Subgroups — #25067499

Order 11008.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144599	C₂	1	1	yes	maximal, characteristic
2	#19143544	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143330	C₂	1	1	yes	maximal, characteristic
4	#19133482	C₂	1	2	yes	maximal, complemented
5	#19133435	C₂	1	2	yes	maximal, complemented
6	#19133434	C₂	1	2	yes	maximal, complemented
7	#19133392	C₂	1	2	yes	maximal, complemented
8	#19133367	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
10	C₈×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₃	—	2	1	no	—
13	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
14	#14583227	C₄	1	2	yes	—
15	#14583186	C₄	1	1	yes	characteristic
16	#14583186	C₄	1	1	yes	characteristic
17	#14583101	C₄	1	1	yes	characteristic
18	#14583101	C₄	1	1	yes	characteristic
19	#14583049	C₄	1	2	yes	—
20	#14583030	—	2	2	no	—
21	#14583030	C₂²	1	2	yes	complemented
22	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
23	C₄×#10621884	C₂²	1	2	yes	—
24	C₄×#10621884	C₂²	1	2	yes	—
25	#14582976	C₂²	1	2	yes	—
26	#14582969	—	2	2	no	—
27	#14582964	C₂²	1	2	yes	—
28	#14582952	C₂²	1	1	yes	characteristic
29	#14582926	—	2	1	no	—
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	#14582862	—	2	1	no	—
32	#14582855	—	2	1	no	—
33	C₄×#10621877	C₂²	1	1	yes	characteristic
34	#14582649	C₂²	1	2	yes	complemented
35	#14582649	C₂²	1	2	yes	complemented
36	#14582628	C₂²	1	1	yes	characteristic
37	#14582628	C₂²	1	1	yes	characteristic
38	#14582628	C₂²	1	1	yes	characteristic
39	#14582628	C₂²	1	1	yes	characteristic
40	#14582621	C₂²	1	2	yes	complemented
41	C₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
42	C₄₃×#533	C₂²	1	1	yes	characteristic
43	C₄₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
46	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	complemented
47	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₃	—	2	1	no	—
49	C₂×#10621884	C₂×C₄	1	2	yes	—
50	C₂×#10621884	C₂×C₄	1	2	yes	—
51	C₂×#10621877	D₄	1	1	yes	characteristic
52	C₂×#10621877	D₄	1	1	yes	characteristic
53	C₂×#10621872	—	2	2	no	—
54	M₁₆×D₄₃	—	4	4	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	C₂×C₈×D₄₃	—	2	2	no	—
57	C₄×D₁₇₂	—	2	1	no	—
58	C₄×D₁₇₂	—	2	1	no	—
59	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
60	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
61	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
62	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
65	#13063256	C₂×C₄	1	2	yes	—
66	#13063256	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
70	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
71	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
74	#13063249	C₂×C₄	1	2	yes	—
75	#13063249	C₂×C₄	1	2	yes	—
76	#13063245	C₂×C₄	1	2	yes	—
77	#13063245	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
79	(C₂×D₄₃)⋊C₈	—	2	2	no	—
80	(C₂×D₄₃)⋊C₈	—	2	2	no	—
81	#13063236	—	2	2	no	—
82	#13063236	D₄	1	2	yes	—
83	C₄×C₄₃⋊C₈	—	2	2	no	—
84	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
85	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂²×C₈×C₄₃	—	2	1	no	—
88	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
90	#125×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
95	#117×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₃	—	2	1	no	—
98	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
99	C₄×C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂³×D₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×Dic₄₃	—	2	1	no	—
109	C₂×D₁₇₂	—	2	1	no	—
110	C₂×D₁₇₂	—	2	2	no	—
111	C₂×D₁₇₂	—	4	1	no	—
112	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	2	1	no	—
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×C₄×D₄₃	—	4	2	no	—
119	C₂×C₄×D₄₃	—	4	2	no	—
120	M₁₆×C₄₃	—	4	2	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	4	2	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂²⋊C₄×C₄₃	—	2	2	no	—
132	C₄²×C₄₃	—	2	2	no	—
133	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₃	#41	1	1	yes	characteristic
