Finite Group Databasebeta

← #13080921

Subgroups — #13080921

Order 1408.

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

normal subgroups only

This group has 420 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×#547C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic, complemented
3#10622851C212yesmaximal, complemented
4#10622845C212yesmaximal, complemented
5#10622696C211yesmaximal, characteristic, complemented
6#10622694C211yesmaximal, characteristic, complemented
7#10622662C212yesmaximal, complemented
8#10622657C212yesmaximal, complemented
9C4×#4323C211yesmaximal, characteristic, complemented
10#10622625C211yesmaximal, characteristic, complemented
11#10622620C211yesmaximal, characteristic, complemented
12C2×C11×#41C2212yes—
13C2×#4341—21no—
14C11×C4⋊Q8C2211yescharacteristic
15C11×#123—22no—
16C11×C22⋊Q8C2212yes—
17C11×#121—21no—
18C4×D4×C11C2211yescharacteristic
19C4×D4×C11C2211yescharacteristic
20C2×C11×C4⋊C4—21no—
21C2×#4325C2212yes—
22C2×#4323C2211yescharacteristic
23#66983C2212yes—
24C2×C4⋊Dic11C2212yes—
25C2×#4318C2212yes—
26#66950—21no—
27#66939—22no—
28C4×D44C2211yescharacteristic
29#66922C2211yescharacteristic
30#66899C2212yes—
31#66899C2212yes—
32#66899C2212yes—
33#66896C2211yescharacteristic
34#66896C2212yes—
35C22⋊(C11⋊C8)C2212yes—
36#66873C2211yescharacteristic
37#66871C2212yes—
38#66871C2211yescharacteristic
39C4⋊(C11⋊C8)C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C11×#41—24no—
42C11×#41—42no—
43C2×Q8×C11C2312yes—
44C2×D4×C11—22no—
45C2×D4×C11D411yescharacteristic
46C2×D4×C11C2311yescharacteristic
47C22×C4×C11—21no—
48C22×C4×C11—22no—
49C22×C4×C11C2312yes—
50C2×C22⋊D11—22no—
51C22×Dic11—22no—
52#4341—44no—
53C2×D44C2311yescharacteristic
54C2×C4×D11—21no—
55C2×Dic22—21no—
56C11×C4⋊C4—21no—
57C11×C4⋊C4—22no—
58C11×C4⋊C4—21no—
59C11×C4⋊C4D411yescharacteristic
60C11×C4⋊C4C2311yescharacteristic
61C11×C22⋊C4—22no—
62C11×C22⋊C4—21no—
63C11×C22⋊C4D412yes—
64C42×C11C2311yescharacteristic
65#4325—42no—
66#4323—22no—
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#3330—111nomaximal, Sylow
78C23×C11—21no—
79C23×C11C2×D412yes—
80C22×D11—21no—
81Q8×C11—22no—
82Q8×C11—22no—
83D4×C11—22no—
84D4×C11—21no—
85D4×C11—44no—
86D4×C11#4112yescomplemented
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11—21no—
90C2×C4×C11—22no—
91C2×C4×C11—44no—
92C2×C4×C11—42no—
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11C2×D412yes—
95C2×C4×C11C2×D411yescharacteristic
96C2×C4×C11C2411yescharacteristic
97C22⋊D11—44no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—44no—
101D44—21no—
102D44—21no—
103C4×D11—42no—
104Dic22—42no—
105C11⋊C8—21no—
106C11⋊C8—21no—
107C11⋊C8—22no—
108#547—111no—
109#547D1111yescharacteristic, complemented
110#487—111no—
111#484—112no—
112#474—111no—
113#468—112no—
114#461—111no—
115#449—112no—
116C4×D8—111no—
117#436—111no—
118#417—112no—
119C22×C11—22no—
120C22×C11—22no—
121C22×C11—22no—
122C22×C11—22no—
123C22×C11—41no—
124C22×C11—41no—
125C22×C11C22×D411yescharacteristic
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C4×C11—22no—
130C4×C11—21no—
131C4×C11—42no—
132C4×C11—41no—
133C4×C11AGL(1,ℤ/8)12yes—
134C4×C11C2×#4111yescharacteristic
