Subgroups — #25065314

Order 11008.

896 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148411	C₂	1	1	yes	maximal, characteristic
2	#19143714	C₂	1	1	yes	maximal, characteristic
3	#19143262	C₂	1	1	yes	maximal, characteristic
4	#19133326	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133322	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133319	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133306	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133304	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133282	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133276	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133274	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133274	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133249	C₂	1	1	yes	maximal, characteristic, complemented
14	#333×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1558	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583629	—	2	1	no	—
17	#14583624	C₄	1	2	yes	—
18	#14583610	—	2	1	no	—
19	#14583604	—	2	1	no	—
20	#14583604	—	2	1	no	—
21	#14583564	C₄	1	2	yes	—
22	Q₈×C₂²⋊D₄₃	C₄	1	2	yes	—
23	Q₈×C₂²⋊D₄₃	C₄	1	2	yes	—
24	#14583530	—	2	1	no	—
25	#14583526	—	2	1	no	—
26	#14583526	—	2	1	no	—
27	#14583456	C₂²	1	1	yes	characteristic
28	#14583454	C₂²	1	1	yes	characteristic
29	#14583454	C₂²	1	1	yes	characteristic
30	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
31	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
32	#14583380	—	2	1	no	—
33	C₄×#10621898	C₂²	1	1	yes	characteristic
34	#14583027	—	2	1	no	—
35	#14582974	—	2	1	no	—
36	#14582973	—	2	1	no	—
37	#14582972	—	2	1	no	—
38	#14582961	—	2	1	no	—
39	#14582957	—	2	1	no	—
40	#14582955	C₂²	1	1	yes	characteristic
41	#14582955	C₂²	1	1	yes	characteristic
42	#14582952	C₂²	1	1	yes	characteristic
43	#14582951	C₂²	1	1	yes	characteristic
44	#14582951	C₂²	1	1	yes	characteristic
45	#14582923	C₂²	1	1	yes	characteristic
46	#14582921	C₂²	1	1	yes	characteristic
47	#14582921	C₂²	1	1	yes	characteristic
48	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
49	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
50	#14582864	—	2	1	no	—
51	#14582856	—	2	1	no	—
52	#14582648	C₂²	1	1	yes	characteristic
53	#14582648	C₂²	1	1	yes	characteristic
54	#14582648	C₂²	1	1	yes	characteristic
55	#14582648	C₂²	1	1	yes	characteristic
56	#14582647	C₂²	1	1	yes	characteristic
57	#14582647	C₂²	1	1	yes	characteristic
58	#14582647	C₂²	1	1	yes	characteristic
59	#14582647	C₂²	1	1	yes	characteristic
60	#14582646	C₂²	1	1	yes	characteristic
61	#14582646	C₂²	1	1	yes	characteristic
62	#14582644	C₂²	1	1	yes	characteristic
63	#14582644	C₂²	1	1	yes	characteristic
64	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
