Finite Group Databasebeta

← #13076651

Subgroups — #13076651

Order 1408.

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

normal subgroups only

This group has 444 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×C22⋊Q8C211yesmaximal, characteristic
2C2×#66977C211yesmaximal, characteristic
3#10622842C212yesmaximal, complemented
4#10622824C211yesmaximal, characteristic
5#10622599C212yesmaximal, complemented
6#10622595C212yesmaximal, complemented
7#10622592C212yesmaximal, complemented
8#10622565C214yesmaximal
9C22×Q8×C11C2211yescharacteristic
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C11×C22⋊Q8—24no—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19#66977—24no—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2214yes—
22C11⋊#95C2214yes—
23C11⋊#95C2214yes—
24C11⋊#95C2214yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C2×Q8×C11—22no—
29C2×Q8×C11—42no—
30C22×C4×C11—42no—
31C22×C4×C11D414yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2314yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C2×Dic22—22no—
40C2×Dic22—42no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—24no—
43C11×C22⋊C4—24no—
44C22⋊Dic11—24no—
45C22⋊Dic11—42no—
46C4⋊Dic11—22no—
47Dic11⋊C4—24no—
48Dic11⋊C4—44no—
49#2817—111nomaximal, Sylow
50C23×C11—22no—
51C23×C11—22no—
52C23×C11—22no—
53C23×C11C2×D412yes—
54C23×C11C2411yescharacteristic
55Q8×C11—44no—
56C2×C4×C11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—24no—
61C2×C4×C11—24no—
62C2×C4×C11—44no—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×D412yes—
65C2×Dic11—22no—
66C2×Dic11—22no—
67C2×Dic11—24no—
68C2×Dic11—24no—
69C2×Dic11—24no—
70C2×Dic11—24no—
71C2×Dic11—24no—
72Dic22—44no—
73C2×C22⋊Q8—111no—
74C2×C22⋊Q8D1111yescharacteristic
75#400—112no—
76#400—112no—
77#397—114no—
78#395—112no—
79#395—112no—
80#381—111no—
81C22×C11—22no—
82C22×C11—22no—
83C22×C11—22no—
84C22×C11—44no—
85C22×C11C22×D411yescharacteristic
86C22×C11H(5,𝔽2)12yes—
87C22×C112−1+412yes—
88C22×C112−1+412yes—
89C4×C11—22no—
90C4×C11—22no—
91C4×C11—42no—
92C4×C11—42no—
93Dic11—42no—
94Dic11—42no—
95Dic11—44no—
96C22×Q8—111no—
97C22×Q8C2×D1111yescharacteristic
98C23×C4C2×D1111yescharacteristic
99C22⋊Q8—24no—
100C22⋊Q8—224no—
101C2×C4⋊C4—112no—
102C2×C4⋊C4—111no—
103C2×C4⋊C4—114no—
104C2×C4⋊C4C2×D1112yes—
105C2×C4⋊C4C2×D1111yescharacteristic
106C2×C22⋊C4—112no—
107C2×C22⋊C4—112no—
108C2×C22⋊C4C2×D1112yes—
109#95—112no—
110#95—112no—
111#95—114no—
112#95—114no—
113#95—114no—
114C2×C11—42no—
115C2×C11#53411yescharacteristic
116C2×C11#53611yescharacteristic
117C2×C11#53611yescharacteristic
118C2×C11#56314yes—
119C24C22×D1111yescharacteristic
120C2×Q8—22no—
121C2×Q8—42no—
122C2×Q8—222no—
123C2×Q8—442no—
124C22×C4—42no—
125C22×C4—114no—
126C22×C4—112no—
127C22×C4—112no—
128C22×C4C22⋊D1114yes—
129C22×C4C22×D1112yes—
130C22×C4C22×D1112yes—
131C22×C4C22×D1111yescharacteristic
132C22×C4C22×D1111yescharacteristic
133C4⋊C4—22no—
134C4⋊C4—24no—
135C4⋊C4—224no—
136C4⋊C4—222no—
137C4⋊C4—444no—
138C22⋊C4—24no—
139C22⋊C4—224no—
140C22⋊C4—442no—
141C11#281711yescharacteristic, complemented, Sylow
142C23—22no—
143C23—22no—
144C23—22no—
145C23C2×C22⋊D1112yes—
146C23C23×D1111yescharacteristic
147Q8—44no—
148Q8—444no—
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—24no—
152C2×C4—24no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—44no—
156C2×C4—224no—
157C2×C4—224no—
158C2×C4—224no—
159C2×C4—224no—
160C2×C4—224no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4C2×C22⋊D1112yes—
164C2×C4C2×C22⋊D1112yes—
165C22—22no—
166C22—22no—
167C22—22no—
168C22—44no—
169C22#6703712yes—
170C22#6704012yes—
171C22#6704312yes—
172C22C22×C22⋊D1111yescharacteristic
173C4—22no—
174C4—22no—
175C4—42no—
176C4—42no—
177C4—442no—
178C4—442no—
179C4—444no—
180C2—42no—
181C2#1062317714yes—
182C2#1062333511yescharacteristic
183C2#1062334711yescharacteristic
184C2#1062335611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C22⋊Q8C2
prime radicalC24×C11C23
hypercenterC2×C22⋊Q8D11
hypocenterC11#2817
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10622842C2semidirect
5. #10622599C2semidirect
6. #10622595C2semidirect
7. #10622592C2semidirect
141. C11#2817semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C22⋊Q82
C2×#669772
#106228422
#106228242
#106225992
#106225952
#106225922
#106225652
#281711