Subgroups — #25977235

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148396	C₂	1	2	yes	maximal, complemented
2	#19147556	C₂	1	4	yes	maximal, complemented
3	#19147499	C₂	1	4	yes	maximal, complemented
4	#19147464	C₂	1	2	yes	maximal, complemented
5	#19147459	C₂	1	4	yes	maximal, complemented
6	#19147447	C₂	1	2	yes	maximal, complemented
7	#19145135	C₂	1	2	yes	maximal, complemented
8	#19144429	C₂	1	4	yes	maximal, complemented
9	#19144388	C₂	1	2	yes	maximal, complemented
10	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143446	C₂	1	2	yes	maximal
12	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
15	#14583610	C₂²	1	4	yes	complemented
16	#14583609	—	2	2	no	—
17	#14583609	—	2	4	no	—
18	#14583605	C₂²	1	8	yes	complemented
19	Q₈×D₁₇₂	—	2	2	no	—
20	#14583564	C₂²	1	4	yes	complemented
21	#14583527	C₂²	1	4	yes	—
22	#14583524	—	2	4	no	—
23	#14583456	C₂²	1	1	yes	characteristic
24	C₂²⋊Q₈×D₄₃	—	2	4	no	—
25	#14583373	C₂²	1	4	yes	—
26	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
27	#14583306	C₂²	1	8	yes	complemented
28	#14583303	C₂²	1	4	yes	complemented
29	#14583300	C₂²	1	4	yes	complemented
30	#14583202	C₂²	1	8	yes	complemented
31	#14583198	C₂²	1	8	yes	complemented
32	#14583196	C₂²	1	8	yes	complemented
33	#14583188	C₂²	1	8	yes	complemented
34	#14583186	C₂²	1	4	yes	complemented
35	#14583178	C₂²	1	8	yes	complemented
36	#14583176	C₂²	1	4	yes	complemented
37	#14583029	C₂²	1	2	yes	complemented
38	#14583029	C₂²	1	2	yes	complemented
39	C₈×Dic₈₆	C₂²	1	2	yes	complemented
40	C₈×Dic₈₆	C₂²	1	2	yes	complemented
41	#14583010	C₂²	1	8	yes	—
42	C₄×D₃₄₄	C₂²	1	2	yes	—
43	C₄×D₃₄₄	C₂²	1	2	yes	—
44	C₄×D₃₄₄	C₂²	1	2	yes	—
45	C₄×D₃₄₄	C₂²	1	2	yes	—
46	#14582981	C₂²	1	4	yes	—
47	#14582981	C₂²	1	4	yes	—
48	#14582942	C₂²	1	4	yes	—
49	C₂×#13063259	C₂²	1	1	yes	characteristic
50	#14582925	C₂²	1	2	yes	—
51	#14582923	C₂²	1	1	yes	characteristic
52	#14582903	C₂²	1	4	yes	—
53	C₂×#13063247	C₂²	1	2	yes	—
54	#14582854	C₂²	1	2	yes	—
55	C₄₃×#533	C₂²	1	2	yes	—
56	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
57	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
58	C₄₃×#499	C₂²	1	2	yes	complemented
59	C₄₃×#499	C₂²	1	2	yes	complemented
60	C₄₃×#498	C₂²	1	2	yes	complemented
61	C₄₃×#427	C₂²	1	2	yes	—
62	C₄₃×#427	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
64	C₂×Q₈×D₄₃	—	2	4	no	—
65	C₂²×D₁₇₂	C₂³	1	2	yes	—
66	C₂²×C₄×D₄₃	—	2	2	no	—
67	C₂×D₃₄₄	Q₈	1	8	yes	complemented
68	C₂×D₃₄₄	C₂³	1	2	yes	—
69	C₂×D₃₄₄	C₂³	1	2	yes	—
70	C₂×#10621877	C₂³	1	2	yes	—
71	#13063325	—	2	4	no	—
72	#13063325	D₄	1	1	yes	characteristic
73	#13063325	D₄	1	1	yes	characteristic
74	#13063324	C₂³	1	8	yes	—
