Finite Group Databasebeta

← #13073086

Subgroups — #13073086

Order 1408.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#66991C211yesmaximal, characteristic
2C2×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C2×#66936C214yesmaximal, complemented
4C11×#390C211yesmaximal, characteristic, complemented
5#10622834C211yesmaximal, characteristic, complemented
6#10622589C211yesmaximal, characteristic, complemented
7#10622562C214yesmaximal, complemented
8C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
9#10622548C211yesmaximal, characteristic, complemented
10C22×D4×C11C2211yescharacteristic
11C22×C22⋊D11C2212yes—
12C22×C4×D11C2212yes—
13C22×C4×D11C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2214yes—
16C2×C42×C11C2211yescharacteristic
17C2×C22⋊Dic11C2214yes—
18C2×C22⋊Dic11C2212yes—
19#66991—24no—
20C2×(C2×D11)⋊C4C2212yes—
21C2×C4⋊Dic11C2214yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2214yes—
25C2×Dic11⋊C4C2212yes—
26C2×C4×Dic11C2211yescharacteristic
27C4⋊C4×D11—24no—
28#66936—216no—
29C11⋊#95C2212yes—
30C24×C11C2312yes—
31C23×D11C2311yescharacteristic
32C2×D4×C11—22no—
33C2×D4×C11—22no—
34C2×D4×C11—22no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—28no—
39C2×C22⋊D11—24no—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2311yescharacteristic
43C22×Dic11C2312yes—
44C2×C4×D11—28no—
45C2×C4×D11—24no—
46C2×C4×D11—22no—
47C2×C4×D11—22no—
48C2×C4×D11D414yes—
49C11×C4⋊C4—22no—
50C11×C22⋊C4—28no—
51C42×C11—22no—
52C22⋊Dic11—28no—
53C22⋊Dic11—24no—
54(C2×D11)⋊C4D418yescomplemented
55C4⋊Dic11—28no—
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58Dic11⋊C4—28no—
59Dic11⋊C4—24no—
60C4×Dic11—22no—
61#2501—111nomaximal, Sylow
62C23×C11—24no—
63C23×C11—22no—
64C23×C11—22no—
65C23×C11—22no—
66C23×C11—24no—
67C23×C11C2411yescharacteristic
68C22×D11—21no—
69C22×D11—21no—
70C22×D11—22no—
71C22×D11C2×D414yes—
72C22×D11C2×D412yes—
73D4×C11—44no—
74C2×C4×C11—22no—
75C2×C4×C11—22no—
76C2×C4×C11—24no—
77C2×C4×C11—22no—
78C2×C4×C11C2×D414yes—
79C2×C4×C11C2×D412yes—
80C2×C4×C11#4112yes—
81C2×C4×C11#4112yes—
82C22⋊D11—48no—
83C2×Dic11—22no—
84C2×Dic11—21no—
85C2×Dic11—21no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—24no—
89C2×Dic11—24no—
90C2×Dic11—22no—
91C2×Dic11C2×D414yes—
92C2×Dic11C2×D412yes—
93C4×D11—28no—
94C4×D11—48no—
95C2×#123—114no—
96C2×#121—111no—
97C22×C4⋊C4—111no—
98#399—114no—
99#390—111no—
100#390D1111yescharacteristic, complemented
101#384—111no—
102#384—111no—
103C4×C22⋊C4—111no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11—42no—
107C22×C11—44no—
108C22×C11—44no—
109C22×C11C22×D411yescharacteristic
110C22×C11C22×D412yes—
111C22×C11C2×#4111yescharacteristic
112C22×C11C2×#4111yescharacteristic
113C22×C112−1+412yes—
114C2×D11—22no—
115C2×D11—22no—
116C2×D11—24no—
117C2×D11—24no—
118C2×D11#12714yes—
119C4×C11—24no—
120C4×C11—42no—
121C4×C11#12314yescomplemented
122Dic11—22no—
123Dic11—24no—
124Dic11—42no—
125Dic11—42no—
