Finite Group Databasebeta

← #13076672

Subgroups — #13076672

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×#66943C211yesmaximal, characteristic, complemented
2C2×#66938C211yesmaximal, characteristic
3C11×#397C211yesmaximal, characteristic, complemented
4#10622606C211yesmaximal, characteristic, complemented
5#10622574C212yesmaximal
6#10622562C211yesmaximal, characteristic, complemented
7#10622561C212yesmaximal, complemented
8#10622290C211yesmaximal, characteristic, complemented
9#10622289C212yesmaximal, complemented
10#10622269C212yesmaximal, complemented
11#10622263C211yesmaximal, characteristic, complemented
12C22×C22⋊D11C2211yescharacteristic
13C22×Dic22C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2211yescharacteristic
16C2×C11×C22⋊C4C2212yes—
17C2×C22⋊Dic11C2211yescharacteristic
18C2×C22⋊Dic11C2212yes—
19C2×(C2×D11)⋊C4C2211yescharacteristic
20C2×(C2×D11)⋊C4C2211yescharacteristic
21C2×(C2×D11)⋊C4C2212yes—
22C2×(C2×D11)⋊C4C2212yes—
23C2×C4⋊Dic11C2212yes—
24C2×C4⋊Dic11C2211yescharacteristic
25C2×C4⋊Dic11C2212yes—
26C2×Dic11⋊C4C2212yes—
27C2×Dic11⋊C4C2212yes—
28C2×Dic11⋊C4C2212yes—
29C2×C4×Dic11C2211yescharacteristic
30#66943—24no—
31#66938—24no—
32C11×#95C2211yescharacteristic
33C11×#95C2212yes—
34C11⋊#95C2212yes—
35C11⋊#95C2211yescharacteristic
36C11⋊#95C2212yes—
37C24×C11C2311yescharacteristic
38C23×D11C2311yescharacteristic
39C22×C4×C11C2312yes—
40C22×C4×C11C2312yes—
41C22×C4×C11C2311yescharacteristic
42C22×C4×C11C2311yescharacteristic
43C2×C22⋊D11—22no—
44C2×C22⋊D11—42no—
45C22×Dic11C2312yes—
46C22×Dic11C2311yescharacteristic
47C22×Dic11C2312yes—
48C22×Dic11C2311yescharacteristic
49C22×Dic11C2311yescharacteristic
50C2×Dic22—22no—
51C2×Dic22—42no—
52C11×C4⋊C4—22no—
53C11×C22⋊C4—22no—
54C11×C22⋊C4—42no—
55C22⋊Dic11—22no—
56C22⋊Dic11—42no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59(C2×D11)⋊C4—42no—
60(C2×D11)⋊C4—42no—
61C4⋊Dic11—24no—
62C4⋊Dic11—22no—
63C4⋊Dic11—42no—
64Dic11⋊C4—24no—
65Dic11⋊C4—42no—
66Dic11⋊C4—42no—
67C4×Dic11D414yes—
68#2820—111nomaximal, Sylow
69C23×C11—21no—
70C23×C11—22no—
71C23×C11—21no—
72C23×C11—22no—
73C23×C11—21no—
74C23×C11C2411yescharacteristic
75C22×D11—21no—
76C22×D11—21no—
77C22×D11—22no—
78C22×D11—22no—
79C22×D11—21no—
80C2×C4×C11—22no—
81C2×C4×C11—22no—
82C2×C4×C11—21no—
83C2×C4×C11—22no—
84C2×C4×C11—22no—
85C2×C4×C11—22no—
86C2×C4×C11—22no—
87C2×C4×C11—22no—
88C2×C4×C11—22no—
89C2×C4×C11C2×D412yes—
90C22⋊D11—44no—
91C2×Dic11—21no—
92C2×Dic11—22no—
93C2×Dic11—21no—
94C2×Dic11—22no—
95C2×Dic11—21no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—22no—
101C2×Dic11—22no—
102C2×Dic11C2×D412yes—
103C2×Dic11C2×D412yes—
104Dic22—44no—
105C2×#125—111no—
106C2×#124—111no—
107#399—111no—
108#399—111no—
109#397—111no—
110#397D1111yescharacteristic, complemented
111#396—112no—
112#396—112no—
113#395—112no—
114#394—112no—
115#382—111no—
116C22×C11—41no—
117C22×C11—41no—
118C22×C11—41no—
119C22×C11—42no—
120C22×C11—42no—
121C22×C11C22×D411yescharacteristic
122C22×C11H(5,𝔽2)11yescharacteristic
123C22×C11H(5,𝔽2)12yes—
124C22×C112−1+412yes—
125C22×C112−1+411yescharacteristic
126C2×D11—41no—
127C2×D11—41no—
128C2×D11—41no—