136	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
137	#10621884	—	2	4	no	—
138	#10621884	—	4	2	no	—
139	(C₂×D₄₃)⋊C₄	—	2	1	no	—
140	(C₂×D₄₃)⋊C₄	—	2	1	no	—
141	(C₂×D₄₃)⋊C₄	—	2	1	no	—
142	(C₂×D₄₃)⋊C₄	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
146	#10621877	—	2	2	no	—
147	#10621877	SD₁₆	1	4	yes	complemented
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	4	2	no	—
151	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
152	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
155	#10621872	—	4	4	no	—
156	C₈×D₄₃	—	4	4	no	—
157	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₄₃	—	2	1	no	—
159	C₂²×D₄₃	—	2	1	no	—
160	C₂²×D₄₃	—	4	2	no	—
161	C₂²×D₄₃	—	4	2	no	—
162	C₂²×D₄₃	—	8	1	no	—
163	Q₈×C₄₃	—	2	2	no	—
164	Q₈×C₄₃	—	2	2	no	—
165	Q₈×C₄₃	—	8	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₄₃	—	2	1	no	—
180	C₂×Dic₄₃	—	2	1	no	—
181	C₂×Dic₄₃	—	4	2	no	—
182	D₁₇₂	—	2	1	no	—
183	D₁₇₂	—	2	1	no	—
184	D₁₇₂	—	2	1	no	—
185	D₁₇₂	—	4	2	no	—
186	D₁₇₂	#131	1	2	yes	—
187	C₄×D₄₃	—	4	1	no	—
188	C₄×D₄₃	—	4	1	no	—
189	C₄×D₄₃	—	4	1	no	—
190	C₄×D₄₃	—	4	1	no	—
191	C₄×D₄₃	—	4	2	no	—
192	C₄×D₄₃	—	4	2	no	—
193	C₈×C₄₃	—	2	2	no	—
194	C₈×C₄₃	—	4	1	no	—
195	C₈×C₄₃	—	4	2	no	—
196	C₄₃⋊C₈	—	2	2	no	—
197	C₄₃⋊C₈	—	2	2	no	—
198	C₄₃⋊C₈	—	2	2	no	—
199	C₄₃⋊C₈	—	4	1	no	—
200	C₄₃⋊C₈	—	4	1	no	—
201	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
202	#17995	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	C₄×SD₁₆	1	2	yes	—
206	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	4	1	no	—
209	C₂×D₄₃	—	4	1	no	—
210	C₂×D₄₃	—	4	1	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	—	4	1	no	—
213	C₂×D₄₃	—	8	4	no	—
214	C₄×C₄₃	—	2	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	4	2	no	—
218	C₄×C₄₃	—	4	2	no	—
219	C₄×C₄₃	C₄×SD₁₆	1	2	yes	—
220	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
221	C₄×C₄₃	#568	1	1	yes	characteristic
222	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
223	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
224	Dic₄₃	—	4	1	no	—
225	Dic₄₃	—	4	1	no	—
226	#3101	—	43	1	no	—
227	#2962	—	43	1	no	—
228	D₄×M₁₆	—	43	1	no	—
229	#1590	—	43	2	no	—
230	#1583	—	43	2	no	—
231	#1582	—	43	2	no	—
232	C₈×SD₁₆	—	43	2	no	—
233	#1570	—	43	1	no	—
234	#1493	D₄₃	1	1	yes	characteristic, complemented
235	C₂×D₄⋊C₈	—	43	1	no	—
236	C₈×M₁₆	—	43	1	no	—
237	C₂×C₄₃	—	2	2	no	—
238	C₂×C₄₃	#2933	1	1	yes	characteristic
239	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
240	C₂×C₄₃	#2956	1	1	yes	characteristic
241	D₄₃	—	4	2	no	—
242	D₄₃	—	8	1	no	—
243	C₂²×M₁₆	—	86	1	no	—
244	#533	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×D₄	—	43	1	no	—
246	#483	—	43	2	no	—
247	#476	—	43	1	no	—
248	#476	—	43	1	no	—
249	#461	—	43	1	no	—
250	#461	—	43	1	no	—
251	#450	—	43	2	no	—
252	#446	—	43	2	no	—
253	#446	—	86	2	no	—
254	C₈×Q₈	—	43	2	no	—
255	C₄×SD₁₆	—	43	2	no	—
256	C₄×SD₁₆	—	43	2	no	—
257	#436	—	43	2	no	—
258	#435	—	86	2	no	—
259	C₈×D₄	—	43	2	no	—
260	#431	—	43	1	no	—
261	#424	—	86	1	no	—
262	#423	C₂×D₄₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	—	43	1	no	—
264	#407	—	86	1	no	—
265	#405	—	86	1	no	—
266	C₄×M₁₆	—	43	1	no	—
267	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
268	#334	—	43	2	no	—
269	#334	—	43	2	no	—
270	Q₈⋊C₈	C₂×D₄₃	1	2	yes	complemented
271	Q₈⋊C₈	C₂×D₄₃	1	2	yes	complemented
272	D₄⋊C₈	—	43	1	no	—
273	D₄⋊C₈	—	43	1	no	—
274	D₄⋊C₈	—	43	1	no	—
275	D₄⋊C₈	—	43	1	no	—
276	#322	—	43	2	no	—
277	C₈²	—	43	2	no	—
278	C₄₃	#17995	1	1	yes	characteristic, complemented, Sylow
279	C₂²×D₄	—	43	1	no	—
280	C₂³×C₄	—	86	1	no	—
281	C₂×SD₁₆	—	43	2	no	—
282	C₂×SD₁₆	—	43	2	no	—
283	C₂×M₁₆	—	2	1	no	—
284	C₂×M₁₆	—	43	1	no	—
285	C₂×M₁₆	—	43	1	no	—
286	C₂×M₁₆	—	86	2	no	—
287	C₂×M₁₆	—	172	4	no	—
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	86	2	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
292	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
293	#125	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
298	C₄×D₄	—	43	1	no	—
