Subgroups — #25979163

Order 11008.

2010 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148627	C₂	1	2	yes	maximal, complemented
2	#19147569	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147460	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147300	C₂	1	2	yes	maximal, complemented
5	#19147019	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146993	C₂	1	2	yes	maximal, complemented
7	#19146839	C₂	1	2	yes	maximal, complemented
8	#19146732	C₂	1	4	yes	maximal, complemented
9	D₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
10	D₈×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
11	#19145241	C₂	1	2	yes	maximal, complemented
12	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144835	C₂	1	4	yes	maximal, complemented
14	#19144686	C₂	1	2	yes	maximal, complemented
15	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143442	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₈×D₄₃	C₂²	1	2	yes	—
19	#14583614	C₂²	1	2	yes	complemented
20	#14583606	C₂²	1	2	yes	complemented
21	#14583597	C₂²	1	4	yes	complemented
22	#14583595	—	2	2	no	—
23	#14583570	C₂²	1	2	yes	complemented
24	#14583545	—	2	2	no	—
25	#14583539	—	2	4	no	—
26	D₄×D₁₇₂	C₂²	1	2	yes	complemented
27	D₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
28	#14583500	C₂²	1	4	yes	complemented
29	#14583482	—	2	4	no	—
30	#14583449	C₂²	1	2	yes	complemented
31	#14583433	C₂²	1	1	yes	characteristic
32	#14583410	—	2	2	no	—
33	C₂×#13063299	—	2	2	no	—
34	#14583371	C₂²	1	4	yes	complemented
35	#14583304	C₂²	1	1	yes	characteristic, complemented
36	#14583300	C₂²	1	2	yes	complemented
37	#14583276	C₂²	1	1	yes	characteristic, complemented
38	#14583274	C₂²	1	2	yes	complemented
39	#14583262	C₂²	1	4	yes	complemented
40	#14583246	C₂²	1	2	yes	complemented
41	#14583226	C₂²	1	4	yes	complemented
42	#14583221	C₂²	1	4	yes	complemented
43	#14583217	C₂²	1	4	yes	complemented
44	#14583202	C₂²	1	4	yes	complemented
45	#14583197	C₂²	1	4	yes	complemented
46	#14583189	C₂²	1	2	yes	complemented
47	#14583189	C₂²	1	2	yes	complemented
48	#14583151	C₂²	1	4	yes	complemented
49	#14583136	C₂²	1	2	yes	complemented
50	#14583135	C₂²	1	2	yes	complemented
51	#14583135	C₂²	1	2	yes	complemented
52	#14583132	C₂²	1	2	yes	complemented
53	#14583094	C₂²	1	2	yes	complemented
54	#14583094	C₂²	1	2	yes	complemented
55	#14583093	C₂²	1	4	yes	complemented
56	#14583092	C₂²	1	4	yes	complemented
57	#14583034	C₂²	1	4	yes	complemented
58	#14583033	C₂²	1	4	yes	complemented
59	#14583031	C₂²	1	4	yes	complemented
60	#14583029	C₂²	1	1	yes	characteristic, complemented
61	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
62	#14583009	C₂²	1	4	yes	complemented
63	#14583009	C₂²	1	4	yes	complemented
64	#14583008	C₂²	1	4	yes	complemented
65	C₄×D₃₄₄	C₂²	1	2	yes	complemented
66	C₄×D₃₄₄	C₂²	1	2	yes	complemented
67	D₈×Dic₄₃	C₂²	1	2	yes	—
68	#14582981	C₂²	1	2	yes	complemented
69	#14582978	C₂²	1	1	yes	characteristic, complemented
70	#14582970	C₂²	1	2	yes	complemented
71	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
72	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
73	#14582958	C₂²	1	2	yes	complemented
74	#14582956	C₂²	1	1	yes	characteristic, complemented
75	#14582936	C₂²	1	2	yes	complemented
