Subgroups — C₂×C₄×#63241 #14545936

Order 2176.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂²×C₄	#3633
commutator, hypocenter	C₁₇	C₂×C₄×C₁₆
Frattini	C₂²	C₂²×#3633
Fitting	C₂²×C₄×C₁₇	C₈
socle, prime radical	C₂³×C₁₇	C₂×C₈
cosocle	C₂×#3624	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
2. C₄×#63241	C₂	direct (N × H)
6. C₂×#63241	C₄	direct (N × H)
19. #63241	C₂×C₄	direct (N × H)
23. C₂×C₄×C₁₇	C₁₆	semidirect
25. C₂×Dic₁₇	C₁₆	semidirect
39. C₄×C₁₇	C₂×C₁₆	semidirect
41. Dic₁₇	C₂×C₁₆	semidirect
47. C₂×C₁₇	C₄×C₁₆	semidirect
58. C₁₇	C₂×C₄×C₁₆	semidirect
77. C₂×C₄	#63241	direct (N × H)
90. C₄	C₂×#63241	direct (N × H)
91. C₂	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
C₂²×#63241	2
C₄×#63241	2
C₂×C₄×#3624	2
C₂×C₄×C₁₆	17

Subgroups — C2×C4×#63241 #14545936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#63241 #14545936