Finite Group Databasebeta

← #13079618

Subgroups — #13079618

Order 1408.

400 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#67000C211yesmaximal, characteristic
2#10623153C211yesmaximal, characteristic, complemented
3C11×#451C211yesmaximal, characteristic, complemented
4#10622841C211yesmaximal, characteristic, complemented
5#10622803C212yesmaximal, complemented
6#10622798C212yesmaximal, complemented
7#10622659C211yesmaximal, characteristic
8#10622411C212yesmaximal, complemented
9#10622408C212yesmaximal, complemented
10#10622344C211yesmaximal, characteristic
11#10622332C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C2×C11×Q16C2212yescomplemented
15C11×C22⋊Q8C2211yescharacteristic
16#67000—21no—
17#67000—21no—
18#67000C2212yes—
19#67000C2212yes—
20Q8×Dic11C2211yescharacteristic, complemented
21#66997C2211yescharacteristic, complemented
22C2×#4326C2212yescomplemented
23C2×#4325C2212yes—
24C2×(C2×D11)⋊C4—21no—
25C2×(C2×D11)⋊C4—21no—
26#66977C2211yescharacteristic
27C2×C4×Dic11C2211yescharacteristic
28C2×#4314C2212yes—
29#66942—21no—
30#66941C2211yescharacteristic, complemented
31#66940—21no—
32#66940C2211yescharacteristic, complemented
33#66931—21no—
34#66930—21no—
35C11×#103C2212yescomplemented
36C11×C22⋊C8C2211yescharacteristic
37#66899C2212yescomplemented
38C22⋊(C11⋊C8)C2211yescharacteristic
39#66885C2212yes—
40#66879C2212yescomplemented
41Dic11⋊C8C2212yescomplemented
42#66873C2212yes—
43C23×D11—21no—
44C2×Q8×C11—21no—
45C2×Q8×C11—42no—
46C2×Q8×C11C2312yes—
47C2×Q8×C11C2311yescharacteristic
48C22×C4×C11—21no—
49C22×C4×C11C2311yescharacteristic
50C22×Dic11D411yescharacteristic
51C22×Dic11D411yescharacteristic
52C2×D44—21no—
53C2×D44—42no—
54C2×D44C2312yes—
55C2×Dic22—21no—
56C2×Dic22C2311yescharacteristic
57C11×Q16—42no—
58C2×C8×C11C2312yes—
59C11×C4⋊C4—21no—
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—21no—
62C22⋊Dic11—21no—
63#4326—42no—
64#4325—42no—
65(C2×D11)⋊C4—22no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4—22no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11C2311yescharacteristic
71Dic11⋊C4—21no—
72Dic11⋊C4—21no—
73Dic11⋊C4—21no—
74Dic11⋊C4—21no—
75Dic11⋊C4—21no—
76C4×Dic11—21no—
77C4×Dic11—21no—
78C4×Dic11D411yescharacteristic
79C4×Dic11D411yescharacteristic
80C4×Dic11C2311yescharacteristic
81C4×Dic11C2311yescharacteristic
82C2×C11⋊C8C2312yes—
83#4314—42no—
84#3215—111nomaximal, Sylow
85C23×C11C2×D411yescharacteristic
86C22×D11—22no—
87C22×D11—42no—
88C22×D11—42no—
89C22×D11—42no—
90Q8×C11—22no—
91Q8×C11—22no—
92Q8×C11—22no—
93Q8×C11—42no—
94C2×C4×C11—22no—
95C2×C4×C11—21no—
96C2×C4×C11—21no—
97C2×C4×C11—22no—
98C2×C4×C11—42no—
99C2×C4×C11C2×D411yescharacteristic
100C2×C4×C11C2411yescharacteristic
101C2×Dic11—22no—
102C2×Dic11—21no—
103C2×Dic11—21no—
104C2×Dic11—41no—
105C2×Dic11C2×D411yescharacteristic
106C2×Dic11C2×D411yescharacteristic
107C2×Dic11C2×D411yescharacteristic
108C2×Dic11C2×D411yescharacteristic
109D44—22no—
110D44—22no—
111D44—42no—
112Dic22—22no—
113Dic22—42no—
114C8×C11—22no—
115C11⋊C8—22no—
116#533—111no—
117C2×#124—111no—
118#497—112no—
119#489—112no—
120#464—112no—
121#464—112no—
122#451—111no—
123#451D1111yescharacteristic, complemented
124#450—111no—
125#450—111no—
126#432—111no—
127C22×C11—21no—
128C22×C11—21no—
129C22×C11#13712yes—
130C22×C11C22×D411yescharacteristic
131C2×D11—42no—
132C2×D11—42no—
133C2×D11—42no—
134C2×D11—84no—
135C4×C11—21no—
136C4×C11—42no—
