Subgroups — #25961165

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143600	C₂	1	8	yes	maximal, complemented
2	#19143591	C₂	1	8	yes	maximal, complemented
3	#19143536	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143530	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143313	C₂	1	1	yes	maximal, characteristic, complemented
6	#19143307	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143299	C₂	1	2	yes	maximal, complemented
8	#19143290	C₂	1	2	yes	maximal, complemented
9	#19143239	C₂	1	2	yes	maximal, complemented
10	#19143233	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143023	C₂	1	2	yes	maximal, complemented
12	C₂×#14582855	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₃×#3455	C₂	1	1	yes	maximal, characteristic
14	C₂×#13063332	C₂²	1	2	yes	—
15	C₂×#13063332	C₂²	1	2	yes	—
16	C₂²×#10621877	C₂²	1	1	yes	characteristic
17	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14583030	C₂²	1	4	yes	complemented
19	#14583030	C₂²	1	8	yes	complemented
20	Q₈×C₄₃⋊C₈	C₂²	1	4	yes	complemented
21	#14582977	C₂²	1	8	yes	—
22	#14582977	C₂²	1	4	yes	complemented
23	#14582971	C₂²	1	8	yes	—
24	#14582971	C₂²	1	8	yes	—
25	#14582971	C₂²	1	8	yes	complemented
26	D₄×C₄₃⋊C₈	C₂²	1	8	yes	—
27	D₄×C₄₃⋊C₈	C₂²	1	4	yes	complemented
28	#14582960	C₂²	1	8	yes	—
29	#14582960	C₂²	1	8	yes	complemented
30	#14582952	C₂²	1	8	yes	complemented
31	#14582926	C₂²	1	2	yes	—
32	#14582926	C₂²	1	2	yes	—
33	#14582923	C₂²	1	1	yes	characteristic
34	#14582923	C₂²	1	1	yes	characteristic
35	#14582866	C₂²	1	2	yes	—
36	#14582866	C₂²	1	2	yes	—
37	#14582863	C₂²	1	2	yes	—
38	#14582855	C₂²	1	4	yes	—
39	#14582855	C₂²	1	4	yes	—
40	#14582855	C₂²	1	2	yes	—
41	#14582855	C₂²	1	2	yes	—
42	#14582855	C₂²	1	4	yes	complemented
43	#14582855	C₂²	1	4	yes	complemented
44	C₄×#10621877	C₂²	1	2	yes	—
45	C₄×#10621877	C₂²	1	4	yes	complemented
46	C₂×#13063236	C₂²	1	1	yes	characteristic
47	C₂×#13063236	C₂²	1	1	yes	characteristic
48	C₂×#13063236	C₂²	1	4	yes	complemented
49	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
51	C₄₃×#542	C₄	1	4	yes	—
52	C₄₃×#541	C₄	1	2	yes	—
53	C₄₃×#540	C₄	1	2	yes	—
54	C₄₃×#539	C₄	1	4	yes	—
55	C₄₃×#538	C₄	1	4	yes	—
56	C₄₃×#533	C₂²	1	1	yes	characteristic
57	C₄₃×#532	C₂²	1	1	yes	characteristic
58	C₄₃×#529	C₂²	1	8	yes	—
59	C₄₃×#525	C₂²	1	2	yes	—
60	C₄×#41×C₄₃	C₂²	1	2	yes	—
61	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
62	#13063332	—	2	8	no	—
63	#13063332	—	2	8	no	—
64	C₂×#10621877	—	2	4	no	—
65	C₂×#10621877	C₂³	1	2	yes	—
66	C₂×#10621877	C₂³	1	2	yes	—
67	C₂×#10621877	C₂³	1	4	yes	—
68	C₂×#10621877	C₂³	1	4	yes	—
69	C₂×#10621877	C₂³	1	2	yes	—
70	C₂×#10621877	C₂³	1	2	yes	—
71	C₂²×C₄₃⋊C₈	—	2	4	no	—
72	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
75	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
76	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	—
77	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
81	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
82	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
83	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
84	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
85	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
86	#13063236	C₂³	1	2	yes	—
87	#13063236	C₂³	1	2	yes	—
88	#13063236	C₂³	1	4	yes	—
89	#13063236	C₂³	1	4	yes	—
90	#13063236	C₂³	1	4	yes	—
91	#13063236	C₂³	1	4	yes	—
92	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
93	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
94	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
