Subgroups — #25063140

Order 11008.

1268 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583449	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133013	C₂	1	4	yes	maximal, complemented
4	#19132995	C₂	1	4	yes	maximal, complemented
5	#19132987	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#10621898	—	2	1	no	—
8	#14583449	—	2	1	no	—
9	#14583449	—	2	1	no	—
10	#14583449	—	2	1	no	—
11	#14583449	—	2	1	no	—
12	#14583449	C₄	1	2	yes	—
13	#14583449	C₄	1	2	yes	—
14	#14583449	C₂²	1	2	yes	—
15	#14583449	C₂²	1	2	yes	—
16	C₂×#13063325	C₄	1	1	yes	characteristic
17	C₂×#13063322	C₄	1	1	yes	characteristic
18	C₂×#13063313	—	2	1	no	—
19	C₂×#13063299	—	2	1	no	—
20	C₂×#13063299	C₄	1	2	yes	—
21	C₂×C₄×D₁₇₂	—	2	1	no	—
22	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
23	#14582952	—	2	1	no	—
24	#14582952	—	2	1	no	—
25	#14582952	C₂²	1	2	yes	—
26	#14582952	C₂²	1	2	yes	complemented
27	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
29	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
30	#14582628	C₂²	1	16	yes	complemented
31	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#432	—	2	1	no	—
33	C₄₃×#432	—	2	1	no	—
34	C₄₃×#431	C₂²	1	2	yes	—
35	C₄₃×#431	C₂²	1	2	yes	complemented
36	C₄₃×#423	—	2	1	no	—
37	C₄₃×#407	—	2	1	no	—
38	C₄×M₁₆×C₄₃	C₂²	1	2	yes	complemented
39	C₂×#10621898	—	2	2	no	—
40	C₂×#10621898	—	2	2	no	—
41	C₂×#10621898	—	2	2	no	—
42	C₂×#10621898	—	2	2	no	—
43	C₂×#10621898	—	4	8	no	—
44	C₂²×Dic₈₆	—	2	1	no	—
45	C₂²×D₁₇₂	—	2	1	no	—
46	C₂²×D₁₇₂	—	2	1	no	—
47	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
48	C₂²×C₂²⋊D₄₃	—	2	2	no	—
49	C₂²×C₄×D₄₃	—	2	2	no	—
50	C₂²×C₄₃⋊C₈	—	2	2	no	—
51	#13063325	—	2	1	no	—
52	#13063325	—	2	1	no	—
53	#13063325	C₂×C₄	1	2	yes	—
54	#13063325	C₂×C₄	1	2	yes	—
55	#13063322	—	2	1	no	—
56	#13063322	—	2	1	no	—
57	#13063322	C₂×C₄	1	2	yes	—
58	#13063322	C₂×C₄	1	2	yes	—
59	#13063313	—	2	2	no	—
60	#13063313	—	2	2	no	—
61	#13063313	—	2	2	no	—
62	#13063313	—	2	2	no	—
63	#13063299	—	2	2	no	—
64	#13063299	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	#13063299	—	2	2	no	—
67	#13063299	—	2	2	no	—
68	#13063299	—	2	2	no	—
69	#13063299	C₂×C₄	1	4	yes	—
70	#13063299	C₂×C₄	1	4	yes	—
71	C₄×D₁₇₂	—	2	2	no	—
72	C₄×D₁₇₂	—	2	2	no	—
73	C₄×D₁₇₂	—	2	2	no	—
74	C₄×D₁₇₂	—	2	2	no	—
75	C₄×D₁₇₂	—	2	2	no	—
76	C₄×D₁₇₂	—	2	2	no	—
77	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
78	C₄×D₁₇₂	C₂³	1	4	yes	—
79	C₂×C₄⋊Dic₄₃	—	2	1	no	—
80	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
81	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
82	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
83	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
84	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
85	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
87	C₄×C₄₃⋊C₈	—	2	2	no	—
88	C₄×C₄₃⋊C₈	—	2	2	no	—
89	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	—	2	2	no	—
93	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	—	2	2	no	—
106	C₄⋊C₈×C₄₃	—	2	2	no	—
107	C₂²⋊C₈×C₄₃	—	2	2	no	—
108	C₂²⋊C₈×C₄₃	—	2	2	no	—
109	#97×C₄₃	—	2	2	no	—
110	C₄×C₈×C₄₃	C₂³	1	4	yes	—
111	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×D₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₃	—	2	4	no	—
135	C₂×C₂²⋊D₄₃	—	2	4	no	—
136	C₂×C₂²⋊D₄₃	—	4	8	no	—
137	C₂²×Dic₄₃	—	2	2	no	—
138	#10621898	—	4	8	no	—
139	#10621898	—	4	8	no	—
140	#10621898	—	4	8	no	—
141	#10621898	—	4	8	no	—
142	C₂×D₁₇₂	—	2	2	no	—
143	C₂×D₁₇₂	—	2	2	no	—
144	C₂×D₁₇₂	—	2	2	no	—
145	C₂×D₁₇₂	—	2	2	no	—
