Subgroups — C₂×#26018469 #36475477

Order 22784.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₄₂₄	C₂	1	1	yes	maximal, characteristic
2	#26018469	C₂	1	4	yes	maximal, direct product factor
3	C₂×#19151317	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₆₄×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₁₂	—	2	1	no	—
6	Dic₁₄₂₄	—	2	1	no	—
7	Dic₁₄₂₄	C₂²	1	2	yes	—
8	#19151317	C₂²	1	2	yes	—
9	C₂×Q₃₂×C₈₉	—	2	1	no	—
10	Q₆₄×C₈₉	—	2	1	no	—
11	Q₆₄×C₈₉	C₂²	1	2	yes	—
12	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×Dic₃₅₆	—	4	1	no	—
14	Dic₇₁₂	—	2	2	no	—
15	Dic₇₁₂	—	4	1	no	—
16	C₂×Q₁₆×C₈₉	—	4	1	no	—
17	Q₃₂×C₈₉	—	2	2	no	—
18	Q₃₂×C₈₉	—	4	1	no	—
19	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
20	C₃₂×C₈₉	D₄	1	1	yes	characteristic
21	C₃₂×C₈₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₇₈	—	8	1	no	—
23	Dic₃₅₆	—	4	2	no	—
24	Dic₃₅₆	—	8	1	no	—
25	C₂×Q₈×C₈₉	—	8	1	no	—
26	Q₁₆×C₈₉	—	4	2	no	—
27	Q₁₆×C₈₉	—	8	1	no	—
28	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
29	C₁₆×C₈₉	D₈	1	1	yes	characteristic
30	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₈₉	—	8	2	no	—
32	Q₈×C₈₉	—	16	1	no	—
33	C₂×C₄×C₈₉	—	16	1	no	—
34	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
35	C₂×Dic₈₉	—	16	1	no	—
36	Dic₁₇₈	—	8	2	no	—
37	Dic₁₇₈	—	16	1	no	—
38	C₈×C₈₉	D₁₆	1	1	yes	characteristic
39	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
40	C₂²×C₈₉	D₃₂	1	1	yes	characteristic
41	C₄×C₈₉	—	16	2	no	—
42	C₄×C₈₉	D₃₂	1	1	yes	characteristic
43	C₄×C₈₉	C₂×D₁₆	1	1	yes	characteristic
44	Dic₈₉	—	16	2	no	—
45	C₂×Q₁₂₈	—	89	1	no	maximal, Sylow
46	C₂×C₈₉	Q₁₂₈	1	2	yes	complemented
47	C₂×C₈₉	C₂×D₃₂	1	1	yes	characteristic
48	C₂×Q₆₄	—	89	1	no	—
49	C₂×Q₆₄	D₈₉	1	1	yes	characteristic
50	Q₁₂₈	—	89	4	no	—
51	C₂×C₆₄	—	89	1	no	—
52	C₈₉	C₂×Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
53	C₂×Q₃₂	—	2	1	no	—
54	C₂×Q₃₂	—	178	1	no	—
55	Q₆₄	—	2	1	no	—
56	Q₆₄	—	89	2	no	—
57	Q₆₄	—	178	1	no	—
58	Q₆₄	C₂×D₈₉	1	2	yes	—
59	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
60	C₆₄	—	89	2	no	—
61	C₂×Q₁₆	—	4	1	no	—
62	C₂×Q₁₆	—	356	1	no	—
63	Q₃₂	—	2	2	no	—
64	Q₃₂	—	4	1	no	—
65	Q₃₂	—	356	1	no	—
66	Q₃₂	—	178	2	no	—
67	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
68	C₃₂	C₂²⋊D₈₉	1	1	yes	characteristic
69	C₃₂	C₂²×D₈₉	1	1	yes	characteristic
70	C₂×Q₈	—	8	1	no	—
71	C₂×Q₈	—	712	1	no	—
72	Q₁₆	—	4	2	no	—
73	Q₁₆	—	8	1	no	—
74	Q₁₆	—	356	2	no	—
75	Q₁₆	—	712	1	no	—
76	C₂×C₈	#13083559	1	1	yes	characteristic
77	C₁₆	#13083559	1	1	yes	characteristic
78	C₁₆	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
79	Q₈	—	8	2	no	—
80	Q₈	—	16	1	no	—
81	Q₈	—	1424	1	no	—
82	Q₈	—	712	2	no	—
83	C₂×C₄	—	16	1	no	—
84	C₂×C₄	—	1424	1	no	—
85	C₂×C₄	#15667953	1	1	yes	characteristic
86	C₈	#15667953	1	1	yes	characteristic
87	C₈	C₂×#13083559	1	1	yes	characteristic
88	C₂²	#19151433	1	1	yes	characteristic
89	C₄	—	16	2	no	—
90	C₄	—	1424	2	no	—
91	C₄	#19151433	1	1	yes	characteristic
92	C₄	C₂×#15667953	1	1	yes	characteristic
93	C₂	#26018469	1	2	yes	direct product factor
94	C₂	C₂×#19151433	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19151433
commutator, cosocle	C₃₂×C₈₉	C₂³
Frattini	C₃₂	C₂²×D₈₉
Fitting	C₂×Q₆₄×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	D₃₂
hypercenter	C₂×Q₆₄	D₈₉
hypocenter	C₈₉	C₂×Q₁₂₈
LCS	G ▷ C₃₂×C₈₉ ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ C₂×Q₆₄

Complements

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

N	H ≅ G/N	type
2. #26018469	C₂	direct (N × H)
46. C₂×C₈₉	Q₁₂₈	semidirect
52. C₈₉	C₂×Q₁₂₈	semidirect
93. C₂	#26018469	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×Dic₁₄₂₄	2
#26018469	2
C₂×#19151317	2
C₂×Q₆₄×C₈₉	2
C₂×Q₁₂₈	89

Subgroups — C2×#26018469 #36475477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26018469 #36475477