Finite Group Databasebeta

← #13081333

Subgroups — #13081333

Order 1408.

372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623258C211yesmaximal, characteristic, complemented
2#10623073C211yesmaximal, characteristic, complemented
3C11×#474C211yesmaximal, characteristic, complemented
4#10622706C211yesmaximal, characteristic, complemented
5C4×#4323C211yesmaximal, characteristic
6#10622502C212yesmaximal, complemented
7#10622488C212yesmaximal, complemented
8#10622454C211yesmaximal, characteristic, complemented
9#10622444C211yesmaximal, characteristic, complemented
10#10622400C212yesmaximal
11#10622378C212yesmaximal, complemented
12C2×Q8×D11—21no—
13C11×C4⋊Q8C2211yescharacteristic
14C4×D4×C11C2211yescharacteristic
15#66999—21no—
16#66989C2212yes—
17C2×#4323C2211yescharacteristic
18#66979—21no—
19#66977—21no—
20C2×#4314C2212yes—
21#66949—22no—
22#66946C2212yes—
23#66941C2212yes—
24#66940C2212yes—
25#66932—22no—
26C4×D44C2211yescharacteristic
27#66922C2211yescharacteristic
28C4×Dic22C2211yescharacteristic
29C11×#107C2212yes—
30C11×C4⋊C8C2211yescharacteristic
31C11×#102C2212yes—
32#66896C2211yescharacteristic
33#66880C2212yes—
34#66879C2212yes—
35Dic11⋊C8C2212yes—
36#66874C2212yes—
37#66874C2212yes—
38#66873C2211yescharacteristic
39#66871C2211yescharacteristic
40C4×C11⋊C8C2211yescharacteristic
41C2×Q8×C11—21no—
42C2×D4×C11C2311yescharacteristic
43C22×C4×C11—21no—
44Q8×D11—44no—
45C2×D44C2311yescharacteristic
46C2×C4×D11—22no—
47C2×C4×D11—21no—
48C2×Dic22—22no—
49C2×Dic22D411yescharacteristic
50C2×Dic22C2312yes—
51C2×C8×C11C2312yes—
52C11×C4⋊C4—21no—
53C11×C4⋊C4C2311yescharacteristic
54C11×C4⋊C4C2312yes—
55C11×C22⋊C4—21no—
56C42×C11C2311yescharacteristic
57C22⋊Dic11—22no—
58C22⋊Dic11—22no—
59#4323—22no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—21no—
62C4⋊Dic11—21no—
63C4⋊Dic11—21no—
64C4⋊Dic11D411yescharacteristic
65C4⋊Dic11C2311yescharacteristic
66Dic11⋊C4—22no—
67Dic11⋊C4—22no—
68Dic11⋊C4D412yes—
69C4×Dic11—22no—
70C4×Dic11C2312yes—
71C2×C11⋊C8C2311yescharacteristic
72C2×C11⋊C8C2311yescharacteristic
73#4314—24no—
74#3367—111nomaximal, Sylow
75C23×C11—21no—
76C22×D11—21no—
77Q8×C11—42no—
78D4×C11—21no—
79D4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—42no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11C2×D412yes—
89C2×Dic11C2×D412yes—
90D44—21no—
91D44#4112yes—
92C4×D11—44no—
93C4×D11—42no—
94Dic22—22no—
95Dic22—22no—
96Dic22—22no—
97Dic22—44no—
98C8×C11—22no—
99C11⋊C8—21no—
100C11⋊C8—21no—
101#556—111no—
102D4×Q8—111no—
103#489—112no—
104#487—111no—
105#477—112no—
106#474D1111yescharacteristic, complemented
107#463—112no—
108#461—111no—
109#446—111no—
110#440—112no—
111C4×D8—111no—
112C22×C11—41no—
113C22×C11—41no—
114C22×C11—41no—
115C22×C11C22×D411yescharacteristic
116C2×D11—22no—
117C2×D11—41no—
118C2×D11—41no—
119C4×C11—21no—
120C4×C11—41no—
121C4×C11—42no—
122C4×C11AGL(1,ℤ/8)12yes—
123C4×C11C2×#4111yescharacteristic
