Subgroups — #25001789

Order 11008.

926 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×#14582854	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582663	C₂	1	1	yes	maximal, characteristic
4	#19134311	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582660	C₂	1	1	yes	maximal, characteristic
6	C₂×#14582658	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
12	#14582854	—	2	2	no	—
13	#14582854	C₄	1	4	yes	complemented
14	C₂×#13063235	—	2	1	no	—
15	C₂×C₈×Dic₄₃	—	2	2	no	—
16	C₂×C₈×Dic₄₃	—	2	2	no	—
17	C₂×C₈×Dic₄₃	—	2	1	no	—
18	C₂×C₈×Dic₄₃	C₄	1	4	yes	complemented
19	#14582663	C₄	1	4	yes	complemented
20	#14582661	C₄	1	4	yes	complemented
21	#14582660	C₄	1	4	yes	complemented
22	#14582658	C₄	1	4	yes	complemented
23	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
24	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#405	—	2	2	no	—
27	C₄₃×#405	C₄	1	4	yes	complemented
28	C₂×#97×C₄₃	—	2	1	no	—
29	C₂×C₄×C₈×C₄₃	—	2	1	no	—
30	C₂³×Dic₄₃	—	2	1	no	—
31	C₂×#10621877	—	2	1	no	—
32	C₂×#10621877	—	2	1	no	—
33	C₂×#10621877	—	2	1	no	—
34	C₂×#10621877	C₂×C₄	1	2	yes	—
35	C₂×#10621877	C₂×C₄	1	2	yes	—
36	C₂×#10621877	C₂×C₄	1	2	yes	—
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃⋊C₈	—	2	1	no	—
41	C₂²×C₄₃⋊C₈	—	2	1	no	—
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
45	#13063284	—	2	1	no	—
46	#13063284	—	2	1	no	—
47	#13063284	C₂×C₄	1	2	yes	—
48	#13063284	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
50	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄×Dic₄₃	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	C₂×C₄×Dic₄₃	—	2	1	no	—
55	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
58	#13063235	—	2	4	no	—
59	C₈×Dic₄₃	—	2	8	no	—
60	C₈×Dic₄₃	—	2	4	no	—
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₄₃	—	2	1	no	—
63	C₂×M₁₆×C₄₃	—	2	1	no	—
64	C₂×M₁₆×C₄₃	—	2	1	no	—
65	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
66	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
67	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₃	D₄	1	2	yes	—
73	C₂²×C₈×C₄₃	D₄	1	2	yes	—
74	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	Q₈	1	2	yes	—
77	#117×C₄₃	—	2	1	no	—
78	#117×C₄₃	—	2	1	no	—
79	#117×C₄₃	C₂×C₄	1	2	yes	—
80	#117×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	#97×C₄₃	—	2	4	no	—
85	C₄×C₈×C₄₃	—	2	4	no	—
86	C₂⁴×C₄₃	#41	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
102	C₂²×Dic₄₃	—	2	8	no	—
103	C₂²×Dic₄₃	—	2	2	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	C₂²×Dic₄₃	—	2	2	no	—
106	C₂²×Dic₄₃	—	2	2	no	—
107	M₁₆×C₄₃	—	2	2	no	—
108	M₁₆×C₄₃	—	2	2	no	—
109	M₁₆×C₄₃	—	2	2	no	—
110	M₁₆×C₄₃	C₄²	1	4	yes	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	C₄²	1	4	yes	—
115	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
116	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
118	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
119	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
121	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
122	C₂×C₈×C₄₃	C₄⋊C₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₄⋊C₄	1	4	yes	—
124	C₄⋊C₄×C₄₃	—	2	2	no	—
125	C₄⋊C₄×C₄₃	C₄²	1	4	yes	—
126	C₂²⋊C₄×C₄₃	—	2	2	no	—
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₂²⋊Dic₄₃	—	2	2	no	—
131	C₂²⋊Dic₄₃	—	2	2	no	—
132	C₄⋊Dic₄₃	—	2	2	no	—
133	C₄⋊Dic₄₃	C₄²	1	4	yes	—
134	C₄×Dic₄₃	—	2	2	no	—
135	C₄×Dic₄₃	—	2	2	no	—
136	C₄×Dic₄₃	—	2	2	no	—
137	C₄×Dic₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	C₄²	1	4	yes	—
140	#10621877	—	2	2	no	—
141	#10621877	—	2	2	no	—
142	#10621877	—	2	2	no	—
143	#10621877	C₄²	1	4	yes	—
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	C₄²	1	4	yes	—
154	C₂³×C₄₃	—	2	4	no	—
155	C₂³×C₄₃	#117	1	1	yes	characteristic
156	C₂³×C₄₃	#117	1	1	yes	characteristic
157	C₂³×C₄₃	#117	1	1	yes	characteristic
158	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
159	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
160	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#117	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	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₄×D₄	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×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
