Subgroups — #25002207

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582654	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582653	C₂	1	1	yes	maximal, characteristic
6	C₄×C₄₃⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#336	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₄₃	—	2	2	no	—
13	C₂×C₈×Dic₄₃	—	2	2	no	—
14	C₂×C₈×Dic₄₃	C₄	1	4	yes	complemented
15	C₂×C₄₃⋊#95	C₄	1	2	yes	—
16	C₂×C₄₃⋊#95	C₄	1	2	yes	—
17	#14582654	—	2	2	no	—
18	#14582653	—	2	2	no	—
19	#14582653	—	2	2	no	—
20	#14582653	C₄	1	4	yes	complemented
21	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#336	—	2	2	no	—
25	C₂³×Dic₄₃	C₂×C₄	1	2	yes	—
26	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×Dic₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄₃⋊C₈	—	2	1	no	—
29	C₂²×C₄₃⋊C₈	—	2	1	no	—
30	C₂²×C₄₃⋊C₈	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₂²×C₄₃⋊C₈	—	2	1	no	—
33	C₂²×C₄₃⋊C₈	—	2	1	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
39	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
40	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
41	C₂²×C₄₃⋊C₈	Q₈	1	2	yes	—
42	C₂×C₄×Dic₄₃	—	2	1	no	—
43	C₂×C₄×Dic₄₃	—	2	1	no	—
44	C₂×C₄×Dic₄₃	—	2	1	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	C₂×C₄×Dic₄₃	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₂×C₄×Dic₄₃	—	2	1	no	—
49	C₂×C₄×Dic₄₃	—	2	1	no	—
50	C₂×C₄×Dic₄₃	—	2	1	no	—
51	C₂×C₄×Dic₄₃	—	2	1	no	—
52	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
54	C₈×Dic₄₃	—	2	8	no	—
55	C₄₃⋊#95	—	2	4	no	—
56	C₄₃⋊#95	C₈	1	8	yes	complemented
57	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
58	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₃	—	2	1	no	—
60	C₂²×C₈×C₄₃	—	2	1	no	—
61	C₂²×C₈×C₄₃	—	2	1	no	—
62	C₂²×C₈×C₄₃	—	2	1	no	—
63	C₂²×C₈×C₄₃	—	2	1	no	—
64	C₂²×C₈×C₄₃	—	2	1	no	—
65	C₂²×C₈×C₄₃	—	2	1	no	—
66	C₂²×C₈×C₄₃	—	2	1	no	—
67	C₂²×C₈×C₄₃	—	2	1	no	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₄₃	D₄	1	2	yes	—
72	C₂²×C₈×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	—	2	1	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	1	no	—
78	C₂×C₄²×C₄₃	—	2	1	no	—
79	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	C₂×C₈	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
101	C₂²×Dic₄₃	—	2	2	no	—
102	C₂²×Dic₄₃	—	2	1	no	—
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	—	2	1	no	—
105	C₂²×Dic₄₃	—	2	1	no	—
106	C₂²×Dic₄₃	—	2	2	no	—
107	C₂²×Dic₄₃	—	2	2	no	—
108	C₂²×Dic₄₃	—	2	2	no	—
109	C₂²×Dic₄₃	—	2	2	no	—
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	C₄²	1	2	yes	—
114	C₂²×Dic₄₃	C₄²	1	2	yes	—
115	C₂²×Dic₄₃	C₂×C₈	1	4	yes	—
116	C₂²×Dic₄₃	C₂×C₈	1	4	yes	—
117	C₂²×Dic₄₃	M₁₆	1	4	yes	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	4	1	no	—
128	C₂×C₈×C₄₃	—	4	1	no	—
129	C₂×C₈×C₄₃	—	4	1	no	—
130	C₂×C₈×C₄₃	—	4	1	no	—
131	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₄₃	—	4	1	no	—
