Subgroups — #25978104

Order 11008.

2000 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148205	C₂	1	2	yes	maximal, complemented
2	#19147605	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147460	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147253	C₂	1	2	yes	maximal, complemented
5	#19146997	C₂	1	2	yes	maximal, complemented
6	#19146989	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146446	C₂	1	4	yes	maximal, complemented
8	#19146421	C₂	1	2	yes	maximal, complemented
9	#19146274	C₂	1	2	yes	maximal, complemented
10	D₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145168	C₂	1	2	yes	maximal, complemented
13	#19144655	C₂	1	2	yes	maximal, complemented
14	#19144646	C₂	1	4	yes	maximal, complemented
15	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×D₈×D₄₃	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×D₈×D₄₃	C₂²	1	2	yes	—
19	#14583634	C₂²	1	2	yes	complemented
20	#14583609	C₂²	1	2	yes	—
21	#14583606	C₂²	1	2	yes	complemented
22	#14583595	—	2	2	no	—
23	#14583593	C₂²	1	4	yes	complemented
24	#14583573	—	2	4	no	—
25	#14583545	—	2	2	no	—
26	#14583537	C₂²	1	4	yes	complemented
27	D₄×D₁₇₂	C₂²	1	2	yes	—
28	#14583449	C₂²	1	2	yes	complemented
29	#14583436	C₂²	1	4	yes	complemented
30	#14583433	—	2	2	no	—
31	#14583408	—	2	4	no	—
32	C₄×#10621898	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₁₇₂	—	2	2	no	—
34	C₄×D₄×D₄₃	C₂²	1	4	yes	complemented
35	#14583304	C₂²	1	1	yes	characteristic, complemented
36	#14583300	C₂²	1	2	yes	complemented
37	#14583284	C₂²	1	2	yes	complemented
38	#14583276	C₂²	1	1	yes	characteristic
39	#14583255	C₂²	1	4	yes	complemented
40	#14583246	C₂²	1	2	yes	complemented
41	#14583233	C₂²	1	4	yes	complemented
42	#14583223	C₂²	1	4	yes	complemented
43	#14583219	C₂²	1	4	yes	complemented
44	#14583198	C₂²	1	4	yes	complemented
45	#14583197	C₂²	1	4	yes	complemented
46	#14583194	C₂²	1	2	yes	complemented
47	#14583189	C₂²	1	2	yes	complemented
48	#14583137	C₂²	1	2	yes	complemented
49	#14583136	C₂²	1	2	yes	—
50	#14583135	C₂²	1	2	yes	complemented
51	#14583135	C₂²	1	2	yes	complemented
52	#14583131	C₂²	1	4	yes	complemented
53	#14583117	C₂²	1	4	yes	complemented
54	#14583116	C₂²	1	4	yes	complemented
55	#14583099	C₂²	1	2	yes	complemented
56	#14583094	C₂²	1	2	yes	—
57	#14583048	C₂²	1	4	yes	complemented
58	#14583044	C₂²	1	4	yes	complemented
59	#14583034	C₂²	1	4	yes	—
60	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
61	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
62	C₄×#10621884	C₂²	1	4	yes	complemented
63	C₄×D₃₄₄	C₂²	1	2	yes	complemented
64	C₄×D₃₄₄	C₂²	1	2	yes	complemented
65	D₈×Dic₄₃	C₂²	1	2	yes	—
66	#14582981	C₂²	1	2	yes	complemented
67	C₄×#10621882	C₂²	1	4	yes	complemented
68	#14582979	C₂²	1	4	yes	complemented
69	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
70	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
71	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
72	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
73	#14582952	C₂²	1	1	yes	characteristic, complemented
