Subgroups — C₂×#27159341 #38734553

Order 24896.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₃₈₉	C₂	1	1	yes	maximal, characteristic
2	#27159341	C₂	1	8	yes	maximal, direct product factor
3	C₂×#20261945	C₂	1	2	yes	maximal, complemented
4	C₂×#20261943	C₂	1	2	yes	maximal
5	C₂×C₄×Dic₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄²×C₃₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₃₈₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃₈₉	C₂²	1	2	yes	—
9	C₂²×Dic₃₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₃₈₉	C₄	1	8	yes	complemented
11	C₂×C₄×D₃₈₉	C₂²	1	4	yes	—
12	#20261945	C₂²	1	8	yes	complemented
13	#20261943	C₂²	1	8	yes	—
14	C₄×Dic₃₈₉	C₂²	1	4	yes	complemented
15	C₂²×C₄×C₃₈₉	C₂²	1	2	yes	—
16	C₂²×C₄×C₃₈₉	C₂²	1	1	yes	characteristic
17	C₄²×C₃₈₉	C₂²	1	4	yes	complemented
18	C₂²×D₃₈₉	—	2	4	no	—
19	C₂²×D₃₈₉	C₂×C₄	1	4	yes	—
20	C₂²×D₃₈₉	C₂³	1	2	yes	—
21	C₂×Dic₃₈₉	—	2	4	no	—
22	C₂×Dic₃₈₉	C₂×C₄	1	4	yes	—
23	C₂×Dic₃₈₉	C₂³	1	4	yes	—
24	C₂×Dic₃₈₉	C₂³	1	2	yes	—
25	C₄×D₃₈₉	C₂×C₄	1	16	yes	complemented
26	C₂³×C₃₈₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₃₈₉	—	2	4	no	—
28	C₂×C₄×C₃₈₉	C₂×C₄	1	4	yes	—
29	C₂×C₄×C₃₈₉	C₂³	1	4	yes	—
30	C₂×C₄×C₃₈₉	C₂³	1	2	yes	—
31	C₂²×C₃₈₉	C₂²×C₄	1	2	yes	—
32	C₂²×C₃₈₉	#41	1	4	yes	—
33	C₂²×C₃₈₉	C₂⁴	1	1	yes	characteristic
34	C₂×D₃₈₉	—	2	8	no	—
35	C₂×D₃₈₉	—	2	4	no	—
36	C₂×D₃₈₉	C₂²×C₄	1	4	yes	—
37	C₄×C₃₈₉	—	2	4	no	—
38	C₄×C₃₈₉	C₂²×C₄	1	4	yes	—
39	Dic₃₈₉	—	2	4	no	—
40	Dic₃₈₉	C₂²×C₄	1	4	yes	—
41	C₂×C₃₈₉	#117	1	4	yes	complemented
42	C₂×C₃₈₉	C₂³×C₄	1	1	yes	characteristic
43	C₂×C₃₈₉	C₂×#41	1	2	yes	—
44	D₃₈₉	—	2	4	no	—
45	C₃₈₉	C₂×#117	1	1	yes	characteristic, complemented, Sylow
46	C₂×#117	—	389	1	no	maximal, Sylow
47	C₂³×C₄	—	389	1	no	—
48	#117	—	389	8	no	—
49	C₂×C₄⋊C₄	—	389	2	no	—
50	C₂×C₂²⋊C₄	—	389	2	no	—
51	C₂×C₄²	—	389	1	no	—
52	C₂×C₄²	D₃₈₉	1	1	yes	characteristic, complemented
53	C₂⁴	—	389	1	no	—
54	C₂²×C₄	—	389	2	no	—
55	C₂²×C₄	—	389	1	no	—
56	C₂²×C₄	—	389	4	no	—
57	C₂²×C₄	—	389	8	no	—
58	C₂²×C₄	C₂×D₃₈₉	1	2	yes	—
59	C₂²×C₄	C₂×D₃₈₉	1	1	yes	characteristic
60	C₄⋊C₄	—	389	8	no	—
61	C₂²⋊C₄	—	389	8	no	—
62	C₄²	—	389	4	no	—
63	C₄²	C₂×D₃₈₉	1	4	yes	complemented
64	C₂³	—	778	4	no	—
65	C₂³	—	389	4	no	—
66	C₂³	—	389	2	no	—
67	C₂³	C₂²×D₃₈₉	1	1	yes	characteristic
68	C₂×C₄	—	2	4	no	—
69	C₂×C₄	—	778	4	no	—
70	C₂×C₄	—	389	4	no	—
71	C₂×C₄	—	389	4	no	—
72	C₂×C₄	—	389	2	no	—
73	C₂×C₄	—	389	16	no	—
74	C₂×C₄	C₄×D₃₈₉	1	4	yes	—
75	C₂×C₄	C₂²×D₃₈₉	1	4	yes	—
76	C₂×C₄	C₂²×D₃₈₉	1	2	yes	—
77	C₂²	—	778	8	no	—
78	C₂²	—	778	4	no	—
79	C₂²	—	389	4	no	—
80	C₂²	C₂×C₄×D₃₈₉	1	2	yes	—
81	C₂²	#20261966	1	4	yes	—
82	C₂²	C₂³×D₃₈₉	1	1	yes	characteristic
83	C₄	—	2	4	no	—
84	C₄	—	778	4	no	—
85	C₄	—	389	4	no	—
86	C₄	C₂×C₄×D₃₈₉	1	4	yes	—
87	C₂	—	778	4	no	—
88	C₂	#27159341	1	4	yes	direct product factor
89	C₂	C₂²×C₄×D₃₈₉	1	1	yes	characteristic
90	C₂	C₂×#20261966	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₃₈₉
commutator	C₂×C₃₈₉	C₂³×C₄
Frattini	C₂²	C₂³×D₃₈₉
Fitting	C₂×C₄²×C₃₈₉	C₂
socle	C₂³×C₃₈₉	C₂³
prime radical	C₂³×D₃₈₉	C₂²
cosocle	C₂²×C₃₈₉	C₂⁴
hypercenter	C₂×C₄²	D₃₈₉
hypocenter	C₃₈₉	C₂×#117
LCS	G ▷ C₂×C₃₈₉ ▷ C₃₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #27159341	C₂	direct (N × H)
3. C₂×#20261945	C₂	semidirect
5. C₂×C₄×Dic₃₈₉	C₂	semidirect
6. C₂×C₄²×C₃₈₉	C₂	semidirect
10. C₂×C₄×D₃₈₉	C₄	semidirect
12. #20261945	C₂²	semidirect
14. C₄×Dic₃₈₉	C₂²	semidirect
17. C₄²×C₃₈₉	C₂²	semidirect
25. C₄×D₃₈₉	C₂×C₄	semidirect
41. C₂×C₃₈₉	#117	semidirect
45. C₃₈₉	C₂×#117	semidirect
52. C₂×C₄²	D₃₈₉	semidirect
63. C₄²	C₂×D₃₈₉	semidirect
88. C₂	#27159341	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₃₈₉	2
#27159341	2
C₂×#20261945	2
C₂×#20261943	2
C₂×C₄×Dic₃₈₉	2
C₂×C₄²×C₃₈₉	2
C₂×#117	389

Subgroups — C2×#27159341 #38734553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27159341 #38734553