Subgroups — #25065495

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148506	C₂	1	1	yes	maximal, characteristic
2	#19143720	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133323	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133318	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133313	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133306	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133298	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133291	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133288	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133283	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133273	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133250	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133245	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14582646	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583622	—	2	1	no	—
17	#14583614	—	2	1	no	—
18	#14583609	—	2	1	no	—
19	#14583595	—	2	1	no	—
20	#14583595	—	2	1	no	—
21	#14583558	—	2	1	no	—
22	#14583558	—	2	1	no	—
23	#14583554	—	2	1	no	—
24	#14583520	C₄	1	2	yes	—
25	#14583520	C₄	1	2	yes	—
26	#14583477	C₄	1	2	yes	—
27	#14583456	C₂²	1	1	yes	characteristic
28	#14583456	C₂²	1	1	yes	characteristic
29	#14583449	C₂²	1	1	yes	characteristic
30	#14583449	C₂²	1	1	yes	characteristic
31	#14583449	C₂²	1	1	yes	characteristic
32	C₂×#13063325	C₂²	1	1	yes	characteristic
33	#14583379	C₄	1	2	yes	—
34	#14583030	—	2	1	no	—
35	#14582971	—	2	1	no	—
36	#14582971	—	2	1	no	—
37	D₄×C₄₃⋊C₈	—	2	1	no	—
38	#14582956	C₂²	1	1	yes	characteristic
39	#14582956	C₂²	1	1	yes	characteristic
40	#14582952	C₂²	1	1	yes	characteristic
41	#14582923	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
44	#14582647	C₂²	1	1	yes	characteristic
45	#14582647	C₂²	1	1	yes	characteristic
46	#14582647	C₂²	1	1	yes	characteristic
47	#14582647	C₂²	1	1	yes	characteristic
48	#14582646	C₂²	1	1	yes	characteristic
49	#14582646	C₂²	1	1	yes	characteristic
50	#14582646	C₂²	1	1	yes	characteristic
51	#14582646	C₂²	1	1	yes	characteristic
52	#14582646	C₂²	1	1	yes	characteristic
53	#14582646	C₂²	1	1	yes	characteristic
54	#14582646	C₂²	1	1	yes	characteristic
55	#14582646	C₂²	1	1	yes	characteristic
56	#14582642	C₂²	1	1	yes	characteristic
57	#14582642	C₂²	1	1	yes	characteristic
58	#14582642	C₂²	1	1	yes	characteristic
59	#14582642	C₂²	1	1	yes	characteristic
60	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
61	C₄₃×#446	—	2	1	no	—
62	C₄₃×#435	—	2	1	no	—
63	C₄₃×#435	—	2	1	no	—
64	C₈×D₄×C₄₃	—	2	1	no	—
65	C₄₃×#432	C₂²	1	1	yes	characteristic
66	C₄₃×#432	C₂²	1	1	yes	characteristic
67	C₄₃×#431	C₂²	1	1	yes	characteristic
68	C₄₃×#423	C₂²	1	1	yes	characteristic
69	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
71	C₂×#10621898	—	2	1	no	—
72	C₂×#10621898	—	2	1	no	—
73	C₂×#10621898	C₂×C₄	1	2	yes	—
74	C₂²×Dic₈₆	—	2	1	no	—
75	C₂×#10621877	—	2	1	no	—
76	C₂²×C₄₃⋊C₈	—	2	1	no	—
77	C₂²×C₄₃⋊C₈	—	2	1	no	—
78	#13063325	—	2	1	no	—
79	#13063325	—	2	1	no	—
80	#13063325	C₂×C₄	1	2	yes	—
81	#13063325	C₂³	1	1	yes	characteristic
82	#13063325	C₂³	1	1	yes	characteristic
83	#13063325	C₂³	1	1	yes	characteristic
84	#13063322	C₂³	1	1	yes	characteristic
85	#13063320	—	2	2	no	—
86	#13063320	—	2	2	no	—
87	#13063317	—	2	1	no	—
