Subgroups — #25003609

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063253	C₂	1	1	yes	maximal, characteristic
2	#19143112	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582872	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582669	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134304	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582659	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	C₂×#13063253	—	2	2	no	—
13	C₂×#13063253	—	2	2	no	—
14	C₂×#13063253	—	2	2	no	—
15	#14582907	C₄	1	2	yes	complemented
16	#14582903	C₄	1	2	yes	complemented
17	#14582898	—	2	2	no	—
18	#14582893	—	2	2	no	—
19	#14582872	—	2	2	no	—
20	#14582872	—	2	2	no	—
21	C₂×#13063239	—	2	2	no	—
22	#14582669	—	2	2	no	—
23	#14582659	—	2	2	no	—
24	#14582658	—	2	2	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#389	—	2	2	no	—
29	C₄₃×#385	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
31	C₂×#10621898	—	2	1	no	—
32	C₂×#10621898	—	2	1	no	—
33	C₂×#10621898	—	2	1	no	—
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	D₄	1	2	yes	—
42	C₂×#10621898	Q₈	1	2	yes	—
43	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₂²⋊D₄₃	—	2	1	no	—
46	C₂²×C₄×D₄₃	—	2	1	no	—
47	C₂×#10621877	—	2	1	no	—
48	C₂×#10621877	—	2	1	no	—
49	C₂×#10621877	—	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	C₂×C₄	1	2	yes	—
58	C₂×#10621877	D₄	1	2	yes	—
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	C₂²×C₄₃⋊C₈	—	2	1	no	—
61	#13063284	—	2	1	no	—
62	#13063284	—	2	1	no	—
63	#13063284	—	2	1	no	—
64	#13063284	D₄	1	2	yes	—
65	C₂×C₄⋊Dic₄₃	—	2	1	no	—
66	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
67	C₂×C₄×Dic₄₃	—	2	1	no	—
68	#13063253	—	2	8	no	—
69	#13063248	—	2	4	no	—
70	#13063245	—	2	4	no	—
71	#13063239	—	2	8	no	—
72	C₂³×C₄×C₄₃	—	2	1	no	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	#117×C₄₃	—	2	1	no	—
75	#117×C₄₃	—	2	1	no	—
76	#117×C₄₃	—	2	1	no	—
77	#117×C₄₃	—	2	1	no	—
78	#117×C₄₃	—	2	1	no	—
79	#117×C₄₃	—	2	1	no	—
80	#117×C₄₃	C₂×C₄	1	2	yes	—
81	#117×C₄₃	D₄	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
85	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
87	C₂×C₄²×C₄₃	—	2	1	no	—
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	—	2	1	no	—
91	C₂×C₄²×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	—	2	1	no	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	D₄	1	2	yes	—
95	#95×C₄₃	—	2	4	no	—
96	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂³×D₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	4	4	no	—
102	C₂²×C₄×C₄₃	—	4	1	no	—
103	C₂²×C₄×C₄₃	—	4	1	no	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	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	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×Q₈	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	#41	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	C₂²×Dic₄₃	—	4	1	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	—	2	2	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	#10621898	—	4	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	—	2	1	no	—
147	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	complemented