76	#14582902	C₂²	1	4	yes	complemented
77	#14582853	C₂²	1	2	yes	complemented
78	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
80	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
81	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
82	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
84	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
86	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
87	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10621898	—	2	2	no	—
90	C₂×#10621898	—	2	2	no	—
91	C₂²×D₁₇₂	—	2	2	no	—
92	C₂²×C₂²⋊D₄₃	—	2	4	no	—
93	C₂×D₄×D₄₃	C₂³	1	4	yes	—
94	C₂×D₃₄₄	C₂³	1	2	yes	—
95	C₂×D₃₄₄	C₂³	1	2	yes	—
96	C₂×#10621882	C₂³	1	4	yes	—
97	C₂×#10621882	C₂³	1	4	yes	—
98	D₈×D₄₃	—	2	8	no	—
99	C₂×#10621872	C₂³	1	2	yes	—
100	C₂×C₈×D₄₃	C₂³	1	2	yes	—
101	#13063325	C₂³	1	2	yes	—
102	#13063322	C₂³	1	2	yes	—
103	#13063321	C₂³	1	4	yes	—
104	#13063320	—	2	4	no	—
105	#13063319	D₄	1	2	yes	—
106	#13063317	D₄	1	1	yes	characteristic
107	#13063316	C₂³	1	4	yes	—
108	#13063313	—	2	2	no	—
109	#13063313	D₄	1	1	yes	characteristic
110	#13063311	—	2	4	no	—
111	#13063310	—	2	4	no	—
112	#13063308	—	2	4	no	—
113	#13063308	D₄	1	2	yes	—
114	#13063307	—	2	4	no	—
115	#13063304	—	2	2	no	—
116	#13063304	D₄	1	1	yes	characteristic
117	#13063302	—	2	4	no	—
118	#13063300	C₂³	1	4	yes	—
119	#13063299	—	2	2	no	—
120	#13063299	—	2	4	no	—
121	#13063299	—	2	2	no	—
122	#13063299	—	2	4	no	—
123	#13063299	—	2	2	no	—
124	#13063299	—	2	2	no	—
125	#13063299	D₄	1	1	yes	characteristic
126	#13063299	C₂³	1	4	yes	—
127	#13063298	—	2	4	no	—
128	#13063298	—	2	4	no	—
129	#13063297	—	2	4	no	—
130	#13063296	C₂³	1	4	yes	—
131	#13063295	—	2	4	no	—
132	#13063294	—	2	4	no	—
133	#13063293	—	2	4	no	—
134	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
135	C₄×D₁₇₂	—	2	2	no	—
136	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
137	C₄×D₁₇₂	C₂³	1	4	yes	—
138	D₄×Dic₄₃	C₂³	1	4	yes	—
139	#13063287	C₂³	1	4	yes	—
140	C₄×C₂²⋊D₄₃	—	2	4	no	—
141	C₄×C₂²⋊D₄₃	—	2	4	no	—
142	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
143	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
144	#13063284	—	2	2	no	—
145	#13063283	C₂³	1	4	yes	—
146	#13063282	C₂³	1	2	yes	—
147	C₂×C₄⋊Dic₄₃	—	2	2	no	—
148	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
149	C₂²⋊C₄×D₄₃	—	2	4	no	—
150	#13063259	C₂³	1	2	yes	—
151	#13063259	C₂³	1	2	yes	—
152	#13063256	C₂³	1	4	yes	—
153	#13063256	C₂³	1	4	yes	—
154	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
155	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
156	Dic₄₃⋊C₈	C₂³	1	2	yes	—
157	Dic₄₃⋊C₈	C₂³	1	2	yes	—
158	#13063247	C₂³	1	4	yes	—
159	#13063247	C₂³	1	4	yes	—
160	#13063246	C₂³	1	4	yes	—
161	#13063246	C₂³	1	4	yes	—
162	#13063245	C₂³	1	4	yes	—
163	#13063245	C₂³	1	4	yes	—
164	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
165	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
166	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
167	#13063236	C₂³	1	2	yes	—
168	#13063235	C₂³	1	2	yes	—
169	C₈×Dic₄₃	C₂³	1	2	yes	—
170	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
171	C₂³×C₄×C₄₃	—	2	2	no	—
172	C₂×D₈×C₄₃	—	2	4	no	—
173	C₂×D₈×C₄₃	C₂³	1	2	yes	—
