Finite Group Databasebeta

← #13074486

Subgroups — #13074486

Order 1408.

512 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 129 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×#66946C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic, complemented
3C11×#398C211yesmaximal, characteristic, complemented
4#10622605C212yesmaximal, complemented
5#10622604C211yesmaximal, characteristic
6#10622602C212yesmaximal, complemented
7#10622593C211yesmaximal, characteristic, complemented
8#10622288C212yesmaximal, complemented
9#10622285C211yesmaximal, characteristic
10#10622281C212yesmaximal, complemented
11#10622264C211yesmaximal, characteristic, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2212yes—
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×Dic11⋊C4C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×C4×Dic11C2211yescharacteristic
29#66946—24no—
30#66942—24no—
31C11×#95C2211yescharacteristic
32C11×#95C2212yes—
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C22×C4×C11C2312yes—
39C22×C4×C11C2312yes—
40C22×C4×C11C2311yescharacteristic
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C22×Dic11C2312yes—
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2311yescharacteristic
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C2×D44—24no—
49C2×D44—22no—
50C2×C4×D11—24no—
51C2×C4×D11—42no—
52C2×C4×D11—42no—
53C11×C4⋊C4—22no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—42no—
56(C2×D11)⋊C4—24no—
57(C2×D11)⋊C4—24no—
58(C2×D11)⋊C4—24no—
59(C2×D11)⋊C4—42no—
60(C2×D11)⋊C4—42no—
61C4⋊Dic11—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—22no—
66Dic11⋊C4—42no—
67C4×Dic11D414yes—
68#2633—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11#4114yes—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—21no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11C2×D412yes—
90C2×Dic11—21no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—21no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—22no—
101C2×Dic11C2×D412yes—
102C2×Dic11C2×D412yes—
103D44—28no—
104C4×D11—48no—
105C2×#125—111no—
106C2×C4×D4—111no—
107#399—112no—
108#398—111no—
109#398D1111yescharacteristic, complemented
110#397—112no—
111#394—111no—
112#394—111no—
113#385—112no—
114#385—112no—
115#383—111no—
116C22×C11C22×D411yescharacteristic
117C22×C11C2×#4112yes—
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C11H(5,𝔽2)11yescharacteristic
120C22×C112−1+412yes—
121C2×D11—24no—
122C2×D11—24no—
123C2×D11—24no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C4×C11—22no—
129C4×C11—41no—
130C4×C11—41no—
131C4×C11—42no—
132C4×C11—42no—
133Dic11—22no—
134Dic11—22no—
135Dic11—41no—
136Dic11—41no—
137Dic11—42no—
138C22×D4—111no—
139C23×C4—112no—
140#125—224no—
141C4×D4—224no—
142C2×C4⋊C4—111no—
143C2×C4⋊C4—111no—
144C2×C4⋊C4—111no—
145C2×C4⋊C4—111no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4C2×D1111yescharacteristic
149C2×C4⋊C4C2×D1111yescharacteristic
150C2×C4⋊C4C2×D1112yes—
151C2×C22⋊C4—112no—
152C2×C22⋊C4—112no—
153C2×C22⋊C4—112no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C42—111no—
157#95—112no—
158#95—111no—
159#95—112no—
160#95—112no—
161#95C2×D1111yescharacteristic
162#95C2×D1112yes—
163C2×C11#52511yescharacteristic
164C2×C11#53511yescharacteristic
165C2×C11#53611yescharacteristic
166C2×C11#53912yes—
167C2×C11#53912yes—
168D11—44no—
169C24—112no—
170C2×D4—224no—
171C2×D4—222no—
172C22×C4—111no—
173C22×C4—111no—
174C22×C4—112no—
175C22×C4—111no—
176C22×C4—111no—
177C22×C4—224no—
178C22×C4—442no—
179C22×C4—442no—
180C22×C4C22×D1112yes—
181C22×C4C22×D1112yes—
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1111yescharacteristic
184C22×C4C22×D1111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—42no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—222no—
192C4⋊C4—222no—
193C4⋊C4—442no—
194C22⋊C4—224no—
195C22⋊C4—224no—
196C22⋊C4—224no—
197C22⋊C4—442no—
198C22⋊C4—442no—
199C42—114no—
200C11#263311yescharacteristic, complemented, Sylow
201C23—114no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23—222no—
208C23C23×D1111yescharacteristic
209D4—228no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—112no—
223C2×C4—112no—
224C2×C4—221no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—448no—
236C2×C4D4×D1112yes—
237C22—224no—
238C22—224no—
239C22—224no—
240C22—442no—
241C22—442no—
242C22—442no—
243C22—442no—
244C22C2×D4×D1111yescharacteristic
245C22#6703711yescharacteristic
246C22#6704012yes—
247C22#41×D1112yes—
248C22#6704211yescharacteristic
249C4—22no—
250C4—42no—
251C4—41no—
252C4—42no—
253C4—41no—
254C4—222no—
255C4—222no—
256C4—441no—
257C4—441no—
258C4—442no—
259C2—444no—
260C2#1062313811yescharacteristic
261C2#1062316912yes—
262C2#1062318711yescharacteristic
263C2#1062322312yes—
264C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC22×D44C22
hypercenter#398D11
hypocenterC11#2633
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
2. C2×#66942C2semidirect
3. C11×#398C2semidirect
4. #10622605C2semidirect
6. #10622602C2semidirect
7. #10622593C2semidirect
8. #10622288C2semidirect
10. #10622281C2semidirect
11. #10622264C2semidirect
109. #398D11semidirect
200. C11#2633semidirect

Maximal subgroups

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

subgroupindex
C2×#669462
C2×#669422
C11×#3982
#106226052
#106226042
#106226022
#106225932
#106222882
#106222852
#106222812
#106222642
#263311