Finite Group Databasebeta

← #13079342

Subgroups — #13079342

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#10623211C212yesmaximal, complemented
2C11×#495C211yesmaximal, characteristic, complemented
3#10622802C211yesmaximal, characteristic, complemented
4#10622797C211yesmaximal, characteristic, complemented
5#10622787C212yesmaximal, complemented
6#10622777C212yesmaximal, complemented
7#10622772C211yesmaximal, characteristic
8#10622765C211yesmaximal, characteristic, complemented
9#10622669C212yesmaximal, complemented
10C4×#4313C211yesmaximal, characteristic, complemented
11#10622296C211yesmaximal, characteristic, complemented
12C2×C11×Q16C2211yescharacteristic
13C2×C11×SD16C2212yes—
14C2×C11×D8C2211yescharacteristic
15C11×#124C2212yes—
16#66999C2212yes—
17Q8×Dic11C2212yes—
18#66991C2212yes—
19D4×Dic11C2212yes—
20C2×#4313C2211yescharacteristic
21C2×#4313C2211yescharacteristic
22#66936—22no—
23(C22⋊D11)⋊C4—22no—
24#66932—22no—
25#66930—22no—
26C42×D11C2211yescharacteristic
27#66923C2212yes—
28C4×C8×C11C2211yescharacteristic
29#66899C2212yes—
30#66899C2212yes—
31#66896C2212yes—
32#66896C2212yes—
33#66882C2212yes—
34#66881C2211yescharacteristic
35#66881C2211yescharacteristic
36#66879C2211yescharacteristic
37#66879C2211yescharacteristic
38C4×C11⋊C8C2211yescharacteristic
39C2×Q8×C11C2312yes—
40C2×D4×C11C2312yes—
41C2×C22⋊D11—22no—
42C22×Dic11—22no—
43C2×C4×D11D412yes—
44C2×C4×D11C2311yescharacteristic
45C11×Q16—22no—
46C11×SD16—24no—
47C11×D8—22no—
48C2×C8×C11C2311yescharacteristic
49C2×C8×C11C2311yescharacteristic
50C11×C22⋊C4—22no—
51C11×C22⋊C4—22no—
52C42×C11C2311yescharacteristic
53C22⋊Dic11—22no—
54C22⋊Dic11—22no—
55(C2×D11)⋊C4—22no—
56C4⋊Dic11—22no—
57C4⋊Dic11C2312yes—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61Dic11⋊C4—22no—
62C4×Dic11—22no—
63C4×Dic11D412yes—
64C4×Dic11C2311yescharacteristic
65C2×C11⋊C8C2311yescharacteristic
66C2×C11⋊C8C2311yescharacteristic
67#4313—22no—
68#4313—22no—
69#3183—111nomaximal, Sylow
70C23×C11—22no—
71C22×D11C2×D411yescharacteristic
72Q8×C11—22no—
73Q8×C11—22no—
74D4×C11—22no—
75D4×C11—22no—
76C2×C4×C11—22no—
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—44no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—44no—
83C2×Dic11C2×D412yes—
84C2×Dic11C2×D411yescharacteristic
85C4×D11—21no—
86C4×D11—21no—
87C4×D11—42no—
88C8×C11#4112yes—
89C8×C11#4112yes—
90C11⋊C8—21no—
91C11⋊C8—21no—
92#529—112no—
93#499—111no—
94#495D1111yescharacteristic, complemented
95#488—112no—
96#470—111no—
97#469—111no—
98#468—112no—
99#442—111no—
100#441—111no—
101#440—112no—
102C4×M16—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×Q16C2×D1111yescharacteristic
118C2×SD16C2×D1112yes—
119C2×D8C2×D1111yescharacteristic
120C2×M16—111no—
121C2×M16—111no—
122#126—222no—
123#125—112no—
124#124C2×D1112yes—
125#123—222no—
126C22⋊Q8—112no—
127#121—112no—
128C4×Q8—112no—
129C4×D4—112no—
130C4×D4—222no—
131#117—222no—
132C2×C42—111no—
133#107—112no—
134#106—111no—
135#106—111no—
136#103—112no—
137#103—112no—
138#102—112no—
139#102—112no—
140#97—111no—
141#97—111no—
142C4×C8—111no—
143C4×C8C2×D1111yescharacteristic
144C2×C11—82no—
145C2×C11#53211yescharacteristic
146C2×C11#57512yes—
147D11—41no—
148C2×Q8C22×D1112yes—
149C2×D4—222no—
150C2×D4C22×D1112yes—
151C22×C4—111no—
152C22×C4—112no—
153C22×C4—222no—
154Q16—22no—
155SD16—24no—
156D8—22no—
157M16—222no—
158M16—222no—
159C2×C8—111no—
160C2×C8—111no—
161C2×C8C22×D1111yescharacteristic
162C2×C8C22×D1111yescharacteristic
163C4⋊C4—112no—
164C4⋊C4—112no—
165C4⋊C4—222no—
166C4⋊C4—222no—
167C4⋊C4—222no—
168C4⋊C4—222no—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—112no—
175C42—111no—
176C42—222no—
177C42C22×D1111yescharacteristic
178C11#318311yescharacteristic, complemented, Sylow
179C23—22no—
180C23—111no—
181Q8—22no—
182Q8—22no—
183D4—22no—
184D4—22no—
185D4—444no—
186C2×C4—22no—
187C2×C4—112no—
188C2×C4—111no—
189C2×C4—221no—
190C2×C4—221no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—442no—
194C2×C4—444no—
195C2×C4D4×D1112yes—
196C2×C4C23×D1111yescharacteristic
197C8—221no—
198C8—221no—
199C8#434112yes—
200C8#434112yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—221no—
205C22—222no—
206C22C2×D4×D1111yescharacteristic
207C4—22no—
208C4—42no—
209C4—221no—
210C4—222no—
211C4—442no—
212C4—442no—
213C4C2×#434111yescharacteristic
214C4C2×#434111yescharacteristic
215C2—82no—
216C2—441no—
217C2#1062324711yescharacteristic
218C2#1062329912yes—
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#495C2
socleC22×C11C22×D4
prime radical#10622772C2
hypercenter#495D11
hypocenterC11#3183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #10623211C2semidirect
2. C11×#495C2semidirect
3. #10622802C2semidirect
4. #10622797C2semidirect
5. #10622787C2semidirect
6. #10622777C2semidirect
8. #10622765C2semidirect
9. #10622669C2semidirect
10. C4×#4313C2semidirect
11. #10622296C2semidirect
94. #495D11semidirect
178. C11#3183semidirect

Maximal subgroups

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

subgroupindex
#106232112
C11×#4952
#106228022
#106227972
#106227872
#106227772
#106227722
#106227652
#106226692
C4×#43132
#106222962
#318311