74	#14582950	C₂²	1	2	yes	complemented
75	#107×D₄₃	C₂²	1	2	yes	complemented
76	#102×D₄₃	C₂²	1	4	yes	complemented
77	C₄×C₈×D₄₃	C₂²	1	2	yes	complemented
78	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
79	C₄×#41×C₄₃	C₂²	1	2	yes	complemented
80	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
84	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
85	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
86	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
87	C₄₃×#416	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	D₄	1	1	yes	characteristic
91	C₂²×D₁₇₂	—	2	2	no	—
92	C₂×D₄×D₄₃	C₂³	1	4	yes	—
93	C₂²×C₄×D₄₃	—	2	4	no	—
94	C₂×#10621884	C₂³	1	4	yes	—
95	C₂×D₃₄₄	C₂³	1	2	yes	—
96	C₂×D₃₄₄	C₂³	1	2	yes	—
97	C₂×#10621882	C₂³	1	4	yes	—
98	D₈×D₄₃	—	2	8	no	—
99	C₂×C₈×D₄₃	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	#13063320	—	2	4	no	—
104	#13063319	—	2	4	no	—
105	#13063317	—	2	2	no	—
106	#13063316	C₂³	1	4	yes	—
107	#13063314	C₂³	1	4	yes	—
108	#13063313	—	2	2	no	—
109	#13063313	—	2	2	no	—
110	#13063310	—	2	4	no	—
111	#13063310	—	2	4	no	—
112	#13063308	—	2	4	no	—
113	#13063307	—	2	4	no	—
114	#13063304	—	2	2	no	—
115	#13063303	—	2	4	no	—
116	#13063302	—	2	4	no	—
117	#13063301	C₂³	1	4	yes	—
118	#13063300	C₂³	1	4	yes	—
119	#13063299	—	2	2	no	—
120	#13063299	—	2	2	no	—
121	#13063299	C₂³	1	4	yes	—
122	#13063298	—	2	4	no	—
123	#13063297	—	2	4	no	—
124	#13063295	—	2	4	no	—
125	#13063293	—	2	4	no	—
126	C₄×Dic₈₆	D₄	1	1	yes	characteristic
127	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
128	C₄×D₁₇₂	—	2	2	no	—
129	C₄×D₁₇₂	—	2	4	no	—
130	C₄×D₁₇₂	—	2	2	no	—
131	C₄×D₁₇₂	—	2	4	no	—
132	C₄×D₁₇₂	—	2	2	no	—
133	C₄×D₁₇₂	D₄	1	1	yes	characteristic
134	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
135	C₄×D₁₇₂	C₂³	1	4	yes	—
136	D₄×Dic₄₃	C₂³	1	4	yes	—
137	#13063287	C₂³	1	4	yes	—
138	C₄×C₂²⋊D₄₃	—	2	4	no	—
139	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
140	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
141	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
142	#13063284	D₄	1	1	yes	characteristic
143	#13063282	—	2	4	no	—
144	#13063282	D₄	1	2	yes	—
145	C₂×C₄⋊Dic₄₃	—	2	2	no	—
146	C₄⋊C₄×D₄₃	C₂³	1	4	yes	—
147	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
148	C₂²⋊C₄×D₄₃	—	2	4	no	—
149	C₄²×D₄₃	C₂³	1	2	yes	—
150	#13063259	C₂³	1	2	yes	—
151	#13063259	C₂³	1	2	yes	—
152	#13063258	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	#13063249	C₂³	1	4	yes	—
159	#13063247	C₂³	1	4	yes	—
160	#13063247	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	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
168	C₈×Dic₄₃	C₂³	1	2	yes	—
169	C₈×Dic₄₃	C₂³	1	2	yes	—
170	C₂×#41×C₄₃	C₂³	1	2	yes	—
171	#135×C₄₃	—	2	4	no	—
172	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
173	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
174	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
178	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
179	C₄×D₄×C₄₃	—	2	2	no	—
180	C₄×D₄×C₄₃	—	2	2	no	—
