Subgroups — #20295384

Order 6976.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16812698	C₂	1	1	yes	maximal, characteristic, complemented
2	#16812686	C₂	1	1	yes	maximal, characteristic
3	#16812624	C₂	1	1	yes	maximal, characteristic, complemented
4	#16812622	C₂	1	1	yes	maximal, characteristic, complemented
5	#16812620	C₂	1	1	yes	maximal, characteristic
6	#16812609	C₂	1	1	yes	maximal, characteristic, complemented
7	#102×C₁₀₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₁₈	—	2	1	no	—
9	C₂×Dic₂₁₈	C₂²	1	1	yes	characteristic
10	C₂×#11724784	C₂²	1	1	yes	characteristic
11	C₄⋊Dic₁₀₉	C₂²	1	1	yes	characteristic
12	#13182008	—	2	1	no	—
13	C₂²⋊Dic₁₀₉	—	2	1	no	—
14	C₂²⋊Dic₁₀₉	—	2	1	no	—
15	C₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
16	C₂×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂³×C₁₀₉	—	2	1	no	—
20	D₄×C₁₀₉	—	2	1	no	—
21	D₄×C₁₀₉	—	2	1	no	—
22	C₂×C₄×C₁₀₉	—	2	1	no	—
23	C₂×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
24	C₂×Dic₁₀₉	—	2	1	no	—
25	C₂×Dic₁₀₉	—	2	1	no	—
26	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
27	C₂×Dic₁₀₉	D₄	1	1	yes	characteristic
28	Dic₂₁₈	—	2	1	no	—
29	Dic₂₁₈	—	2	1	no	—
30	Dic₂₁₈	—	4	2	no	—
31	C₈×C₁₀₉	—	2	1	no	—
32	#11724784	—	2	1	no	—
33	C₂²×C₁₀₉	—	4	1	no	—
34	C₂²×C₁₀₉	—	4	1	no	—
35	C₂²×C₁₀₉	—	4	1	no	—
36	C₂²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
37	C₄×C₁₀₉	—	4	1	no	—
38	C₄×C₁₀₉	#41	1	1	yes	characteristic
39	C₄×C₁₀₉	#41	1	1	yes	characteristic
40	Dic₁₀₉	—	2	1	no	—
41	Dic₁₀₉	—	2	1	no	—
42	Dic₁₀₉	—	4	1	no	—
43	Dic₁₀₉	—	4	1	no	—
44	C₂×C₁₀₉	—	8	1	no	—
45	C₂×C₁₀₉	#124	1	1	yes	characteristic
46	C₂×C₁₀₉	AGL(1,ℤ/8)	1	1	yes	characteristic
47	C₂×C₁₀₉	#137	1	1	yes	characteristic
48	C₁₀₉	#489	1	1	yes	characteristic, complemented, Sylow
49	#489	—	109	1	no	maximal, Sylow
50	C₄⋊Q₈	—	109	1	no	—
51	#124	—	109	1	no	—
52	#103	—	109	1	no	—
53	#103	—	109	1	no	—
54	#102	—	109	1	no	—
55	#102	D₁₀₉	1	1	yes	characteristic
56	#97	—	109	1	no	—
57	C₂×Q₈	—	109	1	no	—
58	C₂×Q₈	—	218	1	no	—
59	C₂×D₄	C₂×D₁₀₉	1	1	yes	characteristic
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	C₂×D₁₀₉	1	1	yes	characteristic
65	C₂²⋊C₄	—	218	1	no	—
66	C₂²⋊C₄	—	218	1	no	—
67	C₄²	—	109	1	no	—
68	C₂³	—	2	1	no	—
69	Q₈	—	436	2	no	—
70	Q₈	—	218	1	no	—
71	Q₈	—	218	1	no	—
72	D₄	—	2	1	no	—
73	D₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	109	1	no	—
76	C₂×C₄	—	109	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	—	4	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	D₄×D₁₀₉	1	1	yes	characteristic
86	C₄	—	4	1	no	—
87	C₄	—	436	1	no	—
88	C₄	—	436	1	no	—
89	C₄	—	218	1	no	—
90	C₄	—	218	1	no	—
91	C₄	#13182028	1	1	yes	characteristic
92	C₄	#13182029	1	1	yes	characteristic
93	C₂	—	8	1	no	—
94	C₂	#16812685	1	1	yes	characteristic
95	C₂	#16812723	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	#102×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂×D₄
hypercenter	#102	D₁₀₉
hypocenter	C₁₀₉	#489
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

Complements

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

N	H ≅ G/N	type
1. #16812698	C₂	semidirect
3. #16812624	C₂	semidirect
4. #16812622	C₂	semidirect
6. #16812609	C₂	semidirect
48. C₁₀₉	#489	semidirect