Subgroups — C₄×#19151320 #36443777

Order 22784.

654 conjugacy classes of subgroups.

The subgroup lattice has 132 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×#10623494	C₂	1	1	yes	maximal, characteristic
2	C₄²×#10623494	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151320	C₂	1	4	yes	maximal
4	C₄²×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#10623494	C₄	1	4	yes	—
6	C₂×C₄×#10623494	C₄	1	4	yes	—
7	C₂×C₄×#10623494	C₂²	1	2	yes	—
8	C₂×C₄×#10623494	C₂²	1	2	yes	—
9	#19151320	C₄	1	16	yes	direct product factor
10	C₂×C₄×C₈×C₈₉	C₄	1	4	yes	—
11	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
12	C₄³×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×#10623494	C₂×C₄	1	4	yes	—
14	C₂²×#10623494	C₂×C₄	1	4	yes	—
15	C₄×#10623494	—	2	8	no	—
16	C₄×#10623494	C₈	1	16	yes	complemented
17	C₄×#10623494	C₂×C₄	1	8	yes	—
18	C₄×#10623494	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₈₉	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
24	C₄×C₈×C₈₉	—	2	8	no	—
25	C₄×C₈×C₈₉	C₂×C₄	1	8	yes	—
26	C₂×#10623494	—	2	8	no	—
27	C₂×#10623494	C₄²	1	8	yes	—
28	C₂×#10623494	C₄²	1	8	yes	—
29	C₂×#10623494	C₂×C₈	1	16	yes	—
30	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
31	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
33	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₈×C₈₉	—	2	8	no	—
35	C₂×C₈×C₈₉	C₄²	1	8	yes	—
36	C₄²×C₈₉	C₂×C₈	1	8	yes	—
37	C₄²×C₈₉	M₁₆	1	8	yes	—
38	C₄²×C₈₉	M₁₆	1	8	yes	—
39	C₄²×C₈₉	C₂²×C₄	1	4	yes	—
40	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
41	C₂×C₄×C₈₉	C₄×C₈	1	8	yes	—
42	C₂×C₄×C₈₉	#97	1	8	yes	—
43	C₂×C₄×C₈₉	#97	1	8	yes	—
44	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
45	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
46	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
47	C₂×C₄×C₈₉	C₂²×C₈	1	4	yes	—
48	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
49	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
50	C₈×C₈₉	—	2	8	no	—
51	#10623494	—	2	8	no	—
52	#10623494	C₄×C₈	1	16	yes	complemented
53	C₂²×C₈₉	C₄³	1	1	yes	characteristic
54	C₂²×C₈₉	C₂×C₄×C₈	1	2	yes	—
55	C₂²×C₈₉	C₂×#97	1	2	yes	—
56	C₂²×C₈₉	C₂×#97	1	2	yes	—
57	C₄×C₈₉	#322	1	16	yes	complemented
58	C₄×C₈₉	C₂×C₄×C₈	1	4	yes	—
59	C₄×C₈₉	C₄×M₁₆	1	4	yes	—
60	C₄×C₈₉	C₄×M₁₆	1	4	yes	—
61	C₄×#322	—	89	1	no	maximal, Sylow
62	C₂×C₈₉	C₂×#322	1	4	yes	—
63	C₂×C₈₉	C₄²×C₈	1	1	yes	characteristic
64	C₂×C₈₉	C₄×#97	1	1	yes	characteristic
65	C₂×C₈₉	C₄×#97	1	1	yes	characteristic
66	C₄²×C₈	—	89	1	no	—
67	C₄²×C₈	—	89	1	no	—
68	C₄²×C₈	D₈₉	1	1	yes	characteristic
69	C₂×#322	—	89	4	no	—
70	C₈₉	C₄×#322	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₄×C₈	—	89	4	no	—
72	C₂×C₄×C₈	—	89	2	no	—