95	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
96	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
97	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
98	C₂×#41×C₄₃	C₂³	1	2	yes	—
99	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
102	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
103	#126×C₄₃	C₂×C₄	1	8	yes	—
104	#126×C₄₃	C₂×C₄	1	8	yes	—
105	#125×C₄₃	C₂×C₄	1	8	yes	—
106	#125×C₄₃	C₂×C₄	1	2	yes	—
107	#124×C₄₃	C₂×C₄	1	8	yes	—
108	#124×C₄₃	C₂×C₄	1	2	yes	—
109	#123×C₄₃	C₂×C₄	1	4	yes	—
110	#123×C₄₃	C₂×C₄	1	8	yes	—
111	#123×C₄₃	C₂×C₄	1	8	yes	—
112	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
113	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
114	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
115	#121×C₄₃	C₂×C₄	1	4	yes	—
116	#121×C₄₃	C₂×C₄	1	8	yes	—
117	#121×C₄₃	C₂×C₄	1	4	yes	—
118	#120×C₄₃	C₂×C₄	1	4	yes	—
119	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
120	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
121	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
122	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
123	C₄×D₄×C₄₃	C₂³	1	8	yes	—
124	C₄×D₄×C₄₃	C₂³	1	4	yes	—
125	#117×C₄₃	C₂×C₄	1	2	yes	—
126	#117×C₄₃	C₂×C₄	1	2	yes	—
127	#117×C₄₃	C₂³	1	4	yes	—
128	#117×C₄₃	C₂³	1	2	yes	—
129	#117×C₄₃	C₂³	1	4	yes	—
130	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
131	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
132	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
135	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	#41×C₄₃	—	2	4	no	—
137	#41×C₄₃	—	2	4	no	—
138	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
139	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
140	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
143	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
148	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
151	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
155	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
156	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
157	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
158	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
159	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
160	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
161	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
162	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
163	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
164	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
165	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
166	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
167	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
168	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
169	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
170	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂²×C₄	1	8	yes	—
173	C₄²×C₄₃	C₂⁴	1	2	yes	—
174	C₄²×C₄₃	C₂⁴	1	2	yes	—
175	C₄²×C₄₃	C₂⁴	1	4	yes	—
176	#10621877	—	2	4	no	—
177	#10621877	—	2	4	no	—
178	#10621877	—	2	4	no	—
179	#10621877	—	2	4	no	—
180	#10621877	—	2	8	no	—
181	#10621877	—	2	8	no	—
182	C₂×C₄₃⋊C₈	—	2	2	no	—
183	C₂×C₄₃⋊C₈	—	2	2	no	—
184	C₂×C₄₃⋊C₈	—	2	8	no	—
185	C₂×C₄₃⋊C₈	—	2	8	no	—
186	C₂×C₄₃⋊C₈	—	2	8	no	—
187	C₂×C₄₃⋊C₈	#41	1	4	yes	—
188	C₂×C₄₃⋊C₈	#41	1	4	yes	—
189	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
190	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
191	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