75	#13063317	—	2	4	no	—
76	#13063317	D₄	1	2	yes	—
77	#13063316	C₂³	1	8	yes	—
78	#13063305	—	2	4	no	—
79	#13063305	—	2	8	no	—
80	#13063304	D₄	1	2	yes	—
81	#13063304	D₄	1	2	yes	—
82	#13063303	—	2	8	no	—
83	#13063303	—	2	8	no	—
84	#13063303	—	2	8	no	—
85	#13063302	—	2	8	no	—
86	#13063301	—	2	4	no	—
87	#13063301	—	2	8	no	—
88	C₄×Dic₈₆	C₂³	1	2	yes	—
89	C₄×Dic₈₆	C₂³	1	2	yes	—
90	C₄×D₁₇₂	—	2	2	no	—
91	C₄×D₁₇₂	—	2	2	no	—
92	C₄×D₁₇₂	—	2	4	no	—
93	C₄×D₁₇₂	—	2	4	no	—
94	C₄×D₁₇₂	C₂³	1	4	yes	—
95	C₄×D₁₇₂	C₂³	1	4	yes	—
96	#13063287	C₂³	1	8	yes	—
97	#13063287	C₂³	1	8	yes	—
98	#13063284	C₂³	1	2	yes	—
99	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
100	C₄⋊C₄×D₄₃	—	2	4	no	—
101	C₄⋊C₄×D₄₃	—	2	8	no	—
102	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
103	C₂²⋊C₄×D₄₃	—	2	8	no	—
104	#13063259	C₂³	1	2	yes	—
105	#13063259	C₂³	1	2	yes	—
106	#13063258	C₂³	1	8	yes	—
107	#13063256	C₂³	1	8	yes	—
108	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
109	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
110	Dic₄₃⋊C₈	C₂³	1	4	yes	—
111	Dic₄₃⋊C₈	C₂³	1	4	yes	—
112	#13063247	C₂³	1	4	yes	—
113	#13063247	C₂³	1	4	yes	—
114	#13063245	C₂³	1	8	yes	—
115	#13063245	C₂³	1	8	yes	—
116	#13063235	C₂³	1	4	yes	—
117	C₈×Dic₄₃	C₂³	1	4	yes	—
118	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
122	#125×C₄₃	C₂³	1	4	yes	—
123	C₂²⋊Q₈×C₄₃	—	2	2	no	—
124	C₂²⋊Q₈×C₄₃	—	2	2	no	—
125	C₄×Q₈×C₄₃	—	2	2	no	—
126	C₄×Q₈×C₄₃	—	2	2	no	—
127	#117×C₄₃	C₂³	1	4	yes	—
128	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
129	#107×C₄₃	C₂³	1	2	yes	—
130	#107×C₄₃	C₂³	1	2	yes	—
131	#107×C₄₃	C₂³	1	2	yes	—
132	#107×C₄₃	C₂³	1	2	yes	—
133	#106×C₄₃	C₂³	1	4	yes	—
134	#106×C₄₃	C₂³	1	4	yes	—
135	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₂³×D₄₃	—	2	2	no	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₄₃	—	2	2	no	—
146	Q₈×D₄₃	—	8	8	no	—
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	4	no	—
149	C₂×D₁₇₂	C₂×Q₈	1	8	yes	complemented
150	C₂×D₁₇₂	C₂⁴	1	4	yes	—
151	C₂×C₄×D₄₃	—	2	4	no	—
152	C₂×C₄×D₄₃	—	2	4	no	—
153	C₂×C₄×D₄₃	—	2	8	no	—
154	C₂×C₄×D₄₃	—	2	8	no	—
155	C₂×C₄×D₄₃	—	8	4	no	—
156	C₂×Dic₈₆	—	2	8	no	—
157	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
158	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₄₃	—	2	2	no	—
160	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	complemented
161	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₄₃	—	2	4	no	—
166	C₄⋊C₄×C₄₃	—	2	4	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
170	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
171	C₂²⋊C₄×C₄₃	—	2	4	no	—
172	C₄²×C₄₃	—	2	4	no	—
