Subgroups — C₂×#31773725 #46838144

Order 34688.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#22576094	C₂	1	2	yes	maximal
2	#31773725	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₂₇₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₂₇₁	—	2	2	no	—
5	#22576094	—	2	2	no	—
6	#22576094	C₂²	1	4	yes	—
7	C₂²×C₈×C₂₇₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₂₇₁	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₂₇₁	C₂²	1	2	yes	—
10	C₂²×Dic₂₇₁	—	4	2	no	—
11	C₄⋊Dic₂₇₁	—	2	4	no	—
12	C₄⋊Dic₂₇₁	—	4	2	no	—
13	C₂²×C₄×C₂₇₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₂₇₁	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₇₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₂₇₁	Q₈	1	2	yes	—
17	C₂×C₈×C₂₇₁	C₂³	1	1	yes	characteristic
18	C₁₆×C₂₇₁	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₂₇₁	—	4	4	no	—
20	C₂×Dic₂₇₁	—	8	4	no	—
21	C₂³×C₂₇₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₇₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₇₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₂₇₁	Q₁₆	1	2	yes	—
25	C₂×C₄×C₂₇₁	C₂×D₄	1	1	yes	characteristic
26	C₈×C₂₇₁	C₄⋊C₄	1	2	yes	—
27	C₈×C₂₇₁	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₂₇₁	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₂₇₁	#107	1	2	yes	—
30	C₂²×C₂₇₁	SD₃₂	1	4	yes	—
31	C₂²×C₂₇₁	C₂×D₈	1	1	yes	characteristic
32	C₄×C₂₇₁	#107	1	2	yes	—
33	C₄×C₂₇₁	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₄×C₂₇₁	C₂×Q₁₆	1	1	yes	characteristic
35	Dic₂₇₁	—	8	4	no	—
36	C₂×C₂₇₁	#367	1	4	yes	complemented
37	C₂×C₂₇₁	C₂×#107	1	1	yes	characteristic
38	C₂×C₂₇₁	C₂×SD₃₂	1	2	yes	—
39	C₂₇₁	C₂×#367	1	1	yes	characteristic, complemented, Sylow
40	C₂×#367	—	271	1	no	maximal, Sylow
41	C₂²×C₁₆	D₂₇₁	1	1	yes	characteristic
42	C₂×#107	—	271	2	no	—
43	#367	—	271	4	no	—
44	C₂²×C₈	C₂×D₂₇₁	1	1	yes	characteristic
45	C₂×C₄⋊C₄	—	542	2	no	—
46	C₂×C₁₆	Dic₂₇₁	1	4	yes	complemented
47	C₂×C₁₆	C₂×D₂₇₁	1	2	yes	—
48	#107	—	271	4	no	—
49	#107	—	542	2	no	—
50	C₂²×C₄	—	1084	2	no	—
51	C₂²×C₄	D₁₀₈₄	1	1	yes	characteristic
52	C₂×C₈	C₂×Dic₂₇₁	1	2	yes	—
53	C₂×C₈	D₁₀₈₄	1	1	yes	characteristic
54	C₂×C₈	Dic₅₄₂	1	2	yes	—
55	C₂×C₈	C₂²×D₂₇₁	1	1	yes	characteristic
56	C₄⋊C₄	—	542	4	no	—
57	C₄⋊C₄	—	1084	2	no	—
58	C₁₆	C₂×Dic₂₇₁	1	4	yes	complemented
59	C₂³	D₂₁₆₈	1	1	yes	characteristic
60	C₂×C₄	—	1084	4	no	—
61	C₂×C₄	—	2168	4	no	—
62	C₂×C₄	C₄⋊Dic₂₇₁	1	2	yes	—
63	C₂×C₄	D₂₁₆₈	1	1	yes	characteristic
64	C₂×C₄	Dic₁₀₈₄	1	2	yes	—
65	C₂×C₄	C₂×D₁₀₈₄	1	1	yes	characteristic
66	C₈	C₄⋊Dic₂₇₁	1	2	yes	—
67	C₈	C₂²×Dic₂₇₁	1	1	yes	characteristic
68	C₈	C₂×Dic₅₄₂	1	1	yes	characteristic
69	C₂²	#22576094	1	2	yes	—
70	C₂²	#22576105	1	4	yes	—
71	C₂²	C₂×D₂₁₆₈	1	1	yes	characteristic
72	C₄	—	2168	4	no	—
73	C₄	#22576094	1	2	yes	—
74	C₄	C₂×C₄⋊Dic₂₇₁	1	1	yes	characteristic
75	C₄	C₂×Dic₁₀₈₄	1	1	yes	characteristic
76	C₂	#31773725	1	4	yes	direct product factor
77	C₂	C₂×#22576094	1	1	yes	characteristic
78	C₂	C₂×#22576105	1	2	yes	—

	subgroup	G/H
center	C₂³	D₂₁₆₈
commutator	C₈×C₂₇₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₂₇₁
Fitting	C₂²×C₁₆×C₂₇₁	C₂
socle, prime radical	C₂³×C₂₇₁	D₈
cosocle	C₂×C₈×C₂₇₁	C₂³
hypercenter	C₂²×C₁₆	D₂₇₁
hypocenter	C₂₇₁	C₂×#367
LCS	G ▷ C₈×C₂₇₁ ▷ C₄×C₂₇₁ ▷ C₂×C₂₇₁ ▷ C₂₇₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #31773725	C₂	direct (N × H)
8. C₂×C₁₆×C₂₇₁	C₄	semidirect
18. C₁₆×C₂₇₁	C₂×C₄	semidirect
36. C₂×C₂₇₁	#367	semidirect
39. C₂₇₁	C₂×#367	semidirect
46. C₂×C₁₆	Dic₂₇₁	semidirect
58. C₁₆	C₂×Dic₂₇₁	semidirect
76. C₂	#31773725	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×#22576094	2
#31773725	2
C₂²×C₁₆×C₂₇₁	2
C₂×#367	271

Subgroups — C2×#31773725 #46838144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#31773725 #46838144