Subgroups — #131×D₁₇₂ #25960567

Order 11008.

2814 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#131×D₄₃	C₂	1	2	yes	maximal, complemented
2	#41×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	#19143341	C₂	1	3	yes	maximal, complemented
4	M₁₆×D₁₇₂	C₂	1	3	yes	maximal, complemented
5	#19143323	C₂	1	6	yes	maximal, complemented
6	#19143308	C₂	1	3	yes	maximal, complemented
7	#19143291	C₂	1	6	yes	maximal, complemented
8	C₂×C₈×D₁₇₂	C₂	1	3	yes	maximal, complemented
9	#19143163	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143042	C₂	1	2	yes	maximal, complemented
11	C₄×#131×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#41×D₄₃	C₂²	1	2	yes	—
13	C₂×#13063333	C₂²	1	6	yes	complemented
14	C₂×#13063332	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	6	yes	complemented
16	#131×D₄₃	—	2	16	no	—
17	C₂×M₁₆×D₄₃	C₂²	1	6	yes	complemented
18	C₂²×C₈×D₄₃	C₂²	1	6	yes	complemented
19	#14583571	C₄	1	1	yes	characteristic
20	Q₈×D₁₇₂	C₄	1	1	yes	characteristic
21	#14583561	C₄	1	2	yes	—
22	#14583553	C₄	1	3	yes	—
23	#14583544	C₄	1	6	yes	—
24	D₄×D₁₇₂	C₄	1	3	yes	—
25	#14583449	C₂²	1	3	yes	—
26	#14583411	C₂²	1	6	yes	—
27	C₂×C₄×D₁₇₂	C₂²	1	3	yes	—
28	#14582978	C₂²	1	6	yes	complemented
29	#14582978	C₂²	1	6	yes	complemented
30	#14582972	C₂²	1	12	yes	complemented
31	#14582972	C₂²	1	12	yes	complemented
32	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
33	C₈×D₁₇₂	C₂²	1	3	yes	—
34	C₈×D₁₇₂	C₂²	1	6	yes	complemented
35	C₈×D₁₇₂	C₂²	1	3	yes	complemented
36	C₈×D₁₇₂	C₂²	1	6	yes	complemented
37	C₈×D₁₇₂	C₂²	1	3	yes	complemented
38	C₈×D₁₇₂	C₂²	1	6	yes	complemented
39	#14582926	C₂²	1	6	yes	complemented
40	#14582923	C₂²	1	3	yes	complemented
41	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	3	yes	complemented
42	#14582867	C₂²	1	6	yes	complemented
43	#14582865	C₂²	1	6	yes	complemented
44	#14582862	C₂²	1	6	yes	complemented
45	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	6	yes	complemented
46	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
48	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
49	C₄₃×#405	C₂²	1	3	yes	complemented
50	C₄₃×#405	C₂²	1	3	yes	complemented
51	C₄×M₁₆×C₄₃	C₂²	1	3	yes	complemented
52	C₂×C₄×C₈×C₄₃	C₂²	1	3	yes	complemented
53	C₂×#10621902	C₂×C₄	1	2	yes	—
54	C₂×#10621898	C₂³	1	6	yes	—
55	C₂×#10621900	C₂×C₄	1	6	yes	—
56	#41×D₄₃	—	2	8	no	—
57	#41×D₄₃	—	2	8	no	—
58	C₂×Q₈×D₄₃	C₂×C₄	1	2	yes	—
59	C₂²×D₁₇₂	C₂×C₄	1	3	yes	—
60	C₂×D₄×D₄₃	C₂×C₄	1	6	yes	—
61	C₂²×C₄×D₄₃	C₂³	1	6	yes	—
62	#13063333	—	2	24	no	—
63	#13063332	—	2	8	no	—