88	#13063317	—	2	1	no	—
89	#13063313	—	2	1	no	—
90	#13063313	—	2	1	no	—
91	#13063313	C₂×C₄	1	2	yes	—
92	#13063311	—	2	2	no	—
93	#13063311	—	2	2	no	—
94	#13063307	—	2	2	no	—
95	#13063307	—	2	2	no	—
96	#13063304	—	2	1	no	—
97	#13063304	—	2	1	no	—
98	#13063304	C₂×C₄	1	2	yes	—
99	#13063304	C₂×C₄	1	2	yes	—
100	#13063303	—	2	2	no	—
101	#13063303	—	2	2	no	—
102	#13063301	—	2	2	no	—
103	#13063299	—	2	1	no	—
104	#13063299	—	2	1	no	—
105	#13063299	—	2	1	no	—
106	#13063299	—	2	1	no	—
107	#13063299	C₂×C₄	1	2	yes	—
108	#13063299	C₂×C₄	1	2	yes	—
109	#13063297	—	2	2	no	—
110	#13063297	—	2	2	no	—
111	#13063296	—	2	2	no	—
112	C₄×Dic₈₆	—	2	1	no	—
113	C₄×Dic₈₆	—	2	1	no	—
114	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
115	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
116	C₄×D₁₇₂	—	2	1	no	—
117	C₄×D₁₇₂	—	2	1	no	—
118	C₄×D₁₇₂	—	2	1	no	—
119	C₄×D₁₇₂	—	2	1	no	—
120	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
121	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
122	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
123	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
124	#13063284	—	2	1	no	—
125	#13063284	—	2	1	no	—
126	#13063283	—	2	2	no	—
127	C₂×C₄⋊Dic₄₃	—	2	1	no	—
128	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
129	C₄⋊C₄×D₄₃	—	2	2	no	—
130	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
131	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
132	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
133	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
134	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
135	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
136	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
137	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
138	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
139	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
140	#13063236	—	2	1	no	—
141	#13063236	—	2	1	no	—
142	C₄×C₄₃⋊C₈	—	2	1	no	—
143	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
144	C₂×M₁₆×C₄₃	—	2	1	no	—
145	C₂²×C₈×C₄₃	—	2	1	no	—
146	C₂²×C₈×C₄₃	—	2	1	no	—
147	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
149	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
150	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
151	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
152	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
153	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
154	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
155	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
156	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
157	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
158	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
160	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
161	C₄⋊C₈×C₄₃	—	2	1	no	—
162	C₄⋊C₈×C₄₃	—	2	1	no	—
163	C₄⋊C₈×C₄₃	—	2	1	no	—
164	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
165	C₄⋊C₈×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	C₂²⋊C₈×C₄₃	—	2	1	no	—
169	C₂²⋊C₈×C₄₃	—	2	1	no	—
170	C₂²⋊C₈×C₄₃	—	2	1	no	—
171	#97×C₄₃	—	2	1	no	—
172	#97×C₄₃	—	2	1	no	—
173	C₄×C₈×C₄₃	—	2	1	no	—
174	#41×C₄₃	—	4	2	no	—
175	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₂²⋊D₄₃	—	2	2	no	—
189	C₂×C₂²⋊D₄₃	—	2	2	no	—
