Subgroups — #25099114

Order 11008.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582948	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	#19143014	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135245	C₂	1	8	yes	maximal, complemented
6	C₂×#14582658	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2896	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
13	#14582948	—	2	4	no	—
14	C₂×#13063261	C₂²	1	4	yes	complemented
15	C₂×#13063252	—	2	4	no	—
16	C₂×#13063252	C₂²	1	4	yes	—
17	#14582866	—	2	2	no	—
18	#14582866	C₂²	1	4	yes	—
19	#14582863	—	2	2	no	—
20	#14582855	—	2	2	no	—
21	#14582855	C₂²	1	4	yes	complemented
22	C₄×#10621877	—	2	2	no	—
23	#14582658	C₂²	1	4	yes	complemented
24	#14582653	C₂²	1	4	yes	complemented
25	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
26	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#419	C₄	1	2	yes	complemented
29	C₄₃×#418	C₄	1	2	yes	complemented
30	C₄₃×#417	C₄	1	4	yes	complemented
31	C₄₃×#416	C₂²	1	4	yes	—
32	C₂³×Dic₄₃	—	2	1	no	—
33	C₂×#10621877	—	2	1	no	—
34	C₂×#10621877	—	2	2	no	—
35	C₂×#10621877	—	2	2	no	—
36	C₂×#10621877	—	2	2	no	—
37	C₂×#10621877	—	2	1	no	—
38	C₂×#10621877	—	2	2	no	—
39	C₂×#10621877	—	2	2	no	—
40	C₂×#10621877	D₄	1	4	yes	—
41	C₂×#10621877	D₄	1	2	yes	—
42	C₂×#10621877	D₄	1	2	yes	—
43	C₂×#10621877	C₂³	1	2	yes	—
44	C₂×#10621877	C₂³	1	2	yes	—
45	C₂²×C₄₃⋊C₈	—	2	1	no	—
46	C₂²×C₄₃⋊C₈	—	2	1	no	—
47	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
48	C₂×C₄×Dic₄₃	—	2	2	no	—
49	C₂×C₄×Dic₄₃	—	2	2	no	—
50	C₂×C₄×Dic₄₃	—	2	1	no	—
51	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
52	#13063261	—	2	8	no	—
53	#13063252	—	2	8	no	—
54	C₂²⋊(C₄₃⋊C₈)	—	2	8	no	—
55	#13063236	—	2	4	no	—
56	C₄×C₄₃⋊C₈	—	2	4	no	—
57	C₂×#41×C₄₃	—	2	1	no	—
58	C₂×#41×C₄₃	—	2	1	no	—
59	C₂×#41×C₄₃	—	2	2	no	—
60	C₂×#41×C₄₃	—	2	2	no	—
61	C₂×#41×C₄₃	—	2	2	no	—
62	C₂×#41×C₄₃	—	2	2	no	—
63	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
64	C₂×#41×C₄₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₄₃	—	2	1	no	—
67	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₃	—	2	1	no	—
69	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
73	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
75	#117×C₄₃	—	2	1	no	—
76	#117×C₄₃	—	2	1	no	—
77	#117×C₄₃	C₂×C₄	1	2	yes	—
78	#117×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	—	2	1	no	—
82	#103×C₄₃	C₂×C₄	1	8	yes	complemented
83	#102×C₄₃	C₂×C₄	1	8	yes	complemented
84	C₂⁴×C₄₃	—	2	1	no	—
85	C₂⁴×C₄₃	#41	1	1	yes	characteristic
86	#41×C₄₃	—	2	4	no	—
87	#41×C₄₃	—	2	4	no	—
88	#41×C₄₃	—	2	2	no	—
89	#41×C₄₃	—	2	2	no	—
90	#41×C₄₃	—	2	2	no	—
91	#41×C₄₃	—	2	2	no	—
92	#41×C₄₃	—	4	2	no	—
93	#41×C₄₃	—	4	2	no	—
94	#41×C₄₃	—	4	2	no	—
95	#41×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₄₃	—	2	1	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	2	2	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	4	2	no	—
