Finite Group Databasebeta

← #17994581

Subgroups — #17994581

Order 4736.

380 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 97 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×C4×C22⋊D37C211yesmaximal, characteristic
2C2×#11924450C212yesmaximal
3#14557393C211yesmaximal, characteristic, complemented
4#14557299C212yesmaximal, complemented
5C37×#380C211yesmaximal, characteristic, complemented
6C22×C22⋊D37C2211yescharacteristic
7C22×C4×D37C411yescharacteristic, complemented
8C4×C22⋊D37—21no—
9C4×C22⋊D37—21no—
10C4×C22⋊D37—21no—
11C4×C22⋊D37—21no—
12C2×C4⋊Dic37—21no—
13C2×#10596936C411yescharacteristic, complemented
14C2×C22⋊Dic37C2212yes—
15C2×C22⋊Dic37C2211yescharacteristic
16C2×#10596938C411yescharacteristic, complemented
17C2×C4×Dic37C411yescharacteristic, complemented
18#11924450—24no—
19#11924443—21no—
20C23×C4×C37C2211yescharacteristic
21C2×C4⋊C4×C37—21no—
22C2×C22⋊C4×C37C2212yes—
23#95×C37—21no—
24C24×C37C2311yescharacteristic
25C23×D37C2×C411yescharacteristic
26C22×C4×C37—22no—
27C22×C4×C37—42no—
28C22×C4×C37C2×C411yescharacteristic
29C22×C4×C37C2×C411yescharacteristic
30C22×C4×C37D411yescharacteristic
31C22×C4×C37D411yescharacteristic
32C22×C4×C37D411yescharacteristic
33C22×C4×C37D411yescharacteristic
34C2×C22⋊D37—21no—
35C2×C22⋊D37—21no—
36C2×C22⋊D37—21no—
37C2×C22⋊D37—21no—
38C2×C22⋊D37D412yes—
39C2×C22⋊D37Q812yes—
40C22×Dic37—22no—
41C22×Dic37C2×C411yescharacteristic
42C22×Dic37C2×C411yescharacteristic
43C22×Dic37C2×C411yescharacteristic
44C2×C4×D37—21no—
45C2×C4×D37—21no—
46C2×C4×D37—42no—
47C4⋊C4×C37—42no—
48C22⋊C4×C37—22no—
49C22⋊C4×C37—22no—
50C22⋊Dic37—21no—
51C22⋊Dic37—21no—
52C22⋊Dic37—22no—
53C22⋊Dic37—22no—
54#10596938—21no—
55#10596938—21no—
56C4⋊Dic37—42no—
57#10596936—21no—
58#10596936—21no—
59C4×Dic37—21no—
60C4×Dic37—21no—
61C23×C37—41no—
62C23×C37—41no—
63C23×C37C22×C411yescharacteristic
64C23×C37C2×D411yescharacteristic
65C23×C37C2×D411yescharacteristic
66C23×C37C2×D411yescharacteristic
67C23×C37C2×Q811yescharacteristic
68C23×C37#4111yescharacteristic
69C23×C37#4111yescharacteristic
70C22×D37—21no—
71C22×D37—21no—
72C22×D37—41no—
73C22×D37—41no—
74C22×D37C4⋊C412yescomplemented
75C2×C4×C37—22no—
76C2×C4×C37—22no—
77C2×C4×C37—22no—
78C2×C4×C37—41no—
79C2×C4×C37—41no—
80C2×C4×C37—41no—
81C2×C4×C37—42no—
82C2×C4×C37—42no—
83C2×C4×C37—42no—
84C2×C4×C37C22⋊C411yescharacteristic
85C2×C4×C37C22⋊C411yescharacteristic
86C2×C4×C37C22⋊C411yescharacteristic
87C2×C4×C37C22⋊C411yescharacteristic
88C22⋊D37—22no—
89C22⋊D37—22no—
90C22⋊D37—22no—
91C22⋊D37—22no—
92C2×Dic37—21no—
93C2×Dic37—21no—
94C2×Dic37—21no—
95C2×Dic37—21no—
96C2×Dic37—41no—
97C2×Dic37—41no—
98C2×Dic37—42no—
99C2×Dic37—42no—
100C2×Dic37—42no—
101C2×Dic37C4⋊C412yescomplemented
102C4×D37—42no—
103C4×D37—42no—
104C22×C37—21no—
105C22×C37—21no—
106C22×C37—21no—
107C22×C37—21no—
108C22×C37—21no—
109C22×C37—21no—
110C22×C37—41no—
111C22×C37—41no—
112C22×C37—41no—
113C22×C37—41no—
114C22×C37C2×C22⋊C411yescharacteristic
115C22×C37C2×C4⋊C411yescharacteristic
116C22×C37#11711yescharacteristic
117C22×C37#12111yescharacteristic
118C22×C37#12111yescharacteristic
119C22×C37C22⋊Q811yescharacteristic
120C22×C37C22⋊Q811yescharacteristic
121C2×D37—22no—
122C2×D37—42no—
123C2×D37—41no—
124C2×D37—41no—
125C2×D37—42no—
126C4×C37—21no—
127C4×C37—21no—
128C4×C37—21no—
129C4×C37—82no—
130C4×C37#9912yescomplemented
131Dic37—22no—
132Dic37—41no—
133Dic37—41no—
134Dic37—82no—
135#1799—371nomaximal, Sylow
136C2×C37—21no—
137C2×C37—21no—
138C2×C37—21no—
139C2×C37—21no—
140C2×C37—21no—
141C2×C37—21no—
142C2×C37#38011yescharacteristic