174	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
175	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₄₃	—	2	2	no	—
179	C₄×D₄×C₄₃	—	2	2	no	—
180	C₄×D₄×C₄₃	C₂³	1	2	yes	—
181	C₄×D₄×C₄₃	C₂³	1	2	yes	—
182	C₄×D₄×C₄₃	C₂³	1	2	yes	—
183	C₄×D₄×C₄₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
186	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
187	#107×C₄₃	C₂³	1	1	yes	characteristic
188	#107×C₄₃	C₂³	1	1	yes	characteristic
189	#107×C₄₃	C₂³	1	2	yes	—
190	#102×C₄₃	C₂³	1	2	yes	—
191	#102×C₄₃	C₂³	1	2	yes	—
192	#102×C₄₃	C₂³	1	2	yes	—
193	#102×C₄₃	C₂³	1	2	yes	—
194	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
198	C₂⁴×C₄₃	—	2	2	no	—
199	C₂³×D₄₃	—	2	4	no	—
200	C₂×D₄×C₄₃	—	2	2	no	—
201	C₂×D₄×C₄₃	—	2	4	no	—
202	C₂×D₄×C₄₃	—	4	2	no	—
203	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
204	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
205	C₂²×C₄×C₄₃	—	2	2	no	—
206	C₂²×C₄×C₄₃	—	2	2	no	—
207	C₂²×C₄×C₄₃	—	2	2	no	—
208	C₂²×C₄×C₄₃	—	2	2	no	—
209	C₂²×C₄×C₄₃	—	2	2	no	—
210	C₂²×C₄×C₄₃	—	8	4	no	—
211	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₂²⋊D₄₃	—	2	4	no	—
215	C₂×C₂²⋊D₄₃	—	2	4	no	—
216	C₂×C₂²⋊D₄₃	—	2	4	no	—
217	C₂×C₂²⋊D₄₃	—	2	4	no	—
218	C₂×C₂²⋊D₄₃	—	2	4	no	—
219	C₂×C₂²⋊D₄₃	—	8	8	no	—
220	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
221	C₂²×Dic₄₃	—	2	4	no	—
222	D₄×D₄₃	—	2	8	no	—
223	D₄×D₄₃	—	4	4	no	—
224	#10621898	—	8	4	no	—
225	#10621898	—	8	4	no	—
226	C₂×D₁₇₂	—	2	2	no	—
227	C₂×D₁₇₂	—	2	2	no	—
228	C₂×D₁₇₂	—	2	4	no	—
229	C₂×D₁₇₂	—	8	4	no	—
230	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
231	C₂×D₁₇₂	C₂⁴	1	4	yes	—
232	C₂×C₄×D₄₃	—	2	4	no	—
233	C₂×C₄×D₄₃	—	2	4	no	—
234	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
235	C₂×Dic₈₆	—	2	2	no	—
236	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
237	D₈×C₄₃	—	2	4	no	—
238	D₈×C₄₃	—	2	2	no	—
239	D₈×C₄₃	#41	1	4	yes	complemented
240	C₂×C₈×C₄₃	—	2	2	no	—
241	C₂×C₈×C₄₃	—	4	1	no	—
242	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₄⋊C₄×C₄₃	—	2	2	no	—
247	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
248	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
249	C₂²⋊C₄×C₄₃	—	2	2	no	—
250	C₂²⋊C₄×C₄₃	—	2	2	no	—
251	C₂²⋊C₄×C₄₃	—	2	2	no	—
252	C₂²⋊C₄×C₄₃	—	2	2	no	—
253	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊Dic₄₃	—	2	4	no	—
258	C₂²⋊Dic₄₃	—	2	4	no	—
259	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
260	#10621882	—	2	8	no	—
261	#10621882	—	4	4	no	—
262	(C₂×D₄₃)⋊C₄	—	2	4	no	—
263	(C₂×D₄₃)⋊C₄	—	2	4	no	—
264	(C₂×D₄₃)⋊C₄	—	2	4	no	—
265	(C₂×D₄₃)⋊C₄	—	2	4	no	—
266	(C₂×D₄₃)⋊C₄	—	2	4	no	—
267	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
268	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
269	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
270	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
271	C₄⋊Dic₄₃	—	2	2	no	—
272	C₄⋊Dic₄₃	—	2	4	no	—
273	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
274	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
275	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
276	Dic₄₃⋊C₄	—	2	4	no	—
277	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
278	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
