Subgroups — C₂×#14583473 #19147912

Order 5504.

1512 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10621898	C₂	1	1	yes	maximal, characteristic
2	#14583473	C₂	1	16	yes	maximal, direct product factor
3	C₂×#13063323	C₂	1	2	yes	maximal, complemented
4	C₂×#13063314	C₂	1	2	yes	maximal, complemented
5	C₂×#13063308	C₂	1	4	yes	maximal, complemented
6	C₂×#13063301	C₂	1	4	yes	maximal, complemented
7	C₂×#13063284	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10621898	—	2	8	no	—
10	C₂×#10621898	C₂²	1	8	yes	—
11	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
12	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊D₄₃	C₂²	1	2	yes	—
14	C₂²×C₄×D₄₃	C₂²	1	2	yes	—
15	#13063323	C₂²	1	16	yes	complemented
16	#13063314	C₂²	1	16	yes	complemented
17	#13063308	C₂²	1	32	yes	complemented
18	#13063301	C₂²	1	32	yes	complemented
19	#13063284	C₂²	1	8	yes	complemented
20	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
21	C₂×Dic₄₃⋊C₄	C₂²	1	8	yes	—
22	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
23	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	8	yes	—
24	C₂×C₄×Dic₄₃	C₂²	1	2	yes	—
25	C₂²×Q₈×C₄₃	—	2	8	no	—
26	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
27	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
28	C₂²×Q₈×C₄₃	C₂²	1	8	yes	complemented
29	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
30	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×D₄₃	C₂³	1	2	yes	—
33	C₂×Q₈×C₄₃	—	2	8	no	—
34	C₂×Q₈×C₄₃	—	2	8	no	—
35	C₂×Q₈×C₄₃	—	2	32	no	—
36	C₂×Q₈×C₄₃	C₂³	1	8	yes	—
37	C₂×Q₈×C₄₃	C₂³	1	8	yes	—
38	C₂²×C₄×C₄₃	—	2	8	no	—
39	C₂²×C₄×C₄₃	D₄	1	8	yes	—
40	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
41	C₂²×C₄×C₄₃	C₂³	1	8	yes	—
42	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
45	C₂×C₂²⋊D₄₃	—	2	8	no	—
46	C₂×C₂²⋊D₄₃	C₂³	1	8	yes	—
47	C₂²×Dic₄₃	C₂³	1	4	yes	—
48	C₂²×Dic₄₃	C₂³	1	2	yes	—
49	#10621898	—	2	32	no	—
50	C₂×D₁₇₂	—	2	4	no	—
51	C₂×D₁₇₂	C₂³	1	4	yes	—
52	C₂×C₄×D₄₃	—	2	8	no	—
53	C₂×C₄×D₄₃	C₂³	1	8	yes	—
54	C₂×Dic₈₆	—	2	4	no	—
55	C₂×Dic₈₆	C₂³	1	4	yes	—
56	C₂²⋊Dic₄₃	C₂³	1	8	yes	—
57	(C₂×D₄₃)⋊C₄	C₂³	1	32	yes	—
58	C₄⋊Dic₄₃	C₂³	1	8	yes	—
59	Dic₄₃⋊C₄	C₂³	1	32	yes	—
60	C₄×Dic₄₃	C₂³	1	8	yes	—
61	C₂³×C₄₃	—	2	4	no	—
62	C₂³×C₄₃	C₂×D₄	1	4	yes	—
63	C₂³×C₄₃	C₂⁴	1	2	yes	—
64	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
65	C₂²×D₄₃	—	2	4	no	—
66	C₂²×D₄₃	—	2	8	no	—
67	C₂²×D₄₃	C₂⁴	1	4	yes	—
68	Q₈×C₄₃	—	2	16	no	—
69	Q₈×C₄₃	—	2	16	no	—
70	C₂×C₄×C₄₃	—	2	16	no	—
71	C₂×C₄×C₄₃	—	2	8	no	—
72	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