148	C₂×C₄×D₄₃	—	2	2	no	—
149	C₂×C₄×D₄₃	—	2	2	no	—
150	C₂×C₄×D₄₃	—	4	1	no	—
151	C₂×C₄×D₄₃	—	4	1	no	—
152	C₂×C₄×D₄₃	—	4	1	no	—
153	C₂×C₄×D₄₃	—	4	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	—	2	1	no	—
159	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	complemented
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	4	8	no	—
162	C₄⋊C₄×C₄₃	—	4	1	no	—
163	C₄⋊C₄×C₄₃	—	4	1	no	—
164	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
165	C₂²⋊C₄×C₄₃	—	2	2	no	—
166	C₂²⋊C₄×C₄₃	—	2	2	no	—
167	C₂²⋊C₄×C₄₃	—	2	2	no	—
168	C₂²⋊C₄×C₄₃	—	2	2	no	—
169	C₄²×C₄₃	—	2	2	no	—
170	C₄²×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	—	2	2	no	—
172	C₄²×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	—	4	1	no	—
174	C₄²×C₄₃	—	4	1	no	—
175	C₄²×C₄₃	—	4	1	no	—
176	C₄²×C₄₃	—	4	1	no	—
177	C₂²⋊Dic₄₃	—	2	2	no	—
178	C₂²⋊Dic₄₃	—	4	1	no	—
179	C₄⋊Dic₄₃	—	2	2	no	—
180	C₄⋊Dic₄₃	—	4	1	no	—
181	C₄×Dic₄₃	—	2	2	no	—
182	C₄×Dic₄₃	—	4	1	no	—
183	#10621877	—	2	2	no	—
184	#10621877	—	2	2	no	—
185	#10621877	—	2	2	no	—
186	#10621877	—	2	2	no	—
187	#10621877	—	4	1	no	—
188	#10621877	—	4	1	no	—
189	#10621877	—	4	1	no	—
190	#10621877	—	4	1	no	—
191	C₂×C₄₃⋊C₈	—	2	2	no	—
192	C₂×C₄₃⋊C₈	—	2	2	no	—
193	C₂×C₄₃⋊C₈	—	4	1	no	—
194	C₂×C₄₃⋊C₈	—	4	1	no	—
195	C₂×C₄₃⋊C₈	—	4	1	no	—
196	C₂×C₄₃⋊C₈	—	4	1	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂³×C₄₃	#120	1	1	yes	characteristic
200	C₂³×C₄₃	#120	1	1	yes	characteristic
201	C₂³×C₄₃	#121	1	1	yes	characteristic
202	C₂³×C₄₃	#121	1	1	yes	characteristic
203	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
204	C₂³×C₄₃	#124	1	1	yes	characteristic
205	C₂²×D₄₃	—	2	2	no	—
206	C₂²×D₄₃	—	4	1	no	—
207	C₂²×D₄₃	—	4	1	no	—
208	C₂²×D₄₃	—	8	2	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	4	4	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	4	no	—
214	C₂×C₄×C₄₃	—	4	4	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	4	no	—
217	C₂×C₄×C₄₃	—	4	2	no	—
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	#117	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	#120	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	#121	1	1	yes	characteristic
230	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#126	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
246	C₂²⋊D₄₃	—	4	2	no	—
247	C₂²⋊D₄₃	—	4	2	no	—
248	C₂²⋊D₄₃	—	4	2	no	—
249	C₂²⋊D₄₃	—	4	2	no	—
250	C₂×Dic₄₃	—	2	2	no	—
251	C₂×Dic₄₃	—	4	1	no	—
252	C₂×Dic₄₃	—	4	1	no	—
253	C₂×Dic₄₃	—	4	2	no	—
254	C₂×Dic₄₃	—	8	2	no	—
255	D₁₇₂	—	2	2	no	—
256	D₁₇₂	—	2	2	no	—
257	D₁₇₂	—	4	1	no	—
258	D₁₇₂	—	4	1	no	—
259	C₄×D₄₃	—	4	2	no	—
260	C₄×D₄₃	—	4	2	no	—
261	C₄×D₄₃	—	4	2	no	—
262	C₄×D₄₃	—	4	2	no	—
263	Dic₈₆	—	2	2	no	—
264	Dic₈₆	—	2	2	no	—
265	Dic₈₆	—	4	1	no	—
266	Dic₈₆	—	4	1	no	—
267	C₄₃⋊C₈	—	4	2	no	—
268	C₄₃⋊C₈	—	4	2	no	—
269	#11060	—	43	1	no	maximal, Sylow
270	C₂²×C₄₃	—	2	2	no	—
271	C₂²×C₄₃	—	2	2	no	—
272	C₂²×C₄₃	—	2	2	no	—
273	C₂²×C₄₃	—	4	1	no	—
274	C₂²×C₄₃	—	4	1	no	—
275	C₂²×C₄₃	—	4	1	no	—
276	C₂²×C₄₃	—	4	1	no	—
277	C₂²×C₄₃	#385	1	1	yes	characteristic
278	C₂²×C₄₃	#386	1	1	yes	characteristic
279	C₂²×C₄₃	#388	1	1	yes	characteristic
280	C₂²×C₄₃	#392	1	1	yes	characteristic
