Subgroups — #25975362

Order 11008.

1842 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148162	C₂	1	2	yes	maximal, complemented
2	#19147220	C₂	1	2	yes	maximal, complemented
3	#19147209	C₂	1	2	yes	maximal, complemented
4	#19147199	C₂	1	2	yes	maximal, complemented
5	#19147189	C₂	1	2	yes	maximal, complemented
6	#19147178	C₂	1	2	yes	maximal, complemented
7	#19147168	C₂	1	2	yes	maximal, complemented
8	#19147154	C₂	1	4	yes	maximal, complemented
9	#19144512	C₂	1	4	yes	maximal, complemented
10	#19144377	C₂	1	2	yes	maximal, complemented
11	#19144205	C₂	1	2	yes	maximal, complemented
12	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14582978	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143183	C₂	1	2	yes	maximal, complemented
15	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063347	C₂²	1	1	yes	characteristic
17	C₂²×#10621872	C₂²	1	2	yes	—
18	#14583623	C₂²	1	2	yes	—
19	#14583615	C₂²	1	2	yes	—
20	#14583610	C₂²	1	2	yes	—
21	#14583602	C₂²	1	4	yes	—
22	#14583591	—	2	2	no	—
23	#14583587	C₂²	1	4	yes	—
24	#14583576	—	2	4	no	—
25	#14583552	C₂²	1	2	yes	—
26	#14583540	—	2	2	no	—
27	#14583436	—	2	2	no	—
28	#14583436	—	2	4	no	—
29	#14583411	C₂²	1	4	yes	—
30	C₄×#10621902	—	2	2	no	—
31	C₄×#10621898	C₂²	1	2	yes	—
32	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
33	#117×D₄₃	C₂²	1	4	yes	—
34	#14583243	C₂²	1	4	yes	complemented
35	#14583242	C₂²	1	4	yes	complemented
36	#14583236	C₂²	1	4	yes	complemented
37	#14583231	C₂²	1	4	yes	complemented
38	#14583226	C₂²	1	4	yes	complemented
39	#14583225	C₂²	1	4	yes	complemented
40	#14583219	C₂²	1	4	yes	complemented
41	#14583214	C₂²	1	4	yes	complemented
42	#14583203	C₂²	1	4	yes	complemented
43	#14583196	C₂²	1	4	yes	complemented
44	#14583191	C₂²	1	2	yes	complemented
45	#14583186	C₂²	1	2	yes	complemented
46	#14583181	C₂²	1	2	yes	complemented
47	#14583176	C₂²	1	2	yes	complemented
48	#14583158	C₂²	1	4	yes	complemented
49	#14583153	C₂²	1	4	yes	complemented
50	#14583146	C₂²	1	4	yes	complemented
51	#14583146	C₂²	1	4	yes	complemented
52	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
53	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
54	C₄×#10621873	C₂²	1	2	yes	complemented
55	C₄×#10621873	C₂²	1	2	yes	complemented
56	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
58	#14582978	C₂²	1	2	yes	—
59	#14582978	C₂²	1	2	yes	—
60	#14582978	C₂²	1	2	yes	—
61	#14582978	C₂²	1	2	yes	—
62	#14582940	C₂²	1	4	yes	complemented
63	#14582940	C₂²	1	4	yes	complemented
64	#14582938	C₂²	1	4	yes	complemented
65	#14582938	C₂²	1	4	yes	complemented
66	#14582937	C₂²	1	1	yes	characteristic
67	#14582935	C₂²	1	4	yes	—
68	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
69	#14582896	C₂²	1	2	yes	—
70	#14582893	C₂²	1	4	yes	—
