Subgroups — #25103130

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#19137288	C₂	1	2	yes	maximal, complemented
4	#19135461	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135328	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135292	C₂	1	2	yes	maximal, complemented
7	#19135033	C₂	1	2	yes	maximal, complemented
8	#19134624	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13063259	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134421	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
13	C₂×#13063299	C₂²	1	2	yes	—
14	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
15	#14583135	C₄	1	8	yes	complemented
16	C₄×D₃₄₄	—	2	4	no	—
17	C₂×#13063259	C₂²	1	1	yes	characteristic
18	C₂×#13063259	C₂²	1	1	yes	characteristic
19	C₂×#13063259	C₂²	1	1	yes	characteristic
20	C₂×#13063247	C₂²	1	2	yes	—
21	C₂×#13063247	C₂²	1	2	yes	—
22	C₂×#13063247	C₂²	1	2	yes	—
23	#14582801	C₂²	1	2	yes	—
24	#14582799	—	2	2	no	—
25	#14582797	C₂²	1	2	yes	—
26	#14582789	—	2	2	no	—
27	#14582775	—	2	2	no	—
28	#14582770	—	2	2	no	—
29	#14582759	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
31	#14582662	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#405	—	2	4	no	—
38	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂²×D₁₇₂	C₂³	1	2	yes	—
43	C₂²×C₂²⋊D₄₃	—	2	2	no	—
44	C₂²×C₄×D₄₃	—	2	2	no	—
45	C₂×D₃₄₄	—	2	2	no	—
46	C₂×D₃₄₄	—	2	2	no	—
47	C₂×D₃₄₄	C₂×C₄	1	4	yes	—
48	#13063299	—	2	4	no	—
49	#13063299	C₂×C₄	1	8	yes	complemented
50	C₄×D₁₇₂	—	2	4	no	—
51	C₄×D₁₇₂	—	2	4	no	—
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
57	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
60	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	#13063259	—	2	2	no	—
63	#13063259	—	2	2	no	—
64	#13063259	C₂×C₄	1	4	yes	complemented
65	#13063247	—	2	4	no	—
66	#13063247	—	2	4	no	—
67	#13063247	C₂×C₄	1	8	yes	complemented
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₄₃	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	2	no	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂²×C₈×C₄₃	—	2	2	no	—
76	C₂²×C₈×C₄₃	—	2	2	no	—
77	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	#117×C₄₃	—	2	2	no	—
83	#117×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	#97×C₄₃	—	2	2	no	—
91	#97×C₄₃	—	2	2	no	—
92	C₄×C₈×C₄₃	—	2	2	no	—
93	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂³×D₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₃	—	2	8	no	—
109	C₂×C₂²⋊D₄₃	—	8	2	no	—
110	C₂×C₂²⋊D₄₃	—	8	2	no	—
111	C₂²×Dic₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	—	2	2	no	—
114	C₂×D₁₇₂	—	2	2	no	—
115	C₂×D₁₇₂	—	2	2	no	—
116	C₂×D₁₇₂	—	2	2	no	—
117	C₂×D₁₇₂	—	2	2	no	—
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
120	C₂×C₄×D₄₃	—	4	4	no	—
121	C₂×C₄×D₄₃	—	8	2	no	—
122	C₂×C₄×D₄₃	—	8	2	no	—
123	M₁₆×C₄₃	—	2	8	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	—	2	1	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	8	no	—
131	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
132	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₃	#41	1	2	yes	—
136	C₂×C₈×C₄₃	#41	1	2	yes	—
137	C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₂²⋊C₄×C₄₃	—	2	2	no	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₄²×C₄₃	—	2	1	no	—
143	C₄²×C₄₃	C₂×D₄	1	2	yes	—
144	C₄²×C₄₃	#41	1	2	yes	—
145	C₂²⋊Dic₄₃	—	8	2	no	—
146	(C₂×D₄₃)⋊C₄	—	2	8	no	—
