Finite Group Databasebeta

← #17996267

Subgroups — #17996267

Order 4736.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#14558097C211yesmaximal, characteristic
2#14557507C211yesmaximal, characteristic, complemented
3#14557325C214yesmaximal, complemented
4C37×#410C211yesmaximal, characteristic, complemented
5C22×D148C411yescharacteristic, complemented
6#11924532C2212yes—
7#11924525C412yescomplemented
8#11924510—21no—
9#11924510—21no—
10#11924504—21no—
11#11924504—21no—
12#11924495—21no—
13#11924495C411yescharacteristic, complemented
14#11924451—21no—
15#11924451C2212yescomplemented
16C2×#41×C37C2211yescharacteristic
17#117×C37—21no—
18#99×C37—21no—
19#99×C37C2212yescomplemented
20C23×D37—21no—
21#41×C37—41no—
22#41×C37—41no—
23C2×Q8×C37C2×C411yescharacteristic
24C2×D4×C37D411yescharacteristic
25C2×D4×C37D411yescharacteristic
26C2×D4×C37C2311yescharacteristic
27C22×C4×C37C2×C411yescharacteristic
28C22×C4×C37D411yescharacteristic
29C22×C4×C37D411yescharacteristic
30C2×C22⋊D37—22no—
31C2×C22⋊D37—22no—
32C2×D148—21no—
33C2×D148—41no—
34C2×D148—41no—
35C2×D148C2×C412yes—
36C4⋊C4×C37—41no—
37C22⋊C4×C37—22no—
38C42×C37—41no—
39C22⋊Dic37—21no—
40C22⋊Dic37—22no—
41#10596938—22no—
42#10596938—22no—
43C4⋊Dic37—21no—
44C4⋊Dic37—41no—
45C4×Dic37—41no—
46C4×Dic37C2×C412yes—
47C23×C37C22⋊C411yescharacteristic
48C23×C37C2×D411yescharacteristic
49C23×C37C2×D411yescharacteristic
50C22×D37—22no—
51C22×D37—42no—
52C22×D37—82no—
53Q8×C37—41no—
54D4×C37—41no—
55D4×C37—41no—
56D4×C37—41no—
57C2×C4×C37—21no—
58C2×C4×C37—21no—
59C2×C4×C37—21no—
60C2×C4×C37—21no—
61C2×C4×C37—21no—
62C2×C4×C37—21no—
63C2×C4×C37—42no—
64C2×C4×C37C22⋊C411yescharacteristic
65C2×C4×C37C22⋊C411yescharacteristic
66C2×C4×C37C22⋊C411yescharacteristic
67C2×C4×C37C22×C411yescharacteristic
68C22⋊D37—82no—
69C22⋊D37—82no—
70C2×Dic37—22no—
71C2×Dic37—42no—
72D148—42no—
73D148—41no—
74D148—41no—
75C22×C37—21no—
76C22×C37—21no—
77C22×C37—21no—
78C22×C37—41no—
79C22×C37—41no—
80C22×C37—41no—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—42no—
83C2×D37—42no—
84C2×D37—42no—
85C2×D37—84no—
86C4×C37—21no—
87C4×C37—21no—
88C4×C37—21no—
89C4×C37—82no—
90C4×C37#9911yescharacteristic
91C4×C37#9911yescharacteristic
92Dic37—42no—
93Dic37—82no—
94#2128—371nomaximal, Sylow
95C2×C37—21no—
96C2×C37—41no—
97C2×C37—41no—
98C2×C37—41no—
99C2×C37C2×#9911yescharacteristic
100D37—82no—
101#535—371no—
102#410—371no—
103#410D3711yescharacteristic, complemented
104#353—374no—
105C37#212811yescharacteristic, complemented, Sylow
106C2×#41C2×D3711yescharacteristic
107C22×D4—371no—
108#127—372no—
109#124—372no—
110#121—741no—
111#121—741no—
112#120—741no—
113#120—741no—
114#117—21no—
115#117—371no—
116#117—741no—
117#99—21no—
118#99—372no—
119#99—741no—
120#99C2×D3712yescomplemented
121C24—741no—
122#41—41no—
123#41—41no—
124C2×Q8C4×D3711yescharacteristic
125C2×D4—372no—
126C2×D4—742no—
127C2×D4—742no—
128C2×D4—741no—
129C2×D4—1481no—
130C2×D4—1481no—
131C2×D4D14811yescharacteristic
132C2×D4C22⋊D3711yescharacteristic
133C2×D4C22×D3711yescharacteristic
134C22×C4C4×D3711yescharacteristic
135C22×C4D14811yescharacteristic
136C22×C4C22⋊D3711yescharacteristic
137C4⋊C4—41no—
138C4⋊C4—741no—
139C4⋊C4—1481no—
140C22⋊C4—22no—
141C22⋊C4—741no—
142C22⋊C4—742no—
143C22⋊C4—742no—
144C22⋊C4—742no—
145C42—41no—
146C42—372no—
147C42—1481no—
148C23—2962no—
149C23—742no—
150C23—1482no—
151C23#1059693811yescharacteristic
152C23C2×D14811yescharacteristic
153C23C2×C22⋊D3711yescharacteristic
154Q8—41no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—2962no—
159D4—2962no—
160D4—1482no—
161D4—1481no—
162D4—1481no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—42no—
170C2×C4—742no—
171C2×C4—1482no—
172C2×C4#1059693811yescharacteristic
173C2×C4#1059693811yescharacteristic
174C2×C4#1059693811yescharacteristic
175C2×C4C2×C4×D3711yescharacteristic
176C22—21no—
177C22—21no—
178C22—21no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—2964no—
183C22—1482no—
184C22—1482no—
185C22—1482no—
186C22C2×#1059693811yescharacteristic
187C4—21no—
188C4—21no—
189C4—21no—
190C4—82no—
191C4—2962no—
192C4—1482no—
193C4#1192445011yescharacteristic
194C4#1192445011yescharacteristic
195C2—21no—
196C2—41no—
197C2—41no—
198C2—41no—
199C2—2962no—
200C2C2×#1192445011yescharacteristic
subgroupG/H
centerC2C2×#11924450
commutatorC2×C4×C37C22×C4
FrattiniC2×D4C22×D37
FittingC37×#410C2
socleC2×C37C2×#99
prime radical#14558097C2
cosocleC2×D4×C37C23
hypercenter#410D37
hypocenterC37#2128
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14557507C2semidirect
3. #14557325C2semidirect
4. C37×#410C2semidirect
5. C22×D148C4semidirect
7. #11924525C4semidirect
13. #11924495C4semidirect
15. #11924451C22semidirect
19. #99×C37C22semidirect
103. #410D37semidirect
105. C37#2128semidirect
120. #99C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580972
#145575072
#145573252
C37×#4102
#212837