Subgroups — #22624869

Order 9344.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#11924031	C₂	1	2	yes	maximal
2	#17988614	C₂	1	1	yes	maximal, characteristic
3	C₂×#11924031	—	2	2	no	—
4	C₂×#11924012	C₄	1	1	yes	characteristic
5	C₂²×#10596831	C₂²	1	1	yes	characteristic
6	C₄⋊#10596831	—	2	2	no	—
7	#117×C₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	4	2	no	—
9	#11924012	—	4	1	no	—
10	C₂×#10596831	—	2	1	no	—
11	C₂×#10596831	—	4	1	no	—
12	C₂×#10596831	D₄	1	2	yes	—
13	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₄×C₇₃	C₈	1	2	yes	—
15	C₂²⋊C₄×C₇₃	—	2	1	no	—
16	C₄²×C₇₃	—	2	1	no	—
17	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
18	C₂×C₄×C₇₃	—	2	1	no	—
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	—	2	2	no	—
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	#10596831	—	2	2	no	—
24	#10596831	—	4	1	no	—
25	C₂²×C₇₃	—	2	1	no	—
26	C₂²×C₇₃	—	2	2	no	—
27	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₇₃	—	2	1	no	—
29	C₄×C₇₃	—	4	2	no	—
30	C₄×C₇₃	#99	1	1	yes	characteristic
31	C₄×C₇₃	#101	1	1	yes	characteristic
32	C₂×C₇₃	—	4	1	no	—
33	C₂×C₇₃	#324	1	1	yes	characteristic
34	C₂×C₇₃	#350	1	2	yes	—
35	#1323	—	73	1	no	maximal, Sylow
36	C₇₃	#1323	1	1	yes	characteristic, complemented, Sylow
37	#424	—	73	1	no	—
38	C₂²⋊C₁₆	—	73	2	no	—
39	C₂×M₁₆	—	73	1	no	—
40	C₂²×C₈	—	73	1	no	—
41	#117	#64408	1	1	yes	characteristic
42	C₂×C₁₆	—	146	2	no	—
43	C₄⋊C₈	—	146	2	no	—
44	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
45	M₁₆	—	292	1	no	—
46	C₂×C₈	—	292	1	no	—
47	C₂×C₈	—	73	2	no	—
48	C₂×C₈	—	146	1	no	—
49	C₄⋊C₄	#10596833	1	2	yes	—
50	C₂²⋊C₄	—	2	1	no	—
51	C₄²	—	2	1	no	—
52	C₁₆	—	292	2	no	—
53	C₂³	#11924037	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
58	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
59	C₈	—	292	1	no	—
60	C₈	—	146	2	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	2	2	no	—
63	C₂²	C₂²⋊#10596833	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	4	2	no	—
66	C₄	#14556650	1	1	yes	characteristic
67	C₄	#14556652	1	1	yes	characteristic
68	C₂	—	4	1	no	—
69	C₂	#17989432	1	1	yes	characteristic
70	C₂	#17989485	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	#117×C₇₃	C₄
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	#117	#64408
hypocenter	C₇₃	#1323
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
36. C₇₃	#1323	semidirect