Finite Group Databasebeta

← #13080918

Subgroups — #13080918

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#10623257C211yesmaximal, characteristic, complemented
2#10623086C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5C4×#4323C211yesmaximal, characteristic, complemented
6#10622499C212yesmaximal, complemented
7#10622497C212yesmaximal, complemented
8#10622454C211yesmaximal, characteristic, complemented
9#10622451C211yesmaximal, characteristic, complemented
10#10622394C212yesmaximal, complemented
11#10622384C212yesmaximal, complemented
12C2×#4343—21no—
13C2×#4341C2212yes—
14C11×C4⋊Q8C2211yescharacteristic
15C4×D4×C11C2211yescharacteristic
16#66999—21no—
17C2×#4323C2211yescharacteristic
18#66983—21no—
19C2×C4⋊Dic11—21no—
20C2×#4314C2212yes—
21C2×#4313C2212yes—
22#66950C2212yes—
23#66948C2212yes—
24#66947—22no—
25C4⋊C4×D11C2212yes—
26#66939—22no—
27C4×D44C2211yescharacteristic
28C4×D44C2211yescharacteristic
29#66922C2211yescharacteristic
30C11×#107C2212yes—
31C11×C4⋊C8C2211yescharacteristic
32C11×#102C2212yes—
33#66896C2211yescharacteristic
34(C2×D11)⋊C8C2212yes—
35#66880C2212yes—
36#66874C2212yes—
37#66874C2212yes—
38#66873C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44C2×C22⋊D11—22no—
45C22×Dic11—22no—
46#4343—44no—
47#4341—24no—
48#4341—42no—
49C2×D44—22no—
50C2×D44D411yescharacteristic
51C2×D44C2311yescharacteristic
52C2×C4×D11—22no—
53C2×C4×D11—21no—
54C2×C4×D11C2312yes—
55C2×Dic22C2312yes—
56C2×C8×C11C2312yes—
57C11×C4⋊C4—21no—
58C11×C4⋊C4C2311yescharacteristic
59C11×C4⋊C4C2312yes—
60C11×C22⋊C4—21no—
61C42×C11C2311yescharacteristic
62#4323—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4—21no—
66(C2×D11)⋊C4D412yes—
67C4⋊Dic11—22no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11D411yescharacteristic
71C4⋊Dic11C2311yescharacteristic
72Dic11⋊C4—22no—
73C2×C11⋊C8C2311yescharacteristic
74C2×C11⋊C8C2311yescharacteristic
75#4314—42no—
76#4313—42no—
77#3330—111nomaximal, Sylow
78C23×C11—21no—
79C22×D11—21no—
80C22×D11C2×D412yes—
81Q8×C11—42no—
82D4×C11—21no—
83D4×C11#4112yescomplemented
84C2×C4×C11—22no—
85C2×C4×C11—21no—
86C2×C4×C11—42no—
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2×D411yescharacteristic
89C2×C4×C11C2411yescharacteristic
90C22⋊D11—44no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—44no—
94C2×Dic11C2×D412yes—
95D44—22no—
96D44—21no—
97D44—21no—
98D44—44no—
99C4×D11—22no—
100C4×D11—22no—
101C4×D11—44no—
102C4×D11—42no—
103Dic22—22no—
104Dic22—22no—
105C8×C11—22no—
106C11⋊C8—21no—
107C11⋊C8—21no—
108#547—111no—
109#547—111no—
110#487—111no—
111#484—112no—
112#474D1111yescharacteristic, complemented
113#468—112no—
114#461—111no—
115#449—112no—
116C4×D8—111no—
117#436—111no—
118#417—112no—
119C22×C11—22no—
120C22×C11—41no—
121C22×C11—41no—
122C22×C11C22×D411yescharacteristic
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—22no—
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C4×C11—21no—
130C4×C11—41no—
131C4×C11—42no—
132C4×C11AGL(1,ℤ/8)12yes—
133C4×C11C2×#4111yescharacteristic
134C4×C11H(5,𝔽2)11yescharacteristic
135Dic11—22no—
136Dic11—42no—
137Dic11—41no—
138C2×#41—112no—
