Finite Group Databasebeta

← #35611119

Subgroups — #35611119

Order 21248.

1356 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24915712C211yesmaximal, characteristic, complemented
2#24915707C211yesmaximal, characteristic, complemented
3#24915706C211yesmaximal, characteristic, complemented
4#24915667C211yesmaximal, characteristic
5#24915666C211yesmaximal, characteristic
6#24915661C211yesmaximal, characteristic
7#24915658C211yesmaximal, characteristic
8#24915643C211yesmaximal, characteristic, complemented
9#24915640C211yesmaximal, characteristic, complemented
10#24915637C211yesmaximal, characteristic, complemented
11#24915636C211yesmaximal, characteristic, complemented
12#24915626C211yesmaximal, characteristic
13#24915625C211yesmaximal, characteristic
14#24915617C211yesmaximal, characteristic
15#24915616C211yesmaximal, characteristic
16#24910769C211yesmaximal, characteristic, complemented
17#24910769C211yesmaximal, characteristic, complemented
18#24910767C211yesmaximal, characteristic, complemented
19#24910767C211yesmaximal, characteristic, complemented
20#24910767C211yesmaximal, characteristic, complemented
21#24910762C211yesmaximal, characteristic
22#24910762C211yesmaximal, characteristic
23#24910762C211yesmaximal, characteristic
24#24910762C211yesmaximal, characteristic
25#24910755C211yesmaximal, characteristic, complemented
26#24910740C211yesmaximal, characteristic
27#24910736C211yesmaximal, characteristic
28#24909955C211yesmaximal, characteristic
29#24909936C211yesmaximal, characteristic, complemented
30#24909934C211yesmaximal, characteristic, complemented
31C83×#2839C211yesmaximal, characteristic, complemented
32C2×#14581757C2211yescharacteristic
33C2×#14581757C2211yescharacteristic
34C2×#14581750C2211yescharacteristic
35C83⋊#401C2211yescharacteristic
36C83⋊#401C2211yescharacteristic
37C83⋊#401C2211yescharacteristic
38C83⋊#401C2211yescharacteristic
39#19127643C2211yescharacteristic
40#19127643C2211yescharacteristic
41#19127643C2211yescharacteristic
42#19127643C2211yescharacteristic
43#19127643C2211yescharacteristic
44#19127643C2211yescharacteristic
45#19127643C2211yescharacteristic
46#19127643C2211yescharacteristic
47#19127643C2211yescharacteristic
48#19127643C2211yescharacteristic
49#19127642C2211yescharacteristic
50#19127642C2211yescharacteristic
51#19127642C2211yescharacteristic
52#19127642C2211yescharacteristic
53#19127641C2211yescharacteristic
54#19127641C2211yescharacteristic
55#19127641C2211yescharacteristic
56#19127641C2211yescharacteristic
57#19127641C2211yescharacteristic
58#19127641C2211yescharacteristic
59#19127641C2211yescharacteristic
60#19127640C2211yescharacteristic
61#19127640C2211yescharacteristic
62#19127640C2211yescharacteristic
63#19127639C2211yescharacteristic
64#19127639C2211yescharacteristic
65#19127639C2211yescharacteristic
66#19127636C2211yescharacteristic
67#19127636C2211yescharacteristic
68#19127635C2211yescharacteristic
69#19127635C2211yescharacteristic
70#19127635C2211yescharacteristic
71#19127635C2211yescharacteristic
72#19127635C2211yescharacteristic
73#19127635C2211yescharacteristic
74#19127635C2211yescharacteristic
75#19127635C2211yescharacteristic
76#19127634C2211yescharacteristic
77#19127634C2211yescharacteristic
78#19127634C2211yescharacteristic
79#19127634C2211yescharacteristic
80#19127634C2211yescharacteristic
81#19127634C2211yescharacteristic
82#19127633C2211yescharacteristic
83#19127633C2211yescharacteristic
84#19127633C2211yescharacteristic
85#19127632C2211yescharacteristic
86#19127632C2211yescharacteristic
87#19127632C2211yescharacteristic
88#19127631C2211yescharacteristic
89#19127631C2211yescharacteristic
90#19127631C2211yescharacteristic
91#19127630C2211yescharacteristic
92#19127630C2211yescharacteristic
93#19127630C2211yescharacteristic