281	C₂²×C₄₃	#393	1	1	yes	characteristic
282	C₂²×C₄₃	#394	1	1	yes	characteristic
283	C₂²×C₄₃	#396	1	1	yes	characteristic
284	C₂×D₄₃	—	4	2	no	—
285	C₂×D₄₃	—	8	2	no	—
286	C₂×D₄₃	—	8	2	no	—
287	C₂×D₄₃	—	8	2	no	—
288	C₄×C₄₃	—	4	4	no	—
289	C₄×C₄₃	—	4	4	no	—
290	C₄×C₄₃	—	8	2	no	—
291	C₄×C₄₃	#380	1	1	yes	characteristic
292	C₄×C₄₃	#385	1	1	yes	characteristic
293	C₄×C₄₃	#388	1	1	yes	characteristic
294	C₄×C₄₃	#390	1	1	yes	characteristic
295	C₄×C₄₃	#394	1	1	yes	characteristic
296	C₄×C₄₃	#396	1	1	yes	characteristic
297	C₄×C₄₃	#397	1	1	yes	characteristic
298	C₄×C₄₃	#399	1	1	yes	characteristic
299	Dic₄₃	—	4	2	no	—
300	Dic₄₃	—	8	2	no	—
301	C₂²×#104	—	43	1	no	—
302	#2896	—	43	1	no	—
303	C₂×#410	—	43	1	no	—
304	#2296	D₄₃	1	1	yes	characteristic, complemented
305	C₂×#344	—	43	1	no	—
306	#1733	—	43	1	no	—
307	C₂×#339	—	43	1	no	—
308	C₂×C₄₃	—	2	1	no	—
309	C₂×C₄₃	—	2	1	no	—
310	C₂×C₄₃	—	2	1	no	—
311	C₂×C₄₃	—	2	1	no	—
312	C₂×C₄₃	—	2	1	no	—
313	C₂×C₄₃	—	2	1	no	—
314	C₂×C₄₃	#1439	1	1	yes	characteristic
315	C₂×C₄₃	#1906	1	2	yes	—
316	D₄₃	—	8	2	no	—
317	C₂²×#41	—	43	1	no	—
318	C₂²×M₁₆	—	43	1	no	—
319	C₂²×M₁₆	—	43	1	no	—
320	C₂×#117	—	43	1	no	—
321	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
322	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
323	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
324	C₂×#104	—	86	2	no	—
325	C₂×#104	—	86	2	no	—
326	C₂×#104	—	86	2	no	—
327	#419	—	43	2	no	—
328	#418	—	43	2	no	—
329	#417	—	86	2	no	—
330	#416	—	86	2	no	—
331	#410	—	86	2	no	—
332	#410	—	86	2	no	—
333	C₂×#99	—	86	2	no	—
334	#389	—	2	2	no	—
335	#385	—	2	2	no	—
336	C₄×C₄⋊C₄	—	2	2	no	—
337	#344	—	86	2	no	—
338	#339	—	86	2	no	—
339	#339	—	86	2	no	—
340	C₄₃	#11060	1	1	yes	characteristic, complemented, Sylow
341	C₂×#41	—	43	2	no	—
342	C₂×#41	—	43	2	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	C₂×#41	—	86	1	no	—
352	C₂×#41	—	86	1	no	—
353	C₂²×Q₈	—	43	1	no	—
354	C₂²×D₄	—	43	1	no	—
355	C₂²×D₄	—	86	1	no	—
356	C₂³×C₄	—	2	1	no	—
357	C₂³×C₄	—	86	1	no	—
358	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
359	C₂×M₁₆	—	43	2	no	—
360	C₂×M₁₆	—	43	2	no	—
361	C₂×M₁₆	—	86	1	no	—
362	C₂×M₁₆	—	86	1	no	—
363	C₂×M₁₆	—	86	1	no	—
364	C₂×M₁₆	—	86	1	no	—
365	C₂×M₁₆	—	86	1	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	C₂²×C₈	—	86	1	no	—
372	C₂²×C₈	—	86	1	no	—
373	#117	—	2	1	no	—
374	#117	—	2	1	no	—
375	#117	—	2	1	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	43	2	no	—
380	#117	—	86	1	no	—
381	#117	—	86	1	no	—
382	#117	—	86	1	no	—
383	#117	C₄×D₄₃	1	2	yes	—
384	#117	D₁₇₂	1	2	yes	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	86	1	no	—
388	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	86	1	no	—
391	C₂×C₂²⋊C₄	C₂²⋊D₄₃	1	2	yes	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	—	2	1	no	—
396	C₂×C₄²	—	2	1	no	—
397	C₂×C₄²	—	2	1	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	—	86	1	no	—
400	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
401	#104	—	86	8	no	—
402	#103	—	86	4	no	—
403	#102	—	86	4	no	—
404	#99	—	86	8	no	—
405	#95	—	2	4	no	—
406	C₂⁴	—	86	1	no	—
407	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
