Subgroups — #107×D₁₁₃ #20298630

Order 7232.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₁₃	C₂	1	2	yes	maximal
3	#16813556	C₂	1	1	yes	maximal, characteristic, complemented
4	#16813555	C₂	1	2	yes	maximal, complemented
5	#107×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₁₁₃	—	2	2	no	—
7	C₂×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
8	C₂×#11744751	C₂²	1	1	yes	characteristic
9	C₈×D₁₁₃	C₄	1	4	yes	complemented
10	C₄⋊Dic₁₁₃	C₂²	1	2	yes	—
11	#14268626	—	2	2	no	—
12	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
14	C₂²×D₁₁₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₁₃	—	2	2	no	—
16	C₂×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₁₃	—	2	2	no	—
18	C₂×Dic₁₁₃	D₄	1	1	yes	characteristic
19	C₄×D₁₁₃	—	4	4	no	—
20	C₄×D₁₁₃	C₂×C₄	1	2	yes	—
21	C₄×D₁₁₃	Q₈	1	2	yes	—
22	C₈×C₁₁₃	C₂×C₄	1	2	yes	complemented
23	#11744751	C₂×C₄	1	2	yes	complemented
24	C₂²×C₁₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₁₁₃	C₄⋊C₄	1	2	yes	—
26	C₂×D₁₁₃	D₈	1	2	yes	—
27	C₂×D₁₁₃	Q₁₆	1	2	yes	—
28	C₄×C₁₁₃	—	4	2	no	—
29	C₄×C₁₁₃	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₁₁₃	C₂×Q₈	1	1	yes	characteristic
31	Dic₁₁₃	—	4	2	no	—
32	Dic₁₁₃	C₄⋊C₄	1	2	yes	—
33	C₂×C₁₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₁₁₃	C₂×D₈	1	1	yes	characteristic
35	C₂×C₁₁₃	C₂×Q₁₆	1	1	yes	characteristic
36	D₁₁₃	#107	1	4	yes	direct product factor
37	C₁₁₃	C₂×#107	1	1	yes	characteristic, complemented, Sylow
38	C₂×#107	—	113	1	no	maximal, Sylow
39	C₂²×C₈	—	113	1	no	—
40	C₂×C₄⋊C₄	—	113	2	no	—
41	#107	—	113	1	no	—
42	#107	—	113	2	no	—
43	#107	D₁₁₃	1	1	yes	characteristic, direct product factor
44	C₂²×C₄	—	113	1	no	—
45	C₂²×C₄	—	226	2	no	—
46	C₂×C₈	—	113	1	no	—
47	C₂×C₈	—	113	4	no	—
48	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
49	C₄⋊C₄	—	113	2	no	—
50	C₄⋊C₄	—	226	2	no	—
51	C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
52	C₂³	—	113	1	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	113	1	no	—
55	C₂×C₄	—	113	2	no	—
56	C₂×C₄	—	113	2	no	—
57	C₂×C₄	—	452	4	no	—
58	C₂×C₄	—	226	2	no	—
59	C₂×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
60	C₈	—	113	2	no	—
61	C₈	C₄×D₁₁₃	1	2	yes	complemented
62	C₂²	—	113	2	no	—
63	C₂²	—	113	2	no	—
64	C₂²	—	113	2	no	—
65	C₂²	D₄×D₁₁₃	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	113	2	no	—
68	C₄	—	452	2	no	—
69	C₄	C₂×C₄×D₁₁₃	1	1	yes	characteristic
70	C₄	Q₈×D₁₁₃	1	1	yes	characteristic
71	C₂	—	113	4	no	—
72	C₂	C₄⋊C₄×D₁₁₃	1	1	yes	characteristic
73	C₂	D₈×D₁₁₃	1	1	yes	characteristic
74	C₂	Q₁₆×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₁₃
commutator	C₄×C₁₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₁₃
Fitting	#107×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂×D₄
hypercenter	#107	D₁₁₃
hypocenter	C₁₁₃	C₂×#107
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
3. #16813556	C₂	semidirect
4. #16813555	C₂	semidirect
5. #107×C₁₁₃	C₂	semidirect
9. C₈×D₁₁₃	C₄	semidirect
22. C₈×C₁₁₃	C₂×C₄	semidirect
23. #11744751	C₂×C₄	semidirect
36. D₁₁₃	#107	direct (N × H)
37. C₁₁₃	C₂×#107	semidirect
43. #107	D₁₁₃	direct (N × H)
61. C₈	C₄×D₁₁₃	semidirect

Subgroups — #107×D113 #20298630

Conjugacy classes of subgroups

Complements

Subgroups — #107×D₁₁₃ #20298630