94#19127630C2211yescharacteristic
95#19127628C2211yescharacteristic
96#19127628C2211yescharacteristic
97#19127628C2211yescharacteristic
98#19127628C2211yescharacteristic
99#19127627C2211yescharacteristic
100#19127627C2211yescharacteristic
101#19127627C2211yescharacteristic
102#19127627C2211yescharacteristic
103#19127625C2211yescharacteristic
104#19127625C2211yescharacteristic
105#19127623C2211yescharacteristic
106#19127623C2211yescharacteristic
107#19127623C2211yescharacteristic
108#19127623C2211yescharacteristic
109#19127623C2211yescharacteristic
110#19127623C2211yescharacteristic
111#19127622C2211yescharacteristic
112#19127622C2211yescharacteristic
113#19127621C2211yescharacteristic
114#19127621C2211yescharacteristic
115#19127621C2211yescharacteristic
116#19127621C2211yescharacteristic
117#19127614C2211yescharacteristic
118#19127614C2211yescharacteristic
119#19127607C2211yescharacteristic
120#19127606C2211yescharacteristic
121#19127605C2211yescharacteristic
122#19127605C2211yescharacteristic
123#19127600C2211yescharacteristic
124#19127598C2211yescharacteristic
125#19127596C2211yescharacteristic
126#19127593C2211yescharacteristic
127#19127592C2211yescharacteristic
128#19127591C2211yescharacteristic
129#19127590C2211yescharacteristic
130#19127588C2211yescharacteristic
131#19127588C2211yescharacteristic
132#19127587C2211yescharacteristic
133#19127587C2211yescharacteristic
134#19127586C2211yescharacteristic
135#19127585C2211yescharacteristic
136#19127584C2211yescharacteristic
137#19127583C2211yescharacteristic
138#19127582C2211yescharacteristic
139#19127582C2211yescharacteristic
140C4⋊C4×Dic83C2211yescharacteristic
141C4⋊C4×Dic83C2211yescharacteristic
142C4⋊C4×Dic83C2211yescharacteristic
143C4⋊C4×Dic83C2211yescharacteristic
144C4⋊C4×Dic83C2211yescharacteristic
145C4⋊C4×Dic83C2211yescharacteristic
146C4⋊C4×Dic83C2211yescharacteristic
147C4⋊C4×Dic83C2211yescharacteristic
148C4⋊C4×Dic83C2211yescharacteristic
149C4⋊C4×Dic83C2211yescharacteristic
150C4⋊C4×Dic83C2211yescharacteristic
151#19127552C2211yescharacteristic
152#19127552C2211yescharacteristic
153#19127552C2211yescharacteristic
154#19127552C2211yescharacteristic
155#19127552C2211yescharacteristic
156#19127552C2211yescharacteristic
157#19127552C2211yescharacteristic
158#19127552C2211yescharacteristic
159#19127552C2211yescharacteristic
160#19127548C2211yescharacteristic
161#19127548C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165#19127548C2211yescharacteristic
166#19127546C2211yescharacteristic
167#19127546C2211yescharacteristic
168#19127546C2211yescharacteristic
169#19127546C2211yescharacteristic
170#19127546C2211yescharacteristic
171C42×Dic83C2211yescharacteristic
172#400×C83C2211yescharacteristic
173#400×C83C2211yescharacteristic
174#400×C83C2211yescharacteristic
175#400×C83C2211yescharacteristic
176#400×C83C2211yescharacteristic
177#400×C83C2211yescharacteristic
178#400×C83C2211yescharacteristic
179#398×C83C2211yescharacteristic
180#398×C83C2211yescharacteristic
181#398×C83C2211yescharacteristic
182#398×C83C2211yescharacteristic
183#398×C83C2211yescharacteristic
184#389×C83C2211yescharacteristic
185#387×C83C2211yescharacteristic
186#387×C83C2211yescharacteristic
187C22×Dic166C2311yescharacteristic
188C22×Dic166C2311yescharacteristic
189C22×C4×D83C2311yescharacteristic
190#14581757—24no—
191#14581757—24no—
192#14581750—24no—
193C2×C4⋊Dic83C2311yescharacteristic
194C2×C4⋊Dic83C2311yescharacteristic
195C2×C4⋊Dic83C2311yescharacteristic
196C2×C4⋊Dic83C2311yescharacteristic
197C2×C4⋊Dic83C2311yescharacteristic
198C2×C4⋊Dic83C2311yescharacteristic
199C2×C4⋊Dic83C2311yescharacteristic
200C2×C4⋊Dic83C2311yescharacteristic
201C2×C4⋊Dic83C2311yescharacteristic
202C2×C4⋊Dic83C2311yescharacteristic
203C2×C4⋊Dic83C2311yescharacteristic