65	C₄₃×#432	C₂²	1	1	yes	characteristic
66	C₄₃×#432	C₂²	1	1	yes	characteristic
67	C₄₃×#333	C₂²	1	1	yes	characteristic
68	C₄₃×#333	C₂²	1	1	yes	characteristic
69	C₄₃×#333	C₂²	1	1	yes	characteristic
70	C₄₃×#333	C₂²	1	1	yes	characteristic
71	C₂×#10621898	D₄	1	1	yes	characteristic
72	C₂×Q₈×D₄₃	C₂×C₄	1	2	yes	—
73	C₂×Q₈×D₄₃	C₂×C₄	1	2	yes	—
74	C₂×#10621877	—	2	1	no	—
75	C₂×#10621872	—	2	1	no	—
76	C₂×#10621872	—	2	1	no	—
77	C₂×C₈×D₄₃	—	2	1	no	—
78	C₂×C₈×D₄₃	—	2	1	no	—
79	#13063325	C₂³	1	1	yes	characteristic
80	#13063325	C₂³	1	1	yes	characteristic
81	#13063324	—	2	2	no	—
82	#13063324	—	2	1	no	—
83	#13063324	—	2	1	no	—
84	#13063324	—	2	1	no	—
85	#13063324	—	2	1	no	—
86	#13063323	—	2	2	no	—
87	#13063323	—	2	2	no	—
88	#13063323	C₂×C₄	1	2	yes	—
89	#13063323	C₂×C₄	1	2	yes	—
90	#13063317	—	2	1	no	—
91	#13063316	—	2	2	no	—
92	#13063316	—	2	1	no	—
93	#13063316	—	2	1	no	—
94	#13063315	—	2	2	no	—
95	#13063315	—	2	2	no	—
96	#13063305	—	2	1	no	—
97	#13063305	—	2	1	no	—
98	#13063304	—	2	1	no	—
99	#13063304	—	2	2	no	—
100	#13063304	—	2	2	no	—
101	#13063304	C₂×C₄	1	2	yes	—
102	#13063303	—	2	2	no	—
103	#13063303	—	2	2	no	—
104	#13063301	—	2	2	no	—
105	#13063301	—	2	2	no	—
106	#13063301	C₂×C₄	1	2	yes	—
107	#13063301	C₂×C₄	1	2	yes	—
108	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
109	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
110	C₄×Dic₈₆	—	2	1	no	—
111	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
112	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
113	C₄×Dic₈₆	D₄	1	1	yes	characteristic
114	#13063290	—	2	2	no	—
115	#13063290	—	2	1	no	—
116	#13063290	—	2	1	no	—
117	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
118	C₄×D₁₇₂	D₄	1	1	yes	characteristic
119	#13063287	—	2	2	no	—
120	C₄×C₂²⋊D₄₃	—	2	2	no	—
121	C₄×C₂²⋊D₄₃	—	2	2	no	—
122	C₄×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
123	C₄×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
124	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
125	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
126	#13063284	—	2	1	no	—
127	#13063284	D₄	1	1	yes	characteristic
128	#13063283	—	2	1	no	—
129	#13063283	—	2	1	no	—
130	#13063282	D₄	1	1	yes	characteristic
131	#13063282	D₄	1	1	yes	characteristic
132	C₄⋊C₄×D₄₃	—	2	1	no	—
133	C₄⋊C₄×D₄₃	—	2	1	no	—
134	C₄⋊C₄×D₄₃	—	2	1	no	—
135	C₄⋊C₄×D₄₃	—	2	1	no	—
136	C₄²×D₄₃	C₂³	1	1	yes	characteristic
137	C₄²×D₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
139	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
140	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
141	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
142	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
143	Dic₄₃⋊C₈	—	2	1	no	—
144	Dic₄₃⋊C₈	—	2	1	no	—
