Subgroups — #25065932

Order 11008.

594 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143720	C₂	1	1	yes	maximal, characteristic
2	#19143562	C₂	1	1	yes	maximal, characteristic
3	#19133381	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133378	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133376	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133373	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133371	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133369	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133363	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133360	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133356	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133348	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14582651	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#2990	C₂	1	1	yes	maximal, characteristic
16	#14583030	—	2	1	no	—
17	#14583030	C₄	1	1	yes	characteristic
18	#14583030	C₄	1	1	yes	characteristic
19	#14582977	C₄	1	1	yes	characteristic
20	#14582977	C₄	1	1	yes	characteristic
21	#14582971	—	2	1	no	—
22	#14582971	—	2	1	no	—
23	#14582971	C₄	1	1	yes	characteristic
24	#14582971	C₄	1	1	yes	characteristic
25	#14582971	C₄	1	1	yes	characteristic
26	#14582971	C₄	1	1	yes	characteristic
27	D₄×C₄₃⋊C₈	—	2	1	no	—
28	#14582956	C₂²	1	1	yes	characteristic
29	#14582956	C₂²	1	1	yes	characteristic
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582952	C₂²	1	1	yes	characteristic
32	#14582952	C₂²	1	1	yes	characteristic
33	#14582952	C₂²	1	1	yes	characteristic
34	#14582923	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
37	C₄×#10621877	C₂²	1	1	yes	characteristic
38	C₄×#10621877	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	#14582651	C₂²	1	1	yes	characteristic
41	#14582651	C₂²	1	1	yes	characteristic
42	#14582651	C₂²	1	1	yes	characteristic
43	#14582651	C₂²	1	1	yes	characteristic
44	#14582651	C₂²	1	1	yes	characteristic
45	#14582651	C₂²	1	1	yes	characteristic
46	#14582651	C₂²	1	1	yes	characteristic
47	#14582651	C₂²	1	1	yes	characteristic
48	#14582651	C₂²	1	1	yes	characteristic
49	#14582651	C₂²	1	1	yes	characteristic
50	#14582649	C₂²	1	1	yes	characteristic
51	#14582649	C₂²	1	1	yes	characteristic
52	#14582649	C₂²	1	1	yes	characteristic
53	#14582649	C₂²	1	1	yes	characteristic
54	#14582649	C₂²	1	1	yes	characteristic
55	#14582649	C₂²	1	1	yes	characteristic
56	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#446	—	2	1	no	—
58	C₄₃×#435	—	2	1	no	—
59	C₄₃×#435	—	2	1	no	—
60	C₈×D₄×C₄₃	—	2	1	no	—
61	C₄₃×#432	C₂²	1	1	yes	characteristic
62	C₄₃×#432	C₂²	1	1	yes	characteristic
63	C₄₃×#431	C₂²	1	1	yes	characteristic
64	C₄₃×#423	C₂²	1	1	yes	characteristic
65	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
66	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
67	C₂×#10621877	—	2	1	no	—
68	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
69	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
71	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₄₃⋊C₈	—	2	1	no	—
73	C₂²×C₄₃⋊C₈	—	2	1	no	—
74	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
84	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
86	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
88	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
89	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
92	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
94	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	#13063236	—	2	1	no	—
99	#13063236	—	2	1	no	—
100	#13063236	C₂×C₄	1	1	yes	characteristic
101	#13063236	C₂×C₄	1	1	yes	characteristic
102	#13063236	C₂×C₄	1	1	yes	characteristic
103	#13063236	C₂×C₄	1	1	yes	characteristic
104	C₄×C₄₃⋊C₈	—	2	1	no	—
105	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
110	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×#41×C₄₃	Q₈	1	1	yes	characteristic
112	C₂×M₁₆×C₄₃	—	2	1	no	—
113	C₂²×C₈×C₄₃	—	2	1	no	—
114	C₂²×C₈×C₄₃	—	2	1	no	—
115	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
117	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
