Subgroups — C₄×#13063348 #19143367

Order 5504.

500 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13063348	C₂	1	1	yes	maximal, characteristic
2	C₄×#10621902	C₂	1	2	yes	maximal, complemented
3	Q₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#10621884	C₂	1	2	yes	maximal, complemented
5	#14582984	C₂	1	2	yes	maximal, complemented
6	C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
7	#14582981	C₂	1	1	yes	maximal, characteristic, complemented
8	#14582936	C₂	1	1	yes	maximal, characteristic, complemented
9	#14582894	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10621902	C₂²	1	2	yes	—
13	#13063348	C₄	1	8	yes	direct product factor
14	C₂×#10621884	C₂²	1	2	yes	—
15	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic
18	Q₈×Dic₄₃	C₂²	1	2	yes	—
19	C₄×D₁₇₂	—	2	2	no	—
20	C₄×D₁₇₂	C₂²	1	2	yes	—
21	#13063287	—	2	2	no	—
22	#13063287	C₂²	1	2	yes	—
23	#13063283	—	2	2	no	—
24	#13063283	C₂²	1	2	yes	—
25	C₄²×D₄₃	—	2	2	no	—
26	C₄²×D₄₃	C₂²	1	1	yes	characteristic
27	#13063259	C₂²	1	1	yes	characteristic
28	#13063256	C₂²	1	2	yes	—
29	#13063249	C₂²	1	2	yes	—
30	#13063247	C₂²	1	2	yes	—
31	#13063245	C₂²	1	2	yes	—
32	C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₄×Q₈×C₄₃	C₂²	1	2	yes	—
37	#107×C₄₃	C₂²	1	1	yes	characteristic
38	#103×C₄₃	C₂²	1	2	yes	—
39	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
41	#10621902	—	2	4	no	—
42	#10621902	C₂×C₄	1	8	yes	complemented
43	C₂×D₁₇₂	—	2	2	no	—
44	C₂×D₁₇₂	C₂³	1	2	yes	—
45	C₂×C₄×D₄₃	—	2	2	no	—
46	C₂×C₄×D₄₃	—	2	2	no	—
47	C₂×C₄×D₄₃	—	2	2	no	—
48	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
49	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
51	Q₁₆×C₄₃	C₂×C₄	1	4	yes	complemented
52	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
56	C₄²×C₄₃	—	2	2	no	—
57	C₄²×C₄₃	C₂³	1	1	yes	characteristic
58	#10621884	C₂×C₄	1	8	yes	complemented
59	(C₂×D₄₃)⋊C₄	—	2	2	no	—
60	(C₂×D₄₃)⋊C₄	—	2	2	no	—
61	(C₂×D₄₃)⋊C₄	—	2	2	no	—
62	C₄⋊Dic₄₃	—	2	2	no	—
63	C₄⋊Dic₄₃	C₂³	1	2	yes	—
64	C₄×Dic₄₃	—	2	2	no	—
65	C₄×Dic₄₃	—	2	2	no	—
66	C₄×Dic₄₃	D₄	1	1	yes	characteristic
67	C₄×Dic₄₃	D₄	1	1	yes	characteristic
68	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
71	D₃₄₄	C₂×C₄	1	4	yes	complemented
72	C₈×D₄₃	—	2	2	no	—
73	C₈×D₄₃	C₂×C₄	1	4	yes	complemented
74	C₂²×D₄₃	—	2	2	no	—
75	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
76	Q₈×C₄₃	—	2	2	no	—
77	Q₈×C₄₃	C₂²×C₄	1	4	yes	—
78	C₂×C₄×C₄₃	—	2	2	no	—
79	C₂×C₄×C₄₃	—	2	2	no	—
80	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
83	C₂×Dic₄₃	—	2	2	no	—
84	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
87	D₁₇₂	—	2	8	no	—
88	D₁₇₂	—	2	2	no	—
