Subgroups — #25106035

Order 11008.

1006 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583453	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582961	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582959	C₂	1	1	yes	maximal, characteristic
4	#19135535	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135533	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135533	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135532	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135530	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135529	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135529	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134665	C₂	1	1	yes	maximal, characteristic
12	#19134665	C₂	1	1	yes	maximal, characteristic
13	#19134662	C₂	1	1	yes	maximal, characteristic
14	#19134662	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583453	—	2	4	no	—
17	#14583453	—	2	4	no	—
18	C₂×#13063324	C₄	1	1	yes	characteristic
19	C₂×#13063323	C₄	1	1	yes	characteristic
20	C₂×#13063315	C₄	1	1	yes	characteristic
21	C₂×#13063315	C₄	1	1	yes	characteristic
22	C₂×#13063305	C₄	1	1	yes	characteristic
23	C₂×#13063303	C₄	1	1	yes	characteristic
24	C₂×#13063303	C₄	1	1	yes	characteristic
25	C₂×#13063301	C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
29	C₂×#13063282	C₂²	1	1	yes	characteristic
30	C₂×#13063282	C₂²	1	1	yes	characteristic
31	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
32	#14582961	—	2	4	no	—
33	#14582959	—	2	4	no	—
34	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×#13063235	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
44	#14582654	C₂²	1	1	yes	characteristic
45	#14582654	C₂²	1	1	yes	characteristic
46	#14582654	C₂²	1	1	yes	characteristic
47	#14582654	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	#14582653	C₂²	1	1	yes	characteristic
51	#14582653	C₂²	1	1	yes	characteristic
52	#14582653	C₂²	1	1	yes	characteristic
53	#14582653	C₂²	1	1	yes	characteristic
54	#14582653	C₂²	1	1	yes	characteristic
55	#14582653	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
58	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₄₃×#336	C₂²	1	1	yes	characteristic
62	C₄₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
65	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
73	#13063324	—	2	4	no	—
74	#13063323	—	2	4	no	—
75	#13063315	—	2	4	no	—
76	#13063315	—	2	4	no	—
77	#13063305	—	2	4	no	—
78	#13063303	—	2	4	no	—
79	#13063303	—	2	4	no	—
80	#13063301	—	2	4	no	—
81	C₄×Dic₈₆	—	2	2	no	—
82	C₄×Dic₈₆	—	2	2	no	—
83	C₄×Dic₈₆	—	2	2	no	—
84	C₄×Dic₈₆	—	2	2	no	—
85	C₄×Dic₈₆	—	2	2	no	—
