Subgroups — #25975116

Order 11008.

1874 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148153	C₂	1	2	yes	maximal, complemented
2	#19147026	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147018	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147009	C₂	1	2	yes	maximal, complemented
5	#19146998	C₂	1	2	yes	maximal, complemented
6	#19146988	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146976	C₂	1	4	yes	maximal, complemented
8	#19146964	C₂	1	2	yes	maximal, complemented
9	#19146953	C₂	1	2	yes	maximal, complemented
10	#19146943	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144510	C₂	1	4	yes	maximal, complemented
13	#19144385	C₂	1	2	yes	maximal, complemented
14	#19144176	C₂	1	2	yes	maximal, complemented
15	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14582937	C₂	1	2	yes	maximal, complemented
17	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13063347	C₂²	1	1	yes	characteristic
19	#14583619	C₂²	1	2	yes	—
20	#14583614	C₂²	1	2	yes	—
21	#14583606	C₂²	1	2	yes	—
22	#14583595	C₂²	1	4	yes	—
23	#14583589	C₂²	1	4	yes	—
24	#14583584	—	2	2	no	—
25	#14583575	—	2	4	no	—
26	#14583553	C₂²	1	2	yes	—
27	#14583543	—	2	2	no	—
28	#14583456	C₂²	1	2	yes	—
29	#14583431	—	2	2	no	—
30	#14583429	—	2	4	no	—
31	#14583410	C₂²	1	4	yes	—
32	C₄×#10621898	C₂²	1	2	yes	—
33	C₄×#10621900	—	2	2	no	—
34	C₂×#13063284	C₂²	1	4	yes	—
35	#14583304	C₂²	1	1	yes	characteristic, complemented
36	#14583304	C₂²	1	1	yes	characteristic, complemented
37	#14583301	C₂²	1	2	yes	complemented
38	#14583301	C₂²	1	2	yes	complemented
39	#14583297	C₂²	1	2	yes	complemented
40	#14583241	C₂²	1	4	yes	complemented
41	#14583241	C₂²	1	4	yes	complemented
42	#14583235	C₂²	1	4	yes	complemented
43	#14583230	C₂²	1	4	yes	complemented
44	#14583224	C₂²	1	4	yes	complemented
45	#14583224	C₂²	1	4	yes	complemented
46	#14583218	C₂²	1	4	yes	complemented
47	#14583213	C₂²	1	4	yes	complemented
48	#14583207	C₂²	1	4	yes	complemented
49	#14583200	C₂²	1	4	yes	complemented
50	#14583195	C₂²	1	2	yes	complemented
51	#14583190	C₂²	1	2	yes	complemented
52	#14583185	C₂²	1	2	yes	complemented
53	#14583180	C₂²	1	2	yes	complemented
54	#14583140	C₂²	1	2	yes	complemented
55	#14583140	C₂²	1	2	yes	complemented
56	#14583135	C₂²	1	2	yes	complemented
57	#14583135	C₂²	1	2	yes	complemented
58	#14583128	C₂²	1	4	yes	complemented
59	#14583128	C₂²	1	4	yes	complemented
60	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
61	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
62	C₄×#10621873	C₂²	1	2	yes	complemented
63	C₄×#10621873	C₂²	1	2	yes	complemented
64	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
65	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
66	#14582937	C₂²	1	1	yes	characteristic
67	#14582937	C₂²	1	4	yes	—
68	#14582937	C₂²	1	2	yes	—
69	#14582937	C₂²	1	2	yes	—
70	#14582937	C₂²	1	4	yes	complemented
71	#14582937	C₂²	1	2	yes	complemented
72	#14582937	C₂²	1	2	yes	complemented
73	C₂×#13063259	C₂²	1	2	yes	complemented
74	C₂×#13063259	C₂²	1	2	yes	complemented
75	C₂×#13063257	C₂²	1	4	yes	complemented
76	#14582896	C₂²	1	2	yes	—
77	#14582896	C₂²	1	4	yes	—
