Subgroups — #25976010

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148447	C₂	1	2	yes	maximal, complemented
2	#19147202	C₂	1	4	yes	maximal, complemented
3	#19147192	C₂	1	4	yes	maximal, complemented
4	#19147019	C₂	1	2	yes	maximal, complemented
5	#19146999	C₂	1	4	yes	maximal, complemented
6	#19146944	C₂	1	2	yes	maximal, complemented
7	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
8	#19144549	C₂	1	4	yes	maximal, complemented
9	#19144392	C₂	1	2	yes	maximal, complemented
10	#19144239	C₂	1	2	yes	maximal, complemented
11	#19143308	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143191	C₂	1	2	yes	maximal, complemented
13	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13063331	C₂²	1	2	yes	—
15	#14583632	—	2	4	no	—
16	#14583619	—	2	2	no	—
17	#14583614	C₂²	1	4	yes	complemented
18	#14583599	C₂²	1	8	yes	complemented
19	#14583570	—	2	2	no	—
20	#14583554	C₂²	1	4	yes	complemented
21	#14583487	—	2	4	no	—
22	#14583466	C₂²	1	4	yes	—
23	#14583456	C₂²	1	2	yes	—
24	#14583449	C₂²	1	1	yes	characteristic
25	#14583410	—	2	4	no	—
26	#14583380	C₂²	1	4	yes	—
27	#14583304	C₂²	1	1	yes	characteristic, complemented
28	#14583304	C₂²	1	1	yes	characteristic, complemented
29	#14583301	C₂²	1	2	yes	complemented
30	#14583301	C₂²	1	2	yes	complemented
31	#14583297	C₂²	1	2	yes	complemented
32	#14583222	C₂²	1	8	yes	complemented
33	#14583221	C₂²	1	8	yes	complemented
34	#14583216	C₂²	1	8	yes	complemented
35	#14583211	C₂²	1	8	yes	complemented
36	#14583199	C₂²	1	8	yes	complemented
37	#14583189	C₂²	1	4	yes	complemented
38	#14583179	C₂²	1	4	yes	complemented
39	#14583149	C₂²	1	8	yes	—
40	#14583132	C₂²	1	4	yes	—
41	#14583132	C₂²	1	4	yes	—
42	#14582978	C₂²	1	2	yes	complemented
43	#14582978	C₂²	1	2	yes	complemented
44	C₈×D₁₇₂	C₂²	1	2	yes	complemented
45	C₈×D₁₇₂	C₂²	1	2	yes	complemented
46	#14582940	C₂²	1	8	yes	complemented
47	#14582939	C₂²	1	4	yes	—
48	#14582937	C₂²	1	2	yes	—
49	#14582937	C₂²	1	2	yes	—
50	#14582936	C₂²	1	4	yes	complemented
51	#107×D₄₃	C₂²	1	4	yes	complemented
52	#14582923	C₂²	1	1	yes	characteristic
53	#14582904	C₂²	1	4	yes	—
54	#14582865	C₂²	1	2	yes	—
55	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
57	C₄×D₈×C₄₃	C₂²	1	2	yes	—
58	C₄×D₈×C₄₃	C₂²	1	2	yes	—
59	C₄×D₈×C₄₃	C₂²	1	2	yes	—
60	C₄×D₈×C₄₃	C₂²	1	2	yes	—
61	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
62	C₂×#102×C₄₃	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
64	C₂×#10621898	—	2	4	no	—
65	C₂×#10621898	C₂³	1	2	yes	—
66	#13063331	—	2	8	no	—
67	C₂×#10621877	C₂³	1	2	yes	—
68	C₂×#10621872	C₂³	1	4	yes	—
69	C₂×C₈×D₄₃	C₂³	1	4	yes	—
70	#13063325	D₄	1	1	yes	characteristic
71	#13063325	C₂³	1	2	yes	—
72	#13063325	C₂³	1	2	yes	—
73	#13063322	D₄	1	1	yes	characteristic
74	#13063321	—	2	4	no	—
75	#13063318	—	2	8	no	—
76	#13063317	C₂³	1	4	yes	—
77	#13063313	D₄	1	2	yes	—
