Subgroups — #25066548

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144613	C₂	1	1	yes	maximal, characteristic
2	#19143564	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133470	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133463	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133456	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133449	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133416	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133411	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133410	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133404	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133376	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133004	C₂	1	1	yes	maximal, characteristic, complemented
14	#19132888	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1488	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583433	C₂²	1	1	yes	characteristic
17	#14583240	C₄	1	1	yes	characteristic
18	#14583223	C₄	1	1	yes	characteristic
19	#14583206	C₄	1	1	yes	characteristic
20	#14583199	C₄	1	1	yes	characteristic
21	#14583121	C₄	1	1	yes	characteristic
22	#14583114	C₄	1	1	yes	characteristic
23	#14583061	C₄	1	1	yes	characteristic
24	#14583044	C₄	1	1	yes	characteristic
25	#14583026	C₂²	1	1	yes	characteristic
26	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	#14583023	C₂²	1	1	yes	characteristic
29	C₄×#10621885	C₂²	1	1	yes	characteristic
30	C₄×#10621884	C₂²	1	1	yes	characteristic
31	C₄×#10621883	C₂²	1	1	yes	characteristic
32	C₄×#10621882	C₂²	1	1	yes	characteristic
33	#14582976	C₂²	1	1	yes	characteristic
34	#14582967	—	2	1	no	—
35	D₄×C₄₃⋊C₈	—	2	1	no	—
36	D₄×C₄₃⋊C₈	—	2	1	no	—
37	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
39	#14582964	C₂²	1	1	yes	characteristic
40	(C₂²⋊D₄₃)⋊C₈	—	2	1	no	—
41	#14582961	—	2	1	no	—
42	#14582952	—	2	1	no	—
43	#14582952	C₂²	1	1	yes	characteristic
44	#14582952	C₂²	1	1	yes	characteristic
45	#14582856	—	2	1	no	—
46	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
47	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
48	#14582651	C₂²	1	1	yes	characteristic
49	#14582651	C₂²	1	1	yes	characteristic
50	#14582649	C₂²	1	1	yes	characteristic
51	#14582649	C₂²	1	1	yes	characteristic
52	#14582631	C₂²	1	1	yes	characteristic
53	#14582631	C₂²	1	1	yes	characteristic
54	#14582628	C₂²	1	1	yes	characteristic
55	#14582628	C₂²	1	1	yes	characteristic
56	#14582621	C₂²	1	1	yes	characteristic
57	#14582621	C₂²	1	1	yes	characteristic
58	#14582620	C₂²	1	1	yes	characteristic
59	#14582620	C₂²	1	1	yes	characteristic
60	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
61	C₄₃×#432	C₂²	1	1	yes	characteristic
62	C₄₃×#431	C₂²	1	1	yes	characteristic
63	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
68	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
69	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
71	C₂×#10621872	—	2	1	no	—
72	C₂²×C₄₃⋊C₈	—	2	1	no	—
73	C₂²×C₄₃⋊C₈	—	2	1	no	—
74	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
75	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
76	C₂×C₈×D₄₃	—	2	1	no	—
77	#13063319	—	2	1	no	—
78	#13063317	C₂×C₄	1	1	yes	characteristic
79	#13063313	C₂×C₄	1	1	yes	characteristic
