Subgroups — #22626898

Order 9344.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989645	C₂	1	8	yes	maximal, complemented
2	C₂×#14556665	C₂	1	6	yes	maximal, complemented
3	C₂×#14556598	C₂	1	1	yes	maximal, characteristic
4	#14556665	C₂²	1	4	yes	—
5	#14556665	C₂²	1	12	yes	complemented
6	C₂×#11924031	C₂²	1	12	yes	complemented
7	#14556598	C₄	1	4	yes	—
8	#14556598	C₂²	1	4	yes	—
9	C₂×#11924012	C₄	1	3	yes	—
10	C₂²×#10596831	C₂²	1	3	yes	—
11	C₂×#41×C₇₃	C₄	1	1	yes	characteristic
12	#11924031	C₂³	1	8	yes	—
13	#11924012	C₂×C₄	1	12	yes	—
14	C₂×#10596831	C₂×C₄	1	3	yes	—
15	C₂×#10596831	C₂×C₄	1	6	yes	—
16	C₂×#10596831	C₂³	1	1	yes	characteristic
17	C₂×#10596831	C₂³	1	6	yes	—
18	#41×C₇₃	C₈	1	4	yes	—
19	#41×C₇₃	C₂×C₄	1	4	yes	—
20	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic
21	C₂×D₄×C₇₃	C₈	1	3	yes	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	3	yes	—
23	C₂³×C₇₃	C₂×C₈	1	3	yes	—
24	Q₈×C₇₃	C₂×C₈	1	4	yes	—
25	D₄×C₇₃	C₂×C₈	1	12	yes	—
26	C₂×C₄×C₇₃	C₂×C₈	1	3	yes	—
27	C₂×C₄×C₇₃	C₂×C₈	1	6	yes	—
28	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₄×C₇₃	C₂²×C₄	1	6	yes	—
30	#10596831	C₂²×C₄	1	1	yes	characteristic
31	#10596831	C₂²×C₄	1	6	yes	—
32	#10596831	C₂⁴	1	1	yes	characteristic
33	C₂²×C₇₃	—	4	3	no	—
34	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
35	C₂²×C₇₃	C₂²×C₈	1	6	yes	—
36	C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
37	C₄×C₇₃	C₂²×C₈	1	6	yes	—
38	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
39	C₂×C₇₃	—	2	1	no	—
40	C₂×C₇₃	—	2	6	no	—
41	C₂×C₇₃	C₂³×C₈	1	1	yes	characteristic
42	#3407	—	73	1	no	maximal, Sylow
43	C₇₃	#3407	1	1	yes	characteristic, complemented, Sylow
44	C₂×#131	—	73	1	no	—
45	#504	—	73	8	no	—
46	C₂×M₃₂	—	73	6	no	—
47	C₂×#41	#64408	1	1	yes	characteristic
48	#131	—	73	4	no	—
49	#131	—	73	4	no	—
50	C₂×M₁₆	—	73	3	no	—
51	C₂²×C₈	—	73	3	no	—
52	M₃₂	—	73	4	no	—
53	M₃₂	—	73	12	no	—
54	C₂×C₁₆	—	73	12	no	—
55	#41	#10596833	1	4	yes	—
56	#41	C₂×#64408	1	4	yes	—
57	C₂×Q₈	#10596833	1	1	yes	characteristic
58	C₂×D₄	#10596833	1	3	yes	—
59	C₂²×C₄	C₂×#64408	1	3	yes	—
60	M₁₆	—	73	12	no	—
61	C₂×C₈	—	73	3	no	—
62	C₂×C₈	—	73	6	no	—
63	C₂×C₈	—	73	6	no	—
64	C₂×C₈	—	73	1	no	—
65	C₁₆	—	73	8	no	—
66	C₂³	C₂×#10596833	1	3	yes	—
67	Q₈	C₂×#10596833	1	4	yes	—
68	D₄	C₂×#10596833	1	12	yes	—
69	C₂×C₄	C₂×#10596833	1	3	yes	—
70	C₂×C₄	C₂×#10596833	1	6	yes	—
71	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
72	C₂×C₄	C₂²×#64408	1	6	yes	—
73	C₈	—	73	1	no	—
74	C₈	—	73	1	no	—
75	C₈	—	73	6	no	—
76	C₂²	—	4	3	no	—
77	C₂²	C₂²×#10596833	1	1	yes	characteristic
78	C₂²	C₂²×#10596833	1	6	yes	—
79	C₄	C₂²×#10596833	1	1	yes	characteristic
80	C₄	C₂²×#10596833	1	6	yes	—
81	C₄	C₂³×#64408	1	1	yes	characteristic
82	C₂	—	2	1	no	—
83	C₂	—	2	6	no	—
84	C₂	C₂³×#10596833	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄	C₂³×#64408
commutator, socle	C₂×C₇₃	C₂³×C₈
Fitting	C₂×#41×C₇₃	C₄
hypercenter	C₂×#41	#64408
hypocenter	C₇₃	#3407
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #17989645	C₂	semidirect
2. C₂×#14556665	C₂	semidirect
5. #14556665	C₂²	semidirect
6. C₂×#11924031	C₂²	semidirect
43. C₇₃	#3407	semidirect