146	C₂×D₁₇₂	—	2	2	no	—
147	C₂×D₁₇₂	—	2	8	no	—
148	C₂×D₁₇₂	—	4	4	no	—
149	C₂×D₁₇₂	—	4	4	no	—
150	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
151	C₂×C₄×D₄₃	—	2	4	no	—
152	C₂×C₄×D₄₃	—	2	4	no	—
153	C₂×C₄×D₄₃	—	4	8	no	—
154	C₂×Dic₈₆	—	2	2	no	—
155	C₂×Dic₈₆	—	2	2	no	—
156	C₂×Dic₈₆	—	4	4	no	—
157	M₁₆×C₄₃	—	4	4	no	—
158	C₂×C₈×C₄₃	—	2	4	no	—
159	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
160	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
161	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
175	(C₂×D₄₃)⋊C₄	—	2	4	no	—
176	(C₂×D₄₃)⋊C₄	—	2	4	no	—
177	(C₂×D₄₃)⋊C₄	—	2	4	no	—
178	(C₂×D₄₃)⋊C₄	—	2	4	no	—
179	C₄⋊Dic₄₃	—	2	2	no	—
180	C₄⋊Dic₄₃	—	2	2	no	—
181	C₄⋊Dic₄₃	—	2	2	no	—
182	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
183	C₂×C₄₃⋊C₈	—	2	4	no	—
184	C₂×C₄₃⋊C₈	—	4	4	no	—
185	C₂³×C₄₃	—	2	2	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	4	1	no	—
188	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
189	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂²×D₄₃	—	2	4	no	—
192	C₂²×D₄₃	—	4	4	no	—
193	C₂²×D₄₃	—	4	4	no	—
194	C₂²×D₄₃	—	4	4	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	#131	1	4	yes	—
221	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
222	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
225	C₂²⋊D₄₃	—	4	8	no	—
226	C₂²⋊D₄₃	—	4	8	no	—
227	C₂×Dic₄₃	—	2	4	no	—
228	C₂×Dic₄₃	—	4	4	no	—
229	D₁₇₂	—	2	8	no	—
230	D₁₇₂	—	4	4	no	—
231	D₁₇₂	—	4	4	no	—
232	D₁₇₂	—	4	4	no	—
233	D₁₇₂	—	4	4	no	—
234	D₁₇₂	—	4	4	no	—
235	C₄×D₄₃	—	4	8	no	—
236	C₄×D₄₃	—	4	8	no	—
237	Dic₈₆	—	4	4	no	—
238	Dic₈₆	—	4	4	no	—
239	C₈×C₄₃	—	4	4	no	—
240	C₄₃⋊C₈	—	4	4	no	—
241	#17463	—	43	1	no	maximal, Sylow
242	C₂²×C₄₃	—	2	1	no	—
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	—	2	1	no	—
245	C₂²×C₄₃	—	2	1	no	—
246	C₂²×C₄₃	—	2	1	no	—
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	—	4	4	no	—
250	C₂²×C₄₃	#408	1	2	yes	—
251	C₂²×C₄₃	#418	1	2	yes	—
252	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
253	C₂×D₄₃	—	4	4	no	—
254	C₂×D₄₃	—	4	4	no	—
255	C₂×D₄₃	—	4	4	no	—
256	C₂×D₄₃	—	8	8	no	—
257	C₄×C₄₃	—	2	1	no	—
258	C₄×C₄₃	—	2	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	2	1	no	—
261	C₄×C₄₃	—	2	1	no	—
262	C₄×C₄₃	—	2	1	no	—
263	C₄×C₄₃	—	2	1	no	—
264	C₄×C₄₃	#408	1	2	yes	—
265	C₄×C₄₃	#418	1	2	yes	—
266	C₄×C₄₃	#421	1	2	yes	—
267	C₄×C₄₃	C₂×#131	1	2	yes	—
268	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
269	Dic₄₃	—	4	4	no	—
270	C₂×#532	—	43	1	no	—
271	#2920	D₄₃	1	1	yes	characteristic, complemented
272	C₂×#431	—	43	1	no	—
273	#1484	—	43	4	no	—
274	#1480	—	43	4	no	—
275	#1478	—	43	4	no	—
276	C₂×C₄₃	—	2	2	no	—
277	C₂×C₄₃	—	2	2	no	—
278	C₂×C₄₃	—	4	1	no	—
279	C₂×C₄₃	C₂×#408	1	1	yes	characteristic
280	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
281	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
282	D₄₃	—	8	4	no	—
283	C₂²×#41	—	86	1	no	—
284	#532	—	43	2	no	—
285	#532	—	43	2	no	—
286	#532	—	43	2	no	—
287	#532	—	43	2	no	—
288	#532	—	86	1	no	—
289	#532	—	86	1	no	—
290	#532	—	86	1	no	—
291	#532	—	86	1	no	—
292	C₂×C₄⋊Q₈	—	43	1	no	—
293	C₂×#127	—	43	1	no	—
294	C₂×#124	—	86	1	no	—
295	C₂×#121	—	43	2	no	—
296	C₂×#121	—	86	1	no	—
297	C₂×C₄×D₄	—	43	2	no	—
298	C₂×C₄×D₄	—	86	1	no	—
299	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
300	#432	—	2	1	no	—
301	#432	—	2	1	no	—
302	#431	—	43	2	no	—
303	#431	—	43	2	no	—
304	#431	—	86	1	no	—
305	#431	—	86	1	no	—
306	#431	C₂×D₄₃	1	2	yes	—
307	#431	C₂×D₄₃	1	2	yes	complemented
