Subgroups — #25095218

Order 11008.

958 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583028	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583027	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063290	C₂	1	1	yes	maximal, characteristic
4	#19134470	C₂	1	1	yes	maximal, characteristic
5	#19134469	C₂	1	1	yes	maximal, characteristic
6	#19134466	C₂	1	1	yes	maximal, characteristic
7	#19134463	C₂	1	1	yes	maximal, characteristic
8	#19134461	C₂	1	1	yes	maximal, characteristic
9	C₄⋊C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
10	#19134443	C₂	1	1	yes	maximal, characteristic
11	#19134443	C₂	1	1	yes	maximal, characteristic
12	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic
13	#97×Dic₄₃	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1771	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	C₂×#13063290	C₄	1	2	yes	—
18	#14583028	C₄	1	8	yes	complemented
19	#14583027	C₄	1	8	yes	complemented
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×#13063236	C₂²	1	1	yes	characteristic
26	C₂×#13063236	C₂²	1	1	yes	characteristic
27	C₂×#13063235	C₂²	1	1	yes	characteristic
28	C₂×#13063235	C₂²	1	1	yes	characteristic
29	C₂×#13063235	C₂²	1	1	yes	characteristic
30	C₂×#13063235	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×Dic₄₃	C₄	1	2	yes	—
39	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
41	#14582750	C₄	1	2	yes	—
42	#14582750	C₄	1	2	yes	—
43	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
44	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
45	C₄²×Dic₄₃	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	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#336	C₂²	1	1	yes	characteristic
56	C₄₃×#336	C₂²	1	1	yes	characteristic
57	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
63	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
64	#13063290	—	2	8	no	—
65	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
67	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
72	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
73	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
81	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
82	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
83	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
85	#13063236	—	2	2	no	—
86	#13063236	C₂×C₄	1	4	yes	—
87	#13063235	—	2	2	no	—
88	#13063235	—	2	2	no	—
89	#13063235	C₂×C₄	1	4	yes	—
90	#13063235	C₂×C₄	1	4	yes	—
91	C₄×C₄₃⋊C₈	—	2	2	no	—
92	C₈×Dic₄₃	—	2	2	no	—
93	C₈×Dic₄₃	—	2	2	no	—
94	C₈×Dic₄₃	—	2	2	no	—
95	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
96	C₈×Dic₄₃	C₂×C₄	1	4	yes	—
97	C₈×Dic₄₃	Q₈	1	4	yes	complemented
98	C₄₃⋊#95	C₂×C₄	1	2	yes	—
99	C₄₃⋊#95	C₂×C₄	1	2	yes	—
100	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
109	#97×C₄₃	—	2	2	no	—
110	#97×C₄₃	C₂×C₄	1	4	yes	—
111	C₄×C₈×C₄₃	—	2	2	no	—
112	#95×C₄₃	C₂×C₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
124	C₂×Dic₈₆	—	2	4	no	—
125	C₂×Dic₈₆	C₄²	1	4	yes	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	1	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
137	C₂×C₈×C₄₃	#41	1	2	yes	—
138	C₄⋊C₄×C₄₃	—	2	4	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₄²×C₄₃	—	2	1	no	—
