Subgroups — #24991957

Order 11008.

670 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×#10621872	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063305	C₂	1	1	yes	maximal, characteristic
3	#19134572	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582631	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582629	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621872	—	2	1	no	—
9	C₂×#13063305	C₄	1	1	yes	characteristic
10	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
11	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
14	C₄×#10621872	—	2	2	no	—
15	C₄×#10621872	—	2	2	no	—
16	C₂×#13063235	—	2	1	no	—
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582804	C₄	1	1	yes	characteristic
19	#14582798	C₄	1	1	yes	characteristic
20	#14582784	—	2	1	no	—
21	#14582773	—	2	1	no	—
22	#14582756	C₄	1	1	yes	characteristic
23	C₄×C₄⋊Dic₄₃	—	2	1	no	—
24	C₄×(C₂×D₄₃)⋊C₄	—	2	1	no	—
25	#14582653	—	2	1	no	—
26	#14582631	—	2	2	no	—
27	#14582629	—	2	2	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
31	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
35	C₂×#10621872	—	2	4	no	—
36	C₂×#10621872	—	2	4	no	—
37	C₂×#10621872	—	2	4	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	—	2	1	no	—
40	#13063305	—	2	2	no	—
41	#13063305	—	2	2	no	—
42	C₄×Dic₈₆	—	2	1	no	—
43	C₄×Dic₈₆	—	2	1	no	—
44	C₄×Dic₈₆	—	2	1	no	—
45	C₄×Dic₈₆	—	2	1	no	—
46	C₂×C₄⋊Dic₄₃	—	2	1	no	—
47	C₂×C₄⋊Dic₄₃	—	2	1	no	—
48	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
49	C₂×Dic₄₃⋊C₄	—	2	1	no	—
50	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
51	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
56	C₄²×D₄₃	—	2	1	no	—
57	C₄²×D₄₃	—	2	1	no	—
58	C₄²×D₄₃	—	2	1	no	—
59	C₄²×D₄₃	—	2	1	no	—
60	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
62	(C₂×D₄₃)⋊C₈	—	4	2	no	—
63	#13063235	—	2	4	no	—
64	C₄×C₄₃⋊C₈	—	2	1	no	—
65	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
66	C₄₃⋊#95	—	2	1	no	—
67	C₄₃⋊#95	—	2	1	no	—
68	C₄₃⋊#95	—	2	1	no	—
69	C₄₃⋊#95	—	2	1	no	—
70	C₂²×C₈×C₄₃	—	2	1	no	—
71	C₂²×C₈×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₄₃	—	2	1	no	—
77	C₄⋊C₈×C₄₃	—	2	1	no	—
78	C₄×C₈×C₄₃	—	2	1	no	—
79	C₄×C₈×C₄₃	D₄	1	2	yes	—
80	#95×C₄₃	—	2	1	no	—
81	C₂³×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₄₃	—	2	1	no	—
88	C₂²×Dic₄₃	—	2	1	no	—
89	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₄₃	—	2	1	no	—
93	C₂×C₄×D₄₃	—	2	1	no	—
94	C₂×C₄×D₄₃	—	2	2	no	—
95	C₂×C₄×D₄₃	—	2	1	no	—
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
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	2	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	—	2	1	no	—
112	C₂×Dic₈₆	—	2	1	no	—
113	C₂×Dic₈₆	M₁₆	1	2	yes	complemented
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	—	2	1	no	—
123	C₄⋊C₄×C₄₃	M₁₆	1	2	yes	complemented
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	4	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	2	1	no	—
135	C₄⋊Dic₄₃	—	4	2	no	—
136	Dic₄₃⋊C₄	—	4	1	no	—
137	Dic₄₃⋊C₄	—	4	1	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	#10621872	—	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	—	2	1	no	—
159	C₂²×D₄₃	—	2	1	no	—
160	C₂²×D₄₃	#104	1	2	yes	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
179	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
183	C₂×Dic₄₃	—	2	1	no	—
184	C₂×Dic₄₃	—	2	1	no	—
185	C₂×Dic₄₃	—	2	1	no	—
186	C₂×Dic₄₃	—	2	1	no	—
187	C₂×Dic₄₃	—	2	1	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	1	no	—
190	C₂×Dic₄₃	—	2	1	no	—
