Subgroups — #25979081

Order 11008.

1900 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148551	C₂	1	2	yes	maximal, complemented
2	#19147609	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147447	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147392	C₂	1	2	yes	maximal, complemented
5	#19147025	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147014	C₂	1	2	yes	maximal, complemented
7	#19146825	C₂	1	2	yes	maximal, complemented
8	#19146757	C₂	1	4	yes	maximal, complemented
9	#19146283	C₂	1	2	yes	maximal, complemented
10	#19146270	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145230	C₂	1	2	yes	maximal, complemented
12	#19144775	C₂	1	4	yes	maximal, complemented
13	#19144740	C₂	1	2	yes	maximal, complemented
14	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143442	C₂	1	2	yes	maximal, complemented
16	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063347	C₂²	1	1	yes	characteristic
19	C₂×D₈×D₄₃	C₂²	1	2	yes	—
20	#14583635	C₂²	1	2	yes	complemented
21	#14583623	C₂²	1	2	yes	—
22	#14583613	C₂²	1	4	yes	complemented
23	#14583578	—	2	4	no	—
24	#14583564	C₂²	1	2	yes	complemented
25	#14583556	—	2	2	no	—
26	#14583546	C₂²	1	4	yes	complemented
27	#14583537	—	2	2	no	—
28	#14583534	C₂²	1	2	yes	—
29	#14583514	C₂²	1	4	yes	complemented
30	#14583481	—	2	4	no	—
31	#14583433	C₂²	1	1	yes	characteristic
32	#14583428	—	2	2	no	—
33	#124×D₄₃	—	2	2	no	—
34	#14583371	C₂²	1	4	yes	complemented
35	C₄×#10621898	C₂²	1	2	yes	complemented
36	#14583303	C₂²	1	2	yes	complemented
37	#14583282	C₂²	1	2	yes	complemented
38	#14583257	C₂²	1	4	yes	complemented
39	#14583242	C₂²	1	4	yes	complemented
40	#14583222	C₂²	1	4	yes	complemented
41	#14583220	C₂²	1	4	yes	complemented
42	#14583187	C₂²	1	4	yes	complemented
43	#14583181	C₂²	1	2	yes	complemented
44	#14583178	C₂²	1	4	yes	complemented
45	#14583176	C₂²	1	2	yes	complemented
46	#14583144	C₂²	1	4	yes	complemented
47	#14583141	C₂²	1	2	yes	complemented
48	#14583132	C₂²	1	2	yes	—
49	#14583113	C₂²	1	4	yes	complemented
50	#14583112	C₂²	1	4	yes	complemented
51	#14583096	C₂²	1	2	yes	complemented
52	#14583091	C₂²	1	2	yes	—
53	#14583051	C₂²	1	4	yes	complemented
54	#14583042	C₂²	1	4	yes	complemented
55	#14583031	C₂²	1	4	yes	—
56	#14583029	C₂²	1	1	yes	characteristic, complemented
57	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
58	#14583009	C₂²	1	4	yes	complemented
59	#14583008	C₂²	1	4	yes	complemented
60	#14582999	C₂²	1	4	yes	complemented
61	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
62	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
63	C₄×#10621873	C₂²	1	2	yes	complemented
64	C₄×#10621873	C₂²	1	2	yes	complemented
65	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
66	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
67	D₈×Dic₄₃	C₂²	1	2	yes	complemented
68	#14582981	C₂²	1	2	yes	—
69	#14582978	C₂²	1	1	yes	characteristic
70	#14582970	C₂²	1	2	yes	complemented
71	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
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	#14582937	C₂²	1	1	yes	characteristic, complemented
