Finite Group Databasebeta

← #28404571

Subgroups — #28404571

Order 14464.

1122 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299324C211yesmaximal, characteristic, complemented
2#20299295C213yesmaximal, complemented
3#20299294C213yesmaximal, complemented
4#20299268C213yesmaximal, complemented
5#20299267C211yesmaximal, characteristic, complemented
6#20299267C211yesmaximal, characteristic, complemented
7#20299248C213yesmaximal, complemented
8#20299202C213yesmaximal, complemented
9#20299201C213yesmaximal, complemented
10#20299143C213yesmaximal, complemented
11#20299128C213yesmaximal, complemented
12#20299081C211yesmaximal, characteristic, complemented
13#20299080C211yesmaximal, characteristic, complemented
14#41×Dic113C211yesmaximal, characteristic, complemented
15#550×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2216yes—
18#16813621C2213yes—
19#16813618C2213yes—
20#16813618C2213yes—
21#16813617C2213yes—
22#16813615C2213yes—
23#16813614C2213yes—
24#16813613C2213yes—
25#16813612C2211yescharacteristic
26#16813608C2213yes—
27#16813606C2213yes—
28#16813604C2216yes—
29#16813603C2216yes—
30#16813603C2213yes—
31#16813599C2213yes—
32#16813596C2213yes—
33#16813596C2213yes—
34#16813594C2213yes—
35#16813594C2216yes—
36#16813594C2216yes—
37#16813593C2213yes—
38#16813593C2213yes—
39#16813593C2216yes—
40Q8×Dic113C2211yescharacteristic
41Q8×Dic113C2211yescharacteristic
42Q8×Dic113C2211yescharacteristic
43C4×Dic226C2213yes—
44C4×D452C2213yes—
45D4×Dic113C2213yes—
46D4×Dic113C2213yes—
47D4×Dic113C2213yes—
48D4×Dic113C2213yes—
49#16813584C2213yes—
50C4×C22⋊D113C2213yes—
51C4×C22⋊D113C2213yes—
52#16813582C2216yes—
53#16813581C2213yes—
54#16813581C2213yes—
55#16813579C2213yes—
56C2×C4⋊Dic113C2213yes—
57C4⋊C4×D113C2213yes—
58C2×C4×Dic113C2213yes—
59C2×#41×C113C2211yescharacteristic
60C2×#41×C113C2211yescharacteristic
61#127×C113C2213yes—
62#121×C113C2213yes—
63#121×C113C2213yes—
64C4×Q8×C113C2211yescharacteristic
65C4×D4×C113C2213yes—
66#14268648—24no—
67#14268646—412no—
68C2×Dic226C2313yes—
69C2×D452C2313yes—
70C2×C22⋊D113C2313yes—
71C2×C22⋊D113C2316yes—
72C2×C22⋊D113C2313yes—
73C2×C22⋊D113C2316yes—
74C22×Dic113C2313yes—
75C22×Dic113C2313yes—
76C22×Dic113C2316yes—
77C2×C4×D113C2313yes—
78C2×C4×D113C2316yes—
79C4⋊Dic113C2313yes—
80C4⋊Dic113C2313yes—
81C4⋊Dic113C2313yes—
82C4⋊Dic113C2311yescharacteristic
83C4⋊Dic113C2313yes—
84C4⋊Dic113C2313yes—
85#14268626C2313yes—
86#14268626C2311yescharacteristic
87#14268626C2316yes—
88#14268626C2311yescharacteristic
89#14268626C2311yescharacteristic
90#14268626C2311yescharacteristic
91#14268626C2313yes—
92C22⋊Dic113C2313yes—
93C22⋊Dic113C2316yes—
94C22⋊Dic113C2313yes—
95C22⋊Dic113C2313yes—
96C22⋊Dic113C2313yes—
97#14268624C2313yes—
98#14268624C2313yes—
99#14268624C2313yes—
100#14268624C2313yes—
101C4×Dic113C2311yescharacteristic
102C4×Dic113C2313yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105C4×Dic113C2313yes—
106#41×C113—24no—
107#41×C113—24no—
108C2×Q8×C113C2311yescharacteristic
