Subgroups — #25066700

Order 11008.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144667	C₂	1	1	yes	maximal, characteristic
2	#19143704	C₂	1	1	yes	maximal, characteristic
3	#19143692	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133465	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133451	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133444	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133430	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133413	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133406	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133401	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133394	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133027	C₂	1	1	yes	maximal, characteristic
13	#19132997	C₂	1	1	yes	maximal, characteristic, complemented
14	#19132895	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583456	C₂²	1	1	yes	characteristic
17	C₄×#10621898	C₂²	1	1	yes	characteristic
18	#14583241	C₄	1	1	yes	characteristic
19	#14583241	C₄	1	1	yes	characteristic
20	#14583185	C₄	1	1	yes	characteristic
21	#14583180	C₄	1	1	yes	characteristic
22	#14583110	C₄	1	1	yes	characteristic
23	#14583105	C₄	1	1	yes	characteristic
24	#14583063	C₄	1	1	yes	characteristic
25	#14583063	C₄	1	1	yes	characteristic
26	#14583027	—	2	1	no	—
27	#14583027	—	2	1	no	—
28	#14583026	C₂²	1	1	yes	characteristic
29	#14583026	C₂²	1	1	yes	characteristic
30	#14583023	C₂²	1	1	yes	characteristic
31	#14583023	C₂²	1	1	yes	characteristic
32	#14583023	C₂²	1	1	yes	characteristic
33	#14583023	C₂²	1	1	yes	characteristic
34	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
35	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
36	C₄×#10621873	C₂²	1	1	yes	characteristic
37	C₄×#10621873	C₂²	1	1	yes	characteristic
38	#14582964	C₂²	1	1	yes	characteristic
39	#14582964	C₂²	1	1	yes	characteristic
40	C₈×C₂²⋊D₄₃	—	2	1	no	—
41	C₈×C₂²⋊D₄₃	—	2	1	no	—
42	#14582957	—	2	1	no	—
43	#14582957	—	2	1	no	—
44	#14582952	C₂²	1	1	yes	characteristic
45	#14582952	C₂²	1	1	yes	characteristic
46	#14582951	—	2	1	no	—
47	C₄⋊C₈×D₄₃	—	2	1	no	—
48	#14582629	C₂²	1	1	yes	characteristic
49	#14582629	C₂²	1	1	yes	characteristic
50	#14582629	C₂²	1	1	yes	characteristic
51	#14582629	C₂²	1	1	yes	characteristic
52	#14582629	C₂²	1	1	yes	characteristic
53	#14582629	C₂²	1	1	yes	characteristic
54	#14582626	C₂²	1	1	yes	characteristic
55	#14582626	C₂²	1	1	yes	characteristic
56	#14582621	C₂²	1	1	yes	characteristic
57	#14582621	C₂²	1	1	yes	characteristic
58	#14582620	C₂²	1	1	yes	characteristic
59	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₄₃×#432	C₂²	1	1	yes	characteristic
61	C₄₃×#431	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
