Subgroups — #25068337

Order 11008.

718 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143629	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#10621882	C₂	1	1	yes	maximal, characteristic
3	#19133507	C₂	1	2	yes	maximal, complemented
4	#19133424	C₂	1	2	yes	maximal, complemented
5	#19133422	C₂	1	2	yes	maximal, complemented
6	#19133417	C₂	1	2	yes	maximal, complemented
7	#19133356	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133038	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133037	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621882	C₄	1	1	yes	characteristic
13	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
14	C₄×#10621882	C₄	1	1	yes	characteristic
15	C₄×#10621882	C₄	1	1	yes	characteristic
16	C₄×#10621882	C₄	1	1	yes	characteristic
17	C₄×#10621882	C₄	1	1	yes	characteristic
18	C₄×#10621882	C₂²	1	1	yes	characteristic
19	C₄×#10621882	C₂²	1	1	yes	characteristic
20	C₄×#10621882	C₂²	1	1	yes	characteristic
21	C₄×#10621882	C₂²	1	1	yes	characteristic
22	#14582978	C₂²	1	2	yes	complemented
23	#14582969	—	2	2	no	—
24	C₈×D₁₇₂	C₂²	1	2	yes	complemented
25	#14582956	C₂²	1	1	yes	characteristic
26	C₂×#13063258	C₄	1	1	yes	characteristic
27	C₂×#13063246	C₄	1	1	yes	characteristic
28	C₂×#13063245	C₄	1	1	yes	characteristic
29	#14582861	—	2	1	no	—
30	C₂²⋊C₈×D₄₃	—	2	1	no	—
31	C₄×#10621877	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
33	#14582651	C₂²	1	2	yes	complemented
34	#14582649	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
36	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
37	#14582626	C₂²	1	2	yes	complemented
38	#14582626	C₂²	1	2	yes	complemented
39	#14582621	C₂²	1	2	yes	complemented
40	#14582620	C₂²	1	2	yes	complemented
41	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#436	C₂²	1	2	yes	complemented
43	C₄₃×#435	—	2	2	no	—
44	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
45	C₄₃×#432	C₂²	1	1	yes	characteristic
46	C₄₃×#431	C₂²	1	1	yes	characteristic
47	C₄₃×#407	—	2	1	no	—
48	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
49	C₂²×D₁₇₂	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	—	2	1	no	—
51	C₂×#10621882	—	2	4	no	—
52	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
55	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621872	—	2	2	no	—
58	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₄₃	—	2	2	no	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	—	2	1	no	—
63	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
64	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
66	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
69	#13063258	C₂×C₄	1	1	yes	characteristic
70	#13063258	C₂×C₄	1	1	yes	characteristic
71	#13063258	C₂×C₄	1	1	yes	characteristic
72	#13063258	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063246	C₂×C₄	1	1	yes	characteristic
75	#13063246	C₂×C₄	1	1	yes	characteristic
76	#13063246	C₂×C₄	1	1	yes	characteristic
77	#13063246	C₂×C₄	1	1	yes	characteristic
78	#13063245	C₂×C₄	1	1	yes	characteristic
79	#13063245	C₂×C₄	1	1	yes	characteristic
80	#13063245	C₂×C₄	1	1	yes	characteristic
