Finite Group Databasebeta

← #13073570

Subgroups — #13073570

Order 1408.

676 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 189 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66999C214yesmaximal, complemented
3C2×C4×D44C211yesmaximal, characteristic
4#10622605C214yesmaximal, complemented
5#10622601C212yesmaximal
6#10622589C212yesmaximal, complemented
7C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
8C22×Q8×C11C2212yes—
9C22×D44C2211yescharacteristic
10C22×C4×D11C2212yes—
11C11×C4⋊Q8—24no—
12C2×C11×C4⋊C4C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C42×C11C2211yescharacteristic
15#66999—216no—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2218yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2218yes—
21C2×C4×Dic11C2212yes—
22C4×D44—24no—
23C11⋊#95C2212yes—
24C23×D11C2312yes—
25C2×Q8×C11—28no—
26C2×Q8×C11—24no—
27C22×C4×C11C2314yes—
28C22×C4×C11C2311yescharacteristic
29C22×C4×C11C2311yescharacteristic
30C22×C4×C11C2311yescharacteristic
31C22×Dic11C2312yes—
32C22×Dic11C2314yes—
33C2×D44—22no—
34C2×D44—22no—
35C2×D44Q814yescomplemented
36C2×C4×D11—24no—
37C2×C4×D11—28no—
38C11×C4⋊C4—24no—
39C11×C4⋊C4—24no—
40C42×C11D414yes—
41(C2×D11)⋊C4—216no—
42(C2×D11)⋊C4—24no—
43C4⋊Dic11—22no—
44C4⋊Dic11D418yescomplemented
45Dic11⋊C4—216no—
46C4×Dic11—24no—
47#2542—111nomaximal, Sylow
48C23×C11C2411yescharacteristic
49C22×D11—24no—
50C22×D11—22no—
51C22×D11—22no—
52C22×D11—24no—
53C22×D11C2×Q814yes—
54Q8×C11—48no—
55C2×C4×C11—22no—
56C2×C4×C11—28no—
57C2×C4×C11—24no—
58C2×C4×C11C2×D414yes—
59C2×C4×C11C2×D412yes—
60C2×C4×C11C2×D412yes—
61C2×C4×C11C2×D412yes—
62C2×C4×C11C2×Q812yes—
63C2×C4×C11#4112yes—
64C2×Dic11—24no—
65C2×Dic11—24no—
66C2×Dic11—24no—
67C2×Dic11—22no—
68C2×Dic11C2×D418yes—
69D44—28no—
70C4×D11—48no—
71C2×C4⋊Q8D1111yescharacteristic, complemented
72C2×C22⋊Q8—114no—
73C2×C4×D4—111no—
74#399—114no—
75#390—112no—
76#384—112no—
77C4×C4⋊C4—111no—
78C22×C11C22×D412yes—
79C22×C11C22×D411yescharacteristic
80C22×C11C22×Q811yescharacteristic
81C22×C11C2×#4111yescharacteristic
82C22×C112−1+412yes—
83C2×D11—24no—
84C2×D11—28no—
85C2×D11—42no—
86C2×D11—42no—
87C2×D11—44no—
88C4×C11—22no—
89C4×C11—44no—
90C4×C11C22⋊Q814yescomplemented
91C4×C11#12714yes—
92Dic11—28no—
93Dic11—42no—
94C22×Q8C2×D1112yes—
95C22×D4—111no—
96C23×C4—112no—
97C4⋊Q8—24no—
98C22⋊Q8—2216no—
99C4×D4—224no—
100C2×C4⋊C4—112no—
101C2×C4⋊C4—111no—
102C2×C4⋊C4—118no—
103C2×C4⋊C4C2×D1112yes—
104C2×C4⋊C4C2×D1112yes—
105C2×C22⋊C4—112no—
106C2×C22⋊C4—118no—
107C2×C42—112no—
108C2×C42C2×D1111yescharacteristic
109#95—112no—
110C2×C11C2×C22⋊Q811yescharacteristic
111C2×C11C2×#12711yescharacteristic
112C2×C11#53611yescharacteristic
113C2×C11#54712yes—
114C2×C11D4×Q812yes—
115D11—44no—
116C24—112no—
117C2×Q8—28no—
118C2×Q8—24no—
119C2×D4—114no—
120C2×D4—222no—
121C2×D4—222no—
122C22×C4—114no—
123C22×C4—112no—
124C22×C4—228no—
125C22×C4—224no—
126C22×C4C22×D1114yes—
127C22×C4C22×D1111yescharacteristic
128C22×C4C22×D1111yescharacteristic
129C22×C4C22×D1111yescharacteristic
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—118no—
133C4⋊C4—2216no—
134C4⋊C4—222no—
135C22⋊C4—2216no—
136C22⋊C4—224no—
137C42—224no—
138C42C22⋊D1114yes—
139C11#254211yescharacteristic, complemented, Sylow
140C23—114no—
141C23—224no—
142C23—222no—
143C23—224no—
144C23—222no—
145C23C23×D1111yescharacteristic
146Q8—48no—
147D4—228no—
148C2×C4—22no—
149C2×C4—28no—
150C2×C4—24no—
151C2×C4—118no—
152C2×C4—224no—
153C2×C4—224no—
154C2×C4—224no—
155C2×C4—222no—
156C2×C4—448no—
157C2×C4D4×D1114yes—
158C2×C4Q8×D1112yes—
159C2×C4#434312yes—
160C2×C4C2×C22⋊D1112yes—
161C2×C4C2×C22⋊D1112yes—
162C2×C4C2×C22⋊D1112yes—
163C22—228no—
164C22—224no—
165C22—444no—
166C22—442no—
167C22—442no—
168C22C2×D4×D1112yes—
169C22C2×Q8×D1111yescharacteristic
170C22C2×#434311yescharacteristic
171C22#6704012yes—
172C22C22×C22⋊D1111yescharacteristic
173C4—22no—
174C4—44no—
175C4—228no—
176C4—442no—
177C4#6699314yes—
178C4#6699914yescomplemented
179C2—444no—
180C2#1062325712yes—
181C2#1062325812yes—
182C2C2×#6699311yescharacteristic
183C2C2×#6699911yescharacteristic
184C2#1062334711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
prime radicalC22×D44C22
hypercenterC2×C4⋊Q8D11
hypocenterC11#2542
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×C11×C4⋊Q8C2semidirect
2. C2×#66999C2semidirect
4. #10622605C2semidirect
6. #10622589C2semidirect
7. C4×C4⋊Dic11C2semidirect
35. C2×D44Q8semidirect
44. C4⋊Dic11D4semidirect
71. C2×C4⋊Q8D11semidirect
90. C4×C11C22⋊Q8semidirect
139. C11#2542semidirect
178. C4#66999semidirect

Maximal subgroups

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

subgroupindex
C2×C11×C4⋊Q82
C2×#669992
C2×C4×D442
#106226052
#106226012
#106225892
C4×C4⋊Dic112
#254211