78	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
79	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
81	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
82	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
83	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
84	C₈×D₄×C₄₃	C₂²	1	2	yes	—
85	C₈×D₄×C₄₃	C₂²	1	2	yes	—
86	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
87	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
89	C₂×#10621898	C₂³	1	2	yes	—
90	C₂×#10621900	—	2	2	no	—
91	#13063347	—	2	4	no	—
92	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
93	C₂×#10621873	C₂³	1	2	yes	—
94	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
95	#13063325	C₂³	1	2	yes	—
96	#13063325	C₂³	1	2	yes	—
97	#13063320	—	2	4	no	—
98	#13063318	—	2	4	no	—
99	#13063318	—	2	4	no	—
100	#13063317	C₂³	1	4	yes	—
101	#13063316	—	2	2	no	—
102	#13063315	—	2	4	no	—
103	#13063312	—	2	2	no	—
104	#13063311	—	2	4	no	—
105	#13063309	—	2	4	no	—
106	#13063308	—	2	4	no	—
107	#13063307	—	2	4	no	—
108	#13063306	—	2	4	no	—
109	#13063305	—	2	2	no	—
110	#13063304	—	2	2	no	—
111	#13063304	—	2	2	no	—
112	#13063304	C₂³	1	4	yes	—
113	#13063304	C₂³	1	4	yes	—
114	#13063302	—	2	4	no	—
115	#13063299	C₂³	1	4	yes	—
116	#13063299	C₂³	1	4	yes	—
117	#13063297	—	2	4	no	—
118	#13063296	—	2	2	no	—
119	#13063294	—	2	4	no	—
120	C₄×Dic₈₆	—	2	2	no	—
121	C₄×Dic₈₆	—	2	2	no	—
122	C₄×Dic₈₆	C₂³	1	2	yes	—
123	C₄×Dic₈₆	C₂³	1	2	yes	—
124	#13063290	—	2	2	no	—
125	C₄×D₁₇₂	C₂³	1	2	yes	—
126	C₄×D₁₇₂	C₂³	1	2	yes	—
127	D₄×Dic₄₃	—	2	2	no	—
128	C₄×C₂²⋊D₄₃	—	2	2	no	—
129	C₄×C₂²⋊D₄₃	—	2	2	no	—
130	C₄×C₂²⋊D₄₃	—	2	4	no	—
131	C₄×C₂²⋊D₄₃	—	2	4	no	—
132	(C₂²⋊D₄₃)⋊C₄	—	2	4	no	—
133	#13063284	—	2	4	no	—
134	#13063284	—	2	4	no	—
135	#13063284	C₂³	1	4	yes	—
136	#13063284	C₂³	1	4	yes	—
137	#13063284	C₂³	1	2	yes	—
138	#13063284	C₂³	1	4	yes	—
139	#13063283	—	2	2	no	—
140	#13063282	—	2	2	no	—
141	#13063281	—	2	4	no	—
142	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
143	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊Dic₄₃	—	2	4	no	—
145	C₂×C₄×Dic₄₃	—	2	4	no	—
146	C₄²×D₄₃	—	2	2	no	—
147	#13063259	C₂³	1	2	yes	—
148	#13063259	C₂³	1	2	yes	—
149	#13063259	C₂³	1	2	yes	—
150	#13063259	C₂³	1	2	yes	—
151	#13063259	C₂³	1	4	yes	—
152	#13063259	C₂³	1	1	yes	characteristic
153	#13063259	C₂³	1	1	yes	characteristic
154	#13063259	C₂³	1	4	yes	—
155	#13063257	C₂³	1	4	yes	—
156	#13063257	C₂³	1	4	yes	—
157	#13063257	C₂³	1	4	yes	—
158	#13063257	C₂³	1	2	yes	—
159	#13063257	C₂³	1	4	yes	—
160	#13063250	C₂³	1	4	yes	—
161	#13063250	C₂³	1	4	yes	—
162	#13063250	C₂³	1	2	yes	—
163	#13063250	C₂³	1	2	yes	—
164	#13063247	C₂³	1	4	yes	—
165	#13063247	C₂³	1	4	yes	—
166	#13063247	C₂³	1	2	yes	—
167	#13063247	C₂³	1	2	yes	—
168	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
169	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
170	C₂²×C₈×C₄₃	—	2	8	no	—
171	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
172	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
173	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
174	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
