Subgroups — #19132767

Order 5504.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583267	C₂	1	1	yes	maximal, characteristic
2	#14582698	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#356	C₂	1	1	yes	maximal, characteristic
4	#13063317	C₄	1	1	yes	characteristic
5	#13063249	—	2	1	no	—
6	#13063249	—	2	1	no	—
7	#13063244	—	2	1	no	—
8	#13063236	C₄	1	1	yes	characteristic
9	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	#101×C₄₃	—	2	1	no	—
11	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
12	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
13	M₁₆×C₄₃	—	4	1	no	—
14	C₄⋊C₄×C₄₃	—	4	1	no	—
15	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
16	C₄⋊Dic₄₃	—	2	1	no	—
17	Dic₄₃⋊C₄	—	4	1	no	—
18	#10621877	—	4	1	no	—
19	C₂×C₄₃⋊C₈	—	2	1	no	—
20	Q₈×C₄₃	—	4	1	no	—
21	Q₈×C₄₃	—	4	1	no	—
22	C₂×C₄×C₄₃	—	2	1	no	—
23	C₂×C₄×C₄₃	—	2	1	no	—
24	C₂×C₄×C₄₃	—	2	1	no	—
25	C₂×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
26	C₂×Dic₄₃	—	4	1	no	—
27	C₈×C₄₃	—	8	1	no	—
28	C₄₃⋊C₈	—	4	1	no	—
29	C₄₃⋊C₈	—	8	1	no	—
30	C₂²×C₄₃	#99	1	1	yes	characteristic
31	C₄×C₄₃	—	2	1	no	—
32	C₄×C₄₃	—	4	1	no	—
33	C₄×C₄₃	—	4	1	no	—
34	C₄×C₄₃	—	4	1	no	—
35	Dic₄₃	—	8	1	no	—
36	#1413	—	43	1	no	maximal, Sylow
37	C₂×C₄₃	—	2	1	no	—
38	C₂×C₄₃	#354	1	1	yes	characteristic
39	#491	—	43	1	no	—
40	#356	—	43	1	no	—
41	#356	D₄₃	1	1	yes	characteristic
42	C₄₃	#1413	1	1	yes	characteristic, complemented, Sylow
43	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
44	#125	—	43	1	no	—
45	#103	—	86	1	no	—
46	#103	—	86	1	no	—
47	#101	—	2	1	no	—
48	#101	—	86	1	no	—
49	#97	—	43	1	no	—
50	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
51	C₂×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
52	M₁₆	—	4	1	no	—
53	M₁₆	—	172	1	no	—
54	C₂×C₈	—	86	1	no	—
55	C₄⋊C₄	—	4	1	no	—
56	C₄⋊C₄	—	86	1	no	—
57	C₄⋊C₄	—	172	1	no	—
58	C₄²	C₄×D₄₃	1	1	yes	characteristic
59	Q₈	—	4	1	no	—
60	Q₈	—	4	1	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	2	1	no	—
63	C₂×C₄	—	2	1	no	—
64	C₂×C₄	—	172	1	no	—
65	C₂×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
66	C₈	—	8	1	no	—
67	C₈	—	344	1	no	—
68	C₈	—	172	1	no	—
69	C₂²	#13063239	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	1	no	—
73	C₄	—	4	1	no	—
74	C₄	—	344	1	no	—
75	C₂	—	2	1	no	—
76	C₂	#14582693	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#14582693
commutator	C₄²×C₄₃	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₄₃
Fitting	C₄₃×#356	C₂
socle	C₂×C₄₃	#354
hypercenter	#356	D₄₃
hypocenter	C₄₃	#1413
LCS	G ▷ C₄²×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #356

Complements

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

N	H ≅ G/N	type
42. C₄₃	#1413	semidirect