Finite Group Databasebeta

← #17995575

Subgroups — #17995575

Order 4736.

244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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#14558086C211yesmaximal, characteristic
2#14557556C211yesmaximal, characteristic
3#14557379C211yesmaximal, characteristic
4#14557294C211yesmaximal, characteristic
5#14557293C211yesmaximal, characteristic
6#14557292C211yesmaximal, characteristic
7C37×#339C211yesmaximal, characteristic
8C2×#10596934C2211yescharacteristic
9#11924535C412yescomplemented
10#11924527C412yescomplemented
11#11924513—22no—
12C4×Dic74—22no—
13#11924495C2211yescharacteristic
14C2×C4×Dic37C2211yescharacteristic
15C2×C4×Dic37C2211yescharacteristic
16#11924465—22no—
17#11924443—22no—
18C2×M16×C37C2211yescharacteristic
19#117×C37C2211yescharacteristic
20C2×C42×C37C2211yescharacteristic
21C22×C4×C37—21no—
22C22×C4×C37C2311yescharacteristic
23C22×Dic37—21no—
24C22×Dic37D412yes—
25C2×Dic74—22no—
26M16×C37—21no—
27M16×C37—21no—
28C2×C8×C37—21no—
29C4⋊C4×C37C2×C412yes—
30C22⋊C4×C37—21no—
31C42×C37—21no—
32C42×C37—21no—
33C42×C37Q812yescomplemented
34C22⋊Dic37—21no—
35C4⋊Dic37—22no—
36C4⋊Dic37C2×C412yes—
37#10596936—22no—
38#10596936—22no—
39C4×Dic37—21no—
40C4×Dic37—21no—
41C4×Dic37C2×C411yescharacteristic
42C4×Dic37C2×C411yescharacteristic
43C4×Dic37D412yes—
44C4×Dic37Q812yescomplemented
45#10596934—21no—
46#10596934—21no—
47C2×#64436—21no—
48C23×C37C2×D411yescharacteristic
49C2×C4×C37—22no—
50C2×C4×C37—22no—
51C2×C4×C37—42no—
52C2×C4×C37C22×C411yescharacteristic
53C2×C4×C37C2×D411yescharacteristic
54C2×C4×C37C2×Q811yescharacteristic
55C2×C4×C37C2×Q811yescharacteristic
56C2×C4×C37#4111yescharacteristic
57C2×C4×C37#4111yescharacteristic
58C2×Dic37—22no—
59C2×Dic37—22no—
60C2×Dic37—42no—
61C2×Dic37—42no—
62C2×Dic37C22⋊C412yes—
63C2×Dic37C22⋊C412yes—
64Dic74—44no—
65C8×C37—41no—
66#64436—41no—
67C22×C37—22no—
68C22×C37C2×C22⋊C411yescharacteristic
69C22×C37C22⋊Q811yescharacteristic
70C22×C37C22⋊Q811yescharacteristic
71C4×C37—42no—
72C4×C37—42no—
73C4×C37C4×Q811yescharacteristic
74C4×C37C4×Q811yescharacteristic
75C4×C37#12411yescharacteristic
76C4×C37C4⋊Q811yescharacteristic
77Dic37—22no—
78Dic37—22no—
79Dic37—42no—
80Dic37—42no—
81#1995—371nomaximal, Sylow
82C2×C37—21no—
83C2×C37—21no—
84C2×C37#39111yescharacteristic
85C2×C37#42112yes—
86#533—371no—
87#423—371no—
88#376—371no—
89#339—371no—
90#339—371no—
91#339—371no—
92#339D3711yescharacteristic
93C37#199511yescharacteristic, complemented, Sylow
94C2×M16—371no—
95C2×M16C2×D3711yescharacteristic
96C4⋊Q8—372no—
97#125—372no—
98C22⋊Q8—742no—
99C4×Q8—742no—
100#117—371no—
101#117C2×D3711yescharacteristic
102C2×C42—371no—
103C2×C42—371no—
104C2×C42C2×D3711yescharacteristic
105C4⋊C8—742no—
106#95—742no—
107C2×Q8—742no—
108C22×C4—21no—
109C22×C4—372no—
110C22×C4—741no—
111C22×C4C22×D3711yescharacteristic
112M16—21no—
113M16—21no—
114M16—741no—
115M16—741no—
116C2×C8—21no—
117C2×C8—741no—
118C4⋊C4—372no—
119C4⋊C4—742no—
120C4⋊C4—742no—
121C4⋊C4—742no—
122C4⋊C4C4×D3712yes—
123C22⋊C4—21no—
124C22⋊C4—741no—
125C42—21no—
126C42—21no—
127C42—371no—
128C42—371no—
129C42—372no—
130C42—372no—
131C42—741no—
132C42—741no—
133C42Dic7412yescomplemented
134C23D4×D3711yescharacteristic
135Q8—1484no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—372no—
140C2×C4—372no—
141C2×C4—742no—
142C2×C4—742no—
143C2×C4—1482no—
144C2×C4—1482no—
145C2×C4C2×Dic7411yescharacteristic
146C2×C4C2×C4×D3711yescharacteristic
147C2×C4#1059696211yescharacteristic
148C2×C4D4×D3711yescharacteristic
149C2×C4#1059696411yescharacteristic
150C2×C4Q8×D3711yescharacteristic
151C8—41no—
152C8—1481no—
153C22—22no—
154C22C22⋊C4×D3711yescharacteristic
155C22#1192451311yescharacteristic
156C22#1192451411yescharacteristic
157C4—42no—
158C4—42no—
159C4—742no—
160C4—742no—
161C4—1482no—
162C4—1482no—
163C4#1192450111yescharacteristic
164C4C4×Dic7411yescharacteristic
165C4#1192452211yescharacteristic
166C4#1192453511yescharacteristic
167C2—21no—
168C2—21no—
169C2#1455743711yescharacteristic
170C2#1455754812yes—
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37C2×C22⋊C4
prime radicalC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1995
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #11924535C4semidirect
10. #11924527C4semidirect
33. C42×C37Q8semidirect
44. C4×Dic37Q8semidirect
93. C37#1995semidirect
133. C42Dic74semidirect

Maximal subgroups

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

subgroupindex
#145580862
#145575562
#145573792
#145572942
#145572932
#145572922
C37×#3392
#199537