Subgroups — #25108898

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144377	C₂	1	1	yes	maximal, characteristic
2	#19143237	C₂	1	1	yes	maximal, characteristic
3	#19135540	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135368	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135340	C₂	1	2	yes	maximal, complemented
6	#19135298	C₂	1	2	yes	maximal
7	#19135243	C₂	1	2	yes	maximal
8	#19135194	C₂	1	2	yes	maximal, complemented
9	#19134612	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10621898	C₂²	1	1	yes	characteristic
13	#14583203	C₄	1	2	yes	complemented
14	#14583196	C₄	1	2	yes	complemented
15	#14583191	C₄	1	1	yes	characteristic, complemented
16	#14583186	C₄	1	1	yes	characteristic, complemented
17	#14583181	C₄	1	1	yes	characteristic, complemented
18	#14583176	C₄	1	1	yes	characteristic, complemented
19	#14582958	—	2	1	no	—
20	#14582958	—	2	1	no	—
21	#14582950	—	2	1	no	—
22	#14582950	—	2	1	no	—
23	C₂×#13063260	C₂²	1	2	yes	—
24	#14582935	C₂²	1	2	yes	—
25	#14582925	C₂²	1	1	yes	characteristic
26	#14582925	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×#13063251	C₂²	1	2	yes	—
29	#14582893	C₂²	1	2	yes	—
30	#14582865	C₂²	1	1	yes	characteristic
31	#14582865	C₂²	1	1	yes	characteristic
32	C₄×#10621877	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
34	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
35	#14582663	C₂²	1	2	yes	—
36	#14582660	C₂²	1	2	yes	—
37	#14582658	C₂²	1	2	yes	—
38	#14582658	C₂²	1	2	yes	—
39	#14582653	C₂²	1	2	yes	—
40	C₄₃×#533	C₂²	1	1	yes	characteristic
41	C₄₃×#446	—	2	1	no	—
42	C₄₃×#446	—	2	1	no	—
43	C₈×Q₈×C₄₃	—	2	1	no	—
44	C₈×Q₈×C₄₃	—	2	1	no	—
45	C₄₃×#424	C₂²	1	2	yes	—
46	C₄₃×#423	C₂²	1	1	yes	characteristic
47	C₄₃×#405	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	C₂×#10621877	C₂³	1	1	yes	characteristic
51	C₂×#10621877	C₂³	1	1	yes	characteristic
52	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
53	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
54	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
55	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
56	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
57	C₄×C₂²⋊D₄₃	—	2	1	no	—
58	C₄×C₂²⋊D₄₃	—	2	1	no	—
59	#13063284	C₂³	1	1	yes	characteristic
60	#13063282	—	2	1	no	—
61	C₂×C₄⋊Dic₄₃	—	2	1	no	—
62	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
63	C₄²×D₄₃	—	2	1	no	—
64	#13063260	—	4	2	no	—
65	#13063258	C₂×C₄	1	2	yes	—
66	#13063258	C₂×C₄	1	2	yes	—
67	#13063256	C₂×C₄	1	2	yes	—
68	#13063256	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
71	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
72	Dic₄₃⋊C₈	—	2	1	no	—
73	Dic₄₃⋊C₈	—	2	1	no	—
74	Dic₄₃⋊C₈	—	2	1	no	—
75	Dic₄₃⋊C₈	—	2	1	no	—
76	#13063251	—	4	2	no	—
77	#13063248	C₂×C₄	1	2	yes	—
78	#13063248	C₂×C₄	1	2	yes	—
79	#13063245	C₂×C₄	1	2	yes	—
80	#13063245	C₂×C₄	1	2	yes	—
81	(C₂×D₄₃)⋊C₈	—	2	1	no	—
82	(C₂×D₄₃)⋊C₈	—	2	1	no	—
83	(C₂×D₄₃)⋊C₈	—	2	1	no	—
84	(C₂×D₄₃)⋊C₈	—	2	1	no	—
85	#13063236	—	2	1	no	—
86	C₄×C₄₃⋊C₈	—	2	1	no	—
87	C₈×Dic₄₃	—	4	2	no	—
88	C₄₃⋊#95	—	2	1	no	—
89	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
90	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
94	#125×C₄₃	C₂×C₄	1	2	yes	—
95	C₂²⋊Q₈×C₄₃	—	2	1	no	—
96	C₂²⋊Q₈×C₄₃	—	2	1	no	—
97	C₄×Q₈×C₄₃	—	2	1	no	—
