Subgroups — C₂×#4699 #78474

Order 384.

552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₂	C₂	1	4	yes	maximal
2	C₂×#869	C₂	1	2	yes	maximal
3	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	#4699	C₂	1	8	yes	maximal, direct product factor
5	C₂×#494	—	3	1	no	maximal, Sylow
6	C₂²×Dic₆	C₂²	1	4	yes	—
7	C₂²×C₃×C₈	C₂²	1	2	yes	—
8	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₃	—	2	4	no	—
10	C₂×Dic₁₂	—	2	16	no	—
11	C₂×Dic₁₂	C₂²	1	16	yes	—
12	#869	—	2	4	no	—
13	#869	C₂²	1	8	yes	—
14	C₃×C₄×C₈	C₂²	1	4	yes	—
15	C₂²×Q₁₆	—	3	4	no	—
16	C₂×C₄⋊Q₈	—	3	2	no	—
17	#494	—	3	8	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	16	no	—
23	C₂×Dic₆	—	2	4	no	—
24	C₂×Dic₆	C₂³	1	8	yes	—
25	C₂×C₃×C₈	D₄	1	8	yes	—
26	C₂×C₃×C₈	C₂³	1	4	yes	—
27	C₃×C₄²	D₄	1	2	yes	—
28	C₃×C₄²	C₂³	1	2	yes	—
29	C₄⋊Dic₃	—	2	16	no	—
30	Dic₁₂	—	2	32	no	—
31	C₂²×Q₈	—	3	4	no	—
32	C₂×Q₁₆	—	3	16	no	—
33	C₂×Q₁₆	—	6	16	no	—
34	C₂²×C₈	C₂×D₃	1	2	yes	—
35	C₄⋊Q₈	—	3	8	no	—
36	C₄⋊Q₈	—	6	4	no	—
37	C₂×C₄⋊C₄	—	6	4	no	—
38	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
39	C₄×C₈	C₂×D₃	1	4	yes	—
40	C₂³×C₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₃×C₄	Q₁₆	1	8	yes	complemented
42	C₂×C₃×C₄	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃×C₄	C₂×D₄	1	4	yes	—
44	C₂×C₃×C₄	C₂×D₄	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	—	2	16	no	—
49	Dic₆	—	4	8	no	—
50	C₃×C₈	C₂×D₄	1	8	yes	—
51	C₂×Q₈	—	3	8	no	—
52	C₂×Q₈	—	6	4	no	—
53	C₂×Q₈	—	6	16	no	—
54	C₂²×C₄	—	6	4	no	—
55	C₂²×C₄	D₁₂	1	2	yes	—
56	C₂²×C₄	C₂²×D₃	1	1	yes	characteristic
57	Q₁₆	—	6	32	no	—
58	C₂×C₈	D₁₂	1	8	yes	—
59	C₂×C₈	C₂²×D₃	1	4	yes	—
60	C₄⋊C₄	—	6	16	no	—
61	C₄²	D₁₂	1	2	yes	—
62	C₄²	C₂²×D₃	1	2	yes	—
63	C₂²×C₃	#127	1	2	yes	—
64	C₂²×C₃	C₂×Q₁₆	1	4	yes	—
65	C₂²×C₃	C₂²×D₄	1	1	yes	characteristic
66	C₃×C₄	#127	1	2	yes	—
67	C₃×C₄	C₂×Q₁₆	1	8	yes	complemented
68	C₃×C₄	C₂²×D₄	1	2	yes	—
69	Dic₃	—	4	8	no	—
70	C₂³	C₂×D₁₂	1	1	yes	characteristic
71	Q₈	—	6	16	no	—
72	Q₈	—	12	8	no	—
73	C₂×C₄	—	6	8	no	—
74	C₂×C₄	—	12	8	no	—
75	C₂×C₄	Dic₁₂	1	8	yes	complemented
76	C₂×C₄	C₂×D₁₂	1	1	yes	characteristic
77	C₂×C₄	C₂×D₁₂	1	4	yes	—
78	C₂×C₄	C₂×D₁₂	1	4	yes	—
79	C₂×C₄	C₂³×D₃	1	1	yes	characteristic
80	C₈	C₂×D₁₂	1	8	yes	—
81	C₂×C₃	#494	1	4	yes	complemented
82	C₂×C₃	C₂×#127	1	1	yes	characteristic
83	C₂×C₃	C₂²×Q₁₆	1	2	yes	—
84	C₂²	#874	1	2	yes	—
85	C₂²	C₂×Dic₁₂	1	4	yes	—
86	C₂²	C₂²×D₁₂	1	1	yes	characteristic
87	C₄	—	12	8	no	—
88	C₄	#874	1	2	yes	—
89	C₄	C₂×Dic₁₂	1	8	yes	complemented
90	C₄	C₂²×D₁₂	1	2	yes	—
91	C₃	C₂×#494	1	1	yes	characteristic, complemented, Sylow
92	C₂	#4699	1	4	yes	direct product factor
93	C₂	C₂×#874	1	1	yes	characteristic
94	C₂	C₂²×Dic₁₂	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×#494
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. #4699	C₂	direct (N × H)
41. C₂×C₃×C₄	Q₁₆	semidirect
67. C₃×C₄	C₂×Q₁₆	semidirect
75. C₂×C₄	Dic₁₂	semidirect
81. C₂×C₃	#494	semidirect
89. C₄	C₂×Dic₁₂	semidirect
91. C₃	C₂×#494	semidirect
92. C₂	#4699	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×Dic₁₂	2
C₂×#869	2
C₂×C₃×C₄×C₈	2
#4699	2
C₂×#494	3

Subgroups — C2×#4699 #78474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4699 #78474