Subgroups — #25096951

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063284	C₂	1	1	yes	maximal, characteristic
2	#19134739	C₂	1	2	yes	maximal, complemented
3	#19134711	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134711	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134664	C₂	1	2	yes	maximal
6	#19134575	C₂	1	1	yes	maximal, characteristic
7	#19134450	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134363	C₂	1	2	yes	maximal
10	#19134345	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063284	C₂²	1	1	yes	characteristic
13	C₂×#13063284	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13063235	C₂²	1	2	yes	—
18	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
19	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
20	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
21	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
22	C₄×C₄⋊Dic₄₃	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊Dic₄₃	C₄	1	1	yes	characteristic
24	C₄×C₂²⋊Dic₄₃	C₄	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₃	C₄	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₃	C₄	1	1	yes	characteristic
27	#14582745	C₂²	1	1	yes	characteristic
28	#14582745	C₂²	1	1	yes	characteristic
29	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
30	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
31	#14582654	C₂²	1	2	yes	—
32	#14582653	C₂²	1	2	yes	—
33	#14582653	C₂²	1	2	yes	—
34	#14582653	C₂²	1	2	yes	—
35	#14582653	C₂²	1	2	yes	—
36	#14582653	C₂²	1	2	yes	—
37	#14582653	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	#13063284	—	2	2	no	—
46	#13063284	—	2	2	no	—
47	#13063284	—	2	2	no	—
48	#13063284	—	2	2	no	—
49	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
72	#13063235	—	2	4	no	—
73	C₈×Dic₄₃	—	2	4	no	—
74	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
75	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
76	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₃	—	2	2	no	—
88	C₂×C₄²×C₄₃	—	2	2	no	—
89	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	—	2	2	no	—
94	C₄⋊C₈×C₄₃	—	2	2	no	—
95	C₂²⋊C₈×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	4	1	no	—
106	C₂²×C₄×C₄₃	—	4	1	no	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	2	yes	—
113	C₂²×C₄×C₄₃	#41	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	#41	1	2	yes	—
134	C₄²×C₄₃	#41	1	2	yes	—
135	C₂²⋊Dic₄₃	—	2	2	no	—
136	C₂²⋊Dic₄₃	—	2	2	no	—
137	C₂²⋊Dic₄₃	—	2	2	no	—
138	C₂²⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	C₄×Dic₄₃	—	2	2	no	—
145	C₄×Dic₄₃	—	2	2	no	—
146	C₄×Dic₄₃	—	2	2	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₄×Dic₄₃	—	2	1	no	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	1	no	—
152	C₄×Dic₄₃	—	2	1	no	—
153	C₄×Dic₄₃	—	4	1	no	—
154	C₄×Dic₄₃	—	4	1	no	—
155	C₄×Dic₄₃	—	4	1	no	—
156	C₄×Dic₄₃	—	4	1	no	—
157	C₄×Dic₄₃	#41	1	2	yes	—
158	C₄×Dic₄₃	#41	1	2	yes	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	2	no	—
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂³×C₄₃	—	2	1	no	—
166	C₂³×C₄₃	—	2	1	no	—
167	C₂³×C₄₃	—	2	1	no	—
168	C₂³×C₄₃	—	2	1	no	—
