Subgroups — #22612217

Order 9344.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988992	C₂	1	1	yes	maximal, characteristic
2	#17988989	C₂	1	1	yes	maximal, characteristic
3	#17988415	C₂	1	2	yes	maximal
4	#17988413	C₂	1	2	yes	maximal
5	#346×C₇₃	C₂	1	1	yes	maximal, characteristic
6	#14556591	—	2	1	no	—
7	#14556583	—	2	1	no	—
8	#14556525	—	2	1	no	—
9	#14556525	C₂²	1	1	yes	characteristic
10	#14556525	C₂²	1	2	yes	—
11	#14556525	C₂²	1	1	yes	characteristic
12	#14556523	—	2	1	no	—
13	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
14	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	4	1	no	—
16	C₄⋊Dic₇₃	—	2	1	no	—
17	C₄⋊Dic₇₃	—	2	1	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	—	4	1	no	—
20	#11924007	—	4	1	no	—
21	#11924007	—	4	1	no	—
22	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
23	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
24	C₄²×C₇₃	D₄	1	1	yes	characteristic
25	C₁₆×C₇₃	Q₈	1	4	yes	complemented
26	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
28	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
29	C₂×Dic₇₃	—	4	1	no	—
30	C₂×Dic₇₃	—	4	1	no	—
31	C₂×Dic₇₃	—	4	2	no	—
32	Dic₁₄₆	—	8	2	no	—
33	C₈×C₇₃	Q₁₆	1	2	yes	—
34	C₈×C₇₃	C₂×Q₈	1	2	yes	—
35	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₇₃	—	2	1	no	—
37	C₄×C₇₃	—	2	1	no	—
38	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
39	C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
40	Dic₇₃	—	8	2	no	—
41	Dic₇₃	—	8	1	no	—
42	Dic₇₃	—	8	1	no	—
43	C₂×C₇₃	#500	1	1	yes	characteristic
44	C₂×C₇₃	#509	1	1	yes	characteristic
45	C₂×C₇₃	#510	1	1	yes	characteristic
46	#2255	—	73	1	no	maximal, Sylow
47	C₇₃	#2255	1	1	yes	characteristic, complemented, Sylow
48	#500	—	73	1	no	—
49	#499	—	73	1	no	—
50	#367	—	73	2	no	—
51	#366	—	73	2	no	—
52	#346	D₇₃	1	1	yes	characteristic
53	C₄⋊Q₈	—	146	1	no	—
54	#125	—	146	1	no	—
55	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
56	#107	—	73	1	no	—
57	#107	—	73	2	no	—
58	#107	—	73	1	no	—
59	#107	—	146	1	no	—
60	#106	—	146	1	no	—
61	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
62	C₂×Q₈	—	292	1	no	—
63	C₂×C₈	D₂₉₂	1	1	yes	characteristic
64	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
65	C₄⋊C₄	—	292	1	no	—
66	C₄⋊C₄	—	292	1	no	—
67	C₄⋊C₄	—	292	1	no	—
68	C₄⋊C₄	—	146	1	no	—
69	C₄⋊C₄	—	146	1	no	—
70	C₄⋊C₄	—	146	2	no	—
71	C₄²	D₂₉₂	1	1	yes	characteristic
72	C₁₆	Dic₁₄₆	1	4	yes	complemented
73	Q₈	—	584	2	no	—
74	C₂×C₄	—	292	1	no	—
75	C₂×C₄	—	292	1	no	—
76	C₂×C₄	—	292	2	no	—
77	C₂×C₄	D₅₈₄	1	1	yes	characteristic
78	C₂×C₄	D₅₈₄	1	1	yes	characteristic
79	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
80	C₈	Dic₂₉₂	1	2	yes	—
81	C₈	C₂×Dic₁₄₆	1	2	yes	—
82	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	2	1	no	—
85	C₄	—	584	2	no	—
86	C₄	—	584	1	no	—
87	C₄	—	584	1	no	—
88	C₄	#14556591	1	1	yes	characteristic
89	C₄	C₂×Dic₂₉₂	1	1	yes	characteristic
90	C₂	#17988992	1	1	yes	characteristic
91	C₂	#17989025	1	1	yes	characteristic
92	C₂	#17989030	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅₈₄
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#346×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#346	D₇₃
hypocenter	C₇₃	#2255
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
25. C₁₆×C₇₃	Q₈	semidirect
47. C₇₃	#2255	semidirect
72. C₁₆	Dic₁₄₆	semidirect