308	#423	—	2	1	no	—
309	C₂×C₄⋊C₈	—	43	2	no	—
310	#407	—	2	1	no	—
311	C₂×C₂²⋊C₈	—	86	1	no	—
312	C₄×M₁₆	C₂×D₄₃	1	2	yes	complemented
313	C₂×C₄×C₈	—	86	1	no	—
314	D₄⋊C₈	—	43	16	no	—
315	C₄₃	#17463	1	1	yes	characteristic, complemented, Sylow
316	C₂×#41	—	86	2	no	—
317	C₂×#41	—	86	2	no	—
318	C₂×#41	—	86	2	no	—
319	C₂×#41	—	86	2	no	—
320	C₂×#41	—	172	8	no	—
321	C₂²×Q₈	—	86	1	no	—
322	C₂²×D₄	—	43	2	no	—
323	C₂²×D₄	—	86	2	no	—
324	C₂²×D₄	—	86	1	no	—
325	C₂²×D₄	—	86	1	no	—
326	C₂³×C₄	—	86	2	no	—
327	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
328	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
329	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₂²×C₈	—	86	2	no	—
332	C₄⋊Q₈	—	43	2	no	—
333	C₄⋊Q₈	—	43	2	no	—
334	C₄⋊Q₈	—	86	1	no	—
335	C₄⋊Q₈	—	86	1	no	—
336	#127	—	43	2	no	—
337	#127	—	43	2	no	—
338	#127	—	86	1	no	—
339	#127	—	86	1	no	—
340	#124	—	86	2	no	—
341	#124	—	86	2	no	—
342	#124	—	86	2	no	—
343	#124	—	86	2	no	—
344	#121	—	43	4	no	—
345	#121	—	43	4	no	—
346	#121	—	86	2	no	—
347	#121	—	86	2	no	—
348	#121	—	86	2	no	—
349	#121	—	86	2	no	—
350	#121	—	86	2	no	—
351	#121	—	86	2	no	—
352	C₄×D₄	—	43	4	no	—
353	C₄×D₄	—	43	4	no	—
354	C₄×D₄	—	86	2	no	—
355	C₄×D₄	—	86	2	no	—
356	C₄×D₄	—	86	2	no	—
357	C₄×D₄	—	86	2	no	—
358	C₄×D₄	—	86	2	no	—
359	C₄×D₄	—	86	2	no	—
360	C₂×C₄⋊C₄	—	43	2	no	—
361	C₂×C₄⋊C₄	—	86	1	no	—
362	C₂×C₂²⋊C₄	—	86	2	no	—
363	C₂×C₂²⋊C₄	—	86	2	no	—
364	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
365	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
366	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
367	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
368	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
369	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
370	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
371	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
372	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
373	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
374	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
376	C₄⋊C₈	—	2	2	no	—
377	C₄⋊C₈	—	2	2	no	—
378	C₄⋊C₈	—	43	4	no	—
379	C₄⋊C₈	—	86	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	C₂²⋊C₈	—	2	2	no	—
382	C₂²⋊C₈	—	86	2	no	—
383	C₂²⋊C₈	—	86	2	no	—
384	#97	—	2	2	no	—
385	C₄×C₈	—	86	2	no	—
386	C₄×C₈	—	86	2	no	—
387	C₄×C₈	C₂²×D₄₃	1	4	yes	—
388	C₂⁴	—	86	2	no	—
389	C₂⁴	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
390	#41	—	172	8	no	—
391	#41	—	172	8	no	—
392	#41	—	172	8	no	—
393	#41	—	172	8	no	—
394	C₂×Q₈	—	86	2	no	—
395	C₂×Q₈	—	86	2	no	—
396	C₂×Q₈	—	172	4	no	—
397	C₂×D₄	—	43	4	no	—
398	C₂×D₄	—	86	4	no	—
399	C₂×D₄	—	86	4	no	—
400	C₂×D₄	—	86	2	no	—
401	C₂×D₄	—	86	2	no	—
402	C₂×D₄	—	86	2	no	—
403	C₂×D₄	—	86	2	no	—
404	C₂×D₄	—	86	2	no	—
405	C₂×D₄	—	86	8	no	—
406	C₂×D₄	—	172	4	no	—
407	C₂×D₄	—	172	4	no	—
408	C₂×D₄	—	172	8	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	86	2	no	—
413	C₂²×C₄	—	86	4	no	—
414	C₂²×C₄	—	86	4	no	—
415	C₂²×C₄	—	172	8	no	—
416	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
417	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
418	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
419	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
424	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
434	M₁₆	—	4	4	no	—
435	C₂×C₈	—	2	4	no	—
436	C₂×C₈	—	86	4	no	—
437	C₂×C₈	—	172	4	no	—
438	C₄⋊C₄	—	43	4	no	—
439	C₄⋊C₄	—	86	2	no	—
440	C₄⋊C₄	—	86	2	no	—
441	C₄⋊C₄	—	86	2	no	—
442	C₂²⋊C₄	—	86	4	no	—
