Subgroups — C₂×#14557363 #17996388

Order 4736.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11924472	C₂	1	2	yes	maximal
2	#14557363	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₃₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10596934	—	2	2	no	—
5	#11924472	—	2	2	no	—
6	#11924472	C₂²	1	4	yes	—
7	C₂²×C₈×C₃₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₃₇	C₄	1	2	yes	—
9	C₂×C₁₆×C₃₇	C₄	1	2	yes	—
10	C₂×C₁₆×C₃₇	C₂²	1	2	yes	—
11	C₂²×C₄×C₃₇	D₄	1	1	yes	characteristic
12	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
15	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
16	C₂×C₈×C₃₇	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₃₇	C₂³	1	1	yes	characteristic
18	#10596934	—	2	4	no	—
19	#10596934	—	4	2	no	—
20	C₂×#64436	—	4	2	no	—
21	C₁₆×C₃₇	C₂×C₄	1	4	yes	—
22	C₂³×C₃₇	Q₁₆	1	1	yes	characteristic
23	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₃₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
26	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
27	C₂×C₄×C₃₇	Q₁₆	1	1	yes	characteristic
28	C₂×C₄×C₃₇	C₂×D₄	1	1	yes	characteristic
29	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
30	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
31	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
32	C₈×C₃₇	C₂×Q₈	1	1	yes	characteristic
33	#64436	—	4	4	no	—
34	C₂²×C₃₇	—	2	2	no	—
35	C₂²×C₃₇	#107	1	1	yes	characteristic
36	C₂²×C₃₇	#107	1	1	yes	characteristic
37	C₂²×C₃₇	C₂×Q₁₆	1	1	yes	characteristic
38	C₄×C₃₇	#107	1	1	yes	characteristic
39	C₄×C₃₇	#107	1	1	yes	characteristic
40	C₄×C₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₃₇	C₂×D₈	1	1	yes	characteristic
42	C₂×#368	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	2	1	no	—
44	C₂×C₃₇	—	2	1	no	—
45	C₂×C₃₇	#368	1	2	yes	complemented
46	C₂×C₃₇	C₂×#107	1	1	yes	characteristic
47	C₂²×C₁₆	D₃₇	1	1	yes	characteristic
48	C₂×#108	—	37	2	no	—
49	#368	—	37	4	no	—
50	C₃₇	C₂×#368	1	1	yes	characteristic, complemented, Sylow
51	C₂×M₁₆	—	74	2	no	—
52	C₂²×C₈	C₂×D₃₇	1	1	yes	characteristic
53	C₂×C₁₆	Dic₃₇	1	2	yes	—
54	C₂×C₁₆	Dic₃₇	1	2	yes	—
55	C₂×C₁₆	C₂×D₃₇	1	2	yes	—
56	#108	—	37	4	no	—
57	#108	—	74	2	no	—
58	C₂²×C₄	D₁₄₈	1	1	yes	characteristic
59	M₁₆	—	74	4	no	—
60	M₁₆	—	148	2	no	—
61	C₂×C₈	—	148	2	no	—
62	C₂×C₈	Dic₇₄	1	1	yes	characteristic
63	C₂×C₈	Dic₇₄	1	1	yes	characteristic
64	C₂×C₈	D₁₄₈	1	1	yes	characteristic
65	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
66	C₂×C₈	C₂×Dic₃₇	1	1	yes	characteristic
67	C₂×C₈	C₂²×D₃₇	1	1	yes	characteristic
68	C₁₆	C₂×Dic₃₇	1	4	yes	—
69	C₂³	Dic₁₄₈	1	1	yes	characteristic
70	C₂×C₄	D₂₉₆	1	1	yes	characteristic
71	C₂×C₄	D₂₉₆	1	1	yes	characteristic
72	C₂×C₄	Dic₁₄₈	1	1	yes	characteristic
73	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
74	C₂×C₄	C₄⋊Dic₃₇	1	1	yes	characteristic
75	C₂×C₄	C₂×D₁₄₈	1	1	yes	characteristic
76	C₈	—	148	4	no	—
77	C₈	C₄⋊Dic₃₇	1	1	yes	characteristic
78	C₈	C₄⋊Dic₃₇	1	1	yes	characteristic
79	C₈	C₂×Dic₇₄	1	1	yes	characteristic
80	C₈	C₂²×Dic₃₇	1	1	yes	characteristic
81	C₂²	—	2	2	no	—
82	C₂²	#11924470	1	1	yes	characteristic
83	C₂²	#11924470	1	1	yes	characteristic
84	C₂²	C₂×Dic₁₄₈	1	1	yes	characteristic
85	C₄	#11924470	1	1	yes	characteristic
86	C₄	#11924470	1	1	yes	characteristic
87	C₄	C₂×C₄⋊Dic₃₇	1	1	yes	characteristic
88	C₄	C₂×D₂₉₆	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	2	1	no	—
91	C₂	#14557363	1	2	yes	direct product factor
92	C₂	C₂×#11924470	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₂₉₆
commutator	C₈×C₃₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₃₇
Fitting	C₂²×C₁₆×C₃₇	C₂
socle	C₂²×C₃₇	#107
prime radical	C₂³×C₃₇	Q₁₆
cosocle	C₂×C₈×C₃₇	C₂³
hypercenter	C₂²×C₁₆	D₃₇
hypocenter	C₃₇	C₂×#368
LCS	G ▷ C₈×C₃₇ ▷ C₄×C₃₇ ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #14557363	C₂	direct (N × H)
45. C₂×C₃₇	#368	semidirect
50. C₃₇	C₂×#368	semidirect
91. C₂	#14557363	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11924472	2
#14557363	2
C₂²×C₁₆×C₃₇	2
C₂×#368	37

Subgroups — C2×#14557363 #17996388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14557363 #17996388