Subgroups — #25002101

Order 11008.

1218 conjugacy classes of subgroups.

The subgroup lattice has 644 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×#14582915	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582893	C₂	1	1	yes	maximal, characteristic
4	#19134327	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134311	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134293	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	#14583380	—	2	2	no	—
11	#14583379	C₄	1	4	yes	complemented
12	#14583376	—	2	1	no	—
13	#14583373	—	2	1	no	—
14	#14583372	—	2	2	no	—
15	C₄×#10621898	—	2	2	no	—
16	#14583367	—	2	2	no	—
17	C₂×#13063284	C₂²	1	1	yes	characteristic
18	C₂×#13063284	C₂²	1	1	yes	characteristic
19	#117×D₄₃	—	2	2	no	—
20	#14582915	—	2	2	no	—
21	#14582915	C₄	1	4	yes	complemented
22	C₂×#13063251	—	2	2	no	—
23	#14582893	—	2	2	no	—
24	#14582893	C₄	1	4	yes	complemented
25	C₂×#13063248	—	2	1	no	—
26	C₂×#13063245	—	2	1	no	—
27	#14582665	—	2	2	no	—
28	#14582661	—	2	2	no	—
29	#14582653	—	2	2	no	—
30	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#339	—	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	C₂×C₄	1	2	yes	—
41	C₂×#10621898	C₂×C₄	1	2	yes	—
42	C₂×#10621898	C₂×C₄	1	2	yes	—
43	C₂×#10621898	D₄	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	—	2	1	no	—
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	C₂²×C₄₃⋊C₈	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	complemented
57	C₄×Dic₈₆	—	2	4	no	—
58	#13063290	—	2	4	no	—
59	C₄×D₁₇₂	—	2	4	no	—
60	#13063287	—	2	4	no	—
61	C₄×C₂²⋊D₄₃	—	2	8	no	—
62	(C₂²⋊D₄₃)⋊C₄	—	2	8	no	—
63	#13063284	—	2	1	no	—
64	#13063284	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063284	—	2	1	no	—
67	#13063284	—	2	1	no	—
68	#13063284	—	2	1	no	—
69	#13063284	—	2	1	no	—
70	#13063284	C₂×C₄	1	2	yes	complemented
71	#13063283	—	2	4	no	—
72	#13063282	—	2	4	no	—
73	#13063281	—	2	4	no	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
76	C₄⋊C₄×D₄₃	—	2	4	no	—
77	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
78	C₂×C₂²⋊Dic₄₃	D₄	1	2	yes	—
79	C₂²⋊C₄×D₄₃	—	2	4	no	—
80	C₂×C₄×Dic₄₃	—	2	1	no	—
81	C₂×C₄×Dic₄₃	D₄	1	2	yes	—
82	C₄²×D₄₃	—	2	4	no	—
83	#13063251	—	2	8	no	—
84	#13063248	—	2	4	no	—
85	#13063245	—	2	4	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	#117×C₄₃	—	2	1	no	—
95	#117×C₄₃	—	2	1	no	—
96	#117×C₄₃	—	2	1	no	—
97	#117×C₄₃	—	2	1	no	—
98	#117×C₄₃	—	2	1	no	—
99	#117×C₄₃	C₂×C₄	1	2	yes	—
100	#117×C₄₃	C₂×C₄	1	2	yes	complemented
101	#117×C₄₃	D₄	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₄²×C₄₃	—	2	1	no	—
107	C₂×C₄²×C₄₃	—	2	1	no	—
108	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂³×D₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	4	1	no	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂²×C₄	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×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂×Q₈	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	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