81	#13063245	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
83	(C₂×D₄₃)⋊C₈	—	2	2	no	—
84	(C₂×D₄₃)⋊C₈	—	2	2	no	—
85	#13063236	—	2	1	no	—
86	#13063236	—	2	1	no	—
87	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
90	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
91	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
92	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	—	2	1	no	—
94	C₂×M₁₆×C₄₃	—	2	2	no	—
95	C₂²×C₈×C₄₃	—	2	2	no	—
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₄₃	—	2	1	no	—
108	C₂²⋊C₈×C₄₃	—	2	2	no	—
109	C₂²⋊C₈×C₄₃	—	2	2	no	—
110	C₂²⋊C₈×C₄₃	D₄	1	1	yes	characteristic
111	C₂²⋊C₈×C₄₃	D₄	1	1	yes	characteristic
112	#97×C₄₃	—	2	1	no	—
113	C₄×C₈×C₄₃	C₂³	1	2	yes	—
114	C₂⁴×C₄₃	—	2	1	no	—
115	C₂³×D₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	4	1	no	—
119	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	8	2	no	—
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
130	C₂²×Dic₄₃	—	2	1	no	—
131	C₂×D₁₇₂	—	2	1	no	—
132	C₂×D₁₇₂	—	2	2	no	—
133	C₂×D₁₇₂	—	4	1	no	—
134	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×C₄×D₄₃	—	2	1	no	—
138	C₂×C₄×D₄₃	—	2	1	no	—
139	C₂×C₄×D₄₃	—	2	1	no	—
140	C₂×C₄×D₄₃	—	8	2	no	—
141	M₁₆×C₄₃	—	8	2	no	—
142	C₂×C₈×C₄₃	—	2	2	no	—
143	C₂×C₈×C₄₃	—	8	2	no	—
144	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₄₃	—	2	1	no	—
147	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²⋊C₄×C₄₃	—	2	1	no	—
150	C₂²⋊C₄×C₄₃	—	2	1	no	—
151	C₂²⋊C₄×C₄₃	—	2	1	no	—
152	C₂²⋊C₄×C₄₃	—	2	1	no	—
153	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₃	#41	1	1	yes	characteristic
156	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
157	#10621882	—	2	2	no	—
158	#10621882	—	2	2	no	—
159	#10621882	—	2	2	no	—
160	#10621882	M₁₆	1	4	yes	complemented
161	(C₂×D₄₃)⋊C₄	—	2	1	no	—
162	(C₂×D₄₃)⋊C₄	—	2	1	no	—
163	(C₂×D₄₃)⋊C₄	—	2	1	no	—
164	(C₂×D₄₃)⋊C₄	—	2	1	no	—
165	C₄⋊Dic₄₃	—	2	1	no	—
166	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
168	#10621877	—	4	2	no	—
169	C₂×C₄₃⋊C₈	—	2	2	no	—
170	C₂×C₄₃⋊C₈	—	2	2	no	—
171	C₂×C₄₃⋊C₈	—	2	2	no	—
172	C₂×C₄₃⋊C₈	—	4	1	no	—
173	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	#10621872	—	8	2	no	—
178	C₈×D₄₃	—	8	2	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	1	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	8	1	no	—
184	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂²×D₄₃	—	2	1	no	—
186	C₂²×D₄₃	—	2	1	no	—
187	C₂²×D₄₃	—	4	2	no	—
188	C₂²×D₄₃	—	4	2	no	—
189	C₂²×D₄₃	—	8	1	no	—
190	D₄×C₄₃	—	2	1	no	—
191	D₄×C₄₃	—	2	1	no	—
192	D₄×C₄₃	—	2	1	no	—
193	D₄×C₄₃	—	4	2	no	—
194	D₄×C₄₃	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	8	1	no	—
204	C₂×C₄×C₄₃	—	8	1	no	—
205	C₂×C₄×C₄₃	—	8	1	no	—
206	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
212	C₂×Dic₄₃	—	2	1	no	—
213	C₂×Dic₄₃	—	2	1	no	—
214	C₂×Dic₄₃	—	8	1	no	—
215	D₁₇₂	—	2	1	no	—
216	D₁₇₂	—	2	1	no	—
217	D₁₇₂	—	2	1	no	—
218	D₁₇₂	—	4	2	no	—
219	D₁₇₂	C₂×M₁₆	1	2	yes	—
220	C₄×D₄₃	—	4	2	no	—
221	C₄×D₄₃	—	4	2	no	—
222	C₄×D₄₃	—	8	1	no	—
223	C₄×D₄₃	—	8	1	no	—
224	C₈×C₄₃	—	2	2	no	—
225	C₈×C₄₃	—	2	2	no	—
226	C₈×C₄₃	—	4	2	no	—
227	C₄₃⋊C₈	—	2	1	no	—
228	C₄₃⋊C₈	—	2	1	no	—
