Finite Group Databasebeta

← #30594470

Subgroups — #30594470

Order 15616.

192 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 46 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#21462189C211yesmaximal, characteristic
2#21461042C211yesmaximal, characteristic
3#21445966C211yesmaximal, characteristic
4C4×#11758217—21no—
5#16840684—21no—
6#16840658—21no—
7#16840655C412yescomplemented
8#92420⋊C8—21no—
9#16840603C411yescharacteristic, complemented
10C8×#92420C411yescharacteristic, complemented
11M16×Dic61C2211yescharacteristic
12#16839532—21no—
13#16839521—21no—
14#16839520C411yescharacteristic
15C61×H(3,ℤ/4)C411yescharacteristic
16C2×#11758217—22no—
17#14519851—22no—
18#14519832—22no—
19C4×#92420—21no—
20C4×#92420—21no—
21C2×#11758194—21no—
22C2×#11758194D411yescharacteristic
23C2×C4×Dic61D411yescharacteristic
24#14519687C2×C411yescharacteristic
25#14519687Q811yescharacteristic
26C8×Dic61C2×C411yescharacteristic
27C8×Dic61D411yescharacteristic
28C2×M16×C61C2×C411yescharacteristic
29#117×C61—21no—
30C22×C4×C61C22⋊C411yescharacteristic
31C22×Dic61—21no—
32#11758217—44no—
33C2×#92420—22no—
34C2×#92420—22no—
35M16×C61—41no—
36C2×C8×C61C4211yescharacteristic
37C2×C8×C61C4⋊C411yescharacteristic
38C4⋊C4×C61—41no—
39C22⋊C4×C61—41no—
40C42×C61—41no—
41C4×Dic61—21no—
42C4×Dic61C22⋊C411yescharacteristic
43C4×Dic61C4⋊C411yescharacteristic
44#11758194—41no—
45#11758194—41no—
46#11758194—41no—
47C2×#92418—41no—
48C2×#92418C22⋊C411yescharacteristic
49C2×#92418C4⋊C411yescharacteristic
50#11758187—42no—
51C23×C61#10411yescharacteristic
52C2×C4×C61—21no—
53C2×C4×C61—21no—
54C2×C4×C61—81no—
55C2×C4×C61#9511yescharacteristic
56C2×C4×C61#10411yescharacteristic
57C2×Dic61—21no—
58C2×Dic61—21no—
59C2×Dic61—42no—
60#92420—24no—
61#92420—42no—
62C8×C61—21no—
63C8×C61—21no—
64#92418—21no—
65#92418—21no—
66#92418—81no—
67#7225—611nomaximal, Sylow
68C22×C61—21no—
69C22×C61—41no—
70C22×C61#33911yescharacteristic
71C4×C61—21no—
72C4×C61—161no—
73C4×C61H(3,ℤ/4)11yescharacteristic
74C4×C61#34411yescharacteristic
75Dic61—22no—
76Dic61—41no—
77#2165—611no—
78#1841—611no—
79#1455—611no—
80C2×C61—21no—
81C2×C61—41no—
82C2×C61#128811yescharacteristic
83C4×M16—611no—
84C4×M16—1221no—
85#364—1221no—
86#349—1221no—
87#347—612no—
88#344—1221no—
89#339—1221no—
90#338—611no—
91H(3,ℤ/4)#692311yescharacteristic
92#322—611no—
93#322—1221no—
94C82—611no—
95C61#722511yescharacteristic, complemented, Sylow
96C2×M16—611no—
97C2×M16—1222no—
98C2×M16—1221no—
99C2×M16C2×#692311yescharacteristic
100#117—21no—
101C2×C42—611no—
102M32—1222no—
103#97—611no—
104#97—611no—
105#97—1222no—
106C4×C8—611no—
107C4×C8—611no—
108C4×C8—1221no—
109C4×C8—1221no—
110C22×C4—1221no—
111C22×C4C22⋊#692311yescharacteristic
112M16—41no—
113M16—2441no—
114M16—2444no—
115M16—2441no—
116M16—2441no—
117C2×C8—611no—
118C2×C8—611no—
119C2×C8—1222no—
120C2×C8—1222no—
121C2×C8—2441no—
122C2×C8C4×#692311yescharacteristic
123C2×C8C4⋊#692311yescharacteristic
124C4⋊C4—41no—
125C22⋊C4—41no—
126C42—41no—
127C42—611no—
128C42—611no—
129C42—1221no—
130C16—2442no—
131C23#1451984111yescharacteristic
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—81no—
135C2×C4—1221no—
136C2×C4—1221no—
137C2×C4—2442no—
138C2×C4(C2×#6923)⋊C411yescharacteristic
139C2×C4#1451984211yescharacteristic
140C8—21no—
141C8—21no—
142C8—1224no—
143C8—1221no—
144C8—1221no—
145C8—4881no—
146C8—2442no—
147C22—21no—
148C22—41no—
149C22#1684063211yescharacteristic
150C4—21no—
151C4—161no—
152C4—1222no—
153C4—2441no—
154C4#1684062911yescharacteristic
155C4#1684064311yescharacteristic
156C2—21no—
157C2—41no—
158C2#2146067811yescharacteristic
subgroupG/H
centerC4#16840629
commutatorC2×C8×C61C42
FrattiniC2×M16C2×#6923
FittingC61×H(3,ℤ/4)C4
socleC2×C61#1288
prime radicalC23×C61#104
cosocleM16×Dic61C22
hypercenterH(3,ℤ/4)#6923
hypocenterC61#7225
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C8 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
7. #16840655C4semidirect
9. #16840603C4semidirect
10. C8×#92420C4semidirect
95. C61#7225semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214610422
#214459662
#722561