Subgroups — C₄×#13063372 #19147805

Order 5504.

1492 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063372	C₂	1	1	yes	maximal, characteristic
2	#14583382	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583379	C₂	1	3	yes	maximal, complemented
4	#14583378	C₂	1	6	yes	maximal, complemented
5	#14583376	C₂	1	3	yes	maximal, complemented
6	#14583375	C₂	1	2	yes	maximal, complemented
7	C₄×#10621898	C₂	1	3	yes	maximal, complemented
8	C₄×#10621900	C₂	1	6	yes	maximal, complemented
9	C₂×C₄×Dic₈₆	C₂	1	3	yes	maximal, complemented
10	C₄×Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
11	C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#13063372	C₄	1	16	yes	direct product factor
13	C₂×#10621898	C₂²	1	3	yes	—
14	C₂×#10621900	C₂²	1	6	yes	—
15	C₂²×Dic₈₆	C₂²	1	3	yes	—
16	C₂×Q₈×D₄₃	C₂²	1	2	yes	—
17	Q₈×Dic₄₃	C₂²	1	2	yes	—
18	C₄×Dic₈₆	C₂²	1	6	yes	—
19	C₄×Dic₈₆	C₂²	1	3	yes	—
20	C₄×Dic₈₆	C₂²	1	6	yes	—
21	C₄×Dic₈₆	C₂²	1	6	yes	—
22	C₄×Dic₈₆	C₂²	1	3	yes	—
23	#13063290	C₂²	1	6	yes	—
24	#13063290	C₂²	1	6	yes	—
25	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
26	C₄×D₁₇₂	C₂²	1	3	yes	—
27	D₄×Dic₄₃	C₂²	1	6	yes	—
28	C₄×C₂²⋊D₄₃	C₂²	1	6	yes	—
29	C₄×C₂²⋊D₄₃	C₂²	1	6	yes	—
30	(C₂²⋊D₄₃)⋊C₄	C₂²	1	12	yes	—
31	#13063284	C₂²	1	3	yes	—
32	#13063283	C₂²	1	6	yes	—
33	#13063282	C₂²	1	6	yes	—
34	#13063281	C₂²	1	12	yes	—
35	C₂×C₄⋊Dic₄₃	C₂²	1	3	yes	—
36	C₂×Dic₄₃⋊C₄	C₂²	1	6	yes	—
37	C₄⋊C₄×D₄₃	C₂²	1	6	yes	—
38	C₂×C₄×Dic₄₃	C₂²	1	6	yes	—
39	C₄²×D₄₃	C₂²	1	6	yes	—
40	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄×D₄×C₄₃	C₂²	1	3	yes	—
44	C₄×D₄×C₄₃	C₂²	1	3	yes	—
45	#117×C₄₃	C₂²	1	3	yes	—
46	C₂×C₄²×C₄₃	C₂²	1	3	yes	—
47	#41×C₄₃	C₂×C₄	1	8	yes	complemented
48	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×D₄×C₄₃	C₂³	1	3	yes	—
50	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
51	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
52	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
53	C₂×C₂²⋊D₄₃	C₂³	1	6	yes	—
54	C₂²×Dic₄₃	C₂³	1	6	yes	—
55	C₂²×Dic₄₃	C₂³	1	6	yes	—
56	Q₈×D₄₃	C₂×C₄	1	16	yes	complemented
57	#10621900	C₂×C₄	1	48	yes	complemented
58	#10621898	C₂×C₄	1	24	yes	complemented
59	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
60	C₂×C₄×D₄₃	C₂³	1	2	yes	—
61	C₂×C₄×D₄₃	C₂³	1	6	yes	—
62	C₂×C₄×D₄₃	C₂³	1	6	yes	—
