Finite Group Databasebeta

← #18010088

Subgroups — #18010088

Order 4736.

194 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 56 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#14558556C211yesmaximal, characteristic
2#14558556C211yesmaximal, characteristic
3#14558390C214yesmaximal, complemented
4#14558088C211yesmaximal, characteristic
5#11924603—21no—
6#11924603—21no—
7#11924593—21no—
8#11924593—21no—
9#11924591C2212yes—
10#11924591C2212yes—
11#11924536C411yescharacteristic
12#11924527C2212yes—
13#11924516—21no—
14#11924512—21no—
15Q8×Dic37—21no—
16#11924501—21no—
17#11924494C412yes—
18C42×D37C2211yescharacteristic
19C4⋊Q8×C37C411yescharacteristic
20C2×Q8×C37—21no—
21C2×C4×D37C2×C411yescharacteristic
22C2×C4×D37D411yescharacteristic
23C2×C4×D37D411yescharacteristic
24C2×Dic74—21no—
25C2×#64438—22no—
26C2×#64438—22no—
27C4⋊C4×C37—21no—
28C4⋊C4×C37C2×C412yes—
29C42×C37C2×C411yescharacteristic
30#10596938—22no—
31C4⋊Dic37—21no—
32C4⋊Dic37—22no—
33C4⋊Dic37C2×C412yes—
34#10596936—22no—
35C4×Dic37—22no—
36C4×Dic37D411yescharacteristic
37C4×Dic37D411yescharacteristic
38C4×Dic37C2311yescharacteristic
39C22×D37C22⋊C411yescharacteristic
40Q8×C37—42no—
41C2×C4×C37—22no—
42C2×C4×C37C22⋊C411yescharacteristic
43C2×C4×C37C22⋊C411yescharacteristic
44C2×C4×C37C22×C411yescharacteristic
45C2×Dic37—22no—
46C2×Dic37C22⋊C411yescharacteristic
47C2×Dic37C2×D411yescharacteristic
48C2×Dic37C2×D411yescharacteristic
49C4×D37—22no—
50C4×D37—41no—
51C4×D37—41no—
52Dic74—42no—
53#64438—42no—
54#64438—42no—
55C22×C37C2×C22⋊C411yescharacteristic
56C2×D37—21no—
57C2×D37—21no—
58C2×D37—21no—
59C4×C37—21no—
60C4×C37—21no—
61C4×C37—21no—
62C4×C37—42no—
63Dic37—21no—
64Dic37—21no—
65Dic37—42no—
66Dic37#10112yes—
67#1537—371nomaximal, Sylow
68C2×C37C2×#10111yescharacteristic
69C2×C37#42111yescharacteristic
70C2×C37#42111yescharacteristic
71D37—41no—
72#533—371no—
73#432—371no—
74#432—371no—
75#330—374no—
76C37#153711yescharacteristic, complemented, Sylow
77C4⋊Q8—371no—
78C4⋊Q8#386611yescharacteristic
79#125—372no—
80C22⋊Q8—741no—
81C22⋊Q8—741no—
82C4×Q8—741no—
83C4×Q8—741no—
84#117—372no—
85C2×C42—371no—
86C4⋊C8—741no—
87C4⋊C8—741no—
88C22⋊C8—741no—
89C22⋊C8—741no—
90#97—372no—
91#97—372no—
92C2×Q8—21no—
93C2×Q8—741no—
94C22×C4—371no—
95C22×C4—371no—
96C22×C4—371no—
97C2×C8—742no—
98C2×C8—742no—
99C4⋊C4—21no—
100C4⋊C4—372no—
101C4⋊C4—742no—
102C4⋊C4—742no—
103C4⋊C4—741no—
104C4⋊C4C2×#386612yes—
105C22⋊C4—742no—
106C42—371no—
107C42—371no—
108C42—371no—
109C42—742no—
110C42C2×#386611yescharacteristic
111C23—371no—
112Q8—42no—
113Q8—1482no—
114C2×C4—22no—
115C2×C4—371no—
116C2×C4—371no—
117C2×C4—371no—
118C2×C4—742no—
119C2×C4—742no—
120C2×C4—1481no—
121C2×C4—1481no—
122C2×C4C22⋊#386611yescharacteristic
123C2×C4C22⋊#386611yescharacteristic
124C2×C4C22×#386611yescharacteristic
125C8—1482no—
126C8—1482no—
127C22—741no—
128C22—741no—
129C22—741no—
130C22C2×C22⋊#386611yescharacteristic
131C4—21no—
132C4—21no—
133C4—21no—
134C4—42no—
135C4—372no—
136C4—741no—
137C4—741no—
138C4—1482no—
139C2—1481no—
140C2D37⋊#10111yescharacteristic
141C2#1455853111yescharacteristic
142C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC4⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC4×Dic37C23
hypercenterC4⋊Q8#3866
hypocenterC37#1537
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
3. #14558390C2semidirect
76. C37#1537semidirect

Maximal subgroups

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

subgroupindex
#145585562
#145583902
#145580882
#153737