Finite Group Databasebeta

← #17995025

Subgroups — #17995025

Order 4736.

432 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C23×#64436C211yesmaximal, characteristic, complemented
2C2×#11924457C212yesmaximal, complemented
3#14557393C211yesmaximal, characteristic, complemented
4#14557295C212yesmaximal, complemented
5C2×#121×C37C211yesmaximal, characteristic
6C22×#64436—22no—
7C22×#64436—24no—
8C22×#64436C2212yes—
9C2×C4⋊Dic37C2212yes—
10C2×C22⋊Dic37—21no—
11#11924457—24no—
12#11924443—21no—
13C22×D4×C37—21no—
14C22×D4×C37C2211yescharacteristic
15C23×C4×C37C2211yescharacteristic
16#121×C37—22no—
17#121×C37C414yescomplemented
18C2×C4⋊C4×C37C2211yescharacteristic
19C2×C22⋊C4×C37—21no—
20C24×C37—21no—
21C24×C37D411yescharacteristic
22C2×D4×C37—24no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37—22no—
26C2×D4×C37—42no—
27C2×D4×C37—42no—
28C2×D4×C37C2×C412yes—
29C22×C4×C37—22no—
30C22×C4×C37—22no—
31C22×C4×C37—21no—
32C22×C4×C37C2×C412yes—
33C22×C4×C37D411yescharacteristic
34C22×C4×C37D412yes—
35C22×C4×C37C2311yescharacteristic
36C22×Dic37—22no—
37C4⋊C4×C37—21no—
38C4⋊C4×C37C2×C412yes—
39C22⋊C4×C37—24no—
40C22⋊Dic37—42no—
41C4⋊Dic37—22no—
42C4⋊Dic37—22no—
43C2×#64436—28no—
44C2×#64436—22no—
45C2×#64436—22no—
46C2×#64436D414yescomplemented
47C23×C37—22no—
48C23×C37—22no—
49C23×C37—22no—
50C23×C37—42no—
51C23×C37—41no—
52C23×C37—41no—
53C23×C37—42no—
54C23×C37C22⋊C412yes—
55C23×C37D812yes—
56C23×C37SD1612yes—
57C23×C37C2×D411yescharacteristic
58D4×C37—24no—
59D4×C37—48no—
60D4×C37—41no—
61D4×C37—41no—
62C2×C4×C37—22no—
63C2×C4×C37—24no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—22no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37C22⋊C412yes—
70C2×C4×C37C22×C411yescharacteristic
71C2×C4×C37C2×D412yes—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37#4112yes—
74C2×Dic37—42no—
75C2×Dic37—42no—
76C2×Dic37—42no—
77#64436—24no—
78C22×C37—22no—
79C22×C37—22no—
80C22×C37—24no—
81C22×C37—24no—
82C22×C37—42no—
83C22×C37—42no—
84C22×C37—42no—
85C22×C37—82no—
86C22×C37—82no—
87C22×C37#10214yescomplemented
88C22×C37C2×C22⋊C411yescharacteristic
89C22×C37#12112yes—
90C22×C37C2×D811yescharacteristic
91C22×C37C2×SD1611yescharacteristic
92C22×C37#13512yes—
93C4×C37—22no—
94C4×C37—42no—
95C4×C37C4×D412yes—
96C4×C37#12011yescharacteristic
97C4×C37#12311yescharacteristic
98Dic37—82no—
99#1893—371nomaximal, Sylow
100C2×C37—24no—
101C2×C37—82no—
102C2×C37#38611yescharacteristic
103C2×C37C2×#10211yescharacteristic
104C2×C37#41611yescharacteristic
105C2×C37#46512yes—
106C2×C37#46612yes—
107C23×C8—371no—
108C2×#121D3711yescharacteristic
109C2×#102—372no—
110#380—371no—
111#340—372no—
112C37#189311yescharacteristic, complemented, Sylow
113C22×D4—21no—
114C22×D4C2×D3711yescharacteristic
115C23×C4C2×D3711yescharacteristic
116C22×C8—372no—
117C22×C8—744no—
118C22×C8—742no—
119#121—22no—
120#121Dic3714yescomplemented
121C2×C4⋊C4—372no—
122C2×C4⋊C4C2×D3711yescharacteristic
123C2×C22⋊C4—21no—
124C2×C22⋊C4—741no—
125#102—744no—
126#95—741no—
127C24—21no—
128C24C22⋊D3711yescharacteristic
129C2×D4—24no—
130C2×D4—22no—
131C2×D4—22no—
132C2×D4—21no—
133C2×D4—42no—
134C2×D4—42no—
135C2×D4C2×Dic3712yes—
136C22×C4—22no—
137C22×C4—22no—
138C22×C4—21no—
139C22×C4—742no—
140C22×C4C2×Dic3712yes—
141C22×C4C22⋊D3711yescharacteristic
142C22×C4C22⋊D3712yes—
143C22×C4C22×D3711yescharacteristic
144C2×C8—374no—
145C2×C8—748no—
146C2×C8—742no—
147C2×C8—742no—
148C4⋊C4—21no—
149C4⋊C4—742no—
150C4⋊C4—742no—
151C4⋊C4C2×Dic3712yes—
152C22⋊C4—24no—
153C22⋊C4—1482no—
154C23—22no—
155C23—22no—
156C23—22no—
157C23—42no—
158C23—41no—
159C23—41no—
160C23—42no—
161C23#1059693912yes—
162C23#1059694012yes—
163C23C22⋊Dic3712yes—
164C23C2×C22⋊D3711yescharacteristic
165D4—24no—
166D4—48no—
167D4—41no—
168D4—41no—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—1482no—
177C2×C4—1482no—
178C2×C4—1482no—
179C2×C4C22⋊Dic3712yes—
180C2×C4D4×D3712yes—
181C2×C4#1059696412yes—
182C2×C4C22×Dic3711yescharacteristic
183C2×C4C2×C22⋊D3711yescharacteristic
184C8—744no—
185C22—24no—
186C22—24no—
187C22—22no—
188C22—22no—
189C22—42no—
190C22—42no—
191C22—42no—
192C22—82no—
193C22—82no—
194C22#1192445714yescomplemented
195C22C2×C22⋊Dic3711yescharacteristic
196C22#1192450812yes—
197C22C2×#1059693911yescharacteristic
198C22C2×#1059694011yescharacteristic
199C22#1192455612yes—
200C4—22no—
201C4—42no—
202C4—2962no—
203C4D4×Dic3712yes—
204C4#1192450411yescharacteristic
205C4#1192451711yescharacteristic
206C2—24no—
207C2—82no—
208C2#1455741311yescharacteristic
209C2C2×#1192445711yescharacteristic
210C2#1455752911yescharacteristic
211C2#1455776012yes—
212C2#1455776712yes—
subgroupG/H
centerC23C2×C22⋊D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC2×#121×C37C2
socleC23×C37C2×D4
cosocleC22×C4×C37C23
hypercenterC2×#121D37
hypocenterC37#1893
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C23×#64436C2semidirect
2. C2×#11924457C2semidirect
3. #14557393C2semidirect
4. #14557295C2semidirect
17. #121×C37C4semidirect
46. C2×#64436D4semidirect
87. C22×C37#102semidirect
112. C37#1893semidirect
120. #121Dic37semidirect
194. C22#11924457semidirect

Maximal subgroups

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

subgroupindex
C23×#644362
C2×#119244572
#145573932
#145572952
C2×#121×C372
#189337