Finite Group Databasebeta

← #18005346

Subgroups — #18005346

Order 4736.

520 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 121 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×#11924511C211yesmaximal, characteristic, complemented
2#121×D37C211yesmaximal, characteristic, complemented
3#14557848C212yesmaximal, complemented
4#14557846C211yesmaximal, characteristic, complemented
5#14557770C212yesmaximal, complemented
6#14557768C212yesmaximal, complemented
7#14557669C211yesmaximal, characteristic, complemented
8#14557668C212yesmaximal, complemented
9#14557666C211yesmaximal, characteristic, complemented
10C22⋊C8×D37C211yesmaximal, characteristic, complemented
11C37×#480C211yesmaximal, characteristic, complemented
12C22×D148—21no—
13C22×D148C2211yescharacteristic, complemented
14C2×D4×D37—21no—
15C2×D4×D37C2211yescharacteristic, complemented
16C22×C4×D37C2211yescharacteristic
17C2×D296C2212yescomplemented
18C2×#10596939C2212yescomplemented
19C2×C8×D37C2212yescomplemented
20#11924511—21no—
21#11924511—21no—
22#11924511C2212yes—
23#11924511C2211yescharacteristic, complemented
24#11924511C2212yescomplemented
25#11924510C2211yescharacteristic
26#11924509—21no—
27#11924508—21no—
28#11924507C2211yescharacteristic, complemented
29C4⋊C4×D37C2211yescharacteristic, complemented
30C2×#10596938—21no—
31C22⋊C4×D37—21no—
32#11924469C2212yescomplemented
33#11924458C2212yescomplemented
34#11924456C2212yescomplemented
35#11924456C2212yescomplemented
36C22⋊#64436C2211yescharacteristic, complemented
37#11924448C2212yescomplemented
38#121×C37C2211yescharacteristic
39C2×C4⋊C4×C37C2211yescharacteristic, complemented
40#107×C37C2212yescomplemented
41#102×C37C2212yescomplemented
42C22⋊C8×C37C2211yescharacteristic, complemented
43C23×D37—21no—
44C23×D37—21no—
45C23×D37D411yescharacteristic
46C2×D4×C37—21no—
47C2×D4×C37C2311yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37C2311yescharacteristic
50C2×C22⋊D37—21no—
51C2×C22⋊D37—21no—
52C2×C22⋊D37—21no—
53C22×Dic37D411yescharacteristic
54D4×D37—42no—
55D4×D37—44no—
56C2×D148—21no—
57C2×D148—22no—
58C2×D148—22no—
59C2×D148—21no—
60C2×D148—42no—
61C2×D148—44no—
62C2×D148C2311yescharacteristic
63C2×D148C2312yes—
64C2×C4×D37—21no—
65C2×C4×D37—42no—
66C2×C4×D37D411yescharacteristic
67C2×C4×D37D411yescharacteristic
68C2×C4×D37C2311yescharacteristic
69C2×C4×D37C2311yescharacteristic
70C2×C8×C37C2312yes—
71C4⋊C4×C37—21no—
72C4⋊C4×C37C2311yescharacteristic
73C4⋊C4×C37C2312yes—
74C22⋊C4×C37—21no—
75C22⋊Dic37—21no—
76#10596939—42no—
77#10596938—21no—
78#10596938—21no—
79#10596938—22no—
80#10596938—22no—
81C4⋊Dic37C2311yescharacteristic
82#10596936—21no—
83C2×#64436C2312yes—
84D296—42no—
85C8×D37—42no—
86C23×C37—21no—
87C23×C37C2×D411yescharacteristic
88C22×D37—22no—
89C22×D37—21no—
90C22×D37—41no—
91C22×D37—41no—
92C22×D37—42no—
93C22×D37—42no—
94C22×D37—42no—
95C22×D37—42no—
