Subgroups — #22607758

Order 9344.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10596831	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×#10596831	C₄	1	4	yes	—
4	C₄×#10596831	—	2	2	no	—
5	C₄×#10596831	—	2	2	no	—
6	C₂²×C₈×C₇₃	C₄	1	2	yes	—
7	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
8	C₄×C₈×C₇₃	—	2	2	no	—
9	C₂×#10596831	—	2	4	no	—
10	C₂×#10596831	—	2	4	no	—
11	C₂×#10596831	C₈	1	8	yes	complemented
12	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
13	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₇₃	—	2	2	no	—
15	C₂×C₈×C₇₃	—	2	2	no	—
16	C₂×C₈×C₇₃	C₈	1	4	yes	complemented
17	C₄²×C₇₃	D₄	1	1	yes	characteristic
18	C₄²×C₇₃	D₄	1	2	yes	—
19	C₄²×C₇₃	Q₈	1	1	yes	characteristic
20	C₂³×C₇₃	C₄²	1	1	yes	characteristic
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
22	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
24	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₂×C₈	1	4	yes	—
26	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₇₃	M₁₆	1	4	yes	—
28	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
29	C₈×C₇₃	—	2	4	no	—
30	#10596831	—	2	8	no	—
31	C₂²×C₇₃	#95	1	1	yes	characteristic
32	C₂²×C₇₃	C₄×C₈	1	2	yes	—
33	C₂²×C₇₃	C₄×C₈	1	1	yes	characteristic
34	C₂²×C₇₃	#97	1	2	yes	—
35	C₂²×C₇₃	#97	1	1	yes	characteristic
36	C₄×C₇₃	C₂²⋊C₈	1	4	yes	—
37	C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
38	C₄×C₇₃	C₄⋊C₈	1	4	yes	—
39	C₄×C₇₃	C₄⋊C₈	1	2	yes	—
40	C₂×C₇₃	C₈²	1	1	yes	characteristic
41	C₂×C₇₃	#322	1	1	yes	characteristic
42	C₂×C₇₃	#322	1	2	yes	—
43	C₂×C₇₃	#336	1	2	yes	—
44	C₂×C₇₃	#336	1	1	yes	characteristic
45	#1273	—	73	1	no	maximal, Sylow
46	C₇₃	#1273	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₄×C₈	—	73	2	no	—
48	C₂×C₄×C₈	D₇₃	1	1	yes	characteristic
49	C₂²×C₈	—	73	4	no	—
50	C₂²×C₈	Dic₇₃	1	2	yes	—
51	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
52	C₄×C₈	—	2	2	no	—
53	C₄×C₈	—	146	2	no	—
54	C₄×C₈	—	146	2	no	—
55	C₂²×C₄	C₄×D₇₃	1	2	yes	—
56	C₂²×C₄	C₂×Dic₇₃	1	1	yes	characteristic
57	C₂×C₈	—	2	2	no	—
58	C₂×C₈	—	2	2	no	—
59	C₂×C₈	—	73	8	no	—
60	C₂×C₈	—	146	4	no	—
61	C₂×C₈	—	146	4	no	—
62	C₂×C₈	#10596831	1	4	yes	complemented
63	C₄²	Dic₁₄₆	1	1	yes	characteristic
64	C₄²	D₂₉₂	1	1	yes	characteristic
65	C₄²	C₂²⋊D₇₃	1	2	yes	—
66	C₂³	C₄×Dic₇₃	1	1	yes	characteristic
67	C₂×C₄	#11924005	1	2	yes	—
68	C₂×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
69	C₂×C₄	#11924007	1	2	yes	—
70	C₂×C₄	C₄⋊Dic₇₃	1	1	yes	characteristic
71	C₂×C₄	C₈×D₇₃	1	4	yes	—
72	C₂×C₄	C₂×#10596831	1	2	yes	—
73	C₂×C₄	#11924011	1	4	yes	—
74	C₂×C₄	#11924012	1	2	yes	—
75	C₈	—	2	4	no	—
76	C₈	—	146	8	no	—
77	C₂²	#14556498	1	1	yes	characteristic
78	C₂²	C₈×Dic₇₃	1	2	yes	—
79	C₂²	C₄×#10596831	1	1	yes	characteristic
80	C₂²	#14556501	1	2	yes	—
81	C₂²	#14556502	1	1	yes	characteristic
82	C₄	#14556503	1	4	yes	—
83	C₄	C₂²⋊#10596831	1	2	yes	—
84	C₄	#14556520	1	4	yes	—
85	C₄	C₄⋊#10596831	1	2	yes	—
86	C₂	C₈×#10596831	1	1	yes	characteristic
87	C₂	#17988308	1	1	yes	characteristic
88	C₂	#17988309	1	2	yes	—
89	C₂	#17988341	1	2	yes	—
90	C₂	#17988342	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂×D₇₃
commutator	C₂×C₇₃	C₈²
Fitting	C₂×C₄×C₈×C₇₃	C₂
socle	C₂³×C₇₃	C₄²
hypercenter	C₂×C₄×C₈	D₇₃
hypocenter	C₇₃	#1273
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
11. C₂×#10596831	C₈	semidirect
16. C₂×C₈×C₇₃	C₈	semidirect
46. C₇₃	#1273	semidirect
62. C₂×C₈	#10596831	semidirect