Finite Group Databasebeta

← #13080901

Subgroups — #13080901

Order 1408.

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

normal subgroups only

This group has 374 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#10623115C211yesmaximal, characteristic
2Q8×D44C211yesmaximal, characteristic
3C4×C11×Q16C211yesmaximal, characteristic, complemented
4#10622799C212yesmaximal, complemented
5#10622644C211yesmaximal, characteristic, complemented
6#10622633C211yesmaximal, characteristic, complemented
7#10622501C212yesmaximal, complemented
8#10622429C212yesmaximal, complemented
9#10622415C212yesmaximal, complemented
10#10622301C211yesmaximal, characteristic
11#10622294C211yesmaximal, characteristic, complemented
12C2×Q8×D11C2212yes—
13C2×C11×Q16C2211yescharacteristic
14C4×Q8×C11C2211yescharacteristic
15C4×Q8×C11C2211yescharacteristic
16#66999C2212yes—
17C2×#4326C2212yes—
18C2×#4313C2212yes—
19#66951—22no—
20#66950—22no—
21#66950C2212yes—
22#66945C2212yes—
23#66928—21no—
24C4×D44—21no—
25C4×D44C2211yescharacteristic
26#66922—21no—
27#66922C2211yescharacteristic
28#66922C2211yescharacteristic
29C4×Dic22—21no—
30C11×#107C2211yescharacteristic
31C11×#103C2211yescharacteristic
32C11×#103C2211yescharacteristic
33C4×C8×C11C2211yescharacteristic
34#66899C2212yes—
35(C2×D11)⋊C8C2212yes—
36#66880C2212yes—
37#66880C2212yes—
38#66874C2212yes—
39#66872C2212yes—
40C4⋊(C11⋊C8)C2211yescharacteristic
41C2×Q8×C11C2311yescharacteristic
42C2×Q8×C11C2311yescharacteristic
43Q8×D11—24no—
44Q8×D11—42no—
45C2×D44D411yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11C2312yes—
48C2×Dic22—22no—
49C2×Dic22—21no—
50C2×Dic22C2312yes—
51C11×Q16—22no—
52C2×C8×C11C2311yescharacteristic
53C2×C8×C11C2311yescharacteristic
54C11×C4⋊C4—21no—
55C11×C4⋊C4—21no—
56C11×C4⋊C4C2311yescharacteristic
57C11×C4⋊C4C2311yescharacteristic
58C42×C11—21no—
59C42×C11—21no—
60C42×C11C2311yescharacteristic
61#4326—42no—
62(C2×D11)⋊C4—22no—
63(C2×D11)⋊C4—22no—
64(C2×D11)⋊C4—22no—
65(C2×D11)⋊C4D412yes—
66C4⋊Dic11—22no—
67C4⋊Dic11—21no—
68C4⋊Dic11—21no—
69C4⋊Dic11—21no—
70C4⋊Dic11D411yescharacteristic
71C4⋊Dic11C2312yes—
72Dic11⋊C4—22no—
73C4×Dic11—22no—
74C2×C11⋊C8C2312yes—
75#4313—42no—
76#3328—111nomaximal, Sylow
77C22×D11C2×D412yes—
78Q8×C11—21no—
79Q8×C11—21no—
80Q8×C11—21no—
81Q8×C11#4112yes—
82C2×C4×C11—21no—
83C2×C4×C11—21no—
84C2×C4×C11—21no—
85C2×C4×C11—21no—
86C2×C4×C11C2×D411yescharacteristic
87C2×C4×C11C2×D411yescharacteristic
88C2×C4×C11C2411yescharacteristic
89C2×Dic11—22no—
90C2×Dic11—22no—
91C2×Dic11C2×D412yes—
92D44—22no—
93C4×D11—22no—
94C4×D11—22no—
95C4×D11—44no—
96Dic22—22no—
97Dic22—22no—
98Dic22—44no—
99Dic22—42no—
100C8×C11—21no—
101C8×C11—21no—
102C11⋊C8—22no—
103#556—111no—
104D4×Q8—111no—
105#487—111no—
106#485—112no—
107#475—111no—
108#470—112no—
109#462—111no—
110#451—112no—
111C4×Q16D1111yescharacteristic, complemented
112#436—111no—
113#419—112no—
114C22×C11C22×D411yescharacteristic
115C2×D11—22no—
116C2×D11—22no—
117C2×D11—22no—
118C4×C11—22no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—41no—
