Subgroups — #22609538

Order 9344.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988964	C₂	1	1	yes	maximal, characteristic
2	#17988935	C₂	1	4	yes	maximal, complemented
3	C₈×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
4	#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₅₈₄	—	2	2	no	—
6	#14556588	C₂²	1	2	yes	—
7	#14556511	—	2	8	no	—
8	C₄×#10596831	C₂²	1	2	yes	—
9	C₂×Q₁₆×C₇₃	—	2	2	no	—
10	C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
11	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×D₂₉₂	—	2	4	no	—
13	C₂×D₂₉₂	—	2	2	no	—
14	D₅₈₄	—	4	4	no	—
15	C₂×#10596831	D₄	1	4	yes	—
16	C₂×Q₈×C₇₃	—	2	2	no	—
17	Q₁₆×C₇₃	—	4	4	no	—
18	C₂×C₈×C₇₃	D₄	1	2	yes	—
19	C₄⋊C₄×C₇₃	—	2	4	no	—
20	C₄²×C₇₃	C₂³	1	1	yes	characteristic
21	C₂²×D₇₃	—	4	2	no	—
22	Q₈×C₇₃	—	4	4	no	—
23	C₂×C₄×C₇₃	—	4	2	no	—
24	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
25	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
26	D₂₉₂	—	4	4	no	—
27	D₂₉₂	—	4	8	no	—
28	C₈×C₇₃	D₈	1	4	yes	—
29	#10596831	—	2	4	no	—
30	C₂²×C₇₃	#127	1	1	yes	characteristic
31	C₂×D₇₃	—	8	2	no	—
32	C₂×D₇₃	—	8	4	no	—
33	C₄×C₇₃	—	8	2	no	—
34	C₄×C₇₃	C₂×D₈	1	2	yes	—
35	C₄×C₇₃	#135	1	4	yes	—
36	C₂×C₇₃	#493	1	1	yes	characteristic
37	C₂×C₇₃	#495	1	2	yes	—
38	D₇₃	—	16	2	no	—
39	#1709	—	73	1	no	maximal, Sylow
40	C₇₃	#1709	1	1	yes	characteristic, complemented, Sylow
41	#494	D₇₃	1	1	yes	characteristic, complemented
42	#493	—	73	1	no	—
43	#486	—	73	4	no	—
44	C₈²	—	73	1	no	—
45	C₂×Q₁₆	—	2	2	no	—
46	C₂×D₈	—	146	2	no	—
47	C₄⋊Q₈	C₂×D₇₃	1	2	yes	—
48	#127	—	73	2	no	—
49	#102	—	146	8	no	—
50	C₄×C₈	—	73	2	no	—
51	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
52	C₂×Q₈	—	2	2	no	—
53	C₂×D₄	—	146	4	no	—
54	C₂×D₄	—	146	2	no	—
55	Q₁₆	—	4	4	no	—
56	D₈	—	292	4	no	—
57	C₂×C₈	—	73	4	no	—
58	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
59	C₄⋊C₄	—	2	4	no	—
60	C₄²	C₂²×D₇₃	1	1	yes	characteristic
61	C₂³	—	292	2	no	—
62	Q₈	—	4	4	no	—
63	D₄	—	292	4	no	—
64	D₄	—	292	8	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	D₄×D₇₃	1	2	yes	—
67	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
68	C₈	—	146	4	no	—
69	C₈	#11924013	1	4	yes	—
70	C₂²	—	584	2	no	—
71	C₂²	—	584	4	no	—
72	C₂²	#14556587	1	1	yes	characteristic
73	C₄	—	8	2	no	—
74	C₄	C₂×#11924013	1	2	yes	—
75	C₄	#14556614	1	4	yes	—
76	C₂	—	1168	2	no	—
77	C₂	#17988963	1	1	yes	characteristic
78	C₂	#17988972	1	2	yes	—

	subgroup	G/H
center	C₂²	#14556587
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#494×C₇₃	C₂
socle	C₂²×C₇₃	#127
hypercenter	#494	D₇₃
hypocenter	C₇₃	#1709
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #494

Complements

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

N	H ≅ G/N	type
2. #17988935	C₂	semidirect
3. C₈×#10596831	C₂	semidirect
4. #494×C₇₃	C₂	semidirect
40. C₇₃	#1709	semidirect
41. #494	D₇₃	semidirect