192	C₂×Dic₄₃	—	2	8	no	—
193	C₂×Dic₄₃	—	2	8	no	—
194	C₂×Dic₄₃	—	2	8	no	—
195	C₂×Dic₄₃	—	2	4	no	—
196	C₂×Dic₄₃	—	2	4	no	—
197	C₂×Dic₄₃	—	4	4	no	—
198	C₈×C₄₃	—	2	4	no	—
199	C₈×C₄₃	#95	1	4	yes	—
200	C₈×C₄₃	#95	1	4	yes	—
201	C₄₃⋊C₈	—	2	4	no	—
202	C₄₃⋊C₈	—	2	4	no	—
203	#10706	—	43	1	no	maximal, Sylow
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	#376	1	1	yes	characteristic
211	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
213	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
214	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
217	C₂²×C₄₃	#443	1	4	yes	—
218	C₄×C₄₃	—	4	4	no	—
219	C₄×C₄₃	C₄³	1	1	yes	characteristic
220	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
221	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
222	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
223	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
226	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
227	Dic₄₃	—	2	8	no	—
228	Dic₄₃	—	4	4	no	—
229	C₂×#405	—	43	1	no	—
230	C₂×#405	D₄₃	1	1	yes	characteristic
231	C₂²×C₄×C₈	—	43	1	no	—
232	C₂×#341	—	43	1	no	—
233	#1735	—	43	1	no	—
234	C₂×#339	—	43	1	no	—
235	C₂×#339	—	43	1	no	—
236	C₂×C₄₃	—	2	1	no	—
237	C₂×C₄₃	—	2	1	no	—
238	C₂×C₄₃	—	2	1	no	—
239	C₂×C₄₃	—	2	1	no	—
240	C₂×C₄₃	C₄×#95	1	1	yes	characteristic
241	C₂×C₄₃	#1764	1	2	yes	—
242	C₂×C₄₃	#1764	1	2	yes	—
243	C₂×C₄₃	#1772	1	2	yes	—
244	C₂²×M₁₆	—	43	1	no	—
245	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
246	C₂³×C₈	—	43	1	no	—
247	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
248	C₂×#117	—	43	1	no	—
249	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
250	C₂²×C₄²	—	43	1	no	—
251	#405	—	2	2	no	—
252	#405	—	43	4	no	—
253	#405	—	86	2	no	—
254	#405	Dic₄₃	1	4	yes	complemented
255	C₂×#97	—	2	1	no	—
256	C₂×#97	—	86	1	no	—
257	C₂×C₄×C₈	—	2	1	no	—
258	C₂×C₄×C₈	—	43	4	no	—
259	C₂×C₄×C₈	—	86	2	no	—
260	C₂×C₄×C₈	—	86	2	no	—
261	C₂×C₄×C₈	—	86	1	no	—
262	#341	—	43	4	no	—
263	#340	—	43	4	no	—
264	#339	—	43	4	no	—
265	#339	—	43	4	no	—
266	C₄₃	#10706	1	1	yes	characteristic, complemented, Sylow
267	C₂³×C₄	—	86	1	no	—
268	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	43	2	no	—
273	C₂×M₁₆	—	43	2	no	—
274	C₂×M₁₆	—	43	2	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂×M₁₆	—	86	1	no	—
277	C₂×M₁₆	—	86	1	no	—
278	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
279	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
280	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	43	2	no	—
283	C₂²×C₈	—	43	2	no	—
284	C₂²×C₈	—	43	2	no	—
285	C₂²×C₈	—	86	1	no	—
286	C₂²×C₈	—	86	1	no	—
287	C₂²×C₈	—	86	1	no	—
288	C₂²×C₈	—	86	1	no	—
289	C₂²×C₈	—	86	1	no	—
290	C₂²×C₈	Dic₈₆	1	2	yes	—
291	C₂²×C₈	C₄×D₄₃	1	2	yes	—
292	C₂²×C₈	C₄×D₄₃	1	2	yes	—
293	C₂²×C₈	D₁₇₂	1	2	yes	—
294	C₂²×C₈	C₂×Dic₄₃	1	2	yes	—
295	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
296	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	—	43	2	no	—
301	#117	—	43	2	no	—
302	#117	—	86	1	no	—
303	#117	—	86	1	no	—
304	#117	C₄×D₄₃	1	2	yes	—
305	#117	C₂×Dic₄₃	1	2	yes	—
306	C₂×C₄⋊C₄	—	43	2	no	—
307	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	86	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	43	2	no	—
312	C₂×C₄²	—	43	2	no	—
313	C₂×C₄²	—	43	2	no	—
314	C₂×C₄²	—	86	1	no	—
315	C₂×C₄²	—	86	1	no	—
316	C₂×C₄²	—	86	1	no	—
317	C₂×C₄²	—	86	1	no	—
318	#97	—	2	4	no	—
319	#97	—	86	4	no	—
320	C₄×C₈	—	2	4	no	—
321	C₄×C₈	—	86	8	no	—
322	C₄×C₈	—	86	4	no	—
323	C₂⁴	#10621898	1	1	yes	characteristic
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	86	8	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	86	2	no	—
328	C₂²×C₄	—	86	2	no	—
329	C₂²×C₄	—	86	2	no	—
330	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
338	C₂²×C₄	#10621898	1	1	yes	characteristic
339	C₂²×C₄	#10621898	1	1	yes	characteristic
340	C₂²×C₄	#10621898	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	43	4	no	—
348	M₁₆	—	86	2	no	—
349	M₁₆	—	86	2	no	—
350	M₁₆	—	86	2	no	—