279	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
280	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
281	C₄×Dic₄₃	—	2	4	no	—
282	C₄×Dic₄₃	C₂⁴	1	2	yes	—
283	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
284	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
285	D₃₄₄	—	2	4	no	—
286	D₃₄₄	—	4	2	no	—
287	#10621872	—	4	2	no	—
288	C₈×D₄₃	—	2	4	no	—
289	C₂³×C₄₃	—	2	2	no	—
290	C₂³×C₄₃	—	2	2	no	—
291	C₂³×C₄₃	—	4	4	no	—
292	C₂³×C₄₃	—	4	4	no	—
293	C₂³×C₄₃	—	8	2	no	—
294	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
295	C₂²×D₄₃	—	2	4	no	—
296	C₂²×D₄₃	—	4	8	no	—
297	C₂²×D₄₃	—	8	4	no	—
298	C₂²×D₄₃	—	8	4	no	—
299	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
300	D₄×C₄₃	—	2	2	no	—
301	D₄×C₄₃	—	2	2	no	—
302	D₄×C₄₃	—	2	2	no	—
303	D₄×C₄₃	—	4	4	no	—
304	D₄×C₄₃	C₂×#41	1	4	yes	—
305	C₂×C₄×C₄₃	—	2	2	no	—
306	C₂×C₄×C₄₃	—	2	2	no	—
307	C₂×C₄×C₄₃	—	2	1	no	—
308	C₂×C₄×C₄₃	—	2	1	no	—
309	C₂×C₄×C₄₃	—	2	2	no	—
310	C₂×C₄×C₄₃	—	2	2	no	—
311	C₂×C₄×C₄₃	—	4	4	no	—
312	C₂×C₄×C₄₃	—	4	4	no	—
313	C₂×C₄×C₄₃	—	8	2	no	—
314	C₂×C₄×C₄₃	—	8	2	no	—
315	C₂×C₄×C₄₃	—	8	2	no	—
316	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
321	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
322	C₂²⋊D₄₃	—	2	4	no	—
323	C₂²⋊D₄₃	—	4	8	no	—
324	C₂²⋊D₄₃	—	4	8	no	—
325	C₂²⋊D₄₃	—	8	4	no	—
326	C₂²⋊D₄₃	—	8	4	no	—
327	C₂²⋊D₄₃	—	8	4	no	—
328	C₂×Dic₄₃	—	2	4	no	—
329	C₂×Dic₄₃	—	8	4	no	—
330	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
331	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
332	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
333	D₁₇₂	—	2	2	no	—
334	D₁₇₂	—	2	4	no	—
335	D₁₇₂	—	2	4	no	—
336	D₁₇₂	—	4	4	no	—
337	D₁₇₂	—	8	2	no	—
338	D₁₇₂	—	8	4	no	—
339	C₄×D₄₃	—	2	2	no	—
340	C₄×D₄₃	—	2	2	no	—
341	C₄×D₄₃	—	8	4	no	—
342	C₄×D₄₃	—	8	4	no	—
343	Dic₈₆	—	2	2	no	—
344	Dic₈₆	—	8	2	no	—
345	C₈×C₄₃	—	2	1	no	—
346	C₈×C₄₃	—	2	1	no	—
347	C₈×C₄₃	—	2	1	no	—
348	C₈×C₄₃	C₂×#41	1	2	yes	—
349	C₄₃⋊C₈	—	2	2	no	—
350	C₄₃⋊C₈	—	2	2	no	—
351	#61480	—	43	1	no	maximal, Sylow
352	C₂²×C₄₃	—	2	1	no	—
353	C₂²×C₄₃	—	2	1	no	—
354	C₂²×C₄₃	—	2	4	no	—
355	C₂²×C₄₃	—	4	2	no	—
356	C₂²×C₄₃	—	4	2	no	—
357	C₂²×C₄₃	—	4	2	no	—
358	C₂²×C₄₃	—	4	2	no	—
359	C₂²×C₄₃	—	4	2	no	—
360	C₂²×C₄₃	—	8	8	no	—
361	C₂²×C₄₃	#576	1	2	yes	—
362	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
363	C₂×D₄₃	—	2	2	no	—
364	C₂×D₄₃	—	2	2	no	—
365	C₂×D₄₃	—	2	2	no	—
366	C₂×D₄₃	—	4	4	no	—
367	C₂×D₄₃	—	4	4	no	—
368	C₂×D₄₃	—	4	4	no	—
369	C₂×D₄₃	—	16	8	no	—
370	C₄×C₄₃	—	2	1	no	—
371	C₄×C₄₃	—	2	1	no	—
372	C₄×C₄₃	—	2	1	no	—
373	C₄×C₄₃	—	2	1	no	—
374	C₄×C₄₃	—	4	2	no	—
375	C₄×C₄₃	—	4	2	no	—
376	C₄×C₄₃	#576	1	2	yes	—
377	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
378	C₄×C₄₃	#585	1	1	yes	characteristic
379	Dic₄₃	—	2	2	no	—
380	Dic₄₃	—	2	2	no	—
381	Dic₄₃	—	2	2	no	—
382	Dic₄₃	—	4	4	no	—
383	#3519	—	43	2	no	—
384	#3391	—	43	1	no	—
385	#3380	—	43	1	no	—
386	#3366	—	43	2	no	—
387	#3341	—	43	1	no	—
388	#3339	—	43	2	no	—
389	#3325	—	43	2	no	—
390	#3318	—	43	4	no	—
391	D₄×D₈	—	43	1	no	—
392	D₄×D₈	—	43	2	no	—
393	#3176	—	43	2	no	—
394	#3169	—	43	1	no	—
395	#3122	—	43	4	no	—
396	#3109	—	43	2	no	—
397	#2966	—	43	1	no	—
398	#2948	—	43	2	no	—
399	C₂×C₄×D₈	D₄₃	1	1	yes	characteristic, complemented