126C22×D4—112no—
127C22×D4C2×D1111yescharacteristic
128C23×C4—111no—
129C23×C4—112no—
130#123—2216no—
131#121—224no—
132C2×C4⋊C4—111no—
133C2×C4⋊C4—112no—
134C2×C4⋊C4—111no—
135C2×C4⋊C4—114no—
136C2×C4⋊C4—114no—
137C2×C4⋊C4—224no—
138C2×C4⋊C4C2×D1111yescharacteristic
139C2×C22⋊C4—112no—
140C2×C22⋊C4—112no—
141C2×C22⋊C4—114no—
142C2×C22⋊C4C2×D1114yes—
143C2×C42—111no—
144C2×C42C2×D1111yescharacteristic
145#95—112no—
146C2×C11—82no—
147C2×C11C2×#12311yescharacteristic
148C2×C11C2×#12711yescharacteristic
149C2×C11#53611yescharacteristic
150C2×C11#54712yes—
151C2×C11#54712yes—
152D11—24no—
153C24—111no—
154C24C22×D1112yes—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—22no—
158C2×D4—224no—
159C2×D4—228no—
160C22×C4—111no—
161C22×C4—112no—
162C22×C4—114no—
163C22×C4—112no—
164C22×C4—112no—
165C22×C4—224no—
166C22×C4—228no—
167C22×C4—222no—
168C22×C4—222no—
169C22×C4C22×D1112yes—
170C22×C4C22×D1112yes—
171C22×C4C22×D1111yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—224no—
174C4⋊C4—228no—
175C4⋊C4—222no—
176C4⋊C4—222no—
177C4⋊C4—228no—
178C22⋊C4—28no—
179C22⋊C4—118no—
180C22⋊C4—224no—
181C22⋊C4—228no—
182C42—22no—
183C42—222no—
184C11#250111yescharacteristic, complemented, Sylow
185C23—22no—
186C23—24no—
187C23—22no—
188C23—22no—
189C23—24no—
190C23—114no—
191C23—112no—
192C23—221no—
193C23—221no—
194C23—222no—
195C23C23×D1111yescharacteristic
196D4—44no—
197D4—448no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—114no—
203C2×C4—112no—
204C2×C4—222no—
205C2×C4—221no—
206C2×C4—221no—
207C2×C4—222no—
208C2×C4—228no—
209C2×C4—224no—
210C2×C4—222no—
211C2×C4—222no—
212C2×C4—224no—
213C2×C4—448no—
214C2×C4#433912yes—
215C2×C4D4×D1114yes—
216C2×C4D4×D1112yes—
217C2×C4#434112yes—
218C22—42no—
219C22—42no—
220C22—44no—
221C22—44no—
222C22—42no—
223C22—114no—
224C22—222no—
225C22—224no—
226C22—224no—
227C22—222no—
228C22C2×#433911yescharacteristic
229C22C2×D4×D1111yescharacteristic
230C22C2×D4×D1112yes—
231C22C2×#434111yescharacteristic
232C22#6704312yes—
233C4—24no—
234C4—42no—
235C4—222no—
236C4—224no—
237C4—442no—
238C4—442no—
239C4#6693614yescomplemented
240C2—82no—
241C2—224no—
242C2C2×#6693611yescharacteristic
243C2#1062308212yes—
244C2#1062314212yes—
245C2#1062320611yescharacteristic
246C2D11×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#390C2
prime radicalC2×#66991C2
hypercenter#390D11
hypocenterC11#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D11C2semidirect
3. C2×#66936C2semidirect
4. C11×#390C2semidirect
5. #10622834C2semidirect
6. #10622589C2semidirect
7. #10622562C2semidirect
8. C4×(C2×D11)⋊C4C2semidirect
9. #10622548C2semidirect
54. (C2×D11)⋊C4D4semidirect
100. #390D11semidirect
121. C4×C11#123semidirect
184. C11#2501semidirect
239. C4#66936semidirect

Maximal subgroups

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

subgroupindex
C2×#669912
C2×C4⋊C4×D112
C2×#669362
C11×#3902
#106228342
#106225892
#106225622
C4×(C2×D11)⋊C42
#106225482
#250111