Subgroups — #24989320

Order 11008.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19134575	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582633	C₂	1	2	yes	maximal
3	#19132825	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132473	C₂	1	2	yes	maximal, complemented
5	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊Dic₄₃	—	2	1	no	—
7	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
8	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₄₃⋊#95	—	2	1	no	—
10	C₂×C₄₃⋊#95	C₂²	1	2	yes	—
11	#14582654	—	2	1	no	—
12	#14582633	—	2	4	no	—
13	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₃	—	2	1	no	—
15	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#390	C₄	1	1	yes	characteristic, complemented
18	C₄₃×#389	C₄	1	1	yes	characteristic, complemented
19	C₄₃×#388	—	2	1	no	—
20	C₄₃×#386	—	2	1	no	—
21	C₄₃×#380	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic, complemented
23	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
24	C₂³×Dic₄₃	—	2	2	no	—
25	C₂²×C₄₃⋊C₈	—	2	2	no	—
26	C₂×C₄⋊Dic₄₃	—	2	4	no	—
27	C₂×C₄⋊Dic₄₃	—	4	2	no	—
28	C₂×C₄⋊Dic₄₃	—	4	2	no	—
29	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
30	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
31	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
32	C₄₃⋊#95	—	2	2	no	—
33	C₄₃⋊#95	—	2	2	no	—
34	C₄₃⋊#95	—	4	2	no	—
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	—	2	1	no	—
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	#121×C₄₃	—	2	1	no	—
42	#121×C₄₃	—	2	1	no	—
43	#121×C₄₃	D₄	1	2	yes	—
44	#121×C₄₃	Q₈	1	2	yes	—
45	C₄×D₄×C₄₃	—	4	2	no	—
46	C₄×D₄×C₄₃	—	4	2	no	—
47	C₄×D₄×C₄₃	—	4	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
53	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄²×C₄₃	—	2	1	no	—
58	C₂×C₄²×C₄₃	—	4	2	no	—
59	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
63	#95×C₄₃	—	2	1	no	—
64	#95×C₄₃	—	2	1	no	—
65	#95×C₄₃	—	2	1	no	—
66	C₂⁴×C₄₃	—	2	1	no	—
67	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
68	C₂×D₄×C₄₃	—	2	1	no	—
69	C₂×D₄×C₄₃	—	2	2	no	—
70	C₂×D₄×C₄₃	—	2	2	no	—
71	C₂×D₄×C₄₃	—	4	1	no	—
72	C₂×D₄×C₄₃	—	4	1	no	—
73	C₂×D₄×C₄₃	—	4	1	no	—
74	C₂×D₄×C₄₃	—	4	1	no	—
75	C₂×D₄×C₄₃	—	4	1	no	—
76	C₂×D₄×C₄₃	—	4	1	no	—
77	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	complemented
78	C₂²×C₄×C₄₃	—	2	2	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	1	no	—
81	C₂²×C₄×C₄₃	—	2	1	no	—
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	4	1	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	—	4	1	no	—
88	C₂²×C₄×C₄₃	—	4	1	no	—
89	C₂²×C₄×C₄₃	—	4	2	no	—
90	C₂²×C₄×C₄₃	—	4	2	no	—
91	C₂²×C₄×C₄₃	—	4	2	no	—
92	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	D₈	1	2	yes	—
97	C₂²×C₄×C₄₃	SD₁₆	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂²×Dic₄₃	—	2	4	no	—
105	C₂²×Dic₄₃	—	4	2	no	—
106	C₂²×Dic₄₃	—	4	2	no	—
107	C₂²×Dic₄₃	—	4	2	no	—
108	C₂²×Dic₄₃	—	4	2	no	—
109	C₂²×Dic₄₃	—	4	2	no	—
110	C₂²×Dic₄₃	—	4	2	no	—
111	C₄⋊C₄×C₄₃	—	2	1	no	—
112	C₄⋊C₄×C₄₃	—	4	1	no	—
