Finite Group Databasebeta

← #13076632

Subgroups — #13076632

Order 1408.

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

normal subgroups only

This group has 478 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×#66950C211yesmaximal, characteristic, complemented
2C2×#66947C211yesmaximal, characteristic
3C11×#398C211yesmaximal, characteristic, complemented
4#10622607C212yesmaximal, complemented
5#10622606C212yesmaximal, complemented
6#10622606C211yesmaximal, characteristic, complemented
7#10622592C211yesmaximal, characteristic, complemented
8#10622286C211yesmaximal, characteristic, complemented
9#10622285C212yesmaximal
10#10622280C211yesmaximal, characteristic, complemented
11#10622270C212yesmaximal, complemented
12C22×D44C2211yescharacteristic
13C22×C4×D11C2211yescharacteristic
14C22×Dic22C2211yescharacteristic
15C2×C11×C4⋊C4C2211yescharacteristic
16C2×C11×C4⋊C4C2211yescharacteristic
17C2×C11×C4⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2211yescharacteristic
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×(C2×D11)⋊C4C2212yes—
24C2×(C2×D11)⋊C4C2212yes—
25C2×C4⋊Dic11C2212yes—
26C2×Dic11⋊C4C2211yescharacteristic
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29#66950—24no—
30#66947—24no—
31C11×#95C2212yes—
32C11×#95C2211yescharacteristic
33C11⋊#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C23×D11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×C4×C11C2312yes—
42C22×C4×C11C2311yescharacteristic
43C22×C4×C11C2311yescharacteristic
44C22×Dic11C2311yescharacteristic
45C22×Dic11C2312yes—
46C22×Dic11C2312yes—
47C22×Dic11C2311yescharacteristic
48C2×D44—22no—
49C2×D44—42no—
50C2×C4×D11—42no—
51C2×C4×D11D414yes—
52C2×Dic22—22no—
53C2×Dic22—42no—
54C11×C4⋊C4—22no—
55C11×C4⋊C4—22no—
56C11×C4⋊C4—42no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—24no—
60(C2×D11)⋊C4—22no—
61(C2×D11)⋊C4—42no—
62(C2×D11)⋊C4—42no—
63(C2×D11)⋊C4—42no—
64C4⋊Dic11—24no—
65Dic11⋊C4—22no—
66Dic11⋊C4—42no—
67Dic11⋊C4—42no—
68#2814—111nomaximal, Sylow
69C23×C11C2411yescharacteristic
70C22×D11—21no—
71C22×D11—22no—
72C22×D11—22no—
73C22×D11—21no—
74C22×D11—21no—
75C22×D11—21no—
76C22×D11—22no—
77C22×D11—22no—
78C22×D11—21no—
79C22×D11C2×D412yes—
80C2×C4×C11—22no—
81C2×C4×C11—21no—
82C2×C4×C11—22no—
83C2×C4×C11—21no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—21no—
89C2×C4×C11—22no—
90C2×C4×C11—21no—
91C2×C4×C11—22no—
92C2×C4×C11C2×D412yes—
93C2×Dic11—22no—
94C2×Dic11—21no—
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103D44—44no—
104C4×D11—44no—
105Dic22—44no—
106C2×#123—111no—
107C2×C22⋊Q8—111no—
108#398—112no—
109#398D1111yescharacteristic, complemented
110#397—111no—
111#397—112no—
112#396—112no—
113#395—111no—
114#394—112no—
115#393—111no—
116#380—111no—
117C22×C11C22×D411yescharacteristic
118C22×C11H(5,𝔽2)11yescharacteristic
119C22×C11H(5,𝔽2)12yes—
120C22×C112−1+412yes—
121C22×C112−1+411yescharacteristic
122C2×D11—22no—
123C2×D11—22no—
124C2×D11—22no—
125C2×D11—42no—
126C2×D11—42no—
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—41no—
