Finite Group Databasebeta

← #13074485

Subgroups — #13074485

Order 1408.

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

normal subgroups only

This group has 512 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
1C2×C11×#125C211yesmaximal, characteristic, complemented
2C2×C4×D44C211yesmaximal, characteristic
3#10622606C212yesmaximal, complemented
4#10622605C212yesmaximal, complemented
5#10622604C212yesmaximal
6#10622602C214yesmaximal, complemented
7#10622596C212yesmaximal, complemented
8#10622550C211yesmaximal, characteristic, complemented
9C22×D44C2211yescharacteristic
10C22×C4×D11C2212yes—
11C11×#125—24no—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C42×C11C2211yescharacteristic
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2214yes—
19C2×(C2×D11)⋊C4C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2214yes—
22C4×D44—24no—
23C11⋊#95C2212yes—
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—24no—
36C2×D44—22no—
37C2×C4×D11—24no—
38C2×C4×D11—44no—
39C11×C4⋊C4—24no—
40C11×C4⋊C4—22no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—24no—
43C42×C11D414yes—
44(C2×D11)⋊C4—28no—
45(C2×D11)⋊C4—24no—
46(C2×D11)⋊C4—44no—
47C4⋊Dic11—22no—
48Dic11⋊C4—44no—
49#2633—111nomaximal, Sylow
50C23×C11C2411yescharacteristic
51C22×D11—22no—
52C22×D11—22no—
53C22×D11—24no—
54C22×D11—24no—
55C22×D11#4114yes—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—24no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11C2×D412yes—
65C2×C4×C11C2×D412yes—
66C2×C4×C11C2×D412yes—
67C2×Dic11—22no—
68C2×Dic11—24no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72D44—28no—
73C4×D11—48no—
74C2×#125D1111yescharacteristic, complemented
75C2×C4×D4—111no—
76#399—112no—
77#398—112no—
78#397—112no—
79#394—112no—
80#385—114no—
81#383—111no—
82C22×C11C22×D411yescharacteristic
83C22×C11C2×#4112yes—
84C22×C11H(5,𝔽2)12yes—
85C22×C112−1+412yes—
86C2×D11—24no—
87C2×D11—28no—
88C2×D11—42no—
89C2×D11—42no—
90C2×D11—44no—
91C4×C11—22no—
92C4×C11—22no—
93C4×C11—22no—
94C4×C11—42no—
95C4×C11—42no—
96Dic11—42no—
97Dic11—44no—
98C22×D4—111no—
99C23×C4—112no—
100#125—24no—
101C4×D4—224no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—114no—
104C2×C4⋊C4C2×D1112yes—
105C2×C4⋊C4C2×D1112yes—
106C2×C4⋊C4C2×D1111yescharacteristic
107C2×C4⋊C4C2×D1111yescharacteristic
108C2×C22⋊C4—112no—
109C2×C22⋊C4—114no—
110C2×C22⋊C4—114no—
111C2×C42C2×D1111yescharacteristic
112#95—112no—
113#95—112no—
114#95—112no—
115#95—114no—
116C2×C11#52511yescharacteristic
117C2×C11#53511yescharacteristic
118C2×C11#53611yescharacteristic
119C2×C11#53914yes—
120D11—44no—
121C24—112no—
122C2×D4—224no—
123C2×D4—222no—
124C22×C4—114no—
125C22×C4—112no—
126C22×C4—224no—
127C22×C4—444no—
128C22×C4C22×D1112yes—
129C22×C4C22×D1112yes—
130C22×C4C22×D1111yescharacteristic
131C22×C4C22×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—22no—
135C4⋊C4—24no—
136C4⋊C4—24no—
137C4⋊C4—222no—
138C4⋊C4—444no—
139C22⋊C4—228no—
140C22⋊C4—224no—
141C22⋊C4—444no—
142C42C22⋊D1114yes—
143C11#263311yescharacteristic, complemented, Sylow
144C23—114no—
145C23—224no—
146C23—222no—
147C23—224no—
148C23—222no—
149C23C23×D1111yescharacteristic
150D4—228no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—24no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—22no—
159C2×C4—224no—
160C2×C4—224no—
161C2×C4—224no—
162C2×C4—224no—
163C2×C4—222no—
164C2×C4—448no—
165C2×C4C2×C22⋊D1112yes—
166C2×C4C2×C22⋊D1112yes—
167C2×C4C2×C22⋊D1112yes—
168C22—224no—
169C22—228no—
170C22—442no—
171C22—442no—
172C22—444no—
173C22#6704012yes—
174C22#41×D1112yes—
175C22#6704212yes—
176C22C22×C22⋊D1111yescharacteristic
177C4—22no—
178C4—22no—
179C4—22no—
180C4—42no—
181C4—42no—
182C4—442no—
183C4—444no—
184C2—444no—
185C2#1062322314yes—
186C2#1062334711yescharacteristic
187C2#1062335911yescharacteristic
188C2#1062336111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#125C2
prime radicalC22×D44C22
hypercenterC2×#125D11
hypocenterC11#2633
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. #10622606C2semidirect
4. #10622605C2semidirect
6. #10622602C2semidirect
7. #10622596C2semidirect
8. #10622550C2semidirect
74. C2×#125D11semidirect
143. C11#2633semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1252
C2×C4×D442
#106226062
#106226052
#106226042
#106226022
#106225962
#106225502
#263311