98	C₄×Q₈×C₄₃	—	2	1	no	—
99	#117×C₄₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	C₄⋊C₈×C₄₃	—	2	2	no	—
103	C₄⋊C₈×C₄₃	—	2	1	no	—
104	C₄⋊C₈×C₄₃	—	2	1	no	—
105	#97×C₄₃	—	2	2	no	—
106	C₄×C₈×C₄₃	—	2	2	no	—
107	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
109	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
110	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₃	—	2	1	no	—
117	C₂²×Dic₄₃	—	2	2	no	—
118	#10621898	—	2	1	no	—
119	#10621898	—	2	1	no	—
120	#10621898	—	2	1	no	—
121	#10621898	—	2	1	no	—
122	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₃	—	2	1	no	—
124	C₂×C₄×D₄₃	—	2	1	no	—
125	C₂×C₄×D₄₃	—	2	1	no	—
126	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
127	M₁₆×C₄₃	—	2	2	no	—
128	M₁₆×C₄₃	—	2	2	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	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	—	2	2	no	—
146	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²⋊Dic₄₃	—	2	1	no	—
151	(C₂×D₄₃)⋊C₄	—	2	1	no	—
152	(C₂×D₄₃)⋊C₄	—	2	1	no	—
153	C₄⋊Dic₄₃	—	2	4	no	—
154	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
156	Dic₄₃⋊C₄	—	2	1	no	—
157	Dic₄₃⋊C₄	—	2	1	no	—
158	C₄×Dic₄₃	—	2	1	no	—
159	C₄×Dic₄₃	—	2	1	no	—
160	C₄×Dic₄₃	—	2	1	no	—
161	C₄×Dic₄₃	—	2	2	no	—
162	C₄×Dic₄₃	—	2	2	no	—
163	#10621877	—	2	1	no	—
164	#10621877	—	2	1	no	—
165	#10621877	—	2	1	no	—
166	#10621877	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
172	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
173	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂²×D₄₃	—	2	1	no	—
175	Q₈×C₄₃	—	4	2	no	—
176	Q₈×C₄₃	—	4	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	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
191	C₂²⋊D₄₃	—	4	1	no	—
192	C₂²⋊D₄₃	—	4	1	no	—
193	C₂×Dic₄₃	—	2	4	no	—
194	C₂×Dic₄₃	—	2	1	no	—
195	C₂×Dic₄₃	—	2	1	no	—
196	C₂×Dic₄₃	—	2	1	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	D₁₇₂	—	2	1	no	—
200	D₁₇₂	—	2	1	no	—
201	C₄×D₄₃	—	4	2	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	—	4	1	no	—
204	C₄×D₄₃	—	4	2	no	—
205	Dic₈₆	—	2	1	no	—
206	Dic₈₆	—	2	1	no	—
207	C₈×C₄₃	—	2	1	no	—
208	C₈×C₄₃	—	2	1	no	—
209	C₈×C₄₃	—	2	1	no	—
210	C₈×C₄₃	—	2	1	no	—
211	C₈×C₄₃	—	4	2	no	—
212	C₄₃⋊C₈	—	2	2	no	—
213	C₄₃⋊C₈	—	2	2	no	—
214	C₄₃⋊C₈	—	4	1	no	—
215	C₄₃⋊C₈	—	4	1	no	—
216	#22130	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	—	2	1	no	—
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₃	#541	1	1	yes	characteristic
221	C₂²×C₄₃	#542	1	1	yes	characteristic
222	C₂×D₄₃	—	4	1	no	—
223	C₂×D₄₃	—	4	1	no	—
224	C₂×D₄₃	—	4	1	no	—
225	C₄×C₄₃	—	2	1	no	—
226	C₄×C₄₃	—	2	1	no	—
227	C₄×C₄₃	—	2	1	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	#443	1	2	yes	—
231	C₄×C₄₃	#519	1	1	yes	characteristic
232	C₄×C₄₃	#520	1	1	yes	characteristic
233	C₄×C₄₃	#536	1	1	yes	characteristic
234	C₄×C₄₃	#537	1	1	yes	characteristic
235	Dic₄₃	—	4	4	no	—
236	Dic₄₃	—	4	1	no	—
237	Dic₄₃	—	4	1	no	—
238	Dic₄₃	—	4	1	no	—
239	#3076	—	43	1	no	—
240	#2960	D₄₃	1	1	yes	characteristic, complemented
241	#2922	—	43	1	no	—
242	#1986	—	43	1	no	—
243	#1950	—	43	1	no	—
244	#1945	—	43	2	no	—
245	#1937	—	43	2	no	—
246	#1929	—	43	2	no	—
247	#1922	—	43	2	no	—
248	#1806	—	43	1	no	—
249	C₈×C₄⋊C₄	—	43	1	no	—
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	#2323	1	1	yes	characteristic
