Subgroups — C₂×C₄⋊#15667918 #36474908

Order 22784.

230 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667918	C₂	1	2	yes	maximal
2	C₄⋊#15667918	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667918	—	2	4	no	—
5	C₂×#15667918	C₂²	1	4	yes	—
6	C₂²×C₁₆×C₈₉	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₈₉	C₄	1	1	yes	characteristic
9	C₄×C₁₆×C₈₉	C₄	1	2	yes	—
10	C₄×C₁₆×C₈₉	C₂²	1	2	yes	—
11	#15667918	—	2	4	no	—
12	C₂²×C₈×C₈₉	C₈	1	1	yes	characteristic
13	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄²×C₈₉	C₈	1	1	yes	characteristic
15	C₂×C₁₆×C₈₉	—	2	2	no	—
16	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
17	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
19	C₂×C₁₆×C₈₉	Q₈	1	2	yes	—
20	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
21	C₄×C₈×C₈₉	C₈	1	2	yes	—
22	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₈₉	C₁₆	1	1	yes	characteristic
24	C₂²×C₄×C₈₉	C₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
26	C₂×C₈×C₈₉	—	2	2	no	—
27	C₂×C₈×C₈₉	C₄⋊C₄	1	2	yes	—
28	C₂×C₈×C₈₉	C₂×C₈	1	2	yes	—
29	C₂×C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
30	C₂×C₈×C₈₉	M₁₆	1	2	yes	—
31	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
32	C₄²×C₈₉	C₁₆	1	2	yes	—
33	C₄²×C₈₉	C₂×C₈	1	2	yes	—
34	C₁₆×C₈₉	—	2	2	no	—
35	C₁₆×C₈₉	C₄⋊C₄	1	2	yes	—
36	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
37	C₁₆×C₈₉	C₂×Q₈	1	1	yes	characteristic
38	C₂³×C₈₉	C₂×C₁₆	1	1	yes	characteristic
39	C₂×C₄×C₈₉	—	2	2	no	—
40	C₂×C₄×C₈₉	C₃₂	1	4	yes	complemented
41	C₂×C₄×C₈₉	C₄⋊C₈	1	2	yes	—
42	C₂×C₄×C₈₉	C₂×C₁₆	1	2	yes	—
43	C₂×C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
44	C₂×C₄×C₈₉	C₂×C₁₆	1	2	yes	—
45	C₂×C₄×C₈₉	M₃₂	1	2	yes	—
46	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
47	C₈×C₈₉	—	2	2	no	—
48	C₈×C₈₉	C₄⋊C₈	1	2	yes	—
49	C₈×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
50	C₈×C₈₉	C₂×M₁₆	1	1	yes	characteristic
51	C₂²×C₈₉	C₄⋊C₁₆	1	2	yes	—
52	C₂²×C₈₉	C₂×C₃₂	1	2	yes	—
53	C₂²×C₈₉	M₆₄	1	2	yes	—
54	C₂²×C₈₉	C₂²×C₁₆	1	1	yes	characteristic
55	C₄×C₈₉	—	2	2	no	—
56	C₄×C₈₉	C₄⋊C₁₆	1	2	yes	—
57	C₄×C₈₉	C₂×C₃₂	1	4	yes	complemented
58	C₄×C₈₉	C₂×C₄⋊C₈	1	1	yes	characteristic
59	C₄×C₈₉	C₂×M₃₂	1	1	yes	characteristic
60	C₂×C₄⋊C₃₂	—	89	1	no	maximal, Sylow
61	C₂×C₈₉	C₄⋊C₃₂	1	4	yes	complemented
62	C₂×C₈₉	C₂×C₄⋊C₁₆	1	1	yes	characteristic
63	C₂×C₈₉	C₂²×C₃₂	1	1	yes	characteristic
64	C₂×C₈₉	C₂×M₆₄	1	1	yes	characteristic
65	C₂²×C₃₂	—	89	2	no	—
66	C₂×C₄×C₁₆	D₈₉	1	1	yes	characteristic
67	C₄⋊C₃₂	—	89	4	no	—
68	C₈₉	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₁₆	Dic₈₉	1	1	yes	characteristic
70	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