147	(C₂×D₄₃)⋊C₄	—	4	4	no	—
148	(C₂×D₄₃)⋊C₄	—	8	2	no	—
149	(C₂×D₄₃)⋊C₄	—	8	2	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₄⋊Dic₄₃	—	2	2	no	—
152	C₄⋊Dic₄₃	—	2	2	no	—
153	C₄⋊Dic₄₃	—	2	2	no	—
154	C₄⋊Dic₄₃	—	2	2	no	—
155	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
156	Dic₄₃⋊C₄	—	8	2	no	—
157	C₄×Dic₄₃	—	8	2	no	—
158	D₃₄₄	—	2	8	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	—	2	1	no	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	—	2	1	no	—
165	C₂³×C₄₃	C₄×D₄	1	2	yes	—
166	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂²×D₄₃	—	2	4	no	—
168	C₂²×D₄₃	—	4	2	no	—
169	C₂²×D₄₃	—	4	2	no	—
170	C₂²×D₄₃	—	4	2	no	—
171	C₂²×D₄₃	—	4	2	no	—
172	C₂²×D₄₃	—	4	2	no	—
173	C₂²×D₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₃	#121	1	2	yes	—
192	C₂×C₄×C₄₃	#121	1	2	yes	—
193	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₄₃	—	8	8	no	—
200	C₂×Dic₄₃	—	2	4	no	—
201	C₂×Dic₄₃	—	4	2	no	—
202	C₂×Dic₄₃	—	4	2	no	—
203	C₂×Dic₄₃	—	4	2	no	—
204	C₂×Dic₄₃	—	4	2	no	—
205	C₂×Dic₄₃	—	4	2	no	—
206	C₂×Dic₄₃	—	4	2	no	—
207	C₂×Dic₄₃	—	4	2	no	—
208	C₂×Dic₄₃	—	4	2	no	—
209	D₁₇₂	—	2	4	no	—
210	D₁₇₂	—	2	4	no	—
211	D₁₇₂	—	4	2	no	—
212	D₁₇₂	—	4	2	no	—
213	C₄×D₄₃	—	8	8	no	—
214	C₈×C₄₃	—	2	2	no	—
215	C₈×C₄₃	—	2	2	no	—
216	C₈×C₄₃	—	2	2	no	—
217	C₈×C₄₃	C₄×D₄	1	4	yes	—
218	#21524	—	43	1	no	maximal, Sylow
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	2	2	no	—
222	C₂²×C₄₃	—	4	1	no	—
223	C₂²×C₄₃	—	4	1	no	—
224	C₂²×C₄₃	—	4	1	no	—
225	C₂²×C₄₃	—	4	1	no	—
226	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
228	C₂²×C₄₃	#532	1	1	yes	characteristic
229	C₂²×C₄₃	#576	1	1	yes	characteristic
230	C₂²×C₄₃	#576	1	1	yes	characteristic
231	C₂²×C₄₃	#576	1	1	yes	characteristic
232	C₂²×C₄₃	#578	1	1	yes	characteristic
233	C₂×D₄₃	—	4	4	no	—
234	C₂×D₄₃	—	4	4	no	—
235	C₂×D₄₃	—	4	4	no	—
236	C₂×D₄₃	—	8	2	no	—
237	C₂×D₄₃	—	8	2	no	—
238	C₂×D₄₃	—	8	2	no	—
239	C₂×D₄₃	—	8	2	no	—
240	C₄×C₄₃	—	2	2	no	—
241	C₄×C₄₃	—	2	2	no	—
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	4	1	no	—
244	C₄×C₄₃	—	4	1	no	—
245	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
247	C₄×C₄₃	#525	1	1	yes	characteristic
248	C₄×C₄₃	#529	1	1	yes	characteristic
249	Dic₄₃	—	4	4	no	—
250	Dic₄₃	—	8	2	no	—
251	Dic₄₃	—	8	2	no	—
252	C₂×#466	—	43	1	no	—
253	C₂×C₄×D₈	—	43	1	no	—
254	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
255	#2324	—	43	2	no	—
256	#1970	—	43	1	no	—
257	#1942	—	43	1	no	—
258	#1936	—	43	2	no	—
259	#1895	—	43	2	no	—
260	#1808	—	43	1	no	—
261	C₄×#107	—	43	1	no	—
262	#1762	—	43	2	no	—
263	C₂×C₄₃	—	4	2	no	—
264	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
265	C₂×C₄₃	#2948	1	1	yes	characteristic
266	C₂×C₄₃	#2951	1	1	yes	characteristic
267	C₂×C₄₃	#3058	1	1	yes	characteristic
268	C₂×C₄₃	#3061	1	1	yes	characteristic
269	C₂×C₄₃	#3175	1	1	yes	characteristic
270	C₂×C₄₃	#3176	1	1	yes	characteristic
271	D₄₃	—	8	4	no	—
272	C₂²×D₈	—	43	1	no	—
273	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
274	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
275	C₂×#121	—	43	2	no	—
276	C₂×C₄×D₄	—	43	2	no	—
277	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
278	#466	—	43	8	no	—
279	C₄×D₈	—	86	4	no	—
280	C₂×#107	—	43	1	no	—
281	C₂×#107	—	43	1	no	—
282	C₂×#107	—	43	1	no	—
283	C₂×#102	—	43	2	no	—
284	C₂×#102	—	43	2	no	—
285	C₂×#102	—	43	2	no	—
