Subgroups — #14583510

Order 2752.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063320	C₂	1	4	yes	maximal
2	#13063317	C₂	1	1	yes	maximal, characteristic, complemented
3	#13063315	C₂	1	4	yes	maximal, complemented
4	#13063301	C₂	1	2	yes	maximal
5	Q₈×Dic₄₃	C₂	1	2	yes	maximal, complemented
6	#13063282	C₂	1	1	yes	maximal, characteristic
7	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₄₃	C₂²	1	2	yes	—
9	C₂×C₄×D₄₃	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
13	(C₂×D₄₃)⋊C₄	C₂²	1	4	yes	—
14	C₄⋊Dic₄₃	C₂²	1	2	yes	—
15	C₄⋊Dic₄₃	C₂²	1	4	yes	—
16	Dic₄₃⋊C₄	C₂²	1	2	yes	—
17	Dic₄₃⋊C₄	C₂²	1	4	yes	—
18	Dic₄₃⋊C₄	C₂²	1	4	yes	—
19	C₄×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₄×Dic₄₃	C₂²	1	4	yes	—
21	C₂²×D₄₃	C₂³	1	1	yes	characteristic
22	Q₈×C₄₃	—	2	4	no	—
23	C₂×C₄×C₄₃	C₂³	1	4	yes	—
24	C₂×C₄×C₄₃	C₂³	1	2	yes	—
25	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
26	C₂×Dic₄₃	C₂³	1	2	yes	—
27	C₂×Dic₄₃	C₂³	1	4	yes	—
28	C₂×Dic₄₃	C₂³	1	1	yes	characteristic
29	C₄×D₄₃	—	2	2	no	—
30	C₂²×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂×D₄₃	—	2	1	no	—
32	C₂×D₄₃	—	2	2	no	—
33	C₄×C₄₃	—	2	4	no	—
34	C₄×C₄₃	—	2	2	no	—
35	C₄×C₄₃	#41	1	2	yes	—
36	Dic₄₃	—	2	1	no	—
37	Dic₄₃	—	2	2	no	—
38	Dic₄₃	—	2	4	no	—
39	C₂×C₄₃	C₂×#41	1	1	yes	characteristic
40	C₂×C₄₃	2₋¹⁺⁴	1	2	yes	—
41	D₄₃	—	4	1	no	—
42	#541	—	43	1	no	maximal, Sylow
43	C₄₃	#541	1	1	yes	characteristic, complemented, Sylow
44	C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
45	#126	—	43	4	no	—
46	#125	—	43	4	no	—
47	#125	—	43	1	no	—
48	C₂²⋊Q₈	—	43	2	no	—
49	C₄×Q₈	—	43	2	no	—
50	#117	—	43	1	no	—
51	C₂×Q₈	C₂×D₄₃	1	2	yes	—
52	C₂²×C₄	—	43	1	no	—
53	C₄⋊C₄	—	43	2	no	—
54	C₄⋊C₄	—	43	2	no	—
55	C₄⋊C₄	—	43	4	no	—
56	C₄⋊C₄	—	43	4	no	—
57	C₄⋊C₄	—	43	4	no	—
58	C₄⋊C₄	C₂×D₄₃	1	4	yes	—
59	C₂²⋊C₄	—	43	2	no	—
60	C₂²⋊C₄	—	43	4	no	—
61	C₄²	—	43	1	no	—
62	C₄²	—	43	4	no	—
63	C₄²	C₂×D₄₃	1	1	yes	characteristic
64	C₂³	—	43	1	no	—
65	Q₈	—	2	4	no	—
66	C₂×C₄	—	43	2	no	—
67	C₂×C₄	—	43	4	no	—
68	C₂×C₄	—	43	1	no	—
69	C₂×C₄	—	86	2	no	—
70	C₂×C₄	C₂²×D₄₃	1	4	yes	—
71	C₂×C₄	C₂²×D₄₃	1	2	yes	—
72	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
73	C₂²	—	86	1	no	—
74	C₂²	—	86	2	no	—
75	C₂²	C₂³×D₄₃	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	2	2	no	—
78	C₄	—	86	1	no	—
79	C₄	—	86	2	no	—
80	C₄	—	86	4	no	—
81	C₄	#10621900	1	2	yes	—
82	C₂	—	172	1	no	—
83	C₂	C₂×#10621900	1	1	yes	characteristic
84	C₂	#13063373	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁴
Fitting	C₄⋊Q₈×C₄₃	C₂
prime radical	C₂²×D₄₃	C₂³
hypercenter	C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#541
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #13063317	C₂	semidirect
3. #13063315	C₂	semidirect
5. Q₈×Dic₄₃	C₂	semidirect
7. C₄⋊Q₈×C₄₃	C₂	semidirect
43. C₄₃	#541	semidirect
44. C₄⋊Q₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063320	2
#13063317	2
#13063315	2
#13063301	2
Q₈×Dic₄₃	2
#13063282	2
C₄⋊Q₈×C₄₃	2
#541	43