73	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
74	C₂×C₄×C₄₃	C₂×D₄	1	16	yes	—
75	C₂×C₄×C₄₃	C₂⁴	1	8	yes	—
76	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
77	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
78	C₂²⋊D₄₃	—	2	16	no	—
79	C₂×Dic₄₃	—	2	4	no	—
80	C₂×Dic₄₃	—	2	8	no	—
81	C₂×Dic₄₃	C₂⁴	1	8	yes	—
82	C₂×Dic₄₃	C₂⁴	1	4	yes	—
83	D₁₇₂	—	2	8	no	—
84	C₄×D₄₃	—	2	16	no	—
85	Dic₈₆	—	2	8	no	—
86	C₂²×C₄₃	—	2	8	no	—
87	C₂²×C₄₃	—	2	4	no	—
88	C₂²×C₄₃	C₂²×D₄	1	4	yes	—
89	C₂²×C₄₃	C₂²×D₄	1	2	yes	—
90	C₂²×C₄₃	2₋¹⁺⁴	1	4	yes	—
91	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
92	C₂×D₄₃	—	2	4	no	—
93	C₂×D₄₃	—	2	8	no	—
94	C₂×D₄₃	—	4	8	no	—
95	C₄×C₄₃	—	2	8	no	—
96	C₄×C₄₃	C₂²×D₄	1	4	yes	—
97	C₄×C₄₃	C₂²×D₄	1	4	yes	—
98	Dic₄₃	—	2	4	no	—
99	Dic₄₃	—	2	8	no	—
100	C₂×#536	—	43	1	no	maximal, Sylow
101	C₂×C₄₃	—	2	4	no	—
102	C₂×C₄₃	#536	1	4	yes	complemented
103	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
104	C₂×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
105	D₄₃	—	4	4	no	—
106	C₂²×#41	—	43	1	no	—
107	C₂³×Q₈	D₄₃	1	1	yes	characteristic, complemented
108	#536	—	43	16	no	—
109	C₂×C₄⋊Q₈	—	43	2	no	—
110	C₂×#124	—	43	2	no	—
111	C₂×#123	—	43	4	no	—
112	C₂×C₂²⋊Q₈	—	43	4	no	—
113	C₂×#117	—	43	1	no	—
114	C₄₃	C₂×#536	1	1	yes	characteristic, complemented, Sylow
115	C₂×#41	—	43	8	no	—
116	C₂×#41	—	86	8	no	—
117	C₂²×Q₈	—	2	8	no	—
118	C₂²×Q₈	—	43	1	no	—
119	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
120	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
121	C₂²×Q₈	C₂×D₄₃	1	8	yes	complemented
122	C₂²×D₄	—	43	2	no	—
123	C₂²×D₄	—	43	1	no	—
124	C₂³×C₄	—	43	2	no	—
125	C₂³×C₄	C₂×D₄₃	1	2	yes	—
126	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
127	C₄⋊Q₈	—	43	16	no	—
128	#124	—	43	16	no	—
129	#123	—	43	32	no	—
130	C₂²⋊Q₈	—	43	32	no	—
131	#117	—	43	8	no	—
132	C₂×C₄⋊C₄	—	43	2	no	—
133	C₂×C₄⋊C₄	—	43	8	no	—
134	C₂×C₂²⋊C₄	—	43	2	no	—
135	C₂×C₂²⋊C₄	—	43	8	no	—
136	C₂×C₄²	—	43	2	no	—
137	C₂⁴	—	43	2	no	—
138	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
139	#41	—	86	32	no	—
140	C₂×Q₈	—	2	8	no	—
141	C₂×Q₈	—	2	8	no	—
142	C₂×Q₈	—	2	32	no	—
143	C₂×Q₈	—	43	4	no	—
144	C₂×Q₈	—	86	4	no	—
145	C₂×Q₈	C₂²×D₄₃	1	8	yes	—
146	C₂×Q₈	C₂²×D₄₃	1	8	yes	—
147	C₂×D₄	—	43	8	no	—
148	C₂×D₄	—	43	4	no	—
149	C₂×D₄	—	86	8	no	—
150	C₂×D₄	—	86	4	no	—
151	C₂²×C₄	—	2	8	no	—
152	C₂²×C₄	—	43	4	no	—
153	C₂²×C₄	—	43	2	no	—
154	C₂²×C₄	—	43	8	no	—
155	C₂²×C₄	—	86	8	no	—
156	C₂²×C₄	C₂²⋊D₄₃	1	8	yes	—
157	C₂²×C₄	C₂²×D₄₃	1	8	yes	—