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	C₂²⋊Dic₄₃	C₂×D₄	1	4	yes	—
178	(C₂×D₄₃)⋊C₄	—	2	4	no	—
179	(C₂×D₄₃)⋊C₄	—	2	4	no	—
180	(C₂×D₄₃)⋊C₄	—	2	8	no	—
181	(C₂×D₄₃)⋊C₄	—	2	8	no	—
182	C₄⋊Dic₄₃	—	2	2	no	—
183	C₄⋊Dic₄₃	—	2	8	no	—
184	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
185	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
186	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
188	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
189	Dic₄₃⋊C₄	—	2	8	no	—
190	Dic₄₃⋊C₄	—	2	8	no	—
191	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
192	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
193	C₄×Dic₄₃	C₂⁴	1	4	yes	—
194	#10621877	—	2	4	no	—
195	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
196	D₃₄₄	C₂×Q₈	1	8	yes	complemented
197	D₃₄₄	C₂×Q₈	1	8	yes	complemented
198	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂²×D₄₃	—	2	4	no	—
200	C₂²×D₄₃	—	2	8	no	—
201	C₂²×D₄₃	—	8	2	no	—
202	C₂²×D₄₃	—	8	2	no	—
203	Q₈×C₄₃	—	4	4	no	—
204	Q₈×C₄₃	—	8	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
216	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
217	C₂×Dic₄₃	—	2	4	no	—
218	C₂×Dic₄₃	—	8	2	no	—
219	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
220	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
221	D₁₇₂	—	2	8	no	—
222	D₁₇₂	—	2	4	no	—
223	D₁₇₂	C₂²×Q₈	1	8	yes	—
224	C₄×D₄₃	—	4	8	no	—
225	C₄×D₄₃	—	8	8	no	—
226	C₄×D₄₃	—	8	8	no	—
227	C₄×D₄₃	—	8	4	no	—
228	Dic₈₆	—	2	4	no	—
229	Dic₈₆	—	4	2	no	—
230	Dic₈₆	—	8	8	no	—
231	C₈×C₄₃	—	2	1	no	—
232	C₈×C₄₃	—	2	1	no	—
233	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
234	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
235	C₄₃⋊C₈	—	2	4	no	—
236	#61370	—	43	1	no	maximal, Sylow
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	—	2	1	no	—
239	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
240	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
241	C₂×D₄₃	—	2	8	no	—
242	C₂×D₄₃	—	4	4	no	—
243	C₂×D₄₃	—	4	4	no	—
244	C₂×D₄₃	—	8	8	no	—
245	C₄×C₄₃	—	2	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	—	4	4	no	—
249	C₄×C₄₃	—	4	4	no	—
250	C₄×C₄₃	D₄×Q₈	1	2	yes	—
251	C₄×C₄₃	#576	1	2	yes	—
252	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
253	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	Dic₄₃	—	2	4	no	—
255	Dic₄₃	—	2	4	no	—
256	Dic₄₃	—	4	4	no	—
257	#3501	—	43	2	no	—
258	#3389	—	43	4	no	—
259	#3384	—	43	4	no	—
260	#3380	—	43	2	no	—
261	#3380	—	43	4	no	—
262	Q₈×D₈	—	43	2	no	—
263	#3164	—	43	2	no	—
264	#3160	D₄₃	1	1	yes	characteristic, complemented
265	#3081	—	43	4	no	—
266	#3077	—	43	2	no	—
267	#2960	—	43	1	no	—
268	#2948	—	43	2	no	—
269	C₂×C₄×D₈	—	43	1	no	—