86	C₄×Dic₈₆	—	2	2	no	—
87	#13063282	—	2	2	no	—
88	#13063282	—	2	2	no	—
89	#13063282	D₄	1	4	yes	—
90	#13063282	D₄	1	4	yes	—
91	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
113	C₄²×D₄₃	—	2	2	no	—
114	C₄²×D₄₃	—	2	2	no	—
115	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
116	Dic₄₃⋊C₈	—	2	2	no	—
117	Dic₄₃⋊C₈	—	2	2	no	—
118	(C₂×D₄₃)⋊C₈	—	2	2	no	—
119	(C₂×D₄₃)⋊C₈	—	2	2	no	—
120	(C₂×D₄₃)⋊C₈	—	2	2	no	—
121	(C₂×D₄₃)⋊C₈	—	2	2	no	—
122	#13063235	—	2	2	no	—
123	C₄×C₄₃⋊C₈	—	2	2	no	—
124	C₈×Dic₄₃	—	2	2	no	—
125	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
126	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
130	C₄×Q₈×C₄₃	—	2	2	no	—
131	C₄×Q₈×C₄₃	—	2	2	no	—
132	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
135	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₄₃	—	2	2	no	—
139	#97×C₄₃	—	2	2	no	—
140	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂×Q₈×C₄₃	—	2	2	no	—
143	C₂×Q₈×C₄₃	—	4	1	no	—
144	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₄₃	—	2	1	no	—
159	C₂×C₄×D₄₃	—	2	1	no	—
160	C₂×C₄×D₄₃	—	2	1	no	—
161	C₂×C₄×D₄₃	—	2	1	no	—
162	C₂×C₄×D₄₃	—	2	2	no	—
163	C₂×C₄×D₄₃	—	2	2	no	—
164	C₂×C₄×D₄₃	—	2	2	no	—
165	C₂×C₄×D₄₃	—	2	2	no	—
166	C₂×C₄×D₄₃	—	4	1	no	—
167	C₂×C₄×D₄₃	—	4	1	no	—
168	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
169	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
170	C₂×Dic₈₆	—	2	2	no	—
171	C₂×Dic₈₆	—	2	2	no	—
172	C₂×Dic₈₆	—	2	2	no	—
173	C₂×Dic₈₆	—	2	2	no	—
174	C₂×Dic₈₆	—	2	2	no	—
175	C₂×Dic₈₆	—	2	2	no	—
176	C₂×Dic₈₆	—	4	1	no	—
177	C₂×Dic₈₆	—	4	1	no	—
178	C₂×Dic₈₆	—	4	1	no	—
179	C₂×C₈×C₄₃	—	2	1	no	—
180	C₂×C₈×C₄₃	—	2	1	no	—
181	C₂×C₈×C₄₃	—	2	1	no	—
182	C₂×C₈×C₄₃	—	2	1	no	—
183	C₂×C₈×C₄₃	—	2	1	no	—
184	C₂×C₈×C₄₃	—	2	1	no	—
185	C₂×C₈×C₄₃	—	2	1	no	—
186	C₂×C₈×C₄₃	—	2	1	no	—
187	C₂×C₈×C₄₃	—	2	1	no	—
188	C₂×C₈×C₄₃	—	2	1	no	—
189	C₂×C₈×C₄₃	—	2	1	no	—
190	C₂×C₈×C₄₃	—	2	1	no	—
191	C₄⋊C₄×C₄₃	—	2	2	no	—
192	C₄⋊C₄×C₄₃	—	2	2	no	—
193	C₄⋊C₄×C₄₃	—	2	2	no	—
194	C₄²×C₄₃	—	2	1	no	—
195	C₄²×C₄₃	—	2	1	no	—
196	C₄²×C₄₃	—	2	1	no	—
197	C₄²×C₄₃	—	2	1	no	—
198	C₄²×C₄₃	C₂×D₄	1	2	yes	—
199	C₄²×C₄₃	C₂×D₄	1	2	yes	—
200	(C₂×D₄₃)⋊C₄	—	2	2	no	—
201	(C₂×D₄₃)⋊C₄	—	2	2	no	—
202	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	4	yes	—
203	(C₂×D₄₃)⋊C₄	C₂²⋊C₄	1	4	yes	—
204	C₄⋊Dic₄₃	—	2	2	no	—
205	C₄⋊Dic₄₃	—	2	2	no	—
206	C₄⋊Dic₄₃	—	2	2	no	—
207	Dic₄₃⋊C₄	—	2	2	no	—
208	Dic₄₃⋊C₄	—	2	2	no	—
209	Dic₄₃⋊C₄	—	2	2	no	—
210	Dic₄₃⋊C₄	—	2	2	no	—
211	Dic₄₃⋊C₄	—	2	2	no	—
212	Dic₄₃⋊C₄	—	2	2	no	—
213	Dic₄₃⋊C₄	—	2	2	no	—
214	Dic₄₃⋊C₄	—	2	2	no	—
215	Dic₄₃⋊C₄	C₂²⋊C₄	1	4	yes	—
216	Dic₄₃⋊C₄	C₂²⋊C₄	1	4	yes	—
