Finite Group Databasebeta

← #30599329

Subgroups — #30599329

Order 15616.

418 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461720C211yesmaximal, characteristic
2#21461716C211yesmaximal, characteristic
3#21460667C214yesmaximal
4#21448314C211yesmaximal, characteristic
5#16840734C2212yes—
6#16840705C2212yes—
7#16840642—22no—
8#16840640—22no—
9C2×#14519734C2211yescharacteristic
10#16839651—22no—
11#16839644—22no—
12C4×#11758196C412yescomplemented
13C4×#11758198C2212yes—
14C42×Dic61C411yescharacteristic, complemented
15C61×#376C411yescharacteristic, complemented
16C2×#11758217—22no—
17C2×C22⋊#6923—22no—
18#14519834—24no—
19(C2×#6923)⋊C4—24no—
20C22×C4×D61C2311yescharacteristic
21#14519734—24no—
22C2×#11758196—22no—
23C2×#11758196D412yes—
24C2×#11758198—22no—
25C2×#11758198D412yes—
26C2×C4×Dic61—22no—
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61C2×C412yes—
29#14519684—22no—
30#14519684—22no—
31C2×C42×C61C2×C411yescharacteristic
32C2×C42×C61C2×C412yes—
33#95×C61—22no—
34C23×D61C2×D411yescharacteristic
35C22×#6923—42no—
36C22×C4×C61—22no—
37C22×C4×C61C22⋊C412yes—
38C22×C4×C61C22×C411yescharacteristic
39C22×Dic61—22no—
40C22×Dic61C22⋊C412yes—
41C22×Dic61C2×D411yescharacteristic
42C2×C4×D61—42no—
43C2×C4×D61#4114yes—
44C22⋊#6923—44no—
45#11758217—44no—
46C2×#92420—42no—
47C42×C61—22no—
48C42×C61—42no—
49#11758198—24no—
50#11758198—44no—
51#11758196—24no—
52#11758196—44no—
53C4×Dic61—22no—
54C4×Dic61—44no—
55C4×Dic61—42no—
56C23×C61C2×C22⋊C411yescharacteristic
57C22×D61—22no—
58C22×D61—42no—
59C22×D61#12312yes—
60C2×#6923—82no—
61C2×#6923—84no—
62C2×C4×C61—22no—
63C2×C4×C61—22no—
64C2×C4×C61—42no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61#11712yes—
69C2×Dic61—22no—
70C2×Dic61—24no—
71C2×Dic61—22no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61—42no—
75C2×Dic61#12312yes—
76C4×D61—44no—
77#92420—82no—
78#8741—611nomaximal, Sylow
79C22×C61—22no—
80C22×C61#38111yescharacteristic
81C22×C61#41012yes—
82C2×D61—22no—
83C2×D61—24no—
84C2×D61—82no—
85#6923—162no—
86C4×C61—22no—
87C4×C61—42no—
88C4×C61—82no—
89Dic61—22no—
90Dic61—44no—
91Dic61—42no—
92#2298—611no—
93#1822—611no—
94#1820—611no—
95#1284—614no—
96C2×C61—22no—
97C2×C61#182011yescharacteristic
98C2×C61#182712yes—
99D61—42no—
100C2×#117—611no—
101#407—612no—
102#388—1222no—
103#387—1222no—
104#381—612no—
105C4×C4⋊C4—612no—
106C4×C22⋊C4—612no—
107#376#692311yescharacteristic, complemented
108C43—611no—
109#343—1222no—
110#342—1222no—
111C61#874111yescharacteristic, complemented, Sylow
112C23×C4—611no—
113C2×M16—1222no—
114#117—1224no—
115C2×C4⋊C4—612no—
116C2×C4⋊C4—1222no—
117C2×C22⋊C4—612no—
118C2×C22⋊C4—1222no—
119C2×C22⋊C4—1222no—
120C2×C42—611no—
121C2×C42—612no—
122C2×C42—1222no—
123C2×C42C2×#692311yescharacteristic
124C2×C42C2×#692312yes—
125C22⋊C8—1224no—
126#95—22no—
127#95—1222no—
128#95—1222no—
129#95—1224no—
130C24—611no—
131C22×C4—22no—
132C22×C4—611no—
133C22×C4—614no—
134C22×C4—612no—
135C22×C4—1222no—
136C22×C4—2442no—
137C22×C4—2442no—
138C22×C4C22⋊#692312yes—
139C22×C4C22×#692311yescharacteristic
140M16—2444no—
141C2×C8—2442no—
142C4⋊C4—1224no—
143C4⋊C4—2444no—
144C22⋊C4—1224no—
145C22⋊C4—2444no—
146C22⋊C4—2444no—
147C42—22no—
148C42—42no—
149C42—1222no—
150C42—2442no—
151C42—2444no—
152C23—612no—
153C23—1222no—
154C23—2442no—
155C23C2×C22⋊#692311yescharacteristic
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—612no—
163C2×C4—1222no—
164C2×C4—1224no—
165C2×C4—1222no—
166C2×C4—4882no—
167C2×C4—4884no—
168C2×C4—2444no—
169C2×C4—2442no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4#1451985612yes—
173C8—4882no—
174C22—22no—
175C22—1222no—
176C22—1224no—
177C22—4882no—
178C22#1684070511yescharacteristic
179C22#1684074112yes—
180C4—22no—
181C4—42no—
182C4—82no—
183C4—1222no—
184C4—9762no—
185C4—2444no—
186C4—2442no—
187C2—22no—
188C2—2442no—
189C2#2146171611yescharacteristic
190C2#2146172912yes—
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#376C4
socleC22×C61#381
prime radicalC23×D61C2×D4
cosocleC22×C4×D61C23
hypercenter#376#6923
hypocenterC61#8741
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
12. C4×#11758196C4semidirect
14. C42×Dic61C4semidirect
15. C61×#376C4semidirect
107. #376#6923semidirect
111. C61#8741semidirect

Maximal subgroups

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

subgroupindex
#214617202
#214617162
#214606672
#214483142
#874161