Finite Group Databasebeta

← #17993151

Subgroups — #17993151

Order 4736.

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

normal subgroups only

This group has 284 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
1#14558046C211yesmaximal, characteristic
2C22⋊C8×D37C211yesmaximal, characteristic, complemented
3#14557395C211yesmaximal, characteristic, complemented
4#14557270C211yesmaximal, characteristic, complemented
5#14557268C211yesmaximal, characteristic, complemented
6#14557266C211yesmaximal, characteristic, complemented
7C37×#328C211yesmaximal, characteristic, complemented
8C2×#10596966C411yescharacteristic, complemented
9C22×C4×D37C2211yescharacteristic
10C2×C8×D37—21no—
11#11924521—21no—
12#11924512C411yescharacteristic, complemented
13#11924511C411yescharacteristic, complemented
14#11924510C2211yescharacteristic
15#11924506—21no—
16#11924498—21no—
17#11924496—21no—
18#11924494C411yescharacteristic, complemented
19C2×#10596938—21no—
20C22⋊#64436C2211yescharacteristic
21#11924448—21no—
22#11924443—21no—
23#11924443C2211yescharacteristic
24C22⋊Q8×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26#95×C37C2211yescharacteristic
27C23×D37D411yescharacteristic
28C2×Q8×C37C2×C411yescharacteristic
29C22×C4×C37—21no—
30C22×C4×C37C2311yescharacteristic
31C2×C22⋊D37—21no—
32C22×Dic37—21no—
33C22×Dic37D411yescharacteristic
34#10596966—42no—
35C2×D148—21no—
36C2×D148—21no—
37C2×D148C2×C411yescharacteristic
38C2×C4×D37—21no—
39C2×C4×D37—42no—
40C2×C4×D37C2×C411yescharacteristic
41C2×C4×D37C2×C411yescharacteristic
42C2×C4×D37D411yescharacteristic
43C2×C4×D37D411yescharacteristic
44C2×C8×C37—21no—
45C4⋊C4×C37—21no—
46C4⋊C4×C37C2×C411yescharacteristic
47C22⋊C4×C37—21no—
48#10596938—21no—
49#10596938—21no—
50#10596938—21no—
51#10596938—21no—
52#10596938—42no—
53C4⋊Dic37C2×C411yescharacteristic
54#10596936—21no—
55C4×Dic37—21no—
56C2×#64436—21no—
57C8×D37—42no—
58C23×C37C2×D411yescharacteristic
59C22×D37—21no—
60C22×D37—21no—
61C22×D37—22no—
62C22×D37—21no—
63C22×D37—41no—
64C22×D37C22⋊C411yescharacteristic
65C22×D37C22⋊C411yescharacteristic
66Q8×C37—41no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37—41no—
72C2×C4×C37—41no—
73C2×C4×C37C22×C411yescharacteristic
74C2×C4×C37C2×D411yescharacteristic
75C22⋊D37—41no—
76C22⋊D37—41no—
77C2×Dic37—21no—
78C2×Dic37—41no—
79C2×Dic37—41no—
80C2×Dic37—41no—
81C2×Dic37—41no—
82C2×Dic37C22⋊C411yescharacteristic
83C2×Dic37C22⋊C411yescharacteristic
84D148—41no—
85D148—42no—
86D148—42no—
87C4×D37—22no—
88C4×D37—22no—
89C4×D37—41no—
90C4×D37—41no—
91C4×D37—42no—
92C8×C37—41no—
93#64436—41no—
94C22×C37—21no—
95C22×C37—21no—
96C22×C37C2×C22⋊C411yescharacteristic
97C22×C37#13511yescharacteristic
98C22×C37#13511yescharacteristic
99C2×D37—21no—
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#9912yes—
110C4×C37—21no—
111C4×C37—21no—
112C4×C37—41no—
113C4×C37—41no—
114C4×C37—81no—
115Dic37—21no—
116Dic37—21no—
117Dic37—41no—
118Dic37—81no—
119#1516—371nomaximal, Sylow
120C2×C37—21no—
121C2×C37—21no—
122C2×C37C2×#9911yescharacteristic
123C2×C37#41611yescharacteristic