71	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	2	yes	—
72	C₄₃×#533	C₂²	1	2	yes	—
73	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
74	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
75	C₄₃×#499	C₂²	1	2	yes	complemented
76	C₄₃×#499	C₂²	1	2	yes	complemented
77	C₄₃×#498	C₂²	1	2	yes	complemented
78	C₄₃×#427	C₂²	1	2	yes	—
79	C₄₃×#427	C₂²	1	2	yes	—
80	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
81	C₂×#10621902	—	2	2	no	—
82	C₂×#10621898	C₂³	1	2	yes	—
83	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
84	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
85	#13063347	—	2	4	no	—
86	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
87	C₂×#10621873	C₂³	1	2	yes	—
88	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
89	C₂×#10621872	—	2	8	no	—
90	C₂×#10621872	C₂³	1	4	yes	—
91	C₂×#10621872	C₂³	1	4	yes	—
92	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
93	#13063320	—	2	4	no	—
94	#13063320	—	2	4	no	—
95	#13063320	—	2	4	no	—
96	#13063316	—	2	4	no	—
97	#13063316	—	2	2	no	—
98	#13063314	—	2	2	no	—
99	#13063314	—	2	4	no	—
100	#13063310	—	2	4	no	—
101	#13063310	—	2	4	no	—
102	#13063310	—	2	4	no	—
103	#13063309	—	2	4	no	—
104	#13063305	C₂³	1	4	yes	—
105	#13063305	C₂³	1	4	yes	—
106	#13063301	—	2	4	no	—
107	#13063301	—	2	2	no	—
108	#13063300	—	2	4	no	—
109	#13063300	—	2	2	no	—
110	#13063300	C₂³	1	4	yes	—
111	#13063300	C₂³	1	4	yes	—
112	#13063295	—	2	4	no	—
113	Q₈×Dic₄₃	—	2	2	no	—
114	C₄×Dic₈₆	C₂³	1	2	yes	—
115	C₄×Dic₈₆	C₂³	1	2	yes	—
116	C₄×D₁₇₂	—	2	4	no	—
117	C₄×D₁₇₂	—	2	4	no	—
118	C₄×D₁₇₂	D₄	1	2	yes	—
119	C₄×D₁₇₂	D₄	1	2	yes	—
120	C₄×D₁₇₂	C₂³	1	2	yes	—
121	C₄×D₁₇₂	C₂³	1	2	yes	—
122	C₄×D₁₇₂	C₂³	1	2	yes	—
123	C₄×D₁₇₂	C₂³	1	2	yes	—
124	#13063287	—	2	2	no	—
125	#13063287	—	2	4	no	—
126	C₄×C₂²⋊D₄₃	—	2	2	no	—
127	C₄×C₂²⋊D₄₃	—	2	2	no	—
128	#13063284	C₂³	1	2	yes	—
129	#13063283	—	2	4	no	—
130	#13063283	—	2	2	no	—
131	#13063283	C₂³	1	4	yes	—
132	#13063283	C₂³	1	4	yes	—
133	#13063282	—	2	4	no	—
134	#13063282	—	2	2	no	—
135	#13063281	—	2	4	no	—
136	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
137	C₄⋊C₄×D₄₃	C₂³	1	4	yes	—
138	C₄⋊C₄×D₄₃	C₂³	1	4	yes	—
139	C₂×(C₂×D₄₃)⋊C₄	D₄	1	2	yes	—
140	C₂²⋊C₄×D₄₃	—	2	4	no	—
141	C₄²×D₄₃	—	2	4	no	—
142	C₄²×D₄₃	—	2	2	no	—
143	#13063259	C₂³	1	1	yes	characteristic
144	#13063259	C₂³	1	1	yes	characteristic
145	#13063258	C₂³	1	4	yes	—
146	#13063258	C₂³	1	4	yes	—
147	#13063257	C₂³	1	2	yes	—
148	#13063256	C₂³	1	4	yes	—
149	#13063256	C₂³	1	4	yes	—
150	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
151	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
152	#13063250	C₂³	1	2	yes	—
153	#13063250	C₂³	1	2	yes	—
154	#13063248	C₂³	1	4	yes	—
155	#13063248	C₂³	1	4	yes	—
156	#13063247	C₂³	1	2	yes	—