76	#14582936	C₂²	1	2	yes	complemented
77	#14582902	C₂²	1	4	yes	complemented
78	#14582896	C₂²	1	2	yes	complemented
79	#14582853	C₂²	1	2	yes	complemented
80	C₄₃×#532	C₂²	1	2	yes	complemented
81	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
82	C₄₃×#493	C₂²	1	1	yes	characteristic
83	C₄₃×#486	C₂²	1	2	yes	complemented
84	C₄₃×#466	C₂²	1	2	yes	complemented
85	C₄₃×#466	C₂²	1	2	yes	complemented
86	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
87	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
88	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
89	C₂×#10621898	C₂³	1	2	yes	—
90	C₂×Q₈×D₄₃	—	2	2	no	—
91	C₂×D₄×D₄₃	—	2	2	no	—
92	C₂×D₄×D₄₃	C₂³	1	4	yes	—
93	#13063347	—	2	4	no	—
94	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
95	C₂×#10621873	C₂³	1	2	yes	—
96	C₂×#10621883	C₂³	1	4	yes	—
97	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
98	C₂×#10621882	C₂³	1	4	yes	—
99	D₈×D₄₃	—	2	8	no	—
100	C₂×#10621872	C₂³	1	2	yes	—
101	C₂×C₈×D₄₃	C₂³	1	2	yes	—
102	#13063324	C₂³	1	4	yes	—
103	#13063320	—	2	4	no	—
104	#13063319	D₄	1	2	yes	—
105	#13063318	—	2	4	no	—
106	#13063317	D₄	1	1	yes	characteristic
107	#13063314	—	2	2	no	—
108	#13063313	D₄	1	1	yes	characteristic
109	#13063312	—	2	2	no	—
110	#13063312	—	2	4	no	—
111	#13063312	C₂³	1	4	yes	—
112	#13063311	—	2	4	no	—
113	#13063311	—	2	4	no	—
114	#13063308	—	2	4	no	—
115	#13063308	D₄	1	2	yes	—
116	#13063307	—	2	4	no	—
117	#13063306	—	2	4	no	—
118	#13063305	C₂³	1	4	yes	—
119	#13063304	—	2	4	no	—
120	#13063304	D₄	1	1	yes	characteristic
121	#13063303	—	2	4	no	—
122	#13063301	—	2	2	no	—
123	#13063299	D₄	1	1	yes	characteristic
124	#13063297	—	2	4	no	—
125	#13063296	—	2	4	no	—
126	#13063296	—	2	2	no	—
127	#13063296	C₂³	1	4	yes	—
128	#13063293	—	2	4	no	—
129	#13063293	—	2	4	no	—
130	Q₈×Dic₄₃	—	2	2	no	—
131	C₄×Dic₈₆	C₂³	1	2	yes	—
132	C₄×Dic₈₆	C₂³	1	2	yes	—
133	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
134	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
135	C₄×D₁₇₂	C₂³	1	2	yes	—
136	C₄×D₁₇₂	C₂³	1	2	yes	—
137	D₄×Dic₄₃	—	2	2	no	—
138	D₄×Dic₄₃	C₂³	1	4	yes	—
139	#13063287	C₂³	1	4	yes	—
140	C₄×C₂²⋊D₄₃	—	2	2	no	—
141	C₄×C₂²⋊D₄₃	—	2	2	no	—
142	C₄×C₂²⋊D₄₃	—	2	4	no	—
143	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
144	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
145	#13063284	C₂³	1	2	yes	—
146	#13063283	C₂³	1	4	yes	—
147	#13063282	—	2	2	no	—
148	#13063282	C₂³	1	2	yes	—
149	#13063281	—	2	4	no	—
150	C₂×(C₂×D₄₃)⋊C₄	—	2	4	no	—
151	C₂²⋊C₄×D₄₃	—	2	4	no	—
152	C₂²⋊C₄×D₄₃	—	2	4	no	—
153	C₄²×D₄₃	—	2	2	no	—
154	#13063259	C₂³	1	1	yes	characteristic
155	#13063259	C₂³	1	1	yes	characteristic
156	#13063258	C₂³	1	4	yes	—
157	#13063257	C₂³	1	2	yes	—
158	#13063256	C₂³	1	4	yes	—
159	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
160	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
161	Dic₄₃⋊C₈	C₂³	1	2	yes	—
162	Dic₄₃⋊C₈	C₂³	1	2	yes	—
163	#13063250	C₂³	1	2	yes	—
164	#13063250	C₂³	1	2	yes	—
165	#13063248	C₂³	1	4	yes	—
166	#13063247	C₂³	1	2	yes	—
167	#13063247	C₂³	1	2	yes	—
