Subgroups — #31804580

Order 17792.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22581307	C₂	1	1	yes	maximal, characteristic
2	#22580748	C₂	1	1	yes	maximal, characteristic
3	#355×C₁₃₉	C₂	1	1	yes	maximal, characteristic
4	#17984834	C₄	1	1	yes	characteristic, complemented
5	#17984766	—	2	1	no	—
6	#17984763	—	2	1	no	—
7	#17984757	—	2	1	no	—
8	C₄×C₁₃₉⋊C₈	C₄	1	1	yes	characteristic, complemented
9	#124×C₁₃₉	C₂²	1	1	yes	characteristic
10	#101×C₁₃₉	—	2	1	no	—
11	C₂×C₁₃₉⋊C₈	—	2	1	no	—
12	C₄⋊Dic₁₃₉	—	2	1	no	—
13	Dic₁₃₉⋊C₄	—	4	1	no	—
14	C₂²⋊Dic₁₃₉	—	4	1	no	—
15	C₂×Q₈×C₁₃₉	D₄	1	1	yes	characteristic
16	C₂×D₄×C₁₃₉	D₄	1	1	yes	characteristic
17	M₁₆×C₁₃₉	—	4	1	no	—
18	C₂²⋊C₄×C₁₃₉	—	4	1	no	—
19	C₄²×C₁₃₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₃₉	—	4	1	no	—
21	C₂×Dic₁₃₉	—	8	1	no	—
22	C₁₃₉⋊C₈	—	4	1	no	—
23	C₂³×C₁₃₉	—	2	1	no	—
24	Q₈×C₁₃₉	—	4	1	no	—
25	D₄×C₁₃₉	—	4	1	no	—
26	C₂×C₄×C₁₃₉	—	2	1	no	—
27	C₂×C₄×C₁₃₉	—	2	1	no	—
28	C₂×C₄×C₁₃₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₈×C₁₃₉	—	8	1	no	—
30	C₂²×C₁₃₉	—	4	1	no	—
31	C₂²×C₁₃₉	—	8	1	no	—
32	C₂²×C₁₃₉	#99	1	1	yes	characteristic
33	C₄×C₁₃₉	—	2	1	no	—
34	C₄×C₁₃₉	—	4	1	no	—
35	C₄×C₁₃₉	—	4	1	no	—
36	Dic₁₃₉	—	8	1	no	—
37	Dic₁₃₉	—	16	1	no	—
38	C₂×C₁₃₉	—	2	1	no	—
39	C₂×C₁₃₉	—	8	1	no	—
40	C₂×C₁₃₉	#354	1	1	yes	characteristic
41	C₁₃₉	#1414	1	1	yes	characteristic, complemented, Sylow
42	#1414	—	139	1	no	maximal, Sylow
43	#488	—	139	1	no	—
44	#355	D₁₃₉	1	1	yes	characteristic
45	#354	—	139	1	no	—
46	#125	—	139	1	no	—
47	#124	C₂×D₁₃₉	1	1	yes	characteristic
48	#103	—	278	1	no	—
49	#102	—	278	1	no	—
50	#101	—	2	1	no	—
51	#99	—	278	1	no	—
52	C₄×C₈	—	139	1	no	—
53	C₂×Q₈	C₂²⋊D₁₃₉	1	1	yes	characteristic
54	C₂×D₄	D₅₅₆	1	1	yes	characteristic
55	M₁₆	—	4	1	no	—
56	C₂×C₈	—	278	1	no	—
57	C₄⋊C₄	—	278	1	no	—
58	C₄⋊C₄	—	556	1	no	—
59	C₂²⋊C₄	—	4	1	no	—
60	C₂²⋊C₄	—	556	1	no	—
61	C₄²	C₄×D₁₃₉	1	1	yes	characteristic
62	C₂³	—	2	1	no	—
63	Q₈	—	4	1	no	—
64	D₄	—	4	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	1	no	—
67	C₂×C₄	—	556	1	no	—
68	C₂×C₄	—	1112	1	no	—
69	C₂×C₄	(C₂×D₁₃₉)⋊C₄	1	1	yes	characteristic
70	C₈	—	8	1	no	—
71	C₈	—	556	1	no	—
72	C₂²	—	4	1	no	—
73	C₂²	—	8	1	no	—
74	C₂²	#17984756	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	—	4	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	1112	1	no	—
79	C₄	—	2224	1	no	—
80	C₂	—	2	1	no	—
81	C₂	—	8	1	no	—
82	C₂	#22580747	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#22580747
commutator	C₄²×C₁₃₉	C₂×C₄
Frattini	#124	C₂×D₁₃₉
Fitting	#355×C₁₃₉	C₂
socle	C₂×C₁₃₉	#354
prime radical	C₂×D₄×C₁₃₉	D₄
cosocle	#124×C₁₃₉	C₂²
hypercenter	#355	D₁₃₉
hypocenter	C₁₃₉	#1414
LCS	G ▷ C₄²×C₁₃₉ ▷ C₂×C₄×C₁₃₉ ▷ C₂²×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #355

Complements

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

N	H ≅ G/N	type
4. #17984834	C₄	semidirect
8. C₄×C₁₃₉⋊C₈	C₄	semidirect
41. C₁₃₉	#1414	semidirect

Maximal subgroups

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

subgroup	index
#22581307	2
#22580748	2
#355×C₁₃₉	2
#1414	139