Subgroups — #25099359

Order 11008.

1054 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143159	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063252	C₂	1	1	yes	maximal, characteristic
3	#19143040	C₂	1	1	yes	maximal, characteristic
4	C₂×M₁₆×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135308	C₂	1	4	yes	maximal, complemented
6	#19135301	C₂	1	4	yes	maximal, complemented
7	#19134322	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14582658	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2896	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂²×#10621877	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
14	#14582926	—	2	2	no	—
15	#14582926	C₂²	1	4	yes	complemented
16	#14582923	—	2	2	no	—
17	C₂×#13063252	—	2	4	no	—
18	C₂×#13063252	C₂²	1	2	yes	—
19	C₂×#13063252	C₂²	1	2	yes	—
20	#14582866	—	2	2	no	—
21	#14582866	C₂²	1	4	yes	—
22	#14582863	—	2	2	no	—
23	M₁₆×Dic₄₃	—	2	4	no	—
24	C₂×#13063235	C₂²	1	2	yes	complemented
25	C₂×C₈×Dic₄₃	C₂²	1	2	yes	complemented
26	#14582664	C₂²	1	4	yes	complemented
27	#14582658	C₂²	1	2	yes	complemented
28	#14582658	C₂²	1	2	yes	complemented
29	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#419	C₄	1	2	yes	complemented
33	C₄₃×#418	C₄	1	2	yes	complemented
34	C₄₃×#417	C₄	1	4	yes	complemented
35	C₄₃×#416	C₂²	1	4	yes	—
36	C₂³×Dic₄₃	—	2	1	no	—
37	C₂×#10621877	—	2	2	no	—
38	C₂×#10621877	—	2	2	no	—
39	C₂×#10621877	—	2	1	no	—
40	C₂×#10621877	—	2	1	no	—
41	C₂×#10621877	—	2	2	no	—
42	C₂×#10621877	—	2	2	no	—
43	C₂×#10621877	—	2	2	no	—
44	C₂×#10621877	—	2	2	no	—
45	C₂×#10621877	D₄	1	2	yes	—
46	C₂×#10621877	D₄	1	2	yes	—
47	C₂×#10621877	C₂³	1	2	yes	—
48	C₂×#10621877	C₂³	1	2	yes	—
49	C₂²×C₄₃⋊C₈	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
52	C₂×C₄×Dic₄₃	—	2	2	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	C₂×C₄×Dic₄₃	D₄	1	4	yes	—
55	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
57	C₄⋊(C₄₃⋊C₈)	—	2	8	no	—
58	#13063252	—	2	4	no	—
59	#13063252	—	2	4	no	—
60	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
61	#13063235	—	2	4	no	—
62	C₈×Dic₄₃	—	2	4	no	—
63	C₂×#41×C₄₃	—	2	1	no	—
64	C₂×#41×C₄₃	—	2	1	no	—
65	C₂×#41×C₄₃	—	2	2	no	—
66	C₂×#41×C₄₃	—	2	2	no	—
67	C₂×#41×C₄₃	—	2	2	no	—
68	C₂×#41×C₄₃	—	2	2	no	—
69	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
70	C₂×#41×C₄₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂²×D₄×C₄₃	—	2	1	no	—
73	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	—	2	1	no	—
75	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×M₁₆×C₄₃	—	2	2	no	—
77	C₂×M₁₆×C₄₃	—	2	2	no	—
78	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
81	#117×C₄₃	—	2	1	no	—
82	#117×C₄₃	—	2	1	no	—
83	#117×C₄₃	C₂×C₄	1	2	yes	—
84	#117×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	—	2	1	no	—
88	#103×C₄₃	C₂×C₄	1	8	yes	complemented
89	#102×C₄₃	C₂×C₄	1	8	yes	complemented
90	C₂⁴×C₄₃	—	2	1	no	—
91	C₂⁴×C₄₃	#41	1	1	yes	characteristic
92	#41×C₄₃	—	2	4	no	—
93	#41×C₄₃	—	2	4	no	—
94	#41×C₄₃	—	2	2	no	—
95	#41×C₄₃	—	2	2	no	—
96	#41×C₄₃	—	2	2	no	—
97	#41×C₄₃	—	2	2	no	—
98	#41×C₄₃	—	4	2	no	—
99	#41×C₄₃	—	4	2	no	—
100	#41×C₄₃	—	4	2	no	—
101	#41×C₄₃	—	4	2	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	2	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	4	2	no	—
112	C₂×D₄×C₄₃	—	4	2	no	—
