Finite Group Databasebeta

← #18010030

Subgroups — #18010030

Order 4736.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#14558551C211yesmaximal, characteristic
2#14558477C211yesmaximal, characteristic
3#14558387C214yesmaximal
4#14558088C211yesmaximal, characteristic
5C2×C4⋊#3866—21no—
6#11924603—21no—
7#11924593C2212yes—
8C4×#64438—21no—
9(C2×#3866)⋊C4—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—42no—
28C4⋊C4×C37—21no—
29C4⋊C4×C37—21no—
30C42×C37C2×C411yescharacteristic
31#10596938—22no—
32C4⋊Dic37—21no—
33C4⋊Dic37—22no—
34C4⋊Dic37C2×C412yes—
35#10596936—22no—
36C4×Dic37—22no—
37C4×Dic37C2×C411yescharacteristic
38C4×Dic37D411yescharacteristic
39C4×Dic37D411yescharacteristic
40C22×D37C2×D411yescharacteristic
41C2×#3866—42no—
42C2×#3866—42no—
43C2×#3866—42no—
44Q8×C37—42no—
45C2×C4×C37—22no—
46C2×C4×C37C22⋊C411yescharacteristic
47C2×C4×C37C22⋊C411yescharacteristic
48C2×C4×C37C22×C411yescharacteristic
49C2×Dic37—22no—
50C2×Dic37C22⋊C411yescharacteristic
51C2×Dic37C22⋊C411yescharacteristic
52C2×Dic37C2×D411yescharacteristic
53C4×D37—41no—
54C4×D37—41no—
55C4×D37SD1612yes—
56C4×D37Q1612yes—
57Dic74—42no—
58#64438—42no—
59C22×C37C2×C22⋊C411yescharacteristic
60C2×D37—21no—
61C2×D37—21no—
62C2×D37C2×SD1611yescharacteristic
63C2×D37C2×Q1611yescharacteristic
64#3866—82no—
65C4×C37—21no—
66C4×C37—21no—
67C4×C37—42no—
68C4×C37#10312yes—
69Dic37—21no—
70Dic37—21no—
71Dic37—42no—
72Dic37#10312yes—
73#1518—371nomaximal, Sylow
74C2×C37#41011yescharacteristic
75C2×C37C2×#10311yescharacteristic
76C2×C37#42111yescharacteristic
77D37—21no—
78D37—21no—
79#533—371no—
80#431—371no—
81#382—371no—
82#328—374no—
83C37#151811yescharacteristic, complemented, Sylow
84C4⋊Q8—371no—
85C4⋊Q8#386611yescharacteristic, complemented
86#125—741no—
87C22⋊Q8—372no—
88C22⋊Q8—741no—
89C4×Q8—372no—
90C4×Q8—741no—
91#117—741no—
92C2×C4⋊C4—741no—
93C2×C42—371no—
94C4⋊C8—741no—
95C22⋊C8—372no—
96C4×C8—741no—
97#95—372no—
98#95—741no—
99C2×Q8—741no—
100C2×Q8C2×#386612yes—
101C22×C4—371no—
102C22×C4—371no—
103C22×C4—371no—
104C22×C4—742no—
105C2×C8—742no—
106C4⋊C4—21no—
107C4⋊C4—21no—
108C4⋊C4—372no—
109C4⋊C4—742no—
110C4⋊C4—742no—
111C4⋊C4—741no—
112C4⋊C4—1482no—
113C22⋊C4—742no—
114C42—371no—
115C42—371no—
116C42—371no—
117C42—742no—
118C42C2×#386611yescharacteristic
119C23—371no—
120Q8—42no—
121Q8—1482no—
122C2×C4—22no—
123C2×C4—371no—
124C2×C4—372no—
125C2×C4—372no—
126C2×C4—371no—
127C2×C4—371no—
128C2×C4—742no—
129C2×C4—1481no—
130C2×C4—1481no—
131C2×C4—1482no—
132C2×C4—1482no—
133C2×C4—1482no—
134C2×C4C22⋊#386611yescharacteristic
135C2×C4C22⋊#386611yescharacteristic
136C2×C4C22×#386611yescharacteristic
137C8—1482no—
138C22—371no—
139C22—371no—
140C22—741no—
141C22—741no—
142C22C2×C22⋊#386611yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—372no—
147C4—2962no—
148C4—741no—
149C4—741no—
150C4—1482no—
151C4#1192459912yes—
152C2—741no—
153C2—741no—
154C2#1455851311yescharacteristic
155C2C2×#1192459911yescharacteristic
156C2#1455853211yescharacteristic
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#1518
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
83. C37#1518semidirect
85. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585512
#145584772
#145583872
#145580882
#151837