Finite Group Databasebeta

← #18009980

Subgroups — #18009980

Order 4736.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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#14558552C211yesmaximal, characteristic
2C4×C4⋊#3866C211yesmaximal, characteristic
3#14558387C214yesmaximal
4#14558088C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6C2×C4×#3866—21no—
7C4⋊#64438—21no—
8#11924593C2212yes—
9C4×#64438—21no—
10(C2×#3866)⋊C4C2212yes—
11#11924536C411yescharacteristic, complemented
12#11924527—21no—
13#11924516—21no—
14#11924512C2212yes—
15Q8×Dic37C412yescomplemented
16#11924501—21no—
17#11924494—21no—
18C42×D37C2211yescharacteristic
19C4⋊Q8×C37C411yescharacteristic, complemented
20C22×#3866—22no—
21C2×Q8×C37C2×C412yes—
22C2×C4×D37D411yescharacteristic
23C2×C4×D37D411yescharacteristic
24C2×C4×D37C2311yescharacteristic
25C2×Dic74—21no—
26C2×#64438—22no—
27C4⋊#3866—24no—
28C4×#3866—42no—
29C4⋊C4×C37—21no—
30C4⋊C4×C37—21no—
31C42×C37C2×C411yescharacteristic
32#10596938—22no—
33C4⋊Dic37—21no—
34C4⋊Dic37—22no—
35C4⋊Dic37C2×C412yes—
36#10596936—22no—
37C4×Dic37—22no—
38C4×Dic37C2×C411yescharacteristic
39C4×Dic37D411yescharacteristic
40C4×Dic37D411yescharacteristic
41C22×D37C2×D411yescharacteristic
42C2×#3866—24no—
43C2×#3866—42no—
44C2×#3866—42no—
45Q8×C37—42no—
46C2×C4×C37—22no—
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22⋊C411yescharacteristic
49C2×C4×C37C22×C411yescharacteristic
50C2×Dic37—22no—
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C22⋊C411yescharacteristic
53C2×Dic37C2×D411yescharacteristic
54C4×D37—22no—
55C4×D37—41no—
56C4×D37SD1612yes—
57C4×D37Q1612yes—
58Dic74—42no—
59#64438—42no—
60C22×C37C2×C22⋊C411yescharacteristic
61C2×D37—21no—
62C2×D37—21no—
63C2×D37C2×SD1611yescharacteristic
64C2×D37C2×Q1611yescharacteristic
65#3866—44no—
66C4×C37—21no—
67C4×C37—42no—
68C4×C37#10312yes—
69C4×C37#10412yes—
70Dic37—21no—
71Dic37—21no—
72Dic37—42no—
73Dic37#10312yes—
74#1503—371nomaximal, Sylow
75C2×C37#41011yescharacteristic
76C2×C37C2×#10311yescharacteristic
77C2×C37C2×#10411yescharacteristic
78D37—21no—
79D37—21no—
80#533—371no—
81#431—371no—
82C4×C4⋊C4—371no—
83#328—374no—
84C37#150311yescharacteristic, complemented, Sylow
85C4⋊Q8—371no—
86C4⋊Q8#386611yescharacteristic, complemented
87#125—741no—
88C22⋊Q8—372no—
89C22⋊Q8—741no—
90C4×Q8—372no—
91C4×Q8—741no—
92#117—741no—
93C2×C4⋊C4—741no—
94C2×C42—371no—
95C2×C42—741no—
96C4⋊C8—741no—
97C22⋊C8—372no—
98C4×C8—741no—
99#95—372no—
100C2×Q8—741no—
101C2×Q8C2×#386612yes—
102C22×C4—371no—
103C22×C4—371no—
104C22×C4—371no—
105C22×C4—742no—
106C2×C8—742no—
107C4⋊C4—21no—
108C4⋊C4—21no—
109C4⋊C4—372no—
110C4⋊C4—742no—
111C4⋊C4—742no—
112C4⋊C4—744no—
113C4⋊C4—741no—
114C22⋊C4—742no—
115C42—371no—
116C42—371no—
117C42—371no—
118C42—742no—
119C42—1482no—
120C42C2×#386611yescharacteristic
121C23—371no—
122Q8—42no—
123Q8—1482no—
124C2×C4—22no—
125C2×C4—371no—
126C2×C4—372no—
127C2×C4—372no—
128C2×C4—371no—
129C2×C4—371no—
130C2×C4—742no—
131C2×C4—744no—
132C2×C4—742no—
133C2×C4—1481no—
134C2×C4—1482no—
135C2×C4—1482no—
136C2×C4C22⋊#386611yescharacteristic
137C2×C4C22⋊#386611yescharacteristic
138C2×C4C22×#386611yescharacteristic
139C8—1482no—
140C22—371no—
141C22—371no—
142C22—741no—
143C22—741no—
144C22C2×C22⋊#386611yescharacteristic
145C4—21no—
146C4—42no—
147C4—372no—
148C4—741no—
149C4—741no—
150C4—1484no—
151C4—1482no—
152C4#1192459912yes—
153C4#1192460112yes—
154C2—741no—
155C2—741no—
156C2#1455851311yescharacteristic
157C2C2×#1192459911yescharacteristic
158C2C2×#1192460111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C2×D4
cosocleC2×C4×D37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1503
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #11924536C4semidirect
15. Q8×Dic37C4semidirect
19. C4⋊Q8×C37C4semidirect
84. C37#1503semidirect
86. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585522
C4×C4⋊#38662
#145583872
#145580882
#150337