Finite Group Databasebeta

← #30595650

Subgroups — #30595650

Order 15616.

384 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 94 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#21461747C212yesmaximal
2#21460637C214yesmaximal
3#125×Dic61C211yesmaximal, characteristic
4#16840628—22no—
5#16840628—22no—
6#16840628C2214yes—
7#16839661C2212yes—
8#16839648—22no—
9#16839628C411yescharacteristic
10C4⋊C4×Dic61—22no—
11C4⋊C4×Dic61C412yes—
12C42×Dic61C2211yescharacteristic
13C2×#125×C61C411yescharacteristic
14C22×#92420—24no—
15C2×C4⋊Dic61—22no—
16C2×C4⋊Dic61C2×C412yes—
17C2×C4×Dic61—22no—
18C2×C4×Dic61C2×C411yescharacteristic
19C2×C4×Dic61D412yes—
20C2×C4×Dic61D412yes—
21C2×C4×Dic61C2311yescharacteristic
22#14519684—22no—
23#14519684—22no—
24#14519684—22no—
25#125×C61—24no—
26C2×C4⋊C4×C61—22no—
27C2×C4⋊C4×C61C2×C412yes—
28C2×C42×C61C2×C411yescharacteristic
29C22×C4×C61—22no—
30C22×C4×C61C22⋊C412yes—
31C22×C4×C61C22×C411yescharacteristic
32C22×Dic61—22no—
33C22×Dic61C22⋊C411yescharacteristic
34C22×Dic61C22⋊C411yescharacteristic
35C22×Dic61C2×D412yes—
36C2×#92420—44no—
37C2×#92420—44no—
38C2×#92420—44no—
39C4⋊C4×C61—28no—
40C4⋊C4×C61—22no—
41C4⋊C4×C61M1614yes—
42C42×C61—22no—
43C4⋊Dic61—44no—
44C4⋊Dic61—42no—
45C4×Dic61—22no—
46C4×Dic61—24no—
47C4×Dic61—42no—
48C4×Dic61—41no—
49C4×Dic61—44no—
50C23×C61C2×C22⋊C411yescharacteristic
51C2×C4×C61—21no—
52C2×C4×C61—21no—
53C2×C4×C61—22no—
54C2×C4×C61—24no—
55C2×C4×C61—22no—
56C2×C4×C61—22no—
57C2×C4×C61—42no—
58C2×C4×C61—42no—
59C2×C4×C61C2×M1612yes—
60C2×Dic61—22no—
61C2×Dic61—22no—
62C2×Dic61—22no—
63C2×Dic61—21no—
64C2×Dic61—22no—
65C2×Dic61—42no—
66C2×Dic61—42no—
67C2×Dic61—42no—
68C2×Dic61#10112yes—
69C2×Dic61#13514yes—
70#92420—84no—
71#7650—611nomaximal, Sylow
72C22×C61#40711yescharacteristic
73C22×C61#41011yescharacteristic
74C22×C61C2×#10111yescharacteristic
75C22×C61#41612yes—
76C22×C61#42112yes—
77C4×C61—22no—
78C4×C61—42no—
79C4×C61—44no—
80Dic61—24no—
81Dic61—22no—
82Dic61—41no—
83Dic61—82no—
84C4×#125—611no—
85#1839—612no—
86#1271—614no—
87C2×C61#146711yescharacteristic
88C2×C61#148812yes—
89C2×C61#152112yes—
90C2×C61#153411yescharacteristic
91C2×C61#154411yescharacteristic
92C2×#125#692311yescharacteristic
93#389—612no—
94#387—1222no—
95#382—611no—
96C4×C4⋊C4—612no—
97C4×C4⋊C4—1222no—
98C43—611no—
99#336—614no—
100#336—1222no—
101#336—1222no—
102C61#765011yescharacteristic, complemented, Sylow
103C22×C8—1224no—
104#125—24no—
105C2×C4⋊C4—22no—
106C2×C4⋊C4—612no—
107C2×C4⋊C4—1222no—
108C2×C4⋊C4C2×#692312yes—
109C2×C42—612no—
110C2×C42—611no—
111C2×C42—612no—
112C2×C42—611no—
113C2×C42—1222no—
114C2×C42C2×#692311yescharacteristic
115#95—1222no—
116#95—1222no—
117#95—1222no—
118C22×C4—22no—
119C22×C4—612no—
120C22×C4—611no—
121C22×C4—611no—
122C22×C4—1222no—
123C22×C4C22⋊#692312yes—
124C22×C4C22×#692311yescharacteristic
125C2×C8—2444no—
126C2×C8—2444no—
127C2×C8—2444no—
128C4⋊C4—28no—
129C4⋊C4—22no—
130C4⋊C4—2442no—
131C4⋊C4—2444no—
132C4⋊C4#1175821714yes—
133C42—22no—
134C42—1222no—
135C42—1224no—
136C42—2441no—
137C42—2442no—
138C42—2444no—
139C23C2×C22⋊#692311yescharacteristic
140C2×C4—21no—
141C2×C4—21no—
142C2×C4—22no—
143C2×C4—24no—
144C2×C4—22no—
145C2×C4—22no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—612no—
149C2×C4—614no—
150C2×C4—1222no—
151C2×C4—1222no—
152C2×C4—1222no—
153C2×C4—1221no—
154C2×C4—1222no—
155C2×C4—2442no—
156C2×C4—2442no—
157C2×C4—2442no—
158C2×C4C2×#1175821712yes—
159C8—4884no—
160C22#1684073211yescharacteristic
161C22#1684074311yescharacteristic
162C22D61⋊#10111yescharacteristic
163C22#1684075212yes—
164C22#1684075912yes—
165C4—22no—
166C4—42no—
167C4—44no—
168C4—1224no—
169C4—1222no—
170C4—4882no—
171C4—2441no—
172C2#2146108211yescharacteristic
173C2#2146115012yes—
174C2#2146126212yes—
175C2#2146130211yescharacteristic
176C2#2146132511yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#125×C61C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#125#6923
hypocenterC61#7650
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
102. C61#7650semidirect

Maximal subgroups

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

subgroupindex
#214617472
#214606372
#125×Dic612
#765061