145	Dic₄₃⋊C₈	—	2	1	no	—
146	Dic₄₃⋊C₈	—	2	1	no	—
147	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
148	(C₂×D₄₃)⋊C₈	—	2	1	no	—
149	(C₂×D₄₃)⋊C₈	—	2	1	no	—
150	(C₂×D₄₃)⋊C₈	—	2	1	no	—
151	(C₂×D₄₃)⋊C₈	—	2	1	no	—
152	#13063235	—	2	1	no	—
153	#13063235	—	2	1	no	—
154	C₄×C₄₃⋊C₈	—	2	1	no	—
155	C₈×Dic₄₃	—	2	1	no	—
156	C₈×Dic₄₃	—	2	1	no	—
157	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
158	C₄⋊Q₈×C₄₃	—	2	1	no	—
159	C₄⋊Q₈×C₄₃	—	2	1	no	—
160	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
161	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
162	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
166	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
167	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
168	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
169	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
170	C₂²⋊C₈×C₄₃	—	2	1	no	—
171	C₂²⋊C₈×C₄₃	—	2	1	no	—
172	#97×C₄₃	—	2	1	no	—
173	#97×C₄₃	—	2	1	no	—
174	C₂×Q₈×C₄₃	—	2	2	no	—
175	C₂×Q₈×C₄₃	—	8	2	no	—
176	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
177	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
178	C₂²×C₄×C₄₃	—	2	2	no	—
179	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₂²⋊D₄₃	C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₂²⋊D₄₃	C₂²⋊C₄	1	1	yes	characteristic
184	Q₈×D₄₃	—	8	2	no	—
185	Q₈×D₄₃	—	8	2	no	—
186	#10621898	—	2	2	no	—
187	#10621898	—	2	2	no	—
188	C₂×D₁₇₂	C₂²⋊C₄	1	1	yes	characteristic
189	C₂×C₄×D₄₃	—	2	2	no	—
190	C₂×C₄×D₄₃	—	2	2	no	—
191	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
192	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
193	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
197	C₂×Dic₈₆	—	2	1	no	—
198	C₂×Dic₈₆	—	2	2	no	—
199	C₂×Dic₈₆	—	2	2	no	—
200	C₂×Dic₈₆	C₂²⋊C₄	1	1	yes	characteristic
201	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
202	C₂×C₈×C₄₃	—	2	1	no	—
203	C₂×C₈×C₄₃	—	2	1	no	—
204	C₂×C₈×C₄₃	—	2	1	no	—
205	C₂×C₈×C₄₃	—	2	1	no	—
206	C₄⋊C₄×C₄₃	—	2	2	no	—
207	C₄⋊C₄×C₄₃	—	2	2	no	—
208	C₄⋊C₄×C₄₃	—	2	1	no	—
209	C₄⋊C₄×C₄₃	—	2	1	no	—
210	C₄⋊C₄×C₄₃	—	2	1	no	—
211	C₄⋊C₄×C₄₃	—	2	1	no	—
212	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
214	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
215	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
216	C₂²⋊Dic₄₃	—	2	2	no	—
217	C₂²⋊Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
218	C₂²⋊Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
219	(C₂×D₄₃)⋊C₄	—	2	2	no	—
220	(C₂×D₄₃)⋊C₄	—	2	2	no	—
221	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
222	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
223	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
224	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