113	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	4	2	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₄₃	#41	1	2	yes	—
126	C₂²×C₄×C₄₃	#41	1	2	yes	—
127	C₂²×C₄×C₄₃	#41	1	2	yes	—
128	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂²×Dic₄₃	—	2	4	no	—
131	C₂²×Dic₄₃	—	2	1	no	—
132	C₂²×Dic₄₃	—	2	1	no	—
133	C₂²×Dic₄₃	—	4	4	no	—
134	M₁₆×C₄₃	—	2	4	no	—
135	M₁₆×C₄₃	—	2	4	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₂²⋊C₄×C₄₃	—	2	2	no	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	—	2	2	no	—
145	C₄×Dic₄₃	—	2	4	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
149	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
150	#10621877	—	2	4	no	—
151	#10621877	—	2	4	no	—
152	#10621877	—	2	2	no	—
153	#10621877	—	2	2	no	—
154	#10621877	—	2	2	no	—
155	#10621877	—	2	2	no	—
156	#10621877	—	4	2	no	—
157	#10621877	—	4	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	4	2	no	—
163	C₂×C₄₃⋊C₈	—	4	2	no	—
164	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	8	2	no	—
169	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂³×C₄₃	#123	1	2	yes	—
172	C₂³×C₄₃	#126	1	2	yes	—
173	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	2	no	—
176	Q₈×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	2	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	D₄×C₄₃	—	4	4	no	—
182	D₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	—	8	2	no	—
190	C₂×C₄×C₄₃	#117	1	2	yes	—
191	C₂×C₄×C₄₃	#117	1	2	yes	—
192	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	2	yes	—
197	C₂×C₄×C₄₃	#121	1	2	yes	—
198	C₂×C₄×C₄₃	#123	1	2	yes	—
199	C₂×C₄×C₄₃	#124	1	2	yes	—
200	C₂×C₄×C₄₃	#124	1	2	yes	—
201	C₂×C₄×C₄₃	#126	1	2	yes	—
202	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
208	C₂×Dic₄₃	—	2	4	no	—
209	C₂×Dic₄₃	—	2	2	no	—
210	C₂×Dic₄₃	—	2	2	no	—
211	C₂×Dic₄₃	—	4	8	no	—
212	C₂×Dic₄₃	—	4	2	no	—
213	C₈×C₄₃	—	2	4	no	—
214	C₄₃⋊C₈	—	2	4	no	—
215	C₄₃⋊C₈	—	4	2	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	#21099	—	43	1	no	maximal, Sylow
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	4	2	no	—
222	C₂²×C₄₃	—	4	2	no	—
223	C₂²×C₄₃	—	4	4	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	8	4	no	—
226	C₂²×C₄₃	#388	1	2	yes	—
227	C₂²×C₄₃	#388	1	2	yes	—
228	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
230	C₂²×C₄₃	C₂×#126	1	1	yes	characteristic
231	C₄×C₄₃	—	4	4	no	—
232	C₄×C₄₃	—	4	2	no	—
233	C₄×C₄₃	#388	1	2	yes	—
234	C₄×C₄₃	#388	1	2	yes	—
235	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
236	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
237	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
238	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
239	Dic₄₃	—	2	4	no	—
240	Dic₄₃	—	4	2	no	—
241	#2905	—	43	1	no	—
242	C₂²×#104	—	43	1	no	—
243	#2896	D₄₃	1	1	yes	characteristic
244	#2879	—	43	1	no	—
245	C₂×C₄×M₁₆	—	43	1	no	—
246	#1938	—	43	4	no	—
247	#1937	—	43	4	no	—
248	#1738	—	43	1	no	—
249	C₂×#339	—	43	1	no	—
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	2	no	—
252	C₂×C₄₃	—	2	1	no	—
253	C₂×C₄₃	—	2	2	no	—
254	C₂×C₄₃	—	8	2	no	—
255	C₂×C₄₃	C₂×#388	1	1	yes	characteristic
256	C₂×C₄₃	#2956	1	2	yes	—
257	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
258	C₂²×M₁₆	—	43	1	no	—
259	C₂²×M₁₆	—	43	1	no	—
260	C₂²×M₁₆	—	43	1	no	—
261	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
263	C₂²×C₄²	—	43	1	no	—
