Subgroups — #25097709

Order 11008.

1320 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583665	C₂	1	1	yes	maximal, characteristic
2	#19143159	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143158	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582872	C₂	1	1	yes	maximal, characteristic
5	#19143039	C₂	1	1	yes	maximal, characteristic
6	#19134882	C₂	1	8	yes	maximal, complemented
7	C₂×#14582671	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621898	C₂²	1	1	yes	characteristic
10	#14583665	—	2	2	no	—
11	#14583665	—	2	2	no	—
12	#14583665	—	2	2	no	—
13	#14583665	C₂²	1	4	yes	—
14	C₂×#13063333	—	2	2	no	—
15	C₂×#13063331	—	2	2	no	—
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂²×#10621877	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×D₄₃	—	2	2	no	—
19	C₂×#13063284	C₂²	1	1	yes	characteristic
20	#14582927	C₂²	1	4	yes	complemented
21	#14582926	—	2	2	no	—
22	#14582926	C₂²	1	4	yes	complemented
23	#14582925	—	2	2	no	—
24	#14582923	—	2	2	no	—
25	#14582922	—	2	2	no	—
26	#14582872	C₄	1	4	yes	—
27	#14582872	C₂²	1	4	yes	—
28	C₂×#13063239	C₄	1	4	yes	—
29	#14582867	C₂²	1	4	yes	—
30	#14582865	—	2	2	no	—
31	#14582862	—	2	2	no	—
32	#14582671	C₂²	1	4	yes	complemented
33	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#344	C₂²	1	4	yes	complemented
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂×#10621898	—	2	1	no	—
44	C₂×#10621898	—	2	1	no	—
45	C₂×#10621898	C₂×C₄	1	2	yes	—
46	C₂×#10621898	D₄	1	2	yes	—
47	C₂×#10621898	Q₈	1	2	yes	—
48	C₂×#10621898	C₂³	1	2	yes	—
49	C₂²×Dic₈₆	Q₈	1	1	yes	characteristic
50	C₂²×D₁₇₂	Q₈	1	1	yes	characteristic
51	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
52	C₂²×C₄×D₄₃	D₄	1	2	yes	—
53	#13063333	—	2	8	no	—
54	#13063333	—	2	8	no	—
55	#13063331	—	2	8	no	—
56	#13063331	—	2	8	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	—	2	1	no	—
60	C₂×#10621877	—	2	1	no	—
61	C₂×#10621877	—	2	1	no	—
62	C₂×#10621877	—	2	1	no	—
63	C₂×#10621877	—	2	1	no	—
64	C₂×#10621877	—	2	1	no	—
65	C₂×#10621877	—	2	1	no	—
66	C₂×#10621877	—	2	1	no	—
67	C₂×#10621877	D₄	1	2	yes	—
68	C₂×#10621877	C₂³	1	2	yes	—
69	C₂×#10621872	—	2	4	no	—
70	M₁₆×D₄₃	—	2	8	no	—
71	M₁₆×D₄₃	—	2	8	no	—
72	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
73	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₈×D₄₃	—	2	4	no	—
75	#13063284	—	2	1	no	—
76	#13063284	—	2	1	no	—
77	#13063284	C₂×C₄	1	2	yes	—
78	#13063284	C₂³	1	2	yes	—
79	C₂×C₄⋊Dic₄₃	—	2	1	no	—
80	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
81	C₂×C₄×Dic₄₃	—	2	1	no	—
82	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
83	Dic₄₃⋊C₈	—	2	8	no	—
84	#13063239	C₂×C₄	1	16	yes	—
85	(C₂×D₄₃)⋊C₈	—	2	8	no	—
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	—	2	1	no	—
93	C₂×M₁₆×C₄₃	—	2	1	no	—
94	C₂×M₁₆×C₄₃	—	2	1	no	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
97	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
98	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₃	—	2	1	no	—
100	C₂²×C₈×C₄₃	D₄	1	2	yes	—
101	#117×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	#117×C₄₃	C₂×C₄	1	2	yes	—
104	#117×C₄₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₄₃	—	2	1	no	—
108	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂³×D₄₃	C₄⋊C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₃	—	2	2	no	—
126	C₂×C₂²⋊D₄₃	—	2	2	no	—
