Subgroups — #25001810

Order 11008.

842 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582857	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582857	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582855	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582670	C₂	1	1	yes	maximal, characteristic
5	#19134333	C₂	1	1	yes	maximal, characteristic
6	#19134327	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#344	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂×#13063284	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	#14582857	—	2	2	no	—
13	#14582857	—	2	1	no	—
14	#14582857	—	2	1	no	—
15	#14582857	—	2	1	no	—
16	#14582857	—	2	1	no	—
17	#14582857	C₄	1	4	yes	complemented
18	#14582855	—	2	2	no	—
19	#14582855	C₄	1	4	yes	complemented
20	C₂×#13063236	—	2	1	no	—
21	C₂×#13063235	—	2	1	no	—
22	C₂×#13063235	C₄	1	2	yes	complemented
23	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
24	C₂×C₈×Dic₄₃	—	2	1	no	—
25	C₂×C₈×Dic₄₃	C₄	1	2	yes	complemented
26	#14582670	C₄	1	4	yes	complemented
27	#14582667	C₄	1	4	yes	complemented
28	#14582665	C₄	1	4	yes	—
29	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#344	C₄	1	4	yes	complemented
33	C₂×#10621877	—	2	1	no	—
34	C₂×#10621877	—	2	1	no	—
35	C₂×#10621877	—	2	1	no	—
36	C₂×#10621877	C₂×C₄	1	2	yes	—
37	C₂×#10621877	C₂×C₄	1	2	yes	—
38	C₂×#10621877	C₂×C₄	1	2	yes	—
39	C₂²×C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
43	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
44	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
45	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
46	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
49	C₂²×C₄₃⋊C₈	Q₈	1	2	yes	—
50	#13063284	—	2	1	no	—
51	#13063284	—	2	1	no	—
52	#13063284	—	2	1	no	—
53	#13063284	—	2	1	no	—
54	#13063284	—	2	1	no	—
55	#13063284	—	2	1	no	—
56	#13063284	C₂×C₄	1	2	yes	—
57	#13063284	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊Dic₄₃	—	2	1	no	—
59	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
60	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
62	C₂×C₄×Dic₄₃	—	2	1	no	—
63	C₂×C₄×Dic₄₃	C₂×C₄	1	2	yes	—
64	#13063236	—	2	4	no	—
65	#13063235	—	2	4	no	—
66	#13063235	—	2	2	no	—
67	#13063235	—	2	2	no	—
68	C₄×C₄₃⋊C₈	—	2	4	no	—
69	C₈×Dic₄₃	—	2	4	no	—
70	C₈×Dic₄₃	—	2	2	no	—
71	C₈×Dic₄₃	—	2	2	no	—
72	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂×M₁₆×C₄₃	—	2	1	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	1	no	—
77	C₂×M₁₆×C₄₃	—	2	1	no	—
78	C₂×M₁₆×C₄₃	—	2	1	no	—
79	C₂×M₁₆×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
81	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
85	C₂²×C₈×C₄₃	—	2	1	no	—
86	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
87	#117×C₄₃	—	2	1	no	—
88	#117×C₄₃	—	2	1	no	—
89	#117×C₄₃	C₂×C₄	1	2	yes	—
90	#117×C₄₃	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	C₄²	1	4	yes	—
112	M₁₆×C₄₃	—	2	2	no	—
113	M₁₆×C₄₃	—	2	2	no	—
114	M₁₆×C₄₃	—	2	2	no	—
115	M₁₆×C₄₃	—	2	2	no	—
116	M₁₆×C₄₃	—	2	2	no	—
117	M₁₆×C₄₃	—	2	2	no	—
118	M₁₆×C₄₃	—	2	2	no	—
119	M₁₆×C₄₃	C₄²	1	4	yes	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	C₄²	1	4	yes	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₂²⋊C₄×C₄₃	—	2	2	no	—
129	C₂²⋊C₄×C₄₃	C₄²	1	4	yes	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₄²×C₄₃	—	2	2	no	—
132	C₂²⋊Dic₄₃	—	2	2	no	—
133	C₂²⋊Dic₄₃	—	2	2	no	—
