Subgroups — #15689518

Order 3008.

124 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10625337	C₂	1	2	yes	maximal, complemented
2	C₂×#10625335	C₂	1	2	yes	maximal
3	#13094024	C₂	1	1	yes	maximal, characteristic, complemented
4	#13093935	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₄₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₉₄	C₂²	1	2	yes	—
9	C₂²⋊C₄×C₄₇	—	2	2	no	—
10	C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	#10625337	—	2	4	no	—
12	#10625335	—	2	4	no	—
13	C₄⋊Dic₄₇	—	2	2	no	—
14	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂³×C₄₇	—	2	1	no	—
16	Q₈×C₄₇	—	2	2	no	—
17	D₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	2	1	no	—
19	C₂×C₄×C₄₇	D₄	1	2	yes	—
20	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₇	—	2	2	no	—
22	Dic₉₄	—	2	2	no	—
23	Dic₉₄	—	2	2	no	—
24	C₄₇⋊C₈	D₄	1	4	yes	—
25	C₂²×C₄₇	—	4	1	no	—
26	C₂²×C₄₇	—	4	2	no	—
27	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₇	—	2	2	no	—
29	C₄×C₄₇	—	4	1	no	—
30	C₄×C₄₇	C₂×D₄	1	2	yes	—
31	Dic₄₇	—	4	2	no	—
32	C₂×C₄₇	—	8	1	no	—
33	C₂×C₄₇	#127	1	1	yes	characteristic
34	C₂×C₄₇	#137	1	2	yes	—
35	#497	—	47	1	no	maximal, Sylow
36	C₄₇	#497	1	1	yes	characteristic, complemented, Sylow
37	C₂×Q₁₆	—	47	2	no	—
38	C₂×SD₁₆	—	47	2	no	—
39	C₄⋊Q₈	—	47	1	no	—
40	#124	D₄₇	1	1	yes	characteristic
41	#97	—	47	1	no	—
42	C₂×Q₈	—	47	2	no	—
43	C₂×Q₈	C₂×D₄₇	1	1	yes	characteristic
44	C₂×D₄	C₂×D₄₇	1	1	yes	characteristic
45	Q₁₆	—	94	4	no	—
46	SD₁₆	—	94	4	no	—
47	C₂×C₈	—	47	2	no	—
48	C₄⋊C₄	—	94	2	no	—
49	C₂²⋊C₄	—	2	2	no	—
50	C₄²	C₂×D₄₇	1	1	yes	characteristic
51	C₂³	—	2	1	no	—
52	Q₈	—	2	2	no	—
53	Q₈	—	94	2	no	—
54	Q₈	—	94	2	no	—
55	D₄	—	2	2	no	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	94	2	no	—
58	C₂×C₄	C₂²⋊D₄₇	1	2	yes	—
59	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
60	C₈	—	47	4	no	—
61	C₂²	—	4	1	no	—
62	C₂²	—	4	2	no	—
63	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
64	C₄	—	2	2	no	—
65	C₄	—	4	1	no	—
66	C₄	—	188	2	no	—
67	C₄	D₄×D₄₇	1	2	yes	—
68	C₂	—	8	1	no	—
69	C₂	#13094020	1	1	yes	characteristic
70	C₂	#13094054	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂³
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	#124×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
prime radical	C₂×D₄×C₄₇	C₂²
hypercenter	#124	D₄₇
hypocenter	C₄₇	#497
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. C₂×#10625337	C₂	semidirect
3. #13094024	C₂	semidirect
4. #13093935	C₂	semidirect
36. C₄₇	#497	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10625337	2
C₂×#10625335	2
#13094024	2
#13093935	2
#124×C₄₇	2
#497	47