Subgroups — C₃×#89454 #13055115

Order 1344.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6432	C₂	1	2	yes	maximal
2	C₃×C₄×C₇×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#6392	C₂	1	4	yes	maximal
4	#89454	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×Dic₁₄	—	2	2	no	—
6	C₂×C₃×C₇×C₈	C₂²	1	2	yes	—
7	C₃×C₄²×C₇	C₂²	1	1	yes	characteristic
8	C₃×C₄⋊Dic₇	—	2	2	no	—
9	C₃×C₄⋊Dic₇	C₂²	1	4	yes	—
10	#6432	C₂×C₃	1	2	yes	—
11	C₄×C₇×C₈	C₂×C₃	1	1	yes	characteristic
12	#6392	C₂×C₃	1	4	yes	—
13	C₃×#500	—	7	1	no	maximal, Hall
14	C₂×C₃×C₄×C₇	D₄	1	1	yes	characteristic
15	C₂×C₃×C₄×C₇	D₄	1	1	yes	characteristic
16	C₂×C₃×C₄×C₇	C₂³	1	1	yes	characteristic
17	C₂×C₃×Dic₇	—	2	4	no	—
18	C₃×Dic₁₄	—	4	4	no	—
19	C₃×C₇×C₈	Q₈	1	4	yes	complemented
20	C₂×Dic₁₄	—	2	2	no	—
21	C₂×C₇×C₈	C₂²×C₃	1	2	yes	—
22	C₄²×C₇	C₂²×C₃	1	1	yes	characteristic
23	C₄⋊Dic₇	—	2	2	no	—
24	C₄⋊Dic₇	C₂²×C₃	1	4	yes	—
25	C₃×C₄⋊Q₈	—	7	2	no	—
26	C₃×#107	—	7	4	no	—
27	C₃×C₄×C₈	D₇	1	1	yes	characteristic
28	C₂²×C₃×C₇	C₂×D₄	1	1	yes	characteristic
29	C₃×C₄×C₇	D₈	1	2	yes	—
30	C₃×C₄×C₇	Q₁₆	1	2	yes	—
31	C₃×C₄×C₇	C₂×Q₈	1	2	yes	—
32	C₃×Dic₇	—	4	4	no	—
33	#500	—	7	1	no	Sylow
34	C₂×C₄×C₇	C₃×D₄	1	1	yes	characteristic
35	C₂×C₄×C₇	C₃×D₄	1	1	yes	characteristic
36	C₂×C₄×C₇	C₂³×C₃	1	1	yes	characteristic
37	C₂×Dic₇	—	2	4	no	—
38	Dic₁₄	—	4	4	no	—
39	C₇×C₈	C₃×Q₈	1	4	yes	complemented
40	C₂×C₃×Q₈	—	14	2	no	—
41	C₂×C₃×C₈	C₂×D₇	1	2	yes	—
42	C₃×C₄⋊C₄	—	7	4	no	—
43	C₃×C₄⋊C₄	—	14	2	no	—
44	C₃×C₄²	C₂×D₇	1	1	yes	characteristic
45	C₂×C₃×C₇	C₄⋊Q₈	1	1	yes	characteristic
46	C₂×C₃×C₇	C₂×D₈	1	1	yes	characteristic
47	C₂×C₃×C₇	C₂×Q₁₆	1	1	yes	characteristic
48	C₄⋊Q₈	—	7	2	no	—
49	#107	—	7	4	no	—
50	C₄×C₈	C₃×D₇	1	1	yes	characteristic
51	C₂²×C₇	C₂×C₃×D₄	1	1	yes	characteristic
52	C₄×C₇	C₃×D₈	1	2	yes	—
53	C₄×C₇	C₃×Q₁₆	1	2	yes	—
54	C₄×C₇	C₂×C₃×Q₈	1	2	yes	—
55	Dic₇	—	4	4	no	—
56	C₃×Q₈	—	28	4	no	—
57	C₂×C₃×C₄	—	14	4	no	—
58	C₂×C₃×C₄	D₂₈	1	1	yes	characteristic
59	C₂×C₃×C₄	D₂₈	1	1	yes	characteristic
60	C₂×C₃×C₄	C₂²×D₇	1	1	yes	characteristic
61	C₃×C₈	Dic₁₄	1	4	yes	complemented
62	C₃×C₇	#500	1	1	yes	characteristic, complemented, Hall
63	C₂×Q₈	—	14	2	no	—
64	C₂×C₈	C₂×C₃×D₇	1	2	yes	—
65	C₄⋊C₄	—	7	4	no	—
66	C₄⋊C₄	—	14	2	no	—
67	C₄²	C₂×C₃×D₇	1	1	yes	characteristic
68	C₂×C₇	C₃×C₄⋊Q₈	1	1	yes	characteristic
69	C₂×C₇	C₂×C₃×D₈	1	1	yes	characteristic
70	C₂×C₇	C₂×C₃×Q₁₆	1	1	yes	characteristic
71	C₂²×C₃	C₂×D₂₈	1	1	yes	characteristic
72	C₃×C₄	—	28	4	no	—
73	C₃×C₄	D₅₆	1	2	yes	—
74	C₃×C₄	Dic₂₈	1	2	yes	—
75	C₃×C₄	C₂×Dic₁₄	1	2	yes	—
76	Q₈	—	28	4	no	—
77	C₂×C₄	—	14	4	no	—
78	C₂×C₄	C₃×D₂₈	1	1	yes	characteristic
79	C₂×C₄	C₃×D₂₈	1	1	yes	characteristic
80	C₂×C₄	C₂²×C₃×D₇	1	1	yes	characteristic
81	C₈	C₃×Dic₁₄	1	4	yes	complemented
82	C₇	C₃×#500	1	1	yes	characteristic, complemented, Sylow
83	C₂×C₃	#6432	1	1	yes	characteristic
84	C₂×C₃	C₂×D₅₆	1	1	yes	characteristic
85	C₂×C₃	C₂×Dic₂₈	1	1	yes	characteristic
86	C₂²	C₂×C₃×D₂₈	1	1	yes	characteristic
87	C₄	—	28	4	no	—
88	C₄	C₃×D₅₆	1	2	yes	—
89	C₄	C₃×Dic₂₈	1	2	yes	—
90	C₄	C₂×C₃×Dic₁₄	1	2	yes	—
91	C₃	#89454	1	1	yes	characteristic, direct product factor, Sylow
92	C₂	C₃×#6432	1	1	yes	characteristic
93	C₂	C₂×C₃×D₅₆	1	1	yes	characteristic
94	C₂	C₂×C₃×Dic₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₂₈
commutator, cosocle	C₂×C₄×C₇	C₂³×C₃
Frattini	C₂×C₄	C₂²×C₃×D₇
Fitting	C₃×C₄×C₇×C₈	C₂
socle, prime radical	C₂²×C₃×C₇	C₂×D₄
hypercenter	C₃×C₄×C₈	D₇
hypocenter	C₇	C₃×#500
LCS	G ▷ C₂×C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #89454	C₃	direct (N × H)
19. C₃×C₇×C₈	Q₈	semidirect
39. C₇×C₈	C₃×Q₈	semidirect
61. C₃×C₈	Dic₁₄	semidirect
62. C₃×C₇	#500	semidirect
81. C₈	C₃×Dic₁₄	semidirect
82. C₇	C₃×#500	semidirect
91. C₃	#89454	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#6432	2
C₃×C₄×C₇×C₈	2
C₃×#6392	2
#89454	3
C₃×#500	7

Subgroups — C3×#89454 #13055115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#89454 #13055115