127	C₂×C₂²⋊D₄₃	—	2	2	no	—
128	C₂×C₂²⋊D₄₃	—	2	2	no	—
129	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	4	yes	—
130	C₂×C₂²⋊D₄₃	C₂²×C₄	1	4	yes	—
131	C₂²×Dic₄₃	—	2	2	no	—
132	C₂²×Dic₄₃	C₄⋊C₄	1	2	yes	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	#10621898	—	2	2	no	—
142	#10621898	—	2	2	no	—
143	#10621898	—	2	2	no	—
144	#10621898	—	2	2	no	—
145	#10621898	—	2	2	no	—
146	#10621898	—	2	2	no	—
147	#10621898	—	2	2	no	—
148	#10621898	—	2	2	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
154	C₂×D₁₇₂	C₂×Q₈	1	2	yes	—
155	C₂×C₄×D₄₃	—	2	2	no	—
156	C₂×C₄×D₄₃	—	2	2	no	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
160	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	—	2	1	no	—
163	C₂×Dic₈₆	—	2	1	no	—
164	C₂×Dic₈₆	—	2	1	no	—
165	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
166	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
167	M₁₆×C₄₃	—	2	2	no	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	2	2	no	—
172	M₁₆×C₄₃	—	2	2	no	—
173	M₁₆×C₄₃	—	4	1	no	—
174	M₁₆×C₄₃	—	4	1	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	2	2	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₂×C₈×C₄₃	—	4	1	no	—
179	C₂×C₈×C₄₃	—	4	1	no	—
180	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	2	2	no	—
183	C₂²⋊C₄×C₄₃	—	2	2	no	—
184	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₂²⋊Dic₄₃	—	2	2	no	—
188	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
189	C₄⋊Dic₄₃	—	2	2	no	—
190	C₄⋊Dic₄₃	—	2	2	no	—
191	C₄×Dic₄₃	—	2	2	no	—
192	C₄×Dic₄₃	—	2	2	no	—
193	#10621877	—	2	2	no	—
194	#10621877	—	2	2	no	—
195	#10621877	—	2	2	no	—
196	#10621877	—	2	2	no	—
197	#10621877	—	4	1	no	—
198	#10621877	—	4	1	no	—
199	#10621877	—	4	1	no	—
200	#10621877	—	4	1	no	—
201	C₂×C₄₃⋊C₈	—	2	2	no	—
202	C₂×C₄₃⋊C₈	—	2	2	no	—
203	C₂×C₄₃⋊C₈	—	2	2	no	—
204	C₂×C₄₃⋊C₈	—	2	2	no	—
205	C₂×C₄₃⋊C₈	—	2	2	no	—
206	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
207	#10621872	—	2	16	no	—
208	C₈×D₄₃	—	2	16	no	—
209	C₂³×C₄₃	—	8	1	no	—
210	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
212	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
213	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
217	C₂²×D₄₃	—	2	2	no	—
218	C₂²×D₄₃	—	2	2	no	—
219	C₂²×D₄₃	—	8	2	no	—
220	C₂²×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
221	C₂×C₄×C₄₃	—	2	4	no	—
222	C₂×C₄×C₄₃	—	8	2	no	—
223	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₄₃	—	2	4	no	—
252	C₂²⋊D₄₃	—	2	4	no	—
253	C₂²⋊D₄₃	—	2	4	no	—
254	C₂²⋊D₄₃	—	2	4	no	—
255	C₂×Dic₄₃	—	2	2	no	—
256	C₂×Dic₄₃	—	2	2	no	—
257	C₂×Dic₄₃	—	2	4	no	—
258	C₂×Dic₄₃	—	8	2	no	—
259	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
260	D₁₇₂	—	2	2	no	—
261	D₁₇₂	—	2	2	no	—
262	D₁₇₂	—	2	2	no	—
263	D₁₇₂	—	2	2	no	—
264	C₄×D₄₃	—	2	4	no	—
265	C₄×D₄₃	—	2	4	no	—
266	C₄×D₄₃	—	2	4	no	—
267	C₄×D₄₃	—	2	4	no	—
268	Dic₈₆	—	2	2	no	—
269	Dic₈₆	—	2	2	no	—
270	Dic₈₆	—	2	2	no	—
271	Dic₈₆	—	2	2	no	—
272	C₈×C₄₃	—	2	4	no	—
273	C₈×C₄₃	—	4	2	no	—
274	C₄₃⋊C₈	—	2	4	no	—
275	C₄₃⋊C₈	—	4	2	no	—
276	#20892	—	43	1	no	maximal, Sylow
277	C₂²×C₄₃	—	4	1	no	—
278	C₂²×C₄₃	—	4	1	no	—
279	C₂²×C₄₃	—	4	1	no	—
280	C₂²×C₄₃	—	4	1	no	—
281	C₂²×C₄₃	—	4	1	no	—
282	C₂²×C₄₃	—	4	1	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	#385	1	1	yes	characteristic
285	C₂²×C₄₃	#385	1	1	yes	characteristic
286	C₂²×C₄₃	#385	1	1	yes	characteristic
