Finite Group Databasebeta

← #30595036

Subgroups — #30595036

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#21460760C211yesmaximal, characteristic
2#21460695C211yesmaximal, characteristic
3#21447170C211yesmaximal, characteristic
4C2×#14519832—21no—
5#16840607—21no—
6#16840393C411yescharacteristic
7#16839804—21no—
8#16839627C2211yescharacteristic
9#16839523—21no—
10C61×#343C411yescharacteristic
11C22×#92420—41no—
12C22⋊#92420—41no—
13#14519832—22no—
14#14519832—41no—
15#14519776—41no—
16#14519768—41no—
17#14519756—41no—
18#14519736—21no—
19C2×C4⋊Dic61D411yescharacteristic
20C2×C4×Dic61D411yescharacteristic
21#14519711—41no—
22#14519709—41no—
23#14519684—41no—
24C2×M16×C61—21no—
25C2×C4⋊C4×C61C2×C411yescharacteristic
26C22×C4×C61—21no—
27C22×C4×C61C22⋊C411yescharacteristic
28C22×Dic61—21no—
29C22×Dic61—21no—
30C2×Dic122—41no—
31C2×#92420—42no—
32C2×#92420—42no—
33C2×#92420—42no—
34C2×#92420—81no—
35M16×C61—22no—
36M16×C61—41no—
37C2×C8×C61—41no—
38C4⋊C4×C61—41no—
39C22⋊Dic61—41no—
40C4⋊Dic61—21no—
41C4⋊Dic61—21no—
42C4⋊Dic61—41no—
43C4⋊Dic61—41no—
44#11758196—42no—
45C4×Dic61—21no—
46C4×Dic61—41no—
47C4×Dic61SD1611yescharacteristic
48C4×Dic61Q1611yescharacteristic
49C23×C61#9911yescharacteristic
50C2×C4×C61—21no—
51C2×C4×C61—21no—
52C2×C4×C61—41no—
53C2×C4×C61—81no—
54C2×C4×C61#10311yescharacteristic
55C2×C4×C61#10411yescharacteristic
56C2×Dic61—21no—
57C2×Dic61—21no—
58C2×Dic61—41no—
59C2×Dic61—41no—
60C2×Dic61—41no—
61C2×Dic61—41no—
62C2×Dic61—41no—
63C2×Dic61—81no—
64Dic122—161no—
65#92420—44no—
66#92420—161no—
67C8×C61—42no—
68#7442—611nomaximal, Sylow
69C22×C61—21no—
70C22×C61—21no—
71C22×C61#32811yescharacteristic
72C22×C61AΣL(1,𝔽16)11yescharacteristic
73C22×C61#35611yescharacteristic
74C4×C61—21no—
75C4×C61—21no—
76C4×C61—81no—
77Dic61—41no—
78Dic61—41no—
79Dic61—81no—
80Dic61—81no—
81Dic61—81no—
82#2061—611no—
83#1324—611no—
84#1295—611no—
85C2×C61—21no—
86C2×C61—21no—
87C2×C61#135411yescharacteristic
88C2×C61#140311yescharacteristic
89C2×C61#140411yescharacteristic
90#544—611no—
91#428—1221no—
92C2×#97—1221no—
93#382—611no—
94#343#692311yescharacteristic
95#339—1221no—
96#324—1221no—
97C61#744211yescharacteristic, complemented, Sylow
98C2×M16—21no—
99C22×C8—2441no—
100C4⋊Q8—2441no—
101#125—2441no—
102C22⋊Q8—2441no—
103#117—1221no—
104C2×C4⋊C4—611no—
105C2×C4⋊C4C2×#692311yescharacteristic
106C2×C42—611no—
107#107—2441no—
108#106—2441no—
109C22⋊C8—2441no—
110#97—1222no—
111#97—2441no—
112#95—2441no—
113C2×Q8—2441no—
114C22×C4—21no—
115C22×C4—1221no—
116C22×C4—1221no—
117C22×C4C22⋊#692311yescharacteristic
118M16—22no—
119M16—41no—
120C2×C8—41no—
121C2×C8—4881no—
122C2×C8—2442no—
123C2×C8—2442no—
124C2×C8—2442no—
125C4⋊C4—41no—
126C4⋊C4—1221no—
127C4⋊C4—1221no—
128C4⋊C4—2441no—
129C4⋊C4—2441no—
130C4⋊C4—2442no—
131C22⋊C4—2441no—
132C42—611no—
133C42—611no—
134C42—1221no—
135C42—2441no—
136C23#1451983611yescharacteristic
137Q8—9761no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—81no—
142C2×C4—1221no—
143C2×C4—1221no—
144C2×C4—4881no—
145C2×C4—2441no—
146C2×C4—2441no—
147C2×C4—2441no—
148C2×C4—2441no—
149C2×C4—2441no—
150C2×C4#1451984011yescharacteristic
151C2×C4#1451984111yescharacteristic
152C8—42no—
153C8—9761no—
154C8—2444no—
155C22—21no—
156C22—21no—
157C22#1684061511yescharacteristic
158C22#1684066311yescharacteristic
159C22#1684067311yescharacteristic
160C4—21no—
161C4—21no—
162C4—81no—
163C4—4881no—
164C4—4881no—
165C4—4881no—
166C4—2441no—
167C4—2441no—
168C2—21no—
169C2—21no—
170C2#2146081911yescharacteristic
171C2#2146094111yescharacteristic
172C2#2146094311yescharacteristic
subgroupG/H
centerC22#16840663
commutatorC2×C4⋊C4×C61C2×C4
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61AΣL(1,𝔽16)
prime radicalC23×C61#99
cosocle#16839627C22
hypercenter#343#6923
hypocenterC61#7442
LCSG ▷ C2×C4⋊C4×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
97. C61#7442semidirect

Maximal subgroups

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

subgroupindex
#214607602
#214606952
#214471702
#744261