Finite Group Databasebeta

← #17993209

Subgroups — #17993209

Order 4736.

212 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 61 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#14558089C211yesmaximal, characteristic
2#14557588C211yesmaximal, characteristic
3#97×D37C211yesmaximal, characteristic
4#14557275C211yesmaximal, characteristic, complemented
5#14557274C211yesmaximal, characteristic, complemented
6#14557274C211yesmaximal, characteristic, complemented
7C37×#330C211yesmaximal, characteristic, complemented
8C2×C8×D37—21no—
9#11924535C411yescharacteristic
10#11924535C411yescharacteristic
11#11924528C2211yescharacteristic
12#11924514—21no—
13#11924514—21no—
14#11924501—21no—
15#11924501—21no—
16#11924494C411yescharacteristic
17#11924494C411yescharacteristic
18C42×D37C2211yescharacteristic
19#11924465—21no—
20#11924448—21no—
21#11924447C2211yescharacteristic
22#11924447C2211yescharacteristic
23#11924446—21no—
24#125×C37C2211yescharacteristic
25#97×C37C2211yescharacteristic
26#97×C37C2211yescharacteristic
27C2×C4×D37C2×C411yescharacteristic
28C2×C4×D37D411yescharacteristic
29C2×C4×D37D411yescharacteristic
30C2×Dic74—21no—
31C2×Dic74—21no—
32C2×C8×C37—21no—
33C2×C8×C37—21no—
34C4⋊C4×C37—21no—
35C4⋊C4×C37—21no—
36C4⋊C4×C37C2×C411yescharacteristic
37C4⋊C4×C37C2×C411yescharacteristic
38C42×C37C2311yescharacteristic
39#10596938—21no—
40#10596938—21no—
41C4⋊Dic37C2×C411yescharacteristic
42C4⋊Dic37C2×C411yescharacteristic
43#10596936—21no—
44#10596936—21no—
45#10596936—21no—
46#10596936—21no—
47C4×Dic37—21no—
48C4×Dic37—21no—
49C4×Dic37C2×C411yescharacteristic
50C4×Dic37D411yescharacteristic
51C4×Dic37D411yescharacteristic
52C2×#64436—21no—
53C2×#64436—21no—
54C8×D37—24no—
55C22×D37C22⋊C411yescharacteristic
56C2×C4×C37—21no—
57C2×C4×C37—21no—
58C2×C4×C37C22×C411yescharacteristic
59C2×C4×C37C2×D411yescharacteristic
60C2×C4×C37C2×D411yescharacteristic
61C2×Dic37—21no—
62C2×Dic37—21no—
63C2×Dic37C22⋊C411yescharacteristic
64C2×Dic37C22⋊C411yescharacteristic
65C2×Dic37C22⋊C411yescharacteristic
66C4×D37—22no—
67C4×D37—22no—
68C4×D37—41no—
69Dic74—42no—
70Dic74—42no—
71C8×C37—22no—
72C8×C37—41no—
73#64436—22no—
74#64436—41no—
75C22×C37C2×C22⋊C411yescharacteristic
76C2×D37—21no—
77C2×D37—21no—
78C2×D37#10112yes—
79C4×C37—21no—
80C4×C37—21no—
81C4×C37—21no—
82C4×C37—41no—
83C4×C37—41no—
84Dic37—21no—
85Dic37—21no—
86Dic37—41no—
87Dic37—41no—
88Dic37#10412yes—
89#1531—371nomaximal, Sylow
90C2×C37C2×#10111yescharacteristic
91C2×C37C2×#10411yescharacteristic
92C2×C37#42111yescharacteristic
93D37—22no—
94#533—371no—
95#432—371no—
96C2×#97—371no—
97#330—371no—
98#330—371no—
99#330—371no—
100#330D3711yescharacteristic, complemented
101C37#153111yescharacteristic, complemented, Sylow
102C22×C8—741no—
103C4⋊Q8—371no—
104C4⋊Q8—371no—
105#125—371no—
106#125C2×D3711yescharacteristic
107C22⋊Q8—741no—
108C22⋊Q8—741no—
109C4×Q8—741no—
110C4×Q8—741no—
111#117—371no—
112#117—371no—
113C2×C42—371no—
114C4⋊C8—741no—
115C22⋊C8—741no—
116#97—371no—
117#97—371no—
118#97—741no—
119#97C2×D3711yescharacteristic
120#97C2×D3711yescharacteristic
121C2×Q8—741no—
122C2×Q8—741no—
123C22×C4—371no—
124C22×C4—371no—
125C22×C4—371no—
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—744no—
129C2×C8—741no—
130C2×C8—741no—
131C4⋊C4—21no—
132C4⋊C4—21no—
133C4⋊C4—371no—
134C4⋊C4—371no—
135C4⋊C4—741no—
136C4⋊C4—741no—
137C4⋊C4—741no—
138C4⋊C4—741no—
139C4⋊C4C4×D3711yescharacteristic
140C4⋊C4C4×D3711yescharacteristic
141C22⋊C4—741no—
142C22⋊C4—741no—
143C42—371no—
144C42—371no—
145C42—371no—
146C42—741no—
147C42—741no—
148C42C22×D3711yescharacteristic
149C23—371no—
150Q8—1482no—
151Q8—1482no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—371no—
155C2×C4—371no—
156C2×C4—371no—
157C2×C4—742no—
158C2×C4—742no—
159C2×C4—741no—
160C2×C4—741no—
161C2×C4—1481no—
162C2×C4C2×C4×D3711yescharacteristic
163C2×C4D4×D3711yescharacteristic
164C2×C4D4×D3711yescharacteristic
165C8—22no—
166C8—41no—
167C8—742no—
168C8—1481no—
169C22—372no—
170C22—741no—
171C22—741no—
172C22C22⋊C4×D3711yescharacteristic
173C4—21no—
174C4—21no—
175C4—21no—
176C4—41no—
177C4—41no—
178C4—372no—
179C4—741no—
180C4—741no—
181C4—1481no—
182C4—1481no—
183C2—742no—
184C2#101×D3711yescharacteristic
185C2#104×D3711yescharacteristic
186C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC42C22×D37
FittingC37×#330C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D37C22⋊C4
cosocleC42×C37C23
hypercenter#330D37
hypocenterC37#1531
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
4. #14557275C2semidirect
5. #14557274C2semidirect
6. #14557274C2semidirect
7. C37×#330C2semidirect
100. #330D37semidirect
101. C37#1531semidirect

Maximal subgroups

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

subgroupindex
#145580892
#145575882
#97×D372
#145572752
#145572742
C37×#3302
#153137