Subgroups — #25099187

Order 11008.

1000 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582948	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582917	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582917	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
5	#19143014	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135265	C₂	1	8	yes	maximal, complemented
7	C₂×#14582669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10621898	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂²×#10621877	C₂²	1	1	yes	characteristic
12	C₂²×#10621877	C₂²	1	1	yes	characteristic
13	#14582948	—	2	2	no	—
14	#14582948	C₂²	1	4	yes	complemented
15	C₂×#13063261	—	2	2	no	—
16	#14582917	—	2	2	no	—
17	#14582917	—	2	2	no	—
18	#14582917	—	2	2	no	—
19	#14582917	C₂²	1	4	yes	—
20	C₂×#13063253	—	2	2	no	—
21	C₂×#13063253	C₂²	1	4	yes	—
22	#14582881	C₄	1	4	yes	complemented
23	#14582881	C₂²	1	4	yes	—
24	C₂×#13063243	C₄	1	2	yes	complemented
25	C₂×#13063241	C₄	1	2	yes	complemented
26	#14582855	—	2	2	no	—
27	#14582855	—	2	2	no	—
28	C₄×#10621877	C₂²	1	4	yes	complemented
29	#14582669	C₂²	1	4	yes	complemented
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#339	C₂²	1	4	yes	complemented
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	—	2	1	no	—
43	C₂×#10621898	—	2	1	no	—
44	C₂×#10621898	C₂×C₄	1	2	yes	—
45	C₂×#10621898	C₂³	1	2	yes	—
46	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₂²⋊D₄₃	—	2	1	no	—
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	—	2	1	no	—
60	C₂×#10621877	—	2	1	no	—
61	C₂×#10621877	C₂×C₄	1	2	yes	—
62	C₂×#10621877	C₂×C₄	1	2	yes	—
63	C₂×#10621877	D₄	1	2	yes	—
64	C₂×#10621877	D₄	1	2	yes	—
65	C₂×#10621877	C₂³	1	2	yes	—
66	C₂×#10621877	C₂³	1	2	yes	—
67	C₂×#10621877	C₂³	1	2	yes	—
68	C₂²×C₄₃⋊C₈	—	2	1	no	—
69	C₂²×C₄₃⋊C₈	—	2	1	no	—
70	C₂²×C₄₃⋊C₈	—	2	1	no	—
71	#13063261	—	2	8	no	—
72	#13063253	—	2	8	no	—
73	#13063253	—	2	8	no	—
74	#13063243	C₂×C₄	1	8	yes	complemented
75	#13063241	C₂×C₄	1	8	yes	complemented
76	#13063236	—	2	4	no	—
77	C₄×C₄₃⋊C₈	—	2	4	no	—
78	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×M₁₆×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	—	2	1	no	—
81	C₂×M₁₆×C₄₃	—	2	1	no	—
82	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	#117×C₄₃	—	2	1	no	—
87	#117×C₄₃	—	2	1	no	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	—	2	1	no	—
90	#117×C₄₃	—	2	1	no	—
91	#117×C₄₃	D₄	1	2	yes	—
92	#117×C₄₃	D₄	1	2	yes	—
93	#117×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	—	2	1	no	—
99	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
100	C₂⁴×C₄₃	#41	1	1	yes	characteristic
101	C₂³×D₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	4	1	no	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₃	—	2	2	no	—