168	#13063246	C₂³	1	4	yes	—
169	#13063246	C₂³	1	4	yes	—
170	#13063245	C₂³	1	4	yes	—
171	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
172	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
173	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
174	#13063236	C₂³	1	2	yes	—
175	#13063235	C₂³	1	2	yes	—
176	C₈×Dic₄₃	C₂³	1	2	yes	—
177	C₂×#41×C₄₃	—	2	2	no	—
178	C₂×D₈×C₄₃	C₂³	1	2	yes	—
179	C₂×D₈×C₄₃	C₂³	1	2	yes	—
180	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
182	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
183	#127×C₄₃	C₂³	1	2	yes	—
184	#124×C₄₃	—	2	2	no	—
185	#121×C₄₃	—	2	2	no	—
186	#121×C₄₃	C₂³	1	4	yes	—
187	C₄×D₄×C₄₃	—	2	2	no	—
188	C₄×D₄×C₄₃	C₂³	1	4	yes	—
189	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
190	#107×C₄₃	C₂³	1	2	yes	—
191	#107×C₄₃	C₂³	1	2	yes	—
192	#102×C₄₃	C₂³	1	4	yes	—
193	#102×C₄₃	C₂³	1	4	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	—	8	4	no	—
200	C₂×Q₈×C₄₃	—	2	2	no	—
201	C₂×D₄×C₄₃	—	2	2	no	—
202	C₂×D₄×C₄₃	—	2	2	no	—
203	C₂×D₄×C₄₃	—	2	4	no	—
204	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
205	C₂²×C₄×C₄₃	—	2	4	no	—
206	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₂²⋊D₄₃	—	2	4	no	—
210	C₂×C₂²⋊D₄₃	—	2	2	no	—
211	C₂×C₂²⋊D₄₃	—	2	4	no	—
212	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
213	C₂²×Dic₄₃	—	2	4	no	—
214	Q₈×D₄₃	—	8	4	no	—
215	D₄×D₄₃	—	2	8	no	—
216	D₄×D₄₃	—	4	4	no	—
217	D₄×D₄₃	—	8	4	no	—
218	#10621898	—	2	4	no	—
219	#10621898	—	4	2	no	—
220	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
221	C₂×D₁₇₂	C₂⁴	1	2	yes	—
222	C₂×C₄×D₄₃	—	2	2	no	—
223	C₂×C₄×D₄₃	—	2	2	no	—
224	C₂×C₄×D₄₃	—	2	2	no	—
225	C₂×C₄×D₄₃	—	2	4	no	—
226	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
227	C₂×Dic₈₆	—	2	4	no	—
228	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
229	C₂×Dic₈₆	C₂⁴	1	2	yes	—
230	D₈×C₄₃	—	2	4	no	—
231	D₈×C₄₃	—	4	2	no	—
232	C₂×C₈×C₄₃	—	2	2	no	—
233	C₂×C₈×C₄₃	—	4	1	no	—
234	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₄⋊C₄×C₄₃	—	2	2	no	—
239	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
240	C₂²⋊C₄×C₄₃	—	2	4	no	—
241	C₂²⋊C₄×C₄₃	—	2	4	no	—
242	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
243	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
244	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
246	C₂²⋊Dic₄₃	—	2	4	no	—
247	C₂²⋊Dic₄₃	—	2	4	no	—
248	C₂²⋊Dic₄₃	—	2	4	no	—
249	C₂²⋊Dic₄₃	—	2	4	no	—
250	C₂²⋊Dic₄₃	—	2	2	no	—
251	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
252	#10621883	—	4	4	no	—
253	#10621882	—	2	8	no	—
254	(C₂×D₄₃)⋊C₄	—	2	2	no	—
255	(C₂×D₄₃)⋊C₄	—	2	2	no	—
256	(C₂×D₄₃)⋊C₄	—	2	4	no	—
257	(C₂×D₄₃)⋊C₄	—	2	4	no	—
258	(C₂×D₄₃)⋊C₄	—	2	4	no	—
259	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
260	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
261	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
262	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
263	C₄⋊Dic₄₃	—	2	4	no	—
264	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
265	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
