Subgroups — C₂×#13093955 #15689153

Order 3008.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#13093955	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×C₄₇	—	2	1	no	—
6	C₂²×C₄×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₇	—	2	1	no	—
8	C₄⋊C₄×C₄₇	—	2	1	no	—
9	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₄⋊Dic₄₇	—	2	1	no	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₂×C₄₇⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂³×C₄₇	D₄	1	1	yes	characteristic
15	C₂×C₄×C₄₇	—	2	2	no	—
16	C₂×C₄×C₄₇	—	4	2	no	—
17	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄×C₄₇	Q₈	1	2	yes	—
20	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
21	C₂×Dic₄₇	—	2	2	no	—
22	C₂×Dic₄₇	—	4	2	no	—
23	C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
24	C₂²×C₄₇	C₄⋊C₄	1	2	yes	—
25	C₂²×C₄₇	SD₁₆	1	2	yes	—
26	C₂²×C₄₇	SD₁₆	1	2	yes	—
27	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₇	—	4	2	no	—
29	C₄×C₄₇	C₄⋊C₄	1	2	yes	—
30	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
32	Dic₄₇	—	4	2	no	—
33	C₂×C₄₇	#106	1	4	yes	complemented
34	C₂×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
36	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
37	C₂×#106	—	47	1	no	maximal, Sylow
38	C₄₇	C₂×#106	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₈	—	47	1	no	—
40	C₂×C₄⋊C₄	—	47	1	no	—
41	C₂×C₄⋊C₄	D₄₇	1	1	yes	characteristic
42	#106	—	47	4	no	—
43	C₂²×C₄	—	2	1	no	—
44	C₂²×C₄	—	94	1	no	—
45	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
46	C₂×C₈	—	47	4	no	—
47	C₂×C₈	—	47	2	no	—
48	C₄⋊C₄	—	2	1	no	—
49	C₄⋊C₄	—	47	2	no	—
50	C₄⋊C₄	—	94	1	no	—
51	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
52	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	4	2	no	—
55	C₂×C₄	—	94	2	no	—
56	C₂×C₄	—	188	2	no	—
57	C₂×C₄	Dic₉₄	1	2	yes	—
58	C₂×C₄	C₄×D₄₇	1	2	yes	—
59	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
60	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
61	C₈	—	47	4	no	—
62	C₂²	Dic₄₇⋊C₄	1	2	yes	—
63	C₂²	#10625335	1	2	yes	—
64	C₂²	#10625336	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	188	2	no	—
68	C₄	Dic₄₇⋊C₄	1	2	yes	—
69	C₄	C₂×Dic₉₄	1	1	yes	characteristic
70	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
71	C₂	#13093955	1	4	yes	direct product factor
72	C₂	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
73	C₂	C₂×#10625336	1	1	yes	characteristic
74	C₂	C₂×#10625335	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting	C₂×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂³×C₄₇	D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×C₄⋊C₄	D₄₇
hypocenter	C₄₇	C₂×#106
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #13093955	C₂	direct (N × H)
12. C₂×C₄₇⋊C₈	C₄	semidirect
23. C₄₇⋊C₈	C₂×C₄	semidirect
33. C₂×C₄₇	#106	semidirect
38. C₄₇	C₂×#106	semidirect
71. C₂	#13093955	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄₇⋊C₈	2
C₂×C₄⋊Dic₄₇	2
#13093955	2
C₂×C₄⋊C₄×C₄₇	2
C₂×#106	47

Subgroups — C2×#13093955 #15689153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093955 #15689153