Finite Group Databasebeta

← #17993164

Subgroups — #17993164

Order 4736.

340 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×C22⋊#64436C211yesmaximal, characteristic, complemented
2#14557393C211yesmaximal, characteristic, complemented
3#14557267C214yesmaximal, complemented
4C2×#121×C37C211yesmaximal, characteristic
5C22×#64436—21no—
6C2×C4⋊Dic37—21no—
7C2×C22⋊Dic37—21no—
8C22⋊#64436—21no—
9C22⋊#64436C2212yescomplemented
10#11924443C2212yescomplemented
11C22×D4×C37—21no—
12C22×D4×C37C411yescharacteristic, complemented
13C23×C4×C37C2211yescharacteristic
14#121×C37—21no—
15#121×C37—21no—
16#121×C37C412yescomplemented
17#121×C37C2212yes—
18C2×C4⋊C4×C37C411yescharacteristic, complemented
19C2×C22⋊C4×C37—21no—
20C24×C37—21no—
21C24×C37D411yescharacteristic
22C2×D4×C37—22no—
23C2×D4×C37—22no—
24C2×D4×C37—21no—
25C2×D4×C37—42no—
26C2×D4×C37—42no—
27C2×D4×C37—42no—
28C2×D4×C37C2×C412yes—
29C22×C4×C37—21no—
30C22×C4×C37—42no—
31C22×C4×C37C2×C411yescharacteristic
32C22×C4×C37C2×C411yescharacteristic
33C22×C4×C37D411yescharacteristic
34C22×C4×C37D411yescharacteristic
35C22×C4×C37D411yescharacteristic
36C22×C4×C37C2311yescharacteristic
37C22×Dic37—22no—
38C4⋊C4×C37—21no—
39C4⋊C4×C37C2×C412yes—
40C22⋊C4×C37—22no—
41C22⋊C4×C37—22no—
42C22⋊Dic37—42no—
43C4⋊Dic37—42no—
44C2×#64436—22no—
45C2×#64436—42no—
46C23×C37—22no—
47C23×C37—41no—
48C23×C37—41no—
49C23×C37—42no—
50C23×C37—42no—
51C23×C37—42no—
52C23×C37C22⋊C411yescharacteristic
53C23×C37C22⋊C411yescharacteristic
54C23×C37D812yes—
55C23×C37SD1612yes—
56C23×C37C2×D411yescharacteristic
57D4×C37—42no—
58D4×C37—44no—
59D4×C37—42no—
60D4×C37—42no—
61D4×C37—42no—
62C2×C4×C37—22no—
63C2×C4×C37—22no—
64C2×C4×C37—22no—
65C2×C4×C37—22no—
66C2×C4×C37—41no—
67C2×C4×C37—41no—
68C2×C4×C37—41no—
69C2×C4×C37—42no—
70C2×C4×C37C22⋊C411yescharacteristic
71C2×C4×C37C22⋊C411yescharacteristic
72C2×C4×C37C22×C411yescharacteristic
73C2×C4×C37C2×D411yescharacteristic
74C2×Dic37—42no—
75C2×Dic37—42no—
76C2×Dic37—42no—
77#64436—42no—
78C22×C37—21no—
79C22×C37—21no—
80C22×C37—21no—
81C22×C37—21no—
82C22×C37—21no—
83C22×C37—21no—
84C22×C37—42no—
85C22×C37—42no—
86C22×C37—42no—
87C22×C37—42no—
88C22×C37—42no—
89C22×C37—84no—
90C22×C37#10212yes—
91C22×C37#10212yes—
92C22×C37C2×C22⋊C411yescharacteristic
93C22×C37C2×D811yescharacteristic
94C22×C37C2×SD1611yescharacteristic
95C4×C37—21no—
96C4×C37—21no—
97C4×C37—21no—
98C4×C37—42no—
99C4×C37#9912yes—
100Dic37—82no—
101#1519—371nomaximal, Sylow
102C2×C37—21no—
103C2×C37—22no—
104C2×C37—22no—
105C2×C37—21no—
106C2×C37—82no—
107C2×C37C2×#9911yescharacteristic
108C2×C37C2×#10211yescharacteristic
109C2×C37#42111yescharacteristic
110C2×#121D3711yescharacteristic
111C2×C22⋊C8—371no—
112#380—371no—
113#327—374no—
