Subgroups — #25062608

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	#19143228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
3	#19132955	C₂	1	4	yes	maximal, complemented
4	#19132947	C₂	1	4	yes	maximal, complemented
5	#19132916	C₂	1	4	yes	maximal, complemented
6	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
7	#14582956	—	2	1	no	—
8	#14582956	C₂²	1	2	yes	—
9	#14582952	—	2	1	no	—
10	#14582952	—	2	1	no	—
11	#14582952	—	2	1	no	—
12	#14582952	C₂²	1	2	yes	—
13	#14582952	C₂²	1	2	yes	—
14	#14582952	C₂²	1	2	yes	—
15	#14582923	—	2	1	no	—
16	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
17	#14582863	C₂²	1	2	yes	—
18	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
19	C₄×#10621877	—	2	1	no	—
20	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
21	#14582623	C₂²	1	16	yes	—
22	C₂²×#41×C₄₃	C₄	1	2	yes	—
23	C₄₃×#532	—	2	1	no	—
24	C₄₃×#532	—	2	1	no	—
25	C₄₃×#532	—	2	1	no	—
26	C₄₃×#532	—	2	1	no	—
27	C₄₃×#532	—	2	1	no	—
28	C₄₃×#532	—	2	1	no	—
29	C₄₃×#532	—	2	1	no	—
30	C₄₃×#532	—	2	1	no	—
31	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
32	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
33	C₂×#124×C₄₃	C₂²	1	2	yes	—
34	C₂×#121×C₄₃	C₄	1	2	yes	—
35	C₂×#121×C₄₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
37	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
38	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#10621877	—	2	2	no	—
40	C₂²×C₄₃⋊C₈	—	2	2	no	—
41	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
42	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
43	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
44	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
45	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
46	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
47	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
48	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
49	#13063236	—	2	2	no	—
50	C₄×C₄₃⋊C₈	—	2	2	no	—
51	C₄×C₄₃⋊C₈	—	2	2	no	—
52	C₄×C₄₃⋊C₈	—	2	2	no	—
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	2	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	2	no	—
57	C₂×#41×C₄₃	—	4	8	no	—
58	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
59	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
60	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
61	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
62	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₃	—	2	1	no	—
68	C₄⋊Q₈×C₄₃	—	2	1	no	—
69	C₄⋊Q₈×C₄₃	—	2	1	no	—
70	C₄⋊Q₈×C₄₃	—	2	1	no	—
71	#127×C₄₃	—	2	1	no	—
72	#127×C₄₃	—	2	1	no	—
73	#127×C₄₃	—	2	1	no	—
74	#127×C₄₃	—	2	1	no	—
75	#124×C₄₃	—	2	2	no	—
76	#124×C₄₃	—	2	2	no	—
77	#124×C₄₃	—	2	2	no	—
78	#124×C₄₃	—	2	2	no	—
79	#121×C₄₃	—	2	2	no	—
80	#121×C₄₃	—	2	2	no	—
81	#121×C₄₃	—	2	2	no	—
82	#121×C₄₃	—	2	2	no	—
83	#121×C₄₃	—	2	2	no	—
84	#121×C₄₃	—	2	2	no	—
85	#121×C₄₃	—	2	2	no	—
86	#121×C₄₃	—	2	2	no	—
87	C₄×D₄×C₄₃	—	2	2	no	—
88	C₄×D₄×C₄₃	—	2	2	no	—
89	C₄×D₄×C₄₃	—	2	2	no	—
90	C₄×D₄×C₄₃	—	2	2	no	—
91	C₄×D₄×C₄₃	—	2	2	no	—
92	C₄×D₄×C₄₃	—	2	2	no	—
93	C₄×D₄×C₄₃	—	2	2	no	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
96	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
98	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
99	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
111	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
113	#41×C₄₃	—	4	8	no	—
114	#41×C₄₃	—	4	8	no	—
115	#41×C₄₃	—	4	8	no	—
116	#41×C₄₃	—	4	8	no	—
117	C₂×Q₈×C₄₃	—	2	2	no	—
118	C₂×Q₈×C₄₃	—	2	2	no	—
119	C₂×Q₈×C₄₃	—	4	4	no	—
120	C₂×D₄×C₄₃	—	2	2	no	—
121	C₂×D₄×C₄₃	—	2	2	no	—
122	C₂×D₄×C₄₃	—	2	2	no	—
123	C₂×D₄×C₄₃	—	2	2	no	—
124	C₂×D₄×C₄₃	—	2	2	no	—
125	C₂×D₄×C₄₃	—	2	2	no	—
126	C₂×D₄×C₄₃	—	2	8	no	—
127	C₂×D₄×C₄₃	—	2	4	no	—
128	C₂×D₄×C₄₃	—	2	4	no	—
129	C₂×D₄×C₄₃	—	4	8	no	—
130	C₂×D₄×C₄₃	—	4	4	no	—
131	C₂×D₄×C₄₃	—	4	4	no	—
132	C₂²×C₄×C₄₃	—	2	4	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	2	4	no	—
135	C₂²×C₄×C₄₃	—	2	4	no	—
136	C₂²×C₄×C₄₃	—	4	2	no	—
137	C₂²×C₄×C₄₃	—	4	8	no	—
138	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
151	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₄₃	—	2	2	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₂²⋊C₄×C₄₃	—	2	4	no	—
162	C₂²⋊C₄×C₄₃	—	2	4	no	—
163	C₂²⋊C₄×C₄₃	—	2	4	no	—