143	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
144	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
145	C₄⋊Dic₄₃	C₄²	1	4	yes	—
146	Dic₄₃⋊C₄	—	2	4	no	—
147	Dic₄₃⋊C₄	—	2	4	no	—
148	Dic₄₃⋊C₄	C₄²	1	4	yes	—
149	Dic₄₃⋊C₄	C₄²	1	4	yes	—
150	C₄×Dic₄₃	—	2	1	no	—
151	C₄×Dic₄₃	—	2	1	no	—
152	C₄×Dic₄₃	—	2	4	no	—
153	C₄×Dic₄₃	—	2	4	no	—
154	C₄×Dic₄₃	—	2	4	no	—
155	C₄×Dic₄₃	—	2	4	no	—
156	C₄×Dic₄₃	—	2	4	no	—
157	C₄×Dic₄₃	M₁₆	1	8	yes	—
158	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
159	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
160	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
161	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
162	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
163	C₄×Dic₄₃	#41	1	2	yes	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	—	2	1	no	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	1	no	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
174	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
175	C₂×C₄₃⋊C₈	#41	1	2	yes	—
176	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
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	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
185	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
186	C₂×C₄×C₄₃	C₂×M₁₆	1	4	yes	—
187	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
193	C₂×Dic₄₃	—	2	2	no	—
194	C₂×Dic₄₃	—	2	2	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	—	2	2	no	—
197	C₂×Dic₄₃	—	2	2	no	—
198	C₂×Dic₄₃	—	2	2	no	—
199	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
200	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
201	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
202	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
203	C₂×Dic₄₃	C₄×Q₈	1	4	yes	—
204	C₂×Dic₄₃	C₂×M₁₆	1	4	yes	—
205	C₂×Dic₄₃	C₂×M₁₆	1	4	yes	—
206	C₂×Dic₄₃	#131	1	4	yes	—
207	Dic₈₆	—	2	8	no	—
208	C₈×C₄₃	—	2	2	no	—
209	C₈×C₄₃	—	2	2	no	—
210	C₈×C₄₃	—	2	2	no	—
211	C₈×C₄₃	C₄×Q₈	1	4	yes	complemented
212	C₄₃⋊C₈	—	2	2	no	—
213	C₄₃⋊C₈	—	2	2	no	—
214	C₄₃⋊C₈	—	2	2	no	—
215	C₄₃⋊C₈	C₄×Q₈	1	4	yes	complemented
216	C₄×#446	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
218	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
219	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
220	C₂²×C₄₃	C₂²×M₁₆	1	2	yes	—
221	C₂²×C₄₃	C₂×#131	1	2	yes	—
222	C₄×C₄₃	—	2	2	no	—
223	C₄×C₄₃	—	2	2	no	—
224	C₄×C₄₃	—	2	4	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
227	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
228	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
229	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
230	Dic₄₃	—	2	2	no	—
231	Dic₄₃	—	2	2	no	—
232	Dic₄₃	—	2	2	no	—
233	Dic₄₃	—	4	2	no	—
234	Dic₄₃	C₄×M₁₆	1	4	yes	—
235	Dic₄₃	#446	1	8	yes	complemented
236	C₂×#446	—	43	1	no	—
237	C₂×#446	—	43	1	no	—
238	C₄²×Q₈	—	43	1	no	—
239	#1771	—	43	1	no	—
240	#1771	—	43	1	no	—
241	#1771	—	43	1	no	—
242	#1771	D₄₃	1	1	yes	characteristic
243	#1770	—	43	1	no	—
244	#1770	—	43	1	no	—
245	C₄×C₄⋊C₈	—	43	1	no	—
246	C₄×C₄⋊C₈	—	43	1	no	—
247	C₄×C₄⋊C₈	—	43	1	no	—
248	C₄×#97	—	43	1	no	—
249	C₄×#97	—	43	1	no	—
250	C₄²×C₈	—	43	1	no	—
251	C₂×C₄₃	C₄²×Q₈	1	1	yes	characteristic
