Subgroups — #22581297

Order 8896.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17984822	C₂	1	1	yes	maximal, characteristic
2	#17984800	C₂	1	1	yes	maximal, characteristic
3	#17984775	C₂	1	1	yes	maximal, characteristic, complemented
4	#17984767	C₂	1	1	yes	maximal, characteristic, complemented
5	#17984765	C₂	1	1	yes	maximal, characteristic, complemented
6	(C₂×D₁₃₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#106×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₇₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₃₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₃₉⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₃₉	—	2	1	no	—
12	C₄⋊Dic₁₃₉	C₂²	1	1	yes	characteristic
13	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
14	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
15	C₄×Dic₁₃₉	—	2	1	no	—
16	C₂×C₈×C₁₃₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₃₉	C₂²	1	1	yes	characteristic
19	C₂²×D₁₃₉	D₄	1	1	yes	characteristic
20	Dic₂₇₈	—	2	1	no	—
21	Dic₂₇₈	—	2	1	no	—
22	C₂×Dic₁₃₉	—	2	1	no	—
23	C₂×Dic₁₃₉	—	2	1	no	—
24	C₂×Dic₁₃₉	D₄	1	1	yes	characteristic
25	C₄×D₁₃₉	—	2	1	no	—
26	C₄×D₁₃₉	—	2	1	no	—
27	C₁₃₉⋊C₈	—	2	1	no	—
28	C₂×C₄×C₁₃₉	—	2	1	no	—
29	C₂×C₄×C₁₃₉	—	2	1	no	—
30	C₂×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
31	C₈×C₁₃₉	—	2	1	no	—
32	C₂²×C₁₃₉	C₂×D₄	1	1	yes	characteristic
33	C₂×D₁₃₉	—	2	1	no	—
34	C₂×D₁₃₉	—	2	1	no	—
35	C₂×D₁₃₉	—	2	1	no	—
36	C₄×C₁₃₉	—	4	1	no	—
37	C₄×C₁₃₉	—	4	1	no	—
38	C₄×C₁₃₉	#41	1	1	yes	characteristic
39	C₄×C₁₃₉	#41	1	1	yes	characteristic
40	Dic₁₃₉	—	2	1	no	—
41	Dic₁₃₉	—	4	1	no	—
42	Dic₁₃₉	—	4	1	no	—
43	C₂×C₁₃₉	#123	1	1	yes	characteristic
44	C₂×C₁₃₉	#135	1	1	yes	characteristic
45	C₂×C₁₃₉	#137	1	1	yes	characteristic
46	D₁₃₉	—	4	1	no	—
47	C₁₃₉	#485	1	1	yes	characteristic, complemented, Sylow
48	#485	—	139	1	no	maximal, Sylow
49	C₂²⋊Q₈	—	139	1	no	—
50	#117	—	139	1	no	—
51	#107	—	139	1	no	—
52	#106	D₁₃₉	1	1	yes	characteristic, complemented
53	#103	—	139	1	no	—
54	#103	—	139	1	no	—
55	C₂²⋊C₈	—	139	1	no	—
56	C₂×Q₈	—	139	1	no	—
57	C₂²×C₄	—	139	1	no	—
58	C₂×C₈	—	139	1	no	—
59	C₂×C₈	C₂×D₁₃₉	1	1	yes	characteristic
60	C₄⋊C₄	—	278	1	no	—
61	C₄⋊C₄	—	139	1	no	—
62	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
63	C₄⋊C₄	C₂×D₁₃₉	1	1	yes	characteristic
64	C₂²⋊C₄	—	278	1	no	—
65	C₂²⋊C₄	—	278	1	no	—
66	C₄²	—	278	1	no	—
67	C₂³	—	139	1	no	—
68	Q₈	—	278	1	no	—
69	Q₈	—	278	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	278	1	no	—
73	C₂×C₄	—	278	1	no	—
74	C₂×C₄	—	278	1	no	—
75	C₂×C₄	—	278	1	no	—
76	C₂×C₄	—	139	1	no	—
77	C₂×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	278	1	no	—
80	C₂²	—	278	1	no	—
81	C₂²	—	278	1	no	—
82	C₂²	—	278	1	no	—
83	C₂²	D₄×D₁₃₉	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	278	1	no	—
87	C₄	—	556	1	no	—
88	C₄	—	556	1	no	—
89	C₄	#14555785	1	1	yes	characteristic
90	C₄	#14555786	1	1	yes	characteristic
91	C₂	—	556	1	no	—
92	C₂	#17984827	1	1	yes	characteristic
93	C₂	#17984863	1	1	yes	characteristic
94	C₂	#17984871	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₃₉
commutator	C₂×C₄×C₁₃₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₃₉
Fitting	#106×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂×D₄
hypercenter	#106	D₁₃₉
hypocenter	C₁₃₉	#485
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #17984775	C₂	semidirect
4. #17984767	C₂	semidirect
5. #17984765	C₂	semidirect
7. #106×C₁₃₉	C₂	semidirect
47. C₁₃₉	#485	semidirect
52. #106	D₁₃₉	semidirect