63	C₄₃×#335	C₂²	1	1	yes	characteristic
64	C₄₃×#335	C₂²	1	1	yes	characteristic
65	C₄₃×#334	C₂²	1	1	yes	characteristic
66	C₄₃×#334	C₂²	1	1	yes	characteristic
67	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
71	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₄₃	—	2	1	no	—
73	C₂×C₈×D₄₃	—	2	1	no	—
74	#13063325	C₂×C₄	1	1	yes	characteristic
75	#13063325	C₂×C₄	1	1	yes	characteristic
76	#13063317	—	2	1	no	—
77	#13063304	—	2	1	no	—
78	#13063304	C₂×C₄	1	1	yes	characteristic
79	#13063304	C₂×C₄	1	1	yes	characteristic
80	C₄×Dic₈₆	—	2	1	no	—
81	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
83	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
84	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
85	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
86	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
87	C₄×C₂²⋊D₄₃	—	2	1	no	—
88	C₄×C₂²⋊D₄₃	—	2	1	no	—
89	#13063284	—	2	1	no	—
90	#13063284	C₂×C₄	1	1	yes	characteristic
91	#13063282	—	2	1	no	—
92	C₄²×D₄₃	—	2	1	no	—
93	#13063259	C₂×C₄	1	1	yes	characteristic
94	#13063259	C₂×C₄	1	1	yes	characteristic
95	#13063257	C₂×C₄	1	1	yes	characteristic
96	#13063257	C₂×C₄	1	1	yes	characteristic
97	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
98	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
99	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
100	Dic₄₃⋊C₈	—	2	1	no	—
101	Dic₄₃⋊C₈	—	2	1	no	—
102	Dic₄₃⋊C₈	—	2	1	no	—
103	Dic₄₃⋊C₈	—	2	1	no	—
104	Dic₄₃⋊C₈	—	2	1	no	—
105	Dic₄₃⋊C₈	—	2	1	no	—
106	#13063250	C₂×C₄	1	1	yes	characteristic
107	#13063250	C₂×C₄	1	1	yes	characteristic
108	#13063250	C₂×C₄	1	1	yes	characteristic
109	#13063250	C₂×C₄	1	1	yes	characteristic
110	#13063250	C₂×C₄	1	1	yes	characteristic
111	#13063250	C₂×C₄	1	1	yes	characteristic
112	#13063247	C₂×C₄	1	1	yes	characteristic
113	#13063247	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
115	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
116	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
117	(C₂×D₄₃)⋊C₈	—	2	1	no	—
118	(C₂×D₄₃)⋊C₈	—	2	1	no	—
119	#13063235	—	2	1	no	—
120	#13063235	—	2	1	no	—
121	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₄₃	—	2	1	no	—
126	C₈×Dic₄₃	—	2	1	no	—
127	C₈×Dic₄₃	—	2	1	no	—
128	C₈×Dic₄₃	—	2	1	no	—
129	C₂²×C₈×C₄₃	—	2	1	no	—
130	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
131	C₄⋊C₈×C₄₃	—	2	1	no	—
132	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
135	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
138	C₂²⋊C₈×C₄₃	—	2	1	no	—
139	C₂²⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
140	C₂²⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
141	#97×C₄₃	—	2	1	no	—
