Finite Group Databasebeta

← #13076599

Subgroups — #13076599

Order 1408.

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

normal subgroups only

This group has 368 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×#400C211yesmaximal, characteristic
2#10622599C211yesmaximal, characteristic
3#10622597C212yesmaximal
4#10622587C211yesmaximal, characteristic
5#10622270C212yesmaximal
6#10622266C212yesmaximal
7#10622265C212yesmaximal
8#10622260C212yesmaximal
9#10622259C212yesmaximal
10C22×Dic22C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C4⋊Dic11C2212yes—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4C2212yes—
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×C4×Dic11C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21C11×#95C2212yes—
22C11×#95C2211yescharacteristic
23C11×#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—41no—
41C2×Dic22—41no—
42C2×Dic22Q814yes—
43C11×C4⋊C4—41no—
44C11×C4⋊C4—41no—
45C4⋊Dic11—24no—
46C4⋊Dic11—41no—
47Dic11⋊C4—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—42no—
50Dic11⋊C4—42no—
51C4×Dic11—41no—
52C4×Dic11—42no—
53#2809—111nomaximal, Sylow
54C23×C11C2411yescharacteristic
55C2×C4×C11—21no—
56C2×C4×C11—21no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11C2×Q812yes—
68C2×Dic11—22no—
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×Dic11C2×Q814yes—
79C2×Dic11#4114yes—
80Dic22—44no—
81#400—111no—
82#400D1111yescharacteristic
83#398—112no—
84#398—112no—
85#391—111no—
86#391—112no—
87#389—112no—
88#387—112no—
89#387—112no—
90C22×C11C22×Q811yescharacteristic
91C22×C11C2×#4112yes—
92C22×C11H(5,𝔽2)11yescharacteristic
93C22×C11H(5,𝔽2)11yescharacteristic
94C22×C112−1+412yes—
95C4×C11—22no—
96C4×C11—42no—
97C4×C11—42no—
98C4×C11—41no—
99C4×C11—41no—
100Dic11—24no—
101Dic11—24no—
102Dic11—42no—
103Dic11—42no—
104C22×Q8—111no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—111no—
111C2×C4⋊C4C2×D1111yescharacteristic
112C2×C4⋊C4C2×D1111yescharacteristic
113C2×C42—112no—
114C2×C42—111no—
115#95—111no—
116#95—112no—
117#95—112no—
118#95—112no—
119#95—112no—
120#95—112no—
121#95—112no—
122#95C2×D1111yescharacteristic
123#95C2×D1112yes—
124#95C2×D1112yes—
125C2×C11#53912yes—
126C2×C11#54311yescharacteristic
127C2×C11#55511yescharacteristic
128C2×C11#55712yes—
129C2×C11#56311yescharacteristic
130C2×Q8—114no—
131C2×Q8—441no—
132C2×Q8—441no—
133C22×C4—112no—
134C22×C4—112no—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4C22×D1111yescharacteristic
138C22×C4C22×D1111yescharacteristic
139C22×C4C22×D1112yes—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C4⋊C4—41no—
143C4⋊C4—41no—
144C4⋊C4—224no—
145C4⋊C4—224no—
146C4⋊C4—224no—
147C4⋊C4—442no—
148C4⋊C4—442no—
149C4⋊C4—441no—
150C42—441no—
151C42—442no—
152C11#280911yescharacteristic, complemented, Sylow
153C23C23×D1111yescharacteristic
154Q8—444no—
155C2×C4—21no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—114no—
168C2×C4—114no—
169C2×C4—222no—
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×C4Q8×D1112yes—
180C22#6703711yescharacteristic
181C22C2×Q8×D1111yescharacteristic
182C22#41×D1112yes—
183C22#6704211yescharacteristic
184C22#6704312yes—
185C4—22no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—42no—
190C4—224no—
191C4—224no—
192C4—442no—
193C4—442no—
194C2#1062316511yescharacteristic
195C2#1062318211yescharacteristic
196C2#1062320111yescharacteristic
197C2#1062321612yes—
198C2#1062323812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#400C2
hypercenter#400D11
hypocenterC11#2809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
152. C11#2809semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106225992
#106225972
#106225872
#106222702
#106222662
#106222652
#106222602
#106222592
#280911