Finite Group Databasebeta

← #13074277

Subgroups — #13074277

Order 1408.

444 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4×C11×C22⋊C4C211yesmaximal, characteristic
2#10622824C211yesmaximal, characteristic
3C4×C22⋊Dic11C211yesmaximal, characteristic
4#10622562C212yesmaximal
5#10622560C212yesmaximal
6#10622546C212yesmaximal, complemented
7#10622542C212yesmaximal, complemented
8#10622267C212yesmaximal, complemented
9#10622259C212yesmaximal, complemented
10C23×C4×C11C2211yescharacteristic
11C22×Dic22C2212yes—
12C2×C11×C22⋊C4C2212yes—
13C2×C42×C11C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15C2×C22⋊Dic11C2212yes—
16C2×C22⋊Dic11C2211yescharacteristic
17C2×C22⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2212yes—
19C2×Dic11⋊C4C2212yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2211yescharacteristic
22C2×C4×Dic11C2211yescharacteristic
23C11×#95C2212yes—
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2212yes—
29C11⋊#95C2212yes—
30C11⋊#95C2212yes—
31C24×C11C2311yescharacteristic
32C22×C4×C11—41no—
33C22×C4×C11—41no—
34C22×C4×C11Q814yescomplemented
35C22×C4×C11C2312yes—
36C22×C4×C11C2311yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C22×C4×C11C2312yes—
39C22×Dic11C2312yes—
40C22×Dic11C2312yes—
41C22×Dic11C2312yes—
42C22×Dic11C2312yes—
43C2×Dic22—24no—
44C2×Dic22—24no—
45C2×Dic22—42no—
46C11×C22⋊C4—24no—
47C42×C11—41no—
48C42×C11—41no—
49C22⋊Dic11—24no—
50C22⋊Dic11—41no—
51C22⋊Dic11—41no—
52C4⋊Dic11—24no—
53Dic11⋊C4—24no—
54Dic11⋊C4—42no—
55C4×Dic11—41no—
56C4×Dic11—41no—
57#2607—111nomaximal, Sylow
58C23×C11—22no—
59C23×C11—22no—
60C23×C11—21no—
61C23×C11—21no—
62C23×C11C2×Q812yes—
63C23×C11C2411yescharacteristic
64C2×C4×C11—22no—
65C2×C4×C11—21no—
66C2×C4×C11—21no—
67C2×C4×C11—22no—
68C2×C4×C11—21no—
69C2×C4×C11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11—44no—
74C2×C4×C11C2×Q812yes—
75C2×C4×C11C2×Q812yes—
76C2×C4×C11#4114yes—
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—22no—
86C2×Dic11—22no—
87C2×Dic11—22no—
88C2×Dic11#4114yes—
89Dic22—48no—
90#399—112no—
91#393—112no—
92#391—112no—
93#391—112no—
94#387—112no—
95#387—112no—
96#381—111no—
97C4×C22⋊C4—111no—
98C4×C22⋊C4D1111yescharacteristic
99C22×C11—22no—
100C22×C11—22no—
101C22×C11—22no—
102C22×C11—42no—
103C22×C11—42no—
104C22×C11C22×Q811yescharacteristic
105C22×C11C2×#4112yes—
106C22×C11C2×#4112yes—
107C22×C11H(5,𝔽2)11yescharacteristic
108C22×C11H(5,𝔽2)11yescharacteristic
109C4×C11—22no—
110C4×C11—22no—
111C4×C11—24no—
112C4×C11—42no—
113Dic11—24no—
114Dic11—42no—
115Dic11—42no—
116Dic11—42no—
117C22×Q8—112no—
118C23×C4C2×D1111yescharacteristic
119C2×C4⋊C4—112no—
120C2×C4⋊C4—112no—
121C2×C4⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—111no—
124C2×C22⋊C4—111no—
125C2×C22⋊C4C2×D1112yes—
126C2×C42—111no—
127C2×C42—111no—
128C2×C42C2×D1111yescharacteristic
129C2×C42C2×D1111yescharacteristic
130#95—112no—
131#95—112no—
132#95—112no—
133#95—112no—
134#95—112no—
135#95—112no—
136#95—112no—
137#95C2×D1112yes—
138C2×C11—42no—
139C2×C11#53311yescharacteristic
140C2×C11#53311yescharacteristic
141C2×C11#54311yescharacteristic
142C2×C11#55112yes—
143C2×C11#55912yes—
144C24C22×D1111yescharacteristic
145C2×Q8—224no—
146C2×Q8—224no—
147C2×Q8—442no—
148C22×C4—41no—
149C22×C4—41no—
150C22×C4—112no—
151C22×C4—112no—
152C22×C4—112no—
153C22×C4—112no—
154C22×C4Dic2214yescomplemented
155C22×C4C22×D1112yes—
156C22×C4C22×D1111yescharacteristic
157C22×C4C22×D1111yescharacteristic
158C22×C4C22×D1112yes—
159C4⋊C4—224no—
160C4⋊C4—224no—
161C4⋊C4—442no—
162C22⋊C4—24no—
163C22⋊C4—224no—
164C22⋊C4—441no—
165C22⋊C4—441no—
166C42—41no—
167C42—41no—
168C42—441no—
169C42—441no—
170C11#260711yescharacteristic, complemented, Sylow
171C23—22no—
172C23—21no—
173C23—21no—
174C23—22no—
175C23C2×Dic2212yes—
176C23C23×D1111yescharacteristic
177Q8—448no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—44no—
188C2×C4—114no—
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—222no—
199C2×C4—222no—
200C2×C4C2×Dic2212yes—
201C2×C4C2×Dic2212yes—
202C2×C4#433914yes—
203C22—22no—
204C22—22no—
205C22—22no—
206C22—42no—
207C22—42no—
208C22C22×Dic2211yescharacteristic
209C22C2×#433912yes—
210C22#6703711yescharacteristic
211C22#6703711yescharacteristic
212C22#41×D1112yes—
213C4—22no—
214C4—22no—
215C4—24no—
216C4—42no—
217C4—224no—
218C4—442no—
219C4—442no—
220C4—442no—
221C2—42no—
222C2#1062300111yescharacteristic
223C2#1062301411yescharacteristic
224C2#1062304811yescharacteristic
225C2#1062308712yes—
226C2#1062309012yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC4×C11×C22⋊C4C2
prime radicalC24×C11C23
hypercenterC4×C22⋊C4D11
hypocenterC11#2607
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
6. #10622546C2semidirect
7. #10622542C2semidirect
8. #10622267C2semidirect
9. #10622259C2semidirect
34. C22×C4×C11Q8semidirect
154. C22×C4Dic22semidirect
170. C11#2607semidirect

Maximal subgroups

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

subgroupindex
C4×C11×C22⋊C42
#106228242
C4×C22⋊Dic112
#106225622
#106225602
#106225462
#106225422
#106222672
#106222592
#260711