118	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
119	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
120	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
121	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
122	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
123	#117×C₄₃	Q₈	1	1	yes	characteristic
124	#117×C₄₃	Q₈	1	1	yes	characteristic
125	#117×C₄₃	Q₈	1	1	yes	characteristic
126	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
129	C₄⋊C₈×C₄₃	—	2	1	no	—
130	C₄⋊C₈×C₄₃	—	2	1	no	—
131	C₄⋊C₈×C₄₃	—	2	1	no	—
132	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
134	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₂²⋊C₈×C₄₃	—	2	1	no	—
137	C₂²⋊C₈×C₄₃	—	2	1	no	—
138	C₂²⋊C₈×C₄₃	—	2	1	no	—
139	#97×C₄₃	—	2	1	no	—
140	#97×C₄₃	—	2	1	no	—
141	C₄×C₈×C₄₃	—	2	1	no	—
142	#41×C₄₃	—	4	2	no	—
143	C₂×Q₈×C₄₃	C₄⋊C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
145	C₂×D₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
146	C₂×D₄×C₄₃	C₄⋊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	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
156	M₁₆×C₄₃	—	8	1	no	—
157	C₂×C₈×C₄₃	—	2	1	no	—
158	C₂×C₈×C₄₃	—	2	1	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	8	1	no	—
162	C₂×C₈×C₄₃	—	8	1	no	—
163	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
166	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
167	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
169	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
173	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
174	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₄₃	C₂²×C₄	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	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
182	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
183	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
184	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
185	#10621877	—	2	2	no	—
186	#10621877	—	2	2	no	—
187	#10621877	—	4	1	no	—
188	#10621877	—	4	1	no	—
189	#10621877	—	8	1	no	—
190	C₂×C₄₃⋊C₈	—	2	2	no	—
191	C₂×C₄₃⋊C₈	—	2	1	no	—
192	C₂×C₄₃⋊C₈	—	2	1	no	—
193	C₂×C₄₃⋊C₈	—	2	1	no	—
194	C₂×C₄₃⋊C₈	—	2	1	no	—
195	C₂×C₄₃⋊C₈	—	4	1	no	—
196	C₂×C₄₃⋊C₈	—	8	1	no	—
197	C₂×C₄₃⋊C₈	—	8	1	no	—
198	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
206	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	Q₈×C₄₃	—	4	1	no	—
210	D₄×C₄₃	—	2	2	no	—
211	D₄×C₄₃	—	2	2	no	—
212	D₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	1	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
240	C₈×C₄₃	—	4	1	no	—
241	C₈×C₄₃	—	4	1	no	—
242	C₈×C₄₃	—	4	1	no	—
243	C₈×C₄₃	—	4	1	no	—
244	C₄₃⋊C₈	—	2	1	no	—
245	C₄₃⋊C₈	—	2	1	no	—
246	C₄₃⋊C₈	—	2	1	no	—
247	C₄₃⋊C₈	—	2	1	no	—
248	C₄₃⋊C₈	—	2	1	no	—
249	C₄₃⋊C₈	—	2	1	no	—
250	C₄₃⋊C₈	—	2	1	no	—
251	C₄₃⋊C₈	—	4	1	no	—
252	C₄₃⋊C₈	—	4	1	no	—
253	C₄₃⋊C₈	—	4	1	no	—
254	C₄₃⋊C₈	—	4	1	no	—
255	C₄₃⋊C₈	#131	1	2	yes	—
256	#17840	—	43	1	no	maximal, Sylow
257	C₂²×C₄₃	—	2	1	no	—
258	C₂²×C₄₃	—	2	1	no	—
259	C₂²×C₄₃	—	2	1	no	—
260	C₂²×C₄₃	—	2	1	no	—
261	C₂²×C₄₃	—	2	1	no	—
262	C₂²×C₄₃	—	2	1	no	—
263	C₂²×C₄₃	—	2	1	no	—
264	C₂²×C₄₃	—	2	1	no	—
265	C₂²×C₄₃	#430	1	2	yes	—
266	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
267	C₄×C₄₃	—	2	1	no	—
268	C₄×C₄₃	—	2	1	no	—
269	C₄×C₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	2	1	no	—
272	C₄×C₄₃	—	2	1	no	—
273	C₄×C₄₃	—	2	1	no	—
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	1	no	—
277	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
278	C₄×C₄₃	#568	1	1	yes	characteristic
279	C₄×C₄₃	#576	1	1	yes	characteristic
280	C₄×C₄₃	#578	1	1	yes	characteristic
281	#2990	—	43	1	no	—
282	#2990	D₄₃	1	1	yes	characteristic
283	#2965	—	43	1	no	—
284	#1573	—	43	1	no	—
285	#1573	—	43	1	no	—
286	#1572	—	43	1	no	—
287	#1572	—	43	1	no	—
288	#1571	—	43	1	no	—
289	#1571	—	43	1	no	—
290	#1569	—	43	1	no	—
291	#1569	—	43	1	no	—
292	#1568	—	43	1	no	—
293	#1565	—	43	1	no	—
294	#1565	—	43	1	no	—
295	C₂×#335	—	43	1	no	—
296	C₂×C₄₃	—	2	2	no	—
297	C₂×C₄₃	—	4	1	no	—
298	C₂×C₄₃	—	4	1	no	—
