Subgroups — #25001951

Order 11008.

1214 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147796	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582881	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582865	C₂	1	1	yes	maximal, characteristic
4	#19134334	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134333	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134291	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂²×#10621877	C₂²	1	1	yes	characteristic
10	C₂²×#10621877	C₂²	1	1	yes	characteristic
11	#14583380	—	2	2	no	—
12	#14583379	—	2	2	no	—
13	#14583376	—	2	1	no	—
14	#14583373	—	2	1	no	—
15	#14583372	C₄	1	4	yes	—
16	C₄×#10621898	—	2	2	no	—
17	#14583367	—	2	2	no	—
18	C₂×#13063284	C₂²	1	1	yes	characteristic
19	#117×D₄₃	—	2	2	no	—
20	#14582881	—	2	2	no	—
21	#14582881	C₄	1	4	yes	complemented
22	C₂×#13063243	—	2	1	no	—
23	C₂×#13063241	—	2	1	no	—
24	#14582865	—	2	2	no	—
25	#14582865	C₄	1	4	yes	complemented
26	C₂×(C₂×D₄₃)⋊C₈	—	2	2	no	—
27	#14582668	—	2	2	no	—
28	#14582667	—	2	2	no	—
29	#14582653	—	2	2	no	—
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#336	—	2	2	no	—
34	C₂×#10621898	—	2	1	no	—
35	C₂×#10621898	—	2	1	no	—
36	C₂×#10621898	—	2	1	no	—
37	C₂×#10621898	—	2	1	no	—
38	C₂×#10621898	—	2	1	no	—
39	C₂×#10621898	—	2	1	no	—
40	C₂×#10621898	—	2	1	no	—
41	C₂×#10621898	—	2	1	no	—
42	C₂×#10621898	C₂×C₄	1	2	yes	—
43	C₂×#10621898	C₂×C₄	1	2	yes	—
44	C₂×#10621898	D₄	1	2	yes	—
45	C₂×#10621898	Q₈	1	2	yes	—
46	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
47	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
48	C₂²×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
49	C₂²×C₄×D₄₃	D₄	1	2	yes	—
50	C₂×#10621877	—	2	1	no	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	—	2	1	no	—
54	C₂×#10621877	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂×#10621877	—	2	1	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂×#10621877	—	2	1	no	—
59	C₂×#10621877	—	2	1	no	—
60	C₂×#10621877	C₂×C₄	1	2	yes	complemented
61	C₂×#10621877	C₂×C₄	1	2	yes	complemented
62	C₂²×C₄₃⋊C₈	—	2	1	no	—
63	C₂²×C₄₃⋊C₈	—	2	1	no	—
64	C₄×Dic₈₆	—	2	4	no	—
65	#13063290	—	2	4	no	—
66	C₄×D₁₇₂	—	2	4	no	—
67	#13063287	—	2	4	no	—
68	C₄×C₂²⋊D₄₃	—	2	8	no	—
69	(C₂²⋊D₄₃)⋊C₄	—	2	8	no	—
70	#13063284	—	2	1	no	—
71	#13063284	—	2	1	no	—
72	#13063284	—	2	1	no	—
73	#13063284	—	2	1	no	—
74	#13063283	—	2	4	no	—
75	#13063282	—	2	4	no	—
76	#13063281	—	2	4	no	—
77	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
78	C₄⋊C₄×D₄₃	—	2	4	no	—
79	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	2	yes	—
80	C₂²⋊C₄×D₄₃	—	2	4	no	—
81	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
82	C₄²×D₄₃	—	2	4	no	—
83	#13063243	—	2	4	no	—
84	#13063241	—	2	4	no	—
85	(C₂×D₄₃)⋊C₈	—	2	8	no	—
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂×M₁₆×C₄₃	—	2	1	no	—
89	C₂×M₁₆×C₄₃	—	2	1	no	—
90	C₂×M₁₆×C₄₃	—	2	1	no	—
91	C₂×M₁₆×C₄₃	—	2	1	no	—
92	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	complemented