351	M₁₆	C₄×Dic₄₃	1	4	yes	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	43	4	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	86	2	no	—
359	C₂×C₈	—	86	2	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	86	2	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	86	2	no	—
365	C₂×C₈	C₄×Dic₄₃	1	4	yes	—
366	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
367	C₂×C₈	Dic₄₃⋊C₄	1	4	yes	—
368	C₂×C₈	Dic₄₃⋊C₄	1	2	yes	—
369	C₂×C₈	C₄⋊Dic₄₃	1	4	yes	—
370	C₂×C₈	(C₂×D₄₃)⋊C₄	1	4	yes	—
371	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
372	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
373	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
374	C₂×C₈	C₂²⋊Dic₄₃	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	43	4	no	—
377	C₄⋊C₄	—	86	2	no	—
378	C₄⋊C₄	C₄×Dic₄₃	1	4	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	86	2	no	—
382	C₂²⋊C₄	—	86	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	43	4	no	—
386	C₄²	—	86	2	no	—
387	C₄²	—	86	2	no	—
388	C₄²	—	86	2	no	—
389	C₄²	—	86	2	no	—
390	C₄²	—	86	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	#13063282	1	1	yes	characteristic
393	C₂³	#13063282	1	1	yes	characteristic
394	C₂³	#13063284	1	1	yes	characteristic
395	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
397	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
398	C₂³	C₄×Dic₈₆	1	1	yes	characteristic
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	86	8	no	—
402	C₂×C₄	—	86	8	no	—
403	C₂×C₄	—	86	8	no	—
404	C₂×C₄	—	86	4	no	—
405	C₂×C₄	—	86	4	no	—
406	C₂×C₄	—	172	4	no	—
407	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
415	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
416	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
418	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
420	C₂×C₄	#13063282	1	1	yes	characteristic
421	C₂×C₄	#13063282	1	1	yes	characteristic
422	C₂×C₄	#13063284	1	1	yes	characteristic
423	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
425	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
430	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
431	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
432	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
433	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
434	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	86	4	no	—
437	C₈	—	86	4	no	—
438	C₈	C₄₃⋊#95	1	4	yes	—
439	C₈	C₄₃⋊#95	1	4	yes	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	#14582745	1	1	yes	characteristic
447	C₂²	C₄×C₂²⋊Dic₄₃	1	1	yes	characteristic
448	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
449	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
450	C₂²	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
451	C₂²	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
452	C₂²	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
453	C₂²	#14583014	1	4	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	86	8	no	—
456	C₄	—	172	4	no	—
457	C₄	C₄²×Dic₄₃	1	1	yes	characteristic
458	C₄	C₂×C₄₃⋊#95	1	1	yes	characteristic
459	C₄	C₄×C₂²⋊Dic₄₃	1	1	yes	characteristic
460	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
461	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
462	C₄	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
463	C₄	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
464	C₄	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	C₄×C₄₃⋊#95	1	1	yes	characteristic
470	C₂	#19134430	1	2	yes	—
471	C₂	#19134434	1	2	yes	—
472	C₂	#19134475	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²⋊D₄₃
commutator	C₄×C₄₃	C₄³
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#10706
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
13. #14582854	C₄	semidirect
18. C₂×C₈×Dic₄₃	C₄	semidirect
19. #14582663	C₄	semidirect
20. #14582661	C₄	semidirect
21. #14582660	C₄	semidirect
22. #14582658	C₄	semidirect
27. C₄₃×#405	C₄	semidirect
254. #405	Dic₄₃	semidirect
266. C₄₃	#10706	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582854	2
C₂²×C₈×Dic₄₃	2
C₂×#14582663	2
#19134311	2
C₂×#14582660	2
C₂×#14582658	2
C₂×C₄₃×#405	2
#10706	43