Subgroups — C₄×C₄₃⋊#95 #19132815

Order 5504.

752 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Dic₄₃	C₂	1	2	yes	maximal
2	C₂×C₄₃⋊#95	C₂	1	4	yes	maximal
3	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₄₃	C₂²	1	4	yes	—
5	C₂×C₄×Dic₄₃	—	2	4	no	—
6	C₂×C₄×Dic₄₃	—	2	4	no	—
7	C₂×C₄×Dic₄₃	C₄	1	8	yes	complemented
8	C₄₃⋊#95	C₄	1	16	yes	direct product factor
9	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	—	2	4	no	—
12	C₂×C₄²×C₄₃	C₄	1	4	yes	complemented
13	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	—	2	4	no	—
15	C₂²×C₄×C₄₃	—	2	4	no	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	8	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
20	C₂²×C₄×C₄₃	D₄	1	2	yes	—
21	C₂²×C₄×C₄₃	D₄	1	4	yes	—
22	C₂²×C₄×C₄₃	Q₈	1	2	yes	—
23	C₂²×Dic₄₃	—	2	4	no	—
24	C₂²×Dic₄₃	—	2	4	no	—
25	C₂²×Dic₄₃	—	2	8	no	—
26	C₂²×Dic₄₃	C₂×C₄	1	16	yes	—
27	C₂²×Dic₄₃	C₂×C₄	1	8	yes	—
28	C₄²×C₄₃	—	2	8	no	—
29	C₄×Dic₄₃	—	2	16	no	—
30	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
31	C₂³×C₄₃	C₂²×C₄	1	4	yes	—
32	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂³×C₄₃	C₂×D₄	1	2	yes	—
35	C₂³×C₄₃	C₂×Q₈	1	1	yes	characteristic
36	C₂³×C₄₃	#41	1	4	yes	—
37	C₂×C₄×C₄₃	—	2	4	no	—
38	C₂×C₄×C₄₃	—	2	4	no	—
39	C₂×C₄×C₄₃	—	2	16	no	—
40	C₂×C₄×C₄₃	C₄²	1	4	yes	—
41	C₂×C₄×C₄₃	C₄²	1	8	yes	complemented
42	C₂×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
43	C₂×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
44	C₂×C₄×C₄₃	C₄⋊C₄	1	8	yes	—
45	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
46	C₂×Dic₄₃	—	2	8	no	—
47	C₂×Dic₄₃	—	2	8	no	—
48	C₂×Dic₄₃	—	2	16	no	—
49	C₂×Dic₄₃	—	2	16	no	—
50	C₂×Dic₄₃	C₄²	1	16	yes	complemented
51	C₂²×C₄₃	C₂×C₄²	1	4	yes	—
52	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
53	C₂²×C₄₃	C₂×C₄²	1	2	yes	—
54	C₂²×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
57	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄₃	#117	1	4	yes	—
59	C₂²×C₄₃	#117	1	2	yes	—
60	C₂²×C₄₃	C₄×D₄	1	8	yes	—
61	C₂²×C₄₃	C₄×D₄	1	4	yes	—
62	C₂²×C₄₃	C₄×Q₈	1	4	yes	—
63	C₄×C₄₃	—	2	8	no	—
64	C₄×C₄₃	#95	1	8	yes	complemented
65	Dic₄₃	—	2	16	no	—
66	C₄×#95	—	43	1	no	maximal, Sylow
67	C₂×C₄₃	C₄³	1	1	yes	characteristic
68	C₂×C₄₃	C₂×#95	1	1	yes	characteristic
69	C₂×C₄₃	#376	1	1	yes	characteristic
70	C₂×C₄₃	C₄×C₂²⋊C₄	1	2	yes	—
71	C₂×C₄₃	C₄×C₂²⋊C₄	1	4	yes	—
72	C₂×C₄₃	C₄×C₄⋊C₄	1	2	yes	—
73	C₂×C₄₃	C₄×C₄⋊C₄	1	4	yes	—
74	C₂²×C₄²	—	43	2	no	—
75	C₂²×C₄²	D₄₃	1	1	yes	characteristic
76	C₂×#95	—	43	4	no	—
77	C₄₃	C₄×#95	1	1	yes	characteristic, complemented, Sylow
78	C₂³×C₄	—	43	4	no	—
79	C₂³×C₄	C₂×D₄₃	1	2	yes	—
80	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
81	C₂×C₄²	—	2	4	no	—
82	C₂×C₄²	—	43	8	no	—
83	C₂×C₄²	—	86	4	no	—