119	C₂×C₂²⋊D₄₃	—	2	2	no	—
120	C₂×C₂²⋊D₄₃	—	4	1	no	—
121	C₂×C₂²⋊D₄₃	—	4	1	no	—
122	C₂×C₂²⋊D₄₃	—	4	1	no	—
123	C₂×C₂²⋊D₄₃	—	4	1	no	—
124	C₂²×Dic₄₃	—	2	1	no	—
125	#10621898	—	2	2	no	—
126	#10621898	—	2	2	no	—
127	#10621898	—	2	2	no	—
128	#10621898	—	2	2	no	—
129	#10621898	—	2	2	no	—
130	#10621898	—	2	2	no	—
131	#10621898	—	2	2	no	—
132	#10621898	—	2	2	no	—
133	#10621898	—	4	1	no	—
134	#10621898	—	4	1	no	—
135	#10621898	—	4	1	no	—
136	#10621898	—	4	1	no	—
137	#10621898	—	4	1	no	—
138	#10621898	—	4	1	no	—
139	#10621898	—	4	1	no	—
140	#10621898	—	4	1	no	—
141	C₂×D₁₇₂	—	2	1	no	—
142	C₂×D₁₇₂	—	2	1	no	—
143	C₂×D₁₇₂	—	2	1	no	—
144	C₂×D₁₇₂	—	2	1	no	—
145	C₂×D₁₇₂	—	2	1	no	—
146	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
147	C₂×C₄×D₄₃	—	2	2	no	—
148	C₂×C₄×D₄₃	—	2	2	no	—
149	C₂×C₄×D₄₃	—	4	1	no	—
150	C₂×C₄×D₄₃	—	4	1	no	—
151	C₂×C₄×D₄₃	—	4	1	no	—
152	C₂×C₄×D₄₃	—	4	1	no	—
153	C₂×Dic₈₆	—	2	1	no	—
154	C₂×Dic₈₆	—	2	1	no	—
155	C₂×Dic₈₆	—	2	1	no	—
156	C₂×Dic₈₆	—	2	1	no	—
157	C₂×Dic₈₆	—	2	1	no	—
158	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
159	M₁₆×C₄₃	—	2	2	no	—
160	M₁₆×C₄₃	—	2	2	no	—
161	M₁₆×C₄₃	—	2	2	no	—
162	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
163	C₂×C₈×C₄₃	—	2	2	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	2	2	no	—
169	C₄⋊C₄×C₄₃	—	4	1	no	—
170	C₂²⋊C₄×C₄₃	—	2	2	no	—
171	C₂²⋊C₄×C₄₃	—	2	2	no	—
172	C₂²⋊C₄×C₄₃	—	2	2	no	—
173	C₂²⋊C₄×C₄₃	—	4	1	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	—	4	1	no	—
177	C₄²×C₄₃	C₂×D₄	1	4	yes	—
178	#10621877	—	2	2	no	—
179	#10621877	—	2	2	no	—
180	#10621877	—	2	2	no	—
181	#10621877	—	2	2	no	—
182	#10621877	—	2	2	no	—
183	#10621877	—	2	2	no	—
184	#10621877	—	2	2	no	—
185	#10621877	—	2	2	no	—
186	#10621877	—	4	1	no	—
187	#10621877	—	4	1	no	—
188	#10621877	C₂²×C₄	1	4	yes	—
189	#10621877	C₂×D₄	1	4	yes	—
190	C₂×C₄₃⋊C₈	—	2	2	no	—
191	C₂×C₄₃⋊C₈	—	2	2	no	—
192	C₂×C₄₃⋊C₈	—	2	2	no	—
193	C₂×C₄₃⋊C₈	—	2	2	no	—
194	C₂×C₄₃⋊C₈	—	2	2	no	—
195	C₂×C₄₃⋊C₈	—	2	2	no	—
196	C₂×C₄₃⋊C₈	—	2	2	no	—
197	C₂×C₄₃⋊C₈	—	4	1	no	—
198	C₂×C₄₃⋊C₈	—	4	1	no	—
199	C₂³×C₄₃	—	8	1	no	—
200	C₂³×C₄₃	#117	1	1	yes	characteristic
201	C₂³×C₄₃	#117	1	1	yes	characteristic
202	C₂³×C₄₃	#123	1	1	yes	characteristic
203	C₂³×C₄₃	#123	1	1	yes	characteristic
204	C₂³×C₄₃	#124	1	1	yes	characteristic
205	C₂³×C₄₃	#124	1	1	yes	characteristic
206	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
207	C₂²×D₄₃	—	2	2	no	—
208	C₂²×D₄₃	—	4	1	no	—
209	C₂²×D₄₃	—	4	1	no	—
210	C₂²×D₄₃	—	8	2	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	8	2	no	—
214	C₂×C₄×C₄₃	—	8	2	no	—
215	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
216	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
226	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