89	D₁₇₂	C₂²×C₄	1	4	yes	—
90	C₄×D₄₃	—	2	2	no	—
91	C₄×D₄₃	—	2	8	no	—
92	C₄×D₄₃	—	2	2	no	—
93	C₄×D₄₃	—	4	4	no	—
94	C₄×D₄₃	—	4	4	no	—
95	C₄×D₄₃	C₂²×C₄	1	2	yes	—
96	C₄×D₄₃	#41	1	2	yes	—
97	C₈×C₄₃	—	2	1	no	—
98	C₈×C₄₃	C₂²×C₄	1	2	yes	—
99	C₄₃⋊C₈	—	2	1	no	—
100	C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
101	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
102	C₂×D₄₃	—	2	1	no	—
103	C₂×D₄₃	—	2	1	no	—
104	C₂×D₄₃	—	2	4	no	—
105	C₂×D₄₃	—	4	2	no	—
106	C₂×D₄₃	—	4	2	no	—
107	C₂×D₄₃	C₄×D₄	1	2	yes	—
108	C₄×C₄₃	—	2	4	no	—
109	C₄×C₄₃	—	2	1	no	—
110	C₄×C₄₃	—	4	2	no	—
111	C₄×C₄₃	#135	1	2	yes	complemented
112	C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
113	C₄×C₄₃	C₂×#41	1	1	yes	characteristic
114	Dic₄₃	—	2	1	no	—
115	Dic₄₃	—	4	2	no	—
116	Dic₄₃	C₄×D₄	1	2	yes	—
117	Dic₄₃	#135	1	2	yes	complemented
118	C₄×#135	—	43	1	no	maximal, Sylow
119	C₂×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
120	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
121	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
122	D₄₃	—	2	2	no	—
123	D₄₃	—	4	4	no	—
124	C₂×#135	—	43	1	no	—
125	C₄×#41	—	43	2	no	—
126	C₄×Q₁₆	—	43	1	no	—
127	C₄×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
128	C₄×SD₁₆	—	43	2	no	—
129	C₄×SD₁₆	—	43	2	no	—
130	C₄×D₈	—	43	1	no	—
131	C₄×D₈	—	43	1	no	—
132	#427	—	43	1	no	—
133	#416	—	43	2	no	—
134	C₂×C₄×C₈	—	43	1	no	—
135	C₄₃	C₄×#135	1	1	yes	characteristic, complemented, Sylow
136	C₂×#41	—	43	2	no	—
137	#135	—	43	8	no	—
138	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
139	C₂×SD₁₆	—	43	2	no	—
140	C₂×D₈	—	43	1	no	—
141	C₂²×C₈	—	43	1	no	—
142	C₂²×C₈	—	43	1	no	—
143	C₄×Q₈	—	43	2	no	—
144	C₄×Q₈	C₂×D₄₃	1	2	yes	—
145	C₄×D₄	—	43	2	no	—
146	C₄×D₄	—	43	2	no	—
147	C₄×D₄	—	86	2	no	—
148	C₄×D₄	—	86	2	no	—
149	#117	—	43	2	no	—
150	#117	—	86	2	no	—
151	C₂×C₄²	—	43	1	no	—
152	C₂×C₄²	—	86	2	no	—
153	#107	—	43	1	no	—
154	#107	C₂×D₄₃	1	1	yes	characteristic
155	#106	—	43	2	no	—
156	#103	—	43	2	no	—
157	#103	C₂×D₄₃	1	2	yes	—
158	#102	—	43	2	no	—
159	#102	—	43	2	no	—
160	C₄×C₈	—	43	1	no	—
161	C₄×C₈	—	43	1	no	—
162	C₄×C₈	—	43	1	no	—
163	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
164	#41	—	43	8	no	—
165	#41	—	86	4	no	—
166	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
167	C₂×D₄	—	43	2	no	—
168	C₂×D₄	—	86	2	no	—
169	C₂²×C₄	—	43	1	no	—
170	C₂²×C₄	—	43	1	no	—
171	C₂²×C₄	—	43	1	no	—
172	C₂²×C₄	—	86	2	no	—
173	C₂²×C₄	—	86	2	no	—
174	C₂²×C₄	—	86	2	no	—
175	Q₁₆	C₄×D₄₃	1	4	yes	complemented
176	SD₁₆	—	43	8	no	—
177	D₈	—	43	4	no	—
178	C₂×C₈	—	43	1	no	—
179	C₂×C₈	—	43	4	no	—
180	C₂×C₈	—	43	1	no	—
181	C₂×C₈	—	86	2	no	—