84	C₂×C₄²	—	86	4	no	—
85	C₂×C₄²	Dic₄₃	1	4	yes	complemented
86	#95	—	43	16	no	—
87	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
88	C₂²×C₄	—	2	4	no	—
89	C₂²×C₄	—	2	4	no	—
90	C₂²×C₄	—	43	16	no	—
91	C₂²×C₄	—	43	8	no	—
92	C₂²×C₄	—	86	4	no	—
93	C₂²×C₄	—	86	8	no	—
94	C₂²×C₄	—	86	4	no	—
95	C₂²×C₄	Dic₈₆	1	2	yes	—
96	C₂²×C₄	C₄×D₄₃	1	8	yes	—
97	C₂²×C₄	C₄×D₄₃	1	4	yes	—
98	C₂²×C₄	D₁₇₂	1	2	yes	—
99	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
100	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
101	C₂²×C₄	C₂²⋊D₄₃	1	4	yes	—
102	C₄²	—	2	8	no	—
103	C₄²	—	86	16	no	—
104	C₂³	C₂×Dic₈₆	1	1	yes	characteristic
105	C₂³	C₂×C₄×D₄₃	1	2	yes	—
106	C₂³	C₂×C₄×D₄₃	1	4	yes	—
107	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
108	C₂³	#10621898	1	4	yes	—
109	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
110	C₂³	C₂×C₂²⋊D₄₃	1	2	yes	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	2	4	no	—
113	C₂×C₄	—	2	16	no	—
114	C₂×C₄	—	43	16	no	—
115	C₂×C₄	—	86	8	no	—
116	C₂×C₄	—	86	8	no	—
117	C₂×C₄	—	86	16	no	—
118	C₂×C₄	—	86	16	no	—
119	C₂×C₄	C₄×Dic₄₃	1	4	yes	—
120	C₂×C₄	C₄×Dic₄₃	1	8	yes	complemented
121	C₂×C₄	Dic₄₃⋊C₄	1	8	yes	—
122	C₂×C₄	C₄⋊Dic₄₃	1	4	yes	—
123	C₂×C₄	(C₂×D₄₃)⋊C₄	1	8	yes	—
124	C₂×C₄	C₂²⋊Dic₄₃	1	4	yes	—
125	C₂²	C₄²×D₄₃	1	4	yes	—
126	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
127	C₂²	C₂×C₄×Dic₄₃	1	2	yes	—
128	C₂²	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
129	C₂²	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
130	C₂²	C₂×Dic₄₃⋊C₄	1	2	yes	—
131	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
132	C₂²	#13063282	1	4	yes	—
133	C₂²	#13063284	1	2	yes	—
134	C₂²	C₄×C₂²⋊D₄₃	1	8	yes	—
135	C₂²	C₄×D₁₇₂	1	4	yes	—
136	C₂²	C₄×Dic₈₆	1	4	yes	—
137	C₄	—	2	8	no	—
138	C₄	—	86	16	no	—
139	C₄	C₄₃⋊#95	1	8	yes	direct product factor
140	C₂	C₄²×Dic₄₃	1	1	yes	characteristic
141	C₂	C₂×C₄₃⋊#95	1	1	yes	characteristic
142	C₂	#14582745	1	1	yes	characteristic
143	C₂	C₄×C₂²⋊Dic₄₃	1	2	yes	—
144	C₂	C₄×(C₂×D₄₃)⋊C₄	1	4	yes	—
145	C₂	C₄×C₄⋊Dic₄₃	1	2	yes	—
146	C₂	C₄×Dic₄₃⋊C₄	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂×D₄₃
commutator	C₂×C₄₃	C₄³
Frattini	C₂⁴	C₂²×D₄₃
Fitting	C₂²×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	C₄×#95
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
7. C₂×C₄×Dic₄₃	C₄	semidirect
8. C₄₃⋊#95	C₄	direct (N × H)
12. C₂×C₄²×C₄₃	C₄	semidirect
41. C₂×C₄×C₄₃	C₄²	semidirect
50. C₂×Dic₄₃	C₄²	semidirect
64. C₄×C₄₃	#95	semidirect
77. C₄₃	C₄×#95	semidirect
85. C₂×C₄²	Dic₄₃	semidirect
120. C₂×C₄	C₄×Dic₄₃	semidirect
139. C₄	C₄₃⋊#95	direct (N × H)

Subgroups — C4×C43⋊#95 #19132815

Conjugacy classes of subgroups

Complements

Subgroups — C₄×C₄₃⋊#95 #19132815