Finite Group Databasebeta

← #18009679

Subgroups — #18009679

Order 4736.

234 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D37⋊#100C211yesmaximal, characteristic
2#14558481C211yesmaximal, characteristic
3#99×D37C211yesmaximal, characteristic
4C23×#3866C411yescharacteristic, complemented
5D37⋊M16—21no—
6C2×C22⋊#3866—21no—
7C2×C22⋊#3866C411yescharacteristic, complemented
8#11924596—21no—
9#11924596C412yescomplemented
10(C2×#3866)⋊C4—21no—
11C2×D4×D37C2211yescharacteristic
12C22⋊C4×D37—21no—
13#11924451C411yescharacteristic, complemented
14#11924450—21no—
15#99×C37C411yescharacteristic, complemented
16C23×D37C2×C411yescharacteristic
17C23×D37D411yescharacteristic
18C22×#3866—21no—
19C22×#3866—21no—
20C22×#3866—42no—
21C22×#3866—41no—
22C2×D4×C37C2×C411yescharacteristic
23C2×C22⋊D37C2×C411yescharacteristic
24C2×C22⋊D37D411yescharacteristic
25D4×D37—41no—
26D4×D37—41no—
27C2×D148Q811yescharacteristic
28C2×C4×D37—41no—
29C2×C4×D37D411yescharacteristic
30C22⋊#3866—42no—
31C22⋊#3866—41no—
32#10596957—22no—
33#10596953—41no—
34D37⋊C8—41no—
35C22⋊C4×C37—21no—
36C22⋊Dic37—21no—
37#10596938—41no—
38C23×C37C4211yescharacteristic
39C23×C37C22⋊C411yescharacteristic
40C22×D37—21no—
41C22×D37—21no—
42C22×D37—21no—
43C22×D37—21no—
44C22×D37—41no—
45C22×D37—41no—
46C22×D37—41no—
47C22×D37—41no—
48C22×D37C22⋊C411yescharacteristic
49C22×D37C4⋊C411yescharacteristic
50C22×D37C4⋊C411yescharacteristic
51C2×#3866—22no—
52C2×#3866—41no—
53C2×#3866—42no—
54C2×#3866—41no—
55C2×#3866—42no—
56C2×#3866—41no—
57C2×#3866—41no—
58C2×#3866—41no—
59D4×C37—41no—
60C2×C4×C37—41no—
61C2×C4×C37C4⋊C411yescharacteristic
62C22⋊D37—41no—
63C22⋊D37—41no—
64C2×Dic37—41no—
65C2×Dic37C22⋊C411yescharacteristic
66D148—41no—
67C4×D37—21no—
68C4×D37—21no—
69C4×D37—81no—
70C4×D37—81no—
71#64438—42no—
72C22×C37—21no—
73C22×C37—21no—
74C22×C37—41no—
75C22×C37—41no—
76C22×C37#9511yescharacteristic
77C2×D37—21no—
78C2×D37—21no—
79C2×D37—21no—
80C2×D37—21no—
81C2×D37—42no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—41no—
88C2×D37—81no—
89C2×D37#9911yescharacteristic
90C2×D37#9911yescharacteristic
91#3866—42no—
92#3866—81no—
93C4×C37—21no—
94C4×C37—81no—
95Dic37—21no—
96Dic37—81no—
97#1390—371nomaximal, Sylow
98C2×C37—21no—
99C2×C37—41no—
100C2×C37—41no—
101C2×C37#34211yescharacteristic
102D37—21no—
103D37—41no—
104D37—41no—
105D37AΣL(1,𝔽16)11yescharacteristic
106D37#35211yescharacteristic
107C2×#100—371no—
108C2×#99—371no—
109#386—371no—
110C37#139011yescharacteristic, complemented, Sylow
111C22×D4—371no—
112C23×C4—371no—
113C2×M16—741no—
114C2×C22⋊C4—371no—
115C2×C22⋊C4—741no—
116C2×C22⋊C4—741no—
117#100—372no—
118#100—741no—
119#99—371no—
120#99—741no—
121#99#386611yescharacteristic, complemented
122#95—741no—
123C24—371no—
124C24—371no—
125C2×D4—371no—
126C2×D4—371no—
127C2×D4—371no—
128C2×D4—1481no—
129C2×D4—1481no—
130C2×D4C2×#386611yescharacteristic
131C22×C4—371no—
132C22×C4—741no—
133C22×C4—741no—
134C22×C4—1481no—
135C22×C4—1482no—
136C22×C4—1481no—
137M16—742no—
138M16—1481no—
139C2×C8—1481no—
140C22⋊C4—21no—
141C22⋊C4—741no—
142C22⋊C4—1481no—
143C22⋊C4—1482no—
144C22⋊C4—1481no—
145C23—371no—
146C23—371no—
147C23—371no—
148C23—741no—
149C23—741no—
150C23—741no—
151C23—741no—
152C23—1481no—
153C23—1481no—
154C23—1481no—
155C23—1481no—
156C23C4×#386611yescharacteristic
157C23C22⋊#386611yescharacteristic
158D4—41no—
159D4—1481no—
160D4—1481no—
161D4—1481no—
162C2×C4—41no—
163C2×C4—371no—
164C2×C4—2961no—
165C2×C4—2961no—
166C2×C4—741no—
167C2×C4—741no—
168C2×C4—742no—
169C2×C4—1481no—
170C2×C4—1481no—
171C2×C4—1481no—
172C2×C4—1481no—
173C2×C4—1481no—
174C2×C4—1481no—
175C2×C4—1482no—
176C2×C4—1482no—
177C2×C4C4⋊#386611yescharacteristic
178C8—1482no—
179C22—21no—
180C22—21no—
181C22—41no—
182C22—41no—
183C22—371no—
184C22—371no—
185C22—2961no—
186C22—741no—
187C22—741no—
188C22—741no—
189C22—741no—
190C22—1481no—
191C22—1481no—
192C22—1481no—
193C22—1481no—
194C22—1481no—
195C22—1481no—
196C22—1482no—
197C22(C2×#3866)⋊C411yescharacteristic
198C4—21no—
199C4—81no—
200C4—2961no—
201C4—2961no—
202C4—741no—
203C4—1482no—
204C2—21no—
205C2—41no—
206C2—41no—
207C2—371no—
208C2—371no—
209C2—741no—
210C2—1481no—
211C2—1481no—
212C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC23×C37C42
FrattiniC2×D4C2×#3866
Fitting#99×C37C4
socleC2×C37#342
prime radical, cosocleC2×D4×D37C22
hypercenter#99#3866
hypocenterC37#1390
LCSG ▷ C23×C37 ▷ C22×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. C23×#3866C4semidirect
7. C2×C22⋊#3866C4semidirect
9. #11924596C4semidirect
13. #11924451C4semidirect
15. #99×C37C4semidirect
110. C37#1390semidirect
121. #99#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#1002
#145584812
#99×D372
#139037