78	#13063312	—	2	4	no	—
79	#13063311	—	2	8	no	—
80	#13063308	—	2	8	no	—
81	#13063307	—	2	8	no	—
82	#13063304	—	2	2	no	—
83	#13063304	—	2	2	no	—
84	#13063304	—	2	4	no	—
85	#13063299	—	2	4	no	—
86	#13063299	D₄	1	2	yes	—
87	#13063299	D₄	1	2	yes	—
88	#13063298	—	2	8	no	—
89	#13063296	C₂³	1	8	yes	—
90	#13063296	C₂³	1	8	yes	—
91	#13063294	—	2	8	no	—
92	C₄×Dic₈₆	—	2	2	no	—
93	C₄×Dic₈₆	—	2	2	no	—
94	#13063290	—	2	4	no	—
95	C₄×D₁₇₂	C₂³	1	2	yes	—
96	C₄×D₁₇₂	C₂³	1	2	yes	—
97	#13063287	—	2	4	no	—
98	C₄×C₂²⋊D₄₃	—	2	8	no	—
99	C₄×C₂²⋊D₄₃	—	2	8	no	—
100	#13063284	—	2	4	no	—
101	#13063284	C₂³	1	4	yes	—
102	#13063283	C₂³	1	8	yes	—
103	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
104	#13063259	C₂³	1	2	yes	—
105	#13063259	C₂³	1	2	yes	—
106	#13063259	C₂³	1	2	yes	—
107	#13063259	C₂³	1	2	yes	—
108	#13063258	C₂³	1	8	yes	—
109	#13063257	C₂³	1	4	yes	—
110	#13063257	C₂³	1	4	yes	—
111	#13063256	C₂³	1	8	yes	—
112	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
113	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
114	#13063246	C₂³	1	8	yes	—
115	#13063246	C₂³	1	8	yes	—
116	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
117	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
118	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₄₃	—	2	2	no	—
120	C₂×D₈×C₄₃	—	2	4	no	—
121	C₂×D₈×C₄₃	C₂³	1	2	yes	—
122	C₂×D₈×C₄₃	C₂³	1	2	yes	—
123	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₄×D₄×C₄₃	—	2	2	no	—
126	C₄×D₄×C₄₃	—	2	2	no	—
127	C₄×D₄×C₄₃	C₂³	1	4	yes	—
128	C₄×D₄×C₄₃	C₂³	1	4	yes	—
129	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
131	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
132	#107×C₄₃	C₂³	1	2	yes	—
133	#107×C₄₃	C₂³	1	2	yes	—
134	#102×C₄₃	C₂³	1	4	yes	—
135	#102×C₄₃	C₂³	1	4	yes	—
136	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
140	C₂⁴×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	2	2	no	—
142	C₂×D₄×C₄₃	—	2	4	no	—
143	C₂×D₄×C₄₃	—	2	4	no	—
144	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	4	no	—
147	C₂²×C₄×C₄₃	—	2	2	no	—
148	C₂²×C₄×C₄₃	—	8	4	no	—
149	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₂²⋊D₄₃	—	2	8	no	—
153	C₂×C₂²⋊D₄₃	—	2	8	no	—
154	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
155	#10621898	—	2	4	no	—
156	#10621898	—	2	4	no	—
157	#10621898	—	8	8	no	—
158	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
159	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
160	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
161	C₂×C₄×D₄₃	—	2	8	no	—
162	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
163	C₂×Dic₈₆	—	2	2	no	—
164	C₂×Dic₈₆	—	2	2	no	—
165	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
166	D₈×C₄₃	—	2	4	no	—
167	D₈×C₄₃	—	2	4	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	#41	1	4	yes	complemented
