Subgroups — C₄₃×#14697 #24934714

Order 11008.

2574 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#389	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#385	C₂	1	2	yes	maximal
4	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1436	C₂	1	4	yes	maximal, complemented
7	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₄₃×C₂²⋊#95	C₂	1	2	yes	maximal
9	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₃	—	2	4	no	—
19	C₂²×C₄²×C₄₃	—	2	8	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
22	C₄₃×#389	—	2	8	no	—
23	C₄₃×#385	—	2	8	no	—
24	C₄₃×#380	—	2	4	no	—
25	C₄₃×#380	C₄	1	8	yes	complemented
26	C₂×#95×C₄₃	C₂²	1	4	yes	—
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	4	yes	—
29	C₂×#95×C₄₃	C₂²	1	2	yes	—
30	C₂×#95×C₄₃	C₂²	1	2	yes	—
31	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	—	2	2	no	—
33	C₂³×C₄×C₄₃	—	2	2	no	—
34	C₂³×C₄×C₄₃	—	2	2	no	—
35	C₂³×C₄×C₄₃	—	2	2	no	—
36	C₂³×C₄×C₄₃	—	2	4	no	—
37	C₂³×C₄×C₄₃	—	2	4	no	—
38	C₂³×C₄×C₄₃	—	2	4	no	—
39	C₂³×C₄×C₄₃	—	2	4	no	—
40	C₂³×C₄×C₄₃	—	2	4	no	—
41	C₂³×C₄×C₄₃	—	2	4	no	—
42	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
43	C₂³×C₄×C₄₃	D₄	1	4	yes	—
44	C₂³×C₄×C₄₃	D₄	1	4	yes	—
45	C₂³×C₄×C₄₃	Q₈	1	4	yes	—
46	C₂³×C₄×C₄₃	Q₈	1	4	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
64	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
69	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
70	C₂×C₄²×C₄₃	—	2	32	no	—
71	C₂×C₄²×C₄₃	—	2	4	no	—
72	C₂×C₄²×C₄₃	—	2	4	no	—
73	C₂×C₄²×C₄₃	—	2	4	no	—
74	C₂×C₄²×C₄₃	—	2	4	no	—
75	C₂×C₄²×C₄₃	—	2	4	no	—
76	C₂×C₄²×C₄₃	D₄	1	8	yes	—
77	#95×C₄₃	—	2	4	no	—
78	#95×C₄₃	—	2	8	no	—
79	#95×C₄₃	—	2	8	no	—
80	#95×C₄₃	—	2	8	no	—
81	#95×C₄₃	C₂×C₄	1	8	yes	complemented
82	C₂⁴×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	2	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
87	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
88	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
89	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
90	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂⁴×C₄₃	#41	1	2	yes	—
92	C₂⁴×C₄₃	#41	1	2	yes	—
93	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	—	2	8	no	—
95	C₂²×C₄×C₄₃	—	2	8	no	—
96	C₂²×C₄×C₄₃	—	2	8	no	—
97	C₂²×C₄×C₄₃	—	2	8	no	—
98	C₂²×C₄×C₄₃	—	2	16	no	—
99	C₂²×C₄×C₄₃	—	2	16	no	—
100	C₂²×C₄×C₄₃	—	2	16	no	—
101	C₂²×C₄×C₄₃	—	2	8	no	—
102	C₂²×C₄×C₄₃	—	2	16	no	—
103	C₂²×C₄×C₄₃	—	2	16	no	—
104	C₂²×C₄×C₄₃	—	2	16	no	—
105	C₂²×C₄×C₄₃	—	2	8	no	—
106	C₂²×C₄×C₄₃	—	2	8	no	—
107	C₂²×C₄×C₄₃	—	2	8	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	4	no	—
126	C₂²×C₄×C₄₃	—	2	4	no	—
127	C₂²×C₄×C₄₃	—	2	4	no	—
128	C₂²×C₄×C₄₃	—	2	4	no	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
135	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
136	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
146	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₄₃	#41	1	4	yes	—
148	C₂²×C₄×C₄₃	#41	1	4	yes	—
149	C₂²×C₄×C₄₃	#41	1	4	yes	—
150	C₄⋊C₄×C₄₃	—	2	16	no	—
151	C₄⋊C₄×C₄₃	—	4	4	no	—
152	C₄⋊C₄×C₄₃	—	4	16	no	—
153	C₄⋊C₄×C₄₃	—	4	4	no	—
154	C₂²⋊C₄×C₄₃	—	2	16	no	—
155	C₂²⋊C₄×C₄₃	—	4	8	no	—
156	C₄²×C₄₃	—	2	16	no	—
157	C₄²×C₄₃	—	2	16	no	—
158	C₂³×C₄₃	—	2	4	no	—
159	C₂³×C₄₃	—	2	4	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	4	no	—
162	C₂³×C₄₃	—	2	4	no	—
163	C₂³×C₄₃	—	2	4	no	—
164	C₂³×C₄₃	—	2	2	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	2	4	no	—
168	C₂³×C₄₃	—	2	4	no	—
169	C₂³×C₄₃	—	2	4	no	—
170	C₂³×C₄₃	—	2	4	no	—
171	C₂³×C₄₃	—	2	4	no	—
172	C₂³×C₄₃	—	2	4	no	—
173	C₂³×C₄₃	—	2	4	no	—
174	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
175	C₂³×C₄₃	C₄×D₄	1	4	yes	—
176	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
177	C₂³×C₄₃	#121	1	4	yes	—
178	C₂³×C₄₃	C₂²⋊Q₈	1	4	yes	—
179	C₂³×C₄₃	#125	1	4	yes	—
180	C₂³×C₄₃	C₄⋊Q₈	1	4	yes	—
181	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