227	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
228	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
229	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
231	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
232	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
233	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
234	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
235	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
243	C₂²⋊D₄₃	—	4	2	no	—
244	C₂²⋊D₄₃	—	4	2	no	—
245	C₂²⋊D₄₃	—	4	2	no	—
246	C₂²⋊D₄₃	—	4	2	no	—
247	C₂×Dic₄₃	—	2	2	no	—
248	C₂×Dic₄₃	—	4	1	no	—
249	C₂×Dic₄₃	—	4	1	no	—
250	D₁₇₂	—	2	2	no	—
251	D₁₇₂	—	2	2	no	—
252	D₁₇₂	—	4	1	no	—
253	D₁₇₂	—	4	1	no	—
254	C₄×D₄₃	—	4	2	no	—
255	C₄×D₄₃	—	4	2	no	—
256	C₄×D₄₃	—	4	2	no	—
257	C₄×D₄₃	—	4	2	no	—
258	Dic₈₆	—	2	2	no	—
259	Dic₈₆	—	2	2	no	—
260	Dic₈₆	—	4	1	no	—
261	Dic₈₆	—	4	1	no	—
262	C₈×C₄₃	—	2	4	no	—
263	C₄₃⋊C₈	—	2	4	no	—
264	C₄₃⋊C₈	—	2	4	no	—
265	C₄₃⋊C₈	—	4	2	no	—
266	#21080	—	43	1	no	maximal, Sylow
267	C₂²×C₄₃	—	4	1	no	—
268	C₂²×C₄₃	—	4	1	no	—
269	C₂²×C₄₃	—	4	1	no	—
270	C₂²×C₄₃	—	4	1	no	—
271	C₂²×C₄₃	—	4	1	no	—
272	C₂²×C₄₃	—	4	1	no	—
273	C₂²×C₄₃	—	4	1	no	—
274	C₂²×C₄₃	#388	1	1	yes	characteristic
275	C₂²×C₄₃	#388	1	1	yes	characteristic
276	C₂²×C₄₃	#388	1	1	yes	characteristic
277	C₂²×C₄₃	#388	1	1	yes	characteristic
278	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
279	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
280	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
281	C₂×D₄₃	—	4	2	no	—
282	C₂×D₄₃	—	8	2	no	—
283	C₂×D₄₃	—	8	2	no	—
284	C₂×D₄₃	—	8	2	no	—
285	C₄×C₄₃	—	4	4	no	—
286	C₄×C₄₃	—	8	2	no	—
287	C₄×C₄₃	#388	1	1	yes	characteristic
288	C₄×C₄₃	#388	1	1	yes	characteristic
289	C₄×C₄₃	#388	1	1	yes	characteristic
290	C₄×C₄₃	#388	1	1	yes	characteristic
291	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
294	C₄×C₄₃	C₂×#126	1	1	yes	characteristic
295	Dic₄₃	—	4	2	no	—
296	C₂×#430	—	43	1	no	—
297	C₂×#421	—	43	1	no	—
298	C₂×#421	—	43	1	no	—
299	C₂×#413	—	43	1	no	—
300	#2873	—	43	1	no	—
301	#1932	—	43	8	no	—
302	C₂×#344	—	43	1	no	—
303	#1733	D₄₃	1	1	yes	characteristic, complemented
304	C₂×C₄₃	—	2	1	no	—
305	C₂×C₄₃	—	2	1	no	—
306	C₂×C₄₃	—	2	1	no	—
307	C₂×C₄₃	—	2	1	no	—
308	C₂×C₄₃	—	2	1	no	—
309	C₂×C₄₃	—	2	1	no	—
310	C₂×C₄₃	—	2	1	no	—
311	C₂×C₄₃	C₂×#388	1	1	yes	characteristic
312	D₄₃	—	8	2	no	—
313	C₂²×#41	—	43	1	no	—
314	C₂²×M₁₆	—	43	1	no	—
315	C₂²×M₁₆	—	43	1	no	—
316	C₂²×M₁₆	—	43	1	no	—
317	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
318	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
319	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
320	#430	—	43	4	no	—
321	#430	—	86	2	no	—
322	C₂×#108	—	86	2	no	—
323	#421	—	43	4	no	—
324	#421	—	86	2	no	—
325	#421	—	86	2	no	—
