Subgroups — C₂×#401×D₆₇ #31022124

Order 17152.

2942 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₇⋊#401	C₂	1	7	yes	maximal, complemented
2	#401×D₆₇	C₂	1	16	yes	maximal, direct product factor
3	C₂×#95×D₆₇	C₂	1	7	yes	maximal
4	C₂×#401×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₄×D₆₇	C₂²	1	7	yes	—
6	C₆₇⋊#401	C₂²	1	56	yes	complemented
7	C₂×C₆₇⋊#95	C₂²	1	21	yes	—
8	#95×D₆₇	C₂²	1	56	yes	—
9	#401×C₆₇	C₂²	1	8	yes	complemented
10	C₂×#95×C₆₇	C₂²	1	7	yes	—
11	C₂⁴×D₆₇	C₂³	1	1	yes	characteristic
12	C₂³×Dic₆₇	C₂³	1	7	yes	—
13	C₂²×C₄×D₆₇	—	2	84	no	—
14	C₂²×C₄×D₆₇	C₂³	1	28	yes	—
15	C₆₇⋊#95	C₂³	1	84	yes	—
16	C₂³×C₄×C₆₇	C₂³	1	7	yes	—
17	#95×C₆₇	C₂³	1	28	yes	—
18	C₂³×D₆₇	#41	1	28	yes	—
19	C₂³×D₆₇	C₂⁴	1	2	yes	—
20	C₂²×Dic₆₇	—	2	42	no	—
21	C₂²×Dic₆₇	C₂⁴	1	14	yes	—
22	C₂×C₄×D₆₇	—	2	168	no	—
23	C₂×C₄×D₆₇	—	4	112	no	—
24	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
25	C₂²×C₄×C₆₇	—	2	42	no	—
26	C₂²×C₄×C₆₇	C₂⁴	1	14	yes	—
27	C₂³×C₆₇	C₂×#41	1	14	yes	—
28	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
29	C₂²×D₆₇	#126	1	112	yes	—
30	C₂²×D₆₇	C₂×#41	1	28	yes	—
31	C₂×C₄×C₆₇	—	2	42	no	—
32	C₂×C₄×C₆₇	—	4	28	no	—
33	C₂×Dic₆₇	—	2	42	no	—
34	C₂×Dic₆₇	—	4	28	no	—
35	C₄×D₆₇	—	4	112	no	—
36	C₂²×C₆₇	C₂×#126	1	28	yes	—
37	C₂²×C₆₇	C₂²×#41	1	7	yes	—
38	C₂×D₆₇	#401	1	64	yes	direct product factor
39	C₂×D₆₇	C₂×#126	1	56	yes	—
40	C₄×C₆₇	—	4	14	no	—
41	Dic₆₇	—	4	14	no	—
42	C₂²×#401	—	67	1	no	maximal, Sylow
43	C₂×C₆₇	C₂×#401	1	8	yes	complemented
44	C₂×C₆₇	C₂²×#126	1	7	yes	—
45	D₆₇	C₂×#401	1	16	yes	direct product factor
46	C₂×#401	—	67	16	no	—
47	C₂×#401	—	67	7	no	—
48	C₂×#401	D₆₇	1	1	yes	characteristic, direct product factor
49	C₂²×#95	—	67	7	no	—
50	C₆₇	C₂²×#401	1	1	yes	characteristic, complemented, Sylow
51	C₂⁴×C₄	—	67	7	no	—
52	#401	—	67	56	no	—
53	#401	C₂×D₆₇	1	8	yes	direct product factor
54	C₂×#95	—	67	21	no	—
55	C₂×#95	—	67	56	no	—
56	C₂×#95	C₂×D₆₇	1	7	yes	—
57	C₂⁵	—	67	1	no	—
58	C₂³×C₄	—	67	7	no	—
59	C₂³×C₄	—	67	28	no	—
60	C₂³×C₄	—	134	84	no	—
61	C₂³×C₄	C₂²×D₆₇	1	7	yes	—
62	#95	—	67	84	no	—
63	#95	C₂²×D₆₇	1	28	yes	—
64	C₂⁴	—	67	28	no	—
65	C₂⁴	—	67	2	no	—
66	C₂⁴	C₂³×D₆₇	1	1	yes	characteristic
67	C₂²×C₄	—	2	42	no	—
68	C₂²×C₄	—	268	112	no	—
69	C₂²×C₄	—	67	14	no	—
70	C₂²×C₄	—	134	168	no	—
71	C₂²×C₄	—	134	42	no	—
72	C₂²×C₄	C₂³×D₆₇	1	14	yes	—
73	C₂³	—	67	112	no	—
74	C₂³	—	67	28	no	—
75	C₂³	#41×D₆₇	1	14	yes	—
76	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
77	C₂×C₄	—	2	42	no	—
78	C₂×C₄	—	4	28	no	—
79	C₂×C₄	—	268	112	no	—
80	C₂×C₄	—	268	28	no	—
81	C₂×C₄	—	134	42	no	—
82	C₂²	—	67	56	no	—
83	C₂²	—	67	64	no	—
84	C₂²	#126×D₆₇	1	28	yes	—
85	C₂²	C₂×#41×D₆₇	1	7	yes	—
86	C₄	—	4	14	no	—
87	C₄	—	268	14	no	—
88	C₂	—	67	16	no	—
89	C₂	#401×D₆₇	1	8	yes	direct product factor
90	C₂	C₂×#126×D₆₇	1	7	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₆₇
commutator, cosocle	C₂³×C₆₇	C₂⁵
Frattini	C₂³	C₂⁴×D₆₇
Fitting	C₂×#401×C₆₇	C₂
socle	C₂⁴×C₆₇	C₂⁴
prime radical	C₂⁴×D₆₇	C₂³
hypercenter	C₂×#401	D₆₇
hypocenter	C₆₇	C₂²×#401
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₇⋊#401	C₂	semidirect
2. #401×D₆₇	C₂	direct (N × H)
4. C₂×#401×C₆₇	C₂	semidirect
6. C₆₇⋊#401	C₂²	semidirect
9. #401×C₆₇	C₂²	semidirect
38. C₂×D₆₇	#401	direct (N × H)
43. C₂×C₆₇	C₂×#401	semidirect
45. D₆₇	C₂×#401	direct (N × H)
48. C₂×#401	D₆₇	direct (N × H)
50. C₆₇	C₂²×#401	semidirect
53. #401	C₂×D₆₇	direct (N × H)
89. C₂	#401×D₆₇	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×C₆₇⋊#401	2
#401×D₆₇	2
C₂×#95×D₆₇	2
C₂×#401×C₆₇	2
C₂²×#401	67

Subgroups — C2×#401×D67 #31022124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#401×D₆₇ #31022124