Finite Group Databasebeta

← #13073526

Subgroups — #13073526

Order 1408.

604 conjugacy classes of subgroups; only the 161 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 161 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×#66950C212yesmaximal, complemented
2C2×C4×D44C211yesmaximal, characteristic
3C2×C4×Dic22C211yesmaximal, characteristic, complemented
4C11×#382C211yesmaximal, characteristic, complemented
5#10622600C212yesmaximal, complemented
6#10622285C212yesmaximal
7#10622283C214yesmaximal, complemented
8#10622274C212yesmaximal, complemented
9C22×D44C2211yescharacteristic
10C22×C4×D11C2212yes—
11C22×Dic22C2211yescharacteristic
12C2×C11×C4⋊C4C2212yes—
13C2×C42×C11C2211yescharacteristic
14C2×(C2×D11)⋊C4C2212yes—
15C2×(C2×D11)⋊C4C2214yes—
16C2×(C2×D11)⋊C4C2214yes—
17C2×C4⋊Dic11C2211yescharacteristic
18C2×C4⋊Dic11C2211yescharacteristic
19C2×C4⋊Dic11C2214yes—
20C2×Dic11⋊C4C2212yes—
21C2×C4×Dic11C2212yes—
22#66950—28no—
23C4×D44—24no—
24C4×Dic22—24no—
25C11×#95C2212yes—
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C23×D11C2312yes—
29C22×C4×C11C2314yes—
30C22×C4×C11C2311yescharacteristic
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×Dic11C2312yes—
34C22×Dic11C2312yes—
35C22×Dic11C2312yes—
36C2×D44—24no—
37C2×D44—22no—
38C2×C4×D11—24no—
39C2×C4×D11—24no—
40C2×C4×D11—24no—
41C2×Dic22—22no—
42C2×Dic22—22no—
43C2×Dic22D414yescomplemented
44C11×C4⋊C4—24no—
45C42×C11D414yes—
46(C2×D11)⋊C4—28no—
47(C2×D11)⋊C4—28no—
48(C2×D11)⋊C4—24no—
49C4⋊Dic11—28no—
50C4⋊Dic11—22no—
51C4⋊Dic11—22no—
52Dic11⋊C4—24no—
53C4×Dic11—24no—
54#2536—111nomaximal, Sylow
55C23×C11C2411yescharacteristic
56C22×D11—22no—
57C22×D11—22no—
58C22×D11—22no—
59C22×D11—22no—
60C22×D11—22no—
61C22×D11—22no—
62C22×D11#4114yes—
63C2×C4×C11—22no—
64C2×C4×C11—22no—
65C2×C4×C11—24no—
66C2×C4×C11—24no—
67C2×C4×C11—24no—
68C2×C4×C11C2×D412yes—
69C2×C4×C11C2×D412yes—
70C2×C4×C11C2×D412yes—
71C2×C4×C11C2×D412yes—
72C2×C4×C11#4112yes—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11—22no—
78C2×Dic11—24no—
79C2×Dic11—22no—
80C2×Dic11C2×D414yes—
81D44—28no—
82C4×D11—48no—
83Dic22—28no—
84C2×C22⋊Q8—112no—
85C2×C4×Q8—111no—
86C2×C4×D4—111no—
87#398—112no—
88#394—112no—
89#388—114no—
90#382D1111yescharacteristic, complemented
91#380—112no—
92C22×C11C22×D411yescharacteristic
93C22×C11C22×D411yescharacteristic
94C22×C11C2×#4111yescharacteristic
95C22×C11C2×#4112yes—
96C22×C112−1+412yes—
97C2×D11—24no—
98C2×D11—24no—
99C2×D11—24no—
100C2×D11—42no—
101C2×D11—42no—
102C2×D11—42no—
103C2×D11—42no—
104C4×C11—22no—
105C4×C11—22no—
106C4×C11—44no—
107C4×C11#12114yes—
108Dic11—24no—
109Dic11—42no—
110Dic11—42no—
111C22×Q8—111no—
112C22×D4—111no—
113C23×C4—112no—
114C22⋊Q8—228no—
115C4×Q8—224no—
116C4×D4—224no—
117C2×C4⋊C4—111no—
118C2×C4⋊C4—111no—
119C2×C4⋊C4—112no—
120C2×C4⋊C4—114no—
121C2×C4⋊C4C2×D1112yes—
122C2×C22⋊C4—112no—
123C2×C22⋊C4—114no—
124C2×C22⋊C4—114no—
125C2×C42—112no—
126C2×C42C2×D1111yescharacteristic
127#95—114no—
128#95C2×D1112yes—
129#95C2×D1112yes—
130C2×C11C2×#12111yescharacteristic
131C2×C11#52511yescharacteristic
132C2×C11#53611yescharacteristic
133C2×C11#54812yes—
134C2×C11#55212yes—
135D11—44no—
136C24—112no—
137C2×Q8—114no—
138C2×Q8—222no—
139C2×Q8—222no—
140C2×D4—224no—
141C2×D4—222no—
142C22×C4—112no—
143C22×C4—112no—
144C22×C4—112no—
145C22×C4—224no—
146C22×C4—224no—
147C22×C4—224no—
148C22×C4C22×D1114yes—
149C22×C4C22×D1111yescharacteristic
150C22×C4C22×D1111yescharacteristic
151C22×C4C22×D1111yescharacteristic
152C4⋊C4—24no—
153C4⋊C4—228no—
154C4⋊C4—222no—
155C4⋊C4—224no—
156C4⋊C4—222no—
157C22⋊C4—228no—
158C22⋊C4—228no—
159C22⋊C4—224no—
160C42—224no—
161C42D4414yes—
162C11#253611yescharacteristic, complemented, Sylow
163C23—114no—
164C23—222no—
165C23—222no—
166C23—222no—
167C23—222no—
168C23—222no—
169C23—222no—
170C23C23×D1111yescharacteristic
171Q8—228no—
172D4—228no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—24no—
178C2×C4—114no—
179C2×C4—222no—
180C2×C4—222no—
181C2×C4—222no—
182C2×C4—222no—
183C2×C4—222no—
184C2×C4—222no—
185C2×C4—224no—
186C2×C4—448no—
187C2×C4C2×D4412yes—
188C2×C4C2×D4412yes—
189C2×C4C2×D4412yes—
190C2×C4D4×D1112yes—
191C2×C4#434312yes—
192C22—224no—
193C22—224no—
194C22—224no—
195C22—442no—
196C22—442no—
197C22—442no—
198C22—442no—
199C22C22×D4411yescharacteristic
200C22C2×D4×D1111yescharacteristic
201C22C2×#434311yescharacteristic
202C22#41×D1112yes—
203C22#6704312yes—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—224no—
208C4—442no—
209C4—442no—
210C4#6694814yes—
211C2—444no—
212C2C2×#6694811yescharacteristic
213C2#1062305511yescharacteristic
214C2#1062305711yescharacteristic
215C2#1062320812yes—
216C2#1062322512yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#382C2
prime radicalC22×D44C22
hypercenter#382D11
hypocenterC11#2536
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
1. C2×#66950C2semidirect
3. C2×C4×Dic22C2semidirect
4. C11×#382C2semidirect
5. #10622600C2semidirect
7. #10622283C2semidirect
8. #10622274C2semidirect
43. C2×Dic22D4semidirect
90. #382D11semidirect
162. C11#2536semidirect

Maximal subgroups

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

subgroupindex
C2×#669502
C2×C4×D442
C2×C4×Dic222
C11×#3822
#106226002
#106222852
#106222832
#106222742
#253611