Finite Group Databasebeta

← #17992935

Subgroups — #17992935

Order 4736.

300 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 69 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
1C2×#11924496C211yesmaximal, characteristic
2#14557587C212yesmaximal, complemented
3#14557257C211yesmaximal, characteristic, complemented
4#14557256C212yesmaximal, complemented
5C37×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C411yescharacteristic
7C23×Dic37C411yescharacteristic
8C22×C4×D37C411yescharacteristic
9#11924496—22no—
10#11924496—22no—
11C2×#10596936C411yescharacteristic
12C2×#10596938C2211yescharacteristic
13C2×C4×Dic37C2211yescharacteristic
14#11924465—22no—
15C22⋊#64436C2212yes—
16#11924446—22no—
17C2×C22⋊C4×C37C2211yescharacteristic
18C22⋊C8×C37C2212yes—
19C24×C37C2×C411yescharacteristic
20C23×D37C2×C411yescharacteristic
21C22×C4×C37C2×C411yescharacteristic
22C22×C4×C37C2311yescharacteristic
23C2×C22⋊D37—22no—
24C2×C22⋊D37—22no—
25C2×C22⋊D37—22no—
26C22×Dic37—21no—
27C22×Dic37—21no—
28C22×Dic37—42no—
29C22×Dic37C2×C411yescharacteristic
30C22×Dic37C2×C411yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C2×C4×D37—21no—
33C2×C4×D37—21no—
34C2×C4×D37—42no—
35C2×C8×C37—22no—
36C22⋊C4×C37—22no—
37#10596938—22no—
38#10596936—22no—
39C4×Dic37D412yes—
40C4×Dic37D412yes—
41C2×#64436—22no—
42C23×C37—21no—
43C23×C37—21no—
44C23×C37—41no—
45C23×C37—41no—
46C23×C37M1612yes—
47C23×C37C22×C411yescharacteristic
48C22×D37—21no—
49C22×D37—21no—
50C22×D37—41no—
51C22×D37—41no—
52C22×D37M1612yes—
53C2×C4×C37—21no—
54C2×C4×C37—41no—
55C2×C4×C37—41no—
56C2×C4×C37C2×D412yes—
57C22⋊D37—28no—
58C2×Dic37—21no—
59C2×Dic37—21no—
60C2×Dic37—22no—
61C2×Dic37—21no—
62C2×Dic37—42no—
63C2×Dic37—42no—
64C2×Dic37—41no—
65C2×Dic37C22⋊C412yes—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C22⋊C411yescharacteristic
68C4×D37—42no—
69C4×D37—42no—
70C8×C37—42no—
71#64436—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—22no—
75C22×C37—42no—
76C22×C37—42no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37C2×C22⋊C411yescharacteristic
80C22×C37C2×M1611yescharacteristic
81C22×C37C2×M1611yescharacteristic
82C2×D37—22no—
83C2×D37—42no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—42no—
87C4×C37—22no—
88C4×C37—41no—
89Dic37—22no—
90Dic37—21no—
91Dic37—41no—
92Dic37#10012yes—
93#1466—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—21no—
96C2×C37—42no—
97C2×C37#40711yescharacteristic
98C2×C37#41011yescharacteristic
99C2×C37C2×#10011yescharacteristic
100D37—42no—
101C2×C4×D4—371no—
102#432—372no—
103#323—371no—
104#323—372no—
105#323D3711yescharacteristic, complemented
106C37#146611yescharacteristic, complemented, Sylow
107C22×D4—371no—
108C23×C4—371no—
109C23×C4—371no—
110C4×D4—742no—
111C4×D4—742no—
112C2×C4⋊C4—371no—
113C2×C22⋊C4—371no—
114C2×C22⋊C4C2×D3711yescharacteristic
115C2×C42—371no—
116C4⋊C8—742no—
117C22⋊C8—372no—
118C22⋊C8C2×D3712yes—
119#97—742no—
120C24—371no—
121C24C4×D3711yescharacteristic
122C2×D4—742no—
123C2×D4—742no—
124C2×D4—742no—
125C22×C4—371no—
126C22×C4—371no—
127C22×C4—371no—
128C22×C4—741no—
129C22×C4—741no—
130C22×C4—741no—
131C22×C4—741no—
132C22×C4—1482no—
133C22×C4—1482no—
134C22×C4C4×D3711yescharacteristic
135C22×C4C22×D3711yescharacteristic
136C2×C8—22no—
137C2×C8—742no—
138C4⋊C4—742no—
139C22⋊C4—22no—
140C22⋊C4—742no—
141C42—372no—
142C42—372no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—372no—
148C23—741no—
149C23—741no—
150C23—1481no—
151C23—1481no—
152C23#1059692912yes—
153C23C2×C4×D3711yescharacteristic
154D4—748no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—371no—
159C2×C4—372no—
160C2×C4—371no—
161C2×C4—742no—
162C2×C4—741no—
163C2×C4—741no—
164C2×C4—741no—
165C2×C4—1482no—
166C2×C4—1482no—
167C2×C4—1482no—
168C2×C4—1482no—
169C2×C4—1481no—
170C2×C4D4×D3712yes—
171C8—42no—
172C8—1482no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—742no—
181C22—1482no—
182C22—1482no—
183C22—1481no—
184C22—1481no—
185C22C22⋊C4×D3711yescharacteristic
186C22M16×D3711yescharacteristic
187C22C2×#1059692911yescharacteristic
188C4—22no—
189C4—41no—
190C4—372no—
191C4—742no—
192C4—741no—
193C4—1481no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—1482no—
198C2#1455749511yescharacteristic
199C2#1455750511yescharacteristic
200C2#100×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#323C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C4
cosocleC22×C4×C37C23
hypercenter#323D37
hypocenterC37#1466
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14557587C2semidirect
3. #14557257C2semidirect
4. #14557256C2semidirect
5. C37×#323C2semidirect
105. #323D37semidirect
106. C37#1466semidirect

Maximal subgroups

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

subgroupindex
C2×#119244962
#145575872
#145572572
#145572562
C37×#3232
#146637