Subgroups — #19136851

Order 5504.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063270	C₂	1	4	yes	maximal, complemented
2	#14583279	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583276	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₁₇₂	—	2	1	no	—
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	C₂×D₃₄₄	—	2	1	no	—
8	C₂×D₃₄₄	C₂²	1	2	yes	—
9	#13063325	—	2	1	no	—
10	#13063322	—	2	1	no	—
11	#13063270	—	2	8	no	—
12	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×D₁₇₂	—	2	2	no	—
15	C₂×D₁₇₂	—	4	2	no	—
16	C₂×Dic₈₆	—	2	2	no	—
17	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	D₄	1	1	yes	characteristic
20	C₄⋊Dic₄₃	—	4	2	no	—
21	Dic₁₇₂	—	2	4	no	—
22	Dic₁₇₂	—	4	2	no	—
23	D₃₄₄	—	2	4	no	—
24	D₃₄₄	—	4	2	no	—
25	C₁₆×C₄₃	D₄	1	4	yes	complemented
26	C₂²×D₄₃	—	4	2	no	—
27	C₂×C₄×C₄₃	D₈	1	2	yes	—
28	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₄₃	—	4	2	no	—
30	D₁₇₂	—	4	2	no	—
31	D₁₇₂	—	4	2	no	—
32	D₁₇₂	—	8	4	no	—
33	Dic₈₆	—	4	2	no	—
34	Dic₈₆	—	4	2	no	—
35	C₈×C₄₃	D₈	1	2	yes	—
36	C₈×C₄₃	C₂×D₄	1	2	yes	—
37	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
38	C₂×D₄₃	—	8	2	no	—
39	C₂×D₄₃	—	8	4	no	—
40	C₄×C₄₃	SD₃₂	1	4	yes	complemented
41	C₄×C₄₃	#127	1	1	yes	characteristic
42	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
43	Dic₄₃	—	8	2	no	—
44	#2248	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	#493	1	1	yes	characteristic
46	C₂×C₄₃	C₂×SD₃₂	1	2	yes	—
47	D₄₃	—	16	2	no	—
48	C₂×SD₃₂	—	43	4	no	—
49	#494	—	43	1	no	—
50	#493	—	43	1	no	—
51	C₄×C₁₆	D₄₃	1	1	yes	characteristic, complemented
52	C₄₃	#2248	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₁₆	—	43	2	no	—
54	C₂×Q₁₆	—	86	1	no	—
55	C₂×D₈	—	43	2	no	—
56	C₂×D₈	—	86	1	no	—
57	C₄⋊Q₈	—	86	1	no	—
58	#127	—	86	1	no	—
59	SD₃₂	—	86	8	no	—
60	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
61	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
62	C₂×Q₈	—	86	2	no	—
63	C₂×D₄	—	86	2	no	—
64	C₂×D₄	—	172	2	no	—
65	Q₁₆	—	86	4	no	—
66	Q₁₆	—	172	2	no	—
67	D₈	—	86	4	no	—
68	D₈	—	172	2	no	—
69	C₂×C₈	D₁₇₂	1	1	yes	characteristic
70	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
71	C₄⋊C₄	—	172	2	no	—
72	C₄²	D₁₇₂	1	1	yes	characteristic
73	C₁₆	D₁₇₂	1	4	yes	complemented
74	C₂³	—	172	2	no	—
75	Q₈	—	172	2	no	—
76	Q₈	—	172	2	no	—
77	D₄	—	344	4	no	—
78	D₄	—	172	2	no	—
79	D₄	—	172	2	no	—
80	C₂×C₄	—	172	2	no	—
81	C₂×C₄	D₃₄₄	1	2	yes	—
82	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
83	C₈	D₃₄₄	1	2	yes	—
84	C₈	C₂×D₁₇₂	1	2	yes	—
85	C₂²	—	344	4	no	—
86	C₂²	—	344	2	no	—
87	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
88	C₄	—	344	2	no	—
89	C₄	#13063270	1	4	yes	complemented
90	C₄	#13063322	1	1	yes	characteristic
91	C₄	C₂×D₃₄₄	1	1	yes	characteristic
92	C₂	—	688	2	no	—
93	C₂	#14583276	1	1	yes	characteristic
94	C₂	C₂×#13063270	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄×C₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₄×C₁₆	D₄₃
hypocenter	C₄₃	#2248
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#13063270	C₂	semidirect
2. #14583279	C₂	semidirect
4. C₄×C₁₆×C₄₃	C₂	semidirect
25. C₁₆×C₄₃	D₄	semidirect
40. C₄×C₄₃	SD₃₂	semidirect
51. C₄×C₁₆	D₄₃	semidirect
52. C₄₃	#2248	semidirect
73. C₁₆	D₁₇₂	semidirect
89. C₄	#13063270	semidirect