106	C₂×D₄×C₄₃	—	4	2	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	4	2	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	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	2	yes	—
119	C₂²×C₄×C₄₃	#41	1	2	yes	—
120	C₂²×C₄×C₄₃	#41	1	2	yes	—
121	C₂²×C₄×C₄₃	#41	1	2	yes	—
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²×Dic₄₃	—	2	2	no	—
125	C₂²×Dic₄₃	—	4	4	no	—
126	C₂²×Dic₄₃	—	4	2	no	—
127	M₁₆×C₄₃	—	2	4	no	—
128	M₁₆×C₄₃	—	2	4	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
134	C₂²⋊C₄×C₄₃	—	2	2	no	—
135	C₂²⋊C₄×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄×Dic₄₃	—	2	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	4	2	no	—
141	#10621877	—	2	4	no	—
142	#10621877	—	2	4	no	—
143	#10621877	—	2	4	no	—
144	#10621877	—	2	2	no	—
145	#10621877	—	2	2	no	—
146	#10621877	—	2	2	no	—
147	#10621877	—	4	2	no	—
148	#10621877	C₂×D₄	1	4	yes	—
149	C₂×C₄₃⋊C₈	—	2	4	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	4	2	no	—
155	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	2	no	—
159	C₂³×C₄₃	—	8	2	no	—
160	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
162	C₂³×C₄₃	#124	1	2	yes	—
163	C₂³×C₄₃	#126	1	2	yes	—
164	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
165	Q₈×C₄₃	—	2	2	no	—
166	Q₈×C₄₃	—	2	2	no	—
167	Q₈×C₄₃	—	4	2	no	—
168	D₄×C₄₃	—	2	2	no	—
169	D₄×C₄₃	—	2	2	no	—
170	D₄×C₄₃	—	4	2	no	—
171	D₄×C₄₃	—	4	2	no	—
172	D₄×C₄₃	—	4	4	no	—
173	D₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	8	2	no	—
181	C₂×C₄×C₄₃	#117	1	2	yes	—
182	C₂×C₄×C₄₃	#117	1	2	yes	—
183	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
185	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#121	1	2	yes	—
188	C₂×C₄×C₄₃	#121	1	2	yes	—
189	C₂×C₄×C₄₃	#123	1	2	yes	—
190	C₂×C₄×C₄₃	#123	1	2	yes	—
191	C₂×C₄×C₄₃	#124	1	2	yes	—
192	C₂×C₄×C₄₃	#126	1	2	yes	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₄₃	—	2	4	no	—
200	C₂×Dic₄₃	—	4	2	no	—
201	C₂×Dic₄₃	—	4	8	no	—
202	C₂×Dic₄₃	—	4	2	no	—
203	C₈×C₄₃	—	2	4	no	—
204	C₄₃⋊C₈	—	2	4	no	—
205	C₄₃⋊C₈	—	2	4	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	#21071	—	43	1	no	maximal, Sylow
208	C₂²×C₄₃	—	2	2	no	—
209	C₂²×C₄₃	—	2	2	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	4	2	no	—
212	C₂²×C₄₃	—	4	2	no	—
213	C₂²×C₄₃	—	4	4	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	—	8	4	no	—
216	C₂²×C₄₃	#388	1	2	yes	—
217	C₂²×C₄₃	#388	1	2	yes	—
218	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
219	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
220	C₂²×C₄₃	C₂×#126	1	1	yes	characteristic
221	C₄×C₄₃	—	4	4	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	#388	1	2	yes	—
224	C₄×C₄₃	#388	1	2	yes	—
225	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
226	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
228	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
229	Dic₄₃	—	4	4	no	—
230	C₂×#430	—	43	1	no	—
231	C₂²×#104	—	43	1	no	—
232	#2896	D₄₃	1	1	yes	characteristic
233	#2879	—	43	1	no	—
234	#2873	—	43	1	no	—
235	#1929	—	43	8	no	—
236	C₂×#339	—	43	1	no	—
237	#1728	—	43	1	no	—
238	C₂×C₄₃	—	2	1	no	—