326	#421	—	86	2	no	—
327	C₂×#104	—	43	4	no	—
328	C₂×#104	—	86	2	no	—
329	#413	—	43	4	no	—
330	#413	—	43	4	no	—
331	C₂×#101	—	43	2	no	—
332	C₂×#100	—	43	2	no	—
333	#405	—	86	2	no	—
334	#405	—	86	2	no	—
335	C₄×M₁₆	—	43	4	no	—
336	#344	—	43	4	no	—
337	#339	C₂×D₄₃	1	4	yes	complemented
338	C₄₃	#21080	1	1	yes	characteristic, complemented, Sylow
339	C₂×#41	—	43	2	no	—
340	C₂×#41	—	43	2	no	—
341	C₂×#41	—	86	1	no	—
342	C₂×#41	—	86	1	no	—
343	C₂×#41	—	86	1	no	—
344	C₂×#41	—	86	1	no	—
345	C₂×#41	—	86	1	no	—
346	C₂×#41	—	86	1	no	—
347	C₂×#41	—	86	1	no	—
348	C₂×#41	—	86	1	no	—
349	C₂×#41	—	86	1	no	—
350	C₂×#41	—	86	1	no	—
351	C₂²×Q₈	—	43	1	no	—
352	C₂²×D₄	—	43	1	no	—
353	C₂²×D₄	—	86	1	no	—
354	C₂³×C₄	—	86	1	no	—
355	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	43	2	no	—
360	C₂×M₁₆	—	43	2	no	—
361	C₂×M₁₆	—	43	2	no	—
362	C₂×M₁₆	—	43	2	no	—
363	C₂×M₁₆	—	43	2	no	—
364	C₂×M₁₆	—	43	2	no	—
365	C₂×M₁₆	—	43	2	no	—
366	C₂×M₁₆	—	86	1	no	—
367	C₂×M₁₆	—	86	1	no	—
368	C₂×M₁₆	—	86	1	no	—
369	C₂×M₁₆	—	86	1	no	—
370	C₂×M₁₆	—	86	1	no	—
371	C₂×M₁₆	—	86	1	no	—
372	C₂×M₁₆	—	86	1	no	—
373	C₂×M₁₆	—	86	1	no	—
374	C₂×M₁₆	—	86	1	no	—
375	C₂×M₁₆	—	86	1	no	—
376	C₂×M₁₆	—	86	1	no	—
377	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
378	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
379	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	86	1	no	—
382	C₂²×C₈	—	86	1	no	—
383	C₂²×C₈	—	86	1	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	—	2	1	no	—
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	D₁₇₂	1	2	yes	—
390	#117	D₁₇₂	1	2	yes	—
391	#117	C₂²×D₄₃	1	2	yes	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
398	#108	—	86	8	no	—
399	#104	—	86	8	no	—
400	#104	—	86	8	no	—
401	#101	—	43	8	no	—
402	#100	—	43	8	no	—
403	#97	—	86	4	no	—
404	C₄×C₈	—	86	4	no	—
405	C₂⁴	—	86	1	no	—
406	C₂⁴	#10621900	1	1	yes	characteristic
407	#41	—	86	2	no	—
408	#41	—	86	2	no	—
409	#41	—	86	2	no	—
410	#41	—	86	2	no	—
411	#41	—	86	2	no	—
412	#41	—	86	2	no	—
413	#41	—	86	2	no	—
414	#41	—	86	2	no	—
415	#41	—	172	1	no	—
416	#41	—	172	1	no	—
417	#41	—	172	1	no	—
418	#41	—	172	1	no	—
419	#41	—	172	1	no	—
420	#41	—	172	1	no	—
421	#41	—	172	1	no	—
422	#41	—	172	1	no	—
423	C₂×Q₈	—	43	2	no	—
424	C₂×Q₈	—	86	1	no	—
425	C₂×Q₈	—	86	1	no	—
426	C₂×Q₈	—	86	1	no	—
427	C₂×Q₈	—	86	1	no	—
428	C₂×Q₈	—	86	1	no	—
429	C₂×D₄	—	43	2	no	—
430	C₂×D₄	—	86	2	no	—
431	C₂×D₄	—	86	2	no	—
432	C₂×D₄	—	86	1	no	—
433	C₂×D₄	—	86	1	no	—
434	C₂×D₄	—	86	1	no	—
435	C₂×D₄	—	86	1	no	—
436	C₂×D₄	—	86	1	no	—
437	C₂×D₄	—	172	1	no	—
438	C₂×D₄	—	172	1	no	—
439	C₂×D₄	—	172	1	no	—
440	C₂×D₄	—	172	1	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	86	1	no	—
444	C₂²×C₄	—	86	2	no	—
445	C₂²×C₄	—	86	2	no	—
446	C₂²×C₄	—	172	1	no	—