287	C₂²×C₄₃	#385	1	1	yes	characteristic
288	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
289	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
290	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂×D₄₃	—	2	4	no	—
292	C₂×D₄₃	—	4	4	no	—
293	C₂×D₄₃	—	4	4	no	—
294	C₂×D₄₃	—	8	2	no	—
295	C₄×C₄₃	—	4	4	no	—
296	C₄×C₄₃	#385	1	1	yes	characteristic
297	C₄×C₄₃	#385	1	1	yes	characteristic
298	C₄×C₄₃	#385	1	1	yes	characteristic
299	C₄×C₄₃	#385	1	1	yes	characteristic
300	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
301	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
302	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
304	Dic₄₃	—	2	4	no	—
305	Dic₄₃	—	4	4	no	—
306	C₂×#568	—	43	1	no	—
307	#2905	—	43	1	no	—
308	#2905	—	43	1	no	—
309	C₂×#410	—	43	1	no	—
310	#2879	—	43	1	no	—
311	#1868	—	43	8	no	—
312	C₂×#344	—	43	1	no	—
313	C₂×#344	D₄₃	1	1	yes	characteristic, complemented
314	C₂×C₄₃	—	2	1	no	—
315	C₂×C₄₃	—	2	1	no	—
316	C₂×C₄₃	—	2	1	no	—
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
322	D₄₃	—	4	4	no	—
323	C₂²×#41	—	43	1	no	—
324	#568	—	43	4	no	—
325	#568	—	86	2	no	—
326	#568	—	86	2	no	—
327	#568	—	86	2	no	—
328	C₂×#131	—	86	2	no	—
329	C₂×#131	—	86	2	no	—
330	C₂²×M₁₆	—	43	1	no	—
331	C₂²×M₁₆	—	43	1	no	—
332	C₂²×M₁₆	—	86	2	no	—
333	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
334	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
335	C₂×#117	—	43	1	no	—
336	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
337	#424	—	43	4	no	—
338	#424	—	43	4	no	—
339	#424	—	86	2	no	—
340	#424	—	86	2	no	—
341	#423	—	86	2	no	—
342	#423	—	86	2	no	—
343	#410	—	43	4	no	—
344	#410	—	43	4	no	—
345	C₂×#99	—	43	4	no	—
346	#408	—	43	4	no	—
347	#408	—	86	2	no	—
348	#407	—	86	2	no	—
349	#344	—	43	4	no	—
350	#344	C₂×D₄₃	1	4	yes	complemented
351	C₄₃	#20892	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	43	2	no	—
353	C₂×#41	—	43	2	no	—
354	C₂×#41	—	43	2	no	—
355	C₂×#41	—	43	2	no	—
356	C₂×#41	—	86	1	no	—
357	C₂×#41	—	86	1	no	—
358	C₂×#41	—	86	1	no	—
359	C₂×#41	—	86	1	no	—
360	C₂×#41	—	86	1	no	—
361	C₂×#41	—	86	1	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂²×Q₈	—	43	1	no	—
365	C₂²×D₄	—	43	2	no	—
366	C₂²×D₄	—	43	1	no	—
367	C₂³×C₄	—	43	2	no	—
368	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
369	#131	—	86	8	no	—
370	#131	—	86	8	no	—
371	#131	—	86	8	no	—
372	#131	—	86	8	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	43	2	no	—
383	C₂×M₁₆	—	43	2	no	—
384	C₂×M₁₆	—	86	4	no	—
385	C₂×M₁₆	—	86	8	no	—
386	C₂×M₁₆	—	86	8	no	—
387	C₂×M₁₆	—	86	1	no	—
388	C₂×M₁₆	—	86	1	no	—
389	C₂×M₁₆	—	86	1	no	—
390	C₂×M₁₆	—	86	1	no	—
391	C₂×M₁₆	—	86	1	no	—
392	C₂×M₁₆	—	86	1	no	—
393	C₂×M₁₆	—	86	1	no	—
394	C₂×M₁₆	—	86	1	no	—
395	C₂×M₁₆	—	86	1	no	—
396	C₂×M₁₆	—	86	1	no	—
397	C₂×M₁₆	D₁₇₂	1	2	yes	—
398	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
399	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
400	C₂²×C₈	—	2	1	no	—
401	C₂²×C₈	—	43	2	no	—
402	C₂²×C₈	—	43	2	no	—
403	C₂²×C₈	—	86	4	no	—
404	C₂²×C₈	D₁₇₂	1	2	yes	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	43	2	no	—
408	#117	—	43	2	no	—
409	#117	—	86	1	no	—
410	#117	—	86	1	no	—
411	#117	C₄×D₄₃	1	2	yes	—
412	#117	C₂²×D₄₃	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	86	1	no	—
415	C₂×C₂²⋊C₄	—	43	2	no	—
