696C25—831no—
697C25—831no—
698C22×Q8—3324no—
699C22×Q8—831no—
700C22×Q8—832no—
701C22×Q8—1664no—
702C22×Q8C22×D8311yescharacteristic
703C22×D4—831no—
704C22×D4—831no—
705C22×D4—838no—
706C22×D4—831no—
707C22×D4—1664no—
708C22×D4—1664no—
709C22×D4C22×D8311yescharacteristic
710C23×C4—3324no—
711C23×C4—3324no—
712C23×C4—838no—
713C23×C4—831no—
714C23×C4—831no—
715C23×C4—832no—
716C23×C4—831no—
717C23×C4—832no—
718C23×C4—831no—
719C23×C4—832no—
720C23×C4—831no—
721C23×C4—831no—
722C23×C4—831no—
723C23×C4—831no—
724C23×C4—831no—
725C23×C4—831no—
726C23×C4—831no—
727C23×C4—1664no—
728C23×C4C22×D8312yes—
729C23×C4C22×D8311yescharacteristic
730C23×C4C22×D8311yescharacteristic
731C22⋊Q8—24no—
732C22⋊Q8—3324no—
733C22⋊Q8—3324no—
734C22⋊Q8—1668no—
735C22⋊Q8—1668no—
736C22⋊Q8—1664no—
737C22⋊Q8—1664no—
738C22⋊Q8—1664no—
739C4×D4—24no—
740C4×D4—1664no—
741C4×D4—1664no—
742C4×D4—1664no—
743C4×D4—1664no—
744C4×D4—1664no—
745C4×D4—1664no—
746C4×D4—1664no—
747C2×C4⋊C4—3324no—
748C2×C4⋊C4—832no—
749C2×C4⋊C4—832no—
750C2×C4⋊C4—832no—
751C2×C4⋊C4—832no—
752C2×C4⋊C4—832no—
753C2×C4⋊C4—832no—
754C2×C4⋊C4—832no—
755C2×C4⋊C4—832no—
756C2×C4⋊C4—831no—
757C2×C4⋊C4—831no—
758C2×C4⋊C4—831no—
759C2×C4⋊C4—832no—
760C2×C4⋊C4—832no—
761C2×C4⋊C4—832no—
762C2×C4⋊C4—832no—
763C2×C4⋊C4—831no—
764C2×C4⋊C4—832no—
765C2×C4⋊C4—832no—
766C2×C4⋊C4—1664no—
767C2×C4⋊C4—1664no—
768C2×C4⋊C4—1668no—
769C2×C4⋊C4C22×D8311yescharacteristic
770C2×C4⋊C4C22×D8312yes—
771C2×C4⋊C4C22×D8311yescharacteristic
772C2×C4⋊C4C22×D8312yes—
773C2×C4⋊C4C22×D8312yes—
774C2×C22⋊C4—832no—
775C2×C22⋊C4—832no—
776C2×C22⋊C4—832no—
777C2×C22⋊C4—832no—
778C2×C22⋊C4—832no—
779C2×C22⋊C4—832no—
780C2×C22⋊C4—831no—
781C2×C22⋊C4—831no—
782C2×C22⋊C4—832no—
783C2×C22⋊C4—831no—
784C2×C22⋊C4—831no—
785C2×C22⋊C4—831no—
786C2×C22⋊C4—831no—
787C2×C22⋊C4—832no—
788C2×C22⋊C4—832no—
789C2×C22⋊C4—832no—
790C2×C22⋊C4—832no—
791C2×C22⋊C4—832no—
792C2×C22⋊C4—832no—
793C2×C22⋊C4—1664no—
794C2×C22⋊C4—1664no—
795C2×C22⋊C4—1668no—
796C2×C22⋊C4—1668no—
797C2×C22⋊C4C22×D8311yescharacteristic
798C2×C22⋊C4C22×D8311yescharacteristic
799C2×C22⋊C4C22×D8312yes—
800C2×C22⋊C4C22×D8312yes—
801C2×C22⋊C4C22×D8312yes—
802C2×C42—831no—
803C2×C42—831no—
804C2×C42—831no—
805C2×C42—1664no—
806C2×C42C22×D8311yescharacteristic
807#95—832no—
808#95—831no—
809#95—831no—
810#95—832no—
811#95—832no—
812#95—832no—
813#95—832no—
814#95—832no—
815#95—832no—
816#95—832no—
817#95—832no—
818#95—832no—
819#95—832no—
820#95—832no—
821#95—832no—
822#95C22×D8312yes—
823#95C22×D8311yescharacteristic
824#95C22×D8311yescharacteristic
825#95C22×D8312yes—
826#95C22×D8312yes—
827#95C22×D8312yes—
828#95C22×D8312yes—
829C24—3322no—
830C24—3322no—
831C24—3322no—
832C24—3322no—
833C24—834no—
834C24—834no—
835C24—834no—
836C24—834no—
837C24—831no—
838C24—831no—
839C24—831no—
