Finite Group Databasebeta

← #13080943

Subgroups — #13080943

Order 1408.

430 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C11×#550C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic, complemented
3#10622851C212yesmaximal, complemented
4#10622845C212yesmaximal, complemented
5#10622685C211yesmaximal, characteristic, complemented
6#10622683C211yesmaximal, characteristic, complemented
7#10622652C212yesmaximal, complemented
8#10622647C212yesmaximal, complemented
9C4×#4325C211yesmaximal, characteristic, complemented
10#10622633C211yesmaximal, characteristic, complemented
11#10622625C211yesmaximal, characteristic, complemented
12C2×C11×#41C2212yes—
13C2×#4341—21no—
14C11×#127—21no—
15C11×#127C2211yescharacteristic
16C11×#121—22no—
17C11×#121C2212yes—
18C4×Q8×C11C2211yescharacteristic
19C4×D4×C11—21no—
20C4×D4×C11C2211yescharacteristic
21C2×#4325C2211yescharacteristic
22C2×#4323C2212yes—
23#66983C2212yes—
24C2×C4⋊Dic11C2212yes—
25C2×#4318C2212yes—
26#66950—21no—
27#66939—22no—
28C4×D44C2211yescharacteristic
29#66922C2211yescharacteristic
30#66899C2211yescharacteristic
31#66899C2212yes—
32#66896C2212yes—
33#66896C2212yes—
34#66896C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66873C2211yescharacteristic
37#66872C2212yes—
38#66872C2211yescharacteristic
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C11×#41—24no—
42C11×#41—42no—
43C2×Q8×C11C2311yescharacteristic
44C2×D4×C11—22no—
45C2×D4×C11—22no—
46C2×D4×C11—21no—
47C2×D4×C11—21no—
48C2×D4×C11D411yescharacteristic
49C2×D4×C11C2312yes—
50C22×C4×C11—22no—
51C22×C4×C11C2312yes—
52C2×C22⋊D11—22no—
53C22×Dic11—22no—
54#4341—44no—
55C2×D44C2311yescharacteristic
56C2×C4×D11—21no—
57C2×Dic22—21no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4D411yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—22no—
62C11×C22⋊C4D412yes—
63C42×C11—21no—
64C42×C11C2311yescharacteristic
65#4325—22no—
66#4323—42no—
67(C2×D11)⋊C4—21no—
68(C2×D11)⋊C4—22no—
69C4⋊Dic11—21no—
70C4⋊Dic11—22no—
71C4⋊Dic11C2312yes—
72C4⋊Dic11C2311yescharacteristic
73#4318—42no—
74C2×C11⋊C8C2311yescharacteristic
75C2×C11⋊C8C2311yescharacteristic
76C2×C11⋊C8C2312yes—
77#3332—111nomaximal, Sylow
78C23×C11—22no—
79C23×C11C2×D412yes—
80C22×D11—21no—
81Q8×C11—21no—
82Q8×C11#4112yescomplemented
83D4×C11—22no—
84D4×C11—22no—
85D4×C11—22no—
86D4×C11—44no—
87D4×C11—42no—
88D4×C11—81no—
89D4×C11—82no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11—22no—
93C2×C4×C11—21no—
94C2×C4×C11—44no—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2×D412yes—
97C2×C4×C11C2×D411yescharacteristic
98C2×C4×C11C2411yescharacteristic
99C22⋊D11—44no—
100C2×Dic11—22no—
101C2×Dic11—21no—
102C2×Dic11—44no—
103D44—21no—
104D44—21no—
105C4×D11—42no—
106Dic22—42no—
107C11⋊C8—21no—
108C11⋊C8—21no—
109C11⋊C8—22no—
110#550D1111yescharacteristic, complemented
111#547—111no—
112#486—111no—
113#481—112no—
114#475—111no—
115#469—112no—
116#459—111no—
117#449—112no—
118C4×SD16—111no—
119#436—111no—
120#417—112no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—22no—
124C22×C11—42no—
125C22×C11—42no—
126C22×C11—42no—
127C22×C11C22×D411yescharacteristic
128C2×D11—41no—
129C2×D11—41no—
130C2×D11—41no—
131C4×C11—22no—
132C4×C11—22no—
133C4×C11—21no—
134C4×C11—41no—