175	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
176	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
179	C₄×D₄×C₄₃	D₄	1	2	yes	—
180	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
181	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₄₃	C₂³	1	2	yes	—
183	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
186	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
187	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
188	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
189	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
193	C₂²⋊C₈×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	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₄₃	—	2	4	no	—
200	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
201	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
202	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₄₃	—	2	4	no	—
204	C₂²×C₄×C₄₃	—	2	4	no	—
205	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
206	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
207	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
208	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
209	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₂²⋊D₄₃	—	2	4	no	—
214	C₂×C₂²⋊D₄₃	—	2	2	no	—
215	C₂×C₂²⋊D₄₃	—	2	4	no	—
216	C₂²×Dic₄₃	—	2	4	no	—
217	C₂²×Dic₄₃	—	2	4	no	—
218	#10621900	—	4	8	no	—
219	#10621898	—	2	4	no	—
220	#10621898	—	2	4	no	—
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×Dic₈₆	—	2	2	no	—
226	C₂×Dic₈₆	—	2	2	no	—
227	C₂×Dic₈₆	C₂⁴	1	2	yes	—
228	C₂×C₈×C₄₃	—	2	4	no	—
229	C₂×C₈×C₄₃	—	2	2	no	—
230	C₂×C₈×C₄₃	—	2	4	no	—
231	C₂×C₈×C₄₃	—	2	4	no	—
232	C₂×C₈×C₄₃	—	2	4	no	—
233	C₂×C₈×C₄₃	—	2	4	no	—
234	C₂×C₈×C₄₃	#41	1	4	yes	complemented
235	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
239	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
243	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
244	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
245	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
246	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
247	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
248	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
249	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
250	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
251	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₂²⋊Dic₄₃	—	2	2	no	—
253	C₂²⋊Dic₄₃	—	2	4	no	—
254	C₂²⋊Dic₄₃	—	2	4	no	—
255	C₂²⋊Dic₄₃	—	2	4	no	—
256	C₂²⋊Dic₄₃	—	2	4	no	—
257	C₂²⋊Dic₄₃	—	2	4	no	—
258	(C₂×D₄₃)⋊C₄	—	2	2	no	—
259	(C₂×D₄₃)⋊C₄	—	2	2	no	—
260	(C₂×D₄₃)⋊C₄	—	2	4	no	—
261	(C₂×D₄₃)⋊C₄	—	2	4	no	—
262	C₄⋊Dic₄₃	—	2	4	no	—
263	C₄⋊Dic₄₃	—	2	4	no	—
264	C₄⋊Dic₄₃	—	2	2	no	—
265	C₄⋊Dic₄₃	—	2	2	no	—
266	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
267	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
268	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
269	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
270	Dic₄₃⋊C₄	—	2	4	no	—
271	Dic₄₃⋊C₄	—	2	4	no	—
272	Dic₄₃⋊C₄	—	2	2	no	—
273	Dic₄₃⋊C₄	—	2	2	no	—
274	Dic₄₃⋊C₄	—	2	4	no	—
275	Dic₄₃⋊C₄	—	2	4	no	—
