Finite Group Databasebeta

← #13076587

Subgroups — #13076587

Order 1408.

408 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 133 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×#399C211yesmaximal, characteristic
2#10622598C212yesmaximal, complemented
3#10622596C212yesmaximal, complemented
4#10622595C212yesmaximal, complemented
5#10622563C212yesmaximal
6#10622562C211yesmaximal, characteristic
7#10622559C211yesmaximal, characteristic
8#10622558C212yesmaximal
9#10622260C212yesmaximal, complemented
10C23×Dic11C2211yescharacteristic
11C2×C11×C4⋊C4C2212yes—
12C2×C11×C4⋊C4C2211yescharacteristic
13C2×C11×C22⋊C4C2212yes—
14C2×C11×C22⋊C4C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22C2×Dic11⋊C4C2212yes—
23C2×C4×Dic11C2212yes—
24C11×#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2211yescharacteristic
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×Dic11—42no—
37C22×Dic11—41no—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C11×C4⋊C4—24no—
43C11×C4⋊C4—41no—
44C11×C22⋊C4—24no—
45C11×C22⋊C4—41no—
46C22⋊Dic11—42no—
47C22⋊Dic11Q814yes—
48C4⋊Dic11—42no—
49C4⋊Dic11—41no—
50C4⋊Dic11—42no—
51Dic11⋊C4—24no—
52Dic11⋊C4—42no—
53Dic11⋊C4—42no—
54C4×Dic11—42no—
55#2807—111nomaximal, Sylow
56C23×C11—22no—
57C23×C11—22no—
58C23×C11—21no—
59C23×C11—21no—
60C23×C11C2×Q812yes—
61C23×C11C2411yescharacteristic
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—21no—
69C2×C4×C11—22no—
70C2×C4×C11—21no—
71C2×C4×C11#4114yes—
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—44no—
84C2×Dic11C2×Q814yes—
85#400—112no—
86#399—111no—
87#399D1111yescharacteristic
88#398—112no—
89#389—112no—
90#389—112no—
91#388—112no—
92#385—111no—
93#385—112no—
94C22×C11—22no—
95C22×C11—24no—
96C22×C11—42no—
97C22×C11—41no—
98C22×C11—41no—
99C22×C11C22×Q811yescharacteristic
100C22×C11C2×#4112yes—
101C22×C11H(5,𝔽2)11yescharacteristic
102C22×C11H(5,𝔽2)12yes—
103C22×C112−1+411yescharacteristic
104C4×C11—24no—
105C4×C11—42no—
106C4×C11—41no—
107C4×C11—41no—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111Dic11—42no—
112C23×C4—111no—
113C2×C4⋊C4—112no—
114C2×C4⋊C4—112no—
115C2×C4⋊C4—112no—
116C2×C4⋊C4—112no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4C2×D1112yes—
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C22⋊C4—111no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4C2×D1112yes—
124C2×C22⋊C4C2×D1111yescharacteristic
125C2×C42—112no—
126#95—112no—
127#95—112no—
128#95—112no—
129#95—112no—
130#95—112no—
131#95—111no—
132#95C2×D1111yescharacteristic
133C2×C11—42no—
134C2×C11#53912yes—
135C2×C11#54411yescharacteristic
136C2×C11#55412yes—
137C2×C11#55911yescharacteristic
138C2×C11#56011yescharacteristic
139C24C22×D1111yescharacteristic
140C22×C4—112no—
141C22×C4—112no—
142C22×C4—112no—
143C22×C4—112no—
144C22×C4—441no—
145C22×C4—442no—
146C22×C4C22×D1112yes—
147C22×C4C22×D1111yescharacteristic
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1112yes—
150C4⋊C4—24no—
151C4⋊C4—41no—
152C4⋊C4—224no—
153C4⋊C4—442no—
154C4⋊C4—442no—
155C4⋊C4—442no—
156C4⋊C4—441no—
157C4⋊C4—442no—
158C22⋊C4—24no—
159C22⋊C4—41no—
160C22⋊C4—114no—
161C22⋊C4—442no—
162C42—442no—
163C11#280711yescharacteristic, complemented, Sylow
164C23—22no—
165C23—21no—
166C23—22no—
167C23—21no—
168C23Q8×D1112yes—
169C23C23×D1111yescharacteristic
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—114no—
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×C4—222no—
191C2×C4—444no—
192C2×C4#434114yes—
193C22—22no—
194C22—24no—
195C22—41no—
196C22—42no—
197C22—41no—
198C22C2×#434112yes—
199C22#6703711yescharacteristic
200C22C2×Q8×D1111yescharacteristic
201C22#6704212yes—
202C22#6704311yescharacteristic
203C4—24no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—224no—
208C4—442no—
209C4—442no—
210C4—442no—
211C2—42no—
212C2#1062315411yescharacteristic
213C2#1062316612yes—
214C2#1062319612yes—
215C2#1062319711yescharacteristic
216C2#1062324411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#399C2
prime radicalC24×C11C23
hypercenter#399D11
hypocenterC11#2807
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #399

Complements

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

NH ≅ G/Ntype
2. #10622598C2semidirect
3. #10622596C2semidirect
4. #10622595C2semidirect
9. #10622260C2semidirect
163. C11#2807semidirect

Maximal subgroups

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

subgroupindex
C11×#3992
#106225982
#106225962
#106225952
#106225632
#106225622
#106225592
#106225582
#106222602
#280711