Subgroups — C₂³×#13083561 #26034970

Order 11392.

1720 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₃₅₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13083561	C₂	1	28	yes	maximal, direct product factor
3	C₂³×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₈₉	—	2	1	no	—
6	C₂²×D₃₅₆	—	2	7	no	—
7	C₂²×D₃₅₆	C₂²	1	14	yes	—
8	C₂×#13083561	C₂²	1	112	yes	direct product factor
9	C₂²×#10623494	C₂²	1	14	yes	complemented
10	C₂²×Q₈×C₈₉	—	2	7	no	—
11	C₂²×Q₈×C₈₉	C₂²	1	14	yes	complemented
12	C₂³×C₄×C₈₉	—	2	1	no	—
13	C₂³×C₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₈₉	—	2	14	no	—
15	C₂³×D₈₉	—	4	8	no	—
16	C₂×D₃₅₆	—	2	42	no	—
17	C₂×D₃₅₆	C₂³	1	28	yes	—
18	#13083561	C₂³	1	64	yes	direct product factor
19	C₂×#10623494	C₂³	1	28	yes	complemented
20	C₂⁴×C₈₉	D₄	1	1	yes	characteristic
21	C₂×Q₈×C₈₉	—	2	42	no	—
22	C₂×Q₈×C₈₉	C₂³	1	28	yes	complemented
23	C₂²×C₄×C₈₉	—	2	14	no	—
24	C₂²×C₄×C₈₉	D₄	1	7	yes	—
25	C₂²×C₄×C₈₉	C₂³	1	7	yes	—
26	C₂³×C₈₉	SD₁₆	1	8	yes	complemented
27	C₂³×C₈₉	C₂×D₄	1	7	yes	—
28	C₂²×D₈₉	—	2	28	no	—
29	C₂²×D₈₉	—	4	56	no	—
30	Q₈×C₈₉	—	2	28	no	—
31	Q₈×C₈₉	C₂⁴	1	8	yes	complemented
32	C₂×C₄×C₈₉	—	2	28	no	—
33	C₂×C₄×C₈₉	C₂×D₄	1	21	yes	—
34	C₂×C₄×C₈₉	C₂⁴	1	7	yes	—
35	D₃₅₆	—	2	28	no	—
36	D₃₅₆	C₂⁴	1	8	yes	—
37	#10623494	C₂⁴	1	8	yes	complemented
38	C₂²×C₈₉	C₂×SD₁₆	1	28	yes	complemented
39	C₂²×C₈₉	C₂²×D₄	1	7	yes	—
40	C₂×D₈₉	—	2	8	no	—
41	C₂×D₈₉	—	4	56	no	—
42	C₄×C₈₉	—	2	8	no	—
43	C₄×C₈₉	C₂²×D₄	1	7	yes	—
44	C₄×C₈₉	C₂⁵	1	1	yes	characteristic
45	C₂×C₈₉	C₂²×SD₁₆	1	14	yes	complemented
46	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
47	D₈₉	—	4	8	no	—
48	C₂³×SD₁₆	—	89	1	no	maximal, Sylow
49	C₈₉	C₂³×SD₁₆	1	1	yes	characteristic, complemented, Sylow
50	C₂³×Q₈	D₈₉	1	1	yes	characteristic, complemented
51	C₂³×D₄	—	89	1	no	—
52	C₂²×SD₁₆	—	89	28	no	—
53	C₂³×C₈	—	89	1	no	—
54	C₂⁵	—	178	1	no	—
55	C₂²×Q₈	—	2	7	no	—
56	C₂²×Q₈	C₂×D₈₉	1	14	yes	complemented
57	C₂²×D₄	—	89	14	no	—
58	C₂²×D₄	—	178	7	no	—
59	C₂³×C₄	—	2	1	no	—
60	C₂³×C₄	C₂×D₈₉	1	1	yes	characteristic
61	C₂×SD₁₆	—	89	112	no	—
62	C₂²×C₈	—	89	14	no	—
63	C₂⁴	—	356	8	no	—
