Finite Group Databasebeta

← #18003990

Subgroups — #18003990

Order 4736.

766 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#14558369C211yesmaximal, characteristic, complemented
2#14558045C212yesmaximal, complemented
3#14558040C211yesmaximal, characteristic, complemented
4#14557724C214yesmaximal, complemented
5#14557721C214yesmaximal, complemented
6#14557506C212yesmaximal, complemented
7C37×#410C211yesmaximal, characteristic, complemented
8#11924584—21no—
9#11924583—22no—
10#11924582—22no—
11#11924581—21no—
12#11924581C2214yes—
13C2×#10596962—22no—
14C2×#10596962C2212yes—
15#41×D37—24no—
16C22×C4×D37C2211yescharacteristic, complemented
17#11924520C2214yescomplemented
18#11924517C2212yescomplemented
19#11924516—22no—
20#11924512—21no—
21#11924511—22no—
22#11924507—21no—
23#11924506C2214yescomplemented
24#11924504C2212yescomplemented
25C4×D148—24no—
26C4×C22⋊D37—22no—
27#11924495C2211yescharacteristic, complemented
28#11924450C2218yescomplemented
29C2×#41×C37C2211yescharacteristic
30#117×C37C2212yescomplemented
31#99×C37C2214yescomplemented
32C23×D37C2311yescharacteristic
33#41×C37—22no—
34#41×C37—22no—
35C2×Q8×C37D411yescharacteristic, complemented
36C2×D4×C37D411yescharacteristic, complemented
37C2×D4×C37C2312yes—
38C22×C4×C37D412yescomplemented
39C22×C4×C37C2311yescharacteristic
40C2×C22⋊D37—24no—
41C2×C22⋊D37—22no—
42C2×C22⋊D37C2314yes—
43C22×Dic37C2311yescharacteristic
44#10596966—24no—
45Q8×D37—24no—
46#10596964—24no—
47#10596964—28no—
48D4×D37—24no—
49D4×D37—28no—
50#10596962—24no—
51#10596962—24no—
52#10596962—22no—
53#10596962—22no—
54#10596962—24no—
55#10596962—22no—
56#10596962—22no—
57C2×D148—22no—
58C2×D148—24no—
59C2×D148D412yescomplemented
60C2×C4×D37—24no—
61C2×C4×D37—21no—
62C2×C4×D37—22no—
63C2×C4×D37—21no—
64C2×C4×D37—22no—
65C2×C4×D37D414yescomplemented
66C2×Dic74—22no—
67C2×Dic74D412yescomplemented
68C4⋊C4×C37—22no—
69C22⋊C4×C37C2314yes—
70C42×C37—22no—
71C22⋊Dic37—22no—
72C22⋊Dic37C2312yes—
73#10596938—24no—
74#10596938—22no—
75#10596938—24no—
76C4⋊Dic37—21no—
77C4⋊Dic37—24no—
78#10596936—22no—
79C4×Dic37—21no—
80C23×C37C2×D412yes—
81C23×C37C2411yescharacteristic
82C22×D37—22no—
83C22×D37—21no—
84C22×D37—24no—
85C22×D37—42no—
86C22×D37C2×D414yes—
87Q8×C37—22no—
88D4×C37—24no—
89D4×C37—22no—
90C2×C4×C37—22no—
91C2×C4×C37—22no—
92C2×C4×C37—24no—
93C2×C4×C37C2×D412yes—
94C2×C4×C37C2×D411yescharacteristic
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37C2×D412yes—
97C2×C4×C37C2×D412yes—
98C22⋊D37—28no—
99C22⋊D37—24no—
100C22⋊D37—24no—
101C22⋊D37—44no—
102C2×Dic37—24no—
103C2×Dic37—22no—
104C2×Dic37—21no—
105C2×Dic37—22no—
106C2×Dic37C2×D414yes—
107D148—24no—
108D148—22no—
109D148—22no—
110D148—48no—
111C4×D37—28no—
112C4×D37—24no—
113C4×D37—24no—
114C4×D37—41no—
115C4×D37—42no—
116C4×D37—41no—
117Dic74—24no—
118Dic74—22no—
119Dic74—22no—
120C22×C37—22no—
121C22×C37—41no—
122C22×C37—42no—
123C22×C37C22×D412yes—
124C22×C37C22×D411yescharacteristic
125C2×D37—24no—
126C2×D37—22no—
127C2×D37—24no—
128C2×D37—41no—
129C2×D37—42no—
130C2×D37—41no—
131C2×D37—44no—
132C2×D37—84no—
133C4×C37—22no—
134C4×C37—44no—
135C4×C37#12011yescharacteristic
136C4×C37#12012yes—
137C4×C37#12011yescharacteristic
138Dic37—24no—
139Dic37—42no—
140Dic37—41no—
141#3025—371nomaximal, Sylow
142C2×C37—21no—
143C2×C37—22no—
144C2×C37—42no—
145C2×C37C2×#12011yescharacteristic
146D37—42no—
147D37—44no—
148#585—371no—
149#525—371no—
150#525—372no—
151#458—374no—
152B(4,𝔽2)—374no—
153#410—372no—
154#410D3711yescharacteristic, complemented
155C37#302511yescharacteristic, complemented, Sylow
1562−1+4—742no—
1572−1+4—741no—
