Subgroups — C₄×C₄₃×#418 #24940429

Order 11008.

2018 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#418	C₂	1	2	yes	maximal
3	C₂×C₄×M₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#117×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1762	C₂	1	4	yes	maximal, complemented
6	C₄×#102×C₄₃	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1736	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	—	2	1	no	—
10	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₄₃	—	2	1	no	—
12	C₂×C₄×D₄×C₄₃	—	2	1	no	—
13	C₂×C₄×D₄×C₄₃	—	2	4	no	—
14	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	complemented
15	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
17	C₂×#117×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#418	C₄	1	16	yes	direct product factor
22	C₂×#102×C₄₃	C₂²	1	8	yes	—
23	C₄×M₁₆×C₄₃	—	2	4	no	—
24	C₂×#97×C₄₃	C₂²	1	2	yes	complemented
25	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	complemented
26	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
27	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	complemented
28	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
29	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
30	C₄₃×#376	—	2	1	no	—
31	C₄³×C₄₃	—	2	1	no	—
32	C₄₃×#340	C₂²	1	8	yes	complemented
33	C₂⁵×C₄₃	—	2	1	no	—
34	C₂²×D₄×C₄₃	—	2	2	no	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	—	2	4	no	—
37	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
38	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂³×C₄×C₄₃	—	2	8	no	—
42	C₂³×C₄×C₄₃	—	2	2	no	—
43	C₂³×C₄×C₄₃	—	2	2	no	—
44	C₂³×C₄×C₄₃	—	4	8	no	—
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₄₃	—	2	4	no	—
49	C₂×M₁₆×C₄₃	—	2	4	no	—
50	C₂×M₁₆×C₄₃	C₂×C₄	1	8	yes	complemented
51	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
52	C₄×D₄×C₄₃	—	2	8	no	—
53	C₄×D₄×C₄₃	—	2	8	no	—
54	C₄×D₄×C₄₃	—	2	4	no	—
55	C₄×D₄×C₄₃	—	2	4	no	—
56	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
58	#117×C₄₃	—	2	4	no	—
59	#117×C₄₃	C₂×C₄	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
73	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	D₄	1	4	yes	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	#102×C₄₃	C₂×C₄	1	32	yes	complemented
79	#97×C₄₃	—	2	4	no	—
80	C₄×C₈×C₄₃	—	2	4	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	4	no	—
84	C₂⁴×C₄₃	—	2	8	no	—
85	C₂⁴×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	—	4	4	no	—
87	C₂⁴×C₄₃	—	4	4	no	—
88	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×D₄×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	2	8	no	—
91	C₂×D₄×C₄₃	—	2	8	no	—
92	C₂×D₄×C₄₃	—	2	16	no	—
93	C₂×D₄×C₄₃	—	2	2	no	—
94	C₂×D₄×C₄₃	—	2	4	no	—
95	C₂×D₄×C₄₃	C₄²	1	16	yes	complemented
96	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
97	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	8	no	—
100	C₂²×C₄×C₄₃	—	2	8	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	—	4	4	no	—
106	C₂²×C₄×C₄₃	—	4	32	no	—
107	C₂²×C₄×C₄₃	—	4	8	no	—
108	C₂²×C₄×C₄₃	—	4	8	no	—
109	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
110	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₄₃	—	2	16	no	—
122	C₂×C₈×C₄₃	—	2	4	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	8	yes	complemented
125	C₄⋊C₄×C₄₃	—	2	4	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
129	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	complemented
130	C₂²⋊C₄×C₄₃	—	2	8	no	—
131	C₂²⋊C₄×C₄₃	—	2	8	no	—
132	C₂²⋊C₄×C₄₃	—	2	8	no	—
133	C₄²×C₄₃	—	2	8	no	—
134	C₄²×C₄₃	—	4	4	no	—
135	C₄²×C₄₃	—	4	4	no	—
136	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
137	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
138	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₄₃	C₂×D₄	1	2	yes	—
141	C₄²×C₄₃	C₂×D₄	1	2	yes	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	4	no	—
145	C₂³×C₄₃	—	2	8	no	—
146	C₂³×C₄₃	—	2	16	no	—
147	C₂³×C₄₃	—	4	8	no	—
148	C₂³×C₄₃	—	4	8	no	—
149	C₂³×C₄₃	—	4	32	no	—
150	C₂³×C₄₃	—	4	4	no	—
151	C₂³×C₄₃	—	4	4	no	—
152	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₄₃	C₄×D₄	1	4	yes	—
154	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
155	D₄×C₄₃	—	2	4	no	—
156	D₄×C₄₃	—	2	8	no	—
157	D₄×C₄₃	—	2	16	no	—
158	D₄×C₄₃	C₂×C₄²	1	8	yes	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	8	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	16	no	—
167	C₂×C₄×C₄₃	—	4	8	no	—