142	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
147	C₂×C₂²⋊D₄₃	—	2	1	no	—
148	#10621898	—	2	2	no	—
149	#10621898	—	2	2	no	—
150	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₄₃	—	2	1	no	—
152	C₂×C₄×D₄₃	—	2	1	no	—
153	C₂×C₄×D₄₃	—	2	1	no	—
154	C₂×Dic₈₆	—	2	1	no	—
155	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
162	C₂×C₈×C₄₃	—	8	1	no	—
163	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₄₃	#41	1	1	yes	characteristic
170	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
171	C₂²⋊Dic₄₃	—	2	1	no	—
172	C₂²⋊Dic₄₃	—	2	1	no	—
173	C₂²⋊Dic₄₃	—	2	1	no	—
174	(C₂×D₄₃)⋊C₄	—	2	1	no	—
175	(C₂×D₄₃)⋊C₄	—	2	1	no	—
176	C₄⋊Dic₄₃	—	2	1	no	—
177	C₄⋊Dic₄₃	—	2	1	no	—
178	C₄⋊Dic₄₃	—	2	1	no	—
179	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
181	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
183	Dic₄₃⋊C₄	—	2	1	no	—
184	Dic₄₃⋊C₄	—	2	1	no	—
185	Dic₄₃⋊C₄	—	2	1	no	—
186	Dic₄₃⋊C₄	—	2	1	no	—
187	Dic₄₃⋊C₄	—	2	1	no	—
188	Dic₄₃⋊C₄	—	2	1	no	—
189	C₄×Dic₄₃	—	2	1	no	—
190	C₄×Dic₄₃	—	2	1	no	—
191	C₄×Dic₄₃	—	2	1	no	—
192	C₄×Dic₄₃	—	2	1	no	—
193	C₄×Dic₄₃	—	2	1	no	—
194	C₂×C₄₃⋊C₈	—	2	1	no	—
195	C₂×C₄₃⋊C₈	—	2	1	no	—
196	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
199	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
200	Dic₁₇₂	—	2	2	no	—
201	Dic₁₇₂	—	2	2	no	—
202	#10621873	—	2	2	no	—
203	#10621873	—	2	2	no	—
204	C₈×D₄₃	—	8	1	no	—
205	C₈×D₄₃	—	8	1	no	—
206	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂²×D₄₃	—	2	1	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
219	C₂²⋊D₄₃	—	2	4	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	1	no	—
222	C₂×Dic₄₃	—	2	1	no	—
223	C₂×Dic₄₃	—	2	1	no	—
224	C₂×Dic₄₃	—	2	1	no	—
225	C₂×Dic₄₃	—	2	1	no	—
226	C₂×Dic₄₃	—	2	1	no	—
227	D₁₇₂	—	2	1	no	—
228	D₁₇₂	#131	1	2	yes	—
229	C₄×D₄₃	—	2	4	no	—
230	C₄×D₄₃	—	4	1	no	—
231	C₄×D₄₃	—	4	1	no	—
232	C₄×D₄₃	—	8	1	no	—
233	Dic₈₆	—	2	1	no	—
234	Dic₈₆	—	2	1	no	—
235	Dic₈₆	—	2	1	no	—
236	Dic₈₆	—	2	1	no	—
237	Dic₈₆	—	2	1	no	—
238	Dic₈₆	—	8	1	no	—
239	Dic₈₆	#131	1	2	yes	—
240	C₈×C₄₃	—	2	1	no	—
241	C₈×C₄₃	—	2	1	no	—
242	C₈×C₄₃	—	2	1	no	—
243	C₈×C₄₃	—	2	1	no	—
244	C₈×C₄₃	—	4	1	no	—
245	C₈×C₄₃	—	4	1	no	—
246	C₈×C₄₃	—	4	1	no	—
247	C₈×C₄₃	—	4	1	no	—
248	C₄₃⋊C₈	—	2	1	no	—
249	C₄₃⋊C₈	—	2	1	no	—
250	C₄₃⋊C₈	—	2	1	no	—
251	C₄₃⋊C₈	—	2	1	no	—
252	C₄₃⋊C₈	—	4	1	no	—
253	C₄₃⋊C₈	—	4	1	no	—
254	#17921	—	43	1	no	maximal, Sylow
255	C₂²×C₄₃	—	2	1	no	—
256	C₂²×C₄₃	—	2	1	no	—
257	C₂²×C₄₃	—	2	1	no	—
258	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₄₃	—	2	2	no	—
260	C₂×D₄₃	—	4	1	no	—
261	C₂×D₄₃	—	4	1	no	—
262	C₄×C₄₃	—	2	1	no	—
263	C₄×C₄₃	—	2	1	no	—
264	C₄×C₄₃	—	2	1	no	—
265	C₄×C₄₃	—	2	1	no	—
266	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
