Subgroups — C₂×#14558465 #18011016

Order 4736.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14558465	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11924586	C₂	1	2	yes	maximal, complemented
3	C₂²×#10596925	C₂	1	1	yes	maximal, characteristic
4	#11924586	C₂²	1	4	yes	complemented
5	C₂×#10596925	C₄	1	2	yes	—
6	C₂×#10596925	C₄	1	1	yes	characteristic
7	C₂×#10596925	C₂²	1	2	yes	—
8	C₂×#10596925	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₃₇	C₄	1	1	yes	characteristic
10	C₂²×C₄×C₃₇	C₈	1	1	yes	characteristic
11	C₂×C₈×C₃₇	C₈	1	1	yes	characteristic
12	C₂×C₈×C₃₇	C₈	1	2	yes	—
13	C₂×C₈×C₃₇	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₃₇	C₂×C₄	1	1	yes	characteristic
15	#10596925	C₂×C₄	1	2	yes	—
16	#10596925	C₂×C₄	1	1	yes	characteristic
17	#10596925	C₂³	1	1	yes	characteristic
18	C₂³×C₃₇	C₁₆	1	1	yes	characteristic
19	C₂×C₄×C₃₇	C₁₆	1	2	yes	—
20	C₂×C₄×C₃₇	C₁₆	1	1	yes	characteristic
21	C₂×C₄×C₃₇	C₂×C₈	1	2	yes	—
22	C₂×C₄×C₃₇	C₂×C₈	1	1	yes	characteristic
23	C₈×C₃₇	C₂×C₈	1	2	yes	—
24	C₈×C₃₇	C₂×C₈	1	1	yes	characteristic
25	C₈×C₃₇	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₃₇	—	2	2	no	—
27	C₂²×C₃₇	C₂×C₁₆	1	2	yes	—
28	C₂²×C₃₇	C₂×C₁₆	1	1	yes	characteristic
29	C₄×C₃₇	C₂×C₁₆	1	2	yes	—
30	C₄×C₃₇	C₂×C₁₆	1	1	yes	characteristic
31	C₄×C₃₇	C₂²×C₈	1	1	yes	characteristic
32	C₂×M₆₄	—	37	1	no	maximal, Sylow
33	C₂×C₃₇	—	2	2	no	—
34	C₂×C₃₇	M₆₄	1	2	yes	complemented
35	C₂×C₃₇	C₂²×C₁₆	1	1	yes	characteristic
36	C₂²×C₁₆	—	37	1	no	—
37	M₆₄	—	37	4	no	—
38	C₂×C₃₂	—	37	2	no	—
39	C₃₇	C₂×M₆₄	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₈	#3866	1	1	yes	characteristic
41	C₂×C₁₆	—	37	2	no	—
42	C₂×C₁₆	—	37	2	no	—
43	C₂×C₁₆	—	37	1	no	—
44	C₂×C₁₆	—	37	1	no	—
45	C₃₂	—	37	4	no	—
46	C₂²×C₄	#64438	1	1	yes	characteristic
47	C₂×C₈	#64438	1	1	yes	characteristic
48	C₂×C₈	#64438	1	2	yes	—
49	C₂×C₈	C₂×#3866	1	2	yes	—
50	C₂×C₈	C₂×#3866	1	1	yes	characteristic
51	C₁₆	—	37	2	no	—
52	C₁₆	—	37	1	no	—
53	C₁₆	—	37	1	no	—
54	C₂³	#10596927	1	1	yes	characteristic
55	C₂×C₄	#10596927	1	2	yes	—
56	C₂×C₄	#10596927	1	1	yes	characteristic
57	C₂×C₄	C₂×#64438	1	2	yes	—
58	C₂×C₄	C₂×#64438	1	1	yes	characteristic
59	C₈	C₂×#64438	1	2	yes	—
60	C₈	C₂×#64438	1	1	yes	characteristic
61	C₈	C₂²×#3866	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	C₂×#10596927	1	2	yes	—
64	C₂²	C₂×#10596927	1	1	yes	characteristic
65	C₄	C₂×#10596927	1	2	yes	—
66	C₄	C₂×#10596927	1	1	yes	characteristic
67	C₄	C₂²×#64438	1	1	yes	characteristic
68	C₂	—	2	2	no	—
69	C₂	#14558465	1	2	yes	direct product factor
70	C₂	C₂²×#10596927	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#3866
commutator	C₂×C₃₇	C₂²×C₁₆
Frattini	C₈	C₂²×#3866
Fitting	C₂²×C₈×C₃₇	C₄
socle	C₂²×C₃₇	C₂×C₁₆
prime radical	C₂³×C₃₇	C₁₆
cosocle	#10596925	C₂³
hypercenter	C₂²×C₈	#3866
hypocenter	C₃₇	C₂×M₆₄
LCS	G ▷ C₂×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #14558465	C₂	direct (N × H)
2. C₂×#11924586	C₂	semidirect
4. #11924586	C₂²	semidirect
34. C₂×C₃₇	M₆₄	semidirect
39. C₃₇	C₂×M₆₄	semidirect
69. C₂	#14558465	direct (N × H)

Maximal subgroups

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

subgroup	index
#14558465	2
C₂×#11924586	2
C₂²×#10596925	2
C₂×M₆₄	37

Subgroups — C2×#14558465 #18011016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14558465 #18011016