Finite Group Databasebeta

← #13074925

Subgroups — #13074925

Order 1408.

544 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 149 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×#66997C212yesmaximal, complemented
2C2×#66931C212yesmaximal
3C11×#393C211yesmaximal, characteristic
4#10622562C211yesmaximal, characteristic
5#10622559C211yesmaximal, characteristic
6#10622558C212yesmaximal
7#10622270C212yesmaximal, complemented
8#10622269C212yesmaximal, complemented
9#10622265C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C23×Dic11C2211yescharacteristic
12C22×Dic22C2212yes—
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17#66997—28no—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26#66931—28no—
27C11×#95C2212yes—
28C11×#95C2211yescharacteristic
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2212yes—
33C24×C11C2311yescharacteristic
34C2×Q8×C11—24no—
35C2×Q8×C11—41no—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×Dic11—24no—
41C22×Dic11—41no—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22×Dic11C2312yes—
46C2×Dic22—24no—
47C2×Dic22—24no—
48C2×Dic22—42no—
49C11×C22⋊C4—24no—
50C11×C22⋊C4—41no—
51C22⋊Dic11—24no—
52C22⋊Dic11Q814yescomplemented
53C4⋊Dic11—24no—
54C4⋊Dic11—41no—
55Dic11⋊C4—24no—
56Dic11⋊C4—24no—
57Dic11⋊C4—24no—
58Dic11⋊C4—24no—
59Dic11⋊C4D418yes—
60C4×Dic11—24no—
61#2677—111nomaximal, Sylow
62C23×C11—22no—
63C23×C11—21no—
64C23×C11—21no—
65C23×C11—22no—
66C23×C11C2×Q812yes—
67C23×C11C2411yescharacteristic
68Q8×C11—44no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D414yes—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—44no—
89C2×Dic11C2×D414yes—
90C2×Dic11C2×D414yes—
91C2×Dic11C2×Q814yes—
92Dic22—48no—
93C2×C4⋊Q8—112no—
94C2×C22⋊Q8—112no—
95#399—111no—
96#398—112no—
97#395—112no—
98#393D1111yescharacteristic
99#388—112no—
100#387—112no—
101#385—111no—
102C22×C11—22no—
103C22×C11—24no—
104C22×C11—42no—
105C22×C11—41no—
106C22×C11—41no—
107C22×C11C22×D412yes—
108C22×C11C22×Q811yescharacteristic
109C22×C11H(5,𝔽2)11yescharacteristic
110C22×C112−1+411yescharacteristic
111C22×C112−1+412yes—
112C4×C11—24no—
113C4×C11—42no—
114C4×C11—41no—
115C4×C11—41no—
116Dic11—24no—
117Dic11—24no—
118Dic11—24no—
119Dic11—42no—
120C22×Q8—112no—
121C22×Q8C2×D1111yescharacteristic
122C23×C4—111no—
123C4⋊Q8—228no—
124C22⋊Q8—228no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—112no—
128C2×C4⋊C4—112no—
129C2×C4⋊C4—112no—
130C2×C4⋊C4—112no—
131C2×C4⋊C4—111no—
132C2×C22⋊C4—111no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4C2×D1112yes—
135C2×C22⋊C4C2×D1111yescharacteristic
136C2×C42—112no—
137#95—112no—
138#95—111no—
139#95—112no—
140#95—112no—
141#95C2×D1112yes—
142#95C2×D1111yescharacteristic
143C2×C11—42no—
144C2×C11#53612yes—
145C2×C11#54411yescharacteristic
146C2×C11D4211yescharacteristic
147C2×C11D4×Q812yes—
148C2×C11#56311yescharacteristic
149C24C22×D1111yescharacteristic
150C2×Q8—24no—
151C2×Q8—41no—
152C2×Q8—224no—
153C2×Q8—224no—
154C2×Q8—442no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4—224no—
160C22×C4—441no—
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1112yes—
163C22×C4C22×D1111yescharacteristic
164C22×C4C22×D1112yes—
165C4⋊C4—118no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—224no—
169C4⋊C4—224no—
170C4⋊C4—224no—
171C4⋊C4—441no—
172C22⋊C4—24no—
173C22⋊C4—41no—
174C22⋊C4—114no—
175C22⋊C4—224no—
176C42—224no—
177C11#267711yescharacteristic, complemented, Sylow
178C23—22no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23Q8×D1112yes—
183C23C23×D1111yescharacteristic
184Q8—44no—
185Q8—448no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—114no—
196C2×C4—114no—
197C2×C4—114no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—444no—
208C2×C4D4×D1114yes—
209C22—22no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22C2×D4×D1112yes—
215C22#6703711yescharacteristic
216C22C2×Q8×D1111yescharacteristic
217C22#6704311yescharacteristic
218C22#6704312yes—
219C4—24no—
220C4—41no—
221C4—41no—
222C4—42no—
223C4—224no—
224C4—224no—
225C4—224no—
226C4—442no—
227C2—42no—
228C2#1062312111yescharacteristic
229C2#1062315411yescharacteristic
230C2#1062316312yes—
231C2#1062320311yescharacteristic
232C2#1062320612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#393C2
prime radicalC24×C11C23
hypercenter#393D11
hypocenterC11#2677
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#66997C2semidirect
7. #10622270C2semidirect
8. #10622269C2semidirect
9. #10622265C2semidirect
52. C22⋊Dic11Q8semidirect
177. C11#2677semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669312
C11×#3932
#106225622
#106225592
#106225582
#106222702
#106222692
#106222652
#267711