443	C₂²⋊C₄	—	86	4	no	—
444	C₂²⋊C₄	—	86	4	no	—
445	C₂²⋊C₄	—	86	4	no	—
446	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
447	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
448	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
449	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
450	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
451	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
453	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
454	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
455	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
456	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
457	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
458	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
459	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
461	C₄²	C₂³×D₄₃	1	1	yes	characteristic
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	4	1	no	—
465	C₂³	—	86	4	no	—
466	C₂³	—	172	4	no	—
467	C₂³	—	172	4	no	—
468	C₂³	—	172	4	no	—
469	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
470	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
471	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
472	Q₈	—	172	4	no	—
473	Q₈	—	172	4	no	—
474	D₄	—	86	8	no	—
475	D₄	—	172	4	no	—
476	D₄	—	172	4	no	—
477	D₄	—	172	8	no	—
478	D₄	—	172	8	no	—
479	D₄	—	172	4	no	—
480	D₄	—	172	4	no	—
481	D₄	—	172	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	86	4	no	—
499	C₂×C₄	—	172	8	no	—
500	C₂×C₄	—	172	4	no	—
501	C₂×C₄	—	172	8	no	—
502	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
503	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
504	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
505	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
506	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
509	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
511	C₂×C₄	#13063333	1	4	yes	—
512	C₂×C₄	#13063353	1	4	yes	—
513	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
516	C₈	—	4	4	no	—
517	C₈	—	172	4	no	—
518	C₂²	—	2	1	no	—
519	C₂²	—	2	1	no	—
520	C₂²	—	2	1	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	344	8	no	—
527	C₂²	—	172	4	no	—
528	C₂²	—	172	4	no	—
529	C₂²	—	172	4	no	—
530	C₂²	#14582867	1	2	yes	—
531	C₂²	#14582905	1	2	yes	—
532	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	172	4	no	—
541	C₄	#14582867	1	2	yes	—
542	C₄	#14582905	1	2	yes	—
543	C₄	#14582917	1	2	yes	—
544	C₄	C₂×#13063333	1	2	yes	—
545	C₄	C₂×#13063353	1	2	yes	—
546	C₂	—	2	2	no	—
547	C₂	—	2	2	no	—
548	C₂	—	4	1	no	—
549	C₂	—	344	4	no	—
550	C₂	C₂×#14582867	1	1	yes	characteristic
551	C₂	C₂×#14582905	1	1	yes	characteristic
552	C₂	C₂×#14582917	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2920	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#14583449	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2920	D₄₃
hypocenter	C₄₃	#17463
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
2. C₂×#14582952	C₂	semidirect
3. #19133013	C₂	semidirect
4. #19132995	C₂	semidirect
5. #19132987	C₂	semidirect
6. C₄₃×#2920	C₂	semidirect
26. #14582952	C₂²	semidirect
27. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
30. #14582628	C₂²	semidirect
35. C₄₃×#431	C₂²	semidirect
38. C₄×M₁₆×C₄₃	C₂²	semidirect
271. #2920	D₄₃	semidirect
307. #431	C₂×D₄₃	semidirect
312. C₄×M₁₆	C₂×D₄₃	semidirect
315. C₄₃	#17463	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583449	2
C₂×#14582952	2
#19133013	2
#19132995	2
#19132987	2
C₄₃×#2920	2
#17463	43