Finite Group Databasebeta

← #17995045

Subgroups — #17995045

Order 4736.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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×#11924495C211yesmaximal, characteristic, complemented
2C2×#11924463C212yesmaximal, complemented
3#14557497C211yesmaximal, characteristic, complemented
4#14557292C212yesmaximal, complemented
5C37×#525C211yesmaximal, characteristic
6C2×#10596934C2212yes—
7#11924495—24no—
8C2×C4⋊Dic37—21no—
9C2×C22⋊Dic37—21no—
10C2×C4×Dic37C2212yes—
11#11924463—24no—
12C22⋊#64436—22no—
13C2×#41×C37C2211yescharacteristic
14C23×C4×C37C2211yescharacteristic
15#123×C37—21no—
16C22⋊Q8×C37C412yescomplemented
17#121×C37C412yescomplemented
18#120×C37—21no—
19C4×D4×C37—22no—
20#117×C37C2211yescharacteristic
21C24×C37D411yescharacteristic
22#41×C37—22no—
23#41×C37—22no—
24C2×Q8×C37C2×C411yescharacteristic
25C2×D4×C37—22no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37—22no—
29C22×C4×C37—22no—
30C22×C4×C37—21no—
31C22×C4×C37C2×C412yes—
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D412yes—
34C22×C4×C37C2311yescharacteristic
35C22×Dic37—22no—
36C4⋊C4×C37—22no—
37C4⋊C4×C37C2×C412yes—
38C22⋊C4×C37—22no—
39C22⋊C4×C37—21no—
40C22⋊C4×C37—22no—
41C42×C37—21no—
42C22⋊Dic37—24no—
43C4⋊Dic37—24no—
44C4×Dic37—22no—
45C4×Dic37D414yescomplemented
46#10596934—22no—
47#10596934—22no—
48C2×#64436—22no—
49C23×C37—21no—
50C23×C37—21no—
51C23×C37—21no—
52C23×C37—42no—
53C23×C37C22⋊C412yes—
54C23×C37C2×D411yescharacteristic
55Q8×C37—22no—
56D4×C37—22no—
57D4×C37—44no—
58D4×C37—41no—
59D4×C37—41no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—24no—
63C2×C4×C37—24no—
64C2×C4×C37—22no—
65C2×C4×C37—21no—
66C2×C4×C37—42no—
67C2×C4×C37C22⋊C412yes—
68C2×C4×C37C22×C411yescharacteristic
69C2×C4×C37C2×D412yes—
70C2×C4×C37C2×D411yescharacteristic
71C2×C4×C37#4112yes—
72C2×Dic37—24no—
73C2×Dic37—44no—
74#64436—42no—
75C22×C37—22no—
76C22×C37—22no—
77C22×C37—22no—
78C22×C37—22no—
79C22×C37—42no—
80C22×C37—42no—
81C22×C37—41no—
82C22×C37—42no—
83C22×C37C2×C22⋊C411yescharacteristic
84C22×C37#12011yescharacteristic
85C22×C37#12311yescharacteristic
86C4×C37—22no—
87C4×C37—41no—
88C4×C37—42no—
89C4×C37C4×D412yes—
90C4×C37#12112yes—
91Dic37—44no—
92#1897—371nomaximal, Sylow
93C2×C37—21no—
94C2×C37—21no—
95C2×C37—42no—
96C2×C37—81no—
97C2×C37#38611yescharacteristic
98C2×C37#42112yes—
99#525D3711yescharacteristic
100C2×#117—371no—
101C2×#104—372no—
102#407—371no—
103#339—372no—
104C37#189711yescharacteristic, complemented, Sylow
105C2×#41C2×D3711yescharacteristic
106C23×C4C2×D3711yescharacteristic
107C2×M16—372no—
108#123—21no—
109C22⋊Q8Dic3712yescomplemented
110#121Dic3712yescomplemented
111#120—21no—
112C4×D4—22no—
113#117—744no—
114#117C2×D3711yescharacteristic
115C2×C4⋊C4—741no—
116C2×C22⋊C4—741no—
117C2×C42—372no—
118#104—744no—
119C22⋊C8—742no—
120C24C22⋊D3711yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic3711yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic3711yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—742no—
131C22×C4C2×Dic3712yes—
132C22×C4C22⋊D3711yescharacteristic
133C22×C4C22⋊D3712yes—
134C22×C4C22×D3711yescharacteristic
135M16—742no—
136M16—742no—
137C2×C8—742no—
138C4⋊C4—22no—
139C4⋊C4—744no—
140C4⋊C4C2×Dic3712yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—744no—
145C42—21no—
146C42—374no—
147C42—742no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic3712yes—
153C23C2×C22⋊D3711yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—744no—
167C2×C4—1484no—
168C2×C4C22⋊Dic3712yes—
169C2×C4D4×D3712yes—
170C2×C4#1059696412yes—
171C2×C4C22×Dic3711yescharacteristic
172C2×C4C2×C22⋊D3711yescharacteristic
173C8—1482no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22C2×C22⋊Dic3711yescharacteristic
183C22#1192450411yescharacteristic
184C22#1192451711yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—1484no—
189C4D4×Dic3712yes—
190C4#1192450812yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#1455741311yescharacteristic
196C2#1455755012yes—
subgroupG/H
centerC2×C4C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC37×#525C2
socleC22×C37C2×C22⋊C4
cosocleC22×C4×C37C23
hypercenter#525D37
hypocenterC37#1897
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11924495C2semidirect
2. C2×#11924463C2semidirect
3. #14557497C2semidirect
4. #14557292C2semidirect
16. C22⋊Q8×C37C4semidirect
17. #121×C37C4semidirect
45. C4×Dic37D4semidirect
104. C37#1897semidirect
109. C22⋊Q8Dic37semidirect
110. #121Dic37semidirect

Maximal subgroups

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

subgroupindex
C2×#119244952
C2×#119244632
#145574972
#145572922
C37×#5252
#189737