Subgroups — C₄×#322×C₁₃₇ #46857225

Order 35072.

654 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₈×C₁₃₇	C₂	1	2	yes	maximal
2	C₄²×C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#322×C₁₃₇	C₂	1	4	yes	maximal
4	C₂×C₄×C₈×C₁₃₇	C₄	1	8	yes	—
5	C₂×C₄×C₈×C₁₃₇	C₄	1	4	yes	—
6	C₂×C₄×C₈×C₁₃₇	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₁₃₇	C₂²	1	2	yes	—
8	C₄³×C₁₃₇	C₂²	1	1	yes	characteristic
9	#322×C₁₃₇	C₄	1	16	yes	direct product factor
10	C₂²×C₈×C₁₃₇	C₂×C₄	1	8	yes	—
11	C₂²×C₈×C₁₃₇	C₂×C₄	1	4	yes	—
12	C₂×C₄²×C₁₃₇	C₂×C₄	1	2	yes	—
13	C₂×C₄²×C₁₃₇	C₂×C₄	1	4	yes	—
14	C₂×C₄²×C₁₃₇	C₂³	1	1	yes	characteristic
15	C₄×C₈×C₁₃₇	—	2	16	no	—
16	C₄×C₈×C₁₃₇	C₈	1	16	yes	complemented
17	C₄×C₈×C₁₃₇	C₂×C₄	1	16	yes	—
18	C₄×C₈×C₁₃₇	C₂×C₄	1	8	yes	—
19	C₂²×C₄×C₁₃₇	C₄²	1	4	yes	—
20	C₂²×C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₁₃₇	C₂²×C₄	1	2	yes	—
22	C₂×C₈×C₁₃₇	—	2	16	no	—
23	C₂×C₈×C₁₃₇	C₄²	1	16	yes	—
24	C₂×C₈×C₁₃₇	C₄²	1	8	yes	—
25	C₂×C₈×C₁₃₇	C₂×C₈	1	16	yes	—
26	C₄²×C₁₃₇	C₂×C₈	1	8	yes	—
27	C₄²×C₁₃₇	M₁₆	1	16	yes	—
28	C₄²×C₁₃₇	C₂²×C₄	1	4	yes	—
29	C₂³×C₁₃₇	C₂×C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₃₇	C₄×C₈	1	8	yes	—
31	C₂×C₄×C₁₃₇	#97	1	16	yes	—
32	C₂×C₄×C₁₃₇	C₂×C₄²	1	2	yes	—
33	C₂×C₄×C₁₃₇	C₂×C₄²	1	4	yes	—
34	C₂×C₄×C₁₃₇	C₂²×C₈	1	4	yes	—
35	C₂×C₄×C₁₃₇	C₂×M₁₆	1	8	yes	—
36	C₈×C₁₃₇	—	2	16	no	—
37	C₈×C₁₃₇	C₄×C₈	1	16	yes	complemented
38	C₂²×C₁₃₇	C₄³	1	1	yes	characteristic
39	C₂²×C₁₃₇	C₂×C₄×C₈	1	2	yes	—
40	C₂²×C₁₃₇	C₂×#97	1	4	yes	—
41	C₄×C₁₃₇	#322	1	16	yes	direct product factor
42	C₄×C₁₃₇	C₂×C₄×C₈	1	4	yes	—
43	C₄×C₁₃₇	C₄×M₁₆	1	8	yes	—
44	C₂×C₁₃₇	C₂×#322	1	4	yes	—
45	C₂×C₁₃₇	C₄²×C₈	1	1	yes	characteristic
46	C₂×C₁₃₇	C₄×#97	1	2	yes	—
47	C₄×#322	C₁₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₁₃₇	C₄×#322	1	1	yes	characteristic, direct product factor, Sylow
49	C₄²×C₈	C₂×C₁₃₇	1	2	yes	—
50	C₄²×C₈	C₂×C₁₃₇	1	1	yes	characteristic
51	C₂×#322	C₂×C₁₃₇	1	4	yes	—
52	C₂×C₄×C₈	C₄×C₁₃₇	1	8	yes	—
53	C₂×C₄×C₈	C₄×C₁₃₇	1	4	yes	—
54	C₂×C₄×C₈	C₂²×C₁₃₇	1	4	yes	—
55	C₂×C₄×C₈	C₂²×C₁₃₇	1	2	yes	—