252	C₂×C₄₃	C₂×C₄×M₁₆	1	1	yes	characteristic
253	C₂×C₄₃	C₄×#131	1	1	yes	characteristic
254	C₂×C₄₃	C₂×#446	1	2	yes	—
255	C₂×C₄₃	#2965	1	2	yes	—
256	C₂×C₄×Q₈	—	43	2	no	—
257	C₂×C₄×Q₈	—	43	1	no	—
258	#446	—	43	8	no	—
259	#446	—	43	8	no	—
260	C₂×C₄⋊C₈	—	43	1	no	—
261	C₂×C₄⋊C₈	—	43	1	no	—
262	C₂×C₄⋊C₈	—	43	1	no	—
263	C₂×C₄⋊C₈	—	43	1	no	—
264	C₂×C₄⋊C₈	—	43	1	no	—
265	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
266	C₂×#97	—	43	1	no	—
267	C₂×#97	—	43	1	no	—
268	C₂×#97	—	43	1	no	—
269	C₂×#97	—	43	1	no	—
270	C₂×#97	—	43	1	no	—
271	C₂×#97	—	43	1	no	—
272	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
273	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
274	C₂×C₄×C₈	—	43	1	no	—
275	C₂×C₄×C₈	—	43	1	no	—
276	C₂×C₄×C₈	—	43	1	no	—
277	C₂×C₄×C₈	—	43	1	no	—
278	C₂×C₄×C₈	—	43	1	no	—
279	C₂×C₄×C₈	—	43	1	no	—
280	C₂×C₄×C₈	—	43	1	no	—
281	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
282	C₄×C₄⋊C₄	—	43	2	no	—
283	C₄×C₄⋊C₄	—	43	1	no	—
284	C₄×C₄⋊C₄	—	43	1	no	—
285	C₄×C₄⋊C₄	—	43	2	no	—
286	C₄×C₄⋊C₄	—	43	2	no	—
287	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
288	C₄³	—	43	1	no	—
289	C₄³	—	43	1	no	—
290	C₄³	—	43	1	no	—
291	#336	—	43	1	no	—
292	#336	—	43	1	no	—
293	#336	—	43	1	no	—
294	#336	—	43	1	no	—
295	#336	C₂×D₄₃	1	1	yes	characteristic
296	#336	C₂×D₄₃	1	1	yes	characteristic
297	C₄₃	C₄×#446	1	1	yes	characteristic, complemented, Sylow
298	C₂²×Q₈	—	43	1	no	—
299	C₂²×C₈	—	43	1	no	—
300	C₂²×C₈	—	43	1	no	—
301	C₂²×C₈	—	43	1	no	—
302	C₂²×C₈	—	43	1	no	—
303	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
307	C₄×Q₈	—	43	4	no	—
308	C₄×Q₈	—	43	4	no	—
309	C₄×Q₈	—	86	8	no	—
310	C₂×C₄⋊C₄	—	43	1	no	—
311	C₂×C₄⋊C₄	—	43	1	no	—
312	C₂×C₄⋊C₄	—	43	1	no	—
313	C₂×C₄⋊C₄	—	43	2	no	—
314	C₂×C₄⋊C₄	—	43	2	no	—
315	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
316	C₂×C₄²	—	43	2	no	—
317	C₂×C₄²	—	43	1	no	—
318	C₂×C₄²	—	43	1	no	—
319	C₂×C₄²	—	43	1	no	—
320	C₂×C₄²	—	43	2	no	—
321	C₂×C₄²	—	43	2	no	—
322	C₂×C₄²	—	43	2	no	—
323	C₂×C₄²	—	43	2	no	—
324	C₂×C₄²	—	43	2	no	—
325	C₂×C₄²	—	43	1	no	—
326	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
329	C₄⋊C₈	—	43	4	no	—
330	C₄⋊C₈	—	43	4	no	—
331	C₄⋊C₈	—	43	4	no	—
332	C₄⋊C₈	—	43	4	no	—
333	C₄⋊C₈	—	43	4	no	—
334	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
335	#97	—	2	2	no	—
336	#97	—	43	4	no	—
337	#97	—	43	4	no	—
338	#97	—	43	4	no	—
339	#97	—	86	2	no	—
340	#97	—	86	2	no	—
341	#97	—	86	2	no	—
342	#97	C₄×D₄₃	1	4	yes	—
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	—	43	4	no	—
345	C₄×C₈	—	43	4	no	—
346	C₄×C₈	—	43	4	no	—
347	C₄×C₈	—	86	2	no	—
348	C₄×C₈	—	86	2	no	—
349	C₄×C₈	—	86	2	no	—
350	C₄×C₈	—	86	2	no	—
351	#95	—	43	2	no	—
352	#95	—	43	2	no	—
353	#95	C₄×D₄₃	1	2	yes	—
354	C₂×Q₈	—	43	4	no	—
355	C₂×Q₈	—	86	4	no	—
356	C₂²×C₄	—	43	2	no	—
357	C₂²×C₄	—	43	1	no	—
358	C₂²×C₄	—	43	1	no	—
359	C₂²×C₄	—	43	1	no	—
360	C₂²×C₄	—	43	1	no	—
361	C₂²×C₄	—	43	2	no	—
362	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
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	2	yes	—
366	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	43	2	no	—
374	C₂×C₈	—	43	2	no	—
375	C₂×C₈	—	43	2	no	—
376	C₂×C₈	—	43	2	no	—
377	C₂×C₈	—	43	2	no	—