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	C₂²×C₈×C₄₃	—	2	1	no	—
95	C₂²×C₈×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	—	2	1	no	—
97	C₂²×C₈×C₄₃	—	2	1	no	—
98	C₂²×C₈×C₄₃	—	2	1	no	—
99	C₂²×C₈×C₄₃	—	2	1	no	—
100	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	complemented
101	#117×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	#117×C₄₃	—	2	1	no	—
104	#117×C₄₃	—	2	1	no	—
105	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
106	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×C₄²×C₄₃	D₄	1	2	yes	—
108	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂³×D₄₃	C₂²⋊C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₃	—	2	2	no	—
126	C₂×C₂²⋊D₄₃	—	2	2	no	—
127	C₂×C₂²⋊D₄₃	—	2	2	no	—
128	C₂×C₂²⋊D₄₃	—	2	2	no	—
129	C₂×C₂²⋊D₄₃	C₄²	1	4	yes	—
130	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	4	yes	—
131	C₂²×Dic₄₃	C₂²⋊C₄	1	2	yes	—
132	C₂²×Dic₄₃	C₂²⋊C₄	1	4	yes	—
133	#10621898	—	2	2	no	—
134	#10621898	—	2	2	no	—
135	#10621898	—	2	2	no	—
136	#10621898	—	2	2	no	—
137	#10621898	—	2	2	no	—
138	#10621898	—	2	2	no	—
139	#10621898	—	2	2	no	—
140	#10621898	—	2	2	no	—
141	#10621898	—	2	2	no	—
142	#10621898	—	2	2	no	—
143	#10621898	—	2	2	no	—
144	#10621898	—	2	2	no	—
145	#10621898	—	2	2	no	—
146	#10621898	—	2	2	no	—
147	#10621898	—	2	2	no	—
148	#10621898	—	2	2	no	—
149	C₂×D₁₇₂	—	2	1	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
154	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
155	C₂×C₄×D₄₃	—	2	2	no	—
156	C₂×C₄×D₄₃	—	2	2	no	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×C₄×D₄₃	—	2	8	no	—
160	C₂×C₄×D₄₃	C₂²⋊C₄	1	4	yes	—
161	C₂×C₄×D₄₃	C₄⋊C₄	1	4	yes	—
162	C₂×Dic₈₆	—	2	1	no	—
163	C₂×Dic₈₆	—	2	1	no	—
164	C₂×Dic₈₆	—	2	1	no	—
165	C₂×Dic₈₆	—	2	1	no	—
166	C₂×Dic₈₆	C₂²⋊C₄	1	2	yes	—
167	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
168	M₁₆×C₄₃	—	2	2	no	—
169	M₁₆×C₄₃	—	2	2	no	—
170	M₁₆×C₄₃	—	4	1	no	—
171	M₁₆×C₄₃	—	4	1	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₂×C₈×C₄₃	—	4	1	no	—
177	C₂×C₈×C₄₃	—	4	1	no	—
178	C₂×C₈×C₄₃	—	4	1	no	—
179	C₂×C₈×C₄₃	—	4	1	no	—
180	C₂×C₈×C₄₃	—	4	1	no	—
181	C₂×C₈×C₄₃	—	4	1	no	—
182	C₄⋊C₄×C₄₃	—	2	2	no	—
183	C₄⋊C₄×C₄₃	—	2	2	no	—
184	C₂²⋊C₄×C₄₃	—	2	2	no	—
185	C₂²⋊C₄×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₂²⋊Dic₄₃	—	2	2	no	—
189	C₂²⋊Dic₄₃	—	2	2	no	—
190	(C₂×D₄₃)⋊C₄	—	2	8	no	—
191	C₄⋊Dic₄₃	—	2	2	no	—
192	C₄⋊Dic₄₃	—	2	2	no	—
193	Dic₄₃⋊C₄	—	2	8	no	—
194	C₄×Dic₄₃	—	2	8	no	—
195	C₄×Dic₄₃	—	2	2	no	—
196	C₄×Dic₄₃	—	2	2	no	—
197	#10621877	—	2	2	no	—
198	#10621877	—	2	2	no	—
199	#10621877	—	2	2	no	—
200	#10621877	—	2	2	no	—
201	#10621877	—	4	1	no	—
202	#10621877	—	4	1	no	—
203	#10621877	—	4	1	no	—
204	#10621877	—	4	1	no	—
205	C₂×C₄₃⋊C₈	—	2	2	no	—
206	C₂×C₄₃⋊C₈	—	2	2	no	—
207	C₂×C₄₃⋊C₈	—	4	1	no	—
208	C₂×C₄₃⋊C₈	—	4	1	no	—
209	C₂×C₄₃⋊C₈	—	4	1	no	—
210	C₂×C₄₃⋊C₈	—	4	1	no	—
211	C₂³×C₄₃	—	4	2	no	—
212	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
213	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
