Finite Group Databasebeta

← #28404399

Subgroups — #28404399

Order 14464.

988 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299327C211yesmaximal, characteristic, complemented
2#20299324C211yesmaximal, characteristic, complemented
3#20299324C211yesmaximal, characteristic, complemented
4#20299309C213yesmaximal, complemented
5#20299308C213yesmaximal, complemented
6#20299304C213yesmaximal, complemented
7#20299304C213yesmaximal, complemented
8#20299228C213yesmaximal, complemented
9#20299225C213yesmaximal, complemented
10#20299152C213yesmaximal, complemented
11#125×D113C213yesmaximal, complemented
12#20299080C211yesmaximal, characteristic
13#20299080C211yesmaximal, characteristic
14C4×#14268648C211yesmaximal, characteristic
15#557×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17#16813622C2213yes—
18#16813621C2213yes—
19#16813621C2213yes—
20#16813621C2213yes—
21#16813620C2213yes—
22#16813614C2213yes—
23#16813614C2213yes—
24#16813613C2213yes—
25#16813613C2213yes—
26#16813613C2213yes—
27#16813613C2213yes—
28#16813612C2213yes—
29#16813612C2216yes—
30#16813612C2211yescharacteristic
31#16813602C2213yes—
32#16813602C2216yes—
33#16813600C2213yes—
34#16813600C2216yes—
35#16813600C2216yes—
36#16813600C2213yes—
37#16813598C2216yes—
38#16813598C2213yes—
39Q8×Dic113C2211yescharacteristic
40Q8×Dic113C2211yescharacteristic
41Q8×Dic113C2211yescharacteristic
42C4×Dic226C2213yes—
43C4×Dic226C2213yes—
44C4×Dic226C2213yes—
45C4×D452C2213yes—
46C4×D452C2213yes—
47C4×D452C2213yes—
48#16813584C2213yes—
49#16813584C2213yes—
50#16813584C2213yes—
51#16813580C2213yes—
52#16813579C2213yes—
53#16813579C2213yes—
54C4⋊C4×D113C2216yes—
55C4⋊C4×D113C2216yes—
56C4⋊C4×D113C2213yes—
57C4⋊C4×D113C2213yes—
58C42×D113C2213yes—
59C4⋊Q8×C113C2213yes—
60#125×C113C2213yes—
61#125×C113C2213yes—
62C4×Q8×C113C2213yes—
63C4×Q8×C113C2211yescharacteristic
64C4×Q8×C113C2211yescharacteristic
65C4×Q8×C113C2211yescharacteristic
66#14268648Q818yescomplemented
67C2×Dic226C2313yes—
68C2×Dic226C2313yes—
69C2×Dic226C2313yes—
70C2×D452C2313yes—
71C2×C4×D113C2313yes—
72C2×C4×D113C2313yes—
73C2×C4×D113C2316yes—
74C2×C4×D113C2316yes—
75C2×C4×D113C2313yes—
76C4⋊Dic113C2313yes—
77C4⋊Dic113C2313yes—
78C4⋊Dic113C2313yes—
79C4⋊Dic113C2316yes—
80C4⋊Dic113C2313yes—
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2313yes—
83#14268626C2313yes—
84#14268626C2313yes—
85#14268626C2313yes—
86#14268626C2313yes—
87#14268626C2316yes—
88#14268626C2316yes—
89#14268626C2311yescharacteristic
90#14268626C2311yescharacteristic
91#14268626C2311yescharacteristic
92#14268626C2311yescharacteristic
93#14268626C2313yes—
94#14268626C2313yes—
95#14268624C2313yes—
96#14268624C2313yes—
97#14268624C2313yes—
98#14268624C2313yes—
99#14268624C2316yes—
100C4×Dic113C2311yescharacteristic
