Finite Group Databasebeta

← #17992943

Subgroups — #17992943

Order 4736.

280 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 63 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×#11924521C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic, complemented
3C22⋊C8×D37C211yesmaximal, characteristic, complemented
4#14557259C211yesmaximal, characteristic, complemented
5#14557256C211yesmaximal, characteristic, complemented
6#14557256C211yesmaximal, characteristic, complemented
7C37×#324C211yesmaximal, characteristic, complemented
8C22×D148C411yescharacteristic
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—21no—
11C2×C8×D37—21no—
12#11924521—21no—
13#11924521—21no—
14#11924521—21no—
15#11924521—21no—
16C2×#10596936C411yescharacteristic
17C2×#10596938C411yescharacteristic
18C2×#10596938C411yescharacteristic
19C2×#10596938C2211yescharacteristic
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22#11924448—21no—
23#11924448—21no—
24C2×C4⋊C4×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26C22⋊C8×C37C2211yescharacteristic
27C23×D37C2×C411yescharacteristic
28C23×D37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2×C411yescharacteristic
31C22×C4×C37C2311yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C2×D148—21no—
35C2×D148—21no—
36C2×D148—42no—
37C2×C4×D37—42no—
38C2×C4×D37D411yescharacteristic
39C2×C4×D37D411yescharacteristic
40C2×C4×D37D411yescharacteristic
41C2×C4×D37D411yescharacteristic
42C2×C8×C37—21no—
43C2×C8×C37—21no—
44C4⋊C4×C37—21no—
45C4⋊C4×C37—21no—
46#10596938—21no—
47#10596938—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51#10596938—21no—
52#10596936—21no—
53#10596936—21no—
54C2×#64436—21no—
55C2×#64436—21no—
56#10596929—42no—
57C8×D37—42no—
58C23×C37C22×C411yescharacteristic
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—22no—
62C22×D37—21no—
63C22×D37—21no—
64C22×D37—21no—
65C22×D37—41no—
66C22×D37—41no—
67C22×D37—41no—
68C22×D37C22⋊C411yescharacteristic
69C22×D37C22⋊C411yescharacteristic
70C2×C4×C37—21no—
71C2×C4×C37—21no—
72C2×C4×C37—21no—
73C2×C4×C37—21no—
74C2×C4×C37—41no—
75C2×C4×C37—41no—
76C2×C4×C37C2×D411yescharacteristic
77C2×C4×C37C2×D411yescharacteristic
78C2×Dic37—21no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37C22⋊C411yescharacteristic
82C2×Dic37C22⋊C411yescharacteristic
83D148—42no—
84D148—42no—
85C4×D37—22no—
86C4×D37—22no—
87C4×D37—41no—
88C4×D37—41no—
89C8×C37—41no—
90C8×C37—41no—
91#64436—41no—
92#64436—41no—
93C22×C37—21no—
94C22×C37—21no—
95C22×C37C2×C22⋊C411yescharacteristic
96C22×C37#13111yescharacteristic
97C22×C37#13111yescharacteristic
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—21no—
102C2×D37—21no—
103C2×D37—42no—
104C2×D37—42no—
105C2×D37—41no—
106C2×D37—41no—
107C2×D37—41no—
108C2×D37—81no—
109C2×D37—81no—
110C2×D37#9912yes—
111C4×C37—21no—
112C4×C37—21no—
113C4×C37—41no—
114C4×C37—41no—
115Dic37—21no—
116Dic37—21no—
117Dic37—41no—
118#1468—371nomaximal, Sylow
119C2×C37—21no—
120C2×C37—21no—
121C2×C37#40811yescharacteristic
122C2×C37C2×#9911yescharacteristic
123C2×C37#41311yescharacteristic
124D37—22no—
125D37—41no—
126D37—81no—
127C2×#123—371no—
128#407—371no—
129C2×C22⋊C8—371no—
130#324—371no—
131#324D3711yescharacteristic, complemented
132#323—371no—
133#323—371no—
134C37#146811yescharacteristic, complemented, Sylow
135C22×D4—371no—
136C23×C4—371no—
137C2×M16—741no—
138C22×C8—741no—
139#123—741no—
140#123—741no—
141#123—741no—
142#123—741no—
143C2×C4⋊C4—371no—
144C2×C4⋊C4C2×D3711yescharacteristic
145C2×C22⋊C4—371no—
146C2×C22⋊C4—371no—
147C2×C22⋊C4—371no—
148C22⋊C8—371no—
149C22⋊C8—371no—
150C22⋊C8—741no—
151C22⋊C8—741no—
152C22⋊C8C2×D3711yescharacteristic
153C22⋊C8C2×D3711yescharacteristic
154C24—371no—
155C24—371no—
156C2×D4—741no—
157C2×D4—741no—
158C2×D4—1482no—
159C22×C4—371no—
160C22×C4—371no—
161C22×C4—371no—
162C22×C4—371no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—1482no—
166C22×C4C4×D3711yescharacteristic
167C22×C4C4×D3711yescharacteristic
168C22×C4C22×D3711yescharacteristic
169M16—1482no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—741no—
173C2×C8—741no—
174C2×C8—1482no—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—741no—
178C4⋊C4—741no—
179C22⋊C4—741no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—741no—
185C23—371no—
186C23—371no—
187C23—742no—
188C23—741no—
189C23—741no—
190C23—741no—
191C23—741no—
192C23—741no—
193C23—1481no—
194C23—1481no—
195C23—1481no—
196C23C2×C4×D3711yescharacteristic
197D4—1482no—
198D4—1482no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—371no—
206C2×C4—371no—
207C2×C4—742no—
208C2×C4—742no—
209C2×C4—741no—
210C2×C4—1481no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1481no—
214C2×C4D4×D3711yescharacteristic
215C2×C4D4×D3711yescharacteristic
216C8—41no—
217C8—41no—
218C8—1481no—
219C8—1481no—
220C22—21no—
221C22—21no—
222C22—372no—
223C22—2961no—
224C22—2961no—
225C22—741no—
226C22—741no—
227C22—741no—
228C22—741no—
229C22—741no—
230C22—1482no—
231C22—1482no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22C22⋊C4×D3711yescharacteristic
236C22#1192454211yescharacteristic
237C22#1192454411yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—741no—
243C4—741no—
244C4—1481no—
245C2—21no—
246C2—21no—
247C2—2961no—
248C2—742no—
249C2—1481no—
250C2#1455749811yescharacteristic
251C2#99×D3711yescharacteristic
252C2#1455751611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37C2×C22⋊C4
prime radicalC22×D148C4
cosocleC22×C4×C37C23
hypercenter#324D37
hypocenterC37#1468
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14557495C2semidirect
3. C22⋊C8×D37C2semidirect
4. #14557259C2semidirect
5. #14557256C2semidirect
6. #14557256C2semidirect
7. C37×#324C2semidirect
131. #324D37semidirect
134. C37#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#119245212
#145574952
C22⋊C8×D372
#145572592
#145572562
C37×#3242
#146837