Finite Group Databasebeta

← #13076783

Subgroups — #13076783

Order 1408.

416 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 117 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×#391C211yesmaximal, characteristic, complemented
2#10622844C212yesmaximal, complemented
3#10622604C211yesmaximal, characteristic
4#10622592C211yesmaximal, characteristic, complemented
5#10622553C212yesmaximal, complemented
6#10622288C212yesmaximal, complemented
7#10622286C212yesmaximal, complemented
8#10622285C212yesmaximal
9#10622271C212yesmaximal, complemented
10C22×Q8×C11C2211yescharacteristic
11C22×D44C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C11×#95C2212yes—
24C11×#95C2212yes—
25C11⋊#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C2×Q8×C11—22no—
33C2×Q8×C11—41no—
34C2×Q8×C11—41no—
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×D44—42no—
44C2×D44—41no—
45C2×Dic22—42no—
46C2×Dic22—41no—
47C11×C4⋊C4—41no—
48C42×C11—41no—
49(C2×D11)⋊C4—24no—
50(C2×D11)⋊C4—42no—
51(C2×D11)⋊C4—42no—
52(C2×D11)⋊C4—42no—
53(C2×D11)⋊C4—42no—
54(C2×D11)⋊C4—42no—
55Dic11⋊C4—42no—
56Dic11⋊C4—42no—
57#2832—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—
66Q8×C11—44no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
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—22no—
76C2×C4×C11—21no—
77C2×C4×C11—21no—
78C2×C4×C11—22no—
79C2×C4×C11#4112yes—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89D44—44no—
90Dic22—44no—
91#400—112no—
92#397—112no—
93#395—111no—
94#394—111no—
95#394—112no—
96#393—112no—
97#393—112no—
98#391D1111yescharacteristic, complemented
99#388—112no—
100C22×C11C2×#4111yescharacteristic
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C11H(5,𝔽2)12yes—
104C22×C112−1+412yes—
105C2×D11—42no—
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C2×D11—42no—
110C2×D11—42no—
111C2×D11—42no—
112C4×C11—22no—
113C4×C11—42no—
114C4×C11—41no—
115C4×C11—41no—
116C4×C11—42no—
117Dic11—42no—
118Dic11—42no—
119Dic11—42no—
120C22×Q8—111no—
121C22×Q8C2×D1111yescharacteristic
122C22×D4—111no—
123C2×C4⋊C4—112no—
124C2×C4⋊C4—112no—
125C2×C4⋊C4C2×D1111yescharacteristic
126C2×C22⋊C4—112no—
127C2×C22⋊C4—112no—
128C2×C22⋊C4—112no—
129C2×C22⋊C4—112no—
130C2×C22⋊C4—112no—
131C2×C22⋊C4—112no—
132C2×C42C2×D1111yescharacteristic
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95—111no—
138#95—111no—
139#95C2×D1112yes—
140#95C2×D1112yes—
141C2×C11#53811yescharacteristic
142C2×C11#54212yes—
143C2×C11H(3,𝔽4)11yescharacteristic
144C2×C11#56212yes—
145C2×C11#56311yescharacteristic
146D11—82no—
147C24—112no—
148C2×Q8—22no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—441no—
152C2×Q8—442no—
153C2×D4—441no—
154C2×D4—442no—
155C22×C4—112no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4C22×D1112yes—
159C22×C4C22×D1112yes—
160C22×C4C22×D1111yescharacteristic
161C22×C4C22×D1111yescharacteristic
162C22×C4C22×D1111yescharacteristic
163C4⋊C4—41no—
164C4⋊C4—442no—
165C4⋊C4—442no—
166C22⋊C4—224no—
167C22⋊C4—442no—
168C22⋊C4—442no—
169C22⋊C4—442no—
170C22⋊C4—442no—
171C22⋊C4—442no—
172C42—41no—
173C11#283211yescharacteristic, complemented, Sylow
174C23—222no—
175C23—222no—
176C23—222no—
177C23—222no—
178C23—222no—
179C23—222no—
180C23—222no—
181C23C23×D1111yescharacteristic
182Q8—44no—
183Q8—444no—
184D4—444no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—222no—
198C2×C4—222no—
199C2×C4—222no—
200C2×C4—222no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4#433912yes—
207C22—442no—
208C22—442no—
209C22—442no—
210C22—442no—
211C22—442no—
212C22—442no—
213C22—442no—
214C22C2×#433911yescharacteristic
215C22#6703711yescharacteristic
216C22#6703711yescharacteristic
217C22#6704012yes—
218C22#6704212yes—
219C4—22no—
220C4—42no—
221C4—42no—
222C4—41no—
223C4—41no—
224C4—442no—
225C4—442no—
226C4—442no—
227C2—882no—
228C2#1062302511yescharacteristic
229C2#1062311312yes—
230C2#1062317812yes—
231C2#1062321411yescharacteristic
232C2#1062326611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#391C2
prime radicalC22×D44C22
hypercenter#391D11
hypocenterC11#2832
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C11×#391C2semidirect
2. #10622844C2semidirect
4. #10622592C2semidirect
5. #10622553C2semidirect
6. #10622288C2semidirect
7. #10622286C2semidirect
9. #10622271C2semidirect
98. #391D11semidirect
173. C11#2832semidirect

Maximal subgroups

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

subgroupindex
C11×#3912
#106228442
#106226042
#106225922
#106225532
#106222882
#106222862
#106222852
#106222712
#283211