190	C₂×C₂²⋊D₄₃	—	2	2	no	—
191	C₂²×Dic₄₃	—	2	2	no	—
192	#10621898	—	4	4	no	—
193	#10621898	—	8	1	no	—
194	#10621898	—	8	1	no	—
195	#10621898	—	8	1	no	—
196	#10621898	—	8	1	no	—
197	C₂×D₁₇₂	—	2	1	no	—
198	C₂×D₁₇₂	—	2	1	no	—
199	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
200	C₂×C₄×D₄₃	—	2	2	no	—
201	C₂×C₄×D₄₃	—	2	2	no	—
202	C₂×C₄×D₄₃	—	2	2	no	—
203	C₂×Dic₈₆	—	2	1	no	—
204	C₂×Dic₈₆	—	2	1	no	—
205	C₂×Dic₈₆	—	2	2	no	—
206	C₂×Dic₈₆	—	8	1	no	—
207	C₂×Dic₈₆	—	8	1	no	—
208	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
209	M₁₆×C₄₃	—	8	1	no	—
210	C₂×C₈×C₄₃	—	2	1	no	—
211	C₂×C₈×C₄₃	—	2	1	no	—
212	C₂×C₈×C₄₃	—	2	1	no	—
213	C₂×C₈×C₄₃	—	2	1	no	—
214	C₂×C₈×C₄₃	—	8	1	no	—
215	C₂×C₈×C₄₃	—	8	1	no	—
216	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
217	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
218	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
219	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
220	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
221	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
222	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
223	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
224	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
225	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
226	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
227	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
228	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
229	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
230	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
231	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
237	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂²⋊Dic₄₃	—	2	2	no	—
239	C₂²⋊Dic₄₃	—	2	2	no	—
240	(C₂×D₄₃)⋊C₄	—	2	2	no	—
241	(C₂×D₄₃)⋊C₄	—	2	2	no	—
242	(C₂×D₄₃)⋊C₄	—	2	2	no	—
243	(C₂×D₄₃)⋊C₄	—	2	2	no	—
244	(C₂×D₄₃)⋊C₄	—	2	2	no	—
245	(C₂×D₄₃)⋊C₄	—	2	2	no	—
246	C₄⋊Dic₄₃	—	2	2	no	—
247	C₄⋊Dic₄₃	—	2	2	no	—
248	C₄⋊Dic₄₃	—	2	1	no	—
249	C₄⋊Dic₄₃	—	2	1	no	—
250	C₄⋊Dic₄₃	—	2	1	no	—
251	C₄⋊Dic₄₃	—	2	1	no	—
252	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
253	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
254	Dic₄₃⋊C₄	—	2	2	no	—
255	Dic₄₃⋊C₄	—	2	2	no	—
256	Dic₄₃⋊C₄	—	2	2	no	—
257	Dic₄₃⋊C₄	—	2	2	no	—
258	C₄×Dic₄₃	—	2	2	no	—
259	C₄×Dic₄₃	—	2	2	no	—
260	#10621877	—	8	1	no	—
261	C₂×C₄₃⋊C₈	—	2	1	no	—
262	C₂×C₄₃⋊C₈	—	2	1	no	—
263	C₂×C₄₃⋊C₈	—	2	1	no	—
264	C₂×C₄₃⋊C₈	—	2	1	no	—
265	C₂×C₄₃⋊C₈	—	8	1	no	—
266	C₂×C₄₃⋊C₈	—	8	1	no	—
267	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂²×D₄₃	—	2	2	no	—
271	Q₈×C₄₃	—	4	1	no	—
272	D₄×C₄₃	—	2	2	no	—
273	D₄×C₄₃	—	2	2	no	—
274	D₄×C₄₃	—	4	1	no	—
275	C₂×C₄×C₄₃	—	2	2	no	—
276	C₂×C₄×C₄₃	—	2	1	no	—
277	C₂×C₄×C₄₃	—	2	1	no	—
278	C₂×C₄×C₄₃	—	2	1	no	—
279	C₂×C₄×C₄₃	—	2	1	no	—
280	C₂×C₄×C₄₃	—	2	1	no	—
281	C₂×C₄×C₄₃	—	2	1	no	—
282	C₂×C₄×C₄₃	—	2	1	no	—
283	C₂×C₄×C₄₃	—	2	1	no	—
284	C₂×C₄×C₄₃	—	2	1	no	—
285	C₂×C₄×C₄₃	—	2	1	no	—
286	C₂×C₄×C₄₃	—	2	1	no	—
287	C₂×C₄×C₄₃	—	2	1	no	—
288	C₂×C₄×C₄₃	—	4	1	no	—
289	C₂×C₄×C₄₃	—	4	1	no	—
290	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
291	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
298	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
300	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