276	C₄×Dic₄₃	—	2	2	no	—
277	C₄×Dic₄₃	—	2	2	no	—
278	C₄×Dic₄₃	—	2	2	no	—
279	C₄×Dic₄₃	—	2	4	no	—
280	C₄×Dic₄₃	—	2	4	no	—
281	C₄×Dic₄₃	—	2	4	no	—
282	Dic₁₇₂	—	2	2	no	—
283	D₃₄₄	—	2	2	no	—
284	#10621873	—	2	4	no	—
285	C₂³×C₄₃	—	2	4	no	—
286	C₂³×C₄₃	—	2	4	no	—
287	C₂³×C₄₃	—	4	2	no	—
288	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
289	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
290	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
291	C₂²×D₄₃	—	2	2	no	—
292	D₄×C₄₃	—	2	4	no	—
293	D₄×C₄₃	—	2	2	no	—
294	D₄×C₄₃	#135	1	4	yes	complemented
295	C₂×C₄×C₄₃	—	2	4	no	—
296	C₂×C₄×C₄₃	—	2	4	no	—
297	C₂×C₄×C₄₃	—	2	4	no	—
298	C₂×C₄×C₄₃	—	2	2	no	—
299	C₂×C₄×C₄₃	—	2	2	no	—
300	C₂×C₄×C₄₃	—	2	2	no	—
301	C₂×C₄×C₄₃	—	2	2	no	—
302	C₂×C₄×C₄₃	—	2	2	no	—
303	C₂×C₄×C₄₃	—	4	1	no	—
304	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
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	C₂×#41	1	2	yes	—
312	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
313	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
314	C₂²⋊D₄₃	—	4	4	no	—
315	C₂²⋊D₄₃	—	4	8	no	—
316	C₂²⋊D₄₃	—	8	4	no	—
317	C₂×Dic₄₃	—	2	2	no	—
318	C₂×Dic₄₃	—	2	2	no	—
319	C₂×Dic₄₃	—	2	2	no	—
320	C₂×Dic₄₃	—	2	4	no	—
321	C₂×Dic₄₃	—	2	4	no	—
322	C₂×Dic₄₃	—	4	8	no	—
323	C₂×Dic₄₃	—	8	4	no	—
324	D₁₇₂	—	2	2	no	—
325	D₁₇₂	—	2	2	no	—
326	C₄×D₄₃	—	4	4	no	—
327	C₄×D₄₃	—	4	4	no	—
328	C₄×D₄₃	—	8	2	no	—
329	Dic₈₆	—	2	2	no	—
330	Dic₈₆	—	2	2	no	—
331	Dic₈₆	—	4	4	no	—
332	Dic₈₆	—	8	2	no	—
333	C₈×C₄₃	—	2	2	no	—
334	C₈×C₄₃	—	2	2	no	—
335	C₈×C₄₃	—	2	1	no	—
336	C₈×C₄₃	—	2	1	no	—
337	C₈×C₄₃	C₂×#41	1	2	yes	—
338	C₈×C₄₃	C₂×#41	1	2	yes	—
339	#61234	—	43	1	no	maximal, Sylow
340	C₂²×C₄₃	—	2	1	no	—
341	C₂²×C₄₃	—	2	2	no	—
342	C₂²×C₄₃	—	2	2	no	—
343	C₂²×C₄₃	—	2	1	no	—
344	C₂²×C₄₃	—	2	2	no	—
345	C₂²×C₄₃	—	2	2	no	—
346	C₂²×C₄₃	—	2	2	no	—
347	C₂²×C₄₃	—	4	8	no	—
348	C₂²×C₄₃	#547	1	2	yes	—
349	C₂²×C₄₃	C₂×#135	1	4	yes	—
350	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
351	C₂×D₄₃	—	4	2	no	—
352	C₂×D₄₃	—	4	2	no	—
353	C₂×D₄₃	—	4	2	no	—
354	C₄×C₄₃	—	2	1	no	—
355	C₄×C₄₃	—	2	1	no	—
356	C₄×C₄₃	—	2	2	no	—
357	C₄×C₄₃	—	2	2	no	—
358	C₄×C₄₃	—	2	1	no	—
359	C₄×C₄₃	#547	1	2	yes	—
360	C₄×C₄₃	C₂×#135	1	2	yes	—
361	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
362	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
363	Dic₄₃	—	4	4	no	—
364	Dic₄₃	—	4	2	no	—
365	Dic₄₃	—	4	2	no	—
366	Dic₄₃	—	4	4	no	—
367	Dic₄₃	—	4	2	no	—
368	#3475	—	43	2	no	—
369	#3342	—	43	1	no	—
370	#3341	—	43	1	no	—
371	#3340	—	43	2	no	—
372	#3339	—	43	2	no	—
373	#3338	—	43	1	no	—
374	#3337	—	43	4	no	—
375	#3336	—	43	2	no	—
376	#3335	—	43	2	no	—
377	#3334	—	43	1	no	—
378	#3160	—	43	1	no	—
379	#3091	—	43	4	no	—
380	#3076	—	43	2	no	—
381	#3050	—	43	2	no	—
382	C₄×#135	—	43	1	no	—
383	C₂×C₈×D₄	D₄₃	1	1	yes	characteristic, complemented
384	C₂×#427	—	43	2	no	—
385	C₂×C₄₃	—	2	2	no	—
386	C₂×C₄₃	—	2	4	no	—
387	C₂×C₄₃	—	4	2	no	—
388	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
389	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
390	C₂×C₄₃	#3584	1	1	yes	characteristic
391	D₄₃	—	8	2	no	—
392	C₂×#135	—	43	1	no	—