267	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
268	C₄×C₄₃	#577	1	1	yes	characteristic
269	C₄×C₄₃	#578	1	1	yes	characteristic
270	Dic₄₃	—	2	2	no	—
271	Dic₄₃	—	4	1	no	—
272	Dic₄₃	—	4	1	no	—
273	Dic₄₃	—	4	1	no	—
274	Dic₄₃	—	4	1	no	—
275	Dic₄₃	—	4	1	no	—
276	Dic₄₃	—	4	1	no	—
277	#3107	—	43	1	no	—
278	#2988	—	43	1	no	—
279	#2985	—	43	1	no	—
280	#1587	—	43	1	no	—
281	#1585	—	43	1	no	—
282	#1584	—	43	1	no	—
283	#1582	—	43	1	no	—
284	#1579	—	43	1	no	—
285	SD₁₆⋊C₈	—	43	1	no	—
286	C₈×Q₁₆	—	43	1	no	—
287	C₈×SD₁₆	—	43	1	no	—
288	#1573	D₄₃	1	1	yes	characteristic, complemented
289	#1488	—	43	1	no	—
290	#1481	—	43	1	no	—
291	#1454	—	43	1	no	—
292	C₂×C₄₃	—	4	1	no	—
293	C₂×C₄₃	#2929	1	1	yes	characteristic
294	C₂×C₄₃	#2947	1	1	yes	characteristic
295	C₂×C₄₃	#2957	1	1	yes	characteristic
296	D₄₃	—	4	2	no	—
297	#533	—	43	1	no	—
298	C₄×#41	—	43	1	no	—
299	#485	—	43	1	no	—
300	#485	—	43	1	no	—
301	#475	—	43	1	no	—
302	#474	—	43	1	no	—
303	#462	—	43	1	no	—
304	#461	—	43	1	no	—
305	#452	—	43	1	no	—
306	#452	—	43	1	no	—
307	#446	—	43	1	no	—
308	#446	—	43	1	no	—
309	#446	—	86	1	no	—
310	#446	—	86	1	no	—
311	C₈×Q₈	—	43	1	no	—
312	C₈×Q₈	—	43	1	no	—
313	C₈×Q₈	—	43	1	no	—
314	C₈×Q₈	—	43	1	no	—
315	C₄×Q₁₆	—	43	1	no	—
316	C₄×Q₁₆	—	43	1	no	—
317	C₄×SD₁₆	—	43	1	no	—
318	C₄×SD₁₆	—	43	1	no	—
319	C₈×D₄	—	43	1	no	—
320	C₈×D₄	—	43	1	no	—
321	C₈×D₄	—	86	1	no	—
322	C₈×D₄	—	86	1	no	—
323	#433	—	86	1	no	—
324	#433	—	86	1	no	—
325	#432	C₂×D₄₃	1	1	yes	characteristic
326	#431	—	43	1	no	—
327	#431	—	43	1	no	—
328	#431	—	86	1	no	—
329	#431	C₂×D₄₃	1	1	yes	characteristic
330	C₂×C₄⋊C₈	—	86	1	no	—
331	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
332	#335	C₂×D₄₃	1	1	yes	characteristic
333	#335	C₂×D₄₃	1	1	yes	characteristic
334	#334	C₂×D₄₃	1	1	yes	characteristic
335	#334	C₂×D₄₃	1	1	yes	characteristic
336	Q₈⋊C₈	—	43	1	no	—
337	Q₈⋊C₈	—	43	1	no	—
338	Q₈⋊C₈	—	43	1	no	—
339	Q₈⋊C₈	—	43	1	no	—
340	Q₈⋊C₈	—	43	1	no	—
341	Q₈⋊C₈	—	43	1	no	—
342	D₄⋊C₈	—	43	1	no	—
343	D₄⋊C₈	—	43	1	no	—
344	#322	—	43	1	no	—
345	#322	—	43	1	no	—
346	#322	—	43	1	no	—
347	C₈²	—	43	1	no	—
348	C₄₃	#17921	1	1	yes	characteristic, complemented, Sylow
349	C₂×#41	—	43	1	no	—
350	C₂×Q₁₆	—	43	1	no	—
351	C₂×Q₁₆	—	43	1	no	—
352	C₂×SD₁₆	—	43	1	no	—
353	C₂×SD₁₆	—	43	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	86	1	no	—
356	C₂²×C₈	—	86	1	no	—
357	C₄⋊Q₈	—	43	1	no	—
358	C₄⋊Q₈	—	43	1	no	—
359	#125	—	86	1	no	—
360	C₂²⋊Q₈	—	43	1	no	—
361	C₂²⋊Q₈	—	43	1	no	—
362	C₂²⋊Q₈	—	86	1	no	—
363	C₄×Q₈	—	43	1	no	—
364	C₄×Q₈	—	43	1	no	—
365	C₄×Q₈	—	43	1	no	—
366	C₄×Q₈	—	43	1	no	—
367	C₄×Q₈	—	86	1	no	—
368	C₄×D₄	—	43	1	no	—
369	C₄×D₄	—	43	1	no	—
370	C₄×D₄	—	86	1	no	—