225	C₄⋊Dic₄₃	—	2	1	no	—
226	C₄⋊Dic₄₃	—	2	1	no	—
227	C₄⋊Dic₄₃	—	2	1	no	—
228	C₄⋊Dic₄₃	—	2	2	no	—
229	C₄⋊Dic₄₃	—	2	2	no	—
230	C₄⋊Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
231	C₄⋊Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
232	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
233	Dic₄₃⋊C₄	—	2	2	no	—
234	Dic₄₃⋊C₄	—	2	2	no	—
235	Dic₄₃⋊C₄	—	2	2	no	—
236	Dic₄₃⋊C₄	—	2	2	no	—
237	Dic₄₃⋊C₄	—	2	2	no	—
238	Dic₄₃⋊C₄	—	2	2	no	—
239	Dic₄₃⋊C₄	—	2	2	no	—
240	Dic₄₃⋊C₄	—	2	2	no	—
241	Dic₄₃⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
242	Dic₄₃⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
243	Dic₄₃⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
244	Dic₄₃⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
245	C₄×Dic₄₃	—	2	2	no	—
246	C₄×Dic₄₃	—	2	2	no	—
247	C₄×Dic₄₃	—	2	2	no	—
248	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
249	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
250	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
251	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
252	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
253	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
254	#10621877	—	8	1	no	—
255	C₂×C₄₃⋊C₈	—	2	1	no	—
256	C₂×C₄₃⋊C₈	—	2	1	no	—
257	C₂×C₄₃⋊C₈	—	2	1	no	—
258	C₂×C₄₃⋊C₈	—	2	1	no	—
259	#10621872	—	4	2	no	—
260	#10621872	—	8	1	no	—
261	C₈×D₄₃	—	4	2	no	—
262	C₈×D₄₃	—	8	1	no	—
263	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×D₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×D₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	Q₈×C₄₃	—	4	2	no	—
267	Q₈×C₄₃	—	4	2	no	—
268	Q₈×C₄₃	—	8	2	no	—
269	C₂×C₄×C₄₃	—	2	1	no	—
270	C₂×C₄×C₄₃	—	2	1	no	—
271	C₂×C₄×C₄₃	—	2	1	no	—
272	C₂×C₄×C₄₃	—	2	1	no	—
273	C₂×C₄×C₄₃	—	2	2	no	—
274	C₂×C₄×C₄₃	—	2	2	no	—
275	C₂×C₄×C₄₃	—	4	1	no	—
276	C₂×C₄×C₄₃	—	8	2	no	—
277	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
283	C₂²⋊D₄₃	—	2	2	no	—
284	C₂²⋊D₄₃	—	2	2	no	—
285	C₂×Dic₄₃	—	2	2	no	—
286	C₂×Dic₄₃	—	2	2	no	—
287	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
288	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
289	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
290	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	D₁₇₂	—	2	2	no	—
294	C₄×D₄₃	—	2	1	no	—
295	C₄×D₄₃	—	2	1	no	—
296	C₄×D₄₃	—	2	1	no	—
297	C₄×D₄₃	—	2	1	no	—
298	C₄×D₄₃	—	2	1	no	—
299	C₄×D₄₃	—	2	1	no	—
300	C₄×D₄₃	—	4	1	no	—
301	C₄×D₄₃	—	4	1	no	—
302	C₄×D₄₃	—	8	2	no	—
303	C₄×D₄₃	—	8	2	no	—
304	C₄×D₄₃	#137	1	2	yes	—
305	C₄×D₄₃	#137	1	2	yes	—
306	Dic₈₆	—	2	2	no	—
307	Dic₈₆	—	4	1	no	—
308	Dic₈₆	—	4	1	no	—
309	Dic₈₆	—	4	2	no	—
310	Dic₈₆	—	8	2	no	—
311	Dic₈₆	—	8	2	no	—
312	C₈×C₄₃	—	4	1	no	—
313	C₈×C₄₃	—	4	1	no	—
