Subgroups — #22616041

Order 9344.

612 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556591	C₂	1	3	yes	maximal, complemented
2	C₂×#14556579	C₂	1	3	yes	maximal
3	#17988524	C₂	1	8	yes	maximal, complemented
4	#376×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×Dic₁₄₆	C₂²	1	3	yes	—
6	C₂²×D₂₉₂	C₂²	1	1	yes	characteristic
7	#14556591	—	2	12	no	—
8	#14556579	—	2	12	no	—
9	C₂×C₄⋊Dic₇₃	C₂²	1	12	yes	—
10	C₂×#11924005	C₂²	1	12	yes	—
11	C₂×C₄²×C₇₃	C₂²	1	3	yes	—
12	#95×C₇₃	C₂²	1	4	yes	—
13	C₂³×D₇₃	C₂³	1	2	yes	—
14	C₂×Dic₁₄₆	—	2	6	no	—
15	C₂×Dic₁₄₆	—	2	12	no	—
16	C₂×D₂₉₂	—	2	6	no	—
17	C₂²×Dic₇₃	C₂³	1	6	yes	—
18	C₄⋊Dic₇₃	—	2	24	no	—
19	#11924005	—	2	24	no	—
20	C₂²×C₄×C₇₃	C₂³	1	6	yes	—
21	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
22	C₄²×C₇₃	D₄	1	12	yes	—
23	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
24	C₂²×D₇₃	—	2	6	no	—
25	C₂²×D₇₃	—	2	8	no	—
26	C₂×C₄×C₇₃	—	2	12	no	—
27	C₂×C₄×C₇₃	C₂×D₄	1	12	yes	—
28	C₂×C₄×C₇₃	C₂×D₄	1	6	yes	—
29	C₂×Dic₇₃	—	2	6	no	—
30	C₂×Dic₇₃	—	2	12	no	—
31	D₂₉₂	—	4	4	no	—
32	Dic₁₄₆	—	4	12	no	—
33	C₂²×C₇₃	C₂²×D₄	1	3	yes	—
34	C₂²×C₇₃	2₋¹⁺⁴	1	4	yes	—
35	C₂×D₇₃	—	4	2	no	—
36	C₂×D₇₃	—	4	12	no	—
37	C₄×C₇₃	—	2	12	no	—
38	C₄×C₇₃	#127	1	4	yes	—
39	Dic₇₃	—	4	6	no	—
40	C₂×C₇₃	C₂×#127	1	1	yes	characteristic
41	C₂×C₇₃	#536	1	6	yes	—
42	D₇₃	—	8	2	no	—
43	#2658	—	73	1	no	maximal, Sylow
44	C₇₃	#2658	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₄⋊Q₈	—	73	3	no	—
46	C₂×#124	—	73	3	no	—
47	#399	—	73	8	no	—
48	#376	D₇₃	1	1	yes	characteristic, complemented
49	C₂²×Q₈	—	73	3	no	—
50	C₂²×D₄	—	73	1	no	—
51	C₄⋊Q₈	—	146	12	no	—
52	#124	—	146	12	no	—
53	C₂×C₄⋊C₄	—	73	12	no	—
54	C₂×C₂²⋊C₄	—	73	12	no	—
55	C₂×C₄²	C₂×D₇₃	1	3	yes	—
56	#95	C₂×D₇₃	1	4	yes	—
57	C₂⁴	—	73	2	no	—
58	C₂×Q₈	—	146	6	no	—
59	C₂×Q₈	—	146	12	no	—
60	C₂×D₄	—	146	6	no	—
61	C₂²×C₄	—	73	6	no	—
62	C₂²×C₄	C₂²×D₇₃	1	6	yes	—
63	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
64	C₄⋊C₄	—	146	24	no	—
65	C₂²⋊C₄	—	146	24	no	—
66	C₄²	D₂₉₂	1	12	yes	—
67	C₂³	—	146	6	no	—
68	C₂³	—	146	8	no	—
69	C₂³	C₂³×D₇₃	1	1	yes	characteristic
70	Q₈	—	292	12	no	—
71	D₄	—	292	4	no	—
72	C₂×C₄	—	2	12	no	—
73	C₂×C₄	—	146	6	no	—
74	C₂×C₄	—	146	12	no	—
75	C₂×C₄	C₂×D₂₉₂	1	12	yes	—
76	C₂×C₄	C₂×D₂₉₂	1	6	yes	—
77	C₂²	—	292	2	no	—
78	C₂²	—	292	12	no	—
79	C₂²	C₂²×D₂₉₂	1	3	yes	—
80	C₂²	#14556638	1	4	yes	—
81	C₄	—	2	12	no	—
82	C₄	—	292	6	no	—
83	C₄	#14556588	1	4	yes	—
84	C₂	—	584	2	no	—
85	C₂	C₂×#14556588	1	1	yes	characteristic
86	C₂	#17989163	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₃
commutator, socle	C₂³×C₇₃	C₂⁴
Fitting	#376×C₇₃	C₂
hypercenter	#376	D₇₃
hypocenter	C₇₃	#2658
LCS	G ▷ C₂³×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ #376

Complements

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

N	H ≅ G/N	type
1. C₂×#14556591	C₂	semidirect
3. #17988524	C₂	semidirect
4. #376×C₇₃	C₂	semidirect
44. C₇₃	#2658	semidirect
48. #376	D₇₃	semidirect