Subgroups — #22611036

Order 9344.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989387	C₂	1	3	yes	maximal, complemented
2	#17988555	C₂	1	3	yes	maximal, complemented
3	#338×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11924028	C₂²	1	3	yes	—
5	#14556624	—	2	6	no	—
6	#14556619	—	2	6	no	—
7	#14556613	—	2	6	no	—
8	C₂²×#10596831	C₂²	1	1	yes	characteristic
9	#14556503	—	2	6	no	—
10	C₂×M₁₆×C₇₃	C₂²	1	3	yes	—
11	#11924028	—	2	6	no	—
12	#11924028	—	2	6	no	—
13	C₂×Dic₁₄₆	D₄	1	3	yes	—
14	C₂×D₂₉₂	D₄	1	3	yes	—
15	C₂×C₂²⋊D₇₃	—	2	3	no	—
16	C₂×C₄×D₇₃	—	2	3	no	—
17	Dic₂₉₂	—	2	6	no	—
18	#11924017	—	2	12	no	—
19	D₅₈₄	—	2	6	no	—
20	C₂×#10596831	—	2	3	no	—
21	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
22	M₁₆×C₇₃	—	2	6	no	—
23	C₂×C₈×C₇₃	D₄	1	6	yes	—
24	C₂³×C₇₃	#41	1	1	yes	characteristic
25	C₂²×D₇₃	—	2	3	no	—
26	C₂×C₄×C₇₃	C₂×D₄	1	3	yes	—
27	C₂×C₄×C₇₃	C₂×D₄	1	3	yes	—
28	C₂²⋊D₇₃	—	4	6	no	—
29	C₂×Dic₇₃	—	2	3	no	—
30	D₂₉₂	—	2	6	no	—
31	C₄×D₇₃	—	4	3	no	—
32	C₄×D₇₃	—	4	3	no	—
33	Dic₁₄₆	—	2	6	no	—
34	C₈×C₇₃	—	2	6	no	—
35	#10596831	—	4	1	no	—
36	C₂²×C₇₃	—	4	1	no	—
37	C₂²×C₇₃	#121	1	3	yes	—
38	C₂×D₇₃	—	4	6	no	—
39	C₂×D₇₃	—	4	3	no	—
40	C₄×C₇₃	#120	1	3	yes	—
41	C₄×C₇₃	#127	1	1	yes	characteristic
42	Dic₇₃	—	4	3	no	—
43	C₂×C₇₃	—	2	3	no	—
44	C₂×C₇₃	#392	1	1	yes	characteristic
45	D₇₃	—	8	3	no	—
46	#2017	—	73	1	no	maximal, Sylow
47	C₇₃	#2017	1	1	yes	characteristic, complemented, Sylow
48	#575	—	73	3	no	—
49	#408	—	73	3	no	—
50	#338	D₇₃	1	1	yes	characteristic, complemented
51	C₂×#41	—	73	3	no	—
52	#137	—	146	6	no	—
53	AGL(1,ℤ/8)	—	146	6	no	—
54	#135	—	146	6	no	—
55	C₂×M₁₆	C₂×D₇₃	1	3	yes	—
56	C₂²×C₈	—	73	1	no	—
57	C₂²⋊C₈	—	146	6	no	—
58	#41	—	146	6	no	—
59	#41	—	146	6	no	—
60	C₂×Q₈	—	73	3	no	—
61	C₂×D₄	—	73	3	no	—
62	C₂×D₄	—	146	3	no	—
63	C₂²×C₄	—	146	3	no	—
64	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
65	Q₁₆	—	146	6	no	—
66	SD₁₆	—	146	12	no	—
67	D₈	—	146	6	no	—
68	M₁₆	—	2	6	no	—
69	C₂×C₈	—	146	3	no	—
70	C₂×C₈	D₂₉₂	1	6	yes	—
71	C₂³	—	146	3	no	—
72	C₂³	#11924029	1	1	yes	characteristic
73	Q₈	—	146	6	no	—
74	D₄	—	292	6	no	—
75	D₄	—	146	6	no	—
76	C₂×C₄	—	292	3	no	—
77	C₂×C₄	—	292	3	no	—
78	C₂×C₄	—	146	3	no	—
79	C₂×C₄	D₄×D₇₃	1	3	yes	—
80	C₂×C₄	C₂×D₂₉₂	1	3	yes	—
81	C₈	—	2	6	no	—
82	C₈	—	292	1	no	—
83	C₂²	—	4	1	no	—
84	C₂²	—	292	6	no	—
85	C₂²	—	292	3	no	—
86	C₂²	#14556566	1	3	yes	—
87	C₄	—	292	3	no	—
88	C₄	#14556561	1	3	yes	—
89	C₄	#14556588	1	1	yes	characteristic
90	C₂	—	2	3	no	—
91	C₂	—	584	3	no	—
92	C₂	#17988497	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556588
commutator	C₂²×C₄×C₇₃	C₂³
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#338×C₇₃	C₂
socle	C₂×C₇₃	#392
hypercenter	#338	D₇₃
hypocenter	C₇₃	#2017
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #338

Complements

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

N	H ≅ G/N	type
1. #17989387	C₂	semidirect
2. #17988555	C₂	semidirect
3. #338×C₇₃	C₂	semidirect
47. C₇₃	#2017	semidirect
50. #338	D₇₃	semidirect