393	C₂³×C₈	C₂×D₄₃	1	2	yes	—
394	#556	—	43	2	no	—
395	#555	—	43	2	no	—
396	#554	—	43	2	no	—
397	#553	—	43	4	no	—
398	#552	—	43	4	no	—
399	#552	—	86	2	no	—
400	#551	—	86	4	no	—
401	#547	—	43	2	no	—
402	#546	—	86	2	no	—
403	#533	—	43	2	no	—
404	#529	—	86	4	no	—
405	#529	—	86	2	no	—
406	#525	—	43	4	no	—
407	C₄×#41	—	43	2	no	—
408	C₄×#41	—	86	2	no	—
409	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
410	C₂×#117	—	43	4	no	—
411	#500	—	43	1	no	—
412	#500	—	43	1	no	—
413	#499	—	43	2	no	—
414	#499	—	43	2	no	—
415	#498	—	43	2	no	—
416	#485	—	43	4	no	—
417	#485	—	43	4	no	—
418	#484	—	43	4	no	—
419	#483	—	43	4	no	—
420	#482	—	43	4	no	—
421	#482	—	43	4	no	—
422	#481	—	43	4	no	—
423	#480	—	43	4	no	—
424	#479	—	43	4	no	—
425	#478	—	43	4	no	—
426	#477	—	43	2	no	—
427	#476	—	43	2	no	—
428	#475	—	43	2	no	—
429	#474	—	43	2	no	—
430	#467	—	43	2	no	—
431	#467	—	43	2	no	—
432	#466	—	43	2	no	—
433	#466	—	43	2	no	—
434	#465	—	43	4	no	—
435	#465	—	43	4	no	—
436	C₄×Q₁₆	—	43	1	no	—
437	C₄×Q₁₆	—	43	1	no	—
438	C₄×SD₁₆	—	43	2	no	—
439	C₄×SD₁₆	—	43	2	no	—
440	C₄×D₈	—	43	1	no	—
441	C₄×D₈	—	43	1	no	—
442	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
443	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
444	C₈×D₄	C₂×D₄₃	1	2	yes	—
445	C₈×D₄	C₂×D₄₃	1	2	yes	—
446	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
447	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
448	#427	—	43	4	no	—
449	#427	—	43	2	no	—
450	#427	—	43	4	no	—
451	#427	—	43	2	no	—
452	#427	—	43	2	no	—
453	#427	—	43	2	no	—
454	#427	—	43	1	no	—
455	C₂×#107	—	43	2	no	—
456	C₂×#107	—	43	2	no	—
457	C₂×#106	—	43	4	no	—
458	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
459	#416	—	43	4	no	—
460	#416	—	43	2	no	—
461	C₂×C₂²⋊C₈	C₂×D₄₃	1	2	yes	—
462	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
463	C₄₃	#61234	1	1	yes	characteristic, complemented, Sylow
464	C₂×#41	—	43	2	no	—
465	C₂×#41	—	86	2	no	—
466	C₂²×D₄	D₁₇₂	1	1	yes	characteristic
467	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
468	#135	—	86	4	no	—
469	C₂×Q₁₆	—	43	1	no	—
470	C₂×SD₁₆	—	43	2	no	—
471	C₂×D₈	—	43	1	no	—
472	C₂²×C₈	—	2	8	no	—
473	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
474	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
475	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
476	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
477	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
478	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
479	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
480	C₄⋊Q₈	—	43	2	no	—
481	C₄⋊Q₈	—	43	2	no	—
482	#126	—	86	4	no	—
483	#126	—	86	4	no	—
484	#126	—	86	4	no	—
485	#125	—	43	4	no	—
486	#125	—	86	4	no	—
487	#125	—	86	2	no	—
488	#124	—	86	2	no	—
489	#124	—	86	4	no	—
490	#123	—	86	4	no	—
491	#123	—	86	4	no	—
492	#123	—	86	4	no	—
493	#123	—	86	4	no	—
494	C₂²⋊Q₈	—	43	4	no	—
495	C₂²⋊Q₈	—	43	4	no	—
496	C₂²⋊Q₈	—	86	2	no	—
497	C₂²⋊Q₈	—	86	2	no	—
498	C₂²⋊Q₈	—	86	2	no	—
499	C₂²⋊Q₈	—	86	4	no	—
500	#121	—	43	4	no	—
501	#121	—	43	4	no	—
502	#121	—	86	4	no	—
503	#121	—	86	2	no	—
504	#120	—	86	4	no	—
505	C₄×Q₈	—	43	2	no	—