181	C₄×D₄×C₄₃	C₂³	1	2	yes	—
182	C₄×D₄×C₄₃	C₂³	1	2	yes	—
183	#117×C₄₃	—	2	2	no	—
184	#117×C₄₃	C₂³	1	2	yes	—
185	C₂×C₄²×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	#106×C₄₃	C₂³	1	2	yes	—
190	#103×C₄₃	C₂³	1	2	yes	—
191	#103×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	C₂³×D₄₃	—	2	4	no	—
199	#41×C₄₃	—	2	4	no	—
200	#41×C₄₃	—	4	2	no	—
201	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₄₃	—	2	2	no	—
203	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₄₃	—	2	2	no	—
205	C₂²×C₄×C₄₃	—	2	2	no	—
206	C₂²×C₄×C₄₃	—	2	2	no	—
207	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
210	C₂×C₂²⋊D₄₃	—	2	4	no	—
211	C₂×C₂²⋊D₄₃	—	2	4	no	—
212	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
213	C₂²×Dic₄₃	—	2	4	no	—
214	D₄×D₄₃	—	2	8	no	—
215	D₄×D₄₃	—	4	4	no	—
216	#10621898	—	2	4	no	—
217	#10621898	—	8	4	no	—
218	C₂×D₁₇₂	—	2	2	no	—
219	C₂×D₁₇₂	—	2	2	no	—
220	C₂×D₁₇₂	—	2	4	no	—
221	C₂×D₁₇₂	—	4	8	no	—
222	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
223	C₂×D₁₇₂	C₂⁴	1	4	yes	—
224	C₂×C₄×D₄₃	—	2	4	no	—
225	C₂×C₄×D₄₃	—	2	4	no	—
226	C₂×C₄×D₄₃	—	2	4	no	—
227	C₂×C₄×D₄₃	—	8	8	no	—
228	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
229	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
230	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
231	C₂×Dic₈₆	—	2	2	no	—
232	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
233	Q₁₆×C₄₃	—	2	2	no	—
234	SD₁₆×C₄₃	—	2	4	no	—
235	D₈×C₄₃	#41	1	4	yes	complemented
236	C₂×C₈×C₄₃	—	2	2	no	—
237	C₂×C₈×C₄₃	—	4	1	no	—
238	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₄₃	—	2	2	no	—
243	C₄⋊C₄×C₄₃	—	2	2	no	—
244	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
245	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
246	C₂²⋊C₄×C₄₃	—	2	2	no	—
247	C₂²⋊C₄×C₄₃	—	2	2	no	—
248	C₂²⋊C₄×C₄₃	—	2	2	no	—
249	C₄²×C₄₃	—	2	2	no	—
250	C₄²×C₄₃	—	2	2	no	—
251	C₄²×C₄₃	—	2	2	no	—
252	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
253	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
254	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊Dic₄₃	—	2	4	no	—
257	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
258	#10621884	—	4	4	no	—
259	#10621882	—	2	8	no	—
260	(C₂×D₄₃)⋊C₄	—	2	4	no	—
261	(C₂×D₄₃)⋊C₄	—	2	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	C₄⋊Dic₄₃	—	2	2	no	—
270	C₄⋊Dic₄₃	—	2	4	no	—
271	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
272	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
273	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
274	Dic₄₃⋊C₄	—	2	4	no	—
275	Dic₄₃⋊C₄	—	2	4	no	—
276	Dic₄₃⋊C₄	—	2	4	no	—
277	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
278	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
279	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
280	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
281	C₄×Dic₄₃	C₂⁴	1	2	yes	—
282	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
283	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
284	D₃₄₄	—	2	4	no	—
285	D₃₄₄	—	4	2	no	—
286	C₈×D₄₃	—	2	4	no	—
