Finite Group Databasebeta

← #18010033

Subgroups — #18010033

Order 4736.

340 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 70 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⋊(C22⋊C8)C211yesmaximal, characteristic, complemented
2#14558475C211yesmaximal, characteristic, complemented
3#14558385C214yesmaximal, complemented
4C2×#11924511C211yesmaximal, characteristic
5C2×D37⋊C8—21no—
6C2×C4⋊#3866—21no—
7C2×C22⋊#3866—21no—
8#11924593C2212yescomplemented
9C22⋊#64438—21no—
10(C2×#3866)⋊C4C2212yescomplemented
11C22×D148—21no—
12C22×D148C411yescharacteristic, complemented
13C22×C4×D37C2211yescharacteristic
14#11924511—21no—
15#11924511—21no—
16#11924511C412yescomplemented
17#11924511C2212yes—
18C2×#10596938—21no—
19C2×C4⋊C4×C37C411yescharacteristic, complemented
20C23×D37—21no—
21C23×D37D411yescharacteristic
22C22×#3866—22no—
23C22×C4×C37—21no—
24C22×C4×C37C2×C411yescharacteristic
25C22×Dic37D411yescharacteristic
26C2×D148—22no—
27C2×D148—22no—
28C2×D148—21no—
29C2×D148—42no—
30C2×D148—42no—
31C2×D148—42no—
32C2×D148C2×C412yes—
33C2×C4×D37—42no—
34C2×C4×D37C2×C411yescharacteristic
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37C2311yescharacteristic
38C22⋊#3866—42no—
39C2×#64438—22no—
40C4⋊#3866—42no—
41D37⋊C8—42no—
42C4⋊C4×C37—21no—
43C4⋊C4×C37C2×C412yes—
44#10596938—22no—
45#10596938—22no—
46C23×C37C22⋊C411yescharacteristic
47C22×D37—22no—
48C22×D37—41no—
49C22×D37—41no—
50C22×D37—42no—
51C22×D37—42no—
52C22×D37—42no—
53C22×D37C22⋊C411yescharacteristic
54C22×D37D812yes—
55C22×D37SD1612yes—
56C22×D37C2×D411yescharacteristic
57C2×#3866—42no—
58C2×#3866—42no—
59C2×#3866—42no—
60C2×C4×C37—22no—
61C2×C4×C37—22no—
62C2×C4×C37—42no—
63C2×C4×C37C22⋊C411yescharacteristic
64C2×C4×C37C22×C411yescharacteristic
65C2×Dic37—41no—
66C2×Dic37C22⋊C411yescharacteristic
67C2×Dic37C2×D411yescharacteristic
68D148—42no—
69D148—44no—
70D148—42no—
71D148—42no—
72D148—42no—
73C4×D37—22no—
74C4×D37—22no—
75C4×D37—41no—
76C4×D37—41no—
77#64438—42no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37#10212yes—
81C22×C37C2×C22⋊C411yescharacteristic
82C2×D37—21no—
83C2×D37—21no—
84C2×D37—21no—
85C2×D37—21no—
86C2×D37—42no—
87C2×D37—42no—
88C2×D37—42no—
89C2×D37—42no—
90C2×D37—42no—
91C2×D37—84no—
92C2×D37#10212yes—
93C2×D37C2×D811yescharacteristic
94C2×D37C2×SD1611yescharacteristic
95#3866—82no—
96C4×C37—21no—
97C4×C37—42no—
98C4×C37#9912yes—
99Dic37—21no—
100Dic37—21no—
101#1519—371nomaximal, Sylow
102C2×C37—22no—
103C2×C37C2×#9911yescharacteristic
104C2×C37C2×#10211yescharacteristic
105C2×C37#42111yescharacteristic
106D37—21no—
107D37—22no—
108D37—21no—
109D37—82no—
110C2×#121—371no—
111C2×C22⋊C8—371no—
112#380—371no—
113#327—374no—
114C37#151911yescharacteristic, complemented, Sylow
115C22×D4—371no—
116C22×D4—741no—
117C23×C4—371no—
118C22×C8—741no—
119#121—372no—
120#121—372no—
121#121—741no—
122#121—741no—
123C2×C4⋊C4—741no—
124C2×C4⋊C4#386611yescharacteristic, complemented
125C2×C22⋊C4—741no—
126C2×C22⋊C4—741no—
127C22⋊C8—372no—
128C22⋊C8—741no—
129#95—372no—
130C24—371no—
131C24—741no—
132C2×D4—372no—
133C2×D4—742no—
134C2×D4—742no—
135C2×D4—741no—
136C2×D4—1482no—
137C2×D4—1482no—
138C2×D4—1482no—
139C22×C4—21no—
140C22×C4—371no—
141C22×C4—371no—
142C22×C4—371no—
143C22×C4—371no—
144C22×C4—371no—
145C22×C4—742no—
146C22×C4—1482no—
147C22×C4C2×#386611yescharacteristic
148C2×C8—742no—
149C2×C8—1482no—
150C4⋊C4—21no—
151C4⋊C4—1482no—
152C4⋊C4C2×#386612yes—
153C22⋊C4—742no—
154C22⋊C4—742no—
155C22⋊C4—1482no—
156C23—371no—
157C23—371no—
158C23—372no—
159C23—372no—
160C23—742no—
161C23—1482no—
162C23—1482no—
163C23—1481no—
164C23—1481no—
165C23—1482no—
166C23C22⋊#386611yescharacteristic
167D4—1482no—
168D4—1482no—
169D4—1484no—
170D4—1482no—
171D4—1482no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—371no—
176C2×C4—371no—
177C2×C4—742no—
178C2×C4—742no—
179C2×C4—1481no—
180C2×C4—1481no—
181C2×C4—1482no—
182C2×C4—1482no—
183C2×C4—1482no—
184C2×C4—1481no—
185C2×C4C22⋊#386611yescharacteristic
186C2×C4C22×#386611yescharacteristic
187C8—1482no—
188C22—21no—
189C22—21no—
190C22—371no—
191C22—372no—
192C22—371no—
193C22—2964no—
194C22—741no—
195C22—741no—
196C22—741no—
197C22—741no—
198C22—1482no—
199C22—1482no—
200C22—1482no—
201C22—1482no—
202C22—1482no—
203C22#1192459812yes—
204C22C2×C22⋊#386611yescharacteristic
205C4—21no—
206C4—42no—
207C4—2962no—
208C4—741no—
209C4—741no—
210C4#1192459512yes—
211C2—22no—
212C2—2962no—
213C2—741no—
214C2—742no—
215C2—741no—
216C2C2×#1192459511yescharacteristic
217C2C2×#1192459811yescharacteristic
218C2#1455853211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
FittingC2×C4⋊C4×C37C4
socleC22×C37C2×C22⋊C4
prime radicalC2×#11924511C2
cosocleC2×C4×D37C23
hypercenterC2×C4⋊C4#3866
hypocenterC37#1519
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. D37⋊(C22⋊C8)C2semidirect
2. #14558475C2semidirect
3. #14558385C2semidirect
8. #11924593C22semidirect
10. (C2×#3866)⋊C4C22semidirect
12. C22×D148C4semidirect
16. #11924511C4semidirect
19. C2×C4⋊C4×C37C4semidirect
114. C37#1519semidirect
124. C2×C4⋊C4#3866semidirect

Maximal subgroups

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

subgroupindex
D37⋊(C22⋊C8)2
#145584752
#145583852
C2×#119245112
#151937