168	C₂×C₄×C₄₃	—	4	4	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	16	no	—
172	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
173	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	#117	1	4	yes	—
179	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
180	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
186	C₈×C₄₃	—	2	8	no	—
187	C₄×#418	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	2	8	no	—
191	C₂²×C₄₃	—	2	8	no	—
192	C₂²×C₄₃	—	4	32	no	—
193	C₂²×C₄₃	—	4	4	no	—
194	C₂²×C₄₃	—	4	4	no	—
195	C₂²×C₄₃	—	4	16	no	—
196	C₂²×C₄₃	C₄×C₂²⋊C₄	1	4	yes	—
197	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
199	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	C₂²×C₄₃	#575	1	2	yes	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	4	4	no	—
205	C₄×C₄₃	—	4	8	no	—
206	C₄×C₄₃	C₄×C₂²⋊C₄	1	4	yes	—
207	C₄×C₄₃	#418	1	4	yes	direct product factor
208	C₄×C₄₃	C₂²×C₄²	1	1	yes	characteristic
209	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
210	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
211	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
212	C₂×#418	C₂×C₄₃	1	2	yes	—
213	C₂×C₄×M₁₆	C₂×C₄₃	1	1	yes	characteristic, complemented
214	C₄×#117	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#1762	C₂×C₄₃	1	4	yes	complemented
216	C₄×#102	C₂×C₄₃	1	4	yes	complemented
217	#1736	C₂×C₄₃	1	2	yes	complemented
218	C₂×C₄₃	—	2	4	no	—
219	C₂×C₄₃	—	4	8	no	—
220	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
222	C₂×C₄₃	#2896	1	1	yes	characteristic
223	C₂×C₄₃	C₄×AGL(1,ℤ/8)	1	4	yes	—
224	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
225	C₂⁴×C₄	—	2	1	no	—
226	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	—	2	1	no	—
229	C₂×C₄×D₄	—	2	4	no	—
230	C₂×C₄×D₄	C₄×C₄₃	1	8	yes	complemented
231	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
232	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
233	C₂×#117	C₂²×C₄₃	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
237	#418	C₄×C₄₃	1	16	yes	direct product factor
238	C₂×#102	C₂²×C₄₃	1	8	yes	—
239	C₄×M₁₆	—	2	4	no	—
240	C₂×#97	C₂²×C₄₃	1	2	yes	complemented
241	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	complemented
242	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
243	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	complemented
244	C₄×C₂²⋊C₄	—	2	1	no	—
245	C₄×C₂²⋊C₄	—	2	1	no	—
246	#376	—	2	1	no	—
247	C₄³	—	2	1	no	—
248	#340	C₂²×C₄₃	1	8	yes	complemented
249	C₄₃	C₄×#418	1	1	yes	characteristic, direct product factor, Sylow
250	C₂⁵	—	2	1	no	—
251	C₂²×D₄	—	2	1	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	4	no	—
254	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
255	C₂²×D₄	C₂×C₄×C₄₃	1	8	yes	—
256	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
257	C₂³×C₄	—	2	1	no	—
258	C₂³×C₄	—	2	8	no	—
259	C₂³×C₄	—	2	2	no	—
260	C₂³×C₄	—	2	2	no	—
261	C₂³×C₄	—	4	8	no	—
262	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
263	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
265	C₂×M₁₆	—	2	4	no	—
266	C₂×M₁₆	—	2	4	no	—
267	C₂×M₁₆	C₂×C₄×C₄₃	1	8	yes	complemented
268	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
269	C₄×D₄	—	2	8	no	—
270	C₄×D₄	—	2	8	no	—
271	C₄×D₄	—	2	4	no	—
272	C₄×D₄	—	2	4	no	—
273	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	—
274	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	—
275	#117	—	2	4	no	—
276	#117	C₂×C₄×C₄₃	1	8	yes	complemented
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
290	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
291	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	D₄×C₄₃	1	4	yes	—
293	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
295	#102	C₂×C₄×C₄₃	1	32	yes	complemented
296	#97	—	2	4	no	—
297	C₄×C₈	—	2	4	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	C₄²×C₄₃	1	16	yes	complemented
313	C₂×D₄	C₂²×C₄×C₄₃	1	8	yes	—
314	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	8	no	—
323	C₂²×C₄	—	4	32	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	4	8	no	—
326	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
327	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
328	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
329	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
330	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂²×C₄	#41×C₄₃	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
338	M₁₆	—	2	16	no	—