101C4×Dic113C2313yes—
102C4×Dic113C2313yes—
103C4×Dic113C2313yes—
104C4×Dic113C2313yes—
105C2×Q8×C113C2313yes—
106C2×Q8×C113C2311yescharacteristic
107C4⋊C4×C113C2313yes—
108C4⋊C4×C113C2313yes—
109C4⋊C4×C113C2313yes—
110C4⋊C4×C113C2316yes—
111C4⋊C4×C113C2313yes—
112C4⋊C4×C113C2311yescharacteristic
113C4⋊C4×C113C2313yes—
114C42×C113C2313yes—
115C42×C113C2313yes—
116C42×C113C2313yes—
117C22×D113C2413yes—
118Q8×C113—43no—
119Q8×C113C2×Q814yes—
120C2×C4×C113C2411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C2×C4×C113C2411yescharacteristic
123C2×C4×C113C2413yes—
124C2×C4×C113C2413yes—
125C2×C4×C113C2413yes—
126C2×C4×C113C2413yes—
127C2×Dic113C2411yescharacteristic
128C2×Dic113C2411yescharacteristic
129C2×Dic113C2411yescharacteristic
130C2×Dic113C2413yes—
131C2×Dic113C2413yes—
132C2×Dic113C2413yes—
133C2×Dic113C2411yescharacteristic
134D452C2×Q8112yes—
135C4×D113—43no—
136C4×D113—46no—
137C4×D113—46no—
138C4×D113—43no—
139C4×D113C2×Q8112yes—
140Dic226—43no—
141Dic226—43no—
142Dic226—43no—
143C22×C113C2511yescharacteristic
144C2×D113—23no—
145C2×D113—23no—
146C2×D113C22×Q816yes—
147C4×C113—21no—
148C4×C113—23no—
149C4×C113—23no—
150C4×C113—21no—
151C4×C113—23no—
152C4×C113—21no—
153C4×C113C22×Q816yes—
154Dic113—21no—
155Dic113—21no—
156Dic113—23no—
157Dic113—23no—
158Dic113—23no—
159Dic113—21no—
160Dic113C22×Q812yes—
161C2×C113C23×Q811yescharacteristic
162C2×C113#58511yescharacteristic
163C2×C113#58511yescharacteristic
164D113—26no—
165#3504—1131nomaximal, Sylow
166C113#350411yescharacteristic, complemented, Sylow
167#557—1131no—
168#557—1131no—
169#557—1131no—
170#557D11311yescharacteristic, complemented
171#554—1133no—
172#554—1133no—
173#554—1133no—
174#554—1133no—
175#544—1133no—
176#544—1133no—
177#533—1133no—
178C2×#125—1133no—
179#520—1131no—
180#520—1131no—
181C4×#41—1131no—
182C2×#41—1131no—
183C4⋊Q8—1133no—
184C4⋊Q8—1133no—
185C4⋊Q8—1133no—
186C4⋊Q8—1133no—
187C4⋊Q8—1133no—
188C4⋊Q8C2×D11313yes—
189#125—1133no—
190#125—1136no—
191#125—1133no—
192#125—1133no—
193#125—1131no—
194#125—1133no—
195#125—1133no—
196#125—1133no—
197#125—1133no—
198#125C2×D11313yes—
199#125C2×D11313yes—
200C22⋊Q8—1133no—
201C22⋊Q8—1136no—
202C22⋊Q8—1133no—
203C22⋊Q8—1133no—
204C22⋊Q8—1133no—
205C22⋊Q8—1136no—
206C22⋊Q8—1136no—
207C22⋊Q8—1136no—
208C4×Q8—1131no—
209C4×Q8—1131no—
210C4×Q8—1131no—
211C4×Q8—1133no—
212C4×Q8—1133no—
213C4×Q8—1133no—
214C4×Q8C2×D11311yescharacteristic
215C4×Q8C2×D11311yescharacteristic
216C4×Q8C2×D11311yescharacteristic
217C4×Q8C2×D11313yes—
218C4×D4—1133no—
219C4×D4—1133no—
220C4×D4—1133no—
221C4×D4—1133no—
222C4×D4—1133no—
223C4×D4—1133no—
224#117—1133no—
225#117—1133no—
226#117—1133no—
227C2×C4⋊C4—1133no—
228C2×C4⋊C4—1133no—
229C2×C4⋊C4—1136no—
230C2×C4⋊C4—1136no—
231C2×C42—1133no—
232#41—1138no—