133	C₄²×C₄₃	—	4	1	no	—
134	C₄²×C₄₃	—	4	1	no	—
135	C₄²×C₄₃	—	4	1	no	—
136	C₄×Dic₄₃	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	4	1	no	—
141	C₄×Dic₄₃	—	4	1	no	—
142	C₄×Dic₄₃	—	4	1	no	—
143	C₄×Dic₄₃	—	4	1	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂×C₄₃⋊C₈	—	2	2	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	4	1	no	—
154	C₂×C₄₃⋊C₈	—	4	1	no	—
155	C₂×C₄₃⋊C₈	—	4	1	no	—
156	C₂×C₄₃⋊C₈	—	4	1	no	—
157	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
158	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
159	C₂³×C₄₃	#117	1	1	yes	characteristic
160	C₂³×C₄₃	#117	1	1	yes	characteristic
161	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
165	C₂³×C₄₃	C₂²×C₈	1	2	yes	—
166	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
167	C₂³×C₄₃	#131	1	2	yes	—
168	C₂³×C₄₃	#131	1	2	yes	—
169	C₂×C₄×C₄₃	—	2	4	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
179	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
193	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
194	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
195	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
198	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
199	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
200	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
201	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
202	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
203	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
204	C₂×Dic₄₃	—	2	2	no	—
205	C₂×Dic₄₃	—	2	2	no	—
206	C₂×Dic₄₃	—	2	2	no	—
207	C₂×Dic₄₃	—	2	2	no	—
208	C₂×Dic₄₃	—	2	4	no	—
209	C₂×Dic₄₃	—	2	4	no	—
210	C₂×Dic₄₃	—	2	4	no	—
211	C₂×Dic₄₃	—	2	4	no	—
212	C₂×Dic₄₃	—	2	4	no	—
213	C₂×Dic₄₃	—	2	4	no	—
214	C₂×Dic₄₃	—	2	4	no	—
215	C₂×Dic₄₃	—	4	2	no	—
216	C₂×Dic₄₃	—	4	2	no	—
217	C₂×Dic₄₃	—	4	2	no	—
218	C₂×Dic₄₃	—	4	2	no	—
219	C₂×Dic₄₃	C₄×C₈	1	4	yes	—
220	C₂×Dic₄₃	#97	1	4	yes	—
221	C₈×C₄₃	—	2	4	no	—
222	C₈×C₄₃	—	4	2	no	—
223	C₄₃⋊C₈	—	2	4	no	—
224	C₄₃⋊C₈	—	4	2	no	—
225	#10797	—	43	1	no	maximal, Sylow
226	C₂²×C₄₃	#376	1	1	yes	characteristic
227	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₄₃	#387	1	1	yes	characteristic
230	C₂²×C₄₃	#387	1	1	yes	characteristic
231	C₂²×C₄₃	#388	1	1	yes	characteristic
232	C₂²×C₄₃	#388	1	1	yes	characteristic
233	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
234	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
235	C₂²×C₄₃	#405	1	1	yes	characteristic
236	C₂²×C₄₃	#405	1	1	yes	characteristic
237	C₂²×C₄₃	#431	1	2	yes	—
238	C₂²×C₄₃	#431	1	2	yes	—
239	C₂²×C₄₃	#433	1	2	yes	—
240	C₂²×C₄₃	#433	1	2	yes	—
241	C₂²×C₄₃	C₈×D₄	1	2	yes	—
242	C₂²×C₄₃	C₈×D₄	1	2	yes	—
243	C₂²×C₄₃	C₈×D₄	1	2	yes	—
244	C₂²×C₄₃	#435	1	2	yes	—
245	C₂²×C₄₃	#435	1	2	yes	—
246	C₂²×C₄₃	#436	1	2	yes	—
247	C₂²×C₄₃	C₈×Q₈	1	2	yes	—
248	C₂²×C₄₃	#446	1	2	yes	—
