Finite Group Databasebeta

← #13076671

Subgroups — #13076671

Order 1408.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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×#67000C211yesmaximal, characteristic
2C2×#66942C211yesmaximal, characteristic, complemented
3C11×#395C211yesmaximal, characteristic, complemented
4#10622842C211yesmaximal, characteristic, complemented
5#10622607C212yesmaximal, complemented
6#10622605C212yesmaximal, complemented
7#10622604C211yesmaximal, characteristic
8#10622289C212yesmaximal, complemented
9#10622288C212yesmaximal, complemented
10#10622285C211yesmaximal, characteristic
11#10622263C211yesmaximal, characteristic, complemented
12C22×Q8×C11C2211yescharacteristic
13C22×D44C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C4⋊C4C2212yes—
16#67000—24no—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2211yescharacteristic
24C2×Dic11⋊C4C2211yescharacteristic
25C2×Dic11⋊C4C2211yescharacteristic
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2211yescharacteristic
28C2×Dic11⋊C4C2212yes—
29C2×Dic11⋊C4C2212yes—
30C2×C4×Dic11C2211yescharacteristic
31#66942—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2312yes—
38C2×Q8×C11—22no—
39C2×Q8×C11—42no—
40C22×C4×C11C2312yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×C4×C11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2311yescharacteristic
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×D44—22no—
51C2×D44—42no—
52C11×C4⋊C4—22no—
53C11×C4⋊C4—42no—
54(C2×D11)⋊C4—24no—
55(C2×D11)⋊C4—24no—
56(C2×D11)⋊C4—42no—
57(C2×D11)⋊C4—42no—
58(C2×D11)⋊C4—42no—
59(C2×D11)⋊C4—42no—
60C4⋊Dic11—22no—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65Dic11⋊C4—42no—
66Dic11⋊C4—42no—
67C4×Dic11D414yes—
68#2820—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—22no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—22no—
74C22×D11—22no—
75C22×D11—22no—
76C22×D11—22no—
77Q8×C11—44no—
78C2×C4×C11—22no—
79C2×C4×C11—21no—
80C2×C4×C11—21no—
81C2×C4×C11—22no—
82C2×C4×C11—22no—
83C2×C4×C11—22no—
84C2×C4×C11—21no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11C2×D412yes—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—21no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—21no—
100C2×Dic11—21no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103C2×Dic11C2×D412yes—
104D44—44no—
105C2×#125—111no—
106C2×#124—111no—
107#399—112no—
108#397—112no—
109#396—112no—
110#396—112no—
111#395—111no—
112#395D1111yescharacteristic, complemented
113#394—111no—
114#394—111no—
115#382—111no—
116C22×C11C22×D411yescharacteristic
117C22×C11H(5,𝔽2)12yes—
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C112−1+412yes—
120C22×C112−1+411yescharacteristic
121C2×D11—42no—
122C2×D11—42no—
123C2×D11—42no—
124C2×D11—42no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—42no—
128C4×C11—22no—
129C4×C11—41no—
130C4×C11—42no—
131C4×C11—41no—
132C4×C11—42no—
133Dic11—22no—
134Dic11—22no—
135Dic11—41no—
136Dic11—41no—
137Dic11—42no—
138C22×Q8C2×D1111yescharacteristic
139C22×D4—111no—
140#125—224no—
141#124—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⋊C4—112no—
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×C22⋊C4—112no—
157C2×C42—111no—
158#95—111no—
159#95—112no—
160#95—112no—
161#95C2×D1111yescharacteristic
162#95C2×D1112yes—
163C2×C11#53511yescharacteristic
164C2×C11#53611yescharacteristic
165C2×C11#53711yescharacteristic
166C2×C11#56212yes—
167C2×C11#56312yes—
168D11—82no—
169C24—112no—
170C2×Q8—22no—
171C2×Q8—42no—
172C2×D4—222no—
173C2×D4—442no—
174C22×C4—111no—
175C22×C4—111no—
176C22×C4—112no—
177C22×C4—111no—
178C22×C4—111no—
179C22×C4C22×D1112yes—
180C22×C4C22×D1112yes—
181C22×C4C22×D1111yescharacteristic
182C22×C4C22×D1111yescharacteristic
183C22×C4C22×D1111yescharacteristic
184C4⋊C4—22no—
185C4⋊C4—42no—
186C4⋊C4—222no—
187C4⋊C4—222no—
188C4⋊C4—222no—
189C4⋊C4—222no—
190C4⋊C4—222no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C22⋊C4—224no—
194C22⋊C4—224no—
195C22⋊C4—442no—
196C22⋊C4—442no—
197C22⋊C4—442no—
198C22⋊C4—442no—
199C42—114no—
200C11#282011yescharacteristic, complemented, Sylow
201C23—222no—
202C23—222no—
203C23—222no—
204C23—222no—
205C23—222no—
206C23—222no—
207C23—222no—
208C23C23×D1111yescharacteristic
209Q8—44no—
210D4—444no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—112no—
224C2×C4—112no—
225C2×C4—222no—
226C2×C4—221no—
227C2×C4—221no—
228C2×C4—221no—
229C2×C4—221no—
230C2×C4—222no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—221no—
235C2×C4—222no—
236C2×C4D4×D1112yes—
237C22—442no—
238C22—442no—
239C22—442no—
240C22—442no—
241C22—442no—
242C22—442no—
243C22—442no—
244C22C2×D4×D1111yescharacteristic
245C22#6703712yes—
246C22#6704012yes—
247C22#6704011yescharacteristic
248C22#6704211yescharacteristic
249C4—22no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—42no—
254C4—222no—
255C4—222no—
256C4—441no—
257C4—441no—
258C4—442no—
259C2—882no—
260C2#1062312311yescharacteristic
261C2#1062316011yescharacteristic
262C2#1062317812yes—
263C2#1062325511yescharacteristic
264C2#1062326612yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#395C2
prime radicalC22×D44C22
hypercenter#395D11
hypocenterC11#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
2. C2×#66942C2semidirect
3. C11×#395C2semidirect
4. #10622842C2semidirect
5. #10622607C2semidirect
6. #10622605C2semidirect
8. #10622289C2semidirect
9. #10622288C2semidirect
11. #10622263C2semidirect
112. #395D11semidirect
200. C11#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#670002
C2×#669422
C11×#3952
#106228422
#106226072
#106226052
#106226042
#106222892
#106222882
#106222852
#106222632
#282011