Finite Group Databasebeta

← #18009990

Subgroups — #18009990

Order 4736.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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#14558555C211yesmaximal, characteristic
2#14558469C211yesmaximal, characteristic
3#14558387C214yesmaximal
4#14558088C211yesmaximal, characteristic
5C2×C4×#3866—21no—
6C4⋊#64438—21no—
7#11924593C2212yes—
8#11924591—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—24no—
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—24no—
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—22no—
54C4×D37—22no—
55C4×D37—41no—
56Dic74—42no—
57#64438—42no—
58C22×C37C2×C22⋊C411yescharacteristic
59C2×D37—21no—
60C2×D37—21no—
61C2×D37#13712yes—
62#3866—44no—
63C4×C37—21no—
64C4×C37—21no—
65C4×C37—42no—
66C4×C37#10412yes—
67Dic37—21no—
68Dic37—21no—
69Dic37—21no—
70Dic37—42no—
71#1506—371nomaximal, Sylow
72C2×C37#41011yescharacteristic
73C2×C37#41911yescharacteristic
74C2×C37C2×#10411yescharacteristic
75D37—22no—
76#533—371no—
77#432—371no—
78#376—371no—
79#328—374no—
80C37#150611yescharacteristic, complemented, Sylow
81C4⋊Q8—371no—
82C4⋊Q8#386611yescharacteristic, complemented
83#125—741no—
84C22⋊Q8—372no—
85C22⋊Q8—741no—
86C4×Q8—372no—
87C4×Q8—741no—
88#117—741no—
89C2×C42—371no—
90C2×C42—741no—
91C4⋊C8—741no—
92C22⋊C8—372no—
93#97—741no—
94#95—372no—
95#95—741no—
96C2×Q8—741no—
97C2×Q8C2×#386612yes—
98C22×C4—371no—
99C22×C4—371no—
100C22×C4—371no—
101C22×C4—742no—
102C2×C8—742no—
103C4⋊C4—21no—
104C4⋊C4—21no—
105C4⋊C4—372no—
106C4⋊C4—742no—
107C4⋊C4—742no—
108C4⋊C4—741no—
109C22⋊C4—742no—
110C42—371no—
111C42—371no—
112C42—371no—
113C42—742no—
114C42—744no—
115C42C2×#386611yescharacteristic
116C23—371no—
117Q8—42no—
118Q8—1482no—
119C2×C4—22no—
120C2×C4—371no—
121C2×C4—371no—
122C2×C4—371no—
123C2×C4—742no—
124C2×C4—742no—
125C2×C4—744no—
126C2×C4—742no—
127C2×C4—1481no—
128C2×C4—1482no—
129C2×C4—1482no—
130C2×C4C22⋊#386611yescharacteristic
131C2×C4C22⋊#386611yescharacteristic
132C2×C4C22×#386611yescharacteristic
133C8—1482no—
134C22—372no—
135C22—741no—
136C22—741no—
137C22C2×C22⋊#386611yescharacteristic
138C4—21no—
139C4—21no—
140C4—42no—
141C4—741no—
142C4—741no—
143C4—741no—
144C4—1484no—
145C4—1482no—
146C4#1192460112yes—
147C2—742no—
148C2#1455851311yescharacteristic
149C2#1455852611yescharacteristic
150C2C2×#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#1506
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
80. C37#1506semidirect
82. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585552
#145584692
#145583872
#145580882
#150637