182	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
184	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
187	C₂³×C₄₃	C₂×#41	1	2	yes	—
188	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
189	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₂³×C₄₃	C₂×#41	1	2	yes	—
191	C₂³×C₄₃	C₂×#41	1	2	yes	—
192	C₂×C₄×C₄₃	—	2	32	no	—
193	C₂×C₄×C₄₃	—	2	32	no	—
194	C₂×C₄×C₄₃	—	2	4	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	4	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	4	no	—
199	C₂×C₄×C₄₃	—	2	4	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	4	no	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	32	no	—
211	C₂×C₄×C₄₃	—	2	8	no	—
212	C₂×C₄×C₄₃	—	2	8	no	—
213	C₂×C₄×C₄₃	—	2	8	no	—
214	C₂×C₄×C₄₃	—	4	4	no	—
215	C₂×C₄×C₄₃	—	4	4	no	—
216	C₂×C₄×C₄₃	—	4	4	no	—
217	C₂×C₄×C₄₃	—	4	4	no	—
218	C₂×C₄×C₄₃	—	4	2	no	—
219	C₂×C₄×C₄₃	—	4	2	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	4	no	—
222	C₂×C₄×C₄₃	—	4	2	no	—
223	C₂×C₄×C₄₃	—	4	4	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	no	—
226	C₂×C₄×C₄₃	—	4	4	no	—
227	C₂×C₄×C₄₃	—	4	4	no	—
228	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
229	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
230	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
231	C₂×C₄×C₄₃	#120	1	4	yes	—
232	C₂×C₄×C₄₃	#121	1	8	yes	—
233	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
234	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
235	C₂×C₄×C₄₃	#123	1	4	yes	—
236	#14697	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	2	4	no	—
239	C₂²×C₄₃	—	2	8	no	—
240	C₂²×C₄₃	—	2	4	no	—
241	C₂²×C₄₃	—	2	4	no	—
242	C₂²×C₄₃	—	2	8	no	—
243	C₂²×C₄₃	—	2	4	no	—
244	C₂²×C₄₃	—	2	4	no	—
245	C₂²×C₄₃	—	2	8	no	—
246	C₂²×C₄₃	—	2	8	no	—
247	C₂²×C₄₃	#389	1	8	yes	complemented
248	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
250	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
252	C₂²×C₄₃	C₄×#41	1	2	yes	—
253	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
255	C₂²×C₄₃	C₂×#121	1	2	yes	—
256	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
257	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
258	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
259	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
260	C₂²×C₄₃	#525	1	2	yes	—
261	C₂²×C₄₃	#525	1	1	yes	characteristic
262	C₂²×C₄₃	#525	1	2	yes	—
263	C₂²×C₄₃	#525	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×#125	1	1	yes	characteristic
265	C₂²×C₄₃	#529	1	2	yes	—
266	C₂²×C₄₃	#529	1	2	yes	—
267	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
268	C₂²×C₄₃	#532	1	2	yes	—
269	C₂²×C₄₃	#533	1	2	yes	—
270	C₂²×C₄₃	#533	1	2	yes	—
271	C₄×C₄₃	—	2	8	no	—
272	C₄×C₄₃	—	2	8	no	—
273	C₄×C₄₃	—	2	4	no	—
274	C₄×C₄₃	—	4	8	no	—
275	C₄×C₄₃	—	8	2	no	—
276	C₄×C₄₃	—	8	2	no	—
277	C₄×C₄₃	#385	1	8	yes	complemented
278	C₂³×C₄²	C₂×C₄₃	1	1	yes	characteristic
279	C₂×#389	C₂×C₄₃	1	2	yes	complemented
280	C₂×#385	C₂×C₄₃	1	2	yes	—
281	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
282	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
283	#1436	C₂×C₄₃	1	4	yes	complemented
284	C₄⋊#95	C₂×C₄₃	1	2	yes	complemented
285	C₂²⋊#95	C₂×C₄₃	1	2	yes	—
286	C₂×C₄₃	—	2	8	no	—
287	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
288	C₂×C₄₃	C₂×#389	1	1	yes	characteristic
289	C₂×C₄₃	#2296	1	1	yes	characteristic
290	C₂×C₄₃	C₄×#121	1	2	yes	—
291	C₂×C₄₃	C₄×C₂²⋊Q₈	1	2	yes	—
292	C₂×C₄₃	#2847	1	1	yes	characteristic
293	C₂×C₄₃	#2848	1	1	yes	characteristic
294	C₂×C₄₃	#2851	1	2	yes	—
295	C₂×C₄₃	#2854	1	1	yes	characteristic
296	C₂×C₄₃	#2855	1	1	yes	characteristic
297	C₂×C₄₃	#2857	1	2	yes	—
298	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
299	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
300	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
306	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
