Subgroups — #14583247

Order 2752.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063322	C₂	1	1	yes	maximal, characteristic
2	#13063245	C₂	1	4	yes	maximal, complemented
3	C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈×C₄₃	—	2	1	no	—
6	C₂×D₁₇₂	—	2	1	no	—
7	C₂×D₁₇₂	—	2	1	no	—
8	C₂×D₁₇₂	C₂²	1	2	yes	—
9	C₄⋊C₄×C₄₃	—	2	1	no	—
10	C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄₃⋊C₈	C₂²	1	2	yes	—
13	C₂²×D₄₃	—	2	2	no	—
14	Q₈×C₄₃	—	4	2	no	—
15	C₂×C₄×C₄₃	—	2	2	no	—
16	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
17	C₂×C₄×C₄₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	D₁₇₂	—	2	4	no	—
20	D₁₇₂	—	4	2	no	—
21	D₁₇₂	—	4	2	no	—
22	C₄₃⋊C₈	—	2	2	no	—
23	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₂×D₄₃	—	4	2	no	—
25	C₂×D₄₃	—	4	2	no	—
26	C₂×D₄₃	—	4	2	no	—
27	C₄×C₄₃	—	4	2	no	—
28	C₄×C₄₃	D₈	1	2	yes	—
29	C₄×C₄₃	SD₁₆	1	2	yes	—
30	C₄×C₄₃	#41	1	2	yes	—
31	C₂×C₄₃	#124	1	1	yes	characteristic
32	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
33	C₂×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
34	D₄₃	—	8	2	no	—
35	#486	—	43	1	no	maximal, Sylow
36	C₄₃	#486	1	1	yes	characteristic, complemented, Sylow
37	C₄⋊Q₈	D₄₃	1	1	yes	characteristic, complemented
38	#127	—	43	1	no	—
39	#102	—	43	4	no	—
40	C₄×C₈	—	43	1	no	—
41	C₂×Q₈	—	2	1	no	—
42	C₂×D₄	—	43	2	no	—
43	C₂×D₄	—	86	1	no	—
44	C₂×D₄	—	86	1	no	—
45	C₂×C₈	—	43	2	no	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	C₂×D₄₃	1	2	yes	—
48	C₄²	C₂×D₄₃	1	1	yes	characteristic
49	C₂³	—	86	2	no	—
50	Q₈	—	4	2	no	—
51	D₄	—	86	4	no	—
52	D₄	—	172	2	no	—
53	D₄	—	172	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
57	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
58	C₈	—	86	2	no	—
59	C₂²	—	172	2	no	—
60	C₂²	—	172	2	no	—
61	C₂²	—	172	2	no	—
62	C₂²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
63	C₄	—	4	2	no	—
64	C₄	#10621882	1	2	yes	—
65	C₄	#10621884	1	2	yes	—
66	C₄	#10621902	1	2	yes	—
67	C₂	—	344	2	no	—
68	C₂	#13063314	1	1	yes	characteristic
69	C₂	C₂×#10621882	1	1	yes	characteristic
70	C₂	C₂×#10621884	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊Q₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	#13063322	C₂
hypercenter	C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#486
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #13063245	C₂	semidirect
3. C₄×C₄₃⋊C₈	C₂	semidirect
4. C₄⋊Q₈×C₄₃	C₂	semidirect
36. C₄₃	#486	semidirect
37. 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
#13063322	2
#13063245	2
C₄×C₄₃⋊C₈	2
C₄⋊Q₈×C₄₃	2
#486	43