Finite Group Databasebeta

← #13076561

Subgroups — #13076561

Order 1408.

480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 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#10622602C212yesmaximal, complemented
3#10622601C211yesmaximal, characteristic
4#10622599C211yesmaximal, characteristic, complemented
5#10622286C212yesmaximal, complemented
6#10622286C212yesmaximal, complemented
7#10622281C212yesmaximal, complemented
8#10622278C212yesmaximal
9#10622259C212yesmaximal, complemented
10C22×D44C2211yescharacteristic
11C22×C4×D11C2212yes—
12C22×Dic22C2212yes—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4C2212yes—
16C2×(C2×D11)⋊C4C2212yes—
17C2×(C2×D11)⋊C4C2212yes—
18C2×(C2×D11)⋊C4C2212yes—
19C2×(C2×D11)⋊C4C2212yes—
20C2×C4⋊Dic11C2211yescharacteristic
21C2×Dic11⋊C4C2212yes—
22C2×C4×Dic11C2211yescharacteristic
23C11×#95C2212yes—
24C11×#95C2212yes—
25C11×#95C2211yescharacteristic
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C23×D11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2312yes—
34C22×C4×C11C2312yes—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C2×D44—41no—
41C2×D44—41no—
42C2×D44Q814yescomplemented
43C2×C4×D11—42no—
44C2×C4×D11—42no—
45C2×C4×D11—42no—
46C2×Dic22—24no—
47C2×Dic22—42no—
48C2×Dic22—42no—
49C11×C4⋊C4—41no—
50C11×C4⋊C4—41no—
51(C2×D11)⋊C4—24no—
52(C2×D11)⋊C4—24no—
53(C2×D11)⋊C4—42no—
54(C2×D11)⋊C4—42no—
55(C2×D11)⋊C4—42no—
56C4⋊Dic11—41no—
57Dic11⋊C4—42no—
58C4×Dic11—41no—
59#2804—111nomaximal, Sylow
60C23×C11C2411yescharacteristic
61C22×D11—22no—
62C22×D11—22no—
63C22×D11—22no—
64C22×D11—22no—
65C22×D11—22no—
66C22×D11—22no—
67C22×D11C2×Q814yes—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—22no—
74C2×C4×C11—21no—
75C2×C4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11—22no—
78C2×C4×C11—21no—
79C2×C4×C11—22no—
80C2×C4×C11C2×Q812yes—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11—22no—
84C2×Dic11—22no—
85C2×Dic11—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11#4114yes—
90D44—44no—
91C4×D11—48no—
92Dic22—48no—
93#400—111no—
94#400D1111yescharacteristic, complemented
95#393—112no—
96#393—112no—
97#391—112no—
98#390—111no—
99#386—112no—
100#385—112no—
101#385—112no—
102C22×C11C22×Q811yescharacteristic
103C22×C11C2×#4112yes—
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C11H(5,𝔽2)11yescharacteristic
106C22×C11H(5,𝔽2)12yes—
107C2×D11—24no—
108C2×D11—24no—
109C2×D11—24no—
110C2×D11—42no—
111C2×D11—42no—
112C2×D11—42no—
113C2×D11—42no—
114C4×C11—22no—
115C4×C11—42no—
116C4×C11—41no—
117C4×C11—41no—
118C4×C11—42no—
119Dic11—24no—
120Dic11—42no—
121Dic11—42no—
122C22×Q8—112no—
123C22×D4—111no—
124C23×C4—112no—
125C2×C4⋊C4—112no—
126C2×C4⋊C4—111no—
127C2×C4⋊C4C2×D1111yescharacteristic
128C2×C4⋊C4C2×D1111yescharacteristic
129C2×C22⋊C4—112no—
130C2×C22⋊C4—112no—
131C2×C22⋊C4—112no—
132C2×C22⋊C4—112no—
133C2×C22⋊C4—112no—
134C2×C42—111no—
135#95—112no—
136#95—112no—
137#95—112no—
138#95—112no—
139#95—111no—
140#95C2×D1112yes—
141#95C2×D1112yes—
142#95C2×D1111yescharacteristic
143C2×C11#53812yes—
144C2×C11#54311yescharacteristic
145C2×C11#55412yes—
146C2×C11#55911yescharacteristic
147C2×C11H(3,𝔽4)11yescharacteristic
148D11—44no—
149C24—112no—
150C2×Q8—224no—
151C2×Q8—442no—
152C2×Q8—442no—
153C2×D4—114no—
154C2×D4—441no—
155C2×D4—441no—
156C22×C4—112no—
157C22×C4—112no—
158C22×C4—112no—
159C22×C4—442no—
160C22×C4—442no—
161C22×C4—442no—
162C22×C4C22×D1111yescharacteristic
163C22×C4C22×D1112yes—
164C22×C4C22×D1111yescharacteristic
165C22×C4C22×D1112yes—
166C22×C4C22×D1111yescharacteristic
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—442no—
170C4⋊C4—441no—
171C22⋊C4—224no—
172C22⋊C4—224no—
173C22⋊C4—442no—
174C22⋊C4—442no—
175C22⋊C4—442no—
176C42—441no—
177C11#280411yescharacteristic, complemented, Sylow
178C23—114no—
179C23—222no—
180C23—222no—
181C23—222no—
182C23—222no—
183C23—222no—
184C23—222no—
185C23C23×D1111yescharacteristic
186Q8—448no—
187D4—444no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—114no—
201C2×C4—222no—
202C2×C4—222no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—222no—
206C2×C4—222no—
207C2×C4—222no—
208C2×C4—222no—
209C2×C4—448no—
210C2×C4Q8×D1112yes—
211C22—224no—
212C22—224no—
213C22—224no—
214C22—442no—
215C22—442no—
216C22—442no—
217C22—442no—
218C22#6703711yescharacteristic
219C22C2×Q8×D1111yescharacteristic
220C22#41×D1112yes—
221C22#6704211yescharacteristic
222C22#6704212yes—
223C4—22no—
224C4—42no—
225C4—41no—
226C4—41no—
227C4—42no—
228C4—224no—
229C4—442no—
230C4—442no—
231C2—444no—
232C2#1062316511yescharacteristic
233C2#1062319511yescharacteristic
234C2#1062321411yescharacteristic
235C2#1062322112yes—
236C2#1062323512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#400C2
prime radicalC22×D44C22
hypercenter#400D11
hypocenterC11#2804
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. #10622602C2semidirect
4. #10622599C2semidirect
5. #10622286C2semidirect
6. #10622286C2semidirect
7. #10622281C2semidirect
9. #10622259C2semidirect
42. C2×D44Q8semidirect
94. #400D11semidirect
177. C11#2804semidirect

Maximal subgroups

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

subgroupindex
C11×#4002
#106226022
#106226012
#106225992
#106222862
#106222812
#106222782
#106222592
#280411