Subgroups — #31806153

Order 17792.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17984753	C₂	1	2	yes	maximal
2	#22580708	C₂	1	4	yes	maximal
3	C₄³×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₃₉⋊C₈	C₂²	1	4	yes	—
5	#17984753	C₄	1	8	yes	complemented
6	C₂×C₄²×C₁₃₉	C₄	1	4	yes	—
7	C₂×C₄²×C₁₃₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₁₃₉	C₂²	1	1	yes	characteristic
9	C₂×C₁₃₉⋊C₈	—	2	8	no	—
10	C₂×C₁₃₉⋊C₈	C₂×C₄	1	8	yes	—
11	C₂²×C₄×C₁₃₉	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₁₃₉	C₂×C₄	1	4	yes	—
13	C₂²×C₄×C₁₃₉	C₂³	1	1	yes	characteristic
14	C₄²×C₁₃₉	—	2	8	no	—
15	C₄²×C₁₃₉	—	2	4	no	—
16	C₄²×C₁₃₉	C₂×C₄	1	4	yes	—
17	C₁₃₉⋊C₈	—	2	8	no	—
18	C₂³×C₁₃₉	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₄×C₁₃₉	—	2	4	no	—
20	C₂×C₄×C₁₃₉	—	2	4	no	—
21	C₂×C₄×C₁₃₉	—	2	4	no	—
22	C₂×C₄×C₁₃₉	C₄²	1	4	yes	—
23	C₂×C₄×C₁₃₉	M₁₆	1	8	yes	—
24	C₂×C₄×C₁₃₉	C₂²×C₄	1	2	yes	—
25	C₂×C₄×C₁₃₉	#41	1	4	yes	—
26	C₂²×C₁₃₉	C₂×C₄²	1	1	yes	characteristic
27	C₂²×C₁₃₉	#117	1	2	yes	—
28	C₂²×C₁₃₉	C₂×M₁₆	1	4	yes	—
29	C₄×C₁₃₉	—	2	4	no	—
30	C₄×C₁₃₉	—	2	8	no	—
31	C₄×C₁₃₉	#117	1	4	yes	—
32	C₂×C₁₃₉	#376	1	1	yes	characteristic
33	C₂×C₁₃₉	C₄×M₁₆	1	2	yes	—
34	C₂×C₁₃₉	#432	1	4	yes	—
35	C₁₃₉	#1745	1	1	yes	characteristic, complemented, Sylow
36	#1745	—	139	1	no	maximal, Sylow
37	C₂×#97	—	139	2	no	—
38	C₄³	D₁₃₉	1	1	yes	characteristic
39	#336	—	139	4	no	—
40	C₂²×C₈	—	139	4	no	—
41	C₂×C₄²	Dic₁₃₉	1	4	yes	—
42	C₂×C₄²	C₂×D₁₃₉	1	2	yes	—
43	C₂×C₄²	C₂×D₁₃₉	1	1	yes	characteristic
44	#97	—	139	8	no	—
45	C₂²×C₄	C₂×Dic₁₃₉	1	2	yes	—
46	C₂²×C₄	C₂×Dic₁₃₉	1	4	yes	—
47	C₂²×C₄	C₂²×D₁₃₉	1	1	yes	characteristic
48	C₂×C₈	—	278	8	no	—
49	C₂×C₈	—	139	8	no	—
50	C₄²	—	2	8	no	—
51	C₄²	—	2	4	no	—
52	C₄²	C₄×D₁₃₉	1	4	yes	—
53	C₂³	C₂²×Dic₁₃₉	1	1	yes	characteristic
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	C₄×Dic₁₃₉	1	4	yes	—
58	C₂×C₄	#14555769	1	8	yes	—
59	C₂×C₄	C₂×C₄×D₁₃₉	1	2	yes	—
60	C₂×C₄	#14555785	1	4	yes	—
61	C₈	—	278	8	no	—
62	C₂²	C₂×C₄×Dic₁₃₉	1	1	yes	characteristic
63	C₂²	#17984801	1	2	yes	—
64	C₂²	C₂×#14555769	1	4	yes	—
65	C₄	—	2	8	no	—
66	C₄	—	2	4	no	—
67	C₄	#17984799	1	4	yes	—
68	C₂	#22580799	1	1	yes	characteristic
69	C₂	C₄×#14555769	1	2	yes	—
70	C₂	#22581010	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₃₉
commutator	C₂²×C₁₃₉	C₂×C₄²
Fitting	C₄³×C₁₃₉	C₂
socle, prime radical	C₂³×C₁₃₉	C₂²×C₄
cosocle	C₂²×C₄×C₁₃₉	C₂³
hypercenter	C₄³	D₁₃₉
hypocenter	C₁₃₉	#1745
LCS	G ▷ C₂²×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³

Complements

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

N	H ≅ G/N	type
5. #17984753	C₄	semidirect
35. C₁₃₉	#1745	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17984753	2
#22580708	2
C₄³×C₁₃₉	2
#1745	139