Finite Group Databasebeta

← #13073567

Subgroups — #13073567

Order 1408.

676 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 676 conjugacy classes of subgroups — too many to draw. Only its 185 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×D4×Dic11C211yesmaximal, characteristic
2C2×#66941C211yesmaximal, characteristic, complemented
3C2×#66931C214yesmaximal, complemented
4C11×#390C211yesmaximal, characteristic
5#10622834C211yesmaximal, characteristic
6#10622589C211yesmaximal, characteristic, complemented
7#10622562C214yesmaximal, complemented
8#10622548C211yesmaximal, characteristic, complemented
9C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C23×Dic11C2212yes—
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C22⋊C4C2214yes—
15C2×C42×C11C2211yescharacteristic
16C2×C22⋊Dic11C2214yes—
17C2×C22⋊Dic11C2212yes—
18D4×Dic11—24no—
19C2×C4⋊Dic11C2214yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22C2×Dic11⋊C4C2214yes—
23C2×Dic11⋊C4C2212yes—
24C2×Dic11⋊C4C2212yes—
25C2×C4×Dic11C2211yescharacteristic
26C2×C4×Dic11C2211yescharacteristic
27#66941—24no—
28#66931—216no—
29C11⋊#95C2212yes—
30C24×C11C2312yes—
31C2×D4×C11—22no—
32C2×D4×C11—22no—
33C2×D4×C11Q814yescomplemented
34C22×C4×C11C2312yes—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11—28no—
38C22×Dic11—24no—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2311yescharacteristic
42C22×Dic11C2312yes—
43C22×Dic11C2311yescharacteristic
44C2×Dic22—28no—
45C2×Dic22—24no—
46C11×C4⋊C4—22no—
47C11×C22⋊C4—28no—
48C42×C11—22no—
49C22⋊Dic11—28no—
50C22⋊Dic11—24no—
51C4⋊Dic11—28no—
52C4⋊Dic11—22no—
53C4⋊Dic11—22no—
54Dic11⋊C4—28no—
55Dic11⋊C4—24no—
56Dic11⋊C4D418yescomplemented
57C4×Dic11—22no—
58C4×Dic11D414yes—
59#2542—111nomaximal, Sylow
60C23×C11—24no—
61C23×C11—22no—
62C23×C11—22no—
63C23×C11—24no—
64C23×C11C2×Q814yes—
65C23×C11C2411yescharacteristic
66D4×C11—28no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—24no—
70C2×C4×C11—22no—
71C2×C4×C11C2×D414yes—
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×Q812yes—
74C2×C4×C11#4112yes—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81C2×Dic11—22no—
82C2×Dic11—48no—
83C2×Dic11C2×D412yes—
84C2×Dic11C2×D414yes—
85C2×Dic11C2×D412yes—
86C2×Dic11C2×D414yes—
87Dic22—48no—
88C2×C4⋊Q8—111no—
89C2×C22⋊Q8—114no—
90C2×C4×D4—111no—
91#399—114no—
92#390—111no—
93#390D1111yescharacteristic
94#384—111no—
95#384—111no—
96C4×C4⋊C4—111no—
97C22×C11—24no—
98C22×C11—28no—
99C22×C11—42no—
100C22×C11—42no—
101C22×C11—44no—
102C22×C11C22×D411yescharacteristic
103C22×C11C22×D412yes—
104C22×C11C22×Q811yescharacteristic
105C22×C11C2×#4111yescharacteristic
106C22×C112−1+412yes—
107C4×C11—24no—
108C4×C11—42no—
109C4×C11C22⋊Q814yescomplemented
110Dic11—22no—
111Dic11—24no—
112Dic11—42no—
113Dic11—42no—
114Dic11#12714yes—
115C22×Q8—112no—
116C22×D4C2×D1111yescharacteristic
117C23×C4—112no—
118C4⋊Q8—224no—
119C22⋊Q8—2216no—
120C4×D4—224no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4—114no—
124C2×C4⋊C4—114no—
125C2×C4⋊C4—111no—
126C2×C4⋊C4—112no—
127C2×C4⋊C4C2×D1111yescharacteristic
128C2×C22⋊C4—112no—
129C2×C22⋊C4—114no—
130C2×C22⋊C4C2×D1114yes—
131C2×C42—111no—
132C2×C42—111no—
133C2×C42C2×D1111yescharacteristic
134#95—112no—
135C2×C11—44no—
136C2×C11C2×C22⋊Q811yescharacteristic
137C2×C11C2×#12711yescharacteristic
138C2×C11#53611yescharacteristic
139C2×C11#54712yes—
140C2×C11D4×Q812yes—
141C24C22×D1112yes—
142C2×Q8—228no—
143C2×Q8—224no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4Dic2214yescomplemented
147C22×C4—111no—
148C22×C4—111no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—224no—
153C22×C4—228no—
154C22×C4C22×D1112yes—
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C4⋊C4—22no—
158C4⋊C4—118no—
159C4⋊C4—228no—
160C4⋊C4—224no—
161C4⋊C4—222no—
162C4⋊C4—228no—
163C4⋊C4—222no—
164C22⋊C4—28no—
165C22⋊C4—224no—
166C22⋊C4—228no—
167C42—22no—
168C42—114no—
169C42—222no—
170C11#254211yescharacteristic, complemented, Sylow
171C23—24no—
172C23—22no—
173C23—22no—
174C23—24no—
175C23C2×Dic2214yes—
176C23C23×D1111yescharacteristic
177Q8—448no—
178D4—28no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—22no—
183C2×C4—112no—
184C2×C4—114no—
185C2×C4—112no—
186C2×C4—114no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—224no—
192C2×C4—224no—
193C2×C4—222no—
194C2×C4—448no—
195C2×C4C2×Dic2212yes—
196C2×C4D4×D1114yes—
197C2×C4D4×D1112yes—
198C2×C4#434112yes—
199C22—24no—
200C22—28no—
201C22—42no—
202C22—44no—
203C22—42no—
204C22C22×Dic2211yescharacteristic
205C22C2×D4×D1111yescharacteristic
206C22C2×D4×D1112yes—
207C22C2×#434111yescharacteristic
208C22#6704312yes—
209C4—24no—
210C4—42no—
211C4—114no—
212C4—224no—
213C4—222no—
214C4—442no—
215C4—442no—
216C4#6693114yescomplemented
217C2—44no—
218C2C2×#6693111yescharacteristic
219C2D4×Dic2212yes—
220C2#1062314212yes—
221C2#1062320611yescharacteristic
222C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC22×D4×C11C22
hypercenter#390D11
hypocenterC11#2542
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#66941C2semidirect
3. C2×#66931C2semidirect
6. #10622589C2semidirect
7. #10622562C2semidirect
8. #10622548C2semidirect
9. C4×Dic11⋊C4C2semidirect
33. C2×D4×C11Q8semidirect
56. Dic11⋊C4D4semidirect
109. C4×C11C22⋊Q8semidirect
146. C2×D4Dic22semidirect
170. C11#2542semidirect
216. C4#66931semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic112
C2×#669412
C2×#669312
C11×#3902
#106228342
#106225892
#106225622
#106225482
C4×Dic11⋊C42
#254211