169	C₂³×C₄₃	—	2	1	no	—
170	C₂³×C₄₃	—	2	1	no	—
171	C₂³×C₄₃	#117	1	2	yes	—
172	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	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	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	#117	1	2	yes	—
190	C₂×C₄×C₄₃	#117	1	2	yes	—
191	C₂×C₄×C₄₃	#117	1	2	yes	—
192	C₂×C₄×C₄₃	#131	1	2	yes	—
193	C₂×C₄×C₄₃	#131	1	2	yes	—
194	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₄₃	—	2	1	no	—
201	C₂×Dic₄₃	—	2	1	no	—
202	C₂×Dic₄₃	—	2	1	no	—
203	C₂×Dic₄₃	—	2	1	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	1	no	—
206	C₂×Dic₄₃	—	2	1	no	—
207	C₂×Dic₄₃	—	2	1	no	—
208	C₂×Dic₄₃	—	2	1	no	—
209	C₂×Dic₄₃	—	2	1	no	—
210	C₂×Dic₄₃	—	2	1	no	—
211	C₂×Dic₄₃	—	2	1	no	—
212	C₂×Dic₄₃	—	2	1	no	—
213	C₂×Dic₄₃	—	2	1	no	—
214	C₂×Dic₄₃	—	2	1	no	—
215	C₂×Dic₄₃	—	2	1	no	—
216	C₂×Dic₄₃	—	2	1	no	—
217	C₂×Dic₄₃	—	2	1	no	—
218	C₂×Dic₄₃	—	2	1	no	—
219	C₂×Dic₄₃	—	2	1	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	1	no	—
222	C₂×Dic₄₃	#117	1	2	yes	—
223	C₂×Dic₄₃	#117	1	2	yes	—
224	C₈×C₄₃	—	4	2	no	—
225	C₈×C₄₃	—	4	2	no	—
226	C₄₃⋊C₈	—	4	2	no	—
227	C₄₃⋊C₈	—	4	2	no	—
228	#20786	—	43	1	no	maximal, Sylow
229	C₂²×C₄₃	—	2	2	no	—
230	C₂²×C₄₃	—	2	2	no	—
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	4	1	no	—
233	C₂²×C₄₃	—	4	1	no	—
234	C₂²×C₄₃	—	4	1	no	—
235	C₂²×C₄₃	—	4	1	no	—
236	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
237	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
238	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
239	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
240	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
241	C₂²×C₄₃	#568	1	1	yes	characteristic
242	C₂²×C₄₃	#568	1	1	yes	characteristic
243	C₄×C₄₃	—	2	2	no	—
244	C₄×C₄₃	—	2	2	no	—
245	C₄×C₄₃	—	4	1	no	—
246	C₄×C₄₃	—	4	1	no	—
247	C₄×C₄₃	#433	1	4	yes	—
248	C₄×C₄₃	#529	1	1	yes	characteristic
249	C₄×C₄₃	#529	1	1	yes	characteristic
250	C₄×C₄₃	#529	1	1	yes	characteristic
251	C₄×C₄₃	#529	1	1	yes	characteristic
252	Dic₄₃	—	2	2	no	—
253	Dic₄₃	—	2	2	no	—
254	Dic₄₃	—	4	1	no	—
255	Dic₄₃	—	4	1	no	—
256	Dic₄₃	—	4	1	no	—
257	Dic₄₃	—	4	1	no	—
258	Dic₄₃	—	4	1	no	—
259	Dic₄₃	—	4	1	no	—
260	C₄×#117	—	43	1	no	—
261	#1840	—	43	2	no	—
262	#1831	—	43	1	no	—
263	#1831	—	43	1	no	—
264	#1818	—	43	2	no	—
265	#1797	—	43	1	no	—
266	#1797	D₄₃	1	1	yes	characteristic
267	#1767	—	43	1	no	—
268	C₄×C₄⋊C₈	—	43	1	no	—
269	#1750	—	43	2	no	—
270	#1746	—	43	2	no	—
271	C₂×C₄₃	—	4	2	no	—
272	C₂×C₄₃	#2283	1	1	yes	characteristic
273	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
274	C₂×C₄₃	#2921	1	1	yes	characteristic
275	C₂×C₄₃	#2925	1	1	yes	characteristic
276	C₂×C₄₃	#2925	1	1	yes	characteristic
277	C₂×C₄₃	#2925	1	1	yes	characteristic
278	C₂×C₄₃	#2925	1	1	yes	characteristic
279	C₂×#117	—	43	1	no	—
280	C₂×#117	—	43	1	no	—
281	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
282	C₂×C₄⋊C₈	—	43	1	no	—
283	C₂×C₄⋊C₈	—	43	1	no	—
284	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₂²⋊C₈	—	43	2	no	—
287	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
288	C₂×#97	—	43	2	no	—