299	C₂×C₄₃	#2906	1	1	yes	characteristic
300	C₂×C₄₃	#2913	1	1	yes	characteristic
301	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
302	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
303	#446	—	2	1	no	—
304	#446	—	43	1	no	—
305	#446	—	43	1	no	—
306	#446	—	86	1	no	—
307	#436	—	43	1	no	—
308	#436	—	43	1	no	—
309	#435	—	2	1	no	—
310	#435	—	2	1	no	—
311	#435	—	43	1	no	—
312	#435	—	43	1	no	—
313	#435	—	43	1	no	—
314	#435	—	43	1	no	—
315	#435	—	86	1	no	—
316	#435	—	86	1	no	—
317	C₈×D₄	—	2	1	no	—
318	C₈×D₄	—	86	1	no	—
319	#432	—	43	1	no	—
320	#432	—	43	1	no	—
321	#432	C₂×D₄₃	1	1	yes	characteristic
322	#432	C₂×D₄₃	1	1	yes	characteristic
323	#431	—	43	1	no	—
324	#431	—	43	1	no	—
325	#431	—	43	1	no	—
326	#431	—	43	1	no	—
327	#431	C₂×D₄₃	1	1	yes	characteristic
328	#423	—	43	1	no	—
329	#423	C₂×D₄₃	1	1	yes	characteristic
330	C₂×C₄⋊C₈	—	43	1	no	—
331	C₂×C₄⋊C₈	—	43	1	no	—
332	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
333	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
334	C₄×M₁₆	—	43	1	no	—
335	C₄×M₁₆	—	43	1	no	—
336	C₂×C₄×C₈	—	43	1	no	—
337	#335	—	43	1	no	—
338	#335	—	43	1	no	—
339	#335	—	43	1	no	—
340	#335	—	43	1	no	—
341	#335	—	43	1	no	—
342	#335	—	43	1	no	—
343	#335	—	43	1	no	—
344	#335	—	43	1	no	—
345	#335	—	43	1	no	—
346	#335	—	43	1	no	—
347	#334	—	43	1	no	—
348	#334	—	43	1	no	—
349	#334	—	43	1	no	—
350	#334	—	43	1	no	—
351	#334	—	43	1	no	—
352	#334	—	43	1	no	—
353	C₄₃	#17840	1	1	yes	characteristic, complemented, Sylow
354	C₂×#41	Dic₈₆	1	1	yes	characteristic
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	43	1	no	—
357	C₂×M₁₆	—	43	1	no	—
358	C₂×M₁₆	—	43	1	no	—
359	C₂×M₁₆	—	43	1	no	—
360	C₂×M₁₆	—	86	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	43	1	no	—
364	C₂²×C₈	—	43	1	no	—
365	C₂²×C₈	—	86	1	no	—
366	C₂²×C₈	—	86	1	no	—
367	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
368	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
369	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
370	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
371	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
372	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
373	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
374	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
375	#117	Dic₈₆	1	1	yes	characteristic
376	#117	Dic₈₆	1	1	yes	characteristic
377	#117	Dic₈₆	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	43	1	no	—
385	C₄⋊C₈	—	43	1	no	—
386	C₄⋊C₈	—	43	1	no	—
387	C₄⋊C₈	—	43	1	no	—
388	C₄⋊C₈	—	43	1	no	—
389	C₄⋊C₈	—	43	1	no	—
390	C₄⋊C₈	—	43	1	no	—
391	C₄⋊C₈	—	43	1	no	—
392	C₄⋊C₈	—	43	1	no	—
393	C₄⋊C₈	—	43	1	no	—
394	C₄⋊C₈	—	86	1	no	—
395	C₄⋊C₈	—	86	1	no	—
396	C₄⋊C₈	—	86	1	no	—
397	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
400	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	43	1	no	—
405	C₂²⋊C₈	—	43	1	no	—
406	C₂²⋊C₈	—	43	1	no	—
407	C₂²⋊C₈	—	43	1	no	—
408	C₂²⋊C₈	—	43	1	no	—
409	C₂²⋊C₈	—	43	1	no	—
410	C₂²⋊C₈	—	86	1	no	—
411	C₂²⋊C₈	—	86	1	no	—
412	C₂²⋊C₈	—	86	1	no	—
413	#97	—	2	1	no	—
414	#97	—	2	1	no	—
415	#97	—	43	1	no	—
416	#97	—	43	1	no	—
417	#97	—	43	1	no	—
418	#97	—	43	1	no	—
419	#97	—	86	1	no	—
420	#97	—	86	1	no	—
421	C₄×C₈	—	2	1	no	—
422	C₄×C₈	—	43	1	no	—
423	C₄×C₈	—	43	1	no	—
424	C₄×C₈	—	43	1	no	—
425	C₄×C₈	—	43	1	no	—
426	C₄×C₈	—	43	1	no	—
427	C₄×C₈	—	43	1	no	—
428	C₄×C₈	—	86	1	no	—
429	#41	—	4	2	no	—
430	C₂×Q₈	Dic₄₃⋊C₄	1	1	yes	characteristic
431	C₂×D₄	Dic₄₃⋊C₄	1	1	yes	characteristic
432	C₂×D₄	Dic₄₃⋊C₄	1	1	yes	characteristic
433	C₂×D₄	Dic₄₃⋊C₄	1	1	yes	characteristic
434	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
435	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
436	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
443	M₁₆	—	8	1	no	—
444	M₁₆	—	86	2	no	—
445	M₁₆	—	86	2	no	—
446	M₁₆	—	344	1	no	—
447	M₁₆	—	172	1	no	—
448	M₁₆	—	172	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	8	1	no	—
454	C₂×C₈	—	8	1	no	—
455	C₂×C₈	—	43	1	no	—
456	C₂×C₈	—	43	1	no	—
457	C₂×C₈	—	43	1	no	—
458	C₂×C₈	—	43	1	no	—
459	C₂×C₈	—	43	1	no	—