73	C₂×C₄×C₈	—	89	2	no	—
74	C₂×C₄×C₈	—	89	4	no	—
75	C₂×C₄×C₈	Dic₈₉	1	4	yes	—
76	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
77	C₄³	C₂×D₈₉	1	1	yes	characteristic
78	#322	—	89	16	no	—
79	C₂²×C₈	—	89	4	no	—
80	C₂²×C₈	—	89	4	no	—
81	C₂²×C₈	C₂×Dic₈₉	1	4	yes	—
82	C₂×C₄²	C₄×D₈₉	1	2	yes	—
83	C₂×C₄²	C₄×D₈₉	1	2	yes	—
84	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
85	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
86	C₄×C₈	—	2	8	no	—
87	C₄×C₈	—	89	16	no	—
88	C₄×C₈	—	89	8	no	—
89	C₄×C₈	—	89	8	no	—
90	C₄×C₈	—	178	8	no	—
91	C₄×C₈	C₄×D₈₉	1	8	yes	—
92	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
93	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
94	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
95	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
96	C₂×C₈	—	2	8	no	—
97	C₂×C₈	—	89	16	no	—
98	C₂×C₈	—	89	8	no	—
99	C₂×C₈	—	89	8	no	—
100	C₂×C₈	—	178	8	no	—
101	C₂×C₈	C₄×Dic₈₉	1	8	yes	—
102	C₄²	C₈×D₈₉	1	8	yes	—
103	C₄²	#13083557	1	8	yes	—
104	C₄²	#13083558	1	8	yes	—
105	C₄²	C₂×C₄×D₈₉	1	4	yes	—
106	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
107	C₂×C₄	C₈×Dic₈₉	1	8	yes	—
108	C₂×C₄	#15667922	1	8	yes	—
109	C₂×C₄	#15667923	1	8	yes	—
110	C₂×C₄	C₄²×D₈₉	1	2	yes	—
111	C₂×C₄	C₄²×D₈₉	1	2	yes	—
112	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
113	C₂×C₄	C₂×C₈×D₈₉	1	4	yes	—
114	C₂×C₄	C₂×#13083557	1	4	yes	—
115	C₂×C₄	C₂×#13083558	1	4	yes	—
116	C₈	—	2	8	no	—
117	C₈	—	89	16	no	—
118	C₈	—	178	8	no	—
119	C₂²	C₄²×Dic₈₉	1	1	yes	characteristic
120	C₂²	C₂×C₈×Dic₈₉	1	2	yes	—
121	C₂²	C₂×#15667922	1	2	yes	—
122	C₂²	C₂×#15667923	1	2	yes	—
123	C₄	#19151320	1	16	yes	direct product factor
124	C₄	C₄×C₈×D₈₉	1	4	yes	—
125	C₄	C₄×#13083557	1	4	yes	—
126	C₄	C₄×#13083558	1	4	yes	—
127	C₂	C₂×#19151320	1	4	yes	—
128	C₂	C₄×C₈×Dic₈₉	1	1	yes	characteristic
129	C₂	C₄×#15667922	1	1	yes	characteristic
130	C₂	C₄×#15667923	1	1	yes	characteristic

	subgroup	G/H
center	C₄³	C₂×D₈₉
commutator	C₂×C₈₉	C₄²×C₈
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₄²×C₈×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂×C₄²
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₄²×C₈	D₈₉
hypocenter	C₈₉	C₄×#322
LCS	G ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄³ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
9. #19151320	C₄	direct (N × H)
16. C₄×#10623494	C₈	semidirect
52. #10623494	C₄×C₈	semidirect
57. C₄×C₈₉	#322	semidirect
70. C₈₉	C₄×#322	semidirect
123. C₄	#19151320	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×#10623494	2
C₂×#19151320	2
C₄²×C₈×C₈₉	2
C₄×#322	89

Subgroups — C4×#19151320 #36443777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151320 #36443777