135C4×C11AGL(1,ℤ/8)12yes—
136C4×C11C2×#4111yescharacteristic
137C4×C11H(5,𝔽2)11yescharacteristic
138Dic11—42no—
139Dic11—41no—
140C2×#41—221no—
141C2×#41C2×D1112yes—
142C2×SD16—111no—
143C2×D8—112no—
144C2×M16—112no—
145C4⋊Q8—111no—
146#127—21no—
147#127C2×D1111yescharacteristic
148#123—222no—
149C22⋊Q8—221no—
150#121—22no—
151#121—112no—
152#121C2×D1112yes—
153C4×Q8C2×D1111yescharacteristic
154C4×D4—21no—
155C4×D4—111no—
156C4×D4C2×D1111yescharacteristic
157C2×C4⋊C4—112no—
158#106—111no—
159#106—112no—
160C4⋊C8—111no—
161#103—111no—
162#103—112no—
163#102—112no—
164#102—112no—
165#102—112no—
166#102—111no—
167C22⋊C8—112no—
168C4×C8—111no—
169C2×C11—42no—
170C2×C11—82no—
171C2×C11#54611yescharacteristic
172C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
173C2×C11#57711yescharacteristic
174D11—81no—
175#41—24no—
176#41—42no—
177#41—444no—
178C2×Q8—221no—
179C2×Q8C22×D1111yescharacteristic
180C2×D4—22no—
181C2×D4—22no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—111no—
185C2×D4—222no—
186C2×D4C22⋊D1111yescharacteristic
187C2×D4C22×D1112yes—
188C22×C4—22no—
189C22×C4—222no—
190C22×C4—221no—
191C22×C4C22×D1112yes—
192SD16—222no—
193D8—442no—
194M16—442no—
195C2×C8—111no—
196C2×C8—111no—
197C2×C8—112no—
198C4⋊C4—21no—
199C4⋊C4—111no—
200C4⋊C4—112no—
201C4⋊C4—222no—
202C4⋊C4—221no—
203C4⋊C4C22⋊D1111yescharacteristic
204C4⋊C4C22×D1111yescharacteristic
205C22⋊C4—22no—
206C22⋊C4—221no—
207C22⋊C4—222no—
208C22⋊C4C22⋊D1112yes—
209C42—21no—
210C42C22×D1111yescharacteristic
211C11#333211yescharacteristic, complemented, Sylow
212C23—22no—
213C23—221no—
214C23C2×C22⋊D1112yes—
215Q8—21no—
216Q8—442no—
217Q8#434112yescomplemented
218D4—22no—
219D4—22no—
220D4—22no—
221D4—44no—
222D4—42no—
223D4—81no—
224D4—82no—
225D4—221no—
226D4—221no—
227D4—444no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—44no—
233C2×C4—221no—
234C2×C4—222no—
235C2×C4—444no—
236C2×C4—442no—
237C2×C4C2×C22⋊D1111yescharacteristic
238C2×C4C2×C22⋊D1112yes—
239C2×C4C2×C22⋊D1111yescharacteristic
240C2×C4C23×D1111yescharacteristic
241C8—221no—
242C8—221no—
243C8—222no—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—441no—
251C22—441no—
252C22—441no—
253C22C22×C22⋊D1111yescharacteristic
254C4—22no—
255C4—22no—
256C4—21no—
257C4—41no—
258C4—441no—
259C4—442no—
260C4#6700212yes—
261C4C2×#434111yescharacteristic
262C4#6703711yescharacteristic
263C2—42no—
264C2—82no—
265C2—881no—
266C2#1062333711yescharacteristic
267C2C2×#6700211yescharacteristic
268C2#1062336711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#550C2
socleC22×C11C22×D4
hypercenter#550D11
hypocenterC11#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C11×#550C2semidirect
2. #10623086C2semidirect
3. #10622851C2semidirect
4. #10622845C2semidirect
5. #10622685C2semidirect
6. #10622683C2semidirect
7. #10622652C2semidirect
8. #10622647C2semidirect
9. C4×#4325C2semidirect
10. #10622633C2semidirect
11. #10622625C2semidirect
82. Q8×C11#41semidirect
110. #550D11semidirect
211. C11#3332semidirect
217. Q8#4341semidirect

Maximal subgroups

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

subgroupindex
C11×#5502
#106230862
#106228512
#106228452
#106226852
#106226832
#106226522
#106226472
C4×#43252
#106226332
#106226252
#333211