157	#13063247	C₂³	1	2	yes	—
158	#13063245	C₂³	1	4	yes	—
159	#13063245	C₂³	1	4	yes	—
160	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
161	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
162	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
163	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
164	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
166	#125×C₄₃	C₂³	1	4	yes	—
167	C₂²⋊Q₈×C₄₃	—	2	2	no	—
168	C₂²⋊Q₈×C₄₃	—	2	2	no	—
169	C₄×Q₈×C₄₃	—	2	2	no	—
170	C₄×Q₈×C₄₃	—	2	2	no	—
171	#117×C₄₃	C₂³	1	4	yes	—
172	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
173	#107×C₄₃	C₂³	1	2	yes	—
174	#107×C₄₃	C₂³	1	2	yes	—
175	#107×C₄₃	C₂³	1	2	yes	—
176	#107×C₄₃	C₂³	1	2	yes	—
177	#106×C₄₃	C₂³	1	4	yes	—
178	#106×C₄₃	C₂³	1	4	yes	—
179	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
180	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
181	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
183	C₂³×D₄₃	C₂×D₄	1	2	yes	—
184	C₂×Q₈×C₄₃	—	2	2	no	—
185	C₂×Q₈×C₄₃	—	2	2	no	—
186	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	C₂×C₂²⋊D₄₃	—	2	2	no	—
190	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
191	#10621902	—	4	8	no	—
192	#10621898	—	2	4	no	—
193	#10621898	—	2	4	no	—
194	C₂×D₁₇₂	—	2	4	no	—
195	C₂×D₁₇₂	—	2	4	no	—
196	C₂×D₁₇₂	—	4	2	no	—
197	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
198	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
199	C₂×D₁₇₂	C₂⁴	1	2	yes	—
200	C₂×C₄×D₄₃	—	2	4	no	—
201	C₂×C₄×D₄₃	—	2	4	no	—
202	C₂×C₄×D₄₃	—	2	2	no	—
203	C₂×C₄×D₄₃	—	2	2	no	—
204	C₂×C₄×D₄₃	—	2	2	no	—
205	C₂×C₄×D₄₃	—	2	4	no	—
206	C₂×C₄×D₄₃	—	2	4	no	—
207	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
208	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
209	C₂×Dic₈₆	C₂⁴	1	2	yes	—
210	C₂×C₈×C₄₃	—	2	2	no	—
211	C₂×C₈×C₄₃	#41	1	4	yes	complemented
212	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
213	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
215	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
216	C₄⋊C₄×C₄₃	—	2	4	no	—
217	C₄⋊C₄×C₄₃	—	2	4	no	—
218	C₄⋊C₄×C₄₃	—	2	2	no	—
219	C₄⋊C₄×C₄₃	—	2	2	no	—
220	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
221	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
222	C₂²⋊C₄×C₄₃	—	2	4	no	—
223	C₄²×C₄₃	—	2	4	no	—
224	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
227	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
228	C₂²⋊Dic₄₃	—	2	2	no	—
229	(C₂×D₄₃)⋊C₄	—	2	2	no	—
230	(C₂×D₄₃)⋊C₄	—	2	2	no	—
231	(C₂×D₄₃)⋊C₄	—	2	4	no	—
232	(C₂×D₄₃)⋊C₄	—	2	4	no	—
233	(C₂×D₄₃)⋊C₄	—	2	4	no	—
234	(C₂×D₄₃)⋊C₄	—	2	4	no	—
235	(C₂×D₄₃)⋊C₄	—	2	4	no	—
236	(C₂×D₄₃)⋊C₄	—	2	4	no	—
237	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
238	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
