Finite Group Databasebeta

← #17995009

Subgroups — #17995009

Order 4736.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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×#11924517C211yesmaximal, characteristic
2C2×#11924451C211yesmaximal, characteristic
3#14557394C212yesmaximal, complemented
4#14557300C212yesmaximal, complemented
5C37×#518C211yesmaximal, characteristic
6C23×Dic37C2211yescharacteristic
7#11924517—22no—
8#11924517C414yescomplemented
9C2×#10596936—21no—
10C2×C22⋊Dic37—21no—
11C2×C22⋊Dic37C2212yes—
12C2×C22⋊Dic37C2211yescharacteristic
13#11924451—22no—
14#11924443—24no—
15C22×D4×C37C2211yescharacteristic
16C4×D4×C37—24no—
17#117×C37—21no—
18C2×C22⋊C4×C37—21no—
19C2×C22⋊C4×C37C2212yes—
20C24×C37D411yescharacteristic
21C24×C37C2311yescharacteristic
22C2×D4×C37—22no—
23C2×D4×C37—22no—
24C2×D4×C37C2×C412yes—
25C2×D4×C37D412yes—
26C22×C4×C37—22no—
27C22×C4×C37D411yescharacteristic
28C22×C4×C37D414yes—
29C22×Dic37—21no—
30C22×Dic37—21no—
31C22×Dic37—21no—
32C22×Dic37—22no—
33C22×Dic37—22no—
34C22×Dic37—22no—
35C22×Dic37C2×C412yescomplemented
36C4⋊C4×C37—22no—
37C22⋊C4×C37—22no—
38C22⋊C4×C37—22no—
39C22⋊C4×C37—22no—
40C42×C37—22no—
41C22⋊Dic37—24no—
42C22⋊Dic37—21no—
43C22⋊Dic37—22no—
44C22⋊Dic37—22no—
45C22⋊Dic37C2×C412yescomplemented
46#10596936—24no—
47C23×C37—21no—
48C23×C37—21no—
49C23×C37—42no—
50C23×C37—42no—
51C23×C37C22⋊C412yes—
52C23×C37C22×C411yescharacteristic
53C23×C37C2×D411yescharacteristic
54C23×C37C2×D411yescharacteristic
55C23×C37C2×D412yes—
56C23×C37#4112yes—
57D4×C37—24no—
58D4×C37—24no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—24no—
62C2×C4×C37—44no—
63C2×C4×C37—82no—
64C2×C4×C37C22⋊C412yes—
65C2×Dic37—22no—
66C2×Dic37—22no—
67C2×Dic37—24no—
68C2×Dic37—42no—
69C2×Dic37—41no—
70C2×Dic37—42no—
71C2×Dic37—41no—
72C2×Dic37—44no—
73C2×Dic37—42no—
74C22×C37—24no—
75C22×C37—22no—
76C22×C37—22no—
77C22×C37—41no—
78C22×C37—41no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37—42no—
82C22×C37—81no—
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37C4×D412yes—
85C22×C37#12011yescharacteristic
86C22×C37#12112yes—
87C22×C37#12311yescharacteristic
88C4×C37—22no—
89C4×C37—44no—
90Dic37—42no—
91Dic37—42no—
92Dic37—82no—
93#1890—371nomaximal, Sylow
94C2×C37—21no—
95C2×C37—22no—
96C2×C37—21no—
97C2×C37—22no—
98C2×C37—42no—
99C2×C37#38611yescharacteristic
100C2×C37#45812yes—
101C2×#123—371no—
102#518D3711yescharacteristic
103C2×#99—371no—
104#381—372no—
105#342—372no—
106C37#189011yescharacteristic, complemented, Sylow
107C22×D4C2×D3711yescharacteristic
108C23×C4—371no—
109#123—374no—
110#123—742no—
111C4×D4—24no—
112#117—21no—
113C2×C4⋊C4—741no—
114C2×C22⋊C4—21no—
115C2×C22⋊C4—371no—
116C2×C22⋊C4—372no—
117C2×C22⋊C4—741no—
118C2×C22⋊C4C2×D3712yes—
119#99—742no—
120#95—744no—
121C24C22⋊D3711yescharacteristic
122C24C22×D3711yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C4×D3712yes—
126C2×D4D14812yes—
127C22×C4—22no—
128C22×C4—372no—
129C22×C4—741no—
130C22×C4—742no—
131C22×C4—742no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4—742no—
135C22×C4C22⋊D3711yescharacteristic
136C22×C4C22⋊D3714yes—
137C4⋊C4—22no—
138C4⋊C4—744no—
139C22⋊C4—22no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—372no—
143C22⋊C4—744no—
144C22⋊C4—741no—
145C22⋊C4—742no—
146C22⋊C4—742no—
147C42—22no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23#1059693812yes—
153C23C2×C4×D3711yescharacteristic
154C23C2×D14811yescharacteristic
155C23#1059696212yes—
156C23C2×C22⋊D3711yescharacteristic
157C23C2×C22⋊D3712yes—
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—44no—
164C2×C4—82no—
165C2×C4—742no—
166C2×C4—742no—
167C2×C4—744no—
168C2×C4—1484no—
169C2×C4—1482no—
170C2×C4—1482no—
171C2×C4—1481no—
172C2×C4—1482no—
173C2×C4—1481no—
174C2×C4#1059693812yes—
175C22—24no—
176C22—22no—
177C22—22no—
178C22—41no—
179C22—41no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22C2×#1059693811yescharacteristic
185C22C4×C22⋊D3712yes—
186C22#1192450511yescharacteristic
187C22#1192451012yes—
188C22#1192451911yescharacteristic
189C4—22no—
190C4—44no—
191C4—2962no—
192C4—1482no—
193C4—1482no—
194C2—22no—
195C2—21no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1455741211yescharacteristic
200C2#1455772312yes—
subgroupG/H
centerC22#11924505
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#518C2
socleC22×C37#120
prime radicalC22×D4×C37C22
cosocleC24×C37C23
hypercenter#518D37
hypocenterC37#1890
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
3. #14557394C2semidirect
4. #14557300C2semidirect
8. #11924517C4semidirect
35. C22×Dic37C2×C4semidirect
45. C22⋊Dic37C2×C4semidirect
106. C37#1890semidirect

Maximal subgroups

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

subgroupindex
C2×#119245172
C2×#119244512
#145573942
#145573002
C37×#5182
#189037