Finite Group Databasebeta

← #30594851

Subgroups — #30594851

Order 15616.

176 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 40 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#21460759C211yesmaximal, characteristic
2#21460759C211yesmaximal, characteristic
3#21446784C211yesmaximal, characteristic
4#16840607—21no—
5#16840607—21no—
6C2×#14519769C411yescharacteristic
7#16839628C2211yescharacteristic
8#16839525—21no—
9#16839525—21no—
10C2×C4×C8×C61C411yescharacteristic
11C22⋊#92420—41no—
12C22⋊#92420—41no—
13#14519769—21no—
14#14519769—41no—
15#14519769C812yescomplemented
16C2×C4⋊Dic61—21no—
17C2×C4⋊Dic61D411yescharacteristic
18C2×C4⋊Dic61D411yescharacteristic
19C2×#11758196—41no—
20#14519684—41no—
21C22×C8×C61—21no—
22C2×C42×C61C2×C411yescharacteristic
23C4×C8×C61—41no—
24C22×C4×C61—21no—
25C22×C4×C61C22⋊C411yescharacteristic
26C22×Dic61—21no—
27C22×Dic61—21no—
28C22×Dic61—41no—
29C2×#92420—81no—
30C2×#92420—81no—
31C2×C8×C61—22no—
32C2×C8×C61—41no—
33C2×C8×C61—41no—
34C42×C61—21no—
35C42×C61C2×C811yescharacteristic
36C42×C61M1611yescharacteristic
37C4⋊Dic61—22no—
38C4⋊Dic61—41no—
39C4⋊Dic61—41no—
40C4⋊Dic61—41no—
41#11758196—42no—
42#11758196—42no—
43C23×C61#9911yescharacteristic
44C2×C4×C61—21no—
45C2×C4×C61—21no—
46C2×C4×C61—21no—
47C2×C4×C61—21no—
48C2×C4×C61—41no—
49C2×C4×C61—41no—
50C2×C4×C61C22⋊C811yescharacteristic
51C2×C4×C61#10011yescharacteristic
52C2×Dic61—42no—
53C2×Dic61—41no—
54C2×Dic61—41no—
55C2×Dic61—81no—
56C2×Dic61—81no—
57C2×Dic61—81no—
58C2×Dic61—81no—
59#92420—161no—
60#92420—161no—
61C8×C61—42no—
62#7359—611nomaximal, Sylow
63C22×C61—21no—
64C22×C61—21no—
65C22×C61#32311yescharacteristic
66C22×C61#35411yescharacteristic
67C22×C61#35611yescharacteristic
68C4×C61—21no—
69C4×C61—21no—
70C4×C61—41no—
71C4×C61—41no—
72Dic61—82no—
73Dic61—81no—
74Dic61—81no—
75#1991—611no—
76#1324—611no—
77#1324—611no—
78C2×C61—21no—
79C2×C61—21no—
80C2×C61#131911yescharacteristic
81C2×C61#141411yescharacteristic
82C2×C61#141411yescharacteristic
83C2×#125—611no—
84C2×C4×C8#692311yescharacteristic
85#382—611no—
86#340—1221no—
87#340—1221no—
88#324—1221no—
89#324—1221no—
90C61#735911yescharacteristic, complemented, Sylow
91C22×C8—21no—
92#125—612no—
93#125—1221no—
94#125—2441no—
95C2×C4⋊C4—611no—
96C2×C4⋊C4—611no—
97C2×C4⋊C4—1221no—
98C2×C4⋊C4—2441no—
99C2×C42C2×#692311yescharacteristic
100C22⋊C8—2441no—
101C22⋊C8—2441no—
102C4×C8—41no—
103#95—2441no—
104C22×C4—21no—
105C22×C4—1221no—
106C22×C4—1221no—
107C22×C4—2441no—
108C22×C4C22⋊#692311yescharacteristic
109C2×C8—22no—
110C2×C8—41no—
111C2×C8—41no—
112C2×C8—4881no—
113C2×C8—4881no—
114C4⋊C4—1222no—
115C4⋊C4—2441no—
116C4⋊C4—2441no—
117C4⋊C4—2442no—
118C4⋊C4—2442no—
119C4⋊C4—2441no—
120C42—21no—
121C42D61⋊C811yescharacteristic
122C42#1175821311yescharacteristic
123C23#1451983611yescharacteristic
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—4881no—
131C2×C4—4881no—
132C2×C4—4881no—
133C2×C4—4881no—
134C2×C4—2442no—
135C2×C4—2441no—
136C2×C4—2441no—
137C2×C4#1451983411yescharacteristic
138C2×C4#1451983711yescharacteristic
139C8—42no—
140C8—9761no—
141C8—9761no—
142C22—21no—
143C22—21no—
144C22#1684060611yescharacteristic
145C22#1684066911yescharacteristic
146C22#1684067311yescharacteristic
147C4—21no—
148C4—21no—
149C4—41no—
150C4—41no—
151C4—4882no—
152C4—4881no—
153C4—4881no—
154C2—21no—
155C2—21no—
156C2#2146075011yescharacteristic
157C2#2146096611yescharacteristic
158C2#2146096711yescharacteristic
subgroupG/H
centerC22#16840669
commutatorC42×C61C2×C8
FrattiniC2×C42C2×#6923
FittingC2×C4×C8×C61C4
socleC22×C61#354
prime radicalC23×C61#99
cosocle#16839628C22
hypercenterC2×C4×C8#6923
hypocenterC61#7359
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
15. #14519769C8semidirect
90. C61#7359semidirect

Maximal subgroups

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

subgroupindex
#214607592
#214467842
#735961