447	C₂²×C₄	—	172	1	no	—
448	C₂²×C₄	—	172	1	no	—
449	C₂²×C₄	—	172	1	no	—
450	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
454	C₂²×C₄	#10621898	1	1	yes	characteristic
455	C₂²×C₄	#10621898	1	1	yes	characteristic
456	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
457	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
458	C₂²×C₄	#10621900	1	1	yes	characteristic
459	C₂²×C₄	#10621900	1	1	yes	characteristic
460	C₂²×C₄	#10621900	1	1	yes	characteristic
461	C₂²×C₄	#10621902	1	1	yes	characteristic
462	C₂²×C₄	#10621902	1	1	yes	characteristic
463	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	43	4	no	—
468	M₁₆	—	43	4	no	—
469	M₁₆	—	86	2	no	—
470	M₁₆	—	86	2	no	—
471	M₁₆	—	86	2	no	—
472	M₁₆	—	86	2	no	—
473	M₁₆	—	86	2	no	—
474	M₁₆	—	86	2	no	—
475	M₁₆	—	86	2	no	—
476	M₁₆	—	86	2	no	—
477	M₁₆	—	172	1	no	—
478	M₁₆	—	172	1	no	—
479	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	86	2	no	—
484	C₂×C₈	—	86	2	no	—
485	C₂×C₈	—	86	2	no	—
486	C₂×C₈	—	86	2	no	—
487	C₂×C₈	—	86	2	no	—
488	C₂×C₈	—	86	2	no	—
489	C₂×C₈	—	86	2	no	—
490	C₂×C₈	—	172	1	no	—
491	C₂×C₈	—	172	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	4	1	no	—
503	C₄²	C₂×D₁₇₂	1	4	yes	—
504	C₂³	—	8	1	no	—
505	C₂³	—	86	2	no	—
506	C₂³	—	344	2	no	—
507	C₂³	—	172	1	no	—
508	C₂³	—	172	1	no	—
509	C₂³	#13063283	1	1	yes	characteristic
510	C₂³	#13063283	1	1	yes	characteristic
511	C₂³	#13063309	1	1	yes	characteristic
512	C₂³	#13063309	1	1	yes	characteristic
513	C₂³	#13063311	1	1	yes	characteristic
514	C₂³	#13063311	1	1	yes	characteristic
515	C₂³	C₂×#10621900	1	1	yes	characteristic
516	Q₈	—	86	2	no	—
517	Q₈	—	86	2	no	—
518	Q₈	—	172	1	no	—
519	Q₈	—	172	1	no	—
520	D₄	—	86	2	no	—
521	D₄	—	86	2	no	—
522	D₄	—	172	2	no	—
523	D₄	—	172	2	no	—
524	D₄	—	172	2	no	—
525	D₄	—	172	2	no	—
526	D₄	—	172	1	no	—
527	D₄	—	172	1	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	8	2	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	86	2	no	—
533	C₂×C₄	—	172	1	no	—
534	C₂×C₄	—	172	1	no	—
535	C₂×C₄	—	172	2	no	—
536	C₂×C₄	—	172	2	no	—
537	C₂×C₄	—	172	2	no	—
538	C₂×C₄	—	172	2	no	—
539	C₂×C₄	#13063283	1	1	yes	characteristic
540	C₂×C₄	#13063283	1	1	yes	characteristic
541	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
542	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
543	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
544	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
545	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
546	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
547	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
548	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
549	C₂×C₄	#13063300	1	1	yes	characteristic
550	C₂×C₄	#13063300	1	1	yes	characteristic
