Finite Group Databasebeta

← #17997835

Subgroups — #17997835

Order 4736.

696 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×Dic37C211yesmaximal, characteristic, complemented
2C2×#11924496C212yesmaximal, complemented
3C2×#11924494C211yesmaximal, characteristic, complemented
4#14557463C211yesmaximal, characteristic, complemented
5#14557460C211yesmaximal, characteristic, complemented
6#14557456C212yesmaximal, complemented
7#14557448C212yesmaximal, complemented
8#14557441C211yesmaximal, characteristic
9#14557384C211yesmaximal, characteristic, complemented
10C22⋊C4×Dic37C212yesmaximal, complemented
11C37×#394C211yesmaximal, characteristic, complemented
12C22×C22⋊D37C2212yes—
13C23×Dic37C2212yes—
14C22×C4×D37C2211yescharacteristic
15D4×Dic37—24no—
16#11924496—28no—
17#11924494—24no—
18C2×C4⋊Dic37C2211yescharacteristic
19C2×C4⋊Dic37C2211yescharacteristic
20C2×#10596936C2212yes—
21C2×#10596936C2212yes—
22C2×C22⋊Dic37C2212yes—
23C2×C22⋊Dic37C2212yes—
24C2×#10596938C2211yescharacteristic
25C2×#10596938C2211yescharacteristic
26C2×#10596938C2212yes—
27C2×C4×Dic37C2211yescharacteristic
28C2×C4×Dic37C2212yes—
29C2×C4×Dic37C2211yescharacteristic
30#11924443C2211yescharacteristic
31#11924443C2212yes—
32#11924443C2212yes—
33C22×D4×C37C2211yescharacteristic
34C2×C4⋊C4×C37C2211yescharacteristic
35C2×C22⋊C4×C37C2212yes—
36C2×C22⋊C4×C37C2212yes—
37#95×C37C2211yescharacteristic
38C24×C37C2312yes—
39C23×D37C2311yescharacteristic
40C2×D4×C37—24no—
41C2×D4×C37—22no—
42C22×C4×C37C2312yes—
43C22×C4×C37C2311yescharacteristic
44C22×C4×C37C2311yescharacteristic
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—24no—
47C2×C22⋊D37—24no—
48C2×C22⋊D37—24no—
49C22×Dic37—24no—
50C22×Dic37—24no—
51C22×Dic37—24no—
52C22×Dic37C2311yescharacteristic
53C22×Dic37C2312yes—
54C22×Dic37C2311yescharacteristic
55C22×Dic37C2312yes—
56C22×Dic37C2311yescharacteristic
57C2×C4×D37—22no—
58C2×C4×D37—22no—
59C2×C4×D37D414yescomplemented
60C4⋊C4×C37—22no—
61C22⋊C4×C37—24no—
62C22⋊C4×C37—24no—
63C22⋊Dic37—24no—
64C22⋊Dic37—24no—
65#10596938—24no—
66#10596938—22no—
67#10596938—22no—
68C4⋊Dic37—22no—
69C4⋊Dic37—22no—
70#10596936—24no—
71#10596936—24no—
72C4×Dic37—22no—
73C4×Dic37—24no—
74C4×Dic37D414yescomplemented
75C23×C37—22no—
76C23×C37—22no—
77C23×C37—22no—
78C23×C37—22no—
79C23×C37—22no—
80C23×C37—22no—
81C23×C37#4114yes—
82C23×C37C2411yescharacteristic
83C22×D37—21no—
84C22×D37—21no—
85C22×D37—22no—
86C22×D37—22no—
87C22×D37C2×D412yes—
88D4×C37—28no—
89C2×C4×C37—21no—
90C2×C4×C37—21no—
91C2×C4×C37—22no—
92C2×C4×C37—22no—
93C2×C4×C37—21no—
94C2×C4×C37—22no—
95C2×C4×C37—22no—
96C2×C4×C37—22no—
97C2×C4×C37C2×D412yes—
98C2×C4×C37C2×D412yes—
99C22⋊D37—216no—
100C2×Dic37—22no—
101C2×Dic37—22no—
102C2×Dic37—22no—
103C2×Dic37—21no—
104C2×Dic37—22no—
105C2×Dic37—22no—
106C2×Dic37—22no—
107C2×Dic37—22no—
108C2×Dic37—48no—
109C2×Dic37C2×D412yes—
110C2×Dic37C2×D412yes—
111C2×Dic37C2×D412yes—
112C2×Dic37#4114yes—
113C2×Dic37#4112yes—
114C4×D37—28no—
115C22×C37—24no—
116C22×C37—24no—
117C22×C37—24no—
118C22×C37—42no—
119C22×C37—42no—
120C22×C37—42no—
121C22×C37—42no—
122C22×C37C22×D411yescharacteristic
123C22×C37C22×D411yescharacteristic
124C22×C37C2×#4111yescharacteristic
125C22×C37C2×#4112yes—
126C22×C37C2×#4112yes—
127C2×D37—22no—
128C2×D37—24no—
129C2×D37—41no—
130C2×D37—42no—
131C2×D37—41no—
132C4×C37—22no—
133C4×C37—22no—
134C4×C37—41no—
135C4×C37—42no—
136Dic37—24no—
137Dic37—22no—
138Dic37—42no—
139Dic37—41no—
140Dic37#12114yes—
141#2392—371nomaximal, Sylow
142C2×C37—44no—