307	C₂²×C₄²	—	2	4	no	—
308	C₂²×C₄²	—	2	8	no	—
309	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
310	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
311	#389	—	2	8	no	—
312	#385	—	2	8	no	—
313	#380	—	2	4	no	—
314	#380	C₄×C₄₃	1	8	yes	complemented
315	C₂×#95	C₂²×C₄₃	1	4	yes	—
316	C₂×#95	C₂²×C₄₃	1	4	yes	—
317	C₂×#95	C₂²×C₄₃	1	4	yes	—
318	C₂×#95	C₂²×C₄₃	1	2	yes	—
319	C₂×#95	C₂²×C₄₃	1	2	yes	—
320	C₄₃	#14697	1	1	yes	characteristic, direct product factor, Sylow
321	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂³×C₄	—	2	2	no	—
326	C₂³×C₄	—	2	4	no	—
327	C₂³×C₄	—	2	4	no	—
328	C₂³×C₄	—	2	4	no	—
329	C₂³×C₄	—	2	4	no	—
330	C₂³×C₄	—	2	4	no	—
331	C₂³×C₄	—	2	4	no	—
332	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
333	C₂³×C₄	D₄×C₄₃	1	4	yes	—
334	C₂³×C₄	D₄×C₄₃	1	4	yes	—
335	C₂³×C₄	Q₈×C₄₃	1	4	yes	—
336	C₂³×C₄	Q₈×C₄₃	1	4	yes	—
337	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
339	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
340	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	8	no	—
349	C₂×C₄⋊C₄	—	2	4	no	—
350	C₂×C₄⋊C₄	—	2	8	no	—
351	C₂×C₄⋊C₄	—	2	8	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
354	C₂×C₂²⋊C₄	—	2	4	no	—
355	C₂×C₂²⋊C₄	—	2	4	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	—	2	4	no	—
358	C₂×C₂²⋊C₄	—	2	4	no	—
359	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
360	C₂×C₄²	—	2	32	no	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	—	2	4	no	—
363	C₂×C₄²	—	2	4	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	—	2	4	no	—
366	C₂×C₄²	D₄×C₄₃	1	8	yes	—
367	#95	—	2	4	no	—
368	#95	—	2	8	no	—
369	#95	—	2	8	no	—
370	#95	—	2	8	no	—
371	#95	C₂×C₄×C₄₃	1	8	yes	complemented
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
377	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
378	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
379	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
380	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
381	C₂⁴	#41×C₄₃	1	2	yes	—
382	C₂⁴	#41×C₄₃	1	2	yes	—
383	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	16	no	—
387	C₂²×C₄	—	2	16	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	8	no	—
391	C₂²×C₄	—	2	8	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	16	no	—
403	C₂²×C₄	—	2	8	no	—
404	C₂²×C₄	—	2	16	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
425	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
426	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
427	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
429	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
430	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
431	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
432	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
434	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
435	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
436	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
437	C₂²×C₄	#41×C₄₃	1	4	yes	—
438	C₂²×C₄	#41×C₄₃	1	4	yes	—
439	C₂²×C₄	#41×C₄₃	1	4	yes	—
440	C₄⋊C₄	—	2	16	no	—
441	C₄⋊C₄	—	4	4	no	—
442	C₄⋊C₄	—	4	16	no	—
443	C₄⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	2	16	no	—
445	C₂²⋊C₄	—	4	8	no	—
446	C₄²	—	2	16	no	—
447	C₄²	—	2	16	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	2	4	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	2	4	no	—
463	C₂³	—	2	4	no	—
464	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
465	C₂³	C₄×D₄×C₄₃	1	4	yes	—
466	C₂³	C₄×Q₈×C₄₃	1	4	yes	—
467	C₂³	#121×C₄₃	1	4	yes	—
468	C₂³	C₂²⋊Q₈×C₄₃	1	4	yes	—
469	C₂³	#125×C₄₃	1	4	yes	—
470	C₂³	C₄⋊Q₈×C₄₃	1	4	yes	—
471	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
472	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
473	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
474	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
