Finite Group Databasebeta

← #13074438

Subgroups — #13074438

Order 1408.

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

normal subgroups only

This group has 488 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×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#66925C211yesmaximal, characteristic
3#10622844C212yesmaximal
4#10622842C212yesmaximal, complemented
5#10622605C212yesmaximal
6#10622600C212yesmaximal
7#10622595C212yesmaximal, complemented
8#10622586C212yesmaximal, complemented
9#10622549C211yesmaximal, characteristic, complemented
10C22×Q8×C11C2212yes—
11C22×C4×D11C2211yescharacteristic
12C11×C4⋊Q8—24no—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2212yes—
15C2×C42×C11C2211yescharacteristic
16C2×(C2×D11)⋊C4C2211yescharacteristic
17C2×(C2×D11)⋊C4C2211yescharacteristic
18C2×(C2×D11)⋊C4C2214yes—
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2214yes—
23C2×C4×Dic11C2211yescharacteristic
24#66925—24no—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C23×D11C2311yescharacteristic
30C2×Q8×C11—24no—
31C2×Q8×C11—44no—
32C22×C4×C11C2314yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×Dic11C2311yescharacteristic
37C22×Dic11C2314yes—
38C22×Dic11C2311yescharacteristic
39C22×Dic11C2311yescharacteristic
40C2×C4×D11—22no—
41C2×C4×D11—22no—
42C2×C4×D11Q814yescomplemented
43C11×C4⋊C4—24no—
44C11×C4⋊C4—24no—
45C42×C11D414yes—
46(C2×D11)⋊C4—22no—
47(C2×D11)⋊C4—22no—
48(C2×D11)⋊C4—44no—
49C4⋊Dic11—24no—
50Dic11⋊C4—22no—
51Dic11⋊C4—22no—
52Dic11⋊C4—44no—
53C4×Dic11—22no—
54#2628—111nomaximal, Sylow
55C23×C11C2411yescharacteristic
56C22×D11—21no—
57C22×D11—21no—
58C22×D11—22no—
59C22×D11—22no—
60C22×D11C2×Q812yes—
61Q8×C11—48no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—24no—
65C2×C4×C11—24no—
66C2×C4×C11—24no—
67C2×C4×C11C2×D412yes—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×Q812yes—
71C2×C4×C11#4112yes—
72C2×Dic11—21no—
73C2×Dic11—21no—
74C2×Dic11—21no—
75C2×Dic11—21no—
76C2×Dic11—24no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—22no—
80C2×Dic11—24no—
81C2×Dic11C2×Q812yes—
82C4×D11—28no—
83C2×C4⋊Q8D1111yescharacteristic, complemented
84C2×#117—111no—
85#400—112no—
86#399—112no—
87#395—112no—
88#393—112no—
89#389—112no—
90#382—111no—
91#380—112no—
92C22×C11C22×D411yescharacteristic
93C22×C11C22×Q811yescharacteristic
94C22×C11C2×#4111yescharacteristic
95C22×C11H(5,𝔽2)12yes—
96C22×C112−1+412yes—
97C2×D11—22no—
98C2×D11—24no—
99C2×D11—41no—
100C2×D11—41no—
101C2×D11—42no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—44no—
105C4×C11C22⋊Q814yes—
106Dic11—22no—
107Dic11—41no—
108Dic11—41no—
109Dic11—44no—
110C22×Q8C2×D1112yes—
111C23×C4—111no—
112C4⋊Q8—24no—
113#117—224no—
114C2×C4⋊C4—111no—
115C2×C4⋊C4—111no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—114no—
118C2×C4⋊C4C2×D1112yes—
119C2×C4⋊C4C2×D1112yes—
120C2×C22⋊C4—111no—
121C2×C22⋊C4—111no—
122C2×C22⋊C4—114no—
123C2×C42—111no—
124C2×C42C2×D1111yescharacteristic
125#95—114no—
126#95—112no—
127#95—112no—
128#95—114no—
129C2×C11C2×C22⋊Q811yescharacteristic
130C2×C11#53511yescharacteristic
131C2×C11#53611yescharacteristic
132C2×C11#54212yes—
133C2×C11#54412yes—
134D11—42no—
135C24—111no—
136C2×Q8—24no—
137C2×Q8—44no—
138C22×C4—111no—
139C22×C4—114no—
140C22×C4—111no—
141C22×C4—114no—
142C22×C4—111no—
143C22×C4—222no—
144C22×C4—222no—
145C22×C4C22×D1114yes—
146C22×C4C22×D1111yescharacteristic
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1111yescharacteristic
149C4⋊C4—24no—
150C4⋊C4—24no—
151C4⋊C4—224no—
152C4⋊C4—222no—
153C4⋊C4—222no—
154C4⋊C4—444no—
155C22⋊C4—222no—
156C22⋊C4—222no—
157C22⋊C4—444no—
158C42—222no—
159C42C22⋊D1114yes—
160C11#262811yescharacteristic, complemented, Sylow
161C23—112no—
162C23—222no—
163C23—221no—
164C23—222no—
165C23—221no—
166C23C23×D1111yescharacteristic
167Q8—48no—
168C2×C4—22no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—24no—
172C2×C4—24no—
173C2×C4—112no—
174C2×C4—221no—
175C2×C4—221no—
176C2×C4—228no—
177C2×C4—224no—
178C2×C4—222no—
179C2×C4—224no—
180C2×C4—224no—
181C2×C4—222no—
182C2×C4—221no—
183C2×C4—221no—
184C2×C4Q8×D1112yes—
185C2×C4#434312yes—
186C2×C4C2×C22⋊D1112yes—
187C2×C4C2×C22⋊D1112yes—
188C2×C4C2×C22⋊D1112yes—
189C22—224no—
190C22—222no—
191C22—442no—
192C22—441no—
193C22—441no—
194C22#6703712yes—
195C22C2×Q8×D1111yescharacteristic
196C22C2×#434311yescharacteristic
197C22#6704012yes—
198C22C22×C22⋊D1111yescharacteristic
199C4—22no—
200C4—22no—
201C4—44no—
202C4—222no—
203C4—444no—
204C4—441no—
205C4—441no—
206C4#6699914yes—
207C2—442no—
208C2#1062326012yes—
209C2#1062326412yes—
210C2#1062333611yescharacteristic
211C2C2×#6699911yescharacteristic
212C2#1062334711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×C4⋊Q8C2
prime radicalC23×D11C23
hypercenterC2×C4⋊Q8D11
hypocenterC11#2628
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
4. #10622842C2semidirect
7. #10622595C2semidirect
8. #10622586C2semidirect
9. #10622549C2semidirect
42. C2×C4×D11Q8semidirect
83. C2×C4⋊Q8D11semidirect
160. C11#2628semidirect

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×#669252
#106228442
#106228422
#106226052
#106226002
#106225952
#106225862
#106225492
#262811