249	C₄×C₄₃	—	4	4	no	—
250	C₄×C₄₃	#380	1	1	yes	characteristic
251	C₄×C₄₃	#381	1	1	yes	characteristic
252	C₄×C₄₃	#382	1	1	yes	characteristic
253	C₄×C₄₃	#383	1	1	yes	characteristic
254	C₄×C₄₃	#387	1	1	yes	characteristic
255	C₄×C₄₃	#387	1	1	yes	characteristic
256	C₄×C₄₃	#388	1	1	yes	characteristic
257	C₄×C₄₃	#388	1	1	yes	characteristic
258	Dic₄₃	—	2	4	no	—
259	Dic₄₃	—	2	4	no	—
260	Dic₄₃	—	4	4	no	—
261	C₂²×C₄×C₈	—	43	1	no	—
262	C₂×#336	—	43	1	no	—
263	C₂×#336	—	43	1	no	—
264	C₂×#336	—	43	1	no	—
265	C₂×#336	—	43	1	no	—
266	C₂×#336	D₄₃	1	1	yes	characteristic
267	C₄×#95	—	43	1	no	—
268	C₂×C₄₃	#1434	1	1	yes	characteristic
269	C₂×C₄₃	#1744	1	1	yes	characteristic
270	C₂×C₄₃	#1746	1	1	yes	characteristic
271	C₂×C₄₃	C₈×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄₃	#1752	1	1	yes	characteristic
273	C₂×C₄₃	C₈×C₄⋊C₄	1	1	yes	characteristic
274	C₂×C₄₃	#1770	1	1	yes	characteristic
275	C₂×C₄₃	#1916	1	2	yes	—
276	C₂×C₄₃	#1916	1	2	yes	—
277	C₂×C₄₃	#1923	1	2	yes	—
278	C₂×C₄₃	#1923	1	2	yes	—
279	C₂³×C₈	—	43	1	no	—
280	C₂³×C₈	—	43	1	no	—
281	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
282	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
283	C₂²×C₄²	—	43	1	no	—
284	C₂²×C₄²	—	43	1	no	—
285	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄×C₈	—	43	4	no	—
287	C₂×C₄×C₈	—	86	2	no	—
288	C₂×C₄×C₈	—	86	2	no	—
289	C₂×#95	—	43	2	no	—
290	C₂×#95	—	43	2	no	—
291	#336	—	2	2	no	—
292	#336	—	43	4	no	—
293	#336	—	86	2	no	—
294	#336	—	86	2	no	—
295	#336	—	86	2	no	—
296	C₄₃	#10797	1	1	yes	characteristic, complemented, Sylow
297	C₂³×C₄	—	43	1	no	—
298	C₂³×C₄	—	43	1	no	—
299	C₂³×C₄	—	43	2	no	—
300	C₂³×C₄	C₄×D₄₃	1	2	yes	—
301	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	2	1	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	1	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	43	2	no	—
313	C₂²×C₈	—	43	2	no	—
314	C₂²×C₈	—	43	2	no	—
315	C₂²×C₈	—	43	2	no	—
316	C₂²×C₈	—	86	1	no	—
317	C₂²×C₈	—	86	1	no	—
318	C₂²×C₈	—	86	1	no	—
319	C₂²×C₈	—	86	1	no	—
320	C₂²×C₈	—	86	1	no	—
321	C₂²×C₈	—	86	1	no	—
322	C₂²×C₈	—	86	1	no	—
323	C₂²×C₈	—	86	1	no	—
324	C₂²×C₈	—	86	1	no	—
325	C₂²×C₈	—	86	1	no	—
326	C₂²×C₈	C₄×D₄₃	1	2	yes	—
327	C₂²×C₈	C₄×D₄₃	1	2	yes	—
328	C₂²×C₈	D₁₇₂	1	2	yes	—
329	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	43	2	no	—
337	C₂×C₄²	—	43	2	no	—
338	C₂×C₄²	—	86	1	no	—
339	C₂×C₄²	—	86	1	no	—
340	C₂×C₄²	—	86	1	no	—
341	C₂×C₄²	—	86	1	no	—
342	C₂×C₄²	—	86	1	no	—
343	C₂×C₄²	—	86	1	no	—
344	C₂×C₄²	—	86	1	no	—
345	C₂×C₄²	—	86	1	no	—
346	C₂×C₄²	—	86	1	no	—
347	C₂×C₄²	—	86	1	no	—
348	C₄×C₈	—	86	8	no	—
349	#95	—	43	8	no	—
350	#95	—	86	4	no	—
351	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	43	2	no	—
359	C₂²×C₄	—	43	2	no	—
360	C₂²×C₄	—	43	4	no	—
361	C₂²×C₄	—	43	4	no	—
362	C₂²×C₄	—	43	4	no	—
363	C₂²×C₄	—	86	1	no	—
364	C₂²×C₄	—	86	1	no	—
365	C₂²×C₄	—	86	1	no	—
