Subgroups — #25106914

Order 11008.

1042 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582863	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#19134800	C₂	1	4	yes	maximal, complemented
4	#19134799	C₂	1	4	yes	maximal, complemented
5	#19134631	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₃×#407	C₂	1	1	yes	maximal, characteristic
7	C₂²×#10621877	C₂²	1	2	yes	—
8	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
9	C₂×#13063260	C₂²	1	8	yes	complemented
10	#14582863	—	2	1	no	—
11	#14582863	—	2	1	no	—
12	#14582863	C₂²	1	2	yes	—
13	#14582863	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
15	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
16	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
17	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
18	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
19	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	2	yes	—
20	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
22	#14582663	C₂²	1	8	yes	complemented
23	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#407	—	2	1	no	—
26	C₄₃×#407	—	2	1	no	—
27	C₄₃×#407	C₂²	1	2	yes	—
28	C₄₃×#407	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
31	C₂×#10621877	—	2	2	no	—
32	C₂×#10621877	—	4	4	no	—
33	C₂×#10621877	C₂³	1	4	yes	—
34	C₂²×C₄₃⋊C₈	—	2	2	no	—
35	C₂²×C₄₃⋊C₈	—	4	4	no	—
36	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
37	C₂²×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
38	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
39	#13063260	—	4	8	no	—
40	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
41	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
43	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
44	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
45	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
46	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
47	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
48	C₂⁵×C₄₃	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	—	4	4	no	—
50	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
59	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
60	C₂³×C₄×C₄₃	Q₈	1	1	yes	characteristic
61	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₄₃	—	2	2	no	—
65	C₂×M₁₆×C₄₃	—	4	4	no	—
66	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
67	C₂²×C₈×C₄₃	—	2	2	no	—
68	C₂²⋊C₈×C₄₃	—	2	2	no	—
69	C₂²⋊C₈×C₄₃	—	2	2	no	—
70	C₂²⋊C₈×C₄₃	—	2	2	no	—
71	C₂²⋊C₈×C₄₃	—	2	2	no	—
72	C₂⁴×C₄₃	—	2	4	no	—
73	C₂⁴×C₄₃	—	4	2	no	—
74	C₂⁴×C₄₃	—	4	2	no	—
75	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
76	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂⁴×C₄₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
80	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
81	C₂⁴×C₄₃	C₂×Q₈	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	—	2	4	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	4	2	no	—
86	C₂²×C₄×C₄₃	—	4	2	no	—
87	C₂²×C₄×C₄₃	—	4	2	no	—
88	C₂²×C₄×C₄₃	—	4	2	no	—
89	C₂²×C₄×C₄₃	—	4	2	no	—
90	C₂²×C₄×C₄₃	—	4	2	no	—
91	C₂²×C₄×C₄₃	—	4	2	no	—
92	C₂²×C₄×C₄₃	—	4	2	no	—
93	C₂²×C₄×C₄₃	—	4	2	no	—
94	C₂²×C₄×C₄₃	—	4	2	no	—
95	C₂²×C₄×C₄₃	—	4	2	no	—
96	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	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×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	M₁₆×C₄₃	—	2	8	no	—
125	M₁₆×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	—	2	4	no	—
127	C₂×C₈×C₄₃	—	4	4	no	—
128	#10621877	—	2	8	no	—
129	#10621877	—	4	4	no	—
130	C₂×C₄₃⋊C₈	—	2	8	no	—
131	C₂×C₄₃⋊C₈	—	2	4	no	—
132	C₂×C₄₃⋊C₈	—	4	4	no	—
133	C₂×C₄₃⋊C₈	—	4	4	no	—
134	C₂×C₄₃⋊C₈	—	4	4	no	—
135	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	2	2	no	—
138	C₂³×C₄₃	—	2	2	no	—
139	C₂³×C₄₃	—	2	2	no	—
140	C₂³×C₄₃	—	2	2	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	4	1	no	—