302	C₂²⋊D₄₃	—	4	4	no	—
303	C₂²⋊D₄₃	—	8	2	no	—
304	C₂²⋊D₄₃	—	8	2	no	—
305	C₂×Dic₄₃	—	2	2	no	—
306	C₂×Dic₄₃	—	2	2	no	—
307	C₂×Dic₄₃	—	2	2	no	—
308	C₂×Dic₄₃	—	8	2	no	—
309	D₁₇₂	—	4	2	no	—
310	D₁₇₂	—	4	1	no	—
311	D₁₇₂	—	4	1	no	—
312	D₁₇₂	—	4	1	no	—
313	D₁₇₂	—	4	1	no	—
314	C₄×D₄₃	—	4	4	no	—
315	C₄×D₄₃	—	8	2	no	—
316	C₄×D₄₃	—	8	2	no	—
317	Dic₈₆	—	4	1	no	—
318	Dic₈₆	—	4	1	no	—
319	Dic₈₆	—	4	1	no	—
320	Dic₈₆	—	4	1	no	—
321	Dic₈₆	—	4	2	no	—
322	Dic₈₆	—	8	2	no	—
323	C₈×C₄₃	—	4	1	no	—
324	C₈×C₄₃	—	4	1	no	—
325	C₈×C₄₃	—	4	1	no	—
326	C₈×C₄₃	—	4	1	no	—
327	C₄₃⋊C₈	—	4	1	no	—
328	C₄₃⋊C₈	—	4	1	no	—
329	C₄₃⋊C₈	—	4	1	no	—
330	C₄₃⋊C₈	—	4	1	no	—
331	#17775	—	43	1	no	maximal, Sylow
332	C₂²×C₄₃	—	2	1	no	—
333	C₂²×C₄₃	—	2	1	no	—
334	C₂²×C₄₃	—	2	1	no	—
335	C₂²×C₄₃	—	2	1	no	—
336	C₂²×C₄₃	—	2	1	no	—
337	C₂²×C₄₃	—	2	1	no	—
338	C₂²×C₄₃	—	2	1	no	—
339	C₂²×C₄₃	—	2	1	no	—
340	C₂²×C₄₃	#413	1	2	yes	—
341	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×D₄₃	—	4	2	no	—
343	C₂×D₄₃	—	4	2	no	—
344	C₂×D₄₃	—	4	2	no	—
345	C₄×C₄₃	—	2	1	no	—
346	C₄×C₄₃	—	2	1	no	—
347	C₄×C₄₃	—	2	1	no	—
348	C₄×C₄₃	—	2	1	no	—
349	C₄×C₄₃	—	2	1	no	—
350	C₄×C₄₃	—	2	1	no	—
351	C₄×C₄₃	—	2	1	no	—
352	C₄×C₄₃	—	2	1	no	—
353	C₄×C₄₃	—	2	1	no	—
354	C₄×C₄₃	—	2	1	no	—
355	C₄×C₄₃	#576	1	1	yes	characteristic
356	C₄×C₄₃	#577	1	1	yes	characteristic
357	C₄×C₄₃	#577	1	1	yes	characteristic
358	C₄×C₄₃	#578	1	1	yes	characteristic
359	Dic₄₃	—	4	2	no	—
360	Dic₄₃	—	4	2	no	—
361	Dic₄₃	—	4	2	no	—
362	#3511	—	43	1	no	—
363	#2990	—	43	1	no	—
364	#2990	D₄₃	1	1	yes	characteristic, complemented
365	#1559	—	43	1	no	—
366	#1557	—	43	1	no	—
367	#1556	—	43	1	no	—
368	#1554	—	43	1	no	—
369	#1553	—	43	1	no	—
370	#1551	—	43	1	no	—
371	#1551	—	43	1	no	—
372	#1550	—	43	1	no	—
373	#1547	—	43	1	no	—
374	#1542	—	43	1	no	—
375	#1540	—	43	1	no	—
376	C₂×#332	—	43	1	no	—
377	C₂×C₄₃	—	2	2	no	—
378	C₂×C₄₃	—	4	1	no	—
379	C₂×C₄₃	—	4	1	no	—
380	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
381	C₂×C₄₃	#2897	1	1	yes	characteristic
382	C₂×C₄₃	#2898	1	1	yes	characteristic
383	D₄₃	—	8	2	no	—
384	#556	—	86	1	no	—
385	#555	—	86	1	no	—
386	#554	—	86	1	no	—
387	#553	—	86	1	no	—
388	#553	—	86	1	no	—
389	#548	—	86	1	no	—
390	#548	—	86	1	no	—
391	#547	—	86	1	no	—
392	#542	—	43	2	no	—
393	#542	—	43	2	no	—
394	#537	—	43	2	no	—
395	#533	—	43	1	no	—
396	#533	—	43	1	no	—
397	#532	—	43	1	no	—
398	#532	—	43	1	no	—
399	#532	—	43	1	no	—
400	C₂×C₄⋊Q₈	—	43	1	no	—
401	#520	—	43	2	no	—
402	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
403	#446	—	2	1	no	—
404	#446	—	86	1	no	—
405	#435	—	2	1	no	—
406	#435	—	2	1	no	—
407	#435	—	86	1	no	—
408	#435	—	86	1	no	—
409	C₈×D₄	—	2	1	no	—
410	C₈×D₄	—	86	1	no	—
411	#432	—	43	1	no	—
412	#432	—	43	1	no	—
413	#432	C₂×D₄₃	1	1	yes	characteristic
414	#432	C₂×D₄₃	1	1	yes	characteristic
415	#431	—	43	1	no	—
416	#431	C₂×D₄₃	1	1	yes	characteristic
417	#423	—	43	1	no	—
418	#423	C₂×D₄₃	1	1	yes	characteristic
419	C₂×C₄⋊C₈	—	43	1	no	—
420	C₂×C₄⋊C₈	—	43	1	no	—
421	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
422	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
423	#333	—	43	1	no	—
424	#333	—	43	1	no	—
425	#333	—	43	1	no	—
426	#333	—	43	1	no	—
427	#332	—	43	1	no	—
428	#332	—	43	1	no	—
429	#332	—	43	1	no	—
430	#332	—	43	1	no	—
