Finite Group Databasebeta

← #18010031

Subgroups — #18010031

Order 4736.

340 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 68 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×#11924593C211yesmaximal, characteristic, complemented
2#14558475C211yesmaximal, characteristic, complemented
3#14558385C212yesmaximal, complemented
4#14558384C212yesmaximal, complemented
5#121×D37C211yesmaximal, characteristic
6C22×#64438—21no—
7C2×C4⋊#3866—21no—
8C2×C22⋊#3866—21no—
9#11924593—21no—
10#11924593C2212yescomplemented
11(C2×#3866)⋊C4C2212yescomplemented
12C2×D4×D37—21no—
13C2×D4×D37C411yescharacteristic, complemented
14C22×C4×D37C2211yescharacteristic
15#11924511C2211yescharacteristic
16#11924510C411yescharacteristic, complemented
17#11924509—21no—
18#11924508—21no—
19#11924507C2211yescharacteristic
20C4⋊C4×D37C411yescharacteristic, complemented
21C22⋊C4×D37—21no—
22#121×C37C411yescharacteristic, complemented
23C23×D37—21no—
24C23×D37D411yescharacteristic
25C22×#3866—22no—
26C2×D4×C37—21no—
27C2×D4×C37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C2×C22⋊D37—21no—
30C2×C22⋊D37—21no—
31C2×C22⋊D37—21no—
32C22×Dic37D411yescharacteristic
33D4×D37—42no—
34D4×D37—42no—
35D4×D37—42no—
36C2×D148—21no—
37C2×D148C2×C411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—42no—
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C4×D37C2311yescharacteristic
44C22⋊#3866—42no—
45C2×#64438—22no—
46C2×#64438—42no—
47C4⋊#3866—42no—
48C4⋊C4×C37C2×C411yescharacteristic
49C22⋊C4×C37—21no—
50C22⋊Dic37—21no—
51#10596938—21no—
52#10596938—21no—
53C4⋊Dic37C2×C411yescharacteristic
54#10596936—21no—
55C23×C37—21no—
56C23×C37C22⋊C411yescharacteristic
57C22×D37—21no—
58C22×D37—41no—
59C22×D37—41no—
60C22×D37—42no—
61C22×D37—42no—
62C22×D37—42no—
63C22×D37C22⋊C411yescharacteristic
64C22×D37D812yes—
65C22×D37SD1612yes—
66C22×D37C2×D411yescharacteristic
67C2×#3866—42no—
68C2×#3866—42no—
69C2×#3866—42no—
70D4×C37—41no—
71D4×C37—42no—
72C2×C4×C37—21no—
73C2×C4×C37—41no—
74C2×C4×C37C22⋊C411yescharacteristic
75C2×C4×C37C22×C411yescharacteristic
76C22⋊D37—42no—
77C22⋊D37—41no—
78C22⋊D37—41no—
79C22⋊D37—42no—
80C2×Dic37—22no—
81C2×Dic37—21no—
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C2×D411yescharacteristic
84D148—41no—
85D148—41no—
86D148—41no—
87C4×D37—22no—
88C4×D37—22no—
89C4×D37—41no—
90C4×D37—41no—
91C4×D37—42no—
92#64438—42no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37—41no—
96C22×C37—41no—
97C22×C37—41no—
98C22×C37#10212yes—
99C22×C37C2×C22⋊C411yescharacteristic
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—21no—
103C2×D37—21no—
104C2×D37—42no—
105C2×D37—42no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—41no—
109C2×D37—84no—
110C2×D37#10212yes—
111C2×D37C2×D811yescharacteristic
112C2×D37C2×SD1611yescharacteristic
113#3866—82no—
114C4×C37—21no—
115C4×C37—21no—
116C4×C37—41no—
117Dic37—21no—
118Dic37—41no—
119Dic37#9912yes—
120#1519—371nomaximal, Sylow
121C2×C37—22no—
122C2×C37—81no—
123C2×C37C2×#9911yescharacteristic
124C2×C37C2×#10211yescharacteristic
125C2×C37#42111yescharacteristic