253	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
254	C₂×C₄₃	#2955	1	1	yes	characteristic
255	D₄₃	—	8	1	no	—
256	#533	C₂×D₄₃	1	1	yes	characteristic
257	C₄×#41	—	43	1	no	—
258	#479	—	43	2	no	—
259	#478	—	43	2	no	—
260	#477	—	43	1	no	—
261	#476	—	43	1	no	—
262	#475	—	43	1	no	—
263	#474	—	43	1	no	—
264	#446	—	2	1	no	—
265	#446	—	2	1	no	—
266	C₈×Q₈	—	2	1	no	—
267	C₈×Q₈	—	2	1	no	—
268	#433	—	86	1	no	—
269	#433	—	86	1	no	—
270	#431	—	86	1	no	—
271	#431	—	86	1	no	—
272	C₂×#108	—	43	2	no	—
273	#427	—	43	2	no	—
274	#424	—	43	1	no	—
275	#424	—	43	1	no	—
276	#424	C₂×D₄₃	1	2	yes	—
277	#423	C₂×D₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	—	43	1	no	—
279	C₂×#104	—	43	2	no	—
280	#416	—	43	2	no	—
281	#408	—	43	1	no	—
282	#408	—	43	1	no	—
283	#405	C₂×D₄₃	1	2	yes	—
284	C₄×M₁₆	—	43	1	no	—
285	C₂×C₄×C₈	—	43	2	no	—
286	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
287	C₄×C₄⋊C₄	—	43	1	no	—
288	#341	—	43	2	no	—
289	#339	—	43	2	no	—
290	#339	—	43	2	no	—
291	#339	—	43	2	no	—
292	#336	—	43	2	no	—
293	C₄₃	#22130	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	43	1	no	—
295	C₂×M₁₆	—	43	1	no	—
296	C₂×M₁₆	—	43	1	no	—
297	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
298	C₂²×C₈	—	43	2	no	—
299	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
302	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
303	#125	C₄×D₄₃	1	2	yes	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	43	1	no	—
309	C₄×Q₈	—	43	1	no	—
310	C₄×D₄	—	43	1	no	—
311	C₄×D₄	—	43	1	no	—
312	C₄×D₄	—	86	1	no	—
313	C₄×D₄	—	86	1	no	—
314	#117	—	43	1	no	—
315	#117	—	86	1	no	—
316	#117	C₂²×D₄₃	1	2	yes	—
317	C₂×C₄⋊C₄	—	86	1	no	—
318	C₂×C₄²	—	43	2	no	—
319	C₂×C₄²	—	86	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#108	—	172	2	no	—
322	#107	—	43	2	no	—
323	#107	—	43	2	no	—
324	#106	—	43	2	no	—
325	#106	—	43	2	no	—
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	—	2	2	no	—
328	C₄⋊C₈	—	2	1	no	—
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	43	1	no	—
331	C₄⋊C₈	—	43	1	no	—
332	C₄⋊C₈	—	43	2	no	—
333	C₄⋊C₈	—	86	1	no	—
334	C₄⋊C₈	—	86	1	no	—
335	C₄⋊C₈	—	86	1	no	—
336	C₄⋊C₈	—	86	1	no	—
337	#104	—	172	2	no	—
338	#103	—	43	2	no	—
339	#103	—	43	2	no	—
340	#102	—	43	2	no	—
341	#102	—	43	2	no	—
342	C₂²⋊C₈	—	86	1	no	—
343	C₂²⋊C₈	—	86	1	no	—
344	C₂²⋊C₈	—	86	1	no	—
345	C₂²⋊C₈	—	86	1	no	—
346	#97	—	2	2	no	—
347	#97	—	86	1	no	—
348	C₄×C₈	—	2	2	no	—
349	C₄×C₈	—	86	1	no	—
350	C₄×C₈	—	172	2	no	—
351	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
352	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
353	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
354	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
355	#95	—	86	1	no	—
356	#41	—	86	1	no	—
357	#41	—	86	1	no	—
358	#41	—	86	1	no	—
359	#41	—	86	1	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	43	1	no	—
363	C₂×D₄	—	43	1	no	—
364	C₂×D₄	—	86	1	no	—
365	C₂²×C₄	—	86	2	no	—
366	C₂²×C₄	—	86	1	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	#10621898	1	1	yes	characteristic
370	C₂²×C₄	#10621898	1	1	yes	characteristic
371	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	86	1	no	—
375	M₁₆	—	86	1	no	—
376	M₁₆	—	86	1	no	—
377	M₁₆	—	86	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	43	2	no	—
384	C₂×C₈	—	43	2	no	—