840C24—1662no—
841C24—1662no—
842C24C23×D8311yescharacteristic
843C24C23×D8311yescharacteristic
844C2×Q8—22no—
845C2×Q8—42no—
846C2×Q8—3322no—
847C2×Q8—33216no—
848C2×Q8—1664no—
849C2×Q8—1664no—
850C2×Q8—1664no—
851C2×Q8—1662no—
852C2×D4—22no—
853C2×D4—22no—
854C2×D4—834no—
855C2×D4—834no—
856C2×D4—834no—
857C2×D4—1662no—
858C2×D4—1662no—
859C2×D4—16632no—
860C2×D4—1662no—
861C2×D4—1662no—
862C2×D4—1662no—
863C2×D4—1662no—
864C2×D4Q8×D8314yescomplemented
865C22×C4—24no—
866C22×C4—22no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—3322no—
872C22×C4—3322no—
873C22×C4—3322no—
874C22×C4—3322no—
875C22×C4—3322no—
876C22×C4—3322no—
877C22×C4—3322no—
878C22×C4—3322no—
879C22×C4—3322no—
880C22×C4—33216no—
881C22×C4—33216no—
882C22×C4—3322no—
883C22×C4—3322no—
884C22×C4—834no—
885C22×C4—834no—
886C22×C4—831no—
887C22×C4—834no—
888C22×C4—831no—
889C22×C4—831no—
890C22×C4—834no—
891C22×C4—834no—
892C22×C4—834no—
893C22×C4—832no—
894C22×C4—832no—
895C22×C4—831no—
896C22×C4—832no—
897C22×C4—832no—
898C22×C4—831no—
899C22×C4—1662no—
900C22×C4—1664no—
901C22×C4—1662no—
902C22×C4—1664no—
903C22×C4—1662no—
904C22×C4—1664no—
905C22×C4—1664no—
906C22×C4—1664no—
907C22×C4—1662no—
908C22×C4—1662no—
909C22×C4—1662no—
910C22×C4—1664no—
911C22×C4—1662no—
912C22×C4—1664no—
913C22×C4—1664no—
914C22×C4D4×D8314yes—
915C22×C4C23×D8312yes—
916C22×C4C23×D8311yescharacteristic
917C22×C4C23×D8312yes—
918C22×C4C23×D8312yes—
919C22×C4C23×D8311yescharacteristic
920C22×C4C23×D8312yes—
921C22×C4C23×D8311yescharacteristic
922C22×C4C23×D8311yescharacteristic
923C22×C4C23×D8311yescharacteristic
924C4⋊C4—22no—
925C4⋊C4—22no—
926C4⋊C4—24no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—3322no—
930C4⋊C4—3322no—
931C4⋊C4—3322no—
932C4⋊C4—3322no—
933C4⋊C4—3322no—
934C4⋊C4—3322no—
935C4⋊C4—3322no—
936C4⋊C4—3322no—
937C4⋊C4—1664no—
938C4⋊C4—1664no—
939C4⋊C4—1662no—
940C4⋊C4—1662no—
941C4⋊C4—1664no—
942C4⋊C4—1664no—
943C4⋊C4—1664no—
944C4⋊C4—1662no—
945C4⋊C4—1664no—
946C4⋊C4—1662no—
947C22⋊C4—22no—
948C22⋊C4—24no—
949C22⋊C4—22no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—3322no—
953C22⋊C4—3322no—
954C22⋊C4—3322no—
955C22⋊C4—3322no—
956C22⋊C4—3322no—
957C22⋊C4—3322no—
958C22⋊C4—1662no—
959C22⋊C4—1662no—
960C22⋊C4—1662no—
961C22⋊C4—1664no—
962C22⋊C4—1664no—
963C22⋊C4—1664no—
964C22⋊C4—1664no—
965C22⋊C4—1664no—
966C22⋊C4—1664no—
967C22⋊C4—1662no—
968C22⋊C4—1662no—
969C22⋊C4—1664no—
970C22⋊C4—1662no—
971C42—22no—
972C42—1662no—
973C42—1662no—
974C42—1662no—
975C23—22no—
976C23—22no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—3324no—
982C23—3328no—
983C23—3328no—
984C23—3324no—
985C23—3328no—
986C23—3324no—
987C23—3328no—
988C23—3324no—
989C23—8316no—
990C23—832no—
991C23—832no—
992C23—832no—
993C23—832no—
994C23—832no—
995C23—832no—
996C23—832no—