239	C₂×C₄₃	—	2	2	no	—
240	C₂×C₄₃	—	2	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	8	2	no	—
243	C₂×C₄₃	C₂×#388	1	1	yes	characteristic
244	C₂×C₄₃	#2956	1	2	yes	—
245	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
246	C₂²×M₁₆	—	43	1	no	—
247	C₂²×M₁₆	—	43	1	no	—
248	C₂²×M₁₆	—	43	1	no	—
249	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
250	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
251	C₂²×C₄²	—	43	1	no	—
252	#430	—	86	4	no	—
253	C₂×#108	—	43	4	no	—
254	C₂×#104	—	43	4	no	—
255	C₂×#104	—	86	4	no	—
256	#419	Dic₄₃	1	2	yes	complemented
257	#418	Dic₄₃	1	2	yes	complemented
258	#417	Dic₄₃	1	4	yes	complemented
259	#416	C₂×D₄₃	1	4	yes	—
260	#408	—	43	4	no	—
261	#408	—	86	2	no	—
262	#407	—	86	2	no	—
263	#405	—	43	4	no	—
264	#405	—	86	2	no	—
265	C₄×M₁₆	—	86	2	no	—
266	#339	—	43	4	no	—
267	#336	—	43	4	no	—
268	C₄₃	#21071	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	C₂×Dic₄₃	1	2	yes	—
276	C₂×#41	C₂²×D₄₃	1	2	yes	—
277	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂³×C₄	—	86	1	no	—
282	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	43	2	no	—
286	C₂×M₁₆	—	43	2	no	—
287	C₂×M₁₆	—	43	4	no	—
288	C₂×M₁₆	—	43	2	no	—
289	C₂×M₁₆	—	43	2	no	—
290	C₂×M₁₆	—	86	2	no	—
291	C₂×M₁₆	—	86	2	no	—
292	C₂×M₁₆	—	86	1	no	—
293	C₂×M₁₆	—	86	2	no	—
294	C₂×M₁₆	—	86	1	no	—
295	C₂×M₁₆	—	86	2	no	—
296	C₂×M₁₆	—	86	2	no	—
297	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
298	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
299	C₂²×C₈	—	43	2	no	—
300	C₂²×C₈	—	86	1	no	—
301	C₂²×C₈	—	86	1	no	—
302	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
303	#117	—	2	1	no	—
304	#117	—	2	1	no	—
305	#117	C₂×Dic₄₃	1	2	yes	—
306	#117	C₂²×D₄₃	1	2	yes	—
307	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	43	2	no	—
311	C₂×C₄²	—	86	2	no	—
312	C₂×C₄²	—	86	2	no	—
313	C₂×C₄²	—	86	1	no	—
314	#108	—	86	8	no	—
315	#104	—	86	8	no	—
316	#103	C₂×Dic₄₃	1	8	yes	complemented
317	#102	C₂×Dic₄₃	1	8	yes	complemented
318	C₂²⋊C₈	—	86	8	no	—
319	#97	—	86	4	no	—
320	C₄×C₈	—	86	4	no	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	#10621900	1	1	yes	characteristic
323	#41	—	2	4	no	—
324	#41	—	2	4	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	2	no	—
329	#41	—	4	2	no	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	—	4	2	no	—
344	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	—	4	2	no	—
351	C₂²×C₄	—	86	2	no	—
352	C₂²×C₄	—	172	4	no	—
353	C₂²×C₄	—	172	2	no	—
354	C₂²×C₄	#10621898	1	2	yes	—
355	C₂²×C₄	#10621898	1	2	yes	—
356	C₂²×C₄	D₄×D₄₃	1	2	yes	—
357	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
359	C₂²×C₄	#10621900	1	2	yes	—
360	C₂²×C₄	#10621900	1	1	yes	characteristic
361	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	4	no	—
366	M₁₆	—	43	4	no	—
367	M₁₆	—	86	4	no	—
368	M₁₆	—	86	4	no	—
369	M₁₆	—	86	4	no	—
370	M₁₆	—	86	2	no	—
371	M₁₆	—	86	2	no	—
372	M₁₆	—	86	2	no	—
373	M₁₆	—	172	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	43	4	no	—
