Subgroups — C₂×#16813557 #20298643

Order 7232.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268631	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11744751	C₂	1	1	yes	maximal, characteristic
3	#16813557	C₂	1	4	yes	maximal, direct product factor
4	C₂×M₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
5	#14268631	—	2	1	no	—
6	#14268631	C₂²	1	2	yes	—
7	C₂×#11744751	—	2	1	no	—
8	C₂×#11744751	C₄	1	2	yes	—
9	C₂×#11744751	C₄	1	2	yes	—
10	C₂×#11744751	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
12	M₁₆×C₁₁₃	—	2	1	no	—
13	M₁₆×C₁₁₃	C₂²	1	2	yes	—
14	C₂×C₈×C₁₁₃	—	2	1	no	—
15	C₂³×C₁₁₃	Q₈	1	1	yes	characteristic
16	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₁₃	Q₈	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
22	C₈×C₁₁₃	—	2	2	no	—
23	#11744751	—	2	2	no	—
24	#11744751	C₂×C₄	1	4	yes	—
25	C₂²×C₁₁₃	—	2	2	no	—
26	C₂²×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂²×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
29	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
30	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₁₃	—	2	1	no	—
34	C₂×C₁₁₃	—	2	1	no	—
35	C₂×C₁₁₃	#108	1	2	yes	complemented
36	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₁₁₃	C₂×#108	1	1	yes	characteristic, complemented, Sylow
38	C₂×#108	—	113	1	no	maximal, Sylow
39	C₂×M₁₆	—	113	1	no	—
40	C₂×M₁₆	D₁₁₃	1	1	yes	characteristic
41	C₂²×C₈	—	113	1	no	—
42	#108	—	113	4	no	—
43	C₂²×C₄	C₂×D₁₁₃	1	1	yes	characteristic
44	M₁₆	—	2	1	no	—
45	M₁₆	—	113	2	no	—
46	M₁₆	—	226	1	no	—
47	M₁₆	C₂×D₁₁₃	1	2	yes	—
48	C₂×C₈	—	2	1	no	—
49	C₂×C₈	—	113	2	no	—
50	C₂×C₈	—	113	2	no	—
51	C₂×C₈	—	113	2	no	—
52	C₂×C₈	—	226	1	no	—
53	C₂³	Dic₂₂₆	1	1	yes	characteristic
54	C₂×C₄	Dic₂₂₆	1	1	yes	characteristic
55	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
56	C₂×C₄	C₄×D₁₁₃	1	1	yes	characteristic
57	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
58	C₂×C₄	C₂²⋊D₁₁₃	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
60	C₈	—	2	2	no	—
61	C₈	—	113	4	no	—
62	C₈	—	226	2	no	—
63	C₂²	—	2	2	no	—
64	C₂²	#14268626	1	1	yes	characteristic
65	C₂²	#14268626	1	1	yes	characteristic
66	C₂²	C₂×Dic₂₂₆	1	1	yes	characteristic
67	C₄	#14268626	1	1	yes	characteristic
68	C₄	#14268626	1	1	yes	characteristic
69	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
70	C₄	C₂×C₂²⋊D₁₁₃	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	2	1	no	—
73	C₂	#16813557	1	2	yes	direct product factor
74	C₂	C₂×#14268626	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₁₃
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	C₂×M₁₆×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₄⋊C₄
hypercenter	C₂×M₁₆	D₁₁₃
hypocenter	C₁₁₃	C₂×#108
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
3. #16813557	C₂	direct (N × H)
35. C₂×C₁₁₃	#108	semidirect
37. C₁₁₃	C₂×#108	semidirect
73. C₂	#16813557	direct (N × H)

Subgroups — C2×#16813557 #20298643

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#16813557 #20298643