Finite Group Databasebeta

← #18004174

Subgroups — #18004174

Order 4736.

520 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924556C211yesmaximal, characteristic, complemented
2C23×#64436C211yesmaximal, characteristic, complemented
3#14558044C211yesmaximal, characteristic, complemented
4#14557772C212yesmaximal, complemented
5#14557767C212yesmaximal, complemented
6#14557764C212yesmaximal, complemented
7#14557760C212yesmaximal, complemented
8#14557569C211yesmaximal, characteristic, complemented
9#14557529C211yesmaximal, characteristic, complemented
10#14557527C211yesmaximal, characteristic, complemented
11C37×#525C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13#11924556—24no—
14C2×#10596942C2211yescharacteristic, complemented
15C2×#10596940C2211yescharacteristic, complemented
16C2×#10596941C2211yescharacteristic, complemented
17C2×#10596939C2211yescharacteristic, complemented
18C22×#64436—24no—
19C22×#64436C2212yes—
20C22×#64436C2212yes—
21C22×#64436C2211yescharacteristic
22C22×#64436C2211yescharacteristic
23#11924519—21no—
24#11924515C2212yes—
25#11924510C2212yes—
26#11924505—21no—
27C4×C22⋊D37—22no—
28#11924495C2211yescharacteristic
29#11924469C2212yescomplemented
30#11924467C2212yescomplemented
31#11924460C2212yescomplemented
32#11924459C2212yescomplemented
33#11924457C2212yescomplemented
34#11924456C2212yescomplemented
35C2×#41×C37C2211yescharacteristic
36C23×C4×C37C2211yescharacteristic
37#123×C37—21no—
38C22⋊Q8×C37C2212yes—
39#121×C37C2212yes—
40#120×C37—21no—
41C4×D4×C37—22no—
42#117×C37C2211yescharacteristic
43C24×C37D411yescharacteristic
44#41×C37—22no—
45#41×C37—22no—
46C2×Q8×C37C2311yescharacteristic
47C2×D4×C37—22no—
48C2×D4×C37—21no—
49C2×D4×C37C2311yescharacteristic
50C22×C4×C37—22no—
51C22×C4×C37—22no—
52C22×C4×C37—21no—
53C22×C4×C37D412yes—
54C22×C4×C37D411yescharacteristic
55C22×C4×C37C2312yes—
56C22×C4×C37C2311yescharacteristic
57C2×C22⋊D37—22no—
58C2×C22⋊D37—21no—
59#10596962—22no—
60#10596962—22no—
61C2×D148C2311yescharacteristic
62C2×C4×D37—21no—
63C2×Dic74C2311yescharacteristic
64C4⋊C4×C37—22no—
65C4⋊C4×C37C2312yes—
66C22⋊C4×C37—21no—
67C22⋊C4×C37—22no—
68C22⋊C4×C37—22no—
69C42×C37—21no—
70C22⋊Dic37—21no—
71C22⋊Dic37—22no—
72#10596942—22no—
73#10596941—22no—
74#10596940—22no—
75#10596939—22no—
76#10596938—22no—
77C4⋊Dic37C2312yes—
78#10596936—22no—
79C4×Dic37—21no—
80C2×#64436—22no—
81C2×#64436—24no—
82C2×#64436—24no—
83C2×#64436D414yescomplemented
84C2×#64436C2312yes—
85C2×#64436C2311yescharacteristic
86C2×#64436C2311yescharacteristic
87C23×C37—22no—
88C23×C37—24no—
89C23×C37—21no—
90C23×C37C2×D411yescharacteristic
91C23×C37C2×D412yes—
92C22×D37—21no—
93Q8×C37—21no—
94Q8×C37—21no—
95D4×C37—21no—
96D4×C37—21no—
97D4×C37—42no—
98D4×C37—44no—
99C2×C4×C37—22no—
100C2×C4×C37—24no—
101C2×C4×C37—22no—
102C2×C4×C37—22no—
103C2×C4×C37—22no—
104C2×C4×C37—21no—
105C2×C4×C37—42no—
106C2×C4×C37C2×D412yes—
107C2×C4×C37C2×D412yes—
108C2×C4×C37C2×D411yescharacteristic
109C2×C4×C37#4112yes—
110C2×C4×C37C2411yescharacteristic
111C22⋊D37—42no—
112C22⋊D37—44no—
113C2×Dic37—22no—
114C2×Dic37—21no—
115D148—21no—
116D148—21no—
117C4×D37—42no—
118Dic74—21no—
119Dic74—21no—
120#64436—22no—
121#64436C2×D412yes—
122#64436C2×D412yes—
123C22×C37—28no—
124C22×C37—22no—
125C22×C37—22no—
126C22×C37—22no—
127C22×C37—41no—
128C22×C37—42no—
129C22×C37#12112yes—
130C22×C37#13514yescomplemented
131C22×C37C22×D411yescharacteristic
132C2×D37—41no—
133C2×D37—42no—
134C4×C37—22no—
135C4×C37—41no—
136C4×C37—42no—
137C4×C37#12112yes—
138C4×C37C22×D411yescharacteristic
139C4×C37C2×#4111yescharacteristic
140Dic37—41no—
141Dic37—42no—
142#3050—371nomaximal, Sylow
143C2×C37—22no—
144C2×C37—24no—
145C2×C37—81no—
146C2×C37C2×#12111yescharacteristic
147C2×C37C2×#13512yes—