191	C₂×Dic₄₃	—	2	1	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	C₂×Dic₄₃	—	4	1	no	—
195	C₂×Dic₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	4	1	no	—
197	C₂×Dic₄₃	#104	1	2	yes	—
198	C₄×D₄₃	—	2	4	no	—
199	C₄×D₄₃	—	2	4	no	—
200	C₄×D₄₃	—	4	1	no	—
201	C₄×D₄₃	—	4	1	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	—	4	1	no	—
204	C₄×D₄₃	—	4	1	no	—
205	C₄×D₄₃	—	4	1	no	—
206	C₄×D₄₃	—	4	1	no	—
207	C₄×D₄₃	—	4	1	no	—
208	Dic₈₆	—	2	2	no	—
209	Dic₈₆	—	2	2	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	4	1	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	#9077	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	#386	1	1	yes	characteristic
218	C₂²×C₄₃	#407	1	1	yes	characteristic
219	C₂²×C₄₃	#408	1	1	yes	characteristic
220	C₂²×C₄₃	#417	1	1	yes	characteristic
221	C₂²×C₄₃	#419	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	—	4	1	no	—
228	C₂×D₄₃	—	4	1	no	—
229	C₂×D₄₃	—	4	1	no	—
230	C₂×D₄₃	—	4	1	no	—
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	#435	1	1	yes	characteristic
236	C₄×C₄₃	#435	1	1	yes	characteristic
237	C₄×C₄₃	#436	1	1	yes	characteristic
238	C₄×C₄₃	#436	1	1	yes	characteristic
239	C₄×C₄₃	#468	1	1	yes	characteristic
240	C₄×C₄₃	#468	1	1	yes	characteristic
241	C₄×C₄₃	#470	1	1	yes	characteristic
242	C₄×C₄₃	#470	1	1	yes	characteristic
243	Dic₄₃	—	2	2	no	—
244	Dic₄₃	—	4	2	no	—
245	Dic₄₃	—	4	1	no	—
246	Dic₄₃	—	4	1	no	—
247	Dic₄₃	—	8	1	no	—
248	C₂×C₄×M₁₆	—	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	—	43	1	no	—
253	#1279	—	43	1	no	—
254	#1279	D₄₃	1	1	yes	characteristic, complemented
255	C₂×C₄₃	#1483	1	1	yes	characteristic
256	C₂×C₄₃	#1485	1	1	yes	characteristic
257	C₂×C₄₃	#1489	1	1	yes	characteristic
258	C₂×C₄₃	#1491	1	1	yes	characteristic
259	C₂×C₄₃	#1870	1	1	yes	characteristic
260	C₂×C₄₃	#1894	1	1	yes	characteristic
261	C₂×C₄₃	#1896	1	1	yes	characteristic
262	D₄₃	—	4	2	no	—
263	C₂²×M₁₆	—	86	1	no	—
264	C₂×C₂²⋊Q₈	—	43	1	no	—
265	C₂×C₄×Q₈	—	43	1	no	—
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	C₄×M₁₆	—	86	2	no	—
271	C₄×M₁₆	—	86	2	no	—
272	C₂×#97	—	86	1	no	—
273	C₂×C₄×C₈	—	43	1	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	—	86	1	no	—
281	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
282	C₄×C₂²⋊C₄	—	86	1	no	—
283	#336	—	86	1	no	—
284	Q₈⋊C₈	—	86	2	no	—
285	Q₈⋊C₈	—	86	2	no	—
286	C₄₃	#9077	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	—	43	1	no	—
288	C₂³×C₄	—	43	1	no	—
289	C₂³×C₄	—	43	1	no	—
290	C₂³×C₄	—	43	1	no	—
291	C₂×M₁₆	—	86	4	no	—
292	C₂×M₁₆	—	86	4	no	—
293	C₂×M₁₆	—	86	4	no	—
294	C₂²×C₈	—	2	1	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	86	1	no	—
297	C₂²×C₈	—	86	1	no	—
298	C₂²⋊Q₈	—	86	2	no	—
299	C₂²⋊Q₈	—	86	2	no	—
300	C₄×Q₈	—	86	1	no	—
301	C₄×Q₈	—	86	1	no	—
302	C₄×Q₈	—	86	1	no	—
303	C₄×Q₈	—	86	1	no	—
304	C₂×C₄⋊C₄	—	43	1	no	—
305	C₂×C₄⋊C₄	—	86	1	no	—
306	C₂×C₄⋊C₄	—	86	1	no	—
307	C₂×C₄⋊C₄	—	86	1	no	—
308	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
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	#97	—	86	4	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	43	2	no	—
330	C₄×C₈	—	86	1	no	—
331	C₄×C₈	D₁₇₂	1	2	yes	—
332	#95	—	2	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	—	43	2	no	—
339	C₂×Q₈	—	86	1	no	—
340	C₂×Q₈	—	86	1	no	—
341	C₂×Q₈	—	86	1	no	—
342	C₂×Q₈	—	86	1	no	—
343	C₂×Q₈	—	86	1	no	—
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	—	86	2	no	—
350	C₂²×C₄	—	86	2	no	—
351	C₂²×C₄	—	86	1	no	—
352	C₂²×C₄	—	86	1	no	—
353	C₂²×C₄	—	86	1	no	—