64	#13063331	—	2	24	no	—
65	C₂×#10621877	C₂³	1	6	yes	—
66	C₂×#10621872	C₂³	1	12	yes	—
67	M₁₆×D₄₃	—	2	24	no	—
68	C₂²×C₄₃⋊C₈	C₂³	1	6	yes	—
69	C₂×C₈×D₄₃	—	2	24	no	—
70	C₂×C₈×D₄₃	C₂³	1	2	yes	—
71	C₂×C₈×D₄₃	C₂³	1	6	yes	—
72	C₂×C₈×D₄₃	C₂³	1	6	yes	—
73	C₂×C₈×D₄₃	C₂³	1	6	yes	—
74	#13063325	C₂×C₄	1	3	yes	—
75	#13063322	C₂×C₄	1	3	yes	—
76	#13063313	C₂×C₄	1	6	yes	—
77	#13063309	C₂×C₄	1	12	yes	—
78	#13063305	C₂×C₄	1	6	yes	—
79	#13063305	C₂×C₄	1	6	yes	—
80	#13063300	C₂×C₄	1	6	yes	—
81	#13063300	C₂×C₄	1	6	yes	—
82	#13063299	C₂×C₄	1	6	yes	—
83	#13063299	C₂×C₄	1	6	yes	—
84	#13063295	C₂×C₄	1	12	yes	—
85	C₄×D₁₇₂	C₂×C₄	1	3	yes	—
86	C₄×D₁₇₂	C₂×C₄	1	6	yes	—
87	C₄×D₁₇₂	C₂×C₄	1	3	yes	—
88	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
89	C₄×D₁₇₂	C₂³	1	6	yes	—
90	C₄×D₁₇₂	C₂³	1	3	yes	—
91	C₄×D₁₇₂	C₂³	1	6	yes	—
92	C₂×C₄⋊Dic₄₃	C₂×C₄	1	3	yes	—
93	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	6	yes	—
94	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
95	C₄⋊(C₄₃⋊C₈)	C₂³	1	3	yes	—
96	C₄⋊(C₄₃⋊C₈)	C₂³	1	6	yes	—
97	C₄⋊(C₄₃⋊C₈)	C₂³	1	6	yes	—
98	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
99	(C₂×D₄₃)⋊C₈	C₂³	1	6	yes	—
100	(C₂×D₄₃)⋊C₈	C₂³	1	6	yes	—
101	(C₂×D₄₃)⋊C₈	C₂³	1	6	yes	—
102	(C₂×D₄₃)⋊C₈	C₂³	1	12	yes	—
103	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
104	#131×C₄₃	—	2	4	no	—
105	#131×C₄₃	D₄	1	8	yes	complemented
106	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
107	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
108	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
109	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
110	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
111	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
112	C₄×D₄×C₄₃	C₂×C₄	1	3	yes	—
113	C₄×D₄×C₄₃	C₂×C₄	1	3	yes	—
114	#117×C₄₃	C₂³	1	3	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	3	yes	—
116	#97×C₄₃	C₂³	1	6	yes	—
117	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₄×C₈×C₄₃	C₂³	1	3	yes	—
119	C₄×C₈×C₄₃	C₂³	1	3	yes	—
120	C₄×C₈×C₄₃	C₂³	1	3	yes	—
121	C₂³×D₄₃	C₂²×C₄	1	6	yes	—
122	#41×C₄₃	C₂×D₄	1	4	yes	—
123	#41×C₄₃	#41	1	4	yes	—
124	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₄₃	C₂²×C₄	1	3	yes	—
126	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
127	C₂²×C₄×C₄₃	C₂²×C₄	1	3	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
129	C₂×C₂²⋊D₄₃	C₂²×C₄	1	12	yes	—
130	C₂²×Dic₄₃	C₂²×C₄	1	6	yes	—
131	#10621902	—	2	8	no	—
132	Q₈×D₄₃	—	2	8	no	—
133	#10621900	—	2	24	no	—
134	D₄×D₄₃	—	2	24	no	—
135	#10621898	—	2	12	no	—
