Finite Group Databasebeta

← #13079330

Subgroups — #13079330

Order 1408.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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×#532C211yesmaximal, characteristic
2#10623001C211yesmaximal, characteristic, complemented
3#10622706C211yesmaximal, characteristic, complemented
4#10622691C211yesmaximal, characteristic, complemented
5#10622689C211yesmaximal, characteristic, complemented
6#10622683C211yesmaximal, characteristic, complemented
7#10622655C214yesmaximal, complemented
8#10622631C214yesmaximal, complemented
9C4×#4318C211yesmaximal, characteristic, complemented
10C2×C11×#41—21no—
11C11×C4⋊Q8C2211yescharacteristic
12C11×#127C2211yescharacteristic
13C11×#124—21no—
14C11×#121—21no—
15C11×#121C2212yes—
16C4×D4×C11—21no—
17C4×D4×C11C2212yes—
18C2×C42×C11C2211yescharacteristic
19C2×#4324C2214yes—
20#66979—21no—
21#66977—21no—
22#66977C2212yes—
23C2×#4318C2212yes—
24#66923—21no—
25#66922C2211yescharacteristic
26#66922C2211yescharacteristic
27C4×Dic22—21no—
28C4×Dic22C2212yes—
29#66896C2214yes—
30#66874C2214yes—
31#66871C2214yes—
32#66867C2212yes—
33C4×C11⋊C8C2211yescharacteristic
34C4×C11⋊C8C2211yescharacteristic
35C11×#41—44no—
36C2×Q8×C11—21no—
37C2×D4×C11—22no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11C2312yes—
41C22×C4×C11—22no—
42C22×C4×C11D411yescharacteristic
43C22×C4×C11D411yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C2×Dic22—21no—
46C2×Dic22C2312yes—
47C11×C4⋊C4—21no—
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C11×C22⋊C4—22no—
51C42×C11D411yescharacteristic
52C42×C11D411yescharacteristic
53C42×C11C2311yescharacteristic
54C42×C11C2311yescharacteristic
55C22⋊Dic11—22no—
56#4324—28no—
57C4⋊Dic11—21no—
58C4⋊Dic11—21no—
59C4⋊Dic11—21no—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63C4×Dic11—22no—
64#4318—24no—
65C2×C11⋊C8C2312yes—
66C2×C11⋊C8C2312yes—
67#3182—111nomaximal, Sylow
68C23×C11—22no—
69C23×C11C2×D411yescharacteristic
70Q8×C11—42no—
71D4×C11—24no—
72D4×C11—44no—
73D4×C11—42no—
74D4×C11—42no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—22no—
79C2×C4×C11—44no—
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11C2×D411yescharacteristic
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D411yescharacteristic
85C2×C4×C11C2411yescharacteristic
86C2×Dic11—22no—
87C2×Dic11—22no—
88Dic22—24no—
89Dic22—42no—
90C11⋊C8—22no—
91C11⋊C8#4114yescomplemented
92#533—111no—
93#532D1111yescharacteristic
94#500—111no—
95#492—111no—
96#487—111no—
97#486—111no—
98#468—114no—
99#440—114no—
100C4×M16—111no—
101C22×C11—21no—
102C22×C11—21no—
103C22×C11—21no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11C22×D411yescharacteristic
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—21no—
111C4×C11—42no—
112C4×C11AGL(1,ℤ/8)12yes—
113C4×C11#13712yes—
114C4×C11C2×#4112yes—
115Dic11—42no—
116Dic11—42no—
117C2×#41—21no—
118C2×SD16—114no—
119C2×M16—112no—
120C4⋊Q8—111no—
121C4⋊Q8—111no—
122C4⋊Q8C2×D1111yescharacteristic
123#127C2×D1111yescharacteristic
124#125—221no—
125#124—21no—
126C22⋊Q8—112no—
127C22⋊Q8—221no—
128#121—21no—
129#121C2×D1112yes—
130C4×Q8—112no—
131C4×Q8—221no—
132C4×D4—21no—
133C4×D4C2×D1112yes—
134#117—221no—
135C2×C42C2×D1111yescharacteristic
136#107—114no—
137#103—114no—
138#102—114no—
139#97—112no—
140C4×C8—111no—
141C4×C8—111no—
142C2×C11—41no—
143C2×C11—82no—
144C2×C11#53211yescharacteristic
145C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
146C2×C11C2×#13711yescharacteristic
147#41—44no—
148C2×Q8—21no—
149C2×Q8—112no—
150C2×Q8—221no—
151C2×D4—22no—
152C2×D4—21no—
153C2×D4—21no—
154C2×D4C22×D1112yes—
155C22×C4—22no—
156C22×C4C22⋊D1111yescharacteristic
157C22×C4C22⋊D1111yescharacteristic
158C22×C4C22×D1111yescharacteristic
159SD16—228no—
160M16—224no—
161C2×C8—112no—
162C2×C8—112no—
163C4⋊C4—21no—
164C4⋊C4—112no—
165C4⋊C4—221no—
166C4⋊C4—221no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C4⋊C4—221no—
170C4⋊C4C22×D1112yes—
171C22⋊C4—22no—
172C22⋊C4—22no—
173C22⋊C4—222no—
174C42—222no—
175C42C22⋊D1111yescharacteristic
176C42C22⋊D1111yescharacteristic
177C42C22×D1111yescharacteristic
178C42C22×D1111yescharacteristic
179C11#318211yescharacteristic, complemented, Sylow
180C23—22no—
181C23C2×C22⋊D1111yescharacteristic
182Q8—42no—
183Q8—224no—
184Q8—442no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4C2×C22⋊D1111yescharacteristic
197C2×C4C2×C22⋊D1111yescharacteristic
198C2×C4C2×C22⋊D1111yescharacteristic
199C2×C4C2×C22⋊D1111yescharacteristic
200C2×C4C2×C22⋊D1111yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—114no—
203C8—222no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C22×C22⋊D1111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—442no—
216C4—442no—
217C4#6698512yes—
218C4#6700412yes—
219C4#41×D1112yes—
220C2—41no—
221C2—82no—
222C2C2×#6698511yescharacteristic
223C2C2×#6700411yescharacteristic
224C2#1062336311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#532C2
socleC22×C11C22×D4
hypercenter#532D11
hypocenterC11#3182
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
2. #10623001C2semidirect
3. #10622706C2semidirect
4. #10622691C2semidirect
5. #10622689C2semidirect
6. #10622683C2semidirect
7. #10622655C2semidirect
8. #10622631C2semidirect
9. C4×#4318C2semidirect
91. C11⋊C8#41semidirect
179. C11#3182semidirect

Maximal subgroups

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

subgroupindex
C11×#5322
#106230012
#106227062
#106226912
#106226892
#106226832
#106226552
#106226312
C4×#43182
#318211