Subgroups — C₂×#13093947 #15689113

Order 3008.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13093947	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	C₂×Dic₉₄	—	2	1	no	—
9	C₂×Dic₉₄	—	2	2	no	—
10	C₂×Dic₉₄	C₄	1	4	yes	complemented
11	C₂×Dic₉₄	C₂²	1	2	yes	—
12	C₄⋊C₄×C₄₇	—	2	1	no	—
13	C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄₇⋊C₈	—	2	2	no	—
15	C₂×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂³×C₄₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₇	—	2	2	no	—
18	C₂×C₄×C₄₇	—	4	2	no	—
19	C₂×C₄×C₄₇	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₄₇	D₄	1	2	yes	—
21	C₂×C₄×C₄₇	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
23	C₂×Dic₄₇	—	2	4	no	—
24	C₂×Dic₄₇	—	2	2	no	—
25	Dic₉₄	—	2	4	no	—
26	Dic₉₄	—	2	2	no	—
27	Dic₉₄	C₂×C₄	1	4	yes	complemented
28	C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₄₇	SD₁₆	1	2	yes	—
31	C₂²×C₄₇	Q₁₆	1	2	yes	—
32	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₄₇	—	4	2	no	—
34	C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
35	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
37	Dic₄₇	—	2	4	no	—
38	C₂×C₄₇	#103	1	4	yes	complemented
39	C₂×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
42	C₂×#103	—	47	1	no	maximal, Sylow
43	C₄₇	C₂×#103	1	1	yes	characteristic, complemented, Sylow
44	C₂²×Q₈	—	47	1	no	—
45	C₂²×C₈	—	47	1	no	—
46	C₂×C₄⋊C₄	D₄₇	1	1	yes	characteristic
47	#103	—	47	4	no	—
48	C₂×Q₈	—	47	4	no	—
49	C₂×Q₈	—	47	2	no	—
50	C₂×Q₈	—	94	2	no	—
51	C₂×Q₈	—	94	1	no	—
52	C₂²×C₄	—	2	1	no	—
53	C₂²×C₄	—	94	1	no	—
54	C₂²×C₄	C₂×D₄₇	1	1	yes	characteristic
55	C₂×C₈	—	47	2	no	—
56	C₂×C₈	—	94	2	no	—
57	C₄⋊C₄	—	2	1	no	—
58	C₄⋊C₄	C₂×D₄₇	1	2	yes	—
59	C₂³	C₂²⋊D₄₇	1	1	yes	characteristic
60	Q₈	—	47	4	no	—
61	Q₈	—	94	4	no	—
62	Q₈	—	94	2	no	—
63	C₂×C₄	—	2	2	no	—
64	C₂×C₄	—	4	2	no	—
65	C₂×C₄	—	94	4	no	—
66	C₂×C₄	—	94	2	no	—
67	C₂×C₄	C₄×D₄₇	1	2	yes	—
68	C₂×C₄	D₁₈₈	1	2	yes	—
69	C₂×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
71	C₈	—	94	2	no	—
72	C₂²	(C₂×D₄₇)⋊C₄	1	2	yes	—
73	C₂²	#10625335	1	2	yes	—
74	C₂²	#10625337	1	2	yes	—
75	C₂²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
76	C₄	—	4	2	no	—
77	C₄	—	94	4	no	—
78	C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
79	C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
80	C₄	C₂×D₁₈₈	1	1	yes	characteristic
81	C₂	#13093947	1	4	yes	direct product factor
82	C₂	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
83	C₂	C₂×#10625335	1	1	yes	characteristic
84	C₂	C₂×#10625337	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×#103
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. #13093947	C₂	direct (N × H)
10. C₂×Dic₉₄	C₄	semidirect
27. Dic₉₄	C₂×C₄	semidirect
38. C₂×C₄₇	#103	semidirect
43. C₄₇	C₂×#103	semidirect
81. C₂	#13093947	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×Dic₉₄	2
C₂²×C₄₇⋊C₈	2
#13093947	2
C₂×C₄⋊C₄×C₄₇	2
C₂×#103	47

Subgroups — C2×#13093947 #15689113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093947 #15689113