Subgroups — #24991925

Order 11008.

726 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063301	C₂	1	1	yes	maximal, characteristic
3	#19134572	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₃	—	2	1	no	—
9	C₂×#13063301	C₄	1	1	yes	characteristic
10	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
13	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₈×Dic₄₃	—	2	1	no	—
15	C₄×C₈×D₄₃	—	2	2	no	—
16	C₄×C₈×D₄₃	—	2	2	no	—
17	#14582806	C₄	1	1	yes	characteristic
18	#14582795	C₄	1	1	yes	characteristic
19	#14582780	—	2	1	no	—
20	#14582770	—	2	1	no	—
21	#14582756	C₄	1	1	yes	characteristic
22	C₄×Dic₄₃⋊C₄	—	2	1	no	—
23	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
24	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
25	#14582653	—	2	1	no	—
26	Q₈⋊(C₄₃⋊C₈)	—	2	2	no	—
27	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×Q₈⋊C₈	—	2	2	no	—
31	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂×C₈×D₄₃	—	2	4	no	—
37	C₂×C₈×D₄₃	—	2	4	no	—
38	C₂×C₈×D₄₃	—	2	4	no	—
39	#13063301	—	2	2	no	—
40	#13063301	C₈	1	4	yes	complemented
41	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂×Dic₄₃⋊C₄	—	2	1	no	—
44	C₂×Dic₄₃⋊C₄	—	2	1	no	—
45	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
51	C₄²×D₄₃	—	2	1	no	—
52	C₄²×D₄₃	—	2	1	no	—
53	C₄²×D₄₃	—	2	1	no	—
54	C₄²×D₄₃	—	2	1	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
57	(C₂×D₄₃)⋊C₈	—	4	2	no	—
58	C₄×C₄₃⋊C₈	—	2	1	no	—
59	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
60	C₈×Dic₄₃	—	2	4	no	—
61	C₄₃⋊#95	—	2	1	no	—
62	C₄₃⋊#95	—	2	1	no	—
63	C₄₃⋊#95	—	2	1	no	—
64	C₄₃⋊#95	—	2	1	no	—
65	C₄₃⋊#95	—	2	1	no	—
66	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₄₃	—	2	1	no	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₄×Q₈×C₄₃	—	2	1	no	—
70	C₄×Q₈×C₄₃	—	2	1	no	—
71	C₄×Q₈×C₄₃	—	2	1	no	—
72	C₄×Q₈×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₃	—	2	1	no	—
78	C₄⋊C₈×C₄₃	—	2	1	no	—
79	C₄×C₈×C₄₃	—	2	1	no	—
80	C₄×C₈×C₄₃	D₄	1	2	yes	—
81	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₃	—	2	1	no	—
83	C₂×Q₈×C₄₃	—	2	1	no	—
84	C₂×Q₈×C₄₃	—	2	1	no	—
85	C₂×Q₈×C₄₃	—	2	1	no	—
86	C₂×Q₈×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	C₂×C₈	1	2	yes	complemented
88	C₂²×C₄×C₄₃	—	2	1	no	—
89	C₂²×C₄×C₄₃	—	2	1	no	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×Dic₄₃	—	2	1	no	—
94	C₂²×Dic₄₃	—	2	1	no	—
95	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₃	—	2	1	no	—
99	C₂×C₄×D₄₃	—	2	1	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	1	no	—
103	C₂×C₄×D₄₃	—	2	1	no	—
104	C₂×C₄×D₄₃	—	2	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	—	2	1	no	—
107	C₂×C₄×D₄₃	—	2	1	no	—