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	—	86	2	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	#41	—	172	1	no	—
424	C₂×Q₈	—	43	2	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×Q₈	—	86	1	no	—
430	C₂×D₄	—	43	2	no	—
431	C₂×D₄	—	86	2	no	—
432	C₂×D₄	—	86	2	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	—	86	1	no	—
438	C₂×D₄	—	172	1	no	—
439	C₂×D₄	—	172	1	no	—
440	C₂×D₄	—	172	1	no	—
441	C₂×D₄	—	172	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	4	4	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	—	4	1	no	—
448	C₂²×C₄	—	86	1	no	—
449	C₂²×C₄	—	86	2	no	—
450	C₂²×C₄	—	86	2	no	—
451	C₂²×C₄	—	172	1	no	—
452	C₂²×C₄	—	172	1	no	—
453	C₂²×C₄	—	172	1	no	—
454	C₂²×C₄	—	172	1	no	—
455	C₂²×C₄	—	172	1	no	—
456	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
458	C₂²×C₄	#10621898	1	1	yes	characteristic
459	C₂²×C₄	#10621898	1	1	yes	characteristic
460	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
461	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
462	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
463	C₂²×C₄	#10621900	1	1	yes	characteristic
464	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
465	C₂²×C₄	#10621902	1	1	yes	characteristic
466	C₂²×C₄	#10621902	1	1	yes	characteristic
467	C₂²×C₄	#10621902	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
470	M₁₆	—	86	2	no	—
471	M₁₆	—	86	2	no	—
472	M₁₆	—	86	2	no	—
473	M₁₆	—	86	2	no	—
474	M₁₆	—	172	1	no	—
475	M₁₆	—	172	1	no	—
476	M₁₆	—	172	1	no	—
477	M₁₆	—	172	1	no	—
478	C₂×C₈	—	86	2	no	—
479	C₂×C₈	—	86	2	no	—
480	C₂×C₈	—	172	1	no	—
481	C₂×C₈	—	172	1	no	—
482	C₂×C₈	—	172	1	no	—
483	C₂×C₈	—	172	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	4	8	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	86	2	no	—
489	C₄⋊C₄	—	172	1	no	—
490	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	86	2	no	—
496	C₂²⋊C₄	—	172	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	4	1	no	—
502	C₄²	—	4	1	no	—
503	C₄²	—	4	1	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	86	2	no	—
506	C₄²	—	172	1	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	86	2	no	—
509	C₂³	—	344	2	no	—
510	C₂³	—	172	1	no	—
511	C₂³	—	172	1	no	—
512	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
513	C₂³	#13063293	1	1	yes	characteristic
514	C₂³	#13063294	1	1	yes	characteristic
515	C₂³	#13063297	1	1	yes	characteristic
516	C₂³	#13063299	1	1	yes	characteristic
517	C₂³	#13063301	1	1	yes	characteristic
518	C₂³	#13063314	1	1	yes	characteristic
519	Q₈	—	86	2	no	—
520	Q₈	—	86	2	no	—
521	Q₈	—	172	1	no	—
522	Q₈	—	172	1	no	—
523	D₄	—	86	2	no	—
524	D₄	—	86	2	no	—
525	D₄	—	172	2	no	—
526	D₄	—	172	2	no	—
527	D₄	—	172	2	no	—
528	D₄	—	172	2	no	—
529	D₄	—	172	1	no	—
530	D₄	—	172	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	4	4	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	4	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	86	2	no	—
541	C₂×C₄	—	344	2	no	—
542	C₂×C₄	—	172	2	no	—
543	C₂×C₄	—	172	1	no	—
544	C₂×C₄	—	172	1	no	—
545	C₂×C₄	—	172	2	no	—
546	C₂×C₄	—	172	2	no	—
547	C₂×C₄	—	172	2	no	—
548	C₂×C₄	—	172	2	no	—