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	—	2	2	no	—
130	C₂×C₂²⋊D₄₃	—	2	2	no	—
131	C₂×C₂²⋊D₄₃	—	2	2	no	—
132	C₂²×Dic₄₃	—	2	1	no	—
133	C₂²×Dic₄₃	—	4	1	no	—
134	C₂²×Dic₄₃	C₂²⋊C₄	1	4	yes	—
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	C₄²	1	4	yes	—
148	#10621898	C₂²⋊C₄	1	4	yes	—
149	#10621898	C₄⋊C₄	1	4	yes	—
150	#10621898	C₄⋊C₄	1	4	yes	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×D₁₇₂	—	2	1	no	—
154	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
155	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
156	C₂×D₁₇₂	C₄⋊C₄	1	2	yes	—
157	C₂×C₄×D₄₃	—	2	2	no	—
158	C₂×C₄×D₄₃	—	2	2	no	—
159	C₂×C₄×D₄₃	—	2	2	no	—
160	C₂×C₄×D₄₃	—	2	2	no	—
161	C₂×C₄×D₄₃	—	2	2	no	—
162	C₂×C₄×D₄₃	—	2	2	no	—
163	C₂×C₄×D₄₃	—	2	8	no	—
164	C₂×Dic₈₆	—	2	1	no	—
165	C₂×Dic₈₆	—	2	1	no	—
166	C₂×Dic₈₆	—	2	1	no	—
167	C₂×Dic₈₆	C₂²⋊C₄	1	2	yes	—
168	C₂×Dic₈₆	C₂²⋊C₄	1	2	yes	—
169	C₂×Dic₈₆	C₄⋊C₄	1	2	yes	—
170	M₁₆×C₄₃	—	2	2	no	—
171	M₁₆×C₄₃	—	2	2	no	—
172	M₁₆×C₄₃	—	4	1	no	—
173	M₁₆×C₄₃	—	4	1	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	4	1	no	—
176	C₂×C₈×C₄₃	—	4	1	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	2	2	no	—
179	C₄⋊C₄×C₄₃	—	4	1	no	—
180	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
181	C₂²⋊C₄×C₄₃	—	2	2	no	—
182	C₂²⋊C₄×C₄₃	—	2	2	no	—
183	C₂²⋊C₄×C₄₃	—	2	2	no	—
184	C₂²⋊C₄×C₄₃	—	4	1	no	—
185	C₄²×C₄₃	—	2	2	no	—
186	C₄²×C₄₃	—	2	2	no	—
187	C₄²×C₄₃	—	2	2	no	—
188	C₄²×C₄₃	—	4	1	no	—
189	C₂²⋊Dic₄₃	—	2	2	no	—
190	C₂²⋊Dic₄₃	—	2	2	no	—
191	C₂²⋊Dic₄₃	—	2	2	no	—
192	C₂²⋊Dic₄₃	—	4	1	no	—
193	(C₂×D₄₃)⋊C₄	—	2	8	no	—
194	C₄⋊Dic₄₃	—	2	2	no	—
195	C₄⋊Dic₄₃	—	2	2	no	—
196	C₄⋊Dic₄₃	—	2	2	no	—
197	C₄⋊Dic₄₃	—	4	1	no	—
198	Dic₄₃⋊C₄	—	2	8	no	—
199	C₄×Dic₄₃	—	2	8	no	—
200	C₄×Dic₄₃	—	2	2	no	—
201	C₄×Dic₄₃	—	2	2	no	—
202	C₄×Dic₄₃	—	2	2	no	—
203	C₄×Dic₄₃	—	4	1	no	—
204	C₂×C₄₃⋊C₈	—	2	2	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×C₂²⋊C₄	1	1	yes	characteristic
213	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
214	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂³×C₄₃	#120	1	1	yes	characteristic
216	C₂³×C₄₃	#120	1	1	yes	characteristic
217	C₂³×C₄₃	#121	1	1	yes	characteristic
218	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂²×D₄₃	—	2	2	no	—
220	C₂²×D₄₃	—	2	2	no	—
221	C₂²×D₄₃	—	2	2	no	—
222	C₂²×D₄₃	—	8	2	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	8	2	no	—
226	C₂×C₄×C₄₃	—	8	2	no	—
227	C₂×C₄×C₄₃	C₂×C₄²	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×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	#117	1	1	yes	characteristic
236	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
243	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
244	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