997C23—1668no—
998C23—1661no—
999C23—1661no—
1000C23—1662no—
1001C23—1662no—
1002C23—1662no—
1003C23—1662no—
1004C23—1662no—
1005C23—1662no—
1006C23C2×D4×D8312yes—
1007C23C2×Q8×D8312yes—
1008C23C2×Q8×D8312yes—
1009C23#41×D8312yes—
1010C23C24×D8311yescharacteristic
1011Q8—44no—
1012Q8—3324no—
1013Q8—3328no—
1014D4—28no—
1015D4—1668no—
1016D4—1668no—
1017D4—1668no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—21no—
1023C2×C4—22no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—44no—
1039C2×C4—44no—
1040C2×C4—84no—
1041C2×C4—3324no—
1042C2×C4—3324no—
1043C2×C4—3324no—
1044C2×C4—3324no—
1045C2×C4—3328no—
1046C2×C4—3328no—
1047C2×C4—3324no—
1048C2×C4—3324no—
1049C2×C4—3324no—
1050C2×C4—832no—
1051C2×C4—834no—
1052C2×C4—832no—
1053C2×C4—832no—
1054C2×C4—6644no—
1055C2×C4—1668no—
1056C2×C4—1668no—
1057C2×C4—1668no—
1058C2×C4—1661no—
1059C2×C4—1662no—
1060C2×C4—1661no—
1061C2×C4—1662no—
1062C2×C4—1662no—
1063C2×C4—1662no—
1064C2×C4—1662no—
1065C2×C4—1662no—
1066C2×C4—1662no—
1067C2×C4—1662no—
1068C2×C4—1662no—
1069C2×C4—1662no—
1070C2×C4—1662no—
1071C2×C4—1662no—
1072C2×C4—1662no—
1073C2×C4—1662no—
1074C2×C4—1668no—
1075C2×C4—1661no—
1076C2×C4—1661no—
1077C2×C4—1662no—
1078C2×C4C2×D4×D8312yes—
1079C2×C4C2×D4×D8312yes—
1080C2×C4C2×Q8×D8312yes—
1081C22—24no—
1082C22—22no—
1083C22—24no—
1084C22—22no—
1085C22—22no—
1086C22—24no—
1087C22—41no—
1088C22—42no—
1089C22—41no—
1090C22—33216no—
1091C22—33216no—
1092C22—3321no—
1093C22—3322no—
1094C22—3321no—
1095C22—834no—
1096C22—834no—
1097C22—1662no—
1098C22—1664no—
1099C22—1664no—
1100C22—1664no—
1101C22—1662no—
1102C22—1662no—
1103C22—1664no—
1104C22—1664no—
1105C22—1662no—
1106C22—1662no—
1107C22C22⋊Q8×D8314yes—
1108C22C22×D4×D8311yescharacteristic
1109C22C22×Q8×D8311yescharacteristic
1110C22C2×#41×D8311yescharacteristic
1111C22H(5,𝔽2)×D8312yes—
1112C22#1912853712yes—
1113C4—22no—
1114C4—22no—
1115C4—22no—
1116C4—41no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—41no—
1121C4—42no—
1122C4—3321no—
1123C4—3322no—
1124C4—3322no—
1125C4—3322no—
1126C4—3321no—
1127C4—3322no—
1128C4—834no—
1129C4—1662no—
1130C4—1662no—
1131C2—24no—
1132C2—42no—
1133C2—3322no—
1134C2—1664no—
1135C2—1664no—
1136C2C2×C22⋊Q8×D8311yescharacteristic
1137C2#534×D8311yescharacteristic
1138C2#2492079011yescharacteristic
1139C2#2492126212yes—
1140C2#2492129412yes—
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2564C2
prime radicalC22×D4×D83C22
hypercenter#2564D83
hypocenterC83#35010
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2564

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊Q8×D83C2semidirect
3. #24915798C2semidirect
4. #24915749C2semidirect
5. #24913277C2semidirect
6. #24913275C2semidirect
7. #24913269C2semidirect
8. #24913267C2semidirect
9. #24912814C2semidirect
10. #24912808C2semidirect