314	C₈×C₄₃	—	4	1	no	—
315	C₈×C₄₃	—	4	1	no	—
316	C₄₃⋊C₈	—	4	1	no	—
317	C₄₃⋊C₈	—	4	1	no	—
318	C₄₃⋊C₈	—	4	1	no	—
319	C₄₃⋊C₈	—	4	1	no	—
320	#17760	—	43	1	no	maximal, Sylow
321	C₂²×C₄₃	—	2	1	no	—
322	C₂²×C₄₃	—	2	1	no	—
323	C₂²×C₄₃	—	2	1	no	—
324	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
325	C₂×D₄₃	—	2	1	no	—
326	C₂×D₄₃	—	2	1	no	—
327	C₂×D₄₃	—	2	1	no	—
328	C₂×D₄₃	—	2	1	no	—
329	C₂×D₄₃	—	2	1	no	—
330	C₂×D₄₃	#419	1	2	yes	—
331	C₄×C₄₃	—	2	1	no	—
332	C₄×C₄₃	—	2	1	no	—
333	C₄×C₄₃	—	2	1	no	—
334	C₄×C₄₃	—	2	1	no	—
335	C₄×C₄₃	—	4	2	no	—
336	C₄×C₄₃	—	4	2	no	—
337	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
338	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
339	C₄×C₄₃	#577	1	1	yes	characteristic
340	C₄×C₄₃	#578	1	1	yes	characteristic
341	Dic₄₃	—	2	1	no	—
342	Dic₄₃	—	2	1	no	—
343	Dic₄₃	—	2	1	no	—
344	Dic₄₃	—	2	1	no	—
345	Dic₄₃	—	2	1	no	—
346	Dic₄₃	—	4	2	no	—
347	Dic₄₃	—	4	2	no	—
348	Dic₄₃	#419	1	2	yes	—
349	#3503	—	43	1	no	—
350	#2989	—	43	1	no	—
351	#2925	—	43	1	no	—
352	#1559	—	43	1	no	—
353	#1559	—	43	1	no	—
354	#1558	—	43	1	no	—
355	#1558	D₄₃	1	1	yes	characteristic, complemented
356	#1554	—	43	1	no	—
357	#1554	—	43	1	no	—
358	#1550	—	43	1	no	—
359	#1548	—	43	1	no	—
360	#1548	—	43	1	no	—
361	#1548	—	43	1	no	—
362	#1542	—	43	1	no	—
363	C₂×#333	—	43	1	no	—
364	C₂×C₄₃	—	4	1	no	—
365	C₂×C₄₃	#2888	1	1	yes	characteristic
366	C₂×C₄₃	C₂×#419	1	1	yes	characteristic
367	C₂×C₄₃	#2898	1	1	yes	characteristic
368	D₄₃	—	2	2	no	—
369	D₄₃	—	4	1	no	—
370	Q₈²	—	86	1	no	—
371	#557	—	43	2	no	—
372	#554	—	86	1	no	—
373	#554	—	86	1	no	—
374	#554	—	86	1	no	—
375	D₄×Q₈	—	43	2	no	—
376	D₄×Q₈	—	43	2	no	—
377	D₄×Q₈	—	43	2	no	—
378	#544	—	86	1	no	—
379	#544	—	86	1	no	—
380	#544	—	86	1	no	—
381	#533	—	43	1	no	—
382	#533	—	43	1	no	—
383	#533	—	43	1	no	—
384	C₂×C₄⋊Q₈	—	43	1	no	—
385	C₂×C₄⋊Q₈	—	43	1	no	—
386	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
387	#520	—	86	1	no	—
388	C₄×#41	—	43	1	no	—
389	#446	—	86	1	no	—
390	#436	—	86	1	no	—
391	#435	—	86	1	no	—
392	#435	—	86	1	no	—
393	#433	—	86	1	no	—
394	#433	—	86	1	no	—
395	#432	—	43	1	no	—
396	#432	—	43	1	no	—
397	#432	C₂×D₄₃	1	1	yes	characteristic
398	#432	C₂×D₄₃	1	1	yes	characteristic
399	#431	—	43	1	no	—
400	#431	—	43	1	no	—
401	#431	—	43	1	no	—
402	#423	—	43	1	no	—
403	#423	—	43	1	no	—
404	#423	—	43	1	no	—
405	C₂×C₄⋊C₈	—	43	1	no	—
406	C₂×C₄⋊C₈	—	43	1	no	—
407	#408	—	86	1	no	—
408	#405	—	86	1	no	—
409	#333	—	43	1	no	—
410	#333	—	43	1	no	—
411	#333	—	43	1	no	—
412	#333	—	43	1	no	—
413	#333	—	43	1	no	—
414	#333	—	43	1	no	—
415	#333	—	43	1	no	—
416	#333	—	43	1	no	—
417	#333	C₂×D₄₃	1	1	yes	characteristic
418	#333	C₂×D₄₃	1	1	yes	characteristic
419	#333	C₂×D₄₃	1	1	yes	characteristic