299	C₄×D₄	—	43	1	no	—
300	C₄×D₄	—	43	1	no	—
301	C₄×D₄	—	43	1	no	—
302	C₄×D₄	—	86	1	no	—
303	C₄×D₄	—	86	1	no	—
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	43	1	no	—
306	C₂×C₂²⋊C₄	—	86	1	no	—
307	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
308	#106	—	43	2	no	—
309	#106	—	43	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	43	1	no	—
313	C₄⋊C₈	—	43	1	no	—
314	C₄⋊C₈	—	43	1	no	—
315	C₄⋊C₈	—	86	2	no	—
316	C₄⋊C₈	—	86	2	no	—
317	C₄⋊C₈	—	86	1	no	—
318	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
319	#103	—	43	2	no	—
320	#103	—	43	2	no	—
321	#102	—	43	2	no	—
322	#102	—	43	2	no	—
323	C₂²⋊C₈	—	43	2	no	—
324	C₂²⋊C₈	—	86	2	no	—
325	C₂²⋊C₈	—	86	2	no	—
326	#97	—	43	2	no	—
327	#97	—	86	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	43	2	no	—
330	C₄×C₈	—	43	2	no	—
331	C₄×C₈	—	86	2	no	—
332	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
334	C₂⁴	—	86	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
337	C₂×D₄	—	43	1	no	—
338	C₂×D₄	—	43	1	no	—
339	C₂×D₄	—	86	2	no	—
340	C₂×D₄	—	86	1	no	—
341	C₂×D₄	—	172	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	86	1	no	—
345	C₂²×C₄	—	86	1	no	—
346	C₂²×C₄	—	86	1	no	—
347	C₂²×C₄	—	172	2	no	—
348	C₂²×C₄	—	172	2	no	—
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	#10621900	1	1	yes	characteristic
352	SD₁₆	—	86	4	no	—
353	SD₁₆	—	172	2	no	—
354	M₁₆	—	4	2	no	—
355	M₁₆	—	43	4	no	—
356	M₁₆	—	86	2	no	—
357	M₁₆	—	172	4	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	—	43	2	no	—
363	C₂×C₈	—	43	2	no	—
364	C₂×C₈	—	43	2	no	—
365	C₂×C₈	—	43	2	no	—
366	C₂×C₈	—	86	1	no	—
367	C₂×C₈	—	86	1	no	—
368	C₂×C₈	—	172	4	no	—
369	C₂×C₈	—	172	2	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	43	1	no	—
376	C₄⋊C₄	—	43	1	no	—
377	C₄⋊C₄	—	86	1	no	—
378	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
379	C₂²⋊C₄	—	2	2	no	—
380	C₂²⋊C₄	—	86	1	no	—
381	C₂²⋊C₄	—	86	1	no	—
382	C₂²⋊C₄	—	86	1	no	—
383	C₂²⋊C₄	—	86	1	no	—
384	C₄²	—	2	2	no	—
385	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
386	C₄²	D₄×D₄₃	1	1	yes	characteristic
387	C₄²	#10621900	1	1	yes	characteristic
388	C₄²	C₂³×D₄₃	1	1	yes	characteristic
389	C₂³	—	86	1	no	—
390	C₂³	—	86	1	no	—
391	C₂³	—	344	1	no	—
392	C₂³	—	172	2	no	—
393	C₂³	—	172	2	no	—
394	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
395	Q₈	—	2	2	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	8	1	no	—
398	D₄	—	43	2	no	—
399	D₄	—	86	1	no	—
400	D₄	—	86	1	no	—
401	D₄	—	86	1	no	—
402	D₄	—	172	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	86	1	no	—
409	C₂×C₄	—	86	1	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	—	172	2	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
418	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
419	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
420	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
421	C₂×C₄	#13063348	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₈	—	43	4	no	—
429	C₈	—	86	2	no	—
430	C₈	—	86	2	no	—
431	C₈	—	86	2	no	—
432	C₈	—	172	1	no	—
433	C₈	—	172	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	86	2	no	—
437	C₂²	—	344	4	no	—
438	C₂²	—	172	1	no	—
439	C₂²	—	172	1	no	—
440	C₂²	—	172	1	no	—
441	C₂²	—	172	1	no	—
442	C₂²	—	172	1	no	—
443	C₂²	#14582984	1	2	yes	—
444	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	172	1	no	—
451	C₄	—	172	1	no	—
452	C₄	#14582984	1	2	yes	—
453	C₄	#131×D₄₃	1	1	yes	characteristic
454	C₄	#14583664	1	1	yes	characteristic
455	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
456	C₄	C₂×#13063348	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	344	1	no	—
459	C₂	—	172	2	no	—
460	C₂	#19143325	1	1	yes	characteristic
461	C₂	C₂×#14582984	1	1	yes	characteristic
462	C₂	#19143501	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1493	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂²×D₁₇₂	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1493	D₄₃
hypocenter	C₄₃	#17995
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1493