416	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
417	C₂×C₄²	—	2	1	no	—
418	C₂×C₄²	—	86	1	no	—
419	C₄⋊C₈	—	86	8	no	—
420	C₄⋊C₈	—	86	8	no	—
421	#99	—	43	16	no	—
422	C₂²⋊C₈	—	86	8	no	—
423	C₂⁴	—	43	2	no	—
424	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
425	#41	—	86	2	no	—
426	#41	—	86	2	no	—
427	#41	—	86	2	no	—
428	#41	—	86	2	no	—
429	#41	—	86	2	no	—
430	#41	—	86	2	no	—
431	#41	—	86	2	no	—
432	#41	—	86	2	no	—
433	#41	—	86	2	no	—
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	#41	—	86	2	no	—
437	#41	—	86	2	no	—
438	#41	—	86	2	no	—
439	#41	—	86	2	no	—
440	#41	—	86	2	no	—
441	C₂×Q₈	—	43	2	no	—
442	C₂×Q₈	—	43	2	no	—
443	C₂×Q₈	—	86	1	no	—
444	C₂×Q₈	—	86	1	no	—
445	C₂×Q₈	—	86	1	no	—
446	C₂×Q₈	—	86	1	no	—
447	C₂×D₄	—	43	4	no	—
448	C₂×D₄	—	43	4	no	—
449	C₂×D₄	—	43	2	no	—
450	C₂×D₄	—	43	2	no	—
451	C₂×D₄	—	86	2	no	—
452	C₂×D₄	—	86	2	no	—
453	C₂×D₄	—	86	2	no	—
454	C₂×D₄	—	86	2	no	—
455	C₂×D₄	—	86	1	no	—
456	C₂×D₄	—	86	1	no	—
457	C₂×D₄	—	86	1	no	—
458	C₂×D₄	—	86	1	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	43	2	no	—
461	C₂²×C₄	—	43	4	no	—
462	C₂²×C₄	—	43	4	no	—
463	C₂²×C₄	—	86	2	no	—
464	C₂²×C₄	—	86	2	no	—
465	C₂²×C₄	—	86	2	no	—
466	C₂²×C₄	—	86	2	no	—
467	C₂²×C₄	—	86	2	no	—
468	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
471	C₂²×C₄	#10621898	1	1	yes	characteristic
472	C₂²×C₄	#10621898	1	1	yes	characteristic
473	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
475	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
476	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
477	C₂²×C₄	#10621900	1	1	yes	characteristic
478	C₂²×C₄	#10621900	1	1	yes	characteristic
479	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
480	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
481	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	86	16	no	—
491	M₁₆	—	86	2	no	—
492	M₁₆	—	86	2	no	—
493	M₁₆	—	86	2	no	—
494	M₁₆	—	86	2	no	—
495	M₁₆	—	172	1	no	—
496	M₁₆	—	172	1	no	—
497	M₁₆	—	172	1	no	—
498	M₁₆	—	172	1	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	43	4	no	—
505	C₂×C₈	—	86	16	no	—
506	C₂×C₈	—	86	2	no	—
507	C₂×C₈	—	86	2	no	—
508	C₂×C₈	—	86	2	no	—
509	C₂×C₈	—	86	2	no	—
510	C₂×C₈	—	86	2	no	—
511	C₂×C₈	C₂×D₁₇₂	1	4	yes	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	86	2	no	—
515	C₄⋊C₄	—	86	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	43	4	no	—
518	C₂²⋊C₄	—	86	2	no	—
519	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	86	2	no	—
523	C₄²	—	86	2	no	—
524	C₂³	—	8	1	no	—
525	C₂³	—	43	4	no	—
526	C₂³	—	86	2	no	—
527	C₂³	—	86	2	no	—
528	C₂³	—	344	2	no	—
529	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
530	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
531	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
532	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
533	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
534	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
535	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
536	Q₈	—	86	2	no	—
537	Q₈	—	86	2	no	—
538	Q₈	—	86	2	no	—
539	Q₈	—	86	2	no	—
540	D₄	—	86	4	no	—
541	D₄	—	86	4	no	—
542	D₄	—	86	4	no	—
543	D₄	—	86	4	no	—
544	D₄	—	86	2	no	—
545	D₄	—	86	2	no	—
546	D₄	—	86	2	no	—
547	D₄	—	86	2	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	43	4	no	—
551	C₂×C₄	—	86	2	no	—
552	C₂×C₄	—	86	2	no	—
