Subgroups — #22626334

Order 9344.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989631	C₂	1	2	yes	maximal, complemented
2	#17989516	C₂	1	1	yes	maximal, characteristic, complemented
3	#17989502	C₂	1	2	yes	maximal, complemented
4	#17989474	C₂	1	1	yes	maximal, characteristic, complemented
5	#17989020	C₂	1	1	yes	maximal, characteristic
6	#14556679	—	2	2	no	—
7	#14556664	C₂²	1	1	yes	characteristic
8	#14556662	C₂²	1	2	yes	—
9	#14556656	—	2	2	no	—
10	C₈×#64408	C₂²	1	1	yes	characteristic
11	#14556614	C₂²	1	2	yes	—
12	#14556534	C₄	1	2	yes	complemented
13	D₁₁₆₈	C₄	1	1	yes	characteristic, complemented
14	C₁₆×D₇₃	C₂²	1	1	yes	characteristic
15	Q₃₂×C₇₃	C₄	1	1	yes	characteristic, complemented
16	#11924038	—	2	2	no	—
17	#11924038	—	4	2	no	—
18	#11924036	—	4	2	no	—
19	#11924036	D₄	1	1	yes	characteristic
20	C₄×#64408	D₄	1	1	yes	characteristic
21	#11924031	—	2	1	no	—
22	#11924029	—	2	2	no	—
23	#11924015	—	2	2	no	—
24	D₅₈₄	C₂×C₄	1	2	yes	—
25	C₈×D₇₃	C₂³	1	1	yes	characteristic
26	#11924003	C₂×C₄	1	1	yes	characteristic
27	Q₁₆×C₇₃	C₂×C₄	1	2	yes	—
28	C₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×#64408	—	2	1	no	—
30	Q₈×C₇₃	—	2	2	no	—
31	D₂₉₂	—	2	2	no	—
32	D₂₉₂	—	4	2	no	—
33	C₄×D₇₃	—	4	2	no	—
34	C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
35	#10596833	—	4	2	no	—
36	#10596833	D₈	1	2	yes	—
37	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	#10596831	#41	1	1	yes	characteristic
39	C₂×D₇₃	—	4	2	no	—
40	C₂×D₇₃	#135	1	1	yes	characteristic
41	#64408	—	4	1	no	—
42	C₄×C₇₃	—	4	2	no	—
43	C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
44	Dic₇₃	C₂×D₈	1	1	yes	characteristic
45	C₂×C₇₃	C₄×D₈	1	1	yes	characteristic
46	D₇₃	—	2	1	no	—
47	D₇₃	—	8	2	no	—
48	#2179	—	73	1	no	maximal, Sylow
49	C₇₃	#2179	1	1	yes	characteristic, complemented, Sylow
50	#508	—	73	1	no	—
51	#443	—	73	2	no	—
52	#368	—	73	1	no	—
53	#359	—	73	2	no	—
54	#346	—	73	1	no	—
55	#135	—	73	2	no	—
56	#131	—	146	2	no	—
57	Q₃₂	#64408	1	1	yes	characteristic, complemented
58	SD₃₂	—	73	2	no	—
59	D₁₆	—	73	1	no	—
60	C₂×C₁₆	—	73	1	no	—
61	C₂×C₁₆	—	73	1	no	—
62	#108	—	73	2	no	—
63	#104	—	146	2	no	—
64	C₄×C₈	—	73	1	no	—
65	#41	—	146	2	no	—
66	Q₁₆	C₂×#64408	1	2	yes	—
67	SD₁₆	—	146	2	no	—
68	D₈	—	73	2	no	—
69	M₁₆	—	292	2	no	—
70	M₁₆	—	146	2	no	—
71	C₂×C₈	—	292	2	no	—
72	C₂×C₈	—	73	1	no	—
73	C₂×C₈	—	73	1	no	—
74	C₄²	—	73	1	no	—
75	C₁₆	—	73	1	no	—
76	C₁₆	—	146	1	no	—
77	C₁₆	C₂×#64408	1	1	yes	characteristic
78	Q₈	—	2	2	no	—
79	D₄	—	292	2	no	—
80	D₄	—	146	2	no	—
81	C₂×C₄	—	292	2	no	—
82	C₂×C₄	—	73	1	no	—
83	C₂×C₄	—	146	1	no	—
84	C₈	—	292	2	no	—
85	C₈	—	73	2	no	—
86	C₈	—	73	1	no	—
87	C₈	C₂²×#64408	1	1	yes	characteristic
88	C₂²	—	292	2	no	—
89	C₂²	—	73	1	no	—
90	C₄	—	4	2	no	—
91	C₄	—	292	1	no	—
92	C₄	—	73	1	no	—
93	C₄	D₄×#64408	1	1	yes	characteristic
94	C₂	—	584	2	no	—
95	C₂	—	146	1	no	—
96	C₂	D₈×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₈×#64408
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₈	C₂²×#64408
Fitting	Q₃₂×C₇₃	C₄
socle	C₂×C₇₃	C₄×D₈
hypercenter	Q₃₂	#64408
hypocenter	C₇₃	#2179
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

Complements

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

N	H ≅ G/N	type
1. #17989631	C₂	semidirect
2. #17989516	C₂	semidirect
3. #17989502	C₂	semidirect
4. #17989474	C₂	semidirect
12. #14556534	C₄	semidirect
13. D₁₁₆₈	C₄	semidirect
15. Q₃₂×C₇₃	C₄	semidirect
49. C₇₃	#2179	semidirect
57. Q₃₂	#64408	semidirect