Finite Group Databasebeta

← #18010784

Subgroups — #18010784

Order 4736.

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

normal subgroups only

This group has 244 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#14558538C211yesmaximal, characteristic
2#14558469C211yesmaximal, characteristic
3#14558403C214yesmaximal
4#14558088C211yesmaximal, characteristic
5C2×#10596953C2212yes—
6C2×C4×#3866C2212yes—
7#11924603—21no—
8#11924603—21no—
9(C2×#3866)⋊C4—21no—
10(C2×#3866)⋊C4—21no—
11#11924536C411yescharacteristic, complemented
12#11924527C412yescomplemented
13#11924516—21no—
14#11924512—21no—
15Q8×Dic37—21no—
16#11924501—21no—
17#11924494C2212yes—
18C42×D37C2211yescharacteristic
19C4⋊Q8×C37C411yescharacteristic, complemented
20C22×#3866—22no—
21C2×Q8×C37—21no—
22C2×C4×D37D411yescharacteristic
23C2×C4×D37D411yescharacteristic
24C2×C4×D37C2311yescharacteristic
25C2×Dic74—21no—
26C2×#64438—22no—
27C4×#3866—22no—
28C4×#3866Q814yescomplemented
29#10596953—24no—
30C4⋊C4×C37—21no—
31C4⋊C4×C37C2×C412yes—
32C42×C37C2×C411yescharacteristic
33#10596938—22no—
34C4⋊Dic37—21no—
35C4⋊Dic37—22no—
36C4⋊Dic37C2×C412yes—
37#10596936—22no—
38C4×Dic37—22no—
39C4×Dic37C2×C411yescharacteristic
40C4×Dic37D411yescharacteristic
41C4×Dic37D411yescharacteristic
42C22×D37C2×D411yescharacteristic
43C2×#3866—24no—
44C2×#3866—42no—
45C2×#3866—42no—
46Q8×C37—42no—
47C2×C4×C37—22no—
48C2×C4×C37C22⋊C411yescharacteristic
49C2×C4×C37C22⋊C411yescharacteristic
50C2×C4×C37C22×C411yescharacteristic
51C2×Dic37—22no—
52C2×Dic37C22⋊C411yescharacteristic
53C2×Dic37C22⋊C411yescharacteristic
54C2×Dic37C2×D411yescharacteristic
55C4×D37—41no—
56C4×D37—41no—
57C4×D37C2×Q812yes—
58C4×D37#4112yes—
59Dic74—42no—
60#64438—42no—
61C22×C37C2×C22⋊C411yescharacteristic
62C2×D37—21no—
63C2×D37—21no—
64C2×D37C22⋊Q812yes—
65#3866—44no—
66C4×C37—21no—
67C4×C37—21no—
68C4×C37—42no—
69C4×C37C4×Q812yes—
70Dic37—21no—
71Dic37—21no—
72Dic37—42no—
73Dic37#12411yescharacteristic
74Dic37C4⋊Q811yescharacteristic
75#1995—371nomaximal, Sylow
76C2×C37#39111yescharacteristic
77C2×C37#42111yescharacteristic
78C2×C37#42111yescharacteristic
79D37—22no—
80#533—371no—
81#423—371no—
82#376—371no—
83#339—374no—
84C37#199511yescharacteristic, complemented, Sylow
85C2×M16—372no—
86C4⋊Q8—371no—
87C4⋊Q8#386611yescharacteristic, complemented
88#125—372no—
89C22⋊Q8—741no—
90C22⋊Q8—741no—
91C4×Q8—741no—
92C4×Q8—741no—
93#117—372no—
94C2×C42—371no—
95C2×C42—372no—
96C4⋊C8—741no—
97C4⋊C8—741no—
98#95—741no—
99#95—741no—
100C2×Q8—21no—
101C2×Q8—741no—
102C22×C4—371no—
103C22×C4—371no—
104C22×C4—371no—
105C22×C4—742no—
106M16—744no—
107C2×C8—742no—
108C4⋊C4—21no—
109C4⋊C4—372no—
110C4⋊C4—742no—
111C4⋊C4—742no—
112C4⋊C4—741no—
113C4⋊C4C2×#386612yes—
114C22⋊C4—742no—
115C42—371no—
116C42—371no—
117C42—371no—
118C42—374no—
119C42—742no—
120C42—742no—
121C42C2×#386611yescharacteristic
122C23—371no—
123Q8—42no—
124Q8—1482no—
125C2×C4—22no—
126C2×C4—371no—
127C2×C4—372no—
128C2×C4—372no—
129C2×C4—371no—
130C2×C4—371no—
131C2×C4—744no—
132C2×C4—742no—
133C2×C4—1481no—
134C2×C4—1481no—
135C2×C4—1482no—
136C2×C4—1482no—
137C2×C4C22⋊#386611yescharacteristic
138C2×C4C22⋊#386611yescharacteristic
139C2×C4C22×#386611yescharacteristic
140C8—1482no—
141C22—372no—
142C22—741no—
143C22—741no—
144C22C2×C22⋊#386611yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—371no—
149C4—371no—
150C4—741no—
151C4—741no—
152C4—1484no—
153C4—1482no—
154C4Q8×#386612yes—
155C2—742no—
156C2(C2×#3866)⋊Q811yescharacteristic
157C2#1455853111yescharacteristic
158C2#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#1995
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #11924536C4semidirect
12. #11924527C4semidirect
19. C4⋊Q8×C37C4semidirect
28. C4×#3866Q8semidirect
84. C37#1995semidirect
87. C4⋊Q8#3866semidirect

Maximal subgroups

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

subgroupindex
#145585382
#145584692
#145584032
#145580882
#199537