Subgroups — #31806535

Order 17792.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22580819	C₂	1	2	yes	maximal
2	#22580716	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₁₃₉	C₂²	1	4	yes	—
5	C₁₃₉⋊#95	—	2	4	no	—
6	C₂²×C₈×C₁₃₉	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₁₃₉	C₄	1	4	yes	complemented
9	C₂²×Dic₁₃₉	—	2	4	no	—
10	C₄⋊Dic₁₃₉	—	2	8	no	—
11	C₂²×C₄×C₁₃₉	D₄	1	2	yes	—
12	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₁₃₉	—	2	4	no	—
14	C₂×C₈×C₁₃₉	C₂×C₄	1	4	yes	—
15	C₄²×C₁₃₉	C₂×C₄	1	2	yes	—
16	C₄²×C₁₃₉	Q₈	1	2	yes	—
17	C₂×Dic₁₃₉	—	4	4	no	—
18	C₂×Dic₁₃₉	—	4	8	no	—
19	C₂³×C₁₃₉	C₂×D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₃₉	—	2	4	no	—
21	C₂×C₄×C₁₃₉	C₄⋊C₄	1	4	yes	—
22	C₂×C₄×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₃₉	C₂×Q₈	1	1	yes	characteristic
24	C₂×C₄×C₁₃₉	#41	1	4	yes	—
25	C₈×C₁₃₉	—	2	4	no	—
26	C₂²×C₁₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₃₉	#124	1	2	yes	—
28	C₂²×C₁₃₉	#135	1	4	yes	—
29	C₄×C₁₃₉	—	2	4	no	—
30	C₄×C₁₃₉	#117	1	2	yes	—
31	C₄×C₁₃₉	#125	1	2	yes	—
32	Dic₁₃₉	—	8	4	no	—
33	C₂×C₁₃₉	#382	1	1	yes	characteristic
34	C₂×C₁₃₉	#427	1	2	yes	—
35	C₂×C₁₃₉	#488	1	4	yes	—
36	C₁₃₉	#1835	1	1	yes	characteristic, complemented, Sylow
37	#1835	—	139	1	no	maximal, Sylow
38	C₂×C₄×C₈	D₁₃₉	1	1	yes	characteristic
39	#382	—	139	2	no	—
40	#340	—	139	4	no	—
41	C₂²×C₈	C₂×D₁₃₉	1	2	yes	—
42	C₂×C₄⋊C₄	—	139	4	no	—
43	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
44	C₄×C₈	Dic₁₃₉	1	4	yes	complemented
45	#95	—	278	4	no	—
46	C₂²×C₄	—	278	4	no	—
47	C₂²×C₄	D₅₅₆	1	2	yes	—
48	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
49	C₂×C₈	—	2	4	no	—
50	C₂×C₈	C₂×Dic₁₃₉	1	4	yes	—
51	C₄⋊C₄	—	278	8	no	—
52	C₄²	C₂×Dic₁₃₉	1	2	yes	—
53	C₄²	Dic₂₇₈	1	2	yes	—
54	C₂³	C₂×D₅₅₆	1	1	yes	characteristic
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	556	4	no	—
57	C₂×C₄	—	556	8	no	—
58	C₂×C₄	C₄⋊Dic₁₃₉	1	4	yes	—
59	C₂×C₄	C₂²×Dic₁₃₉	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₂₇₈	1	1	yes	characteristic
61	C₂×C₄	#14555785	1	4	yes	—
62	C₈	—	2	4	no	—
63	C₂²	C₂×C₄⋊Dic₁₃₉	1	1	yes	characteristic
64	C₂²	#17984830	1	2	yes	—
65	C₂²	#17984864	1	4	yes	—
66	C₄	—	2	4	no	—
67	C₄	—	1112	4	no	—
68	C₄	#17984801	1	2	yes	—
69	C₄	#17984834	1	2	yes	—
70	C₂	#22580819	1	1	yes	characteristic
71	C₂	#22580991	1	2	yes	—
72	C₂	#22581308	1	4	yes	—

	subgroup	G/H
center	C₂³	C₂×D₅₅₆
commutator	C₂×C₄×C₁₃₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₁₃₉
Fitting	C₂×C₄×C₈×C₁₃₉	C₂
socle, prime radical	C₂³×C₁₃₉	C₂×D₄
cosocle	C₂²×C₄×C₁₃₉	C₂³
hypercenter	C₂×C₄×C₈	D₁₃₉
hypocenter	C₁₃₉	#1835
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
8. C₄×C₈×C₁₃₉	C₄	semidirect
36. C₁₃₉	#1835	semidirect
44. C₄×C₈	Dic₁₃₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#22580819	2
#22580716	2
C₂×C₄×C₈×C₁₃₉	2
#1835	139