214	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
217	C₂³×C₄₃	#117	1	1	yes	characteristic
218	C₂³×C₄₃	#117	1	1	yes	characteristic
219	C₂²×D₄₃	—	2	2	no	—
220	C₂²×D₄₃	—	2	2	no	—
221	C₂²×D₄₃	—	4	4	no	—
222	C₂²×D₄₃	#95	1	4	yes	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	4	4	no	—
225	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
239	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
240	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
241	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
242	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
245	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
250	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
251	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
253	C₂²⋊D₄₃	—	2	4	no	—
254	C₂²⋊D₄₃	—	2	4	no	—
255	C₂²⋊D₄₃	—	2	4	no	—
256	C₂²⋊D₄₃	—	2	4	no	—
257	C₂×Dic₄₃	—	2	2	no	—
258	C₂×Dic₄₃	—	2	2	no	—
259	C₂×Dic₄₃	—	2	4	no	—
260	C₂×Dic₄₃	—	4	4	no	—
261	C₂×Dic₄₃	#95	1	4	yes	—
262	D₁₇₂	—	2	2	no	—
263	D₁₇₂	—	2	2	no	—
264	D₁₇₂	—	2	2	no	—
265	D₁₇₂	—	2	2	no	—
266	C₄×D₄₃	—	2	4	no	—
267	C₄×D₄₃	—	2	4	no	—
268	C₄×D₄₃	—	2	4	no	—
269	C₄×D₄₃	—	2	4	no	—
270	C₄×D₄₃	—	8	8	no	—
271	Dic₈₆	—	2	2	no	—
272	Dic₈₆	—	2	2	no	—
273	Dic₈₆	—	2	2	no	—
274	Dic₈₆	—	2	2	no	—
275	C₈×C₄₃	—	4	2	no	—
276	C₈×C₄₃	—	4	2	no	—
277	C₄₃⋊C₈	—	4	2	no	—
278	C₄₃⋊C₈	—	4	2	no	—
279	#10747	—	43	1	no	maximal, Sylow
280	C₂²×C₄₃	—	2	2	no	—
281	C₂²×C₄₃	—	2	2	no	—
282	C₂²×C₄₃	—	2	2	no	—
283	C₂²×C₄₃	—	4	1	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	—	4	1	no	—
286	C₂²×C₄₃	—	4	1	no	—
287	C₂²×C₄₃	C₂×#95	1	1	yes	characteristic
288	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
289	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
290	C₂²×C₄₃	#379	1	1	yes	characteristic
291	C₂²×C₄₃	#380	1	1	yes	characteristic
292	C₂²×C₄₃	#380	1	1	yes	characteristic
293	C₂²×C₄₃	#381	1	1	yes	characteristic
294	C₂×D₄₃	—	2	4	no	—
295	C₂×D₄₃	—	4	4	no	—
296	C₂×D₄₃	—	4	4	no	—
297	C₂×D₄₃	—	8	2	no	—
298	C₄×C₄₃	—	4	4	no	—
299	C₄×C₄₃	#385	1	1	yes	characteristic
300	C₄×C₄₃	#385	1	1	yes	characteristic
301	C₄×C₄₃	#385	1	1	yes	characteristic
302	C₄×C₄₃	#385	1	1	yes	characteristic
303	C₄×C₄₃	#386	1	1	yes	characteristic
304	C₄×C₄₃	#386	1	1	yes	characteristic
305	C₄×C₄₃	#386	1	1	yes	characteristic
306	C₄×C₄₃	#386	1	1	yes	characteristic
307	Dic₄₃	—	2	4	no	—
308	Dic₄₃	—	4	4	no	—
309	#3428	—	43	1	no	—
310	C₂×#413	—	43	1	no	—
311	C₂×#408	—	43	1	no	—
312	#1742	—	43	1	no	—
313	#1742	—	43	1	no	—
314	#1729	—	43	1	no	—
315	#1729	D₄₃	1	1	yes	characteristic, complemented
316	C₂×C₄₃	—	2	1	no	—
317	C₂×C₄₃	—	2	1	no	—
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	C₂²⋊#95	1	1	yes	characteristic
323	C₂×C₄₃	#1791	1	2	yes	—
324	D₄₃	—	4	4	no	—
325	C₂²×#41	—	43	1	no	—
326	C₂²×M₁₆	—	43	1	no	—
327	C₂²×M₁₆	—	43	1	no	—
328	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
329	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
330	#520	—	86	2	no	—
331	#520	—	86	2	no	—
