Finite Group Databasebeta

← #13080923

Subgroups — #13080923

Order 1408.

420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#10623086C211yesmaximal, characteristic, complemented
2#10623082C211yesmaximal, characteristic, complemented
3C4×C11×D8C211yesmaximal, characteristic, complemented
4#10622771C212yesmaximal, complemented
5#10622632C211yesmaximal, characteristic, complemented
6#10622620C211yesmaximal, characteristic, complemented
7#10622497C212yesmaximal, complemented
8#10622393C212yesmaximal, complemented
9#10622384C212yesmaximal, complemented
10#10622301C211yesmaximal, characteristic, complemented
11#10622294C211yesmaximal, characteristic, complemented
12C2×#4341C2212yes—
13C2×#4339—21no—
14C2×C11×D8C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16C4×D4×C11C2211yescharacteristic
17#66991C2212yes—
18C2×#4324C2212yes—
19#66983—21no—
20C2×C4⋊Dic11—21no—
21#66977—21no—
22C2×#4313C2212yes—
23#66950C2212yes—
24C4⋊C4×D11C2212yes—
25#66939—22no—
26#66936—22no—
27C4×D44C2211yescharacteristic
28#66922C2211yescharacteristic
29#66922C2211yescharacteristic
30C11×#107C2211yescharacteristic
31C11×#102C2211yescharacteristic
32C11×#102C2211yescharacteristic
33C4×C8×C11C2211yescharacteristic
34#66896C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66880C2212yes—
37#66880C2212yes—
38#66874C2212yes—
39#66871C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×D4×C11C2311yescharacteristic
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C22×C4×C11—21no—
45C2×C22⋊D11—22no—
46C2×C22⋊D11—22no—
47C22×Dic11—22no—
48#4341—24no—
49#4341—42no—
50#4339—44no—
51C2×D44D411yescharacteristic
52C2×C4×D11—22no—
53C2×C4×D11C2312yes—
54C2×Dic22—21no—
55C2×Dic22C2312yes—
56C11×D8—22no—
57C2×C8×C11C2311yescharacteristic
58C2×C8×C11C2311yescharacteristic
59C11×C4⋊C4C2311yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—21no—
62C11×C22⋊C4—21no—
63C42×C11C2311yescharacteristic
64C22⋊Dic11—22no—
65#4324—42no—
66(C2×D11)⋊C4—22no—
67(C2×D11)⋊C4D412yes—
68C4⋊Dic11—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11—21no—
71C4⋊Dic11—21no—
72C4⋊Dic11D411yescharacteristic
73C4⋊Dic11C2312yes—
74Dic11⋊C4—22no—
75C2×C11⋊C8C2312yes—
76#4313—42no—
77#3330—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11—21no—
80C22×D11C2×D412yes—
81D4×C11—21no—
82D4×C11—21no—
83D4×C11—21no—
84D4×C11#4112yescomplemented
85C2×C4×C11—21no—
86C2×C4×C11—21no—
87C2×C4×C11—42no—
88C2×C4×C11—42no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2411yescharacteristic
92C22⋊D11—44no—
93C22⋊D11—44no—
94C2×Dic11—22no—
95C2×Dic11—22no—
96C2×Dic11—44no—
97C2×Dic11C2×D412yes—
98D44—22no—
99C4×D11—22no—
100C4×D11—22no—
101C4×D11—44no—
102Dic22—22no—
103Dic22—22no—
104Dic22—42no—
105C8×C11—21no—
106C8×C11—21no—
107C11⋊C8—22no—
108#547—111no—
109#547—111no—
110#487—111no—
111#484—112no—
112#474—111no—
113#468—112no—
114#461—111no—
115#449—112no—
116C4×D8D1111yescharacteristic, complemented
117#436—111no—
118#417—112no—
119C22×C11—22no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11—41no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11C22×D411yescharacteristic
126C2×D11—22no—
127C2×D11—22no—
128C2×D11—22no—
129C4×C11—21no—
130C4×C11—41no—
131C4×C11—41no—
132C4×C11AGL(1,ℤ/8)12yes—
133C4×C11C2×#4111yescharacteristic