460	C₂×C₈	—	43	1	no	—
461	C₂×C₈	—	43	1	no	—
462	C₂×C₈	—	43	1	no	—
463	C₂×C₈	—	86	2	no	—
464	C₂×C₈	—	86	1	no	—
465	C₂×C₈	—	86	1	no	—
466	C₂×C₈	—	86	1	no	—
467	C₂×C₈	—	86	1	no	—
468	C₂×C₈	—	344	1	no	—
469	C₂×C₈	—	344	1	no	—
470	C₂×C₈	—	172	1	no	—
471	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
472	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
473	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
474	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
475	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
476	C₄⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
477	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
478	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
479	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
480	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
481	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
482	C₂²⋊C₄	Dic₄₃⋊C₄	1	1	yes	characteristic
483	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
484	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
485	C₄²	C₂×Dic₈₆	1	1	yes	characteristic
486	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
487	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
488	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
489	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
490	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
491	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
492	C₄²	C₂³×D₄₃	1	1	yes	characteristic
493	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
494	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
495	C₂³	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
496	Q₈	—	4	1	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	2	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
516	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
517	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
518	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
519	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
520	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
521	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
522	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
523	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
524	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
526	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	1	no	—
531	C₈	—	43	2	no	—
532	C₈	—	86	1	no	—
533	C₈	—	86	1	no	—
534	C₈	—	86	1	no	—
535	C₈	—	86	1	no	—
536	C₈	—	86	1	no	—
537	C₈	—	86	1	no	—
538	C₈	—	86	1	no	—
539	C₈	—	172	1	no	—
540	C₈	—	172	1	no	—
541	C₈	—	172	1	no	—
542	C₈	—	172	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	#14582947	1	2	yes	—
552	C₂²	C₂²×Dic₄₃⋊C₄	1	1	yes	characteristic
553	C₄	—	2	1	no	—
554	C₄	—	2	1	no	—
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	#131×D₄₃	1	1	yes	characteristic
564	C₄	#14583664	1	1	yes	characteristic
565	C₄	#14583702	1	1	yes	characteristic
566	C₄	#14583714	1	1	yes	characteristic
567	C₂	—	2	2	no	—
568	C₂	—	4	1	no	—
569	C₂	—	4	1	no	—
570	C₂	#19143161	1	1	yes	characteristic
571	C₂	#19143193	1	1	yes	characteristic
572	C₂	C₂×#14582947	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×#2990	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₄₃	Q₈
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2990	D₄₃
hypocenter	C₄₃	#17840
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
3. #19133381	C₂	semidirect
4. #19133378	C₂	semidirect
5. #19133376	C₂	semidirect
6. #19133373	C₂	semidirect
7. #19133371	C₂	semidirect
8. #19133369	C₂	semidirect
9. #19133363	C₂	semidirect
10. #19133360	C₂	semidirect
11. #19133356	C₂	semidirect
12. #19133348	C₂	semidirect
13. #19133345	C₂	semidirect
14. C₂×#14582651	C₂	semidirect
353. C₄₃	#17840	semidirect

Maximal subgroups

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

subgroup	index
#19143720	2
#19143562	2
#19133381	2
#19133378	2
#19133376	2
#19133373	2
#19133371	2
#19133369	2
#19133363	2
#19133360	2
#19133356	2
#19133348	2
#19133345	2
C₂×#14582651	2
C₄₃×#2990	2
#17840	43