80	#13063308	—	2	1	no	—
81	#13063304	C₂×C₄	1	1	yes	characteristic
82	#13063299	C₂×C₄	1	1	yes	characteristic
83	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
84	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
85	C₄×C₂²⋊D₄₃	—	2	1	no	—
86	#13063282	—	2	1	no	—
87	#13063258	C₂×C₄	1	1	yes	characteristic
88	#13063258	C₂×C₄	1	1	yes	characteristic
89	#13063256	C₂×C₄	1	1	yes	characteristic
90	#13063256	C₂×C₄	1	1	yes	characteristic
91	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
92	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
93	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
96	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
97	Dic₄₃⋊C₈	—	2	1	no	—
98	Dic₄₃⋊C₈	—	2	1	no	—
99	#13063249	C₂×C₄	1	1	yes	characteristic
100	#13063249	C₂×C₄	1	1	yes	characteristic
101	#13063248	C₂×C₄	1	1	yes	characteristic
102	#13063248	C₂×C₄	1	1	yes	characteristic
103	#13063246	C₂×C₄	1	1	yes	characteristic
104	#13063246	C₂×C₄	1	1	yes	characteristic
105	#13063245	C₂×C₄	1	1	yes	characteristic
106	#13063245	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
108	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
109	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
110	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
112	(C₂×D₄₃)⋊C₈	—	2	1	no	—
113	(C₂×D₄₃)⋊C₈	—	2	1	no	—
114	#13063235	—	2	1	no	—
115	C₄×C₄₃⋊C₈	—	2	1	no	—
116	C₄×C₄₃⋊C₈	—	2	1	no	—
117	C₄×C₄₃⋊C₈	—	2	1	no	—
118	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
119	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
120	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₈×Dic₄₃	—	2	1	no	—
125	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
126	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
127	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₄₃	—	2	1	no	—
129	C₄×D₄×C₄₃	—	2	1	no	—
130	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
132	#117×C₄₃	—	2	1	no	—
133	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₄₃	—	2	1	no	—
135	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₄₃	—	2	1	no	—
137	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₂²⋊C₈×C₄₃	—	2	1	no	—
140	C₂²⋊C₈×C₄₃	—	2	1	no	—
141	#97×C₄₃	—	2	1	no	—
142	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
144	#41×C₄₃	—	2	2	no	—
145	#41×C₄₃	—	2	2	no	—
146	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₄₃	—	2	1	no	—
148	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	1	no	—
151	C₂²×C₄×C₄₃	—	2	1	no	—
152	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
155	C₂×C₂²⋊D₄₃	—	2	1	no	—
156	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₄₃	—	2	1	no	—
158	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₄₃	—	2	1	no	—
168	C₂²⋊C₄×C₄₃	—	2	1	no	—
169	C₂²⋊C₄×C₄₃	—	2	1	no	—
170	C₄²×C₄₃	—	2	1	no	—
171	C₄²×C₄₃	—	2	1	no	—
172	C₄²×C₄₃	—	2	1	no	—
173	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	#41	1	1	yes	characteristic
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂²⋊Dic₄₃	—	2	1	no	—
178	#10621885	—	2	2	no	—
179	#10621884	—	2	2	no	—
180	#10621883	—	2	2	no	—
181	#10621882	—	2	2	no	—
182	(C₂×D₄₃)⋊C₄	—	2	1	no	—
183	(C₂×D₄₃)⋊C₄	—	2	1	no	—
184	(C₂×D₄₃)⋊C₄	—	2	1	no	—