506	C₄×Q₈	—	43	2	no	—
507	C₄×Q₈	—	86	2	no	—
508	C₄×Q₈	—	86	2	no	—
509	C₄×Q₈	—	86	2	no	—
510	C₄×D₄	—	43	2	no	—
511	C₄×D₄	—	43	2	no	—
512	C₄×D₄	—	86	2	no	—
513	C₄×D₄	—	86	2	no	—
514	C₄×D₄	—	86	2	no	—
515	C₄×D₄	—	86	4	no	—
516	C₄×D₄	—	86	4	no	—
517	C₄×D₄	—	86	4	no	—
518	C₄×D₄	D₁₇₂	1	1	yes	characteristic
519	C₄×D₄	D₁₇₂	1	1	yes	characteristic
520	C₄×D₄	D₁₇₂	1	2	yes	—
521	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
522	C₄×D₄	C₂²×D₄₃	1	2	yes	—
523	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
524	#117	—	43	2	no	—
525	#117	—	43	4	no	—
526	#117	—	43	4	no	—
527	#117	—	43	4	no	—
528	#117	—	86	4	no	—
529	#117	—	86	4	no	—
530	#117	—	86	2	no	—
531	#117	—	86	4	no	—
532	#117	—	86	2	no	—
533	C₂×C₄⋊C₄	—	43	4	no	—
534	C₂×C₄⋊C₄	—	43	4	no	—
535	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
536	C₂×C₂²⋊C₄	—	86	4	no	—
537	C₂×C₂²⋊C₄	D₁₇₂	1	2	yes	—
538	C₂×C₄²	—	86	4	no	—
539	C₂×C₄²	—	86	2	no	—
540	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
541	#107	—	43	1	no	—
542	#107	—	43	1	no	—
543	#107	—	43	2	no	—
544	#107	—	43	2	no	—
545	#107	—	43	4	no	—
546	#107	—	43	4	no	—
547	#107	—	43	2	no	—
548	#107	—	43	2	no	—
549	#106	—	43	2	no	—
550	#106	—	43	4	no	—
551	#106	—	43	4	no	—
552	#106	—	43	4	no	—
553	#106	—	43	4	no	—
554	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
555	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
556	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
557	#103	—	43	2	no	—
558	#103	—	43	2	no	—
559	#103	—	43	4	no	—
560	#103	—	43	4	no	—
561	#102	—	43	2	no	—
562	#102	—	43	2	no	—
563	#102	—	43	4	no	—
564	#102	—	43	4	no	—
565	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
566	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
567	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
568	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
569	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
570	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
571	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
572	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
573	C₂⁴	C₂×D₁₇₂	1	2	yes	—
574	#41	—	86	4	no	—
575	#41	—	86	4	no	—
576	#41	—	172	8	no	—
577	C₂×Q₈	—	43	2	no	—
578	C₂×Q₈	—	86	2	no	—
579	C₂×Q₈	—	86	2	no	—
580	C₂×D₄	—	2	4	no	—
581	C₂×D₄	—	43	2	no	—
582	C₂×D₄	—	86	4	no	—
583	C₂×D₄	—	86	2	no	—
584	C₂×D₄	—	86	4	no	—
585	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
586	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
587	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	86	4	no	—
591	C₂²×C₄	—	86	4	no	—
592	C₂²×C₄	—	86	2	no	—
593	C₂²×C₄	—	86	2	no	—
594	C₂²×C₄	—	86	2	no	—
595	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
597	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
598	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
599	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
600	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
601	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
602	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
603	Q₁₆	—	86	2	no	—
604	SD₁₆	—	86	4	no	—
605	D₈	—	86	2	no	—
606	C₂×C₈	—	2	4	no	—