287	C₈×D₄₃	—	4	2	no	—
288	C₂³×C₄₃	—	2	2	no	—
289	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
290	C₂²×D₄₃	—	2	4	no	—
291	C₂²×D₄₃	—	4	8	no	—
292	C₂²×D₄₃	—	4	8	no	—
293	C₂²×D₄₃	—	8	4	no	—
294	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
295	Q₈×C₄₃	—	2	2	no	—
296	Q₈×C₄₃	—	2	2	no	—
297	D₄×C₄₃	—	2	2	no	—
298	D₄×C₄₃	—	4	4	no	—
299	D₄×C₄₃	C₂×#41	1	4	yes	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	—	2	2	no	—
302	C₂×C₄×C₄₃	—	2	1	no	—
303	C₂×C₄×C₄₃	—	2	1	no	—
304	C₂×C₄×C₄₃	—	2	2	no	—
305	C₂×C₄×C₄₃	—	2	2	no	—
306	C₂×C₄×C₄₃	—	2	2	no	—
307	C₂×C₄×C₄₃	—	4	4	no	—
308	C₂×C₄×C₄₃	—	4	4	no	—
309	C₂×C₄×C₄₃	—	4	4	no	—
310	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
313	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
316	C₂²⋊D₄₃	—	2	4	no	—
317	C₂²⋊D₄₃	—	4	8	no	—
318	C₂²⋊D₄₃	—	8	4	no	—
319	C₂×Dic₄₃	—	2	4	no	—
320	C₂×Dic₄₃	—	8	4	no	—
321	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
322	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
323	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
324	D₁₇₂	—	2	4	no	—
325	D₁₇₂	—	2	4	no	—
326	D₁₇₂	—	4	8	no	—
327	D₁₇₂	—	4	4	no	—
328	D₁₇₂	—	8	2	no	—
329	D₁₇₂	#135	1	4	yes	complemented
330	C₄×D₄₃	—	2	4	no	—
331	C₄×D₄₃	—	2	4	no	—
332	C₄×D₄₃	—	2	2	no	—
333	C₄×D₄₃	—	2	2	no	—
334	C₄×D₄₃	—	4	8	no	—
335	C₄×D₄₃	—	8	4	no	—
336	C₄×D₄₃	—	8	4	no	—
337	Dic₈₆	—	2	2	no	—
338	Dic₈₆	—	8	2	no	—
339	C₈×C₄₃	—	2	1	no	—
340	C₈×C₄₃	—	2	1	no	—
341	C₈×C₄₃	—	2	1	no	—
342	C₈×C₄₃	C₂×#41	1	2	yes	—
343	C₄₃⋊C₈	—	2	2	no	—
344	C₄₃⋊C₈	—	2	2	no	—
345	#61431	—	43	1	no	maximal, Sylow
346	C₂²×C₄₃	—	2	4	no	—
347	C₂²×C₄₃	—	2	1	no	—
348	C₂²×C₄₃	—	2	1	no	—
349	C₂²×C₄₃	—	2	1	no	—
350	C₂²×C₄₃	—	4	2	no	—
351	C₂²×C₄₃	—	4	2	no	—
352	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
353	C₂×D₄₃	—	2	2	no	—
354	C₂×D₄₃	—	2	2	no	—
355	C₂×D₄₃	—	4	4	no	—
356	C₂×D₄₃	—	4	4	no	—
357	C₂×D₄₃	—	4	4	no	—
358	C₂×D₄₃	—	8	16	no	—
359	C₂×D₄₃	C₂×#135	1	4	yes	—
360	C₄×C₄₃	—	2	1	no	—
361	C₄×C₄₃	—	2	1	no	—
362	C₄×C₄₃	—	2	1	no	—
363	C₄×C₄₃	—	4	2	no	—
364	C₄×C₄₃	—	4	2	no	—
365	C₄×C₄₃	—	4	2	no	—
366	C₄×C₄₃	C₂×#135	1	2	yes	—
367	C₄×C₄₃	#576	1	2	yes	—
368	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
369	C₄×C₄₃	#585	1	1	yes	characteristic
370	Dic₄₃	—	2	2	no	—
371	Dic₄₃	—	2	2	no	—
372	Dic₄₃	—	2	2	no	—
373	Dic₄₃	—	4	4	no	—
374	#3481	—	43	2	no	—
375	#3396	—	43	1	no	—
376	#3380	—	43	1	no	—
377	#3361	—	43	2	no	—
378	#3339	—	43	2	no	—
379	#3338	—	43	1	no	—
380	#3297	—	43	4	no	—
381	#3295	—	43	2	no	—
382	#3280	—	43	2	no	—
383	D₄×D₈	—	43	1	no	—
384	#3169	—	43	1	no	—
385	#3168	—	43	2	no	—
386	#3106	—	43	2	no	—
387	#3105	—	43	4	no	—
388	C₈×#41	—	43	1	no	—
389	C₄×#135	D₄₃	1	1	yes	characteristic, complemented
390	C₂×C₄×D₈	—	43	2	no	—
391	C₂×C₄₃	—	4	4	no	—
392	C₂×C₄₃	—	4	1	no	—
393	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
394	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
395	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
396	D₄₃	—	2	4	no	—
397	D₄₃	—	8	4	no	—
398	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
