Subgroups — C₄²×#63241 #17982370

Order 4352.

558 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#63241	C₂	1	6	yes	maximal
2	C₄²×#3624	C₂	1	1	yes	maximal, characteristic
3	C₂²×#63241	C₂²	1	4	yes	—
4	C₄×#63241	C₄	1	24	yes	direct product factor
5	C₂×C₄×#3624	C₄	1	3	yes	—
6	C₂×C₄×#3624	C₂²	1	3	yes	—
7	C₄²×Dic₁₇	C₄	1	1	yes	characteristic
8	C₂²×#3624	C₂×C₄	1	3	yes	—
9	C₂²×#3624	C₂³	1	1	yes	characteristic
10	C₂×#63241	C₂×C₄	1	24	yes	—
11	C₂×C₄²×C₁₇	C₈	1	1	yes	characteristic
12	C₂×C₄×Dic₁₇	C₈	1	3	yes	—
13	C₂×C₄×Dic₁₇	C₂×C₄	1	3	yes	—
14	C₄×#3624	C₈	1	12	yes	—
15	C₄×#3624	C₂×C₄	1	12	yes	—
16	C₂²×C₄×C₁₇	C₂×C₈	1	3	yes	—
17	C₂²×Dic₁₇	C₂×C₈	1	3	yes	—
18	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
19	C₂×#3624	C₄²	1	6	yes	—
20	C₂×#3624	C₂×C₈	1	12	yes	—
21	C₂×#3624	C₂²×C₄	1	6	yes	—
22	#63241	C₄²	1	16	yes	direct product factor
23	C₄²×C₁₇	C₁₆	1	4	yes	complemented
24	C₄×Dic₁₇	C₁₆	1	12	yes	complemented
25	C₄×Dic₁₇	C₄²	1	6	yes	—
26	C₄×Dic₁₇	C₂×C₈	1	6	yes	—
27	C₄²×C₁₆	—	17	1	no	maximal, Sylow
28	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₄×C₈	1	6	yes	—
30	C₂×C₄×C₁₇	C₂×C₁₆	1	6	yes	—
31	C₂×C₄×C₁₇	C₂×C₁₆	1	6	yes	—
32	C₂×Dic₁₇	C₄×C₈	1	6	yes	—
33	C₂×Dic₁₇	C₂×C₁₆	1	12	yes	—
34	C₂×Dic₁₇	C₂×C₄²	1	3	yes	—
35	C₂×Dic₁₇	C₂²×C₈	1	3	yes	—
36	#3624	C₄×C₈	1	12	yes	—
37	#3624	C₂×C₄²	1	4	yes	—
38	C₂×C₄×C₁₆	—	17	6	no	—
39	C₄²×C₈	—	17	1	no	—
40	C₂²×C₁₇	C₂×C₄×C₈	1	3	yes	—
41	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
42	C₂²×C₁₇	C₂²×C₁₆	1	3	yes	—
43	C₄×C₁₇	C₄×C₁₆	1	12	yes	complemented
44	Dic₁₇	C₄×C₁₆	1	12	yes	complemented
45	Dic₁₇	C₄³	1	1	yes	characteristic
46	Dic₁₇	C₂×C₄×C₈	1	3	yes	—
47	C₂²×C₁₆	—	17	4	no	—
48	C₂×C₄×C₈	—	17	3	no	—
49	C₂×C₄×C₈	—	17	3	no	—
50	C₄³	—	17	1	no	—
51	C₄×C₁₆	—	17	24	no	—
52	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
53	C₂×C₁₇	C₂×C₄×C₁₆	1	3	yes	—
54	C₂×C₁₇	C₂×C₄×C₁₆	1	3	yes	—
55	C₂²×C₈	—	17	3	no	—
56	C₂²×C₈	—	17	1	no	—
57	C₂×C₄²	—	17	3	no	—
58	C₂×C₄²	—	17	3	no	—
59	C₂×C₄²	#3633	1	1	yes	characteristic
60	C₂×C₁₆	—	17	24	no	—
61	C₄×C₈	—	17	12	no	—
62	C₄×C₈	—	17	12	no	—
63	C₁₇	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	17	3	no	—
65	C₂²×C₄	—	17	1	no	—
66	C₂²×C₄	C₂×#3633	1	3	yes	—
67	C₂×C₈	—	17	6	no	—
68	C₂×C₈	—	17	12	no	—
69	C₂×C₈	—	17	6	no	—
70	C₄²	—	17	12	no	—
71	C₄²	—	17	6	no	—
72	C₄²	—	17	6	no	—
73	C₄²	#63241	1	4	yes	direct product factor
74	C₁₆	—	17	16	no	—
75	C₂³	C₂²×#3633	1	1	yes	characteristic
76	C₂×C₄	—	17	3	no	—
77	C₂×C₄	—	17	3	no	—
78	C₂×C₄	—	17	6	no	—
79	C₂×C₄	—	17	12	no	—
80	C₂×C₄	#10587665	1	6	yes	—
81	C₂×C₄	C₄×#3633	1	6	yes	—
82	C₂×C₄	C₂×#63241	1	6	yes	—
83	C₈	—	17	4	no	—
84	C₈	—	17	12	no	—
85	C₂²	C₂×C₄×#3633	1	3	yes	—
86	C₂²	C₂²×#63241	1	1	yes	characteristic
87	C₂²	C₂×#10587665	1	3	yes	—
88	C₄	—	17	12	no	—
89	C₄	—	17	1	no	—
90	C₄	—	17	3	no	—
91	C₄	C₄×#63241	1	12	yes	direct product factor
92	C₂	C₄²×#3633	1	1	yes	characteristic
93	C₂	C₂×C₄×#63241	1	3	yes	—
94	C₂	C₄×#10587665	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₂×C₄²	#3633
commutator, hypocenter	C₁₇	C₄²×C₁₆
Frattini	C₂³	C₂²×#3633
Fitting	C₂×C₄²×C₁₇	C₈
socle, prime radical	C₂³×C₁₇	C₂²×C₈
cosocle	C₂²×#3624	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
4. C₄×#63241	C₄	direct (N × H)
22. #63241	C₄²	direct (N × H)
23. C₄²×C₁₇	C₁₆	semidirect
24. C₄×Dic₁₇	C₁₆	semidirect
43. C₄×C₁₇	C₄×C₁₆	semidirect
44. Dic₁₇	C₄×C₁₆	semidirect
63. C₁₇	C₄²×C₁₆	semidirect
73. C₄²	#63241	direct (N × H)
91. C₄	C₄×#63241	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×#63241	2
C₄²×#3624	2
C₄²×C₁₆	17

Subgroups — C42×#63241 #17982370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×#63241 #17982370