553	C₂×C₄	—	86	4	no	—
554	C₂×C₄	—	86	4	no	—
555	C₂×C₄	—	86	4	no	—
556	C₂×C₄	—	86	4	no	—
557	C₂×C₄	—	86	4	no	—
558	C₂×C₄	—	344	2	no	—
559	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
560	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
561	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
562	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
564	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
565	C₂×C₄	#13063295	1	1	yes	characteristic
566	C₂×C₄	#13063295	1	1	yes	characteristic
567	C₂×C₄	#13063295	1	1	yes	characteristic
568	C₂×C₄	#13063295	1	1	yes	characteristic
569	C₂×C₄	#13063303	1	1	yes	characteristic
570	C₂×C₄	#13063303	1	1	yes	characteristic
571	C₂×C₄	#13063303	1	1	yes	characteristic
572	C₂×C₄	#13063303	1	1	yes	characteristic
573	C₂×C₄	#13063305	1	1	yes	characteristic
574	C₂×C₄	#13063305	1	1	yes	characteristic
575	C₂×C₄	#13063305	1	1	yes	characteristic
576	C₂×C₄	#13063305	1	1	yes	characteristic
577	C₂×C₄	#13063307	1	1	yes	characteristic
578	C₂×C₄	#13063307	1	1	yes	characteristic
579	C₂×C₄	#13063307	1	1	yes	characteristic
580	C₂×C₄	#13063307	1	1	yes	characteristic
581	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
582	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
583	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
584	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
585	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
586	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
587	C₈	—	2	4	no	—
588	C₈	—	4	2	no	—
589	C₈	—	86	4	no	—
590	C₈	—	172	2	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	86	4	no	—
599	C₂²	—	344	2	no	—
600	C₂²	—	172	4	no	—
601	C₂²	—	172	4	no	—
602	C₂²	#14582773	1	1	yes	characteristic
603	C₂²	#14582773	1	1	yes	characteristic
604	C₂²	#14582773	1	1	yes	characteristic
605	C₂²	#14582773	1	1	yes	characteristic
606	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
607	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
608	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
609	C₄	—	4	4	no	—
610	C₄	—	86	4	no	—
611	C₄	—	172	4	no	—
612	C₄	#14582773	1	1	yes	characteristic
613	C₄	#14582773	1	1	yes	characteristic
614	C₄	#14582773	1	1	yes	characteristic
615	C₄	#14582773	1	1	yes	characteristic
616	C₄	C₂×#13063295	1	1	yes	characteristic
617	C₄	C₂×#13063303	1	1	yes	characteristic
618	C₄	C₂×#13063305	1	1	yes	characteristic
619	C₄	C₂×#13063307	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	172	4	no	—
628	C₂	C₂×#14582773	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13063295
commutator	C₂³×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#344	C₂
socle	C₂×C₄₃	C₂×#385
prime radical	C₂²×#10621898	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#344	D₄₃
hypocenter	C₄₃	#20892
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
2. #19143159	C₂	semidirect
3. #19143158	C₂	semidirect
6. #19134882	C₂	semidirect
7. C₂×#14582671	C₂	semidirect
8. C₂×C₄₃×#344	C₂	semidirect
20. #14582927	C₂²	semidirect
22. #14582926	C₂²	semidirect
32. #14582671	C₂²	semidirect
36. C₄₃×#344	C₂²	semidirect
313. C₂×#344	D₄₃	semidirect
350. #344	C₂×D₄₃	semidirect
351. C₄₃	#20892	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583665	2
#19143159	2
#19143158	2
C₂×#14582872	2
#19143039	2
#19134882	2
C₂×#14582671	2
C₂×C₄₃×#344	2
#20892	43