108	C₂×C₄×D₄₃	—	2	2	no	—
109	C₂×C₄×D₄₃	—	2	2	no	—
110	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
111	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
112	C₂×C₄×D₄₃	SD₁₆	1	2	yes	—
113	C₂×C₄×D₄₃	Q₁₆	1	2	yes	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	4	1	no	—
118	C₂×C₈×C₄₃	—	4	1	no	—
119	C₂×C₈×C₄₃	—	4	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	4	1	no	—
123	C₄⋊C₄×C₄₃	—	4	1	no	—
124	C₄²×C₄₃	—	4	1	no	—
125	C₄²×C₄₃	—	4	1	no	—
126	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₃	#41	1	1	yes	characteristic
129	C₄²×C₄₃	#41	1	1	yes	characteristic
130	(C₂×D₄₃)⋊C₄	—	2	4	no	—
131	(C₂×D₄₃)⋊C₄	—	4	2	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	2	1	no	—
135	C₄⋊Dic₄₃	C₂×C₈	1	2	yes	complemented
136	Dic₄₃⋊C₄	—	2	4	no	—
137	Dic₄₃⋊C₄	—	4	2	no	—
138	C₄×Dic₄₃	—	2	1	no	—
139	C₄×Dic₄₃	—	2	1	no	—
140	C₄×Dic₄₃	—	2	1	no	—
141	C₄×Dic₄₃	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	4	1	no	—
145	C₄×Dic₄₃	—	4	1	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	—	4	1	no	—
150	C₂×C₄₃⋊C₈	—	4	1	no	—
151	C₂×C₄₃⋊C₈	—	4	1	no	—
152	C₈×D₄₃	—	2	16	no	—
153	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×D₄₃	—	2	1	no	—
155	C₂²×D₄₃	—	2	1	no	—
156	C₂²×D₄₃	—	2	1	no	—
157	C₂²×D₄₃	—	2	1	no	—
158	C₂²×D₄₃	C₂²⋊C₈	1	2	yes	—
159	C₂²×D₄₃	#103	1	2	yes	—
160	C₂²×D₄₃	#104	1	2	yes	—
161	Q₈×C₄₃	—	2	2	no	—
162	Q₈×C₄₃	—	2	2	no	—
163	Q₈×C₄₃	—	4	1	no	—
164	Q₈×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
187	C₂×Dic₄₃	—	2	1	no	—
188	C₂×Dic₄₃	—	2	1	no	—
189	C₂×Dic₄₃	—	2	1	no	—
190	C₂×Dic₄₃	—	2	1	no	—
191	C₂×Dic₄₃	—	2	1	no	—
192	C₂×Dic₄₃	—	2	1	no	—
193	C₂×Dic₄₃	—	2	2	no	—
194	C₂×Dic₄₃	—	4	1	no	—
195	C₂×Dic₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	—	4	1	no	—
198	C₂×Dic₄₃	—	4	1	no	—
199	C₂×Dic₄₃	C₂²⋊C₈	1	2	yes	—
200	C₂×Dic₄₃	#103	1	2	yes	—
201	C₂×Dic₄₃	#104	1	2	yes	—
202	C₄×D₄₃	—	2	4	no	—
203	C₄×D₄₃	—	2	4	no	—
204	C₄×D₄₃	—	2	2	no	—
205	C₄×D₄₃	—	2	2	no	—
206	C₄×D₄₃	—	2	2	no	—
207	C₄×D₄₃	—	2	2	no	—
208	C₄×D₄₃	—	2	2	no	—
209	C₄×D₄₃	—	2	2	no	—
210	C₄×D₄₃	—	2	2	no	—
211	C₄×D₄₃	—	2	2	no	—
212	C₈×C₄₃	—	2	4	no	—
213	C₈×C₄₃	—	8	1	no	—
214	C₄₃⋊C₈	—	2	4	no	—
215	C₄₃⋊C₈	—	8	1	no	—
216	#9071	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	#386	1	1	yes	characteristic
218	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
219	C₂²×C₄₃	#408	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#103	1	1	yes	characteristic
221	C₂²×C₄₃	#416	1	1	yes	characteristic
222	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
224	C₂×D₄₃	—	2	2	no	—
225	C₂×D₄₃	—	2	2	no	—
226	C₂×D₄₃	—	2	2	no	—
227	C₂×D₄₃	—	2	2	no	—
228	C₂×D₄₃	—	2	2	no	—