135C4×C11H(5,𝔽2)11yescharacteristic
136Dic11—42no—
137Dic11—41no—
138C2×#41—221no—
139C2×#41C2×D1112yes—
140C2×SD16—112no—
141C2×D8—111no—
142C2×M16—112no—
143C4⋊Q8—111no—
144C4⋊Q8C2×D1111yescharacteristic
145#123—22no—
146#123—222no—
147C22⋊Q8—221no—
148C22⋊Q8C2×D1112yes—
149#121—21no—
150#121—112no—
151C4×D4—111no—
152C4×D4C2×D1111yescharacteristic
153C4×D4C2×D1111yescharacteristic
154C2×C4⋊C4—21no—
155C2×C4⋊C4—112no—
156#107—111no—
157#107—112no—
158C4⋊C8—111no—
159#103—112no—
160#103—112no—
161#103—112no—
162#102—111no—
163#102—112no—
164#102—111no—
165C22⋊C8—112no—
166C4×C8—111no—
167C2×C11—42no—
168C2×C11—42no—
169C2×C11#54611yescharacteristic
170C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
171C2×C11#57811yescharacteristic
172D11—81no—
173#41—24no—
174#41—42no—
175#41—444no—
176C2×Q8—221no—
177C2×Q8C22×D1112yes—
178C2×D4—22no—
179C2×D4—111no—
180C2×D4—222no—
181C2×D4C22⋊D1111yescharacteristic
182C2×D4C22×D1111yescharacteristic
183C22×C4—21no—
184C22×C4—22no—
185C22×C4—222no—
186C22×C4—221no—
187C22×C4C22×D1112yes—
188SD16—442no—
189D8—222no—
190M16—442no—
191C2×C8—111no—
192C2×C8—111no—
193C2×C8—112no—
194C4⋊C4—21no—
195C4⋊C4—22no—
196C4⋊C4—21no—
197C4⋊C4—111no—
198C4⋊C4—112no—
199C4⋊C4—222no—
200C4⋊C4—221no—
201C4⋊C4C22⋊D1111yescharacteristic
202C4⋊C4C22×D1111yescharacteristic
203C22⋊C4—22no—
204C22⋊C4—21no—
205C22⋊C4—221no—
206C22⋊C4—222no—
207C22⋊C4C22⋊D1112yes—
208C42C22×D1111yescharacteristic
209C11#333011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—221no—
212C23C2×C22⋊D1112yes—
213Q8—22no—
214Q8—22no—
215Q8—442no—
216D4—22no—
217D4—21no—
218D4—44no—
219D4—221no—
220D4—221no—
221D4—444no—
222D4#434112yescomplemented
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—44no—
228C2×C4—42no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—444no—
232C2×C4—442no—
233C2×C4C2×C22⋊D1111yescharacteristic
234C2×C4C2×C22⋊D1112yes—
235C2×C4C2×C22⋊D1111yescharacteristic
236C2×C4C23×D1111yescharacteristic
237C8—221no—
238C8—221no—
239C8—222no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—41no—
245C22—41no—
246C22—441no—
247C22—441no—
248C22—441no—
249C22C22×C22⋊D1111yescharacteristic
250C4—22no—
251C4—21no—
252C4—42no—
253C4—41no—
254C4—441no—
255C4—442no—
256C4#6700212yes—
257C4C2×#434111yescharacteristic
258C4#6703711yescharacteristic
259C2—42no—
260C2—42no—
261C2—881no—
262C2#1062333711yescharacteristic
263C2C2×#6700211yescharacteristic
264C2#1062336911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#547C2
socleC22×C11C22×D4
hypercenter#547D11
hypocenterC11#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. C11×#547C2semidirect
2. #10623086C2semidirect
3. #10622851C2semidirect
4. #10622845C2semidirect
5. #10622696C2semidirect
6. #10622694C2semidirect
7. #10622662C2semidirect
8. #10622657C2semidirect
9. C4×#4323C2semidirect
10. #10622625C2semidirect
11. #10622620C2semidirect
86. D4×C11#41semidirect
109. #547D11semidirect
209. C11#3330semidirect
222. D4#4341semidirect

Maximal subgroups

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

subgroupindex
C11×#5472
#106230862
#106228512
#106228452
#106226962
#106226942
#106226622
#106226572
C4×#43232
#106226252
#106226202
#333011