266	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
267	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
268	Dic₄₃⋊C₄	—	2	2	no	—
269	Dic₄₃⋊C₄	—	2	2	no	—
270	Dic₄₃⋊C₄	—	2	4	no	—
271	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
272	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
273	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
274	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
275	C₄×Dic₄₃	—	2	2	no	—
276	C₄×Dic₄₃	—	2	2	no	—
277	C₄×Dic₄₃	—	2	2	no	—
278	C₄×Dic₄₃	—	2	4	no	—
279	C₄×Dic₄₃	C₂⁴	1	2	yes	—
280	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
281	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
282	Dic₁₇₂	—	2	2	no	—
283	D₃₄₄	#41	1	4	yes	complemented
284	#10621873	—	2	4	no	—
285	#10621872	—	4	2	no	—
286	C₈×D₄₃	—	2	4	no	—
287	C₂³×C₄₃	—	2	4	no	—
288	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
289	C₂²×D₄₃	—	2	2	no	—
290	C₂²×D₄₃	—	4	8	no	—
291	C₂²×D₄₃	—	8	4	no	—
292	C₂²×D₄₃	—	8	4	no	—
293	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
294	Q₈×C₄₃	—	4	4	no	—
295	D₄×C₄₃	—	2	4	no	—
296	D₄×C₄₃	—	2	4	no	—
297	D₄×C₄₃	—	4	4	no	—
298	D₄×C₄₃	—	8	2	no	—
299	D₄×C₄₃	—	8	4	no	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	—	2	1	no	—
302	C₂×C₄×C₄₃	—	2	1	no	—
303	C₂×C₄×C₄₃	—	2	4	no	—
304	C₂×C₄×C₄₃	—	4	1	no	—
305	C₂×C₄×C₄₃	—	8	4	no	—
306	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
312	C₂²⋊D₄₃	—	4	2	no	—
313	C₂²⋊D₄₃	—	4	8	no	—
314	C₂²⋊D₄₃	—	4	4	no	—
315	C₂²⋊D₄₃	—	8	4	no	—
316	C₂×Dic₄₃	—	2	2	no	—
317	C₂×Dic₄₃	—	2	2	no	—
318	C₂×Dic₄₃	—	2	2	no	—
319	C₂×Dic₄₃	—	8	4	no	—
320	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
321	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
322	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
323	D₁₇₂	—	2	2	no	—
324	D₁₇₂	—	2	2	no	—
325	D₁₇₂	C₂×#41	1	4	yes	—
326	C₄×D₄₃	—	2	2	no	—
327	C₄×D₄₃	—	2	2	no	—
328	C₄×D₄₃	—	4	4	no	—
329	C₄×D₄₃	—	4	4	no	—
330	C₄×D₄₃	—	8	4	no	—
331	C₄×D₄₃	—	8	2	no	—
332	Dic₈₆	—	2	2	no	—
333	Dic₈₆	—	2	2	no	—
334	Dic₈₆	—	2	2	no	—
335	Dic₈₆	—	8	4	no	—
336	C₈×C₄₃	—	2	1	no	—
337	C₈×C₄₃	—	2	1	no	—
338	C₈×C₄₃	—	2	1	no	—
339	C₈×C₄₃	C₂×#41	1	2	yes	—
340	C₄₃⋊C₈	—	2	2	no	—
341	C₄₃⋊C₈	—	2	2	no	—
342	#61475	—	43	1	no	maximal, Sylow
343	C₂²×C₄₃	—	2	1	no	—
344	C₂²×C₄₃	—	2	1	no	—
345	C₂²×C₄₃	—	2	1	no	—
346	C₂²×C₄₃	—	4	4	no	—
347	C₂²×C₄₃	—	4	4	no	—
348	C₂²×C₄₃	—	4	4	no	—
349	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
350	C₂×D₄₃	—	2	2	no	—
351	C₂×D₄₃	—	2	4	no	—
352	C₂×D₄₃	—	2	2	no	—
353	C₂×D₄₃	—	2	2	no	—
354	C₂×D₄₃	—	4	2	no	—
355	C₂×D₄₃	—	4	2	no	—
356	C₂×D₄₃	—	16	8	no	—
357	C₄×C₄₃	—	2	1	no	—
358	C₄×C₄₃	—	2	1	no	—
359	C₄×C₄₃	—	2	1	no	—
360	C₄×C₄₃	—	2	1	no	—
361	C₄×C₄₃	—	4	4	no	—
362	C₄×C₄₃	#576	1	2	yes	—
363	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
364	C₄×C₄₃	#585	1	1	yes	characteristic
365	Dic₄₃	—	2	2	no	—
366	Dic₄₃	—	2	2	no	—
367	Dic₄₃	—	2	2	no	—
368	Dic₄₃	—	4	2	no	—
369	Dic₄₃	—	4	2	no	—
370	Dic₄₃	—	4	2	no	—
371	#3514	—	43	2	no	—
372	#3396	—	43	1	no	—
373	Q₈×D₈	—	43	1	no	—
374	#3373	—	43	2	no	—
375	#3342	—	43	1	no	—
376	#3341	—	43	2	no	—