270	C₂×C₄₃	—	2	2	no	—
271	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
272	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
273	C₂×C₄₃	#3584	1	1	yes	characteristic
274	D₄₃	—	4	8	no	—
275	C₂²×D₈	—	43	1	no	—
276	#554	—	43	4	no	—
277	#554	—	43	8	no	—
278	#554	—	86	4	no	—
279	#554	—	86	2	no	—
280	D₄×Q₈	—	43	4	no	—
281	D₄×Q₈	—	86	2	no	—
282	#544	—	43	4	no	—
283	#543	—	86	4	no	—
284	#533	—	43	1	no	—
285	#533	C₂×D₄₃	1	2	yes	—
286	C₂×C₂²⋊Q₈	—	86	4	no	—
287	#518	—	43	4	no	—
288	C₂×C₄×D₄	—	43	2	no	—
289	#501	—	43	8	no	—
290	#500	—	43	4	no	—
291	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
292	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
293	#499	—	43	4	no	—
294	#499	C₂×D₄₃	1	2	yes	complemented
295	#499	C₂×D₄₃	1	2	yes	complemented
296	#498	C₂×D₄₃	1	2	yes	complemented
297	#478	—	43	8	no	—
298	#478	—	43	8	no	—
299	#478	—	43	8	no	—
300	#476	—	43	4	no	—
301	#476	—	43	8	no	—
302	#474	—	43	4	no	—
303	#474	—	43	8	no	—
304	#446	—	43	2	no	—
305	#446	—	43	2	no	—
306	C₈×Q₈	—	43	2	no	—
307	C₈×Q₈	—	43	2	no	—
308	#442	—	43	8	no	—
309	C₄×D₈	—	43	4	no	—
310	C₄×D₈	—	43	4	no	—
311	C₄×D₈	—	43	2	no	—
312	C₄×D₈	—	43	2	no	—
313	C₄×D₈	—	43	2	no	—
314	C₄×D₈	—	43	2	no	—
315	#428	—	43	4	no	—
316	#427	C₂×D₄₃	1	2	yes	—
317	#427	C₂×D₄₃	1	2	yes	—
318	C₂×#107	—	43	1	no	—
319	#424	—	43	2	no	—
320	#423	—	43	1	no	—
321	#418	—	43	4	no	—
322	C₂×#102	—	43	2	no	—
323	#405	—	43	2	no	—
324	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
325	C₄₃	#61370	1	1	yes	characteristic, complemented, Sylow
326	C₂²×Q₈	—	86	4	no	—
327	C₂²×D₄	—	43	2	no	—
328	C₂³×C₄	—	86	2	no	—
329	C₂×D₈	—	43	8	no	—
330	C₂×D₈	—	43	2	no	—
331	C₂×D₈	—	43	2	no	—
332	C₂×M₁₆	—	43	2	no	—
333	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
335	C₄⋊Q₈	—	43	8	no	—
336	C₄⋊Q₈	—	43	1	no	—
337	C₄⋊Q₈	—	43	1	no	—
338	C₄⋊Q₈	—	86	4	no	—
339	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
340	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
341	#125	—	43	8	no	—
342	#125	—	43	2	no	—
343	#125	—	86	4	no	—
344	#125	C₂²×D₄₃	1	4	yes	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	43	2	no	—
348	C₂²⋊Q₈	—	43	2	no	—
349	C₂²⋊Q₈	—	86	8	no	—
350	C₂²⋊Q₈	—	86	8	no	—
351	C₂²⋊Q₈	—	86	8	no	—
352	C₂²⋊Q₈	—	86	8	no	—
353	C₂²⋊Q₈	—	86	4	no	—
354	C₂²⋊Q₈	—	86	8	no	—
355	C₂²⋊Q₈	—	86	4	no	—
356	C₂²⋊Q₈	—	86	8	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	43	2	no	—
360	C₄×Q₈	—	43	2	no	—
361	C₄×D₄	—	43	8	no	—
362	C₄×D₄	—	43	8	no	—
363	C₄×D₄	—	43	4	no	—
364	C₄×D₄	—	43	4	no	—
365	C₄×D₄	—	86	4	no	—
366	C₄×D₄	—	86	4	no	—
367	C₄×D₄	—	86	2	no	—
368	C₄×D₄	—	86	2	no	—
369	#117	—	43	2	no	—
370	#117	C₂²×D₄₃	1	4	yes	—
