Finite Group Databasebeta

← #18010122

Subgroups — #18010122

Order 4736.

198 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 58 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#14558553C211yesmaximal, characteristic
2#14558550C211yesmaximal, characteristic
3#14558393C212yesmaximal, complemented
4#14558392C212yesmaximal, complemented
5#14558085C211yesmaximal, characteristic
6#11924603C2212yes—
7#11924603C2212yes—
8C22⋊#64438—21no—
9C22⋊#64438—21no—
10#11924591—21no—
11C4×#64438—21no—
12#11924535C2211yescharacteristic
13#11924534C2211yescharacteristic
14#11924526—21no—
15#11924515C411yescharacteristic
16#11924513—21no—
17Q8×Dic37C411yescharacteristic
18#11924501—21no—
19#11924501C411yescharacteristic
20#11924492—21no—
21C2×C4×Dic37C2211yescharacteristic
22C22⋊Q8×C37C411yescharacteristic
23C2×Q8×C37C2×C411yescharacteristic
24C22×C4×C37C2×C411yescharacteristic
25C22×Dic37D411yescharacteristic
26C22×Dic37D411yescharacteristic
27C2×Dic74—21no—
28C2×Dic74C2×C411yescharacteristic
29C2×#64438—22no—
30C2×#64438—22no—
31C4⋊C4×C37—21no—
32C4⋊C4×C37C2×C411yescharacteristic
33C22⋊C4×C37—21no—
34C22⋊Dic37—21no—
35C4⋊Dic37—21no—
36C4⋊Dic37C2×C411yescharacteristic
37#10596936—21no—
38#10596936—21no—
39#10596936—21no—
40#10596936—21no—
41#10596936—21no—
42C4×Dic37—21no—
43C4×Dic37—21no—
44C4×Dic37C2×C411yescharacteristic
45C4×Dic37D411yescharacteristic
46C4×Dic37D411yescharacteristic
47C4×Dic37C2311yescharacteristic
48C23×C37C22⋊C411yescharacteristic
49Q8×C37—41no—
50C2×C4×C37—21no—
51C2×C4×C37—21no—
52C2×C4×C37—41no—
53C2×C4×C37C22⋊C411yescharacteristic
54C2×C4×C37C22×C411yescharacteristic
55C2×Dic37—22no—
56C2×Dic37—22no—
57C2×Dic37—21no—
58C2×Dic37—21no—
59C2×Dic37C22⋊C411yescharacteristic
60C2×Dic37C22⋊C411yescharacteristic
61C2×Dic37C2×D411yescharacteristic
62C2×Dic37C2×D411yescharacteristic
63Dic74—42no—
64Dic74—41no—
65#64438—42no—
66#64438—42no—
67C22×C37—21no—
68C22×C37—21no—
69C22×C37—21no—
70C22×C37C2×C22⋊C411yescharacteristic
71C4×C37—21no—
72C4×C37—21no—
73C4×C37—41no—
74C4×C37—41no—
75Dic37—21no—
76Dic37—21no—
77Dic37—41no—
78Dic37—41no—
79Dic37#13512yes—
80Dic37#13712yes—
81#1554—371nomaximal, Sylow
82C2×C37—41no—
83C2×C37#41311yescharacteristic
84C2×C37#41611yescharacteristic
85C2×C37#41911yescharacteristic
86#533—371no—
87#432—371no—
88#431—371no—
89#333—372no—
90#332—372no—
91C37#155411yescharacteristic, complemented, Sylow
92C4⋊Q8—371no—
93C4⋊Q8—371no—
94#125—741no—
95C22⋊Q8—371no—
96C22⋊Q8—741no—
97C22⋊Q8#386611yescharacteristic
98C4×Q8—371no—
99C4×Q8—371no—
100C4×Q8—741no—
101#117—741no—
102C2×C42—371no—
103C4⋊C8—372no—
104C4⋊C8—372no—
105C22⋊C8—741no—
106C22⋊C8—741no—
107#97—741no—
108C4×C8—741no—
109C2×Q8—371no—
110C2×Q8—741no—
111C2×Q8C2×#386611yescharacteristic
112C22×C4—371no—
113C22×C4—371no—
114C22×C4C2×#386611yescharacteristic
115C2×C8—742no—
116C2×C8—742no—
117C4⋊C4—21no—
118C4⋊C4—371no—
119C4⋊C4—741no—
120C4⋊C4—741no—
121C4⋊C4—741no—
122C4⋊C4—741no—
123C4⋊C4—741no—
124C4⋊C4—741no—
125C4⋊C4C2×#386611yescharacteristic
126C22⋊C4—21no—
127C22⋊C4—741no—
128C42—371no—
129C42—371no—
130C42—371no—
131C42—371no—
132C42—741no—
133C42—741no—
134C23C22⋊#386611yescharacteristic
135Q8—41no—
136Q8—1481no—
137Q8—1482no—
138C2×C4—21no—
139C2×C4—21no—
140C2×C4—41no—
141C2×C4—371no—
142C2×C4—371no—
143C2×C4—371no—
144C2×C4—371no—
145C2×C4—742no—
146C2×C4—742no—
147C2×C4—741no—
148C2×C4—741no—
149C2×C4C22⋊#386611yescharacteristic
150C2×C4C22×#386611yescharacteristic
151C8—1482no—
152C8—1482no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#386611yescharacteristic
157C4—21no—
158C4—21no—
159C4—41no—
160C4—41no—
161C4—372no—
162C4—372no—
163C4—741no—
164C4—741no—
165C4—1481no—
166C4—1481no—
167C2—41no—
168C2#1455852011yescharacteristic
169C2#1455852311yescharacteristic
170C2#1455852611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC22⋊Q8×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C22⋊C4
cosocleC4×Dic37C23
hypercenterC22⋊Q8#3866
hypocenterC37#1554
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #14558393C2semidirect
4. #14558392C2semidirect
91. C37#1554semidirect

Maximal subgroups

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

subgroupindex
#145585532
#145585502
#145583932
#145583922
#145580852
#155437