Subgroups — #20292731

Order 6848.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133808	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₀₇	C₂	1	1	yes	maximal, characteristic
3	#16812074	C₂	1	1	yes	maximal, characteristic
4	#16812040	C₂	1	1	yes	maximal, characteristic
5	#16812034	C₂	1	1	yes	maximal, characteristic
6	#16812019	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₀₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₁₄	C₂²	1	1	yes	characteristic
9	#13133808	C₄	1	4	yes	complemented
10	C₂×C₁₀₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₇	—	2	1	no	—
12	C₄⋊Dic₁₀₇	C₂²	1	1	yes	characteristic
13	Dic₁₀₇⋊C₄	—	2	1	no	—
14	C₄×Dic₁₀₇	—	2	1	no	—
15	C₄×Dic₁₀₇	—	2	1	no	—
16	C₄×Dic₁₀₇	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₀₇	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₁₀₇	C₂²	1	1	yes	characteristic
20	Q₈×C₁₀₇	—	2	1	no	—
21	Q₈×C₁₀₇	C₂×C₄	1	2	yes	—
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	—	2	1	no	—
27	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
28	C₂×Dic₁₀₇	D₄	1	1	yes	characteristic
29	Dic₂₁₄	—	2	1	no	—
30	Dic₂₁₄	C₂×C₄	1	2	yes	—
31	C₈×C₁₀₇	—	2	1	no	—
32	C₁₀₇⋊C₈	C₂×C₄	1	2	yes	—
33	C₂²×C₁₀₇	C₂×D₄	1	1	yes	characteristic
34	C₄×C₁₀₇	—	2	2	no	—
35	C₄×C₁₀₇	—	4	1	no	—
36	C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
37	C₄×C₁₀₇	#41	1	1	yes	characteristic
38	Dic₁₀₇	—	2	2	no	—
39	Dic₁₀₇	—	2	1	no	—
40	Dic₁₀₇	—	2	1	no	—
41	Dic₁₀₇	—	4	1	no	—
42	C₂×C₁₀₇	C₄×D₄	1	1	yes	characteristic
43	C₂×C₁₀₇	#137	1	1	yes	characteristic
44	C₂×C₁₀₇	#137	1	1	yes	characteristic
45	C₁₀₇	#441	1	1	yes	characteristic, complemented, Sylow
46	#441	—	107	1	no	maximal, Sylow
47	C₂×Q₁₆	—	107	1	no	—
48	C₄×Q₈	—	107	1	no	—
49	C₄×Q₈	—	107	1	no	—
50	#106	—	107	1	no	—
51	#103	—	107	1	no	—
52	#103	D₁₀₇	1	1	yes	characteristic
53	#97	—	107	1	no	—
54	C₂×Q₈	—	107	1	no	—
55	C₂×Q₈	C₂×D₁₀₇	1	1	yes	characteristic
56	Q₁₆	—	107	4	no	—
57	C₂×C₈	—	107	1	no	—
58	C₂×C₈	C₂×D₁₀₇	1	1	yes	characteristic
59	C₄⋊C₄	—	107	1	no	—
60	C₄⋊C₄	—	214	1	no	—
61	C₄⋊C₄	—	214	1	no	—
62	C₄⋊C₄	C₂×D₁₀₇	1	1	yes	characteristic
63	C₄²	—	107	1	no	—
64	C₄²	—	214	1	no	—
65	C₄²	—	214	1	no	—
66	Q₈	—	2	1	no	—
67	Q₈	—	107	2	no	—
68	Q₈	—	214	1	no	—
69	Q₈	C₄×D₁₀₇	1	2	yes	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	107	1	no	—
73	C₂×C₄	—	107	1	no	—
74	C₂×C₄	—	214	1	no	—
75	C₂×C₄	—	214	1	no	—
76	C₂×C₄	C₂²×D₁₀₇	1	1	yes	characteristic
77	C₈	—	2	1	no	—
78	C₈	—	107	2	no	—
79	C₂²	D₄×D₁₀₇	1	1	yes	characteristic
80	C₄	—	2	2	no	—
81	C₄	—	4	1	no	—
82	C₄	—	428	1	no	—
83	C₄	—	214	2	no	—
84	C₄	—	214	1	no	—
85	C₄	—	214	1	no	—
86	C₄	C₂×C₄×D₁₀₇	1	1	yes	characteristic
87	C₄	#13133817	1	1	yes	characteristic
88	C₂	(C₂²⋊D₁₀₇)⋊C₄	1	1	yes	characteristic
89	C₂	#16812138	1	1	yes	characteristic
90	C₂	#16812141	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₇
commutator	C₄×C₁₀₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₀₇
Fitting	#103×C₁₀₇	C₂
socle	C₂²×C₁₀₇	C₂×D₄
hypercenter	#103	D₁₀₇
hypocenter	C₁₀₇	#441
LCS	G ▷ 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
9. #13133808	C₄	semidirect
45. C₁₀₇	#441	semidirect