229	C₂×D₄₃	—	2	2	no	—
230	C₂×D₄₃	Q₈⋊C₈	1	4	yes	complemented
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	1	no	—
233	C₄×C₄₃	—	4	2	no	—
234	C₄×C₄₃	—	8	1	no	—
235	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
236	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
237	C₄×C₄₃	#435	1	1	yes	characteristic
238	C₄×C₄₃	#435	1	1	yes	characteristic
239	C₄×C₄₃	#465	1	1	yes	characteristic
240	C₄×C₄₃	#465	1	1	yes	characteristic
241	C₄×C₄₃	#467	1	1	yes	characteristic
242	C₄×C₄₃	#467	1	1	yes	characteristic
243	Dic₄₃	—	2	2	no	—
244	Dic₄₃	—	2	2	no	—
245	Dic₄₃	—	2	2	no	—
246	Dic₄₃	—	4	2	no	—
247	Dic₄₃	—	8	1	no	—
248	C₂²×C₄×C₈	—	43	1	no	—
249	C₄×C₂²⋊Q₈	—	43	1	no	—
250	#1797	—	43	1	no	—
251	C₂×Q₈⋊C₈	—	43	1	no	—
252	C₂×Q₈⋊C₈	D₄₃	1	1	yes	characteristic, complemented
253	#1279	—	43	1	no	—
254	#1279	—	43	1	no	—
255	C₂×C₄₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
256	C₂×C₄₃	#1476	1	1	yes	characteristic
257	C₂×C₄₃	#1493	1	1	yes	characteristic
258	C₂×C₄₃	#1494	1	1	yes	characteristic
259	C₂×C₄₃	#1869	1	1	yes	characteristic
260	C₂×C₄₃	#1892	1	1	yes	characteristic
261	C₂×C₄₃	#1896	1	1	yes	characteristic
262	D₄₃	—	2	4	no	—
263	C₂³×C₈	—	86	1	no	—
264	C₂×C₂²⋊Q₈	—	43	1	no	—
265	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
266	C₂²×C₄²	—	43	1	no	—
267	C₂×C₄⋊C₈	—	43	1	no	—
268	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	—	86	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₈	—	86	2	no	—
272	C₂×C₄×C₈	—	86	1	no	—
273	C₂×C₄×C₈	—	86	2	no	—
274	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
275	#391	—	43	1	no	—
276	#389	—	43	1	no	—
277	#387	—	86	1	no	—
278	#385	—	86	1	no	—
279	#380	—	43	1	no	—
280	C₄×C₄⋊C₄	—	43	1	no	—
281	C₄×C₄⋊C₄	—	86	1	no	—
282	C₄×C₂²⋊C₄	—	86	1	no	—
283	#336	—	86	1	no	—
284	Q₈⋊C₈	—	2	2	no	—
285	Q₈⋊C₈	—	86	2	no	—
286	C₄₃	#9071	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
288	C₂³×C₄	—	43	1	no	—
289	C₂³×C₄	—	43	1	no	—
290	C₂³×C₄	—	43	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	1	no	—
293	C₂²×C₈	—	86	4	no	—
294	C₂²×C₈	—	86	4	no	—
295	C₂²×C₈	—	86	4	no	—
296	C₂²×C₈	—	86	1	no	—
297	C₂²×C₈	—	86	1	no	—
298	C₂²⋊Q₈	—	43	4	no	—
299	C₂²⋊Q₈	—	86	2	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	43	1	no	—
306	C₂×C₄⋊C₄	—	43	1	no	—
307	C₂×C₄⋊C₄	—	86	1	no	—
308	C₂×C₄⋊C₄	—	86	1	no	—
309	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	86	1	no	—
311	C₂×C₂²⋊C₄	—	86	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	43	1	no	—
314	C₂×C₄²	—	43	1	no	—
315	C₂×C₄²	—	43	1	no	—
316	C₂×C₄²	—	86	1	no	—
317	C₂×C₄²	—	86	1	no	—
318	C₂×C₄²	—	86	1	no	—
319	C₂×C₄²	—	86	1	no	—
320	C₂×C₄²	—	86	1	no	—