143C2×C37C2×#12111yescharacteristic
144C2×C37#52511yescharacteristic
145C2×C37#52512yes—
146C2×C37#52912yes—
147C2×C37#53211yescharacteristic
148D37—42no—
149C2×C4×D4—371no—
150C2×C4×D4—372no—
151C2×#117—371no—
152#398—371no—
153#397—371no—
154#396—372no—
155#394—372no—
156#394D3711yescharacteristic, complemented
157#392—371no—
158C4×C4⋊C4—371no—
159C4×C22⋊C4—372no—
160C37#239211yescharacteristic, complemented, Sylow
161C22×D4—372no—
162C22×D4C2×D3711yescharacteristic
163C23×C4—371no—
164C23×C4—372no—
165C4×D4—744no—
166C4×D4—748no—
167#117—744no—
168C2×C4⋊C4—371no—
169C2×C4⋊C4—372no—
170C2×C4⋊C4—371no—
171C2×C4⋊C4—372no—
172C2×C4⋊C4C2×D3711yescharacteristic
173C2×C22⋊C4—372no—
174C2×C22⋊C4—372no—
175C2×C22⋊C4—371no—
176C2×C22⋊C4—371no—
177C2×C22⋊C4—372no—
178C2×C22⋊C4C2×D3712yes—
179C2×C22⋊C4C2×D3712yes—
180C2×C42—371no—
181C2×C42—371no—
182C2×C42—372no—
183#95—372no—
184#95—372no—
185#95—371no—
186#95C2×D3711yescharacteristic
187C24—371no—
188C24C22×D3712yes—
189C2×D4—24no—
190C2×D4—22no—
191C2×D4—744no—
192C2×D4—744no—
193C2×D4—744no—
194C22×C4—371no—
195C22×C4—372no—
196C22×C4—371no—
197C22×C4—374no—
198C22×C4—371no—
199C22×C4—372no—
200C22×C4—742no—
201C22×C4—742no—
202C22×C4—744no—
203C22×C4—744no—
204C22×C4—744no—
205C22×C4C22×D3711yescharacteristic
206C22×C4C22×D3712yes—
207C22×C4C22×D3711yescharacteristic
208C22×C4C22×D3711yescharacteristic
209C4⋊C4—22no—
210C4⋊C4—744no—
211C4⋊C4—742no—
212C4⋊C4—744no—
213C4⋊C4—742no—
214C22⋊C4—24no—
215C22⋊C4—24no—
216C22⋊C4—742no—
217C22⋊C4—744no—
218C22⋊C4—744no—
219C22⋊C4—744no—
220C22⋊C4—742no—
221C42—374no—
222C42—742no—
223C42—744no—
224C23—22no—
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—372no—
231C23—741no—
232C23—741no—
233C23—742no—
234C23—742no—
235C23#1059696414yes—
236C23C23×D3711yescharacteristic
237D4—28no—
238D4—7416no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—372no—
248C2×C4—372no—
249C2×C4—372no—
250C2×C4—372no—
251C2×C4—374no—
252C2×C4—748no—
253C2×C4—742no—
254C2×C4—742no—
255C2×C4—742no—
256C2×C4—741no—
257C2×C4—742no—
258C2×C4—742no—
259C2×C4—742no—
260C2×C4—742no—
261C2×C4—1488no—
262C2×C4D4×D3712yes—
263C2×C4D4×D3712yes—
264C22—24no—
265C22—24no—
266C22—24no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—742no—
272C22—744no—
273C22—1481no—
274C22—1482no—
275C22—1481no—
276C22C2×D4×D3711yescharacteristic
277C22C2×D4×D3711yescharacteristic
278C22#41×D3711yescharacteristic
279C22#41×D3712yes—
280C22C2×#1059696412yes—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—42no—
285C4—374no—
286C4—744no—
287C4—742no—
288C4—1482no—
289C4—1481no—
290C2—44no—
291C2—1482no—
292C2#121×D3711yescharacteristic
293C2#1455803911yescharacteristic
294C2#1455804312yes—
295C2#1455806012yes—
296C2#1455808211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D37
commutator, socle, cosocleC23×C37C24
FittingC37×#394C2
prime radical#14557441C2
hypercenter#394D37
hypocenterC37#2392
LCSG ▷ C23×C37 ▷ C37
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic37C2semidirect
2. C2×#11924496C2semidirect
3. C2×#11924494C2semidirect
4. #14557463C2semidirect
5. #14557460C2semidirect
6. #14557456C2semidirect
7. #14557448C2semidirect
9. #14557384C2semidirect
10. C22⋊C4×Dic37C2semidirect
11. C37×#394C2semidirect
59. C2×C4×D37D4semidirect
74. C4×Dic37D4semidirect
156. #394D37semidirect
160. C37#2392semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic372
C2×#119244962
C2×#119244942
#145574632
#145574602
#145574562
#145574482
#145574412
#145573842
C22⋊C4×Dic372
C37×#3942
#239237