551	C₂×C₄	#13063300	1	1	yes	characteristic
552	C₂×C₄	#13063300	1	1	yes	characteristic
553	C₂×C₄	#13063309	1	1	yes	characteristic
554	C₂×C₄	#13063309	1	1	yes	characteristic
555	C₂×C₄	#13063311	1	1	yes	characteristic
556	C₂×C₄	#13063311	1	1	yes	characteristic
557	C₂×C₄	#13063320	1	1	yes	characteristic
558	C₂×C₄	#13063320	1	1	yes	characteristic
559	C₂×C₄	#13063320	1	1	yes	characteristic
560	C₂×C₄	#13063320	1	1	yes	characteristic
561	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
562	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
564	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
565	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
566	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
567	C₈	—	2	4	no	—
568	C₈	—	86	4	no	—
569	C₈	—	86	4	no	—
570	C₈	—	172	2	no	—
571	C₂²	—	4	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	344	2	no	—
579	C₂²	—	344	2	no	—
580	C₂²	—	344	2	no	—
581	C₂²	—	172	2	no	—
582	C₂²	#14582791	1	1	yes	characteristic
583	C₂²	#14582791	1	1	yes	characteristic
584	C₂²	#14582791	1	1	yes	characteristic
585	C₂²	#14582791	1	1	yes	characteristic
586	C₂²	C₂×#13063283	1	1	yes	characteristic
587	C₂²	C₂×#13063309	1	1	yes	characteristic
588	C₂²	C₂×#13063311	1	1	yes	characteristic
589	C₄	—	4	4	no	—
590	C₄	—	8	2	no	—
591	C₄	—	172	2	no	—
592	C₄	#14582791	1	1	yes	characteristic
593	C₄	#14582791	1	1	yes	characteristic
594	C₄	#14582791	1	1	yes	characteristic
595	C₄	#14582791	1	1	yes	characteristic
596	C₄	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
597	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
598	C₄	C₂×#13063300	1	1	yes	characteristic
599	C₄	C₂×#13063320	1	1	yes	characteristic
600	C₂	—	2	1	no	—
601	C₂	—	2	1	no	—
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	344	2	no	—
608	C₂	C₂×#14582791	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13063300
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1733	C₂
socle	C₂×C₄₃	C₂×#388
prime radical	C₂²×#10621898	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1733	D₄₃
hypocenter	C₄₃	#21080
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
1. C₂×#14582948	C₂	semidirect
5. #19143014	C₂	semidirect
6. #19135265	C₂	semidirect
7. C₂×#14582669	C₂	semidirect
8. C₄₃×#1733	C₂	semidirect
14. #14582948	C₂²	semidirect
22. #14582881	C₄	semidirect
24. C₂×#13063243	C₄	semidirect
25. C₂×#13063241	C₄	semidirect
28. C₄×#10621877	C₂²	semidirect
29. #14582669	C₂²	semidirect
33. C₄₃×#339	C₂²	semidirect
74. #13063243	C₂×C₄	semidirect
75. #13063241	C₂×C₄	semidirect
303. #1733	D₄₃	semidirect
337. #339	C₂×D₄₃	semidirect
338. C₄₃	#21080	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582948	2
C₂×#14582917	2
C₂×#14582881	2
#19143014	2
#19135265	2
C₂×#14582669	2
C₄₃×#1733	2
#21080	43