399	C₂²×D₈	—	43	2	no	—
400	#559	—	43	2	no	—
401	#554	—	43	2	no	—
402	#554	—	43	2	no	—
403	#553	—	43	4	no	—
404	#553	—	86	2	no	—
405	#551	—	86	4	no	—
406	#546	—	43	4	no	—
407	#546	—	86	2	no	—
408	D₄²	—	43	2	no	—
409	#532	—	43	2	no	—
410	#529	—	43	4	no	—
411	#529	—	86	2	no	—
412	#525	—	86	4	no	—
413	C₄×#41	—	43	1	no	—
414	C₄×#41	C₂×D₄₃	1	2	yes	complemented
415	C₂×C₄×D₄	—	43	4	no	—
416	C₂×C₄×D₄	—	86	2	no	—
417	#500	—	43	1	no	—
418	#499	—	43	2	no	—
419	#495	—	43	2	no	—
420	#493	—	43	1	no	—
421	#488	—	43	4	no	—
422	#486	—	43	2	no	—
423	#484	—	43	4	no	—
424	#482	—	43	4	no	—
425	#481	—	43	4	no	—
426	#478	—	43	4	no	—
427	#478	—	43	4	no	—
428	#477	—	43	2	no	—
429	#476	—	43	2	no	—
430	#467	—	43	2	no	—
431	#466	—	43	2	no	—
432	#466	—	43	2	no	—
433	#466	—	43	2	no	—
434	#465	—	43	4	no	—
435	#463	—	43	4	no	—
436	#463	—	43	4	no	—
437	#460	—	43	2	no	—
438	#459	—	43	2	no	—
439	#450	—	43	4	no	—
440	#449	—	43	4	no	—
441	#447	—	43	4	no	—
442	C₈×Q₈	—	43	1	no	—
443	C₈×Q₈	—	43	1	no	—
444	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
445	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
446	C₄×SD₁₆	—	43	4	no	—
447	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
448	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
449	C₄×D₈	—	43	2	no	—
450	C₄×D₈	—	43	4	no	—
451	C₄×D₈	—	43	2	no	—
452	C₄×D₈	—	43	4	no	—
453	C₄×D₈	—	43	2	no	—
454	C₄×D₈	—	43	2	no	—
455	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
456	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
457	C₈×D₄	—	43	2	no	—
458	C₈×D₄	—	43	2	no	—
459	C₈×D₄	—	43	1	no	—
460	C₈×D₄	—	43	1	no	—
461	#431	—	43	1	no	—
462	#431	—	43	2	no	—
463	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
464	C₂×#107	—	43	2	no	—
465	#416	C₂×D₄₃	1	2	yes	complemented
466	C₂×#102	—	43	4	no	—
467	C₂×C₄×C₈	—	43	2	no	—
468	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
469	C₄₃	#61431	1	1	yes	characteristic, complemented, Sylow
470	C₂×#41	—	43	1	no	—
471	C₂×#41	—	86	2	no	—
472	C₂×#41	C₂²×D₄₃	1	2	yes	—
473	C₂²×D₄	—	43	4	no	—
474	C₂²×D₄	—	86	2	no	—
475	C₂³×C₄	—	86	4	no	—
476	#135	—	2	4	no	—
477	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
478	C₂×SD₁₆	—	43	4	no	—
479	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
480	C₂×D₈	—	43	4	no	—
481	C₂×D₈	—	43	2	no	—
482	C₂×D₈	—	43	2	no	—
483	C₂×D₈	—	86	8	no	—
484	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
485	C₂²×C₈	—	43	2	no	—
486	C₂²×C₈	—	43	2	no	—
487	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
488	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
489	C₄⋊Q₈	—	43	2	no	—
490	#127	—	43	2	no	—
491	#126	—	86	4	no	—
492	#126	—	86	4	no	—
493	#125	—	43	4	no	—
494	#125	—	86	2	no	—
495	#124	—	43	4	no	—
496	#124	—	86	2	no	—
497	#124	—	86	2	no	—
498	#123	—	86	4	no	—
499	#123	—	86	4	no	—
500	#123	—	86	4	no	—
501	#123	—	86	4	no	—
502	C₂²⋊Q₈	—	43	4	no	—
503	C₂²⋊Q₈	—	86	4	no	—
504	C₂²⋊Q₈	—	86	4	no	—
505	C₂²⋊Q₈	—	86	2	no	—
506	#121	—	43	4	no	—
507	#121	—	43	4	no	—
508	#121	—	86	4	no	—
509	#121	—	86	4	no	—
