Finite Group Databasebeta

← #13073641

Subgroups — #13073641

Order 1408.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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
2C2×#66941C212yesmaximal
3C11×#395C211yesmaximal, characteristic
4#10622592C211yesmaximal, characteristic
5#10622589C211yesmaximal, characteristic
6#10622585C212yesmaximal
7#10622269C212yesmaximal
8#10622262C212yesmaximal
9#10622260C212yesmaximal
10C22×Q8×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15#66997—28no—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×Dic11⋊C4C2212yes—
24C2×C4×Dic11C2212yes—
25C2×C4×Dic11C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27#66941—28no—
28C11×#95C2211yescharacteristic
29C11×#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C11⋊#95C2211yescharacteristic
33C2×Q8×C11—24no—
34C2×Q8×C11—41no—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
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×C4⋊C4—41no—
51C4⋊Dic11—24no—
52C4⋊Dic11—41no—
53Dic11⋊C4—24no—
54Dic11⋊C4—24no—
55Dic11⋊C4—24no—
56Dic11⋊C4—24no—
57Dic11⋊C4D418yes—
58Dic11⋊C4Q818yescomplemented
59C4×Dic11—24no—
60C4×Dic11—24no—
61C4×Dic11Q814yescomplemented
62#2551—111nomaximal, Sylow
63C23×C11C2411yescharacteristic
64Q8×C11—44no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—21no—
74C2×C4×C11—21no—
75C2×C4×C11C2×D414yes—
76C2×C4×C11C2×Q812yes—
77C2×C4×C11C2×Q814yes—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11C2×D414yes—
86C2×Dic11C2×D414yes—
87C2×Dic11C2×Q814yes—
88C2×Dic11C2×Q814yes—
89C2×Dic11C2×Q814yes—
90Dic22—44no—
91Dic22—48no—
92C2×C4⋊Q8—112no—
93C2×C4⋊Q8—112no—
94#395—111no—
95#395—112no—
96#395D1111yescharacteristic
97#389—112no—
98#389—112no—
99#384—111no—
100C4×C4⋊C4—112no—
101C22×C11C22×D412yes—
102C22×C11C22×Q811yescharacteristic
103C22×C11C22×Q812yes—
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C112−1+411yescharacteristic
106C4×C11—22no—
107C4×C11—24no—
108C4×C11—24no—
109C4×C11—41no—
110C4×C11—41no—
111Dic11—24no—
112Dic11—24no—
113Dic11—42no—
114Dic11C4⋊Q818yescomplemented
115C22×Q8—111no—
116C22×Q8—112no—
117C22×Q8C2×D1111yescharacteristic
118C4⋊Q8—228no—
119C4⋊Q8—228no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—112no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4—111no—
128C2×C4⋊C4C2×D1112yes—
129C2×C4⋊C4C2×D1111yescharacteristic
130C2×C42—111no—
131C2×C42—112no—
132C2×C42—112no—
133#95—112no—
134#95—111no—
135#95—112no—
136#95C2×D1112yes—
137#95C2×D1111yescharacteristic
138C2×C11C2×C4⋊Q812yes—
139C2×C11#54411yescharacteristic
140C2×C11D4211yescharacteristic
141C2×C11D4×Q812yes—
142C2×C11Q8211yescharacteristic
143C2×Q8—24no—
144C2×Q8—41no—
145C2×Q8—224no—
146C2×Q8—224no—
147C2×Q8—224no—
148C2×Q8—442no—
149C2×Q8—441no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1111yescharacteristic
156C22×C4C22×D1112yes—
157C22×C4C22×D1111yescharacteristic
158C22×C4C22×D1112yes—
159C4⋊C4—24no—
160C4⋊C4—41no—
161C4⋊C4—118no—
162C4⋊C4—118no—
163C4⋊C4—224no—
164C4⋊C4—224no—
165C4⋊C4—224no—
166C4⋊C4—224no—
167C4⋊C4—224no—
168C4⋊C4—441no—
169C42—114no—
170C42—224no—
171C42—224no—
172C11#255111yescharacteristic, complemented, Sylow
173C23C23×D1111yescharacteristic
174Q8—44no—
175Q8—448no—
176Q8—444no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—114no—
188C2×C4—114no—
189C2×C4—114no—
190C2×C4—114no—
191C2×C4—114no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4D4×D1114yes—
200C2×C4Q8×D1112yes—
201C2×C4Q8×D1114yes—
202C22C2×D4×D1112yes—
203C22#6703711yescharacteristic
204C22C2×Q8×D1112yes—
205C22C2×Q8×D1111yescharacteristic
206C22#6704311yescharacteristic
207C4—24no—
208C4—22no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—118no—
213C4—224no—
214C4—224no—
215C4—442no—
216C2#1062312111yescharacteristic
217C2#1062315411yescharacteristic
218C2#1062316312yes—
219C2#1062325311yescharacteristic
220C2D11×C4⋊Q812yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#395C2
hypercenter#395D11
hypocenterC11#2551
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. Dic11⋊C4Q8semidirect
61. C4×Dic11Q8semidirect
114. Dic11C4⋊Q8semidirect
172. C11#2551semidirect

Maximal subgroups

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

subgroupindex
C2×#669972
C2×#669412
C11×#3952
#106225922
#106225892
#106225852
#106222692
#106222622
#106222602
#255111