Subgroups — #19212097

Order 5888.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₇₃₆	C₂	1	1	yes	maximal, characteristic
2	#15671601	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃₆₈	—	2	1	no	—
5	D₇₃₆	—	2	1	no	—
6	D₇₃₆	C₄	1	2	yes	—
7	#13092247	—	2	1	no	—
8	C₂×C₂₃×C₃₂	C₂²	1	1	yes	characteristic
9	C₂₃×C₆₄	—	2	1	no	—
10	C₂×D₁₈₄	—	4	1	no	—
11	C₂×C₁₆×C₂₃	D₄	1	1	yes	characteristic
12	#10625001	—	4	1	no	—
13	D₃₆₈	—	2	2	no	—
14	D₃₆₈	—	4	1	no	—
15	C₂₃×C₃₂	C₂×C₄	1	1	yes	characteristic
16	C₂₃×C₃₂	D₄	1	1	yes	characteristic
17	C₂×D₉₂	—	8	1	no	—
18	C₂×C₈×C₂₃	D₈	1	1	yes	characteristic
19	#67267	—	8	1	no	—
20	D₁₈₄	—	4	2	no	—
21	D₁₈₄	—	8	1	no	—
22	C₁₆×C₂₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₂₃	SD₁₆	1	1	yes	characteristic
24	#7541	—	23	1	no	maximal, Sylow
25	C₂²×D₂₃	—	16	1	no	—
26	C₂×C₄×C₂₃	D₁₆	1	1	yes	characteristic
27	D₉₂	—	8	2	no	—
28	D₉₂	—	16	1	no	—
29	C₈×C₂₃	#102	1	1	yes	characteristic
30	C₈×C₂₃	SD₃₂	1	1	yes	characteristic
31	C₂₃⋊C₈	—	16	1	no	—
32	C₂×D₃₂	—	23	1	no	—
33	M₁₂₈	D₂₃	1	1	yes	characteristic, complemented
34	#1425	—	23	1	no	—
35	C₂²×C₂₃	SD₆₄	1	1	yes	characteristic
36	C₂×D₂₃	—	16	2	no	—
37	C₂×D₂₃	—	32	2	no	—
38	C₄×C₂₃	#357	1	1	yes	characteristic
39	C₄×C₂₃	D₃₂	1	1	yes	characteristic
40	C₂×D₁₆	—	46	1	no	—
41	D₃₂	—	23	2	no	—
42	D₃₂	—	46	1	no	—
43	C₂×C₃₂	C₂×D₂₃	1	1	yes	characteristic
44	#368	—	46	1	no	—
45	C₆₄	—	2	1	no	—
46	C₂×C₂₃	—	2	1	no	—
47	C₂×C₂₃	#1415	1	1	yes	characteristic
48	D₂₃	—	32	2	no	—
49	C₂×D₈	—	92	1	no	—
50	D₁₆	—	46	2	no	—
51	D₁₆	—	92	1	no	—
52	C₂×C₁₆	D₉₂	1	1	yes	characteristic
53	#108	—	92	1	no	—
54	C₃₂	C₄×D₂₃	1	1	yes	characteristic
55	C₃₂	C₂²⋊D₂₃	1	1	yes	characteristic
56	C₂₃	#7541	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₄	—	184	1	no	—
58	D₈	—	92	2	no	—
59	D₈	—	184	1	no	—
60	M₁₆	—	184	1	no	—
61	C₂×C₈	D₁₈₄	1	1	yes	characteristic
62	C₁₆	#67263	1	1	yes	characteristic
63	C₁₆	(C₂×D₂₃)⋊C₄	1	1	yes	characteristic
64	C₂³	—	368	1	no	—
65	D₄	—	368	1	no	—
66	D₄	—	184	2	no	—
67	C₂×C₄	D₃₆₈	1	1	yes	characteristic
68	C₈	—	368	1	no	—
69	C₈	#10624982	1	1	yes	characteristic
70	C₈	#10625003	1	1	yes	characteristic
71	C₂²	—	368	2	no	—
72	C₂²	—	736	2	no	—
73	C₂²	#13092256	1	1	yes	characteristic
74	C₄	#13092219	1	1	yes	characteristic
75	C₄	D₇₃₆	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	736	2	no	—
78	C₂	#15671576	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#15671576
commutator	C₂₃×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₂₃
Fitting	C₂₃×M₁₂₈	C₂
socle	C₂×C₂₃	#1415
hypercenter	M₁₂₈	D₂₃
hypocenter	C₂₃	#7541
LCS	G ▷ C₂₃×C₃₂ ▷ C₁₆×C₂₃ ▷ C₈×C₂₃ ▷ C₄×C₂₃ ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
2. #15671601	C₂	semidirect
3. C₂₃×M₁₂₈	C₂	semidirect
33. M₁₂₈	D₂₃	semidirect
56. C₂₃	#7541	semidirect