510	#121	—	86	2	no	—
511	#121	—	86	2	no	—
512	#120	—	86	4	no	—
513	#120	—	86	4	no	—
514	C₄×Q₈	—	43	1	no	—
515	C₄×Q₈	—	43	1	no	—
516	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
517	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	43	2	no	—
521	C₄×D₄	—	43	2	no	—
522	C₄×D₄	—	43	4	no	—
523	C₄×D₄	—	43	4	no	—
524	C₄×D₄	—	43	1	no	—
525	C₄×D₄	—	43	1	no	—
526	C₄×D₄	—	43	4	no	—
527	C₄×D₄	—	86	4	no	—
528	C₄×D₄	—	86	2	no	—
529	C₄×D₄	—	86	4	no	—
530	C₄×D₄	—	86	2	no	—
531	C₄×D₄	—	86	4	no	—
532	C₄×D₄	—	86	4	no	—
533	C₄×D₄	—	86	2	no	—
534	C₄×D₄	C₂²×D₄₃	1	2	yes	—
535	C₄×D₄	C₂²×D₄₃	1	2	yes	—
536	#117	—	2	2	no	—
537	#117	—	43	1	no	—
538	#117	—	43	2	no	—
539	#117	—	86	4	no	—
540	#117	C₂²×D₄₃	1	2	yes	—
541	C₂×C₄⋊C₄	—	43	4	no	—
542	C₂×C₄⋊C₄	—	86	2	no	—
543	C₂×C₂²⋊C₄	—	86	4	no	—
544	C₂×C₂²⋊C₄	—	86	4	no	—
545	C₂×C₄²	—	2	2	no	—
546	C₂×C₄²	—	43	2	no	—
547	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
548	#107	—	43	2	no	—
549	#107	—	43	2	no	—
550	#107	—	43	4	no	—
551	#107	C₂²×D₄₃	1	1	yes	characteristic
552	#107	C₂²×D₄₃	1	1	yes	characteristic
553	#106	—	43	4	no	—
554	#106	C₂²×D₄₃	1	2	yes	—
555	C₄⋊C₈	—	43	2	no	—
556	C₄⋊C₈	—	43	2	no	—
557	C₄⋊C₈	—	43	1	no	—
558	C₄⋊C₈	—	43	1	no	—
559	#103	—	43	4	no	—
560	#103	C₂²×D₄₃	1	2	yes	—
561	#103	C₂²×D₄₃	1	2	yes	—
562	#102	—	43	4	no	—
563	#102	—	43	4	no	—
564	#102	—	43	4	no	—
565	#102	—	43	4	no	—
566	#102	—	43	4	no	—
567	#102	C₂²×D₄₃	1	2	yes	—
568	#102	C₂²×D₄₃	1	2	yes	—
569	C₂²⋊C₈	—	43	2	no	—
570	C₂²⋊C₈	—	43	2	no	—
571	C₂²⋊C₈	—	43	2	no	—
572	C₄×C₈	—	43	2	no	—
573	C₄×C₈	—	43	2	no	—
574	C₄×C₈	—	43	2	no	—
575	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
576	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
577	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
578	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
579	C₂⁴	—	86	4	no	—
580	#41	—	2	4	no	—
581	#41	—	4	2	no	—
582	#41	—	86	4	no	—
583	#41	—	344	4	no	—
584	C₂×Q₈	—	43	1	no	—
585	C₂×Q₈	—	86	2	no	—
586	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	43	2	no	—
589	C₂×D₄	—	43	1	no	—
590	C₂×D₄	—	43	4	no	—
591	C₂×D₄	—	86	4	no	—
592	C₂×D₄	—	86	4	no	—
593	C₂×D₄	—	86	8	no	—
594	C₂×D₄	—	86	4	no	—
595	C₂×D₄	—	86	2	no	—
596	C₂×D₄	—	86	2	no	—
597	C₂×D₄	—	172	8	no	—
598	C₂×D₄	—	172	4	no	—
599	C₂×D₄	C₂³×D₄₃	1	2	yes	—
600	C₂²×C₄	—	2	2	no	—
601	C₂²×C₄	—	2	2	no	—
602	C₂²×C₄	—	2	2	no	—
603	C₂²×C₄	—	43	2	no	—
604	C₂²×C₄	—	43	2	no	—
605	C₂²×C₄	—	43	2	no	—
606	C₂²×C₄	—	86	4	no	—
607	C₂²×C₄	—	86	4	no	—
608	C₂²×C₄	—	86	4	no	—
609	C₂²×C₄	—	86	4	no	—
610	C₂²×C₄	—	344	8	no	—
611	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
612	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
613	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
614	Q₁₆	—	2	2	no	—
615	SD₁₆	—	2	4	no	—
616	SD₁₆	—	172	4	no	—
617	D₈	—	86	8	no	—
618	D₈	—	86	4	no	—
619	D₈	—	172	2	no	—
620	D₈	#10621898	1	4	yes	complemented
621	C₂×C₈	—	2	2	no	—
622	C₂×C₈	—	4	1	no	—
623	C₂×C₈	—	43	2	no	—
624	C₂×C₈	—	43	2	no	—
625	C₂×C₈	—	86	4	no	—
626	C₂×C₈	—	172	2	no	—
