Subgroups — #25011338

Order 11008.

238 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136877	C₂	1	2	yes	maximal
2	#19136870	C₂	1	2	yes	maximal
3	#19134205	C₂	1	2	yes	maximal
4	C₈×C₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
5	#14583304	C₂²	1	4	yes	—
6	#14583250	—	2	4	no	—
7	#14582727	—	2	4	no	—
8	#14582725	—	2	4	no	—
9	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
10	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₈²×C₄₃	C₂²	1	1	yes	characteristic
12	#13063325	—	2	4	no	—
13	#13063259	—	2	4	no	—
14	#13063259	—	2	4	no	—
15	#13063250	—	4	8	no	—
16	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
17	C₂×C₁₆×C₄₃	D₄	1	2	yes	—
18	C₄×C₈×C₄₃	D₄	1	2	yes	—
19	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₂×Dic₈₆	—	4	4	no	—
21	C₂×C₈×C₄₃	D₈	1	4	yes	—
22	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
23	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
24	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
25	C₄⋊Dic₄₃	—	4	4	no	—
26	C₄⋊Dic₄₃	—	4	4	no	—
27	C₁₆×C₄₃	Q₁₆	1	4	yes	—
28	C₁₆×C₄₃	Q₁₆	1	4	yes	—
29	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
31	C₂×Dic₄₃	—	8	4	no	—
32	Dic₈₆	—	8	8	no	—
33	C₈×C₄₃	—	2	4	no	—
34	C₈×C₄₃	C₂×Q₁₆	1	2	yes	—
35	C₈×C₄₃	C₂×Q₁₆	1	2	yes	—
36	#12522	—	43	1	no	maximal, Sylow
37	C₂²×C₄₃	#493	1	1	yes	characteristic
38	C₄×C₄₃	#494	1	1	yes	characteristic
39	C₄×C₄₃	#494	1	1	yes	characteristic
40	C₄×C₄₃	#508	1	4	yes	—
41	Dic₄₃	—	16	4	no	—
42	#2254	—	43	2	no	—
43	#2252	—	43	2	no	—
44	#1710	—	43	2	no	—
45	C₈×C₁₆	D₄₃	1	1	yes	characteristic
46	C₂×C₄₃	#1713	1	1	yes	characteristic
47	C₂×C₄₃	#2249	1	2	yes	—
48	#500	—	43	4	no	—
49	#487	—	86	4	no	—
50	#367	—	86	4	no	—
51	#366	—	86	4	no	—
52	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
53	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
54	C₈²	C₂×D₄₃	1	1	yes	characteristic
55	C₄₃	#12522	1	1	yes	characteristic, complemented, Sylow
56	C₄⋊Q₈	—	86	4	no	—
57	C₂×C₁₆	D₁₇₂	1	2	yes	—
58	C₂×C₁₆	D₁₇₂	1	2	yes	—
59	#107	—	86	4	no	—
60	#107	—	86	4	no	—
61	#103	—	172	8	no	—
62	C₄×C₈	D₁₇₂	1	2	yes	—
63	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
64	C₂×Q₈	—	172	4	no	—
65	C₂×C₈	D₃₄₄	1	4	yes	—
66	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
67	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
68	C₄⋊C₄	—	172	4	no	—
69	C₄⋊C₄	—	172	4	no	—
70	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
71	C₁₆	Dic₁₇₂	1	4	yes	—
72	C₁₆	Dic₁₇₂	1	4	yes	—
73	Q₈	—	344	8	no	—
74	C₂×C₄	—	344	4	no	—
75	C₂×C₄	#13063322	1	1	yes	characteristic
76	C₂×C₄	C₂×D₃₄₄	1	2	yes	—
77	C₈	—	2	4	no	—
78	C₈	C₂×Dic₁₇₂	1	2	yes	—
79	C₈	C₂×Dic₁₇₂	1	2	yes	—
80	C₂²	#14583276	1	1	yes	characteristic
81	C₄	—	688	4	no	—
82	C₄	#14583279	1	1	yes	characteristic
83	C₄	#14583279	1	1	yes	characteristic
84	C₄	#14583331	1	4	yes	—
85	C₂	#19134213	1	1	yes	characteristic
86	C₂	#19136856	1	2	yes	—

	subgroup	G/H
center	C₂²	#14583276
commutator, cosocle	C₄×C₈×C₄₃	C₂³
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₈×C₁₆×C₄₃	C₂
socle, prime radical	C₂²×C₄₃	#493
hypercenter	C₈×C₁₆	D₄₃
hypocenter	C₄₃	#12522
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
55. C₄₃	#12522	semidirect

Maximal subgroups

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

subgroup	index
#19136877	2
#19136870	2
#19134205	2
C₈×C₁₆×C₄₃	2
#12522	43