Finite Group Databasebeta

← #18006334

Subgroups — #18006334

Order 4736.

482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11924555C211yesmaximal, characteristic, complemented
2C22×Dic148C211yesmaximal, characteristic, complemented
3#14558189C212yesmaximal, complemented
4#14557916C211yesmaximal, characteristic, complemented
5#14557775C211yesmaximal, characteristic, complemented
6#14557754C212yesmaximal, complemented
7#14557696C212yesmaximal, complemented
8#14557671C212yesmaximal, complemented
9#14557627C211yesmaximal, characteristic, complemented
10C8×C22⋊D37C211yesmaximal, characteristic, complemented
11C37×#466C211yesmaximal, characteristic, complemented
12C2×#10596964C2212yes—
13C22×Dic74C2212yes—
14#11924555—24no—
15C2×Dic148—24no—
16C2×Dic148C2212yes—
17C2×Dic148C2211yescharacteristic
18C2×Dic148C2211yescharacteristic
19C2×#10596940C2212yes—
20C2×#10596940C2212yes—
21C2×C8×D37C2211yescharacteristic
22#11924523C2212yes—
23#11924522—22no—
24#11924516C2212yes—
25#11924513—22no—
26#11924508—22no—
27#11924501C2212yes—
28D4×Dic37—22no—
29C4×C22⋊D37C2211yescharacteristic
30#11924465C2211yescharacteristic
31#11924459C2212yes—
32#11924459C2212yes—
33C22⋊#64436C2211yescharacteristic
34#11924448C2211yescharacteristic
35C8×Dic37C2211yescharacteristic
36C2×D8×C37C2211yescharacteristic
37C22×C8×C37C2211yescharacteristic
38#121×C37C2212yes—
39#107×C37C2211yescharacteristic
40#102×C37C2212yes—
41C2×D4×C37—22no—
42C2×D4×C37C2312yes—
43C22×C4×C37C2311yescharacteristic
44C2×C22⋊D37—22no—
45C2×C22⋊D37D411yescharacteristic
46C22×Dic37—22no—
47C22×Dic37—22no—
48#10596964—24no—
49#10596964—42no—
50C2×C4×D37C2311yescharacteristic
51C2×Dic74—24no—
52C2×Dic74—22no—
53C2×Dic74—42no—
54C2×Dic74C2312yes—
55C2×Dic74C2312yes—
56D8×C37—22no—
57C2×C8×C37—22no—
58C2×C8×C37C2311yescharacteristic
59C2×C8×C37C2311yescharacteristic
60C4⋊C4×C37C2312yes—
61C22⋊C4×C37—22no—
62C22⋊Dic37—22no—
63C22⋊Dic37—22no—
64C22⋊Dic37D411yescharacteristic
65#10596940—24no—
66#10596940—42no—
67#10596938—22no—
68#10596938D411yescharacteristic
69C4⋊Dic37—22no—
70#10596936—22no—
71#10596936D411yescharacteristic
72C4×Dic37—22no—
73C4×Dic37C2311yescharacteristic
74C2×#64436C2311yescharacteristic
75C2×#64436C2311yescharacteristic
76Dic148—24no—
77Dic148—22no—
78Dic148D414yescomplemented
79C8×D37—22no—
80C23×C37—22no—
81C23×C37C2×D411yescharacteristic
82C22×D37C2×D411yescharacteristic
83D4×C37—22no—
84D4×C37—22no—
85D4×C37—44no—
86C2×C4×C37—21no—
87C2×C4×C37—21no—
88C2×C4×C37—22no—
89C2×C4×C37C2×D411yescharacteristic
90C2×C4×C37C2411yescharacteristic
91C22⋊D37—22no—
92C22⋊D37—44no—
93C2×Dic37—22no—
94C2×Dic37—22no—
95C2×Dic37—44no—
96C2×Dic37—44no—
97C2×Dic37C2×D411yescharacteristic
98C2×Dic37C2×D411yescharacteristic
99C2×Dic37C2×D411yescharacteristic
100C4×D37—21no—
101C4×D37—21no—
102Dic74—22no—
103Dic74—22no—
104Dic74—22no—
105Dic74—44no—
106Dic74C2×D414yes—
107C8×C37—21no—
108C8×C37C2×D412yes—
109#64436—21no—
110#64436—21no—
111C22×C37—21no—
112C22×C37—21no—
113C22×C37—42no—
114C22×C37—42no—
115C22×C37—42no—
116C22×C37#13512yescomplemented
117C22×C37C22×D411yescharacteristic
118C2×D37—21no—
119C2×D37—21no—
120C2×D37—21no—
121C4×C37—21no—
122C4×C37—42no—
123C4×C37C22×D411yescharacteristic
124C4×C37H(5,𝔽2)11yescharacteristic
125Dic37—24no—
126Dic37—21no—
127Dic37—21no—
128Dic37—21no—
129Dic37—42no—
130#3285—371nomaximal, Sylow
131C2×C37—22no—
132C2×C37—82no—
133C2×C37D4211yescharacteristic
