Subgroups — #25115190

Order 11008.

916 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582976	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582964	C₂	1	1	yes	maximal, characteristic
3	#19137059	C₂	1	1	yes	maximal, characteristic
4	#19135311	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135311	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134779	C₂	1	2	yes	maximal, complemented
7	#19134774	C₂	1	2	yes	maximal, complemented
8	#19134578	C₂	1	2	yes	maximal, complemented
9	C₄×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134290	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₃	C₂²	1	2	yes	—
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	C₂×#13063282	C₂²	1	2	yes	—
16	#14582976	—	2	4	no	—
17	#14582964	—	2	4	no	—
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
21	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
22	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
23	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	#14582801	C₄	1	1	yes	characteristic
27	#14582801	C₄	1	1	yes	characteristic
28	#14582797	C₄	1	1	yes	characteristic
29	#14582797	C₄	1	1	yes	characteristic
30	#14582790	C₄	1	2	yes	—
31	#14582790	C₄	1	2	yes	—
32	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
33	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
34	#14582654	C₂²	1	1	yes	characteristic
35	#14582654	C₂²	1	1	yes	characteristic
36	#14582653	C₂²	1	2	yes	—
37	#14582653	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄³×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
45	C₂×#10621872	—	2	4	no	—
46	C₂×#10621872	—	2	4	no	—
47	C₂×#10621872	—	4	2	no	—
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₄₃	—	2	4	no	—
53	C₂×C₈×D₄₃	—	2	4	no	—
54	C₂×C₈×D₄₃	—	4	2	no	—
55	C₄×D₁₇₂	D₄	1	4	yes	—
56	C₄×D₁₇₂	Q₈	1	4	yes	—
57	#13063282	—	4	2	no	—
58	#13063282	—	4	2	no	—
59	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	Dic₄₃⋊C₈	—	4	2	no	—
73	Dic₄₃⋊C₈	—	4	2	no	—
74	(C₂×D₄₃)⋊C₈	—	2	4	no	—
75	(C₂×D₄₃)⋊C₈	—	2	4	no	—
76	C₄×C₄₃⋊C₈	—	2	2	no	—
77	C₄×C₄₃⋊C₈	—	2	2	no	—
78	C₄₃⋊#95	C₂×C₄	1	2	yes	—
79	C₄₃⋊#95	C₂×C₄	1	2	yes	—
80	C₄₃⋊#95	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	—	2	2	no	—
92	C₂³×D₄₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
102	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
103	C₂×D₁₇₂	—	2	2	no	—
104	C₂×D₁₇₂	—	2	2	no	—
105	C₂×D₁₇₂	C₄⋊C₄	1	4	yes	—
106	C₂×C₄×D₄₃	—	2	2	no	—
107	C₂×C₄×D₄₃	—	2	2	no	—
108	C₂×C₄×D₄₃	—	2	2	no	—
109	C₂×C₄×D₄₃	—	2	2	no	—
110	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
111	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₄²×C₄₃	—	2	2	no	—
119	C₄²×C₄₃	—	2	2	no	—
120	C₄²×C₄₃	—	2	2	no	—
121	C₄²×C₄₃	—	2	1	no	—
122	C₄²×C₄₃	—	2	1	no	—
123	C₄²×C₄₃	—	2	1	no	—
124	C₄²×C₄₃	—	2	1	no	—
125	C₄²×C₄₃	—	4	1	no	—
126	C₄²×C₄₃	C₂×D₄	1	2	yes	—
