Subgroups — #20292988

Order 6848.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812108	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812098	C₂	1	1	yes	maximal, characteristic
3	#16812033	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812031	C₂	1	1	yes	maximal, characteristic
5	#16812029	C₂	1	1	yes	maximal, characteristic
6	#16812019	C₂	1	1	yes	maximal, characteristic, complemented
7	#103×C₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₁₄	—	2	1	no	—
9	C₂×D₄₂₈	C₂²	1	1	yes	characteristic
10	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
12	Dic₁₀₇⋊C₄	—	2	1	no	—
13	(C₂×D₁₀₇)⋊C₄	—	2	1	no	—
14	(C₂×D₁₀₇)⋊C₄	—	2	1	no	—
15	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₇	—	2	1	no	—
20	Q₈×C₁₀₇	—	2	1	no	—
21	Q₈×C₁₀₇	—	2	1	no	—
22	C₂×C₄×C₁₀₇	—	2	1	no	—
23	C₂×C₄×C₁₀₇	—	2	1	no	—
24	C₂×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₇	—	2	1	no	—
26	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
28	D₄₂₈	—	2	1	no	—
29	D₄₂₈	—	2	1	no	—
30	Dic₂₁₄	—	4	2	no	—
31	C₈×C₁₀₇	—	2	1	no	—
32	C₁₀₇⋊C₈	—	2	1	no	—
33	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₀₇	—	4	1	no	—
35	C₂×D₁₀₇	—	4	1	no	—
36	C₂×D₁₀₇	—	4	1	no	—
37	C₄×C₁₀₇	—	4	1	no	—
38	C₄×C₁₀₇	—	4	1	no	—
39	C₄×C₁₀₇	#41	1	1	yes	characteristic
40	C₄×C₁₀₇	#41	1	1	yes	characteristic
41	Dic₁₀₇	—	2	1	no	—
42	Dic₁₀₇	—	2	1	no	—
43	Dic₁₀₇	—	4	1	no	—
44	C₂×C₁₀₇	#124	1	1	yes	characteristic
45	C₂×C₁₀₇	AGL(1,ℤ/8)	1	1	yes	characteristic
46	C₂×C₁₀₇	#137	1	1	yes	characteristic
47	D₁₀₇	—	8	1	no	—
48	C₁₀₇	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	107	1	no	maximal, Sylow
50	C₄⋊Q₈	—	107	1	no	—
51	#124	—	107	1	no	—
52	#103	—	107	1	no	—
53	#103	D₁₀₇	1	1	yes	characteristic, complemented
54	#102	—	107	1	no	—
55	#102	—	107	1	no	—
56	#97	—	107	1	no	—
57	C₂×Q₈	—	214	1	no	—
58	C₂×Q₈	C₂×D₁₀₇	1	1	yes	characteristic
59	C₂×D₄	—	107	1	no	—
60	C₂×C₈	—	107	1	no	—
61	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
62	C₄⋊C₄	—	107	1	no	—
63	C₄⋊C₄	—	214	1	no	—
64	C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
65	C₂²⋊C₄	—	214	1	no	—
66	C₂²⋊C₄	—	214	1	no	—
67	C₄²	—	107	1	no	—
68	C₂³	—	214	1	no	—
69	Q₈	—	2	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	428	2	no	—
72	D₄	—	214	1	no	—
73	D₄	—	214	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	107	1	no	—
77	C₂×C₄	—	107	1	no	—
78	C₂×C₄	—	214	1	no	—
79	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	214	1	no	—
82	C₂²	—	428	1	no	—
83	C₂²	—	428	1	no	—
84	C₂²	—	428	1	no	—
85	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	428	1	no	—
89	C₄	—	214	1	no	—
90	C₄	—	214	1	no	—
91	C₄	#13133817	1	1	yes	characteristic
92	C₄	#13133818	1	1	yes	characteristic
93	C₂	—	856	1	no	—
94	C₂	#16812095	1	1	yes	characteristic
95	C₂	#16812136	1	1	yes	characteristic
96	C₂	#16812141	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₂×C₄×C₁₀₇	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	#103×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	#103	D₁₀₇
hypocenter	C₁₀₇	#489
LCS	G ▷ C₂×C₄×C₁₀₇ ▷ C₂×C₁₀₇ ▷ C₁₀₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
1. #16812108	C₂	semidirect
3. #16812033	C₂	semidirect
6. #16812019	C₂	semidirect
7. #103×C₁₀₇	C₂	semidirect
48. C₁₀₇	#489	semidirect
53. #103	D₁₀₇	semidirect