217	C₄×Dic₄₃	—	2	1	no	—
218	C₄×Dic₄₃	—	2	1	no	—
219	C₄×Dic₄₃	—	2	1	no	—
220	C₄×Dic₄₃	—	2	1	no	—
221	C₄×Dic₄₃	—	2	2	no	—
222	C₄×Dic₄₃	—	2	2	no	—
223	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
224	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
225	C₂×C₄₃⋊C₈	—	2	1	no	—
226	C₂×C₄₃⋊C₈	—	2	1	no	—
227	C₂×C₄₃⋊C₈	—	2	1	no	—
228	C₂×C₄₃⋊C₈	—	2	1	no	—
229	C₂×C₄₃⋊C₈	—	2	1	no	—
230	C₂×C₄₃⋊C₈	—	2	1	no	—
231	C₂×C₄₃⋊C₈	—	2	1	no	—
232	C₂×C₄₃⋊C₈	—	2	1	no	—
233	C₂×C₄₃⋊C₈	—	2	1	no	—
234	C₂×C₄₃⋊C₈	—	2	1	no	—
235	C₂×C₄₃⋊C₈	—	2	1	no	—
236	C₂×C₄₃⋊C₈	—	2	1	no	—
237	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
238	C₂²×D₄₃	—	2	1	no	—
239	C₂²×D₄₃	—	2	1	no	—
240	C₂²×D₄₃	—	2	1	no	—
241	C₂²×D₄₃	—	2	1	no	—
242	C₂²×D₄₃	—	2	1	no	—
243	C₂²×D₄₃	—	2	1	no	—
244	C₂²×D₄₃	C₂×C₂²⋊C₄	1	2	yes	—
245	Q₈×C₄₃	—	4	4	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	—	2	1	no	—
248	C₂×C₄×C₄₃	—	2	1	no	—
249	C₂×C₄×C₄₃	—	2	1	no	—
250	C₂×C₄×C₄₃	—	2	1	no	—
251	C₂×C₄×C₄₃	—	2	1	no	—
252	C₂×C₄×C₄₃	—	2	1	no	—
253	C₂×C₄×C₄₃	—	2	1	no	—
254	C₂×C₄×C₄₃	—	2	1	no	—
255	C₂×C₄×C₄₃	—	2	1	no	—
256	C₂×C₄×C₄₃	—	2	1	no	—
257	C₂×C₄×C₄₃	—	2	1	no	—
258	C₂×C₄×C₄₃	—	2	1	no	—
259	C₂×C₄×C₄₃	—	2	1	no	—
260	C₂×C₄×C₄₃	—	2	1	no	—
261	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
262	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₃	#131	1	2	yes	—
264	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
267	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
268	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
269	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
270	C₂×Dic₄₃	—	2	1	no	—
271	C₂×Dic₄₃	—	2	1	no	—
272	C₂×Dic₄₃	—	2	1	no	—
273	C₂×Dic₄₃	—	2	1	no	—
274	C₂×Dic₄₃	—	2	1	no	—
275	C₂×Dic₄₃	—	2	1	no	—
276	C₂×Dic₄₃	—	2	1	no	—
277	C₂×Dic₄₃	—	2	1	no	—
278	C₂×Dic₄₃	—	2	1	no	—
279	C₂×Dic₄₃	—	2	1	no	—
280	C₂×Dic₄₃	—	2	1	no	—
281	C₂×Dic₄₃	—	2	1	no	—
282	C₂×Dic₄₃	—	2	1	no	—
283	C₂×Dic₄₃	—	2	1	no	—
284	C₂×Dic₄₃	—	2	1	no	—
285	C₂×Dic₄₃	—	2	1	no	—
286	C₂×Dic₄₃	—	2	1	no	—
287	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	2	yes	—
288	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×Dic₄₃	#131	1	2	yes	—
291	C₄×D₄₃	—	2	2	no	—
292	C₄×D₄₃	—	2	2	no	—
293	C₄×D₄₃	—	2	2	no	—
294	C₄×D₄₃	—	2	2	no	—
295	C₄×D₄₃	—	4	4	no	—
296	C₄×D₄₃	—	4	4	no	—
297	Dic₈₆	—	4	4	no	—
298	Dic₈₆	—	4	4	no	—
299	Dic₈₆	—	4	4	no	—
300	C₈×C₄₃	—	4	1	no	—
301	C₈×C₄₃	—	4	1	no	—
302	C₈×C₄₃	—	4	1	no	—
303	C₈×C₄₃	—	4	1	no	—
304	C₄₃⋊C₈	—	4	1	no	—
305	C₄₃⋊C₈	—	4	1	no	—
306	C₄₃⋊C₈	—	4	1	no	—
307	C₄₃⋊C₈	—	4	1	no	—
308	#21824	—	43	1	no	maximal, Sylow
