Finite Group Databasebeta

← #13079231

Subgroups — #13079231

Order 1408.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#10623092C212yesmaximal, complemented
2C11×#442C211yesmaximal, characteristic, complemented
3#10622772C211yesmaximal, characteristic
4#10622768C211yesmaximal, characteristic, complemented
5C4×#4324C212yesmaximal, complemented
6#10622481C211yesmaximal, characteristic, complemented
7#10622468C211yesmaximal, characteristic, complemented
8#10622391C212yesmaximal, complemented
9#10622378C212yesmaximal, complemented
10#10622329C211yesmaximal, characteristic, complemented
11#10622321C211yesmaximal, characteristic, complemented
12C2×C11×D8C2211yescharacteristic
13C4×D4×C11C2212yes—
14#66991C2212yes—
15#66989C2212yes—
16C2×#4324C2212yes—
17#66982—22no—
18#66977—22no—
19C2×Dic44C2211yescharacteristic
20C2×#4313C2211yescharacteristic
21C2×C8×D11C2211yescharacteristic
22#66950C2212yes—
23#66941C2212yes—
24#66938—22no—
25#66932—22no—
26#66925C2211yescharacteristic
27C4×Dic22C2212yes—
28C11×#106C2211yescharacteristic
29C11×#102C2212yes—
30C11×#97C2211yescharacteristic
31#66896C2212yes—
32#66881C2211yescharacteristic
33#66880C2212yes—
34#66879C2211yescharacteristic
35C8×Dic11C2211yescharacteristic
36#66874C2212yes—
37#66872C2212yes—
38C4×C11⋊C8C2211yescharacteristic
39C2×D4×C11C2312yes—
40C22×C4×C11—22no—
41C2×C22⋊D11—22no—
42C2×C4×D11C2311yescharacteristic
43C2×Dic22—22no—
44C2×Dic22C2312yes—
45C11×D8—22no—
46C2×C8×C11C2311yescharacteristic
47C2×C8×C11C2311yescharacteristic
48C11×C4⋊C4C2312yes—
49C11×C22⋊C4—22no—
50C42×C11C2311yescharacteristic
51C22⋊Dic11—22no—
52C22⋊Dic11—22no—
53C22⋊Dic11—22no—
54#4324—24no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4D412yes—
57C4⋊Dic11—22no—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4D412yes—
62C4×Dic11—22no—
63C4×Dic11C2311yescharacteristic
64C2×C11⋊C8C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66Dic44—22no—
67#4313—22no—
68C8×D11—22no—
69#3173—111nomaximal, Sylow
70C23×C11—22no—
71C22×D11C2×D411yescharacteristic
72D4×C11—22no—
73D4×C11—22no—
74C2×C4×C11—22no—
75C2×C4×C11—82no—
76C2×C4×C11C2×D412yes—
77C2×C4×C11C2411yescharacteristic
78C22⋊D11—82no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11C2×D412yes—
82C2×Dic11C2×D411yescharacteristic
83C4×D11—21no—
84C4×D11—21no—
85Dic22—22no—
86Dic22—22no—
87Dic22—82no—
88C8×C11—21no—
89C8×C11#4112yes—
90C11⋊C8—21no—
91C11⋊C8#4112yes—
92#542—112no—
93#498—111no—
94#495—111no—
95#489—112no—
96#470—111no—
97#469—111no—
98#465—112no—
99#442D1111yescharacteristic, complemented
100#441—111no—
101C4×SD16—112no—
102#405—111no—
103C22×C11—42no—
104C22×C11—42no—
105C22×C11—42no—
106C22×C11C22×D411yescharacteristic
107C2×D11—21no—
108C2×D11—22no—
109C4×C11—22no—
110C4×C11—42no—
111C4×C11C2×#4111yescharacteristic
112C4×C11C2×#4111yescharacteristic
113Dic11—21no—
114Dic11—22no—
115Dic11—42no—
116Dic11—42no—
117C2×Q16—111no—
118C2×SD16—112no—
119C2×D8C2×D1111yescharacteristic
120C2×M16—111no—
121C22×C8—111no—
122C4⋊Q8—112no—
123#126—222no—
124#124—112no—
125#124—222no—
126#123—222no—
127C22⋊Q8—112no—
128C22⋊Q8—222no—
129#121—112no—
130C4×Q8—112no—
131C4×D4C2×D1112yes—
132#117—111no—
133#106—111no—
134#106—112no—
135#106C2×D1111yescharacteristic
136#103—112no—
137#103—112no—
138#102—112no—
139#102C2×D1112yes—
140#97—111no—
141#97C2×D1111yescharacteristic
142C4×C8—111no—
143C4×C8—111no—
144C2×C11—82no—
145C2×C11#53211yescharacteristic
146C2×C11#57712yes—
147D11—41no—
148C2×Q8—112no—
149C2×Q8—222no—
150C2×D4—222no—
151C2×D4C22×D1112yes—
152C22×C4—22no—
153C22×C4—111no—
154Q16—222no—
155SD16—224no—
156D8—22no—
157M16—222no—
158C2×C8—111no—
159C2×C8—111no—
160C2×C8—222no—
161C2×C8C22×D1111yescharacteristic
162C2×C8C22×D1111yescharacteristic
163C4⋊C4—112no—
164C4⋊C4—112no—
165C4⋊C4—222no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4C22×D1112yes—
169C22⋊C4—22no—
170C22⋊C4—112no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C22⋊C4—222no—
175C42—111no—
176C42—222no—
177C42C22×D1111yescharacteristic
178C11#317311yescharacteristic, complemented, Sylow
179C23—22no—
180C23—111no—
181Q8—222no—
182Q8—222no—
183Q8—882no—
184D4—22no—
185D4—22no—
186D4—882no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—112no—
190C2×C4—111no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—222no—
194C2×C4—222no—
195C2×C4D4×D1112yes—
196C2×C4C23×D1111yescharacteristic
197C8—21no—
198C8—112no—
199C8—221no—
200C8#433912yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—222no—
205C22—221no—
206C22C2×D4×D1111yescharacteristic
207C4—22no—
208C4—42no—
209C4—222no—
210C4—221no—
211C4—442no—
212C4—442no—
213C4C2×#433911yescharacteristic
214C4#41×D1111yescharacteristic
215C2—82no—
216C2—441no—
217C2#1062307911yescharacteristic
218C2#1062330612yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#442C2
socleC22×C11C22×D4
prime radical#10622772C2
hypercenter#442D11
hypocenterC11#3173
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #10623092C2semidirect
2. C11×#442C2semidirect
4. #10622768C2semidirect
5. C4×#4324C2semidirect
6. #10622481C2semidirect
7. #10622468C2semidirect
8. #10622391C2semidirect
9. #10622378C2semidirect
10. #10622329C2semidirect
11. #10622321C2semidirect
99. #442D11semidirect
178. C11#3173semidirect

Maximal subgroups

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

subgroupindex
#106230922
C11×#4422
#106227722
#106227682
C4×#43242
#106224812
#106224682
#106223912
#106223782
#106223292
#106223212
#317311