109C2×D4×C113C2313yes—
110C2×D4×C113C2313yes—
111C2×D4×C113C2316yes—
112C2×D4×C113C2313yes—
113C22×C4×C113C2313yes—
114C22×C4×C113C2313yes—
115C4⋊C4×C113C2313yes—
116C4⋊C4×C113C2311yescharacteristic
117C22⋊C4×C113C2313yes—
118C22⋊C4×C113C2313yes—
119C42×C113C2313yes—
120C23×C113C2413yes—
121C23×C113C2413yes—
122C22×D113C2413yes—
123Q8×C113#4114yescomplemented
124D4×C113—26no—
125D4×C113—26no—
126D4×C113—43no—
127D4×C113—46no—
128C2×C4×C113—26no—
129C2×C4×C113—26no—
130C2×C4×C113C2411yescharacteristic
131C2×C4×C113C2413yes—
132C2×C4×C113C2411yescharacteristic
133C2×C4×C113C2411yescharacteristic
134C2×C4×C113C2413yes—
135C22⋊D113—26no—
136C22⋊D113—46no—
137C22⋊D113—43no—
138C22⋊D113—46no—
139C2×Dic113—26no—
140C2×Dic113—43no—
141C2×Dic113—46no—
142C2×Dic113C2411yescharacteristic
143C2×Dic113C2411yescharacteristic
144C2×Dic113C2413yes—
145C2×Dic113C2413yes—
146C2×Dic113C2413yes—
147C2×Dic113C2411yescharacteristic
148C2×Dic113C2411yescharacteristic
149D452—26no—
150C4×D113—26no—
151C4×D113—46no—
152Dic226—26no—
153C22×C113—23no—
154C22×C113—23no—
155C22×C113—23no—
156C22×C113—23no—
157C22×C113—23no—
158C22×C113—23no—
159C22×C113C2511yescharacteristic
160C2×D113—23no—
161C2×D113—23no—
162C2×D113—23no—
163C4×C113—21no—
164C4×C113—21no—
165C4×C113—23no—
166C4×C113—21no—
167C4×C113C2×#4116yes—
168Dic113—21no—
169Dic113—23no—
170Dic113—23no—
171Dic113—21no—
172Dic113—23no—
173Dic113—21no—
174Dic113H(5,𝔽2)12yes—
175C2×C113—43no—
176C2×C113—43no—
177C2×C113C22×#4111yescharacteristic
178C2×C113C2×H(5,𝔽2)11yescharacteristic
179C2×C113#58511yescharacteristic
180D113—43no—
181#3517—1131nomaximal, Sylow
182C113#351711yescharacteristic, complemented, Sylow
183#557—1131no—
184#553—1133no—
185#553—1133no—
186#550—1131no—
187#550—1131no—
188#550—1133no—
189#550D11311yescharacteristic, complemented
190#547—1133no—
191#540—1133no—
192#540—1133no—
193#532—1133no—
194#529—1133no—
195#520—1131no—
196#520—1131no—
197C4×#41—1131no—
198C2×#41—1131no—
199C2×#41—1136no—
200C2×#41C2×D11311yescharacteristic
201C2×#41C2×D11311yescharacteristic
202C4⋊Q8—1133no—
203#127—1133no—
204#127—1133no—
205#127C2×D11313yes—
206#126—1133no—
207#126—1133no—
208#125—1131no—
209#125—1133no—
210#125—1133no—
211#124—1133no—
212#123—1133no—
213#123—1136no—
214#123—1133no—
215#123—1136no—
216C22⋊Q8—1133no—
217#121—1133no—
218#121—1136no—
219#121—1133no—
220#121—1136no—
221#121—1133no—
222#121—1136no—
223#121—1133no—
224#121—1133no—
225#121C2×D11313yes—
226#121C2×D11313yes—
227C4×Q8—1131no—
228C4×Q8—1131no—
229C4×Q8—1131no—
230C4×Q8—1133no—
231C4×Q8C2×D11311yescharacteristic
232C4×D4—1133no—
233C4×D4—1133no—
234C4×D4—1133no—
235C4×D4—1133no—
236C4×D4—1133no—
237C4×D4—1133no—
238C4×D4—1133no—
239C4×D4—1136no—
240C4×D4—1133no—
241C4×D4C2×D11313yes—
242#117—1133no—
243#117—1133no—
244#117—1133no—
245C2×C4⋊C4—1133no—
246C2×C4⋊C4—1133no—
247C2×C42—1133no—
248#41—24no—
249#41—24no—
250#41—45212no—
251#41—2264no—
252C2×Q8—1133no—
253C2×Q8C22×D11311yescharacteristic