371	C₄×D₄	—	86	1	no	—
372	#117	—	43	1	no	—
373	#117	—	86	1	no	—
374	#117	—	86	1	no	—
375	C₂×C₄²	—	86	1	no	—
376	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
377	#107	—	43	1	no	—
378	#107	—	43	1	no	—
379	#106	—	43	1	no	—
380	#106	—	43	1	no	—
381	C₄⋊C₈	—	2	1	no	—
382	C₄⋊C₈	—	43	1	no	—
383	C₄⋊C₈	—	43	1	no	—
384	C₄⋊C₈	—	86	1	no	—
385	C₄⋊C₈	—	86	1	no	—
386	C₄⋊C₈	—	86	1	no	—
387	C₄⋊C₈	—	86	1	no	—
388	C₄⋊C₈	—	86	1	no	—
389	C₄⋊C₈	—	86	1	no	—
390	C₄⋊C₈	—	86	1	no	—
391	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
392	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
396	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
397	#103	—	43	1	no	—
398	#103	—	43	1	no	—
399	#103	—	43	1	no	—
400	#103	—	43	1	no	—
401	#103	—	43	1	no	—
402	#103	—	43	1	no	—
403	#102	—	43	1	no	—
404	#102	—	43	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	43	1	no	—
407	C₂²⋊C₈	—	43	1	no	—
408	C₂²⋊C₈	—	86	1	no	—
409	C₂²⋊C₈	—	86	1	no	—
410	C₂²⋊C₈	—	86	1	no	—
411	C₂²⋊C₈	C₄×D₄₃	1	1	yes	characteristic
412	C₂²⋊C₈	C₄×D₄₃	1	1	yes	characteristic
413	#97	—	2	1	no	—
414	#97	—	86	1	no	—
415	#97	—	86	1	no	—
416	C₄×C₈	—	43	1	no	—
417	C₄×C₈	—	43	1	no	—
418	C₄×C₈	—	43	1	no	—
419	C₄×C₈	—	43	1	no	—
420	C₄×C₈	—	86	1	no	—
421	C₄×C₈	—	86	1	no	—
422	C₄×C₈	—	86	1	no	—
423	C₄×C₈	—	86	1	no	—
424	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
425	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
426	#41	—	86	2	no	—
427	#41	—	86	2	no	—
428	C₂×Q₈	—	43	1	no	—
429	C₂×Q₈	—	43	1	no	—
430	C₂×Q₈	—	43	1	no	—
431	C₂×Q₈	—	86	1	no	—
432	C₂×D₄	—	43	1	no	—
433	C₂×D₄	—	86	1	no	—
434	C₂²×C₄	—	86	1	no	—
435	C₂²×C₄	—	86	1	no	—
436	C₂²×C₄	—	86	1	no	—
437	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
439	C₂²×C₄	#10621902	1	1	yes	characteristic
440	Q₁₆	—	86	2	no	—
441	Q₁₆	—	86	2	no	—
442	SD₁₆	—	86	2	no	—
443	SD₁₆	—	86	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	8	1	no	—
449	C₂×C₈	—	43	1	no	—
450	C₂×C₈	—	43	1	no	—
451	C₂×C₈	—	43	1	no	—
452	C₂×C₈	—	43	1	no	—
453	C₂×C₈	—	86	1	no	—
454	C₂×C₈	—	86	1	no	—
455	C₂×C₈	—	344	1	no	—
456	C₂×C₈	—	344	1	no	—
457	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
458	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
459	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
461	C₄⋊C₄	—	43	1	no	—
462	C₄⋊C₄	—	43	1	no	—
463	C₄⋊C₄	—	43	1	no	—
464	C₄⋊C₄	—	43	1	no	—
465	C₄⋊C₄	—	86	1	no	—
466	C₄⋊C₄	—	86	1	no	—
467	C₄⋊C₄	—	86	1	no	—
468	C₄⋊C₄	—	86	1	no	—
469	C₄⋊C₄	—	86	1	no	—
470	C₄⋊C₄	—	86	1	no	—
471	C₄⋊C₄	—	86	1	no	—
472	C₄⋊C₄	—	86	1	no	—
473	C₄⋊C₄	—	86	1	no	—
474	C₂²⋊C₄	—	86	1	no	—
475	C₂²⋊C₄	—	86	1	no	—
476	C₂²⋊C₄	—	86	1	no	—
477	C₂²⋊C₄	—	86	1	no	—
478	C₂²⋊C₄	—	86	1	no	—
479	C₄²	—	86	1	no	—