377	#3324	—	43	2	no	—
378	#3319	—	43	4	no	—
379	#3280	—	43	2	no	—
380	D₄×D₈	—	43	1	no	—
381	#3175	—	43	2	no	—
382	#3169	D₄₃	1	1	yes	characteristic, complemented
383	#3118	—	43	4	no	—
384	#3115	—	43	2	no	—
385	#2966	—	43	1	no	—
386	#2948	—	43	2	no	—
387	C₄×#135	—	43	1	no	—
388	C₂×C₄₃	—	4	1	no	—
389	C₂×C₄₃	—	8	4	no	—
390	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
391	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
392	C₂×C₄₃	#3584	1	1	yes	characteristic
393	D₄₃	—	4	2	no	—
394	D₄₃	—	4	4	no	—
395	C₂×#135	—	43	1	no	—
396	C₂²×D₈	—	43	2	no	—
397	#559	—	43	2	no	—
398	#556	—	43	2	no	—
399	#555	—	43	4	no	—
400	#551	—	86	4	no	—
401	D₄×Q₈	—	43	2	no	—
402	#548	—	86	2	no	—
403	#546	—	43	4	no	—
404	#546	—	86	2	no	—
405	D₄²	—	43	2	no	—
406	#542	—	43	4	no	—
407	#538	—	86	4	no	—
408	#532	C₂×D₄₃	1	2	yes	complemented
409	#529	—	43	1	no	—
410	#529	—	86	2	no	—
411	C₂×#124	—	86	2	no	—
412	#518	—	43	4	no	—
413	C₄×#41	—	43	2	no	—
414	#500	—	43	2	no	—
415	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
416	#495	—	43	2	no	—
417	#493	C₂×D₄₃	1	1	yes	characteristic
418	#489	—	43	4	no	—
419	#486	C₂×D₄₃	1	2	yes	complemented
420	#485	—	43	4	no	—
421	#482	—	43	4	no	—
422	#482	—	43	4	no	—
423	#476	—	43	4	no	—
424	#475	—	43	2	no	—
425	#474	—	43	2	no	—
426	#474	—	43	4	no	—
427	#468	—	43	4	no	—
428	#467	—	43	2	no	—
429	#466	—	43	2	no	—
430	#466	C₂×D₄₃	1	2	yes	complemented
431	#466	C₂×D₄₃	1	2	yes	complemented
432	#463	—	43	4	no	—
433	#463	—	43	4	no	—
434	#460	—	43	2	no	—
435	#459	—	43	2	no	—
436	#450	—	43	4	no	—
437	#449	—	43	4	no	—
438	#447	—	43	4	no	—
439	#446	—	43	1	no	—
440	C₈×Q₈	—	43	1	no	—
441	#442	—	43	4	no	—
442	#442	—	43	4	no	—
443	#440	—	43	4	no	—
444	C₄×Q₁₆	—	43	1	no	—
445	C₄×Q₁₆	—	43	1	no	—
446	C₄×SD₁₆	—	43	2	no	—
447	C₄×SD₁₆	—	43	2	no	—
448	C₄×D₈	—	43	2	no	—
449	C₄×D₈	—	43	2	no	—
450	C₄×D₈	—	43	1	no	—
451	C₄×D₈	—	43	1	no	—
452	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
453	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
454	#436	—	43	1	no	—
455	#435	—	43	2	no	—
456	C₈×D₄	—	43	2	no	—
457	C₈×D₄	—	43	1	no	—
458	#433	—	43	2	no	—
459	#432	—	43	1	no	—
460	#427	—	43	1	no	—
461	#427	—	43	2	no	—
462	#418	—	43	4	no	—
463	#416	—	43	2	no	—
464	#405	—	43	2	no	—
465	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
466	C₄₃	#61475	1	1	yes	characteristic, complemented, Sylow
467	C₂×#41	—	2	2	no	—
468	C₂×#41	—	43	2	no	—
469	C₂²×Q₈	—	86	2	no	—
470	C₂²×D₄	—	43	4	no	—
471	C₂²×D₄	—	86	2	no	—
472	#135	—	86	4	no	—
473	C₂×Q₁₆	—	43	1	no	—
474	C₂×SD₁₆	—	43	4	no	—
475	C₂×SD₁₆	—	43	2	no	—
476	C₂×D₈	—	43	4	no	—
477	C₂×D₈	—	43	1	no	—
478	C₂×D₈	—	86	8	no	—
479	C₂×D₈	C₂²×D₄₃	1	2	yes	—
480	C₂×D₈	C₂²×D₄₃	1	2	yes	—
481	C₂×M₁₆	—	43	2	no	—
482	C₂²×C₈	—	43	2	no	—
483	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
484	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
485	C₄⋊Q₈	—	43	4	no	—
486	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
487	#127	C₂²×D₄₃	1	2	yes	—
488	#126	—	43	2	no	—
489	#126	—	86	4	no	—
490	#126	—	86	4	no	—
491	#125	—	43	1	no	—
