Finite Group Databasebeta

← #13074405

Subgroups — #13074405

Order 1408.

548 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 149 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×#117C211yesmaximal, characteristic, complemented
2C2×#66983C211yesmaximal, characteristic
3#10622825C211yesmaximal, characteristic, complemented
4#10622606C212yesmaximal, complemented
5#10622605C212yesmaximal, complemented
6#10622572C214yesmaximal, complemented
7#10622552C212yesmaximal, complemented
8#10622541C212yesmaximal, complemented
9C23×C4×C11C2211yescharacteristic
10C22×C22⋊D11C2212yes—
11C22×D44C2211yescharacteristic
12C11×#117—24no—
13C2×C11×C4⋊C4C2211yescharacteristic
14C2×C11×C4⋊C4C2211yescharacteristic
15C2×C11×C22⋊C4C2212yes—
16C2×C42×C11C2212yes—
17C2×C22⋊Dic11C2212yes—
18#66983—24no—
19C2×(C2×D11)⋊C4C2212yes—
20C2×(C2×D11)⋊C4C2214yes—
21C2×(C2×D11)⋊C4C2214yes—
22C2×C4⋊Dic11C2211yescharacteristic
23C2×C4⋊Dic11C2212yes—
24C2×Dic11⋊C4C2214yes—
25C11⋊#95C2214yes—
26C11⋊#95C2212yes—
27C24×C11C2311yescharacteristic
28C23×D11C2312yes—
29C22×C4×C11—24no—
30C22×C4×C11D414yes—
31C22×C4×C11C2312yes—
32C22×C4×C11C2312yes—
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C2×C22⋊D11—24no—
36C2×C22⋊D11—44no—
37C22×Dic11C2312yes—
38C22×Dic11C2314yes—
39C2×D44—22no—
40C2×D44—24no—
41C11×C4⋊C4—22no—
42C11×C4⋊C4—22no—
43C11×C22⋊C4—24no—
44C42×C11—24no—
45C22⋊Dic11—42no—
46(C2×D11)⋊C4—24no—
47(C2×D11)⋊C4—44no—
48(C2×D11)⋊C4—44no—
49C4⋊Dic11—22no—
50C4⋊Dic11—24no—
51Dic11⋊C4—44no—
52#2624—111nomaximal, Sylow
53C23×C11—22no—
54C23×C11—21no—
55C23×C11—22no—
56C23×C11—21no—
57C23×C11C2×D412yes—
58C23×C11C2411yescharacteristic
59C22×D11—22no—
60C22×D11—24no—
61C22×D11—22no—
62C22×D11—24no—
63C22×D11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—28no—
66C2×C4×C11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11C2×D412yes—
73C2×C4×C11C2×D412yes—
74C2×C4×C11#4114yes—
75C22⋊D11—48no—
76C2×Dic11—22no—
77C2×Dic11—24no—
78C2×Dic11—24no—
79C2×Dic11—24no—
80C2×Dic11—24no—
81D44—44no—
82C2×#121—111no—
83C2×#117D1111yescharacteristic, complemented
84#399—112no—
85#397—112no—
86#394—114no—
87#390—112no—
88#389—112no—
89#380—111no—
90C22×C11—22no—
91C22×C11—22no—
92C22×C11—22no—
93C22×C11—42no—
94C22×C11—42no—
95C22×C11C22×D411yescharacteristic
96C22×C11C2×#4112yes—
97C22×C11H(5,𝔽2)12yes—
98C22×C11H(5,𝔽2)11yescharacteristic
99C22×C112−1+411yescharacteristic
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—44no—
104C2×D11—44no—
105C4×C11—22no—
106C4×C11—42no—
107C4×C11—42no—
108C4×C11#12314yes—
109Dic11—42no—
110Dic11—44no—
111C22×D4—112no—
112C22×D4—111no—
113C23×C4C2×D1111yescharacteristic
114#121—224no—
115#117—24no—
116C2×C4⋊C4—111no—
117C2×C4⋊C4—112no—
118C2×C4⋊C4—114no—
119C2×C4⋊C4C2×D1111yescharacteristic
120C2×C4⋊C4C2×D1111yescharacteristic
121C2×C22⋊C4—112no—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4—114no—
125C2×C22⋊C4C2×D1112yes—
126C2×C42C2×D1112yes—
127#95—112no—
128#95—114no—
129C2×C11—42no—
130C2×C11C2×#12311yescharacteristic
131C2×C11#53511yescharacteristic
132C2×C11#53711yescharacteristic
133C2×C11#54012yes—
134C2×C11#54212yes—
135D11—82no—
136C24—112no—
137C24C22×D1111yescharacteristic
138C2×D4—224no—
139C2×D4—224no—
140C2×D4—222no—
141C2×D4—444no—
142C22×C4—24no—
143C22×C4—114no—
144C22×C4—112no—
145C22×C4C22⋊D1114yes—
146C22×C4C22×D1112yes—
147C22×C4C22×D1112yes—
148C22×C4C22×D1111yescharacteristic
149C22×C4C22×D1111yescharacteristic
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—224no—
153C4⋊C4—222no—
154C4⋊C4—444no—
155C22⋊C4—24no—
156C22⋊C4—224no—
157C22⋊C4—444no—
158C22⋊C4—444no—
159C22⋊C4—442no—
160C42—24no—
161C11#262411yescharacteristic, complemented, Sylow
162C23—22no—
163C23—21no—
164C23—22no—
165C23—21no—
166C23—224no—
167C23—222no—
168C23—224no—
169C23—222no—
170C23—222no—
171C23C2×C22⋊D1112yes—
172C23C23×D1111yescharacteristic
173D4—448no—
174D4—444no—
175C2×C4—22no—
176C2×C4—28no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—224no—
184C2×C4—224no—
185C2×C4—224no—
186C2×C4—224no—
187C2×C4—222no—
188C2×C4#433914yes—
189C2×C4C2×C22⋊D1112yes—
190C2×C4C2×C22⋊D1112yes—
191C22—22no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—442no—
197C22—444no—
198C22—444no—
199C22—442no—
200C22—442no—
201C22C2×#433912yes—
202C22#6704212yes—
203C22#6704211yescharacteristic
204C22#6704311yescharacteristic
205C22C22×C22⋊D1111yescharacteristic
206C4—22no—
207C4—42no—
208C4—42no—
209C4—444no—
210C4—442no—
211C4#6698214yes—
212C2—42no—
213C2—882no—
214C2#1062306512yes—
215C2#1062306612yes—
216C2C2×#6698211yescharacteristic
217C2#1062336111yescharacteristic
218C2#1062336411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC2×C11×#117C2
prime radicalC2×#66983C2
hypercenterC2×#117D11
hypocenterC11#2624
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C11×#117C2semidirect
3. #10622825C2semidirect
4. #10622606C2semidirect
5. #10622605C2semidirect
6. #10622572C2semidirect
7. #10622552C2semidirect
8. #10622541C2semidirect
83. C2×#117D11semidirect
161. C11#2624semidirect

Maximal subgroups

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

subgroupindex
C2×C11×#1172
C2×#669832
#106228252
#106226062
#106226052
#106225722
#106225522
#106225412
#262411