Finite Group Databasebeta

← #18009689

Subgroups — #18009689

Order 4736.

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

normal subgroups only

This group has 232 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⋊#99C211yesmaximal, characteristic
2#14558485C211yesmaximal, characteristic
3#99×D37C211yesmaximal, characteristic
4C2×C4⋊#3866C411yescharacteristic, complemented
5C2×C22⋊#3866—21no—
6C2×C22⋊#3866—21no—
7C2×C22⋊#3866—21no—
8C2×C4×#3866C411yescharacteristic, complemented
9#11924595C412yescomplemented
10#11924594—21no—
11C2×D4×D37C2211yescharacteristic
12C22⋊C4×D37—21no—
13#11924451C411yescharacteristic, complemented
14#11924450—21no—
15#99×C37C411yescharacteristic, complemented
16C23×D37D411yescharacteristic
17C23×D37D411yescharacteristic
18C22×#3866—21no—
19C22×#3866—21no—
20C22×#3866—41no—
21C2×D4×C37C2×C411yescharacteristic
22C2×C22⋊D37D411yescharacteristic
23C2×C22⋊D37Q811yescharacteristic
24D4×D37—41no—
25D4×D37—41no—
26C2×D148C2×C411yescharacteristic
27C2×C4×D37—41no—
28C2×C4×D37C2×C411yescharacteristic
29C22⋊#3866—22no—
30C22⋊#3866—42no—
31C22⋊#3866—42no—
32C22⋊#3866—41no—
33C4⋊#3866—41no—
34C4×#3866—41no—
35C22⋊C4×C37—21no—
36C22⋊Dic37—21no—
37#10596938—41no—
38C23×C37C22⋊C411yescharacteristic
39C23×C37C4⋊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×D37C22⋊C411yescharacteristic
50C22×D37C4⋊C411yescharacteristic
51C2×#3866—22no—
52C2×#3866—41no—
53C2×#3866—41no—
54C2×#3866—42no—
55C2×#3866—41no—
56C2×#3866—41no—
57C2×#3866—41no—
58C2×#3866—81no—
59C2×#3866—81no—
60D4×C37—41no—
61C2×C4×C37—41no—
62C2×C4×C37C4211yescharacteristic
63C22⋊D37—41no—
64C22⋊D37—41no—
65C2×Dic37—41no—
66C2×Dic37C4⋊C411yescharacteristic
67D148—41no—
68C4×D37—21no—
69C4×D37—21no—
70C4×D37—81no—
71C4×D37—81no—
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—41no—
82C2×D37—41no—
83C2×D37—41no—
84C2×D37—41no—
85C2×D37—41no—
86C2×D37—41no—
87C2×D37—81no—
88C2×D37—81no—
89C2×D37#9911yescharacteristic
90C2×D37#9911yescharacteristic
91#3866—42no—
92#3866—82no—
93#3866—81no—
94C4×C37—21no—
95C4×C37—81no—
96Dic37—21no—
97Dic37—81no—
98#1393—371nomaximal, Sylow
99C2×C37—21no—
100C2×C37—41no—
101C2×C37—41no—
102C2×C37#34211yescharacteristic
103D37—21no—
104D37—41no—
105D37—41no—
106D37#35311yescharacteristic
107D37#35411yescharacteristic
108C2×#99—371no—
109C2×#99—371no—
110#390—371no—
111C37#139311yescharacteristic, complemented, Sylow
112C22×D4—371no—
113C2×C4⋊C4—371no—
114C2×C22⋊C4—741no—
115C2×C22⋊C4—741no—
116C2×C22⋊C4—741no—
117C2×C22⋊C4—741no—
118C2×C42—371no—
119#99—372no—
120#99—371no—
121#99—741no—
122#99—741no—
123#99#386611yescharacteristic, complemented
124C24—371no—
125C24—371no—
126C2×D4—371no—
127C2×D4—371no—
128C2×D4—371no—
129C2×D4—1481no—
130C2×D4—1481no—
131C2×D4C2×#386611yescharacteristic
132C22×C4—371no—
133C22×C4—741no—
134C22×C4—741no—
135C22×C4—1481no—
136C22×C4—1481no—
137C4⋊C4—1481no—
138C22⋊C4—21no—
139C22⋊C4—742no—
140C22⋊C4—741no—
141C22⋊C4—1481no—
142C22⋊C4—1482no—
143C22⋊C4—1482no—
144C22⋊C4—1481no—
145C42—1481no—
146C23—371no—
147C23—371no—
148C23—371no—
149C23—741no—
150C23—741no—
151C23—741no—
152C23—741no—
153C23—1481no—
154C23—1481no—
155C23—1481no—
156C23—1481no—
157C23C4⋊#386611yescharacteristic
158C23C22⋊#386611yescharacteristic
159D4—41no—
160D4—1481no—
161D4—1481no—
162D4—1481no—
163C2×C4—41no—
164C2×C4—371no—
165C2×C4—2961no—
166C2×C4—2961no—
167C2×C4—2961no—
168C2×C4—2961no—
169C2×C4—741no—
170C2×C4—741no—
171C2×C4—742no—
172C2×C4—1481no—
173C2×C4—1481no—
174C2×C4—1482no—
175C2×C4—1481no—
176C2×C4—1481no—
177C2×C4—1481no—
178C2×C4—1481no—
179C2×C4C4×#386611yescharacteristic
180C22—21no—
181C22—21no—
182C22—41no—
183C22—41no—
184C22—371no—
185C22—371no—
186C22—2961no—
187C22—2961no—
188C22—741no—
189C22—741no—
190C22—741no—
191C22—741no—
192C22—1481no—
193C22—1481no—
194C22—1481no—
195C22—1481no—
196C22—1481no—
197C22—1481no—
198C22(C2×#3866)⋊C411yescharacteristic
199C4—21no—
200C4—81no—
201C4—2961no—
202C4—2961no—
203C4—2962no—
204C4—741no—
205C4—1482no—
206C2—21no—
207C2—41no—
208C2—41no—
209C2—371no—
210C2—371no—
211C2—741no—
212C2—1481no—
213C2—1481no—
214C2#1455841011yescharacteristic
subgroupG/H
centerC2#14558410
commutatorC2×C4×C37C42
FrattiniC2×D4C2×#3866
Fitting#99×C37C4
socleC2×C37#342
prime radical, cosocleC2×D4×D37C22
hypercenter#99#3866
hypocenterC37#1393
LCSG ▷ C2×C4×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. C2×C4⋊#3866C4semidirect
8. C2×C4×#3866C4semidirect
9. #11924595C4semidirect
13. #11924451C4semidirect
15. #99×C37C4semidirect
111. C37#1393semidirect
123. #99#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊#992
#145584852
#99×D372
#139337