Subgroups — C₂×#17984833 #22581474

Order 8896.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984833	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₁₃₉	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₃₉⋊C₄	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₁₃₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊C₄×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₃₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₃₉	C₂²	1	2	yes	—
10	C₄⋊Dic₁₃₉	C₂²	1	8	yes	—
11	C₄⋊Dic₁₃₉	C₂²	1	4	yes	—
12	Dic₁₃₉⋊C₄	C₂²	1	8	yes	—
13	C₄×Dic₁₃₉	C₂²	1	4	yes	—
14	C₂²×C₄×C₁₃₉	C₂²	1	2	yes	—
15	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
16	C₄⋊C₄×C₁₃₉	C₂²	1	4	yes	—
17	C₂×Dic₁₃₉	—	2	2	no	—
18	C₂×Dic₁₃₉	—	2	2	no	—
19	C₂×Dic₁₃₉	—	2	4	no	—
20	C₂×Dic₁₃₉	C₂³	1	2	yes	—
21	C₂×Dic₁₃₉	C₂³	1	2	yes	—
22	C₂×Dic₁₃₉	C₂³	1	4	yes	—
23	C₂³×C₁₃₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₁₃₉	—	2	4	no	—
25	C₂×C₄×C₁₃₉	Q₈	1	4	yes	—
26	C₂×C₄×C₁₃₉	C₂³	1	4	yes	—
27	C₂×C₄×C₁₃₉	C₂³	1	2	yes	—
28	C₂²×C₁₃₉	C₂×Q₈	1	2	yes	—
29	C₂²×C₁₃₉	#41	1	2	yes	—
30	C₂²×C₁₃₉	#41	1	2	yes	—
31	C₂²×C₁₃₉	C₂⁴	1	1	yes	characteristic
32	C₄×C₁₃₉	—	2	4	no	—
33	C₄×C₁₃₉	C₂×Q₈	1	4	yes	—
34	Dic₁₃₉	—	2	2	no	—
35	Dic₁₃₉	—	2	2	no	—
36	Dic₁₃₉	—	2	4	no	—
37	C₂×C₁₃₉	#125	1	4	yes	complemented
38	C₂×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
39	C₂×C₁₃₉	C₂×#41	1	1	yes	characteristic
40	C₂×C₁₃₉	C₂×#41	1	1	yes	characteristic
41	C₁₃₉	C₂×#125	1	1	yes	characteristic, complemented, Sylow
42	C₂×#125	—	139	1	no	maximal, Sylow
43	#125	—	139	8	no	—
44	C₂×C₄⋊C₄	—	139	2	no	—
45	C₂×C₄⋊C₄	—	139	2	no	—
46	C₂×C₄⋊C₄	—	139	1	no	—
47	C₂×C₄⋊C₄	D₁₃₉	1	1	yes	characteristic
48	C₂×C₄²	—	139	1	no	—
49	C₂²×C₄	—	139	1	no	—
50	C₂²×C₄	—	139	1	no	—
51	C₂²×C₄	—	139	2	no	—
52	C₂²×C₄	C₂×D₁₃₉	1	2	yes	—
53	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
54	C₄⋊C₄	—	139	8	no	—
55	C₄⋊C₄	—	139	8	no	—
56	C₄⋊C₄	—	139	4	no	—
57	C₄⋊C₄	C₂×D₁₃₉	1	4	yes	—
58	C₄²	—	139	4	no	—
59	C₂³	C₂²×D₁₃₉	1	1	yes	characteristic
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	278	2	no	—
62	C₂×C₄	—	278	2	no	—
63	C₂×C₄	—	278	4	no	—
64	C₂×C₄	—	139	2	no	—
65	C₂×C₄	—	139	2	no	—
66	C₂×C₄	—	139	4	no	—
67	C₂×C₄	Dic₂₇₈	1	4	yes	—
68	C₂×C₄	C₂²×D₁₃₉	1	4	yes	—
69	C₂×C₄	C₂²×D₁₃₉	1	2	yes	—
70	C₂²	C₂×Dic₂₇₈	1	2	yes	—
71	C₂²	#14555784	1	2	yes	—
72	C₂²	#14555786	1	2	yes	—
73	C₂²	C₂³×D₁₃₉	1	1	yes	characteristic
74	C₄	—	2	4	no	—
75	C₄	—	278	2	no	—
76	C₄	—	278	2	no	—
77	C₄	—	278	4	no	—
78	C₄	C₂×Dic₂₇₈	1	4	yes	—
79	C₂	#17984833	1	4	yes	direct product factor
80	C₂	C₂²×Dic₂₇₈	1	1	yes	characteristic
81	C₂	C₂×#14555784	1	1	yes	characteristic
82	C₂	C₂×#14555786	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₃₉
commutator	C₂²×C₁₃₉	C₂⁴
Frattini	C₂²	C₂³×D₁₃₉
Fitting	C₂×C₄⋊C₄×C₁₃₉	C₂
socle	C₂³×C₁₃₉	C₂³
hypercenter	C₂×C₄⋊C₄	D₁₃₉
hypocenter	C₁₃₉	C₂×#125
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. #17984833	C₂	direct (N × H)
37. C₂×C₁₃₉	#125	semidirect
41. C₁₃₉	C₂×#125	semidirect
79. C₂	#17984833	direct (N × H)

Subgroups — C2×#17984833 #22581474

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17984833 #22581474