Finite Group Databasebeta

← #13076412

Subgroups — #13076412

Order 1408.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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×#384C211yesmaximal, characteristic
2#10622597C212yesmaximal
3#10622596C211yesmaximal, characteristic
4#10622592C211yesmaximal, characteristic
5#10622592C212yesmaximal
6#10622591C212yesmaximal
7#10622585C212yesmaximal
8#10622585C212yesmaximal
9#10622546C212yesmaximal
10C22×Dic22C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C42×C11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—41no—
41C2×Dic22—42no—
42C11×C4⋊C4—42no—
43C11×C4⋊C4—41no—
44C11×C4⋊C4—42no—
45C11×C4⋊C4—41no—
46C42×C11—22no—
47C4⋊Dic11—41no—
48Dic11⋊C4—24no—
49Dic11⋊C4—42no—
50Dic11⋊C4—42no—
51Dic11⋊C4—42no—
52Dic11⋊C4Q818yescomplemented
53C4×Dic11—42no—
54#2792—111nomaximal, Sylow
55C23×C11C2411yescharacteristic
56C2×C4×C11—22no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—21no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—21no—
65C2×C4×C11—21no—
66C2×C4×C11—22no—
67C2×C4×C11C2×Q814yes—
68C2×C4×C11#4112yes—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11C2×Q814yes—
80C2×Dic11C2×Q814yes—
81Dic22—44no—
82#398—111no—
83#398—112no—
84#395—111no—
85#395—112no—
86#389—112no—
87#389—112no—
88#387—112no—
89#387—112no—
90#384D1111yescharacteristic
91C22×C11C22×Q812yes—
92C22×C11C2×#4111yescharacteristic
93C22×C11H(5,𝔽2)11yescharacteristic
94C22×C11H(5,𝔽2)12yes—
95C22×C112−1+411yescharacteristic
96C4×C11—22no—
97C4×C11—24no—
98C4×C11—42no—
99C4×C11—41no—
100C4×C11—41no—
101Dic11—24no—
102Dic11—24no—
103Dic11—42no—
104Dic11—42no—
105C22×Q8—111no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4C2×D1112yes—
113C2×C4⋊C4C2×D1111yescharacteristic
114C2×C4⋊C4C2×D1112yes—
115C2×C4⋊C4C2×D1111yescharacteristic
116C2×C42—112no—
117C2×C42C2×D1111yescharacteristic
118#95—111no—
119#95—112no—
120#95—112no—
121#95—112no—
122#95—112no—
123#95—112no—
124#95—112no—
125#95—111no—
126C2×C11#53911yescharacteristic
127C2×C11#54412yes—
128C2×C11#55412yes—
129C2×C11Q8211yescharacteristic
130C2×C11#56011yescharacteristic
131C2×Q8—441no—
132C2×Q8—442no—
133C22×C4—112no—
134C22×C4—112no—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4C22×D1111yescharacteristic
138C22×C4C22×D1112yes—
139C22×C4C22×D1111yescharacteristic
140C22×C4C22×D1111yescharacteristic
141C22×C4C22×D1112yes—
142C4⋊C4—42no—
143C4⋊C4—41no—
144C4⋊C4—42no—
145C4⋊C4—41no—
146C4⋊C4—118no—
147C4⋊C4—224no—
148C4⋊C4—442no—
149C4⋊C4—442no—
150C4⋊C4—442no—
151C4⋊C4—441no—
152C42—22no—
153C42—442no—
154C11#279211yescharacteristic, complemented, Sylow
155C23C23×D1111yescharacteristic
156Q8—444no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—22no—
168C2×C4—114no—
169C2×C4—114no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4#433912yes—
181C2×C4Q8×D1114yes—
182C22C2×#433911yescharacteristic
183C22#6703711yescharacteristic
184C22#6703712yes—
185C22C2×Q8×D1112yes—
186C22#6704011yescharacteristic
187C4—24no—
188C4—22no—
189C4—41no—
190C4—42no—
191C4—41no—
192C4—224no—
193C4—224no—
194C4—442no—
195C4—442no—
196C2#1062304212yes—
197C2#1062304611yescharacteristic
198C2#1062325111yescharacteristic
199C2#1062325311yescharacteristic
200C2#1062326012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#384C2
hypercenter#384D11
hypocenterC11#2792
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #384

Complements

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

NH ≅ G/Ntype
52. Dic11⋊C4Q8semidirect
154. C11#2792semidirect

Maximal subgroups

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

subgroupindex
C11×#3842
#106225972
#106225962
#106225922
#106225912
#106225852
#106225462
#279211