149	C₂³×C₄₃	—	4	1	no	—
150	C₂³×C₄₃	—	4	1	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	—	4	1	no	—
154	C₂³×C₄₃	—	4	1	no	—
155	C₂³×C₄₃	—	4	1	no	—
156	C₂³×C₄₃	—	4	16	no	—
157	C₂³×C₄₃	#108	1	4	yes	complemented
158	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	1	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	1	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
201	C₈×C₄₃	—	4	4	no	—
202	C₄₃⋊C₈	—	2	8	no	—
203	C₄₃⋊C₈	—	4	4	no	—
204	#21948	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	8	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	2	1	no	—
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	2	1	no	—
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	1	no	—
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	—	2	1	no	—
220	C₂²×C₄₃	—	2	1	no	—
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	4	4	no	—
223	C₂²×C₄₃	—	4	4	no	—
224	C₂²×C₄₃	—	4	4	no	—
225	C₂²×C₄₃	—	4	4	no	—
226	C₂²×C₄₃	—	4	4	no	—
227	C₂²×C₄₃	—	4	4	no	—
228	C₂²×C₄₃	C₂×#108	1	2	yes	—
229	C₂²×C₄₃	C₂×#108	1	2	yes	—
230	C₂²×C₄₃	C₂×#108	1	2	yes	—
231	C₂²×C₄₃	#430	1	2	yes	—
232	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₂²×C₄₃	#543	1	2	yes	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	2	1	no	—
238	C₄×C₄₃	—	2	1	no	—
239	C₄×C₄₃	—	2	1	no	—
240	C₄×C₄₃	#518	1	2	yes	—
241	C₄×C₄₃	#534	1	2	yes	—
242	C₂×#407	—	43	1	no	—
243	C₂×#407	D₄₃	1	1	yes	characteristic
244	C₂²×C₂²⋊C₈	—	43	1	no	—
245	#1855	—	43	4	no	—
246	#1855	—	43	4	no	—
247	#1810	—	43	4	no	—
248	C₂×C₄₃	—	2	2	no	—
249	C₂×C₄₃	—	2	2	no	—
250	C₂×C₄₃	—	2	2	no	—
251	C₂×C₄₃	—	2	2	no	—
252	C₂×C₄₃	—	2	2	no	—
253	C₂×C₄₃	—	4	1	no	—
254	C₂×C₄₃	—	4	1	no	—
255	C₂×C₄₃	#2315	1	1	yes	characteristic
256	C₂×C₄₃	C₂²×#108	1	1	yes	characteristic
257	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
258	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic
259	C₂²×M₁₆	—	43	2	no	—
260	C₂²×M₁₆	C₂×D₄₃	1	2	yes	—
261	C₂³×C₈	—	43	2	no	—
262	C₂×#108	—	43	8	no	—
263	#407	—	2	1	no	—
264	#407	—	2	1	no	—
265	#407	—	43	2	no	—
266	#407	—	43	2	no	—
267	#407	—	86	1	no	—
268	#407	—	86	1	no	—
269	#407	C₂×D₄₃	1	2	yes	—
270	#407	C₂×D₄₃	1	2	yes	—
271	C₂×C₂²⋊C₈	—	2	1	no	—
272	C₂×C₂²⋊C₈	—	2	1	no	—
273	C₂×C₂²⋊C₈	—	43	2	no	—
274	C₂×C₂²⋊C₈	—	43	2	no	—
275	C₂×C₂²⋊C₈	—	43	2	no	—
276	C₂×C₂²⋊C₈	—	43	2	no	—
277	C₂×C₂²⋊C₈	—	43	2	no	—
278	C₂×C₂²⋊C₈	—	43	2	no	—
279	C₂×C₂²⋊C₈	—	86	1	no	—
280	C₂×C₂²⋊C₈	—	86	1	no	—
281	#341	—	43	8	no	—
282	C₄₃	#21948	1	1	yes	characteristic, complemented, Sylow
283	C₂⁵	Dic₈₆	1	1	yes	characteristic
284	C₂³×C₄	—	4	4	no	—
285	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
286	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
287	C₂³×C₄	Dic₈₆	1	1	yes	characteristic
288	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
289	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
290	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
291	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
292	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
293	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
294	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
295	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
296	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
297	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
298	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	4	4	no	—
301	C₂×M₁₆	—	43	4	no	—
302	C₂×M₁₆	—	86	2	no	—
303	C₂×M₁₆	—	172	4	no	—
304	C₂×M₁₆	C₂²×D₄₃	1	4	yes	—
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	43	4	no	—
307	C₂²×C₈	—	43	4	no	—
308	C₂²×C₈	—	43	4	no	—
309	C₂²×C₈	—	86	2	no	—
310	C₂²×C₈	—	172	4	no	—
311	#108	—	172	8	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	—	2	2	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	—	43	4	no	—
317	C₂²⋊C₈	—	43	4	no	—
318	C₂²⋊C₈	—	43	4	no	—
