Finite Group Databasebeta

← #13074324

Subgroups — #13074324

Order 1408.

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

normal subgroups only

This group has 388 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×#382C211yesmaximal, characteristic
2#10622599C211yesmaximal, characteristic
3#10622597C212yesmaximal
4#10622592C211yesmaximal, characteristic
5#10622545C212yesmaximal
6#10622268C212yesmaximal
7#10622267C212yesmaximal
8#10622260C212yesmaximal
9#10622259C212yesmaximal
10C22×Dic22C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C4⋊Dic11C2212yes—
15C2×C4⋊Dic11C2211yescharacteristic
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×C4×Dic11C2212yes—
20C2×C4×Dic11C2212yes—
21C11×#95C2212yes—
22C11×#95C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×Dic22—24no—
41C2×Dic22—41no—
42C11×C4⋊C4—41no—
43C11×C4⋊C4—41no—
44C42×C11Q814yescomplemented
45C4⋊Dic11—24no—
46C4⋊Dic11—41no—
47Dic11⋊C4—24no—
48Dic11⋊C4—24no—
49Dic11⋊C4—42no—
50C4×Dic11—24no—
51C4×Dic11—24no—
52#2612—111nomaximal, Sylow
53C23×C11C2411yescharacteristic
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—21no—
64C2×C4×C11—21no—
65C2×C4×C11C2×Q814yes—
66C2×C4×C11C2×Q812yes—
67C2×Dic11—22no—
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#4114yes—
78C2×Dic11#4114yes—
79Dic22—44no—
80#400—111no—
81#398—112no—
82#395—111no—
83#391—112no—
84#389—112no—
85#387—112no—
86#387—112no—
87#382D1111yescharacteristic
88#376—112no—
89C22×C11C22×Q811yescharacteristic
90C22×C11C2×#4112yes—
91C22×C11C2×#4112yes—
92C22×C11H(5,𝔽2)11yescharacteristic
93C22×C112−1+411yescharacteristic
94C4×C11—24no—
95C4×C11—22no—
96C4×C11—41no—
97C4×C11—41no—
98C4×C11—42no—
99Dic11—24no—
100Dic11—24no—
101Dic11—42no—
102Dic11—42no—
103C22×Q8—111no—
104C2×C4⋊C4—112no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—111no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C4⋊C4C2×D1111yescharacteristic
111C2×C42—112no—
112C2×C42—112no—
113C2×C42C2×D1111yescharacteristic
114#95—112no—
115#95—112no—
116#95—112no—
117#95—112no—
118#95—111no—
119#95—111no—
120#95—112no—
121#95—112no—
122#95C2×D1112yes—
123#95C2×D1112yes—
124C2×C11#53312yes—
125C2×C11#54411yescharacteristic
126C2×C11#55111yescharacteristic
127C2×C11#55212yes—
128C2×C11#55511yescharacteristic
129C2×Q8—224no—
130C2×Q8—441no—
131C22×C4—112no—
132C22×C4—112no—
133C22×C4—112no—
134C22×C4—112no—
135C22×C4C22×D1111yescharacteristic
136C22×C4C22×D1111yescharacteristic
137C22×C4C22×D1112yes—
138C22×C4C22×D1111yescharacteristic
139C22×C4C22×D1112yes—
140C4⋊C4—41no—
141C4⋊C4—41no—
142C4⋊C4—224no—
143C4⋊C4—224no—
144C4⋊C4—224no—
145C4⋊C4—442no—
146C4⋊C4—441no—
147C42—224no—
148C42—224no—
149C42Dic2214yescomplemented
150C11#261211yescharacteristic, complemented, Sylow
151C23C23×D1111yescharacteristic
152Q8—444no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—114no—
165C2×C4—114no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4—222no—
171C2×C4—222no—
172C2×C4—222no—
173C2×C4—222no—
174C2×C4—222no—
175C2×C4—222no—
176C2×C4C2×Dic2212yes—
177C2×C4C2×Dic2214yes—
178C22C22×Dic2211yescharacteristic
179C22#6703711yescharacteristic
180C22#6704011yescharacteristic
181C22#41×D1112yes—
182C22#41×D1112yes—
183C4—22no—
184C4—24no—
185C4—42no—
186C4—41no—
187C4—41no—
188C4—224no—
189C4—224no—
190C4—442no—
191C4—442no—
192C2#1062303111yescharacteristic
193C2#1062304812yes—
194C2#1062320111yescharacteristic
195C2#1062321011yescharacteristic
196C2#1062322412yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#382C2
hypercenter#382D11
hypocenterC11#2612
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
44. C42×C11Q8semidirect
149. C42Dic22semidirect
150. C11#2612semidirect

Maximal subgroups

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

subgroupindex
C11×#3822
#106225992
#106225972
#106225922
#106225452
#106222682
#106222672
#106222602
#106222592
#261211