127	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
128	(C₂×D₄₃)⋊C₄	—	2	4	no	—
129	(C₂×D₄₃)⋊C₄	—	4	2	no	—
130	(C₂×D₄₃)⋊C₄	—	4	2	no	—
131	(C₂×D₄₃)⋊C₄	—	4	2	no	—
132	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	8	yes	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
136	Dic₄₃⋊C₄	—	4	2	no	—
137	Dic₄₃⋊C₄	—	4	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	#41	1	2	yes	—
151	C₂×C₄₃⋊C₈	#41	1	2	yes	—
152	#10621872	—	4	8	no	—
153	C₈×D₄₃	—	4	8	no	—
154	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	2	no	—
156	C₂²×D₄₃	—	2	2	no	—
157	C₂²×D₄₃	—	2	2	no	—
158	C₂²×D₄₃	—	2	2	no	—
159	C₂²×D₄₃	—	2	2	no	—
160	C₂²×D₄₃	—	2	2	no	—
161	C₂²×D₄₃	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	#131	1	2	yes	—
178	C₂×C₄×C₄₃	#131	1	2	yes	—
179	C₂×C₄×C₄₃	#131	1	2	yes	—
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	2	2	no	—
194	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
195	D₁₇₂	—	2	8	no	—
196	C₄×D₄₃	—	2	4	no	—
197	C₄×D₄₃	—	2	4	no	—
198	C₄×D₄₃	—	2	4	no	—
199	C₄×D₄₃	—	2	4	no	—
200	C₈×C₄₃	—	4	2	no	—
201	C₈×C₄₃	—	4	2	no	—
202	C₄₃⋊C₈	—	2	2	no	—
203	C₄₃⋊C₈	—	2	2	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	#22701	—	43	1	no	maximal, Sylow
207	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
208	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
209	C₂²×C₄₃	#518	1	1	yes	characteristic
210	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
212	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
213	C₂²×C₄₃	#568	1	1	yes	characteristic
214	C₂×D₄₃	—	2	4	no	—
215	C₂×D₄₃	—	2	4	no	—
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	4	2	no	—
218	C₂×D₄₃	—	4	2	no	—
219	C₂×D₄₃	—	4	2	no	—
220	C₂×D₄₃	—	4	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	4	1	no	—
224	C₄×C₄₃	—	4	1	no	—
225	C₄×C₄₃	—	4	1	no	—
226	C₄×C₄₃	#424	1	4	yes	—
227	C₄×C₄₃	#546	1	1	yes	characteristic
228	C₄×C₄₃	#546	1	1	yes	characteristic
229	C₄×C₄₃	#554	1	1	yes	characteristic
230	C₄×C₄₃	#554	1	1	yes	characteristic
231	Dic₄₃	—	2	4	no	—
232	Dic₄₃	—	4	2	no	—
233	Dic₄₃	—	4	2	no	—
234	C₂×#436	—	43	1	no	—
235	C₂×C₈×D₄	—	43	1	no	—
236	#2293	—	43	1	no	—
237	#1939	—	43	1	no	—
238	#1939	—	43	1	no	—
239	#1851	—	43	2	no	—
240	#1850	—	43	2	no	—
241	#1831	D₄₃	1	1	yes	characteristic, complemented
242	#1798	—	43	2	no	—
243	C₄×C₄⋊C₈	—	43	1	no	—
244	#1729	—	43	2	no	—
245	C₂×C₄₃	#2349	1	1	yes	characteristic
246	C₂×C₄₃	C₂×#424	1	1	yes	characteristic
247	C₂×C₄₃	#2906	1	1	yes	characteristic
248	C₂×C₄₃	#2966	1	1	yes	characteristic
249	C₂×C₄₃	#2969	1	1	yes	characteristic
250	C₂×C₄₃	#2979	1	1	yes	characteristic
251	C₂×C₄₃	#2981	1	1	yes	characteristic
252	D₄₃	—	4	4	no	—
253	C₂²×M₁₆	—	43	2	no	—
254	C₂³×C₈	—	43	2	no	—
255	C₂×C₄×D₄	—	43	1	no	—
256	C₂×#117	—	43	2	no	—
257	#436	—	86	4	no	—
258	C₈×D₄	—	86	4	no	—
259	C₂×C₄⋊C₈	—	43	1	no	—
260	C₂×C₄⋊C₈	—	43	1	no	—
261	C₂×C₄⋊C₈	—	43	2	no	—
