Subgroups — #25108907

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	#19143530	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143240	C₂	1	1	yes	maximal, characteristic
4	#19135370	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135342	C₂	1	2	yes	maximal, complemented
6	#19135300	C₂	1	2	yes	maximal
7	#19135241	C₂	1	2	yes	maximal
8	#19135192	C₂	1	2	yes	maximal, complemented
9	#19134616	C₂	1	1	yes	maximal, characteristic
10	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1986	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	#14583030	—	2	1	no	—
20	#14583030	—	2	1	no	—
21	Q₈×C₄₃⋊C₈	—	2	1	no	—
22	Q₈×C₄₃⋊C₈	—	2	1	no	—
23	#14582961	—	2	1	no	—
24	#14582961	—	2	1	no	—
25	#14582950	—	2	1	no	—
26	#14582950	—	2	1	no	—
27	C₂×#13063260	C₂²	1	2	yes	—
28	#14582935	C₂²	1	2	yes	—
29	#14582927	C₂²	1	1	yes	characteristic
30	#14582927	C₂²	1	1	yes	characteristic
31	#14582926	C₂²	1	2	yes	—
32	#14582923	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#13063253	C₂²	1	2	yes	—
35	#14582893	C₂²	1	2	yes	—
36	#14582867	C₂²	1	1	yes	characteristic
37	#14582867	C₂²	1	1	yes	characteristic
38	#14582855	C₂²	1	2	yes	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
40	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
41	#14582663	C₂²	1	2	yes	—
42	#14582659	C₂²	1	2	yes	—
43	#14582654	C₂²	1	2	yes	—
44	C₄₃×#533	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#339	C₂²	1	2	yes	—
48	C₄₃×#339	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	C₂×#10621877	C₂³	1	2	yes	—
51	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
54	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
56	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
57	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₄₃	—	2	1	no	—
59	C₄×C₂²⋊D₄₃	—	2	1	no	—
60	#13063284	C₂³	1	1	yes	characteristic
61	#13063282	—	2	1	no	—
62	C₄²×D₄₃	—	2	1	no	—
63	#13063260	—	4	2	no	—
64	#13063258	C₂×C₄	1	2	yes	—
65	#13063258	C₂×C₄	1	2	yes	—
66	#13063256	C₂×C₄	1	2	yes	—
67	#13063256	C₂×C₄	1	2	yes	—
68	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
75	Dic₄₃⋊C₈	—	2	1	no	—
76	Dic₄₃⋊C₈	—	2	1	no	—
77	Dic₄₃⋊C₈	—	2	1	no	—
78	Dic₄₃⋊C₈	—	2	1	no	—
79	#13063253	—	4	2	no	—
80	#13063248	C₂×C₄	1	2	yes	—
81	#13063248	C₂×C₄	1	2	yes	—
82	#13063245	C₂×C₄	1	2	yes	—
83	#13063245	C₂×C₄	1	2	yes	—
84	(C₂×D₄₃)⋊C₈	—	2	1	no	—
85	(C₂×D₄₃)⋊C₈	—	2	1	no	—
86	(C₂×D₄₃)⋊C₈	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	1	no	—
88	#13063236	—	2	2	no	—
89	C₄×C₄₃⋊C₈	—	2	2	no	—
90	C₄×C₄₃⋊C₈	—	4	2	no	—
91	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
95	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
96	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
99	#125×C₄₃	C₂×C₄	1	2	yes	—
100	C₂²⋊Q₈×C₄₃	—	2	1	no	—
101	C₂²⋊Q₈×C₄₃	—	2	1	no	—
102	C₄×Q₈×C₄₃	—	2	1	no	—
103	C₄×Q₈×C₄₃	—	2	1	no	—
104	#117×C₄₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	#97×C₄₃	—	2	1	no	—
109	C₄×C₈×C₄₃	—	2	1	no	—
110	#95×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₃	—	2	1	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	1	no	—
128	M₁₆×C₄₃	—	2	1	no	—
129	M₁₆×C₄₃	—	2	1	no	—
130	M₁₆×C₄₃	—	2	1	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
139	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	2	2	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊Dic₄₃	—	2	1	no	—
149	(C₂×D₄₃)⋊C₄	—	2	1	no	—
150	(C₂×D₄₃)⋊C₄	—	2	1	no	—
151	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
153	Dic₄₃⋊C₄	—	2	1	no	—
154	Dic₄₃⋊C₄	—	2	1	no	—
155	C₄×Dic₄₃	—	2	1	no	—
156	C₄×Dic₄₃	—	2	1	no	—
157	C₄×Dic₄₃	—	2	1	no	—
158	#10621877	—	2	2	no	—
159	#10621877	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	1	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	—	2	1	no	—
166	C₂×C₄₃⋊C₈	—	2	2	no	—
167	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
168	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
169	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
170	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
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	4	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
193	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
194	C₂²⋊D₄₃	—	4	1	no	—
195	C₂²⋊D₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	2	1	no	—
197	C₂×Dic₄₃	—	2	1	no	—
198	C₂×Dic₄₃	—	2	1	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	—	4	1	no	—
208	C₈×C₄₃	—	4	1	no	—
209	C₄₃⋊C₈	—	2	2	no	—
210	C₄₃⋊C₈	—	2	2	no	—
211	C₄₃⋊C₈	—	2	1	no	—
212	C₄₃⋊C₈	—	2	1	no	—
213	C₄₃⋊C₈	—	2	1	no	—
214	C₄₃⋊C₈	—	2	1	no	—
215	C₄₃⋊C₈	—	4	2	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	4	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	—	4	2	no	—
231	C₄×C₄₃	#443	1	2	yes	—
232	C₄×C₄₃	#519	1	1	yes	characteristic
233	C₄×C₄₃	#520	1	1	yes	characteristic
234	C₄×C₄₃	#536	1	1	yes	characteristic
235	C₄×C₄₃	#537	1	1	yes	characteristic
236	Dic₄₃	—	4	1	no	—
237	Dic₄₃	—	4	1	no	—