309	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₄₃	#519	1	1	yes	characteristic
311	C₂²×C₄₃	#519	1	1	yes	characteristic
312	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
313	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
314	C₂²×C₄₃	#568	1	1	yes	characteristic
315	C₂²×C₄₃	#568	1	1	yes	characteristic
316	C₂×D₄₃	—	2	2	no	—
317	C₂×D₄₃	—	2	2	no	—
318	C₂×D₄₃	—	2	2	no	—
319	C₂×D₄₃	—	4	1	no	—
320	C₂×D₄₃	—	4	1	no	—
321	C₂×D₄₃	—	4	1	no	—
322	C₂×D₄₃	—	4	1	no	—
323	C₄×C₄₃	—	2	2	no	—
324	C₄×C₄₃	—	2	2	no	—
325	C₄×C₄₃	—	2	2	no	—
326	C₄×C₄₃	—	4	1	no	—
327	C₄×C₄₃	—	4	1	no	—
328	C₄×C₄₃	—	4	1	no	—
329	C₄×C₄₃	#536	1	1	yes	characteristic
330	C₄×C₄₃	#536	1	1	yes	characteristic
331	C₄×C₄₃	#536	1	1	yes	characteristic
332	C₄×C₄₃	#536	1	1	yes	characteristic
333	Dic₄₃	—	2	2	no	—
334	Dic₄₃	—	2	2	no	—
335	Dic₄₃	—	2	2	no	—
336	Dic₄₃	—	2	2	no	—
337	Dic₄₃	—	4	1	no	—
338	Dic₄₃	—	4	1	no	—
339	Dic₄₃	—	4	1	no	—
340	C₂×#533	—	43	1	no	—
341	C₂×#433	—	43	1	no	—
342	C₂×#433	—	43	1	no	—
343	#1985	—	43	1	no	—
344	#1985	—	43	1	no	—
345	#1985	—	43	1	no	—
346	#1985	D₄₃	1	1	yes	characteristic, complemented
347	#1984	—	43	1	no	—
348	#1984	—	43	1	no	—
349	#1984	—	43	1	no	—
350	#1984	—	43	1	no	—
351	#1818	—	43	1	no	—
352	#1818	—	43	1	no	—
353	#1817	—	43	1	no	—
354	#1817	—	43	1	no	—
355	C₂×C₄₃	#2310	1	1	yes	characteristic
356	C₂×C₄₃	#2880	1	1	yes	characteristic
357	C₂×C₄₃	#2880	1	1	yes	characteristic
358	C₂×C₄₃	#2985	1	1	yes	characteristic
359	C₂×C₄₃	#2985	1	1	yes	characteristic
360	C₂×C₄₃	#2986	1	1	yes	characteristic
361	C₂×C₄₃	#2987	1	1	yes	characteristic
362	D₄₃	—	4	2	no	—
363	#533	—	86	4	no	—
364	#533	—	86	4	no	—
365	C₂×C₄⋊Q₈	—	43	1	no	—
366	C₂×C₄⋊Q₈	—	43	1	no	—
367	C₂×#125	—	43	1	no	—
368	C₂×#125	—	43	1	no	—
369	C₂×C₂²⋊Q₈	—	43	1	no	—
370	C₂×C₂²⋊Q₈	—	43	1	no	—
371	C₂×C₂²⋊Q₈	—	43	1	no	—
372	C₂×C₂²⋊Q₈	—	43	1	no	—
373	C₂×C₄×Q₈	—	43	1	no	—
374	C₂×C₄×Q₈	—	43	1	no	—
375	C₂×C₄×Q₈	—	43	1	no	—
376	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
377	C₂×#117	—	43	1	no	—
378	C₂×#117	—	43	1	no	—
379	C₂²×C₄²	—	43	1	no	—
380	#433	—	86	4	no	—
381	#433	—	86	4	no	—
382	C₂×C₄⋊C₈	—	43	1	no	—
383	C₂×C₄⋊C₈	—	43	1	no	—
384	C₂×C₄⋊C₈	—	43	1	no	—
385	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
386	C₂×C₂²⋊C₈	—	43	1	no	—
387	C₂×C₂²⋊C₈	—	43	1	no	—
388	C₂×C₂²⋊C₈	—	43	1	no	—
389	C₂×C₂²⋊C₈	—	43	1	no	—
390	C₂×#97	—	43	1	no	—
391	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
392	C₂×C₄×C₈	—	43	1	no	—
393	C₂×C₄×C₈	—	43	1	no	—
394	#336	—	43	1	no	—
395	#336	—	43	1	no	—
396	#336	—	43	1	no	—
397	#336	—	43	1	no	—
398	#336	—	43	1	no	—
399	#336	—	43	1	no	—
400	#336	—	43	1	no	—
401	#336	—	43	1	no	—