129C2×D11—42no—
130C2×D11—42no—
131C4×C11—22no—
132C4×C11—41no—
133C4×C11—42no—
134C4×C11—42no—
135Dic11—22no—
136Dic11—22no—
137Dic11—41no—
138Dic11—42no—
139Dic11—42no—
140C22×Q8—111no—
141C22×D4—111no—
142#125—224no—
143#124—224no—
144C2×C4⋊C4—112no—
145C2×C4⋊C4—112no—
146C2×C4⋊C4—111no—
147C2×C4⋊C4—112no—
148C2×C4⋊C4—112no—
149C2×C4⋊C4—112no—
150C2×C4⋊C4C2×D1111yescharacteristic
151C2×C22⋊C4—111no—
152C2×C22⋊C4—111no—
153C2×C22⋊C4—111no—
154C2×C22⋊C4—112no—
155C2×C22⋊C4—112no—
156C2×C22⋊C4—112no—
157C2×C22⋊C4C2×D1111yescharacteristic
158C2×C22⋊C4C2×D1112yes—
159C2×C42—111no—
160#95—112no—
161#95—111no—
162#95—112no—
163#95C2×D1111yescharacteristic
164#95C2×D1112yes—
165C2×C11—81no—
166C2×C11#53511yescharacteristic
167C2×C11#53611yescharacteristic
168C2×C11#53711yescharacteristic
169C2×C11#56212yes—
170C2×C11#56312yes—
171D11—81no—
172C24—111no—
173C24C22×D1111yescharacteristic
174C2×Q8—222no—
175C2×Q8—442no—
176C2×D4—222no—
177C2×D4—442no—
178C22×C4—111no—
179C22×C4—111no—
180C22×C4—112no—
181C22×C4—111no—
182C22×C4—112no—
183C22×C4C22×D1112yes—
184C22×C4C22×D1112yes—
185C22×C4C22×D1111yescharacteristic
186C22×C4C22×D1111yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—224no—
189C4⋊C4—224no—
190C4⋊C4—222no—
191C4⋊C4—442no—
192C4⋊C4—442no—
193C4⋊C4—442no—
194C22⋊C4—22no—
195C22⋊C4—42no—
196C22⋊C4—222no—
197C22⋊C4—222no—
198C22⋊C4—222no—
199C22⋊C4—442no—
200C22⋊C4—442no—
201C22⋊C4—442no—
202C42—114no—
203C11#282011yescharacteristic, complemented, Sylow
204C23—21no—
205C23—21no—
206C23—22no—
207C23—21no—
208C23—22no—
209C23—221no—
210C23—221no—
211C23—222no—
212C23—221no—
213C23—222no—
214C23C23×D1111yescharacteristic
215Q8—444no—
216D4—444no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—112no—
227C2×C4—112no—
228C2×C4—221no—
229C2×C4—222no—
230C2×C4—221no—
231C2×C4—221no—
232C2×C4—222no—
233C2×C4—222no—
234C2×C4—222no—
235C2×C4—222no—
236C2×C4—222no—
237C2×C4—222no—
238C2×C4—222no—
239C2×C4D4×D1112yes—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22—41no—
245C22—442no—
246C22—441no—
247C22—441no—
248C22—442no—
249C22—441no—
250C22C2×D4×D1111yescharacteristic
251C22#6703711yescharacteristic
252C22#6704212yes—
253C22#6704311yescharacteristic
254C22#6704312yes—
255C4—22no—
256C4—42no—
257C4—42no—
258C4—41no—
259C4—222no—
260C4—222no—
261C4—442no—
262C4—441no—
263C4—442no—
264C2—81no—
265C2—881no—
266C2#1062313911yescharacteristic
267C2#1062317911yescharacteristic
268C2#1062319812yes—
269C2#1062320511yescharacteristic
270C2#1062324312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC22×C22⋊D11C22
hypercenter#397D11
hypocenterC11#2820
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#66943C2semidirect
3. C11×#397C2semidirect
4. #10622606C2semidirect
6. #10622562C2semidirect
7. #10622561C2semidirect
8. #10622290C2semidirect
9. #10622289C2semidirect
10. #10622269C2semidirect
11. #10622263C2semidirect
110. #397D11semidirect
203. C11#2820semidirect

Maximal subgroups

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

subgroupindex
C2×#669432
C2×#669382
C11×#3972
#106226062
#106225742
#106225622
#106225612
#106222902
#106222892
#106222692
#106222632
#282011