420	#333	C₂×D₄₃	1	1	yes	characteristic
421	#332	—	43	1	no	—
422	#332	—	43	1	no	—
423	#332	—	43	1	no	—
424	#332	—	43	1	no	—
425	C₄₃	#17760	1	1	yes	characteristic, complemented, Sylow
426	C₂×#41	—	43	1	no	—
427	C₂²×Q₈	—	43	2	no	—
428	C₂²×Q₈	—	43	2	no	—
429	C₂²×Q₈	C₄×D₄₃	1	2	yes	—
430	C₂×M₁₆	—	86	1	no	—
431	C₂×M₁₆	—	86	1	no	—
432	C₂×M₁₆	—	86	1	no	—
433	C₂²×C₈	—	86	1	no	—
434	C₂²×C₈	—	86	1	no	—
435	C₄⋊Q₈	—	2	1	no	—
436	C₄⋊Q₈	—	2	1	no	—
437	C₄⋊Q₈	—	43	2	no	—
438	C₄⋊Q₈	—	43	2	no	—
439	C₄⋊Q₈	—	43	1	no	—
440	C₄⋊Q₈	—	43	1	no	—
441	C₄⋊Q₈	—	86	1	no	—
442	C₄⋊Q₈	—	86	1	no	—
443	C₄⋊Q₈	—	86	1	no	—
444	C₄⋊Q₈	—	86	1	no	—
445	C₄⋊Q₈	—	86	2	no	—
446	C₄⋊Q₈	—	86	2	no	—
447	C₄⋊Q₈	—	86	2	no	—
448	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
449	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
450	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
451	#125	—	86	1	no	—
452	#125	—	86	1	no	—
453	#125	—	86	2	no	—
454	#125	—	86	2	no	—
455	#125	—	86	2	no	—
456	#125	—	86	1	no	—
457	C₂²⋊Q₈	—	43	2	no	—
458	C₂²⋊Q₈	—	43	2	no	—
459	C₂²⋊Q₈	—	43	2	no	—
460	C₂²⋊Q₈	—	86	2	no	—
461	C₂²⋊Q₈	—	86	2	no	—
462	C₂²⋊Q₈	—	86	2	no	—
463	C₂²⋊Q₈	—	86	2	no	—
464	C₂²⋊Q₈	—	86	2	no	—
465	C₂²⋊Q₈	—	86	2	no	—
466	C₂²⋊Q₈	—	86	1	no	—
467	C₂²⋊Q₈	—	86	1	no	—
468	C₂²⋊Q₈	—	86	1	no	—
469	C₄×Q₈	—	43	1	no	—
470	C₄×Q₈	—	43	1	no	—
471	C₄×Q₈	—	43	2	no	—
472	C₄×Q₈	—	43	2	no	—
473	C₄×Q₈	—	43	2	no	—
474	C₄×Q₈	—	86	1	no	—
475	C₄×Q₈	—	86	1	no	—
476	C₄×Q₈	—	86	2	no	—
477	C₄×Q₈	—	86	1	no	—
478	C₄×D₄	—	43	1	no	—
479	C₄×D₄	—	43	1	no	—
480	C₄×D₄	—	43	1	no	—
481	C₄×D₄	—	43	1	no	—
482	C₄×D₄	—	43	1	no	—
483	C₄×D₄	—	43	1	no	—
484	C₄×D₄	—	86	2	no	—
485	C₄×D₄	—	86	2	no	—
486	C₄×D₄	—	86	2	no	—
487	#117	—	43	1	no	—
488	#117	—	43	1	no	—
489	#117	—	43	1	no	—
490	#117	—	86	1	no	—
491	#117	—	86	1	no	—
492	#117	—	86	1	no	—
493	C₂×C₄⋊C₄	—	2	1	no	—
494	C₂×C₄⋊C₄	—	2	1	no	—
495	C₂×C₄⋊C₄	—	86	1	no	—
496	C₂×C₄⋊C₄	—	86	1	no	—
497	C₂×C₄⋊C₄	—	86	1	no	—
498	C₂×C₄⋊C₄	—	86	1	no	—
499	C₂×C₄²	—	43	1	no	—
500	C₂×C₄²	—	43	1	no	—
501	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
502	C₄⋊C₈	—	43	1	no	—
503	C₄⋊C₈	—	43	1	no	—
504	C₄⋊C₈	—	43	1	no	—
505	C₄⋊C₈	—	43	1	no	—
506	C₄⋊C₈	—	86	1	no	—
507	C₄⋊C₈	—	86	1	no	—
508	C₄⋊C₈	—	86	1	no	—
509	C₄⋊C₈	—	86	1	no	—
510	C₄⋊C₈	—	86	1	no	—
511	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
512	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
513	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
514	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
515	C₂²⋊C₈	—	2	1	no	—
516	C₂²⋊C₈	—	2	1	no	—
517	C₂²⋊C₈	—	86	1	no	—
518	C₂²⋊C₈	—	86	1	no	—
519	C₂²⋊C₈	—	86	1	no	—
520	C₂²⋊C₈	—	86	1	no	—
521	C₂²⋊C₈	—	86	1	no	—
522	#97	—	2	1	no	—
523	#97	—	2	1	no	—
524	#97	—	86	1	no	—
525	#97	—	86	1	no	—