371	C₂×C₄⋊C₄	—	43	2	no	—
372	C₂×C₄⋊C₄	—	86	8	no	—
373	C₂×C₄⋊C₄	—	86	4	no	—
374	C₂×C₂²⋊C₄	—	86	8	no	—
375	C₂×C₂²⋊C₄	—	86	2	no	—
376	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
377	#107	—	43	2	no	—
378	#107	—	43	2	no	—
379	#107	—	43	8	no	—
380	#107	C₂²×D₄₃	1	2	yes	—
381	#107	C₂²×D₄₃	1	2	yes	—
382	#107	C₂²×D₄₃	1	2	yes	—
383	#107	C₂²×D₄₃	1	2	yes	—
384	#106	—	43	8	no	—
385	#106	C₂²×D₄₃	1	4	yes	—
386	#106	C₂²×D₄₃	1	4	yes	—
387	C₄⋊C₈	—	43	4	no	—
388	C₄⋊C₈	—	43	4	no	—
389	C₄⋊C₈	—	43	2	no	—
390	C₄⋊C₈	—	43	2	no	—
391	#102	—	43	4	no	—
392	#102	—	43	4	no	—
393	#102	—	43	8	no	—
394	#102	—	43	8	no	—
395	#97	—	43	4	no	—
396	C₄×C₈	—	43	4	no	—
397	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
401	C₂⁴	—	86	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	43	2	no	—
405	C₂×Q₈	—	43	2	no	—
406	C₂×Q₈	—	86	8	no	—
407	C₂×Q₈	—	344	8	no	—
408	C₂×D₄	—	43	8	no	—
409	C₂×D₄	—	43	4	no	—
410	C₂×D₄	—	86	2	no	—
411	C₂×D₄	—	86	4	no	—
412	C₂²×C₄	—	86	8	no	—
413	C₂²×C₄	—	86	8	no	—
414	C₂²×C₄	—	86	2	no	—
415	C₂²×C₄	—	86	4	no	—
416	C₂²×C₄	—	86	4	no	—
417	C₂²×C₄	—	344	4	no	—
418	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
419	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
421	D₈	—	43	8	no	—
422	D₈	—	43	8	no	—
423	M₁₆	—	86	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	43	4	no	—
426	C₂×C₈	Q₈×D₄₃	1	4	yes	complemented
427	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
429	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
430	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	43	4	no	—
436	C₄⋊C₄	—	43	2	no	—
437	C₄⋊C₄	—	43	2	no	—
438	C₄⋊C₄	—	43	2	no	—
439	C₄⋊C₄	—	43	4	no	—
440	C₄⋊C₄	—	43	2	no	—
441	C₄⋊C₄	—	43	4	no	—
442	C₄⋊C₄	—	86	8	no	—
443	C₄⋊C₄	—	86	8	no	—
444	C₄⋊C₄	—	86	8	no	—
445	C₄⋊C₄	—	86	2	no	—
446	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
447	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	43	4	no	—
450	C₂²⋊C₄	—	86	8	no	—
451	C₂²⋊C₄	—	86	8	no	—
452	C₂²⋊C₄	—	86	4	no	—
453	C₂²⋊C₄	—	86	4	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	43	4	no	—
456	C₄²	D₄×D₄₃	1	1	yes	characteristic
457	C₄²	D₄×D₄₃	1	1	yes	characteristic
458	C₄²	C₂³×D₄₃	1	1	yes	characteristic
459	C₄²	C₂³×D₄₃	1	1	yes	characteristic
460	C₂³	—	86	8	no	—
461	C₂³	—	86	4	no	—
462	C₂³	—	344	2	no	—
463	C₂³	—	344	2	no	—
464	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
465	Q₈	—	4	4	no	—
466	Q₈	—	8	2	no	—
467	Q₈	—	86	4	no	—
468	Q₈	—	344	8	no	—
469	Q₈	—	172	2	no	—
470	D₄	—	43	8	no	—
471	D₄	—	86	8	no	—
472	D₄	—	86	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	43	4	no	—
478	C₂×C₄	—	43	4	no	—
479	C₂×C₄	—	86	4	no	—