289	C₂×C₄×C₈	—	43	2	no	—
290	C₄×C₄⋊C₄	—	43	1	no	—
291	C₄×C₄⋊C₄	—	43	1	no	—
292	C₄×C₄⋊C₄	—	43	1	no	—
293	C₄×C₄⋊C₄	—	43	1	no	—
294	C₄×C₂²⋊C₄	—	43	1	no	—
295	C₄×C₂²⋊C₄	—	43	1	no	—
296	C₄×C₂²⋊C₄	—	43	1	no	—
297	C₄×C₂²⋊C₄	—	43	1	no	—
298	#376	—	43	1	no	—
299	#376	—	43	1	no	—
300	C₄³	—	43	1	no	—
301	C₄³	—	43	1	no	—
302	#336	—	43	2	no	—
303	#336	—	43	2	no	—
304	#336	—	43	2	no	—
305	#336	—	43	2	no	—
306	#336	—	43	2	no	—
307	#336	—	43	2	no	—
308	#336	—	43	2	no	—
309	#336	C₂×D₄₃	1	2	yes	—
310	C₄₃	#20786	1	1	yes	characteristic, complemented, Sylow
311	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
312	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
313	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
314	C₂²×C₈	—	43	2	no	—
315	C₂²×C₈	—	43	2	no	—
316	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
317	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
318	#117	—	86	2	no	—
319	#117	—	86	2	no	—
320	#117	—	86	2	no	—
321	#117	—	86	2	no	—
322	C₂×C₄⋊C₄	—	43	1	no	—
323	C₂×C₄⋊C₄	—	43	1	no	—
324	C₂×C₄⋊C₄	—	43	1	no	—
325	C₂×C₄⋊C₄	—	43	1	no	—
326	C₂×C₂²⋊C₄	—	43	1	no	—
327	C₂×C₂²⋊C₄	—	43	1	no	—
328	C₂×C₂²⋊C₄	—	43	1	no	—
329	C₂×C₂²⋊C₄	—	43	1	no	—
330	C₂×C₄²	—	2	2	no	—
331	C₂×C₄²	—	2	2	no	—
332	C₂×C₄²	—	43	1	no	—
333	C₂×C₄²	—	43	1	no	—
334	C₂×C₄²	—	43	1	no	—
335	C₂×C₄²	—	43	1	no	—
336	C₂×C₄²	—	43	1	no	—
337	C₂×C₄²	—	43	1	no	—
338	C₂×C₄²	—	43	1	no	—
339	C₂×C₄²	—	43	1	no	—
340	C₂×C₄²	—	43	1	no	—
341	C₂×C₄²	—	43	1	no	—
342	C₂×C₄²	—	43	1	no	—
343	C₂×C₄²	—	43	1	no	—
344	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
345	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
346	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
347	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
348	C₄⋊C₈	—	2	2	no	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	86	2	no	—
351	C₄⋊C₈	—	86	2	no	—
352	C₂²⋊C₈	—	2	4	no	—
353	C₂²⋊C₈	—	86	4	no	—
354	#97	—	86	4	no	—
355	C₄×C₈	—	86	4	no	—
356	#95	—	43	1	no	—
357	#95	—	43	1	no	—
358	#95	—	43	1	no	—
359	#95	—	43	1	no	—
360	#95	—	43	1	no	—
361	#95	—	43	1	no	—
362	#95	—	43	1	no	—
363	#95	—	43	1	no	—
364	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	43	1	no	—
376	C₂²×C₄	—	43	1	no	—
377	C₂²×C₄	—	43	1	no	—
378	C₂²×C₄	—	43	1	no	—
379	C₂²×C₄	—	43	1	no	—
380	C₂²×C₄	—	43	1	no	—
381	C₂²×C₄	—	43	1	no	—
382	C₂²×C₄	—	43	1	no	—
383	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
388	C₂²×C₄	#10621900	1	2	yes	—
389	C₂²×C₄	#10621902	1	2	yes	—
390	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
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	—	86	2	no	—
398	C₂×C₈	—	86	2	no	—
399	C₂×C₈	—	86	2	no	—
400	C₂×C₈	—	86	2	no	—
401	C₂×C₈	—	86	2	no	—
402	C₂×C₈	—	86	2	no	—
403	C₄⋊C₄	—	86	2	no	—
404	C₄⋊C₄	—	86	2	no	—
405	C₄⋊C₄	—	86	2	no	—
406	C₄⋊C₄	—	86	2	no	—
407	C₂²⋊C₄	—	86	2	no	—
408	C₂²⋊C₄	—	86	2	no	—
409	C₂²⋊C₄	—	86	2	no	—
410	C₂²⋊C₄	—	86	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	43	2	no	—
416	C₄²	—	43	2	no	—
417	C₄²	—	86	2	no	—
418	C₄²	—	86	2	no	—
419	C₄²	—	86	2	no	—
420	C₄²	—	86	2	no	—
421	C₄²	—	86	1	no	—
422	C₄²	—	86	1	no	—