137C4×C11—41no—
138C4×C11—41no—
139C4×C11H(5,𝔽2)12yes—
140Dic11—21no—
141Dic11—21no—
142Dic11—21no—
143Dic11—21no—
144Dic11—41no—
145Dic11—41no—
146C22×Q8C2×D1111yescharacteristic
147C22×D4—111no—
148C2×Q16—112no—
149C2×Q16C2×D1112yescomplemented
150C2×SD16—112no—
151C2×SD16—112no—
152C4⋊Q8—111no—
153C4⋊Q8—111no—
154#125—221no—
155#124—112no—
156#124—112no—
157#124—221no—
158#124—221no—
159C22⋊Q8—111no—
160C22⋊Q8—221no—
161C22⋊Q8C2×D1111yescharacteristic
162C4×Q8—111no—
163C4×Q8—111no—
164C4×Q8—221no—
165#117—221no—
166C2×C22⋊C4—221no—
167C2×C22⋊C4—221no—
168C2×C42—111no—
169C4⋊C8—112no—
170#103—112no—
171#103C2×D1112yescomplemented
172#102—112no—
173#102—112no—
174C22⋊C8—111no—
175C22⋊C8C2×D1111yescharacteristic
176#97—112no—
177C2×C11—22no—
178C2×C11#53511yescharacteristic
179C2×C11C2×#13711yescharacteristic
180C2×C11#57511yescharacteristic
181D11—82no—
182C24—221no—
183C2×Q8—21no—
184C2×Q8—42no—
185C2×Q8—111no—
186C2×Q8—221no—
187C2×Q8C22×D1112yes—
188C2×Q8C22×D1111yescharacteristic
189C2×D4—112no—
190C2×D4—221no—
191C2×D4—442no—
192C22×C4—21no—
193C22×C4—111no—
194C22×C4—111no—
195C22×C4C22×D1111yescharacteristic
196Q16—42no—
197Q16—442no—
198SD16—442no—
199SD16—442no—
200C2×C8—112no—
201C2×C8C22×D1112yes—
202C4⋊C4—21no—
203C4⋊C4—111no—
204C4⋊C4—221no—
205C4⋊C4—221no—
206C4⋊C4—221no—
207C4⋊C4—221no—
208C4⋊C4—221no—
209C4⋊C4—221no—
210C4⋊C4C22×D1111yescharacteristic
211C22⋊C4—21no—
212C22⋊C4—222no—
213C22⋊C4—222no—
214C22⋊C4—222no—
215C22⋊C4—222no—
216C22⋊C4—221no—
217C42—111no—
218C42—111no—
219C42—111no—
220C42—111no—
221C42—221no—
222C42—221no—
223C11#321511yescharacteristic, complemented, Sylow
224C23—222no—
225C23—442no—
226C23—442no—
227C23—442no—
228C23D4×D1111yescharacteristic
229Q8—22no—
230Q8—22no—
231Q8—22no—
232Q8—42no—
233Q8—222no—
234Q8—442no—
235D4—222no—
236D4—222no—
237D4—442no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—42no—
243C2×C4—111no—
244C2×C4—111no—
245C2×C4—111no—
246C2×C4—111no—
247C2×C4—222no—
248C2×C4—221no—
249C2×C4—221no—
250C2×C4—441no—
251C2×C4D4×D1111yescharacteristic
252C2×C4C23×D1111yescharacteristic
253C8—22no—
254C8—222no—
255C22—21no—
256C22—21no—
257C22—442no—
258C22—442no—
259C22—442no—
260C22—884no—
261C22#6697112yes—
262C22C2×D4×D1111yescharacteristic
263C4—21no—
264C4—41no—
265C4—42no—
266C4—41no—
267C4—221no—
268C4—221no—
269C4—221no—
270C4—221no—
271C4—441no—
272C4—441no—
273C4#6703712yes—
274C2—22no—
275C2—882no—
276C2#1062312311yescharacteristic
277C2C2×#6697111yescharacteristic
278C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#451C2
socleC22×C11C22×D4
prime radicalC22×D44C22
hypercenter#451D11
hypocenterC11#3215
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #10623153C2semidirect
3. C11×#451C2semidirect
4. #10622841C2semidirect
5. #10622803C2semidirect
6. #10622798C2semidirect
8. #10622411C2semidirect
9. #10622408C2semidirect
11. #10622332C2semidirect
14. C2×C11×Q16C22semidirect
20. Q8×Dic11C22semidirect
21. #66997C22semidirect
22. C2×#4326C22semidirect
30. #66941C22semidirect
32. #66940C22semidirect
35. C11×#103C22semidirect
37. #66899C22semidirect
40. #66879C22semidirect
41. Dic11⋊C8C22semidirect
123. #451D11semidirect
149. C2×Q16C2×D11semidirect
171. #103C2×D11semidirect
223. C11#3215semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
#106231532
C11×#4512
#106228412
#106228032
#106227982
#106226592
#106224112
#106224082
#106223442
#106223322
#321511