366	C₂²×C₄	—	86	1	no	—
367	C₂²×C₄	—	86	2	no	—
368	C₂²×C₄	—	86	2	no	—
369	C₂²×C₄	—	86	2	no	—
370	C₂²×C₄	—	86	2	no	—
371	C₂²×C₄	—	86	2	no	—
372	C₂²×C₄	—	86	2	no	—
373	C₂²×C₄	—	86	2	no	—
374	C₂²×C₄	—	86	2	no	—
375	C₂²×C₄	C₈×D₄₃	1	4	yes	—
376	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
379	C₂²×C₄	#10621898	1	1	yes	characteristic
380	C₂²×C₄	#10621898	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
382	C₂²×C₄	#10621900	1	1	yes	characteristic
383	C₂²×C₄	#10621900	1	1	yes	characteristic
384	C₂²×C₄	#10621900	1	1	yes	characteristic
385	C₂²×C₄	#10621900	1	1	yes	characteristic
386	C₂²×C₄	#10621900	1	1	yes	characteristic
387	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
388	C₂²×C₄	#10621902	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₂×C₈	—	43	4	no	—
404	C₂×C₈	—	86	2	no	—
405	C₂×C₈	—	86	2	no	—
406	C₂×C₈	—	86	2	no	—
407	C₂×C₈	—	86	2	no	—
408	C₂×C₈	—	86	2	no	—
409	C₂×C₈	—	86	2	no	—
410	C₂×C₈	—	86	2	no	—
411	C₂×C₈	—	86	2	no	—
412	C₂×C₈	—	86	2	no	—
413	C₂×C₈	—	172	1	no	—
414	C₂×C₈	—	172	1	no	—
415	C₂×C₈	—	172	1	no	—
416	C₂×C₈	—	172	1	no	—
417	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
418	C₄²	—	4	1	no	—
419	C₄²	—	4	1	no	—
420	C₄²	—	4	1	no	—
421	C₄²	—	4	1	no	—
422	C₄²	—	86	2	no	—
423	C₄²	—	86	2	no	—
424	C₄²	—	86	2	no	—
425	C₄²	—	86	2	no	—
426	C₄²	—	172	1	no	—
427	C₄²	—	172	1	no	—
428	C₄²	—	172	1	no	—
429	C₄²	—	172	1	no	—
430	C₂³	C₄²×D₄₃	1	1	yes	characteristic
431	C₂³	#13063281	1	1	yes	characteristic
432	C₂³	#13063283	1	1	yes	characteristic
433	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
434	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
435	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
436	C₂³	#13063290	1	1	yes	characteristic
437	C₂³	C₂×C₈×D₄₃	1	2	yes	—
438	C₂³	M₁₆×D₄₃	1	2	yes	—
439	C₂³	#13063331	1	2	yes	—
440	C₂³	#13063333	1	2	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	43	4	no	—
449	C₂×C₄	—	43	4	no	—
450	C₂×C₄	—	86	2	no	—
451	C₂×C₄	—	86	2	no	—
452	C₂×C₄	—	86	4	no	—
453	C₂×C₄	—	86	4	no	—
454	C₂×C₄	—	86	4	no	—
455	C₂×C₄	—	86	4	no	—
456	C₂×C₄	—	86	2	no	—
457	C₂×C₄	—	86	2	no	—
458	C₂×C₄	—	86	4	no	—
459	C₂×C₄	—	86	4	no	—
460	C₂×C₄	—	86	4	no	—
461	C₂×C₄	—	172	2	no	—
462	C₂×C₄	—	172	2	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	—	172	2	no	—
465	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
467	C₂×C₄	#13063281	1	1	yes	characteristic
468	C₂×C₄	#13063281	1	1	yes	characteristic
469	C₂×C₄	#13063281	1	1	yes	characteristic
470	C₂×C₄	#13063282	1	1	yes	characteristic
471	C₂×C₄	#13063283	1	1	yes	characteristic
472	C₂×C₄	#13063283	1	1	yes	characteristic
473	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
474	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
475	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
476	C₂×C₄	#13063290	1	1	yes	characteristic
477	C₂×C₄	#13063296	1	1	yes	characteristic
