Finite Group Databasebeta

← #13079755

Subgroups — #13079755

Order 1408.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#10623259C211yesmaximal, characteristic, complemented
2#10623256C211yesmaximal, characteristic
3C11×#500C211yesmaximal, characteristic, complemented
4#10622701C211yesmaximal, characteristic, complemented
5#10622692C211yesmaximal, characteristic, complemented
6#10622504C214yesmaximal, complemented
7#10622498C214yesmaximal, complemented
8#10622307C211yesmaximal, characteristic, complemented
9#10622298C211yesmaximal, characteristic, complemented
10C2×#4343—21no—
11C11×C4⋊Q8C2211yescharacteristic
12C11×C4⋊Q8C2211yescharacteristic
13#67000—21no—
14#66999—21no—
15Q8×Dic11—21no—
16#66950—21no—
17#66948—21no—
18#66948C2212yes—
19#66946—21no—
20#66946C2212yes—
21#66945C2212yes—
22#66943C2212yes—
23#66940—21no—
24#66927C2211yescharacteristic
25C42×D11C2211yescharacteristic
26#66922C2211yescharacteristic
27C11×#107C2214yes—
28C4×C8×C11C2211yescharacteristic
29#66885C2214yes—
30(C2×D11)⋊C8C2212yes—
31Dic11⋊C8C2212yes—
32#66873C2214yes—
33#66872C2214yes—
34C4×C11⋊C8C2211yescharacteristic
35C2×Q8×C11—21no—
36C2×Q8×C11—21no—
37#4343—44no—
38C2×D44—22no—
39C2×D44—21no—
40C2×D44—21no—
41C2×D44C2312yes—
42C2×C4×D11—22no—
43C2×C4×D11D411yescharacteristic
44C2×C4×D11D411yescharacteristic
45C2×C4×D11C2311yescharacteristic
46C2×Dic22—21no—
47C2×C8×C11C2312yes—
48C11×C4⋊C4—21no—
49C11×C4⋊C4—21no—
50C11×C4⋊C4C2312yes—
51C11×C4⋊C4C2312yes—
52C42×C11C2311yescharacteristic
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55(C2×D11)⋊C4—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11—21no—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60C4×Dic11—22no—
61C4×Dic11D411yescharacteristic
62C4×Dic11D411yescharacteristic
63C4×Dic11C2311yescharacteristic
64C2×C11⋊C8C2312yes—
65#3228—111nomaximal, Sylow
66C22×D11—22no—
67C22×D11C2×D411yescharacteristic
68Q8×C11—42no—
69Q8×C11—42no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2411yescharacteristic
75C2×Dic11—22no—
76C2×Dic11C2×D411yescharacteristic
77C2×Dic11C2×D411yescharacteristic
78C2×Dic11C2×D411yescharacteristic
79D44—24no—
80D44—44no—
81D44—42no—
82D44—42no—
83C4×D11—22no—
84C4×D11—22no—
85C4×D11—22no—
86C4×D11—44no—
87Dic22—42no—
88C8×C11—22no—
89C11⋊C8—22no—
90#533—111no—
91#532—111no—
92#500D1111yescharacteristic, complemented
93#498—111no—
94#486—111no—
95#486—111no—
96#482—114no—
97#478—114no—
98#431—111no—
99C22×C11C22×D411yescharacteristic
100C2×D11—21no—
101C2×D11—21no—
102C2×D11—21no—
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C4×C11—42no—
107C4×C11—42no—
108C4×C11#13512yes—
109C4×C11AGL(1,ℤ/8)12yes—
110C4×C112−1+412yes—
111Dic11—21no—
112Dic11—21no—
113Dic11—21no—
114Dic11—42no—
115C2×#41—221no—
116C4⋊Q8—111no—
117C4⋊Q8C2×D1111yescharacteristic
118C4⋊Q8C2×D1111yescharacteristic
119#127—111no—
120#125—112no—
121#124—221no—
122C22⋊Q8—221no—
123C22⋊Q8—221no—
124#121—112no—
125#121—221no—
126C4×Q8—221no—
127C4×Q8—221no—
128C4×D4—112no—
129C4×D4—221no—
130#117—112no—
131C2×C42—111no—
132#107C2×D1114yes—
133#106—114no—
134C4⋊C8—112no—
135#102—114no—
136#102—114no—
137C22⋊C8—112no—
138C4×C8—111no—
139C4×C8C2×D1111yescharacteristic
140C2×C11#53611yescharacteristic
141C2×C11C2×#13511yescharacteristic
142C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
143D11—41no—
144D11—82no—
145#41—444no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—221no—
149C2×D4—112no—
150C2×D4—222no—
151C2×D4—221no—
152C2×D4—221no—
153C22×C4—111no—
154C22×C4—111no—
155C22×C4—111no—
156C22×C4—222no—
157C2×C8—112no—
158C2×C8C22×D1112yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—112no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—221no—
165C4⋊C4C22×D1112yes—
166C4⋊C4C22×D1112yes—
167C22⋊C4—222no—
168C22⋊C4—222no—
169C22⋊C4—222no—
170C42—111no—
171C42—111no—
172C42—111no—
173C42—222no—
174C42C22×D1111yescharacteristic
175C11#322811yescharacteristic, complemented, Sylow
176C23—111no—
177C23—222no—
178Q8—42no—
179Q8—42no—
180Q8—442no—
181D4—224no—
182D4—444no—
183D4—442no—
184D4—442no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—111no—
188C2×C4—111no—
189C2×C4—111no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—222no—
194C2×C4—444no—
195C2×C4D4×D1111yescharacteristic
196C2×C4D4×D1111yescharacteristic
197C2×C4C23×D1111yescharacteristic
198C8—22no—
199C8—222no—
200C22—221no—
201C22—221no—
202C22—221no—
203C22—442no—
204C22—442no—
205C22—442no—
206C22C2×D4×D1111yescharacteristic
207C4—42no—
208C4—42no—
209C4—221no—
210C4—221no—
211C4—221no—
212C4—442no—
213C4#6696412yes—
214C4#6697212yes—
215C4#6704012yes—
216C2—441no—
217C2—882no—
218C2#1062325511yescharacteristic
219C2C2×#6696411yescharacteristic
220C2C2×#6697211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#500C2
socleC22×C11C22×D4
prime radical#10623256C2
hypercenter#500D11
hypocenterC11#3228
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #10623259C2semidirect
3. C11×#500C2semidirect
4. #10622701C2semidirect
5. #10622692C2semidirect
6. #10622504C2semidirect
7. #10622498C2semidirect
8. #10622307C2semidirect
9. #10622298C2semidirect
92. #500D11semidirect
175. C11#3228semidirect

Maximal subgroups

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

subgroupindex
#106232592
#106232562
C11×#5002
#106227012
#106226922
#106225042
#106224982
#106223072
#106222982
#322811