492	#124	—	2	2	no	—
493	#124	—	43	4	no	—
494	#124	—	43	1	no	—
495	#124	—	86	4	no	—
496	#124	—	86	4	no	—
497	#124	—	86	4	no	—
498	#124	—	86	2	no	—
499	#124	—	86	2	no	—
500	#123	—	43	2	no	—
501	#123	—	86	4	no	—
502	#123	—	86	4	no	—
503	#123	—	86	4	no	—
504	C₂²⋊Q₈	—	43	1	no	—
505	C₂²⋊Q₈	—	43	4	no	—
506	C₂²⋊Q₈	—	86	4	no	—
507	C₂²⋊Q₈	—	86	4	no	—
508	C₂²⋊Q₈	—	86	2	no	—
509	#121	—	2	2	no	—
510	#121	—	43	1	no	—
511	#121	—	43	4	no	—
512	#121	—	86	4	no	—
513	#121	—	86	2	no	—
514	#121	—	86	4	no	—
515	#121	C₂²×D₄₃	1	4	yes	—
516	#120	—	86	4	no	—
517	#120	—	86	4	no	—
518	C₄×Q₈	—	43	1	no	—
519	C₄×Q₈	—	43	2	no	—
520	C₄×Q₈	—	43	2	no	—
521	C₄×Q₈	—	86	2	no	—
522	C₄×D₄	—	2	2	no	—
523	C₄×D₄	—	43	2	no	—
524	C₄×D₄	—	43	4	no	—
525	C₄×D₄	—	43	4	no	—
526	C₄×D₄	—	43	1	no	—
527	C₄×D₄	—	43	2	no	—
528	C₄×D₄	—	43	2	no	—
529	C₄×D₄	—	86	4	no	—
530	C₄×D₄	—	86	4	no	—
531	C₄×D₄	—	86	2	no	—
532	C₄×D₄	—	86	2	no	—
533	C₄×D₄	—	86	2	no	—
534	C₄×D₄	C₂²×D₄₃	1	4	yes	—
535	#117	—	43	2	no	—
536	#117	—	43	2	no	—
537	#117	—	43	4	no	—
538	#117	—	86	4	no	—
539	#117	—	86	2	no	—
540	C₂×C₂²⋊C₄	—	86	4	no	—
541	C₂×C₂²⋊C₄	—	86	4	no	—
542	C₂×C₂²⋊C₄	—	86	4	no	—
543	C₂×C₄²	—	86	2	no	—
544	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
545	#107	—	43	1	no	—
546	#107	—	43	1	no	—
547	#107	—	43	4	no	—
548	#107	C₂²×D₄₃	1	2	yes	—
549	#107	C₂²×D₄₃	1	2	yes	—
550	#106	—	43	2	no	—
551	#106	—	43	4	no	—
552	C₄⋊C₈	—	43	2	no	—
553	C₄⋊C₈	—	43	2	no	—
554	C₄⋊C₈	—	43	1	no	—
555	C₄⋊C₈	—	43	1	no	—
556	#103	—	43	2	no	—
557	#103	—	43	2	no	—
558	#103	—	43	4	no	—
559	#102	—	43	4	no	—
560	#102	—	43	4	no	—
561	#102	—	43	2	no	—
562	#102	—	43	2	no	—
563	#102	—	43	4	no	—
564	#102	C₂²×D₄₃	1	4	yes	—
565	#102	C₂²×D₄₃	1	4	yes	—
566	C₂²⋊C₈	—	43	2	no	—
567	C₂²⋊C₈	—	43	2	no	—
568	C₂²⋊C₈	—	43	2	no	—
569	#97	—	43	2	no	—
570	#97	—	43	2	no	—
571	C₄×C₈	—	43	2	no	—
572	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
573	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
574	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
575	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
576	C₂⁴	—	86	4	no	—
577	#41	—	8	4	no	—
578	#41	—	86	4	no	—
579	#41	—	172	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	43	1	no	—
582	C₂×Q₈	—	43	2	no	—
583	C₂×Q₈	—	86	4	no	—
584	C₂×Q₈	—	344	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	2	no	—
587	C₂×D₄	—	2	2	no	—
588	C₂×D₄	—	43	2	no	—
589	C₂×D₄	—	43	1	no	—
590	C₂×D₄	—	43	2	no	—
591	C₂×D₄	—	86	4	no	—
592	C₂×D₄	—	86	8	no	—
593	C₂×D₄	—	86	4	no	—
594	C₂×D₄	—	86	2	no	—
595	C₂×D₄	—	344	4	no	—
596	C₂×D₄	—	172	4	no	—
597	C₂×D₄	C₂³×D₄₃	1	4	yes	—
598	C₂²×C₄	—	2	4	no	—
599	C₂²×C₄	—	43	2	no	—
600	C₂²×C₄	—	86	4	no	—
601	C₂²×C₄	—	86	4	no	—
602	C₂²×C₄	—	86	2	no	—
603	C₂²×C₄	—	86	2	no	—
604	C₂²×C₄	—	86	2	no	—
605	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
606	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
607	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
608	Q₁₆	—	86	2	no	—
609	SD₁₆	—	86	4	no	—
610	SD₁₆	—	172	4	no	—
611	D₈	—	2	4	no	—
612	D₈	—	4	2	no	—
613	D₈	—	43	4	no	—
614	D₈	—	86	8	no	—
