Subgroups — C₄₃×#20736 #24940753

Order 11008.

1358 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1825	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1805	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1804	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1788	C₂	1	2	yes	maximal
8	C₄×#103×C₄₃	C₂	1	2	yes	maximal, complemented
9	C₄×#102×C₄₃	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₄×#41×C₄₃	—	2	4	no	—
12	C₄×#41×C₄₃	C₄	1	8	yes	complemented
13	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₃	—	2	1	no	—
16	C₂×C₄×D₄×C₄₃	—	2	1	no	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₃	—	2	1	no	—
20	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	—	2	1	no	—
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#431	—	2	4	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	4	yes	—
26	C₂×#102×C₄₃	C₂²	1	4	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#383	—	2	1	no	—
30	C₄₃×#382	C₂²	1	2	yes	—
31	C₄₃×#381	—	2	1	no	—
32	C₄₃×#380	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
34	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
35	C₄₃×#376	—	2	1	no	—
36	C₄₃×#340	C₂²	1	4	yes	—
37	C₄₃×#340	C₂²	1	4	yes	—
38	C₂×#41×C₄₃	—	2	4	no	—
39	C₂×#41×C₄₃	—	2	4	no	—
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
52	C₄×Q₈×C₄₃	—	2	2	no	—
53	C₄×Q₈×C₄₃	—	2	2	no	—
54	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₄₃	—	2	8	no	—
57	C₄×D₄×C₄₃	—	2	8	no	—
58	C₄×D₄×C₄₃	—	2	2	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
61	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
62	#117×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	8	no	—
64	#117×C₄₃	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	8	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	D₄	1	4	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₄₃	—	2	4	no	—
86	#103×C₄₃	—	2	8	no	—
87	#102×C₄₃	—	2	8	no	—
88	C₂²⋊C₈×C₄₃	—	2	4	no	—
89	C₄×C₈×C₄₃	—	2	4	no	—
90	#95×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	2	no	—
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	—	2	1	no	—
95	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
96	#41×C₄₃	—	2	16	no	—
97	#41×C₄₃	—	2	8	no	—
98	#41×C₄₃	—	2	8	no	—
99	C₂×Q₈×C₄₃	—	2	1	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₄₃	#41	1	4	yes	—
103	C₂×D₄×C₄₃	—	2	8	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂×D₄×C₄₃	#41	1	4	yes	—
109	C₂²×C₄×C₄₃	—	2	8	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	4	no	—
122	C₂²×C₄×C₄₃	—	4	4	no	—
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
125	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₄₃	—	2	4	no	—
134	C₂×C₈×C₄₃	—	2	4	no	—
135	C₂×C₈×C₄₃	—	2	4	no	—
136	C₄⋊C₄×C₄₃	—	2	4	no	—
137	C₄⋊C₄×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	2	1	no	—
140	C₄⋊C₄×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₄₃	—	2	4	no	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	4	no	—
148	C₄²×C₄₃	—	2	4	no	—
149	C₄²×C₄₃	—	2	4	no	—
150	C₄²×C₄₃	—	2	4	no	—
151	C₄²×C₄₃	—	4	4	no	—
152	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
153	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
154	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
155	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
156	C₄²×C₄₃	C₂×D₄	1	2	yes	—
157	C₄²×C₄₃	C₂×D₄	1	2	yes	—
158	C₂³×C₄₃	—	2	2	no	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	4	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₄₃	—	2	2	no	—
168	Q₈×C₄₃	—	2	4	no	—
169	Q₈×C₄₃	#117	1	4	yes	—
170	D₄×C₄₃	—	2	16	no	—
171	D₄×C₄₃	—	2	2	no	—
172	D₄×C₄₃	—	2	4	no	—
173	D₄×C₄₃	#117	1	4	yes	—
174	C₂×C₄×C₄₃	—	2	16	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	8	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	8	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	8	no	—
192	C₂×C₄×C₄₃	—	4	4	no	—
193	C₂×C₄×C₄₃	—	4	4	no	—
194	C₂×C₄×C₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₄₃	#135	1	4	yes	—
201	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
204	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
205	C₈×C₄₃	—	4	4	no	—
206	#20736	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	4	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	4	4	no	—
212	C₂²×C₄₃	—	4	8	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₃	#525	1	2	yes	—
217	C₂²×C₄₃	C₂×#135	1	2	yes	—
218	C₂²×C₄₃	#575	1	2	yes	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	4	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	8	4	no	—
227	C₄×C₄₃	#416	1	4	yes	—
228	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
229	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
230	C₄×C₄₃	#525	1	2	yes	—
231	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic
232	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
233	#2283	C₂×C₄₃	1	1	yes	characteristic, complemented
234	#1825	C₂×C₄₃	1	2	yes	complemented
235	#1805	C₂×C₄₃	1	2	yes	complemented
236	#1804	C₂×C₄₃	1	2	yes	complemented
237	#1788	C₂×C₄₃	1	2	yes	—
238	C₄×#103	C₂×C₄₃	1	2	yes	complemented
239	C₄×#102	C₂×C₄₃	1	2	yes	complemented
240	C₂×C₄₃	—	4	2	no	—
241	C₂×C₄₃	—	4	4	no	—
242	C₂×C₄₃	#2280	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
244	C₂×C₄₃	#2896	1	1	yes	characteristic
245	C₂×C₄₃	#3102	1	4	yes	—