63	C₂×Dic₈₆	C₂×C₄	1	24	yes	complemented
64	C₂×Dic₈₆	C₂³	1	6	yes	—
65	C₂×Dic₈₆	C₂³	1	3	yes	—
66	C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
67	C₄⋊C₄×C₄₃	C₂³	1	3	yes	—
68	C₂²⋊C₄×C₄₃	C₂³	1	6	yes	—
69	C₄²×C₄₃	C₂³	1	1	yes	characteristic
70	C₄²×C₄₃	C₂³	1	3	yes	—
71	C₄²×C₄₃	C₂³	1	3	yes	—
72	C₄²×C₄₃	C₂³	1	3	yes	—
73	C₂²⋊Dic₄₃	C₂³	1	6	yes	—
74	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
75	(C₂×D₄₃)⋊C₄	C₂³	1	6	yes	—
76	C₄⋊Dic₄₃	C₂³	1	6	yes	—
77	C₄⋊Dic₄₃	C₂³	1	3	yes	—
78	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
79	Dic₄₃⋊C₄	C₂³	1	12	yes	—
80	Dic₄₃⋊C₄	C₂³	1	6	yes	—
81	Dic₄₃⋊C₄	C₂³	1	6	yes	—
82	C₄×Dic₄₃	C₂³	1	6	yes	—
83	C₄×Dic₄₃	C₂³	1	6	yes	—
84	C₄×Dic₄₃	C₂³	1	6	yes	—
85	C₄×Dic₄₃	C₂³	1	12	yes	—
86	C₂³×C₄₃	C₂⁴	1	3	yes	—
87	C₂²×D₄₃	C₂⁴	1	2	yes	—
88	Q₈×C₄₃	C₂²×C₄	1	4	yes	—
89	D₄×C₄₃	C₂²×C₄	1	12	yes	—
90	C₂×C₄×C₄₃	—	2	6	no	—
91	C₂×C₄×C₄₃	—	4	3	no	—
92	C₂×C₄×C₄₃	C₂²×C₄	1	12	yes	—
93	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
94	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
95	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂×C₄×C₄₃	C₂⁴	1	3	yes	—
97	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
98	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
99	C₂²⋊D₄₃	C₂²×C₄	1	24	yes	—
100	C₂×Dic₄₃	—	4	6	no	—
101	C₂×Dic₄₃	C₂²×C₄	1	24	yes	—
102	C₂×Dic₄₃	C₂⁴	1	2	yes	—
103	C₂×Dic₄₃	C₂⁴	1	6	yes	—
104	C₂×Dic₄₃	C₂⁴	1	6	yes	—
105	D₁₇₂	C₂²×C₄	1	4	yes	—
106	C₄×D₄₃	—	2	4	no	—
107	C₄×D₄₃	—	4	6	no	—
108	C₄×D₄₃	C₂²×C₄	1	24	yes	—
109	Dic₈₆	C₂²×C₄	1	12	yes	—
110	Dic₈₆	C₂²×C₄	1	24	yes	—
111	C₂²×C₄₃	—	2	3	no	—
112	C₂²×C₄₃	—	2	3	no	—
113	C₂²×C₄₃	C₂³×C₄	1	6	yes	—
114	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
115	C₂×D₄₃	—	2	2	no	—
116	C₂×D₄₃	—	2	2	no	—
117	C₂×D₄₃	C₂³×C₄	1	4	yes	—
118	C₄×C₄₃	—	2	3	no	—
119	C₄×C₄₃	—	2	3	no	—
120	C₄×C₄₃	—	2	1	no	—
121	C₄×C₄₃	C₂³×C₄	1	2	yes	—
122	C₄×C₄₃	C₂³×C₄	1	6	yes	—
123	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	complemented
124	Dic₄₃	—	2	2	no	—
125	Dic₄₃	—	2	6	no	—
126	Dic₄₃	C₂³×C₄	1	12	yes	—
127	C₄×2₋¹⁺⁴	—	43	1	no	maximal, Sylow
128	C₂×C₄₃	—	2	6	no	—
129	C₂×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
130	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
131	C₂×C₄₃	#585	1	1	yes	characteristic
132	D₄₃	—	2	4	no	—
133	C₂×2₋¹⁺⁴	—	43	1	no	—
134	#520	—	43	1	no	—
