Finite Group Databasebeta

← #17992958

Subgroups — #17992958

Order 4736.

270 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 65 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×#11924514C211yesmaximal, characteristic
2#14557495C211yesmaximal, characteristic
3C22⋊C8×D37C211yesmaximal, characteristic
4#14557259C211yesmaximal, characteristic, complemented
5#14557258C211yesmaximal, characteristic, complemented
6#14557258C211yesmaximal, characteristic, complemented
7C37×#324C211yesmaximal, characteristic, complemented
8C22×Dic74C411yescharacteristic
9C22×C4×D37C2211yescharacteristic
10C2×#10596929—21no—
11C2×C8×D37—21no—
12#11924514—21no—
13#11924514—21no—
14#11924514—21no—
15#11924514—21no—
16C2×#10596936C411yescharacteristic
17C2×#10596936C2211yescharacteristic
18C2×#10596938C411yescharacteristic
19C2×#10596938C411yescharacteristic
20C22⋊#64436C2211yescharacteristic
21C22⋊#64436C2211yescharacteristic
22#11924448—21no—
23#11924448—21no—
24C2×C4⋊C4×C37C2211yescharacteristic
25C22⋊C8×C37C2211yescharacteristic
26C22⋊C8×C37C2211yescharacteristic
27C23×D37C2×C411yescharacteristic
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37C2311yescharacteristic
31C22×Dic37C2×C411yescharacteristic
32C22×Dic37C2×C411yescharacteristic
33C22×Dic37C2×C411yescharacteristic
34C2×C4×D37—42no—
35C2×C4×D37D411yescharacteristic
36C2×C4×D37D411yescharacteristic
37C2×C4×D37D411yescharacteristic
38C2×C4×D37D411yescharacteristic
39C2×Dic74—21no—
40C2×Dic74—21no—
41C2×Dic74—42no—
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#10596936—21no—
51#10596936—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—41no—
63C22×D37C22⋊C411yescharacteristic
64C22×D37C22⋊C411yescharacteristic
65C2×C4×C37—21no—
66C2×C4×C37—21no—
67C2×C4×C37—21no—
68C2×C4×C37—21no—
69C2×C4×C37—41no—
70C2×C4×C37—41no—
71C2×C4×C37C2×D411yescharacteristic
72C2×C4×C37C2×D411yescharacteristic
73C2×Dic37—22no—
74C2×Dic37—21no—
75C2×Dic37—21no—
76C2×Dic37—21no—
77C2×Dic37—21no—
78C2×Dic37—41no—
79C2×Dic37C22⋊C411yescharacteristic
80C2×Dic37C22⋊C411yescharacteristic
81C4×D37—22no—
82C4×D37—22no—
83C4×D37—41no—
84C4×D37—41no—
85Dic74—42no—
86Dic74—42no—
87C8×C37—41no—
88C8×C37—41no—
89#64436—41no—
90#64436—41no—
91C22×C37—21no—
92C22×C37—21no—
93C22×C37C2×C22⋊C411yescharacteristic
94C22×C37#13111yescharacteristic
95C22×C37#13111yescharacteristic
96C2×D37—21no—
97C2×D37—21no—
98C2×D37—21no—
99C2×D37—21no—
100C2×D37—21no—
101C2×D37—42no—
102C2×D37—42no—
103C2×D37#10112yes—
104C4×C37—21no—
105C4×C37—21no—
106C4×C37—41no—
107C4×C37—41no—
108Dic37—21no—
109Dic37—41no—
110Dic37—41no—
111Dic37#9912yes—
112#1472—371nomaximal, Sylow
113C2×C37—21no—
114C2×C37—21no—
115C2×C37#40811yescharacteristic
116C2×C37C2×#9911yescharacteristic
117C2×C37C2×#10111yescharacteristic
