Subgroups — C₂×#4680 #78439

Order 384.

424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#869	C₂	1	2	yes	maximal
2	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#817	C₂	1	4	yes	maximal
4	#4680	C₂	1	8	yes	maximal, direct product factor
5	C₂×#498	—	3	1	no	maximal, Sylow
6	C₂²×Dic₆	—	2	2	no	—
7	C₂²×C₃×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₃	—	2	2	no	—
10	C₂×C₄⋊Dic₃	C₂²	1	4	yes	—
11	#869	—	2	4	no	—
12	#869	C₂²	1	8	yes	—
13	C₃×C₄×C₈	C₂²	1	4	yes	—
14	#817	C₂²	1	16	yes	—
15	C₂×C₄⋊Q₈	—	3	2	no	—
16	#498	—	3	8	no	—
17	C₂×#106	—	3	4	no	—
18	C₂×C₄×C₈	D₃	1	1	yes	characteristic
19	C₂²×C₃×C₄	D₄	1	2	yes	—
20	C₂²×C₃×C₄	C₂³	1	1	yes	characteristic
21	C₂²×Dic₃	—	2	4	no	—
22	C₂×Dic₆	—	2	8	no	—
23	C₂×Dic₆	—	4	8	no	—
24	C₂×C₃×C₈	Q₈	1	8	yes	complemented
25	C₂×C₃×C₈	C₂³	1	4	yes	—
26	C₃×C₄²	D₄	1	2	yes	—
27	C₃×C₄²	C₂³	1	2	yes	—
28	C₄⋊Dic₃	—	2	4	no	—
29	C₄⋊Dic₃	—	2	8	no	—
30	C₄⋊Dic₃	C₂³	1	8	yes	—
31	C₂²×Q₈	—	6	2	no	—
32	C₂²×C₈	C₂×D₃	1	2	yes	—
33	C₄⋊Q₈	—	3	8	no	—
34	C₄⋊Q₈	—	6	4	no	—
35	C₂×C₄⋊C₄	—	3	4	no	—
36	C₂×C₄⋊C₄	—	6	2	no	—
37	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
38	#106	—	3	16	no	—
39	C₄×C₈	C₂×D₃	1	4	yes	—
40	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃×C₄	SD₁₆	1	8	yes	—
42	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂×D₄	1	4	yes	—
44	C₂×C₃×C₄	C₂×Q₈	1	4	yes	—
45	C₂×C₃×C₄	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₃	—	2	8	no	—
47	C₂×Dic₃	—	4	8	no	—
48	Dic₆	—	4	16	no	—
49	C₃×C₈	C₂×Q₈	1	8	yes	complemented
50	C₂×Q₈	—	6	8	no	—
51	C₂×Q₈	—	12	8	no	—
52	C₂²×C₄	—	6	4	no	—
53	C₂²×C₄	D₁₂	1	2	yes	—
54	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₈	Dic₆	1	8	yes	complemented
56	C₂×C₈	C₂²×D₃	1	4	yes	—
57	C₄⋊C₄	—	3	8	no	—
58	C₄⋊C₄	—	6	4	no	—
59	C₄⋊C₄	—	6	8	no	—
60	C₄²	D₁₂	1	2	yes	—
61	C₄²	C₂²×D₃	1	2	yes	—
62	C₂²×C₃	C₄⋊Q₈	1	2	yes	—
63	C₂²×C₃	C₂×SD₁₆	1	4	yes	—
64	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
65	C₃×C₄	C₄⋊Q₈	1	2	yes	—
66	C₃×C₄	C₂×SD₁₆	1	8	yes	—
67	C₃×C₄	C₂²×Q₈	1	2	yes	—
68	Dic₃	—	4	8	no	—
69	C₂³	C₂×D₁₂	1	1	yes	characteristic
70	Q₈	—	12	16	no	—
71	C₂×C₄	—	6	8	no	—
72	C₂×C₄	—	12	8	no	—
73	C₂×C₄	#204	1	8	yes	—
74	C₂×C₄	C₂×Dic₆	1	4	yes	—
75	C₂×C₄	C₂×D₁₂	1	1	yes	characteristic
76	C₂×C₄	C₂×D₁₂	1	4	yes	—
77	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
78	C₈	C₂×Dic₆	1	8	yes	complemented
79	C₂×C₃	#498	1	4	yes	complemented
80	C₂×C₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₃	C₂²×SD₁₆	1	2	yes	—
82	C₂²	#869	1	2	yes	—
83	C₂²	C₂×#204	1	4	yes	—
84	C₂²	C₂²×D₁₂	1	1	yes	characteristic
85	C₄	—	12	8	no	—
86	C₄	#869	1	2	yes	—
87	C₄	C₂×#204	1	8	yes	—
88	C₄	C₂²×Dic₆	1	2	yes	—
89	C₃	C₂×#498	1	1	yes	characteristic, complemented, Sylow
90	C₂	#4680	1	4	yes	direct product factor
91	C₂	C₂×#869	1	1	yes	characteristic
92	C₂	C₂²×#204	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴
Frattini	C₂×C₄	C₂³×D₃
Fitting	C₂×C₃×C₄×C₈	C₂
socle, prime radical	C₂³×C₃	C₂×D₄
hypercenter	C₂×C₄×C₈	D₃
hypocenter	C₃	C₂×#498
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #4680	C₂	direct (N × H)
24. C₂×C₃×C₈	Q₈	semidirect
49. C₃×C₈	C₂×Q₈	semidirect
55. C₂×C₈	Dic₆	semidirect
78. C₈	C₂×Dic₆	semidirect
79. C₂×C₃	#498	semidirect
89. C₃	C₂×#498	semidirect
90. C₂	#4680	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#869	2
C₂×C₃×C₄×C₈	2
C₂×#817	2
#4680	2
C₂×#498	3

Subgroups — C2×#4680 #78439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4680 #78439