Subgroups — #44484705

Order 30592.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21439892	C₂	1	4	yes	maximal
2	#29504642	C₂	1	2	yes	maximal
3	C₂×C₄×C₈×C₂₃₉	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₂₃₉	—	2	4	no	—
5	C₂×C₄⋊Dic₂₃₉	C₂²	1	4	yes	—
6	#21439892	—	2	8	no	—
7	C₂²×C₈×C₂₃₉	C₂²	1	2	yes	—
8	C₂×C₄²×C₂₃₉	C₂²	1	1	yes	characteristic
9	C₄×C₈×C₂₃₉	C₄	1	4	yes	complemented
10	C₂²×Dic₂₃₉	—	2	4	no	—
11	C₄⋊Dic₂₃₉	—	2	8	no	—
12	C₄⋊Dic₂₃₉	—	4	8	no	—
13	C₂²×C₄×C₂₃₉	D₄	1	2	yes	—
14	C₂²×C₄×C₂₃₉	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₂₃₉	C₂×C₄	1	4	yes	—
16	C₂×C₈×C₂₃₉	D₄	1	4	yes	—
17	C₂×C₈×C₂₃₉	Q₈	1	4	yes	—
18	C₄²×C₂₃₉	C₂×C₄	1	2	yes	—
19	C₄²×C₂₃₉	Q₈	1	2	yes	—
20	C₂×Dic₂₃₉	—	4	4	no	—
21	C₂×Dic₂₃₉	—	4	8	no	—
22	C₂³×C₂₃₉	C₂×D₄	1	1	yes	characteristic
23	C₂×C₄×C₂₃₉	C₄⋊C₄	1	4	yes	—
24	C₂×C₄×C₂₃₉	SD₁₆	1	8	yes	—
25	C₂×C₄×C₂₃₉	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₂₃₉	C₂×D₄	1	2	yes	—
27	C₂×C₄×C₂₃₉	C₂×Q₈	1	2	yes	—
28	C₂×C₄×C₂₃₉	C₂×Q₈	1	1	yes	characteristic
29	C₈×C₂₃₉	C₄⋊C₄	1	8	yes	complemented
30	C₂²×C₂₃₉	C₂×C₄⋊C₄	1	1	yes	characteristic
31	C₂²×C₂₃₉	#127	1	1	yes	characteristic
32	C₂²×C₂₃₉	C₄⋊Q₈	1	1	yes	characteristic
33	C₂²×C₂₃₉	C₂×SD₁₆	1	4	yes	—
34	C₄×C₂₃₉	#106	1	8	yes	complemented
35	C₄×C₂₃₉	C₂×C₄⋊C₄	1	2	yes	—
36	C₄×C₂₃₉	C₄⋊Q₈	1	2	yes	—
37	Dic₂₃₉	—	8	4	no	—
38	C₂×C₂₃₉	#384	1	1	yes	characteristic
39	C₂×C₂₃₉	C₂×#106	1	2	yes	—
40	C₂×C₂₃₉	#492	1	2	yes	—
41	C₂×C₂₃₉	#498	1	2	yes	—
42	C₂₃₉	#1844	1	1	yes	characteristic, complemented, Sylow
43	#1844	—	239	1	no	maximal, Sylow
44	C₂×#106	—	239	4	no	—
45	C₂×C₄×C₈	D₂₃₉	1	1	yes	characteristic
46	#384	—	239	2	no	—
47	C₂²×C₈	C₂×D₂₃₉	1	2	yes	—
48	C₂×C₄⋊C₄	—	478	4	no	—
49	C₂×C₄⋊C₄	—	239	4	no	—
50	C₂×C₄²	C₂×D₂₃₉	1	1	yes	characteristic
51	#106	—	478	8	no	—
52	C₄×C₈	Dic₂₃₉	1	4	yes	complemented
53	C₂²×C₄	—	478	4	no	—
54	C₂²×C₄	D₉₅₆	1	2	yes	—
55	C₂²×C₄	C₂²×D₂₃₉	1	1	yes	characteristic
56	C₂×C₈	C₂×Dic₂₃₉	1	4	yes	—
57	C₂×C₈	D₉₅₆	1	4	yes	—
58	C₂×C₈	Dic₄₇₈	1	4	yes	—
59	C₄⋊C₄	—	956	8	no	—
60	C₄⋊C₄	—	478	8	no	—
61	C₄²	C₂×Dic₂₃₉	1	2	yes	—
62	C₄²	Dic₄₇₈	1	2	yes	—
63	C₂³	C₂×D₉₅₆	1	1	yes	characteristic
64	C₂×C₄	—	956	4	no	—
65	C₂×C₄	—	956	8	no	—
66	C₂×C₄	C₄⋊Dic₂₃₉	1	4	yes	—
67	C₂×C₄	#16838537	1	8	yes	—
68	C₂×C₄	C₂²×Dic₂₃₉	1	1	yes	characteristic
69	C₂×C₄	C₂×D₉₅₆	1	2	yes	—
70	C₂×C₄	C₂×Dic₄₇₈	1	2	yes	—
71	C₂×C₄	C₂×Dic₄₇₈	1	1	yes	characteristic
72	C₈	C₄⋊Dic₂₃₉	1	8	yes	complemented
73	C₂²	C₂×C₄⋊Dic₂₃₉	1	1	yes	characteristic
74	C₂²	#21439957	1	1	yes	characteristic
75	C₂²	#21439960	1	1	yes	characteristic
76	C₂²	C₂×#16838537	1	4	yes	—
77	C₄	—	1912	4	no	—
78	C₄	#21439892	1	8	yes	complemented
79	C₄	C₂×C₄⋊Dic₂₃₉	1	2	yes	—
80	C₄	#21439960	1	2	yes	—
81	C₂	#29504642	1	1	yes	characteristic
82	C₂	C₂×#21439892	1	2	yes	—
83	C₂	#29505145	1	2	yes	—
84	C₂	#29505170	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₉₅₆
commutator	C₂×C₄×C₂₃₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₂₃₉
Fitting	C₂×C₄×C₈×C₂₃₉	C₂
socle, prime radical	C₂³×C₂₃₉	C₂×D₄
cosocle	C₂²×C₄×C₂₃₉	C₂³
hypercenter	C₂×C₄×C₈	D₂₃₉
hypocenter	C₂₃₉	#1844
LCS	G ▷ C₂×C₄×C₂₃₉ ▷ C₂×C₂₃₉ ▷ C₂₃₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. C₄×C₈×C₂₃₉	C₄	semidirect
29. C₈×C₂₃₉	C₄⋊C₄	semidirect
34. C₄×C₂₃₉	#106	semidirect
42. C₂₃₉	#1844	semidirect
52. C₄×C₈	Dic₂₃₉	semidirect
72. C₈	C₄⋊Dic₂₃₉	semidirect
78. C₄	#21439892	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21439892	2
#29504642	2
C₂×C₄×C₈×C₂₃₉	2
#1844	239