122C4×C11—41no—
123C4×C11#13712yes—
124C4×C11C2×#4111yescharacteristic
125C4×C11H(5,𝔽2)11yescharacteristic
126Dic11—22no—
127Dic11—42no—
128Dic11—42no—
129C22×Q8—112no—
130C2×Q16—112no—
131C2×Q16C2×D1111yescharacteristic
132C2×M16—112no—
133C4⋊Q8—111no—
134C4⋊Q8—111no—
135C4⋊Q8—221no—
136#126—222no—
137#124—221no—
138C22⋊Q8—112no—
139C22⋊Q8—112no—
140C22⋊Q8—222no—
141C4×Q8—221no—
142C4×Q8C2×D1111yescharacteristic
143C4×Q8C2×D1111yescharacteristic
144C4×D4—111no—
145C4×D4—221no—
146#117—112no—
147#107C2×D1111yescharacteristic
148#106—112no—
149C4⋊C8—111no—
150#103—112no—
151#103—112no—
152#103—112no—
153#103—112no—
154#103C2×D1111yescharacteristic
155#103C2×D1111yescharacteristic
156C22⋊C8—112no—
157C4×C8C2×D1111yescharacteristic
158C2×C11#54611yescharacteristic
159C2×C11C2×#13711yescharacteristic
160C2×C11#57811yescharacteristic
161D11—42no—
162C2×Q8—112no—
163C2×Q8—222no—
164C2×Q8—221no—
165C2×Q8—224no—
166C2×Q8—442no—
167C2×Q8C22×D1111yescharacteristic
168C2×Q8C22×D1111yescharacteristic
169C2×D4—111no—
170C22×C4—112no—
171C22×C4—222no—
172Q16—22no—
173Q16—442no—
174M16—442no—
175C2×C8—112no—
176C2×C8C22×D1111yescharacteristic
177C2×C8C22×D1111yescharacteristic
178C4⋊C4—21no—
179C4⋊C4—21no—
180C4⋊C4—111no—
181C4⋊C4—112no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4—221no—
187C4⋊C4C22×D1111yescharacteristic
188C4⋊C4C22×D1111yescharacteristic
189C22⋊C4—112no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4—222no—
193C42—21no—
194C42—21no—
195C42—222no—
196C42C22×D1111yescharacteristic
197C11#332811yescharacteristic, complemented, Sylow
198C23—112no—
199Q8—21no—
200Q8—21no—
201Q8—21no—
202Q8—222no—
203Q8—222no—
204Q8—444no—
205Q8—442no—
206Q8#433912yes—
207D4—222no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—112no—
213C2×C4—222no—
214C2×C4—222no—
215C2×C4—222no—
216C2×C4—222no—
217C2×C4—444no—
218C2×C4D4×D1111yescharacteristic
219C2×C4D4×D1111yescharacteristic
220C2×C4C23×D1111yescharacteristic
221C8—21no—
222C8—21no—
223C8—222no—
224C22—222no—
225C22—222no—
226C22—222no—
227C22C2×D4×D1111yescharacteristic
228C4—21no—
229C4—22no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—222no—
234C4—442no—
235C4—442no—
236C4#6697112yes—
237C4C2×#433911yescharacteristic
238C4#6704211yescharacteristic
239C2—442no—
240C2#1062308111yescharacteristic
241C2C2×#6697111yescharacteristic
242C2#1062330211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×Q16C2
socleC22×C11C22×D4
prime radicalC2×D44D4
hypercenterC4×Q16D11
hypocenterC11#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
3. C4×C11×Q16C2semidirect
4. #10622799C2semidirect
5. #10622644C2semidirect
6. #10622633C2semidirect
7. #10622501C2semidirect
8. #10622429C2semidirect
9. #10622415C2semidirect
11. #10622294C2semidirect
111. C4×Q16D11semidirect
197. C11#3328semidirect

Maximal subgroups

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

subgroupindex
#106231152
Q8×D442
C4×C11×Q162
#106227992
#106226442
#106226332
#106225012
#106224292
#106224152
#106223012
#106222942
#332811