478	C₂×C₄	#13063300	1	1	yes	characteristic
479	C₂×C₄	#13063301	1	1	yes	characteristic
480	C₂×C₄	#13063305	1	1	yes	characteristic
481	C₂×C₄	#13063306	1	1	yes	characteristic
482	C₂×C₄	#13063306	1	1	yes	characteristic
483	C₂×C₄	#13063309	1	1	yes	characteristic
484	C₂×C₄	#13063309	1	1	yes	characteristic
485	C₂×C₄	#13063311	1	1	yes	characteristic
486	C₂×C₄	#13063311	1	1	yes	characteristic
487	C₂×C₄	#13063315	1	1	yes	characteristic
488	C₂×C₄	#13063315	1	1	yes	characteristic
489	C₂×C₄	#13063318	1	1	yes	characteristic
490	C₂×C₄	#13063318	1	1	yes	characteristic
491	C₂×C₄	#13063320	1	1	yes	characteristic
492	C₂×C₄	#13063320	1	1	yes	characteristic
493	C₈	—	2	4	no	—
494	C₈	—	4	2	no	—
495	C₈	—	86	4	no	—
496	C₈	—	172	2	no	—
497	C₂²	#14582744	1	1	yes	characteristic
498	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
499	C₂²	#14582750	1	1	yes	characteristic
500	C₂²	#14582780	1	1	yes	characteristic
501	C₂²	#14582784	1	1	yes	characteristic
502	C₂²	#14582787	1	1	yes	characteristic
503	C₂²	#14582791	1	1	yes	characteristic
504	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
505	C₂²	#97×D₄₃	1	1	yes	characteristic
506	C₂²	#14582853	1	1	yes	characteristic
507	C₂²	#14582856	1	1	yes	characteristic
508	C₂²	#14582949	1	2	yes	—
509	C₂²	#14582951	1	2	yes	—
510	C₂²	#14582957	1	2	yes	—
511	C₂²	#14582959	1	2	yes	—
512	C₂²	(C₂²⋊D₄₃)⋊C₈	1	2	yes	—
513	C₂²	C₈×C₂²⋊D₄₃	1	2	yes	—
514	C₂²	C₈×D₁₇₂	1	2	yes	—
515	C₂²	#14582968	1	2	yes	—
516	C₂²	#14582972	1	2	yes	—
517	C₂²	#14582974	1	2	yes	—
518	C₂²	#14583023	1	2	yes	—
519	C₂²	#14583028	1	2	yes	—
520	C₄	—	4	4	no	—
521	C₄	—	86	4	no	—
522	C₄	—	86	4	no	—
523	C₄	—	172	4	no	—
524	C₄	#14582756	1	1	yes	characteristic
525	C₄	#14582760	1	1	yes	characteristic
526	C₄	#14582763	1	1	yes	characteristic
527	C₄	#14582766	1	1	yes	characteristic
528	C₄	#14582780	1	1	yes	characteristic
529	C₄	#14582784	1	1	yes	characteristic
530	C₄	#14582787	1	1	yes	characteristic
531	C₄	#14582791	1	1	yes	characteristic
532	C₂	#19132819	1	1	yes	characteristic
533	C₂	#19134339	1	1	yes	characteristic
534	C₂	#19134345	1	1	yes	characteristic
535	C₂	C₈×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
536	C₂	#19134372	1	1	yes	characteristic
537	C₂	#19134456	1	1	yes	characteristic
538	C₂	#19134461	1	1	yes	characteristic
539	C₂	#19135149	1	2	yes	—
540	C₂	#19135153	1	2	yes	—
541	C₂	#19135198	1	2	yes	—
542	C₂	#19135202	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂×C₄×C₈
Fitting	C₂×C₄₃×#336	C₂
socle, prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#336	D₄₃
hypocenter	C₄₃	#10797
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
14. C₂×C₈×Dic₄₃	C₄	semidirect
20. #14582653	C₄	semidirect
56. C₄₃⋊#95	C₈	semidirect
296. C₄₃	#10797	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₈×Dic₄₃	2
C₂×#14582654	2
C₂×#14582653	2
C₄×C₄₃⋊#95	2
C₂×C₄₃×#336	2
#10797	43