262	C₂×C₄⋊C₈	—	43	2	no	—
263	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
265	C₂×C₂²⋊C₈	—	43	2	no	—
266	C₂×C₂²⋊C₈	—	43	2	no	—
267	C₂×C₄×C₈	—	43	1	no	—
268	C₂×C₄×C₈	—	43	1	no	—
269	#390	—	43	1	no	—
270	#390	—	43	1	no	—
271	#389	—	43	1	no	—
272	#389	—	43	1	no	—
273	#388	—	43	2	no	—
274	#388	—	43	2	no	—
275	C₄×C₄⋊C₄	—	43	1	no	—
276	C₄×C₂²⋊C₄	—	43	2	no	—
277	C₄³	C₂×D₄₃	1	1	yes	characteristic
278	#336	—	43	2	no	—
279	#336	—	43	2	no	—
280	#336	—	43	1	no	—
281	#336	—	43	1	no	—
282	#336	C₂×D₄₃	1	2	yes	—
283	#336	C₂×D₄₃	1	2	yes	—
284	C₄₃	#22701	1	1	yes	characteristic, complemented, Sylow
285	C₂²×D₄	—	43	1	no	—
286	C₂³×C₄	—	43	2	no	—
287	C₂×M₁₆	—	86	4	no	—
288	C₂×M₁₆	—	86	4	no	—
289	C₂×M₁₆	—	172	2	no	—
290	C₂²×C₈	—	43	1	no	—
291	C₂²×C₈	—	43	1	no	—
292	C₂²×C₈	—	43	1	no	—
293	C₂²×C₈	—	43	1	no	—
294	C₂²×C₈	—	86	4	no	—
295	C₂²×C₈	—	86	4	no	—
296	C₂²×C₈	—	172	2	no	—
297	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
298	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
299	C₄×D₄	—	43	4	no	—
300	C₄×D₄	—	43	4	no	—
301	#117	—	172	2	no	—
302	#117	—	172	2	no	—
303	C₂×C₄⋊C₄	—	43	1	no	—
304	C₂×C₄⋊C₄	—	43	1	no	—
305	C₂×C₄⋊C₄	—	43	1	no	—
306	C₂×C₄⋊C₄	—	43	2	no	—
307	C₂×C₄⋊C₄	—	43	2	no	—
308	C₂×C₂²⋊C₄	—	43	2	no	—
309	C₂×C₂²⋊C₄	—	43	2	no	—
310	C₂×C₂²⋊C₄	—	43	2	no	—
311	C₂×C₂²⋊C₄	—	43	2	no	—
312	C₂×C₂²⋊C₄	—	43	2	no	—
313	C₂×C₄²	—	43	2	no	—
314	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
315	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
316	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
317	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	86	2	no	—
324	C₄⋊C₈	—	86	2	no	—
325	C₄⋊C₈	—	172	2	no	—
326	C₄⋊C₈	—	172	2	no	—
327	C₂²⋊C₈	—	86	4	no	—
328	C₂²⋊C₈	—	86	4	no	—
329	C₄×C₈	—	86	2	no	—
330	C₄×C₈	—	86	2	no	—
331	#95	—	43	2	no	—
332	#95	—	43	2	no	—
333	#95	—	43	2	no	—
334	C₂⁴	—	43	2	no	—
335	C₂×D₄	—	43	4	no	—
336	C₂×D₄	—	86	2	no	—
337	C₂×D₄	—	86	2	no	—
338	C₂²×C₄	—	43	2	no	—
339	C₂²×C₄	—	43	4	no	—
340	C₂²×C₄	—	43	4	no	—
341	C₂²×C₄	—	43	2	no	—
342	C₂²×C₄	—	43	2	no	—
343	C₂²×C₄	—	86	2	no	—
344	C₂²×C₄	—	86	2	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
354	M₁₆	—	172	8	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	43	2	no	—
362	C₂×C₈	—	43	2	no	—
363	C₂×C₈	—	86	1	no	—
364	C₂×C₈	—	86	1	no	—
365	C₂×C₈	—	86	1	no	—
366	C₂×C₈	—	86	1	no	—
367	C₂×C₈	—	86	1	no	—
368	C₂×C₈	—	86	1	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	1	no	—
371	C₂×C₈	—	86	1	no	—
372	C₂×C₈	—	86	1	no	—
373	C₂×C₈	—	172	8	no	—
374	C₄⋊C₄	—	43	4	no	—
375	C₄⋊C₄	—	86	2	no	—
376	C₄⋊C₄	—	86	2	no	—
377	C₄⋊C₄	—	172	2	no	—
378	C₄⋊C₄	—	172	2	no	—
379	C₂²⋊C₄	—	43	8	no	—
380	C₂²⋊C₄	—	86	4	no	—
381	C₂²⋊C₄	—	172	2	no	—
382	C₂²⋊C₄	—	172	2	no	—
383	C₂²⋊C₄	—	172	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	4	1	no	—
392	C₄²	—	86	2	no	—
393	C₄²	—	86	2	no	—
394	C₄²	D₄×D₄₃	1	2	yes	—