239	C₄⋊Dic₄₃	—	2	4	no	—
240	C₄⋊Dic₄₃	—	2	4	no	—
241	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
242	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
243	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
244	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
245	Dic₄₃⋊C₄	—	2	2	no	—
246	Dic₄₃⋊C₄	—	2	2	no	—
247	Dic₄₃⋊C₄	—	2	4	no	—
248	Dic₄₃⋊C₄	—	2	4	no	—
249	C₄×Dic₄₃	—	2	2	no	—
250	C₄×Dic₄₃	—	2	2	no	—
251	C₄×Dic₄₃	—	2	2	no	—
252	C₄×Dic₄₃	—	2	4	no	—
253	C₄×Dic₄₃	—	2	4	no	—
254	C₂×C₄₃⋊C₈	—	2	4	no	—
255	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
256	Dic₁₇₂	—	2	2	no	—
257	D₃₄₄	—	2	2	no	—
258	#10621873	—	2	4	no	—
259	#10621872	—	2	8	no	—
260	#10621872	—	2	8	no	—
261	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
262	C₂²×D₄₃	—	2	4	no	—
263	C₂²×D₄₃	—	2	2	no	—
264	C₂²×D₄₃	—	4	2	no	—
265	C₂²×D₄₃	—	4	2	no	—
266	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
267	Q₈×C₄₃	—	4	4	no	—
268	Q₈×C₄₃	—	8	2	no	—
269	C₂×C₄×C₄₃	—	2	2	no	—
270	C₂×C₄×C₄₃	—	2	4	no	—
271	C₂×C₄×C₄₃	—	2	4	no	—
272	C₂×C₄×C₄₃	—	4	1	no	—
273	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
279	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
280	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
281	C₂²⋊D₄₃	—	4	4	no	—
282	C₂×Dic₄₃	—	2	4	no	—
283	C₂×Dic₄₃	—	2	2	no	—
284	C₂×Dic₄₃	—	2	2	no	—
285	C₂×Dic₄₃	—	2	2	no	—
286	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
287	D₁₇₂	—	2	4	no	—
288	D₁₇₂	—	2	2	no	—
289	D₁₇₂	—	2	2	no	—
290	D₁₇₂	—	4	2	no	—
291	D₁₇₂	—	4	8	no	—
292	D₁₇₂	—	8	4	no	—
293	C₄×D₄₃	—	2	8	no	—
294	C₄×D₄₃	—	2	4	no	—
295	C₄×D₄₃	—	2	4	no	—
296	C₄×D₄₃	—	4	8	no	—
297	C₄×D₄₃	—	4	4	no	—
298	C₄×D₄₃	—	4	4	no	—
299	C₄×D₄₃	—	8	2	no	—
300	C₄×D₄₃	—	8	4	no	—
301	Dic₈₆	—	2	2	no	—
302	Dic₈₆	—	2	2	no	—
303	C₈×C₄₃	—	2	1	no	—
304	C₈×C₄₃	—	2	1	no	—
305	C₈×C₄₃	C₂×#41	1	2	yes	—
306	C₈×C₄₃	C₂×#41	1	2	yes	—
307	C₄₃⋊C₈	—	2	4	no	—
308	#61251	—	43	1	no	maximal, Sylow
309	C₂²×C₄₃	—	2	1	no	—
310	C₂²×C₄₃	—	2	1	no	—
311	C₂²×C₄₃	#547	1	2	yes	—
312	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
313	C₂×D₄₃	—	2	4	no	—
314	C₂×D₄₃	—	2	4	no	—
315	C₂×D₄₃	—	2	4	no	—
316	C₂×D₄₃	—	4	2	no	—
317	C₂×D₄₃	—	4	2	no	—
318	C₂×D₄₃	—	4	2	no	—
319	C₂×D₄₃	—	8	4	no	—
320	C₄×C₄₃	—	2	1	no	—
321	C₄×C₄₃	—	2	1	no	—
322	C₄×C₄₃	—	2	1	no	—
323	C₄×C₄₃	—	4	4	no	—
324	C₄×C₄₃	—	4	4	no	—
325	C₄×C₄₃	#547	1	2	yes	—
326	C₄×C₄₃	#575	1	2	yes	—
327	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
328	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
329	Dic₄₃	—	2	4	no	—
330	Dic₄₃	—	4	2	no	—
331	Dic₄₃	—	4	2	no	—
332	Dic₄₃	—	4	2	no	—
333	#3475	—	43	2	no	—
334	#3357	—	43	2	no	—
335	#3356	—	43	2	no	—
336	#3355	—	43	2	no	—
337	#3354	—	43	2	no	—
338	#3353	—	43	2	no	—
339	#3352	—	43	2	no	—