Complements

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

N	H ≅ G/N	type
2. #19143544	C₂	semidirect
4. #19133482	C₂	semidirect
5. #19133435	C₂	semidirect
6. #19133434	C₂	semidirect
7. #19133392	C₂	semidirect
8. #19133367	C₂	semidirect
10. C₈×#10621877	C₂	semidirect
11. C₄₃×#1493	C₂	semidirect
21. #14583030	C₂²	semidirect
22. Q₈×C₄₃⋊C₈	C₂²	semidirect
34. #14582649	C₂²	semidirect
35. #14582649	C₂²	semidirect
40. #14582621	C₂²	semidirect
41. C₈×C₄₃⋊C₈	C₂²	semidirect
45. C₄₃×Q₈⋊C₈	C₂²	semidirect
46. C₄₃×Q₈⋊C₈	C₂²	semidirect
147. #10621877	SD₁₆	semidirect
234. #1493	D₄₃	semidirect
270. Q₈⋊C₈	C₂×D₄₃	semidirect
271. Q₈⋊C₈	C₂×D₄₃	semidirect
278. C₄₃	#17995	semidirect

Maximal subgroups

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

subgroup	index
#19144599	2
#19143544	2
#19143330	2
#19133482	2
#19133435	2
#19133434	2
#19133392	2
#19133367	2
C₂×#14582628	2
C₈×#10621877	2
C₄₃×#1493	2
#17995	43