Subgroups — C₂×#11924241 #72245672

Order 2352.

540 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⋊(C₇⋊D₇)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₇⋊D₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₇²×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#11924241	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₄⋊(C₇⋊D₇)	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₇²	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊(C₇⋊D₇)	—	2	2	no	—
8	C₂×C₃⋊(C₇⋊D₇)	C₂²	1	2	yes	complemented
9	C₂×C₃×C₇⋊D₇	—	2	2	no	—
10	C₂×C₃×C₇⋊D₇	C₂²	1	2	yes	complemented
11	C₇²×Dic₃	C₂²	1	2	yes	complemented
12	C₂²×C₇⋊D₇	—	3	1	no	—
13	C₂²×C₇⋊D₇	D₃	1	1	yes	characteristic, complemented
14	C₂×C₄×C₇²	—	3	1	no	—
15	C₄⋊(C₇⋊D₇)	—	3	4	no	—
16	C₂×#4246	—	7	8	no	maximal
17	C₂×C₃×C₇²	D₄	1	2	yes	complemented
18	C₂×C₃×C₇²	C₂³	1	1	yes	characteristic
19	C₃⋊(C₇⋊D₇)	—	2	2	no	—
20	C₃×C₇⋊D₇	—	2	2	no	—
21	C₂²×C₇²	C₂×D₃	1	1	yes	characteristic
22	C₂×C₇⋊D₇	—	2	2	no	—
23	C₂×C₇⋊D₇	—	3	2	no	—
24	C₂×C₇⋊D₇	—	6	2	no	—
25	C₂×C₇⋊D₇	C₂×D₃	1	2	yes	complemented
26	C₄×C₇²	—	3	2	no	—
27	C₂²×D₂₁	—	7	8	no	—
28	C₂²×C₃×D₇	—	7	8	no	—
29	C₂×C₇×Dic₃	D₇	1	8	yes	complemented
30	#4246	—	7	32	no	—
31	C₃×C₇²	C₂×D₄	1	1	yes	characteristic, complemented, Hall
32	C₂×D₂₈	—	21	8	no	—
33	C₂×C₇²	#67	1	2	yes	complemented
34	C₂×C₇²	C₂²×D₃	1	1	yes	characteristic
35	C₇⋊D₇	—	2	2	no	—
36	C₇⋊D₇	—	6	2	no	—
37	C₂²×C₃×C₇	C₂×D₇	1	8	yes	—
38	C₂×D₂₁	—	7	16	no	—
39	C₂×D₂₁	—	14	16	no	—
40	C₂×C₃×D₇	—	7	16	no	—
41	C₂×C₃×D₇	—	14	16	no	—
42	C₇×Dic₃	C₂×D₇	1	16	yes	complemented
43	C₂²×D₇	—	7	8	no	—
44	C₂²×D₇	—	21	8	no	—
45	C₂×C₄×C₇	—	3	8	no	—
46	D₂₈	—	21	32	no	—
47	C₇²	C₂×#67	1	1	yes	characteristic, complemented, Sylow
48	C₂×#67	—	49	1	no	Hall
49	C₂×C₃×C₇	D₂₈	1	16	yes	complemented
50	C₂×C₃×C₇	C₂²×D₇	1	8	yes	—
51	D₂₁	—	14	16	no	—
52	C₃×D₇	—	14	16	no	—
53	C₂²×C₇	D₃×D₇	1	8	yes	—
54	C₂×D₇	—	7	16	no	—
55	C₂×D₇	—	14	16	no	—
56	C₂×D₇	—	21	16	no	—
57	C₂×D₇	—	42	16	no	—
58	C₄×C₇	—	3	16	no	—
59	C₂³×C₃	—	49	1	no	—
60	C₂²×D₃	—	49	1	no	—
61	#67	—	49	4	no	—
62	C₂×Dic₃	C₇⋊D₇	1	1	yes	characteristic, complemented
