Subgroups — #25101293

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137069	C₂	1	1	yes	maximal, characteristic
2	#19135531	C₂	1	1	yes	maximal, characteristic
3	#19135530	C₂	1	1	yes	maximal, characteristic
4	#19135314	C₂	1	1	yes	maximal, characteristic
5	#19135155	C₂	1	2	yes	maximal
6	#19135149	C₂	1	2	yes	maximal
7	#19134454	C₂	1	2	yes	maximal
8	#19134450	C₂	1	1	yes	maximal, characteristic
9	#19134345	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
15	C₂×#13063235	C₂²	1	2	yes	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
21	#14582804	C₄	1	1	yes	characteristic
22	#14582804	C₄	1	1	yes	characteristic
23	#14582795	C₄	1	1	yes	characteristic
24	#14582795	C₄	1	1	yes	characteristic
25	#14582781	C₄	1	2	yes	—
26	#14582781	C₄	1	2	yes	—
27	C₄×Dic₄₃⋊C₄	C₂²	1	2	yes	—
28	#14582745	C₂²	1	2	yes	—
29	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
30	#14582654	C₂²	1	2	yes	—
31	#14582653	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	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	2	yes	—
41	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₄×Dic₈₆	—	2	2	no	—
46	C₄×Dic₈₆	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
57	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
58	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
60	#13063235	—	2	4	no	—
61	C₄×C₄₃⋊C₈	—	2	2	no	—
62	C₈×Dic₄₃	—	2	2	no	—
63	C₈×Dic₄₃	—	2	2	no	—
64	C₈×Dic₄₃	—	2	2	no	—
65	C₈×Dic₄₃	Q₈	1	4	yes	complemented
66	C₄₃⋊#95	C₂×C₄	1	2	yes	—
67	C₄₃⋊#95	C₂×C₄	1	2	yes	—
68	C₄₃⋊#95	C₂×C₄	1	2	yes	—
69	C₄₃⋊#95	C₂×C₄	1	2	yes	—
70	C₄₃⋊#95	C₂×C₄	1	2	yes	—
71	C₄₃⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₃	—	2	4	no	—
80	C₄⋊C₈×C₄₃	—	2	2	no	—
81	C₄×C₈×C₄₃	—	2	2	no	—
82	#95×C₄₃	C₂×C₄	1	2	yes	—
83	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×Dic₈₆	—	2	2	no	—
95	C₂×Dic₈₆	—	2	2	no	—
96	C₂×Dic₈₆	—	2	2	no	—
97	C₂×C₈×C₄₃	—	2	1	no	—
98	C₂×C₈×C₄₃	—	2	1	no	—
99	C₂×C₈×C₄₃	—	2	1	no	—
100	C₂×C₈×C₄₃	—	2	1	no	—
101	C₂×C₈×C₄₃	—	2	2	no	—
102	C₂×C₈×C₄₃	—	2	2	no	—
103	C₂×C₈×C₄₃	—	2	2	no	—
104	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
105	C₂×C₈×C₄₃	#41	1	2	yes	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄²×C₄₃	—	2	2	no	—
109	C₄²×C₄₃	—	2	2	no	—
110	C₄²×C₄₃	#41	1	2	yes	—
111	C₄²×C₄₃	#41	1	2	yes	—
112	C₄⋊Dic₄₃	—	2	2	no	—
113	Dic₄₃⋊C₄	—	2	4	no	—
114	Dic₄₃⋊C₄	—	2	4	no	—
115	Dic₄₃⋊C₄	—	2	4	no	—
116	C₄×Dic₄₃	—	2	2	no	—
117	C₄×Dic₄₃	—	2	2	no	—
118	C₄×Dic₄₃	—	2	1	no	—
119	C₄×Dic₄₃	—	2	1	no	—
120	C₄×Dic₄₃	—	2	2	no	—
121	C₄×Dic₄₃	—	2	2	no	—
122	C₄×Dic₄₃	—	2	2	no	—
123	C₄×Dic₄₃	—	2	2	no	—
124	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
125	C₄×Dic₄₃	#41	1	2	yes	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	2	2	no	—
131	C₂×C₄₃⋊C₈	—	2	2	no	—
132	C₂×C₄₃⋊C₈	—	2	2	no	—
133	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
134	C₂×C₄₃⋊C₈	#41	1	2	yes	—
135	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	#117	1	2	yes	—
145	C₂×C₄×C₄₃	#117	1	2	yes	—
146	C₂×C₄×C₄₃	#131	1	2	yes	—
147	C₂×C₄×C₄₃	#131	1	2	yes	—
148	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
154	C₂×Dic₄₃	—	2	1	no	—
155	C₂×Dic₄₃	—	2	1	no	—
156	C₂×Dic₄₃	—	2	1	no	—
157	C₂×Dic₄₃	—	2	1	no	—
158	C₂×Dic₄₃	—	2	1	no	—
159	C₂×Dic₄₃	—	2	1	no	—
160	C₂×Dic₄₃	—	2	1	no	—
