Finite Group Databasebeta

← #13076566

Subgroups — #13076566

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×#389C211yesmaximal, characteristic
2#10622595C212yesmaximal
3#10622594C212yesmaximal
4#10622592C212yesmaximal
5#10622585C212yesmaximal
6#10622542C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic
8#10622273C212yesmaximal
9#10622266C212yesmaximal
10C22×Dic22C2211yescharacteristic
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
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—
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—22no—
41C2×Dic22—41no—
42C2×Dic22—41no—
43C11×C4⋊C4—22no—
44C11×C4⋊C4—24no—
45C11×C4⋊C4—41no—
46C42×C11—41no—
47C4⋊Dic11—41no—
48C4⋊Dic11—41no—
49C4⋊Dic11Q814yescomplemented
50Dic11⋊C4—24no—
51Dic11⋊C4—42no—
52Dic11⋊C4—42no—
53C4×Dic11—42no—
54#2805—111nomaximal, Sylow
55C23×C11C2411yescharacteristic
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11C2×Q812yes—
69C2×C4×C11#4112yes—
70C2×C4×C11#4112yes—
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×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11C2×Q814yes—
83Dic22—44no—
84#400—112no—
85#400—112no—
86#395—112no—
87#391—111no—
88#389—112no—
89#389—111no—
90#389D1111yescharacteristic
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×Q8—111no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4—112no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4C2×D1112yes—
117C2×C4⋊C4C2×D1111yescharacteristic
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#95—112no—
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—222no—
138C2×Q8—441no—
139C2×Q8—441no—
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—22no—
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—114no—
153C4⋊C4—224no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—441no—
157C4⋊C4—441no—
158C42—41no—
159C42—442no—
160C11#280511yescharacteristic, complemented, Sylow
161C23C23×D1111yescharacteristic
162Q8—444no—
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×C4#434112yes—
189C2×C4Q8×D1112yes—
190C22C2×#433911yescharacteristic
191C22C2×#434111yescharacteristic
192C22#6703711yescharacteristic
193C22C2×Q8×D1111yescharacteristic
194C22#6704011yescharacteristic
195C22#6704211yescharacteristic
196C22#6704311yescharacteristic
197C4—22no—
198C4—22no—
199C4—22no—
200C4—42no—
201C4—42no—
202C4—224no—
203C4—442no—
204C4—442no—
205C4—442no—
206C2#1062304611yescharacteristic
207C2#1062307311yescharacteristic
208C2#1062311011yescharacteristic
209C2#1062314811yescharacteristic
210C2#1062315411yescharacteristic
211C2#1062323011yescharacteristic
212C2#1062325211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2805
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
49. 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×#3892
#106225952
#106225942
#106225922
#106225852
#106225422
#106225412
#106222732
#106222662
#280511