Finite Group Databasebeta

← #13076686

Subgroups — #13076686

Order 1408.

380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66943C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic
4#10622599C211yesmaximal, characteristic
5#10622597C212yesmaximal
6#10622593C211yesmaximal, characteristic
7#10622593C212yesmaximal
8#10622273C212yesmaximal
9#10622272C211yesmaximal, characteristic
10#10622270C212yesmaximal
11#10622263C211yesmaximal, characteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2212yes—
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2211yescharacteristic
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26#66943—24no—
27#66942—24no—
28C11×#95C2211yescharacteristic
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C11×C4⋊C4—22no—
49C11×C4⋊C4—22no—
50C11×C4⋊C4—42no—
51C4⋊Dic11—22no—
52C4⋊Dic11—24no—
53C4⋊Dic11—22no—
54Dic11⋊C4—22no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—24no—
58Dic11⋊C4—22no—
59Dic11⋊C4—42no—
60Dic11⋊C4—42no—
61C4×Dic11D414yes—
62#2822—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64C2×C4×C11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×Dic11—21no—
78C2×Dic11—22no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—24no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—21no—
89C2×Dic11—22no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92C2×#125—111no—
93C2×#125—111no—
94#400—111no—
95#400—111no—
96#400—112no—
97#398—111no—
98#398—112no—
99#398—112no—
100#398—112no—
101#398D1111yescharacteristic
102#382—111no—
103C22×C11C22×D411yescharacteristic
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C112−1+412yes—
106C22×C112−1+412yes—
107C22×C112−1+411yescharacteristic
108C4×C11—22no—
109C4×C11—41no—
110C4×C11—41no—
111C4×C11—42no—
112C4×C11—42no—
113Dic11—22no—
114Dic11—22no—
115Dic11—42no—
116Dic11—41no—
117Dic11—41no—
118Dic11—42no—
119#125—224no—
120#125—224no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—111no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C4⋊C4C2×D1111yescharacteristic
133C2×C4⋊C4C2×D1112yes—
134C2×C42—111no—
135#95—112no—
136#95—111no—
137#95—112no—
138#95—112no—
139#95—112no—
140#95—112no—
141#95—112no—
142#95C2×D1111yescharacteristic
143#95C2×D1112yes—
144C2×C11#53611yescharacteristic
145C2×C11#53611yescharacteristic
146C2×C11#53711yescharacteristic
147C2×C11#56312yes—
148C2×C11#56412yes—
149C22×C4—111no—
150C22×C4—111no—
151C22×C4—112no—
152C22×C4—112no—
153C22×C4—111no—
154C22×C4—111no—
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1111yescharacteristic
158C22×C4C22×D1112yes—
159C22×C4C22×D1111yescharacteristic
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—224no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—224no—
169C4⋊C4—222no—
170C4⋊C4—222no—
171C4⋊C4—442no—
172C4⋊C4—442no—
173C42—114no—
174C11#282211yescharacteristic, complemented, Sylow
175C23C23×D1111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—112no—
189C2×C4—112no—
190C2×C4—221no—
191C2×C4—222no—
192C2×C4—221no—
193C2×C4—222no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—222no—
198C2×C4—224no—
199C2×C4—222no—
200C2×C4—221no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4D4×D1112yes—
204C22C2×D4×D1111yescharacteristic
205C22#6703711yescharacteristic
206C22#6704012yes—
207C22#6704311yescharacteristic
208C22#6704312yes—
209C4—22no—
210C4—41no—
211C4—42no—
212C4—42no—
213C4—41no—
214C4—222no—
215C4—222no—
216C4—442no—
217C4—441no—
218C4—442no—
219C4—441no—
220C2#1062313911yescharacteristic
221C2#1062317712yes—
222C2#1062317911yescharacteristic
223C2C11⋊#56412yes—
224C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2822
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
174. C11#2822semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669422
C11×#3982
#106225992
#106225972
#106225932
#106222732
#106222722
#106222702
#106222632
#282211