114C37#151911yescharacteristic, complemented, Sylow
115C22×D4—21no—
116C22×D4Dic3711yescharacteristic, complemented
117C23×C4C2×D3711yescharacteristic
118C22×C8—741no—
119#121—21no—
120#121—21no—
121#121Dic3712yescomplemented
122#121C2×D3712yes—
123C2×C4⋊C4—741no—
124C2×C4⋊C4Dic3711yescharacteristic, complemented
125C2×C22⋊C4—21no—
126C2×C22⋊C4—741no—
127C22⋊C8—372no—
128C22⋊C8—741no—
129#95—372no—
130C24—21no—
131C24C22⋊D3711yescharacteristic
132C2×D4—22no—
133C2×D4—22no—
134C2×D4—21no—
135C2×D4—42no—
136C2×D4—42no—
137C2×D4—42no—
138C2×D4C2×Dic3712yes—
139C22×C4—21no—
140C22×C4—42no—
141C22×C4—742no—
142C22×C4C2×Dic3711yescharacteristic
143C22×C4C2×Dic3711yescharacteristic
144C22×C4C22⋊D3711yescharacteristic
145C22×C4C22⋊D3711yescharacteristic
146C22×C4C22⋊D3711yescharacteristic
147C22×C4C22×D3711yescharacteristic
148C2×C8—742no—
149C2×C8—1482no—
150C4⋊C4—21no—
151C4⋊C4—1482no—
152C4⋊C4C2×Dic3712yes—
153C22⋊C4—22no—
154C22⋊C4—22no—
155C22⋊C4—1482no—
156C23—22no—
157C23—41no—
158C23—41no—
159C23—42no—
160C23—42no—
161C23—42no—
162C23#1059693912yes—
163C23#1059694012yes—
164C23C22⋊Dic3711yescharacteristic
165C23C22⋊Dic3711yescharacteristic
166C23C2×C22⋊D3711yescharacteristic
167D4—42no—
168D4—42no—
169D4—42no—
170D4—44no—
171D4—42no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—42no—
180C2×C4—1482no—
181C2×C4—1482no—
182C2×C4—1482no—
183C2×C4C22⋊Dic3711yescharacteristic
184C2×C4C22⋊Dic3711yescharacteristic
185C2×C4C22×Dic3711yescharacteristic
186C2×C4C2×C22⋊D3711yescharacteristic
187C8—1482no—
188C22—21no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—21no—
193C22—21no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—42no—
198C22—42no—
199C22—84no—
200C22#1192445712yes—
201C22#1192445712yes—
202C22C2×C22⋊Dic3711yescharacteristic
203C22C2×#1059693911yescharacteristic
204C22C2×#1059694011yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—42no—
209C4—2962no—
210C4#1192445112yes—
211C2—21no—
212C2—22no—
213C2—21no—
214C2—22no—
215C2—82no—
216C2C2×#1192445111yescharacteristic
217C2C2×#1192445711yescharacteristic
218C2#1455755011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
Fitting, prime radicalC2×#121×C37C2
socleC22×C37C2×C22⋊C4
cosocleC22×C4×C37C23
hypercenterC2×#121D37
hypocenterC37#1519
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×C22⋊#64436C2semidirect
2. #14557393C2semidirect
3. #14557267C2semidirect
9. C22⋊#64436C22semidirect
10. #11924443C22semidirect
12. C22×D4×C37C4semidirect
16. #121×C37C4semidirect
18. C2×C4⋊C4×C37C4semidirect
114. C37#1519semidirect
116. C22×D4Dic37semidirect
121. #121Dic37semidirect
124. C2×C4⋊C4Dic37semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊#644362
#145573932
#145572672
C2×#121×C372
#151937