615	M₁₆	—	172	2	no	—
616	C₂×C₈	—	2	2	no	—
617	C₂×C₈	—	4	1	no	—
618	C₂×C₈	—	43	2	no	—
619	C₂×C₈	—	43	2	no	—
620	C₂×C₈	—	86	4	no	—
621	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
622	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
623	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
624	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	43	2	no	—
627	C₄⋊C₄	—	43	2	no	—
628	C₄⋊C₄	—	43	2	no	—
629	C₄⋊C₄	—	43	1	no	—
630	C₄⋊C₄	—	43	1	no	—
631	C₄⋊C₄	—	43	2	no	—
632	C₄⋊C₄	—	43	2	no	—
633	C₄⋊C₄	—	43	2	no	—
634	C₄⋊C₄	—	86	4	no	—
635	C₄⋊C₄	—	86	4	no	—
636	C₄⋊C₄	—	86	2	no	—
637	C₄⋊C₄	—	86	2	no	—
638	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	43	2	no	—
642	C₂²⋊C₄	—	43	2	no	—
643	C₂²⋊C₄	—	43	2	no	—
644	C₂²⋊C₄	—	43	2	no	—
645	C₂²⋊C₄	—	43	2	no	—
646	C₂²⋊C₄	—	86	4	no	—
647	C₂²⋊C₄	—	86	4	no	—
648	C₂²⋊C₄	—	86	4	no	—
649	C₂²⋊C₄	—	86	4	no	—
650	C₂²⋊C₄	—	86	4	no	—
651	C₂²⋊C₄	—	86	4	no	—
652	C₂²⋊C₄	—	86	4	no	—
653	C₂²⋊C₄	—	86	2	no	—
654	C₂²⋊C₄	—	86	2	no	—
655	C₂²⋊C₄	—	86	2	no	—
656	C₄²	—	43	2	no	—
657	C₄²	—	86	4	no	—
658	C₄²	—	86	2	no	—
659	C₄²	—	86	2	no	—
660	C₄²	—	86	2	no	—
661	C₄²	D₄×D₄₃	1	1	yes	characteristic
662	C₄²	D₄×D₄₃	1	1	yes	characteristic
663	C₄²	C₂³×D₄₃	1	1	yes	characteristic
664	C₄²	C₂³×D₄₃	1	1	yes	characteristic
665	C₂³	—	2	4	no	—
666	C₂³	—	43	2	no	—
667	C₂³	—	86	2	no	—
668	C₂³	—	344	4	no	—
669	C₂³	—	344	4	no	—
670	C₂³	—	172	8	no	—
671	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
672	Q₈	—	4	4	no	—
673	Q₈	—	86	2	no	—
674	Q₈	—	86	2	no	—
675	Q₈	—	86	2	no	—
676	Q₈	—	344	4	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	4	no	—
679	D₄	—	4	4	no	—
680	D₄	—	8	2	no	—
681	D₄	—	8	4	no	—
682	D₄	—	43	4	no	—
683	D₄	—	86	2	no	—
684	D₄	—	86	2	no	—
685	D₄	—	344	4	no	—
686	D₄	—	172	2	no	—
687	D₄	—	172	8	no	—
688	D₄	—	172	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	8	4	no	—
695	C₂×C₄	—	43	2	no	—
696	C₂×C₄	—	43	2	no	—
697	C₂×C₄	—	43	2	no	—
698	C₂×C₄	—	86	2	no	—
699	C₂×C₄	—	86	2	no	—
700	C₂×C₄	—	86	2	no	—
701	C₂×C₄	—	86	2	no	—
702	C₂×C₄	—	86	2	no	—
703	C₂×C₄	—	344	2	no	—
704	C₂×C₄	—	344	4	no	—
705	C₂×C₄	—	344	4	no	—
706	C₂×C₄	—	172	4	no	—
707	C₂×C₄	—	172	4	no	—
708	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
709	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
710	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
711	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
712	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
713	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
714	C₈	—	2	1	no	—
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	86	2	no	—
718	C₈	—	86	2	no	—
719	C₈	#41×D₄₃	1	2	yes	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	86	2	no	—
727	C₂²	—	86	2	no	—
728	C₂²	—	86	4	no	—
729	C₂²	—	86	2	no	—
730	C₂²	—	172	2	no	—
731	C₂²	—	172	2	no	—
732	C₂²	—	688	8	no	—
733	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	4	4	no	—
739	C₄	—	86	2	no	—
740	C₄	—	86	2	no	—
741	C₄	—	86	2	no	—
742	C₄	—	172	2	no	—
743	C₄	—	172	2	no	—
744	C₄	—	172	2	no	—
745	C₄	#14583700	1	2	yes	—