264	#424	—	43	4	no	—
265	#424	—	86	2	no	—
266	#423	—	86	2	no	—
267	C₂×#104	—	43	2	no	—
268	C₂×#104	—	43	2	no	—
269	C₂×#104	—	86	4	no	—
270	#419	Dic₄₃	1	2	yes	complemented
271	#418	Dic₄₃	1	2	yes	complemented
272	#417	Dic₄₃	1	4	yes	complemented
273	#416	C₂×D₄₃	1	4	yes	—
274	#408	—	43	4	no	—
275	#408	—	86	2	no	—
276	#407	—	86	2	no	—
277	C₄×M₁₆	—	86	4	no	—
278	C₂×#97	—	43	2	no	—
279	C₂×C₄×C₈	—	43	2	no	—
280	#341	—	43	4	no	—
281	#339	—	43	2	no	—
282	#339	—	43	2	no	—
283	C₄₃	#21099	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	2	1	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	—	2	2	no	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	C₂×Dic₄₃	1	2	yes	—
291	C₂×#41	C₂²×D₄₃	1	2	yes	—
292	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	—	86	1	no	—
297	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
298	C₂×M₁₆	—	2	2	no	—
299	C₂×M₁₆	—	2	2	no	—
300	C₂×M₁₆	—	43	2	no	—
301	C₂×M₁₆	—	43	2	no	—
302	C₂×M₁₆	—	43	2	no	—
303	C₂×M₁₆	—	43	2	no	—
304	C₂×M₁₆	—	86	2	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	—	86	1	no	—
307	C₂×M₁₆	—	86	1	no	—
308	C₂×M₁₆	—	86	2	no	—
309	C₂×M₁₆	—	86	2	no	—
310	C₂×M₁₆	—	86	2	no	—
311	C₂×M₁₆	—	86	2	no	—
312	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
313	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
314	C₂²×C₈	—	43	2	no	—
315	C₂²×C₈	—	86	1	no	—
316	C₂²×C₈	—	86	1	no	—
317	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
318	#117	—	2	1	no	—
319	#117	—	2	1	no	—
320	#117	C₂×Dic₄₃	1	2	yes	—
321	#117	C₂²×D₄₃	1	2	yes	—
322	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	43	4	no	—
326	C₂×C₄²	—	43	1	no	—
327	C₂×C₄²	—	43	1	no	—
328	C₂×C₄²	—	86	2	no	—
329	C₂×C₄²	—	86	1	no	—
330	C₄⋊C₈	—	86	8	no	—
331	#104	—	86	4	no	—
332	#104	—	86	4	no	—
333	#103	C₂×Dic₄₃	1	8	yes	complemented
334	#102	C₂×Dic₄₃	1	8	yes	complemented
335	C₂²⋊C₈	—	86	8	no	—
336	#97	—	86	4	no	—
337	C₄×C₈	—	86	4	no	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	#10621900	1	1	yes	characteristic
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	2	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	—	4	2	no	—
347	#41	—	4	2	no	—
348	#41	—	4	2	no	—
349	#41	—	4	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	—	86	4	no	—
370	C₂²×C₄	—	86	1	no	—
371	C₂²×C₄	—	172	4	no	—
372	C₂²×C₄	#10621898	1	2	yes	—
373	C₂²×C₄	#10621898	1	2	yes	—
374	C₂²×C₄	D₄×D₄₃	1	2	yes	—
375	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
377	C₂²×C₄	#10621900	1	1	yes	characteristic
378	C₂²×C₄	#10621900	1	2	yes	—
379	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
381	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
382	M₁₆	—	2	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	86	4	no	—
385	M₁₆	—	86	4	no	—
386	M₁₆	—	86	2	no	—
387	M₁₆	—	86	2	no	—
388	M₁₆	—	86	2	no	—
389	M₁₆	—	86	2	no	—
390	M₁₆	—	172	2	no	—
391	M₁₆	—	172	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	43	4	no	—
395	C₂×C₈	—	86	2	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	—	86	2	no	—
398	C₂×C₈	—	86	2	no	—
399	C₂×C₈	—	172	2	no	—
400	C₂×C₈	—	172	2	no	—
401	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	43	2	no	—
409	C₄²	—	43	2	no	—
410	C₄²	—	86	4	no	—
411	C₄²	—	86	1	no	—
412	C₄²	—	86	1	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	8	2	no	—
417	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