549	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
550	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
551	C₂×C₄	#13063283	1	1	yes	characteristic
552	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
553	C₂×C₄	#13063287	1	1	yes	characteristic
554	C₂×C₄	#13063287	1	1	yes	characteristic
555	C₂×C₄	#13063293	1	1	yes	characteristic
556	C₂×C₄	#13063296	1	1	yes	characteristic
557	C₂×C₄	#13063297	1	1	yes	characteristic
558	C₂×C₄	#13063299	1	1	yes	characteristic
559	C₂×C₄	#13063300	1	1	yes	characteristic
560	C₂×C₄	#13063300	1	1	yes	characteristic
561	C₂×C₄	#13063300	1	1	yes	characteristic
562	C₂×C₄	#13063301	1	1	yes	characteristic
563	C₂×C₄	#13063301	1	1	yes	characteristic
564	C₂×C₄	#13063303	1	1	yes	characteristic
565	C₂×C₄	#13063303	1	1	yes	characteristic
566	C₂×C₄	#13063305	1	1	yes	characteristic
567	C₂×C₄	#13063308	1	1	yes	characteristic
568	C₂×C₄	#13063310	1	1	yes	characteristic
569	C₂×C₄	#13063310	1	1	yes	characteristic
570	C₂×C₄	#13063310	1	1	yes	characteristic
571	C₂×C₄	#13063310	1	1	yes	characteristic
572	C₂×C₄	#13063314	1	1	yes	characteristic
573	C₂×C₄	#13063314	1	1	yes	characteristic
574	C₂×C₄	#13063320	1	1	yes	characteristic
575	C₂×C₄	#13063320	1	1	yes	characteristic
576	C₂×C₄	#13063321	1	1	yes	characteristic
577	C₈	—	172	2	no	—
578	C₈	—	172	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	4	1	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	344	2	no	—
587	C₂²	—	344	2	no	—
588	C₂²	—	344	2	no	—
589	C₂²	—	172	2	no	—
590	C₂²	#14582770	1	1	yes	characteristic
591	C₂²	#14582778	1	1	yes	characteristic
592	C₂²	#14582789	1	1	yes	characteristic
593	C₂²	#14582807	1	1	yes	characteristic
594	C₂²	#14582810	1	1	yes	characteristic
595	C₂²	#14582816	1	1	yes	characteristic
596	C₂²	#14582821	1	1	yes	characteristic
597	C₄	—	4	4	no	—
598	C₄	—	4	4	no	—
599	C₄	—	8	2	no	—
600	C₄	—	344	2	no	—
601	C₄	—	172	2	no	—
602	C₄	#14582756	1	1	yes	characteristic
603	C₄	#14582770	1	1	yes	characteristic
604	C₄	#14582789	1	1	yes	characteristic
605	C₄	#14582800	1	1	yes	characteristic
606	C₄	#14582816	1	1	yes	characteristic
607	C₄	#14582821	1	1	yes	characteristic
608	C₄	#14582825	1	1	yes	characteristic
609	C₄	#14582834	1	1	yes	characteristic
610	C₂	—	2	1	no	—
611	C₂	—	2	1	no	—
612	C₂	—	2	1	no	—
613	C₂	—	2	1	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	1	no	—
616	C₂	—	344	2	no	—
617	C₂	#19132837	1	1	yes	characteristic
618	C₂	#19135096	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063299
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#2296	C₂
socle	C₂²×C₄₃	#386
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#2296	D₄₃
hypocenter	C₄₃	#11060
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
4. C₂×#14582669	C₂	semidirect
5. #19134304	C₂	semidirect
6. C₂×#14582659	C₂	semidirect
7. C₄₃×#2296	C₂	semidirect
15. #14582907	C₄	semidirect
16. #14582903	C₄	semidirect
147. C₂×D₁₇₂	C₄⋊C₄	semidirect
159. C₂×Dic₈₆	C₄⋊C₄	semidirect
304. #2296	D₄₃	semidirect
340. C₄₃	#11060	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063253	2
#19143112	2
C₂×#14582872	2
C₂×#14582669	2
#19134304	2
C₂×#14582659	2
C₄₃×#2296	2
#11060	43