124C4×C112−1+411yescharacteristic
125Dic11—22no—
126Dic11—22no—
127Dic11—42no—
128Dic11—41no—
129C22×Q8—221no—
130C2×SD16—112no—
131C2×D8—111no—
132C4⋊Q8—112no—
133C4⋊Q8—111no—
134C4⋊Q8C2×D1111yescharacteristic
135#126—222no—
136#124—112no—
137C22⋊Q8—222no—
138C22⋊Q8—221no—
139C22⋊Q8—221no—
140C4×Q8—111no—
141C4×Q8—112no—
142C4×D4—112no—
143C4×D4—111no—
144C4×D4C2×D1111yescharacteristic
145#117—221no—
146#107—111no—
147#107C2×D1112yes—
148C4⋊C8—112no—
149C4⋊C8C2×D1111yescharacteristic
150#103—112no—
151#103—112no—
152#103—112no—
153#102—111no—
154#102—111no—
155#102C2×D1112yes—
156#97—112no—
157C4×C8—111no—
158C2×C11—81no—
159C2×C11#54811yescharacteristic
160C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
161C2×C11#57811yescharacteristic
162D11—42no—
163C2×Q8—21no—
164C2×Q8—111no—
165C2×Q8—112no—
166C2×Q8—222no—
167C2×Q8—444no—
168C2×D4—111no—
169C2×D4C22×D1111yescharacteristic
170C22×C4—21no—
171C22×C4—222no—
172C22×C4—221no—
173SD16—224no—
174D8—222no—
175C2×C8—111no—
176C2×C8—111no—
177C2×C8C22×D1112yes—
178C4⋊C4—21no—
179C4⋊C4—111no—
180C4⋊C4—112no—
181C4⋊C4—111no—
182C4⋊C4—222no—
183C4⋊C4—222no—
184C4⋊C4—221no—
185C4⋊C4—221no—
186C4⋊C4C22×D1111yescharacteristic
187C4⋊C4C22×D1112yes—
188C22⋊C4—21no—
189C22⋊C4—222no—
190C22⋊C4—222no—
191C22⋊C4—222no—
192C22⋊C4—221no—
193C42—112no—
194C42—222no—
195C42C22×D1111yescharacteristic
196C11#336711yescharacteristic, complemented, Sylow
197C23—21no—
198C23—221no—
199Q8—42no—
200Q8—222no—
201Q8—222no—
202Q8—222no—
203Q8—444no—
204D4—21no—
205D4—21no—
206D4—112no—
207D4—221no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—42no—
211C2×C4—112no—
212C2×C4—112no—
213C2×C4—222no—
214C2×C4—221no—
215C2×C4—444no—
216C2×C4—442no—
217C2×C4D4×D1111yescharacteristic
218C2×C4D4×D1111yescharacteristic
219C2×C4C23×D1111yescharacteristic
220C8—22no—
221C8—221no—
222C8—221no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—222no—
227C22—441no—
228C22—441no—
229C22C2×D4×D1111yescharacteristic
230C4—21no—
231C4—41no—
232C4—42no—
233C4—222no—
234C4—222no—
235C4—441no—
236C4—442no—
237C4#6696412yes—
238C4#6704011yescharacteristic
239C4#41×D1111yescharacteristic
240C2—81no—
241C2—442no—
242C2#1062316411yescharacteristic
243C2C2×#6696411yescharacteristic
244C2#1062331011yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#474C2
socleC22×C11C22×D4
prime radicalC2×#4323C22
hypercenter#474D11
hypocenterC11#3367
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. #10623258C2semidirect
2. #10623073C2semidirect
3. C11×#474C2semidirect
4. #10622706C2semidirect
6. #10622502C2semidirect
7. #10622488C2semidirect
8. #10622454C2semidirect
9. #10622444C2semidirect
11. #10622378C2semidirect
106. #474D11semidirect
196. C11#3367semidirect

Maximal subgroups

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

subgroupindex
#106232582
#106230732
C11×#4742
#106227062
C4×#43232
#106225022
#106224882
#106224542
#106224442
#106224002
#106223782
#336711