254C2×D4—1136no—
255C2×D4—1133no—
256C2×D4—1136no—
257C2×D4—1133no—
258C2×D4—1133no—
259C2×D4C22×D11313yes—
260C2×D4C22×D11313yes—
261C2×D4C22×D11313yes—
262C2×D4C22×D11316yes—
263C22×C4—1133no—
264C22×C4—1136no—
265C22×C4—1133no—
266C22×C4—1136no—
267C22×C4—1133no—
268C22×C4C22×D11313yes—
269C22×C4C22×D11313yes—
270C4⋊C4—1133no—
271C4⋊C4—1133no—
272C4⋊C4—1133no—
273C4⋊C4—1133no—
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1133no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4—1136no—
280C4⋊C4—1131no—
281C4⋊C4—1133no—
282C4⋊C4—1133no—
283C4⋊C4C22×D11313yes—
284C4⋊C4C22×D11311yescharacteristic
285C22⋊C4—1133no—
286C22⋊C4—1136no—
287C22⋊C4—1133no—
288C22⋊C4—1133no—
289C22⋊C4—1133no—
290C22⋊C4—1133no—
291C22⋊C4—1133no—
292C22⋊C4—1133no—
293C22⋊C4—1133no—
294C22⋊C4C22×D11313yes—
295C22⋊C4C22×D11313yes—
296C42—1131no—
297C42—1133no—
298C42—1133no—
299C42—1133no—
300C42—1133no—
301C42C22×D11313yes—
302C23—1133no—
303C23C23×D11313yes—
304C23C23×D11313yes—
305Q8—2266no—
306Q8#1426864614yescomplemented
307D4—26no—
308D4—26no—
309D4—46no—
310D4—43no—
311D4—4526no—
312D4—4526no—
313D4—4523no—
314D4—2266no—
315D4—2266no—
316C2×C4—26no—
317C2×C4—26no—
318C2×C4—1131no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1133no—
322C2×C4—1133no—
323C2×C4—1133no—
324C2×C4—1131no—
325C2×C4—4526no—
326C2×C4—4526no—
327C2×C4—4523no—
328C2×C4—2266no—
329C2×C4—2266no—
330C2×C4C23×D11311yescharacteristic
331C2×C4C23×D11311yescharacteristic
332C2×C4C23×D11313yes—
333C2×C4C23×D11311yescharacteristic
334C2×C4C23×D11313yes—
335C22—23no—
336C22—23no—
337C22—23no—
338C22—23no—
339C22—23no—
340C22—23no—
341C22—2263no—
342C22—2263no—
343C22—2263no—
344C22C24×D11311yescharacteristic
345C4—21no—
346C4—21no—
347C4—23no—
348C4—21no—
349C4—1132no—
350C4—2261no—
351C4—2263no—
352C4—2263no—
353C4—2261no—
354C4—2263no—
355C4—2261no—
356C4C2×#1426864616yes—
357C2—43no—
358C2—43no—
359C2—4523no—
360C2C22×#1426864611yescharacteristic
361C2H(5,𝔽2)×D11311yescharacteristic
362C2#2029943411yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#550×C113C2
hypercenter#550D113
hypocenterC113#3517
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #550

Complements

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

NH ≅ G/Ntype
1. #20299324C2semidirect
2. #20299295C2semidirect
3. #20299294C2semidirect
4. #20299268C2semidirect
5. #20299267C2semidirect
6. #20299267C2semidirect
7. #20299248C2semidirect
8. #20299202C2semidirect
9. #20299201C2semidirect
10. #20299143C2semidirect
11. #20299128C2semidirect
12. #20299081C2semidirect
13. #20299080C2semidirect
14. #41×Dic113C2semidirect
15. #550×C113C2semidirect
123. Q8×C113#41semidirect
182. C113#3517semidirect
189. #550D113semidirect
306. Q8#14268646semidirect

Maximal subgroups

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

subgroupindex
#202993242
#202992952
#202992942
#202992682
#202992672
#202992482
#202992022
#202992012
#202991432
#202991282
#202990812
#202990802
#41×Dic1132
#550×C1132
#3517113