Subgroups — #25017111

Order 11008.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582729	C₂	1	2	yes	maximal
2	#19132799	C₂	1	4	yes	maximal, complemented
3	C₂×C₄₃×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂×#13063261	—	2	2	no	—
5	#14582729	—	2	2	no	—
6	#14582729	C₂²	1	4	yes	—
7	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×M₆₄	C₄	1	4	yes	—
9	C₂×C₃₂×C₄₃	C₂²	1	2	yes	—
10	C₂×#10621877	—	4	2	no	—
11	#13063261	—	2	4	no	—
12	#13063261	—	4	2	no	—
13	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂×C₄	1	2	yes	—
15	C₂×C₁₆×C₄₃	D₄	1	1	yes	characteristic
16	C₂×C₁₆×C₄₃	Q₈	1	2	yes	—
17	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
18	C₃₂×C₄₃	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
21	C₂×C₈×C₄₃	D₈	1	1	yes	characteristic
22	C₂×C₈×C₄₃	Q₁₆	1	2	yes	—
23	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
24	#10621877	—	4	4	no	—
25	#10621877	—	8	2	no	—
26	C₂×C₄₃⋊C₈	—	8	2	no	—
27	C₁₆×C₄₃	C₄⋊C₄	1	2	yes	—
28	C₁₆×C₄₃	C₂²×C₄	1	1	yes	characteristic
29	C₁₆×C₄₃	C₂×Q₈	1	1	yes	characteristic
30	C₂³×C₄₃	Q₃₂	1	1	yes	characteristic
31	C₂×C₄×C₄₃	#107	1	2	yes	—
32	C₂×C₄×C₄₃	D₁₆	1	2	yes	—
33	C₂×C₄×C₄₃	Q₃₂	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
35	C₈×C₄₃	#107	1	2	yes	—
36	C₈×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₈×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
38	C₄₃⋊C₈	—	8	4	no	—
39	#13636	—	43	1	no	maximal, Sylow
40	C₂²×C₄₃	—	4	1	no	—
41	C₂²×C₄₃	#366	1	2	yes	—
42	C₂²×C₄₃	C₂×Q₃₂	1	1	yes	characteristic
43	C₄×C₄₃	#366	1	2	yes	—
44	C₄×C₄₃	C₂×#107	1	1	yes	characteristic
45	C₄×C₄₃	C₂×D₁₆	1	1	yes	characteristic
46	C₂×M₆₄	D₄₃	1	1	yes	characteristic
47	C₂×#368	—	43	2	no	—
48	#1425	—	43	4	no	—
49	C₂×C₄₃	—	2	2	no	—
50	C₂×C₄₃	—	2	1	no	—
51	C₂×C₄₃	C₂×#366	1	1	yes	characteristic
52	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
53	C₂×#108	—	86	2	no	—
54	M₆₄	Dic₄₃	1	4	yes	—
55	C₂×C₃₂	C₂×D₄₃	1	2	yes	—
56	#368	—	43	4	no	—
57	#368	—	86	2	no	—
58	C₄₃	#13636	1	1	yes	characteristic, complemented, Sylow
59	C₂×M₁₆	—	172	2	no	—
60	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
61	C₂×C₁₆	Dic₈₆	1	2	yes	—
62	C₂×C₁₆	D₁₇₂	1	1	yes	characteristic
63	C₂×C₁₆	C₂×Dic₄₃	1	2	yes	—
64	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
65	#108	—	86	4	no	—
66	#108	—	172	2	no	—
67	C₃₂	C₂×Dic₄₃	1	4	yes	—
68	C₂²×C₄	D₃₄₄	1	1	yes	characteristic
69	M₁₆	—	344	2	no	—
70	M₁₆	—	172	4	no	—
71	C₂×C₈	—	344	2	no	—
72	C₂×C₈	D₃₄₄	1	1	yes	characteristic
73	C₂×C₈	Dic₁₇₂	1	2	yes	—
74	C₂×C₈	C₄⋊Dic₄₃	1	2	yes	—
75	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
76	C₁₆	C₄⋊Dic₄₃	1	2	yes	—
77	C₁₆	C₂×Dic₈₆	1	1	yes	characteristic
78	C₁₆	C₂²×Dic₄₃	1	1	yes	characteristic
79	C₂³	Dic₃₄₄	1	1	yes	characteristic
80	C₂×C₄	#13063259	1	2	yes	—
81	C₂×C₄	D₆₈₈	1	2	yes	—
82	C₂×C₄	Dic₃₄₄	1	1	yes	characteristic
83	C₂×C₄	C₂×D₃₄₄	1	1	yes	characteristic
84	C₈	—	344	4	no	—
85	C₈	#13063259	1	2	yes	—
86	C₈	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
87	C₈	C₂×Dic₁₇₂	1	1	yes	characteristic
88	C₂²	—	4	1	no	—
89	C₂²	#14582725	1	2	yes	—
90	C₂²	C₂×Dic₃₄₄	1	1	yes	characteristic
91	C₄	#14582725	1	2	yes	—
92	C₄	C₂×#13063259	1	1	yes	characteristic
93	C₄	C₂×D₆₈₈	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2	2	no	—
96	C₂	C₂×#14582725	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₆₈₈
commutator	C₁₆×C₄₃	C₂²×C₄
Frattini	C₂×C₁₆	C₂²×D₄₃
Fitting	C₂×C₄₃×M₆₄	C₂
socle	C₂×C₄₃	C₂×#366
prime radical	C₂³×C₄₃	Q₃₂
cosocle	C₂×C₁₆×C₄₃	C₂³
hypercenter	C₂×M₆₄	D₄₃
hypocenter	C₄₃	#13636
LCS	G ▷ C₁₆×C₄₃ ▷ C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
2. #19132799	C₂	semidirect
58. C₄₃	#13636	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582729	2
#19132799	2
C₂×C₄₃×M₆₄	2
#13636	43