136	#10621898	—	2	12	no	—
137	C₂×D₁₇₂	—	2	12	no	—
138	C₂×D₁₇₂	C₂²×C₄	1	6	yes	—
139	C₂×D₁₇₂	C₂²×C₄	1	3	yes	—
140	C₂×D₁₇₂	C₂²×C₄	1	6	yes	—
141	C₂×D₁₇₂	C₂²×C₄	1	6	yes	—
142	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄×D₄₃	—	2	12	no	—
144	C₂×C₄×D₄₃	—	2	12	no	—
145	C₂×C₄×D₄₃	C₂²×C₄	1	6	yes	—
146	C₂×C₄×D₄₃	C₂²×C₄	1	6	yes	—
147	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
148	C₂×C₄×D₄₃	C₂⁴	1	6	yes	—
149	C₂×Dic₈₆	C₂²×C₄	1	6	yes	—
150	M₁₆×C₄₃	—	2	6	no	—
151	M₁₆×C₄₃	C₂×D₄	1	12	yes	complemented
152	C₂×C₈×C₄₃	—	2	6	no	—
153	C₂×C₈×C₄₃	C₂×D₄	1	12	yes	complemented
154	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
156	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
157	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₄⋊C₄×C₄₃	C₂²×C₄	1	3	yes	—
159	C₄⋊C₄×C₄₃	C₂²×C₄	1	3	yes	—
160	C₂²⋊C₄×C₄₃	C₂²×C₄	1	6	yes	—
161	C₄²×C₄₃	C₂²×C₄	1	3	yes	—
162	C₄²×C₄₃	C₂²×C₄	1	3	yes	—
163	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₄²×C₄₃	C₂⁴	1	3	yes	—
165	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
166	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
167	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
168	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	6	yes	—
169	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	12	yes	—
170	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₄₃	C₂²×C₄	1	3	yes	—
172	C₄⋊Dic₄₃	C₂²×C₄	1	6	yes	—
173	C₄⋊Dic₄₃	C₂²×C₄	1	6	yes	—
174	#10621877	—	2	12	no	—
175	C₂×C₄₃⋊C₈	—	2	12	no	—
176	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
177	C₂×C₄₃⋊C₈	C₂⁴	1	6	yes	—
178	#10621872	—	2	24	no	—
179	C₈×D₄₃	—	2	4	no	—
180	C₈×D₄₃	—	2	12	no	—
181	C₈×D₄₃	—	2	12	no	—
182	C₈×D₄₃	—	2	12	no	—
183	C₂³×C₄₃	C₂³×C₄	1	3	yes	—
184	C₂²×D₄₃	—	2	12	no	—
185	C₂²×D₄₃	—	2	12	no	—
186	C₂²×D₄₃	—	4	6	no	—
187	C₂²×D₄₃	C₂³×C₄	1	6	yes	—
188	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
189	Q₈×C₄₃	C₄×D₄	1	4	yes	—
190	D₄×C₄₃	C₄×D₄	1	12	yes	—
191	C₂×C₄×C₄₃	—	2	6	no	—
192	C₂×C₄×C₄₃	—	4	3	no	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
194	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
195	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂³×C₄	1	3	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
199	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
200	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
201	C₂²⋊D₄₃	—	2	24	no	—
202	C₂×Dic₄₃	—	2	12	no	—
203	C₂×Dic₄₃	C₂³×C₄	1	6	yes	—
204	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
205	D₁₇₂	—	2	12	no	—
206	D₁₇₂	—	2	12	no	—
