Finite Group Databasebeta

← #17994615

Subgroups — #17994615

Order 4736.

312 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 87 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#14558001C211yesmaximal, characteristic
2#14557556C211yesmaximal, characteristic, complemented
3C2×#11924464C211yesmaximal, characteristic
4C2×#11924462C211yesmaximal, characteristic
5C4×#10596936C211yesmaximal, characteristic, complemented
6#14557292C211yesmaximal, characteristic, complemented
7C37×#339C211yesmaximal, characteristic, complemented
8C2×#10596962C2211yescharacteristic
9C2×#10596934C2211yescharacteristic
10#11924501C411yescharacteristic, complemented
11#11924501C411yescharacteristic, complemented
12#11924498C411yescharacteristic, complemented
13#11924498C411yescharacteristic, complemented
14#11924496—21no—
15#11924496—21no—
16#11924493—21no—
17C2×#10596936—21no—
18C2×C4×Dic37C2211yescharacteristic
19C2×C4×Dic37C2211yescharacteristic
20C42×D37—21no—
21#11924465—21no—
22#11924465—21no—
23#11924464—22no—
24#11924462—22no—
25#11924443—21no—
26C2×M16×C37C2211yescharacteristic
27#117×C37C2211yescharacteristic
28C2×C42×C37C2211yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33C22×Dic37D411yescharacteristic
34C22×Dic37D411yescharacteristic
35#10596962—21no—
36#10596962—21no—
37#10596962D412yes—
38#10596962Q812yes—
39C2×D148C2×C411yescharacteristic
40C2×C4×D37—21no—
41C2×C4×D37—21no—
42C2×C4×D37—21no—
43C2×Dic74C2×C411yescharacteristic
44M16×C37—21no—
45M16×C37—21no—
46C2×C8×C37—21no—
47C4⋊C4×C37C2×C411yescharacteristic
48C4⋊C4×C37C2×C411yescharacteristic
49C22⋊C4×C37—21no—
50C42×C37—21no—
51C42×C37—21no—
52C42×C37—21no—
53#10596938—21no—
54#10596938—21no—
55#10596936—24no—
56#10596936—21no—
57#10596936—21no—
58C4×Dic37—21no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C4×Dic37—21no—
62C4×Dic37C2×C411yescharacteristic
63C4×Dic37C2×C411yescharacteristic
64C4×Dic37D411yescharacteristic
65C4×Dic37D411yescharacteristic
66#10596934—21no—
67#10596934—21no—
68C2×#64436—21no—
69C23×C37C2×D411yescharacteristic
70C22×D37—21no—
71C2×C4×C37—22no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37C22×C411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×C4×C37C2×D411yescharacteristic
79C2×C4×C37C2×Q811yescharacteristic
80C2×C4×C37#4111yescharacteristic
81C2×C4×C37#4111yescharacteristic
82C22⋊D37—22no—
83C22⋊D37—22no—
84C2×Dic37—21no—
85C2×Dic37—22no—
86C2×Dic37—22no—
87C2×Dic37—41no—
88C2×Dic37—41no—
89C2×Dic37—41no—
90C2×Dic37C22⋊C411yescharacteristic
91C2×Dic37C22⋊C411yescharacteristic
92C2×Dic37C22⋊C411yescharacteristic
93C2×Dic37C22⋊C411yescharacteristic
94D148—21no—
95D148C4⋊C412yescomplemented
96C4×D37—22no—
97C4×D37—22no—
98C4×D37—42no—
99C4×D37—42no—
100Dic74—21no—
101Dic74C4⋊C412yescomplemented
102C8×C37—41no—
103#64436—41no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37C2×C22⋊C411yescharacteristic
107C22×C37#12111yescharacteristic
108C22×C37C22⋊Q811yescharacteristic
109C2×D37—22no—
110C2×D37—41no—
111C2×D37—41no—
112C4×C37—42no—
113C4×C37—41no—
114C4×C37—41no—
115C4×C37C2×C4⋊C411yescharacteristic
116C4×C37#11711yescharacteristic
117C4×C37#12111yescharacteristic
118C4×C37C22⋊Q811yescharacteristic
119Dic37—22no—
120Dic37—21no—
121Dic37—21no—
122Dic37—21no—
123Dic37—42no—
124Dic37#10412yescomplemented
125#1806—371nomaximal, Sylow
126C2×C37—21no—
127C2×C37—21no—