135	#520	—	43	6	no	—
136	#520	—	43	3	no	—
137	#519	—	43	2	no	—
138	#519	—	43	3	no	—
139	C₄×#41	—	43	6	no	—
140	C₄×#41	—	43	3	no	—
141	C₄×#41	D₄₃	1	1	yes	characteristic, complemented
142	C₂×C₄×Q₈	—	43	2	no	—
143	C₂×C₄×Q₈	—	43	3	no	—
144	C₄₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
145	2₋¹⁺⁴	—	43	16	no	—
146	C₂×#41	—	43	6	no	—
147	C₂×#41	—	43	3	no	—
148	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
149	C₂²×Q₈	—	43	2	no	—
150	C₂²×Q₈	—	43	3	no	—
151	C₄×Q₈	—	43	2	no	—
152	C₄×Q₈	—	43	6	no	—
153	C₄×Q₈	—	43	6	no	—
154	C₄×Q₈	—	43	6	no	—
155	C₄×Q₈	—	43	3	no	—
156	C₄×Q₈	—	43	6	no	—
157	C₄×Q₈	—	43	6	no	—
158	C₄×Q₈	—	43	3	no	—
159	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
160	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
161	C₄×D₄	—	43	6	no	—
162	C₄×D₄	—	43	6	no	—
163	C₄×D₄	—	43	6	no	—
164	C₄×D₄	—	43	12	no	—
165	C₄×D₄	—	43	1	no	—
166	C₄×D₄	—	43	3	no	—
167	C₄×D₄	C₂×D₄₃	1	3	yes	—
168	C₄×D₄	C₂×D₄₃	1	3	yes	—
169	#117	—	43	3	no	—
170	#117	—	43	6	no	—
171	#117	—	43	12	no	—
172	#117	—	43	6	no	—
173	#117	C₂×D₄₃	1	3	yes	—
174	C₂×C₄⋊C₄	—	43	6	no	—
175	C₂×C₄⋊C₄	—	43	3	no	—
176	C₂×C₄⋊C₄	—	43	6	no	—
177	C₂×C₄²	—	43	6	no	—
178	C₂×C₄²	—	43	6	no	—
179	C₂×C₄²	C₂×D₄₃	1	3	yes	—
180	#41	—	43	48	no	—
181	#41	—	43	24	no	—
182	#41	C₄×D₄₃	1	8	yes	complemented
183	C₂×Q₈	—	43	16	no	—
184	C₂×Q₈	—	43	24	no	—
185	C₂×Q₈	—	43	6	no	—
186	C₂×Q₈	—	43	3	no	—
187	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
188	C₂×D₄	—	43	6	no	—
189	C₂×D₄	—	43	1	no	—
190	C₂×D₄	C₂²×D₄₃	1	3	yes	—
191	C₂²×C₄	—	43	6	no	—
192	C₂²×C₄	—	43	6	no	—
193	C₂²×C₄	—	43	6	no	—
194	C₂²×C₄	—	43	2	no	—
195	C₂²×C₄	—	43	6	no	—
196	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
197	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
198	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
199	C₄⋊C₄	—	43	12	no	—
200	C₄⋊C₄	—	43	6	no	—
201	C₄⋊C₄	—	43	6	no	—
202	C₄⋊C₄	—	43	3	no	—
203	C₄⋊C₄	—	43	6	no	—
204	C₄⋊C₄	—	43	1	no	—
205	C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
206	C₄⋊C₄	C₂²×D₄₃	1	3	yes	—
207	C₂²⋊C₄	—	43	6	no	—
208	C₂²⋊C₄	—	43	2	no	—
209	C₂²⋊C₄	—	43	6	no	—
210	C₂²⋊C₄	C₂²×D₄₃	1	6	yes	—
211	C₄²	—	43	6	no	—
212	C₄²	—	43	12	no	—
213	C₄²	—	43	6	no	—
214	C₄²	—	43	6	no	—
215	C₄²	C₂²×D₄₃	1	3	yes	—
216	C₄²	C₂²×D₄₃	1	3	yes	—
217	C₄²	C₂²×D₄₃	1	3	yes	—