158H(5,𝔽2)—374no—
159H(5,𝔽2)—742no—
160H(5,𝔽2)—741no—
161C2×#41—372no—
162C2×#41—744no—
163C2×#41—742no—
164C2×#41C2×D3711yescharacteristic
165C23×C4—371no—
166#123—372no—
167#123—374no—
168C22⋊Q8—742no—
169C22⋊Q8—741no—
170#121—742no—
171#121—741no—
172#120—372no—
173#120—374no—
174C4×D4—744no—
175C4×D4—742no—
176#117—371no—
177#117C2×D3712yescomplemented
178#99—378no—
179#99C2×D3714yescomplemented
180C24—371no—
181#41—22no—
182#41—22no—
183#41—744no—
184#41—744no—
185#41—748no—
186#41—744no—
187#41—744no—
188#41—742no—
189#41—742no—
190#41—744no—
191#41—742no—
192#41—742no—
193C2×Q8—372no—
194C2×Q8—742no—
195C2×Q8—744no—
196C2×Q8D14811yescharacteristic, complemented
197C2×D4—374no—
198C2×D4—372no—
199C2×D4—742no—
200C2×D4—744no—
201C2×D4—748no—
202C2×D4—744no—
203C2×D4—744no—
204C2×D4—742no—
205C2×D4D14811yescharacteristic, complemented
206C2×D4C22×D3712yes—
207C22×C4—374no—
208C22×C4—371no—
209C22×C4—744no—
210C22×C4—741no—
211C22×C4—741no—
212C22×C4—742no—
213C22×C4—742no—
214C22×C4D14812yescomplemented
215C22×C4C22×D3711yescharacteristic
216C4⋊C4—22no—
217C4⋊C4—744no—
218C4⋊C4—742no—
219C4⋊C4—741no—
220C22⋊C4—372no—
221C22⋊C4—744no—
222C22⋊C4—744no—
223C22⋊C4—742no—
224C22⋊C4—742no—
225C22⋊C4C22×D3714yes—
226C42—22no—
227C42—741no—
228C23—374no—
229C23—744no—
230C23—742no—
231C23—741no—
232C23—1482no—
233C23C2×D14812yes—
234C23C23×D3711yescharacteristic
235Q8—22no—
236Q8—744no—
237Q8—742no—
238Q8—742no—
239D4—24no—
240D4—22no—
241D4—744no—
242D4—748no—
243D4—744no—
244D4—744no—
245D4—742no—
246D4—742no—
247D4—1488no—
248D4—1484no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—24no—
252C2×C4—374no—
253C2×C4—748no—
254C2×C4—744no—
255C2×C4—744no—
256C2×C4—744no—
257C2×C4—742no—
258C2×C4—742no—
259C2×C4—741no—
260C2×C4—1481no—
261C2×C4—1482no—
262C2×C4—1481no—
263C2×C4C2×D14812yes—
264C2×C4C2×D14811yescharacteristic
265C2×C4C2×D14811yescharacteristic
266C2×C4D4×D3712yes—
267C2×C4D4×D3712yes—
268C22—22no—
269C22—41no—
270C22—42no—
271C22—2964no—
272C22—744no—
273C22—742no—
274C22—744no—
275C22—1484no—
276C22—1482no—
277C22—1481no—
278C22—1481no—
279C22C2×D4×D3712yes—
280C22C22×D14811yescharacteristic
281C4—22no—
282C4—44no—
283C4—744no—
284C4—1482no—
285C4—1481no—
286C4#1192450611yescharacteristic
287C4#1192450612yes—
288C4#1192450611yescharacteristic
289C2—22no—
290C2—21no—
291C2—42no—
292C2—1484no—
293C2—1482no—
294C2C2×#1192450611yescharacteristic
subgroupG/H
centerC4#11924506
commutator, cosocleC23×C37C24
FrattiniC23C23×D37
FittingC37×#410C2
socleC2×C37C2×#120
hypercenter#410D37
hypocenterC37#3025
LCSG ▷ C23×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C4 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #14558369C2semidirect
2. #14558045C2semidirect
3. #14558040C2semidirect
4. #14557724C2semidirect
5. #14557721C2semidirect
6. #14557506C2semidirect
7. C37×#410C2semidirect
16. C22×C4×D37C22semidirect
17. #11924520C22semidirect
18. #11924517C22semidirect
23. #11924506C22semidirect
24. #11924504C22semidirect
27. #11924495C22semidirect
28. #11924450C22semidirect
30. #117×C37C22semidirect
31. #99×C37C22semidirect
35. C2×Q8×C37D4semidirect
36. C2×D4×C37D4semidirect
38. C22×C4×C37D4semidirect
59. C2×D148D4semidirect
65. C2×C4×D37D4semidirect
67. C2×Dic74D4semidirect
154. #410D37semidirect
155. C37#3025semidirect
177. #117C2×D37semidirect
179. #99C2×D37semidirect
196. C2×Q8D148semidirect
205. C2×D4D148semidirect
214. C22×C4D148semidirect

Maximal subgroups

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

subgroupindex
#145583692
#145580452
#145580402
#145577242
#145577212
#145575062
C37×#4102
#302537