192	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
193	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
194	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
195	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	4	2	no	—
198	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
199	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
200	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
201	Q₈×C₄₃	—	2	4	no	—
202	Q₈×C₄₃	—	4	4	no	—
203	D₄×C₄₃	—	2	8	no	—
204	D₄×C₄₃	—	2	4	no	—
205	D₄×C₄₃	—	4	4	no	—
206	D₄×C₄₃	—	4	8	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	8	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
217	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
219	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
220	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
221	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
225	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
226	C₄₃⋊C₈	—	2	2	no	—
227	C₄₃⋊C₈	—	2	2	no	—
228	C₄₃⋊C₈	—	2	4	no	—
229	C₄₃⋊C₈	—	2	4	no	—
230	C₄₃⋊C₈	C₂×#41	1	4	yes	—
231	C₄₃⋊C₈	C₂×#41	1	2	yes	—
232	C₄₃⋊C₈	C₂×#41	1	2	yes	—
233	#60209	—	43	1	no	maximal, Sylow
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	2	no	—
236	C₂²×C₄₃	—	2	4	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	2	8	no	—
239	C₂²×C₄₃	—	4	4	no	—
240	C₂²×C₄₃	C₄×#41	1	2	yes	—
241	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	2	4	no	—
244	C₄×C₄₃	—	2	4	no	—
245	C₄×C₄₃	—	2	2	no	—
246	C₄×C₄₃	—	2	8	no	—
247	C₄×C₄₃	—	2	2	no	—
248	C₄×C₄₃	C₄×#41	1	2	yes	—
249	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
250	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
251	#3455	D₄₃	1	1	yes	characteristic
252	#2969	—	43	8	no	—
253	#2968	—	43	8	no	—
254	#2961	—	43	1	no	—
255	#2960	—	43	1	no	—
256	#2932	—	43	1	no	—
257	#2931	—	43	1	no	—
258	#2930	—	43	2	no	—
259	#2929	—	43	2	no	—
260	#2922	—	43	2	no	—
261	#2921	—	43	1	no	—
262	#2875	—	43	2	no	—
263	C₂×#405	—	43	1	no	—
264	C₂×C₄₃	—	2	2	no	—
265	C₂×C₄₃	—	4	4	no	—
266	C₂×C₄₃	—	4	2	no	—
267	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
268	C₂×C₄₃	#3573	1	2	yes	—
269	C₂×#131	—	43	2	no	—
270	C₂×#131	—	43	2	no	—
271	C₂²×M₁₆	—	43	1	no	—
272	C₂³×C₈	—	43	1	no	—
273	#542	Dic₄₃	1	4	yes	—
274	#541	Dic₄₃	1	2	yes	—
275	#540	Dic₄₃	1	2	yes	—
276	#539	Dic₄₃	1	4	yes	—
277	#538	Dic₄₃	1	4	yes	—
278	#533	C₂×D₄₃	1	1	yes	characteristic
279	#532	C₂×D₄₃	1	1	yes	characteristic
280	#529	C₂×D₄₃	1	8	yes	—
281	#525	C₂×D₄₃	1	2	yes	—
282	C₄×#41	C₂×D₄₃	1	2	yes	—
283	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
284	#446	—	43	4	no	—
285	#446	—	43	8	no	—
286	C₈×Q₈	—	43	4	no	—
287	#436	—	43	8	no	—
288	#436	—	43	4	no	—
289	#435	—	43	8	no	—
290	#435	—	43	8	no	—
291	#435	—	43	8	no	—
292	C₈×D₄	—	43	8	no	—
293	C₈×D₄	—	43	4	no	—
294	#433	—	43	8	no	—
295	#433	—	43	8	no	—
296	#431	—	43	8	no	—
297	#424	—	43	2	no	—
298	#424	—	43	2	no	—
299	#423	—	43	1	no	—
300	#423	—	43	1	no	—
301	#408	—	43	2	no	—
302	#408	—	43	2	no	—
303	#407	—	43	2	no	—
304	#405	—	43	4	no	—
305	#405	—	43	4	no	—
306	#405	—	43	2	no	—
307	#405	—	43	2	no	—
308	#405	—	43	4	no	—
309	#405	—	43	4	no	—
310	C₄×M₁₆	—	43	2	no	—
311	C₄×M₁₆	—	43	4	no	—
312	C₂×#97	—	43	1	no	—
313	C₂×#97	—	43	1	no	—
314	C₂×#97	—	43	4	no	—
315	C₂×C₄×C₈	—	43	1	no	—
316	C₂×C₄×C₈	—	43	1	no	—
317	C₄₃	#60209	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	C₂²×D₄₃	1	2	yes	—
319	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
320	#131	—	86	8	no	—
321	#131	—	86	8	no	—
322	C₂×M₁₆	—	43	2	no	—