204C2×C4⋊Dic83C2311yescharacteristic
205C2×Dic83⋊C4C2311yescharacteristic
206C2×Dic83⋊C4C2311yescharacteristic
207C2×Dic83⋊C4C2311yescharacteristic
208C2×Dic83⋊C4C2311yescharacteristic
209C2×Dic83⋊C4C2311yescharacteristic
210C2×Dic83⋊C4C2311yescharacteristic
211C2×Dic83⋊C4C2311yescharacteristic
212C2×Dic83⋊C4C2311yescharacteristic
213C2×Dic83⋊C4C2311yescharacteristic
214C2×Dic83⋊C4C2311yescharacteristic
215C2×Dic83⋊C4C2311yescharacteristic
216C2×Dic83⋊C4C2311yescharacteristic
217C2×Dic83⋊C4C2311yescharacteristic
218C2×Dic83⋊C4C2311yescharacteristic
219C2×Dic83⋊C4C2311yescharacteristic
220C2×Dic83⋊C4C2311yescharacteristic
221C2×Dic83⋊C4C2311yescharacteristic
222C2×Dic83⋊C4C2311yescharacteristic
223C2×Dic83⋊C4C2311yescharacteristic
224C2×Dic83⋊C4C2311yescharacteristic
225C2×Dic83⋊C4C2311yescharacteristic
226C2×Dic83⋊C4C2311yescharacteristic
227C2×(C2×D83)⋊C4C2311yescharacteristic
228C2×(C2×D83)⋊C4C2311yescharacteristic
229C2×(C2×D83)⋊C4C2311yescharacteristic
230C2×(C2×D83)⋊C4C2311yescharacteristic
231C2×(C2×D83)⋊C4C2311yescharacteristic
232C2×(C2×D83)⋊C4C2311yescharacteristic
233C2×(C2×D83)⋊C4C2311yescharacteristic
234C2×(C2×D83)⋊C4C2311yescharacteristic
235C2×(C2×D83)⋊C4C2311yescharacteristic
236C2×(C2×D83)⋊C4C2311yescharacteristic
237C2×(C2×D83)⋊C4C2311yescharacteristic
238C2×(C2×D83)⋊C4C2311yescharacteristic
239C2×(C2×D83)⋊C4C2311yescharacteristic
240C2×(C2×D83)⋊C4C2311yescharacteristic
241C2×C4×Dic83C2311yescharacteristic
242C2×C4×Dic83C2311yescharacteristic
243C2×C4×Dic83C2311yescharacteristic
244C2×C4×Dic83C2311yescharacteristic
245C2×C4×Dic83C2311yescharacteristic
246C2×C4×Dic83C2311yescharacteristic
247C2×C4×Dic83C2311yescharacteristic
248C2×C4×Dic83C2311yescharacteristic
249C2×C4×Dic83C2311yescharacteristic
250C2×C4×Dic83C2311yescharacteristic
251C2×C4×Dic83C2311yescharacteristic
252C2×C4×Dic83C2311yescharacteristic
253C2×C4×Dic83C2311yescharacteristic
254C2×C4×Dic83C2311yescharacteristic
255C2×C4×Dic83C2311yescharacteristic
256C2×C4×Dic83C2311yescharacteristic
257C2×C4×Dic83C2311yescharacteristic
258C83⋊#95C2311yescharacteristic
259C83⋊#95C2311yescharacteristic
260C83⋊#95C2311yescharacteristic
261C83⋊#95C2311yescharacteristic
262C83⋊#95C2311yescharacteristic
263C83⋊#95C2311yescharacteristic
264C83⋊#95C2311yescharacteristic
265C83⋊#95C2311yescharacteristic
266C83⋊#95C2311yescharacteristic
267C83⋊#95C2311yescharacteristic
268C83⋊#95C2311yescharacteristic
269C83⋊#95C2311yescharacteristic
270C83⋊#95C2311yescharacteristic
271C83⋊#95C2311yescharacteristic
272C83⋊#95C2311yescharacteristic
273C83⋊#95C2311yescharacteristic
274C83⋊#95C2311yescharacteristic
275C83⋊#95C2311yescharacteristic
276C83⋊#95C2311yescharacteristic
277C83⋊#95C2311yescharacteristic
278C83⋊#95C2311yescharacteristic
279C83⋊#95C2311yescharacteristic
280C83⋊#95C2311yescharacteristic
281C83⋊#95C2311yescharacteristic
282C83⋊#95C2311yescharacteristic
283C83⋊#95C2311yescharacteristic
284C83⋊#95C2311yescharacteristic
285C83⋊#95C2311yescharacteristic
286C83⋊#95C2311yescharacteristic
287C83⋊#95C2311yescharacteristic
288C83⋊#95C2311yescharacteristic
289C83⋊#95C2311yescharacteristic
290C83⋊#95C2311yescharacteristic
291C83⋊#95C2311yescharacteristic
292C83⋊#95C2311yescharacteristic
293C83⋊#95C2311yescharacteristic
294C83⋊#95C2311yescharacteristic
295C83⋊#95C2311yescharacteristic
296C83⋊#95C2311yescharacteristic
297C83⋊#95C2311yescharacteristic
298C83⋊#95C2311yescharacteristic
299C83⋊#95C2311yescharacteristic
300C83⋊#95C2311yescharacteristic
301C83⋊#95C2311yescharacteristic
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C2×C4⋊C4×C83C2311yescharacteristic
311C2×C4⋊C4×C83C2311yescharacteristic
312C2×C4⋊C4×C83C2311yescharacteristic
313C2×C4⋊C4×C83C2311yescharacteristic
314C2×C4⋊C4×C83C2311yescharacteristic
315C2×C4⋊C4×C83C2311yescharacteristic
