Finite Group Databasebeta

← #13076571

Subgroups — #13076571

Order 1408.

368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 133 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×#391C211yesmaximal, characteristic
2#10622842C212yesmaximal
3#10622591C212yesmaximal
4#10622541C211yesmaximal, characteristic
5#10622541C211yesmaximal, characteristic
6#10622273C212yesmaximal
7#10622272C212yesmaximal
8#10622267C212yesmaximal
9#10622260C212yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13C2×C4⋊Dic11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22C11×#95C2212yes—
23C11×#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C2×Q8×C11—22no—
32C2×Q8×C11—41no—
33C2×Q8×C11—41no—
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2311yescharacteristic
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C11×C4⋊C4—41no—
44C42×C11—41no—
45C4⋊Dic11—22no—
46C4⋊Dic11—41no—
47C4⋊Dic11—41no—
48C4⋊Dic11Q814yescomplemented
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—42no—
52Dic11⋊C4—42no—
53C4×Dic11—42no—
54#2805—111nomaximal, Sylow
55C23×C11C2411yescharacteristic
56Q8×C11—44no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11C2×Q812yes—
70C2×C4×C11#4112yes—
71C2×C4×C11#4112yes—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11C2×Q814yes—
84#400—112no—
85#400—112no—
86#395—112no—
87#391D1111yescharacteristic
88#389—111no—
89#389—111no—
90#389—112no—
91#387—112no—
92#387—112no—
93C22×C11C22×Q811yescharacteristic
94C22×C11C2×#4111yescharacteristic
95C22×C11C2×#4111yescharacteristic
96C22×C11H(5,𝔽2)11yescharacteristic
97C22×C11H(5,𝔽2)11yescharacteristic
98C22×C112−1+411yescharacteristic
99C22×C112−1+411yescharacteristic
100C4×C11—22no—
101C4×C11—22no—
102C4×C11—22no—
103C4×C11—42no—
104C4×C11—42no—
105Dic11—24no—
106Dic11—42no—
107Dic11—42no—
108Dic11—42no—
109C22×Q8C2×D1111yescharacteristic
110C2×C4⋊C4—111no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—112no—
113C2×C4⋊C4—111no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4C2×D1111yescharacteristic
119C2×C42—112no—
120C2×C42C2×D1111yescharacteristic
121#95—112no—
122#95—112no—
123#95—112no—
124#95—112no—
125#95—112no—
126#95—112no—
127#95—112no—
128#95C2×D1112yes—
129#95C2×D1112yes—
130C2×C11#53811yescharacteristic
131C2×C11#53911yescharacteristic
132C2×C11#54411yescharacteristic
133C2×C11#55411yescharacteristic
134C2×C11#55611yescharacteristic
135C2×C11#55711yescharacteristic
136C2×C11#56311yescharacteristic
137C2×Q8—22no—
138C2×Q8—41no—
139C2×Q8—41no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4—112no—
143C22×C4—112no—
144C22×C4C22×D1112yes—
145C22×C4C22×D1112yes—
146C22×C4C22×D1111yescharacteristic
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1111yescharacteristic
149C4⋊C4—41no—
150C4⋊C4—114no—
151C4⋊C4—224no—
152C4⋊C4—224no—
153C4⋊C4—222no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—441no—
157C4⋊C4—441no—
158C42—41no—
159C42—442no—
160C11#280511yescharacteristic, complemented, Sylow
161C23C23×D1111yescharacteristic
162Q8—44no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—114no—
176C2×C4—222no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4#433912yes—
188C2×C4Q8×D1112yes—
189C2×C4#434312yes—
190C22C2×#433911yescharacteristic
191C22#6703711yescharacteristic
192C22#6703711yescharacteristic
193C22C2×Q8×D1111yescharacteristic
194C22C2×#434311yescharacteristic
195C22#6704311yescharacteristic
196C22#6704311yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—224no—
203C4—442no—
204C4—442no—
205C4—442no—
206C2#1062302511yescharacteristic
207C2#1062309811yescharacteristic
208C2#1062311511yescharacteristic
209C2#1062315411yescharacteristic
210C2#1062317611yescharacteristic
211C2#1062320311yescharacteristic
212C2#1062326111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2805
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
48. C4⋊Dic11Q8semidirect
160. C11#2805semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228422
#106225912
#106225412
#106222732
#106222722
#106222672
#106222602
#280511