400	C₂×C₄₃	—	2	2	no	—
401	C₂×C₄₃	—	4	4	no	—
402	C₂×C₄₃	—	8	2	no	—
403	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
404	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
405	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
406	D₄₃	—	4	2	no	—
407	D₄₃	—	8	4	no	—
408	C₂²×D₈	—	43	2	no	—
409	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
410	#555	—	43	2	no	—
411	#554	—	43	2	no	—
412	#553	—	43	4	no	—
413	#553	—	86	2	no	—
414	#550	—	43	2	no	—
415	#546	—	86	4	no	—
416	#546	—	86	2	no	—
417	D₄²	—	43	4	no	—
418	D₄²	—	43	2	no	—
419	#540	—	43	4	no	—
420	#538	—	86	4	no	—
421	#532	—	43	2	no	—
422	#529	—	43	1	no	—
423	#525	—	86	2	no	—
424	C₂×#121	—	86	2	no	—
425	#518	—	43	4	no	—
426	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
427	#500	—	43	1	no	—
428	#499	—	43	2	no	—
429	#493	—	43	2	no	—
430	#493	—	43	1	no	—
431	#490	—	43	4	no	—
432	#486	—	43	2	no	—
433	#482	—	43	4	no	—
434	#482	—	43	4	no	—
435	#481	—	43	4	no	—
436	#478	—	43	4	no	—
437	#478	—	43	4	no	—
438	#476	—	43	2	no	—
439	#476	—	43	2	no	—
440	#469	—	43	4	no	—
441	#466	—	43	2	no	—
442	#466	—	43	2	no	—
443	#466	—	43	2	no	—
444	#466	—	43	2	no	—
445	#459	—	43	4	no	—
446	#459	—	43	2	no	—
447	#459	—	43	2	no	—
448	#459	—	43	4	no	—
449	#447	—	43	4	no	—
450	#447	—	43	4	no	—
451	#447	—	43	4	no	—
452	#446	—	43	1	no	—
453	C₈×Q₈	—	43	1	no	—
454	#442	—	43	4	no	—
455	#442	—	43	4	no	—
456	#442	—	43	4	no	—
457	C₄×D₈	—	43	2	no	—
458	C₄×D₈	—	43	2	no	—
459	C₄×D₈	—	43	2	no	—
460	C₄×D₈	—	43	2	no	—
461	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
462	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
463	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
464	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
465	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
466	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
467	#436	—	43	1	no	—
468	#435	—	43	2	no	—
469	C₈×D₄	—	43	2	no	—
470	C₈×D₄	—	43	1	no	—
471	#433	—	43	2	no	—
472	#432	—	43	1	no	—
473	#427	—	43	2	no	—
474	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
475	#418	—	43	4	no	—
476	C₂×#102	C₂×D₄₃	1	2	yes	complemented
477	#405	—	43	2	no	—
478	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
479	C₄₃	#61480	1	1	yes	characteristic, complemented, Sylow
480	C₂×#41	—	86	2	no	—
481	C₂×#41	—	86	2	no	—
482	C₂²×D₄	—	43	4	no	—
483	C₂²×D₄	—	86	2	no	—
484	C₂²×D₄	—	86	4	no	—
485	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
486	C₂³×C₄	—	2	2	no	—
487	C₂×D₈	—	2	4	no	—
488	C₂×D₈	—	43	4	no	—
489	C₂×D₈	—	43	4	no	—
490	C₂×D₈	—	43	2	no	—
491	C₂×D₈	—	43	2	no	—
492	C₂×D₈	—	86	8	no	—
493	C₂×D₈	C₂²×D₄₃	1	2	yes	—
494	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
495	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
496	C₂×M₁₆	—	43	2	no	—
497	C₂²×C₈	—	43	2	no	—
498	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
499	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
500	C₄⋊Q₈	—	43	2	no	—
501	#127	—	43	4	no	—
502	#127	—	43	2	no	—
503	#126	—	43	2	no	—
504	#126	—	86	4	no	—
505	#125	—	43	4	no	—
506	#125	—	43	1	no	—
507	#124	—	43	1	no	—
508	#124	—	86	4	no	—
509	#124	—	86	2	no	—
510	#123	—	43	2	no	—
511	#123	—	86	4	no	—
512	#123	—	86	4	no	—
