Subgroups — C₂×#14583375 #19147784

Order 5504.

1488 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#14583375	C₂	1	16	yes	maximal, direct product factor
3	C₂×Q₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×Dic₈₆	C₂	1	3	yes	maximal, complemented
5	C₂×#13063290	C₂	1	3	yes	maximal, complemented
6	C₂×#13063283	C₂	1	3	yes	maximal
7	C₂×#13063282	C₂	1	3	yes	maximal
8	C₂×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Dic₈₆	C₂²	1	3	yes	—
10	C₂×Q₈×D₄₃	C₄	1	16	yes	complemented
11	C₂×Q₈×D₄₃	C₂²	1	8	yes	—
12	C₂²×C₄×D₄₃	C₂²	1	3	yes	—
13	Q₈×Dic₄₃	C₂²	1	8	yes	complemented
14	C₄×Dic₈₆	C₂²	1	24	yes	complemented
15	#13063290	C₂²	1	24	yes	complemented
16	#13063283	C₂²	1	24	yes	—
17	#13063282	C₂²	1	24	yes	—
18	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
19	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
20	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
21	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
23	C₂×C₄×Dic₄₃	C₂²	1	3	yes	—
24	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
25	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₄₃	C₂²	1	8	yes	complemented
27	C₂×C₄⋊C₄×C₄₃	C₂²	1	3	yes	—
28	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
29	C₂³×D₄₃	C₂³	1	1	yes	characteristic
30	C₂×Q₈×C₄₃	C₂×C₄	1	8	yes	—
31	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
32	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
34	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
35	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
36	C₂²×Dic₄₃	C₂³	1	3	yes	—
37	C₂²×Dic₄₃	C₂³	1	3	yes	—
38	Q₈×D₄₃	C₂×C₄	1	64	yes	complemented
39	C₂×C₄×D₄₃	C₂×C₄	1	24	yes	—
40	C₂×C₄×D₄₃	C₂³	1	12	yes	—
41	C₂×Dic₈₆	C₂×C₄	1	24	yes	—
42	C₂×Dic₈₆	C₂³	1	12	yes	—
43	C₄⋊C₄×C₄₃	C₂³	1	12	yes	—
44	C₄²×C₄₃	C₂³	1	12	yes	—
45	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
46	(C₂×D₄₃)⋊C₄	C₂³	1	12	yes	—
47	C₄⋊Dic₄₃	C₂³	1	12	yes	—
48	Dic₄₃⋊C₄	C₂³	1	12	yes	—
49	Dic₄₃⋊C₄	C₂³	1	12	yes	—
50	C₄×Dic₄₃	C₂³	1	12	yes	—
51	C₄×Dic₄₃	C₂³	1	24	yes	—
52	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
53	C₂²×D₄₃	—	2	2	no	—
54	C₂²×D₄₃	—	2	2	no	—
55	C₂²×D₄₃	C₂²×C₄	1	4	yes	—
56	C₂²×D₄₃	C₂⁴	1	2	yes	—
57	Q₈×C₄₃	C₂²×C₄	1	16	yes	—
58	C₂×C₄×C₄₃	—	2	6	no	—
59	C₂×C₄×C₄₃	—	2	2	no	—
60	C₂×C₄×C₄₃	C₂²×C₄	1	12	yes	—
61	C₂×C₄×C₄₃	C₂⁴	1	6	yes	—
62	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
63	C₂×C₄×C₄₃	C₂⁴	1	6	yes	—
64	C₂×Dic₄₃	—	2	2	no	—
65	C₂×Dic₄₃	—	2	6	no	—
66	C₂×Dic₄₃	C₂²×C₄	1	12	yes	—
67	C₂×Dic₄₃	C₂⁴	1	2	yes	—
68	C₂×Dic₄₃	C₂⁴	1	6	yes	—
69	C₂×Dic₄₃	C₂⁴	1	6	yes	—
70	C₄×D₄₃	C₂²×C₄	1	48	yes	—
71	Dic₈₆	C₂²×C₄	1	48	yes	—
72	C₂²×C₄₃	C₂³×C₄	1	2	yes	—
73	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
74	C₂²×C₄₃	2₋¹⁺⁴	1	2	yes	—
75	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
76	C₂×D₄₃	—	2	8	no	—
77	C₂×D₄₃	—	2	2	no	—
78	C₂×D₄₃	—	2	2	no	—
79	C₂×D₄₃	C₂³×C₄	1	4	yes	—
80	C₄×C₄₃	—	2	6	no	—
81	C₄×C₄₃	—	2	2	no	—
82	C₄×C₄₃	C₂³×C₄	1	12	yes	—
83	Dic₄₃	—	2	2	no	—
84	Dic₄₃	—	2	6	no	—
85	Dic₄₃	C₂³×C₄	1	12	yes	—
86	C₂×#519	—	43	1	no	maximal, Sylow
87	C₂×C₄₃	#519	1	4	yes	complemented
88	C₂×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
89	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
90	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
91	D₄₃	—	2	4	no	—
92	C₂³×Q₈	—	43	1	no	—
93	#519	—	43	16	no	—