118D37—22no—
119D37—41no—
120C2×C22⋊Q8—371no—
121#407—371no—
122C2×C22⋊C8—371no—
123#324—371no—
124#324—371no—
125#324—371no—
126#324D3711yescharacteristic, complemented
127C37#147211yescharacteristic, complemented, Sylow
128C22×Q8—371no—
129C23×C4—371no—
130C2×M16—741no—
131C22×C8—741no—
132C22⋊Q8—741no—
133C22⋊Q8—741no—
134C22⋊Q8—741no—
135C22⋊Q8—741no—
136C2×C4⋊C4—371no—
137C2×C4⋊C4—371no—
138C2×C4⋊C4C2×D3711yescharacteristic
139C2×C22⋊C4—371no—
140C2×C22⋊C4—371no—
141C22⋊C8—371no—
142C22⋊C8—371no—
143C22⋊C8—741no—
144C22⋊C8—741no—
145C22⋊C8C2×D3711yescharacteristic
146C22⋊C8C2×D3711yescharacteristic
147C24—371no—
148C2×Q8—741no—
149C2×Q8—741no—
150C2×Q8—1482no—
151C22×C4—371no—
152C22×C4—371no—
153C22×C4—371no—
154C22×C4—371no—
155C22×C4—371no—
156C22×C4—371no—
157C22×C4—371no—
158C22×C4—1482no—
159C22×C4C4×D3711yescharacteristic
160C22×C4C4×D3711yescharacteristic
161C22×C4C22×D3711yescharacteristic
162M16—1482no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—741no—
166C2×C8—741no—
167C2×C8—1482no—
168C4⋊C4—21no—
169C4⋊C4—21no—
170C4⋊C4—741no—
171C4⋊C4—741no—
172C4⋊C4—741no—
173C4⋊C4—741no—
174C22⋊C4—741no—
175C22⋊C4—741no—
176C22⋊C4—741no—
177C22⋊C4—741no—
178C23—371no—
179C23—371no—
180C23—742no—
181C23—741no—
182C23—741no—
183C23—1481no—
184C23C2×C4×D3711yescharacteristic
185Q8—1482no—
186Q8—1482no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—371no—
194C2×C4—371no—
195C2×C4—742no—
196C2×C4—742no—
197C2×C4—742no—
198C2×C4—741no—
199C2×C4—741no—
200C2×C4—741no—
201C2×C4—741no—
202C2×C4—1481no—
203C2×C4—1481no—
204C2×C4—1481no—
205C2×C4D4×D3711yescharacteristic
206C2×C4D4×D3711yescharacteristic
207C8—41no—
208C8—41no—
209C8—1481no—
210C8—1481no—
211C22—21no—
212C22—21no—
213C22—372no—
214C22—741no—
215C22—741no—
216C22—741no—
217C22—741no—
218C22—741no—
219C22—1482no—
220C22—1482no—
221C22C22⋊C4×D3711yescharacteristic
222C22#1192454211yescharacteristic
223C22#1192454411yescharacteristic
224C4—21no—
225C4—21no—
226C4—41no—
227C4—41no—
228C4—372no—
229C4—741no—
230C4—1481no—
231C4—1481no—
232C2—21no—
233C2—21no—
234C2—742no—
235C2—1481no—
236C2#1455749811yescharacteristic
237C2#99×D3711yescharacteristic
238C2#101×D3711yescharacteristic
subgroupG/H
centerC22C22⋊C4×D37
commutatorC23×C37C22×C4
FrattiniC22×C4C22×D37
FittingC37×#324C2
socleC22×C37C2×C22⋊C4
prime radicalC23×D37C2×C4
cosocleC22×C4×C37C23
hypercenter#324D37
hypocenterC37#1472
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
4. #14557259C2semidirect
5. #14557258C2semidirect
6. #14557258C2semidirect
7. C37×#324C2semidirect
126. #324D37semidirect
127. C37#1472semidirect

Maximal subgroups

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

subgroupindex
C2×#119245142
#145574952
C22⋊C8×D372
#145572592
#145572582
C37×#3242
#147237