316C2×C4⋊C4×C83C2311yescharacteristic
317C2×C4⋊C4×C83C2311yescharacteristic
318C2×C4⋊C4×C83C2311yescharacteristic
319C2×C4⋊C4×C83C2311yescharacteristic
320C2×C4⋊C4×C83C2311yescharacteristic
321C2×C4⋊C4×C83C2311yescharacteristic
322C2×C4⋊C4×C83C2311yescharacteristic
323C2×C4⋊C4×C83C2311yescharacteristic
324C2×C42×C83C2311yescharacteristic
325#95×C83C2311yescharacteristic
326#95×C83C2311yescharacteristic
327#95×C83C2311yescharacteristic
328#95×C83C2311yescharacteristic
329#95×C83C2311yescharacteristic
330#95×C83C2311yescharacteristic
331#95×C83C2311yescharacteristic
332#95×C83C2311yescharacteristic
333#95×C83C2311yescharacteristic
334#95×C83C2311yescharacteristic
335#95×C83C2311yescharacteristic
336#95×C83C2311yescharacteristic
337#95×C83C2311yescharacteristic
338#95×C83C2311yescharacteristic
339#95×C83C2311yescharacteristic
340#95×C83C2311yescharacteristic
341#95×C83C2311yescharacteristic
342#95×C83C2311yescharacteristic
343#95×C83C2311yescharacteristic
344#95×C83C2311yescharacteristic
345C23×D83C2411yescharacteristic
346C2×Dic166—22no—
347C2×Dic166—22no—
348C2×Dic166—41no—
349C2×Dic166—41no—
350C2×Dic166—41no—
351C2×Dic166—41no—
352C22×Dic83C2411yescharacteristic
353C22×Dic83C2411yescharacteristic
354C22×Dic83C2411yescharacteristic
355C22×Dic83C2411yescharacteristic
356C22×Dic83C2411yescharacteristic
357C22×Dic83C2411yescharacteristic
358C22×Dic83C2411yescharacteristic
359C22×Dic83C2411yescharacteristic
360C22×Dic83C2411yescharacteristic
361C22×Dic83C2411yescharacteristic
362C22×Dic83C2411yescharacteristic
363C22×Dic83C2411yescharacteristic
364C22×Dic83C2411yescharacteristic
365C22×Dic83C2411yescharacteristic
366C22×Dic83C2411yescharacteristic
367C2×C4×D83—22no—
368C2×C4×D83—22no—
369C2×C4×D83—22no—
370C4⋊Dic83—22no—
371C4⋊Dic83—41no—
372C4⋊Dic83—41no—
373C4⋊Dic83—41no—
374C4⋊Dic83—41no—
375C4⋊Dic83—41no—
376C4⋊Dic83—41no—
377C4⋊Dic83—41no—
378C4⋊Dic83—41no—
379C4⋊Dic83—41no—
380C4⋊Dic83—41no—
381C4⋊Dic83—41no—
382Dic83⋊C4—22no—
383Dic83⋊C4—22no—
384Dic83⋊C4—22no—
385Dic83⋊C4—22no—
386Dic83⋊C4—41no—
387Dic83⋊C4—41no—
388Dic83⋊C4—41no—
389Dic83⋊C4—41no—
390Dic83⋊C4—41no—
391Dic83⋊C4—41no—
392Dic83⋊C4—41no—
393Dic83⋊C4—41no—
394Dic83⋊C4—41no—
395Dic83⋊C4—41no—
396Dic83⋊C4—41no—
397Dic83⋊C4—41no—
398Dic83⋊C4—41no—
399Dic83⋊C4—41no—
400Dic83⋊C4—41no—
401Dic83⋊C4—41no—
402Dic83⋊C4—41no—
403Dic83⋊C4—41no—
404(C2×D83)⋊C4—22no—
405(C2×D83)⋊C4—22no—
406(C2×D83)⋊C4—41no—
407(C2×D83)⋊C4—41no—
408(C2×D83)⋊C4—41no—
409(C2×D83)⋊C4—41no—
410(C2×D83)⋊C4—41no—
411(C2×D83)⋊C4—41no—
412(C2×D83)⋊C4—41no—
413(C2×D83)⋊C4—41no—
414(C2×D83)⋊C4—41no—
415(C2×D83)⋊C4—41no—
416(C2×D83)⋊C4—41no—
417(C2×D83)⋊C4—41no—
418C4×Dic83—22no—
419C4×Dic83—22no—
420C4×Dic83—22no—
421C4×Dic83—22no—
422C4×Dic83—22no—
423C4×Dic83—22no—
424C4×Dic83—22no—
425C4×Dic83—22no—
426C4×Dic83—22no—
427C4×Dic83—22no—
428C4×Dic83—22no—
429C4×Dic83—22no—
430C4×Dic83—22no—
431C4×Dic83—41no—
432C4×Dic83—41no—
433C4×Dic83—41no—
434C4×Dic83#4114yes—
435C22×C4×C83C2411yescharacteristic
436C22×C4×C83C2411yescharacteristic
437C22×C4×C83C2411yescharacteristic
438C22×C4×C83C2411yescharacteristic
439C22×C4×C83C2411yescharacteristic
440C22×C4×C83C2411yescharacteristic
441C22×C4×C83C2411yescharacteristic
442C22×C4×C83C2411yescharacteristic
443C22×C4×C83C2411yescharacteristic
444C22×C4×C83C2411yescharacteristic
445C22×C4×C83C2411yescharacteristic
446C22×C4×C83C2411yescharacteristic
447C22×C4×C83C2411yescharacteristic
448C22×C4×C83C2411yescharacteristic
449C22×C4×C83C2411yescharacteristic
450C4⋊C4×C83—22no—
451C4⋊C4×C83—22no—
452C4⋊C4×C83—22no—
453C4⋊C4×C83—41no—
454C4⋊C4×C83—41no—
455C4⋊C4×C83—41no—
456C4⋊C4×C83—41no—
457C4⋊C4×C83—41no—
458C4⋊C4×C83—41no—
459C4⋊C4×C83—41no—
460C4⋊C4×C83—41no—
461C4⋊C4×C83—41no—
462C4⋊C4×C83—41no—
463C4⋊C4×C83—41no—