340	#3351	—	43	4	no	—
341	#3160	D₄₃	1	1	yes	characteristic, complemented
342	#3091	—	43	4	no	—
343	#3076	—	43	2	no	—
344	#3054	—	43	2	no	—
345	C₄×#135	—	43	1	no	—
346	C₂×#436	—	43	1	no	—
347	#2911	—	43	2	no	—
348	C₂×C₄₃	—	2	2	no	—
349	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
350	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
351	C₂×C₄₃	#3584	1	1	yes	characteristic
352	D₄₃	—	4	4	no	—
353	D₄₃	—	8	2	no	—
354	C₂×#135	—	43	1	no	—
355	C₂²×M₁₆	—	43	2	no	—
356	#556	—	43	2	no	—
357	#555	—	43	2	no	—
358	#554	—	43	2	no	—
359	#553	—	43	4	no	—
360	#552	—	43	4	no	—
361	#552	—	86	2	no	—
362	#551	—	86	4	no	—
363	#547	—	43	2	no	—
364	#546	—	86	2	no	—
365	#533	C₂×D₄₃	1	2	yes	—
366	#529	—	86	4	no	—
367	#529	—	86	2	no	—
368	#525	—	43	4	no	—
369	C₄×#41	—	43	2	no	—
370	C₄×#41	—	86	2	no	—
371	C₂×C₄×D₄	—	43	1	no	—
372	C₂×#117	—	43	4	no	—
373	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
374	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
375	#499	C₂×D₄₃	1	2	yes	complemented
376	#499	C₂×D₄₃	1	2	yes	complemented
377	#498	C₂×D₄₃	1	2	yes	complemented
378	#485	—	43	4	no	—
379	#485	—	43	4	no	—
380	#484	—	43	4	no	—
381	#483	—	43	4	no	—
382	#482	—	43	4	no	—
383	#482	—	43	4	no	—
384	#481	—	43	4	no	—
385	#480	—	43	4	no	—
386	#479	—	43	4	no	—
387	#478	—	43	4	no	—
388	#477	—	43	2	no	—
389	#476	—	43	2	no	—
390	#475	—	43	2	no	—
391	#474	—	43	2	no	—
392	#470	—	43	4	no	—
393	#469	—	43	4	no	—
394	#468	—	43	4	no	—
395	#468	—	43	4	no	—
396	C₄×Q₁₆	—	43	1	no	—
397	C₄×Q₁₆	—	43	1	no	—
398	C₄×SD₁₆	—	43	2	no	—
399	C₄×SD₁₆	—	43	2	no	—
400	C₄×D₈	—	43	1	no	—
401	C₄×D₈	—	43	1	no	—
402	#436	—	43	2	no	—
403	#436	—	43	2	no	—
404	#436	—	43	2	no	—
405	#436	—	43	2	no	—
406	#428	—	43	4	no	—
407	#428	—	43	4	no	—
408	#428	—	43	4	no	—
409	#428	—	43	4	no	—
410	#427	—	43	1	no	—
411	#427	—	43	4	no	—
412	#427	C₂×D₄₃	1	2	yes	—
413	#427	C₂×D₄₃	1	2	yes	—
414	C₂×C₄⋊C₈	—	43	1	no	—
415	#416	—	43	2	no	—
416	#416	—	43	4	no	—
417	C₂×C₂²⋊C₈	—	43	2	no	—
418	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
419	C₄₃	#61251	1	1	yes	characteristic, complemented, Sylow
420	C₂×#41	—	43	2	no	—
421	C₂×#41	—	86	2	no	—
422	C₂²×D₄	—	43	1	no	—
423	C₂³×C₄	—	43	2	no	—
424	#135	—	86	4	no	—
425	C₂×Q₁₆	—	43	1	no	—
426	C₂×SD₁₆	—	43	2	no	—
427	C₂×D₈	—	43	1	no	—
428	C₂×M₁₆	—	43	4	no	—
429	C₂×M₁₆	—	43	4	no	—
430	C₂×M₁₆	—	86	8	no	—
431	C₂²×C₈	—	43	2	no	—
432	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
433	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
434	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
435	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
436	#126	—	86	4	no	—
437	#126	—	86	4	no	—
438	#126	—	86	4	no	—
439	#125	—	86	4	no	—
440	#125	—	86	2	no	—
441	#125	C₂²×D₄₃	1	4	yes	—