607	C₂×C₈	—	2	2	no	—
608	C₂×C₈	—	2	4	no	—
609	C₂×C₈	—	2	4	no	—
610	C₂×C₈	—	2	4	no	—
611	C₂×C₈	—	2	4	no	—
612	C₂×C₈	#10621900	1	4	yes	complemented
613	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
614	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
615	C₂×C₈	C₂³×D₄₃	1	2	yes	—
616	C₂×C₈	C₂³×D₄₃	1	2	yes	—
617	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
618	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
619	C₄⋊C₄	—	43	2	no	—
620	C₄⋊C₄	—	43	2	no	—
621	C₄⋊C₄	—	43	4	no	—
622	C₄⋊C₄	—	43	4	no	—
623	C₄⋊C₄	—	86	4	no	—
624	C₄⋊C₄	—	86	4	no	—
625	C₄⋊C₄	—	86	2	no	—
626	C₄⋊C₄	—	86	2	no	—
627	C₄⋊C₄	—	86	2	no	—
628	C₄⋊C₄	—	86	4	no	—
629	C₄⋊C₄	—	86	4	no	—
630	C₄⋊C₄	—	86	4	no	—
631	C₄⋊C₄	—	86	4	no	—
632	C₄⋊C₄	—	86	2	no	—
633	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
634	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
635	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
636	C₂²⋊C₄	—	86	2	no	—
637	C₂²⋊C₄	—	86	4	no	—
638	C₂²⋊C₄	—	86	4	no	—
639	C₂²⋊C₄	—	86	4	no	—
640	C₂²⋊C₄	—	86	4	no	—
641	C₂²⋊C₄	—	86	4	no	—
642	C₂²⋊C₄	—	86	2	no	—
643	C₂²⋊C₄	—	86	2	no	—
644	C₂²⋊C₄	—	86	4	no	—
645	C₂²⋊C₄	—	86	4	no	—
646	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
647	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
648	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
649	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
650	C₄²	—	86	4	no	—
651	C₄²	—	86	4	no	—
652	C₄²	—	86	2	no	—
653	C₄²	—	86	2	no	—
654	C₄²	—	86	2	no	—
655	C₄²	—	86	4	no	—
656	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
657	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
658	C₄²	C₂³×D₄₃	1	1	yes	characteristic
659	C₄²	C₂³×D₄₃	1	1	yes	characteristic
660	C₂³	—	2	4	no	—
661	C₂³	—	2	4	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	86	2	no	—
664	C₂³	C₂²×D₁₇₂	1	2	yes	—
665	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
666	C₂³	C₂²×D₁₇₂	1	2	yes	—
667	Q₈	—	86	2	no	—
668	Q₈	—	86	2	no	—
669	Q₈	—	344	2	no	—
670	Q₈	—	172	4	no	—
671	D₄	—	2	4	no	—
672	D₄	—	2	2	no	—
673	D₄	—	86	2	no	—
674	D₄	—	86	2	no	—
675	D₄	—	344	4	no	—
676	D₄	—	172	4	no	—
677	D₄	—	172	8	no	—
678	D₄	#13063347	1	4	yes	complemented
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	86	2	no	—
689	C₂×C₄	—	86	2	no	—
690	C₂×C₄	—	86	4	no	—
691	C₂×C₄	—	86	4	no	—
692	C₂×C₄	—	86	2	no	—
693	C₂×C₄	—	344	2	no	—
694	C₂×C₄	—	344	4	no	—
695	C₂×C₄	—	172	8	no	—
696	C₂×C₄	—	172	4	no	—
697	C₂×C₄	—	172	4	no	—
698	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
699	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
700	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
701	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
702	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
703	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
705	C₂×C₄	C₂×#10621900	1	2	yes	—
706	C₂×C₄	#13063372	1	2	yes	—
707	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
708	C₈	—	2	2	no	—
709	C₈	—	2	2	no	—
710	C₈	—	2	1	no	—
711	C₈	—	2	1	no	—
712	C₈	C₂×#10621900	1	2	yes	—
713	C₈	C₂×#10621900	1	2	yes	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	4	8	no	—
