Finite Group Databasebeta

← #13076039

Subgroups — #13076039

Order 1408.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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×#381C211yesmaximal, characteristic
2#10622823C212yesmaximal
3#10622566C211yesmaximal, characteristic
4#10622560C211yesmaximal, characteristic
5#10622558C212yesmaximal
6#10622271C212yesmaximal, complemented
7#10622270C212yesmaximal, complemented
8#10622264C212yesmaximal, complemented
9#10622259C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2211yescharacteristic
12C2×C11×C22⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2211yescharacteristic
14C2×C22⋊Dic11C2212yes—
15C2×C22⋊Dic11C2212yes—
16C2×C4⋊Dic11C2211yescharacteristic
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2212yes—
21C11×#95C2212yes—
22C11×#95C2212yes—
23C11⋊#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2211yescharacteristic
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C24×C11C2311yescharacteristic
32C22×C4×C11—22no—
33C22×C4×C11—41no—
34C22×C4×C11—41no—
35C22×C4×C11C2311yescharacteristic
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2312yes—
38C22×C4×C11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×Dic22—24no—
44C2×Dic22—41no—
45C11×C22⋊C4—41no—
46C11×C22⋊C4—41no—
47C22⋊Dic11—24no—
48C22⋊Dic11—24no—
49C4⋊Dic11—41no—
50Dic11⋊C4—42no—
51Dic11⋊C4—42no—
52Dic11⋊C4—42no—
53C4×Dic11—24no—
54#2764—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—21no—
57C23×C11—21no—
58C23×C11—22no—
59C23×C11#4112yes—
60C23×C11C2411yescharacteristic
61C2×C4×C11—22no—
62C2×C4×C11—22no—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—22no—
66C2×C4×C11—22no—
67C2×C4×C11—21no—
68C2×C4×C11—21no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—44no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83C2×Dic11#4114yes—
84Dic22—44no—
85#400—112no—
86#398—112no—
87#397—111no—
88#393—111no—
89#391—112no—
90#388—112no—
91#385—112no—
92#383—112no—
93#381D1111yescharacteristic
94C22×C11—22no—
95C22×C11—24no—
96C22×C11—42no—
97C22×C11—41no—
98C22×C11—41no—
99C22×C11C2×#4111yescharacteristic
100C22×C11C2×#4112yes—
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)11yescharacteristic
103C22×C112−1+412yes—
104C4×C11—42no—
105C4×C11—42no—
106C4×C11—41no—
107C4×C11—41no—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C22×Q8—111no—
113C23×C4C2×D1111yescharacteristic
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—111no—
118C2×C22⋊C4—112no—
119C2×C22⋊C4—112no—
120C2×C22⋊C4C2×D1111yescharacteristic
121C2×C22⋊C4C2×D1111yescharacteristic
122C2×C42—112no—
123#95—111no—
124#95—112no—
125#95—112no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—111no—
131#95C2×D1112yes—
132#95C2×D1112yes—
133C2×C11—42no—
134C2×C11#53811yescharacteristic
135C2×C11#54212yes—
136C2×C11#55111yescharacteristic
137C2×C11#55212yes—
138C2×C11#56311yescharacteristic
139C24C22×D1111yescharacteristic
140C2×Q8—224no—
141C2×Q8—441no—
142C22×C4—22no—
143C22×C4—41no—
144C22×C4—41no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4—112no—
148C22×C4—112no—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1112yes—
152C22×C4C22×D1112yes—
153C4⋊C4—442no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—441no—
157C22⋊C4—41no—
158C22⋊C4—41no—
159C22⋊C4—224no—
160C22⋊C4—224no—
161C42—224no—
162C11#276411yescharacteristic, complemented, Sylow
163C23—21no—
164C23—21no—
165C23—22no—
166C23—22no—
167C23#433912yes—
168C23C23×D1111yescharacteristic
169Q8—444no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—44no—
181C2×C4—114no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—222no—
186C2×C4—222no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C22—22no—
194C22—24no—
195C22—41no—
196C22—41no—
197C22—42no—
198C22C2×#433911yescharacteristic
199C22#6703711yescharacteristic
200C22#6703711yescharacteristic
201C22#41×D1112yes—
202C22#6704312yes—
203C4—42no—
204C4—41no—
205C4—41no—
206C4—42no—
207C4—224no—
208C4—442no—
209C4—442no—
210C4—442no—
211C2—42no—
212C2#1062302511yescharacteristic
213C2#1062306212yes—
214C2#1062318211yescharacteristic
215C2#1062319011yescharacteristic
216C2#1062319312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#381C2
prime radicalC24×C11C23
hypercenter#381D11
hypocenterC11#2764
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
6. #10622271C2semidirect
7. #10622270C2semidirect
8. #10622264C2semidirect
9. #10622259C2semidirect
162. C11#2764semidirect

Maximal subgroups

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

subgroupindex
C11×#3812
#106228232
#106225662
#106225602
#106225582
#106222712
#106222702
#106222642
#106222592
#276411