185	(C₂×D₄₃)⋊C₄	—	2	1	no	—
186	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
187	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
188	Dic₄₃⋊C₄	—	2	1	no	—
189	Dic₄₃⋊C₄	—	2	1	no	—
190	Dic₄₃⋊C₄	—	2	1	no	—
191	Dic₄₃⋊C₄	—	2	1	no	—
192	C₄×Dic₄₃	—	2	1	no	—
193	C₂×C₄₃⋊C₈	—	2	1	no	—
194	C₂×C₄₃⋊C₈	—	2	1	no	—
195	C₂×C₄₃⋊C₈	—	4	1	no	—
196	C₂×C₄₃⋊C₈	—	4	1	no	—
197	C₂×C₄₃⋊C₈	—	4	2	no	—
198	C₂×C₄₃⋊C₈	—	4	2	no	—
199	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
207	#10621872	—	4	2	no	—
208	C₈×D₄₃	—	4	2	no	—
209	C₂³×C₄₃	—	2	1	no	—
210	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
211	C₂²×D₄₃	—	2	1	no	—
212	Q₈×C₄₃	—	2	1	no	—
213	Q₈×C₄₃	#131	1	2	yes	—
214	D₄×C₄₃	—	2	4	no	—
215	D₄×C₄₃	—	2	1	no	—
216	D₄×C₄₃	#131	1	2	yes	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
235	C₂²⋊D₄₃	—	4	2	no	—
236	C₂×Dic₄₃	—	2	1	no	—
237	C₂×Dic₄₃	—	2	1	no	—
238	C₂×Dic₄₃	—	2	1	no	—
239	D₁₇₂	—	2	1	no	—
240	D₁₇₂	—	2	1	no	—
241	C₄×D₄₃	—	4	1	no	—
242	C₄×D₄₃	—	4	1	no	—
243	Dic₈₆	—	2	1	no	—
244	Dic₈₆	—	2	1	no	—
245	C₈×C₄₃	—	4	1	no	—
246	C₈×C₄₃	—	4	1	no	—
247	C₈×C₄₃	—	4	1	no	—
248	C₈×C₄₃	—	4	1	no	—
249	C₄₃⋊C₈	—	2	1	no	—
250	C₄₃⋊C₈	—	2	1	no	—
251	C₄₃⋊C₈	—	2	1	no	—
252	C₄₃⋊C₈	—	2	1	no	—
253	C₄₃⋊C₈	—	2	1	no	—
254	C₄₃⋊C₈	—	2	1	no	—
255	C₄₃⋊C₈	—	2	1	no	—
256	C₄₃⋊C₈	—	2	1	no	—
257	C₄₃⋊C₈	—	4	1	no	—
258	C₄₃⋊C₈	—	4	1	no	—
259	#17909	—	43	1	no	maximal, Sylow
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	2	1	no	—
262	C₂²×C₄₃	—	2	1	no	—
263	C₂²×C₄₃	—	2	1	no	—
264	C₂²×C₄₃	—	4	1	no	—
265	C₂²×C₄₃	—	4	1	no	—
266	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂×D₄₃	—	4	1	no	—
268	C₂×D₄₃	—	4	1	no	—
269	C₂×D₄₃	—	4	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	2	2	no	—
272	C₄×C₄₃	—	2	1	no	—
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	—	4	1	no	—
276	C₄×C₄₃	—	4	1	no	—
277	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
278	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
279	C₄×C₄₃	#575	1	1	yes	characteristic
280	C₄×C₄₃	#575	1	1	yes	characteristic
281	Dic₄₃	—	4	1	no	—
282	Dic₄₃	—	4	1	no	—
283	Dic₄₃	—	4	1	no	—
284	#3102	—	43	1	no	—
285	#2966	—	43	1	no	—
286	C₈×#41	—	43	1	no	—
287	#1588	—	43	1	no	—
288	#1587	—	43	1	no	—
289	#1586	—	43	1	no	—
290	#1585	—	43	1	no	—
291	#1580	—	43	1	no	—
292	#1579	—	43	1	no	—
293	SD₁₆⋊C₈	—	43	1	no	—
294	SD₁₆⋊C₈	—	43	1	no	—
295	#1572	—	43	1	no	—
296	#1488	D₄₃	1	1	yes	characteristic, complemented
297	#1482	—	43	1	no	—
298	#1452	—	43	1	no	—
299	C₂×C₄₃	—	4	1	no	—
300	C₂×C₄₃	—	4	2	no	—
301	C₂×C₄₃	#2929	1	1	yes	characteristic
302	C₂×C₄₃	#2943	1	1	yes	characteristic
303	C₂×C₄₃	#2955	1	1	yes	characteristic
304	D₄₃	—	8	1	no	—
305	#529	—	43	1	no	—
306	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
307	#485	—	43	1	no	—
308	#482	—	43	1	no	—
309	#479	—	43	1	no	—
310	#478	—	43	1	no	—
311	#464	—	43	1	no	—
312	#463	—	43	1	no	—
313	#452	—	43	1	no	—
314	#449	—	43	1	no	—
315	#446	—	43	1	no	—
316	C₈×Q₈	—	43	1	no	—
317	C₈×Q₈	—	43	1	no	—
318	C₈×Q₈	—	43	1	no	—
319	C₄×Q₁₆	—	43	1	no	—
320	C₄×SD₁₆	—	43	1	no	—
321	C₄×SD₁₆	—	43	1	no	—
322	C₄×D₈	—	43	1	no	—
323	#436	—	43	1	no	—
324	#435	—	86	1	no	—
325	C₈×D₄	—	43	1	no	—
326	C₈×D₄	—	43	1	no	—
327	C₈×D₄	—	43	1	no	—
328	C₈×D₄	—	86	1	no	—