746	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
747	C₄	#14583735	1	1	yes	characteristic
748	C₂	—	4	1	no	—
749	C₂	—	8	4	no	—
750	C₂	—	172	2	no	—
751	C₂	—	172	4	no	—
752	C₂	#19148081	1	1	yes	characteristic
753	C₂	C₂×#14583700	1	1	yes	characteristic
754	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	C₄₃×#3169	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3169	D₄₃
hypocenter	C₄₃	#61475
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #19148551	C₂	semidirect
2. #19147609	C₂	semidirect
3. #19147447	C₂	semidirect
4. #19147392	C₂	semidirect
5. #19147025	C₂	semidirect
6. #19147014	C₂	semidirect
7. #19146825	C₂	semidirect
8. #19146757	C₂	semidirect
9. #19146283	C₂	semidirect
10. #19146270	C₂	semidirect
11. #19145230	C₂	semidirect
12. #19144775	C₂	semidirect
13. #19144740	C₂	semidirect
14. #19143570	C₂	semidirect
15. #19143442	C₂	semidirect
16. C₄×#13063347	C₂	semidirect
17. C₄₃×#3169	C₂	semidirect
20. #14583635	C₂²	semidirect
22. #14583613	C₂²	semidirect
24. #14583564	C₂²	semidirect
26. #14583546	C₂²	semidirect
29. #14583514	C₂²	semidirect
34. #14583371	C₂²	semidirect
35. C₄×#10621898	C₂²	semidirect
36. #14583303	C₂²	semidirect
37. #14583282	C₂²	semidirect
38. #14583257	C₂²	semidirect
39. #14583242	C₂²	semidirect
40. #14583222	C₂²	semidirect
41. #14583220	C₂²	semidirect
42. #14583187	C₂²	semidirect
43. #14583181	C₂²	semidirect
44. #14583178	C₂²	semidirect
45. #14583176	C₂²	semidirect
46. #14583144	C₂²	semidirect
47. #14583141	C₂²	semidirect
49. #14583113	C₂²	semidirect
50. #14583112	C₂²	semidirect
51. #14583096	C₂²	semidirect
53. #14583051	C₂²	semidirect
54. #14583042	C₂²	semidirect
56. #14583029	C₂²	semidirect
57. C₈×Dic₈₆	C₂²	semidirect
58. #14583009	C₂²	semidirect
59. #14583008	C₂²	semidirect
60. #14582999	C₂²	semidirect
61. C₄×Dic₁₇₂	C₂²	semidirect
62. C₄×Dic₁₇₂	C₂²	semidirect
63. C₄×#10621873	C₂²	semidirect
64. C₄×#10621873	C₂²	semidirect
67. D₈×Dic₄₃	C₂²	semidirect
70. #14582970	C₂²	semidirect
72. C₈×C₂²⋊D₄₃	C₂²	semidirect
73. #14582958	C₂²	semidirect
74. #14582956	C₂²	semidirect
75. #14582937	C₂²	semidirect
76. #14582936	C₂²	semidirect
77. #14582902	C₂²	semidirect
78. #14582896	C₂²	semidirect
79. #14582853	C₂²	semidirect
80. C₄₃×#532	C₂²	semidirect
81. C₄₃×#500	C₂²	semidirect
83. C₄₃×#486	C₂²	semidirect
84. C₄₃×#466	C₂²	semidirect
85. C₄₃×#466	C₂²	semidirect
86. C₄×D₈×C₄₃	C₂²	semidirect
87. C₄×D₈×C₄₃	C₂²	semidirect
88. C₂×C₄×C₈×C₄₃	C₂²	semidirect
283. D₃₄₄	#41	semidirect
382. #3169	D₄₃	semidirect
408. #532	C₂×D₄₃	semidirect
415. #500	C₂×D₄₃	semidirect
419. #486	C₂×D₄₃	semidirect
430. #466	C₂×D₄₃	semidirect
431. #466	C₂×D₄₃	semidirect
452. C₄×D₈	C₂×D₄₃	semidirect
453. C₄×D₈	C₂×D₄₃	semidirect
465. C₂×C₄×C₈	C₂×D₄₃	semidirect
466. C₄₃	#61475	semidirect

Maximal subgroups

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

subgroup	index
#19148551	2
#19147609	2
#19147447	2
#19147392	2
#19147025	2
#19147014	2
#19146825	2
#19146757	2
#19146283	2
#19146270	2
#19145230	2
#19144775	2
#19144740	2
#19143570	2
#19143442	2
C₄×#13063347	2
C₄₃×#3169	2
#61475	43