Finite Group Databasebeta

← #13074497

Subgroups — #13074497

Order 1408.

416 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 131 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×#66940C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic
4#10622599C211yesmaximal, characteristic
5#10622594C212yesmaximal
6#10622593C211yesmaximal, characteristic
7#10622592C212yesmaximal
8#10622272C211yesmaximal, characteristic
9#10622271C212yesmaximal
10#10622268C212yesmaximal
11#10622264C211yesmaximal, characteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4C2211yescharacteristic
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2211yescharacteristic
25#66943—24no—
26#66940—24no—
27C11×#95C2211yescharacteristic
28C11×#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2211yescharacteristic
32C11⋊#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2212yes—
36C11⋊#95C2212yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C22×Dic11C2312yes—
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×Dic22—22no—
49C2×Dic22—22no—
50C2×Dic22—22no—
51C11×C4⋊C4—22no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—24no—
54C4⋊Dic11—24no—
55C4⋊Dic11—22no—
56Dic11⋊C4—22no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61C4×Dic11—22no—
62C4×Dic11D414yes—
63#2634—111nomaximal, Sylow
64C23×C11C2411yescharacteristic
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11#4112yes—
78C2×Dic11—21no—
79C2×Dic11—21no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—22no—
83C2×Dic11—21no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—24no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—22no—
90C2×Dic11C2×D412yes—
91C2×Dic11C2×D412yes—
92C2×Dic11#4112yes—
93Dic22—28no—
94C2×#125—111no—
95C2×C4×Q8—111no—
96#400—111no—
97#400—112no—
98#400—111no—
99#398—111no—
100#398D1111yescharacteristic
101#395—112no—
102#387—112no—
103#387—112no—
104#383—111no—
105C22×C11C22×D411yescharacteristic
106C22×C11C2×#4111yescharacteristic
107C22×C11C2×#4111yescharacteristic
108C22×C112−1+412yes—
109C22×C112−1+412yes—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11—42no—
113C4×C11—41no—
114C4×C11—42no—
115Dic11—22no—
116Dic11—22no—
117Dic11—22no—
118Dic11—42no—
119Dic11—41no—
120Dic11—42no—
121C22×Q8—111no—
122#125—224no—
123C4×Q8—224no—
124C2×C4⋊C4—111no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—111no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4C2×D1111yescharacteristic
131C2×C4⋊C4C2×D1111yescharacteristic
132C2×C4⋊C4C2×D1112yes—
133C2×C42—111no—
134C2×C42—111no—
135C2×C42—111no—
136#95—112no—
137#95—112no—
138#95—111no—
139#95—112no—
140#95—112no—
141#95—112no—
142#95—112no—
143#95—112no—
144#95C2×D1111yescharacteristic
145#95C2×D1112yes—
146C2×C11#52511yescharacteristic
147C2×C11#53611yescharacteristic
148C2×C11#53611yescharacteristic
149C2×C11#54112yes—
150C2×C11#54112yes—
151C2×Q8—222no—
152C2×Q8—222no—
153C2×Q8—222no—
154C22×C4—111no—
155C22×C4—111no—
156C22×C4—111no—
157C22×C4—112no—
158C22×C4—111no—
159C22×C4—112no—
160C22×C4C22×D1112yes—
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1111yescharacteristic
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—222no—
169C4⋊C4—224no—
170C4⋊C4—224no—
171C4⋊C4—224no—
172C4⋊C4—222no—
173C4⋊C4—222no—
174C42—114no—
175C42—222no—
176C42—222no—
177C11#263411yescharacteristic, complemented, Sylow
178C23C23×D1111yescharacteristic
179Q8—228no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—112no—
192C2×C4—112no—
193C2×C4—112no—
194C2×C4—221no—
195C2×C4—221no—
196C2×C4—221no—
197C2×C4—222no—
198C2×C4—221no—
199C2×C4—221no—
200C2×C4—222no—
201C2×C4—224no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4D4×D1112yes—
207C2×C4#434112yes—
208C22C2×D4×D1111yescharacteristic
209C22C2×#434111yescharacteristic
210C22#6704012yes—
211C22#41×D1111yescharacteristic
212C22#6704312yes—
213C4—22no—
214C4—22no—
215C4—42no—
216C4—42no—
217C4—41no—
218C4—222no—
219C4—222no—
220C4—222no—
221C4—442no—
222C4—441no—
223C4—442no—
224C2#1062313711yescharacteristic
225C2#1062315612yes—
226C2#1062317911yescharacteristic
227C2#1062322712yes—
228C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#398C2
hypercenter#398D11
hypocenterC11#2634
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
177. C11#2634semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669402
C11×#3982
#106225992
#106225942
#106225932
#106225922
#106222722
#106222712
#106222682
#106222642
#263411