Subgroups — #44482642

Order 30592.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21439896	C₂	1	2	yes	maximal
2	C₂²×C₁₆×C₂₃₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#16838532	—	2	2	no	—
4	#21439896	—	2	2	no	—
5	#21439896	C₄	1	4	yes	—
6	C₂²×C₈×C₂₃₉	C₂²	1	1	yes	characteristic
7	C₂×C₁₆×C₂₃₉	—	2	2	no	—
8	C₂×C₁₆×C₂₃₉	C₄	1	2	yes	—
9	#16838532	—	2	4	no	—
10	#16838532	—	4	2	no	—
11	C₂×C₂₃₉⋊C₈	—	4	2	no	—
12	C₂²×C₄×C₂₃₉	D₄	1	1	yes	characteristic
13	C₂×C₈×C₂₃₉	C₂×C₄	1	2	yes	—
14	C₂×C₈×C₂₃₉	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₃₉	D₄	1	2	yes	—
16	C₂×C₈×C₂₃₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₃₉	—	2	2	no	—
18	C₂₃₉⋊C₈	—	4	4	no	—
19	C₂³×C₂₃₉	Q₁₆	1	1	yes	characteristic
20	C₂×C₄×C₂₃₉	C₂²⋊C₄	1	2	yes	—
21	C₂×C₄×C₂₃₉	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₂₃₉	D₈	1	1	yes	characteristic
23	C₂×C₄×C₂₃₉	SD₁₆	1	2	yes	—
24	C₈×C₂₃₉	C₄²	1	1	yes	characteristic
25	C₈×C₂₃₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₃₉	C₄⋊C₄	1	2	yes	—
27	C₂²×C₂₃₉	—	2	2	no	—
28	C₂²×C₂₃₉	#103	1	2	yes	—
29	C₂²×C₂₃₉	#107	1	1	yes	characteristic
30	C₄×C₂₃₉	#95	1	1	yes	characteristic
31	C₄×C₂₃₉	#102	1	2	yes	—
32	C₄×C₂₃₉	#106	1	1	yes	characteristic
33	C₂×C₂₃₉	—	2	2	no	—
34	C₂×C₂₃₉	#340	1	1	yes	characteristic
35	C₂×C₂₃₉	#368	1	2	yes	—
36	C₂₃₉	#1381	1	1	yes	characteristic, complemented, Sylow
37	#1381	—	239	1	no	maximal, Sylow
38	C₂²×C₁₆	D₂₃₉	1	1	yes	characteristic
39	C₂×#108	—	239	2	no	—
40	C₂×M₁₆	—	478	2	no	—
41	C₂²×C₈	C₂×D₂₃₉	1	1	yes	characteristic
42	C₂×C₁₆	—	2	2	no	—
43	C₂×C₁₆	Dic₂₃₉	1	2	yes	—
44	#108	—	478	2	no	—
45	#108	—	239	4	no	—
46	C₂²×C₄	D₉₅₆	1	1	yes	characteristic
47	M₁₆	—	956	2	no	—
48	M₁₆	—	478	4	no	—
49	C₂×C₈	—	956	2	no	—
50	C₂×C₈	C₄×D₂₃₉	1	2	yes	—
51	C₂×C₈	C₂×Dic₂₃₉	1	1	yes	characteristic
52	C₂×C₈	C₂²⋊D₂₃₉	1	2	yes	—
53	C₂×C₈	Dic₄₇₈	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Dic₉₅₆	1	1	yes	characteristic
56	C₂×C₄	(C₂×D₂₃₉)⋊C₄	1	2	yes	—
57	C₂×C₄	C₄⋊Dic₂₃₉	1	1	yes	characteristic
58	C₂×C₄	D₁₉₁₂	1	1	yes	characteristic
59	C₂×C₄	#16838537	1	2	yes	—
60	C₈	—	956	4	no	—
61	C₈	C₄×Dic₂₃₉	1	1	yes	characteristic
62	C₈	C₂²⋊Dic₂₃₉	1	1	yes	characteristic
63	C₈	Dic₂₃₉⋊C₄	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	#21439885	1	2	yes	—
66	C₂²	#21439894	1	1	yes	characteristic
67	C₄	C₂₃₉⋊#95	1	1	yes	characteristic
68	C₄	#21439882	1	2	yes	—
69	C₄	#21439892	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	#29504535	1	1	yes	characteristic
72	C₂	#29504602	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	D₁₉₁₂
commutator	C₈×C₂₃₉	C₄²
Frattini	C₂²×C₈	C₂×D₂₃₉
Fitting	C₂²×C₁₆×C₂₃₉	C₂
socle	C₂²×C₂₃₉	#107
prime radical	C₂³×C₂₃₉	Q₁₆
cosocle	C₂²×C₈×C₂₃₉	C₂²
hypercenter	C₂²×C₁₆	D₂₃₉
hypocenter	C₂₃₉	#1381
LCS	G ▷ C₈×C₂₃₉ ▷ C₄×C₂₃₉ ▷ C₂×C₂₃₉ ▷ C₂₃₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
36. C₂₃₉	#1381	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21439896	2
C₂²×C₁₆×C₂₃₉	2
#1381	239