128C2×C37#38011yescharacteristic
129C2×C37C2×#10411yescharacteristic
130C2×C37#42111yescharacteristic
131D37—42no—
132C4×#41—371no—
133#423—371no—
134C2×#104—371no—
135C2×#104—371no—
136C4×C4⋊C4—371no—
137#339—371no—
138#339D3711yescharacteristic, complemented
139C37#180611yescharacteristic, complemented, Sylow
140C2×#41—371no—
141C2×M16—371no—
142C2×M16C2×D3711yescharacteristic
143C4×Q8—371no—
144C4×Q8—371no—
145C4×D4—371no—
146C4×D4—371no—
147C4×D4—741no—
148C4×D4—741no—
149#117—741no—
150#117C2×D3711yescharacteristic
151C2×C4⋊C4—741no—
152C2×C42—371no—
153C2×C42—371no—
154C2×C42—741no—
155C2×C42C2×D3711yescharacteristic
156C4⋊C8—741no—
157C4⋊C8—741no—
158#104—742no—
159#104—742no—
160#95—741no—
161#41—372no—
162#41—372no—
163#41—741no—
164#41—741no—
165C2×Q8—371no—
166C2×D4—371no—
167C2×D4—741no—
168C22×C4—21no—
169C22×C4—371no—
170C22×C4—371no—
171C22×C4—741no—
172C22×C4—741no—
173C22×C4—741no—
174C22×C4—741no—
175C22×C4C22×D3711yescharacteristic
176M16—21no—
177M16—21no—
178M16—741no—
179M16—741no—
180C2×C8—21no—
181C2×C8—741no—
182C4⋊C4—741no—
183C4⋊C4—741no—
184C4⋊C4—744no—
185C4⋊C4C4×D3711yescharacteristic
186C4⋊C4C4×D3711yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—741no—
189C22⋊C4—741no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—371no—
194C42—371no—
195C42—371no—
196C42—371no—
197C42—741no—
198C42—741no—
199C42—741no—
200C42—741no—
201C23—741no—
202C23D4×D3711yescharacteristic
203Q8—372no—
204Q8—741no—
205D4—372no—
206D4—742no—
207D4—742no—
208D4—741no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—371no—
215C2×C4—371no—
216C2×C4—371no—
217C2×C4—371no—
218C2×C4—742no—
219C2×C4—741no—
220C2×C4—742no—
221C2×C4—742no—
222C2×C4—742no—
223C2×C4—1482no—
224C2×C4—1482no—
225C2×C4—1481no—
226C2×C4—1481no—
227C2×C4—1481no—
228C2×C4C2×C4×D3711yescharacteristic
229C2×C4#1059696211yescharacteristic
230C2×C4#1059696211yescharacteristic
231C2×C4D4×D3711yescharacteristic
232C2×C4D4×D3711yescharacteristic
233C2×C4Q8×D3711yescharacteristic
234C8—41no—
235C8—1481no—
236C22—21no—
237C22—21no—
238C22—742no—
239C22—1481no—
240C22—1481no—
241C22C22⋊C4×D3711yescharacteristic
242C22#1192450911yescharacteristic
243C22#1192451411yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—372no—
248C4—741no—
249C4—741no—
250C4—741no—
251C4—742no—
252C4—1482no—
253C4C4⋊C4×D3711yescharacteristic
254C4#1192449311yescharacteristic
255C4#1192450911yescharacteristic
256C4#1192451411yescharacteristic
257C2—21no—
258C2—21no—
259C2—1482no—
260C2#1455739211yescharacteristic
261C2#104×D3711yescharacteristic
262C2#1455754811yescharacteristic
subgroupG/H
centerC2×C4D4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#339C2
socleC22×C37C2×C22⋊C4
prime radicalC2×#10596962C22
cosocleC22×C4×C37C23
hypercenter#339D37
hypocenterC37#1806
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14557556C2semidirect
5. C4×#10596936C2semidirect
6. #14557292C2semidirect
7. C37×#339C2semidirect
10. #11924501C4semidirect
11. #11924501C4semidirect
12. #11924498C4semidirect
13. #11924498C4semidirect
95. D148C4⋊C4semidirect
101. Dic74C4⋊C4semidirect
124. Dic37#104semidirect
138. #339D37semidirect
139. C37#1806semidirect

Maximal subgroups

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

subgroupindex
#145580012
#145575562
C2×#119244642
C2×#119244622
C4×#105969362
#145572922
C37×#3392
#180637