139C2×#41—221no—
140C2×SD16—112no—
141C2×D8—111no—
142C2×M16—112no—
143C4⋊Q8—111no—
144C4⋊Q8C2×D1111yescharacteristic
145#123—222no—
146#123—222no—
147C22⋊Q8—112no—
148C22⋊Q8—221no—
149#121—112no—
150#121—221no—
151C4×D4—111no—
152C4×D4—111no—
153C4×D4C2×D1111yescharacteristic
154C2×C4⋊C4—112no—
155C2×C4⋊C4—221no—
156#107—111no—
157#107C2×D1112yes—
158C4⋊C8C2×D1111yescharacteristic
159#103—112no—
160#103—112no—
161#103—112no—
162#102—111no—
163#102—111no—
164#102C2×D1112yes—
165C22⋊C8—112no—
166C4×C8—111no—
167C2×C11—42no—
168C2×C11#54611yescharacteristic
169C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
170C2×C11#57811yescharacteristic
171D11—42no—
172D11—81no—
173#41—224no—
174#41—442no—
175#41—444no—
176C2×Q8—21no—
177C2×Q8—112no—
178C2×D4—111no—
179C2×D4—111no—
180C2×D4—222no—
181C2×D4—222no—
182C2×D4C22×D1111yescharacteristic
183C22×C4—21no—
184C22×C4—112no—
185C22×C4—222no—
186C22×C4—222no—
187C22×C4—221no—
188SD16—442no—
189D8—222no—
190M16—442no—
191C2×C8—111no—
192C2×C8—111no—
193C2×C8C22×D1112yes—
194C4⋊C4—21no—
195C4⋊C4—111no—
196C4⋊C4—111no—
197C4⋊C4—222no—
198C4⋊C4—222no—
199C4⋊C4—221no—
200C4⋊C4—221no—
201C4⋊C4C22×D1111yescharacteristic
202C4⋊C4C22×D1112yes—
203C22⋊C4—21no—
204C22⋊C4—112no—
205C22⋊C4—222no—
206C22⋊C4—222no—
207C22⋊C4—221no—
208C42C22×D1111yescharacteristic
209C11#333011yescharacteristic, complemented, Sylow
210C23—21no—
211C23—112no—
212C23—221no—
213Q8—42no—
214Q8—222no—
215Q8—222no—
216D4—21no—
217D4—222no—
218D4—221no—
219D4—221no—
220D4—444no—
221D4—444no—
222D4#434312yescomplemented
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—112no—
227C2×C4—222no—
228C2×C4—222no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—444no—
232C2×C4—444no—
233C2×C4—442no—
234C2×C4D4×D1111yescharacteristic
235C2×C4D4×D1111yescharacteristic
236C2×C4C23×D1111yescharacteristic
237C8—22no—
238C8—221no—
239C8—221no—
240C22—22no—
241C22—41no—
242C22—41no—
243C22—222no—
244C22—222no—
245C22—222no—
246C22—441no—
247C22—441no—
248C22—441no—
249C22C2×D4×D1111yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—222no—
254C4—441no—
255C4—442no—
256C4#6696412yes—
257C4C2×#434311yescharacteristic
258C4#6704211yescharacteristic
259C2—42no—
260C2—442no—
261C2—881no—
262C2#1062316111yescharacteristic
263C2C2×#6696411yescharacteristic
264C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
hypercenter#474D11
hypocenterC11#3330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

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

NH ≅ G/Ntype
1. #10623257C2semidirect
2. #10623086C2semidirect
3. C11×#474C2semidirect
4. #10622706C2semidirect
5. C4×#4323C2semidirect
6. #10622499C2semidirect
7. #10622497C2semidirect
8. #10622454C2semidirect
9. #10622451C2semidirect
10. #10622394C2semidirect
11. #10622384C2semidirect
83. D4×C11#41semidirect
112. #474D11semidirect
209. C11#3330semidirect
222. D4#4343semidirect

Maximal subgroups

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

subgroupindex
#106232572
#106230862
C11×#4742
#106227062
C4×#43232
#106224992
#106224972
#106224542
#106224512
#106223942
#106223842
#333011