207	D₁₇₂	—	2	6	no	—
208	D₁₇₂	—	4	6	no	—
209	D₁₇₂	#131	1	4	yes	direct product factor
210	C₄×D₄₃	—	2	12	no	—
211	C₄×D₄₃	—	2	12	no	—
212	C₄×D₄₃	—	2	2	no	—
213	C₄×D₄₃	—	2	6	no	—
214	C₄×D₄₃	—	2	2	no	—
215	C₄×D₄₃	—	2	6	no	—
216	Dic₈₆	—	2	12	no	—
217	C₈×C₄₃	—	2	1	no	—
218	C₈×C₄₃	—	2	3	no	—
219	C₈×C₄₃	C₂²×D₄	1	2	yes	—
220	C₈×C₄₃	C₂²×D₄	1	6	yes	—
221	C₄₃⋊C₈	—	2	2	no	—
222	C₄₃⋊C₈	—	2	6	no	—
223	D₄×#131	—	43	1	no	maximal, Sylow
224	C₂²×C₄₃	—	2	3	no	—
225	C₂²×C₄₃	—	2	3	no	—
226	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
227	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
228	C₂×D₄₃	—	2	2	no	—
229	C₂×D₄₃	—	2	2	no	—
230	C₂×D₄₃	—	2	6	no	—
231	C₂×D₄₃	—	2	6	no	—
232	C₂×D₄₃	—	2	6	no	—
233	C₂×D₄₃	—	4	24	no	—
234	C₂×D₄₃	C₂×#131	1	4	yes	complemented
235	C₄×C₄₃	—	2	3	no	—
236	C₄×C₄₃	—	2	3	no	—
237	C₄×C₄₃	—	2	1	no	—
238	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
239	C₄×C₄₃	C₂×#131	1	2	yes	complemented
240	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
241	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
242	Dic₄₃	—	2	6	no	—
243	Dic₄₃	—	2	2	no	—
244	C₂²×#131	—	43	2	no	—
245	D₄×#41	—	43	1	no	—
246	#2935	—	43	3	no	—
247	D₄×M₁₆	—	43	3	no	—
248	#2933	—	43	6	no	—
249	#2931	—	43	3	no	—
250	#2929	—	43	6	no	—
251	C₂×C₈×D₄	—	43	3	no	—
252	#2906	—	43	1	no	—
253	#2880	—	43	2	no	—
254	C₄×#131	D₄₃	1	1	yes	characteristic, complemented
255	C₂×C₄₃	—	2	6	no	—
256	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
257	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
258	C₂×C₄₃	#3573	1	1	yes	characteristic
259	D₄₃	—	2	4	no	—
260	D₄₃	—	4	6	no	—
261	C₂²×#41	—	43	2	no	—
262	C₂×#131	—	43	2	no	—
263	C₂×#131	—	43	6	no	—
264	C₂×#131	—	43	6	no	—
265	C₂×#131	—	86	16	no	—
266	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
267	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
268	C₂²×M₁₆	—	43	6	no	—
269	C₂³×C₈	—	43	6	no	—
270	#550	—	43	1	no	—
271	D₄×Q₈	—	43	1	no	—
272	#548	—	43	2	no	—
273	#547	—	43	3	no	—
274	#546	—	43	6	no	—
275	D₄²	—	43	3	no	—
276	#532	—	43	3	no	—
277	#525	—	43	6	no	—
278	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
279	C₂×C₄×D₄	—	43	3	no	—
280	#436	—	43	6	no	—
281	#436	—	43	6	no	—
282	#435	—	43	12	no	—
283	#435	—	43	12	no	—
284	C₈×D₄	—	43	1	no	—
285	C₈×D₄	—	43	6	no	—
286	C₈×D₄	—	43	3	no	—
287	C₈×D₄	—	43	6	no	—
288	C₈×D₄	—	43	3	no	—
289	C₈×D₄	—	43	3	no	—
290	C₈×D₄	—	43	6	no	—
291	#424	—	43	6	no	—
292	#423	—	43	3	no	—
293	C₂×C₄⋊C₈	—	43	3	no	—
294	#408	—	43	6	no	—
295	#408	—	43	6	no	—
296	#407	—	43	6	no	—