143C2×C37C2×#9911yescharacteristic
144C2×C37#41011yescharacteristic
145D37—42no—
146C2×C4×D4—371no—
147C2×#99—372no—
148#380—371no—
149#380D3711yescharacteristic, complemented
150#342—372no—
151C37#179911yescharacteristic, complemented, Sylow
152C22×D4—371no—
153C23×C4—371no—
154C23×C4C2×D3711yescharacteristic
155C4×D4—741no—
156C4×D4—741no—
157C4×D4—741no—
158C4×D4—741no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—371no—
161C2×C4⋊C4—741no—
162C2×C22⋊C4—371no—
163C2×C22⋊C4—371no—
164C2×C22⋊C4—372no—
165C2×C22⋊C4C2×D3712yes—
166C2×C42—371no—
167#99—744no—
168#95—21no—
169#95—741no—
170C24—371no—
171C24C22×D3711yescharacteristic
172C2×D4—372no—
173C2×D4—372no—
174C2×D4—741no—
175C2×D4—741no—
176C2×D4—741no—
177C2×D4—741no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—371no—
181C22×C4—371no—
182C22×C4—371no—
183C22×C4—741no—
184C22×C4—741no—
185C22×C4—742no—
186C22×C4—1482no—
187C22×C4C4×D3711yescharacteristic
188C22×C4C4×D3711yescharacteristic
189C22×C4D14811yescharacteristic
190C22×C4D14811yescharacteristic
191C22×C4C22⋊D3711yescharacteristic
192C22×C4C22⋊D3711yescharacteristic
193C4⋊C4—42no—
194C4⋊C4—741no—
195C4⋊C4—741no—
196C4⋊C4—1482no—
197C22⋊C4—22no—
198C22⋊C4—22no—
199C22⋊C4—741no—
200C22⋊C4—741no—
201C22⋊C4—741no—
202C22⋊C4—741no—
203C22⋊C4—742no—
204C22⋊C4—742no—
205C42—741no—
206C42—741no—
207C23—41no—
208C23—41no—
209C23—372no—
210C23—741no—
211C23—741no—
212C23—1481no—
213C23—1481no—
214C23C2×C4×D3711yescharacteristic
215C23C2×D14811yescharacteristic
216C23D4×D3711yescharacteristic
217C23#1059696411yescharacteristic
218C23Q8×D3711yescharacteristic
219C23#1059696611yescharacteristic
220C23C2×C22⋊D3711yescharacteristic
221D4—742no—
222D4—742no—
223D4—742no—
224D4—742no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—372no—
235C2×C4—741no—
236C2×C4—741no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—1482no—
240C2×C4—1482no—
241C2×C4—1482no—
242C2×C4—1482no—
243C2×C4—1482no—
244C2×C4—1481no—
245C2×C4—1481no—
246C2×C4#1059693811yescharacteristic
247C2×C4#1059693811yescharacteristic
248C2×C4#1059693811yescharacteristic
249C2×C4#1059693811yescharacteristic
250C22—21no—
251C22—21no—
252C22—21no—
253C22—21no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—41no—
260C22—742no—
261C22—1482no—
262C22—1482no—
263C22—1481no—
264C22—1481no—
265C22C2×#1059693811yescharacteristic
266C22C4⋊C4×D3711yescharacteristic
267C22#1192449411yescharacteristic
268C22#1192450711yescharacteristic
269C22#1192451111yescharacteristic
270C22#1192451211yescharacteristic
271C22#1192451611yescharacteristic
272C4—21no—
273C4—21no—
274C4—21no—
275C4—82no—
276C4—2962no—
277C4—742no—
278C4—1481no—
279C4—1481no—
280C4#1192445012yescomplemented
281C2—21no—
282C2—21no—
283C2—21no—
284C2—21no—
285C2—21no—
286C2—21no—
287C2—1482no—
288C2#1455739011yescharacteristic
289C2C2×#1192445011yescharacteristic
290C2#1455750611yescharacteristic
subgroupG/H
centerC22C2×#10596938
commutatorC23×C37C22×C4
FrattiniC24C22×D37
FittingC37×#380C2
socleC22×C37C2×C22⋊C4
prime radicalC22×C22⋊D37C22
cosocleC24×C37C23
hypercenter#380D37
hypocenterC37#1799
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #14557393C2semidirect
4. #14557299C2semidirect
5. C37×#380C2semidirect
7. C22×C4×D37C4semidirect
13. C2×#10596936C4semidirect
16. C2×#10596938C4semidirect
17. C2×C4×Dic37C4semidirect
74. C22×D37C4⋊C4semidirect
101. C2×Dic37C4⋊C4semidirect
130. C4×C37#99semidirect
149. #380D37semidirect
151. C37#1799semidirect
280. C4#11924450semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D372
C2×#119244502
#145573932
#145572992
C37×#3802
#179937