Subgroups — C₄²×#11924031 #34012075

Order 18688.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#11924031	C₂	1	6	yes	maximal
2	C₄²×#10596831	C₂	1	1	yes	maximal, characteristic
3	C₂²×#11924031	C₂²	1	4	yes	—
4	C₄×#11924031	C₄	1	24	yes	direct product factor
5	C₂×C₄×#10596831	C₄	1	3	yes	—
6	C₂×C₄×#10596831	C₂²	1	3	yes	—
7	C₄³×C₇₃	C₄	1	1	yes	characteristic
8	C₂×#11924031	C₂×C₄	1	24	yes	—
9	C₂²×#10596831	C₂×C₄	1	3	yes	—
10	C₂²×#10596831	C₂³	1	1	yes	characteristic
11	C₄×#10596831	C₈	1	12	yes	—
12	C₄×#10596831	C₂×C₄	1	12	yes	—
13	C₂×C₄²×C₇₃	C₈	1	4	yes	—
14	C₂×C₄²×C₇₃	C₂×C₄	1	3	yes	—
15	#11924031	C₄²	1	16	yes	direct product factor
16	C₂×#10596831	C₄²	1	6	yes	—
17	C₂×#10596831	C₂×C₈	1	12	yes	—
18	C₂×#10596831	C₂²×C₄	1	6	yes	—
19	C₂²×C₄×C₇₃	C₂×C₈	1	6	yes	—
20	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
21	C₄²×C₇₃	C₁₆	1	16	yes	complemented
22	C₄²×C₇₃	C₄²	1	6	yes	—
23	C₄²×C₇₃	C₂×C₈	1	6	yes	—
24	C₂³×C₇₃	C₂²×C₈	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₄×C₈	1	12	yes	—
26	C₂×C₄×C₇₃	C₂×C₁₆	1	24	yes	—
27	C₂×C₄×C₇₃	C₂×C₄²	1	3	yes	—
28	C₂×C₄×C₇₃	C₂²×C₈	1	3	yes	—
29	#10596831	C₄×C₈	1	12	yes	—
30	#10596831	C₂×C₄²	1	4	yes	—
31	C₂²×C₇₃	C₂×C₄×C₈	1	3	yes	—
32	C₂²×C₇₃	C₂²×C₁₆	1	4	yes	—
33	C₄×C₇₃	C₄×C₁₆	1	24	yes	complemented
34	C₄×C₇₃	C₄³	1	1	yes	characteristic
35	C₄×C₇₃	C₂×C₄×C₈	1	3	yes	—
36	C₄²×C₁₆	—	73	1	no	maximal, Sylow
37	C₂×C₇₃	C₄²×C₈	1	1	yes	characteristic
38	C₂×C₇₃	C₂×C₄×C₁₆	1	6	yes	—
39	C₂×C₄×C₁₆	—	73	6	no	—
40	C₄²×C₈	—	73	1	no	—
41	C₇₃	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
42	C₂²×C₁₆	—	73	4	no	—
43	C₂×C₄×C₈	—	73	3	no	—
44	C₂×C₄×C₈	—	73	3	no	—
45	C₄³	#64408	1	1	yes	characteristic
46	C₄×C₁₆	—	73	24	no	—
47	C₂²×C₈	—	73	3	no	—
48	C₂²×C₈	—	73	1	no	—
49	C₂×C₄²	#10596833	1	4	yes	—
50	C₂×C₄²	C₂×#64408	1	3	yes	—
51	C₂×C₁₆	—	73	24	no	—
52	C₄×C₈	—	73	12	no	—
53	C₄×C₈	—	73	12	no	—
54	C₂²×C₄	C₂×#10596833	1	6	yes	—
55	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
56	C₂×C₈	—	73	12	no	—
57	C₂×C₈	—	73	6	no	—
58	C₂×C₈	—	73	6	no	—
59	C₄²	#11924031	1	16	yes	direct product factor
60	C₄²	C₄×#64408	1	6	yes	—
61	C₄²	#11924036	1	6	yes	—
62	C₁₆	—	73	16	no	—
63	C₂³	C₂²×#10596833	1	1	yes	characteristic
64	C₂×C₄	C₄×#10596833	1	12	yes	—
65	C₂×C₄	C₂×#11924031	1	24	yes	—
66	C₂×C₄	C₂×C₄×#64408	1	3	yes	—
67	C₂×C₄	C₂×#11924036	1	3	yes	—
68	C₈	—	73	4	no	—
69	C₈	—	73	12	no	—
70	C₂²	C₂×C₄×#10596833	1	3	yes	—
71	C₂²	C₂²×#11924031	1	4	yes	—
72	C₄	C₄×#11924031	1	24	yes	direct product factor
73	C₄	C₄²×#64408	1	1	yes	characteristic
74	C₄	C₄×#11924036	1	3	yes	—
75	C₂	C₄²×#10596833	1	1	yes	characteristic
76	C₂	C₂×C₄×#11924031	1	6	yes	—

	subgroup	G/H
center, hypercenter	C₄³	#64408
commutator, hypocenter	C₇₃	C₄²×C₁₆
Frattini	C₂²×C₄	C₂²×#64408
Fitting	C₄³×C₇₃	C₄
socle, prime radical	C₂³×C₇₃	C₂²×C₈
cosocle	C₂²×#10596831	C₂³
LCS	G ▷ C₇₃
UCS	C₁ ◁ C₄³

Complements

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

N	H ≅ G/N	type
4. C₄×#11924031	C₄	direct (N × H)
15. #11924031	C₄²	direct (N × H)
21. C₄²×C₇₃	C₁₆	semidirect
33. C₄×C₇₃	C₄×C₁₆	semidirect
41. C₇₃	C₄²×C₁₆	semidirect
59. C₄²	#11924031	direct (N × H)
72. C₄	C₄×#11924031	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×#11924031	2
C₄²×#10596831	2
C₄²×C₁₆	73

Subgroups — C42×#11924031 #34012075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#11924031 #34012075