627	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
628	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
629	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
630	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	43	1	no	—
634	C₄⋊C₄	—	43	1	no	—
635	C₄⋊C₄	—	43	2	no	—
636	C₄⋊C₄	—	43	2	no	—
637	C₄⋊C₄	—	43	4	no	—
638	C₄⋊C₄	—	86	4	no	—
639	C₄⋊C₄	—	86	4	no	—
640	C₄⋊C₄	—	86	4	no	—
641	C₄⋊C₄	—	86	4	no	—
642	C₄⋊C₄	—	86	2	no	—
643	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
644	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	2	no	—
648	C₂²⋊C₄	—	43	2	no	—
649	C₂²⋊C₄	—	43	2	no	—
650	C₂²⋊C₄	—	43	2	no	—
651	C₂²⋊C₄	—	86	4	no	—
652	C₂²⋊C₄	—	86	4	no	—
653	C₂²⋊C₄	—	86	4	no	—
654	C₂²⋊C₄	—	86	4	no	—
655	C₂²⋊C₄	—	86	4	no	—
656	C₂²⋊C₄	—	86	4	no	—
657	C₂²⋊C₄	—	86	4	no	—
658	C₂²⋊C₄	—	86	4	no	—
659	C₄²	—	2	2	no	—
660	C₄²	—	2	2	no	—
661	C₄²	—	2	2	no	—
662	C₄²	—	43	2	no	—
663	C₄²	—	43	2	no	—
664	C₄²	—	43	2	no	—
665	C₄²	D₄×D₄₃	1	1	yes	characteristic
666	C₄²	D₄×D₄₃	1	1	yes	characteristic
667	C₄²	C₂³×D₄₃	1	1	yes	characteristic
668	C₄²	C₂³×D₄₃	1	1	yes	characteristic
669	C₂³	—	2	2	no	—
670	C₂³	—	43	2	no	—
671	C₂³	—	86	4	no	—
672	C₂³	—	344	4	no	—
673	C₂³	—	172	8	no	—
674	C₂³	—	172	8	no	—
675	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
676	Q₈	—	2	2	no	—
677	Q₈	—	2	2	no	—
678	Q₈	—	86	2	no	—
679	Q₈	—	344	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	4	4	no	—
682	D₄	—	43	4	no	—
683	D₄	—	86	4	no	—
684	D₄	—	86	4	no	—
685	D₄	—	86	4	no	—
686	D₄	—	344	2	no	—
687	D₄	—	344	4	no	—
688	D₄	—	172	8	no	—
689	D₄	—	172	8	no	—
690	D₄	—	172	4	no	—
691	D₄	C₂×#10621898	1	4	yes	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	43	2	no	—
703	C₂×C₄	—	43	2	no	—
704	C₂×C₄	—	43	2	no	—
705	C₂×C₄	—	86	4	no	—
706	C₂×C₄	—	86	4	no	—
707	C₂×C₄	—	86	2	no	—
708	C₂×C₄	—	86	2	no	—
709	C₂×C₄	—	86	4	no	—
710	C₂×C₄	—	344	4	no	—
711	C₂×C₄	—	344	4	no	—
712	C₂×C₄	—	344	4	no	—
713	C₂×C₄	—	172	8	no	—
714	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
715	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
716	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
717	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
718	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
719	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
720	C₈	—	2	1	no	—
721	C₈	—	2	1	no	—
722	C₈	—	2	1	no	—
723	C₈	—	86	2	no	—
724	C₈	—	86	2	no	—
725	C₈	C₂×#10621898	1	2	yes	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	4	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	43	4	no	—
733	C₂²	—	86	2	no	—
734	C₂²	—	86	2	no	—
735	C₂²	—	344	16	no	—
736	C₂²	—	172	4	no	—
737	C₂²	—	172	4	no	—
738	C₂²	—	172	4	no	—
739	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
740	C₄	—	2	1	no	—
741	C₄	—	2	1	no	—
742	C₄	—	2	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	86	2	no	—
747	C₄	—	86	2	no	—
748	C₄	—	86	2	no	—
749	C₄	—	172	4	no	—
750	C₄	#135×D₄₃	1	2	yes	—
751	C₄	#14583701	1	2	yes	—
752	C₄	C₂²×#10621898	1	1	yes	characteristic
753	C₄	#14583735	1	1	yes	characteristic