297	C₂×C₂²⋊C₈	—	43	6	no	—
298	#405	C₂×D₄₃	1	3	yes	complemented
299	#405	C₂×D₄₃	1	3	yes	complemented
300	C₄×M₁₆	C₂×D₄₃	1	3	yes	complemented
301	C₂×C₄×C₈	C₂×D₄₃	1	3	yes	complemented
302	C₄₃	D₄×#131	1	1	yes	characteristic, complemented, Sylow
303	C₂×#41	—	43	2	no	—
304	C₂×#41	—	43	6	no	—
305	C₂×#41	—	43	6	no	—
306	C₂×#41	—	86	8	no	—
307	C₂×#41	—	86	8	no	—
308	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
309	C₂²×Q₈	—	43	2	no	—
310	C₂²×D₄	—	43	6	no	—
311	C₂²×D₄	—	43	3	no	—
312	C₂³×C₄	—	43	6	no	—
313	#131	—	2	4	no	—
314	#131	—	86	8	no	—
315	#131	—	86	24	no	—
316	#131	—	86	24	no	—
317	#131	D₁₇₂	1	8	yes	direct product factor
318	C₂×M₁₆	—	43	6	no	—
319	C₂×M₁₆	—	43	12	no	—
320	C₂×M₁₆	—	86	24	no	—
321	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
322	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
323	C₂²×C₈	—	43	6	no	—
324	C₂²×C₈	—	43	6	no	—
325	C₂²×C₈	—	43	6	no	—
326	C₂²×C₈	—	43	2	no	—
327	C₂²×C₈	—	43	6	no	—
328	C₂²×C₈	—	86	24	no	—
329	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
330	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
331	C₄⋊Q₈	—	43	3	no	—
332	#127	—	43	3	no	—
333	#124	—	43	6	no	—
334	#123	—	43	12	no	—
335	C₂²⋊Q₈	—	43	6	no	—
336	C₂²⋊Q₈	—	43	6	no	—
337	#121	—	43	6	no	—
338	#121	—	43	6	no	—
339	#121	—	43	6	no	—
340	#121	—	43	6	no	—
341	#120	—	43	12	no	—
342	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
343	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
344	C₄×D₄	—	43	3	no	—
345	C₄×D₄	—	43	6	no	—
346	C₄×D₄	—	43	3	no	—
347	C₄×D₄	—	43	1	no	—
348	C₄×D₄	—	43	6	no	—
349	C₄×D₄	—	43	3	no	—
350	C₄×D₄	—	43	6	no	—
351	C₄×D₄	C₄×D₄₃	1	3	yes	—
352	C₄×D₄	C₄×D₄₃	1	3	yes	—
353	#117	C₂²×D₄₃	1	3	yes	—
354	C₂×C₄⋊C₄	—	43	3	no	—
355	C₂×C₂²⋊C₄	—	43	6	no	—
356	C₂×C₄²	C₂²×D₄₃	1	3	yes	—
357	C₄⋊C₈	—	43	1	no	—
358	C₄⋊C₈	—	43	3	no	—
359	C₄⋊C₈	—	43	6	no	—
360	C₄⋊C₈	—	43	6	no	—
361	C₂²⋊C₈	—	43	2	no	—
362	C₂²⋊C₈	—	43	6	no	—
363	C₂²⋊C₈	—	43	6	no	—
364	C₂²⋊C₈	—	43	6	no	—
365	C₂²⋊C₈	—	43	12	no	—
366	#97	C₂²×D₄₃	1	6	yes	—
367	C₄×C₈	C₂²×D₄₃	1	3	yes	—
368	C₄×C₈	C₂²×D₄₃	1	3	yes	—
369	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
370	C₄×C₈	C₂²×D₄₃	1	3	yes	—
371	C₂⁴	—	43	6	no	—
372	#41	—	86	8	no	—
373	#41	—	86	24	no	—
374	#41	—	86	12	no	—
375	#41	—	86	12	no	—
376	#41	C₂×D₁₇₂	1	4	yes	—
377	#41	#10621898	1	4	yes	—
378	C₂×Q₈	—	43	6	no	—
379	C₂×Q₈	—	86	8	no	—
380	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
381	C₂×D₄	—	43	12	no	—
382	C₂×D₄	—	43	1	no	—
383	C₂×D₄	—	43	6	no	—
384	C₂×D₄	—	43	3	no	—
385	C₂×D₄	—	43	6	no	—