377	C₂×C₈	—	86	4	no	—
378	C₂×C₈	—	86	2	no	—
379	C₂×C₈	—	86	2	no	—
380	C₂×C₈	—	86	2	no	—
381	C₂×C₈	—	86	2	no	—
382	C₂×C₈	—	172	2	no	—
383	C₂×C₈	C₂²×Dic₄₃	1	4	yes	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
386	C₂²⋊C₄	—	2	2	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	86	2	no	—
391	C₄²	—	86	2	no	—
392	C₄²	—	172	2	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
398	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
399	C₂³	#13063311	1	2	yes	—
400	C₂³	#13063318	1	2	yes	—
401	C₂³	C₂×#10621900	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	2	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	86	4	no	—
419	C₂×C₄	—	172	2	no	—
420	C₂×C₄	—	172	8	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	#13063284	1	2	yes	—
423	C₂×C₄	#13063284	1	2	yes	—
424	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
425	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
426	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
427	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
428	C₂×C₄	#13063298	1	2	yes	—
429	C₂×C₄	#13063298	1	2	yes	—
430	C₂×C₄	#13063307	1	2	yes	—
431	C₂×C₄	#13063307	1	2	yes	—
432	C₂×C₄	#13063311	1	2	yes	—
433	C₂×C₄	#13063318	1	2	yes	—
434	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
438	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
439	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	86	4	no	—
442	C₈	—	86	4	no	—
443	C₈	—	172	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	4	no	—
452	C₂²	#14582792	1	2	yes	—
453	C₂²	#14582792	1	2	yes	—
454	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
455	C₂²	C₂×#13063311	1	1	yes	characteristic
456	C₂²	C₂×#13063318	1	1	yes	characteristic
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	—	172	4	no	—
460	C₄	#14582792	1	2	yes	—
461	C₄	#14582792	1	2	yes	—
462	C₄	C₂×#13063284	1	1	yes	characteristic
463	C₄	C₂×D₄×Dic₄₃	1	1	yes	characteristic
464	C₄	C₂×#13063298	1	1	yes	characteristic
465	C₄	C₂×#13063307	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	2	no	—
468	C₂	—	2	2	no	—
469	C₂	—	2	1	no	—
470	C₂	—	8	2	no	—
471	C₂	C₂×#14582792	1	1	yes	characteristic
472	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	#21071
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. C₂×#14582948	C₂	semidirect
4. #19143014	C₂	semidirect
5. #19135245	C₂	semidirect
6. C₂×#14582658	C₂	semidirect
7. #19134288	C₂	semidirect
14. C₂×#13063261	C₂²	semidirect
21. #14582855	C₂²	semidirect
23. #14582658	C₂²	semidirect
24. #14582653	C₂²	semidirect
28. C₄₃×#419	C₄	semidirect
29. C₄₃×#418	C₄	semidirect
30. C₄₃×#417	C₄	semidirect
82. #103×C₄₃	C₂×C₄	semidirect
83. #102×C₄₃	C₂×C₄	semidirect
256. #419	Dic₄₃	semidirect
257. #418	Dic₄₃	semidirect
258. #417	Dic₄₃	semidirect
268. C₄₃	#21071	semidirect
316. #103	C₂×Dic₄₃	semidirect
317. #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
C₂×#14582948	2
C₂²×#13063252	2
#19143040	2
#19143014	2
#19135245	2
C₂×#14582658	2
#19134288	2
C₄₃×#2896	2
#21071	43