464C42×C83—41no—
465C23×C83C2511yescharacteristic
466C22×D83—21no—
467C22×D83—21no—
468C22×D83—21no—
469C22×D83—21no—
470C22×D83—21no—
471C22×D83—21no—
472C22×D83—21no—
473C2×C4×C83—21no—
474C2×C4×C83—21no—
475C2×C4×C83—21no—
476C2×C4×C83—21no—
477C2×C4×C83—21no—
478C2×C4×C83—21no—
479C2×C4×C83—21no—
480C2×C4×C83—21no—
481C2×C4×C83—21no—
482C2×C4×C83—21no—
483C2×C4×C83—21no—
484C2×C4×C83—21no—
485C2×C4×C83—21no—
486C2×C4×C83—21no—
487C2×C4×C83—21no—
488C2×C4×C83—21no—
489C2×C4×C83—21no—
490C2×C4×C83—21no—
491C2×C4×C83—21no—
492C2×C4×C83—21no—
493C2×C4×C83—21no—
494C2×C4×C83—21no—
495C2×C4×C83—21no—
496C2×C4×C83—21no—
497C2×C4×C83—21no—
498C2×C4×C83—21no—
499C2×C4×C83—21no—
500C2×C4×C83—21no—
501C2×C4×C83—21no—
502C2×C4×C83—21no—
503C2×C4×C83—21no—
504C2×C4×C83—21no—
505C2×C4×C83—21no—
506C2×C4×C83—21no—
507C2×C4×C83—21no—
508C2×C4×C83—21no—
509C2×C4×C83—21no—
510C2×C4×C83—21no—
511C2×C4×C83—21no—
512C2×C4×C83—21no—
513C2×C4×C83—21no—
514C2×C4×C83—21no—
515C2×C4×C83—21no—
516C2×C4×C83—21no—
517C2×C4×C83C2×#4112yes—
518C2×Dic83—21no—
519C2×Dic83—21no—
520C2×Dic83—21no—
521C2×Dic83—21no—
522C2×Dic83—21no—
523C2×Dic83—21no—
524C2×Dic83—21no—
525C2×Dic83—21no—
526C2×Dic83—21no—
527C2×Dic83—21no—
528C2×Dic83—21no—
529C2×Dic83—21no—
530C2×Dic83—21no—
531C2×Dic83—21no—
532C2×Dic83—21no—
533C2×Dic83—21no—
534C2×Dic83—21no—
535C2×Dic83—21no—
536C2×Dic83—21no—
537C2×Dic83—21no—
538C2×Dic83—21no—
539C2×Dic83—21no—
540C2×Dic83—21no—
541C2×Dic83—21no—
542C2×Dic83—21no—
543C2×Dic83—21no—
544C2×Dic83—21no—
545C2×Dic83—21no—
546C2×Dic83—21no—
547C2×Dic83—21no—
548C2×Dic83—21no—
549C2×Dic83—21no—
550C2×Dic83—21no—
551C2×Dic83—21no—
552C2×Dic83—21no—
553C2×Dic83—21no—
554C2×Dic83—21no—
555C2×Dic83—21no—
556C2×Dic83—21no—
557C2×Dic83—21no—
558C2×Dic83—21no—
559C2×Dic83C2×#4112yes—
560C2×Dic83C2×#4112yes—
561C2×Dic832−1+412yes—
562C2×Dic832−1+412yes—
563C4×D83—44no—
564Dic166—44no—
565Dic166—44no—
566C22×C83C22×#4111yescharacteristic
567C22×C83C2×2−1+411yescharacteristic
568C22×C83C2×2−1+411yescharacteristic
569C22×C83#58511yescharacteristic
570C22×C83#58511yescharacteristic
571C22×C83#58511yescharacteristic
572C22×C83#58511yescharacteristic
573C2×D83—41no—
574C2×D83—41no—
575C2×D83—41no—
576C2×D83—41no—
577C2×D83—41no—
578C2×D83—41no—
579C2×D83—41no—
580C4×C83—22no—
581C4×C83—41no—
582C4×C83—41no—
583C4×C83—41no—
584C4×C83—41no—
585C4×C83—41no—
586C4×C83—41no—
587C4×C83—41no—
588C4×C83—41no—
589C4×C83—41no—
590C4×C83—41no—
591C4×C83—41no—
592C4×C83—41no—
593C4×C83—41no—
594C4×C83—41no—
595Dic83—22no—
596Dic83—41no—
597Dic83—41no—
598Dic83—41no—
599Dic83—41no—
600Dic83—41no—
601Dic83—41no—
602Dic83—41no—
603Dic83—41no—
604Dic83—41no—
605Dic83—41no—
606Dic83—41no—
607Dic83—41no—
608Dic83—41no—
609Dic83#54114yes—
610#36700—831nomaximal, Sylow
611C2×C83C2×#54111yescharacteristic
612C2×C83#345511yescharacteristic
613C2×C83#345511yescharacteristic
614C2×C83#353111yescharacteristic
615C2×C83#353111yescharacteristic
616C2×C83#353111yescharacteristic
617C2×C83#353111yescharacteristic
618D83—81no—
619#2839—831no—
620#2839—831no—
621#2839—831no—
622#2839D8311yescharacteristic, complemented
623#2836—831no—
624#2836—831no—
625#2836—831no—
626#2836—831no—
627#2833—831no—
628#2833—831no—
629#2833—831no—
630#2833—831no—
631#2831—831no—
632#2831—831no—
633#2831—831no—
634#2831—831no—
635#2402—831no—
636#2402—831no—
637#2402—831no—
638#2402—831no—
639#2402—831no—
640#2401—831no—
641#2401—831no—
642#2401—831no—
643#2401—831no—
644#2399—831no—
645#2396—831no—
646#2396—831no—
647#2298—831no—
648#2295—831no—
649#2295—831no—
650C83#3670011yescharacteristic, complemented, Sylow
651C2×C4×Q8—831no—
652C2×C4×Q8—831no—
653C2×#117—831no—
654#401—831no—
655#401—831no—
656#401—831no—
657#401—831no—
658#400—831no—
659#400—831no—
660#400—831no—