754	C₂	—	4	1	no	—
755	C₂	—	4	4	no	—
756	C₂	—	86	4	no	—
757	C₂	—	344	4	no	—
758	C₂	D₄×#10621898	1	1	yes	characteristic
759	C₂	C₂×#135×D₄₃	1	1	yes	characteristic
760	C₂	C₂×#14583701	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#135×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#135	D₄₃
hypocenter	C₄₃	#61431
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #19148205	C₂	semidirect
2. #19147605	C₂	semidirect
3. #19147460	C₂	semidirect
4. #19147253	C₂	semidirect
5. #19146997	C₂	semidirect
6. #19146989	C₂	semidirect
7. #19146446	C₂	semidirect
8. #19146421	C₂	semidirect
9. #19146274	C₂	semidirect
10. D₈×D₁₇₂	C₂	semidirect
11. #19145174	C₂	semidirect
12. #19145168	C₂	semidirect
13. #19144655	C₂	semidirect
14. #19144646	C₂	semidirect
15. C₈×#10621898	C₂	semidirect
16. C₄×D₈×D₄₃	C₂	semidirect
17. C₄×#135×C₄₃	C₂	semidirect
19. #14583634	C₂²	semidirect
21. #14583606	C₂²	semidirect
23. #14583593	C₂²	semidirect
26. #14583537	C₂²	semidirect
28. #14583449	C₂²	semidirect
29. #14583436	C₂²	semidirect
34. C₄×D₄×D₄₃	C₂²	semidirect
35. #14583304	C₂²	semidirect
36. #14583300	C₂²	semidirect
37. #14583284	C₂²	semidirect
39. #14583255	C₂²	semidirect
40. #14583246	C₂²	semidirect
41. #14583233	C₂²	semidirect
42. #14583223	C₂²	semidirect
43. #14583219	C₂²	semidirect
44. #14583198	C₂²	semidirect
45. #14583197	C₂²	semidirect
46. #14583194	C₂²	semidirect
47. #14583189	C₂²	semidirect
48. #14583137	C₂²	semidirect
50. #14583135	C₂²	semidirect
51. #14583135	C₂²	semidirect
52. #14583131	C₂²	semidirect
53. #14583117	C₂²	semidirect
54. #14583116	C₂²	semidirect
55. #14583099	C₂²	semidirect
57. #14583048	C₂²	semidirect
58. #14583044	C₂²	semidirect
60. C₈×Dic₈₆	C₂²	semidirect
61. C₈×Dic₈₆	C₂²	semidirect
62. C₄×#10621884	C₂²	semidirect
63. C₄×D₃₄₄	C₂²	semidirect
64. C₄×D₃₄₄	C₂²	semidirect
66. #14582981	C₂²	semidirect
67. C₄×#10621882	C₂²	semidirect
68. #14582979	C₂²	semidirect
71. C₈×C₂²⋊D₄₃	C₂²	semidirect
72. C₈×C₂²⋊D₄₃	C₂²	semidirect
73. #14582952	C₂²	semidirect
74. #14582950	C₂²	semidirect
75. #107×D₄₃	C₂²	semidirect
76. #102×D₄₃	C₂²	semidirect
77. C₄×C₈×D₄₃	C₂²	semidirect
79. C₄×#41×C₄₃	C₂²	semidirect
80. C₄×Q₁₆×C₄₃	C₂²	semidirect
81. C₄×Q₁₆×C₄₃	C₂²	semidirect
82. C₄×SD₁₆×C₄₃	C₂²	semidirect
83. C₄×SD₁₆×C₄₃	C₂²	semidirect
86. C₄₃×#427	C₂²	semidirect
87. C₄₃×#416	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
235. D₈×C₄₃	#41	semidirect
329. D₁₇₂	#135	semidirect
389. C₄×#135	D₄₃	semidirect
414. C₄×#41	C₂×D₄₃	semidirect
444. C₄×Q₁₆	C₂×D₄₃	semidirect
445. C₄×Q₁₆	C₂×D₄₃	semidirect
447. C₄×SD₁₆	C₂×D₄₃	semidirect
448. C₄×SD₁₆	C₂×D₄₃	semidirect
463. #427	C₂×D₄₃	semidirect
465. #416	C₂×D₄₃	semidirect
468. C₂×C₄×C₈	C₂×D₄₃	semidirect
469. C₄₃	#61431	semidirect
620. D₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148205	2
#19147605	2
#19147460	2
#19147253	2
#19146997	2
#19146989	2
#19146446	2
#19146421	2
#19146274	2
D₈×D₁₇₂	2
#19145174	2
#19145168	2
#19144655	2
#19144646	2
C₈×#10621898	2
C₄×D₈×D₄₃	2
C₄×#135×C₄₃	2
#61431	43