378	C₂×C₈	—	43	2	no	—
379	C₂×C₈	—	86	1	no	—
380	C₂×C₈	—	86	1	no	—
381	C₂×C₈	—	86	1	no	—
382	C₂×C₈	—	86	1	no	—
383	C₂×C₈	—	86	1	no	—
384	C₂×C₈	—	86	1	no	—
385	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
386	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
387	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
388	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
389	C₂×C₈	#10621900	1	2	yes	—
390	C₂×C₈	Q₈×D₄₃	1	2	yes	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	43	4	no	—
393	C₄⋊C₄	—	43	4	no	—
394	C₄⋊C₄	—	43	4	no	—
395	C₄⋊C₄	—	86	4	no	—
396	C₄⋊C₄	—	86	4	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	43	8	no	—
402	C₄²	—	43	2	no	—
403	C₄²	—	43	2	no	—
404	C₄²	—	43	2	no	—
405	C₄²	—	43	2	no	—
406	C₄²	—	43	2	no	—
407	C₄²	—	43	2	no	—
408	C₄²	—	86	4	no	—
409	C₄²	—	86	4	no	—
410	C₄²	—	86	4	no	—
411	C₄²	—	86	4	no	—
412	C₄²	—	86	4	no	—
413	C₄²	—	86	1	no	—
414	C₄²	—	86	1	no	—
415	C₄²	C₂×C₄×D₄₃	1	2	yes	—
416	C₄²	C₂×C₄×D₄₃	1	2	yes	—
417	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
418	Q₈	—	86	8	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	—	43	2	no	—
427	C₂×C₄	—	43	4	no	—
428	C₂×C₄	—	43	4	no	—
429	C₂×C₄	—	43	4	no	—
430	C₂×C₄	—	43	4	no	—
431	C₂×C₄	—	43	2	no	—
432	C₂×C₄	—	43	2	no	—
433	C₂×C₄	—	43	2	no	—
434	C₂×C₄	—	86	2	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	86	2	no	—
438	C₂×C₄	—	86	2	no	—
439	C₂×C₄	—	86	2	no	—
440	C₂×C₄	C₄²×D₄₃	1	2	yes	—
441	C₂×C₄	C₄²×D₄₃	1	2	yes	—
442	C₂×C₄	M₁₆×D₄₃	1	4	yes	—
443	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
445	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
447	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	43	4	no	—
453	C₈	—	86	2	no	—
454	C₈	—	86	2	no	—
455	C₈	—	86	2	no	—
456	C₈	#13063290	1	4	yes	complemented
457	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
458	C₂²	C₄×Q₈×D₄₃	1	1	yes	characteristic
459	C₂²	C₄×#10621900	1	1	yes	characteristic
460	C₂²	C₂×M₁₆×D₄₃	1	2	yes	—
461	C₂²	#131×D₄₃	1	2	yes	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	43	4	no	—
467	C₄	—	43	8	no	—
468	C₄	—	86	2	no	—
469	C₄	—	86	2	no	—
470	C₄	—	86	2	no	—
471	C₄	—	172	2	no	—
472	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
473	C₄	C₂×#13063290	1	1	yes	characteristic
474	C₄	C₄×#10621900	1	1	yes	characteristic
475	C₄	#14583367	1	1	yes	characteristic
476	C₂	C₄×#13063290	1	1	yes	characteristic
477	C₂	C₄×M₁₆×D₄₃	1	1	yes	characteristic
478	C₂	#19143017	1	1	yes	characteristic
479	C₂	#446×D₄₃	1	2	yes	—
480	C₂	#19143555	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#1771	C₂
socle, prime radical	C₂³×C₄₃	C₂³×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1771	D₄₃
hypocenter	C₄₃	C₄×#446
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
18. #14583028	C₄	semidirect
19. #14583027	C₄	semidirect
97. C₈×Dic₄₃	Q₈	semidirect
211. C₈×C₄₃	C₄×Q₈	semidirect
215. C₄₃⋊C₈	C₄×Q₈	semidirect
235. Dic₄₃	#446	semidirect
297. C₄₃	C₄×#446	semidirect
456. C₈	#13063290	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583028	2
C₂×#14583027	2
C₄×#13063290	2
#19134470	2
#19134469	2
#19134466	2
#19134463	2
#19134461	2
C₄⋊C₈×Dic₄₃	2
#19134443	2
#97×Dic₄₃	2
C₄×C₈×Dic₄₃	2
C₄₃×#1771	2
C₄×#446	43