161	C₂×Dic₄₃	—	2	1	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
169	C₂×Dic₄₃	C₄×Q₈	1	2	yes	—
170	C₂×Dic₄₃	#131	1	2	yes	—
171	C₂×Dic₄₃	#131	1	2	yes	—
172	Dic₈₆	—	4	4	no	—
173	C₈×C₄₃	—	2	2	no	—
174	C₈×C₄₃	—	2	2	no	—
175	C₈×C₄₃	—	4	2	no	—
176	C₄₃⋊C₈	—	2	2	no	—
177	C₄₃⋊C₈	—	2	2	no	—
178	C₄₃⋊C₈	—	4	2	no	—
179	#21341	—	43	1	no	maximal, Sylow
180	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
181	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
182	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
186	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	#433	1	4	yes	—
191	C₄×C₄₃	#529	1	1	yes	characteristic
192	C₄×C₄₃	#529	1	1	yes	characteristic
193	C₄×C₄₃	#533	1	1	yes	characteristic
194	C₄×C₄₃	#533	1	1	yes	characteristic
195	Dic₄₃	—	2	2	no	—
196	Dic₄₃	—	2	2	no	—
197	Dic₄₃	—	2	2	no	—
198	Dic₄₃	—	2	2	no	—
199	Dic₄₃	—	4	2	no	—
200	Dic₄₃	—	4	2	no	—
201	#2295	—	43	1	no	—
202	#1984	—	43	1	no	—
203	#1984	—	43	1	no	—
204	#1939	—	43	1	no	—
205	#1939	D₄₃	1	1	yes	characteristic
206	#1916	—	43	2	no	—
207	#1916	—	43	2	no	—
208	#1768	—	43	2	no	—
209	#1767	—	43	1	no	—
210	#1746	—	43	2	no	—
211	C₄²×C₈	—	43	1	no	—
212	C₂×C₄₃	#2295	1	1	yes	characteristic
213	C₂×C₄₃	C₂×#433	1	1	yes	characteristic
214	C₂×C₄₃	#2922	1	1	yes	characteristic
215	C₂×C₄₃	#2960	1	1	yes	characteristic
216	C₂×C₄₃	#2960	1	1	yes	characteristic
217	C₂×C₄₃	#2966	1	1	yes	characteristic
218	C₂×C₄₃	#2966	1	1	yes	characteristic
219	C₂×C₄×Q₈	—	43	1	no	—
220	C₂×C₄⋊C₈	—	43	2	no	—
221	C₂×C₄⋊C₈	—	43	1	no	—
222	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
224	C₂×#97	—	43	2	no	—
225	C₂×C₄×C₈	—	43	1	no	—
226	C₂×C₄×C₈	—	43	1	no	—
227	C₂×C₄×C₈	—	43	1	no	—
228	C₂×C₄×C₈	—	43	1	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
231	#391	—	43	1	no	—
232	#391	—	43	1	no	—
233	#389	—	43	1	no	—
234	#389	—	43	1	no	—
235	#387	—	43	2	no	—
236	#387	—	43	2	no	—
237	C₄×C₄⋊C₄	—	43	2	no	—
238	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
239	#376	—	43	2	no	—
240	C₄³	—	43	1	no	—
241	#336	—	43	2	no	—
242	#336	—	43	2	no	—
243	#336	—	43	2	no	—
244	#336	—	43	2	no	—
245	#336	—	43	2	no	—
246	#336	—	43	2	no	—
247	#336	C₂×D₄₃	1	2	yes	—
248	C₄₃	#21341	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	C₂²×C₈	—	43	2	no	—
253	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
254	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
256	C₄×Q₈	—	86	2	no	—
257	C₄×Q₈	—	86	2	no	—
258	C₂×C₄⋊C₄	—	43	2	no	—
259	C₂×C₄⋊C₄	—	43	1	no	—
260	C₂×C₄⋊C₄	—	43	2	no	—
261	C₂×C₄⋊C₄	—	43	2	no	—
262	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
264	C₂×C₄²	—	43	1	no	—
265	C₂×C₄²	—	43	1	no	—
266	C₂×C₄²	—	43	1	no	—
267	C₂×C₄²	—	43	1	no	—
268	C₂×C₄²	—	43	1	no	—
269	C₂×C₄²	—	43	2	no	—
270	C₂×C₄²	—	43	1	no	—
271	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	86	4	no	—
276	C₄⋊C₈	—	86	2	no	—
277	#97	—	86	4	no	—
278	C₄×C₈	—	2	2	no	—
279	C₄×C₈	—	43	4	no	—
280	C₄×C₈	—	86	2	no	—
281	C₄×C₈	—	86	2	no	—
282	C₄×C₈	—	86	2	no	—
283	C₄×C₈	—	86	2	no	—
284	#95	—	43	2	no	—
285	#95	—	43	2	no	—
286	#95	—	43	2	no	—
287	#95	—	43	2	no	—
288	#95	—	43	2	no	—
289	#95	—	43	2	no	—
290	#95	C₄×D₄₃	1	2	yes	—
291	C₂×Q₈	—	86	2	no	—
292	C₂×Q₈	—	86	2	no	—
293	C₂×Q₈	—	86	2	no	—
294	C₂²×C₄	—	43	1	no	—
295	C₂²×C₄	—	43	1	no	—
296	C₂²×C₄	—	43	1	no	—