386	C₂×D₄	—	43	6	no	—
387	C₂×D₄	—	86	12	no	—
388	C₂×D₄	—	86	24	no	—
389	C₂×D₄	C₂×C₄×D₄₃	1	3	yes	—
390	C₂²×C₄	—	43	6	no	—
391	C₂²×C₄	—	43	6	no	—
392	C₂²×C₄	—	43	6	no	—
393	C₂²×C₄	—	43	2	no	—
394	C₂²×C₄	—	43	6	no	—
395	C₂²×C₄	—	86	12	no	—
396	C₂²×C₄	—	86	12	no	—
397	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
398	C₂²×C₄	C₂×C₄×D₄₃	1	3	yes	—
399	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
400	M₁₆	—	2	6	no	—
401	M₁₆	—	86	12	no	—
402	M₁₆	—	86	24	no	—
403	M₁₆	C₂×D₁₇₂	1	12	yes	complemented
404	C₂×C₈	—	2	6	no	—
405	C₂×C₈	—	43	2	no	—
406	C₂×C₈	—	43	6	no	—
407	C₂×C₈	—	86	12	no	—
408	C₂×C₈	—	86	4	no	—
409	C₂×C₈	—	86	12	no	—
410	C₂×C₈	—	86	12	no	—
411	C₂×C₈	—	86	12	no	—
412	C₂×C₈	C₂×D₁₇₂	1	12	yes	complemented
413	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
414	C₂×C₈	C₂³×D₄₃	1	3	yes	—
415	C₂×C₈	C₂³×D₄₃	1	3	yes	—
416	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
417	C₄⋊C₄	—	43	1	no	—
418	C₄⋊C₄	—	43	3	no	—
419	C₄⋊C₄	—	43	6	no	—
420	C₄⋊C₄	—	43	6	no	—
421	C₄⋊C₄	C₂×C₄×D₄₃	1	3	yes	—
422	C₄⋊C₄	C₂×C₄×D₄₃	1	3	yes	—
423	C₂²⋊C₄	—	43	2	no	—
424	C₂²⋊C₄	—	43	6	no	—
425	C₂²⋊C₄	—	43	6	no	—
426	C₂²⋊C₄	—	43	6	no	—
427	C₂²⋊C₄	—	43	12	no	—
428	C₂²⋊C₄	C₂×C₄×D₄₃	1	6	yes	—
429	C₄²	C₂×C₄×D₄₃	1	3	yes	—
430	C₄²	C₂×C₄×D₄₃	1	3	yes	—
431	C₄²	C₂³×D₄₃	1	1	yes	characteristic
432	C₄²	C₂³×D₄₃	1	3	yes	—
433	C₂³	—	43	2	no	—
434	C₂³	—	43	6	no	—
435	C₂³	—	86	12	no	—
436	C₂³	—	86	12	no	—
437	C₂³	—	172	6	no	—
438	C₂³	C₂²×C₄×D₄₃	1	3	yes	—
439	Q₈	—	86	12	no	—
440	Q₈	C₄×D₁₇₂	1	4	yes	—
441	D₄	—	43	4	no	—
442	D₄	—	86	12	no	—
443	D₄	—	86	24	no	—
444	D₄	—	86	12	no	—
445	D₄	—	86	6	no	—
446	D₄	—	172	6	no	—
447	D₄	C₄×D₁₇₂	1	12	yes	—
448	C₂×C₄	—	2	6	no	—
449	C₂×C₄	—	4	3	no	—
450	C₂×C₄	—	43	2	no	—
451	C₂×C₄	—	43	6	no	—
452	C₂×C₄	—	86	12	no	—
453	C₂×C₄	—	86	12	no	—
454	C₂×C₄	—	86	12	no	—
455	C₂×C₄	—	86	2	no	—
456	C₂×C₄	—	86	6	no	—
457	C₂×C₄	—	86	2	no	—
458	C₂×C₄	—	86	6	no	—
459	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
461	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
462	C₂×C₄	C₂²×C₄×D₄₃	1	3	yes	—
463	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₁₇₂	1	6	yes	—
465	C₂×C₄	C₂×#10621898	1	6	yes	—
466	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
467	C₈	—	2	1	no	—
468	C₈	—	2	3	no	—
469	C₈	—	86	2	no	—
470	C₈	—	86	6	no	—
471	C₈	C₂²×D₁₇₂	1	2	yes	—
472	C₈	C₂²×D₁₇₂	1	6	yes	—
473	C₂²	—	2	3	no	—
474	C₂²	—	2	3	no	—
475	C₂²	—	43	4	no	—
476	C₂²	—	86	2	no	—
477	C₂²	—	86	2	no	—
478	C₂²	—	86	6	no	—
479	C₂²	—	86	6	no	—
480	C₂²	—	86	6	no	—
481	C₂²	—	172	24	no	—