245	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
246	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
247	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
252	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
253	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
254	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
255	C₂²⋊D₄₃	—	2	4	no	—
256	C₂²⋊D₄₃	—	2	4	no	—
257	C₂²⋊D₄₃	—	2	4	no	—
258	C₂²⋊D₄₃	—	2	4	no	—
259	C₂×Dic₄₃	—	2	2	no	—
260	C₂×Dic₄₃	—	2	2	no	—
261	C₂×Dic₄₃	—	2	2	no	—
262	C₂×Dic₄₃	—	2	4	no	—
263	C₂×Dic₄₃	—	4	4	no	—
264	C₂×Dic₄₃	—	4	2	no	—
265	C₂×Dic₄₃	—	8	2	no	—
266	D₁₇₂	—	2	2	no	—
267	D₁₇₂	—	2	2	no	—
268	D₁₇₂	—	2	2	no	—
269	D₁₇₂	#95	1	4	yes	—
270	C₄×D₄₃	—	2	4	no	—
271	C₄×D₄₃	—	2	4	no	—
272	C₄×D₄₃	—	2	4	no	—
273	C₄×D₄₃	—	2	4	no	—
274	C₄×D₄₃	—	8	8	no	—
275	Dic₈₆	—	2	2	no	—
276	Dic₈₆	—	2	2	no	—
277	Dic₈₆	—	2	2	no	—
278	Dic₈₆	#95	1	4	yes	—
279	C₈×C₄₃	—	4	2	no	—
280	C₄₃⋊C₈	—	4	2	no	—
281	#10779	—	43	1	no	maximal, Sylow
282	C₂²×C₄₃	—	2	2	no	—
283	C₂²×C₄₃	—	2	2	no	—
284	C₂²×C₄₃	—	2	2	no	—
285	C₂²×C₄₃	—	4	1	no	—
286	C₂²×C₄₃	—	4	1	no	—
287	C₂²×C₄₃	—	4	1	no	—
288	C₂²×C₄₃	—	4	1	no	—
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	#385	1	1	yes	characteristic
293	C₂²×C₄₃	#385	1	1	yes	characteristic
294	C₂²×C₄₃	#386	1	1	yes	characteristic
295	C₂²×C₄₃	#386	1	1	yes	characteristic
296	C₂×D₄₃	—	2	4	no	—
297	C₂×D₄₃	—	4	4	no	—
298	C₂×D₄₃	—	8	2	no	—
299	C₂×D₄₃	—	8	2	no	—
300	C₄×C₄₃	—	4	4	no	—
301	C₄×C₄₃	—	8	2	no	—
302	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
303	C₄×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×C₄₃	#380	1	1	yes	characteristic
305	C₄×C₄₃	#381	1	1	yes	characteristic
306	C₄×C₄₃	#385	1	1	yes	characteristic
307	C₄×C₄₃	#385	1	1	yes	characteristic
308	C₄×C₄₃	#386	1	1	yes	characteristic
309	C₄×C₄₃	#386	1	1	yes	characteristic
310	Dic₄₃	—	2	4	no	—
311	Dic₄₃	—	4	4	no	—
312	Dic₄₃	—	8	2	no	—
313	#3428	—	43	1	no	—
314	C₂×#421	—	43	1	no	—
315	C₂×#416	—	43	1	no	—
316	#1740	—	43	1	no	—
317	#1735	—	43	1	no	—
318	#1733	D₄₃	1	1	yes	characteristic, complemented
319	#1729	—	43	1	no	—
320	C₂×C₄₃	—	2	1	no	—
321	C₂×C₄₃	—	2	1	no	—
322	C₂×C₄₃	—	2	1	no	—
323	C₂×C₄₃	—	2	1	no	—
324	C₂×C₄₃	—	2	1	no	—
325	C₂×C₄₃	—	2	1	no	—
326	C₂×C₄₃	C₂²⋊#95	1	1	yes	characteristic
327	C₂×C₄₃	#1794	1	2	yes	—
328	D₄₃	—	4	4	no	—
329	C₂²×#41	—	43	1	no	—
330	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
331	C₂³×C₈	—	43	1	no	—
332	#520	—	43	4	no	—
333	#520	—	86	2	no	—
334	#519	—	86	1	no	—
335	#518	—	86	2	no	—
336	#518	—	86	1	no	—
337	C₄×#41	—	86	2	no	—
338	C₄×#41	—	86	2	no	—
339	C₂×#117	—	43	1	no	—
340	C₂×#117	—	43	1	no	—
341	C₂×#117	—	86	2	no	—
342	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
343	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
344	#421	—	43	4	no	—
345	#421	—	86	2	no	—
346	C₂×#104	—	86	2	no	—
347	#416	—	43	4	no	—