113	C₄⋊C₄×C₄₃	—	4	1	no	—
114	C₄⋊C₄×C₄₃	—	4	2	no	—
115	C₄⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	complemented
116	C₂²⋊C₄×C₄₃	—	2	2	no	—
117	C₂²⋊C₄×C₄₃	—	2	2	no	—
118	C₂²⋊C₄×C₄₃	—	4	2	no	—
119	C₂²⋊C₄×C₄₃	—	4	2	no	—
120	C₂²⋊C₄×C₄₃	—	4	2	no	—
121	C₂²⋊C₄×C₄₃	—	4	1	no	—
122	C₂²⋊C₄×C₄₃	—	4	1	no	—
123	C₄²×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	4	1	no	—
126	C₄²×C₄₃	—	4	1	no	—
127	C₄²×C₄₃	—	4	2	no	—
128	C₄⋊Dic₄₃	—	4	8	no	—
129	C₂×C₄₃⋊C₈	—	4	2	no	—
130	C₂×C₄₃⋊C₈	—	4	2	no	—
131	C₂×C₄₃⋊C₈	—	4	2	no	—
132	C₂³×C₄₃	—	2	1	no	—
133	C₂³×C₄₃	—	2	1	no	—
134	C₂³×C₄₃	—	2	1	no	—
135	C₂³×C₄₃	—	2	1	no	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	4	1	no	—
138	C₂³×C₄₃	—	4	1	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	1	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₄₃	#121	1	1	yes	characteristic
145	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
147	C₂³×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
148	C₂³×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂³×C₄₃	#137	1	1	yes	characteristic
150	D₄×C₄₃	—	4	2	no	—
151	D₄×C₄₃	—	4	2	no	—
152	D₄×C₄₃	—	4	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	4	2	no	—
155	D₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	1	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	8	4	no	—
186	C₂×C₄×C₄₃	#99	1	2	yes	—
187	C₂×C₄×C₄₃	#102	1	2	yes	—
188	C₂×C₄×C₄₃	#102	1	2	yes	—
189	C₂×C₄×C₄₃	#104	1	2	yes	—
190	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
194	C₂×Dic₄₃	—	4	4	no	—
195	C₂×Dic₄₃	—	4	4	no	—
196	C₂×Dic₄₃	—	4	4	no	—
197	C₂×Dic₄₃	—	8	2	no	—
198	C₂×Dic₄₃	—	8	2	no	—
199	C₂×Dic₄₃	—	8	2	no	—
200	C₂×Dic₄₃	—	8	2	no	—
201	C₄₃⋊C₈	—	8	2	no	—
202	#8571	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	2	1	no	—
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	4	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	8	1	no	—
219	C₂²×C₄₃	—	8	1	no	—
220	C₂²×C₄₃	—	8	1	no	—
221	C₂²×C₄₃	—	8	1	no	—
222	C₂²×C₄₃	#380	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
224	C₂²×C₄₃	#410	1	1	yes	characteristic
225	C₂²×C₄₃	C₂×#102	1	1	yes	characteristic
226	C₂²×C₄₃	#417	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
228	C₂²×C₄₃	#421	1	1	yes	characteristic
229	C₂²×C₄₃	#459	1	1	yes	characteristic
230	C₂²×C₄₃	#461	1	1	yes	characteristic
231	C₂²×C₄₃	#474	1	1	yes	characteristic
232	C₂²×C₄₃	#476	1	1	yes	characteristic
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	2	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	—	4	1	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	8	1	no	—
242	C₄×C₄₃	—	8	1	no	—
243	C₄×C₄₃	#327	1	4	yes	complemented
244	Dic₄₃	—	8	4	no	—
245	C₄×#121	D₄₃	1	1	yes	characteristic
246	#1797	—	43	1	no	—
247	C₂×#327	—	43	2	no	—
248	C₄⋊#95	—	43	1	no	—
249	#1294	—	43	2	no	—
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	—	2	1	no	—
253	C₂×C₄₃	—	2	1	no	—
254	C₂×C₄₃	—	8	2	no	—
255	C₂×C₄₃	C₂×#327	1	1	yes	characteristic
256	C₂×C₄₃	#1509	1	1	yes	characteristic
