Subgroups — #14582893

Order 2752.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10621898	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063248	C₂	1	2	yes	maximal, complemented
4	#13063245	C₂	1	2	yes	maximal, complemented
5	#117×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₂²⋊D₄₃	—	2	1	no	—
8	#10621898	—	2	2	no	—
9	#10621898	C₄	1	4	yes	complemented
10	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄₃	—	2	1	no	—
12	C₂×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²⋊C₄×C₄₃	—	2	1	no	—
15	C₄²×C₄₃	—	2	1	no	—
16	C₂×C₄₃⋊C₈	—	2	2	no	—
17	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
18	C₂³×C₄₃	D₄	1	1	yes	characteristic
19	C₂²×D₄₃	—	2	1	no	—
20	C₂×C₄×C₄₃	—	2	2	no	—
21	C₂×C₄×C₄₃	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₄₃	D₄	1	2	yes	—
23	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²⋊D₄₃	—	2	4	no	—
26	C₂×Dic₄₃	—	2	1	no	—
27	D₁₇₂	—	2	1	no	—
28	D₁₇₂	C₂×C₄	1	2	yes	—
29	C₄×D₄₃	—	2	4	no	—
30	Dic₈₆	—	2	1	no	—
31	Dic₈₆	C₂×C₄	1	2	yes	—
32	C₄₃⋊C₈	—	2	2	no	—
33	C₂²×C₄₃	—	2	2	no	—
34	C₂²×C₄₃	C₂²⋊C₄	1	2	yes	—
35	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
36	C₂×D₄₃	—	2	2	no	—
37	C₂×D₄₃	—	4	2	no	—
38	C₄×C₄₃	—	4	2	no	—
39	C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
40	C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
42	Dic₄₃	—	2	2	no	—
43	C₂×C₄₃	—	2	2	no	—
44	C₂×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×C₄₃	#135	1	2	yes	—
46	D₄₃	—	4	2	no	—
47	#416	—	43	1	no	maximal, Sylow
48	C₄₃	#416	1	1	yes	characteristic, complemented, Sylow
49	C₂×#41	—	43	1	no	—
50	C₂²×C₈	—	43	1	no	—
51	#117	D₄₃	1	1	yes	characteristic, complemented
52	#103	—	43	2	no	—
53	#102	—	43	2	no	—
54	#41	—	43	4	no	—
55	#41	—	86	2	no	—
56	C₂×Q₈	—	43	1	no	—
57	C₂×D₄	—	43	1	no	—
58	C₂×D₄	—	86	1	no	—
59	C₂²×C₄	—	86	1	no	—
60	C₂²×C₄	C₂×D₄₃	1	1	yes	characteristic
61	C₂×C₈	—	43	2	no	—
62	C₂×C₈	—	86	2	no	—
63	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
64	C₂²⋊C₄	—	2	1	no	—
65	C₄²	—	2	1	no	—
66	C₂³	—	86	1	no	—
67	C₂³	C₂²⋊D₄₃	1	1	yes	characteristic
68	Q₈	—	43	2	no	—
69	Q₈	—	86	1	no	—
70	D₄	—	43	2	no	—
71	D₄	—	86	4	no	—
72	D₄	—	86	1	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	86	1	no	—
75	C₂×C₄	—	86	4	no	—
76	C₂×C₄	C₄×D₄₃	1	2	yes	—
77	C₂×C₄	D₁₇₂	1	2	yes	—
78	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
79	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
80	C₈	—	86	2	no	—
81	C₂²	—	2	2	no	—
82	C₂²	—	86	2	no	—
83	C₂²	—	172	2	no	—
84	C₂²	(C₂×D₄₃)⋊C₄	1	2	yes	—
85	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	—	86	2	no	—
88	C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
89	C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₄	C₂×D₁₇₂	1	1	yes	characteristic
91	C₂	—	2	2	no	—
92	C₂	—	172	2	no	—
93	C₂	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
94	C₂	#13063345	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	#117×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂×#10621898	C₂
cosocle	C₂×C₄×C₄₃	C₂³
hypercenter	#117	D₄₃
hypocenter	C₄₃	#416
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄₃⋊C₈	C₂	semidirect
3. #13063248	C₂	semidirect
4. #13063245	C₂	semidirect
5. #117×C₄₃	C₂	semidirect
9. #10621898	C₄	semidirect
48. C₄₃	#416	semidirect
51. #117	D₄₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10621898	2
C₂²×C₄₃⋊C₈	2
#13063248	2
#13063245	2
#117×C₄₃	2
#416	43