442	#124	—	86	4	no	—
443	#124	—	86	2	no	—
444	#123	—	86	4	no	—
445	#123	—	86	4	no	—
446	#123	—	86	4	no	—
447	#123	—	86	4	no	—
448	C₂²⋊Q₈	—	2	2	no	—
449	C₂²⋊Q₈	—	2	2	no	—
450	C₂²⋊Q₈	—	43	4	no	—
451	C₂²⋊Q₈	—	43	4	no	—
452	C₂²⋊Q₈	—	86	4	no	—
453	C₂²⋊Q₈	—	86	2	no	—
454	#121	—	43	4	no	—
455	#121	—	43	4	no	—
456	#121	—	86	4	no	—
457	#121	—	86	2	no	—
458	#120	—	86	4	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	43	2	no	—
462	C₄×Q₈	—	43	2	no	—
463	C₄×Q₈	—	86	2	no	—
464	C₄×D₄	—	43	2	no	—
465	C₄×D₄	—	43	2	no	—
466	C₄×D₄	—	43	2	no	—
467	C₄×D₄	—	43	2	no	—
468	C₄×D₄	—	43	2	no	—
469	C₄×D₄	—	43	2	no	—
470	C₄×D₄	—	86	4	no	—
471	C₄×D₄	—	86	4	no	—
472	C₄×D₄	—	86	4	no	—
473	C₄×D₄	—	86	2	no	—
474	C₄×D₄	—	86	2	no	—
475	C₄×D₄	—	86	2	no	—
476	#117	—	43	2	no	—
477	#117	—	43	4	no	—
478	#117	—	43	4	no	—
479	#117	—	86	4	no	—
480	#117	—	86	4	no	—
481	#117	—	86	4	no	—
482	#117	—	86	2	no	—
483	#117	—	86	2	no	—
484	#117	C₂²×D₄₃	1	4	yes	—
485	C₂×C₄⋊C₄	—	43	1	no	—
486	C₂×C₄⋊C₄	—	43	4	no	—
487	C₂×C₄⋊C₄	—	43	4	no	—
488	C₂×C₂²⋊C₄	—	43	2	no	—
489	C₂×C₂²⋊C₄	—	86	4	no	—
490	C₂×C₄²	—	86	4	no	—
491	C₂×C₄²	—	86	2	no	—
492	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
493	#107	—	43	1	no	—
494	#107	—	43	1	no	—
495	#107	—	43	4	no	—
496	#107	—	43	4	no	—
497	#107	C₂²×D₄₃	1	2	yes	—
498	#107	C₂²×D₄₃	1	2	yes	—
499	#107	C₂²×D₄₃	1	2	yes	—
500	#107	C₂²×D₄₃	1	2	yes	—
501	#106	—	43	2	no	—
502	#106	—	43	4	no	—
503	#106	—	43	4	no	—
504	#106	C₂²×D₄₃	1	4	yes	—
505	#106	C₂²×D₄₃	1	4	yes	—
506	C₄⋊C₈	—	43	2	no	—
507	C₄⋊C₈	—	43	2	no	—
508	#103	—	43	2	no	—
509	#103	—	43	2	no	—
510	#103	—	43	4	no	—
511	#103	—	43	4	no	—
512	#102	—	43	2	no	—
513	#102	—	43	2	no	—
514	#102	—	43	4	no	—
515	#102	—	43	4	no	—
516	C₂²⋊C₈	—	43	4	no	—
517	C₂²⋊C₈	—	43	4	no	—
518	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
519	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
520	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
521	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
522	C₂⁴	—	43	2	no	—
523	#41	—	86	4	no	—
524	#41	—	86	4	no	—
525	#41	—	172	8	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	43	2	no	—
529	C₂×D₄	—	43	2	no	—
530	C₂×D₄	—	43	2	no	—
531	C₂×D₄	—	43	2	no	—
532	C₂×D₄	—	86	4	no	—
533	C₂×D₄	—	86	4	no	—
534	C₂×D₄	—	86	2	no	—
535	C₂×D₄	—	172	2	no	—
536	C₂²×C₄	—	43	2	no	—
537	C₂²×C₄	—	43	4	no	—
538	C₂²×C₄	—	43	4	no	—
539	C₂²×C₄	—	86	4	no	—
540	C₂²×C₄	—	86	4	no	—
541	C₂²×C₄	—	86	4	no	—
542	C₂²×C₄	—	86	4	no	—
543	C₂²×C₄	—	86	2	no	—
544	C₂²×C₄	—	86	2	no	—
545	C₂²×C₄	—	86	2	no	—
546	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
547	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
548	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
549	Q₁₆	—	86	2	no	—
550	SD₁₆	—	86	4	no	—