526	C₄×C₈	—	86	1	no	—
527	C₄×C₈	—	86	1	no	—
528	C₄×C₈	—	86	1	no	—
529	#41	—	86	2	no	—
530	#41	—	86	2	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	8	2	no	—
533	C₂×Q₈	—	43	1	no	—
534	C₂×Q₈	—	43	2	no	—
535	C₂×Q₈	—	86	2	no	—
536	C₂×Q₈	—	86	2	no	—
537	C₂×Q₈	—	86	1	no	—
538	C₂×Q₈	—	344	2	no	—
539	C₂×Q₈	—	344	2	no	—
540	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
541	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
542	C₂×D₄	—	43	1	no	—
543	C₂×D₄	—	43	1	no	—
544	C₂×D₄	—	43	1	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	43	1	no	—
547	C₂²×C₄	—	43	1	no	—
548	C₂²×C₄	—	43	1	no	—
549	C₂²×C₄	—	43	1	no	—
550	C₂²×C₄	—	43	1	no	—
551	C₂²×C₄	—	43	1	no	—
552	C₂²×C₄	—	86	2	no	—
553	C₂²×C₄	—	86	2	no	—
554	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
555	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
556	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
557	M₁₆	—	344	1	no	—
558	M₁₆	—	344	1	no	—
559	M₁₆	—	172	2	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	86	1	no	—
565	C₂×C₈	—	86	1	no	—
566	C₂×C₈	—	86	1	no	—
567	C₂×C₈	—	86	1	no	—
568	C₂×C₈	—	344	1	no	—
569	C₂×C₈	—	172	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	43	1	no	—
577	C₄⋊C₄	—	43	1	no	—
578	C₄⋊C₄	—	43	1	no	—
579	C₄⋊C₄	—	43	1	no	—
580	C₄⋊C₄	—	43	1	no	—
581	C₄⋊C₄	—	43	1	no	—
582	C₄⋊C₄	—	43	2	no	—
583	C₄⋊C₄	—	86	2	no	—
584	C₄⋊C₄	—	86	2	no	—
585	C₄⋊C₄	—	86	2	no	—
586	C₄⋊C₄	—	86	2	no	—
587	C₄⋊C₄	—	86	2	no	—
588	C₄⋊C₄	—	86	2	no	—
589	C₄⋊C₄	—	86	2	no	—
590	C₄⋊C₄	—	86	2	no	—
591	C₄⋊C₄	—	86	2	no	—
592	C₄⋊C₄	—	86	2	no	—
593	C₄⋊C₄	—	86	1	no	—
594	C₄⋊C₄	—	86	1	no	—
595	C₄⋊C₄	—	86	1	no	—
596	C₂²⋊C₄	—	43	1	no	—
597	C₂²⋊C₄	—	43	1	no	—
598	C₂²⋊C₄	—	43	1	no	—
599	C₂²⋊C₄	—	43	1	no	—
600	C₂²⋊C₄	—	43	1	no	—
601	C₂²⋊C₄	—	43	1	no	—
602	C₂²⋊C₄	—	86	2	no	—
603	C₂²⋊C₄	—	86	2	no	—
604	C₂²⋊C₄	—	86	2	no	—
605	C₄²	—	43	1	no	—
606	C₄²	—	43	1	no	—
607	C₄²	—	43	1	no	—
608	C₄²	—	43	1	no	—
609	C₄²	—	43	1	no	—
610	C₄²	—	43	1	no	—
611	C₄²	—	86	2	no	—
612	C₄²	—	86	2	no	—
613	C₄²	—	86	2	no	—
614	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
615	C₄²	D₄×D₄₃	1	1	yes	characteristic
616	C₄²	D₄×D₄₃	1	1	yes	characteristic
617	C₄²	C₂³×D₄₃	1	1	yes	characteristic
618	C₂³	—	43	1	no	—
619	C₂³	—	43	1	no	—
620	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
621	Q₈	—	4	2	no	—
622	Q₈	—	4	2	no	—
623	Q₈	—	8	2	no	—
624	Q₈	—	86	2	no	—
625	Q₈	—	344	2	no	—
626	Q₈	—	344	2	no	—
627	Q₈	—	172	2	no	—
628	Q₈	—	172	1	no	—
629	Q₈	—	172	1	no	—
630	D₄	—	86	2	no	—
631	D₄	—	86	2	no	—
632	D₄	—	86	2	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	8	2	no	—
641	C₂×C₄	—	43	1	no	—
642	C₂×C₄	—	43	2	no	—
643	C₂×C₄	—	43	2	no	—
644	C₂×C₄	—	43	1	no	—
645	C₂×C₄	—	43	1	no	—
646	C₂×C₄	—	43	1	no	—