402	#336	—	43	1	no	—
403	#336	—	43	1	no	—
404	#336	—	43	1	no	—
405	#336	—	43	1	no	—
406	#336	C₂×D₄₃	1	1	yes	characteristic
407	#336	C₂×D₄₃	1	1	yes	characteristic
408	#336	C₂×D₄₃	1	1	yes	characteristic
409	#336	C₂×D₄₃	1	1	yes	characteristic
410	C₄₃	#21824	1	1	yes	characteristic, complemented, Sylow
411	C₂²×Q₈	—	43	1	no	—
412	C₂²×Q₈	—	43	1	no	—
413	C₂²×Q₈	—	43	1	no	—
414	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
415	C₂³×C₄	—	43	1	no	—
416	C₂³×C₄	—	43	1	no	—
417	C₂³×C₄	—	43	1	no	—
418	C₂²×C₈	—	43	1	no	—
419	C₂²×C₈	—	43	1	no	—
420	C₂²×C₈	—	43	1	no	—
421	C₂²×C₈	—	43	1	no	—
422	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
423	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
424	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
425	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
426	C₄⋊Q₈	—	86	4	no	—
427	C₄⋊Q₈	—	86	4	no	—
428	#125	—	86	4	no	—
429	#125	—	86	4	no	—
430	C₂²⋊Q₈	—	86	4	no	—
431	C₂²⋊Q₈	—	86	4	no	—
432	C₂²⋊Q₈	—	86	4	no	—
433	C₂²⋊Q₈	—	86	4	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	86	2	no	—
437	C₄×Q₈	—	86	2	no	—
438	C₄×Q₈	—	86	2	no	—
439	C₄×Q₈	—	86	2	no	—
440	C₄×Q₈	—	86	2	no	—
441	C₄×Q₈	—	86	2	no	—
442	#117	—	43	4	no	—
443	#117	—	43	4	no	—
444	#117	—	86	2	no	—
445	#117	—	86	2	no	—
446	C₂×C₄⋊C₄	—	43	1	no	—
447	C₂×C₄⋊C₄	—	43	1	no	—
448	C₂×C₄⋊C₄	—	43	1	no	—
449	C₂×C₄⋊C₄	—	43	1	no	—
450	C₂×C₄⋊C₄	—	43	1	no	—
451	C₂×C₄⋊C₄	—	43	1	no	—
452	C₂×C₄⋊C₄	—	43	1	no	—
453	C₂×C₄⋊C₄	—	43	1	no	—
454	C₂×C₄⋊C₄	—	43	1	no	—
455	C₂×C₄⋊C₄	—	43	1	no	—
456	C₂×C₄⋊C₄	—	43	1	no	—
457	C₂×C₄⋊C₄	—	43	1	no	—
458	C₂×C₄⋊C₄	—	43	1	no	—
459	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
460	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	—	43	1	no	—
463	C₂×C₂²⋊C₄	—	43	1	no	—
464	C₂×C₂²⋊C₄	—	43	1	no	—
465	C₂×C₂²⋊C₄	—	43	1	no	—
466	C₂×C₄²	—	43	1	no	—
467	C₂×C₄²	—	43	1	no	—
468	C₂×C₄²	—	43	1	no	—
469	C₂×C₄²	—	43	1	no	—
470	C₂×C₄²	—	43	1	no	—
471	C₂×C₄²	—	86	2	no	—
472	C₂×C₄²	—	86	2	no	—
473	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
474	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
475	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
476	C₄⋊C₈	—	2	2	no	—
477	C₄⋊C₈	—	86	2	no	—
478	C₄⋊C₈	—	86	2	no	—
479	C₄⋊C₈	—	86	2	no	—
480	C₂²⋊C₈	—	86	2	no	—
481	C₂²⋊C₈	—	86	2	no	—
482	C₂²⋊C₈	—	86	2	no	—
483	C₂²⋊C₈	—	86	2	no	—
484	#97	—	2	2	no	—
485	#97	—	86	2	no	—
486	C₄×C₈	—	86	2	no	—
487	C₄×C₈	—	86	2	no	—
488	C₂⁴	—	43	1	no	—
489	C₂×Q₈	—	2	2	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	4	1	no	—
492	C₂×Q₈	—	86	2	no	—
493	C₂×Q₈	—	86	2	no	—
494	C₂×Q₈	—	86	2	no	—
495	C₂×Q₈	—	86	2	no	—
