Subgroups — #22626304

Order 9344.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989510	C₂	1	2	yes	maximal, complemented
2	#17989483	C₂	1	2	yes	maximal
3	#17989479	C₂	1	2	yes	maximal, complemented
4	#17988543	C₂	1	1	yes	maximal, characteristic
5	#14556665	C₂²	1	4	yes	—
6	C₂×#11924012	C₂²	1	1	yes	characteristic
7	C₂²×#10596831	C₄	1	1	yes	characteristic
8	#14556502	C₄	1	1	yes	characteristic
9	#14556502	C₂²	1	1	yes	characteristic
10	C₄×#10596831	C₄	1	1	yes	characteristic
11	C₄×#10596831	C₂²	1	1	yes	characteristic
12	#117×C₇₃	C₄	1	1	yes	characteristic
13	#11924031	—	2	4	no	—
14	#11924012	—	2	2	no	—
15	C₂×#10596831	—	2	2	no	—
16	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₇₃	—	2	1	no	—
22	C₂²⋊C₄×C₇₃	—	2	1	no	—
23	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	2	1	no	—
28	C₂×C₄×C₇₃	—	2	1	no	—
29	C₂×C₄×C₇₃	—	2	1	no	—
30	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
32	#10596831	—	2	1	no	—
33	#10596831	—	2	1	no	—
34	#10596831	M₁₆	1	2	yes	—
35	#10596831	#41	1	2	yes	—
36	C₂²×C₇₃	—	2	1	no	—
37	C₂²×C₇₃	—	4	1	no	—
38	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
39	C₄×C₇₃	—	2	1	no	—
40	C₄×C₇₃	—	4	1	no	—
41	C₄×C₇₃	—	4	1	no	—
42	C₄×C₇₃	#117	1	1	yes	characteristic
43	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	—	4	1	no	—
46	C₂×C₇₃	#432	1	1	yes	characteristic
47	#2166	—	73	1	no	maximal, Sylow
48	C₇₃	#2166	1	1	yes	characteristic, complemented, Sylow
49	#405	—	73	1	no	—
50	#364	—	73	2	no	—
51	#349	—	73	2	no	—
52	#347	—	73	2	no	—
53	C₂×M₁₆	—	73	1	no	—
54	C₂²×C₈	—	73	1	no	—
55	#117	#64408	1	1	yes	characteristic
56	M₃₂	—	73	4	no	—
57	#97	—	73	1	no	—
58	#97	—	73	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₄×C₈	—	73	1	no	—
61	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
62	M₁₆	—	146	2	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	146	2	no	—
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	2	1	no	—
70	C₄²	C₂×#64408	1	1	yes	characteristic
71	C₄²	C₂×#64408	1	1	yes	characteristic
72	C₁₆	—	146	4	no	—
73	C₂³	#11924037	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	#11924037	1	1	yes	characteristic
79	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
80	C₈	—	73	2	no	—
81	C₈	—	73	2	no	—
82	C₈	—	146	1	no	—
83	C₈	—	146	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂×#11924037	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	#14556670	1	1	yes	characteristic
91	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#17989607	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#117×C₇₃	C₄
socle	C₂×C₇₃	#432
hypercenter	#117	#64408
hypocenter	C₇₃	#2166
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₄² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #17989510	C₂	semidirect
3. #17989479	C₂	semidirect
48. C₇₃	#2166	semidirect