Finite Group Databasebeta

← #13079345

Subgroups — #13079345

Order 1408.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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#10623010C212yesmaximal, complemented
2C4×C11×M16C211yesmaximal, characteristic, complemented
3#10622750C211yesmaximal, characteristic, complemented
4#10622748C211yesmaximal, characteristic
5#10622747C212yesmaximal, complemented
6#10622329C211yesmaximal, characteristic, complemented
7#10622324C211yesmaximal, characteristic, complemented
8#10622323C212yesmaximal, complemented
9#10622310C212yesmaximal, complemented
10#10622309C211yesmaximal, characteristic, complemented
11#10622296C211yesmaximal, characteristic, complemented
12C2×C11×M16C2211yescharacteristic
13C2×C11×M16C2211yescharacteristic
14C2×C42×C11C2211yescharacteristic
15#66983C2212yes—
16#66982—22no—
17C4×C22⋊D11—22no—
18#66977C2212yes—
19C2×Dic44C2211yescharacteristic
20C2×D88C2211yescharacteristic
21C2×#4314C2212yes—
22#66929—22no—
23#66928C2212yes—
24C4×D44C2212yes—
25#66925—22no—
26#66923C2212yes—
27C4×Dic22C2212yes—
28C11×#97C2211yescharacteristic
29C11×#97C2211yescharacteristic
30C4×C8×C11C2211yescharacteristic
31C4×C8×C11C2211yescharacteristic
32#66885C2212yes—
33#66885C2212yes—
34#66882C2212yes—
35#66881C2211yescharacteristic
36#66881C2211yescharacteristic
37#66880C2212yes—
38#66880C2212yes—
39C22×C4×C11D412yes—
40C22×C4×C11C2311yescharacteristic
41C2×C22⋊D11—22no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×Dic22C2312yes—
45C11×M16—22no—
46C11×M16—22no—
47C2×C8×C11C2311yescharacteristic
48C2×C8×C11C2311yescharacteristic
49C2×C8×C11C2311yescharacteristic
50C2×C8×C11C2311yescharacteristic
51C42×C11D412yes—
52C42×C11C2311yescharacteristic
53C42×C11C2311yescharacteristic
54C22⋊Dic11—22no—
55(C2×D11)⋊C4—22no—
56(C2×D11)⋊C4—22no—
57(C2×D11)⋊C4—22no—
58(C2×D11)⋊C4—22no—
59C4⋊Dic11C2312yes—
60C4⋊Dic11C2312yes—
61Dic11⋊C4—22no—
62Dic11⋊C4—22no—
63Dic11⋊C4—22no—
64Dic11⋊C4—22no—
65C4×Dic11—22no—
66Dic44—22no—
67D88—22no—
68#4314—24no—
69#3183—111nomaximal, Sylow
70C23×C11C2×D411yescharacteristic
71C22×D11—22no—
72C2×C4×C11—21no—
73C2×C4×C11—21no—
74C2×C4×C11—42no—
75C2×C4×C11C2×D412yes—
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D412yes—
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—44no—
80C2×Dic11—22no—
81C2×Dic11—22no—
82C2×Dic11—22no—
83D44—22no—
84D44—22no—
85C4×D11—44no—
86Dic22—22no—
87Dic22—22no—
88C8×C11—21no—
89C8×C11—21no—
90C8×C11#4112yes—
91C8×C11#4112yes—
92#529—112no—
93#499—111no—
94#495—111no—
95#488—112no—
96#470—111no—
97#469—111no—
98#468—112no—
99#442—111no—
100#441—111no—
101#440—112no—
102C4×M16D1111yescharacteristic, complemented
103C22×C11—21no—
104C22×C11—22no—
105C22×C11C22×D411yescharacteristic
106C2×D11—42no—
107C2×D11—42no—
108C2×D11—42no—
109C4×C11—21no—
110C4×C11—22no—
111C4×C11—22no—
112C4×C11C2×#4111yescharacteristic
113C4×C11C2×#4111yescharacteristic
114Dic11—42no—
115Dic11—42no—
116Dic11—42no—
117C2×Q16—111no—
118C2×SD16—112no—
119C2×D8—111no—
120C2×M16C2×D1111yescharacteristic
121C2×M16C2×D1111yescharacteristic
122#126—222no—
123#125—112no—
124#124—112no—
125#123—222no—
126C22⋊Q8—112no—
127#121—112no—
128C4×Q8—112no—
129C4×D4—112no—
130C4×D4—222no—
131#117—222no—
132C2×C42C2×D1111yescharacteristic
133#107—112no—
134#106—111no—
135#106—111no—
136#103—112no—
137#103—112no—
138#102—112no—
139#102—112no—
140#97C2×D1111yescharacteristic
141#97C2×D1111yescharacteristic
142C4×C8C2×D1111yescharacteristic
143C4×C8C2×D1111yescharacteristic
144C2×C11—41no—
145C2×C11#53211yescharacteristic
146C2×C11#57512yes—
147D11—82no—
148C2×Q8—112no—
149C2×D4—112no—
150C2×D4—222no—
151C22×C4—222no—
152C22×C4D4412yes—
153C22×C4C22×D1111yescharacteristic
154Q16—222no—
155SD16—224no—
156D8—222no—
157M16—22no—
158M16—22no—
159C2×C8C22×D1111yescharacteristic
160C2×C8C22×D1111yescharacteristic
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—222no—
170C22⋊C4—222no—
171C22⋊C4—222no—
172C22⋊C4—222no—
173C22⋊C4—222no—
174C42—222no—
175C42D4412yes—
176C42C22×D1111yescharacteristic
177C42C22×D1111yescharacteristic
178C11#318311yescharacteristic, complemented, Sylow
179C23—222no—
180C23C2×D4411yescharacteristic
181Q8—222no—
182Q8—222no—
183D4—222no—
184D4—222no—
185D4—444no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—42no—
189C2×C4—222no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—444no—
193C2×C4C2×D4412yes—
194C2×C4C2×D4412yes—
195C2×C4C2×D4411yescharacteristic
196C2×C4C23×D1111yescharacteristic
197C8—21no—
198C8—21no—
199C8#433912yes—
200C8#433912yes—
201C22—21no—
202C22—22no—
203C22—442no—
204C22—442no—
205C22—442no—
206C22C22×D4411yescharacteristic
207C4—21no—
208C4—22no—
209C4—22no—
210C4—442no—
211C4—442no—
212C4—442no—
213C4C2×#433911yescharacteristic
214C4C2×#433911yescharacteristic
215C2—41no—
216C2—882no—
217C2#1062300811yescharacteristic
218C2#1062327912yes—
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC4×C11×M16C2
socleC22×C11C22×D4
prime radical#10622748C2
hypercenterC4×M16D11
hypocenterC11#3183
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
1. #10623010C2semidirect
2. C4×C11×M16C2semidirect
3. #10622750C2semidirect
5. #10622747C2semidirect
6. #10622329C2semidirect
7. #10622324C2semidirect
8. #10622323C2semidirect
9. #10622310C2semidirect
10. #10622309C2semidirect
11. #10622296C2semidirect
102. C4×M16D11semidirect
178. C11#3183semidirect

Maximal subgroups

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

subgroupindex
#106230102
C4×C11×M162
#106227502
#106227482
#106227472
#106223292
#106223242
#106223232
#106223102
#106223092
#106222962
#318311