Finite Group Databasebeta

← #13074931

Subgroups — #13074931

Order 1408.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#66977C212yesmaximal
2C2×#66941C212yesmaximal, complemented
3C11×#385C211yesmaximal, characteristic
4#10622597C212yesmaximal, complemented
5#10622564C212yesmaximal
6#10622562C211yesmaximal, characteristic
7#10622560C211yesmaximal, characteristic
8#10622269C212yesmaximal, complemented
9#10622268C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C22⋊Dic11C2212yes—
17C2×C22⋊Dic11C2212yes—
18C2×C4⋊Dic11C2212yes—
19C2×C4⋊Dic11C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21#66977—28no—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2212yes—
26#66941—28no—
27C11×#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C24×C11C2311yescharacteristic
34C22×C4×C11—24no—
35C22×C4×C11—41no—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C2×Dic22—24no—
45C2×Dic22—24no—
46C2×Dic22—24no—
47C2×Dic22—42no—
48C2×Dic22—41no—
49C11×C4⋊C4—24no—
50C11×C22⋊C4—41no—
51C11×C22⋊C4Q814yescomplemented
52C22⋊Dic11—24no—
53C22⋊Dic11—24no—
54C4⋊Dic11—24no—
55C4⋊Dic11—24no—
56C4⋊Dic11—41no—
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
68C2×C4×C11—22no—
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—44no—
77C2×C4×C11C2×D414yes—
78C2×C4×C11C2×Q814yes—
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—22no—
89C2×Dic11C2×D414yes—
90C2×Dic11C2×D414yes—
91Dic22—44no—
92Dic22—48no—
93C2×C4⋊Q8—112no—
94C2×C22⋊Q8—112no—
95#399—111no—
96#398—112no—
97#395—112no—
98#393—111no—
99#388—112no—
100#387—112no—
101#385D1111yescharacteristic
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—24no—
114C4×C11—41no—
115C4×C11—41no—
116Dic11—24no—
117Dic11—24no—
118Dic11—42no—
119Dic11—42no—
120C22×Q8—112no—
121C22×Q8—111no—
122C23×C4C2×D1111yescharacteristic
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—111no—
131C2×C4⋊C4C2×D1112yes—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—112no—
134C2×C22⋊C4C2×D1111yescharacteristic
135C2×C22⋊C4C2×D1111yescharacteristic
136C2×C42—112no—
137#95—111no—
138#95—112no—
139#95—112no—
140#95—112no—
141#95—111no—
142#95C2×D1112yes—
143C2×C11—42no—
144C2×C11#53612yes—
145C2×C11#54411yescharacteristic
146C2×C11D4211yescharacteristic
147C2×C11D4×Q812yes—
148C2×C11#56311yescharacteristic
149C24C22×D1111yescharacteristic
150C2×Q8—224no—
151C2×Q8—224no—
152C2×Q8—224no—
153C2×Q8—442no—
154C2×Q8—441no—
155C22×C4—24no—
156C22×C4—41no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4—112no—
160C22×C4—112no—
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1112yes—
164C22×C4C22×D1112yes—
165C4⋊C4—24no—
166C4⋊C4—118no—
167C4⋊C4—224no—
168C4⋊C4—224no—
169C4⋊C4—224no—
170C4⋊C4—224no—
171C4⋊C4—441no—
172C22⋊C4—41no—
173C22⋊C4—224no—
174C22⋊C4—224no—
175C22⋊C4Dic2214yescomplemented
176C42—224no—
177C11#267711yescharacteristic, complemented, Sylow
178C23—22no—
179C23—21no—
180C23—21no—
181C23—22no—
182C23C2×Dic2212yes—
183C23C23×D1111yescharacteristic
184Q8—448no—
185Q8—444no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—114no—
196C2×C4—114no—
197C2×C4—222no—
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×C4C2×Dic2214yes—
208C2×C4D4×D1114yes—
209C22—22no—
210C22—24no—
211C22—41no—
212C22—42no—
213C22—41no—
214C22C22×Dic2211yescharacteristic
215C22C2×D4×D1112yes—
216C22#6703711yescharacteristic
217C22#6704011yescharacteristic
218C22#6704312yes—
219C4—24no—
220C4—24no—
221C4—41no—
222C4—41no—
223C4—224no—
224C4—224no—
225C4—442no—
226C4—442no—
227C2—42no—
228C2#1062303111yescharacteristic
229C2D4×Dic2212yes—
230C2#1062312111yescharacteristic
231C2#1062315912yes—
232C2#1062318211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#385C2
prime radicalC24×C11C23
hypercenter#385D11
hypocenterC11#2677
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
4. #10622597C2semidirect
8. #10622269C2semidirect
9. #10622268C2semidirect
51. C11×C22⋊C4Q8semidirect
175. C22⋊C4Dic22semidirect
177. C11#2677semidirect

Maximal subgroups

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

subgroupindex
C2×#669772
C2×#669412
C11×#3852
#106225972
#106225642
#106225622
#106225602
#106222692
#106222682
#267711