11. #24912645C2semidirect
12. #24912643C2semidirect
13. #24912639C2semidirect
14. #24911775C2semidirect
15. #24911773C2semidirect
16. #24910913C2semidirect
17. #24910911C2semidirect
18. #24910823C2semidirect
19. #24910821C2semidirect
20. #24910076C2semidirect
22. C2×#19127560C2semidirect
23. C83×#2564C2semidirect
24. C22×Q8×D83C22semidirect
29. C2×#14581771C22semidirect
31. C2×#14581770C22semidirect
32. C2×#14581769C22semidirect
33. C2×#14581769C22semidirect
44. C22×Dic83⋊C4C22semidirect
46. C2×C4⋊C4×D83C22semidirect
47. C2×C4⋊C4×D83C22semidirect
53. #19127641C22semidirect
54. #19127640C22semidirect
55. #19127639C22semidirect
56. #19127638C22semidirect
57. #19127637C22semidirect
58. #19127636C22semidirect
59. #19127635C22semidirect
60. #19127635C22semidirect
61. #19127633C22semidirect
62. #19127632C22semidirect
63. #19127625C22semidirect
64. #19127624C22semidirect
65. #19127624C22semidirect
66. #19127623C22semidirect
67. #19127622C22semidirect
68. #19127621C22semidirect
69. #19127620C22semidirect
70. #19127614C22semidirect
71. #19127613C22semidirect
72. #19127612C22semidirect
73. #19127605C22semidirect
74. #19127605C22semidirect
75. #19127598C22semidirect
76. #19127596C22semidirect
77. #19127586C22semidirect
78. #19127585C22semidirect
79. #19127582C22semidirect
89. #19127575C22semidirect
90. #19127575C22semidirect
91. #19127575C22semidirect
92. #19127574C22semidirect
95. #19127572C22semidirect
96. #19127572C22semidirect
97. #19127572C22semidirect
100. #19127561C22semidirect
104. #19127560C22semidirect
105. #19127560C22semidirect
106. #19127560C22semidirect
107. #19127560C22semidirect
108. #19127559C22semidirect
109. #19127559C22semidirect
110. #19127559C22semidirect
113. C2×C83⋊#95C22semidirect
114. C2×C22⋊Q8×C83C22semidirect
116. #400×C83C22semidirect
117. #399×C83C22semidirect
118. #395×C83C22semidirect
119. #393×C83C22semidirect
120. #387×C83C22semidirect
122. #385×C83C22semidirect
123. #380×C83C22semidirect
124. C2×#95×C83C22semidirect
136. C2×D4×D83Q8semidirect
266. C23×D83C2×Q8semidirect
285. C2×C22⋊D83C2×Q8semidirect
329. C2×C4×D83C2×Q8semidirect
376. C2×D4×C83C2×Q8semidirect
432. C22×D83C22⋊Q8semidirect
584. #2564D83semidirect
594. C83#35010semidirect
607. C2×C22⋊Q8C2×D83semidirect
629. #400C2×D83semidirect
633. #399C2×D83semidirect
645. #395C2×D83semidirect
649. #393C2×D83semidirect
657. #387C2×D83semidirect
677. #385C2×D83semidirect
691. #380C2×D83semidirect
695. C2×#95C2×D83semidirect
864. C2×D4Q8×D83semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×D832
C2×C4×D4×D832
#249157982
#249157492
#249132772
#249132752
#249132692
#249132672
#249128142
#249128082
#249126452
#249126432
#249126392
#249117752
#249117732
#249109132
#249109112
#249108232
#249108212
#249100762
#249100372
C2×#191275602
C83×#25642
#3501083