Finite Group Databasebeta

← #13076602

Subgroups — #13076602

Order 1408.

368 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 137 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#10622843C211yesmaximal, characteristic
3#10622843C211yesmaximal, characteristic
4#10622597C212yesmaximal
5#10622546C212yesmaximal
6#10622273C212yesmaximal
7#10622270C212yesmaximal
8#10622267C212yesmaximal
9#10622260C212yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C42×C11C2211yescharacteristic
13C2×C4⋊Dic11C2212yes—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21C2×C4×Dic11C2211yescharacteristic
22C11×#95C2212yes—
23C11×#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C2×Q8×C11—41no—
32C2×Q8×C11—41no—
33C2×Q8×C11Q814yes—
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—24no—
46C4⋊Dic11—41no—
47C4⋊Dic11—41no—
48Dic11⋊C4—24no—
49Dic11⋊C4—24no—
50Dic11⋊C4—42no—
51Dic11⋊C4—42no—
52C4×Dic11—41no—
53C4×Dic11—41no—
54#2809—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×C11C2×Q812yes—
71C2×C4×C11C2×Q812yes—
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—24no—
82C2×Dic11#4114yes—
83#400—112no—
84#398—112no—
85#398—112no—
86#391—111no—
87#391—111no—
88#391D1111yescharacteristic
89#389—112no—
90#387—112no—
91#387—112no—
92C22×C11C22×Q811yescharacteristic
93C22×C11C2×#4112yes—
94C22×C11H(5,𝔽2)11yescharacteristic
95C22×C11H(5,𝔽2)11yescharacteristic
96C22×C112−1+412yes—
97C4×C11—22no—
98C4×C11—22no—
99C4×C11—22no—
100C4×C11—42no—
101C4×C11—42no—
102Dic11—24no—
103Dic11—42no—
104Dic11—42no—
105Dic11—42no—
106C22×Q8C2×D1111yescharacteristic
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—112no—
110C2×C4⋊C4—112no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4C2×D1111yescharacteristic
115C2×C42—111no—
116C2×C42—111no—
117C2×C42C2×D1111yescharacteristic
118#95—112no—
119#95—112no—
120#95—112no—
121#95—112no—
122#95—112no—
123#95—112no—
124#95—112no—
125#95C2×D1112yes—
126#95C2×D1112yes—
127C2×C11#53912yes—
128C2×C11#54311yescharacteristic
129C2×C11#55511yescharacteristic
130C2×C11#55712yes—
131C2×C11#56311yescharacteristic
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8Dic2214yes—
135C22×C4—112no—
136C22×C4—112no—
137C22×C4—112no—
138C22×C4—112no—
139C22×C4C22×D1112yes—
140C22×C4C22×D1112yes—
141C22×C4C22×D1111yescharacteristic
142C22×C4C22×D1111yescharacteristic
143C22×C4C22×D1111yescharacteristic
144C4⋊C4—41no—
145C4⋊C4—224no—
146C4⋊C4—224no—
147C4⋊C4—224no—
148C4⋊C4—442no—
149C4⋊C4—442no—
150C4⋊C4—441no—
151C4⋊C4—441no—
152C42—41no—
153C42—441no—
154C42—441no—
155C11#280911yescharacteristic, complemented, Sylow
156C23C23×D1111yescharacteristic
157Q8—44no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—114no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4—224no—
177C2×C4—222no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4C2×Dic2212yes—
182C2×C4C2×Dic2212yes—
183C2×C4C2×Dic2212yes—
184C22C22×Dic2211yescharacteristic
185C22#6703711yescharacteristic
186C22#6703711yescharacteristic
187C22#6704012yes—
188C22#41×D1112yes—
189C4—22no—
190C4—22no—
191C4—22no—
192C4—42no—
193C4—42no—
194C4—224no—
195C4—442no—
196C4—442no—
197C4—442no—
198C2#1062301411yescharacteristic
199C2#1062310012yes—
200C2#1062316912yes—
201C2#1062320111yescharacteristic
202C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#391C2
hypercenter#391D11
hypocenterC11#2809
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
155. C11#2809semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228432
#106225972
#106225462
#106222732
#106222702
#106222672
#106222602
#280911