Finite Group Databasebeta

← #13074113

Subgroups — #13074113

Order 1408.

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

normal subgroups only

This group has 440 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
1C11×#400C211yesmaximal, characteristic, complemented
2#10622603C212yesmaximal, complemented
3#10622601C211yesmaximal, characteristic
4#10622596C211yesmaximal, characteristic, complemented
5#10622285C212yesmaximal
6#10622283C212yesmaximal, complemented
7#10622282C212yesmaximal, complemented
8#10622282C212yesmaximal, complemented
9#10622262C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C2×C11×C4⋊C4C2211yescharacteristic
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C4C2212yes—
14C2×(C2×D11)⋊C4C2212yes—
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×C4⋊Dic11C2211yescharacteristic
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2212yes—
23C2×C4×Dic11C2211yescharacteristic
24C2×C4×Dic11C2212yes—
25C11×#95C2212yes—
26C11×#95C2211yescharacteristic
27C11×#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—22no—
41C2×D44—41no—
42C2×D44—41no—
43C11×C4⋊C4—41no—
44C11×C4⋊C4—41no—
45(C2×D11)⋊C4—24no—
46(C2×D11)⋊C4—24no—
47(C2×D11)⋊C4—24no—
48(C2×D11)⋊C4—24no—
49(C2×D11)⋊C4—42no—
50(C2×D11)⋊C4—42no—
51C4⋊Dic11—41no—
52Dic11⋊C4—24no—
53Dic11⋊C4—24no—
54C4×Dic11—24no—
55C4×Dic11—41no—
56C4×Dic11—42no—
57#2593—111nomaximal, Sylow
58C23×C11C2411yescharacteristic
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C2×C4×C11—21no—
67C2×C4×C11—21no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—21no—
76C2×C4×C11—22no—
77C2×C4×C11—21no—
78C2×C4×C11#4112yes—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11#4114yes—
87C2×Dic11#4114yes—
88D44—44no—
89#400D1111yescharacteristic, complemented
90#398—111no—
91#394—112no—
92#390—111no—
93#388—112no—
94#388—112no—
95#388—112no—
96#388—112no—
97C4×C4⋊C4—112no—
98C22×C11C2×#4111yescharacteristic
99C22×C11C2×#4112yes—
100C22×C11C2×#4112yes—
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)11yescharacteristic
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C4×C11—22no—
111C4×C11—42no—
112C4×C11—42no—
113C4×C11—41no—
114C4×C11—41no—
115Dic11—24no—
116Dic11—24no—
117Dic11—42no—
118C22×D4—111no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—111no—
122C2×C4⋊C4C2×D1111yescharacteristic
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C22⋊C4—112no—
125C2×C22⋊C4—112no—
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C42—112no—
131C2×C42—111no—
132C2×C42—112no—
133#95—112no—
134#95—111no—
135#95—112no—
136#95C2×D1112yes—
137#95C2×D1111yescharacteristic
138#95C2×D1112yes—
139C2×C11#52912yes—
140C2×C11#53811yescharacteristic
141C2×C11#55312yes—
142C2×C11#55511yescharacteristic
143C2×C11#55911yescharacteristic
144D11—82no—
145C24—112no—
146C2×D4—222no—
147C2×D4—441no—
148C2×D4—441no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4C22×D1111yescharacteristic
153C22×C4C22×D1112yes—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C4⋊C4—41no—
158C4⋊C4—41no—
159C4⋊C4—224no—
160C4⋊C4—224no—
161C4⋊C4—441no—
162C22⋊C4—224no—
163C22⋊C4—224no—
164C22⋊C4—224no—
165C22⋊C4—224no—
166C22⋊C4—442no—
167C22⋊C4—442no—
168C42—224no—
169C42—441no—
170C42—442no—
171C11#259311yescharacteristic, complemented, Sylow
172C23—222no—
173C23—222no—
174C23—222no—
175C23—222no—
176C23—222no—
177C23—222no—
178C23—222no—
179C23C23×D1111yescharacteristic
180D4—444no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—114no—
194C2×C4—114no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4#434312yes—
203C22—442no—
204C22—442no—
205C22—442no—
206C22—442no—
207C22—442no—
208C22—442no—
209C22—442no—
210C22#6703711yescharacteristic
211C22C2×#434311yescharacteristic
212C22#41×D1112yes—
213C22#41×D1112yes—
214C22#6704211yescharacteristic
215C4—22no—
216C4—42no—
217C4—41no—
218C4—41no—
219C4—42no—
220C4—224no—
221C4—224no—
222C4—442no—
223C2—882no—
224C2#1062317511yescharacteristic
225C2#1062319511yescharacteristic
226C2#1062320111yescharacteristic
227C2#1062322212yes—
228C2#1062324012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2593
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
1. C11×#400C2semidirect
2. #10622603C2semidirect
4. #10622596C2semidirect
6. #10622283C2semidirect
7. #10622282C2semidirect
8. #10622282C2semidirect
9. #10622262C2semidirect
89. #400D11semidirect
171. C11#2593semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106226032
#106226012
#106225962
#106222852
#106222832
#106222822
#106222622
#259311