Finite Group Databasebeta

← #30595024

Subgroups — #30595024

Order 15616.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460916C211yesmaximal, characteristic
2#21460750C211yesmaximal, characteristic
3#21447356C211yesmaximal, characteristic
4C2×#14519838—21no—
5#16840607—21no—
6C2×#14519711—21no—
7C2×#14519702—21no—
8#16839668C2211yescharacteristic
9#16839632C411yescharacteristic
10C61×#336C411yescharacteristic
11C2×#11758217—41no—
12#14519838—22no—
13#14519838—41no—
14C22⋊#92420—41no—
15C22×Dic122D411yescharacteristic
16C2×C4⋊Dic61—21no—
17C2×C4⋊Dic61—41no—
18C2×C4⋊Dic61D411yescharacteristic
19#14519711—42no—
20#14519702—42no—
21#14519684—41no—
22C22×C8×C61—21no—
23C2×C42×C61C2×C411yescharacteristic
24C22×C4×C61—21no—
25C22×C4×C61C22⋊C411yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—41no—
29C2×Dic122—21no—
30C2×Dic122—41no—
31C2×Dic122—41no—
32C2×Dic122SD1611yescharacteristic
33C2×Dic122Q1611yescharacteristic
34#11758217—42no—
35#11758217—81no—
36C2×#92420—81no—
37C2×#92420—81no—
38C2×C8×C61—22no—
39C2×C8×C61—41no—
40C2×C8×C61—41no—
41C42×C61—41no—
42C4⋊Dic61—41no—
43C4⋊Dic61—41no—
44C4⋊Dic61—41no—
45C4⋊Dic61—82no—
46C23×C61#9911yescharacteristic
47C2×C4×C61—21no—
48C2×C4×C61—21no—
49C2×C4×C61—22no—
50C2×C4×C61—41no—
51C2×C4×C61—41no—
52C2×C4×C61#10311yescharacteristic
53C2×C4×C61#10411yescharacteristic
54C2×Dic61—21no—
55C2×Dic61—21no—
56C2×Dic61—41no—
57C2×Dic61—41no—
58C2×Dic61—41no—
59C2×Dic61—81no—
60C2×Dic61—82no—
61C2×Dic61—81no—
62Dic122—41no—
63Dic122—41no—
64Dic122—81no—
65#92420—82no—
66#92420—161no—
67C8×C61—42no—
68#7436—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#32811yescharacteristic
72C22×C61#35211yescharacteristic
73C22×C61#35311yescharacteristic
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—42no—
77Dic61—41no—
78Dic61—41no—
79Dic61—81no—
80Dic61—161no—
81#2095—611no—
82#1394—611no—
83#1319—611no—
84C2×C61—21no—
85C2×C61—21no—
86C2×C61#135211yescharacteristic
87C2×C61#140611yescharacteristic
88C2×C61#141111yescharacteristic
89C2×#107—1221no—
90C2×#103—1221no—
91C2×#101—1221no—
92#391—611no—
93#384—611no—
94#336#692311yescharacteristic
95#324—1221no—
96C61#743611yescharacteristic, complemented, Sylow
97C22×Q8—611no—
98C2×M16—2441no—
99C22×C8—21no—
100C2×C4⋊C4—611no—
101C2×C4⋊C4—1221no—
102C2×C4⋊C4—2441no—
103C2×C42C2×#692311yescharacteristic
104#107—2442no—
105#103—2442no—
106#101—1222no—
107#101—2441no—
108C22⋊C8—2441no—
109#95—2441no—
110C2×Q8—611no—
111C2×Q8—611no—
112C2×Q8—1221no—
113C2×Q8—2441no—
114C2×Q8—2441no—
115C22×C4—21no—
116C22×C4—1221no—
117C22×C4—1221no—
118C22×C4—2441no—
119C22×C4C22⋊#692311yescharacteristic
120M16—4881no—
121M16—2442no—
122C2×C8—22no—
123C2×C8—41no—
124C2×C8—41no—
125C2×C8—4881no—
126C2×C8—4881no—
127C4⋊C4—4882no—
128C4⋊C4—2441no—
129C4⋊C4—2441no—
130C4⋊C4—2441no—
131C42—41no—
132C23#1451983611yescharacteristic
133Q8—4881no—
134Q8—2441no—
135Q8—2441no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—1221no—
142C2×C4—1221no—
143C2×C4—4882no—
144C2×C4—4881no—
145C2×C4—4881no—
146C2×C4—2441no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4#1451984011yescharacteristic
150C2×C4#1451984111yescharacteristic
151C8—42no—
152C8—9761no—
153C8—4882no—
154C22—21no—
155C22—21no—
156C22#1684061511yescharacteristic
157C22#1684066511yescharacteristic
158C22#1684066711yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—9761no—
163C4—4881no—
164C4—2441no—
165C4—2441no—
166C2—21no—
167C2—21no—
168C2#2146081511yescharacteristic
169C2#2146094711yescharacteristic
170C2#2146095711yescharacteristic
subgroupG/H
centerC22#16840667
commutatorC2×C42×C61C2×C4
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC22×C61#353
prime radicalC23×C61#99
cosocle#16839668C22
hypercenter#336#6923
hypocenterC61#7436
LCSG ▷ C2×C42×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
96. C61#7436semidirect

Maximal subgroups

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

subgroupindex
#214609162
#214607502
#214473562
#743661