64	C₂⁴	—	178	14	no	—
65	C₂⁴	C₂²⋊D₈₉	1	1	yes	characteristic
66	C₂×Q₈	—	2	42	no	—
67	C₂×Q₈	C₂²×D₈₉	1	28	yes	complemented
68	C₂×D₄	—	89	28	no	—
69	C₂×D₄	—	178	42	no	—
70	C₂²×C₄	—	2	14	no	—
71	C₂²×C₄	C₂²⋊D₈₉	1	7	yes	—
72	C₂²×C₄	C₂²×D₈₉	1	7	yes	—
73	SD₁₆	—	89	64	no	—
74	C₂×C₈	—	89	28	no	—
75	C₂³	—	356	56	no	—
76	C₂³	—	178	28	no	—
77	C₂³	#13083561	1	8	yes	direct product factor
78	C₂³	C₂×C₂²⋊D₈₉	1	7	yes	—
79	Q₈	—	2	28	no	—
80	Q₈	C₂³×D₈₉	1	8	yes	complemented
81	D₄	—	89	8	no	—
82	D₄	—	178	28	no	—
83	C₂×C₄	—	2	28	no	—
84	C₂×C₄	C₂×C₂²⋊D₈₉	1	21	yes	—
85	C₂×C₄	C₂³×D₈₉	1	7	yes	—
86	C₈	—	89	8	no	—
87	C₂²	—	356	56	no	—
88	C₂²	—	178	8	no	—
89	C₂²	C₂×#13083561	1	28	yes	direct product factor
90	C₂²	C₂²×C₂²⋊D₈₉	1	7	yes	—
91	C₄	—	2	8	no	—
92	C₄	C₂²×C₂²⋊D₈₉	1	7	yes	—
93	C₄	C₂⁴×D₈₉	1	1	yes	characteristic
94	C₂	—	356	8	no	—
95	C₂	C₂²×#13083561	1	14	yes	direct product factor
96	C₂	C₂³×C₂²⋊D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂²⋊D₈₉
commutator, cosocle	C₄×C₈₉	C₂⁵
Frattini	C₄	C₂⁴×D₈₉
Fitting	C₂³×Q₈×C₈₉	C₂
socle	C₂⁴×C₈₉	D₄
prime radical	C₂³×D₃₅₆	C₂
hypercenter	C₂³×Q₈	D₈₉
hypocenter	C₈₉	C₂³×SD₁₆
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
2. C₂²×#13083561	C₂	direct (N × H)
3. C₂³×#10623494	C₂	semidirect
4. C₂³×Q₈×C₈₉	C₂	semidirect
8. C₂×#13083561	C₂²	direct (N × H)
9. C₂²×#10623494	C₂²	semidirect
11. C₂²×Q₈×C₈₉	C₂²	semidirect
18. #13083561	C₂³	direct (N × H)
19. C₂×#10623494	C₂³	semidirect
22. C₂×Q₈×C₈₉	C₂³	semidirect
26. C₂³×C₈₉	SD₁₆	semidirect
31. Q₈×C₈₉	C₂⁴	semidirect
37. #10623494	C₂⁴	semidirect
38. C₂²×C₈₉	C₂×SD₁₆	semidirect
45. C₂×C₈₉	C₂²×SD₁₆	semidirect
49. C₈₉	C₂³×SD₁₆	semidirect
50. C₂³×Q₈	D₈₉	semidirect
56. C₂²×Q₈	C₂×D₈₉	semidirect
67. C₂×Q₈	C₂²×D₈₉	semidirect
77. C₂³	#13083561	direct (N × H)
80. Q₈	C₂³×D₈₉	semidirect
89. C₂²	C₂×#13083561	direct (N × H)
95. C₂	C₂²×#13083561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₃₅₆	2
C₂²×#13083561	2
C₂³×#10623494	2
C₂³×Q₈×C₈₉	2
C₂³×SD₁₆	89

Subgroups — C23×#13083561 #26034970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×#13083561 #26034970