661#400—831no—
662#400—831no—
663#400—831no—
664#400—831no—
665#400—831no—
666#400—831no—
667#400—831no—
668#400—831no—
669#400—831no—
670#400—831no—
671#400—831no—
672#400—831no—
673#400—831no—
674#400—831no—
675#400—831no—
676#400—831no—
677#400—831no—
678#400—831no—
679#400—831no—
680#400—831no—
681#400—831no—
682#400—831no—
683#400—831no—
684#400—831no—
685#400C2×D8311yescharacteristic
686#400C2×D8311yescharacteristic
687#400C2×D8311yescharacteristic
688#400C2×D8311yescharacteristic
689#400C2×D8311yescharacteristic
690#400C2×D8311yescharacteristic
691#400C2×D8311yescharacteristic
692#399—831no—
693#399—831no—
694#398—831no—
695#398—831no—
696#398—831no—
697#398—831no—
698#398—831no—
699#398—831no—
700#398—831no—
701#398—831no—
702#398—831no—
703#398—831no—
704#398—831no—
705#398—831no—
706#398—831no—
707#398—831no—
708#398—831no—
709#398—831no—
710#398—831no—
711#398—831no—
712#398—831no—
713#398—831no—
714#398—831no—
715#398—831no—
716#398—831no—
717#398C2×D8311yescharacteristic
718#398C2×D8311yescharacteristic
719#398C2×D8311yescharacteristic
720#398C2×D8311yescharacteristic
721#398C2×D8311yescharacteristic
722#397—831no—
723#397—831no—
724#397—831no—
725#397—831no—
726#397—831no—
727#397—831no—
728#397—831no—
729#397—831no—
730#397—831no—
731#397—831no—
732#397—831no—
733#397—831no—
734#396—831no—
735#396—831no—
736#396—831no—
737#396—831no—
738#396—831no—
739#396—831no—
740#396—831no—
741#396—831no—
742#395—831no—
743#395—831no—
744#395—831no—
745#395—831no—
746#395—831no—
747#395—831no—
748#393—831no—
749#393—831no—
750#391—831no—
751#391—831no—
752#391—831no—
753#391—831no—
754#389—831no—
755#389—831no—
756#389—831no—
757#389C2×D8311yescharacteristic
758#388—831no—
759#388—831no—
760#388—831no—
761#388—831no—
762#387—831no—
763#387—831no—
764#387—831no—
765#387—831no—
766#387—831no—
767#387—831no—
768#387—831no—
769#387—831no—
770#387—831no—
771#387—831no—
772#387C2×D8311yescharacteristic
773#387C2×D8311yescharacteristic
774C4×C4⋊C4—831no—
775C4×C4⋊C4—831no—
776C4×C4⋊C4—831no—
777C4×C4⋊C4—831no—
778C4×C4⋊C4—831no—
779C4×C4⋊C4—831no—
780C4×C4⋊C4—831no—
781C4×C4⋊C4—831no—
782C4×C4⋊C4—831no—
783C4×C4⋊C4—831no—
784C4×C4⋊C4—831no—
785C4×C4⋊C4—831no—
786C4×C4⋊C4—831no—
787C4×C4⋊C4—831no—
788C4×C4⋊C4—831no—
789C4×C4⋊C4—831no—
790C4×C4⋊C4—831no—
791C4×C4⋊C4—831no—
792C4×C4⋊C4—831no—
793C4×C4⋊C4—831no—
794C4×C22⋊C4—831no—
795C4×C22⋊C4—831no—
796C4×C22⋊C4—831no—
797C4×C22⋊C4—831no—
798C4×C22⋊C4—831no—
799C4×C22⋊C4—831no—
800#376—831no—
801#376—831no—
802#376—831no—
803#376—831no—
804#376—831no—
805C43—831no—
806C22×Q8—831no—
807C22×Q8—831no—
808C23×C4—831no—
809C4×Q8—1664no—
810C4×Q8—1664no—
811#117—1664no—
812C2×C4⋊C4—831no—
813C2×C4⋊C4—831no—
814C2×C4⋊C4—831no—
815C2×C4⋊C4—831no—
816C2×C4⋊C4—831no—
817C2×C4⋊C4—831no—
818C2×C4⋊C4—831no—
819C2×C4⋊C4—831no—
820C2×C4⋊C4—831no—
821C2×C4⋊C4—831no—
822C2×C4⋊C4—831no—
823C2×C4⋊C4—831no—
824C2×C4⋊C4—831no—
825C2×C4⋊C4—831no—
826C2×C4⋊C4—831no—
827C2×C4⋊C4—831no—
828C2×C4⋊C4—831no—
829C2×C4⋊C4—831no—
830C2×C4⋊C4—831no—
831C2×C4⋊C4—831no—
832C2×C4⋊C4—831no—
833C2×C4⋊C4—831no—
834C2×C4⋊C4—831no—
835C2×C4⋊C4—831no—
836C2×C4⋊C4—831no—
837C2×C4⋊C4—831no—
838C2×C4⋊C4—831no—
839C2×C4⋊C4—831no—
840C2×C4⋊C4—831no—
841C2×C4⋊C4—831no—
842C2×C4⋊C4—831no—
843C2×C4⋊C4—831no—
844C2×C4⋊C4—831no—
845C2×C4⋊C4—831no—
846C2×C4⋊C4C22×D8311yescharacteristic
847C2×C4⋊C4C22×D8311yescharacteristic
848C2×C4⋊C4C22×D8311yescharacteristic
849C2×C4⋊C4C22×D8311yescharacteristic
850C2×C4⋊C4C22×D8311yescharacteristic
851C2×C4⋊C4C22×D8311yescharacteristic
852C2×C4⋊C4C22×D8311yescharacteristic
853C2×C4⋊C4C22×D8311yescharacteristic
854C2×C4⋊C4C22×D8311yescharacteristic
855C2×C4⋊C4C22×D8311yescharacteristic
856C2×C4⋊C4C22×D8311yescharacteristic
857C2×C4⋊C4C22×D8311yescharacteristic