134C4×C11H(5,𝔽2)11yescharacteristic
135Dic11—22no—
136Dic11—42no—
137Dic11—42no—
138C2×#41—112no—
139C2×#41—221no—
140C2×SD16—112no—
141C2×D8C2×D1111yescharacteristic
142C2×M16—112no—
143C4⋊Q8—111no—
144C4⋊Q8—111no—
145#123—222no—
146#123—222no—
147C22⋊Q8—112no—
148C22⋊Q8—221no—
149#121—112no—
150#121—221no—
151C4×D4—111no—
152C4×D4C2×D1111yescharacteristic
153C4×D4C2×D1111yescharacteristic
154C2×C4⋊C4—112no—
155C2×C4⋊C4—221no—
156#107—112no—
157#107C2×D1111yescharacteristic
158C4⋊C8—111no—
159#103—112no—
160#103—112no—
161#103—112no—
162#102—112no—
163#102C2×D1111yescharacteristic
164#102C2×D1111yescharacteristic
165C22⋊C8—112no—
166C4×C8C2×D1111yescharacteristic
167C2×C11—42no—
168C2×C11—81no—
169C2×C11#54611yescharacteristic
170C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C11#57811yescharacteristic
172D11—42no—
173#41—224no—
174#41—444no—
175#41—442no—
176C2×Q8—112no—
177C2×Q8—221no—
178C2×D4—111no—
179C2×D4—222no—
180C2×D4—222no—
181C2×D4C22×D1111yescharacteristic
182C2×D4C22×D1111yescharacteristic
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—112no—
186C22×C4—222no—
187C22×C4—222no—
188SD16—442no—
189D8—22no—
190M16—442no—
191C2×C8—112no—
192C2×C8C22×D1111yescharacteristic
193C2×C8C22×D1111yescharacteristic
194C4⋊C4—111no—
195C4⋊C4—112no—
196C4⋊C4—222no—
197C4⋊C4—222no—
198C4⋊C4—221no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4C22×D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C22⋊C4—21no—
204C22⋊C4—21no—
205C22⋊C4—112no—
206C22⋊C4—222no—
207C22⋊C4—222no—
208C42C22×D1111yescharacteristic
209C11#333011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—21no—
212C23—112no—
213Q8—222no—
214Q8—222no—
215Q8—442no—
216D4—21no—
217D4—21no—
218D4—21no—
219D4—222no—
220D4—444no—
221D4—444no—
222D4#433912yescomplemented
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—42no—
227C2×C4—112no—
228C2×C4—222no—
229C2×C4—222no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—444no—
233C2×C4—444no—
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C2×C4C23×D1111yescharacteristic
237C8—21no—
238C8—21no—
239C8—222no—
240C22—22no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22—41no—
246C22—222no—
247C22—222no—
248C22—222no—
249C22C2×D4×D1111yescharacteristic
250C4—21no—
251C4—41no—
252C4—41no—
253C4—222no—
254C4—442no—
255C4—442no—
256C4#6696412yes—
257C4C2×#433911yescharacteristic
258C4#6704211yescharacteristic
259C2—42no—
260C2—81no—
261C2—442no—
262C2#1062308111yescharacteristic
263C2C2×#6696411yescharacteristic
264C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×D8C2
socleC22×C11C22×D4
hypercenterC4×D8D11
hypocenterC11#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #10623086C2semidirect
2. #10623082C2semidirect
3. C4×C11×D8C2semidirect
4. #10622771C2semidirect
5. #10622632C2semidirect
6. #10622620C2semidirect
7. #10622497C2semidirect
8. #10622393C2semidirect
9. #10622384C2semidirect
10. #10622301C2semidirect
11. #10622294C2semidirect
84. D4×C11#41semidirect
116. C4×D8D11semidirect
209. C11#3330semidirect
222. D4#4339semidirect

Maximal subgroups

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

subgroupindex
#106230862
#106230822
C4×C11×D82
#106227712
#106226322
#106226202
#106224972
#106223932
#106223842
#106223012
#106222942
#333011