Finite Group Databasebeta

← #13075566

Subgroups — #13075566

Order 1408.

416 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 141 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×#66942C212yesmaximal
2C11×#389C211yesmaximal, characteristic
3#10622597C212yesmaximal
4#10622593C212yesmaximal
5#10622585C212yesmaximal
6#10622541C211yesmaximal, characteristic
7#10622541C211yesmaximal, characteristic
8#10622270C212yesmaximal
9#10622267C212yesmaximal
10C2×C11×C4⋊C4C2212yes—
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C42×C11C2211yescharacteristic
14C2×C4⋊Dic11C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25#66942—28no—
26C11×#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C11×C4⋊C4—24no—
42C11×C4⋊C4—22no—
43C11×C4⋊C4—41no—
44C42×C11—41no—
45C4⋊Dic11—41no—
46C4⋊Dic11—41no—
47C4⋊Dic11D414yes—
48C4⋊Dic11Q814yes—
49Dic11⋊C4—24no—
50Dic11⋊C4—24no—
51Dic11⋊C4—24no—
52Dic11⋊C4—24no—
53Dic11⋊C4—24no—
54Dic11⋊C4—42no—
55C4×Dic11—24no—
56#2726—111nomaximal, Sylow
57C23×C11C2411yescharacteristic
58C2×C4×C11—21no—
59C2×C4×C11—21no—
60C2×C4×C11—21no—
61C2×C4×C11—21no—
62C2×C4×C11—21no—
63C2×C4×C11—21no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×Q812yes—
72C2×C4×C11#4112yes—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11C2×D414yes—
84C2×Dic11C2×Q814yes—
85C2×#125—112no—
86#398—112no—
87#398—112no—
88#398—112no—
89#389—112no—
90#389—111no—
91#389—111no—
92#389D1111yescharacteristic
93#387—112no—
94C22×C11C22×D411yescharacteristic
95C22×C11C22×Q811yescharacteristic
96C22×C11C2×#4111yescharacteristic
97C22×C11H(5,𝔽2)11yescharacteristic
98C22×C112−1+411yescharacteristic
99C22×C112−1+411yescharacteristic
100C22×C112−1+411yescharacteristic
101C4×C11—22no—
102C4×C11—22no—
103C4×C11—22no—
104C4×C11—42no—
105C4×C11—42no—
106Dic11—24no—
107Dic11—24no—
108Dic11—42no—
109Dic11—42no—
110#125—228no—
111C2×C4⋊C4—111no—
112C2×C4⋊C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—111no—
120C2×C4⋊C4—111no—
121C2×C4⋊C4C2×D1112yes—
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C42—112no—
125C2×C42C2×D1111yescharacteristic
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95C2×D1112yes—
132C2×C11#53711yescharacteristic
133C2×C11#53911yescharacteristic
134C2×C11#54411yescharacteristic
135C2×C11#54711yescharacteristic
136C2×C11D4×Q811yescharacteristic
137C2×C11#55711yescharacteristic
138C2×C11#56411yescharacteristic
139C22×C4—112no—
140C22×C4—112no—
141C22×C4—112no—
142C22×C4—112no—
143C22×C4C22×D1112yes—
144C22×C4C22×D1112yes—
145C22×C4C22×D1111yescharacteristic
146C22×C4C22×D1111yescharacteristic
147C22×C4C22×D1111yescharacteristic
148C4⋊C4—22no—
149C4⋊C4—24no—
150C4⋊C4—41no—
151C4⋊C4—114no—
152C4⋊C4—114no—
153C4⋊C4—224no—
154C4⋊C4—224no—
155C4⋊C4—224no—
156C4⋊C4—224no—
157C4⋊C4—224no—
158C4⋊C4—442no—
159C4⋊C4—441no—
160C4⋊C4—441no—
161C42—41no—
162C42—224no—
163C11#272611yescharacteristic, complemented, Sylow
164C23C23×D1111yescharacteristic
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—114no—
178C2×C4—114no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4#433912yes—
190C2×C4D4×D1112yes—
191C2×C4Q8×D1112yes—
192C22C2×#433911yescharacteristic
193C22C2×D4×D1111yescharacteristic
194C22#6703711yescharacteristic
195C22C2×Q8×D1111yescharacteristic
196C22#6704011yescharacteristic
197C22#6704311yescharacteristic
198C22#6704311yescharacteristic
199C4—22no—
200C4—22no—
201C4—22no—
202C4—42no—
203C4—42no—
204C4—224no—
205C4—224no—
206C4—442no—
207C4—442no—
208C2#1062304611yescharacteristic
209C2#1062308211yescharacteristic
210C2#1062309811yescharacteristic
211C2#1062312811yescharacteristic
212C2#1062315411yescharacteristic
213C2C11⋊#56411yescharacteristic
214C2#1062325811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#389C2
hypercenter#389D11
hypocenterC11#2726
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
163. C11#2726semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C11×#3892
#106225972
#106225932
#106225852
#106225412
#106222702
#106222672
#272611