246	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
247	C₄×#41	—	2	4	no	—
248	C₄×#41	C₄×C₄₃	1	8	yes	complemented
249	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
251	C₂×C₄×D₄	—	2	1	no	—
252	C₂×C₄×D₄	—	2	1	no	—
253	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
255	C₂×#117	—	2	1	no	—
256	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
257	C₂²×C₄²	—	2	1	no	—
258	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
259	#431	—	2	4	no	—
260	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
261	C₂×#103	C₂²×C₄₃	1	4	yes	—
262	C₂×#102	C₂²×C₄₃	1	4	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
265	#383	—	2	1	no	—
266	#382	C₂²×C₄₃	1	2	yes	—
267	#381	—	2	1	no	—
268	#380	C₂²×C₄₃	1	2	yes	—
269	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
270	C₄×C₂²⋊C₄	—	2	1	no	—
271	#376	—	2	1	no	—
272	#340	C₂²×C₄₃	1	4	yes	—
273	#340	C₂²×C₄₃	1	4	yes	—
274	C₄₃	#20736	1	1	yes	characteristic, direct product factor, Sylow
275	C₂×#41	—	2	4	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
279	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
280	C₂²×D₄	—	2	1	no	—
281	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
282	C₂³×C₄	—	2	1	no	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	2	1	no	—
285	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
286	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
287	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
292	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
293	C₄×D₄	—	2	8	no	—
294	C₄×D₄	—	2	8	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	2	2	no	—
297	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
298	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
299	#117	—	2	2	no	—
300	#117	—	2	8	no	—
301	#117	C₂×C₄×C₄₃	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
305	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	8	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
317	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₄₃	1	4	yes	—
320	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
322	C₄⋊C₈	—	2	4	no	—
323	#103	—	2	8	no	—
324	#102	—	2	8	no	—
325	C₂²⋊C₈	—	2	4	no	—
326	C₄×C₈	—	2	4	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
333	#41	—	2	16	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
339	C₂×Q₈	#41×C₄₃	1	4	yes	—
340	C₂×D₄	—	2	8	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
345	C₂×D₄	#41×C₄₃	1	4	yes	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	4	no	—
359	C₂²×C₄	—	4	4	no	—
360	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
361	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
362	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
380	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	4	4	no	—
385	C₄²	—	2	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	4	no	—
388	C₄²	—	4	4	no	—
389	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
390	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
391	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
392	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
393	C₄²	C₂×D₄×C₄₃	1	2	yes	—
394	C₄²	C₂×D₄×C₄₃	1	2	yes	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
403	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
404	Q₈	—	2	2	no	—
405	Q₈	—	2	4	no	—
406	Q₈	#117×C₄₃	1	4	yes	—
407	D₄	—	2	16	no	—
408	D₄	—	2	2	no	—
409	D₄	—	2	4	no	—
410	D₄	#117×C₄₃	1	4	yes	—
411	C₂×C₄	—	2	16	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
435	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
436	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
437	C₂×C₄	#135×C₄₃	1	4	yes	—
438	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
441	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
442	C₈	—	4	4	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	8	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
452	C₂²	C₄₃×#525	1	2	yes	—
453	C₂²	C₂×#135×C₄₃	1	2	yes	—
454	C₂²	C₄₃×#575	1	2	yes	—
455	C₄	—	2	2	no	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	2	no	—
462	C₄	—	8	4	no	—
463	C₄	C₄₃×#416	1	4	yes	—
464	C₄	C₂×#117×C₄₃	1	1	yes	characteristic
465	C₄	C₂×#117×C₄₃	1	1	yes	characteristic
466	C₄	C₄₃×#525	1	2	yes	—
467	C₂	—	4	2	no	—
468	C₂	—	4	4	no	—
469	C₂	C₄₃×#2280	1	1	yes	characteristic
470	C₂	C₂×C₄₃×#416	1	1	yes	characteristic
471	C₂	C₄₃×#2896	1	1	yes	characteristic
472	C₂	C₄₃×#3102	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×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
2. C₂×C₄₃×#431	C₂	semidirect
3. C₄₃×#2283	C₂	semidirect
4. C₄₃×#1825	C₂	semidirect
5. C₄₃×#1805	C₂	semidirect
6. C₄₃×#1804	C₂	semidirect
8. C₄×#103×C₄₃	C₂	semidirect
9. C₄×#102×C₄₃	C₂	semidirect
12. C₄×#41×C₄₃	C₄	semidirect
206. #20736	C₄₃	direct (N × H)
232. C₂×#431	C₂×C₄₃	semidirect
233. #2283	C₂×C₄₃	semidirect
234. #1825	C₂×C₄₃	semidirect
235. #1805	C₂×C₄₃	semidirect
236. #1804	C₂×C₄₃	semidirect
238. C₄×#103	C₂×C₄₃	semidirect
239. C₄×#102	C₂×C₄₃	semidirect
248. C₄×#41	C₄×C₄₃	semidirect
274. C₄₃	#20736	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₄₃	2
C₂×C₄₃×#431	2
C₄₃×#2283	2
C₄₃×#1825	2
C₄₃×#1805	2
C₄₃×#1804	2
C₄₃×#1788	2
C₄×#103×C₄₃	2
C₄×#102×C₄₃	2
#20736	43

Subgroups — C43×#20736 #24940753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20736 #24940753