Subgroups — #22607908

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988705	C₂	1	1	yes	maximal, characteristic
2	#17988408	C₂	1	1	yes	maximal, characteristic, complemented
3	#322×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#14556613	C₄	1	1	yes	characteristic
5	#14556597	—	2	1	no	—
6	#14556531	—	2	1	no	—
7	#14556527	C₄	1	1	yes	characteristic
8	#14556519	—	2	1	no	—
9	C₄×C₈×C₇₃	—	2	1	no	—
10	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	#11924028	—	2	1	no	—
12	Dic₂₉₂	C₈	1	1	yes	characteristic, complemented
13	#11924017	—	2	1	no	—
14	D₅₈₄	C₈	1	1	yes	characteristic, complemented
15	#11924012	—	2	1	no	—
16	#11924011	—	4	1	no	—
17	C₈×D₇₃	—	4	1	no	—
18	#11924003	—	4	1	no	—
19	C₂×C₈×C₇₃	—	2	2	no	—
20	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₄²×C₇₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂²⋊D₇₃	—	4	1	no	—
26	D₂₉₂	—	2	1	no	—
27	C₄×D₇₃	—	4	1	no	—
28	Dic₁₄₆	—	2	1	no	—
29	C₈×C₇₃	—	4	2	no	—
30	C₈×C₇₃	C₂×C₈	1	1	yes	characteristic
31	C₈×C₇₃	M₁₆	1	1	yes	characteristic
32	C₈×C₇₃	D₈	1	1	yes	characteristic
33	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
34	#10596831	—	4	1	no	—
35	C₂²×C₇₃	#104	1	1	yes	characteristic
36	C₂×D₇₃	—	4	1	no	—
37	C₄×C₇₃	—	2	2	no	—
38	C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
39	C₄×C₇₃	#102	1	1	yes	characteristic
40	Dic₇₃	—	4	1	no	—
41	C₂×C₇₃	—	2	1	no	—
42	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
43	D₇₃	—	8	1	no	—
44	#1336	—	73	1	no	maximal, Sylow
45	C₇₃	#1336	1	1	yes	characteristic, complemented, Sylow
46	#443	—	73	1	no	—
47	#364	—	73	1	no	—
48	#322	D₇₃	1	1	yes	characteristic, complemented
49	#135	—	73	1	no	—
50	#131	—	146	1	no	—
51	M₃₂	—	146	1	no	—
52	#108	—	73	1	no	—
53	#104	—	146	1	no	—
54	C₄×C₈	—	2	1	no	—
55	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
56	#41	—	146	1	no	—
57	Q₁₆	—	73	1	no	—
58	SD₁₆	—	146	1	no	—
59	D₈	—	73	1	no	—
60	M₁₆	—	292	1	no	—
61	M₁₆	—	146	1	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	292	1	no	—
64	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
65	C₂×C₈	D₂₉₂	1	1	yes	characteristic
66	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
67	C₁₆	—	292	1	no	—
68	Q₈	—	146	1	no	—
69	D₄	—	292	1	no	—
70	D₄	—	146	1	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	292	1	no	—
73	C₂×C₄	#11924005	1	1	yes	characteristic
74	C₈	—	4	2	no	—
75	C₈	—	292	1	no	—
76	C₈	C₈×D₇₃	1	1	yes	characteristic
77	C₈	#11924011	1	1	yes	characteristic
78	C₈	D₅₈₄	1	1	yes	characteristic
79	C₈	#11924017	1	1	yes	characteristic
80	C₂²	—	292	1	no	—
81	C₂²	#14556519	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	292	1	no	—
84	C₄	#14556503	1	1	yes	characteristic
85	C₄	#14556513	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	584	1	no	—
88	C₂	#17988316	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556513
commutator	C₈×C₇₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₇₃
Fitting	#322×C₇₃	C₂
socle	C₂×C₇₃	D₄⋊C₈
hypercenter	#322	D₇₃
hypocenter	C₇₃	#1336
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #322

Complements

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

N	H ≅ G/N	type
2. #17988408	C₂	semidirect
3. #322×C₇₃	C₂	semidirect
12. Dic₂₉₂	C₈	semidirect
14. D₅₈₄	C₈	semidirect
45. C₇₃	#1336	semidirect
48. #322	D₇₃	semidirect