482	C₂²	C₂×C₄×D₁₇₂	1	6	yes	—
483	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
484	C₄	—	2	3	no	—
485	C₄	—	2	1	no	—
486	C₄	—	2	3	no	—
487	C₄	—	86	2	no	—
488	C₄	—	86	6	no	—
489	C₄	C₂×C₄×D₁₇₂	1	6	yes	—
490	C₄	#131×D₄₃	1	2	yes	complemented
491	C₄	C₂³×D₁₇₂	1	1	yes	characteristic
492	C₄	C₂²×#10621898	1	1	yes	characteristic
493	C₂	—	2	6	no	—
494	C₂	—	86	4	no	—
495	C₂	—	172	6	no	—
496	C₂	C₂²×C₄×D₁₇₂	1	1	yes	characteristic
497	C₂	C₂×#131×D₄₃	1	1	yes	characteristic
498	C₂	#19149306	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#131×C₄₃	C₂
prime radical	#41×D₁₇₂	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₄×#131	D₄₃
hypocenter	C₄₃	D₄×#131
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
1. C₂×#131×D₄₃	C₂	semidirect
3. #19143341	C₂	semidirect
4. M₁₆×D₁₇₂	C₂	semidirect
5. #19143323	C₂	semidirect
6. #19143308	C₂	semidirect
7. #19143291	C₂	semidirect
8. C₂×C₈×D₁₇₂	C₂	semidirect
9. #19143163	C₂	semidirect
10. #19143042	C₂	semidirect
11. C₄×#131×C₄₃	C₂	semidirect
13. C₂×#13063333	C₂²	semidirect
15. C₂×#13063331	C₂²	semidirect
17. C₂×M₁₆×D₄₃	C₂²	semidirect
18. C₂²×C₈×D₄₃	C₂²	semidirect
28. #14582978	C₂²	semidirect
29. #14582978	C₂²	semidirect
30. #14582972	C₂²	semidirect
31. #14582972	C₂²	semidirect
34. C₈×D₁₇₂	C₂²	semidirect
35. C₈×D₁₇₂	C₂²	semidirect
36. C₈×D₁₇₂	C₂²	semidirect
37. C₈×D₁₇₂	C₂²	semidirect
38. C₈×D₁₇₂	C₂²	semidirect
39. #14582926	C₂²	semidirect
40. #14582923	C₂²	semidirect
41. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
42. #14582867	C₂²	semidirect
43. #14582865	C₂²	semidirect
44. #14582862	C₂²	semidirect
45. C₂×(C₂×D₄₃)⋊C₈	C₂²	semidirect
49. C₄₃×#405	C₂²	semidirect
50. C₄₃×#405	C₂²	semidirect
51. C₄×M₁₆×C₄₃	C₂²	semidirect
52. C₂×C₄×C₈×C₄₃	C₂²	semidirect
105. #131×C₄₃	D₄	semidirect
151. M₁₆×C₄₃	C₂×D₄	semidirect
153. C₂×C₈×C₄₃	C₂×D₄	semidirect
209. D₁₇₂	#131	direct (N × H)
234. C₂×D₄₃	C₂×#131	semidirect
239. C₄×C₄₃	C₂×#131	semidirect
254. C₄×#131	D₄₃	semidirect
298. #405	C₂×D₄₃	semidirect
299. #405	C₂×D₄₃	semidirect
300. C₄×M₁₆	C₂×D₄₃	semidirect
301. C₂×C₄×C₈	C₂×D₄₃	semidirect
302. C₄₃	D₄×#131	semidirect
317. #131	D₁₇₂	direct (N × H)
403. M₁₆	C₂×D₁₇₂	semidirect
412. C₂×C₈	C₂×D₁₇₂	semidirect
490. C₄	#131×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#131×D₄₃	2
#41×D₁₇₂	2
#19143341	2
M₁₆×D₁₇₂	2
#19143323	2
#19143308	2
#19143291	2
C₂×C₈×D₁₇₂	2
#19143163	2
#19143042	2
C₄×#131×C₄₃	2
D₄×#131	43

Subgroups — #131×D172 #25960567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #131×D₁₇₂ #25960567