170	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
176	C₂²⋊C₄×C₄₃	—	2	4	no	—
177	C₂²⋊C₄×C₄₃	—	2	4	no	—
178	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
181	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
182	C₂²⋊Dic₄₃	—	2	8	no	—
183	C₂²⋊Dic₄₃	—	2	8	no	—
184	C₂²⋊Dic₄₃	—	2	4	no	—
185	(C₂×D₄₃)⋊C₄	—	2	8	no	—
186	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
187	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
188	C₄⋊Dic₄₃	—	2	2	no	—
189	C₄⋊Dic₄₃	—	2	2	no	—
190	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
191	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
192	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
193	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
194	Dic₄₃⋊C₄	—	2	4	no	—
195	Dic₄₃⋊C₄	—	2	4	no	—
196	Dic₄₃⋊C₄	—	2	8	no	—
197	C₄×Dic₄₃	—	2	4	no	—
198	C₄×Dic₄₃	—	2	8	no	—
199	#10621877	—	2	4	no	—
200	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
201	#10621872	—	2	8	no	—
202	C₈×D₄₃	—	2	8	no	—
203	C₂³×C₄₃	—	2	4	no	—
204	C₂³×C₄₃	—	4	4	no	—
205	C₂³×C₄₃	—	8	2	no	—
206	C₂³×C₄₃	—	8	2	no	—
207	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
208	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
209	D₄×C₄₃	—	2	4	no	—
210	D₄×C₄₃	—	2	4	no	—
211	D₄×C₄₃	—	4	4	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	4	1	no	—
215	C₂×C₄×C₄₃	—	4	8	no	—
216	C₂×C₄×C₄₃	—	8	4	no	—
217	C₂×C₄×C₄₃	—	8	2	no	—
218	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
225	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
226	C₂²⋊D₄₃	—	2	8	no	—
227	C₂²⋊D₄₃	—	8	8	no	—
228	C₂²⋊D₄₃	—	8	8	no	—
229	C₂×Dic₄₃	—	2	4	no	—
230	C₂×Dic₄₃	—	2	4	no	—
231	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
232	D₁₇₂	—	2	4	no	—
233	D₁₇₂	—	2	4	no	—
234	D₁₇₂	—	4	2	no	—
235	C₄×D₄₃	—	2	4	no	—
236	C₄×D₄₃	—	2	4	no	—
237	C₄×D₄₃	—	8	8	no	—
238	Dic₈₆	—	2	4	no	—
239	Dic₈₆	—	4	4	no	—
240	Dic₈₆	—	8	2	no	—
241	C₈×C₄₃	—	2	1	no	—
242	C₈×C₄₃	—	2	1	no	—
243	C₈×C₄₃	C₂×#41	1	2	yes	—
244	C₈×C₄₃	C₂×#41	1	2	yes	—
245	C₄₃⋊C₈	—	2	4	no	—
246	#61284	—	43	1	no	maximal, Sylow
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	—	4	4	no	—
250	C₂²×C₄₃	—	4	4	no	—
251	C₂²×C₄₃	—	4	4	no	—
252	C₂²×C₄₃	—	8	8	no	—
253	C₂²×C₄₃	#547	1	2	yes	—
254	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
255	C₂×D₄₃	—	2	4	no	—
256	C₂×D₄₃	—	2	4	no	—
257	C₂×D₄₃	—	2	4	no	—
258	C₄×C₄₃	—	2	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	2	1	no	—
261	C₄×C₄₃	—	4	4	no	—
262	C₄×C₄₃	#547	1	2	yes	—
263	C₄×C₄₃	#576	1	2	yes	—
264	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
265	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
266	Dic₄₃	—	2	4	no	—
267	Dic₄₃	—	4	4	no	—
268	Dic₄₃	—	4	4	no	—
269	#3506	—	43	2	no	—
270	#3355	—	43	4	no	—
271	#3354	—	43	4	no	—
272	#3341	—	43	2	no	—
273	#3339	—	43	4	no	—
274	#3334	—	43	2	no	—
