Subgroups — C₃⋊#1273 #67653

Order 384.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₃⋊C₈	C₂	1	2	yes	maximal
3	#1273	—	3	1	no	maximal, Sylow
4	C₂²×C₃×C₈	C₄	1	2	yes	—
5	C₂×C₃×C₄²	C₂²	1	1	yes	characteristic
6	C₂²×C₃⋊C₈	C₄	1	4	yes	—
7	C₃×C₄×C₈	—	2	2	no	—
8	C₄×C₃⋊C₈	—	2	2	no	—
9	C₄×C₃⋊C₈	—	2	2	no	—
10	C₂×C₄×C₈	—	3	2	no	—
11	C₂×C₄×C₈	D₃	1	1	yes	characteristic
12	C₂²×C₃×C₄	C₂×C₄	1	2	yes	—
13	C₂²×C₃×C₄	C₂×C₄	1	1	yes	characteristic
14	C₂×C₃×C₈	—	2	2	no	—
15	C₂×C₃×C₈	—	2	2	no	—
16	C₂×C₃×C₈	C₈	1	4	yes	complemented
17	C₃×C₄²	D₄	1	1	yes	characteristic
18	C₃×C₄²	D₄	1	2	yes	—
19	C₃×C₄²	Q₈	1	1	yes	characteristic
20	C₂×C₃⋊C₈	—	2	4	no	—
21	C₂×C₃⋊C₈	—	2	4	no	—
22	C₂×C₃⋊C₈	C₈	1	8	yes	complemented
23	C₂²×C₈	—	3	4	no	—
24	C₂²×C₈	Dic₃	1	2	yes	—
25	C₂×C₄²	C₂×D₃	1	1	yes	characteristic
26	C₄×C₈	—	2	2	no	—
27	C₄×C₈	—	6	2	no	—
28	C₄×C₈	—	6	2	no	—
29	C₂³×C₃	C₄²	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂²⋊C₄	1	2	yes	—
31	C₂×C₃×C₄	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₃×C₄	C₄⋊C₄	1	2	yes	—
33	C₂×C₃×C₄	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₃×C₄	C₂×C₈	1	4	yes	—
35	C₂×C₃×C₄	C₂×C₈	1	2	yes	—
36	C₂×C₃×C₄	M₁₆	1	4	yes	—
37	C₂×C₃×C₄	M₁₆	1	2	yes	—
38	C₃×C₈	—	2	4	no	—
39	C₃⋊C₈	—	2	8	no	—
40	C₂²×C₄	C₄×D₃	1	2	yes	—
41	C₂²×C₄	C₂×Dic₃	1	1	yes	characteristic
42	C₂×C₈	—	2	2	no	—
43	C₂×C₈	—	2	2	no	—
44	C₂×C₈	—	3	8	no	—
45	C₂×C₈	—	6	4	no	—
46	C₂×C₈	—	6	4	no	—
47	C₂×C₈	C₃⋊C₈	1	4	yes	complemented
48	C₄²	Dic₆	1	1	yes	characteristic
49	C₄²	D₁₂	1	1	yes	characteristic
50	C₄²	#67	1	2	yes	—
51	C₂²×C₃	#95	1	1	yes	characteristic
52	C₂²×C₃	C₄×C₈	1	1	yes	characteristic
53	C₂²×C₃	C₄×C₈	1	2	yes	—
54	C₂²×C₃	#97	1	1	yes	characteristic
55	C₂²×C₃	#97	1	2	yes	—
56	C₃×C₄	C₂²⋊C₈	1	4	yes	—
57	C₃×C₄	C₂²⋊C₈	1	2	yes	—
58	C₃×C₄	C₄⋊C₈	1	2	yes	—
59	C₃×C₄	C₄⋊C₈	1	4	yes	—
60	C₂³	C₄×Dic₃	1	1	yes	characteristic
61	C₂×C₄	D₃×C₈	1	4	yes	—
62	C₂×C₄	ΓL(1,𝔽₂₅)	1	4	yes	—
63	C₂×C₄	C₂×C₃⋊C₈	1	2	yes	—
64	C₂×C₄	#208	1	2	yes	—
65	C₂×C₄	Dic₃⋊C₄	1	2	yes	—
66	C₂×C₄	C₄⋊Dic₃	1	1	yes	characteristic
67	C₂×C₄	(C₂×D₃)⋊C₄	1	2	yes	—
68	C₂×C₄	#217	1	1	yes	characteristic
69	C₈	—	2	4	no	—
70	C₈	—	6	8	no	—
71	C₂×C₃	C₈²	1	1	yes	characteristic
72	C₂×C₃	#322	1	2	yes	—
73	C₂×C₃	#322	1	1	yes	characteristic
74	C₂×C₃	#336	1	1	yes	characteristic
75	C₂×C₃	#336	1	2	yes	—
76	C₂²	C₄×C₃⋊C₈	1	1	yes	characteristic
77	C₂²	#803	1	1	yes	characteristic
78	C₂²	C₈×Dic₃	1	2	yes	—
79	C₂²	#815	1	2	yes	—
80	C₂²	C₃⋊#95	1	1	yes	characteristic
81	C₄	C₄⋊(C₃⋊C₈)	1	2	yes	—
82	C₄	Dic₃⋊C₈	1	4	yes	—
83	C₄	(C₂×D₃)⋊C₈	1	4	yes	—
84	C₄	#830	1	2	yes	—
85	C₃	#1273	1	1	yes	characteristic, complemented, Sylow
86	C₂	C₈×C₃⋊C₈	1	1	yes	characteristic
87	C₂	#4454	1	2	yes	—
88	C₂	#4455	1	1	yes	characteristic
89	C₂	#4524	1	1	yes	characteristic
90	C₂	#4550	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂×D₃
commutator	C₂×C₃	C₈²
Fitting	C₂×C₃×C₄×C₈	C₂
socle, prime radical	C₂³×C₃	C₄²
cosocle	C₂×C₃×C₄²	C₂²
hypercenter	C₂×C₄×C₈	D₃
hypocenter	C₃	#1273
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
16. C₂×C₃×C₈	C₈	semidirect
22. C₂×C₃⋊C₈	C₈	semidirect
47. C₂×C₈	C₃⋊C₈	semidirect
85. C₃	#1273	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₈	2
C₂×C₄×C₃⋊C₈	2
#1273	3

Subgroups — C3⋊#1273 #67653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊#1273 #67653