323	C₂×M₁₆	—	43	2	no	—
324	C₂×M₁₆	—	43	2	no	—
325	C₂×M₁₆	—	43	2	no	—
326	C₂×M₁₆	—	43	4	no	—
327	C₂×M₁₆	—	43	4	no	—
328	C₂×M₁₆	—	86	4	no	—
329	C₂²×C₈	—	43	1	no	—
330	C₂²×C₈	—	43	1	no	—
331	C₂²×C₈	—	43	1	no	—
332	C₂²×C₈	—	43	4	no	—
333	C₂²×C₈	—	43	1	no	—
334	C₂²×C₈	—	43	4	no	—
335	C₂²×C₈	—	43	4	no	—
336	C₂²×C₈	—	86	4	no	—
337	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
338	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
339	#127	C₂×Dic₄₃	1	1	yes	characteristic
340	#126	C₂×Dic₄₃	1	8	yes	—
341	#126	C₂×Dic₄₃	1	8	yes	—
342	#125	C₂×Dic₄₃	1	8	yes	—
343	#125	C₂×Dic₄₃	1	2	yes	—
344	#124	C₂×Dic₄₃	1	8	yes	—
345	#124	C₂×Dic₄₃	1	2	yes	—
346	#123	C₂×Dic₄₃	1	4	yes	—
347	#123	C₂×Dic₄₃	1	8	yes	—
348	#123	C₂×Dic₄₃	1	8	yes	—
349	C₂²⋊Q₈	C₂×Dic₄₃	1	4	yes	—
350	C₂²⋊Q₈	C₂×Dic₄₃	1	8	yes	—
351	C₂²⋊Q₈	C₂×Dic₄₃	1	4	yes	—
352	#121	C₂×Dic₄₃	1	4	yes	—
353	#121	C₂×Dic₄₃	1	8	yes	—
354	#121	C₂×Dic₄₃	1	4	yes	—
355	#120	C₂×Dic₄₃	1	4	yes	—
356	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
357	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
358	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
359	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
360	C₄×D₄	C₂²×D₄₃	1	8	yes	—
361	C₄×D₄	C₂²×D₄₃	1	4	yes	—
362	#117	C₂×Dic₄₃	1	2	yes	—
363	#117	C₂×Dic₄₃	1	2	yes	—
364	#117	C₂²×D₄₃	1	4	yes	—
365	#117	C₂²×D₄₃	1	2	yes	—
366	#117	C₂²×D₄₃	1	4	yes	—
367	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
368	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
369	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
371	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
372	C₄⋊C₈	—	43	4	no	—
373	C₄⋊C₈	—	43	4	no	—
374	C₄⋊C₈	—	43	8	no	—
375	C₄⋊C₈	—	43	8	no	—
376	C₂²⋊C₈	—	43	8	no	—
377	C₂²⋊C₈	—	43	8	no	—
378	C₂²⋊C₈	—	43	8	no	—
379	#97	—	43	2	no	—
380	#97	—	43	2	no	—
381	#97	—	43	4	no	—
382	#97	—	43	4	no	—
383	#97	—	43	4	no	—
384	#97	—	43	4	no	—
385	C₄×C₈	—	43	4	no	—
386	C₄×C₈	—	43	2	no	—
387	C₄×C₈	—	43	2	no	—
388	C₄×C₈	—	43	4	no	—
389	C₄×C₈	—	43	4	no	—
390	C₄×C₈	—	43	4	no	—
391	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
395	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
396	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
397	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
398	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
399	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
403	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
404	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
405	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
406	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
407	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
408	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
409	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
410	M₁₆	—	86	4	no	—
411	M₁₆	—	86	4	no	—
412	M₁₆	—	86	8	no	—
413	M₁₆	—	86	8	no	—
414	M₁₆	—	86	4	no	—
415	M₁₆	—	86	4	no	—
416	C₂×C₈	—	43	4	no	—
417	C₂×C₈	—	43	4	no	—
418	C₂×C₈	—	43	1	no	—
419	C₂×C₈	—	43	1	no	—
420	C₂×C₈	—	43	2	no	—
421	C₂×C₈	—	43	2	no	—
422	C₂×C₈	—	43	2	no	—
423	C₂×C₈	—	43	4	no	—
424	C₂×C₈	—	43	4	no	—
425	C₂×C₈	—	86	8	no	—
426	C₂×C₈	—	86	8	no	—
427	C₂×C₈	—	86	8	no	—
428	C₂×C₈	—	86	2	no	—
429	C₂×C₈	—	86	2	no	—
430	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
431	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
432	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
433	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
434	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
