Subgroups — #20295234

Order 6976.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182019	C₂	1	1	yes	maximal, characteristic
2	#16812697	C₂	1	1	yes	maximal, characteristic
3	Q₈×Dic₁₀₉	C₂	1	1	yes	maximal, characteristic
4	#16812628	C₂	1	1	yes	maximal, characteristic
5	#16812624	C₂	1	1	yes	maximal, characteristic
6	#16812623	C₂	1	1	yes	maximal, characteristic
7	C₂×Q₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
9	#13182019	—	2	2	no	—
10	C₂×#11724784	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₉	—	2	1	no	—
12	C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
13	#13182008	—	2	1	no	—
14	#13182008	—	2	1	no	—
15	C₄×Dic₁₀₉	—	2	1	no	—
16	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
19	Q₁₆×C₁₀₉	—	2	2	no	—
20	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
21	Q₈×C₁₀₉	—	2	1	no	—
22	Q₈×C₁₀₉	—	2	1	no	—
23	Q₈×C₁₀₉	—	2	1	no	—
24	Q₈×C₁₀₉	D₄	1	2	yes	—
25	C₂×C₄×C₁₀₉	—	2	1	no	—
26	C₂×C₄×C₁₀₉	—	2	1	no	—
27	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
28	C₂×Dic₁₀₉	—	2	1	no	—
29	C₂×Dic₁₀₉	—	2	1	no	—
30	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
31	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
32	Dic₂₁₈	—	2	1	no	—
33	Dic₂₁₈	—	2	1	no	—
34	C₈×C₁₀₉	—	2	1	no	—
35	#11724784	—	2	1	no	—
36	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₀₉	—	2	2	no	—
38	C₄×C₁₀₉	—	4	1	no	—
39	C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
40	C₄×C₁₀₉	#41	1	1	yes	characteristic
41	Dic₁₀₉	—	2	1	no	—
42	Dic₁₀₉	—	4	1	no	—
43	Dic₁₀₉	—	4	1	no	—
44	Dic₁₀₉	Q₁₆	1	2	yes	complemented
45	C₂×C₁₀₉	#121	1	1	yes	characteristic
46	C₂×C₁₀₉	C₂×Q₁₆	1	1	yes	characteristic
47	C₂×C₁₀₉	#137	1	1	yes	characteristic
48	C₁₀₉	#462	1	1	yes	characteristic, complemented, Sylow
49	#462	—	109	1	no	maximal, Sylow
50	C₂×Q₁₆	—	109	1	no	—
51	C₂×Q₁₆	D₁₀₉	1	1	yes	characteristic
52	C₄⋊Q₈	—	109	1	no	—
53	C₄×Q₈	—	109	1	no	—
54	C₄⋊C₈	—	109	1	no	—
55	#103	—	109	1	no	—
56	#103	—	109	1	no	—
57	C₂×Q₈	—	109	1	no	—
58	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
59	C₂×Q₈	C₂×D₁₀₉	1	1	yes	characteristic
60	Q₁₆	—	2	2	no	—
61	Q₁₆	—	218	2	no	—
62	C₂×C₈	—	109	1	no	—
63	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
64	C₄⋊C₄	—	109	1	no	—
65	C₄⋊C₄	—	218	1	no	—
66	C₄⋊C₄	—	218	1	no	—
67	C₄⋊C₄	—	218	1	no	—
68	C₄²	—	109	1	no	—
69	C₄²	—	218	1	no	—
70	Q₈	—	2	1	no	—
71	Q₈	—	2	1	no	—
72	Q₈	—	2	1	no	—
73	Q₈	—	218	1	no	—
74	Q₈	—	218	1	no	—
75	Q₈	C₂²⋊D₁₀₉	1	2	yes	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	109	1	no	—
79	C₂×C₄	—	109	1	no	—
80	C₂×C₄	—	218	1	no	—
81	C₂×C₄	—	218	1	no	—
82	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	218	1	no	—
85	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
86	C₄	—	2	2	no	—
87	C₄	—	4	1	no	—
88	C₄	—	109	2	no	—
89	C₄	—	436	1	no	—
90	C₄	—	436	1	no	—
91	C₄	—	218	1	no	—
92	C₄	C₂×C₂²⋊D₁₀₉	1	1	yes	characteristic
93	C₄	#13182028	1	1	yes	characteristic
94	C₂	#16812671	1	1	yes	characteristic
95	C₂	Q₁₆×D₁₀₉	1	1	yes	characteristic
96	C₂	#16812731	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	C₂×Q₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	C₂×Q₁₆	D₁₀₉
hypocenter	C₁₀₉	#462
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
44. Dic₁₀₉	Q₁₆	semidirect
48. C₁₀₉	#462	semidirect