134	C₂²⋊Dic₄₃	—	2	2	no	—
135	C₂²⋊Dic₄₃	C₄²	1	4	yes	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	2	2	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	2	2	no	—
143	C₄×Dic₄₃	—	2	2	no	—
144	#10621877	—	2	2	no	—
145	#10621877	—	2	2	no	—
146	#10621877	—	2	2	no	—
147	#10621877	C₄²	1	4	yes	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
152	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
154	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
157	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
158	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
161	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
162	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
163	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
164	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
165	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
169	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
170	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
171	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
173	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
174	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	4	4	no	—
177	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
205	C₂×Dic₄₃	—	2	4	no	—
206	C₂×Dic₄₃	—	2	4	no	—
207	C₂×Dic₄₃	—	4	4	no	—
208	C₂×Dic₄₃	—	4	4	no	—
209	C₈×C₄₃	—	2	4	no	—
210	C₈×C₄₃	—	2	4	no	—
211	C₄₃⋊C₈	—	2	4	no	—
212	C₄₃⋊C₈	#95	1	2	yes	—
213	C₄₃⋊C₈	#95	1	2	yes	—
214	C₄₃⋊C₈	#95	1	2	yes	—
215	C₄₃⋊C₈	#95	1	2	yes	—
216	#10711	—	43	1	no	maximal, Sylow
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	4	1	no	—
221	C₂²×C₄₃	—	4	1	no	—
222	C₂²×C₄₃	—	4	1	no	—
223	C₂²×C₄₃	—	4	1	no	—
224	C₂²×C₄₃	C₄³	1	1	yes	characteristic
225	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
226	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
227	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
230	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
231	C₄×C₄₃	—	4	4	no	—
232	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
233	C₄×C₄₃	#376	1	1	yes	characteristic
234	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
236	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
237	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
238	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
239	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
240	Dic₄₃	—	4	4	no	—
241	Dic₄₃	—	4	4	no	—
242	C₂×#405	—	43	1	no	—
243	C₂×#405	—	43	1	no	—
244	C₂×#405	—	43	1	no	—
245	C₂×#344	—	43	1	no	—
246	C₂×#344	D₄₃	1	1	yes	characteristic
247	#1742	—	43	1	no	—
248	#1740	—	43	1	no	—
249	C₂×C₄₃	—	2	1	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	—	2	1	no	—
255	C₂×C₄₃	C₄×#95	1	1	yes	characteristic
256	C₂×C₄₃	#1757	1	2	yes	—
257	C₂²×M₁₆	—	43	1	no	—
258	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
259	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
260	C₂³×C₈	—	43	1	no	—
261	C₂×#117	—	43	1	no	—
262	C₂×#117	—	43	1	no	—
263	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
264	#405	—	43	4	no	—
265	#405	—	43	4	no	—
266	#405	—	86	2	no	—
267	#405	—	86	1	no	—
268	#405	—	86	1	no	—
269	#405	—	86	1	no	—
270	#405	—	86	1	no	—
271	#405	—	86	2	no	—
272	C₂×#97	—	43	2	no	—
273	C₂×#97	—	86	1	no	—
274	C₂×#97	—	86	1	no	—
275	C₂×C₄×C₈	—	43	2	no	—
276	C₂×C₄×C₈	—	86	1	no	—
277	C₂×C₄×C₈	—	86	1	no	—
278	#344	—	43	4	no	—