164	C₂²⋊C₄×C₄₃	—	2	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
181	#10621877	—	4	4	no	—
182	C₂×C₄₃⋊C₈	—	2	4	no	—
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	—	2	4	no	—
188	C₂³×C₄₃	—	2	8	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	—	4	4	no	—
191	C₂³×C₄₃	—	4	4	no	—
192	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
195	Q₈×C₄₃	—	4	4	no	—
196	Q₈×C₄₃	—	4	4	no	—
197	D₄×C₄₃	—	4	4	no	—
198	D₄×C₄₃	—	4	4	no	—
199	D₄×C₄₃	—	4	8	no	—
200	D₄×C₄₃	—	4	8	no	—
201	D₄×C₄₃	—	4	4	no	—
202	D₄×C₄₃	—	4	4	no	—
203	D₄×C₄₃	—	4	4	no	—
204	D₄×C₄₃	—	4	4	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	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	2	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	—	4	8	no	—
223	C₂×C₄×C₄₃	—	4	8	no	—
224	C₂×C₄×C₄₃	—	4	4	no	—
225	C₂×C₄×C₄₃	#100	1	4	yes	—
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#131	1	4	yes	—
237	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
239	C₄₃⋊C₈	—	4	4	no	—
240	C₄₃⋊C₈	—	4	4	no	—
241	#17384	—	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	—	4	4	no	—
251	C₂²×C₄₃	—	4	4	no	—
252	C₂²×C₄₃	—	4	4	no	—
253	C₂²×C₄₃	—	8	8	no	—
254	C₂²×C₄₃	C₂×#100	1	2	yes	—
255	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×#131	1	2	yes	—
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	—	4	4	no	—
265	C₄×C₄₃	#408	1	2	yes	—
266	C₄×C₄₃	#408	1	2	yes	—
267	C₄×C₄₃	#410	1	2	yes	—
268	C₄×C₄₃	C₂×#100	1	2	yes	—
269	C₄×C₄₃	C₂×#100	1	2	yes	—
270	C₂×#532	D₄₃	1	1	yes	characteristic
271	#2920	—	43	1	no	—
272	C₂×#431	—	43	1	no	—
273	#1471	—	43	4	no	—
274	#1469	—	43	4	no	—
275	#1460	—	43	4	no	—
276	C₂×C₄₃	—	2	2	no	—
277	C₂×C₄₃	—	2	2	no	—
278	C₂×C₄₃	—	4	1	no	—
279	C₂×C₄₃	—	8	4	no	—
280	C₂×C₄₃	C₂×#408	1	1	yes	characteristic
281	C₂×C₄₃	C₂×#410	1	1	yes	characteristic
282	C₂×C₄₃	C₂²×#100	1	1	yes	characteristic
283	C₂²×#41	Dic₄₃	1	2	yes	—
284	#532	—	2	1	no	—
285	#532	—	2	1	no	—
286	#532	—	2	1	no	—
287	#532	—	2	1	no	—
288	#532	—	2	1	no	—
289	#532	—	2	1	no	—
290	#532	—	2	1	no	—
291	#532	—	2	1	no	—
292	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
293	C₂×#127	Dic₄₃	1	1	yes	characteristic
294	C₂×#124	C₂×D₄₃	1	2	yes	—
295	C₂×#121	Dic₄₃	1	2	yes	—
296	C₂×#121	C₂×D₄₃	1	2	yes	—
297	C₂×C₄×D₄	Dic₄₃	1	2	yes	—
298	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
299	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
300	#432	—	43	2	no	—
301	#432	—	86	1	no	—
302	#431	—	43	2	no	—
303	#431	—	43	2	no	—
304	#431	—	43	2	no	—
305	#431	—	86	1	no	—
306	#431	—	86	1	no	—
307	#431	—	86	1	no	—
308	#423	—	86	1	no	—
309	C₂×C₄⋊C₈	—	86	1	no	—
310	#407	—	43	2	no	—
311	C₂×C₂²⋊C₈	—	43	2	no	—
312	C₄×M₁₆	—	86	1	no	—
313	C₂×C₄×C₈	—	86	1	no	—
314	#323	—	43	16	no	—
315	C₄₃	#17384	1	1	yes	characteristic, complemented, Sylow
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	4	8	no	—
321	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
322	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
323	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
324	C₂²×D₄	C₂×Dic₄₃	1	4	yes	—
325	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
326	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
327	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
328	C₂³×C₄	C₂×Dic₄₃	1	4	yes	—
329	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
330	C₂×M₁₆	—	86	2	no	—
331	C₂²×C₈	—	86	2	no	—
332	C₄⋊Q₈	—	2	1	no	—
333	C₄⋊Q₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	#127	—	2	1	no	—
337	#127	—	2	1	no	—
338	#127	—	2	1	no	—
339	#127	—	2	1	no	—
340	#124	—	2	2	no	—
341	#124	—	2	2	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
362	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
363	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
364	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
365	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
367	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
368	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
369	C₂×C₄²	C₂²⋊D₄₃	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	—	86	2	no	—
377	C₄⋊C₈	—	86	2	no	—
378	C₄⋊C₈	—	86	2	no	—
379	C₄⋊C₈	—	86	2	no	—
380	C₂²⋊C₈	—	43	4	no	—
381	C₂²⋊C₈	—	43	4	no	—
382	C₂²⋊C₈	—	86	2	no	—
383	C₂²⋊C₈	—	86	2	no	—
384	#97	—	86	2	no	—
385	C₄×C₈	—	86	2	no	—