339	C₂×C₈	—	2	4	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	C₂²×C₄×C₄₃	1	8	yes	complemented
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
346	C₄⋊C₄	C₂²×C₄×C₄₃	1	8	yes	complemented
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₄²	—	2	8	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	4	4	no	—
353	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
354	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
355	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
356	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
357	C₄²	C₂×D₄×C₄₃	1	2	yes	—
358	C₄²	C₂×D₄×C₄₃	1	2	yes	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	4	8	no	—
366	C₂³	—	4	32	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
370	C₂³	C₄×D₄×C₄₃	1	4	yes	—
371	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
372	D₄	—	2	4	no	—
373	D₄	—	2	8	no	—
374	D₄	—	2	16	no	—
375	D₄	C₂×C₄²×C₄₃	1	8	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	4	no	—
383	C₂×C₄	—	4	16	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	16	no	—
389	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
390	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
391	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
394	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
395	C₂×C₄	#117×C₄₃	1	4	yes	—
396	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
397	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
398	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
399	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂³×C₄×C₄₃	1	2	yes	—
401	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
402	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
403	C₈	—	2	8	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	4	32	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	16	no	—
412	C₂²	C₄×C₂²⋊C₄×C₄₃	1	4	yes	—
413	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
414	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
415	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
416	C₂²	C₄₃×#575	1	2	yes	—
417	C₄	—	2	2	no	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	8	no	—
422	C₄	C₄×C₂²⋊C₄×C₄₃	1	4	yes	—
423	C₄	C₄₃×#418	1	4	yes	direct product factor
424	C₄	C₂²×C₄²×C₄₃	1	1	yes	characteristic
425	C₄	C₂×#117×C₄₃	1	1	yes	characteristic
426	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
427	C₂	—	2	4	no	—
428	C₂	—	4	8	no	—
429	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
430	C₂	C₂×C₄₃×#418	1	1	yes	characteristic
431	C₂	C₄₃×#2896	1	1	yes	characteristic
432	C₂	C₄×AGL(1,ℤ/8)×C₄₃	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₄	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂³×D₄×C₄₃	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×M₁₆×C₄₃	C₂	semidirect
4. C₄×#117×C₄₃	C₂	semidirect
5. C₄₃×#1762	C₂	semidirect
6. C₄×#102×C₄₃	C₂	semidirect
7. C₄₃×#1736	C₂	semidirect
14. C₂×C₄×D₄×C₄₃	C₄	semidirect
21. C₄₃×#418	C₄	direct (N × H)
24. C₂×#97×C₄₃	C₂²	semidirect
25. C₂×C₄×C₈×C₄₃	C₂²	semidirect
26. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
27. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
32. C₄₃×#340	C₂²	semidirect
50. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
59. #117×C₄₃	C₂×C₄	semidirect
78. #102×C₄₃	C₂×C₄	semidirect
95. C₂×D₄×C₄₃	C₄²	semidirect
124. C₂×C₈×C₄₃	C₂²×C₄	semidirect
129. C₄⋊C₄×C₄₃	C₂²×C₄	semidirect
187. C₄×#418	C₄₃	direct (N × H)
207. C₄×C₄₃	#418	direct (N × H)
213. C₂×C₄×M₁₆	C₂×C₄₃	semidirect
214. C₄×#117	C₂×C₄₃	semidirect
215. #1762	C₂×C₄₃	semidirect
216. C₄×#102	C₂×C₄₃	semidirect
217. #1736	C₂×C₄₃	semidirect
230. C₂×C₄×D₄	C₄×C₄₃	semidirect
237. #418	C₄×C₄₃	direct (N × H)
240. C₂×#97	C₂²×C₄₃	semidirect
241. C₂×C₄×C₈	C₂²×C₄₃	semidirect
242. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
243. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
248. #340	C₂²×C₄₃	semidirect
249. C₄₃	C₄×#418	direct (N × H)
267. C₂×M₁₆	C₂×C₄×C₄₃	semidirect
276. #117	C₂×C₄×C₄₃	semidirect
295. #102	C₂×C₄×C₄₃	semidirect
312. C₂×D₄	C₄²×C₄₃	semidirect
341. C₂×C₈	C₂²×C₄×C₄₃	semidirect
346. C₄⋊C₄	C₂²×C₄×C₄₃	semidirect
423. C₄	C₄₃×#418	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#418	2
C₂×C₄×M₁₆×C₄₃	2
C₄×#117×C₄₃	2
C₄₃×#1762	2
C₄×#102×C₄₃	2
C₄₃×#1736	2
C₄×#418	43

Subgroups — C4×C43×#418 #24940429

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×#418 #24940429