513	#123	—	86	4	no	—
514	C₂²⋊Q₈	—	43	1	no	—
515	C₂²⋊Q₈	—	86	4	no	—
516	C₂²⋊Q₈	—	86	2	no	—
517	#121	—	43	1	no	—
518	#121	—	43	4	no	—
519	#121	—	43	4	no	—
520	#121	—	43	4	no	—
521	#121	—	86	4	no	—
522	#121	—	86	4	no	—
523	#121	—	86	4	no	—
524	#121	—	86	2	no	—
525	#121	—	86	2	no	—
526	#121	—	86	4	no	—
527	#121	—	86	4	no	—
528	#121	—	86	2	no	—
529	#121	—	86	2	no	—
530	#120	—	86	4	no	—
531	#120	—	86	4	no	—
532	#120	—	86	4	no	—
533	C₄×Q₈	—	43	1	no	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	43	2	no	—
537	C₄×D₄	—	43	4	no	—
538	C₄×D₄	—	43	4	no	—
539	C₄×D₄	—	43	1	no	—
540	C₄×D₄	—	43	4	no	—
541	C₄×D₄	—	86	4	no	—
542	C₄×D₄	—	86	4	no	—
543	C₄×D₄	—	86	4	no	—
544	C₄×D₄	—	86	2	no	—
545	C₄×D₄	C₂²×D₄₃	1	2	yes	—
546	C₄×D₄	C₂²×D₄₃	1	2	yes	—
547	C₄×D₄	C₂²×D₄₃	1	2	yes	—
548	C₄×D₄	C₂²×D₄₃	1	2	yes	—
549	#117	—	43	2	no	—
550	#117	—	43	4	no	—
551	#117	—	86	2	no	—
552	C₂×C₄⋊C₄	—	86	2	no	—
553	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
554	C₂×C₂²⋊C₄	—	2	2	no	—
555	C₂×C₂²⋊C₄	—	86	4	no	—
556	C₂×C₂²⋊C₄	—	86	4	no	—
557	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
558	#107	—	43	2	no	—
559	#107	—	43	2	no	—
560	#107	C₂²×D₄₃	1	1	yes	characteristic
561	#107	C₂²×D₄₃	1	1	yes	characteristic
562	#107	C₂²×D₄₃	1	2	yes	—
563	#106	—	43	4	no	—
564	#106	—	43	4	no	—
565	C₄⋊C₈	—	43	2	no	—
566	C₄⋊C₈	—	43	2	no	—
567	C₄⋊C₈	—	43	1	no	—
568	C₄⋊C₈	—	43	1	no	—
569	#102	—	43	4	no	—
570	#102	—	43	4	no	—
571	#102	—	43	4	no	—
572	#102	—	43	4	no	—
573	#102	—	43	4	no	—
574	#102	—	43	4	no	—
575	#102	C₂²×D₄₃	1	2	yes	—
576	#102	C₂²×D₄₃	1	2	yes	—
577	#102	C₂²×D₄₃	1	2	yes	—
578	#102	C₂²×D₄₃	1	2	yes	—
579	C₂²⋊C₈	—	43	2	no	—
580	C₂²⋊C₈	—	43	2	no	—
581	C₂²⋊C₈	—	43	2	no	—
582	#97	—	43	2	no	—
583	#97	—	43	2	no	—
584	C₄×C₈	—	43	2	no	—
585	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
586	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
587	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
588	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	86	4	no	—
591	#41	—	344	4	no	—
592	#41	—	344	4	no	—
593	C₂×Q₈	—	43	1	no	—
594	C₂×Q₈	—	86	2	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	4	2	no	—
598	C₂×D₄	—	43	2	no	—
599	C₂×D₄	—	43	1	no	—
600	C₂×D₄	—	43	4	no	—
601	C₂×D₄	—	86	4	no	—
602	C₂×D₄	—	86	4	no	—
603	C₂×D₄	—	86	4	no	—
604	C₂×D₄	—	86	4	no	—
605	C₂×D₄	—	86	8	no	—
606	C₂×D₄	—	86	4	no	—
607	C₂×D₄	—	86	4	no	—
608	C₂×D₄	—	86	2	no	—
609	C₂×D₄	—	86	2	no	—
610	C₂×D₄	—	344	4	no	—
611	C₂×D₄	—	344	8	no	—
612	C₂×D₄	—	172	4	no	—
613	C₂×D₄	C₂³×D₄₃	1	2	yes	—
614	C₂×D₄	C₂³×D₄₃	1	2	yes	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	8	4	no	—
621	C₂²×C₄	—	43	2	no	—
622	C₂²×C₄	—	86	4	no	—
623	C₂²×C₄	—	86	4	no	—
624	C₂²×C₄	—	86	4	no	—
625	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
626	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
627	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
628	D₈	—	2	4	no	—
629	D₈	—	2	2	no	—
630	D₈	—	86	8	no	—
631	D₈	—	86	4	no	—
632	D₈	—	172	2	no	—
633	D₈	—	172	4	no	—
634	D₈	#10621898	1	4	yes	complemented
635	M₁₆	—	172	2	no	—
636	C₂×C₈	—	2	2	no	—
637	C₂×C₈	—	4	1	no	—
638	C₂×C₈	—	43	2	no	—
639	C₂×C₈	—	43	2	no	—
640	C₂×C₈	—	86	4	no	—
641	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