218	C₄²	C₂²×D₄₃	1	1	yes	characteristic
219	C₂³	—	43	2	no	—
220	C₂³	C₂³×D₄₃	1	3	yes	—
221	Q₈	—	43	24	no	—
222	Q₈	—	43	12	no	—
223	Q₈	C₂×C₄×D₄₃	1	4	yes	—
224	D₄	—	43	24	no	—
225	D₄	—	43	4	no	—
226	D₄	C₂×C₄×D₄₃	1	12	yes	—
227	C₂×C₄	—	2	6	no	—
228	C₂×C₄	—	4	3	no	—
229	C₂×C₄	—	43	24	no	—
230	C₂×C₄	—	43	6	no	—
231	C₂×C₄	—	43	24	no	—
232	C₂×C₄	—	43	2	no	—
233	C₂×C₄	—	43	6	no	—
234	C₂×C₄	—	86	4	no	—
235	C₂×C₄	—	172	6	no	—
236	C₂×C₄	—	172	6	no	—
237	C₂×C₄	C₂×C₄×D₄₃	1	12	yes	—
238	C₂×C₄	C₂³×D₄₃	1	3	yes	—
239	C₂×C₄	C₂³×D₄₃	1	3	yes	—
240	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
241	C₂×C₄	C₂³×D₄₃	1	3	yes	—
242	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
243	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
244	C₂²	—	2	3	no	—
245	C₂²	—	2	3	no	—
246	C₂²	—	43	4	no	—
247	C₂²	—	86	2	no	—
248	C₂²	—	86	2	no	—
249	C₂²	C₂²×C₄×D₄₃	1	6	yes	—
250	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
251	C₄	—	2	3	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	3	no	—
254	C₄	—	43	12	no	—
255	C₄	—	86	2	no	—
256	C₄	—	86	6	no	—
257	C₄	C₂²×C₄×D₄₃	1	6	yes	—
258	C₄	C₂²×C₄×D₄₃	1	2	yes	—
259	C₄	#13063372	1	2	yes	direct product factor
260	C₂	—	2	6	no	—
261	C₂	—	86	4	no	—
262	C₂	C₂³×C₄×D₄₃	1	1	yes	characteristic
263	C₂	C₂×#13063372	1	1	yes	characteristic
264	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₄₃
commutator	C₂×C₄₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₄×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂⁵
hypercenter	C₄×#41	D₄₃
hypocenter	C₄₃	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #14583382	C₂	semidirect
3. #14583379	C₂	semidirect
4. #14583378	C₂	semidirect
5. #14583376	C₂	semidirect
6. #14583375	C₂	semidirect
7. C₄×#10621898	C₂	semidirect
8. C₄×#10621900	C₂	semidirect
9. C₂×C₄×Dic₈₆	C₂	semidirect
10. C₄×Q₈×D₄₃	C₂	semidirect
11. C₄×#41×C₄₃	C₂	semidirect
12. #13063372	C₄	direct (N × H)
47. #41×C₄₃	C₂×C₄	semidirect
56. Q₈×D₄₃	C₂×C₄	semidirect
57. #10621900	C₂×C₄	semidirect
58. #10621898	C₂×C₄	semidirect
63. C₂×Dic₈₆	C₂×C₄	semidirect
123. C₄×C₄₃	2₋¹⁺⁴	semidirect
141. C₄×#41	D₄₃	semidirect
144. C₄₃	C₄×2₋¹⁺⁴	semidirect
182. #41	C₄×D₄₃	semidirect
259. C₄	#13063372	direct (N × H)

Subgroups — C4×#13063372 #19147805

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063372 #19147805