Subgroups — C₂×#14558591 #18011560

Order 4736.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558591	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11924610	C₂	1	3	yes	maximal, complemented
3	C₂²×#10596927	C₂	1	3	yes	maximal, complemented
4	C₂×#11924543	C₂	1	1	yes	maximal, characteristic
5	#11924610	C₂²	1	12	yes	complemented
6	C₂×#10596927	C₂²	1	1	yes	characteristic
7	C₂×#10596927	C₂²	1	3	yes	—
8	C₂×#10596927	C₂²	1	12	yes	complemented
9	#11924543	C₄	1	4	yes	—
10	#11924543	C₂²	1	4	yes	—
11	C₂×#10596934	C₄	1	3	yes	—
12	C₂²×#64436	C₂²	1	3	yes	—
13	C₂×#41×C₃₇	C₄	1	1	yes	characteristic
14	#41×C₃₇	C₈	1	4	yes	—
15	#41×C₃₇	C₂×C₄	1	4	yes	—
16	C₂×Q₈×C₃₇	C₈	1	1	yes	characteristic
17	C₂×D₄×C₃₇	C₈	1	3	yes	—
18	C₂²×C₄×C₃₇	C₂×C₄	1	3	yes	—
19	#10596934	C₂×C₄	1	12	yes	—
20	C₂×#64436	C₂×C₄	1	3	yes	—
21	C₂×#64436	C₂×C₄	1	6	yes	—
22	C₂×#64436	C₂³	1	1	yes	characteristic
23	C₂×#64436	C₂³	1	6	yes	—
24	#10596927	C₂³	1	2	yes	—
25	#10596927	C₂³	1	6	yes	—
26	C₂³×C₃₇	C₂×C₈	1	3	yes	—
27	Q₈×C₃₇	C₂×C₈	1	4	yes	—
28	D₄×C₃₇	C₂×C₈	1	12	yes	—
29	C₂×C₄×C₃₇	C₂×C₈	1	3	yes	—
30	C₂×C₄×C₃₇	C₂×C₈	1	6	yes	—
31	C₂×C₄×C₃₇	C₂²×C₄	1	6	yes	—
32	C₂×C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
33	#64436	C₂²×C₄	1	1	yes	characteristic
34	#64436	C₂²×C₄	1	6	yes	—
35	#64436	C₂⁴	1	1	yes	characteristic
36	C₂²×C₃₇	—	2	6	no	—
37	C₂²×C₃₇	C₂²×C₈	1	6	yes	—
38	C₂²×C₃₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₃₇	C₂²×C₈	1	6	yes	—
41	C₄×C₃₇	C₂³×C₄	1	1	yes	characteristic
42	C₂×#504	—	37	1	no	maximal, Sylow
43	C₂×C₃₇	—	2	6	no	—
44	C₂×C₃₇	#504	1	2	yes	complemented
45	C₂×C₃₇	C₂³×C₈	1	1	yes	characteristic
46	C₂×#131	—	37	1	no	—
47	#504	—	37	8	no	—
48	C₂×M₃₂	—	37	3	no	—
49	C₂²×C₁₆	—	37	3	no	—
50	C₃₇	C₂×#504	1	1	yes	characteristic, complemented, Sylow
51	C₂×#41	#3866	1	1	yes	characteristic
52	#131	—	37	4	no	—
53	#131	—	37	4	no	—
54	C₂×M₁₆	—	37	3	no	—
55	C₂²×C₈	—	37	3	no	—
56	M₃₂	—	37	12	no	—
57	C₂×C₁₆	—	37	1	no	—
58	C₂×C₁₆	—	37	3	no	—
59	C₂×C₁₆	—	37	12	no	—
60	#41	#64438	1	4	yes	—
61	#41	C₂×#3866	1	4	yes	—
62	C₂×Q₈	#64438	1	1	yes	characteristic
63	C₂×D₄	#64438	1	3	yes	—
64	C₂²×C₄	C₂×#3866	1	3	yes	—
65	M₁₆	—	37	12	no	—
66	C₂×C₈	—	37	6	no	—
67	C₂×C₈	—	37	6	no	—
68	C₂×C₈	—	37	3	no	—
69	C₂×C₈	—	37	1	no	—
70	C₁₆	—	37	2	no	—
71	C₁₆	—	37	6	no	—
72	C₂³	C₂×#64438	1	3	yes	—
73	Q₈	C₂×#64438	1	4	yes	—
74	D₄	C₂×#64438	1	12	yes	—
75	C₂×C₄	C₂×#64438	1	3	yes	—
76	C₂×C₄	C₂×#64438	1	6	yes	—
77	C₂×C₄	C₂²×#3866	1	6	yes	—
78	C₂×C₄	C₂²×#3866	1	1	yes	characteristic
79	C₈	—	37	1	no	—
80	C₈	—	37	1	no	—
81	C₈	—	37	6	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#64438	1	6	yes	—
84	C₂²	C₂²×#64438	1	1	yes	characteristic
85	C₄	C₂²×#64438	1	1	yes	characteristic
86	C₄	C₂²×#64438	1	6	yes	—
87	C₄	C₂³×#3866	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#14558591	1	2	yes	direct product factor
90	C₂	C₂³×#64438	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#3866
commutator	C₂×C₃₇	C₂³×C₈
Frattini	C₄	C₂³×#3866
Fitting, prime radical	C₂×#41×C₃₇	C₄
socle	C₂²×C₃₇	C₂²×C₈
cosocle	#64436	C₂⁴
hypercenter	C₂×#41	#3866
hypocenter	C₃₇	C₂×#504
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #14558591	C₂	direct (N × H)
2. C₂×#11924610	C₂	semidirect
3. C₂²×#10596927	C₂	semidirect
5. #11924610	C₂²	semidirect
8. C₂×#10596927	C₂²	semidirect
44. C₂×C₃₇	#504	semidirect
50. C₃₇	C₂×#504	semidirect
89. C₂	#14558591	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558591	2
C₂×#11924610	2
C₂²×#10596927	2
C₂×#11924543	2
C₂×#504	37

Subgroups — C2×#14558591 #18011560

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558591 #18011560