63	C₃×C₇	C₂×D₂₈	1	8	yes	complemented
64	C₂×D₄	—	147	1	no	Sylow
65	C₂×C₇	#4246	1	16	yes	complemented
66	C₂×C₇	C₂×D₃×D₇	1	8	yes	—
67	D₇	—	14	16	no	—
68	D₇	—	42	16	no	—
69	C₂²×C₃	—	49	2	no	—
70	C₂²×C₃	—	98	2	no	—
71	C₂²×C₃	C₂×C₇⋊D₇	1	1	yes	characteristic
72	C₂×D₃	—	49	2	no	—
73	C₂×D₃	—	98	2	no	—
74	Dic₃	C₂×C₇⋊D₇	1	2	yes	complemented
75	C₂³	—	49	1	no	—
76	C₂³	—	147	1	no	—
77	D₄	—	147	4	no	—
78	C₂×C₄	—	3	1	no	—
79	C₇	C₂×#4246	1	8	yes	complemented
80	C₂×C₃	—	98	2	no	—
81	C₂×C₃	C₄⋊(C₇⋊D₇)	1	2	yes	complemented
82	C₂×C₃	C₂²×C₇⋊D₇	1	1	yes	characteristic
83	D₃	—	98	2	no	—
84	C₂²	—	294	2	no	—
85	C₂²	—	49	2	no	—
86	C₂²	—	98	2	no	—
87	C₂²	—	147	2	no	—
88	C₂²	D₃×C₇⋊D₇	1	1	yes	characteristic
89	C₄	—	3	2	no	—
90	C₃	C₂×C₄⋊(C₇⋊D₇)	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	294	2	no	—
92	C₂	—	98	2	no	—
93	C₂	#11924241	1	2	yes	direct product factor
94	C₂	C₂×D₃×C₇⋊D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×C₇⋊D₇
commutator, cosocle	C₂×C₃×C₇²	C₂³
Frattini	C₂	C₂×D₃×C₇⋊D₇
Fitting, socle	C₂²×C₃×C₇²	C₂²
hypocenter	C₃×C₇²	C₂×D₄
LCS	G ▷ C₂×C₃×C₇² ▷ C₃×C₇²
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃⋊(C₇⋊D₇)	C₂	semidirect
2. C₂²×C₃×C₇⋊D₇	C₂	semidirect
3. C₂×C₇²×Dic₃	C₂	semidirect
4. #11924241	C₂	direct (N × H)
8. C₂×C₃⋊(C₇⋊D₇)	C₂²	semidirect
10. C₂×C₃×C₇⋊D₇	C₂²	semidirect
11. C₇²×Dic₃	C₂²	semidirect
13. C₂²×C₇⋊D₇	D₃	semidirect
17. C₂×C₃×C₇²	D₄	semidirect
25. C₂×C₇⋊D₇	C₂×D₃	semidirect
29. C₂×C₇×Dic₃	D₇	semidirect
31. C₃×C₇²	C₂×D₄	semidirect
33. C₂×C₇²	#67	semidirect
42. C₇×Dic₃	C₂×D₇	semidirect
47. C₇²	C₂×#67	semidirect
49. C₂×C₃×C₇	D₂₈	semidirect
62. C₂×Dic₃	C₇⋊D₇	semidirect
63. C₃×C₇	C₂×D₂₈	semidirect
65. C₂×C₇	#4246	semidirect
74. Dic₃	C₂×C₇⋊D₇	semidirect
79. C₇	C₂×#4246	semidirect
81. C₂×C₃	C₄⋊(C₇⋊D₇)	semidirect
90. C₃	C₂×C₄⋊(C₇⋊D₇)	semidirect
93. C₂	#11924241	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×C₃⋊(C₇⋊D₇)	2
C₂²×C₃×C₇⋊D₇	2
C₂×C₇²×Dic₃	2
#11924241	2
C₂×C₄⋊(C₇⋊D₇)	3
C₂×#4246	7

Subgroups — C2×#11924241 #72245672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11924241 #72245672