Subgroups — #22581229

Order 8896.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984875	C₂	1	2	yes	maximal
2	C₂×Dic₅₅₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#17984848	C₂	1	1	yes	maximal, characteristic
4	#17984760	C₂	1	2	yes	maximal, complemented
5	#108×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#14555785	C₂²	1	1	yes	characteristic
7	C₂×Dic₂₇₈	C₂²	1	2	yes	—
8	Dic₅₅₆	—	2	2	no	—
9	Dic₅₅₆	—	2	1	no	—
10	Dic₅₅₆	—	2	1	no	—
11	#14555774	—	2	2	no	—
12	#14555769	C₂²	1	1	yes	characteristic
13	#14555768	—	2	1	no	—
14	C₈×D₁₃₉	—	2	1	no	—
15	M₁₆×C₁₃₉	C₂²	1	2	yes	—
16	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	Dic₂₇₈	—	2	2	no	—
18	Dic₂₇₈	—	2	2	no	—
19	Dic₂₇₈	D₄	1	1	yes	characteristic
20	D₅₅₆	D₄	1	1	yes	characteristic
21	C₂²⋊D₁₃₉	—	2	1	no	—
22	C₂×Dic₁₃₉	—	2	2	no	—
23	C₄×D₁₃₉	—	2	1	no	—
24	C₁₃₉⋊C₈	—	2	1	no	—
25	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
26	C₈×C₁₃₉	—	2	2	no	—
27	C₈×C₁₃₉	D₄	1	1	yes	characteristic
28	C₈×C₁₃₉	D₄	1	1	yes	characteristic
29	C₂²×C₁₃₉	#41	1	1	yes	characteristic
30	C₂×D₁₃₉	—	2	1	no	—
31	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
32	C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
33	Dic₁₃₉	—	2	1	no	—
34	Dic₁₃₉	—	4	2	no	—
35	C₂×C₁₃₉	—	2	1	no	—
36	C₂×C₁₃₉	#121	1	1	yes	characteristic
37	D₁₃₉	—	4	1	no	—
38	C₁₃₉	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	139	1	no	maximal, Sylow
40	#137	—	139	2	no	—
41	C₂×Q₁₆	—	139	1	no	—
42	#131	—	139	1	no	—
43	#108	D₁₃₉	1	1	yes	characteristic, complemented
44	#101	—	139	2	no	—
45	#41	—	139	1	no	—
46	C₂×Q₈	—	139	2	no	—
47	Q₁₆	—	278	2	no	—
48	Q₁₆	—	278	1	no	—
49	Q₁₆	—	278	1	no	—
50	SD₁₆	—	278	2	no	—
51	M₁₆	—	278	1	no	—
52	M₁₆	—	139	1	no	—
53	M₁₆	C₂×D₁₃₉	1	2	yes	—
54	C₂×C₈	—	278	1	no	—
55	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
56	Q₈	—	278	2	no	—
57	Q₈	—	278	2	no	—
58	Q₈	—	139	1	no	—
59	D₄	—	278	1	no	—
60	D₄	—	139	1	no	—
61	C₂×C₄	—	278	1	no	—
62	C₂×C₄	—	278	2	no	—
63	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₈	—	278	1	no	—
66	C₈	D₅₅₆	1	1	yes	characteristic
67	C₈	D₅₅₆	1	1	yes	characteristic
68	C₂²	—	278	1	no	—
69	C₂²	#14555786	1	1	yes	characteristic
70	C₄	—	278	1	no	—
71	C₄	—	556	2	no	—
72	C₄	D₄×D₁₃₉	1	1	yes	characteristic
73	C₄	C₂×D₅₅₆	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	556	1	no	—
76	C₂	#17984817	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17984817
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#108×C₁₃₉	C₂
socle	C₂×C₁₃₉	#121
hypercenter	#108	D₁₃₉
hypocenter	C₁₃₉	#473
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₅₆	C₂	semidirect
4. #17984760	C₂	semidirect
5. #108×C₁₃₉	C₂	semidirect
38. C₁₃₉	#473	semidirect
43. #108	D₁₃₉	semidirect