348	#416	—	86	2	no	—
349	C₂×#103	—	86	1	no	—
350	C₂×#102	—	86	1	no	—
351	#342	—	86	2	no	—
352	#340	—	86	2	no	—
353	#339	—	2	2	no	—
354	#336	—	86	2	no	—
355	C₄₃	#10779	1	1	yes	characteristic, complemented, Sylow
356	C₂×#41	—	43	2	no	—
357	C₂×#41	—	43	2	no	—
358	C₂×#41	—	43	2	no	—
359	C₂×#41	—	43	2	no	—
360	C₂×#41	—	43	2	no	—
361	C₂×#41	—	43	2	no	—
362	C₂×#41	—	86	1	no	—
363	C₂×#41	—	86	1	no	—
364	C₂×#41	—	86	1	no	—
365	C₂×#41	—	86	1	no	—
366	C₂×#41	—	86	1	no	—
367	C₂×#41	—	86	1	no	—
368	C₂²×Q₈	—	43	1	no	—
369	C₂²×D₄	—	43	1	no	—
370	C₂²×D₄	—	86	1	no	—
371	C₂³×C₄	—	86	1	no	—
372	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	C₄×D₄₃	1	2	yes	complemented
379	C₂²×C₈	—	2	1	no	—
380	C₂²×C₈	—	43	2	no	—
381	C₂²×C₈	—	86	1	no	—
382	C₂²×C₈	—	86	1	no	—
383	C₂²×C₈	—	86	1	no	—
384	C₂²×C₈	—	86	1	no	—
385	C₂²×C₈	—	86	1	no	—
386	C₂²×C₈	—	86	1	no	—
387	C₄×Q₈	—	86	4	no	—
388	C₄×Q₈	—	86	4	no	—
389	C₄×D₄	—	86	4	no	—
390	C₄×D₄	—	86	8	no	—
391	C₄×D₄	—	86	4	no	—
392	C₄×D₄	—	86	8	no	—
393	#117	—	2	1	no	—
394	#117	—	2	1	no	—
395	#117	—	2	1	no	—
396	#117	—	2	1	no	—
397	#117	—	2	1	no	—
398	#117	—	43	2	no	—
399	#117	—	86	4	no	—
400	#117	—	86	4	no	—
401	#117	—	86	1	no	—
402	#117	—	86	1	no	—
403	#117	—	86	1	no	—
404	#117	—	86	1	no	—
405	#117	—	86	4	no	—
406	#117	—	86	1	no	—
407	#117	—	86	1	no	—
408	#117	—	86	1	no	—
409	#117	C₄×D₄₃	1	2	yes	—
410	#117	C₄×D₄₃	1	2	yes	complemented
411	#117	C₂²⋊D₄₃	1	2	yes	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	43	2	no	—
414	C₂×C₄⋊C₄	—	86	4	no	—
415	C₂×C₄⋊C₄	—	86	1	no	—
416	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	43	2	no	—
420	C₂×C₂²⋊C₄	—	86	4	no	—
421	C₂×C₂²⋊C₄	—	86	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	43	2	no	—
425	C₂×C₄²	—	86	4	no	—
426	C₂×C₄²	—	86	1	no	—
427	#104	—	86	8	no	—
428	#103	—	86	4	no	—
429	#102	—	86	4	no	—
430	C₂⁴	—	86	1	no	—
431	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
432	#41	—	43	4	no	—
433	#41	—	43	4	no	—
434	#41	—	43	4	no	—
435	#41	—	43	4	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	#41	—	86	2	no	—
445	#41	—	86	2	no	—
446	#41	—	86	2	no	—
447	#41	—	86	2	no	—
448	C₂×Q₈	—	43	2	no	—
449	C₂×Q₈	—	43	2	no	—
450	C₂×Q₈	—	43	2	no	—
451	C₂×Q₈	—	86	1	no	—
452	C₂×Q₈	—	86	1	no	—
453	C₂×Q₈	—	86	1	no	—
454	C₂×D₄	—	43	2	no	—
455	C₂×D₄	—	43	2	no	—
456	C₂×D₄	—	43	2	no	—
457	C₂×D₄	—	86	2	no	—
458	C₂×D₄	—	86	2	no	—
459	C₂×D₄	—	86	2	no	—
460	C₂×D₄	—	86	2	no	—
461	C₂×D₄	—	86	2	no	—
462	C₂×D₄	—	86	2	no	—
463	C₂×D₄	—	86	1	no	—
464	C₂×D₄	—	86	1	no	—
465	C₂×D₄	—	86	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	—	43	4	no	—
469	C₂²×C₄	—	86	8	no	—
470	C₂²×C₄	—	86	1	no	—
471	C₂²×C₄	—	86	2	no	—
472	C₂²×C₄	—	86	2	no	—
473	C₂²×C₄	—	86	2	no	—
474	C₂²×C₄	—	86	2	no	—
475	C₂²×C₄	—	86	2	no	—
476	C₂²×C₄	—	86	2	no	—
477	C₂²×C₄	—	172	1	no	—
478	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