286	#405	—	2	4	no	—
287	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
288	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
289	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
290	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
291	#390	—	43	2	no	—
292	#390	—	86	2	no	—
293	#389	—	43	2	no	—
294	#388	—	86	2	no	—
295	#386	—	86	2	no	—
296	#385	—	86	2	no	—
297	#380	—	43	2	no	—
298	C₄×C₄⋊C₄	—	43	2	no	—
299	#340	—	43	2	no	—
300	#340	—	43	2	no	—
301	#340	—	43	2	no	—
302	C₄₃	#21524	1	1	yes	characteristic, complemented, Sylow
303	C₂²×D₄	—	43	2	no	—
304	C₂²×D₄	—	86	2	no	—
305	C₂³×C₄	—	86	2	no	—
306	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
307	C₂×D₈	—	43	4	no	—
308	C₂×D₈	—	86	2	no	—
309	C₂×D₈	—	86	2	no	—
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	—	2	2	no	—
315	C₂²×C₈	C₄×D₄₃	1	4	yes	complemented
316	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
319	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	#121	—	43	8	no	—
321	#121	—	86	4	no	—
322	C₄×D₄	—	86	4	no	—
323	C₄×D₄	—	86	4	no	—
324	#117	—	2	2	no	—
325	#117	—	2	2	no	—
326	C₂×C₄⋊C₄	—	43	2	no	—
327	C₂×C₄⋊C₄	—	43	2	no	—
328	C₂×C₄⋊C₄	—	43	2	no	—
329	C₂×C₄⋊C₄	—	86	2	no	—
330	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₁₇₂	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	—	86	2	no	—
333	C₂×C₂²⋊C₄	—	86	2	no	—
334	C₂×C₂²⋊C₄	—	86	2	no	—
335	C₂×C₂²⋊C₄	—	86	2	no	—
336	C₂×C₂²⋊C₄	—	86	2	no	—
337	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	D₁₇₂	1	1	yes	characteristic
339	C₂×C₄²	—	86	2	no	—
340	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
342	#107	—	43	4	no	—
343	#107	—	86	2	no	—
344	#107	—	86	2	no	—
345	#102	—	43	8	no	—
346	#102	—	86	4	no	—
347	#102	—	86	4	no	—
348	#97	—	2	2	no	—
349	#97	—	2	2	no	—
350	C₄×C₈	—	2	2	no	—
351	C₄×C₈	C₂²⋊D₄₃	1	4	yes	complemented
352	#95	—	86	2	no	—
353	#95	—	86	2	no	—
354	#95	—	86	2	no	—
355	C₂⁴	—	86	2	no	—
356	C₂⁴	C₂×D₁₇₂	1	1	yes	characteristic
357	C₂×D₄	—	43	4	no	—
358	C₂×D₄	—	86	8	no	—
359	C₂×D₄	—	86	2	no	—
360	C₂×D₄	—	86	2	no	—
361	C₂×D₄	—	86	2	no	—
362	C₂×D₄	—	86	2	no	—
363	C₂×D₄	—	86	2	no	—
364	C₂×D₄	—	344	2	no	—
365	C₂×D₄	—	344	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	86	2	no	—
371	C₂²×C₄	—	86	2	no	—
372	C₂²×C₄	—	86	2	no	—
373	C₂²×C₄	—	344	2	no	—
374	C₂²×C₄	—	344	2	no	—
375	C₂²×C₄	—	172	4	no	—
376	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
377	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
382	C₂²×C₄	#10621898	1	2	yes	—
383	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
384	D₈	—	86	8	no	—
385	M₁₆	—	2	8	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	8	no	—
393	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
394	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
395	C₂×C₈	#10621898	1	2	yes	—
396	C₂×C₈	#10621898	1	2	yes	—
397	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
398	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	43	4	no	—
402	C₄⋊C₄	—	86	2	no	—
403	C₄⋊C₄	—	86	2	no	—
404	C₄⋊C₄	—	86	2	no	—
405	C₄⋊C₄	—	86	2	no	—
406	C₄⋊C₄	—	86	2	no	—
407	C₄⋊C₄	—	344	2	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	2	no	—
410	C₂²⋊C₄	—	86	8	no	—
411	C₂²⋊C₄	—	344	2	no	—
412	C₂²⋊C₄	—	344	2	no	—
413	C₂²⋊C₄	—	344	2	no	—
414	C₂²⋊C₄	—	172	4	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	2	1	no	—
