Subgroups — #25011306

Order 11008.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19136824	C₂	1	4	yes	maximal
2	#19134213	C₂	1	1	yes	maximal, characteristic
3	#19132512	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1710	C₂	1	1	yes	maximal, characteristic
5	#14583304	—	2	2	no	—
6	#14583279	C₂²	1	2	yes	—
7	#14582702	—	2	8	no	—
8	C₄×C₄₃⋊C₁₆	C₂²	1	2	yes	—
9	C₄₃×#500	C₂²	1	2	yes	—
10	C₄₃×#487	—	2	2	no	—
11	C₈²×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×Dic₁₇₂	—	2	4	no	—
13	#13063325	—	2	2	no	—
14	C₂×C₄₃⋊C₁₆	D₄	1	4	yes	—
15	#13063259	—	4	4	no	—
16	C₄⋊Q₈×C₄₃	—	2	2	no	—
17	#107×C₄₃	—	2	4	no	—
18	#103×C₄₃	—	4	4	no	—
19	C₄×C₈×C₄₃	D₄	1	2	yes	—
20	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×Q₈×C₄₃	—	4	2	no	—
22	C₂×Dic₈₆	—	4	2	no	—
23	C₂×C₈×C₄₃	D₈	1	4	yes	—
24	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
25	C₄⋊C₄×C₄₃	—	4	2	no	—
26	C₄⋊C₄×C₄₃	—	4	2	no	—
27	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
28	C₄⋊Dic₄₃	—	4	4	no	—
29	Dic₁₇₂	—	4	8	no	—
30	C₄₃⋊C₁₆	—	2	4	no	—
31	Q₈×C₄₃	—	8	4	no	—
32	C₂×C₄×C₄₃	—	8	2	no	—
33	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
34	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
35	C₂×Dic₄₃	—	8	2	no	—
36	Dic₈₆	—	8	4	no	—
37	C₈×C₄₃	—	2	4	no	—
38	C₈×C₄₃	#135	1	4	yes	—
39	#12514	—	43	1	no	maximal, Sylow
40	C₂²×C₄₃	#493	1	1	yes	characteristic
41	C₄×C₄₃	—	16	2	no	—
42	C₄×C₄₃	#495	1	2	yes	—
43	C₄×C₄₃	#510	1	4	yes	—
44	Dic₄₃	—	16	2	no	—
45	#2241	—	43	4	no	—
46	#1713	—	43	1	no	—
47	#1710	D₄₃	1	1	yes	characteristic
48	#1311	—	43	1	no	—
49	C₂×C₄₃	#1709	1	1	yes	characteristic
50	C₂×C₄₃	#2251	1	2	yes	—
51	#500	—	86	2	no	—
52	#500	C₂×D₄₃	1	2	yes	—
53	#494	—	43	2	no	—
54	#487	—	2	2	no	—
55	#358	—	86	8	no	—
56	C₄×C₁₆	—	43	2	no	—
57	C₈²	C₂×D₄₃	1	1	yes	characteristic
58	C₄₃	#12514	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₁₆	—	86	4	no	—
60	C₄⋊Q₈	—	2	2	no	—
61	C₄⋊Q₈	—	86	2	no	—
62	C₂×C₁₆	—	43	4	no	—
63	#107	—	2	4	no	—
64	#107	—	172	4	no	—
65	#103	—	4	4	no	—
66	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
67	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
68	C₂×Q₈	—	4	2	no	—
69	C₂×Q₈	—	172	2	no	—
70	Q₁₆	—	172	8	no	—
71	C₂×C₈	#10621882	1	4	yes	—
72	C₂×C₈	D₄×D₄₃	1	2	yes	—
73	C₄⋊C₄	—	4	2	no	—
74	C₄⋊C₄	—	4	2	no	—
75	C₄⋊C₄	—	172	4	no	—
76	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
77	C₁₆	—	86	4	no	—
78	Q₈	—	8	4	no	—
79	Q₈	—	344	4	no	—
80	C₂×C₄	—	8	2	no	—
81	C₂×C₄	—	344	2	no	—
82	C₂×C₄	#13063321	1	1	yes	characteristic
83	C₂×C₄	C₂×#10621882	1	2	yes	—
84	C₈	—	2	4	no	—
85	C₈	#13063348	1	4	yes	—
86	C₂²	#14583275	1	1	yes	characteristic
87	C₄	—	16	2	no	—
88	C₄	—	688	2	no	—
89	C₄	#14583284	1	2	yes	—
90	C₄	#14583339	1	4	yes	—
91	C₂	#19134202	1	1	yes	characteristic
92	C₂	#19136867	1	2	yes	—

	subgroup	G/H
center	C₂²	#14583275
commutator, cosocle	C₄×C₈×C₄₃	C₂³
Frattini	C₄×C₈	C₂²×D₄₃
Fitting	C₄₃×#1710	C₂
socle, prime radical	C₂²×C₄₃	#493
hypercenter	#1710	D₄₃
hypocenter	C₄₃	#12514
LCS	G ▷ C₄×C₈×C₄₃ ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1710

Complements

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

N	H ≅ G/N	type
58. C₄₃	#12514	semidirect

Maximal subgroups

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

subgroup	index
#19136824	2
#19134213	2
#19132512	2
C₄₃×#1710	2
#12514	43