275	#3160	—	43	1	no	—
276	#3096	—	43	4	no	—
277	#3077	—	43	2	no	—
278	#3058	—	43	2	no	—
279	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic, complemented
280	#2931	—	43	1	no	—
281	#2913	—	43	2	no	—
282	C₂×C₄₃	—	2	2	no	—
283	C₂×C₄₃	—	8	4	no	—
284	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
285	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
286	C₂×C₄₃	#3584	1	1	yes	characteristic
287	D₄₃	—	4	4	no	—
288	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
289	C₂×#131	—	43	2	no	—
290	#559	—	86	4	no	—
291	#556	—	86	2	no	—
292	#555	—	43	4	no	—
293	#553	—	43	8	no	—
294	#550	—	86	2	no	—
295	#547	—	43	4	no	—
296	#538	—	86	4	no	—
297	#535	—	43	4	no	—
298	#533	—	43	2	no	—
299	#532	—	43	1	no	—
300	#525	—	86	4	no	—
301	#520	—	43	4	no	—
302	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
303	#500	—	43	1	no	—
304	#500	—	43	1	no	—
305	#499	—	43	2	no	—
306	#499	—	43	2	no	—
307	#498	—	43	2	no	—
308	#482	—	43	8	no	—
309	#482	—	43	8	no	—
310	#481	—	43	8	no	—
311	#480	—	43	8	no	—
312	#478	—	43	8	no	—
313	#476	—	43	4	no	—
314	#474	—	43	4	no	—
315	#469	—	43	8	no	—
316	#466	—	43	4	no	—
317	#466	—	43	4	no	—
318	C₄×D₈	C₂×D₄₃	1	2	yes	—
319	C₄×D₈	C₂×D₄₃	1	2	yes	—
320	C₄×D₈	C₂×D₄₃	1	2	yes	—
321	C₄×D₈	C₂×D₄₃	1	2	yes	—
322	#436	—	43	2	no	—
323	#436	—	43	2	no	—
324	C₈×D₄	—	43	2	no	—
325	C₈×D₄	—	43	2	no	—
326	#428	—	43	4	no	—
327	#428	—	43	8	no	—
328	#427	—	43	2	no	—
329	#427	—	43	2	no	—
330	#427	—	43	4	no	—
331	C₂×#107	—	43	4	no	—
332	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
333	#423	—	43	1	no	—
334	#418	—	43	4	no	—
335	C₂×#102	C₂×D₄₃	1	2	yes	—
336	#408	—	43	2	no	—
337	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
338	C₄₃	#61284	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	43	2	no	—
340	C₂×#41	—	86	4	no	—
341	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
342	C₂³×C₄	—	2	2	no	—
343	C₂×D₈	—	2	4	no	—
344	C₂×D₈	C₂²×D₄₃	1	2	yes	—
345	C₂×D₈	C₂²×D₄₃	1	2	yes	—
346	#131	—	86	8	no	—
347	C₂×M₁₆	—	43	2	no	—
348	C₂×M₁₆	—	43	4	no	—
349	C₂²×C₈	—	43	4	no	—
350	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₄⋊Q₈	—	43	1	no	—
353	C₄⋊Q₈	—	43	2	no	—
354	C₄⋊Q₈	—	43	2	no	—
355	#127	—	43	1	no	—
356	#127	—	86	4	no	—
357	#126	—	86	8	no	—
358	#125	—	43	4	no	—
359	#124	—	43	2	no	—
360	#124	—	86	8	no	—
361	#124	—	86	4	no	—
362	#123	—	86	8	no	—
363	#123	—	86	8	no	—
364	C₂²⋊Q₈	—	86	4	no	—
365	C₂²⋊Q₈	—	86	2	no	—
366	C₂²⋊Q₈	—	86	2	no	—
367	#121	—	43	2	no	—
368	#121	—	43	2	no	—
369	#121	—	43	8	no	—
370	#121	—	43	8	no	—
371	#121	—	86	8	no	—
372	#121	—	86	4	no	—
373	#120	—	86	8	no	—
374	C₄×Q₈	—	86	4	no	—
375	C₄×Q₈	—	86	2	no	—
376	C₄×Q₈	—	86	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	43	2	no	—
380	C₄×D₄	—	43	2	no	—
381	C₄×D₄	—	86	8	no	—
382	C₄×D₄	—	86	4	no	—
383	C₄×D₄	—	86	8	no	—
384	C₄×D₄	C₂²×D₄₃	1	4	yes	—