279	#344	Dic₄₃	1	4	yes	complemented
280	#343	—	43	4	no	—
281	#342	—	43	4	no	—
282	C₄₃	#10711	1	1	yes	characteristic, complemented, Sylow
283	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
284	C₂×M₁₆	—	2	1	no	—
285	C₂×M₁₆	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	43	2	no	—
292	C₂×M₁₆	—	43	2	no	—
293	C₂×M₁₆	—	43	2	no	—
294	C₂×M₁₆	—	86	1	no	—
295	C₂×M₁₆	—	86	1	no	—
296	C₂×M₁₆	—	86	1	no	—
297	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
298	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
299	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
300	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
301	C₂×M₁₆	C₂×Dic₄₃	1	2	yes	—
302	C₂²×C₈	—	2	1	no	—
303	C₂²×C₈	—	43	1	no	—
304	C₂²×C₈	—	43	1	no	—
305	C₂²×C₈	—	43	2	no	—
306	C₂²×C₈	—	43	2	no	—
307	C₂²×C₈	—	43	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	43	1	no	—
311	C₂²×C₈	—	43	2	no	—
312	C₂²×C₈	—	43	2	no	—
313	C₂²×C₈	—	86	1	no	—
314	C₂²×C₈	C₄×D₄₃	1	2	yes	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	43	2	no	—
318	#117	—	43	2	no	—
319	#117	—	86	1	no	—
320	#117	—	86	1	no	—
321	#117	—	86	1	no	—
322	#117	—	86	1	no	—
323	#117	—	86	1	no	—
324	#117	—	86	1	no	—
325	#117	C₄×D₄₃	1	2	yes	—
326	#117	C₂×Dic₄₃	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	43	2	no	—
329	C₂×C₄⋊C₄	—	86	1	no	—
330	C₂×C₂²⋊C₄	—	43	2	no	—
331	C₂×C₂²⋊C₄	—	43	2	no	—
332	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	43	2	no	—
335	C₂×C₄²	—	86	1	no	—
336	#97	—	86	4	no	—
337	#97	—	86	2	no	—
338	#97	—	86	2	no	—
339	#97	—	86	4	no	—
340	C₄×C₈	—	86	4	no	—
341	C₄×C₈	—	86	2	no	—
342	C₄×C₈	—	86	2	no	—
343	C₄×C₈	—	86	4	no	—
344	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	43	4	no	—
347	C₂²×C₄	—	86	2	no	—
348	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
356	C₂²×C₄	#10621900	1	1	yes	characteristic
357	C₂²×C₄	#10621900	1	1	yes	characteristic
358	C₂²×C₄	#10621900	1	1	yes	characteristic
359	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
360	C₂²×C₄	#10621902	1	1	yes	characteristic
361	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
362	M₁₆	—	2	2	no	—
363	M₁₆	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	—	43	4	no	—
370	M₁₆	—	86	2	no	—
371	M₁₆	—	86	2	no	—
372	M₁₆	—	86	2	no	—
373	M₁₆	C₄×Dic₄₃	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	43	2	no	—
380	C₂×C₈	—	43	2	no	—
381	C₂×C₈	—	43	2	no	—
382	C₂×C₈	—	43	2	no	—
383	C₂×C₈	—	43	2	no	—
384	C₂×C₈	—	43	2	no	—
385	C₂×C₈	—	43	1	no	—
386	C₂×C₈	—	43	1	no	—
387	C₂×C₈	—	43	1	no	—
388	C₂×C₈	—	43	1	no	—
389	C₂×C₈	—	43	2	no	—
390	C₂×C₈	—	43	2	no	—
391	C₂×C₈	—	43	2	no	—
392	C₂×C₈	—	43	2	no	—
393	C₂×C₈	—	43	2	no	—
394	C₂×C₈	—	43	2	no	—
395	C₂×C₈	—	86	2	no	—
396	C₂×C₈	—	86	2	no	—
397	C₂×C₈	—	86	2	no	—
398	C₂×C₈	C₄×Dic₄₃	1	4	yes	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	86	2	no	—
402	C₄⋊C₄	—	86	2	no	—
403	C₄⋊C₄	—	86	2	no	—
404	C₄⋊C₄	—	86	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	43	4	no	—
407	C₂²⋊C₄	—	86	2	no	—
408	C₂²⋊C₄	—	86	2	no	—
409	C₂²⋊C₄	—	86	2	no	—
410	C₂²⋊C₄	C₄×Dic₄₃	1	4	yes	—
411	C₄²	—	2	2	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	86	2	no	—
414	C₄²	—	86	2	no	—
415	C₄²	—	86	2	no	—
416	C₄²	—	86	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	C₄²×D₄₃	1	1	yes	characteristic
419	C₂³	C₄²×D₄₃	1	1	yes	characteristic
420	C₂³	C₂×C₄×Dic₄₃	1	1	yes	characteristic
