Finite Group Databasebeta

← #13076654

Subgroups — #13076654

Order 1408.

444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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×#66931C212yesmaximal
2C11×#397C211yesmaximal, characteristic
3#10622592C212yesmaximal, complemented
4#10622566C211yesmaximal, characteristic
5#10622565C212yesmaximal
6#10622556C211yesmaximal, characteristic
7#10622273C212yesmaximal, complemented
8#10622271C212yesmaximal, complemented
9#10622269C212yesmaximal, complemented
10C23×Dic11C2211yescharacteristic
11C22×Dic22C2212yes—
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×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×Dic11⋊C4C2212yes—
22#66931—28no—
23C11×#95C2212yes—
24C11×#95C2211yescharacteristic
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2211yescharacteristic
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C11⋊#95C2212yes—
32C24×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×C4×C11C2312yes—
37C22×Dic11—41no—
38C22×Dic11—41no—
39C22×Dic11D414yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C22×Dic11C2312yes—
44C2×Dic22—24no—
45C2×Dic22—42no—
46C2×Dic22—42no—
47C11×C4⋊C4—41no—
48C11×C22⋊C4—24no—
49C11×C22⋊C4—41no—
50C22⋊Dic11—24no—
51C22⋊Dic11—41no—
52C4⋊Dic11—24no—
53C4⋊Dic11—41no—
54Dic11⋊C4—24no—
55Dic11⋊C4—24no—
56Dic11⋊C4—42no—
57#2817—111nomaximal, Sylow
58C23×C11—21no—
59C23×C11—21no—
60C23×C11—22no—
61C23×C11—22no—
62C23×C11C2×D412yes—
63C23×C11C2411yescharacteristic
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—22no—
72C2×C4×C11—22no—
73C2×C4×C11—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—
85C2×Dic11—44no—
86C2×Dic11C2×D414yes—
87Dic22—48no—
88C2×C22⋊Q8—112no—
89#400—112no—
90#400—112no—
91#397—112no—
92#397—111no—
93#397D1111yescharacteristic
94#395—112no—
95#395—112no—
96#381—111no—
97C22×C11—22no—
98C22×C11—24no—
99C22×C11—42no—
100C22×C11—41no—
101C22×C11—41no—
102C22×C11C22×D411yescharacteristic
103C22×C11H(5,𝔽2)11yescharacteristic
104C22×C11H(5,𝔽2)11yescharacteristic
105C22×C112−1+412yes—
106C22×C112−1+412yes—
107C4×C11—42no—
108C4×C11—42no—
109C4×C11—41no—
110C4×C11—41no—
111Dic11—24no—
112Dic11—42no—
113Dic11—42no—
114Dic11—42no—
115C22×Q8—112no—
116C23×C4—111no—
117C22⋊Q8—228no—
118C2×C4⋊C4—112no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—112no—
122C2×C4⋊C4—111no—
123C2×C4⋊C4C2×D1111yescharacteristic
124C2×C22⋊C4—112no—
125C2×C22⋊C4—111no—
126C2×C22⋊C4C2×D1112yes—
127C2×C22⋊C4C2×D1111yescharacteristic
128#95—112no—
129#95—112no—
130#95—112no—
131#95—112no—
132#95—112no—
133#95—112no—
134#95—111no—
135#95C2×D1112yes—
136#95C2×D1111yescharacteristic
137C2×C11—42no—
138C2×C11#53411yescharacteristic
139C2×C11#53612yes—
140C2×C11#56312yes—
141C2×C11#56311yescharacteristic
142C2×C11#56311yescharacteristic
143C24C22×D1111yescharacteristic
144C2×Q8—224no—
145C2×Q8—442no—
146C2×Q8—442no—
147C22×C4—112no—
148C22×C4—114no—
149C22×C4—112no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—441no—
153C22×C4—441no—
154C22×C4C22×D1111yescharacteristic
155C22×C4C22×D1111yescharacteristic
156C22×C4C22×D1112yes—
157C22×C4C22×D1112yes—
158C4⋊C4—41no—
159C4⋊C4—224no—
160C4⋊C4—224no—
161C4⋊C4—224no—
162C4⋊C4—442no—
163C4⋊C4—441no—
164C22⋊C4—24no—
165C22⋊C4—41no—
166C22⋊C4—224no—
167C22⋊C4—441no—
168C11#281711yescharacteristic, complemented, Sylow
169C23—21no—
170C23—21no—
171C23—22no—
172C23—22no—
173C23D4×D1112yes—
174C23C23×D1111yescharacteristic
175Q8—448no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—114no—
187C2×C4—222no—
188C2×C4—222no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4—222no—
196C2×C4—222no—
197C2×C4—222no—
198C2×C4—444no—
199C22—22no—
200C22—24no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22C2×D4×D1111yescharacteristic
205C22#6703711yescharacteristic
206C22#6704211yescharacteristic
207C22#6704312yes—
208C22#6704312yes—
209C4—42no—
210C4—42no—
211C4—41no—
212C4—41no—
213C4—224no—
214C4—442no—
215C4—442no—
216C4—442no—
217C2—42no—
218C2#1062313611yescharacteristic
219C2#1062317912yes—
220C2#1062318211yescharacteristic
221C2#1062320311yescharacteristic
222C2#1062324312yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#397C2
prime radicalC24×C11C23
hypercenter#397D11
hypocenterC11#2817
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
3. #10622592C2semidirect
7. #10622273C2semidirect
8. #10622271C2semidirect
9. #10622269C2semidirect
168. C11#2817semidirect

Maximal subgroups

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

subgroupindex
C2×#669312
C11×#3972
#106225922
#106225662
#106225652
#106225562
#106222732
#106222712
#106222692
#281711