385	C₂×C₈	—	86	2	no	—
386	C₂×C₈	—	86	2	no	—
387	C₂×C₈	—	86	1	no	—
388	C₂×C₈	—	86	1	no	—
389	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
390	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
392	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	43	1	no	—
398	C₄⋊C₄	—	43	1	no	—
399	C₄⋊C₄	—	86	4	no	—
400	C₄⋊C₄	—	86	1	no	—
401	C₄⋊C₄	—	86	1	no	—
402	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
403	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	86	1	no	—
406	C₂²⋊C₄	—	86	1	no	—
407	C₂²⋊C₄	—	86	1	no	—
408	C₄²	—	2	2	no	—
409	C₄²	—	86	1	no	—
410	C₄²	—	86	1	no	—
411	C₄²	—	86	1	no	—
412	C₄²	—	86	2	no	—
413	C₄²	—	86	2	no	—
414	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
415	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
416	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
417	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₂³	—	86	1	no	—
419	C₂³	C₂×#10621898	1	1	yes	characteristic
420	Q₈	—	4	2	no	—
421	Q₈	—	4	2	no	—
422	Q₈	—	86	1	no	—
423	Q₈	—	86	1	no	—
424	D₄	—	86	1	no	—
425	D₄	—	86	1	no	—
426	D₄	—	172	1	no	—
427	D₄	—	172	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	86	4	no	—
433	C₂×C₄	—	86	1	no	—
434	C₂×C₄	—	86	1	no	—
435	C₂×C₄	—	86	1	no	—
436	C₂×C₄	—	172	2	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	—	172	1	no	—
440	C₂×C₄	—	172	1	no	—
441	C₂×C₄	—	172	2	no	—
442	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
448	C₂×C₄	#13063371	1	1	yes	characteristic
449	C₂×C₄	#13063372	1	1	yes	characteristic
450	C₂×C₄	#13063373	1	1	yes	characteristic
451	C₂×C₄	#13063373	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	2	1	no	—
456	C₈	—	4	2	no	—
457	C₈	—	86	2	no	—
458	C₈	—	86	2	no	—
459	C₈	—	172	1	no	—
460	C₈	—	172	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	172	1	no	—
464	C₂²	—	172	1	no	—
465	C₂²	—	172	1	no	—
466	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
467	C₂²	#14583507	1	1	yes	characteristic
468	C₂²	#14583521	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	172	4	no	—
475	C₄	—	172	1	no	—
476	C₄	—	172	1	no	—
477	C₄	—	172	1	no	—
478	C₄	#14583014	1	2	yes	—
479	C₄	#14583375	1	1	yes	characteristic
480	C₄	#14583381	1	1	yes	characteristic
481	C₄	#14583473	1	1	yes	characteristic
482	C₄	#14583477	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	344	1	no	—
486	C₂	#19137271	1	1	yes	characteristic
487	C₂	C₂×#14583014	1	1	yes	characteristic
488	C₂	#19143496	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	C₄₃×#2960	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#2960	D₄₃
hypocenter	C₄₃	#22130
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #19135540	C₂	semidirect
4. #19135368	C₂	semidirect
5. #19135340	C₂	semidirect
8. #19135194	C₂	semidirect
10. C₈×C₄⋊Dic₄₃	C₂	semidirect
11. C₄₃×#2960	C₂	semidirect
13. #14583203	C₄	semidirect
14. #14583196	C₄	semidirect
15. #14583191	C₄	semidirect
16. #14583186	C₄	semidirect
17. #14583181	C₄	semidirect
18. #14583176	C₄	semidirect
240. #2960	D₄₃	semidirect
293. C₄₃	#22130	semidirect

Maximal subgroups

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

subgroup	index
#19144377	2
#19143237	2
#19135540	2
#19135368	2
#19135340	2
#19135298	2
#19135243	2
#19135194	2
#19134612	2
C₈×C₄⋊Dic₄₃	2
C₄₃×#2960	2
#22130	43