148D37—81no—
149C2×#135—371no—
150C23×C8—371no—
151#525—371no—
152#525D3711yescharacteristic, complemented
153#467—372no—
154#466—372no—
155#465—372no—
156#465—372no—
157#427—371no—
158#416—371no—
159#416—371no—
160C37#305011yescharacteristic, complemented, Sylow
161C2×#41—371no—
162C2×#41C2×D3711yescharacteristic
163C23×C4C2×D3711yescharacteristic
164#135—744no—
165C2×Q16—371no—
166C2×SD16—371no—
167C2×SD16—371no—
168C2×D8—371no—
169C22×C8—371no—
170C22×C8—371no—
171C22×C8—372no—
172C22×C8—372no—
173C22×C8—744no—
174#123—21no—
175#123—741no—
176C22⋊Q8—372no—
177C22⋊Q8C2×D3712yes—
178#121—372no—
179#121C2×D3712yes—
180#120—21no—
181#120—741no—
182C4×D4—22no—
183C4×D4—742no—
184#117—371no—
185#117C2×D3711yescharacteristic
186#107—372no—
187#106—372no—
188#103—372no—
189#103—372no—
190#102—372no—
191#102—372no—
192C24C22⋊D3711yescharacteristic
193#41—22no—
194#41—22no—
195#41—742no—
196#41—742no—
197C2×Q8—371no—
198C2×Q8C22×D3711yescharacteristic
199C2×D4—22no—
200C2×D4—21no—
201C2×D4—371no—
202C2×D4—742no—
203C2×D4—741no—
204C2×D4C22×D3711yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—741no—
209C22×C4C22⋊D3711yescharacteristic
210C22×C4C22⋊D3712yes—
211C22×C4C22×D3712yes—
212C22×C4C22×D3711yescharacteristic
213Q16—742no—
214SD16—742no—
215SD16—742no—
216D8—742no—
217C2×C8—374no—
218C2×C8—371no—
219C2×C8—371no—
220C2×C8—372no—
221C2×C8—744no—
222C2×C8—744no—
223C2×C8—742no—
224C4⋊C4—22no—
225C4⋊C4—372no—
226C4⋊C4—742no—
227C4⋊C4C22×D3712yes—
228C22⋊C4—21no—
229C22⋊C4—22no—
230C22⋊C4—22no—
231C22⋊C4—741no—
232C22⋊C4—742no—
233C22⋊C4—742no—
234C42—21no—
235C42—741no—
236C23—22no—
237C23—24no—
238C23—21no—
239C23—741no—
240C23C2×C22⋊D3711yescharacteristic
241C23C2×C22⋊D3712yes—
242Q8—21no—
243Q8—21no—
244Q8—741no—
245Q8—741no—
246D4—21no—
247D4—21no—
248D4—42no—
249D4—44no—
250D4—741no—
251D4—741no—
252D4—1482no—
253D4—1484no—
254C2×C4—22no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—742no—
262C2×C4—741no—
263C2×C4—1482no—
264C2×C4D4×D3712yes—
265C2×C4#1059696412yes—
266C2×C4C2×C22⋊D3712yes—
267C2×C4C2×C22⋊D3711yescharacteristic
268C2×C4C23×D3711yescharacteristic
269C8—372no—
270C8—372no—
271C8—742no—
272C22—28no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—42no—
278C22—1481no—
279C22—1482no—
280C22#1192450812yes—
281C22#1192455614yescomplemented
282C22C22×C22⋊D3711yescharacteristic
283C4—22no—
284C4—41no—
285C4—42no—
286C4—1481no—
287C4—1482no—
288C4#1192450812yes—
289C4C2×D4×D3711yescharacteristic
290C4C2×#1059696411yescharacteristic
291C2—22no—
292C2—24no—
293C2—81no—
294C2—2961no—
295C2C2×#1192450811yescharacteristic
296C2C2×#1192455612yes—
subgroupG/H
centerC2×C4C2×C22⋊D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#525C2
socleC22×C37C22×D4
hypercenter#525D37
hypocenterC37#3050
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#11924556C2semidirect
2. C23×#64436C2semidirect
3. #14558044C2semidirect
4. #14557772C2semidirect
5. #14557767C2semidirect
6. #14557764C2semidirect
7. #14557760C2semidirect
8. #14557569C2semidirect
9. #14557529C2semidirect
10. #14557527C2semidirect
11. C37×#525C2semidirect
14. C2×#10596942C22semidirect
15. C2×#10596940C22semidirect
16. C2×#10596941C22semidirect
17. C2×#10596939C22semidirect
29. #11924469C22semidirect
30. #11924467C22semidirect
31. #11924460C22semidirect
32. #11924459C22semidirect
33. #11924457C22semidirect
34. #11924456C22semidirect
83. C2×#64436D4semidirect
130. C22×C37#135semidirect
152. #525D37semidirect
160. C37#3050semidirect
281. C22#11924556semidirect

Maximal subgroups

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

subgroupindex
C2×#119245562
C23×#644362
#145580442
#145577722
#145577672
#145577642
#145577602
#145575692
#145575292
#145575272
C37×#5252
#305037