96C22×D37—42no—
97C22×D37—42no—
98C22×D37D814yescomplemented
99C22×D37C2×D411yescharacteristic
100C22×D37C2×D411yescharacteristic
101D4×C37—22no—
102D4×C37—42no—
103C2×C4×C37—22no—
104C2×C4×C37—21no—
105C2×C4×C37—22no—
106C2×C4×C37—42no—
107C2×C4×C37C2×D411yescharacteristic
108C2×C4×C37C2411yescharacteristic
109C22⋊D37—42no—
110C22⋊D37—42no—
111C22⋊D37—42no—
112C2×Dic37—21no—
113C2×Dic37—41no—
114C2×Dic37C2×D411yescharacteristic
115C2×Dic37C2×D411yescharacteristic
116D148—22no—
117D148—22no—
118D148—22no—
119D148—42no—
120D148—44no—
121D148—44no—
122D148—42no—
123C4×D37—22no—
124C4×D37—22no—
125C4×D37—41no—
126C4×D37—41no—
127C4×D37—42no—
128C8×C37—22no—
129#64436—22no—
130C22×C37—21no—
131C22×C37—21no—
132C22×C37—41no—
133C22×C37—41no—
134C22×C37—41no—
135C22×C37C2×D812yes—
136C22×C37C22×D411yescharacteristic
137C2×D37—21no—
138C2×D37—21no—
139C2×D37—21no—
140C2×D37—21no—
141C2×D37—44no—
142C2×D37—42no—
143C2×D37—41no—
144C2×D37—42no—
145C2×D37—41no—
146C2×D37—42no—
147C2×D37—41no—
148C2×D37—84no—
149C2×D37—84no—
150C2×D37C2×D812yes—
151C2×D37C2×D812yes—
152C4×C37—21no—
153C4×C37—41no—
154C4×C37—42no—
155C4×C37H(5,𝔽2)12yes—
156Dic37—21no—
157Dic37—21no—
158Dic37—41no—
159#3186—371nomaximal, Sylow
160C2×C37—22no—
161C2×C37—81no—
162C2×C37#53411yescharacteristic
163C2×C37C22×D811yescharacteristic
164C2×C37#57511yescharacteristic
165D37—22no—
166D37—22no—
167D37—82no—
168D37—81no—
169C2×#121—371no—
170C2×#121—371no—
171#480—371no—
172#480—372no—
173#480D3711yescharacteristic, complemented
174#466—372no—
175#466—372no—
176#447—371no—
177#447—372no—
178#447—371no—
179C2×C22⋊C8—371no—
180C37#318611yescharacteristic, complemented, Sylow
181C22×D4—371no—
182C22×D4—371no—
183C22×D4—741no—
184C22×D4—741no—
185C23×C4—371no—
186C2×D8—372no—
187C2×D8—372no—
188C22×C8—372no—
189#121—371no—
190#121—371no—
191#121—372no—
192#121—371no—
193#121—372no—
194#121—741no—
195#121—741no—
196#121—741no—
197#121—741no—
198#121C2×D3711yescharacteristic
199C2×C4⋊C4—371no—
200C2×C4⋊C4C2×D3711yescharacteristic, complemented
201C2×C22⋊C4—741no—
202C2×C22⋊C4—741no—
203#107—372no—
204#107C2×D3712yescomplemented
205#102—372no—
206#102—372no—
207#102—372no—
208#102C2×D3712yescomplemented
209C22⋊C8—371no—
210C22⋊C8—372no—
211C22⋊C8C2×D3711yescharacteristic, complemented
212C24—371no—
213C24—741no—
214C24—741no—
215C2×D4—21no—
216C2×D4—371no—
217C2×D4—372no—
218C2×D4—741no—
219C2×D4—742no—
220C2×D4—742no—
221C2×D4—741no—
222C2×D4—741no—
223C2×D4—741no—
224C2×D4—741no—
225C2×D4—1482no—
226C2×D4—1484no—
227C2×D4—1482no—
228C2×D4—1484no—
229C2×D4C22×D3711yescharacteristic
230C22×C4—21no—
231C22×C4—371no—
232C22×C4—371no—
233C22×C4—371no—
234C22×C4—371no—
235C22×C4—371no—
236C22×C4—741no—
237C22×C4—1482no—
238C22×C4C22×D3711yescharacteristic
239D8—1482no—
240D8—1482no—
241C2×C8—372no—
242C2×C8—1482no—
243C2×C8C22×D3712yes—