496	C₂×Q₈	—	86	2	no	—
497	C₂×Q₈	—	86	2	no	—
498	C₂×Q₈	—	172	1	no	—
499	C₂×Q₈	—	172	1	no	—
500	C₂×Q₈	—	172	1	no	—
501	C₂²×C₄	—	43	1	no	—
502	C₂²×C₄	—	43	1	no	—
503	C₂²×C₄	—	43	1	no	—
504	C₂²×C₄	—	43	1	no	—
505	C₂²×C₄	—	43	2	no	—
506	C₂²×C₄	—	43	2	no	—
507	C₂²×C₄	—	43	1	no	—
508	C₂²×C₄	—	43	1	no	—
509	C₂²×C₄	—	43	1	no	—
510	C₂²×C₄	—	86	2	no	—
511	C₂²×C₄	—	86	2	no	—
512	C₂²×C₄	—	86	2	no	—
513	C₂²×C₄	—	86	1	no	—
514	C₂²×C₄	—	86	1	no	—
515	C₂²×C₄	—	86	1	no	—
516	C₂²×C₄	—	86	1	no	—
517	C₂²×C₄	—	86	2	no	—
518	C₂²×C₄	—	172	1	no	—
519	C₂²×C₄	—	172	1	no	—
520	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
522	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
523	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
524	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
525	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
526	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	86	1	no	—
540	C₂×C₈	—	86	1	no	—
541	C₂×C₈	—	86	1	no	—
542	C₂×C₈	—	86	1	no	—
543	C₂×C₈	—	86	1	no	—
544	C₂×C₈	—	86	1	no	—
545	C₂×C₈	—	86	1	no	—
546	C₂×C₈	—	86	1	no	—
547	C₂×C₈	—	86	1	no	—
548	C₂×C₈	—	86	1	no	—
549	C₂×C₈	—	86	1	no	—
550	C₂×C₈	—	86	1	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	43	4	no	—
555	C₄⋊C₄	—	43	4	no	—
556	C₄⋊C₄	—	86	2	no	—
557	C₄⋊C₄	—	86	2	no	—
558	C₄⋊C₄	—	86	2	no	—
559	C₄⋊C₄	—	86	2	no	—
560	C₄⋊C₄	—	86	2	no	—
561	C₄⋊C₄	—	86	2	no	—
562	C₄⋊C₄	—	86	2	no	—
563	C₄⋊C₄	—	86	2	no	—
564	C₄⋊C₄	—	86	2	no	—
565	C₄⋊C₄	—	86	2	no	—
566	C₄⋊C₄	—	86	2	no	—
567	C₂²⋊C₄	—	43	4	no	—
568	C₂²⋊C₄	—	43	4	no	—
569	C₂²⋊C₄	—	86	2	no	—
570	C₂²⋊C₄	—	86	2	no	—
571	C₄²	—	2	1	no	—
572	C₄²	—	2	1	no	—
573	C₄²	—	2	1	no	—
574	C₄²	—	2	1	no	—
575	C₄²	—	43	2	no	—
576	C₄²	—	43	2	no	—
577	C₄²	—	86	2	no	—
578	C₄²	—	86	2	no	—
579	C₄²	—	86	1	no	—
580	C₄²	—	86	1	no	—
581	C₄²	—	86	1	no	—
582	C₄²	—	86	1	no	—
583	C₄²	D₄×D₄₃	1	2	yes	—
584	C₄²	D₄×D₄₃	1	2	yes	—
585	C₂³	—	43	2	no	—
586	C₂³	—	86	1	no	—
587	C₂³	—	86	1	no	—
588	C₂³	—	86	1	no	—
589	C₂³	—	86	1	no	—
590	C₂³	—	86	1	no	—
591	C₂³	—	86	1	no	—
592	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
593	Q₈	—	4	4	no	—
594	Q₈	—	172	4	no	—
595	Q₈	—	172	4	no	—
596	Q₈	—	172	4	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	43	2	no	—
613	C₂×C₄	—	43	2	no	—
614	C₂×C₄	—	43	2	no	—
615	C₂×C₄	—	43	2	no	—
616	C₂×C₄	—	86	1	no	—
617	C₂×C₄	—	86	1	no	—
618	C₂×C₄	—	86	1	no	—
619	C₂×C₄	—	86	1	no	—
620	C₂×C₄	—	86	1	no	—
621	C₂×C₄	—	86	1	no	—
622	C₂×C₄	—	86	1	no	—
623	C₂×C₄	—	86	1	no	—
624	C₂×C₄	—	86	2	no	—
625	C₂×C₄	—	86	2	no	—
626	C₂×C₄	—	86	2	no	—
627	C₂×C₄	—	86	2	no	—
628	C₂×C₄	—	86	1	no	—
629	C₂×C₄	—	86	1	no	—