642	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
643	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
644	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
645	C₄⋊C₄	—	2	2	no	—
646	C₄⋊C₄	—	43	1	no	—
647	C₄⋊C₄	—	43	2	no	—
648	C₄⋊C₄	—	43	2	no	—
649	C₄⋊C₄	—	43	1	no	—
650	C₄⋊C₄	—	43	2	no	—
651	C₄⋊C₄	—	43	2	no	—
652	C₄⋊C₄	—	43	4	no	—
653	C₄⋊C₄	—	86	4	no	—
654	C₄⋊C₄	—	86	4	no	—
655	C₄⋊C₄	—	86	2	no	—
656	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
657	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
658	C₂²⋊C₄	—	2	2	no	—
659	C₂²⋊C₄	—	2	2	no	—
660	C₂²⋊C₄	—	2	2	no	—
661	C₂²⋊C₄	—	2	2	no	—
662	C₂²⋊C₄	—	43	2	no	—
663	C₂²⋊C₄	—	43	2	no	—
664	C₂²⋊C₄	—	43	2	no	—
665	C₂²⋊C₄	—	43	2	no	—
666	C₂²⋊C₄	—	43	2	no	—
667	C₂²⋊C₄	—	86	4	no	—
668	C₂²⋊C₄	—	86	4	no	—
669	C₂²⋊C₄	—	86	4	no	—
670	C₂²⋊C₄	—	86	4	no	—
671	C₂²⋊C₄	—	86	4	no	—
672	C₂²⋊C₄	—	86	4	no	—
673	C₂²⋊C₄	—	86	4	no	—
674	C₄²	—	43	2	no	—
675	C₄²	—	86	4	no	—
676	C₄²	D₄×D₄₃	1	1	yes	characteristic
677	C₄²	D₄×D₄₃	1	1	yes	characteristic
678	C₄²	C₂³×D₄₃	1	1	yes	characteristic
679	C₄²	C₂³×D₄₃	1	1	yes	characteristic
680	C₂³	—	2	2	no	—
681	C₂³	—	2	2	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	4	no	—
684	C₂³	—	8	2	no	—
685	C₂³	—	43	2	no	—
686	C₂³	—	86	4	no	—
687	C₂³	—	344	4	no	—
688	C₂³	—	344	4	no	—
689	C₂³	—	172	8	no	—
690	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
691	Q₈	—	86	2	no	—
692	Q₈	—	344	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	4	no	—
697	D₄	—	86	4	no	—
698	D₄	—	86	2	no	—
699	D₄	—	86	4	no	—
700	D₄	—	86	4	no	—
701	D₄	—	344	2	no	—
702	D₄	—	344	4	no	—
703	D₄	—	344	4	no	—
704	D₄	—	344	4	no	—
705	D₄	—	344	4	no	—
706	D₄	—	172	8	no	—
707	D₄	—	172	8	no	—
708	D₄	—	172	4	no	—
709	D₄	C₂×#10621898	1	4	yes	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	8	2	no	—
719	C₂×C₄	—	8	2	no	—
720	C₂×C₄	—	8	2	no	—
721	C₂×C₄	—	43	2	no	—
722	C₂×C₄	—	43	2	no	—
723	C₂×C₄	—	43	2	no	—
724	C₂×C₄	—	86	2	no	—
725	C₂×C₄	—	86	2	no	—
726	C₂×C₄	—	86	4	no	—
727	C₂×C₄	—	344	4	no	—
728	C₂×C₄	—	344	4	no	—
729	C₂×C₄	—	344	4	no	—
730	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
731	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
732	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
733	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
734	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
735	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
736	C₈	—	2	1	no	—
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	86	2	no	—
740	C₈	—	86	2	no	—
741	C₈	C₂×#10621898	1	2	yes	—
742	C₂²	—	2	1	no	—
743	C₂²	—	2	1	no	—
744	C₂²	—	2	4	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	8	8	no	—
751	C₂²	—	86	2	no	—
752	C₂²	—	86	2	no	—
753	C₂²	—	86	2	no	—
754	C₂²	—	172	4	no	—
755	C₂²	—	172	4	no	—
756	C₂²	—	172	4	no	—
757	C₂²	—	688	8	no	—
758	C₂²	#14583701	1	2	yes	—
759	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
760	C₄	—	2	1	no	—
761	C₄	—	2	1	no	—
762	C₄	—	2	1	no	—
763	C₄	—	2	1	no	—
764	C₄	—	4	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	86	2	no	—
767	C₄	—	86	2	no	—
768	C₄	—	86	2	no	—
769	C₄	—	172	4	no	—
770	C₄	#14583700	1	2	yes	—
771	C₄	C₂²×#10621898	1	1	yes	characteristic