431	#332	—	43	1	no	—
432	#332	—	43	1	no	—
433	#332	—	43	1	no	—
434	#332	—	43	1	no	—
435	#331	—	43	1	no	—
436	#331	—	43	1	no	—
437	#331	—	43	1	no	—
438	#331	—	43	1	no	—
439	C₄₃	#17775	1	1	yes	characteristic, complemented, Sylow
440	C₂×#41	—	43	2	no	—
441	C₂×#41	—	86	1	no	—
442	C₂×#41	—	86	1	no	—
443	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
444	C₂²×Q₈	—	86	1	no	—
445	C₂×M₁₆	—	2	1	no	—
446	C₂×M₁₆	—	86	1	no	—
447	C₂²×C₈	—	2	1	no	—
448	C₂²×C₈	—	2	1	no	—
449	C₂²×C₈	—	86	1	no	—
450	C₂²×C₈	—	86	1	no	—
451	C₄⋊Q₈	—	43	2	no	—
452	C₄⋊Q₈	—	43	1	no	—
453	C₄⋊Q₈	—	43	1	no	—
454	C₄⋊Q₈	—	43	1	no	—
455	C₄⋊Q₈	—	86	1	no	—
456	C₄⋊Q₈	—	86	1	no	—
457	#127	—	43	1	no	—
458	#126	—	86	2	no	—
459	#126	—	86	2	no	—
460	#125	—	86	1	no	—
461	#125	—	86	1	no	—
462	#124	—	43	2	no	—
463	#124	—	86	2	no	—
464	#124	—	86	2	no	—
465	#124	—	86	1	no	—
466	#124	—	86	1	no	—
467	#123	—	86	2	no	—
468	#123	—	86	2	no	—
469	C₂²⋊Q₈	—	43	2	no	—
470	C₂²⋊Q₈	—	43	2	no	—
471	C₂²⋊Q₈	—	86	2	no	—
472	C₂²⋊Q₈	—	86	1	no	—
473	C₂²⋊Q₈	—	86	1	no	—
474	C₂²⋊Q₈	—	86	2	no	—
475	C₂²⋊Q₈	—	86	2	no	—
476	#121	—	43	2	no	—
477	#121	—	43	2	no	—
478	#121	—	86	2	no	—
479	#121	—	86	2	no	—
480	#121	—	86	2	no	—
481	#121	—	86	1	no	—
482	#121	—	86	1	no	—
483	#121	—	86	1	no	—
484	#121	—	86	1	no	—
485	C₄×Q₈	—	43	2	no	—
486	C₄×Q₈	—	43	2	no	—
487	C₄×Q₈	—	86	1	no	—
488	C₄×Q₈	—	86	1	no	—
489	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
490	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
491	C₄×D₄	—	43	2	no	—
492	C₄×D₄	—	43	2	no	—
493	C₄×D₄	—	86	2	no	—
494	C₄×D₄	—	86	2	no	—
495	C₄×D₄	—	86	1	no	—
496	C₄×D₄	—	86	1	no	—
497	C₄×D₄	—	86	1	no	—
498	C₄×D₄	—	86	1	no	—
499	C₄×D₄	D₁₇₂	1	1	yes	characteristic
500	C₄×D₄	D₁₇₂	1	1	yes	characteristic
501	C₄×D₄	D₁₇₂	1	1	yes	characteristic
502	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
503	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
504	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
505	#117	—	86	1	no	—
506	#117	—	86	1	no	—
507	#117	—	86	2	no	—
508	#117	C₄×D₄₃	1	1	yes	characteristic
509	#117	C₄×D₄₃	1	1	yes	characteristic
510	#117	C₄×D₄₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	43	2	no	—
512	C₂×C₄⋊C₄	—	86	1	no	—
513	C₂×C₄⋊C₄	—	86	2	no	—
514	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
515	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
516	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
517	C₄⋊C₈	—	2	1	no	—
518	C₄⋊C₈	—	2	1	no	—
519	C₄⋊C₈	—	2	1	no	—
520	C₄⋊C₈	—	43	1	no	—
521	C₄⋊C₈	—	43	1	no	—
522	C₄⋊C₈	—	43	1	no	—
523	C₄⋊C₈	—	43	1	no	—
524	C₄⋊C₈	—	86	1	no	—
525	C₄⋊C₈	—	86	1	no	—
526	C₄⋊C₈	—	86	1	no	—
527	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
528	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
529	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
530	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
531	C₂²⋊C₈	—	2	1	no	—
532	C₂²⋊C₈	—	2	1	no	—
533	C₂²⋊C₈	—	2	1	no	—
534	C₂²⋊C₈	—	86	1	no	—
535	C₂²⋊C₈	—	86	1	no	—
536	C₂²⋊C₈	—	86	1	no	—
537	#97	—	2	1	no	—
538	#97	—	2	1	no	—
539	#97	—	86	1	no	—
540	#97	—	86	1	no	—
541	C₄×C₈	—	2	1	no	—
542	C₄×C₈	—	86	1	no	—
543	#41	—	4	2	no	—
544	#41	—	344	1	no	—
545	#41	—	344	1	no	—
546	#41	—	344	1	no	—
547	#41	—	344	1	no	—
548	#41	—	172	4	no	—
549	C₂×Q₈	—	43	2	no	—
550	C₂×Q₈	—	86	2	no	—
