Subgroups — #22626346

Order 9344.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924031	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#11924031	C₂	1	2	yes	maximal
3	#17989475	C₂	1	2	yes	maximal
4	C₄×#11924031	C₂	1	1	yes	maximal, characteristic
5	Q₈×#10596831	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924031	C₂²	1	1	yes	characteristic
7	C₂×#11924031	C₂²	1	2	yes	—
8	C₂×#11924031	C₂²	1	1	yes	characteristic
9	C₄⋊#10596831	C₄	1	2	yes	—
10	C₄⋊#10596831	C₄	1	1	yes	characteristic
11	C₄×#10596831	C₂²	1	1	yes	characteristic
12	C₄×#10596831	C₂²	1	2	yes	—
13	C₄×Q₈×C₇₃	C₄	1	1	yes	characteristic
14	#11924031	—	2	1	no	—
15	#11924031	—	2	2	no	—
16	#11924031	Q₈	1	2	yes	complemented
17	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	2	yes	—
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₂×Q₈×C₇₃	C₈	1	1	yes	characteristic
21	C₄⋊C₄×C₇₃	C₈	1	2	yes	—
22	C₄⋊C₄×C₇₃	C₈	1	1	yes	characteristic
23	C₄²×C₇₃	C₂×C₄	1	2	yes	—
24	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
25	Q₈×C₇₃	—	2	2	no	—
26	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
31	#10596831	—	2	1	no	—
32	#10596831	—	2	2	no	—
33	#10596831	C₂×Q₈	1	1	yes	characteristic
34	#10596831	#41	1	1	yes	characteristic
35	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₇₃	—	2	2	no	—
37	C₄×C₇₃	—	2	2	no	—
38	C₄×C₇₃	—	2	1	no	—
39	C₄×C₇₃	M₃₂	1	2	yes	—
40	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
41	C₄×C₇₃	#131	1	1	yes	characteristic
42	C₂×C₇₃	C₈×Q₈	1	1	yes	characteristic
43	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
44	C₂×C₇₃	#504	1	1	yes	characteristic
45	#2183	—	73	1	no	maximal, Sylow
46	C₇₃	#2183	1	1	yes	characteristic, complemented, Sylow
47	C₈×Q₈	—	73	1	no	—
48	C₄⋊C₁₆	—	73	1	no	—
49	C₄⋊C₁₆	—	73	2	no	—
50	#346	—	73	2	no	—
51	C₄×C₁₆	—	73	1	no	—
52	C₄×Q₈	#64408	1	1	yes	characteristic
53	C₂×C₁₆	—	73	1	no	—
54	C₂×C₁₆	—	73	1	no	—
55	C₂×C₁₆	—	73	2	no	—
56	C₄⋊C₈	—	73	2	no	—
57	C₄⋊C₈	—	73	1	no	—
58	C₄×C₈	—	73	1	no	—
59	C₄×C₈	—	73	2	no	—
60	C₂×Q₈	#10596833	1	1	yes	characteristic
61	C₂×C₈	—	73	1	no	—
62	C₂×C₈	—	73	1	no	—
63	C₂×C₈	—	73	2	no	—
64	C₄⋊C₄	#10596833	1	2	yes	—
65	C₄⋊C₄	#10596833	1	1	yes	characteristic
66	C₄²	C₂×#64408	1	2	yes	—
67	C₄²	C₂×#64408	1	1	yes	characteristic
68	C₁₆	—	73	2	no	—
69	C₁₆	—	146	1	no	—
70	C₁₆	—	146	2	no	—
71	Q₈	—	2	2	no	—
72	C₂×C₄	C₂×#10596833	1	2	yes	—
73	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
74	C₂×C₄	C₂×#10596833	1	2	yes	—
75	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
76	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
77	C₈	—	73	1	no	—
78	C₈	—	73	1	no	—
79	C₈	—	146	1	no	—
80	C₈	—	146	2	no	—
81	C₂²	C₂²×#10596833	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	2	2	no	—
84	C₄	—	2	1	no	—
85	C₄	#14556665	1	2	yes	—
86	C₄	Q₈×#64408	1	1	yes	characteristic
87	C₄	#14556679	1	1	yes	characteristic
88	C₂	Q₈×#10596833	1	1	yes	characteristic
89	C₂	C₂×#14556665	1	1	yes	characteristic
90	C₂	#17989645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₄×Q₈×C₇₃	C₄
hypercenter	C₄×Q₈	#64408
hypocenter	C₇₃	#2183
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
16. #11924031	Q₈	semidirect
46. C₇₃	#2183	semidirect