332	#519	—	86	1	no	—
333	#518	—	43	4	no	—
334	#518	—	86	1	no	—
335	C₄×#41	—	86	2	no	—
336	C₄×#41	—	86	2	no	—
337	C₂×#117	—	43	1	no	—
338	C₂×#117	—	86	2	no	—
339	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
340	#413	—	43	4	no	—
341	#413	—	86	2	no	—
342	C₂×#101	—	86	1	no	—
343	C₂×#100	—	86	1	no	—
344	#408	—	43	4	no	—
345	#408	—	86	2	no	—
346	C₂×C₂²⋊C₈	—	86	2	no	—
347	#343	—	86	2	no	—
348	#343	—	86	2	no	—
349	#336	—	2	2	no	—
350	#336	—	86	2	no	—
351	C₄₃	#10747	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	43	2	no	—
353	C₂×#41	—	43	2	no	—
354	C₂×#41	—	43	2	no	—
355	C₂×#41	—	43	2	no	—
356	C₂×#41	—	86	1	no	—
357	C₂×#41	—	86	1	no	—
358	C₂×#41	—	86	1	no	—
359	C₂×#41	—	86	1	no	—
360	C₂×#41	—	86	1	no	—
361	C₂×#41	—	86	1	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂²×Q₈	—	43	1	no	—
365	C₂²×D₄	—	43	2	no	—
366	C₂²×D₄	—	43	1	no	—
367	C₂³×C₄	—	43	2	no	—
368	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
369	C₂×M₁₆	—	2	1	no	—
370	C₂×M₁₆	—	2	1	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	43	2	no	—
375	C₂×M₁₆	—	43	2	no	—
376	C₂×M₁₆	—	86	1	no	—
377	C₂×M₁₆	—	86	1	no	—
378	C₂×M₁₆	—	86	1	no	—
379	C₂×M₁₆	—	86	1	no	—
380	C₂×M₁₆	—	86	1	no	—
381	C₂×M₁₆	—	86	1	no	—
382	C₂×M₁₆	—	86	1	no	—
383	C₂×M₁₆	—	86	1	no	—
384	C₂×M₁₆	—	86	1	no	—
385	C₂×M₁₆	—	86	1	no	—
386	C₂×M₁₆	C₄×D₄₃	1	2	yes	complemented
387	C₂²×C₈	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₂²×C₈	—	2	1	no	—
390	C₂²×C₈	—	2	1	no	—
391	C₂²×C₈	—	2	1	no	—
392	C₂²×C₈	—	2	1	no	—
393	C₂²×C₈	—	2	1	no	—
394	C₂²×C₈	—	86	1	no	—
395	C₂²×C₈	—	86	1	no	—
396	C₂²×C₈	C₄×D₄₃	1	2	yes	complemented
397	C₄×Q₈	—	86	4	no	—
398	C₄×Q₈	—	86	4	no	—
399	C₄×D₄	—	86	4	no	—
400	C₄×D₄	—	86	8	no	—
401	C₄×D₄	—	86	4	no	—
402	C₄×D₄	—	86	8	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	86	4	no	—
408	#117	—	86	4	no	—
409	#117	—	86	4	no	—
410	#117	—	86	1	no	—
411	#117	—	86	1	no	—
412	#117	—	86	1	no	—
413	#117	—	86	1	no	—
414	C₂×C₄⋊C₄	—	43	2	no	—
415	C₂×C₄⋊C₄	—	86	4	no	—
416	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
417	C₂×C₂²⋊C₄	—	43	2	no	—
418	C₂×C₂²⋊C₄	—	86	4	no	—
419	C₂×C₂²⋊C₄	C₄×D₄₃	1	2	yes	—
420	C₂×C₄²	—	43	2	no	—
421	C₂×C₄²	—	86	4	no	—
422	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
423	#101	—	86	4	no	—
424	#100	—	86	4	no	—
425	C₂²⋊C₈	—	86	8	no	—
426	C₂⁴	—	43	2	no	—
427	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
428	#41	—	86	2	no	—
429	#41	—	86	2	no	—
430	#41	—	86	2	no	—
431	#41	—	86	2	no	—
432	#41	—	86	2	no	—
433	#41	—	86	2	no	—
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	#41	—	86	2	no	—
437	#41	—	86	2	no	—
438	#41	—	86	2	no	—
439	#41	—	86	2	no	—
440	#41	—	86	2	no	—
441	#41	—	86	2	no	—
442	#41	—	86	2	no	—
443	#41	—	86	2	no	—
444	C₂×Q₈	—	43	2	no	—
445	C₂×Q₈	—	43	2	no	—
446	C₂×Q₈	—	86	1	no	—
447	C₂×Q₈	—	86	1	no	—
448	C₂×Q₈	—	86	1	no	—
449	C₂×Q₈	—	86	1	no	—
450	C₂×D₄	—	43	4	no	—
451	C₂×D₄	—	43	4	no	—
452	C₂×D₄	—	43	2	no	—
453	C₂×D₄	—	43	2	no	—
454	C₂×D₄	—	86	2	no	—