551	D₈	—	86	2	no	—
552	M₁₆	—	86	8	no	—
553	M₁₆	—	86	8	no	—
554	C₂×C₈	—	2	2	no	—
555	C₂×C₈	—	43	4	no	—
556	C₂×C₈	—	86	4	no	—
557	C₂×C₈	#10621902	1	4	yes	complemented
558	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
559	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
560	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
561	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	4	no	—
564	C₄⋊C₄	—	2	4	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	43	2	no	—
567	C₄⋊C₄	—	43	2	no	—
568	C₄⋊C₄	—	43	2	no	—
569	C₄⋊C₄	—	43	2	no	—
570	C₄⋊C₄	—	86	4	no	—
571	C₄⋊C₄	—	86	4	no	—
572	C₄⋊C₄	—	86	4	no	—
573	C₄⋊C₄	—	86	4	no	—
574	C₄⋊C₄	—	86	2	no	—
575	C₄⋊C₄	—	86	2	no	—
576	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
577	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
578	C₂²⋊C₄	—	2	4	no	—
579	C₂²⋊C₄	—	43	4	no	—
580	C₂²⋊C₄	—	43	4	no	—
581	C₂²⋊C₄	—	86	4	no	—
582	C₂²⋊C₄	—	86	4	no	—
583	C₂²⋊C₄	—	86	4	no	—
584	C₂²⋊C₄	—	86	4	no	—
585	C₂²⋊C₄	—	86	4	no	—
586	C₂²⋊C₄	—	86	4	no	—
587	C₂²⋊C₄	—	86	2	no	—
588	C₂²⋊C₄	—	86	2	no	—
589	C₂²⋊C₄	—	86	2	no	—
590	C₄²	—	2	4	no	—
591	C₄²	—	86	4	no	—
592	C₄²	—	86	4	no	—
593	C₄²	—	86	2	no	—
594	C₄²	—	86	2	no	—
595	C₄²	—	86	2	no	—
596	C₄²	D₄×D₄₃	1	1	yes	characteristic
597	C₄²	D₄×D₄₃	1	1	yes	characteristic
598	C₄²	C₂³×D₄₃	1	1	yes	characteristic
599	C₄²	C₂³×D₄₃	1	1	yes	characteristic
600	C₂³	—	43	4	no	—
601	C₂³	—	86	4	no	—
602	C₂³	—	86	2	no	—
603	C₂³	—	172	2	no	—
604	C₂³	—	172	2	no	—
605	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
606	Q₈	—	4	4	no	—
607	Q₈	—	8	2	no	—
608	Q₈	—	86	2	no	—
609	Q₈	—	86	2	no	—
610	D₄	—	86	4	no	—
611	D₄	—	86	2	no	—
612	D₄	—	86	2	no	—
613	D₄	—	344	4	no	—
614	D₄	—	172	2	no	—
615	D₄	—	172	8	no	—
616	D₄	—	172	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	43	4	no	—
622	C₂×C₄	—	86	4	no	—
623	C₂×C₄	—	86	8	no	—
624	C₂×C₄	—	86	4	no	—
625	C₂×C₄	—	86	4	no	—
626	C₂×C₄	—	86	2	no	—
627	C₂×C₄	—	86	2	no	—
628	C₂×C₄	—	86	2	no	—
629	C₂×C₄	—	344	2	no	—
630	C₂×C₄	—	344	4	no	—
631	C₂×C₄	—	172	8	no	—
632	C₂×C₄	—	172	4	no	—
633	C₂×C₄	—	172	4	no	—
634	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
635	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
636	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
637	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
638	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
639	C₂×C₄	C₂×#10621902	1	2	yes	—
640	C₂×C₄	#13063373	1	2	yes	—
641	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
642	C₈	—	2	1	no	—
643	C₈	—	2	1	no	—
644	C₈	—	86	4	no	—
645	C₈	C₂×#10621902	1	2	yes	—
646	C₈	C₂×#10621902	1	2	yes	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	86	4	no	—
650	C₂²	—	86	4	no	—
651	C₂²	—	86	4	no	—
652	C₂²	—	344	4	no	—
