Subgroups — #14583180

Order 2752.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13063325	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#13063259	C₂	1	2	yes	maximal, complemented
4	#13063247	C₂	1	2	yes	maximal
5	C₄⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₄₃	—	2	1	no	—
8	C₂×Dic₈₆	—	2	1	no	—
9	C₂×C₈×C₄₃	C₂²	1	2	yes	—
10	C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	(C₂×D₄₃)⋊C₄	—	2	1	no	—
12	C₄⋊Dic₄₃	—	2	1	no	—
13	C₄⋊Dic₄₃	C₂²	1	2	yes	—
14	C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
15	C₂²×D₄₃	—	2	1	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	C₂×Dic₄₃	—	2	2	no	—
20	C₂×Dic₄₃	—	2	1	no	—
21	D₁₇₂	—	2	1	no	—
22	D₁₇₂	Q₈	1	2	yes	complemented
23	C₄×D₄₃	—	4	2	no	—
24	Dic₈₆	—	4	2	no	—
25	C₈×C₄₃	—	2	2	no	—
26	C₂²×C₄₃	C₂×D₄	1	1	yes	characteristic
27	C₂×D₄₃	—	2	2	no	—
28	C₂×D₄₃	—	4	1	no	—
29	C₂×D₄₃	—	4	1	no	—
30	C₄×C₄₃	—	2	1	no	—
31	C₄×C₄₃	D₈	1	2	yes	—
32	C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
33	C₄×C₄₃	#41	1	1	yes	characteristic
34	Dic₄₃	—	4	2	no	—
35	Dic₄₃	—	4	1	no	—
36	C₂×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
37	C₂×C₄₃	C₂×D₈	1	1	yes	characteristic
38	C₂×C₄₃	#137	1	1	yes	characteristic
39	D₄₃	—	4	2	no	—
40	#474	—	43	1	no	maximal, Sylow
41	C₄₃	#474	1	1	yes	characteristic, complemented, Sylow
42	C₄⋊Q₈	—	43	1	no	—
43	C₄×D₄	—	43	1	no	—
44	#107	—	43	2	no	—
45	C₄⋊C₈	D₄₃	1	1	yes	characteristic, complemented
46	#102	—	43	2	no	—
47	C₂×Q₈	—	86	1	no	—
48	C₂×D₄	—	43	1	no	—
49	C₂²×C₄	—	86	1	no	—
50	C₂×C₈	C₂×D₄₃	1	2	yes	—
51	C₄⋊C₄	—	43	2	no	—
52	C₄⋊C₄	—	43	1	no	—
53	C₄⋊C₄	—	86	1	no	—
54	C₂²⋊C₄	—	86	1	no	—
55	C₄²	C₂×D₄₃	1	1	yes	characteristic
56	C₂³	—	86	1	no	—
57	Q₈	—	172	2	no	—
58	D₄	—	43	2	no	—
59	D₄	—	86	1	no	—
60	C₂×C₄	—	86	1	no	—
61	C₂×C₄	—	86	2	no	—
62	C₂×C₄	—	172	2	no	—
63	C₂×C₄	D₁₇₂	1	1	yes	characteristic
64	C₂×C₄	D₁₇₂	1	1	yes	characteristic
65	C₂×C₄	C₂²×D₄₃	1	1	yes	characteristic
66	C₈	—	2	2	no	—
67	C₂²	—	86	2	no	—
68	C₂²	—	172	1	no	—
69	C₂²	—	172	1	no	—
70	C₂²	C₂×D₁₇₂	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	172	1	no	—
73	C₄	—	172	2	no	—
74	C₄	D₃₄₄	1	2	yes	—
75	C₄	#10621900	1	1	yes	characteristic
76	C₄	Q₈×D₄₃	1	1	yes	characteristic
77	C₂	—	172	2	no	—
78	C₂	#13063305	1	1	yes	characteristic
79	C₂	C₂×D₃₄₄	1	1	yes	characteristic
80	C₂	#13063358	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂³
Frattini	C₂×C₄	C₂²×D₄₃
Fitting	C₄⋊C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₄
prime radical	C₂×D₁₇₂	C₂²
hypercenter	C₄⋊C₈	D₄₃
hypocenter	C₄₃	#474
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. #13063325	C₂	semidirect
3. #13063259	C₂	semidirect
5. C₄⋊C₈×C₄₃	C₂	semidirect
22. D₁₇₂	Q₈	semidirect
41. C₄₃	#474	semidirect
45. C₄⋊C₈	D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#13063325	2
C₄×D₁₇₂	2
#13063259	2
#13063247	2
C₄⋊C₈×C₄₃	2
#474	43