395	C₄²	Q₈×D₄₃	1	2	yes	—
396	C₂³	—	43	4	no	—
397	C₂³	—	86	2	no	—
398	C₂³	—	86	2	no	—
399	C₂³	—	86	2	no	—
400	C₂³	—	86	2	no	—
401	C₂³	—	86	2	no	—
402	C₂³	—	86	2	no	—
403	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
404	D₄	—	86	8	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	43	4	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	86	4	no	—
422	C₂×C₄	—	86	4	no	—
423	C₂×C₄	—	86	4	no	—
424	C₂×C₄	—	86	4	no	—
425	C₂×C₄	—	86	2	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	86	2	no	—
428	C₂×C₄	—	86	2	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
432	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
433	C₂×C₄	#13063331	1	2	yes	—
434	C₂×C₄	#13063333	1	2	yes	—
435	C₂×C₄	#13063333	1	2	yes	—
436	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
438	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
439	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
440	C₂×C₄	#13063371	1	1	yes	characteristic
441	C₂×C₄	#13063371	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	4	2	no	—
444	C₈	—	86	2	no	—
445	C₈	—	86	2	no	—
446	C₈	—	172	1	no	—
447	C₈	—	172	1	no	—
448	C₂²	—	86	4	no	—
449	C₂²	—	86	4	no	—
450	C₂²	—	86	4	no	—
451	C₂²	—	172	2	no	—
452	C₂²	—	172	2	no	—
453	C₂²	—	172	2	no	—
454	C₂²	—	172	2	no	—
455	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
456	C₂²	#14583367	1	1	yes	characteristic
457	C₂²	#14583373	1	1	yes	characteristic
458	C₂²	C₂×#13063331	1	1	yes	characteristic
459	C₂²	C₂×#13063333	1	1	yes	characteristic
460	C₂²	C₂×#13063333	1	1	yes	characteristic
461	C₂²	#14583665	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	86	4	no	—
468	C₄	—	172	2	no	—
469	C₄	—	172	2	no	—
470	C₄	#14582924	1	4	yes	—
471	C₄	#14583542	1	1	yes	characteristic
472	C₄	#14583542	1	1	yes	characteristic
473	C₄	#14583605	1	1	yes	characteristic
474	C₄	#14583605	1	1	yes	characteristic
475	C₂	—	172	4	no	—
476	C₂	#19137503	1	1	yes	characteristic
477	C₂	C₂×#14582924	1	1	yes	characteristic
478	C₂	#19143164	1	1	yes	characteristic
479	C₂	#19143564	1	1	yes	characteristic
480	C₂	#19143593	1	1	yes	characteristic
481	C₂	#19143661	1	1	yes	characteristic
482	C₂	#19143673	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1831	C₂
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1831	D₄₃
hypocenter	C₄₃	#22701
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
4. #19135311	C₂	semidirect
5. #19135311	C₂	semidirect
6. #19134779	C₂	semidirect
7. #19134774	C₂	semidirect
8. #19134578	C₂	semidirect
9. C₄×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
10. #19134290	C₂	semidirect
11. C₄₃×#1831	C₂	semidirect
241. #1831	D₄₃	semidirect
284. C₄₃	#22701	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582976	2
C₂×#14582964	2
#19137059	2
#19135311	2
#19134779	2
#19134774	2
#19134578	2
C₄×C₄⋊(C₄₃⋊C₈)	2
#19134290	2
C₄₃×#1831	2
#22701	43