329	C₈×D₄	—	86	1	no	—
330	C₈×D₄	—	86	1	no	—
331	#433	—	86	1	no	—
332	#432	C₂×D₄₃	1	1	yes	characteristic
333	#431	—	43	1	no	—
334	#431	—	43	1	no	—
335	#431	—	86	1	no	—
336	#431	C₂×D₄₃	1	1	yes	characteristic
337	#405	—	86	1	no	—
338	C₂×C₄×C₈	—	43	1	no	—
339	C₂×C₄×C₈	—	86	1	no	—
340	#335	—	43	1	no	—
341	#335	—	43	1	no	—
342	#334	—	43	1	no	—
343	#334	—	43	1	no	—
344	Q₈⋊C₈	—	43	1	no	—
345	Q₈⋊C₈	—	43	1	no	—
346	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
347	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
348	D₄⋊C₈	—	43	1	no	—
349	D₄⋊C₈	—	43	1	no	—
350	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
351	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
352	#322	—	43	1	no	—
353	#322	—	43	1	no	—
354	#322	—	43	1	no	—
355	#322	—	43	1	no	—
356	C₄₃	#17909	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
358	C₂×Q₁₆	—	43	1	no	—
359	C₂×SD₁₆	—	43	1	no	—
360	C₂×SD₁₆	—	43	1	no	—
361	C₂×D₈	—	43	1	no	—
362	C₂×M₁₆	—	86	1	no	—
363	C₂²×C₈	—	43	1	no	—
364	C₂²×C₈	—	43	1	no	—
365	C₂²×C₈	—	86	1	no	—
366	C₂²×C₈	—	86	1	no	—
367	C₂²×C₈	—	86	1	no	—
368	#126	—	86	1	no	—
369	#125	—	43	1	no	—
370	#124	—	43	1	no	—
371	#123	—	86	1	no	—
372	C₂²⋊Q₈	—	43	1	no	—
373	#121	—	43	1	no	—
374	C₄×Q₈	—	43	1	no	—
375	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	43	1	no	—
380	C₄×D₄	—	86	1	no	—
381	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	86	1	no	—
385	#117	C₄×D₄₃	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
388	#107	—	43	1	no	—
389	#107	—	43	1	no	—
390	#106	—	43	1	no	—
391	#106	—	43	1	no	—
392	C₄⋊C₈	—	2	1	no	—
393	C₄⋊C₈	—	43	1	no	—
394	C₄⋊C₈	—	43	1	no	—
395	C₄⋊C₈	—	43	1	no	—
396	C₄⋊C₈	—	43	1	no	—
397	C₄⋊C₈	—	86	1	no	—
398	C₄⋊C₈	—	86	1	no	—
399	C₄⋊C₈	—	86	1	no	—
400	C₄⋊C₈	—	86	1	no	—
401	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
403	#103	—	43	1	no	—
404	#103	—	43	1	no	—
405	#103	—	43	1	no	—
406	#103	—	43	1	no	—
407	#102	—	43	1	no	—
408	#102	—	43	1	no	—
409	#102	—	43	1	no	—
410	#102	—	43	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	43	1	no	—
414	C₂²⋊C₈	—	43	1	no	—
415	C₂²⋊C₈	—	86	1	no	—
416	C₂²⋊C₈	—	86	1	no	—
417	C₂²⋊C₈	—	86	1	no	—
418	C₂²⋊C₈	—	86	1	no	—
419	C₂²⋊C₈	—	86	1	no	—
420	#97	—	2	1	no	—
421	#97	—	86	1	no	—
422	C₄×C₈	—	43	1	no	—
423	C₄×C₈	—	43	1	no	—
424	C₄×C₈	—	43	1	no	—
425	C₄×C₈	—	43	1	no	—
426	C₄×C₈	—	43	1	no	—
427	C₄×C₈	—	43	1	no	—
428	C₄×C₈	—	86	1	no	—
429	C₄×C₈	—	86	1	no	—
430	C₄×C₈	—	86	1	no	—
431	C₄×C₈	—	86	1	no	—
432	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	C₂×Q₈	—	43	1	no	—
437	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	43	1	no	—
440	C₂×D₄	—	86	1	no	—
441	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	86	1	no	—
446	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
448	C₂²×C₄	#10621900	1	1	yes	characteristic
449	Q₁₆	—	86	2	no	—
450	SD₁₆	—	86	2	no	—
451	SD₁₆	—	86	2	no	—
452	D₈	—	86	2	no	—
453	M₁₆	—	172	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	43	1	no	—
459	C₂×C₈	—	43	1	no	—
460	C₂×C₈	—	43	1	no	—
461	C₂×C₈	—	43	1	no	—
462	C₂×C₈	—	43	1	no	—
463	C₂×C₈	—	43	1	no	—
464	C₂×C₈	—	43	1	no	—
465	C₂×C₈	—	43	1	no	—
466	C₂×C₈	—	86	1	no	—
467	C₂×C₈	—	86	1	no	—
468	C₂×C₈	—	172	2	no	—
469	C₂×C₈	—	172	1	no	—