480	C₂×C₄	—	344	4	no	—
481	C₂×C₄	—	344	8	no	—
482	C₂×C₄	—	344	8	no	—
483	C₂×C₄	—	344	2	no	—
484	C₂×C₄	—	172	8	no	—
485	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
491	C₂×C₄	#13063373	1	2	yes	—
492	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	86	4	no	—
496	C₈	C₂×Q₈×D₄₃	1	2	yes	—
497	C₈	C₂×Q₈×D₄₃	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	86	8	no	—
501	C₂²	—	344	8	no	—
502	C₂²	—	172	4	no	—
503	C₂²	—	172	4	no	—
504	C₂²	#14583564	1	2	yes	—
505	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	86	4	no	—
512	C₄	—	86	4	no	—
513	C₄	—	172	4	no	—
514	C₄	#14583564	1	2	yes	—
515	C₄	#14583701	1	2	yes	—
516	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
517	C₄	C₂×#13063373	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	172	8	no	—
520	C₂	C₂×#14583564	1	1	yes	characteristic
521	C₂	C₂×#14583701	1	1	yes	characteristic
522	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×#3160	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×D₃₄₄	C₂²
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#61370
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #19148396	C₂	semidirect
2. #19147556	C₂	semidirect
3. #19147499	C₂	semidirect
4. #19147464	C₂	semidirect
5. #19147459	C₂	semidirect
6. #19147447	C₂	semidirect
7. #19145135	C₂	semidirect
8. #19144429	C₂	semidirect
9. #19144388	C₂	semidirect
10. #19143529	C₂	semidirect
13. C₄₃×#3160	C₂	semidirect
15. #14583610	C₂²	semidirect
18. #14583605	C₂²	semidirect
20. #14583564	C₂²	semidirect
27. #14583306	C₂²	semidirect
28. #14583303	C₂²	semidirect
29. #14583300	C₂²	semidirect
30. #14583202	C₂²	semidirect
31. #14583198	C₂²	semidirect
32. #14583196	C₂²	semidirect
33. #14583188	C₂²	semidirect
34. #14583186	C₂²	semidirect
35. #14583178	C₂²	semidirect
36. #14583176	C₂²	semidirect
37. #14583029	C₂²	semidirect
38. #14583029	C₂²	semidirect
39. C₈×Dic₈₆	C₂²	semidirect
40. C₈×Dic₈₆	C₂²	semidirect
56. C₄₃×#500	C₂²	semidirect
57. C₄₃×#500	C₂²	semidirect
58. C₄₃×#499	C₂²	semidirect
59. C₄₃×#499	C₂²	semidirect
60. C₄₃×#498	C₂²	semidirect
67. C₂×D₃₄₄	Q₈	semidirect
149. C₂×D₁₇₂	C₂×Q₈	semidirect
160. C₂×C₈×C₄₃	C₂×Q₈	semidirect
196. D₃₄₄	C₂×Q₈	semidirect
197. D₃₄₄	C₂×Q₈	semidirect
264. #3160	D₄₃	semidirect
291. #500	C₂×D₄₃	semidirect
292. #500	C₂×D₄₃	semidirect
294. #499	C₂×D₄₃	semidirect
295. #499	C₂×D₄₃	semidirect
296. #498	C₂×D₄₃	semidirect
325. C₄₃	#61370	semidirect
426. C₂×C₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19148396	2
#19147556	2
#19147499	2
#19147464	2
#19147459	2
#19147447	2
#19145135	2
#19144429	2
#19144388	2
#19143529	2
#19143446	2
C₂×C₄×D₃₄₄	2
C₄₃×#3160	2
#61370	43