551	C₂×Q₈	—	86	1	no	—
552	C₂×Q₈	—	86	1	no	—
553	C₂×Q₈	—	344	1	no	—
554	C₂×Q₈	—	344	1	no	—
555	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
556	C₂×D₄	—	43	2	no	—
557	C₂×D₄	—	86	2	no	—
558	C₂×D₄	—	86	2	no	—
559	C₂×D₄	—	86	2	no	—
560	C₂×D₄	—	86	1	no	—
561	C₂×D₄	—	86	1	no	—
562	C₂×D₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
563	C₂×D₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
564	C₂×D₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
565	C₂²×C₄	—	86	2	no	—
566	C₂²×C₄	—	86	2	no	—
567	C₂²×C₄	—	86	2	no	—
568	C₂²×C₄	—	86	2	no	—
569	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
571	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
572	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
574	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
575	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
576	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
577	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
578	M₁₆	—	8	1	no	—
579	M₁₆	—	344	1	no	—
580	C₂×C₈	—	2	1	no	—
581	C₂×C₈	—	2	1	no	—
582	C₂×C₈	—	2	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	8	1	no	—
585	C₂×C₈	—	8	1	no	—
586	C₂×C₈	—	86	1	no	—
587	C₂×C₈	—	86	1	no	—
588	C₂×C₈	—	86	1	no	—
589	C₂×C₈	—	86	1	no	—
590	C₂×C₈	—	344	1	no	—
591	C₂×C₈	—	344	1	no	—
592	C₄⋊C₄	—	43	2	no	—
593	C₄⋊C₄	—	43	2	no	—
594	C₄⋊C₄	—	86	2	no	—
595	C₄⋊C₄	—	86	2	no	—
596	C₄⋊C₄	—	86	2	no	—
597	C₄⋊C₄	—	86	2	no	—
598	C₄⋊C₄	—	86	2	no	—
599	C₄⋊C₄	—	86	2	no	—
600	C₄⋊C₄	—	86	1	no	—
601	C₄⋊C₄	—	86	1	no	—
602	C₄⋊C₄	—	86	1	no	—
603	C₄⋊C₄	—	86	1	no	—
604	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
605	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
606	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
607	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
608	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
609	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
610	C₂²⋊C₄	—	86	2	no	—
611	C₂²⋊C₄	—	86	2	no	—
612	C₂²⋊C₄	—	86	2	no	—
613	C₂²⋊C₄	—	86	2	no	—
614	C₂²⋊C₄	—	86	2	no	—
615	C₂²⋊C₄	—	86	2	no	—
616	C₂²⋊C₄	—	86	2	no	—
617	C₂²⋊C₄	—	86	2	no	—
618	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
619	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
620	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
621	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
622	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
623	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
624	C₄²	—	86	2	no	—
625	C₄²	—	86	2	no	—
626	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
627	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
628	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
629	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
630	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
631	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
632	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
633	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
634	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
635	C₄²	C₂³×D₄₃	1	1	yes	characteristic
636	C₂³	—	86	2	no	—
637	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
638	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
639	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