257	C₂×C₄₃	#1513	1	1	yes	characteristic
258	C₂×C₄₃	#1517	1	1	yes	characteristic
259	C₂×C₄₃	#1799	1	1	yes	characteristic
260	C₂×C₄₃	#1802	1	1	yes	characteristic
261	C₂×C₄₃	#1806	1	1	yes	characteristic
262	C₂×#121	C₂×D₄₃	1	1	yes	characteristic
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic, complemented
265	C₂²×C₄⋊C₄	—	86	1	no	—
266	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	—	86	1	no	—
268	C₂×C₂²⋊C₈	—	43	2	no	—
269	#390	Dic₄₃	1	1	yes	characteristic, complemented
270	#389	Dic₄₃	1	1	yes	characteristic, complemented
271	#388	—	2	1	no	—
272	#386	—	2	1	no	—
273	#380	C₂×D₄₃	1	1	yes	characteristic
274	C₄×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic, complemented
275	C₄×C₂²⋊C₄	—	2	1	no	—
276	C₂×#95	—	43	2	no	—
277	C₂×#95	—	86	1	no	—
278	#336	—	86	1	no	—
279	#327	—	86	4	no	—
280	C₄₃	#8571	1	1	yes	characteristic, complemented, Sylow
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	—	86	2	no	—
285	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
286	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
288	C₂²×C₈	—	86	2	no	—
289	#121	—	2	1	no	—
290	#121	—	2	1	no	—
291	#121	Dic₈₆	1	2	yes	—
292	#121	D₁₇₂	1	2	yes	—
293	C₄×D₄	—	4	2	no	—
294	C₄×D₄	—	4	2	no	—
295	C₄×D₄	—	4	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	86	4	no	—
298	C₂×C₄⋊C₄	—	172	2	no	—
299	C₂×C₄⋊C₄	—	172	2	no	—
300	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	4	2	no	—
310	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
311	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
312	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
313	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
314	C₄⋊C₈	—	172	2	no	—
315	C₂²⋊C₈	—	86	2	no	—
316	C₂²⋊C₈	—	86	2	no	—
317	#95	—	2	1	no	—
318	#95	—	2	1	no	—
319	#95	—	2	1	no	—
320	#95	—	86	2	no	—
321	#95	—	86	2	no	—
322	#95	—	172	2	no	—
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	C₄⋊Dic₄₃	1	2	yes	complemented
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	86	4	no	—
350	C₂²×C₄	—	172	2	no	—
351	C₂²×C₄	—	172	2	no	—
352	C₂²×C₄	—	172	2	no	—
353	C₂²×C₄	—	172	2	no	—
354	C₂²×C₄	—	172	2	no	—
355	C₂²×C₄	—	172	2	no	—
356	C₂²×C₄	#10621882	1	2	yes	—
357	C₂²×C₄	#10621883	1	2	yes	—
358	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
361	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
364	C₂²×C₄	#10621898	1	1	yes	characteristic
365	C₂²×C₄	#10621898	1	1	yes	characteristic
366	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
368	C₂×C₈	—	172	2	no	—
369	C₂×C₈	—	172	2	no	—
370	C₂×C₈	—	172	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	172	8	no	—
376	C₄⋊C₄	C₄⋊Dic₄₃	1	2	yes	complemented
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	4	2	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	—	2	1	no	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	4	1	no	—
395	C₂³	—	4	1	no	—
396	C₂³	—	4	1	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	1	no	—
400	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