233C2×Q8—1133no—
234C2×Q8—1133no—
235C2×Q8—1133no—
236C2×Q8C22×D11313yes—
237C2×Q8C22×D11311yescharacteristic
238C2×D4—1133no—
239C22×C4—1133no—
240C22×C4—1133no—
241C22×C4—1133no—
242C22×C4—1136no—
243C22×C4—1136no—
244C4⋊C4—1133no—
245C4⋊C4—1133no—
246C4⋊C4—1133no—
247C4⋊C4—1133no—
248C4⋊C4—1133no—
249C4⋊C4—1133no—
250C4⋊C4—1133no—
251C4⋊C4—1136no—
252C4⋊C4—1136no—
253C4⋊C4—1136no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1133no—
257C4⋊C4—1131no—
258C4⋊C4—1131no—
259C4⋊C4—1131no—
260C4⋊C4—1133no—
261C4⋊C4—1133no—
262C4⋊C4—1133no—
263C4⋊C4C22×D11313yes—
264C4⋊C4C22×D11313yes—
265C4⋊C4C22×D11313yes—
266C4⋊C4C22×D11316yes—
267C4⋊C4C22×D11313yes—
268C4⋊C4C22×D11311yescharacteristic
269C4⋊C4C22×D11313yes—
270C22⋊C4—1133no—
271C22⋊C4—1133no—
272C22⋊C4—1136no—
273C22⋊C4—1133no—
274C22⋊C4—1133no—
275C42—1131no—
276C42—1133no—
277C42—1133no—
278C42—1133no—
279C42—1133no—
280C42C22×D11313yes—
281C42C22×D11313yes—
282C42C22×D11313yes—
283C23—1133no—
284Q8—43no—
285Q8—4523no—
286Q8—4523no—
287Q8—4523no—
288Q8Q8×D11314yes—
289D4—11312no—
290C2×C4—1131no—
291C2×C4—11312no—
292C2×C4—1131no—
293C2×C4—1131no—
294C2×C4—1131no—
295C2×C4—1133no—
296C2×C4—1133no—
297C2×C4—1133no—
298C2×C4—4526no—
299C2×C4—4523no—
300C2×C4—4523no—
301C2×C4—4526no—
302C2×C4C23×D11311yescharacteristic
303C2×C4C23×D11313yes—
304C2×C4C23×D11311yescharacteristic
305C2×C4C23×D11311yescharacteristic
306C2×C4C23×D11313yes—
307C2×C4C23×D11313yes—
308C2×C4C23×D11313yes—
309C22—1136no—
310C22—2263no—
311C22—2263no—
312C22C24×D11311yescharacteristic
313C4—23no—
314C4—23no—
315C4—21no—
316C4—21no—
317C4—23no—
318C4—21no—
319C4—1132no—
320C4—2261no—
321C4—2263no—
322C4—2261no—
323C4—2263no—
324C4—2263no—
325C4—2261no—
326C4C2×Q8×D11316yes—
327C2—2266no—
328C2C22×Q8×D11311yescharacteristic
329C2#2029943411yescharacteristic
330C2#2029943511yescharacteristic
subgroupG/H
center, FrattiniC22C24×D113
commutator, socle, cosocleC22×C113C25
Fitting#557×C113C2
prime radicalC2×#14268648C22
hypercenter#557D113
hypocenterC113#3504
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ #557

Complements

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

NH ≅ G/Ntype
1. #20299327C2semidirect
2. #20299324C2semidirect
3. #20299324C2semidirect
4. #20299309C2semidirect
5. #20299308C2semidirect
6. #20299304C2semidirect
7. #20299304C2semidirect
8. #20299228C2semidirect
9. #20299225C2semidirect
10. #20299152C2semidirect
11. #125×D113C2semidirect
15. #557×C113C2semidirect
66. #14268648Q8semidirect
166. C113#3504semidirect
170. #557D113semidirect

Maximal subgroups

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

subgroupindex
#202993272
#202993242
#202993092
#202993082
#202993042
#202992282
#202992252
#202991522
#125×D1132
#202990802
C4×#142686482
#557×C1132
#3504113