630	C₂×C₄	—	86	1	no	—
631	C₂×C₄	—	86	1	no	—
632	C₂×C₄	—	86	1	no	—
633	C₂×C₄	—	86	1	no	—
634	C₂×C₄	—	86	1	no	—
635	C₂×C₄	—	86	1	no	—
636	C₂×C₄	—	86	1	no	—
637	C₂×C₄	—	172	4	no	—
638	C₂×C₄	—	172	4	no	—
639	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
640	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
641	C₂×C₄	#13063333	1	2	yes	—
642	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
643	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
644	C₂×C₄	#13063372	1	1	yes	characteristic
645	C₂×C₄	#13063372	1	1	yes	characteristic
646	C₂×C₄	#13063373	1	1	yes	characteristic
647	C₂×C₄	#13063373	1	1	yes	characteristic
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	172	1	no	—
653	C₈	—	172	1	no	—
654	C₈	—	172	1	no	—
655	C₈	—	172	1	no	—
656	C₂²	—	86	2	no	—
657	C₂²	—	86	2	no	—
658	C₂²	—	86	2	no	—
659	C₂²	—	172	1	no	—
660	C₂²	—	172	1	no	—
661	C₂²	—	172	1	no	—
662	C₂²	—	172	1	no	—
663	C₂²	C₂×C₂²⋊C₄×D₄₃	1	1	yes	characteristic
664	C₂²	#14583375	1	1	yes	characteristic
665	C₂²	#14583375	1	1	yes	characteristic
666	C₂²	#131×D₄₃	1	1	yes	characteristic
667	C₂²	C₂×#13063333	1	1	yes	characteristic
668	C₂²	#14583664	1	1	yes	characteristic
669	C₂²	#14583665	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	—	4	1	no	—
676	C₄	—	86	2	no	—
677	C₄	—	86	2	no	—
678	C₄	—	86	2	no	—
679	C₄	—	86	2	no	—
680	C₄	—	172	1	no	—
681	C₄	—	172	1	no	—
682	C₄	—	172	1	no	—
683	C₄	#14583469	1	1	yes	characteristic
684	C₄	#14583472	1	1	yes	characteristic
685	C₄	#14583472	1	1	yes	characteristic
686	C₄	#14583474	1	1	yes	characteristic
687	C₂	—	172	2	no	—
688	C₂	#19137178	1	1	yes	characteristic
689	C₂	#19143043	1	1	yes	characteristic
690	C₂	#19143045	1	1	yes	characteristic
691	C₂	#19143688	1	1	yes	characteristic
692	C₂	#19143691	1	1	yes	characteristic
693	C₂	#19143693	1	1	yes	characteristic
694	C₂	#19143698	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1985	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1985	D₄₃
hypocenter	C₄₃	#21824
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1985

Complements

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

N	H ≅ G/N	type
4. #19135535	C₂	semidirect
5. #19135533	C₂	semidirect
6. #19135533	C₂	semidirect
7. #19135532	C₂	semidirect
8. #19135530	C₂	semidirect
9. #19135529	C₂	semidirect
10. #19135529	C₂	semidirect
15. C₄₃×#1985	C₂	semidirect
346. #1985	D₄₃	semidirect
410. C₄₃	#21824	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583453	2
C₂×#14582961	2
C₂×#14582959	2
#19135535	2
#19135533	2
#19135532	2
#19135530	2
#19135529	2
#19134665	2
#19134662	2
C₄₃×#1985	2
#21824	43