455	C₂×D₄	—	86	2	no	—
456	C₂×D₄	—	86	2	no	—
457	C₂×D₄	—	86	2	no	—
458	C₂×D₄	—	86	1	no	—
459	C₂×D₄	—	86	1	no	—
460	C₂×D₄	—	86	1	no	—
461	C₂×D₄	—	86	1	no	—
462	C₂²×C₄	—	43	2	no	—
463	C₂²×C₄	—	43	4	no	—
464	C₂²×C₄	—	43	4	no	—
465	C₂²×C₄	—	43	4	no	—
466	C₂²×C₄	—	86	8	no	—
467	C₂²×C₄	—	86	2	no	—
468	C₂²×C₄	—	86	2	no	—
469	C₂²×C₄	—	86	2	no	—
470	C₂²×C₄	—	86	2	no	—
471	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
472	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
475	C₂²×C₄	#10621898	1	1	yes	characteristic
476	C₂²×C₄	#10621898	1	1	yes	characteristic
477	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
478	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
479	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
480	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
481	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
482	C₂²×C₄	#10621900	1	1	yes	characteristic
483	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
484	C₂²×C₄	#10621902	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
486	M₁₆	—	2	2	no	—
487	M₁₆	—	2	2	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	1	no	—
490	M₁₆	—	86	2	no	—
491	M₁₆	—	86	2	no	—
492	M₁₆	—	86	2	no	—
493	M₁₆	—	86	2	no	—
494	M₁₆	—	172	1	no	—
495	M₁₆	—	172	1	no	—
496	M₁₆	—	172	1	no	—
497	M₁₆	—	172	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	4	1	no	—
508	C₂×C₈	—	86	2	no	—
509	C₂×C₈	—	86	2	no	—
510	C₂×C₈	—	172	1	no	—
511	C₂×C₈	—	172	1	no	—
512	C₂×C₈	—	172	1	no	—
513	C₂×C₈	—	172	1	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	86	8	no	—
517	C₄⋊C₄	—	86	2	no	—
518	C₄⋊C₄	—	86	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	86	8	no	—
522	C₂²⋊C₄	—	86	2	no	—
523	C₂²⋊C₄	—	86	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	86	8	no	—
527	C₄²	—	86	2	no	—
528	C₄²	—	86	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	43	4	no	—
531	C₂³	—	86	2	no	—
532	C₂³	—	86	2	no	—
533	C₂³	—	172	4	no	—
534	C₂³	C₄²×D₄₃	1	1	yes	characteristic
535	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
536	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
537	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
538	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
539	C₂³	#13063282	1	1	yes	characteristic
540	C₂³	#13063283	1	1	yes	characteristic
541	Q₈	—	86	2	no	—
542	Q₈	—	86	2	no	—
543	Q₈	—	86	2	no	—
544	Q₈	—	86	2	no	—
545	D₄	—	86	4	no	—
546	D₄	—	86	4	no	—
547	D₄	—	86	4	no	—
548	D₄	—	86	4	no	—
549	D₄	—	86	2	no	—
550	D₄	—	86	2	no	—
551	D₄	—	86	2	no	—
552	D₄	—	86	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	43	4	no	—
556	C₂×C₄	—	86	2	no	—
557	C₂×C₄	—	86	2	no	—
558	C₂×C₄	—	86	4	no	—
559	C₂×C₄	—	86	4	no	—
560	C₂×C₄	—	86	4	no	—
561	C₂×C₄	—	86	4	no	—
562	C₂×C₄	—	86	4	no	—
563	C₂×C₄	—	344	8	no	—
564	C₂×C₄	—	172	4	no	—
565	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
566	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
567	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