321	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	86	1	no	—
325	C₄⋊C₈	—	86	1	no	—
326	C₂²⋊C₈	—	172	2	no	—
327	C₄×C₈	—	2	1	no	—
328	C₄×C₈	—	43	2	no	—
329	C₄×C₈	—	86	4	no	—
330	C₄×C₈	—	86	1	no	—
331	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
332	#95	—	86	1	no	—
333	#95	—	86	1	no	—
334	#95	—	86	1	no	—
335	#95	—	86	1	no	—
336	#95	—	86	1	no	—
337	C₂⁴	—	43	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	C₈×D₄₃	1	2	yes	complemented
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	43	1	no	—
348	C₂²×C₄	—	43	1	no	—
349	C₂²×C₄	—	43	2	no	—
350	C₂²×C₄	—	43	2	no	—
351	C₂²×C₄	—	43	2	no	—
352	C₂²×C₄	—	43	2	no	—
353	C₂²×C₄	—	86	2	no	—
354	C₂²×C₄	—	86	2	no	—
355	C₂²×C₄	—	86	1	no	—
356	C₂²×C₄	—	86	1	no	—
357	C₂²×C₄	—	86	1	no	—
358	C₂²×C₄	—	86	1	no	—
359	C₂²×C₄	—	86	1	no	—
360	C₂²×C₄	—	86	1	no	—
361	C₂²×C₄	—	86	1	no	—
362	C₂²×C₄	—	86	1	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	C₂×C₄×D₄₃	1	1	yes	characteristic
368	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	86	16	no	—
377	C₂×C₈	—	86	2	no	—
378	C₂×C₈	—	86	2	no	—
379	C₂×C₈	—	86	2	no	—
380	C₂×C₈	—	172	1	no	—
381	C₂×C₈	—	172	1	no	—
382	C₂×C₈	—	172	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	—	43	2	no	—
388	C₄⋊C₄	—	86	4	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₄⋊C₄	—	86	1	no	—
392	C₄⋊C₄	—	172	2	no	—
393	C₂²⋊C₄	—	86	4	no	—
394	C₂²⋊C₄	—	172	2	no	—
395	C₄²	—	4	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	—	86	1	no	—
398	C₄²	—	86	1	no	—
399	C₄²	—	86	1	no	—
400	C₄²	—	86	1	no	—
401	C₄²	—	86	1	no	—
402	C₄²	—	86	1	no	—
403	C₄²	—	172	1	no	—
404	C₄²	—	172	1	no	—
405	C₄²	#10621898	1	1	yes	characteristic
406	C₄²	D₄×D₄₃	1	1	yes	characteristic
407	C₄²	#10621900	1	1	yes	characteristic
408	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂³	—	43	2	no	—
410	C₂³	—	43	2	no	—
411	C₂³	—	43	2	no	—
412	C₂³	—	86	1	no	—
413	C₂³	—	86	1	no	—
414	C₂³	—	86	1	no	—
415	C₂³	—	86	1	no	—
416	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	43	2	no	—
430	C₂×C₄	—	43	2	no	—
431	C₂×C₄	—	43	2	no	—
432	C₂×C₄	—	86	4	no	—
433	C₂×C₄	—	86	4	no	—
434	C₂×C₄	—	86	1	no	—
435	C₂×C₄	—	86	1	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	86	1	no	—
438	C₂×C₄	—	86	1	no	—
439	C₂×C₄	—	86	1	no	—
440	C₂×C₄	—	86	2	no	—
441	C₂×C₄	—	86	2	no	—
442	C₂×C₄	—	86	2	no	—
443	C₂×C₄	—	86	2	no	—
444	C₂×C₄	—	86	2	no	—
445	C₂×C₄	—	86	2	no	—
446	C₂×C₄	—	86	2	no	—
447	C₂×C₄	—	86	2	no	—
448	C₂×C₄	—	86	2	no	—
449	C₂×C₄	—	172	1	no	—
450	C₂×C₄	—	172	1	no	—
451	C₂×C₄	—	172	1	no	—
452	C₂×C₄	—	172	1	no	—
453	C₂×C₄	—	172	1	no	—
454	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
