Subgroups — #26105653

Order 12032.

582 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093934	C₂	1	3	yes	maximal
2	C₂×#15688844	C₂	1	3	yes	maximal
3	C₂×C₈²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#13093934	C₄	1	12	yes	—
5	C₂×C₄×C₄₇⋊C₈	C₂²	1	3	yes	—
6	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
7	#15688844	C₄	1	12	yes	complemented
8	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
9	C₈²×C₄₇	C₄	1	4	yes	complemented
10	C₂²×C₄₇⋊C₈	C₂×C₄	1	6	yes	—
11	C₂×C₄×Dic₄₇	C₂×C₄	1	6	yes	—
12	#13093934	—	2	24	no	—
13	C₄×C₄₇⋊C₈	C₂×C₄	1	12	yes	—
14	C₂²×C₈×C₄₇	C₂×C₄	1	6	yes	—
15	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
16	C₄×C₈×C₄₇	C₂×C₄	1	6	yes	—
17	C₄×C₈×C₄₇	C₂×C₄	1	6	yes	—
18	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
19	C₂²×Dic₄₇	C₄²	1	4	yes	—
20	C₂×C₈×C₄₇	C₄²	1	12	yes	—
21	C₂×C₈×C₄₇	M₁₆	1	24	yes	—
22	C₄²×C₄₇	C₂²×C₄	1	3	yes	—
23	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×Dic₄₇	—	2	12	no	—
25	C₂×C₄₇⋊C₈	—	2	12	no	—
26	C₂×C₄₇⋊C₈	C₄²	1	12	yes	—
27	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
28	C₂×C₄×C₄₇	C₂×C₄²	1	3	yes	—
29	C₂×C₄×C₄₇	C₂×C₄²	1	3	yes	—
30	C₂×C₄×C₄₇	C₂×M₁₆	1	12	yes	—
31	C₂×Dic₄₇	—	2	12	no	—
32	C₈×C₄₇	#97	1	24	yes	complemented
33	C₄₇⋊C₈	—	2	12	no	—
34	#7846	—	47	1	no	maximal, Sylow
35	C₂²×C₄₇	C₄³	1	1	yes	characteristic
36	C₂²×C₄₇	C₄×M₁₆	1	6	yes	—
37	C₄×C₄₇	C₂×#97	1	6	yes	—
38	C₄×C₄₇	C₄×M₁₆	1	6	yes	—
39	Dic₄₇	—	4	4	no	—
40	C₄×#97	—	47	3	no	—
41	C₂×#322	—	47	3	no	—
42	C₂×C₈²	D₄₇	1	1	yes	characteristic
43	C₂×C₄₇	#1455	1	4	yes	—
44	C₂×C₄₇	C₄×#97	1	3	yes	—
45	C₂×#97	—	47	12	no	—
46	C₂×C₄×C₈	—	47	3	no	—
47	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
48	C₄³	—	47	1	no	—
49	#322	—	47	12	no	—
50	C₈²	Dic₄₇	1	4	yes	complemented
51	C₄₇	#7846	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₈	—	47	6	no	—
53	C₂²×C₈	C₄×D₄₇	1	6	yes	—
54	C₂×C₄²	—	47	6	no	—
55	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
56	#97	—	94	24	no	—
57	C₄×C₈	—	47	12	no	—
58	C₄×C₈	C₄×D₄₇	1	6	yes	—
59	C₄×C₈	C₂×Dic₄₇	1	6	yes	—
60	C₂²×C₄	—	47	4	no	—
61	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
62	C₂×C₈	—	47	12	no	—
63	C₂×C₈	—	94	12	no	—
64	C₂×C₈	#10625324	1	24	yes	—
65	C₂×C₈	C₄×Dic₄₇	1	12	yes	—
66	C₄²	—	94	12	no	—
67	C₄²	C₂×C₄×D₄₇	1	3	yes	—
68	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
69	C₂³	C₄²×D₄₇	1	1	yes	characteristic
70	C₂×C₄	—	94	12	no	—
71	C₂×C₄	C₄²×D₄₇	1	3	yes	—
72	C₂×C₄	C₂×C₄×Dic₄₇	1	3	yes	—
73	C₂×C₄	C₂×#10625324	1	12	yes	—
74	C₈	—	94	12	no	—
75	C₈	#13093934	1	24	yes	complemented
76	C₂²	C₄²×Dic₄₇	1	1	yes	characteristic
77	C₂²	C₄×#10625324	1	6	yes	—
78	C₄	—	188	4	no	—
79	C₄	C₂×#13093934	1	6	yes	—
80	C₄	C₄×#10625324	1	6	yes	—
81	C₂	#20241690	1	4	yes	—
82	C₂	C₄×#13093934	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₄₇
commutator	C₂²×C₄₇	C₄³
Fitting	C₂×C₈²×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	C₂×C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×C₈²	D₄₇
hypocenter	C₄₇	#7846
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
7. #15688844	C₄	semidirect
9. C₈²×C₄₇	C₄	semidirect
32. C₈×C₄₇	#97	semidirect
50. C₈²	Dic₄₇	semidirect
51. C₄₇	#7846	semidirect
75. C₈	#13093934	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093934	2
C₂×#15688844	2
C₂×C₈²×C₄₇	2
#7846	47