Subgroups — #22581510

Order 8896.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984842	C₂	1	2	yes	maximal, complemented
2	#17984834	C₂	1	2	yes	maximal, complemented
3	#17984821	C₂	1	4	yes	maximal
4	C₄×Dic₂₇₈	C₂	1	4	yes	maximal, complemented
5	#17984801	C₂	1	2	yes	maximal
6	C₂×C₄²×C₁₃₉	C₂	1	1	yes	maximal, characteristic
7	C₂×Dic₂₇₈	C₂²	1	4	yes	—
8	C₄⋊Dic₁₃₉	C₂²	1	4	yes	—
9	C₄⋊Dic₁₃₉	C₂²	1	4	yes	—
10	Dic₁₃₉⋊C₄	C₂²	1	8	yes	—
11	C₂²⋊Dic₁₃₉	C₂²	1	4	yes	—
12	C₄×Dic₁₃₉	C₂²	1	4	yes	—
13	C₂²×C₄×C₁₃₉	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₃₉	C₂²	1	1	yes	characteristic
15	C₄²×C₁₃₉	C₂²	1	2	yes	—
16	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
18	Dic₂₇₈	—	2	8	no	—
19	C₂×Dic₁₃₉	C₂³	1	8	yes	—
20	C₂³×C₁₃₉	C₂³	1	1	yes	characteristic
21	C₂×C₄×C₁₃₉	—	2	4	no	—
22	C₂×C₄×C₁₃₉	Q₈	1	4	yes	complemented
23	C₂×C₄×C₁₃₉	C₂³	1	2	yes	—
24	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₃₉	C₂³	1	2	yes	—
26	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
27	C₂²×C₁₃₉	—	2	2	no	—
28	C₂²×C₁₃₉	C₂×Q₈	1	2	yes	—
29	C₂²×C₁₃₉	C₂⁴	1	1	yes	characteristic
30	C₄×C₁₃₉	—	2	2	no	—
31	C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
32	C₄×C₁₃₉	C₂×Q₈	1	2	yes	—
33	C₄×C₁₃₉	#41	1	4	yes	—
34	Dic₁₃₉	—	2	8	no	—
35	C₂×C₁₃₉	—	2	2	no	—
36	C₂×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
37	C₂×C₁₃₉	C₂×#41	1	2	yes	—
38	C₁₃₉	#533	1	1	yes	characteristic, complemented, Sylow
39	#533	—	139	1	no	maximal, Sylow
40	C₄⋊Q₈	—	139	2	no	—
41	#125	—	139	2	no	—
42	C₂²⋊Q₈	—	139	4	no	—
43	C₄×Q₈	—	139	4	no	—
44	#117	—	139	2	no	—
45	C₂×C₄²	D₁₃₉	1	1	yes	characteristic
46	C₂×Q₈	—	139	4	no	—
47	C₂²×C₄	C₂×D₁₃₉	1	2	yes	—
48	C₂²×C₄	C₂×D₁₃₉	1	1	yes	characteristic
49	C₄⋊C₄	—	139	8	no	—
50	C₄⋊C₄	—	139	4	no	—
51	C₄⋊C₄	—	139	4	no	—
52	C₂²⋊C₄	—	139	4	no	—
53	C₄²	—	139	4	no	—
54	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
55	C₄²	C₂×D₁₃₉	1	1	yes	characteristic
56	C₄²	C₂×D₁₃₉	1	2	yes	—
57	C₂³	C₂²×D₁₃₉	1	1	yes	characteristic
58	Q₈	—	278	8	no	—
59	C₂×C₄	—	2	4	no	—
60	C₂×C₄	—	139	8	no	—
61	C₂×C₄	Dic₂₇₈	1	4	yes	complemented
62	C₂×C₄	C₂²×D₁₃₉	1	2	yes	—
63	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
64	C₂×C₄	C₂²×D₁₃₉	1	2	yes	—
65	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
66	C₂²	—	2	2	no	—
67	C₂²	C₂×Dic₂₇₈	1	2	yes	—
68	C₂²	C₂³×D₁₃₉	1	1	yes	characteristic
69	C₄	—	2	2	no	—
70	C₄	—	278	8	no	—
71	C₄	C₂×Dic₂₇₈	1	2	yes	—
72	C₄	C₂×Dic₂₇₈	1	2	yes	—
73	C₄	#14555785	1	4	yes	—
74	C₂	—	2	2	no	—
75	C₂	C₂²×Dic₂₇₈	1	1	yes	characteristic
76	C₂	C₂×#14555785	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₃₉
commutator, socle	C₂²×C₁₃₉	C₂⁴
Frattini	C₂²	C₂³×D₁₃₉
Fitting	C₂×C₄²×C₁₃₉	C₂
hypercenter	C₂×C₄²	D₁₃₉
hypocenter	C₁₃₉	#533
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #17984842	C₂	semidirect
2. #17984834	C₂	semidirect
4. C₄×Dic₂₇₈	C₂	semidirect
22. C₂×C₄×C₁₃₉	Q₈	semidirect
38. C₁₃₉	#533	semidirect
61. C₂×C₄	Dic₂₇₈	semidirect