772	C₄	#14583735	1	1	yes	characteristic
773	C₂	—	2	2	no	—
774	C₂	—	4	4	no	—
775	C₂	—	8	2	no	—
776	C₂	—	344	4	no	—
777	C₂	—	172	2	no	—
778	C₂	D₄×#10621898	1	1	yes	characteristic
779	C₂	C₂×#14583700	1	1	yes	characteristic
780	C₂	C₂×#14583701	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	#61480
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. #19148627	C₂	semidirect
2. #19147569	C₂	semidirect
3. #19147460	C₂	semidirect
4. #19147300	C₂	semidirect
5. #19147019	C₂	semidirect
6. #19146993	C₂	semidirect
7. #19146839	C₂	semidirect
8. #19146732	C₂	semidirect
9. D₈×D₁₇₂	C₂	semidirect
10. D₈×C₂²⋊D₄₃	C₂	semidirect
11. #19145241	C₂	semidirect
12. #19145174	C₂	semidirect
13. #19144835	C₂	semidirect
14. #19144686	C₂	semidirect
15. #19143570	C₂	semidirect
16. #19143442	C₂	semidirect
17. C₂×C₄×D₈×C₄₃	C₂	semidirect
19. #14583614	C₂²	semidirect
20. #14583606	C₂²	semidirect
21. #14583597	C₂²	semidirect
23. #14583570	C₂²	semidirect
26. D₄×D₁₇₂	C₂²	semidirect
27. D₄×C₂²⋊D₄₃	C₂²	semidirect
28. #14583500	C₂²	semidirect
30. #14583449	C₂²	semidirect
34. #14583371	C₂²	semidirect
35. #14583304	C₂²	semidirect
36. #14583300	C₂²	semidirect
37. #14583276	C₂²	semidirect
38. #14583274	C₂²	semidirect
39. #14583262	C₂²	semidirect
40. #14583246	C₂²	semidirect
41. #14583226	C₂²	semidirect
42. #14583221	C₂²	semidirect
43. #14583217	C₂²	semidirect
44. #14583202	C₂²	semidirect
45. #14583197	C₂²	semidirect
46. #14583189	C₂²	semidirect
47. #14583189	C₂²	semidirect
48. #14583151	C₂²	semidirect
49. #14583136	C₂²	semidirect
50. #14583135	C₂²	semidirect
51. #14583135	C₂²	semidirect
52. #14583132	C₂²	semidirect
53. #14583094	C₂²	semidirect
54. #14583094	C₂²	semidirect
55. #14583093	C₂²	semidirect
56. #14583092	C₂²	semidirect
57. #14583034	C₂²	semidirect
58. #14583033	C₂²	semidirect
59. #14583031	C₂²	semidirect
60. #14583029	C₂²	semidirect
61. C₈×Dic₈₆	C₂²	semidirect
62. #14583009	C₂²	semidirect
63. #14583009	C₂²	semidirect
64. #14583008	C₂²	semidirect
65. C₄×D₃₄₄	C₂²	semidirect
66. C₄×D₃₄₄	C₂²	semidirect
68. #14582981	C₂²	semidirect
69. #14582978	C₂²	semidirect
70. #14582970	C₂²	semidirect
71. C₈×D₁₇₂	C₂²	semidirect
72. C₈×C₂²⋊D₄₃	C₂²	semidirect
73. #14582958	C₂²	semidirect
74. #14582956	C₂²	semidirect
75. #14582936	C₂²	semidirect
76. #14582902	C₂²	semidirect
77. #14582853	C₂²	semidirect
79. C₂×C₄×D₄×C₄₃	C₂²	semidirect
82. C₄×D₈×C₄₃	C₂²	semidirect
83. C₄×D₈×C₄₃	C₂²	semidirect
84. C₄×D₈×C₄₃	C₂²	semidirect
85. C₄×D₈×C₄₃	C₂²	semidirect
86. C₂×#107×C₄₃	C₂²	semidirect
87. C₂×#102×C₄₃	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
239. D₈×C₄₃	#41	semidirect
399. C₂×C₄×D₈	D₄₃	semidirect
426. C₂×C₄×D₄	C₂×D₄₃	semidirect
463. C₄×D₈	C₂×D₄₃	semidirect
464. C₄×D₈	C₂×D₄₃	semidirect
465. C₄×D₈	C₂×D₄₃	semidirect
466. C₄×D₈	C₂×D₄₃	semidirect
474. C₂×#107	C₂×D₄₃	semidirect
476. C₂×#102	C₂×D₄₃	semidirect
478. C₂×C₄×C₈	C₂×D₄₃	semidirect
479. C₄₃	#61480	semidirect
634. D₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148627	2
#19147569	2
#19147460	2
#19147300	2
#19147019	2
#19146993	2
#19146839	2
#19146732	2
D₈×D₁₇₂	2
D₈×C₂²⋊D₄₃	2
#19145241	2
#19145174	2
#19144835	2
#19144686	2
#19143570	2
#19143442	2
C₂×C₄×D₈×C₄₃	2
#61480	43