386	C₄×C₈	—	86	2	no	—
387	C₄×C₈	—	86	2	no	—
388	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
389	C₂⁴	C₂²×Dic₄₃	1	4	yes	—
390	#41	—	4	8	no	—
391	#41	—	4	8	no	—
392	#41	—	4	8	no	—
393	#41	—	4	8	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	4	4	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	4	8	no	—
415	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
417	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
418	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
419	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
420	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
421	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
428	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₂²⋊D₄₃	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	C₂³×D₄₃	1	1	yes	characteristic
434	M₁₆	—	172	4	no	—
435	C₂×C₈	—	86	4	no	—
436	C₂×C₈	—	86	4	no	—
437	C₂×C₈	—	172	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
447	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
448	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
449	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
450	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
451	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
452	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
453	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
454	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
455	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
456	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
457	C₄²	C₂×C₂²⋊D₄₃	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	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	4	no	—
465	C₂³	—	2	8	no	—
466	C₂³	—	4	1	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
470	C₂³	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
471	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
472	Q₈	—	4	4	no	—
473	Q₈	—	4	4	no	—
474	D₄	—	4	4	no	—
475	D₄	—	4	4	no	—
476	D₄	—	4	8	no	—
477	D₄	—	4	8	no	—
478	D₄	—	4	4	no	—
479	D₄	—	4	4	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	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	—	2	4	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	8	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	#13063242	1	4	yes	—
503	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
504	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
505	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
506	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
507	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
508	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
509	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
510	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
511	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
512	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
513	C₂×C₄	#13063332	1	4	yes	—
514	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
516	C₈	—	172	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	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	8	no	—
530	C₂²	C₂×#13063242	1	2	yes	—
531	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
532	C₂²	C₂×#13063332	1	2	yes	—
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	—	4	4	no	—
541	C₄	#14582866	1	2	yes	—
542	C₄	#14582866	1	2	yes	—
543	C₄	#14582873	1	2	yes	—
544	C₄	C₂×#13063242	1	2	yes	—
545	C₄	C₂×#13063242	1	2	yes	—
546	C₂	—	2	2	no	—
547	C₂	—	2	2	no	—
548	C₂	—	4	1	no	—
549	C₂	—	8	4	no	—
550	C₂	C₂×#14582866	1	1	yes	characteristic
551	C₂	C₂×#14582873	1	1	yes	characteristic
552	C₂	C₂²×#13063242	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₄₃
commutator	C₂³×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting, prime radical	C₂×C₄₃×#532	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	#17384
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #19143228	C₂	semidirect
2. C₂×#14582952	C₂	semidirect
3. #19132955	C₂	semidirect
4. #19132947	C₂	semidirect
5. #19132916	C₂	semidirect
315. C₄₃	#17384	semidirect

Maximal subgroups

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

subgroup	index
#19143228	2
C₂×#14582952	2
#19132955	2
#19132947	2
#19132916	2
C₂×C₄₃×#532	2
#17384	43