385	C₄×D₄	C₂²×D₄₃	1	4	yes	—
386	#117	—	43	4	no	—
387	#117	—	43	8	no	—
388	#117	—	86	4	no	—
389	C₂×C₄⋊C₄	—	43	8	no	—
390	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
391	C₂×C₂²⋊C₄	—	2	2	no	—
392	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
393	#107	—	43	2	no	—
394	#107	—	43	2	no	—
395	#107	—	43	2	no	—
396	#107	—	43	2	no	—
397	#107	—	43	8	no	—
398	#107	C₂²×D₄₃	1	2	yes	—
399	#107	C₂²×D₄₃	1	2	yes	—
400	#106	—	43	4	no	—
401	#106	—	43	4	no	—
402	#106	—	43	8	no	—
403	C₄⋊C₈	—	43	2	no	—
404	C₄⋊C₈	—	43	2	no	—
405	#102	—	43	8	no	—
406	#102	—	43	8	no	—
407	#102	C₂²×D₄₃	1	4	yes	—
408	#102	C₂²×D₄₃	1	4	yes	—
409	C₂²⋊C₈	—	43	4	no	—
410	C₂²⋊C₈	—	43	4	no	—
411	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
412	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
413	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
415	C₂⁴	—	2	2	no	—
416	#41	—	86	4	no	—
417	#41	—	86	4	no	—
418	#41	—	344	8	no	—
419	C₂×Q₈	—	43	2	no	—
420	C₂×Q₈	—	86	2	no	—
421	C₂×Q₈	—	86	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	43	4	no	—
426	C₂×D₄	—	43	2	no	—
427	C₂×D₄	—	43	2	no	—
428	C₂×D₄	—	43	2	no	—
429	C₂×D₄	—	86	8	no	—
430	C₂×D₄	—	86	8	no	—
431	C₂×D₄	C₂³×D₄₃	1	4	yes	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	8	4	no	—
436	C₂²×C₄	—	43	4	no	—
437	C₂²×C₄	—	86	8	no	—
438	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
439	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
441	D₈	—	2	4	no	—
442	D₈	—	2	4	no	—
443	M₁₆	—	86	4	no	—
444	M₁₆	—	86	8	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	43	4	no	—
447	C₂×C₈	—	86	8	no	—
448	C₂×C₈	#10621898	1	4	yes	complemented
449	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
450	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
451	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
452	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	43	2	no	—
455	C₄⋊C₄	—	43	2	no	—
456	C₄⋊C₄	—	43	4	no	—
457	C₄⋊C₄	—	43	4	no	—
458	C₄⋊C₄	—	86	8	no	—
459	C₄⋊C₄	—	86	2	no	—
460	C₄⋊C₄	—	86	4	no	—
461	C₄⋊C₄	—	86	4	no	—
462	C₄⋊C₄	—	86	2	no	—
463	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	43	4	no	—
467	C₂²⋊C₄	—	43	4	no	—
468	C₂²⋊C₄	—	86	8	no	—
469	C₂²⋊C₄	—	86	8	no	—
470	C₂²⋊C₄	—	86	8	no	—
471	C₂²⋊C₄	—	86	4	no	—
472	C₄²	—	86	8	no	—
473	C₄²	—	86	4	no	—
474	C₄²	D₄×D₄₃	1	1	yes	characteristic
475	C₄²	D₄×D₄₃	1	1	yes	characteristic
476	C₄²	C₂³×D₄₃	1	1	yes	characteristic
477	C₄²	C₂³×D₄₃	1	1	yes	characteristic
478	C₂³	—	2	4	no	—
479	C₂³	—	4	4	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	8	2	no	—
482	C₂³	—	43	4	no	—
483	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
484	Q₈	—	86	4	no	—
485	Q₈	—	344	2	no	—
486	Q₈	—	172	4	no	—
487	D₄	—	2	4	no	—
488	D₄	—	2	4	no	—
489	D₄	—	4	4	no	—
490	D₄	—	86	8	no	—
491	D₄	—	86	4	no	—
492	D₄	—	86	4	no	—
493	D₄	—	344	8	no	—