238	Dic₄₃	—	4	1	no	—
239	#3076	—	43	1	no	—
240	#2960	—	43	1	no	—
241	#2922	—	43	1	no	—
242	#1986	D₄₃	1	1	yes	characteristic, complemented
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	—	86	1	no	—
265	#446	—	86	1	no	—
266	C₈×Q₈	—	86	1	no	—
267	C₈×Q₈	—	86	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	—	43	2	no	—
277	#423	—	43	1	no	—
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	—	43	2	no	—
284	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
285	C₂×C₄×C₈	—	43	1	no	—
286	C₂×C₄×C₈	—	43	2	no	—
287	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
288	#341	—	43	2	no	—
289	#339	—	43	2	no	—
290	#339	C₂×D₄₃	1	2	yes	—
291	#339	C₂×D₄₃	1	2	yes	—
292	#336	—	43	2	no	—
293	C₄₃	#22130	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	43	1	no	—
295	C₂×M₁₆	—	43	2	no	—
296	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
297	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
298	C₂²×C₈	—	43	1	no	—
299	C₂²×C₈	—	43	2	no	—
300	C₂²×C₈	—	43	1	no	—
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	—	2	1	no	—
318	C₂×C₄²	—	86	1	no	—
319	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
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	—	43	1	no	—
327	C₄⋊C₈	—	43	1	no	—
328	C₄⋊C₈	—	43	2	no	—
329	C₄⋊C₈	—	86	2	no	—
330	C₄⋊C₈	—	86	2	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	—	86	1	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	1	no	—
347	#97	—	86	2	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	43	1	no	—
350	C₄×C₈	—	43	1	no	—
351	C₄×C₈	—	43	1	no	—
352	C₄×C₈	—	43	1	no	—
353	C₄×C₈	—	86	2	no	—
354	C₄×C₈	—	172	2	no	—
355	#95	—	2	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	—	2	2	no	—
366	C₂²×C₄	—	86	1	no	—
367	C₂²×C₄	—	86	1	no	—
368	C₂²×C₄	—	86	1	no	—
369	C₂²×C₄	#10621900	1	1	yes	characteristic
370	C₂²×C₄	#10621900	1	1	yes	characteristic
371	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	1	no	—
376	M₁₆	—	86	2	no	—
377	M₁₆	—	86	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	43	2	no	—
381	C₂×C₈	—	43	2	no	—
382	C₂×C₈	—	43	1	no	—
383	C₂×C₈	—	43	1	no	—
384	C₂×C₈	—	43	1	no	—
385	C₂×C₈	—	43	1	no	—
386	C₂×C₈	—	86	1	no	—
387	C₂×C₈	—	86	2	no	—
388	C₂×C₈	—	86	1	no	—
389	C₂×C₈	—	86	2	no	—
390	C₂×C₈	—	86	1	no	—
391	C₂×C₈	—	86	1	no	—
392	C₂×C₈	—	86	2	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	43	1	no	—
399	C₄⋊C₄	—	43	1	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	—	2	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	86	1	no	—
412	C₄²	—	86	1	no	—
413	C₄²	—	86	1	no	—
414	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
415	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
416	C₄²	D₄×D₄₃	1	1	yes	characteristic
417	C₄²	D₄×D₄₃	1	1	yes	characteristic
418	C₂³	—	86	1	no	—
419	C₂³	C₂×#10621900	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	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	86	1	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	86	1	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	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
443	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
444	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
445	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂×D₄×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	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₈	—	86	2	no	—
455	C₈	—	86	2	no	—
456	C₈	—	86	1	no	—
457	C₈	—	86	1	no	—
458	C₈	—	86	1	no	—
459	C₈	—	86	1	no	—
460	C₈	—	172	2	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×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
467	C₂²	#14583510	1	1	yes	characteristic
468	C₂²	#14583518	1	1	yes	characteristic
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	4	4	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	172	1	no	—
476	C₄	—	172	1	no	—
477	C₄	—	172	1	no	—
478	C₄	#14583013	1	2	yes	—
479	C₄	#14583375	1	1	yes	characteristic
480	C₄	#14583381	1	1	yes	characteristic
481	C₄	#14583472	1	1	yes	characteristic
482	C₄	#14583479	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	344	1	no	—
486	C₂	#19137280	1	1	yes	characteristic
487	C₂	C₂×#14583013	1	1	yes	characteristic
488	C₂	#19143494	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1986	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1986	D₄₃
hypocenter	C₄₃	#22130
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1986

Complements

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

N	H ≅ G/N	type
2. #19143530	C₂	semidirect
4. #19135370	C₂	semidirect
5. #19135342	C₂	semidirect
8. #19135192	C₂	semidirect
10. C₄⋊C₄×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#1986	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
242. #1986	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
#19143530	2
#19143240	2
#19135370	2
#19135342	2
#19135300	2
#19135241	2
#19135192	2
#19134616	2
C₄⋊C₄×C₄₃⋊C₈	2
C₄₃×#1986	2
#22130	43