229	C₄₃⋊C₈	—	2	1	no	—
230	C₄₃⋊C₈	—	4	2	no	—
231	C₄₃⋊C₈	—	4	2	no	—
232	C₄₃⋊C₈	C₂×M₁₆	1	2	yes	—
233	#18064	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	—	2	1	no	—
235	C₂²×C₄₃	—	2	1	no	—
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	4	1	no	—
238	C₂²×C₄₃	—	4	1	no	—
239	C₂²×C₄₃	—	4	1	no	—
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	—	4	1	no	—
242	C₂²×C₄₃	—	8	4	no	—
243	C₂²×C₄₃	#444	1	2	yes	—
244	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂×D₄₃	—	2	2	no	—
246	C₂×D₄₃	—	4	1	no	—
247	C₂×D₄₃	—	4	1	no	—
248	C₂×D₄₃	—	4	1	no	—
249	C₂×D₄₃	—	4	1	no	—
250	C₂×D₄₃	—	4	1	no	—
251	C₂×D₄₃	—	8	4	no	—
252	C₄×C₄₃	—	2	1	no	—
253	C₄×C₄₃	—	2	1	no	—
254	C₄×C₄₃	—	2	1	no	—
255	C₄×C₄₃	—	2	1	no	—
256	C₄×C₄₃	—	4	1	no	—
257	C₄×C₄₃	—	4	1	no	—
258	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
259	C₄×C₄₃	#568	1	1	yes	characteristic
260	C₄×C₄₃	#576	1	2	yes	—
261	Dic₄₃	—	4	1	no	—
262	Dic₄₃	—	4	1	no	—
263	#2974	—	43	1	no	—
264	#2974	D₄₃	1	1	yes	characteristic, complemented
265	C₂×C₄×D₈	—	43	1	no	—
266	#1594	—	43	2	no	—
267	#1581	—	43	2	no	—
268	#1581	—	43	2	no	—
269	#1580	—	43	2	no	—
270	#1568	—	43	1	no	—
271	#1490	—	43	1	no	—
272	#1490	—	43	1	no	—
273	#1451	—	43	1	no	—
274	C₂×C₄₃	—	2	2	no	—
275	C₂×C₄₃	—	4	2	no	—
276	C₂×C₄₃	—	8	1	no	—
277	C₂×C₄₃	D₄×M₁₆	1	1	yes	characteristic
278	C₂×C₄₃	#2948	1	1	yes	characteristic
279	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
280	D₄₃	—	4	2	no	—
281	D₄₃	—	8	1	no	—
282	C₂²×D₈	—	43	1	no	—
283	C₂×C₄×D₄	—	43	1	no	—
284	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
285	C₄×D₈	—	43	1	no	—
286	C₄×D₈	—	43	1	no	—
287	C₄×D₈	—	43	1	no	—
288	C₄×D₈	—	43	1	no	—
289	C₄×D₈	—	43	1	no	—
290	C₄×D₈	—	43	1	no	—
291	C₄×D₈	—	43	1	no	—
292	C₄×D₈	—	43	1	no	—
293	#436	—	43	2	no	—
294	#436	C₂×D₄₃	1	2	yes	complemented
295	#435	—	2	2	no	—
296	#435	—	86	2	no	—
297	C₈×D₄	—	43	2	no	—
298	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
299	#432	—	43	1	no	—
300	#432	C₂×D₄₃	1	1	yes	characteristic
301	#431	C₂×D₄₃	1	1	yes	characteristic
302	C₂×#107	—	43	1	no	—
303	C₂×#102	—	43	1	no	—
304	C₂×#102	—	43	1	no	—
305	#407	—	2	1	no	—
306	#407	—	86	1	no	—
307	C₂×C₂²⋊C₈	—	2	1	no	—
308	C₂×C₂²⋊C₈	—	86	1	no	—
309	C₄×M₁₆	—	43	1	no	—
310	C₂×C₄×C₈	—	43	1	no	—
311	#335	—	43	2	no	—
312	#334	—	43	2	no	—
313	D₄⋊C₈	—	43	2	no	—
314	D₄⋊C₈	—	43	2	no	—
315	D₄⋊C₈	—	43	2	no	—
316	D₄⋊C₈	—	43	2	no	—
317	#322	—	43	2	no	—
318	#322	—	43	2	no	—
319	C₄₃	#18064	1	1	yes	characteristic, complemented, Sylow
320	C₂²×D₄	—	43	1	no	—
321	C₂²×D₄	C₄×D₄₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	86	1	no	—
324	C₂×D₈	—	43	1	no	—
325	C₂×D₈	—	43	1	no	—
326	C₂×D₈	—	43	1	no	—
327	C₂×D₈	—	43	1	no	—
328	C₂×D₈	—	86	4	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	86	1	no	—
331	C₂×M₁₆	—	86	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	43	1	no	—
334	C₂²×C₈	—	43	1	no	—
335	C₂²×C₈	—	86	2	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	2	1	no	—
338	C₄×D₄	—	43	1	no	—
339	C₄×D₄	—	43	1	no	—
340	C₄×D₄	—	43	1	no	—
341	C₄×D₄	—	43	1	no	—
342	C₄×D₄	—	86	1	no	—
343	C₄×D₄	—	86	1	no	—