421	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
422	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
423	C₂³	#13063287	1	1	yes	characteristic
424	C₂³	#13063290	1	1	yes	characteristic
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	86	4	no	—
428	C₂×C₄	—	86	4	no	—
429	C₂×C₄	—	172	4	no	—
430	C₂×C₄	—	172	4	no	—
431	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
432	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
434	C₂×C₄	C₂×C₄×Dic₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
437	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
438	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
441	C₂×C₄	#13063281	1	1	yes	characteristic
442	C₂×C₄	#13063281	1	1	yes	characteristic
443	C₂×C₄	#13063281	1	1	yes	characteristic
444	C₂×C₄	#13063283	1	1	yes	characteristic
445	C₂×C₄	#13063283	1	1	yes	characteristic
446	C₂×C₄	#13063283	1	1	yes	characteristic
447	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
448	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
449	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
450	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
451	C₂×C₄	#13063287	1	1	yes	characteristic
452	C₂×C₄	#13063287	1	1	yes	characteristic
453	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
454	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
456	C₂×C₄	#13063290	1	1	yes	characteristic
457	C₂×C₄	#13063290	1	1	yes	characteristic
458	C₂×C₄	Q₈×Dic₄₃	1	1	yes	characteristic
459	C₈	—	2	4	no	—
460	C₈	—	2	4	no	—
461	C₈	—	43	2	no	—
462	C₈	—	43	2	no	—
463	C₈	—	43	2	no	—
464	C₈	—	43	2	no	—
465	C₈	—	86	4	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	1	no	—
472	C₂²	—	4	1	no	—
473	C₂²	C₄²×Dic₄₃	1	1	yes	characteristic
474	C₂²	#14582746	1	1	yes	characteristic
475	C₂²	#14582746	1	1	yes	characteristic
476	C₂²	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
477	C₂²	#14582750	1	1	yes	characteristic
478	C₂²	#14582750	1	1	yes	characteristic
479	C₂²	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
480	C₄	—	4	4	no	—
481	C₄	—	172	4	no	—
482	C₄	—	172	4	no	—
483	C₄	#95×D₄₃	1	1	yes	characteristic
484	C₄	#14582744	1	1	yes	characteristic
485	C₄	#14582746	1	1	yes	characteristic
486	C₄	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
487	C₄	C₂²⋊C₄×Dic₄₃	1	1	yes	characteristic
488	C₄	#14582750	1	1	yes	characteristic
489	C₄	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
490	C₄	C₄⋊C₄×Dic₄₃	1	1	yes	characteristic
491	C₂	—	2	1	no	—
492	C₂	—	2	1	no	—
493	C₂	—	2	1	no	—
494	C₂	—	2	1	no	—
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	#95×Dic₄₃	1	1	yes	characteristic
498	C₂	#19134394	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₄³
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#344	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂⁴×C₄₃	C₂²×C₄
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#344	D₄₃
hypocenter	C₄₃	#10711
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
17. #14582857	C₄	semidirect
19. #14582855	C₄	semidirect
22. C₂×#13063235	C₄	semidirect
25. C₂×C₈×Dic₄₃	C₄	semidirect
26. #14582670	C₄	semidirect
27. #14582667	C₄	semidirect
32. C₄₃×#344	C₄	semidirect
279. #344	Dic₄₃	semidirect
282. C₄₃	#10711	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582857	2
C₂×#14582855	2
C₂×#14582670	2
#19134333	2
#19134327	2
C₂×C₄₃×#344	2
#10711	43