653	C₂²	—	172	2	no	—
654	C₂²	—	172	2	no	—
655	C₂²	—	172	2	no	—
656	C₂²	#14583552	1	2	yes	—
657	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
658	C₄	—	2	1	no	—
659	C₄	—	2	1	no	—
660	C₄	—	2	1	no	—
661	C₄	—	4	4	no	—
662	C₄	—	4	4	no	—
663	C₄	—	86	4	no	—
664	C₄	—	172	2	no	—
665	C₄	—	172	2	no	—
666	C₄	—	172	2	no	—
667	C₄	#14583552	1	2	yes	—
668	C₄	#14583696	1	2	yes	—
669	C₄	C₂²×#10621902	1	1	yes	characteristic
670	C₄	C₂×#13063373	1	1	yes	characteristic
671	C₂	—	2	2	no	—
672	C₂	—	344	2	no	—
673	C₂	—	172	4	no	—
674	C₂	C₂×#14583552	1	1	yes	characteristic
675	C₂	C₂×#14583696	1	1	yes	characteristic
676	C₂	#19149364	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	C₄₃×#3160	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#61251
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #19148162	C₂	semidirect
2. #19147220	C₂	semidirect
3. #19147209	C₂	semidirect
4. #19147199	C₂	semidirect
5. #19147189	C₂	semidirect
6. #19147178	C₂	semidirect
7. #19147168	C₂	semidirect
8. #19147154	C₂	semidirect
9. #19144512	C₂	semidirect
10. #19144377	C₂	semidirect
11. #19144205	C₂	semidirect
12. C₄×#13063347	C₂	semidirect
13. C₂×#14582978	C₂	semidirect
14. #19143183	C₂	semidirect
15. C₄₃×#3160	C₂	semidirect
34. #14583243	C₂²	semidirect
35. #14583242	C₂²	semidirect
36. #14583236	C₂²	semidirect
37. #14583231	C₂²	semidirect
38. #14583226	C₂²	semidirect
39. #14583225	C₂²	semidirect
40. #14583219	C₂²	semidirect
41. #14583214	C₂²	semidirect
42. #14583203	C₂²	semidirect
43. #14583196	C₂²	semidirect
44. #14583191	C₂²	semidirect
45. #14583186	C₂²	semidirect
46. #14583181	C₂²	semidirect
47. #14583176	C₂²	semidirect
48. #14583158	C₂²	semidirect
49. #14583153	C₂²	semidirect
50. #14583146	C₂²	semidirect
51. #14583146	C₂²	semidirect
52. C₄×Dic₁₇₂	C₂²	semidirect
53. C₄×Dic₁₇₂	C₂²	semidirect
54. C₄×#10621873	C₂²	semidirect
55. C₄×#10621873	C₂²	semidirect
56. C₄×D₃₄₄	C₂²	semidirect
57. C₄×D₃₄₄	C₂²	semidirect
62. #14582940	C₂²	semidirect
63. #14582940	C₂²	semidirect
64. #14582938	C₂²	semidirect
65. #14582938	C₂²	semidirect
73. C₄₃×#500	C₂²	semidirect
74. C₄₃×#500	C₂²	semidirect
75. C₄₃×#499	C₂²	semidirect
76. C₄₃×#499	C₂²	semidirect
77. C₄₃×#498	C₂²	semidirect
211. C₂×C₈×C₄₃	#41	semidirect
341. #3160	D₄₃	semidirect
373. #500	C₂×D₄₃	semidirect
374. #500	C₂×D₄₃	semidirect
375. #499	C₂×D₄₃	semidirect
376. #499	C₂×D₄₃	semidirect
377. #498	C₂×D₄₃	semidirect
419. C₄₃	#61251	semidirect
557. C₂×C₈	#10621902	semidirect

Maximal subgroups

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

subgroup	index
#19148162	2
#19147220	2
#19147209	2
#19147199	2
#19147189	2
#19147178	2
#19147168	2
#19147154	2
#19144512	2
#19144377	2
#19144205	2
C₄×#13063347	2
C₂×#14582978	2
#19143183	2
C₄₃×#3160	2
#61251	43