401	C₂³	#13063299	1	1	yes	characteristic
402	C₂³	#13063304	1	1	yes	characteristic
403	C₂³	C₂×#10621882	1	1	yes	characteristic
404	C₂³	C₂×#10621883	1	1	yes	characteristic
405	C₂³	#13063350	1	1	yes	characteristic
406	C₂³	#13063355	1	1	yes	characteristic
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	8	4	no	—
443	C₂×C₄	—	344	2	no	—
444	C₂×C₄	—	344	2	no	—
445	C₂×C₄	—	344	2	no	—
446	C₂×C₄	—	344	2	no	—
447	C₂×C₄	—	172	4	no	—
448	C₂×C₄	—	172	4	no	—
449	C₂×C₄	—	172	4	no	—
450	C₂×C₄	#13063240	1	2	yes	—
451	C₂×C₄	#13063246	1	2	yes	—
452	C₂×C₄	#13063246	1	2	yes	—
453	C₂×C₄	#13063252	1	2	yes	—
454	C₂×C₄	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
455	C₂×C₄	#13063284	1	1	yes	characteristic
456	C₂×C₄	#13063299	1	1	yes	characteristic
457	C₂×C₄	#13063304	1	1	yes	characteristic
458	C₈	—	344	2	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	8	1	no	—
476	C₂²	—	8	1	no	—
477	C₂²	—	8	1	no	—
478	C₂²	#14582759	1	1	yes	characteristic
479	C₂²	C₂×#13063240	1	1	yes	characteristic
480	C₂²	#14582873	1	1	yes	characteristic
481	C₂²	C₂×#13063246	1	1	yes	characteristic
482	C₂²	#14582900	1	1	yes	characteristic
483	C₂²	C₂×#13063252	1	1	yes	characteristic
484	C₂²	#14582916	1	1	yes	characteristic
485	C₂²	#14583094	1	1	yes	characteristic
486	C₂²	#14583104	1	1	yes	characteristic
487	C₂²	#14583179	1	1	yes	characteristic
488	C₂²	#14583189	1	1	yes	characteristic
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	—	344	4	no	—
500	C₄	#14582633	1	4	yes	complemented
501	C₂	—	2	1	no	—
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	8	2	no	—
506	C₂	C₂×#14582633	1	1	yes	characteristic
507	C₂	#19133120	1	1	yes	characteristic
508	C₂	#19133138	1	1	yes	characteristic
509	C₂	#19133155	1	1	yes	characteristic
510	C₂	#19134583	1	1	yes	characteristic
511	C₂	#19134595	1	1	yes	characteristic
512	C₂	#19134615	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₃
commutator	C₂²×C₄×C₄₃	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄×#121×C₄₃	C₂
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₄₃	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₄×#121	D₄₃
hypocenter	C₄₃	#8571
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₄×#121

Complements

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

N	H ≅ G/N	type
1. #19134575	C₂	semidirect
3. #19132825	C₂	semidirect
4. #19132473	C₂	semidirect
15. C₂×C₄×D₄×C₄₃	C₄	semidirect
17. C₄₃×#390	C₄	semidirect
18. C₄₃×#389	C₄	semidirect
22. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
77. C₂×D₄×C₄₃	C₄⋊C₄	semidirect
115. C₄⋊C₄×C₄₃	C₄⋊C₄	semidirect
243. C₄×C₄₃	#327	semidirect
264. C₂×C₄×D₄	Dic₄₃	semidirect
269. #390	Dic₄₃	semidirect
270. #389	Dic₄₃	semidirect
274. C₄×C₄⋊C₄	Dic₄₃	semidirect
280. C₄₃	#8571	semidirect
334. C₂×D₄	C₄⋊Dic₄₃	semidirect
376. C₄⋊C₄	C₄⋊Dic₄₃	semidirect
500. C₄	#14582633	semidirect

Maximal subgroups

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

subgroup	index
#19134575	2
C₂×#14582633	2
#19132825	2
#19132473	2
C₄×#121×C₄₃	2
#8571	43