Finite Group Databasebeta

← #13076666

Subgroups — #13076666

Order 1408.

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

normal subgroups only

This group has 464 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
1C2×C11×#125C211yesmaximal, characteristic, complemented
2C2×#66928C211yesmaximal, characteristic
3#10622607C214yesmaximal, complemented
4#10622606C212yesmaximal, complemented
5#10622605C212yesmaximal, complemented
6#10622604C212yesmaximal
7#10622592C212yesmaximal, complemented
8#10622549C211yesmaximal, characteristic, complemented
9C22×D44C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C11×#125—24no—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×C4⋊Dic11C2212yes—
22C2×Dic11⋊C4C2214yes—
23#66928—24no—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2214yes—
27C23×D11C2312yes—
28C22×C4×C11C2312yes—
29C22×C4×C11C2312yes—
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×Dic11C2314yes—
34C22×Dic11C2312yes—
35C2×D44—22no—
36C2×D44—42no—
37C2×Dic22—22no—
38C2×Dic22—42no—
39C11×C4⋊C4—22no—
40C11×C4⋊C4—22no—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—24no—
43C42×C11D414yes—
44(C2×D11)⋊C4—24no—
45(C2×D11)⋊C4—24no—
46(C2×D11)⋊C4—44no—
47(C2×D11)⋊C4—44no—
48C4⋊Dic11—42no—
49Dic11⋊C4—44no—
50#2820—111nomaximal, Sylow
51C23×C11C2411yescharacteristic
52C22×D11—22no—
53C22×D11—22no—
54C22×D11—24no—
55C22×D11—24no—
56C22×D11—22no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—21no—
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—24no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11C2×D412yes—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D412yes—
69C2×Dic11—22no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72C2×Dic11—24no—
73C2×Dic11—24no—
74D44—44no—
75Dic22—44no—
76C2×#125D1111yescharacteristic, complemented
77C2×#124—111no—
78#399—112no—
79#397—112no—
80#396—114no—
81#395—112no—
82#394—112no—
83#382—111no—
84C22×C11C22×D411yescharacteristic
85C22×C11H(5,𝔽2)12yes—
86C22×C11H(5,𝔽2)11yescharacteristic
87C22×C112−1+412yes—
88C22×C112−1+411yescharacteristic
89C2×D11—42no—
90C2×D11—42no—
91C2×D11—42no—
92C2×D11—44no—
93C2×D11—44no—
94C4×C11—22no—
95C4×C11—22no—
96C4×C11—22no—
97C4×C11—42no—
98C4×C11—42no—
99Dic11—42no—
100Dic11—44no—
101C22×Q8—111no—
102C22×D4—111no—
103#125—24no—
104#124—224no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—114no—
107C2×C4⋊C4C2×D1112yes—
108C2×C4⋊C4C2×D1112yes—
109C2×C4⋊C4C2×D1111yescharacteristic
110C2×C4⋊C4C2×D1111yescharacteristic
111C2×C22⋊C4—112no—
112C2×C22⋊C4—112no—
113C2×C22⋊C4—114no—
114C2×C22⋊C4—114no—
115C2×C42C2×D1111yescharacteristic
116#95—112no—
117#95—112no—
118#95—114no—
119C2×C11#53511yescharacteristic
120C2×C11#53611yescharacteristic
121C2×C11#53711yescharacteristic
122C2×C11#56212yes—
123C2×C11#56312yes—
124D11—82no—
125C24—112no—
126C2×Q8—222no—
127C2×Q8—442no—
128C2×D4—222no—
129C2×D4—442no—
130C22×C4—114no—
131C22×C4—112no—
132C22×C4C22×D1112yes—
133C22×C4C22×D1112yes—
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1111yescharacteristic
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—22no—
139C4⋊C4—22no—
140C4⋊C4—24no—
141C4⋊C4—444no—
142C4⋊C4—442no—
143C22⋊C4—224no—
144C22⋊C4—224no—
145C22⋊C4—444no—
146C22⋊C4—444no—
147C42C22⋊D1114yes—
148C11#282011yescharacteristic, complemented, Sylow
149C23—224no—
150C23—222no—
151C23—224no—
152C23—222no—
153C23—222no—
154C23C23×D1111yescharacteristic
155Q8—444no—
156D4—444no—
157C2×C4—22no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—224no—
167C2×C4—224no—
168C2×C4—224no—
169C2×C4—224no—
170C2×C4—222no—
171C2×C4C2×C22⋊D1112yes—
172C2×C4C2×C22⋊D1112yes—
173C2×C4C2×C22⋊D1112yes—
174C22—442no—
175C22—442no—
176C22—442no—
177C22—444no—
178C22—444no—
179C22#6704012yes—
180C22#6704212yes—
181C22#6704211yescharacteristic
182C22#6704311yescharacteristic
183C22C22×C22⋊D1111yescharacteristic
184C4—22no—
185C4—22no—
186C4—22no—
187C4—42no—
188C4—42no—
189C4—442no—
190C4—444no—
191C2—882no—
192C2#1062323012yes—
193C2#1062323112yes—
194C2#1062334711yescharacteristic
195C2#1062336111yescharacteristic
196C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#125C2
prime radicalC22×D44C22
hypercenterC2×#125D11
hypocenterC11#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C11×#125C2semidirect
3. #10622607C2semidirect
4. #10622606C2semidirect
5. #10622605C2semidirect
7. #10622592C2semidirect
8. #10622549C2semidirect
76. C2×#125D11semidirect
148. C11#2820semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×#669282
#106226072
#106226062
#106226052
#106226042
#106225922
#106225492
#282011