354	C₂²×C₄	—	86	1	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	M₁₆	—	86	16	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	4	1	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	—	2	1	no	—
386	C₄⋊C₄	—	86	4	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	172	2	no	—
390	C₄⋊C₄	—	172	1	no	—
391	C₄⋊C₄	—	172	1	no	—
392	C₄⋊C₄	#10621872	1	2	yes	complemented
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	C₂×D₁₇₂	1	1	yes	characteristic
406	C₄²	#10621898	1	1	yes	characteristic
407	C₄²	D₄×D₄₃	1	1	yes	characteristic
408	C₄²	#10621902	1	1	yes	characteristic
409	C₂³	—	43	2	no	—
410	C₂³	—	86	1	no	—
411	C₂³	—	86	1	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	—	86	2	no	—
418	Q₈	—	86	2	no	—
419	Q₈	—	172	1	no	—
420	Q₈	—	172	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	—	86	4	no	—
431	C₂×C₄	—	86	4	no	—
432	C₂×C₄	—	86	1	no	—
433	C₂×C₄	—	86	1	no	—
434	C₂×C₄	—	86	2	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	1	no	—
441	C₂×C₄	—	172	1	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	1	no	—
444	C₂×C₄	—	172	1	no	—
445	C₂×C₄	—	172	1	no	—
446	C₂×C₄	—	172	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	1	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	#13063287	1	1	yes	characteristic
455	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
456	C₂×C₄	#13063295	1	1	yes	characteristic
457	C₂×C₄	#13063298	1	1	yes	characteristic
458	C₂×C₄	#13063300	1	1	yes	characteristic
459	C₂×C₄	#13063310	1	1	yes	characteristic
460	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
461	C₂×C₄	C₂×#10621872	1	1	yes	characteristic
462	C₂×C₄	#13063331	1	1	yes	characteristic
463	C₂×C₄	#13063333	1	1	yes	characteristic
464	C₂×C₄	#13063349	1	1	yes	characteristic
465	C₂×C₄	#13063354	1	1	yes	characteristic
466	C₂×C₄	#13063354	1	1	yes	characteristic
467	C₂×C₄	#13063357	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	—	86	2	no	—
473	C₂²	—	86	2	no	—
474	C₂²	—	86	2	no	—
475	C₂²	—	172	1	no	—
476	C₂²	—	172	1	no	—
477	C₂²	—	172	1	no	—
478	C₂²	—	172	1	no	—
479	C₂²	#14582777	1	1	yes	characteristic
480	C₂²	#14582861	1	1	yes	characteristic
481	C₂²	#14582864	1	1	yes	characteristic
482	C₂²	#14582897	1	1	yes	characteristic
483	C₂²	#14582906	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	—	344	1	no	—
492	C₄	—	172	1	no	—
493	C₄	—	172	1	no	—
494	C₄	—	172	2	no	—
495	C₄	#14582969	1	1	yes	characteristic
496	C₄	#14582972	1	1	yes	characteristic
497	C₄	#14582976	1	1	yes	characteristic
498	C₄	#14582978	1	1	yes	characteristic
499	C₄	#14583144	1	1	yes	characteristic
500	C₄	#14583146	1	1	yes	characteristic
501	C₄	#14583156	1	1	yes	characteristic
502	C₄	#14583158	1	1	yes	characteristic
503	C₂	—	172	2	no	—
504	C₂	#19133005	1	1	yes	characteristic
505	C₂	#19133014	1	1	yes	characteristic
506	C₂	#19133031	1	1	yes	characteristic
507	C₂	#19133040	1	1	yes	characteristic
508	C₂	#19134891	1	1	yes	characteristic
509	C₂	#19135027	1	1	yes	characteristic
510	C₂	#19135037	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1279	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1279	D₄₃
hypocenter	C₄₃	#9077
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. C₂×#14582631	C₂	semidirect
5. C₂×#14582629	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
113. C₂×Dic₈₆	M₁₆	semidirect
123. C₄⋊C₄×C₄₃	M₁₆	semidirect
254. #1279	D₄₃	semidirect
286. C₄₃	#9077	semidirect
392. C₄⋊C₄	#10621872	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#10621872	2
C₄×#13063305	2
#19134572	2
C₂×#14582631	2
C₂×#14582629	2
#19132436	2
C₄₃×#1279	2
#9077	43