158	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
159	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
160	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
161	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
162	C₄⋊C₄	—	43	8	no	—
163	C₄⋊C₄	—	43	32	no	—
164	C₂²⋊C₄	—	43	8	no	—
165	C₂²⋊C₄	—	43	32	no	—
166	C₄²	—	43	8	no	—
167	C₂³	—	2	4	no	—
168	C₂³	—	43	4	no	—
169	C₂³	—	86	4	no	—
170	C₂³	—	86	8	no	—
171	C₂³	C₂×C₂²⋊D₄₃	1	4	yes	—
172	C₂³	C₂³×D₄₃	1	2	yes	—
173	C₂³	C₂³×D₄₃	1	1	yes	characteristic
174	Q₈	—	2	16	no	—
175	Q₈	—	2	16	no	—
176	Q₈	—	86	8	no	—
177	D₄	—	86	16	no	—
178	D₄	—	86	8	no	—
179	C₂×C₄	—	2	16	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	43	8	no	—
182	C₂×C₄	—	43	4	no	—
183	C₂×C₄	—	86	4	no	—
184	C₂×C₄	—	86	8	no	—
185	C₂×C₄	—	86	16	no	—
186	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
187	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
188	C₂×C₄	C₂×C₂²⋊D₄₃	1	16	yes	—
189	C₂×C₄	C₂³×D₄₃	1	8	yes	—
190	C₂×C₄	C₂³×D₄₃	1	2	yes	—
191	C₂×C₄	C₂³×D₄₃	1	2	yes	—
192	C₂²	—	2	8	no	—
193	C₂²	—	2	4	no	—
194	C₂²	—	86	4	no	—
195	C₂²	—	86	8	no	—
196	C₂²	—	172	8	no	—
197	C₂²	C₂²×C₂²⋊D₄₃	1	4	yes	—
198	C₂²	C₂²×C₂²⋊D₄₃	1	2	yes	—
199	C₂²	#13063373	1	4	yes	—
200	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
201	C₄	—	2	8	no	—
202	C₄	—	86	4	no	—
203	C₄	—	86	8	no	—
204	C₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
205	C₄	C₂²×C₂²⋊D₄₃	1	4	yes	—
206	C₂	—	2	4	no	—
207	C₂	—	172	4	no	—
208	C₂	#14583473	1	4	yes	direct product factor
209	C₂	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
210	C₂	C₂×#13063373	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂³×Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁴
hypercenter	C₂³×Q₈	D₄₃
hypocenter	C₄₃	C₂×#536
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂³×Q₈

Complements

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

N	H ≅ G/N	type
2. #14583473	C₂	direct (N × H)
3. C₂×#13063323	C₂	semidirect
4. C₂×#13063314	C₂	semidirect
5. C₂×#13063308	C₂	semidirect
6. C₂×#13063301	C₂	semidirect
7. C₂×#13063284	C₂	semidirect
8. C₂³×Q₈×C₄₃	C₂	semidirect
15. #13063323	C₂²	semidirect
16. #13063314	C₂²	semidirect
17. #13063308	C₂²	semidirect
18. #13063301	C₂²	semidirect
19. #13063284	C₂²	semidirect
28. C₂²×Q₈×C₄₃	C₂²	semidirect
102. C₂×C₄₃	#536	semidirect
107. C₂³×Q₈	D₄₃	semidirect
114. C₄₃	C₂×#536	semidirect
121. C₂²×Q₈	C₂×D₄₃	semidirect
208. C₂	#14583473	direct (N × H)

Subgroups — C2×#14583473 #19147912

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583473 #19147912