56	C₄³	C₂²×C₁₃₇	1	1	yes	characteristic
57	#322	C₄×C₁₃₇	1	16	yes	direct product factor
58	C₂²×C₈	C₂×C₄×C₁₃₇	1	8	yes	—
59	C₂²×C₈	C₂×C₄×C₁₃₇	1	4	yes	—
60	C₂×C₄²	C₂×C₄×C₁₃₇	1	2	yes	—
61	C₂×C₄²	C₂×C₄×C₁₃₇	1	4	yes	—
62	C₂×C₄²	C₂³×C₁₃₇	1	1	yes	characteristic
63	C₄×C₈	—	2	16	no	—
64	C₄×C₈	C₈×C₁₃₇	1	16	yes	complemented
65	C₄×C₈	C₂×C₄×C₁₃₇	1	16	yes	—
66	C₄×C₈	C₂×C₄×C₁₃₇	1	8	yes	—
67	C₂²×C₄	C₄²×C₁₃₇	1	4	yes	—
68	C₂²×C₄	C₂²×C₄×C₁₃₇	1	1	yes	characteristic
69	C₂²×C₄	C₂²×C₄×C₁₃₇	1	2	yes	—
70	C₂×C₈	—	2	16	no	—
71	C₂×C₈	C₄²×C₁₃₇	1	16	yes	—
72	C₂×C₈	C₄²×C₁₃₇	1	8	yes	—
73	C₂×C₈	C₂×C₈×C₁₃₇	1	16	yes	—
74	C₄²	C₂×C₈×C₁₃₇	1	8	yes	—
75	C₄²	M₁₆×C₁₃₇	1	16	yes	—
76	C₄²	C₂²×C₄×C₁₃₇	1	4	yes	—
77	C₂³	C₂×C₄²×C₁₃₇	1	1	yes	characteristic
78	C₂×C₄	C₄×C₈×C₁₃₇	1	8	yes	—
79	C₂×C₄	#97×C₁₃₇	1	16	yes	—
80	C₂×C₄	C₂×C₄²×C₁₃₇	1	2	yes	—
81	C₂×C₄	C₂×C₄²×C₁₃₇	1	4	yes	—
82	C₂×C₄	C₂²×C₈×C₁₃₇	1	4	yes	—
83	C₂×C₄	C₂×M₁₆×C₁₃₇	1	8	yes	—
84	C₈	—	2	16	no	—
85	C₈	C₄×C₈×C₁₃₇	1	16	yes	complemented
86	C₂²	C₄³×C₁₃₇	1	1	yes	characteristic
87	C₂²	C₂×C₄×C₈×C₁₃₇	1	2	yes	—
88	C₂²	C₂×#97×C₁₃₇	1	4	yes	—
89	C₄	#322×C₁₃₇	1	16	yes	direct product factor
90	C₄	C₂×C₄×C₈×C₁₃₇	1	4	yes	—
91	C₄	C₄×M₁₆×C₁₃₇	1	8	yes	—
92	C₂	C₂×#322×C₁₃₇	1	4	yes	—
93	C₂	C₄²×C₈×C₁₃₇	1	1	yes	characteristic
94	C₂	C₄×#97×C₁₃₇	1	2	yes	—

	subgroup	G/H
center	C₄³×C₁₃₇	C₂²
commutator	C₂	C₄²×C₈×C₁₃₇
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃₇
socle, prime radical	C₂³×C₁₃₇	C₂×C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄³×C₁₃₇ ◁ G

Complements

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

N	H ≅ G/N	type
9. #322×C₁₃₇	C₄	direct (N × H)
16. C₄×C₈×C₁₃₇	C₈	semidirect
37. C₈×C₁₃₇	C₄×C₈	semidirect
41. C₄×C₁₃₇	#322	direct (N × H)
47. C₄×#322	C₁₃₇	direct (N × H)
48. C₁₃₇	C₄×#322	direct (N × H)
57. #322	C₄×C₁₃₇	direct (N × H)
64. C₄×C₈	C₈×C₁₃₇	semidirect
85. C₈	C₄×C₈×C₁₃₇	semidirect
89. C₄	#322×C₁₃₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×C₈×C₁₃₇	2
C₂×#322×C₁₃₇	2
C₄×#322	137

Subgroups — C4×#322×C137 #46857225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#322×C₁₃₇ #46857225