Subgroups — #19132751

Order 5504.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583289	C₂	1	1	yes	maximal, characteristic
2	#14582696	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10621884	—	2	1	no	—
5	C₂×#10621882	—	2	1	no	—
6	#13063322	C₄	1	1	yes	characteristic, complemented
7	#13063244	—	2	1	no	—
8	#13063236	C₄	1	1	yes	characteristic, complemented
9	#124×C₄₃	C₂²	1	1	yes	characteristic
10	#99×C₄₃	—	2	1	no	—
11	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
12	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
13	C₂×D₁₇₂	—	2	1	no	—
14	C₂×D₁₇₂	—	4	1	no	—
15	C₂²⋊C₄×C₄₃	—	4	1	no	—
16	C₂²⋊C₄×C₄₃	—	4	1	no	—
17	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
18	#10621884	—	4	2	no	—
19	#10621882	—	4	2	no	—
20	#10621877	—	4	1	no	—
21	C₂×C₄₃⋊C₈	—	2	1	no	—
22	C₂³×C₄₃	—	2	1	no	—
23	C₂²×D₄₃	—	4	1	no	—
24	Q₈×C₄₃	—	4	1	no	—
25	D₄×C₄₃	—	4	1	no	—
26	C₂×C₄×C₄₃	—	2	1	no	—
27	C₂×C₄×C₄₃	—	2	1	no	—
28	C₂×C₄×C₄₃	—	8	1	no	—
29	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
30	D₁₇₂	—	4	1	no	—
31	D₁₇₂	—	4	1	no	—
32	D₁₇₂	—	8	2	no	—
33	C₄₃⋊C₈	—	2	2	no	—
34	C₄₃⋊C₈	—	8	1	no	—
35	C₂²×C₄₃	—	4	1	no	—
36	C₂²×C₄₃	—	8	1	no	—
37	C₂²×C₄₃	#99	1	1	yes	characteristic
38	C₂×D₄₃	—	8	2	no	—
39	C₂×D₄₃	—	8	1	no	—
40	C₄×C₄₃	—	2	1	no	—
41	C₄×C₄₃	—	4	1	no	—
42	C₄×C₄₃	—	4	1	no	—
43	C₄×C₄₃	—	16	1	no	—
44	#1406	—	43	1	no	maximal, Sylow
45	C₂×C₄₃	—	2	1	no	—
46	C₂×C₄₃	—	8	1	no	—
47	C₂×C₄₃	#353	1	1	yes	characteristic
48	D₄₃	—	16	1	no	—
49	#496	—	43	1	no	—
50	#355	—	43	1	no	—
51	#354	D₄₃	1	1	yes	characteristic, complemented
52	C₄₃	#1406	1	1	yes	characteristic, complemented, Sylow
53	C₂×SD₁₆	—	86	1	no	—
54	C₂×D₈	—	86	1	no	—
55	#127	—	43	1	no	—
56	#124	C₂×D₄₃	1	1	yes	characteristic
57	#101	—	86	1	no	—
58	#99	—	2	1	no	—
59	#97	—	43	1	no	—
60	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
61	C₂×D₄	—	86	1	no	—
62	C₂×D₄	—	172	1	no	—
63	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
64	SD₁₆	—	172	2	no	—
65	D₈	—	172	2	no	—
66	M₁₆	—	172	1	no	—
67	C₂×C₈	—	86	1	no	—
68	C₂²⋊C₄	—	4	1	no	—
69	C₂²⋊C₄	—	4	1	no	—
70	C₄²	C₄×D₄₃	1	1	yes	characteristic
71	C₂³	—	2	1	no	—
72	C₂³	—	172	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	344	2	no	—
76	D₄	—	172	1	no	—
77	D₄	—	172	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	2	1	no	—
80	C₂×C₄	—	8	1	no	—
81	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
82	C₈	—	86	2	no	—
83	C₈	—	344	1	no	—
84	C₂²	—	4	1	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	344	2	no	—
87	C₂²	—	344	1	no	—
88	C₂²	#13063239	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	4	1	no	—
92	C₄	—	16	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	8	1	no	—
95	C₂	—	688	1	no	—
96	C₂	#14582691	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582691
commutator	C₄²×C₄₃	C₂×C₄
Frattini	#124	C₂×D₄₃
Fitting	C₄₃×#354	C₂
socle	C₂×C₄₃	#353
hypercenter	#354	D₄₃
hypocenter	C₄₃	#1406
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #354

Complements

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

N	H ≅ G/N	type
2. #14582696	C₂	semidirect
3. C₄₃×#354	C₂	semidirect
6. #13063322	C₄	semidirect
8. #13063236	C₄	semidirect
51. #354	D₄₃	semidirect
52. C₄₃	#1406	semidirect