Finite Group Databasebeta

← #30599338

Subgroups — #30599338

Order 15616.

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

normal subgroups only

This group has 384 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#21461072C212yesmaximal
2#21460670C214yesmaximal, complemented
3#21448314C211yesmaximal, characteristic
4#16840782C2214yes—
5#16840608—22no—
6#16840606—22no—
7C2×#14519734C2211yescharacteristic
8#16839651—22no—
9#16839644—22no—
10C4×#11758196C2212yes—
11C4×#11758198C412yes—
12C42×Dic61C411yescharacteristic
13C61×#376C411yescharacteristic
14#14519844—24no—
15C22⋊#92420—24no—
16#14519832—24no—
17C22×C4×D61C2×C411yescharacteristic
18#14519734—24no—
19C2×#11758196—22no—
20C2×#11758196D412yes—
21C2×#11758198—22no—
22C2×#11758198D412yes—
23C2×C4×Dic61—22no—
24C2×C4×Dic61C2×C412yes—
25C2×C4×Dic61C2311yescharacteristic
26#14519684—22no—
27#14519684—22no—
28C2×C42×C61C2×C411yescharacteristic
29C2×C42×C61C2×C412yes—
30#95×C61—22no—
31C23×D61C22⋊C411yescharacteristic
32C22×C4×C61—22no—
33C22×C4×C61C22⋊C412yes—
34C22×C4×C61C22×C411yescharacteristic
35C22×Dic61—22no—
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×C4×D61—22no—
39C2×C4×D61—42no—
40C2×#92420—44no—
41C42×C61—22no—
42C42×C61—42no—
43#11758198—24no—
44#11758198—44no—
45#11758196—24no—
46#11758196—44no—
47C4×Dic61—44no—
48C4×Dic61—42no—
49C4×Dic61#4114yes—
50C23×C61C2×C22⋊C411yescharacteristic
51C22×D61—21no—
52C22×D61—22no—
53C22×D61—42no—
54C2×C4×C61—22no—
55C2×C4×C61—22no—
56C2×C4×C61—42no—
57C2×C4×C61—42no—
58C2×C4×C61—42no—
59C2×C4×C61—42no—
60C2×C4×C61#11712yes—
61C2×Dic61—24no—
62C2×Dic61—21no—
63C2×Dic61—22no—
64C2×Dic61—42no—
65C2×Dic61—42no—
66C2×Dic61—42no—
67C2×Dic61#12314yes—
68C4×D61—44no—
69#92420—84no—
70#8744—611nomaximal, Sylow
71C22×C61—22no—
72C22×C61#38111yescharacteristic
73C22×C61#41312yes—
74C2×D61—41no—
75C2×D61—42no—
76C2×D61—82no—
77C4×C61—22no—
78C4×C61—42no—
79C4×C61—82no—
80Dic61—24no—
81Dic61—44no—
82Dic61—41no—
83#2298—611no—
84#1464—612no—
85#1285—614no—
86C2×C61—22no—
87C2×C61#182211yescharacteristic
88C2×C61#182712yes—
89D61—81no—
90C2×#117—611no—
91#432—614no—
92#388—1222no—
93#387—1222no—
94C4×C4⋊C4—612no—
95C4×C22⋊C4—612no—
96#376#692311yescharacteristic
97C43—611no—
98#324—1222no—
99#323—1222no—
100C61#874411yescharacteristic, complemented, Sylow
101C23×C4—611no—
102#117—1224no—
103C2×C4⋊C4—612no—
104C2×C4⋊C4—1222no—
105C2×C22⋊C4—612no—
106C2×C22⋊C4—1222no—
107C2×C42—611no—
108C2×C42—612no—
109C2×C42—1222no—
110C2×C42C2×#692311yescharacteristic
111C2×C42C2×#692312yes—
112C4⋊C8—1224no—
113C22⋊C8—1224no—
114#97—1224no—
115#95—22no—
116#95—1222no—
117#95—1222no—
118C24—611no—
119C22×C4—22no—
120C22×C4—612no—
121C22×C4—611no—
122C22×C4—1222no—
123C22×C4—1222no—
124C22×C4—2442no—
125C22×C4C22⋊#692312yes—
126C22×C4C22×#692311yescharacteristic
127C2×C8—2444no—
128C4⋊C4—1224no—
129C4⋊C4—2444no—
130C22⋊C4—1224no—
131C22⋊C4—2444no—
132C42—22no—
133C42—42no—
134C42—614no—
135C42—2442no—
136C42—2444no—
137C23—1222no—
138C23—1221no—
139C23—2442no—
140C23C2×C22⋊#692311yescharacteristic
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—42no—
144C2×C4—42no—
145C2×C4—42no—
146C2×C4—42no—
147C2×C4—614no—
148C2×C4—1224no—
149C2×C4—1221no—
150C2×C4—1222no—
151C2×C4—2444no—
152C2×C4—2442no—
153C2×C4—2442no—
154C2×C4—2442no—
155C2×C4#1451985612yes—
156C8—4884no—
157C22—22no—
158C22—4882no—
159C22—2441no—
160C22—2442no—
161C22#1684070511yescharacteristic
162C22#1684074812yes—
163C4—22no—
164C4—42no—
165C4—82no—
166C4—1224no—
167C4—2444no—
168C4—2441no—
169C2—22no—
170C2—4881no—
171C2#2146172011yescharacteristic
172C2#2146172912yes—
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#376C4
socleC22×C61#381
prime radicalC23×D61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#376#6923
hypocenterC61#8744
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
2. #21460670C2semidirect
100. C61#8744semidirect

Maximal subgroups

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

subgroupindex
#214610722
#214606702
#214483142
#874461