130C2×D11—42no—
131C2×D11—42no—
132C4×C11—22no—
133C4×C11—41no—
134C4×C11—42no—
135C4×C11—41no—
136C4×C11—42no—
137Dic11—22no—
138Dic11—42no—
139Dic11—41no—
140Dic11—42no—
141C22×Q8—111no—
142C22×D4—111no—
143C23×C4—111no—
144#123—224no—
145C22⋊Q8—224no—
146C2×C4⋊C4—112no—
147C2×C4⋊C4—111no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4C2×D1111yescharacteristic
151C2×C4⋊C4C2×D1111yescharacteristic
152C2×C4⋊C4C2×D1112yes—
153C2×C22⋊C4—112no—
154C2×C22⋊C4—111no—
155C2×C22⋊C4—111no—
156C2×C22⋊C4—111no—
157C2×C22⋊C4—112no—
158C2×C22⋊C4—112no—
159C2×C22⋊C4—112no—
160#95—111no—
161#95—112no—
162#95—112no—
163#95—112no—
164#95C2×D1111yescharacteristic
165#95C2×D1112yes—
166C2×C11#53411yescharacteristic
167C2×C11#53611yescharacteristic
168C2×C11#53711yescharacteristic
169C2×C11#56212yes—
170C2×C11#56312yes—
171D11—42no—
172D11—81no—
173C24—111no—
174C24—111no—
175C2×Q8—222no—
176C2×Q8—442no—
177C2×D4—222no—
178C2×D4—442no—
179C22×C4—111no—
180C22×C4—114no—
181C22×C4—111no—
182C22×C4—112no—
183C22×C4—112no—
184C22×C4—442no—
185C22×C4C22×D1111yescharacteristic
186C22×C4C22×D1112yes—
187C22×C4C22×D1112yes—
188C22×C4C22×D1111yescharacteristic
189C22×C4C22×D1111yescharacteristic
190C4⋊C4—22no—
191C4⋊C4—22no—
192C4⋊C4—42no—
193C4⋊C4—224no—
194C4⋊C4—222no—
195C4⋊C4—442no—
196C4⋊C4—442no—
197C22⋊C4—222no—
198C22⋊C4—224no—
199C22⋊C4—222no—
200C22⋊C4—222no—
201C22⋊C4—442no—
202C22⋊C4—442no—
203C22⋊C4—442no—
204C11#281411yescharacteristic, complemented, Sylow
205C23—112no—
206C23—221no—
207C23—222no—
208C23—222no—
209C23—221no—
210C23—221no—
211C23—221no—
212C23—222no—
213C23—222no—
214C23—221no—
215C23C23×D1111yescharacteristic
216Q8—444no—
217D4—444no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—22no—
230C2×C4—112no—
231C2×C4—222no—
232C2×C4—221no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4—222no—
240C2×C4—444no—
241C2×C4D4×D1112yes—
242C22—222no—
243C22—222no—
244C22—222no—
245C22—442no—
246C22—442no—
247C22—441no—
248C22—441no—
249C22—442no—
250C22—441no—
251C22—442no—
252C22C2×D4×D1111yescharacteristic
253C22#6703711yescharacteristic
254C22#6704012yes—
255C22#6704212yes—
256C22#6704311yescharacteristic
257C4—22no—
258C4—41no—
259C4—42no—
260C4—42no—
261C4—41no—
262C4—222no—
263C4—441no—
264C4—442no—
265C4—442no—
266C2—442no—
267C2—881no—
268C2#1062313911yescharacteristic
269C2#1062317812yes—
270C2#1062318411yescharacteristic
271C2#1062323012yes—
272C2#1062325511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#398C2
prime radicalC22×D44C22
hypercenter#398D11
hypocenterC11#2814
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
1. C2×#66950C2semidirect
3. C11×#398C2semidirect
4. #10622607C2semidirect
5. #10622606C2semidirect
6. #10622606C2semidirect
7. #10622592C2semidirect
8. #10622286C2semidirect
10. #10622280C2semidirect
11. #10622270C2semidirect
109. #398D11semidirect
204. C11#2814semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×#669472
C11×#3982
#106226072
#106226062
#106225922
#106222862
#106222852
#106222802
#106222702
#281411