124C2×C37#42111yescharacteristic
125D37—22no—
126D37—41no—
127D37—81no—
128#525—371no—
129C2×C22⋊C8—371no—
130#381—371no—
131#328—371no—
132#328D3711yescharacteristic, complemented
133#327—371no—
134#327—371no—
135C37#151611yescharacteristic, complemented, Sylow
136C2×#41—371no—
137C23×C4—371no—
138C22×C8—741no—
139#123—741no—
140C22⋊Q8—371no—
141C22⋊Q8C2×D3711yescharacteristic
142#121—371no—
143#121—371no—
144#120—741no—
145C4×D4—741no—
146C4×D4—741no—
147#117—371no—
148C2×C22⋊C4—741no—
149C22⋊C8—371no—
150C22⋊C8—741no—
151C22⋊C8C2×D3711yescharacteristic
152#95—371no—
153#95—741no—
154#95C2×D3711yescharacteristic
155C24—371no—
156#41—1482no—
157C2×Q8C4×D3711yescharacteristic
158C2×D4—371no—
159C2×D4—741no—
160C2×D4—741no—
161C2×D4—741no—
162C22×C4—21no—
163C22×C4—371no—
164C22×C4—371no—
165C22×C4—371no—
166C22×C4—371no—
167C22×C4—371no—
168C22×C4—741no—
169C22×C4—741no—
170C22×C4—1482no—
171C22×C4C22×D3711yescharacteristic
172C2×C8—21no—
173C2×C8—741no—
174C2×C8—1482no—
175C4⋊C4—21no—
176C4⋊C4—371no—
177C4⋊C4—741no—
178C4⋊C4C4×D3711yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—741no—
181C22⋊C4—741no—
182C22⋊C4—741no—
183C22⋊C4—741no—
184C22⋊C4—1482no—
185C42—741no—
186C23—371no—
187C23—371no—
188C23—742no—
189C23—741no—
190C23—741no—
191C23—741no—
192C23—1481no—
193C23D4×D3711yescharacteristic
194Q8—41no—
195D4—1481no—
196D4—1482no—
197D4—1482no—
198D4—1481no—
199D4—1481no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—371no—
207C2×C4—371no—
208C2×C4—742no—
209C2×C4—742no—
210C2×C4—741no—
211C2×C4—1481no—
212C2×C4—1481no—
213C2×C4—1482no—
214C2×C4—1481no—
215C2×C4—1481no—
216C2×C4—1481no—
217C2×C4—1481no—
218C2×C4C2×C4×D3711yescharacteristic
219C2×C4D4×D3711yescharacteristic
220C8—41no—
221C8—1481no—
222C22—21no—
223C22—21no—
224C22—372no—
225C22—741no—
226C22—741no—
227C22—741no—
228C22—741no—
229C22—741no—
230C22—1482no—
231C22—1482no—
232C22—1481no—
233C22—1481no—
234C22—1481no—
235C22C22⋊C4×D3711yescharacteristic
236C22#1192455711yescharacteristic
237C22#1192455911yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—41no—
242C4—81no—
243C4—2961no—
244C4—741no—
245C4—741no—
246C4—1481no—
247C2—21no—
248C2—21no—
249C2—2961no—
250C2—742no—
251C2—1481no—
252C2#99×D3711yescharacteristic
253C2#1455752811yescharacteristic
254C2#1455754811yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC2×C4×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#328C2
socleC22×C37C2×C22⋊C4
prime radical#14558046C2
cosocleC22×C4×C37C23
hypercenter#328D37
hypocenterC37#1516
LCSG ▷ C2×C4×C37 ▷ C22×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D37C2semidirect
3. #14557395C2semidirect
4. #14557270C2semidirect
5. #14557268C2semidirect
6. #14557266C2semidirect
7. C37×#328C2semidirect
8. C2×#10596966C4semidirect
12. #11924512C4semidirect
13. #11924511C4semidirect
18. #11924494C4semidirect
132. #328D37semidirect
135. C37#1516semidirect

Maximal subgroups

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

subgroupindex
#145580462
C22⋊C8×D372
#145573952
#145572702
#145572682
#145572662
C37×#3282
#151637