Finite Group Databasebeta

← #13074494

Subgroups — #13074494

Order 1408.

416 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66942C211yesmaximal, characteristic
2C2×#66940C211yesmaximal, characteristic
3C11×#400C211yesmaximal, characteristic
4#10622595C211yesmaximal, characteristic
5#10622592C211yesmaximal, characteristic
6#10622271C212yesmaximal
7#10622270C212yesmaximal
8#10622269C211yesmaximal, characteristic
9#10622268C212yesmaximal
10#10622267C212yesmaximal
11#10622264C211yesmaximal, characteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C4⋊Dic11C2211yescharacteristic
16C2×C4⋊Dic11C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2211yescharacteristic
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24C2×C4×Dic11C2211yescharacteristic
25#66942—24no—
26#66940—24no—
27C11×#95C2211yescharacteristic
28C11×#95C2212yes—
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C2×Dic22—24no—
49C2×Dic22—22no—
50C11×C4⋊C4—22no—
51C11×C4⋊C4—22no—
52C4⋊Dic11—22no—
53C4⋊Dic11—24no—
54Dic11⋊C4—24no—
55Dic11⋊C4—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—22no—
58Dic11⋊C4—24no—
59Dic11⋊C4—22no—
60C4×Dic11—24no—
61C4×Dic11D414yes—
62#2634—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11—24no—
72C2×C4×C11—21no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11C2×D412yes—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—22no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—21no—
88C2×Dic11—22no—
89C2×Dic11C2×D412yes—
90C2×Dic11C2×D412yes—
91C2×Dic11#4114yes—
92Dic22—28no—
93C2×#125—111no—
94C2×C4×Q8—111no—
95#400—111no—
96#400—112no—
97#400D1111yescharacteristic
98#398—112no—
99#395—111no—
100#395—111no—
101#387—112no—
102#387—112no—
103#383—111no—
104C22×C11C22×D411yescharacteristic
105C22×C11C2×#4112yes—
106C22×C112−1+411yescharacteristic
107C22×C112−1+411yescharacteristic
108C22×C112−1+412yes—
109C4×C11—22no—
110C4×C11—41no—
111C4×C11—41no—
112C4×C11—42no—
113C4×C11—42no—
114Dic11—24no—
115Dic11—22no—
116Dic11—22no—
117Dic11—41no—
118Dic11—41no—
119Dic11—42no—
120C22×Q8—111no—
121#125—224no—
122C4×Q8—224no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—111no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—111no—
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×C42—111no—
134C2×C42—112no—
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—
144#95C2×D1112yes—
145C2×C11#52511yescharacteristic
146C2×C11#53611yescharacteristic
147C2×C11#53611yescharacteristic
148C2×C11#54112yes—
149C2×C11#54112yes—
150C2×Q8—224no—
151C2×Q8—222no—
152C22×C4—111no—
153C22×C4—111no—
154C22×C4—112no—
155C22×C4—112no—
156C22×C4—111no—
157C22×C4—111no—
158C22×C4C22×D1112yes—
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—22no—
164C4⋊C4—22no—
165C4⋊C4—224no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C4⋊C4—222no—
170C4⋊C4—224no—
171C4⋊C4—224no—
172C4⋊C4—222no—
173C42—114no—
174C42—224no—
175C11#263411yescharacteristic, complemented, Sylow
176C23C23×D1111yescharacteristic
177Q8—228no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—24no—
189C2×C4—112no—
190C2×C4—112no—
191C2×C4—114no—
192C2×C4—222no—
193C2×C4—221no—
194C2×C4—222no—
195C2×C4—221no—
196C2×C4—222no—
197C2×C4—221no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—221no—
204C2×C4—222no—
205C2×C4D4×D1112yes—
206C22C2×D4×D1111yescharacteristic
207C22#6704011yescharacteristic
208C22#41×D1112yes—
209C22#6704311yescharacteristic
210C22#6704312yes—
211C4—22no—
212C4—42no—
213C4—41no—
214C4—41no—
215C4—42no—
216C4—222no—
217C4—224no—
218C4—222no—
219C4—441no—
220C4—441no—
221C4—442no—
222C2#1062315911yescharacteristic
223C2#1062318711yescharacteristic
224C2#1062320611yescharacteristic
225C2#1062322712yes—
226C2#1062323212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#400C2
hypercenter#400D11
hypocenterC11#2634
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
175. C11#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#669422
C2×#669402
C11×#4002
#106225952
#106225922
#106222712
#106222702
#106222692
#106222682
#106222672
#106222642
#263411