Subgroups — #22607971

Order 9344.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17988960	C₂	1	1	yes	maximal, characteristic
2	#17988408	C₂	1	1	yes	maximal, characteristic, complemented
3	#364×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11924017	—	2	1	no	—
5	C₂×#11924017	—	2	1	no	—
6	#14556591	C₄	1	1	yes	characteristic
7	#14556588	C₄	1	1	yes	characteristic
8	#14556531	—	2	1	no	—
9	M₃₂×C₇₃	—	2	1	no	—
10	C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₄₆	—	2	1	no	—
12	C₂×D₂₉₂	—	2	1	no	—
13	C₂×D₂₉₂	—	4	1	no	—
14	#11924017	—	4	1	no	—
15	#11924017	—	4	1	no	—
16	#11924017	—	4	1	no	—
17	#11924017	—	4	1	no	—
18	C₄⋊Dic₇₃	—	4	1	no	—
19	#11924003	—	4	1	no	—
20	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₁₆×C₇₃	—	4	1	no	—
24	C₂²×D₇₃	—	4	1	no	—
25	C₂×C₄×C₇₃	—	2	1	no	—
26	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×Dic₇₃	—	4	1	no	—
28	D₂₉₂	—	4	1	no	—
29	D₂₉₂	—	4	1	no	—
30	D₂₉₂	—	8	2	no	—
31	Dic₁₄₆	—	4	1	no	—
32	Dic₁₄₆	—	4	1	no	—
33	C₈×C₇₃	D₈	1	1	yes	characteristic
34	C₈×C₇₃	D₈	1	1	yes	characteristic
35	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
36	C₈×C₇₃	SD₁₆	1	1	yes	characteristic
37	C₂²×C₇₃	#100	1	1	yes	characteristic
38	C₂×D₇₃	—	8	2	no	—
39	C₂×D₇₃	—	8	1	no	—
40	C₄×C₇₃	—	2	2	no	—
41	C₄×C₇₃	#102	1	1	yes	characteristic
42	C₄×C₇₃	#102	1	1	yes	characteristic
43	Dic₇₃	—	8	1	no	—
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	#331	1	1	yes	characteristic
46	D₇₃	—	16	1	no	—
47	#1359	—	73	1	no	maximal, Sylow
48	C₇₃	#1359	1	1	yes	characteristic, complemented, Sylow
49	#492	—	73	1	no	—
50	#364	—	73	1	no	—
51	#364	D₇₃	1	1	yes	characteristic, complemented
52	C₂×SD₁₆	—	146	1	no	—
53	C₂×SD₁₆	—	146	1	no	—
54	C₄⋊Q₈	—	73	1	no	—
55	#127	—	73	1	no	—
56	M₃₂	—	2	1	no	—
57	M₃₂	—	146	1	no	—
58	C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
59	C₂×Q₈	—	146	1	no	—
60	C₂×D₄	—	292	1	no	—
61	C₂×D₄	—	146	1	no	—
62	SD₁₆	—	292	1	no	—
63	SD₁₆	—	292	1	no	—
64	SD₁₆	—	292	1	no	—
65	SD₁₆	—	292	1	no	—
66	C₂×C₈	D₂₉₂	1	1	yes	characteristic
67	C₂×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
68	C₄⋊C₄	—	292	1	no	—
69	C₄²	C₄×D₇₃	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	292	1	no	—
72	C₂³	—	292	1	no	—
73	Q₈	—	292	1	no	—
74	Q₈	—	292	1	no	—
75	D₄	—	292	1	no	—
76	D₄	—	292	1	no	—
77	D₄	—	584	2	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	292	1	no	—
80	C₂×C₄	#11924005	1	1	yes	characteristic
81	C₈	#11924013	1	1	yes	characteristic
82	C₈	D₅₈₄	1	1	yes	characteristic
83	C₈	#11924015	1	1	yes	characteristic
84	C₈	#11924017	1	1	yes	characteristic
85	C₂²	—	584	2	no	—
86	C₂²	—	584	1	no	—
87	C₂²	#14556507	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	584	1	no	—
90	C₄	#14556511	1	1	yes	characteristic
91	C₄	#14556513	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	1168	1	no	—
94	C₂	#17988330	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17988330
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄×C₈	C₂×D₇₃
Fitting	#364×C₇₃	C₂
socle	C₂×C₇₃	#331
hypercenter	#364	D₇₃
hypocenter	C₇₃	#1359
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #364

Complements

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

N	H ≅ G/N	type
2. #17988408	C₂	semidirect
3. #364×C₇₃	C₂	semidirect
48. C₇₃	#1359	semidirect
51. #364	D₇₃	semidirect