475	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
476	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
477	C₂³	C₂×#41×C₄₃	1	2	yes	—
478	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
479	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
480	C₂³	C₂×#41×C₄₃	1	2	yes	—
481	C₂³	C₂×#41×C₄₃	1	2	yes	—
482	C₂×C₄	—	2	32	no	—
483	C₂×C₄	—	2	32	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	32	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	—	4	4	no	—
506	C₂×C₄	—	4	4	no	—
507	C₂×C₄	—	4	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	4	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
519	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
520	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
521	C₂×C₄	#120×C₄₃	1	4	yes	—
522	C₂×C₄	#121×C₄₃	1	8	yes	—
523	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
524	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
525	C₂×C₄	#123×C₄₃	1	4	yes	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	8	no	—
529	C₂²	—	2	4	no	—
530	C₂²	—	2	4	no	—
531	C₂²	—	2	8	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	4	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	2	8	no	—
536	C₂²	C₄₃×#389	1	8	yes	complemented
537	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
538	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
539	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
540	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
541	C₂²	C₄×#41×C₄₃	1	2	yes	—
542	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
543	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
544	C₂²	C₂×#121×C₄₃	1	2	yes	—
545	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
546	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
547	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
548	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
549	C₂²	C₄₃×#525	1	2	yes	—
550	C₂²	C₄₃×#525	1	1	yes	characteristic
551	C₂²	C₄₃×#525	1	2	yes	—
552	C₂²	C₄₃×#525	1	1	yes	characteristic
553	C₂²	C₂×#125×C₄₃	1	1	yes	characteristic
554	C₂²	C₄₃×#529	1	2	yes	—
555	C₂²	C₄₃×#529	1	2	yes	—
556	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
557	C₂²	C₄₃×#532	1	2	yes	—
558	C₂²	C₄₃×#533	1	2	yes	—
559	C₂²	C₄₃×#533	1	2	yes	—
560	C₄	—	2	8	no	—
561	C₄	—	2	8	no	—
562	C₄	—	2	4	no	—
563	C₄	—	4	8	no	—
564	C₄	—	8	2	no	—
565	C₄	—	8	2	no	—
566	C₄	C₄₃×#385	1	8	yes	complemented
567	C₂	—	2	8	no	—
568	C₂	C₂×C₄₃×#385	1	1	yes	characteristic
569	C₂	C₂×C₄₃×#389	1	1	yes	characteristic
570	C₂	C₄₃×#2296	1	1	yes	characteristic
571	C₂	C₄×#121×C₄₃	1	2	yes	—
572	C₂	C₄×C₂²⋊Q₈×C₄₃	1	2	yes	—
573	C₂	C₄₃×#2847	1	1	yes	characteristic
574	C₂	C₄₃×#2848	1	1	yes	characteristic
575	C₂	C₄₃×#2851	1	2	yes	—
576	C₂	C₄₃×#2854	1	1	yes	characteristic
577	C₂	C₄₃×#2855	1	1	yes	characteristic
578	C₂	C₄₃×#2857	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂⁵×C₄₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#389	C₂	semidirect
6. C₄₃×#1436	C₂	semidirect
7. C₄₃×C₄⋊#95	C₂	semidirect
25. C₄₃×#380	C₄	semidirect
63. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
81. #95×C₄₃	C₂×C₄	semidirect
134. C₂²×C₄×C₄₃	C₄⋊C₄	semidirect
236. #14697	C₄₃	direct (N × H)
247. C₂²×C₄₃	#389	semidirect
277. C₄×C₄₃	#385	semidirect
279. C₂×#389	C₂×C₄₃	semidirect
283. #1436	C₂×C₄₃	semidirect
284. C₄⋊#95	C₂×C₄₃	semidirect
314. #380	C₄×C₄₃	semidirect
320. C₄₃	#14697	direct (N × H)
353. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
371. #95	C₂×C₄×C₄₃	semidirect
424. C₂²×C₄	C₄⋊C₄×C₄₃	semidirect
536. C₂²	C₄₃×#389	semidirect
566. C₄	C₄₃×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄²×C₄₃	2
C₂×C₄₃×#389	2
C₂×C₄₃×#385	2
C₂×C₄₃×#380	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄₃×C₂²⋊#95	2
#14697	43

Subgroups — C43×#14697 #24934714

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#14697 #24934714