470	C₂×C₈	—	172	1	no	—
471	C₂×C₈	—	172	2	no	—
472	C₂×C₈	—	172	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	43	1	no	—
476	C₄⋊C₄	—	43	1	no	—
477	C₄⋊C₄	—	86	1	no	—
478	C₄⋊C₄	—	86	1	no	—
479	C₄⋊C₄	—	86	1	no	—
480	C₄⋊C₄	—	86	1	no	—
481	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	86	1	no	—
487	C₂²⋊C₄	—	86	1	no	—
488	C₂²⋊C₄	—	86	1	no	—
489	C₂²⋊C₄	—	86	1	no	—
490	C₂²⋊C₄	—	86	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	86	1	no	—
495	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
496	C₄²	D₄×D₄₃	1	1	yes	characteristic
497	C₄²	#10621900	1	1	yes	characteristic
498	C₄²	C₂³×D₄₃	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	86	1	no	—
501	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
502	Q₈	—	2	1	no	—
503	Q₈	—	86	1	no	—
504	Q₈	—	86	1	no	—
505	Q₈	#13063333	1	2	yes	—
506	D₄	—	2	4	no	—
507	D₄	—	2	1	no	—
508	D₄	—	86	1	no	—
509	D₄	—	86	1	no	—
510	D₄	—	172	2	no	—
511	D₄	#13063333	1	2	yes	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	86	1	no	—
525	C₂×C₄	—	86	1	no	—
526	C₂×C₄	—	86	1	no	—
527	C₂×C₄	—	172	1	no	—
528	C₂×C₄	—	172	1	no	—
529	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
530	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
531	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
534	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	86	1	no	—
540	C₈	—	86	1	no	—
541	C₈	—	86	1	no	—
542	C₈	—	86	1	no	—
543	C₈	—	86	1	no	—
544	C₈	—	86	1	no	—
545	C₈	—	86	1	no	—
546	C₈	—	86	1	no	—
547	C₈	—	172	1	no	—
548	C₈	—	172	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	172	1	no	—
556	C₂²	—	172	1	no	—
557	C₂²	—	172	1	no	—
558	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	2	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	172	1	no	—
567	C₄	—	172	1	no	—
568	C₄	—	172	1	no	—
569	C₄	C₂×#13063333	1	1	yes	characteristic
570	C₄	C₂×#13063333	1	1	yes	characteristic
571	C₄	#14583696	1	1	yes	characteristic
572	C₄	#14583696	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	4	2	no	—
575	C₂	—	344	1	no	—
576	C₂	#19143285	1	1	yes	characteristic
577	C₂	#19143391	1	1	yes	characteristic
578	C₂	#19143494	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1488	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#14583044	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1488	D₄₃
hypocenter	C₄₃	#17909
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1488

Complements

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

N	H ≅ G/N	type
2. #19143564	C₂	semidirect
3. #41×C₄₃⋊C₈	C₂	semidirect
4. #19133470	C₂	semidirect
5. #19133463	C₂	semidirect
6. #19133456	C₂	semidirect
7. #19133449	C₂	semidirect
8. #19133416	C₂	semidirect
9. #19133411	C₂	semidirect
10. #19133410	C₂	semidirect
11. #19133404	C₂	semidirect
12. #19133376	C₂	semidirect
13. #19133004	C₂	semidirect
14. #19132888	C₂	semidirect
15. C₄₃×#1488	C₂	semidirect
296. #1488	D₄₃	semidirect
356. C₄₃	#17909	semidirect

Maximal subgroups

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

subgroup	index
#19144613	2
#19143564	2
#41×C₄₃⋊C₈	2
#19133470	2
#19133463	2
#19133456	2
#19133449	2
#19133416	2
#19133411	2
#19133410	2
#19133404	2
#19133376	2
#19133004	2
#19132888	2
C₄₃×#1488	2
#17909	43