Subgroups — #22626306

Order 9344.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989509	C₂	1	2	yes	maximal, complemented
2	#17989484	C₂	1	2	yes	maximal
3	#17989479	C₂	1	2	yes	maximal, complemented
4	#17988541	C₂	1	1	yes	maximal, characteristic
5	#14556665	C₂²	1	4	yes	—
6	C₂×#11924011	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₇₃	C₄	1	1	yes	characteristic
8	#14556548	C₄	1	1	yes	characteristic
9	#14556502	C₂²	1	1	yes	characteristic
10	#14556501	C₄	1	1	yes	characteristic
11	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
13	#11924031	—	2	4	no	—
14	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
15	#11924011	—	2	2	no	—
16	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
17	C₂×#10596831	C₂³	1	1	yes	characteristic
18	C₈×D₇₃	—	2	2	no	—
19	#11924007	—	2	1	no	—
20	#11924005	—	2	1	no	—
21	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	—	2	1	no	—
29	C₂×Dic₇₃	M₁₆	1	1	yes	characteristic
30	C₄×D₇₃	—	2	1	no	—
31	C₄×D₇₃	—	2	1	no	—
32	C₈×C₇₃	—	2	1	no	—
33	C₈×C₇₃	M₁₆	1	2	yes	—
34	#10596831	—	2	1	no	—
35	#10596831	#41	1	2	yes	—
36	C₂²×C₇₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×D₇₃	—	2	1	no	—
38	C₂×D₇₃	—	4	1	no	—
39	C₄×C₇₃	—	4	1	no	—
40	C₄×C₇₃	#117	1	1	yes	characteristic
41	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
42	Dic₇₃	—	2	1	no	—
43	Dic₇₃	—	4	1	no	—
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	#432	1	1	yes	characteristic
46	D₇₃	—	4	1	no	—
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	—	73	1	no	—
56	M₃₂	—	73	4	no	—
57	#97	—	73	1	no	—
58	#97	—	73	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₄×C₈	#64408	1	1	yes	characteristic
61	C₂²×C₄	—	73	1	no	—
62	M₁₆	—	146	2	no	—
63	C₂×C₈	—	73	1	no	—
64	C₂×C₈	—	73	1	no	—
65	C₂×C₈	—	146	2	no	—
66	C₂×C₈	C₂×#64408	1	1	yes	characteristic
67	C₂×C₈	C₂×#64408	1	1	yes	characteristic
68	C₄⋊C₄	—	146	1	no	—
69	C₂²⋊C₄	—	146	1	no	—
70	C₄²	—	73	1	no	—
71	C₄²	C₂×#64408	1	1	yes	characteristic
72	C₁₆	—	146	4	no	—
73	C₂³	—	73	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	73	1	no	—
76	C₂×C₄	—	146	1	no	—
77	C₂×C₄	—	146	1	no	—
78	C₂×C₄	—	146	1	no	—
79	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	73	2	no	—
82	C₈	—	146	1	no	—
83	C₈	#11924038	1	2	yes	—
84	C₂²	—	292	1	no	—
85	C₂²	—	146	1	no	—
86	C₂²	D₇₃⋊M₁₆	1	1	yes	characteristic
87	C₄	—	4	1	no	—
88	C₄	—	292	1	no	—
89	C₄	—	146	1	no	—
90	C₄	#14556670	1	1	yes	characteristic
91	C₄	C₂×#11924038	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	292	1	no	—
94	C₂	#17989609	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556670
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	#432
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#2166
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #17989509	C₂	semidirect
3. #17989479	C₂	semidirect
48. C₇₃	#2166	semidirect