344	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
345	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
346	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
347	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	—	43	1	no	—
349	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	86	1	no	—
352	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
353	#107	—	43	1	no	—
354	#107	—	43	1	no	—
355	#107	—	43	1	no	—
356	#107	—	43	1	no	—
357	C₄⋊C₈	—	43	2	no	—
358	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
359	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
360	#102	—	43	1	no	—
361	#102	—	43	1	no	—
362	#102	—	43	1	no	—
363	#102	—	43	1	no	—
364	#102	—	43	1	no	—
365	#102	—	43	1	no	—
366	#102	—	43	1	no	—
367	#102	—	43	1	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₂²⋊C₈	—	2	2	no	—
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	86	1	no	—
372	C₂²⋊C₈	—	86	2	no	—
373	C₂²⋊C₈	—	86	2	no	—
374	C₂²⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
375	C₂²⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
376	#97	—	2	1	no	—
377	#97	—	86	1	no	—
378	#97	—	86	1	no	—
379	C₄×C₈	—	43	1	no	—
380	C₄×C₈	—	43	1	no	—
381	C₄×C₈	—	43	1	no	—
382	C₄×C₈	—	43	1	no	—
383	C₄×C₈	—	43	2	no	—
384	C₄×C₈	C₂²×D₄₃	1	2	yes	—
385	C₂⁴	—	2	1	no	—
386	C₂⁴	—	86	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	4	1	no	—
390	C₂×D₄	—	43	1	no	—
391	C₂×D₄	—	43	1	no	—
392	C₂×D₄	—	86	2	no	—
393	C₂×D₄	—	86	1	no	—
394	C₂×D₄	—	172	1	no	—
395	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
396	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	8	2	no	—
403	C₂²×C₄	—	86	1	no	—
404	C₂²×C₄	—	86	1	no	—
405	C₂²×C₄	—	86	1	no	—
406	C₂²×C₄	—	86	1	no	—
407	C₂²×C₄	—	86	1	no	—
408	C₂²×C₄	—	344	2	no	—
409	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
410	C₂²×C₄	#10621898	1	1	yes	characteristic
411	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
412	D₈	—	43	4	no	—
413	D₈	—	86	2	no	—
414	D₈	—	86	2	no	—
415	D₈	—	86	2	no	—
416	M₁₆	—	8	2	no	—
417	M₁₆	—	344	2	no	—
418	M₁₆	—	172	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	8	2	no	—
421	C₂×C₈	—	43	1	no	—
422	C₂×C₈	—	43	1	no	—
423	C₂×C₈	—	43	1	no	—
424	C₂×C₈	—	43	1	no	—
425	C₂×C₈	—	86	2	no	—
426	C₂×C₈	—	86	2	no	—
427	C₂×C₈	—	86	2	no	—
428	C₂×C₈	—	344	2	no	—
429	C₂×C₈	—	172	1	no	—
430	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
431	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	43	1	no	—
434	C₄⋊C₄	—	43	1	no	—
435	C₄⋊C₄	—	86	1	no	—
436	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
437	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₂²⋊C₄	—	2	1	no	—
439	C₂²⋊C₄	—	2	1	no	—
440	C₂²⋊C₄	—	2	1	no	—
441	C₂²⋊C₄	—	2	1	no	—
442	C₂²⋊C₄	—	86	1	no	—
443	C₂²⋊C₄	—	86	1	no	—
444	C₂²⋊C₄	—	86	1	no	—
445	C₂²⋊C₄	—	86	1	no	—
446	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₄²	#10621898	1	1	yes	characteristic
448	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
449	C₄²	C₂³×D₄₃	1	1	yes	characteristic
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	8	1	no	—
455	C₂³	—	86	1	no	—
456	C₂³	—	86	1	no	—
457	C₂³	—	344	1	no	—
458	C₂³	—	172	2	no	—