126D37—21no—
127D37—22no—
128D37—21no—
129D37—81no—
130C2×#121—371no—
131C2×C22⋊C8—371no—
132#380—371no—
133#327—372no—
134#327—372no—
135C37#151911yescharacteristic, complemented, Sylow
136C22×D4—371no—
137C22×D4—741no—
138C23×C4—371no—
139C22×C8—741no—
140#121—371no—
141#121—371no—
142#121—371no—
143#121—741no—
144#121—741no—
145#121#386611yescharacteristic, complemented
146C2×C4⋊C4—371no—
147C2×C4⋊C4—741no—
148C2×C22⋊C4—741no—
149C2×C22⋊C4—741no—
150C22⋊C8—372no—
151C22⋊C8—741no—
152#95—372no—
153C24—371no—
154C24—741no—
155C2×D4—21no—
156C2×D4—371no—
157C2×D4—741no—
158C2×D4—741no—
159C2×D4—741no—
160C2×D4—741no—
161C2×D4—1482no—
162C2×D4—1482no—
163C2×D4—1482no—
164C2×D4C2×#386611yescharacteristic
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—371no—
168C22×C4—371no—
169C22×C4—371no—
170C22×C4—741no—
171C22×C4—742no—
172C22×C4—1482no—
173C22×C4C2×#386611yescharacteristic
174C2×C8—742no—
175C2×C8—1482no—
176C4⋊C4—371no—
177C4⋊C4—741no—
178C4⋊C4—1482no—
179C4⋊C4C2×#386611yescharacteristic
180C22⋊C4—21no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—1482no—
185C23—21no—
186C23—371no—
187C23—371no—
188C23—372no—
189C23—372no—
190C23—741no—
191C23—1481no—
192C23—1481no—
193C23—1482no—
194C23—1482no—
195C23—1482no—
196C23C22⋊#386611yescharacteristic
197D4—41no—
198D4—42no—
199D4—1481no—
200D4—1481no—
201D4—1481no—
202D4—1482no—
203D4—1481no—
204D4—1481no—
205D4—1482no—
206C2×C4—21no—
207C2×C4—41no—
208C2×C4—371no—
209C2×C4—371no—
210C2×C4—742no—
211C2×C4—742no—
212C2×C4—742no—
213C2×C4—741no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1482no—
217C2×C4—1482no—
218C2×C4—1482no—
219C2×C4—1482no—
220C2×C4C22⋊#386611yescharacteristic
221C2×C4C22×#386611yescharacteristic
222C8—1482no—
223C22—21no—
224C22—21no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—371no—
229C22—372no—
230C22—371no—
231C22—2964no—
232C22—741no—
233C22—741no—
234C22—741no—
235C22—741no—
236C22—1482no—
237C22—1482no—
238C22—1481no—
239C22—1481no—
240C22—1481no—
241C22#1192459812yes—
242C22C2×C22⋊#386611yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—372no—
247C4—2962no—
248C4—741no—
249C4—1481no—
250C2—22no—
251C2—81no—
252C2—2961no—
253C2—741no—
254C2—742no—
255C2—741no—
256C2D37⋊#9911yescharacteristic
257C2C2×#1192459811yescharacteristic
258C2#1455853011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#3866
commutatorC2×C4×C37C22×C4
FrattiniC2×C4C22×#3866
Fitting#121×C37C4
socleC22×C37C2×C22⋊C4
prime radical#121×D37C2
cosocleC2×C4×D37C23
hypercenter#121#3866
hypocenterC37#1519
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. C2×#11924593C2semidirect
2. #14558475C2semidirect
3. #14558385C2semidirect
4. #14558384C2semidirect
10. #11924593C22semidirect
11. (C2×#3866)⋊C4C22semidirect
13. C2×D4×D37C4semidirect
16. #11924510C4semidirect
20. C4⋊C4×D37C4semidirect
22. #121×C37C4semidirect
135. C37#1519semidirect
145. #121#3866semidirect

Maximal subgroups

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

subgroupindex
C2×#119245932
#145584752
#145583852
#145583842
#121×D372
#151937