722	C₂²	—	172	2	no	—
723	C₂²	—	172	2	no	—
724	C₂²	—	172	2	no	—
725	C₂²	#14583553	1	2	yes	—
726	C₂²	C₂×#13063347	1	4	yes	—
727	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
728	C₄	—	2	1	no	—
729	C₄	—	2	2	no	—
730	C₄	—	2	2	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	1	no	—
733	C₄	—	172	2	no	—
734	C₄	—	172	4	no	—
735	C₄	—	172	2	no	—
736	C₄	—	172	2	no	—
737	C₄	—	172	4	no	—
738	C₄	#14583553	1	2	yes	—
739	C₄	C₂×#13063347	1	2	yes	—
740	C₄	C₂²×#10621900	1	1	yes	characteristic
741	C₄	C₂×#13063372	1	1	yes	characteristic
742	C₂	—	2	2	no	—
743	C₂	—	2	4	no	—
744	C₂	—	4	2	no	—
745	C₂	—	344	2	no	—
746	C₂	C₂×#14583553	1	1	yes	characteristic
747	C₂	C₂²×#13063347	1	1	yes	characteristic
748	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₈×D₄×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×C₈×D₄	D₄₃
hypocenter	C₄₃	#61234
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄ ◁ C₂×C₈×D₄

Complements

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

N	H ≅ G/N	type
1. #19148153	C₂	semidirect
2. #19147026	C₂	semidirect
3. #19147018	C₂	semidirect
4. #19147009	C₂	semidirect
5. #19146998	C₂	semidirect
6. #19146988	C₂	semidirect
7. #19146976	C₂	semidirect
8. #19146964	C₂	semidirect
9. #19146953	C₂	semidirect
10. #19146943	C₂	semidirect
11. #19145109	C₂	semidirect
12. #19144510	C₂	semidirect
13. #19144385	C₂	semidirect
14. #19144176	C₂	semidirect
15. C₄×#13063347	C₂	semidirect
16. C₂×#14582937	C₂	semidirect
17. C₂×C₈×D₄×C₄₃	C₂	semidirect
35. #14583304	C₂²	semidirect
36. #14583304	C₂²	semidirect
37. #14583301	C₂²	semidirect
38. #14583301	C₂²	semidirect
39. #14583297	C₂²	semidirect
40. #14583241	C₂²	semidirect
41. #14583241	C₂²	semidirect
42. #14583235	C₂²	semidirect
43. #14583230	C₂²	semidirect
44. #14583224	C₂²	semidirect
45. #14583224	C₂²	semidirect
46. #14583218	C₂²	semidirect
47. #14583213	C₂²	semidirect
48. #14583207	C₂²	semidirect
49. #14583200	C₂²	semidirect
50. #14583195	C₂²	semidirect
51. #14583190	C₂²	semidirect
52. #14583185	C₂²	semidirect
53. #14583180	C₂²	semidirect
54. #14583140	C₂²	semidirect
55. #14583140	C₂²	semidirect
56. #14583135	C₂²	semidirect
57. #14583135	C₂²	semidirect
58. #14583128	C₂²	semidirect
59. #14583128	C₂²	semidirect
60. C₄×Dic₁₇₂	C₂²	semidirect
61. C₄×Dic₁₇₂	C₂²	semidirect
62. C₄×#10621873	C₂²	semidirect
63. C₄×#10621873	C₂²	semidirect
64. C₄×D₃₄₄	C₂²	semidirect
65. C₄×D₃₄₄	C₂²	semidirect
70. #14582937	C₂²	semidirect
71. #14582937	C₂²	semidirect
72. #14582937	C₂²	semidirect
73. C₂×#13063259	C₂²	semidirect
74. C₂×#13063259	C₂²	semidirect
75. C₂×#13063257	C₂²	semidirect
234. C₂×C₈×C₄₃	#41	semidirect
294. D₄×C₄₃	#135	semidirect
383. C₂×C₈×D₄	D₄₃	semidirect
463. C₄₃	#61234	semidirect
612. C₂×C₈	#10621900	semidirect
678. D₄	#13063347	semidirect

Maximal subgroups

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

subgroup	index
#19148153	2
#19147026	2
#19147018	2
#19147009	2
#19146998	2
#19146988	2
#19146976	2
#19146964	2
#19146953	2
#19146943	2
#19145109	2
#19144510	2
#19144385	2
#19144176	2
C₄×#13063347	2
C₂×#14582937	2
C₂×C₈×D₄×C₄₃	2
#61234	43