455	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
456	C₂×C₄	#13063293	1	1	yes	characteristic
457	C₂×C₄	#13063296	1	1	yes	characteristic
458	C₂×C₄	#13063298	1	1	yes	characteristic
459	C₂×C₄	#13063307	1	1	yes	characteristic
460	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
461	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
462	C₂×C₄	#13063331	1	1	yes	characteristic
463	C₂×C₄	#13063333	1	1	yes	characteristic
464	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
465	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
466	C₂×C₄	#13063346	1	1	yes	characteristic
467	C₂×C₄	#13063348	1	1	yes	characteristic
468	C₈	—	2	4	no	—
469	C₈	—	8	1	no	—
470	C₈	—	86	4	no	—
471	C₈	—	344	1	no	—
472	C₂²	—	43	4	no	—
473	C₂²	—	86	2	no	—
474	C₂²	—	86	2	no	—
475	C₂²	—	86	2	no	—
476	C₂²	—	86	2	no	—
477	C₂²	—	86	2	no	—
478	C₂²	—	86	2	no	—
479	C₂²	#14582775	1	1	yes	characteristic
480	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
481	C₂²	#14582864	1	1	yes	characteristic
482	C₂²	#103×D₄₃	1	1	yes	characteristic
483	C₂²	#14582894	1	1	yes	characteristic
484	C₂²	#104×D₄₃	1	1	yes	characteristic
485	C₂²	#104×D₄₃	1	1	yes	characteristic
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	86	2	no	—
491	C₄	—	86	2	no	—
492	C₄	—	86	2	no	—
493	C₄	—	344	1	no	—
494	C₄	—	172	2	no	—
495	C₄	(C₂²⋊D₄₃)⋊C₈	1	1	yes	characteristic
496	C₄	C₈×C₂²⋊D₄₃	1	1	yes	characteristic
497	C₄	#14582968	1	1	yes	characteristic
498	C₄	#14582973	1	1	yes	characteristic
499	C₄	#14583125	1	1	yes	characteristic
500	C₄	#14583131	1	1	yes	characteristic
501	C₄	#14583137	1	1	yes	characteristic
502	C₄	#14583139	1	1	yes	characteristic
503	C₂	—	86	4	no	—
504	C₂	Q₈⋊C₈×D₄₃	1	1	yes	characteristic
505	C₂	#19132976	1	1	yes	characteristic
506	C₂	#19133048	1	1	yes	characteristic
507	C₂	#19133054	1	1	yes	characteristic
508	C₂	#19134884	1	1	yes	characteristic
509	C₂	#19135015	1	1	yes	characteristic
510	C₂	#19135035	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₂×C₄₃×Q₈⋊C₈	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	C₂×Q₈⋊C₈	D₄₃
hypocenter	C₄₃	#9071
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
4. C₂×Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
5. #19132435	C₂	semidirect
6. #19132434	C₂	semidirect
7. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
40. #13063301	C₈	semidirect
87. C₂×Q₈×C₄₃	C₂×C₈	semidirect
135. C₄⋊Dic₄₃	C₂×C₈	semidirect
230. C₂×D₄₃	Q₈⋊C₈	semidirect
252. C₂×Q₈⋊C₈	D₄₃	semidirect
286. C₄₃	#9071	semidirect
343. C₂×Q₈	C₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₈×D₄₃	2
C₄×#13063301	2
#19134572	2
C₂×Q₈⋊(C₄₃⋊C₈)	2
#19132435	2
#19132434	2
C₂×C₄₃×Q₈⋊C₈	2
#9071	43