244C4⋊C4—21no—
245C4⋊C4—371no—
246C4⋊C4—741no—
247C4⋊C4C22×D3711yescharacteristic
248C4⋊C4C22×D3712yes—
249C22⋊C4—21no—
250C22⋊C4—741no—
251C22⋊C4—742no—
252C22⋊C4—742no—
253C22⋊C4—741no—
254C22⋊C4—741no—
255C23—21no—
256C23—371no—
257C23—371no—
258C23—374no—
259C23—742no—
260C23—741no—
261C23—1482no—
262C23—1482no—
263C23—1481no—
264C23—1481no—
265C23—1482no—
266C23—1482no—
267C23—1482no—
268C23—1482no—
269C23D4×D3711yescharacteristic
270D4—22no—
271D4—42no—
272D4—742no—
273D4—742no—
274D4—742no—
275D4—1482no—
276D4—1484no—
277D4—1484no—
278D4—1482no—
279D4—1482no—
280D4—1482no—
281D4—1482no—
282C2×C4—22no—
283C2×C4—21no—
284C2×C4—22no—
285C2×C4—42no—
286C2×C4—371no—
287C2×C4—371no—
288C2×C4—742no—
289C2×C4—742no—
290C2×C4—741no—
291C2×C4—1481no—
292C2×C4—1481no—
293C2×C4—1482no—
294C2×C4—1481no—
295C2×C4D4×D3711yescharacteristic
296C2×C4C23×D3711yescharacteristic
297C8—22no—
298C8—742no—
299C22—21no—
300C22—21no—
301C22—41no—
302C22—41no—
303C22—41no—
304C22—372no—
305C22—372no—
306C22—2964no—
307C22—2964no—
308C22—741no—
309C22—741no—
310C22—741no—
311C22—741no—
312C22—1484no—
313C22—1482no—
314C22—1481no—
315C22—1482no—
316C22—1481no—
317C22—1482no—
318C22—1481no—
319C22D8×D3712yes—
320C22C2×D4×D3711yescharacteristic
321C4—21no—
322C4—42no—
323C4—41no—
324C4—741no—
325C4—741no—
326C4—1481no—
327C4#1192458212yes—
328C2—22no—
329C2—81no—
330C2—2962no—
331C2—2961no—
332C2—742no—
333C2—742no—
334C2#1455809411yescharacteristic
335C2C2×D8×D3711yescharacteristic
336C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#480C2
socleC22×C37C22×D4
hypercenter#480D37
hypocenterC37#3186
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. C2×#11924511C2semidirect
2. #121×D37C2semidirect
3. #14557848C2semidirect
4. #14557846C2semidirect
5. #14557770C2semidirect
6. #14557768C2semidirect
7. #14557669C2semidirect
8. #14557668C2semidirect
9. #14557666C2semidirect
10. C22⋊C8×D37C2semidirect
11. C37×#480C2semidirect
13. C22×D148C22semidirect
15. C2×D4×D37C22semidirect
17. C2×D296C22semidirect
18. C2×#10596939C22semidirect
19. C2×C8×D37C22semidirect
23. #11924511C22semidirect
24. #11924511C22semidirect
28. #11924507C22semidirect
29. C4⋊C4×D37C22semidirect
32. #11924469C22semidirect
33. #11924458C22semidirect
34. #11924456C22semidirect
35. #11924456C22semidirect
36. C22⋊#64436C22semidirect
37. #11924448C22semidirect
39. C2×C4⋊C4×C37C22semidirect
40. #107×C37C22semidirect
41. #102×C37C22semidirect
42. C22⋊C8×C37C22semidirect
98. C22×D37D8semidirect
173. #480D37semidirect
180. C37#3186semidirect
200. C2×C4⋊C4C2×D37semidirect
204. #107C2×D37semidirect
208. #102C2×D37semidirect
211. C22⋊C8C2×D37semidirect

Maximal subgroups

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

subgroupindex
C2×#119245112
#121×D372
#145578482
#145578462
#145577702
#145577682
#145576692
#145576682
#145576662
C22⋊C8×D372
C37×#4802
#318637