94	C₂×C₄×Q₈	—	43	1	no	—
95	C₂×C₄×Q₈	—	43	3	no	—
96	C₂×C₄×Q₈	—	43	3	no	—
97	C₂×C₄×Q₈	D₄₃	1	1	yes	characteristic, complemented
98	C₂×#117	—	43	3	no	—
99	C₂×#117	—	43	3	no	—
100	C₄₃	C₂×#519	1	1	yes	characteristic, complemented, Sylow
101	C₂²×Q₈	—	43	8	no	—
102	C₂²×Q₈	—	43	16	no	—
103	C₂²×Q₈	—	43	3	no	—
104	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
105	C₂³×C₄	—	43	3	no	—
106	C₄×Q₈	—	43	8	no	—
107	C₄×Q₈	—	43	24	no	—
108	C₄×Q₈	—	43	24	no	—
109	C₄×Q₈	C₂×D₄₃	1	8	yes	complemented
110	#117	—	43	24	no	—
111	#117	—	43	24	no	—
112	C₂×C₄⋊C₄	—	43	3	no	—
113	C₂×C₄⋊C₄	—	43	3	no	—
114	C₂×C₄⋊C₄	—	43	3	no	—
115	C₂×C₄⋊C₄	C₂×D₄₃	1	3	yes	—
116	C₂×C₂²⋊C₄	—	43	3	no	—
117	C₂×C₂²⋊C₄	—	43	1	no	—
118	C₂×C₄²	—	43	6	no	—
119	C₂×C₄²	—	43	3	no	—
120	C₂×C₄²	C₂×D₄₃	1	3	yes	—
121	C₂⁴	—	43	1	no	—
122	C₂×Q₈	—	43	64	no	—
123	C₂×Q₈	—	43	24	no	—
124	C₂×Q₈	—	43	12	no	—
125	C₂×Q₈	C₄×D₄₃	1	8	yes	—
126	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
127	C₂²×C₄	—	43	3	no	—
128	C₂²×C₄	—	43	24	no	—
129	C₂²×C₄	—	43	12	no	—
130	C₂²×C₄	—	43	1	no	—
131	C₂²×C₄	—	43	3	no	—
132	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
133	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
134	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
135	C₄⋊C₄	—	43	12	no	—
136	C₄⋊C₄	—	43	12	no	—
137	C₄⋊C₄	—	43	12	no	—
138	C₄⋊C₄	C₂²×D₄₃	1	12	yes	—
139	C₂²⋊C₄	—	43	12	no	—
140	C₂²⋊C₄	—	43	4	no	—
141	C₄²	—	43	24	no	—
142	C₄²	—	43	12	no	—
143	C₄²	C₂²×D₄₃	1	12	yes	—
144	C₂³	—	43	4	no	—
145	C₂³	—	43	2	no	—
146	C₂³	—	86	2	no	—
147	C₂³	—	86	2	no	—
148	C₂³	C₂³×D₄₃	1	1	yes	characteristic
149	Q₈	—	43	48	no	—
150	Q₈	C₂×C₄×D₄₃	1	16	yes	—
151	C₂×C₄	—	2	6	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	43	12	no	—
154	C₂×C₄	—	43	6	no	—
155	C₂×C₄	—	43	48	no	—
156	C₂×C₄	—	43	2	no	—
157	C₂×C₄	—	43	6	no	—
158	C₂×C₄	—	86	2	no	—
159	C₂×C₄	—	86	6	no	—
160	C₂×C₄	C₂×C₄×D₄₃	1	12	yes	—
161	C₂×C₄	C₂³×D₄₃	1	6	yes	—
162	C₂×C₄	C₂³×D₄₃	1	2	yes	—
163	C₂×C₄	C₂³×D₄₃	1	6	yes	—
164	C₂²	—	43	4	no	—
165	C₂²	—	86	8	no	—
166	C₂²	—	86	2	no	—
167	C₂²	—	86	2	no	—
168	C₂²	C₂²×C₄×D₄₃	1	2	yes	—
169	C₂²	#13063372	1	2	yes	—
170	C₂²	#13063373	1	2	yes	—
171	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
172	C₄	—	2	6	no	—
173	C₄	—	2	2	no	—
174	C₄	—	43	12	no	—
175	C₄	—	86	2	no	—
176	C₄	—	86	6	no	—
177	C₄	C₂²×C₄×D₄₃	1	12	yes	—
178	C₂	—	86	4	no	—
179	C₂	#14583375	1	4	yes	direct product factor
180	C₂	C₂³×C₄×D₄₃	1	1	yes	characteristic
181	C₂	C₂×#13063372	1	1	yes	characteristic
182	C₂	C₂×#13063373	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₄₃
commutator	C₂×C₄₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂×C₄×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₄₃
hypocenter	C₄₃	C₂×#519
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #14583375	C₂	direct (N × H)
3. C₂×Q₈×Dic₄₃	C₂	semidirect
4. C₂×C₄×Dic₈₆	C₂	semidirect
5. C₂×#13063290	C₂	semidirect
8. C₂×C₄×Q₈×C₄₃	C₂	semidirect
10. C₂×Q₈×D₄₃	C₄	semidirect
13. Q₈×Dic₄₃	C₂²	semidirect
14. C₄×Dic₈₆	C₂²	semidirect
15. #13063290	C₂²	semidirect
26. C₄×Q₈×C₄₃	C₂²	semidirect
38. Q₈×D₄₃	C₂×C₄	semidirect
87. C₂×C₄₃	#519	semidirect
97. C₂×C₄×Q₈	D₄₃	semidirect
100. C₄₃	C₂×#519	semidirect
109. C₄×Q₈	C₂×D₄₃	semidirect
179. C₂	#14583375	direct (N × H)

Subgroups — C2×#14583375 #19147784

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583375 #19147784