482	C₂²×C₄	#10621898	1	1	yes	characteristic
483	C₂²×C₄	#10621898	1	1	yes	characteristic
484	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
485	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
486	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
487	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
488	C₂²×C₄	#10621900	1	1	yes	characteristic
489	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
490	C₂²×C₄	#10621902	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	4	1	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	4	1	no	—
498	C₂×C₈	—	4	1	no	—
499	C₂×C₈	—	86	2	no	—
500	C₂×C₈	—	86	2	no	—
501	C₂×C₈	—	86	2	no	—
502	C₂×C₈	—	172	1	no	—
503	C₂×C₈	—	172	1	no	—
504	C₂×C₈	—	172	1	no	—
505	C₂×C₈	—	172	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₄⋊C₄	—	86	8	no	—
510	C₄⋊C₄	—	86	2	no	—
511	C₄⋊C₄	—	86	2	no	—
512	C₄⋊C₄	—	86	2	no	—
513	C₄⋊C₄	—	172	1	no	—
514	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	4	yes	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₂²⋊C₄	—	86	8	no	—
520	C₂²⋊C₄	—	86	2	no	—
521	C₂²⋊C₄	—	86	2	no	—
522	C₂²⋊C₄	—	86	2	no	—
523	C₂²⋊C₄	—	172	1	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	4	1	no	—
528	C₄²	—	86	8	no	—
529	C₄²	—	86	2	no	—
530	C₄²	—	86	2	no	—
531	C₄²	—	86	2	no	—
532	C₄²	—	172	1	no	—
533	C₂³	—	4	2	no	—
534	C₂³	—	86	2	no	—
535	C₂³	—	86	2	no	—
536	C₂³	—	86	2	no	—
537	C₂³	—	344	2	no	—
538	C₂³	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
539	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
540	C₂³	#13063287	1	1	yes	characteristic
541	C₂³	#13063293	1	1	yes	characteristic
542	C₂³	#13063295	1	1	yes	characteristic
543	C₂³	#13063298	1	1	yes	characteristic
544	C₂³	#13063303	1	1	yes	characteristic
545	Q₈	—	43	4	no	—
546	Q₈	—	86	2	no	—
547	Q₈	—	86	2	no	—
548	Q₈	—	86	2	no	—
549	D₄	—	43	4	no	—
550	D₄	—	86	4	no	—
551	D₄	—	86	4	no	—
552	D₄	—	86	4	no	—
553	D₄	—	86	4	no	—
554	D₄	—	86	2	no	—
555	D₄	—	86	2	no	—
556	D₄	—	86	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	8	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	—	86	2	no	—
562	C₂×C₄	—	86	2	no	—
563	C₂×C₄	—	86	2	no	—
564	C₂×C₄	—	86	4	no	—
565	C₂×C₄	—	86	4	no	—
566	C₂×C₄	—	86	4	no	—
567	C₂×C₄	—	86	4	no	—
568	C₂×C₄	—	86	4	no	—
569	C₂×C₄	—	344	8	no	—
570	C₂×C₄	—	344	2	no	—
571	C₂×C₄	—	172	2	no	—
572	C₂×C₄	—	172	4	no	—
573	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
574	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
575	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
576	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
577	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
578	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
579	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
580	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
581	C₂×C₄	#13063282	1	1	yes	characteristic