858C2×C4⋊C4C22×D8311yescharacteristic
859C2×C4⋊C4C22×D8311yescharacteristic
860C2×C22⋊C4—831no—
861C2×C22⋊C4—831no—
862C2×C22⋊C4—831no—
863C2×C22⋊C4—831no—
864C2×C22⋊C4—831no—
865C2×C22⋊C4—831no—
866C2×C22⋊C4—831no—
867C2×C22⋊C4—831no—
868C2×C22⋊C4—831no—
869C2×C22⋊C4—831no—
870C2×C22⋊C4—831no—
871C2×C22⋊C4—831no—
872C2×C22⋊C4—831no—
873C2×C22⋊C4—831no—
874C2×C42—831no—
875C2×C42—831no—
876C2×C42—831no—
877C2×C42—831no—
878C2×C42—831no—
879C2×C42—831no—
880C2×C42—831no—
881C2×C42—831no—
882C2×C42—831no—
883C2×C42—831no—
884C2×C42—831no—
885C2×C42—831no—
886C2×C42—831no—
887C2×C42—831no—
888C2×C42—831no—
889C2×C42—831no—
890C2×C42—831no—
891C2×C42C22×D8311yescharacteristic
892#95—831no—
893#95—831no—
894#95—831no—
895#95—831no—
896#95—831no—
897#95—831no—
898#95—831no—
899#95—831no—
900#95—831no—
901#95—831no—
902#95—831no—
903#95—831no—
904#95—831no—
905#95—831no—
906#95—831no—
907#95—831no—
908#95—831no—
909#95—831no—
910#95—831no—
911#95—831no—
912#95—831no—
913#95—831no—
914#95—831no—
915#95—831no—
916#95—831no—
917#95—831no—
918#95—831no—
919#95—831no—
920#95—831no—
921#95—831no—
922#95—831no—
923#95—831no—
924#95—831no—
925#95—831no—
926#95—831no—
927#95—831no—
928#95—831no—
929#95—831no—
930#95—831no—
931#95—831no—
932#95—831no—
933#95—831no—
934#95—831no—
935#95—831no—
936#95—831no—
937#95—831no—
938#95—831no—
939#95—831no—
940#95—831no—
941#95—831no—
942#95—831no—
943#95—831no—
944#95C22×D8311yescharacteristic
945#95C22×D8311yescharacteristic
946#95C22×D8311yescharacteristic
947#95C22×D8311yescharacteristic
948#95C22×D8311yescharacteristic
949#95C22×D8311yescharacteristic
950#95C22×D8311yescharacteristic
951#95C22×D8311yescharacteristic
952#95C22×D8311yescharacteristic
953#95C22×D8311yescharacteristic
954#95C22×D8311yescharacteristic
955#95C22×D8311yescharacteristic
956#95C22×D8311yescharacteristic
957#95C22×D8311yescharacteristic
958#95C22×D8311yescharacteristic
959#95C22×D8311yescharacteristic
960#95C22×D8311yescharacteristic
961#95C22×D8311yescharacteristic
962#95C22×D8311yescharacteristic
963#95C22×D8311yescharacteristic
964C24—831no—
965C2×Q8—3321no—
966C2×Q8—3321no—
967C2×Q8—3321no—
968C2×Q8—3321no—
969C2×Q8—1662no—
970C2×Q8—1662no—
971C22×C4—831no—
972C22×C4—831no—
973C22×C4—831no—
974C22×C4—831no—
975C22×C4—831no—
976C22×C4—831no—
977C22×C4—831no—
978C22×C4—831no—
979C22×C4—831no—
980C22×C4—831no—
981C22×C4—831no—
982C22×C4—831no—
983C22×C4—831no—
984C22×C4—831no—
985C22×C4—831no—
986C22×C4—1662no—
987C22×C4—1662no—
988C22×C4—1662no—
989C22×C4C23×D8311yescharacteristic
990C22×C4C23×D8311yescharacteristic
991C22×C4C23×D8311yescharacteristic
992C22×C4C23×D8311yescharacteristic
993C22×C4C23×D8311yescharacteristic
994C22×C4C23×D8311yescharacteristic
995C22×C4C23×D8311yescharacteristic
996C22×C4C23×D8311yescharacteristic
997C22×C4C23×D8311yescharacteristic
998C22×C4C23×D8311yescharacteristic
999C22×C4C23×D8311yescharacteristic
1000C22×C4C23×D8311yescharacteristic
1001C22×C4C23×D8311yescharacteristic
1002C22×C4C23×D8311yescharacteristic
1003C22×C4C23×D8311yescharacteristic
1004C4⋊C4—22no—
1005C4⋊C4—22no—
1006C4⋊C4—22no—
1007C4⋊C4—41no—
1008C4⋊C4—41no—
1009C4⋊C4—41no—
1010C4⋊C4—41no—
1011C4⋊C4—41no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—41no—
1018C4⋊C4—3321no—
1019C4⋊C4—3321no—
1020C4⋊C4—3321no—
1021C4⋊C4—3321no—
1022C4⋊C4—3321no—
1023C4⋊C4—3321no—
1024C4⋊C4—3321no—
1025C4⋊C4—3321no—
1026C4⋊C4—3321no—
1027C4⋊C4—3321no—
1028C4⋊C4—3321no—
1029C4⋊C4—3321no—
1030C4⋊C4—3321no—
1031C4⋊C4—3321no—
1032C4⋊C4—3321no—
1033C4⋊C4—3321no—
1034C4⋊C4—3321no—
1035C4⋊C4—3321no—
1036C4⋊C4—3321no—
1037C4⋊C4—3321no—
1038C4⋊C4—3321no—
1039C4⋊C4—3321no—
1040C4⋊C4—3321no—
1041C4⋊C4—3321no—
1042C4⋊C4—3321no—
1043C4⋊C4—3321no—
1044C4⋊C4—3321no—
1045C4⋊C4—3321no—
1046C4⋊C4—3321no—
1047C4⋊C4—1662no—