647	C₂×C₄	—	43	1	no	—
648	C₂×C₄	—	43	1	no	—
649	C₂×C₄	—	86	1	no	—
650	C₂×C₄	—	86	1	no	—
651	C₂×C₄	—	86	1	no	—
652	C₂×C₄	—	86	1	no	—
653	C₂×C₄	—	86	1	no	—
654	C₂×C₄	—	86	1	no	—
655	C₂×C₄	—	86	2	no	—
656	C₂×C₄	—	86	2	no	—
657	C₂×C₄	—	344	2	no	—
658	C₂×C₄	—	344	2	no	—
659	C₂×C₄	—	172	1	no	—
660	C₂×C₄	—	172	1	no	—
661	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
662	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
663	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
664	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
665	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
666	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
667	C₈	—	4	1	no	—
668	C₈	—	4	1	no	—
669	C₈	—	4	1	no	—
670	C₈	—	4	1	no	—
671	C₈	—	172	1	no	—
672	C₈	—	172	1	no	—
673	C₈	—	172	1	no	—
674	C₈	—	172	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	2	1	no	—
678	C₂²	—	43	2	no	—
679	C₂²	—	86	1	no	—
680	C₂²	—	86	1	no	—
681	C₂²	—	86	1	no	—
682	C₂²	—	86	1	no	—
683	C₂²	—	86	1	no	—
684	C₂²	C₂×C₂²⋊C₄×D₄₃	1	1	yes	characteristic
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	1	no	—
688	C₄	—	2	1	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	43	2	no	—
692	C₄	—	86	1	no	—
693	C₄	—	86	1	no	—
694	C₄	—	86	1	no	—
695	C₄	—	86	1	no	—
696	C₄	—	86	1	no	—
697	C₄	—	172	2	no	—
698	C₄	—	172	2	no	—
699	C₄	#137×D₄₃	1	1	yes	characteristic
700	C₄	#137×D₄₃	1	1	yes	characteristic
701	C₄	#14583708	1	1	yes	characteristic
702	C₄	#14583715	1	1	yes	characteristic
703	C₂	—	4	1	no	—
704	C₂	—	86	2	no	—
705	C₂	—	172	1	no	—
706	C₂	#19143071	1	1	yes	characteristic
707	C₂	#419×D₄₃	1	1	yes	characteristic
708	C₂	#19143127	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊C₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1558	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#10621898	D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1558	D₄₃
hypocenter	C₄₃	#17760
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1558

Complements

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

N	H ≅ G/N	type
4. #19133326	C₂	semidirect
5. #19133322	C₂	semidirect
6. #19133319	C₂	semidirect
7. #19133306	C₂	semidirect
8. #19133304	C₂	semidirect
9. #19133282	C₂	semidirect
10. #19133276	C₂	semidirect
11. #19133274	C₂	semidirect
12. #19133274	C₂	semidirect
13. #19133249	C₂	semidirect
14. #333×D₄₃	C₂	semidirect
15. C₄₃×#1558	C₂	semidirect
355. #1558	D₄₃	semidirect
425. C₄₃	#17760	semidirect

Maximal subgroups

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

subgroup	index
#19148411	2
#19143714	2
#19143262	2
#19133326	2
#19133322	2
#19133319	2
#19133306	2
#19133304	2
#19133282	2
#19133276	2
#19133274	2
#19133249	2
#333×D₄₃	2
C₄₃×#1558	2
#17760	43