423	C₄²	—	86	1	no	—
424	C₄²	—	86	1	no	—
425	C₄²	—	86	1	no	—
426	C₄²	—	86	1	no	—
427	C₄²	—	172	1	no	—
428	C₄²	—	172	1	no	—
429	C₄²	—	172	1	no	—
430	C₄²	—	172	1	no	—
431	C₄²	#10621900	1	2	yes	—
432	C₄²	#10621900	1	2	yes	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	#13063283	1	2	yes	—
440	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	43	2	no	—
458	C₂×C₄	—	43	2	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	86	1	no	—
461	C₂×C₄	—	86	1	no	—
462	C₂×C₄	—	86	1	no	—
463	C₂×C₄	—	86	1	no	—
464	C₂×C₄	—	86	1	no	—
465	C₂×C₄	—	86	1	no	—
466	C₂×C₄	—	86	1	no	—
467	C₂×C₄	—	86	1	no	—
468	C₂×C₄	—	86	1	no	—
469	C₂×C₄	—	86	1	no	—
470	C₂×C₄	—	86	1	no	—
471	C₂×C₄	—	86	1	no	—
472	C₂×C₄	—	86	1	no	—
473	C₂×C₄	—	86	1	no	—
474	C₂×C₄	—	86	1	no	—
475	C₂×C₄	—	86	1	no	—
476	C₂×C₄	—	86	1	no	—
477	C₂×C₄	—	86	1	no	—
478	C₂×C₄	—	86	1	no	—
479	C₂×C₄	—	86	1	no	—
480	C₂×C₄	—	86	1	no	—
481	C₂×C₄	#13063281	1	2	yes	—
482	C₂×C₄	#13063281	1	2	yes	—
483	C₂×C₄	#13063283	1	2	yes	—
484	C₂×C₄	#13063331	1	2	yes	—
485	C₂×C₄	#13063333	1	2	yes	—
486	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
487	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
489	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
490	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
491	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
492	C₈	—	4	2	no	—
493	C₈	—	4	2	no	—
494	C₈	—	172	2	no	—
495	C₈	—	172	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	#117×D₄₃	1	1	yes	characteristic
504	C₂²	C₂×#13063281	1	1	yes	characteristic
505	C₂²	C₂×#13063283	1	1	yes	characteristic
506	C₂²	C₂×#13063331	1	1	yes	characteristic
507	C₂²	C₂×#13063333	1	1	yes	characteristic
508	C₂²	#14583665	1	1	yes	characteristic
509	C₂²	#14583665	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	86	2	no	—
515	C₄	—	86	2	no	—
516	C₄	—	172	1	no	—
517	C₄	—	172	1	no	—
518	C₄	—	172	1	no	—
519	C₄	—	172	1	no	—
520	C₄	—	172	1	no	—
521	C₄	—	172	1	no	—
522	C₄	#14582957	1	4	yes	—
523	C₄	#14583430	1	1	yes	characteristic
524	C₄	#14583430	1	1	yes	characteristic
525	C₄	#14583435	1	1	yes	characteristic
526	C₄	#14583435	1	1	yes	characteristic
527	C₂	—	4	2	no	—
528	C₂	#19136990	1	1	yes	characteristic
529	C₂	C₂×#14582957	1	1	yes	characteristic
530	C₂	#19143230	1	1	yes	characteristic
531	C₂	#19143256	1	1	yes	characteristic
532	C₂	#19143260	1	1	yes	characteristic
533	C₂	#19143262	1	1	yes	characteristic
534	C₂	#19143263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1797	C₂
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1797	D₄₃
hypocenter	C₄₃	#20786
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1797

Complements

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

N	H ≅ G/N	type
2. #19134739	C₂	semidirect
3. #19134711	C₂	semidirect
4. #19134711	C₂	semidirect
7. #19134450	C₂	semidirect
8. C₄⋊C₈×Dic₄₃	C₂	semidirect
10. #19134345	C₂	semidirect
310. C₄₃	#20786	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063284	2
#19134739	2
#19134711	2
#19134664	2
#19134575	2
#19134450	2
C₄⋊C₈×Dic₄₃	2
#19134363	2
#19134345	2
C₄₃×#1797	2
#20786	43