319	C₂²⋊C₈	—	43	4	no	—
320	C₂²⋊C₈	—	86	2	no	—
321	C₂²⋊C₈	—	86	2	no	—
322	C₂²⋊C₈	—	86	2	no	—
323	C₂²⋊C₈	—	86	2	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	4	2	no	—
326	C₂⁴	—	4	2	no	—
327	C₂⁴	Dic₄₃⋊C₄	1	1	yes	characteristic
328	C₂⁴	Dic₄₃⋊C₄	1	1	yes	characteristic
329	C₂⁴	Dic₄₃⋊C₄	1	1	yes	characteristic
330	C₂⁴	Dic₄₃⋊C₄	1	1	yes	characteristic
331	C₂⁴	C₂×Dic₈₆	1	1	yes	characteristic
332	C₂⁴	C₂×Dic₈₆	1	1	yes	characteristic
333	C₂⁴	C₂×Dic₈₆	1	1	yes	characteristic
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
349	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
350	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
351	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
352	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
353	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
354	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
355	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
356	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
357	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
358	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
359	C₂²×C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
360	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
361	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
362	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
376	M₁₆	—	2	8	no	—
377	M₁₆	—	4	4	no	—
378	M₁₆	—	86	8	no	—
379	M₁₆	—	172	4	no	—
380	C₂×C₈	—	2	4	no	—
381	C₂×C₈	—	4	4	no	—
382	C₂×C₈	—	43	8	no	—
383	C₂×C₈	—	86	8	no	—
384	C₂×C₈	—	86	4	no	—
385	C₂×C₈	—	172	4	no	—
386	C₂×C₈	—	172	4	no	—
387	C₂×C₈	—	172	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	4	1	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	16	no	—
409	C₂³	#13063260	1	4	yes	complemented
410	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
411	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
412	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
413	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
414	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
415	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
416	C₂³	C₂²×Dic₈₆	1	1	yes	characteristic
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
445	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
447	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
448	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
449	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂×C₄	#13063370	1	4	yes	—
453	C₈	—	4	4	no	—
454	C₈	—	86	8	no	—
455	C₈	—	172	4	no	—
456	C₂²	—	2	8	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	4	4	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	C₂×#13063260	1	2	yes	—
480	C₂²	C₂×#13063260	1	2	yes	—
481	C₂²	C₂×#13063260	1	2	yes	—
482	C₂²	#14582947	1	2	yes	—
483	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
484	C₂²	#14583525	1	2	yes	—
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	#14583372	1	2	yes	—
492	C₄	#14583458	1	2	yes	—
493	C₂	—	2	2	no	—
494	C₂	—	2	2	no	—
495	C₂	—	2	2	no	—
496	C₂	—	2	2	no	—
497	C₂	—	2	2	no	—
498	C₂	—	4	1	no	—
499	C₂	—	4	1	no	—
500	C₂	#19137207	1	1	yes	characteristic
501	C₂	C₂²×#13063260	1	1	yes	characteristic
502	C₂	C₂×#14582947	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#407	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂⁵×C₄₃	Q₈
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#407	D₄₃
hypocenter	C₄₃	#21948
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. #19134800	C₂	semidirect
4. #19134799	C₂	semidirect
5. #19134631	C₂	semidirect
9. C₂×#13063260	C₂²	semidirect
22. #14582663	C₂²	semidirect
157. C₂³×C₄₃	#108	semidirect
282. C₄₃	#21948	semidirect
409. C₂³	#13063260	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582863	2
C₂²×C₂²⋊(C₄₃⋊C₈)	2
#19134800	2
#19134799	2
#19134631	2
C₂×C₄₃×#407	2
#21948	43