Subgroups — #20295358

Order 6976.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812679	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
3	#16812630	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812624	C₂	1	1	yes	maximal, characteristic, complemented
5	#16812622	C₂	1	1	yes	maximal, characteristic, complemented
6	#16812611	C₂	1	1	yes	maximal, characteristic
7	#106×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₀₉	—	2	1	no	—
10	C₂×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
11	C₂×#11724784	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₀₉	—	2	1	no	—
13	C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
14	#13182008	—	2	1	no	—
15	#13182006	—	2	1	no	—
16	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂²×D₁₀₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₀₉	—	2	1	no	—
21	C₂×C₄×C₁₀₉	—	2	1	no	—
22	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₀₉	—	2	1	no	—
24	C₂×Dic₁₀₉	—	2	1	no	—
25	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
26	C₄×D₁₀₉	—	2	1	no	—
27	C₄×D₁₀₉	—	2	1	no	—
28	C₄×D₁₀₉	—	4	2	no	—
29	Dic₂₁₈	—	2	1	no	—
30	Dic₂₁₈	—	2	1	no	—
31	C₈×C₁₀₉	—	2	1	no	—
32	#11724784	—	2	1	no	—
33	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
34	C₂×D₁₀₉	—	2	1	no	—
35	C₂×D₁₀₉	—	2	1	no	—
36	C₂×D₁₀₉	SD₁₆	1	2	yes	—
37	C₄×C₁₀₉	—	4	1	no	—
38	C₄×C₁₀₉	—	4	1	no	—
39	C₄×C₁₀₉	#41	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	C₂×C₁₀₉	#123	1	1	yes	characteristic
45	C₂×C₁₀₉	C₂×SD₁₆	1	1	yes	characteristic
46	C₂×C₁₀₉	#137	1	1	yes	characteristic
47	D₁₀₉	—	2	2	no	—
48	C₁₀₉	#483	1	1	yes	characteristic, complemented, Sylow
49	#483	—	109	1	no	maximal, Sylow
50	C₂²⋊Q₈	—	109	1	no	—
51	C₂×C₄⋊C₄	—	109	1	no	—
52	#106	—	109	1	no	—
53	#106	D₁₀₉	1	1	yes	characteristic, complemented
54	#103	—	109	1	no	—
55	#103	—	109	1	no	—
56	C₂²⋊C₈	—	109	1	no	—
57	C₂×Q₈	—	109	1	no	—
58	C₂²×C₄	—	109	1	no	—
59	C₂²×C₄	—	218	1	no	—
60	C₂×C₈	—	109	1	no	—
61	C₂×C₈	C₂×D₁₀₉	1	1	yes	characteristic
62	C₄⋊C₄	—	109	1	no	—
63	C₄⋊C₄	—	218	1	no	—
64	C₄⋊C₄	—	218	1	no	—
65	C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
66	C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic
67	C₂²⋊C₄	—	218	1	no	—
68	C₂³	—	109	1	no	—
69	Q₈	—	218	1	no	—
70	Q₈	—	218	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	2	1	no	—
73	C₂×C₄	—	109	1	no	—
74	C₂×C₄	—	436	2	no	—
75	C₂×C₄	—	218	1	no	—
76	C₂×C₄	—	218	1	no	—
77	C₂×C₄	—	218	1	no	—
78	C₂×C₄	—	218	1	no	—
79	C₂×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	218	1	no	—
82	C₂²	—	109	2	no	—
83	C₂²	—	218	1	no	—
84	C₂²	—	218	1	no	—
85	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	4	1	no	—
88	C₄	—	436	1	no	—
89	C₄	—	436	1	no	—
90	C₄	—	218	1	no	—
91	C₄	#13182029	1	1	yes	characteristic
92	C₄	#13182030	1	1	yes	characteristic
93	C₂	—	218	2	no	—
94	C₂	#16812684	1	1	yes	characteristic
95	C₂	SD₁₆×D₁₀₉	1	1	yes	characteristic
96	C₂	#16812728	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₀₉
commutator	C₂×C₄×C₁₀₉	C₂³
Frattini	C₂×C₄	C₂²×D₁₀₉
Fitting	#106×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	#106	D₁₀₉
hypocenter	C₁₀₉	#483
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. #16812630	C₂	semidirect
4. #16812624	C₂	semidirect
5. #16812622	C₂	semidirect
7. #106×C₁₀₉	C₂	semidirect
48. C₁₀₉	#483	semidirect
53. #106	D₁₀₉	semidirect