480	C₄²	—	86	1	no	—
481	C₄²	—	86	1	no	—
482	C₄²	—	86	1	no	—
483	C₄²	—	86	1	no	—
484	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
485	C₄²	D₄×D₄₃	1	1	yes	characteristic
486	C₄²	#10621902	1	1	yes	characteristic
487	C₄²	C₂³×D₄₃	1	1	yes	characteristic
488	C₂³	—	86	1	no	—
489	C₂³	#13063287	1	1	yes	characteristic
490	Q₈	—	43	2	no	—
491	Q₈	—	86	1	no	—
492	Q₈	—	86	1	no	—
493	Q₈	—	86	1	no	—
494	Q₈	—	86	1	no	—
495	Q₈	—	86	1	no	—
496	Q₈	—	344	1	no	—
497	D₄	—	43	2	no	—
498	D₄	—	86	4	no	—
499	D₄	—	86	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	86	4	no	—
506	C₂×C₄	—	86	1	no	—
507	C₂×C₄	—	86	1	no	—
508	C₂×C₄	—	86	1	no	—
509	C₂×C₄	—	86	1	no	—
510	C₂×C₄	—	86	1	no	—
511	C₂×C₄	—	86	1	no	—
512	C₂×C₄	—	86	1	no	—
513	C₂×C₄	—	344	1	no	—
514	C₂×C₄	—	172	1	no	—
515	C₂×C₄	—	172	1	no	—
516	C₂×C₄	#13063287	1	1	yes	characteristic
517	C₂×C₄	#13063287	1	1	yes	characteristic
518	C₂×C₄	#13063287	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
521	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	1	no	—
525	C₈	—	2	1	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	86	1	no	—
531	C₈	—	86	1	no	—
532	C₈	—	86	1	no	—
533	C₈	—	86	1	no	—
534	C₈	—	172	1	no	—
535	C₈	—	172	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	86	2	no	—
540	C₂²	—	172	1	no	—
541	C₂²	—	172	1	no	—
542	C₂²	C₂×#13063287	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	86	2	no	—
548	C₄	—	172	1	no	—
549	C₄	—	172	1	no	—
550	C₄	—	172	1	no	—
551	C₄	—	172	1	no	—
552	C₄	—	172	1	no	—
553	C₄	—	172	1	no	—
554	C₄	#131×D₄₃	1	1	yes	characteristic
555	C₄	#131×D₄₃	1	1	yes	characteristic
556	C₄	#14583709	1	1	yes	characteristic
557	C₄	#14583715	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	172	2	no	—
560	C₂	#19143288	1	1	yes	characteristic
561	C₂	#19143436	1	1	yes	characteristic
562	C₂	#19143511	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1573	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1573	D₄₃
hypocenter	C₄₃	#17921
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
3. #19143692	C₂	semidirect
4. #19133465	C₂	semidirect
5. #19133451	C₂	semidirect
6. #19133444	C₂	semidirect
7. #19133430	C₂	semidirect
8. #19133413	C₂	semidirect
9. #19133406	C₂	semidirect
10. #19133401	C₂	semidirect
11. #19133394	C₂	semidirect
13. #19132997	C₂	semidirect
14. #19132895	C₂	semidirect
15. C₄₃×#1573	C₂	semidirect
288. #1573	D₄₃	semidirect
348. C₄₃	#17921	semidirect

Maximal subgroups

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

subgroup	index
#19144667	2
#19143704	2
#19143692	2
#19133465	2
#19133451	2
#19133444	2
#19133430	2
#19133413	2
#19133406	2
#19133401	2
#19133394	2
#19133027	2
#19132997	2
#19132895	2
C₄₃×#1573	2
#17921	43