Finite Group Databasebeta

← #13074367

Subgroups — #13074367

Order 1408.

728 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 157 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×#127C211yesmaximal, characteristic, complemented
2C2×#66991C212yesmaximal, complemented
3C2×#66925C211yesmaximal, characteristic, complemented
4#10622836C214yesmaximal, complemented
5#10622835C214yesmaximal, complemented
6#10622834C212yesmaximal, complemented
7#10622549C211yesmaximal, characteristic, complemented
8C22×D4×C11C2212yes—
9C22×D4×C11C2214yes—
10C22×C22⋊D11C2214yes—
11C22×C4×D11C2211yescharacteristic
12C11×#127—24no—
13C2×C42×C11C2211yescharacteristic
14C2×C22⋊Dic11C2214yes—
15C2×C22⋊Dic11C2218yes—
16#66991—28no—
17C2×(C2×D11)⋊C4C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2211yescharacteristic
21#66925—24no—
22C11⋊#95C2214yes—
23C24×C11C2314yes—
24C23×D11C2311yescharacteristic
25C2×D4×C11—24no—
26C2×D4×C11—28no—
27C2×D4×C11—24no—
28C2×D4×C11—24no—
29C2×D4×C11—48no—
30C22×C4×C11C2312yes—
31C22×C4×C11C2311yescharacteristic
32C2×C22⋊D11—28no—
33C2×C22⋊D11—48no—
34C22×Dic11C2314yes—
35C22×Dic11C2312yes—
36C22×Dic11C2311yescharacteristic
37C2×C4×D11—22no—
38C2×C4×D11—22no—
39C2×C4×D11D414yescomplemented
40C42×C11D414yescomplemented
41C22⋊Dic11—28no—
42C22⋊Dic11—48no—
43(C2×D11)⋊C4—24no—
44C4⋊Dic11—24no—
45Dic11⋊C4—24no—
46C4×Dic11—22no—
47#2619—111nomaximal, Sylow
48C23×C11—24no—
49C23×C11—24no—
50C23×C11—24no—
51C23×C11—28no—
52C23×C11—28no—
53C23×C11C2411yescharacteristic
54C22×D11—21no—
55C22×D11—21no—
56C22×D11—24no—
57C22×D11C2×D412yes—
58D4×C11—416no—
59D4×C11—48no—
60C2×C4×C11—24no—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2×D414yes—
63C2×C4×C11C2×D412yes—
64C2×C4×C11#4112yes—
65C22⋊D11—416no—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—22no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11—28no—
72C2×Dic11C2×D412yes—
73C4×D11—28no—
74C2×#127D1111yescharacteristic, complemented
75C2×#121—112no—
76C2×#117—111no—
77#394—114no—
78#392—114no—
79#390—112no—
80#382—111no—
81C22×C11—44no—
82C22×C11—48no—
83C22×C11—44no—
84C22×C11—44no—
85C22×C11—48no—
86C22×C11C22×D411yescharacteristic
87C22×C11C22×D411yescharacteristic
88C22×C11C2×#4111yescharacteristic
89C22×C11H(5,𝔽2)14yes—
90C2×D11—22no—
91C2×D11—24no—
92C2×D11—42no—
93C2×D11—42no—
94C4×C11—24no—
95C4×C11#12114yes—
96Dic11—22no—
97Dic11—42no—
98Dic11—44no—
99C22×D4—114no—
100C22×D4C2×D1112yes—
101C22×D4C2×D1114yes—
102C23×C4—111no—
103#127—24no—
104#121—228no—
105#117—224no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C22⋊C4—114no—
109C2×C22⋊C4—112no—
110C2×C22⋊C4—118no—
111C2×C42—111no—
112C2×C42C2×D1111yescharacteristic
113#95—114no—
114C2×C11—84no—
115C2×C11C2×#12111yescharacteristic
116C2×C11#53512yes—
117C2×C11#53512yes—
118C2×C11#54012yes—
119D11—42no—
120C24—111no—
121C24C22×D1114yes—
122C2×D4—24no—
123C2×D4—24no—
124C2×D4—28no—
125C2×D4—24no—
126C2×D4—48no—
127C2×D4—228no—
128C2×D4—448no—
129C22×C4—111no—
130C22×C4—114no—
131C22×C4—114no—
132C22×C4—112no—
133C22×C4—222no—
134C22×C4—222no—
135C22×C4C22×D1112yes—
136C22×C4C22×D1111yescharacteristic
137C4⋊C4—224no—
138C4⋊C4—224no—
139C22⋊C4—228no—
140C22⋊C4—224no—
141C22⋊C4—448no—
142C42—222no—
143C42C22⋊D1114yescomplemented
144C11#261911yescharacteristic, complemented, Sylow
145C23—24no—
146C23—24no—
147C23—28no—
148C23—28no—
149C23—24no—
150C23—112no—
151C23—221no—
152C23—224no—
153C23—221no—
154C23C23×D1111yescharacteristic
155D4—416no—
156D4—48no—
157D4—4416no—
158C2×C4—24no—
159C2×C4—112no—
160C2×C4—221no—
161C2×C4—221no—
162C2×C4—228no—
163C2×C4—224no—
164C2×C4—224no—
165C2×C4—228no—
166C2×C4—222no—
167C2×C4D4×D1112yes—
168C2×C4#434112yes—
169C2×C4C2×C22⋊D1114yes—
170C2×C4C2×C22⋊D1112yes—
171C22—44no—
172C22—44no—
173C22—48no—
174C22—44no—
175C22—48no—
176C22—224no—
177C22—222no—
178C22—442no—
179C22—442no—
180C22C2×D4×D1111yescharacteristic
181C22C2×#434111yescharacteristic
182C22#6703714yes—
183C22C22×C22⋊D1111yescharacteristic
184C4—24no—
185C4—222no—
186C4—444no—
187C4—442no—
188C4#6699114yes—
189C2—84no—
190C2—442no—
191C2#1062324612yes—
192C2#1062325012yes—
193C2C2×#6699111yescharacteristic
194C2#1062333612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#127C2
hypercenterC2×#127D11
hypocenterC11#2619
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×C11×#127C2semidirect
2. C2×#66991C2semidirect
3. C2×#66925C2semidirect
4. #10622836C2semidirect
5. #10622835C2semidirect
6. #10622834C2semidirect
7. #10622549C2semidirect
39. C2×C4×D11D4semidirect
40. C42×C11D4semidirect
74. C2×#127D11semidirect
143. C42C22⋊D11semidirect
144. C11#2619semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1272
C2×#669912
C2×#669252
#106228362
#106228352
#106228342
#106225492
#261911