568	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
569	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
570	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
572	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
573	C₂×C₄	#13063287	1	1	yes	characteristic
574	C₂×C₄	#13063287	1	1	yes	characteristic
575	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
576	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
577	C₂×C₄	#13063293	1	1	yes	characteristic
578	C₂×C₄	#13063293	1	1	yes	characteristic
579	C₂×C₄	#13063295	1	1	yes	characteristic
580	C₂×C₄	#13063295	1	1	yes	characteristic
581	C₂×C₄	#13063296	1	1	yes	characteristic
582	C₂×C₄	#13063298	1	1	yes	characteristic
583	C₂×C₄	#13063298	1	1	yes	characteristic
584	C₂×C₄	#13063300	1	1	yes	characteristic
585	C₂×C₄	#13063301	1	1	yes	characteristic
586	C₂×C₄	#13063303	1	1	yes	characteristic
587	C₂×C₄	#13063303	1	1	yes	characteristic
588	C₂×C₄	#13063305	1	1	yes	characteristic
589	C₂×C₄	#13063307	1	1	yes	characteristic
590	C₂×C₄	#13063307	1	1	yes	characteristic
591	C₂×C₄	#13063310	1	1	yes	characteristic
592	C₂×C₄	#13063310	1	1	yes	characteristic
593	C₈	—	4	2	no	—
594	C₈	—	4	2	no	—
595	C₈	—	172	2	no	—
596	C₈	—	172	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	86	4	no	—
605	C₂²	—	344	2	no	—
606	C₂²	—	172	4	no	—
607	C₂²	—	172	4	no	—
608	C₂²	#95×D₄₃	1	1	yes	characteristic
609	C₂²	#14582746	1	1	yes	characteristic
610	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
611	C₂²	#14582754	1	1	yes	characteristic
612	C₂²	#14582756	1	1	yes	characteristic
613	C₂²	#14582758	1	1	yes	characteristic
614	C₂²	#14582761	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	86	4	no	—
617	C₄	—	172	4	no	—
618	C₄	#14582770	1	1	yes	characteristic
619	C₄	#14582770	1	1	yes	characteristic
620	C₄	#14582773	1	1	yes	characteristic
621	C₄	#14582773	1	1	yes	characteristic
622	C₄	#14582775	1	1	yes	characteristic
623	C₄	#14582775	1	1	yes	characteristic
624	C₄	#14582777	1	1	yes	characteristic
625	C₄	#14582777	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	172	4	no	—
633	C₂	(C₂×D₄₃)⋊#95	1	1	yes	characteristic
634	C₂	#19134545	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063293
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1729	C₂
socle	C₂²×C₄₃	#379
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1729	D₄₃
hypocenter	C₄₃	#10747
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. #19134334	C₂	semidirect
5. #19134333	C₂	semidirect
6. #19134291	C₂	semidirect
7. C₄₃×#1729	C₂	semidirect
21. #14582881	C₄	semidirect
25. #14582865	C₄	semidirect
60. C₂×#10621877	C₂×C₄	semidirect
61. C₂×#10621877	C₂×C₄	semidirect
92. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
100. C₂²×C₈×C₄₃	C₂×C₄	semidirect
315. #1729	D₄₃	semidirect
351. C₄₃	#10747	semidirect
386. C₂×M₁₆	C₄×D₄₃	semidirect
396. C₂²×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19147796	2
C₂×#14582881	2
C₂×#14582865	2
#19134334	2
#19134333	2
#19134291	2
C₄₃×#1729	2
#10747	43