494	D₄	—	344	8	no	—
495	D₄	—	172	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	—	8	2	no	—
502	C₂×C₄	—	43	4	no	—
503	C₂×C₄	—	86	4	no	—
504	C₂×C₄	—	86	4	no	—
505	C₂×C₄	—	86	4	no	—
506	C₂×C₄	—	86	4	no	—
507	C₂×C₄	—	344	8	no	—
508	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
509	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
510	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
512	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
513	C₂×C₄	C₂×#10621898	1	2	yes	—
514	C₂×C₄	#13063372	1	2	yes	—
515	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
516	C₈	—	2	1	no	—
517	C₈	—	2	1	no	—
518	C₈	—	86	4	no	—
519	C₈	C₂×#10621898	1	2	yes	—
520	C₈	C₂×#10621898	1	2	yes	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	8	8	no	—
527	C₂²	—	86	4	no	—
528	C₂²	—	86	4	no	—
529	C₂²	—	86	4	no	—
530	C₂²	#14583554	1	2	yes	—
531	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	4	4	no	—
536	C₄	—	86	4	no	—
537	C₄	—	172	4	no	—
538	C₄	—	172	4	no	—
539	C₄	#14583554	1	2	yes	—
540	C₄	#14583700	1	2	yes	—
541	C₄	C₂²×#10621898	1	1	yes	characteristic
542	C₄	C₂×#13063372	1	1	yes	characteristic
543	C₂	—	2	2	no	—
544	C₂	—	8	4	no	—
545	C₂	—	172	4	no	—
546	C₂	C₂×#14583554	1	1	yes	characteristic
547	C₂	C₂×#14583700	1	1	yes	characteristic
548	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×D₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×C₄×D₈	D₄₃
hypocenter	C₄₃	#61284
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #19148447	C₂	semidirect
2. #19147202	C₂	semidirect
3. #19147192	C₂	semidirect
4. #19147019	C₂	semidirect
5. #19146999	C₂	semidirect
6. #19146944	C₂	semidirect
7. #19145109	C₂	semidirect
8. #19144549	C₂	semidirect
9. #19144392	C₂	semidirect
10. #19144239	C₂	semidirect
11. #19143308	C₂	semidirect
12. #19143191	C₂	semidirect
13. C₂×C₄×D₈×C₄₃	C₂	semidirect
17. #14583614	C₂²	semidirect
18. #14583599	C₂²	semidirect
20. #14583554	C₂²	semidirect
27. #14583304	C₂²	semidirect
28. #14583304	C₂²	semidirect
29. #14583301	C₂²	semidirect
30. #14583301	C₂²	semidirect
31. #14583297	C₂²	semidirect
32. #14583222	C₂²	semidirect
33. #14583221	C₂²	semidirect
34. #14583216	C₂²	semidirect
35. #14583211	C₂²	semidirect
36. #14583199	C₂²	semidirect
37. #14583189	C₂²	semidirect
38. #14583179	C₂²	semidirect
42. #14582978	C₂²	semidirect
43. #14582978	C₂²	semidirect
44. C₈×D₁₇₂	C₂²	semidirect
45. C₈×D₁₇₂	C₂²	semidirect
46. #14582940	C₂²	semidirect
50. #14582936	C₂²	semidirect
51. #107×D₄₃	C₂²	semidirect
169. C₂×C₈×C₄₃	#41	semidirect
279. C₂×C₄×D₈	D₄₃	semidirect
338. C₄₃	#61284	semidirect
448. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148447	2
#19147202	2
#19147192	2
#19147019	2
#19146999	2
#19146944	2
#19145109	2
#19144549	2
#19144392	2
#19144239	2
#19143308	2
#19143191	2
C₂×C₄×D₈×C₄₃	2
#61284	43