Finite Group Databasebeta

← #18010760

Subgroups — #18010760

Order 4736.

336 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 74 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×#11924600C214yesmaximal, complemented
2C4×#10596953C211yesmaximal, characteristic, complemented
3C4×C4⋊#3866C211yesmaximal, characteristic, complemented
4#14558081C211yesmaximal, characteristic
5C2×#10596953C2212yes—
6C2×C4⋊#3866—21no—
7C2×C4×#3866C2212yes—
8#11924600—28no—
9#11924591—21no—
10C4×#64438—21no—
11(C2×#3866)⋊C4—21no—
12C2×#10596964C2212yes—
13#11924536C411yescharacteristic, complemented
14#11924523C412yescomplemented
15#11924507—21no—
16#11924507—21no—
17D4×Dic37—21no—
18D4×Dic37—21no—
19C42×D37C2211yescharacteristic
20#127×C37C411yescharacteristic, complemented
21C22×#3866—22no—
22C2×D4×C37—21no—
23C2×D4×C37—21no—
24C2×D4×C37C2×C412yes—
25C2×C22⋊D37—22no—
26C22×Dic37—22no—
27#10596964—24no—
28#10596964—24no—
29C2×C4×D37D411yescharacteristic
30C2×C4×D37D411yescharacteristic
31C2×C4×D37C2311yescharacteristic
32C2×Dic74C2×C412yes—
33C2×#64438—22no—
34C4⋊#3866—24no—
35C4×#3866—24no—
36#10596953—22no—
37#10596953D414yescomplemented
38C42×C37C2×C411yescharacteristic
39C22⋊Dic37—22no—
40C22⋊Dic37—22no—
41C4⋊Dic37—21no—
42C4⋊Dic37—21no—
43C4×Dic37C2×C411yescharacteristic
44C4×Dic37D411yescharacteristic
45C4×Dic37D411yescharacteristic
46C23×C37—22no—
47C22×D37C2×D411yescharacteristic
48C2×#3866—24no—
49C2×#3866—42no—
50C2×#3866—42no—
51D4×C37—24no—
52D4×C37—42no—
53D4×C37—42no—
54C2×C4×C37C22⋊C411yescharacteristic
55C2×C4×C37C22⋊C411yescharacteristic
56C2×C4×C37C22×C411yescharacteristic
57C22⋊D37—42no—
58C22⋊D37—42no—
59C2×Dic37—22no—
60C2×Dic37—44no—
61C2×Dic37C22⋊C411yescharacteristic
62C2×Dic37C22⋊C411yescharacteristic
63C2×Dic37C2×D411yescharacteristic
64C4×D37—22no—
65C4×D37—41no—
66C4×D37C2×D412yes—
67C4×D37#4112yes—
68Dic74—24no—
69#64438—24no—
70C22×C37—42no—
71C22×C37—42no—
72C22×C37—42no—
73C22×C37C2×C22⋊C411yescharacteristic
74C2×D37—21no—
75C2×D37—21no—
76C2×D37#12411yescharacteristic
77C2×D37#12711yescharacteristic
78#3866—44no—
79C4×C37—21no—
80C4×C37#10412yescomplemented
81C4×C37C4×D412yes—
82Dic37—21no—
83Dic37—21no—
84Dic37—42no—
85Dic37#12112yes—
86#1980—371nomaximal, Sylow
87C2×C37—82no—
88C2×C37#39011yescharacteristic
89C2×C37C2×#10411yescharacteristic
90C2×C37#42111yescharacteristic
91D37—21no—
92D37—21no—
93#532—371no—
94C2×#104—374no—
95C4×M16—371no—
96C4×C4⋊C4—371no—
97C37#198011yescharacteristic, complemented, Sylow
98C2×#41—372no—
99C2×M16—372no—
100C4⋊Q8—371no—
101#127#386611yescharacteristic, complemented
102#124—372no—
103#121—741no—
104#121—741no—
105C4×D4—741no—
106C4×D4—741no—
107C2×C4⋊C4—741no—
108C2×C42—371no—
109C2×C42—372no—
110#104—748no—
111#97—741no—
112C4×C8—741no—
113#95—741no—
114#41—744no—
115#41—744no—
116C2×Q8—372no—
117C2×D4—21no—
118C2×D4—21no—
119C2×D4—742no—
120C2×D4C2×#386612yes—
121C22×C4—371no—
122C22×C4—371no—
123C22×C4—371no—
124C22×C4—742no—
125C22×C4—742no—
126M16—374no—
127M16—742no—
128C2×C8—742no—
129C4⋊C4—744no—
130C4⋊C4—741no—
131C4⋊C4—741no—
132C22⋊C4—742no—
133C22⋊C4—742no—
134C42—371no—
135C42—371no—
136C42—371no—
137C42—744no—
138C42C2×#386611yescharacteristic
139C23—22no—
140C23—371no—
141Q8—744no—
142D4—24no—
143D4—42no—
144D4—42no—
145D4—1482no—
146D4—1482no—
147C2×C4—371no—
148C2×C4—372no—
149C2×C4—372no—
150C2×C4—371no—
151C2×C4—371no—
152C2×C4—742no—
153C2×C4—744no—
154C2×C4—742no—
155C2×C4—1481no—
156C2×C4—1484no—
157C2×C4—1482no—
158C2×C4—1482no—
159C2×C4C22⋊#386611yescharacteristic
160C2×C4C22⋊#386611yescharacteristic
161C2×C4C22×#386611yescharacteristic
162C8—744no—
163C22—42no—
164C22—42no—
165C22—42no—
166C22—371no—
167C22—371no—
168C22—741no—
169C22—741no—
170C22C2×C22⋊#386611yescharacteristic
171C4—21no—
172C4—372no—
173C4—741no—
174C4—741no—
175C4—1484no—
176C4—1482no—
177C4#1192460012yescomplemented
178C4D4×#386612yes—
179C2—82no—
180C2—741no—
181C2—741no—
182C2#1455848511yescharacteristic
183C2C2×#1192460011yescharacteristic
184C2#1455853111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#127×C37C4
socleC22×C37C2×C22⋊C4
prime radical#14558081C2
cosocleC2×C4×D37C23
hypercenter#127#3866
hypocenterC37#1980
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C2×#11924600C2semidirect
2. C4×#10596953C2semidirect
3. C4×C4⋊#3866C2semidirect
13. #11924536C4semidirect
14. #11924523C4semidirect
20. #127×C37C4semidirect
37. #10596953D4semidirect
80. C4×C37#104semidirect
97. C37#1980semidirect
101. #127#3866semidirect
177. C4#11924600semidirect

Maximal subgroups

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

subgroupindex
C2×#119246002
C4×#105969532
C4×C4⋊#38662
#145580812
#198037