Subgroups — C₂²×#14556664 #22626891

Order 9344.

440 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556664	C₂	1	12	yes	maximal, direct product factor
2	C₂²×#11924031	C₂	1	2	yes	maximal, complemented
3	C₂²×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#14556664	C₂²	1	16	yes	direct product factor
5	C₂×#11924031	C₂²	1	12	yes	complemented
6	C₂²×C₄×D₇₃	C₄	1	1	yes	characteristic
7	C₂²×#10596831	C₂²	1	1	yes	characteristic
8	C₂×C₈×D₇₃	C₄	1	6	yes	—
9	C₂×C₈×D₇₃	C₂²	1	6	yes	—
10	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
11	#11924031	C₂³	1	8	yes	complemented
12	C₂³×D₇₃	C₈	1	1	yes	characteristic
13	C₂²×Dic₇₃	C₈	1	1	yes	characteristic
14	C₂×C₄×D₇₃	C₈	1	6	yes	—
15	C₂×C₄×D₇₃	C₂×C₄	1	6	yes	—
16	C₂×#10596831	C₂×C₄	1	3	yes	—
17	C₂×#10596831	C₂³	1	3	yes	—
18	C₈×D₇₃	C₂×C₄	1	12	yes	—
19	C₈×D₇₃	C₂³	1	4	yes	—
20	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	C₂×C₄	1	6	yes	—
22	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂²×D₇₃	C₁₆	1	8	yes	complemented
24	C₂²×D₇₃	C₂×C₈	1	6	yes	—
25	C₂×C₄×C₇₃	C₂×C₈	1	3	yes	—
26	C₂×C₄×C₇₃	C₂²×C₄	1	3	yes	—
27	C₂×Dic₇₃	C₂×C₈	1	6	yes	—
28	C₄×D₇₃	C₂×C₈	1	12	yes	—
29	C₄×D₇₃	C₂²×C₄	1	4	yes	—
30	C₈×C₇₃	C₂²×C₄	1	4	yes	—
31	#10596831	C₂²×C₄	1	3	yes	—
32	#10596831	C₂⁴	1	1	yes	characteristic
33	C₂²×C₇₃	C₂×C₁₆	1	4	yes	complemented
34	C₂²×C₇₃	C₂²×C₈	1	3	yes	—
35	C₂×D₇₃	C₂×C₁₆	1	24	yes	complemented
36	C₂×D₇₃	C₂²×C₈	1	4	yes	—
37	C₄×C₇₃	C₂²×C₈	1	3	yes	—
38	C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
39	Dic₇₃	C₂²×C₈	1	4	yes	—
40	C₂×C₇₃	C₂²×C₁₆	1	6	yes	complemented
41	C₂×C₇₃	C₂³×C₈	1	1	yes	characteristic
42	D₇₃	C₂²×C₁₆	1	8	yes	complemented
43	C₂³×C₁₆	—	73	1	no	maximal, Sylow
44	C₇₃	C₂³×C₁₆	1	1	yes	characteristic, complemented, Sylow
45	C₂³×C₈	—	73	1	no	—
46	C₂²×C₁₆	—	73	2	no	—
47	C₂²×C₁₆	—	73	12	no	—
48	C₂³×C₄	—	73	1	no	—
49	C₂²×C₈	—	73	1	no	—
50	C₂²×C₈	—	73	6	no	—
51	C₂²×C₈	—	73	6	no	—
52	C₂²×C₈	#64408	1	1	yes	characteristic
53	C₂×C₁₆	—	73	12	no	—
54	C₂×C₁₆	—	73	16	no	—
55	C₂⁴	—	73	1	no	—
56	C₂²×C₄	—	73	1	no	—
57	C₂²×C₄	—	73	6	no	—
58	C₂²×C₄	—	73	6	no	—
59	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
60	C₂×C₈	—	73	3	no	—
61	C₂×C₈	—	73	3	no	—
62	C₂×C₈	—	73	12	no	—
63	C₂×C₈	—	73	4	no	—
64	C₂×C₈	C₂×#64408	1	6	yes	—
65	C₁₆	—	73	8	no	—
66	C₂³	—	73	6	no	—
67	C₂³	—	73	8	no	—
68	C₂³	#11924036	1	1	yes	characteristic
69	C₂×C₄	—	73	6	no	—
70	C₂×C₄	—	73	12	no	—
71	C₂×C₄	—	73	4	no	—
72	C₂×C₄	#11924036	1	3	yes	—
73	C₂×C₄	C₂²×#64408	1	3	yes	—
74	C₈	—	73	1	no	—
75	C₈	—	73	3	no	—
76	C₈	C₂²×#64408	1	4	yes	—
77	C₂²	—	73	24	no	—
78	C₂²	—	73	4	no	—
79	C₂²	#14556664	1	4	yes	direct product factor
80	C₂²	C₂×#11924036	1	3	yes	—
81	C₄	—	73	4	no	—
82	C₄	C₂×#11924036	1	3	yes	—
83	C₄	C₂³×#64408	1	1	yes	characteristic
84	C₂	—	73	8	no	—
85	C₂	C₂×#14556664	1	6	yes	direct product factor
86	C₂	C₂²×#11924036	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	#64408
commutator, hypocenter	C₇₃	C₂³×C₁₆
Frattini	C₄	C₂³×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂³×C₇₃	C₂×C₈
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. C₂×#14556664	C₂	direct (N × H)
2. C₂²×#11924031	C₂	semidirect
4. #14556664	C₂²	direct (N × H)
5. C₂×#11924031	C₂²	semidirect
11. #11924031	C₂³	semidirect
23. C₂²×D₇₃	C₁₆	semidirect
33. C₂²×C₇₃	C₂×C₁₆	semidirect
35. C₂×D₇₃	C₂×C₁₆	semidirect
40. C₂×C₇₃	C₂²×C₁₆	semidirect
42. D₇₃	C₂²×C₁₆	semidirect
44. C₇₃	C₂³×C₁₆	semidirect
79. C₂²	#14556664	direct (N × H)
85. C₂	C₂×#14556664	direct (N × H)

Subgroups — C22×#14556664 #22626891

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#14556664 #22626891