134C2×C37C2×#13511yescharacteristic
135C2×C37#57811yescharacteristic
136D37—41no—
137C2×#135—371no—
138C22×Q16—371no—
139#548—372no—
140#495—371no—
141#467—371no—
142#466D3711yescharacteristic, complemented
143#464—372no—
144#452—372no—
145#448—372no—
146C4×Q16—371no—
147C8×D4—371no—
148C37#328511yescharacteristic, complemented, Sylow
149C2×#41—372no—
150C22×Q8—372no—
151#135—744no—
152C2×Q16—371no—
153C2×Q16—372no—
154C2×Q16—371no—
155C2×Q16—744no—
156C2×SD16—372no—
157C2×SD16—372no—
158C2×D8C2×D3711yescharacteristic
159C22×C8—371no—
160C22×C8C2×D3711yescharacteristic
161#124—372no—
162#124—742no—
163C22⋊Q8—372no—
164C22⋊Q8—742no—
165#121—742no—
166#121C2×D3712yes—
167C4×Q8—372no—
168C4×D4—371no—
169C4×D4—742no—
170#107C2×D3711yescharacteristic
171C4⋊C8—371no—
172#103—372no—
173#103—372no—
174#102C2×D3712yes—
175C22⋊C8—371no—
176C22⋊C8—371no—
177C4×C8—371no—
178#41—744no—
179#41—1482no—
180C2×Q8—372no—
181C2×Q8—372no—
182C2×Q8—744no—
183C2×Q8—742no—
184C2×Q8—1482no—
185C2×D4—22no—
186C2×D4—371no—
187C2×D4—742no—
188C2×D4C22×D3712yes—
189C22×C4—371no—
190C22×C4—742no—
191C22×C4—742no—
192C22×C4C22×D3711yescharacteristic
193Q16—374no—
194Q16—744no—
195Q16—742no—
196SD16—744no—
197SD16—1482no—
198D8—22no—
199C2×C8—22no—
200C2×C8—371no—
201C2×C8—371no—
202C2×C8—742no—
203C2×C8C22×D3711yescharacteristic
204C2×C8C22×D3711yescharacteristic
205C4⋊C4—371no—
206C4⋊C4—742no—
207C4⋊C4—742no—
208C4⋊C4C22×D3712yes—
209C22⋊C4—22no—
210C22⋊C4—371no—
211C22⋊C4—371no—
212C22⋊C4—742no—
213C22⋊C4—742no—
214C22⋊C4—742no—
215C42—371no—
216C42—742no—
217C23—22no—
218C23—371no—
219C23D4×D3711yescharacteristic
220Q8—374no—
221Q8—742no—
222Q8—742no—
223Q8—742no—
224Q8—1484no—
225D4—22no—
226D4—22no—
227D4—44no—
228D4—742no—
229D4—1484no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—371no—
234C2×C4—371no—
235C2×C4—371no—
236C2×C4—742no—
237C2×C4—741no—
238C2×C4—741no—
239C2×C4—742no—
240C2×C4—1484no—
241C2×C4—1484no—
242C2×C4D4×D3711yescharacteristic
243C2×C4C23×D3711yescharacteristic
244C8—21no—
245C8—741no—
246C8—741no—
247C8D4×D3712yes—
248C22—21no—
249C22—21no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—741no—
254C22—741no—
255C22—741no—
256C22#1192455512yescomplemented
257C22C2×D4×D3711yescharacteristic
258C4—21no—
259C4—42no—
260C4—741no—
261C4—741no—
262C4—741no—
263C4—744no—
264C4—1482no—
265C4C2×D4×D3711yescharacteristic
266C4#1192458211yescharacteristic
267C2—22no—
268C2—82no—
269C2—1481no—
270C2#1455816711yescharacteristic
271C2C2×#1192455511yescharacteristic
272C2#1455834711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#466C2
socleC22×C37C22×D4
hypercenter#466D37
hypocenterC37#3285
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #466

Complements

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

NH ≅ G/Ntype
1. C2×#11924555C2semidirect
2. C22×Dic148C2semidirect
3. #14558189C2semidirect
4. #14557916C2semidirect
5. #14557775C2semidirect
6. #14557754C2semidirect
7. #14557696C2semidirect
8. #14557671C2semidirect
9. #14557627C2semidirect
10. C8×C22⋊D37C2semidirect
11. C37×#466C2semidirect
78. Dic148D4semidirect
116. C22×C37#135semidirect
142. #466D37semidirect
148. C37#3285semidirect
256. C22#11924555semidirect

Maximal subgroups

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

subgroupindex
C2×#119245552
C22×Dic1482
#145581892
#145579162
#145577752
#145577542
#145576962
#145576712
#145576272
C8×C22⋊D372
C37×#4662
#328537