1048C4⋊C4—1662no—
1049C4⋊C4—1662no—
1050C4⋊C4—1662no—
1051C4⋊C4—1662no—
1052C22⋊C4—3321no—
1053C22⋊C4—3321no—
1054C22⋊C4—3321no—
1055C22⋊C4—3321no—
1056C22⋊C4—3321no—
1057C22⋊C4—3321no—
1058C22⋊C4—3321no—
1059C22⋊C4—3321no—
1060C22⋊C4—3321no—
1061C22⋊C4—3321no—
1062C22⋊C4—3321no—
1063C22⋊C4—3321no—
1064C22⋊C4—1662no—
1065C22⋊C4—1662no—
1066C42—41no—
1067C42—3321no—
1068C42—3321no—
1069C42—3321no—
1070C42—834no—
1071C42—1662no—
1072C42—1662no—
1073C42—1662no—
1074C42—1662no—
1075C42—1662no—
1076C42—1662no—
1077C42—1662no—
1078C42—1662no—
1079C42—1662no—
1080C42—1662no—
1081C42—1662no—
1082C42—1662no—
1083C42—1662no—
1084C23—1661no—
1085C23—1661no—
1086C23—1661no—
1087C23—1661no—
1088C23—1661no—
1089C23—1661no—
1090C23—1661no—
1091C23C24×D8311yescharacteristic
1092Q8—3324no—
1093Q8—3324no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—3324no—
1139C2×C4—832no—
1140C2×C4—832no—
1141C2×C4—832no—
1142C2×C4—832no—
1143C2×C4—1661no—
1144C2×C4—1661no—
1145C2×C4—1661no—
1146C2×C4—1661no—
1147C2×C4—1661no—
1148C2×C4—1661no—
1149C2×C4—1661no—
1150C2×C4—1661no—
1151C2×C4—1661no—
1152C2×C4—1661no—
1153C2×C4—1661no—
1154C2×C4—1661no—
1155C2×C4—1661no—
1156C2×C4—1661no—
1157C2×C4—1661no—
1158C2×C4—1661no—
1159C2×C4—1661no—
1160C2×C4—1661no—
1161C2×C4—1661no—
1162C2×C4—1661no—
1163C2×C4—1661no—
1164C2×C4—1661no—
1165C2×C4—1661no—
1166C2×C4—1661no—
1167C2×C4—1661no—
1168C2×C4—1661no—
1169C2×C4—1661no—
1170C2×C4—1661no—
1171C2×C4—1661no—
1172C2×C4—1661no—
1173C2×C4—1661no—
1174C2×C4—1661no—
1175C2×C4—1661no—
1176C2×C4—1661no—
1177C2×C4—1661no—
1178C2×C4—1661no—
1179C2×C4—1661no—
1180C2×C4—1661no—
1181C2×C4—1661no—
1182C2×C4—1661no—
1183C2×C4—1661no—
1184C2×C4#41×D8312yes—
1185C22—3321no—
1186C22—3321no—
1187C22—3321no—
1188C22—3321no—
1189C22—3321no—
1190C22—3321no—
1191C22—3321no—
1192C22C2×#41×D8311yescharacteristic
1193C222−1+4×D8311yescharacteristic
1194C222−1+4×D8311yescharacteristic
1195C22#1912853611yescharacteristic
1196C22#1912853611yescharacteristic
1197C22#1912853811yescharacteristic
1198C22#1912853811yescharacteristic
1199C4—22no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—41no—
1204C4—41no—
1205C4—41no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—3321no—
1215C4—3321no—
1216C4—3321no—
1217C4—3321no—
1218C4—3321no—
1219C4—3321no—
1220C4—3321no—
1221C4—3321no—
1222C4—3321no—
1223C4—3321no—
1224C4—3321no—
1225C4—3321no—
1226C4—3321no—
1227C4—834no—
1228C4—1662no—
1229C2—6641no—
1230C2#541×D8311yescharacteristic
1231C2#2492084911yescharacteristic
1232C2#2492085011yescharacteristic
1233C2#2492160711yescharacteristic
1234C2#2492160911yescharacteristic
1235C2#2492160911yescharacteristic
1236C2#2492161111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2839C2
prime radicalC23×D83C24
hypercenter#2839D83
hypocenterC83#36700
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2839

Complements

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

NH ≅ G/Ntype
1. #24915712C2semidirect
2. #24915707C2semidirect
3. #24915706C2semidirect
8. #24915643C2semidirect
9. #24915640C2semidirect
10. #24915637C2semidirect
11. #24915636C2semidirect
16. #24910769C2semidirect
17. #24910769C2semidirect
18. #24910767C2semidirect
19. #24910767C2semidirect
20. #24910767C2semidirect
25. #24910755C2semidirect
29. #24909936C2semidirect
30. #24909934C2semidirect
31. C83×#2839C2semidirect
622. #2839D83semidirect
650. C83#36700semidirect

Maximal subgroups

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

subgroupindex
#249157122
#249157072
#249157062
#249156672
#249156662
#249156612
#249156582
#249156432
#249156402
#249156372
#249156362
#249156262
#249156252
#249156172
#249156162
#249107692
#249107672
#249107622
#249107552
#249107402
#249107362
#249099552
#249099362
#249099342
C83×#28392
#3670083