640	Q₈	—	4	1	no	—
641	Q₈	—	344	2	no	—
642	Q₈	—	172	2	no	—
643	Q₈	—	172	1	no	—
644	Q₈	—	172	1	no	—
645	Q₈	—	172	1	no	—
646	Q₈	—	172	1	no	—
647	D₄	—	2	2	no	—
648	D₄	—	2	2	no	—
649	D₄	—	4	1	no	—
650	D₄	—	344	2	no	—
651	D₄	—	344	2	no	—
652	D₄	—	172	2	no	—
653	D₄	—	172	4	no	—
654	D₄	—	172	1	no	—
655	D₄	—	172	1	no	—
656	D₄	—	172	1	no	—
657	D₄	—	172	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	86	2	no	—
674	C₂×C₄	—	86	2	no	—
675	C₂×C₄	—	86	2	no	—
676	C₂×C₄	—	344	2	no	—
677	C₂×C₄	—	344	2	no	—
678	C₂×C₄	—	344	2	no	—
679	C₂×C₄	—	172	4	no	—
680	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
681	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
682	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
683	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
684	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
685	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
686	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
687	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
688	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
689	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
690	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
691	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
692	C₈	—	4	1	no	—
693	C₈	—	4	1	no	—
694	C₈	—	4	1	no	—
695	C₈	—	4	1	no	—
696	C₈	—	172	1	no	—
697	C₈	—	172	1	no	—
698	C₈	—	172	1	no	—
699	C₈	—	172	1	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	1	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	2	1	no	—
708	C₂²	—	172	2	no	—
709	C₂²	—	172	2	no	—
710	C₂²	—	172	2	no	—
711	C₂²	#14582881	1	2	yes	—
712	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
713	C₄	—	2	1	no	—
714	C₄	—	2	1	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	1	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	1	no	—
720	C₄	—	2	1	no	—
721	C₄	—	2	1	no	—
722	C₄	—	2	1	no	—
723	C₄	—	172	2	no	—
724	C₄	—	172	2	no	—
725	C₄	—	172	2	no	—
726	C₄	#14583702	1	1	yes	characteristic
727	C₄	#14583707	1	1	yes	characteristic
728	C₄	#14583711	1	1	yes	characteristic
729	C₄	#14583716	1	1	yes	characteristic
730	C₂	—	2	2	no	—
731	C₂	—	4	1	no	—
732	C₂	—	4	1	no	—
733	C₂	—	344	2	no	—
734	C₂	C₂×#14582881	1	1	yes	characteristic
735	C₂	#19143118	1	1	yes	characteristic
736	C₂	#19143129	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2990	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	#19148506	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2990	D₄₃
hypocenter	C₄₃	#17775
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
2. #19143720	C₂	semidirect
3. #19133323	C₂	semidirect
4. #19133318	C₂	semidirect
5. #19133313	C₂	semidirect
6. #19133306	C₂	semidirect
7. #19133298	C₂	semidirect
8. #19133291	C₂	semidirect
9. #19133288	C₂	semidirect
10. #19133283	C₂	semidirect
11. #19133273	C₂	semidirect
12. #19133250	C₂	semidirect
13. #19133245	C₂	semidirect
14. C₂×#14582646	C₂	semidirect
15. C₄₃×#2990	C₂	semidirect
364. #2990	D₄₃	semidirect
439. C₄₃	#17775	semidirect

Maximal subgroups

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

subgroup	index
#19148506	2
#19143720	2
#19133323	2
#19133318	2
#19133313	2
#19133306	2
#19133298	2
#19133291	2
#19133288	2
#19133283	2
#19133273	2
#19133250	2
#19133245	2
C₂×#14582646	2
C₄₃×#2990	2
#17775	43