Finite Group Databasebeta

← #13073840

Subgroups — #13073840

Order 1408.

456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 157 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×C11×#95C211yesmaximal, characteristic
2#10622825C211yesmaximal, characteristic
3#10622825C212yesmaximal
4#10622823C212yesmaximal
5C4×C22⋊Dic11C211yesmaximal, characteristic
6#10622274C212yesmaximal, complemented
7#10622273C212yesmaximal, complemented
8#10622268C212yesmaximal, complemented
9#10622267C212yesmaximal, complemented
10C23×C4×C11C2212yes—
11C23×C4×C11C2211yescharacteristic
12C2×C22⋊Dic11C2211yescharacteristic
13C2×C22⋊Dic11C2211yescharacteristic
14C2×C22⋊Dic11C2212yes—
15C2×C4⋊Dic11C2212yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×C4×Dic11C2212yes—
21C11×#95C2212yes—
22C11×#95C2211yescharacteristic
23C11×#95C2211yescharacteristic
24C11⋊#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C22×C4×C11—24no—
33C22×C4×C11—24no—
34C22×C4×C11—42no—
35C22×C4×C11—42no—
36C22×C4×C11Q814yes—
37C22×C4×C11C2312yes—
38C22×C4×C11C2311yescharacteristic
39C22×C4×C11C2311yescharacteristic
40C22×C4×C11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C22×Dic11C2312yes—
45C22⋊Dic11—22no—
46C22⋊Dic11—22no—
47C22⋊Dic11—24no—
48C4⋊Dic11—24no—
49C4⋊Dic11—42no—
50C4⋊Dic11—42no—
51Dic11⋊C4—24no—
52Dic11⋊C4—42no—
53C4×Dic11—42no—
54#2569—111nomaximal, Sylow
55C23×C11—22no—
56C23×C11—22no—
57C23×C11C2×Q812yes—
58C23×C11#4112yes—
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—22no—
68C2×C4×C11—44no—
69C2×C4×C11—48no—
70C2×C4×C11C2×Q812yes—
71C2×C4×C11C2×Q812yes—
72C2×C4×C11#4114yes—
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—22no—
84C2×Dic11—22no—
85#400—112no—
86#398—112no—
87#387—112no—
88#387—112no—
89#385—112no—
90#380—111no—
91#380—112no—
92C4×C22⋊C4—111no—
93C2×#95D1111yescharacteristic
94C22×C11—22no—
95C22×C11—22no—
96C22×C11—24no—
97C22×C11—24no—
98C22×C11#12514yes—
99C22×C11C22×Q811yescharacteristic
100C22×C11C2×#4112yes—
101C22×C11C2×#4111yescharacteristic
102C22×C11C2×#4111yescharacteristic
103C22×C11H(5,𝔽2)12yes—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—24no—
107C4×C11—42no—
108Dic11—42no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C23×C4C2×D1112yes—
113C23×C4C2×D1111yescharacteristic
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—112no—
119C2×C22⋊C4—111no—
120C2×C22⋊C4—111no—
121C2×C22⋊C4—112no—
122C2×C42—112no—
123#95—112no—
124#95—111no—
125#95—111no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95C2×D1112yes—
131#95C2×D1111yescharacteristic
132#95C2×D1111yescharacteristic
133C2×C11—24no—
134C2×C11C2×#12511yescharacteristic
135C2×C11#53311yescharacteristic
136C2×C11#54311yescharacteristic
137C2×C11#55112yes—
138C2×C11#55312yes—
139C24C22×D1111yescharacteristic
140C22×C4—24no—
141C22×C4—24no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—112no—
145C22×C4—112no—
146C22×C4—112no—
147C22×C4—112no—
148C22×C4Dic2214yes—
149C22×C4C22×D1112yes—
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1111yescharacteristic
152C22×C4C22×D1112yes—
153C4⋊C4—224no—
154C4⋊C4—224no—
155C4⋊C4—442no—
156C4⋊C4—442no—
157C4⋊C4—442no—
158C22⋊C4—222no—
159C22⋊C4—222no—
160C22⋊C4—224no—
161C42—442no—
162C11#256911yescharacteristic, complemented, Sylow
163C23—22no—
164C23—22no—
165C23C2×Dic2212yes—
166C23#434112yes—
167C23#434312yes—
168C23C23×D1111yescharacteristic
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—44no—
177C2×C4—48no—
178C2×C4—222no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
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×C4C2×Dic2212yes—
191C2×C4C2×Dic2212yes—
192C2×C4#433914yes—
193C22—22no—
194C22—22no—
195C22—24no—
196C22—24no—
197C22#6694314yes—
198C22C22×Dic2211yescharacteristic
199C22C2×#433912yes—
200C22C2×#434111yescharacteristic
201C22#6703712yes—
202C22C2×#434311yescharacteristic
203C4—22no—
204C4—22no—
205C4—24no—
206C4—42no—
207C4—442no—
208C4—442no—
209C4—442no—
210C4—442no—
211C2—24no—
212C2#1062300111yescharacteristic
213C2#1062301411yescharacteristic
214C2#1062302612yes—
215C2C2×#6694311yescharacteristic
216C2#1062304512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#95C2
prime radicalC24×C11C23
hypercenterC2×#95D11
hypocenterC11#2569
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
6. #10622274C2semidirect
7. #10622273C2semidirect
8. #10622268C2semidirect
9. #10622267C2semidirect
162. C11#2569semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#952
#106228252
#106228232
C4×C22⋊Dic112
#106222742
#106222732
#106222682
#106222672
#256911