71	C₂×C₄×C₈	Dic₈₉	1	1	yes	characteristic
72	C₂×C₃₂	—	89	4	no	—
73	C₂×C₃₂	—	178	4	no	—
74	C₄×C₁₆	Dic₈₉	1	2	yes	—
75	C₄×C₁₆	C₂×D₈₉	1	2	yes	—
76	C₂²×C₈	#10623494	1	1	yes	characteristic
77	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
78	C₂×C₄²	#10623494	1	1	yes	characteristic
79	C₂×C₁₆	—	2	2	no	—
80	C₂×C₁₆	Dic₁₇₈	1	2	yes	—
81	C₂×C₁₆	D₃₅₆	1	2	yes	—
82	C₂×C₁₆	C₂×Dic₈₉	1	2	yes	—
83	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
84	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
85	C₄×C₈	#10623494	1	2	yes	—
86	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
87	C₃₂	—	178	4	no	—
88	C₂²×C₄	#13083549	1	1	yes	characteristic
89	C₂²×C₄	#13083549	1	1	yes	characteristic
90	C₂²×C₄	C₂×#10623494	1	1	yes	characteristic
91	C₂×C₈	—	2	2	no	—
92	C₂×C₈	C₄⋊Dic₈₉	1	2	yes	—
93	C₂×C₈	C₂×#10623494	1	2	yes	—
94	C₂×C₈	C₂×#10623494	1	1	yes	characteristic
95	C₂×C₈	#13083558	1	2	yes	—
96	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
97	C₄²	#13083549	1	2	yes	—
98	C₄²	C₂×#10623494	1	2	yes	—
99	C₁₆	—	2	2	no	—
100	C₁₆	C₄⋊Dic₈₉	1	2	yes	—
101	C₁₆	C₂×D₃₅₆	1	1	yes	characteristic
102	C₁₆	C₂×Dic₁₇₈	1	1	yes	characteristic
103	C₂³	C₂×#13083549	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	#15667918	1	4	yes	complemented
106	C₂×C₄	C₄⋊#10623494	1	2	yes	—
107	C₂×C₄	C₂×#13083549	1	2	yes	—
108	C₂×C₄	C₂×#13083549	1	1	yes	characteristic
109	C₂×C₄	C₂×#13083549	1	2	yes	—
110	C₂×C₄	#15667952	1	2	yes	—
111	C₂×C₄	C₂²×#10623494	1	1	yes	characteristic
112	C₈	—	2	2	no	—
113	C₈	C₄⋊#10623494	1	2	yes	—
114	C₈	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
115	C₈	C₂×#13083558	1	1	yes	characteristic
116	C₂²	C₄⋊#13083549	1	2	yes	—
117	C₂²	C₂×#15667918	1	2	yes	—
118	C₂²	#19151432	1	2	yes	—
119	C₂²	C₂²×#13083549	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	C₄⋊#13083549	1	2	yes	—
122	C₄	C₂×#15667918	1	4	yes	complemented
123	C₄	C₂×C₄⋊#10623494	1	1	yes	characteristic
124	C₄	C₂×#15667952	1	1	yes	characteristic
125	C₂	C₄⋊#15667918	1	4	yes	direct product factor
126	C₂	C₂×C₄⋊#13083549	1	1	yes	characteristic
127	C₂	C₂²×#15667918	1	1	yes	characteristic
128	C₂	C₂×#19151432	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄⋊#15667918	C₂	direct (N × H)
40. C₂×C₄×C₈₉	C₃₂	semidirect
57. C₄×C₈₉	C₂×C₃₂	semidirect
61. C₂×C₈₉	C₄⋊C₃₂	semidirect
68. C₈₉	C₂×C₄⋊C₃₂	semidirect
105. C₂×C₄	#15667918	semidirect
122. C₄	C₂×#15667918	semidirect
125. C₂	C₄⋊#15667918	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×#15667918	2
C₄⋊#15667918	2
C₂×C₄×C₁₆×C₈₉	2
C₂×C₄⋊C₃₂	89

Subgroups — C2×C4⋊#15667918 #36474908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊#15667918 #36474908