417	C₄²	—	344	2	no	—
418	C₄²	#10621898	1	2	yes	—
419	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	86	4	no	—
427	C₂³	—	172	2	no	—
428	C₂³	—	172	2	no	—
429	C₂³	—	172	2	no	—
430	C₂³	—	172	2	no	—
431	C₂³	—	172	2	no	—
432	C₂³	—	172	2	no	—
433	C₂³	C₄×D₁₇₂	1	2	yes	—
434	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
435	D₄	—	86	4	no	—
436	D₄	—	86	4	no	—
437	D₄	—	344	8	no	—
438	D₄	—	172	2	no	—
439	D₄	—	172	2	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	86	4	no	—
457	C₂×C₄	—	344	8	no	—
458	C₂×C₄	—	172	2	no	—
459	C₂×C₄	—	172	2	no	—
460	C₂×C₄	—	172	2	no	—
461	C₂×C₄	—	172	2	no	—
462	C₂×C₄	—	172	2	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	—	172	2	no	—
465	C₂×C₄	—	172	2	no	—
466	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
467	C₂×C₄	#13063299	1	2	yes	—
468	C₂×C₄	#13063299	1	2	yes	—
469	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
471	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
472	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
473	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
474	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	C₄×C₂²⋊D₄₃	1	4	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	344	2	no	—
487	C₂²	—	344	2	no	—
488	C₂²	—	344	2	no	—
489	C₂²	—	344	2	no	—
490	C₂²	—	172	4	no	—
491	C₂²	—	172	4	no	—
492	C₂²	—	172	4	no	—
493	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
494	C₂²	C₂×#13063299	1	1	yes	characteristic
495	C₂²	#14583449	1	1	yes	characteristic
496	C₂²	#14583704	1	1	yes	characteristic
497	C₂²	#14583704	1	1	yes	characteristic
498	C₂²	#14583704	1	1	yes	characteristic
499	C₂²	#14583716	1	1	yes	characteristic
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	2	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	1	no	—
505	C₄	—	344	2	no	—
506	C₄	—	344	2	no	—
507	C₄	—	172	4	no	—
508	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
509	C₄	C₄×#10621898	1	1	yes	characteristic
510	C₄	#14583410	1	1	yes	characteristic
511	C₄	#14583433	1	1	yes	characteristic
512	C₂	—	4	2	no	—
513	C₂	—	344	4	no	—
514	C₂	C₄×#13063299	1	1	yes	characteristic
515	C₂	#19143448	1	1	yes	characteristic
516	C₂	#19143472	1	1	yes	characteristic
517	C₂	#19144243	1	1	yes	characteristic
518	C₂	#19144265	1	1	yes	characteristic
519	C₂	#19145234	1	1	yes	characteristic
520	C₂	#19145245	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂×#14583135	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#21524
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#117 ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₃₄₄	C₂	semidirect
3. #19137288	C₂	semidirect
4. #19135461	C₂	semidirect
5. #19135328	C₂	semidirect
6. #19135292	C₂	semidirect
7. #19135033	C₂	semidirect
8. #19134624	C₂	semidirect
9. C₄×#13063259	C₂	semidirect
10. #19134421	C₂	semidirect
11. C₂×C₄₃×#405	C₂	semidirect
15. #14583135	C₄	semidirect
49. #13063299	C₂×C₄	semidirect
64. #13063259	C₂×C₄	semidirect
67. #13063247	C₂×C₄	semidirect
77. C₂²×C₈×C₄₃	C₂×C₄	semidirect
93. C₄×C₈×C₄₃	D₄	semidirect
254. C₂×#405	D₄₃	semidirect
302. C₄₃	#21524	semidirect
315. C₂²×C₈	C₄×D₄₃	semidirect
351. C₄×C₈	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583135	2
C₂×C₄×D₃₄₄	2
#19137288	2
#19135461	2
#19135328	2
#19135292	2
#19135033	2
#19134624	2
C₄×#13063259	2
#19134421	2
C₂×C₄₃×#405	2
#21524	43