459	C₂³	—	172	2	no	—
460	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
461	D₄	—	2	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	43	2	no	—
466	D₄	—	86	1	no	—
467	D₄	—	86	1	no	—
468	D₄	—	86	1	no	—
469	D₄	—	172	2	no	—
470	D₄	M₁₆×D₄₃	1	2	yes	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	8	1	no	—
480	C₂×C₄	—	8	1	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	86	1	no	—
483	C₂×C₄	—	86	1	no	—
484	C₂×C₄	—	344	1	no	—
485	C₂×C₄	—	344	1	no	—
486	C₂×C₄	—	344	1	no	—
487	C₂×C₄	—	172	2	no	—
488	C₂×C₄	—	172	2	no	—
489	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
491	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
492	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
493	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
494	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₈	—	4	2	no	—
498	C₈	—	43	2	no	—
499	C₈	—	86	1	no	—
500	C₈	—	86	1	no	—
501	C₈	—	86	1	no	—
502	C₈	—	172	2	no	—
503	C₈	—	172	2	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	2	1	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	8	4	no	—
513	C₂²	—	86	2	no	—
514	C₂²	—	344	4	no	—
515	C₂²	—	172	1	no	—
516	C₂²	—	172	1	no	—
517	C₂²	—	172	1	no	—
518	C₂²	—	172	1	no	—
519	C₂²	—	172	1	no	—
520	C₂²	#14583019	1	2	yes	—
521	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	1	no	—
527	C₄	—	4	1	no	—
528	C₄	—	172	1	no	—
529	C₄	—	172	1	no	—
530	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
531	C₄	#14583665	1	1	yes	characteristic
532	C₄	#14583702	1	2	yes	—
533	C₂	—	2	2	no	—
534	C₂	—	4	2	no	—
535	C₂	—	8	1	no	—
536	C₂	—	344	1	no	—
537	C₂	—	172	2	no	—
538	C₂	M₁₆×C₂²⋊D₄₃	1	1	yes	characteristic
539	C₂	#19143445	1	1	yes	characteristic
540	C₂	C₂×#14583019	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2974	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂²×#10621882	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2974	D₄₃
hypocenter	C₄₃	#18064
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2974

Complements

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

N	H ≅ G/N	type
1. #19143629	C₂	semidirect
3. #19133507	C₂	semidirect
4. #19133424	C₂	semidirect
5. #19133422	C₂	semidirect
6. #19133417	C₂	semidirect
7. #19133356	C₂	semidirect
8. #19133038	C₂	semidirect
9. #19133037	C₂	semidirect
10. #19132885	C₂	semidirect
11. C₄₃×#2974	C₂	semidirect
22. #14582978	C₂²	semidirect
24. C₈×D₁₇₂	C₂²	semidirect
33. #14582651	C₂²	semidirect
34. #14582649	C₂²	semidirect
35. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
36. D₄⋊(C₄₃⋊C₈)	C₂²	semidirect
37. #14582626	C₂²	semidirect
38. #14582626	C₂²	semidirect
39. #14582621	C₂²	semidirect
40. #14582620	C₂²	semidirect
42. C₄₃×#436	C₂²	semidirect
44. C₈×D₄×C₄₃	C₂²	semidirect
160. #10621882	M₁₆	semidirect
264. #2974	D₄₃	semidirect
294. #436	C₂×D₄₃	semidirect
298. C₈×D₄	C₂×D₄₃	semidirect
319. C₄₃	#18064	semidirect

Maximal subgroups

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

subgroup	index
#19143629	2
C₂×C₄×#10621882	2
#19133507	2
#19133424	2
#19133422	2
#19133417	2
#19133356	2
#19133038	2
#19133037	2
#19132885	2
C₄₃×#2974	2
#18064	43