Finite Group Databasebeta

← #18004984

Subgroups — #18004984

Order 4736.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558086C211yesmaximal, characteristic, complemented
2C2×#11924525C211yesmaximal, characteristic
3#14557894C214yesmaximal, complemented
4#14557889C214yesmaximal, complemented
5#14557542C211yesmaximal, characteristic, complemented
6#14557539C211yesmaximal, characteristic
7#14557537C211yesmaximal, characteristic
8M16×Dic37C211yesmaximal, characteristic, complemented
9C37×#419C211yesmaximal, characteristic, complemented
10C22×D148C2211yescharacteristic
11C2×#10596934C2211yescharacteristic
12#11924535C2212yescomplemented
13#11924527C2212yescomplemented
14#11924525—22no—
15#11924525C2212yes—
16#11924525C2212yes—
17#11924513—22no—
18C4×Dic74—22no—
19#11924495C2211yescharacteristic
20C2×#10596938—22no—
21C2×C4×Dic37C2211yescharacteristic
22#11924460C2214yescomplemented
23#11924458C2214yes—
24#11924456C2214yes—
25#11924446C2212yescomplemented
26C8×Dic37C2212yescomplemented
27C22×Q8×C37C2211yescharacteristic
28C2×M16×C37C2211yescharacteristic
29#117×C37C2211yescharacteristic
30#103×C37C2214yescomplemented
31C23×D37—21no—
32C2×Q8×C37—21no—
33C2×Q8×C37—22no—
34C2×Q8×C37—22no—
35C2×Q8×C37C2312yes—
36C22×C4×C37—21no—
37C22×C4×C37C2311yescharacteristic
38C22×Dic37D412yes—
39C2×D148—22no—
40C2×D148—22no—
41C2×D148—21no—
42C2×D148C2312yes—
43C2×Dic74—22no—
44M16×C37—22no—
45C2×C8×C37C2312yes—
46C4⋊C4×C37C2312yes—
47C22⋊C4×C37—21no—
48C42×C37—21no—
49C22⋊Dic37—21no—
50#10596938—24no—
51#10596938—24no—
52C4⋊Dic37—22no—
53C4⋊Dic37C2312yes—
54#10596936—22no—
55#10596936—22no—
56C4×Dic37—21no—
57C4×Dic37D412yes—
58C4×Dic37C2311yescharacteristic
59C4×Dic37C2311yescharacteristic
60#10596934—22no—
61C2×#64436C2312yes—
62C23×C37C2×D411yescharacteristic
63C22×D37—22no—
64C22×D37—44no—
65C22×D37—42no—
66Q8×C37—22no—
67Q8×C37—22no—
68Q8×C37—42no—
69C2×C4×C37—22no—
70C2×C4×C37—22no—
71C2×C4×C37—42no—
72C2×C4×C37C2×D411yescharacteristic
73C2×C4×C37#4112yes—
74C2×C4×C37#4112yes—
75C2×C4×C37C2411yescharacteristic
76C2×Dic37—22no—
77C2×Dic37—42no—
78C2×Dic37C2×D412yes—
79C2×Dic37C2×D412yes—
80D148—22no—
81D148—22no—
82D148—42no—
83Dic74—44no—
84C8×C37—22no—
85#64436—22no—
86C22×C37—22no—
87C22×C37#12412yes—
88C22×C37C22×D411yescharacteristic
89C2×D37—42no—
90C2×D37—44no—
91C2×D37—84no—
92C4×C37—42no—
93C4×C37—42no—
94C4×C37#12412yes—
95C4×C37C2×#4111yescharacteristic
96C4×C37C2×#4111yescharacteristic
97Dic37—22no—
98Dic37—22no—
99Dic37—42no—
100#3140—371nomaximal, Sylow
101C2×C37—22no—
102C2×C37C2×#12411yescharacteristic
103C2×C37#57512yes—
104D37—82no—
105#533—371no—
106C2×#124—371no—
107#489—374no—
108#488—374no—
109#419—371no—
110#419D3711yescharacteristic, complemented
111#418—371no—
112#418—371no—
113C4×M16—371no—
114C37#314011yescharacteristic, complemented, Sylow
115C22×Q8C2×D3711yescharacteristic
116C22×D4—371no—
117C2×M16—371no—
118C2×M16C2×D3711yescharacteristic
119C4⋊Q8—372no—
120#125—372no—
121#124—372no—
122#124—372no—
123#124—742no—
124C22⋊Q8—742no—
125C4×Q8—742no—
126#117—371no—
127#117C2×D3711yescharacteristic
128C2×C22⋊C4—742no—
129C2×C42—371no—
130#103—374no—
131#103C2×D3714yescomplemented
132#102—374no—
133#102—374no—
134#97—372no—
135C4×C8—372no—
136C24—741no—
137C2×Q8—21no—
138C2×Q8—22no—
139C2×Q8—22no—
140C2×Q8—742no—
141C2×Q8C22×D3712yes—
142C2×D4—372no—
143C2×D4—742no—
144C2×D4—741no—
145C2×D4—742no—
146C22×C4—21no—
147C22×C4—372no—
148C22×C4C22×D3711yescharacteristic
149M16—22no—
150M16—742no—
151C2×C8—372no—
152C2×C8C22×D3712yes—
153C4⋊C4—372no—
154C4⋊C4—742no—
155C4⋊C4—742no—
156C4⋊C4—742no—
157C4⋊C4C22×D3712yes—
158C22⋊C4—21no—
159C22⋊C4—744no—
160C22⋊C4—744no—
161C22⋊C4—741no—
162C42—21no—
163C42—372no—
164C42—371no—
165C42—371no—
166C42—741no—
167C23—742no—
168C23—1484no—
169C23—1482no—
170C23D4×D3711yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—42no—
174Q8—1484no—
175D4—742no—
176D4—742no—
177D4—1482no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—372no—
182C2×C4—372no—
183C2×C4—742no—
184C2×C4—1482no—
185C2×C4#1059696212yes—
186C2×C4D4×D3711yescharacteristic
187C2×C4#1059696412yes—
188C2×C4C23×D3711yescharacteristic
189C8—22no—
190C8—742no—
191C22—22no—
192C22—2964no—
193C22—1482no—
194C22—1484no—
195C22#1192452212yes—
196C22C2×D4×D3711yescharacteristic
197C4—42no—
198C4—42no—
199C4—742no—
200C4—742no—
201C4—1482no—
202C4#1192452212yes—
203C4C2×#1059696411yescharacteristic
204C4C2×#1059696211yescharacteristic
205C2—22no—
206C2—2962no—
207C2C2×#1192452211yescharacteristic
208C2#1455833212yes—
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#419C2
socleC22×C37C22×D4
prime radicalC22×D148C22
hypercenter#419D37
hypocenterC37#3140
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
1. #14558086C2semidirect
3. #14557894C2semidirect
4. #14557889C2semidirect
5. #14557542C2semidirect
8. M16×Dic37C2semidirect
9. C37×#419C2semidirect
12. #11924535C22semidirect
13. #11924527C22semidirect
22. #11924460C22semidirect
25. #11924446C22semidirect
26. C8×Dic37C22semidirect
30. #103×C37C22semidirect
110. #419D37semidirect
114. C37#3140semidirect
131. #103C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580862
C2×#119245252
#145578942
#145578892
#145575422
#145575392
#145575372
M16×Dic372
C37×#4192
#314037