435	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
436	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
437	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
438	C₂²⋊C₄	C₂²×Dic₄₃	1	4	yes	—
439	C₂²⋊C₄	C₂²×Dic₄₃	1	4	yes	—
440	C₂²⋊C₄	C₂²×Dic₄₃	1	4	yes	—
441	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
442	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
443	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
444	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
445	C₄²	C₂²×Dic₄₃	1	2	yes	—
446	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
447	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
448	C₄²	C₂²×Dic₄₃	1	8	yes	—
449	C₄²	C₂³×D₄₃	1	2	yes	—
450	C₄²	C₂³×D₄₃	1	2	yes	—
451	C₄²	C₂³×D₄₃	1	4	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	C₂³×Dic₄₃	1	2	yes	—
455	C₂³	C₂³×Dic₄₃	1	4	yes	—
456	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
457	Q₈	—	2	4	no	—
458	Q₈	—	4	4	no	—
459	D₄	—	2	8	no	—
460	D₄	—	2	4	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	8	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	8	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
473	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
474	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
475	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
476	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
477	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
478	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
479	C₂×C₄	#41×D₄₃	1	2	yes	—
480	C₂×C₄	#41×D₄₃	1	2	yes	—
481	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
482	C₈	—	43	4	no	—
483	C₈	—	43	2	no	—
484	C₈	—	43	2	no	—
485	C₈	—	86	2	no	—
486	C₈	—	86	4	no	—
487	C₈	—	86	4	no	—
488	C₈	—	86	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	8	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	#41×Dic₄₃	1	2	yes	—
496	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
497	C₄	—	2	2	no	—
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	8	no	—
502	C₄	—	2	2	no	—
503	C₄	#41×Dic₄₃	1	2	yes	—
504	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
505	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
506	C₂	—	2	2	no	—
507	C₂	—	4	2	no	—
508	C₂	—	4	4	no	—
509	C₂	C₂×#41×Dic₄₃	1	1	yes	characteristic
510	C₂	#19149307	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting, prime radical	C₄₃×#3455	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#3455	D₄₃
hypocenter	C₄₃	#60209
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #19143600	C₂	semidirect
2. #19143591	C₂	semidirect
3. #19143536	C₂	semidirect
4. #19143530	C₂	semidirect
5. #19143313	C₂	semidirect
6. #19143307	C₂	semidirect
7. #19143299	C₂	semidirect
8. #19143290	C₂	semidirect
9. #19143239	C₂	semidirect
10. #19143233	C₂	semidirect
11. #19143023	C₂	semidirect
12. C₂×#14582855	C₂	semidirect
18. #14583030	C₂²	semidirect
19. #14583030	C₂²	semidirect
20. Q₈×C₄₃⋊C₈	C₂²	semidirect
22. #14582977	C₂²	semidirect
25. #14582971	C₂²	semidirect
27. D₄×C₄₃⋊C₈	C₂²	semidirect
29. #14582960	C₂²	semidirect
30. #14582952	C₂²	semidirect
42. #14582855	C₂²	semidirect
43. #14582855	C₂²	semidirect
45. C₄×#10621877	C₂²	semidirect
48. C₂×#13063236	C₂²	semidirect
317. C₄₃	#60209	semidirect

Maximal subgroups

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

subgroup	index
#19143600	2
#19143591	2
#19143536	2
#19143530	2
#19143313	2
#19143307	2
#19143299	2
#19143290	2
#19143239	2
#19143233	2
#19143023	2
C₂×#14582855	2
C₄₃×#3455	2
#60209	43