182	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
183	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	43	2	no	—
186	C₄⋊C₄	—	86	2	no	—
187	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
188	C₂²⋊C₄	—	86	2	no	—
189	C₂²⋊C₄	—	86	2	no	—
190	C₂²⋊C₄	—	86	2	no	—
191	C₄²	—	2	2	no	—
192	C₄²	—	43	1	no	—
193	C₄²	—	43	1	no	—
194	C₄²	—	43	1	no	—
195	C₄²	—	86	2	no	—
196	C₄²	—	86	2	no	—
197	C₄²	C₂²×D₄₃	1	1	yes	characteristic
198	C₂³	—	43	1	no	—
199	C₂³	—	86	2	no	—
200	Q₈	—	2	2	no	—
201	Q₈	C₂×C₄×D₄₃	1	4	yes	—
202	D₄	—	43	4	no	—
203	D₄	—	86	8	no	—
204	D₄	—	86	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	43	1	no	—
208	C₂×C₄	—	43	1	no	—
209	C₂×C₄	—	43	2	no	—
210	C₂×C₄	—	43	2	no	—
211	C₂×C₄	—	43	1	no	—
212	C₂×C₄	—	86	2	no	—
213	C₂×C₄	—	86	8	no	—
214	C₂×C₄	—	86	2	no	—
215	C₂×C₄	—	86	2	no	—
216	C₂×C₄	—	172	4	no	—
217	C₂×C₄	—	172	4	no	—
218	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
219	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
220	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
221	C₈	—	2	1	no	—
222	C₈	—	43	2	no	—
223	C₈	—	86	1	no	—
224	C₈	C₂×C₄×D₄₃	1	2	yes	—
225	C₂²	—	43	2	no	—
226	C₂²	—	86	1	no	—
227	C₂²	—	86	1	no	—
228	C₂²	—	86	4	no	—
229	C₂²	—	172	2	no	—
230	C₂²	—	172	2	no	—
231	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
232	C₄	—	2	4	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	43	2	no	—
236	C₄	—	43	2	no	—
237	C₄	—	86	1	no	—
238	C₄	—	172	2	no	—
239	C₄	#13063348	1	2	yes	direct product factor
240	C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
241	C₄	#41×D₄₃	1	1	yes	characteristic
242	C₂	—	86	2	no	—
243	C₂	—	172	4	no	—
244	C₂	C₄×D₄×D₄₃	1	1	yes	characteristic
245	C₂	#135×D₄₃	1	1	yes	characteristic
246	C₂	C₂×#13063348	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₄×Q₁₆	D₄₃
hypocenter	C₄₃	C₄×#135
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#10621902	C₂	semidirect
3. Q₁₆×Dic₄₃	C₂	semidirect
4. C₄×#10621884	C₂	semidirect
5. #14582984	C₂	semidirect
6. C₄×D₃₄₄	C₂	semidirect
7. #14582981	C₂	semidirect
8. #14582936	C₂	semidirect
9. #14582894	C₂	semidirect
10. C₄×C₈×D₄₃	C₂	semidirect
11. C₄×Q₁₆×C₄₃	C₂	semidirect
13. #13063348	C₄	direct (N × H)
42. #10621902	C₂×C₄	semidirect
51. Q₁₆×C₄₃	C₂×C₄	semidirect
58. #10621884	C₂×C₄	semidirect
71. D₃₄₄	C₂×C₄	semidirect
73. C₈×D₄₃	C₂×C₄	semidirect
111. C₄×C₄₃	#135	semidirect
117. Dic₄₃	#135	semidirect
127. C₄×Q₁₆	D₄₃	semidirect
135. C₄₃	C₄×#135	semidirect
175. Q₁₆	C₄×D₄₃	semidirect
239. C₄	#13063348	direct (N × H)

Subgroups — C4×#13063348 #19143367

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#13063348 #19143367