Subgroups — #20296041

Order 6976.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13182039	C₂	1	1	yes	maximal, characteristic
2	D₁₀₉⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#16812770	C₂	1	2	yes	maximal, complemented
4	#16812769	C₂	1	2	yes	maximal, complemented
5	M₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic
6	#13182039	—	2	1	no	—
7	#13182039	C₂²	1	1	yes	characteristic
8	#13182039	C₂²	1	2	yes	—
9	#13182039	C₂²	1	1	yes	characteristic
10	#13182038	—	2	1	no	—
11	D₁₀₉⋊C₈	—	2	1	no	—
12	C₂×#11724786	—	2	1	no	—
13	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
14	#13182013	C₄	1	1	yes	characteristic
15	#13182012	C₄	1	2	yes	—
16	C₈×D₁₀₉	C₂²	1	2	yes	—
17	M₁₆×C₁₀₉	C₄	1	1	yes	characteristic
18	C₂²×D₁₀₉	Q₈	1	1	yes	characteristic
19	C₂×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
21	C₄×D₁₀₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₁₀₉	D₄	1	1	yes	characteristic
23	C₄×D₁₀₉	Q₈	1	1	yes	characteristic
24	C₄×D₁₀₉	C₂³	1	1	yes	characteristic
25	#11724786	—	2	2	no	—
26	#11724786	—	2	1	no	—
27	#11724786	—	2	1	no	—
28	C₈×C₁₀₉	C₂×C₄	1	2	yes	—
29	#11724784	C₂×C₄	1	2	yes	—
30	C₂²×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₁₀₉	—	4	1	no	—
32	C₂×D₁₀₉	C₄⋊C₄	1	1	yes	characteristic
33	C₂×D₁₀₉	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₀₉	C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
36	Dic₁₀₉	C₄⋊C₄	1	1	yes	characteristic
37	Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₁₀₉	—	2	1	no	—
39	C₂×C₁₀₉	C₂×C₄⋊C₄	1	1	yes	characteristic
40	D₁₀₉	—	2	1	no	—
41	D₁₀₉	—	2	1	no	—
42	C₁₀₉	#430	1	1	yes	characteristic, complemented, Sylow
43	#430	—	109	1	no	maximal, Sylow
44	C₂×M₁₆	—	109	1	no	—
45	C₂×M₁₆	—	109	1	no	—
46	C₂×M₁₆	—	109	1	no	—
47	#108	—	109	2	no	—
48	#108	—	109	2	no	—
49	C₂²×C₄	—	109	1	no	—
50	M₁₆	—	109	1	no	—
51	M₁₆	—	109	2	no	—
52	M₁₆	—	109	1	no	—
53	M₁₆	—	109	2	no	—
54	M₁₆	—	109	1	no	—
55	M₁₆	—	218	1	no	—
56	M₁₆	—	218	1	no	—
57	M₁₆	#89137	1	1	yes	characteristic
58	C₂×C₈	—	109	2	no	—
59	C₂×C₈	—	218	1	no	—
60	C₂×C₈	—	218	1	no	—
61	C₂³	—	109	1	no	—
62	C₂×C₄	—	109	1	no	—
63	C₂×C₄	—	109	1	no	—
64	C₂×C₄	—	109	1	no	—
65	C₂×C₄	—	109	1	no	—
66	C₂×C₄	—	109	1	no	—
67	C₂×C₄	C₂×#89137	1	1	yes	characteristic
68	C₈	—	109	2	no	—
69	C₈	—	218	2	no	—
70	C₈	—	218	1	no	—
71	C₈	—	218	1	no	—
72	C₈	C₂×#89137	1	2	yes	—
73	C₂²	—	109	1	no	—
74	C₂²	—	109	1	no	—
75	C₂²	—	436	1	no	—
76	C₂²	C₄⋊#89137	1	1	yes	characteristic
77	C₄	—	109	1	no	—
78	C₄	—	109	1	no	—
79	C₄	C₄⋊#89137	1	1	yes	characteristic
80	C₄	C₂²×#89137	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	—	218	1	no	—
83	C₂	—	218	1	no	—
84	C₂	C₂×C₄⋊#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₄⋊#89137
commutator	C₄×C₁₀₉	C₂²×C₄
Frattini	C₄	C₂²×#89137
Fitting	M₁₆×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₂×C₄⋊C₄
hypercenter	M₁₆	#89137
hypocenter	C₁₀₉	#430
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
3. #16812770	C₂	semidirect
4. #16812769	C₂	semidirect
42. C₁₀₉	#430	semidirect