297	C₂²×C₄	—	43	1	no	—
298	C₂²×C₄	—	43	2	no	—
299	C₂²×C₄	—	43	2	no	—
300	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
301	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	43	2	no	—
313	C₂×C₈	—	43	2	no	—
314	C₂×C₈	—	86	1	no	—
315	C₂×C₈	—	86	1	no	—
316	C₂×C₈	—	86	1	no	—
317	C₂×C₈	—	86	1	no	—
318	C₂×C₈	—	86	2	no	—
319	C₂×C₈	—	86	2	no	—
320	C₂×C₈	—	86	2	no	—
321	C₂×C₈	#10621900	1	2	yes	—
322	C₂×C₈	Q₈×D₄₃	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	86	4	no	—
326	C₄⋊C₄	—	86	4	no	—
327	C₄⋊C₄	—	86	4	no	—
328	C₄⋊C₄	—	86	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	43	2	no	—
332	C₄²	—	43	2	no	—
333	C₄²	—	86	2	no	—
334	C₄²	—	86	2	no	—
335	C₄²	—	86	2	no	—
336	C₄²	—	86	2	no	—
337	C₄²	—	86	1	no	—
338	C₄²	—	86	1	no	—
339	C₄²	—	86	2	no	—
340	C₄²	—	86	2	no	—
341	C₄²	#10621900	1	2	yes	—
342	C₄²	#10621902	1	2	yes	—
343	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
344	Q₈	—	172	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	43	2	no	—
354	C₂×C₄	—	43	2	no	—
355	C₂×C₄	—	43	2	no	—
356	C₂×C₄	—	43	2	no	—
357	C₂×C₄	—	86	1	no	—
358	C₂×C₄	—	86	1	no	—
359	C₂×C₄	—	86	1	no	—
360	C₂×C₄	—	86	1	no	—
361	C₂×C₄	—	86	1	no	—
362	C₂×C₄	—	86	1	no	—
363	C₂×C₄	—	86	1	no	—
364	C₂×C₄	—	86	1	no	—
365	C₂×C₄	—	86	2	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	86	2	no	—
369	C₂×C₄	—	86	2	no	—
370	C₂×C₄	—	86	2	no	—
371	C₂×C₄	#13063283	1	2	yes	—
372	C₂×C₄	#13063283	1	2	yes	—
373	C₂×C₄	#13063331	1	2	yes	—
374	C₂×C₄	#13063333	1	2	yes	—
375	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
376	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
379	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
380	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	86	2	no	—
385	C₈	—	86	2	no	—
386	C₈	—	172	2	no	—
387	C₂²	C₂×#13063283	1	1	yes	characteristic
388	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
389	C₂²	C₄×#10621900	1	1	yes	characteristic
390	C₂²	#131×D₄₃	1	1	yes	characteristic
391	C₂²	#131×D₄₃	1	1	yes	characteristic
392	C₂²	C₂×#13063331	1	1	yes	characteristic
393	C₂²	C₂×#13063333	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	86	2	no	—
398	C₄	—	86	2	no	—
399	C₄	—	86	2	no	—
400	C₄	—	86	2	no	—
401	C₄	—	172	2	no	—
402	C₄	—	172	2	no	—
403	C₄	#14582959	1	4	yes	—
404	C₄	#14583430	1	1	yes	characteristic
405	C₄	#14583434	1	1	yes	characteristic
406	C₄	#14583451	1	1	yes	characteristic
407	C₄	#14583454	1	1	yes	characteristic
408	C₂	#19137066	1	1	yes	characteristic
409	C₂	C₂×#14582959	1	1	yes	characteristic
410	C₂	#19143238	1	1	yes	characteristic
411	C₂	#19143524	1	1	yes	characteristic
412	C₂	#19143526	1	1	yes	characteristic
413	C₂	#19143567	1	1	yes	characteristic
414	C₂	#19143573	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle, prime radical	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1939	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1939	D₄₃
hypocenter	C₄₃	#21341
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
65. C₈×Dic₄₃	Q₈	semidirect
248. C₄₃	#21341	semidirect

Maximal subgroups

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

subgroup	index
#19137069	2
#19135531	2
#19135530	2
#19135314	2
#19135155	2
#19135149	2
#19134454	2
#19134450	2
#19134345	2
C₄×C₈×Dic₄₃	2
C₄₃×#1939	2
#21341	43