582	C₂×C₄	#13063283	1	1	yes	characteristic
583	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
585	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
586	C₂×C₄	#13063287	1	1	yes	characteristic
587	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
588	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
589	C₂×C₄	#13063293	1	1	yes	characteristic
590	C₂×C₄	#13063295	1	1	yes	characteristic
591	C₂×C₄	#13063296	1	1	yes	characteristic
592	C₂×C₄	#13063298	1	1	yes	characteristic
593	C₂×C₄	#13063300	1	1	yes	characteristic
594	C₂×C₄	#13063301	1	1	yes	characteristic
595	C₂×C₄	#13063303	1	1	yes	characteristic
596	C₂×C₄	#13063305	1	1	yes	characteristic
597	C₂×C₄	#13063307	1	1	yes	characteristic
598	C₂×C₄	#13063307	1	1	yes	characteristic
599	C₂×C₄	#13063310	1	1	yes	characteristic
600	C₂×C₄	#13063310	1	1	yes	characteristic
601	C₈	—	4	2	no	—
602	C₈	—	172	2	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	86	4	no	—
611	C₂²	—	344	2	no	—
612	C₂²	—	344	2	no	—
613	C₂²	—	172	4	no	—
614	C₂²	#14582746	1	1	yes	characteristic
615	C₂²	#14582754	1	1	yes	characteristic
616	C₂²	#14582758	1	1	yes	characteristic
617	C₂²	#14582770	1	1	yes	characteristic
618	C₂²	#14582773	1	1	yes	characteristic
619	C₂²	#14582775	1	1	yes	characteristic
620	C₂²	#14582777	1	1	yes	characteristic
621	C₄	—	4	4	no	—
622	C₄	—	8	2	no	—
623	C₄	—	86	4	no	—
624	C₄	—	344	2	no	—
625	C₄	—	172	4	no	—
626	C₄	#95×D₄₃	1	1	yes	characteristic
627	C₄	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
628	C₄	#14582756	1	1	yes	characteristic
629	C₄	#14582761	1	1	yes	characteristic
630	C₄	#14582770	1	1	yes	characteristic
631	C₄	#14582773	1	1	yes	characteristic
632	C₄	#14582775	1	1	yes	characteristic
633	C₄	#14582777	1	1	yes	characteristic
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	2	1	no	—
640	C₂	—	172	4	no	—
641	C₂	(C₂×D₄₃)⋊#95	1	1	yes	characteristic
642	C₂	#19134557	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063293
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₄₃×#1733	C₂
socle	C₂²×C₄₃	#379
prime radical	C₂²×#10621898	C₂²
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	#1733	D₄₃
hypocenter	C₄₃	#10779
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1733

Complements

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

N	H ≅ G/N	type
4. #19134327	C₂	semidirect
5. #19134311	C₂	semidirect
6. #19134293	C₂	semidirect
7. C₄₃×#1733	C₂	semidirect
11. #14583379	C₄	semidirect
21. #14582915	C₄	semidirect
24. #14582893	C₄	semidirect
56. C₂²×C₄₃⋊C₈	C₂×C₄	semidirect
70. #13063284	C₂×C₄	semidirect
92. C₂×M₁₆×C₄₃	C₂×C₄	semidirect
100. #117×C₄₃	C₂×C₄	semidirect
318. #1733	D₄₃	semidirect
355. C₄₃	#10779	semidirect
378. C₂×M₁₆	C₄×D₄₃	semidirect
410. #117	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×#14582915	2
C₂×#14582893	2
#19134327	2
#19134311	2
#19134293	2
C₄₃×#1733	2
#10779	43