Subgroups — #22612178

Order 9344.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988967	C₂	1	1	yes	maximal, characteristic
2	#17988390	C₂	1	4	yes	maximal
3	#17988363	C₂	1	1	yes	maximal, characteristic
4	#499×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₉₂	—	2	1	no	—
6	C₂×Dic₂₉₂	C₂²	1	2	yes	—
7	#14556591	—	2	1	no	—
8	C₂×#11924003	C₂²	1	2	yes	—
9	#125×C₇₃	—	2	1	no	—
10	#107×C₇₃	C₂²	1	2	yes	—
11	#106×C₇₃	—	2	1	no	—
12	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×Dic₁₄₆	—	2	2	no	—
14	Dic₂₉₂	—	2	4	no	—
15	Dic₂₉₂	—	4	2	no	—
16	C₄⋊Dic₇₃	—	4	2	no	—
17	#11924003	—	2	2	no	—
18	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
20	C₄⋊C₄×C₇₃	—	2	2	no	—
21	C₄⋊C₄×C₇₃	—	4	2	no	—
22	C₄²×C₇₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₇₃	—	4	2	no	—
24	C₂×C₄×C₇₃	D₈	1	2	yes	—
25	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
26	C₂×Dic₇₃	—	4	2	no	—
27	Dic₁₄₆	—	4	2	no	—
28	Dic₁₄₆	—	4	2	no	—
29	C₈×C₇₃	SD₁₆	1	2	yes	—
30	C₈×C₇₃	#41	1	2	yes	—
31	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
32	C₄×C₇₃	—	2	2	no	—
33	C₄×C₇₃	—	8	2	no	—
34	C₄×C₇₃	#124	1	1	yes	characteristic
35	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
36	Dic₇₃	—	8	2	no	—
37	C₂×C₇₃	#486	1	1	yes	characteristic
38	C₂×C₇₃	#510	1	2	yes	—
39	#2245	—	73	1	no	maximal, Sylow
40	C₇₃	#2245	1	1	yes	characteristic, complemented, Sylow
41	#499	D₇₃	1	1	yes	characteristic
42	#494	—	73	1	no	—
43	#358	—	73	4	no	—
44	#346	—	73	1	no	—
45	C₂×Q₁₆	—	73	2	no	—
46	C₂×Q₁₆	—	146	1	no	—
47	C₄⋊Q₈	—	146	1	no	—
48	#125	—	2	1	no	—
49	C₂×C₁₆	—	73	2	no	—
50	#107	C₂×D₇₃	1	2	yes	—
51	#106	—	2	1	no	—
52	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
53	C₂×Q₈	—	146	2	no	—
54	Q₁₆	—	292	2	no	—
55	Q₁₆	—	146	4	no	—
56	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
57	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
58	C₄⋊C₄	—	2	2	no	—
59	C₄⋊C₄	—	4	2	no	—
60	C₄⋊C₄	—	292	2	no	—
61	C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
62	C₁₆	—	146	2	no	—
63	Q₈	—	292	2	no	—
64	Q₈	—	292	2	no	—
65	C₂×C₄	—	4	2	no	—
66	C₂×C₄	—	292	2	no	—
67	C₂×C₄	#11924013	1	2	yes	—
68	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
69	C₈	#11924015	1	2	yes	—
70	C₈	#11924029	1	2	yes	—
71	C₂²	C₂×#11924013	1	1	yes	characteristic
72	C₄	—	2	2	no	—
73	C₄	—	8	2	no	—
74	C₄	—	584	2	no	—
75	C₄	#14556580	1	1	yes	characteristic
76	C₄	C₂×#11924015	1	1	yes	characteristic
77	C₂	#17988935	1	1	yes	characteristic
78	C₂	#17989027	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#11924013
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#499×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#499	D₇₃
hypocenter	C₇₃	#2245
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #499

Complements

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

N	H ≅ G/N	type
40. C₇₃	#2245	semidirect