418	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
419	C₂³	#13063307	1	2	yes	—
420	C₂³	#13063318	1	2	yes	—
421	C₂³	C₂×#10621900	1	1	yes	characteristic
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	4	2	no	—
425	D₄	—	2	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	4	4	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	—	86	4	no	—
439	C₂×C₄	—	86	2	no	—
440	C₂×C₄	—	86	2	no	—
441	C₂×C₄	—	172	8	no	—
442	C₂×C₄	—	172	2	no	—
443	C₂×C₄	#13063284	1	2	yes	—
444	C₂×C₄	#13063284	1	2	yes	—
445	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
446	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
447	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
448	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
449	C₂×C₄	#13063298	1	2	yes	—
450	C₂×C₄	#13063298	1	2	yes	—
451	C₂×C₄	#13063307	1	2	yes	—
452	C₂×C₄	#13063311	1	2	yes	—
453	C₂×C₄	#13063311	1	2	yes	—
454	C₂×C₄	#13063318	1	2	yes	—
455	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
456	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
457	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
458	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
459	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
460	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
461	C₈	—	2	4	no	—
462	C₈	—	86	4	no	—
463	C₈	—	172	2	no	—
464	C₈	—	172	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	4	no	—
473	C₂²	#14582792	1	2	yes	—
474	C₂²	#14582792	1	2	yes	—
475	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
476	C₂²	C₂×#13063307	1	1	yes	characteristic
477	C₂²	C₂×#13063318	1	1	yes	characteristic
478	C₄	—	4	2	no	—
479	C₄	—	4	4	no	—
480	C₄	—	86	4	no	—
481	C₄	—	172	2	no	—
482	C₄	#14582792	1	2	yes	—
483	C₄	#14582792	1	2	yes	—
484	C₄	C₂×#13063284	1	1	yes	characteristic
485	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
486	C₄	C₂×#13063298	1	1	yes	characteristic
487	C₄	C₂×#13063311	1	1	yes	characteristic
488	C₂	—	2	1	no	—
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	2	1	no	—
492	C₂	—	8	2	no	—
493	C₂	C₂×#14582792	1	1	yes	characteristic
494	C₂	#19143505	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2896	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂²×#41×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2896	D₄₃
hypocenter	C₄₃	#21099
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2896

Complements

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

N	H ≅ G/N	type
1. #19143159	C₂	semidirect
4. C₂×M₁₆×Dic₄₃	C₂	semidirect
5. #19135308	C₂	semidirect
6. #19135301	C₂	semidirect
7. #19134322	C₂	semidirect
8. C₂×#14582658	C₂	semidirect
15. #14582926	C₂²	semidirect
24. C₂×#13063235	C₂²	semidirect
25. C₂×C₈×Dic₄₃	C₂²	semidirect
26. #14582664	C₂²	semidirect
27. #14582658	C₂²	semidirect
28. #14582658	C₂²	semidirect
32. C₄₃×#419	C₄	semidirect
33. C₄₃×#418	C₄	semidirect
34. C₄₃×#417	C₄	semidirect
88. #103×C₄₃	C₂×C₄	semidirect
89. #102×C₄₃	C₂×C₄	semidirect
270. #419	Dic₄₃	semidirect
271. #418	Dic₄₃	semidirect
272. #417	Dic₄₃	semidirect
283. C₄₃	#21099	semidirect
333. #103	C₂×Dic₄₃	semidirect
334. #102	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19143159	2
C₂²×#13063252	2
#19143040	2
C₂×M₁₆×Dic₄₃	2
#19135308	2
#19135301	2
#19134322	2
C₂×#14582658	2
C₄₃×#2896	2
#21099	43