Subgroups — #25115019

Order 11008.

986 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×Dic₄₃	C₂	1	2	yes	maximal
2	#19137516	C₂	1	1	yes	maximal, characteristic, complemented
3	#19137505	C₂	1	1	yes	maximal, characteristic
4	#19135324	C₂	1	2	yes	maximal, complemented
5	#19134851	C₂	1	2	yes	maximal, complemented
6	#19134844	C₂	1	2	yes	maximal
7	#19134759	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134610	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134605	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₃	C₂²	1	2	yes	—
14	SD₁₆×Dic₄₃	—	2	8	no	—
15	C₂×#13063259	C₂²	1	2	yes	—
16	C₂×#13063257	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#13063249	C₂²	1	2	yes	—
19	C₂×#13063246	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
21	#14582798	—	2	2	no	—
22	#14582798	C₂²	1	2	yes	—
23	#14582798	C₂²	1	2	yes	—
24	#14582774	—	2	2	no	—
25	#14582765	—	2	1	no	—
26	#14582765	C₂²	1	1	yes	characteristic
27	#14582765	C₂²	1	1	yes	characteristic
28	#14582759	—	2	1	no	—
29	C₄×C₄⋊Dic₄₃	—	2	1	no	—
30	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄₃⋊#95	—	2	1	no	—
32	#14582661	C₂²	1	2	yes	—
33	#14582661	C₂²	1	2	yes	—
34	#14582653	C₂²	1	2	yes	—
35	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
38	C₄×SD₁₆×C₄₃	C₄	1	8	yes	complemented
39	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₂³×Dic₄₃	—	2	2	no	—
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	Q₈×Dic₄₃	—	2	4	no	—
46	Q₈×Dic₄₃	—	4	2	no	—
47	D₄×Dic₄₃	—	2	4	no	—
48	D₄×Dic₄₃	—	4	2	no	—
49	C₂×C₄⋊Dic₄₃	—	2	2	no	—
50	C₂×C₄⋊Dic₄₃	—	2	2	no	—
51	C₂×C₄⋊Dic₄₃	—	2	2	no	—
52	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
56	C₂×C₄×Dic₄₃	—	2	2	no	—
57	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
58	#13063259	—	4	2	no	—
59	#13063257	—	2	4	no	—
60	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
61	#13063249	—	2	4	no	—
62	#13063246	—	2	4	no	—
63	C₈×Dic₄₃	—	2	4	no	—
64	C₄₃⋊#95	—	2	1	no	—
65	C₄₃⋊#95	—	2	1	no	—
66	C₄₃⋊#95	—	2	1	no	—
67	C₄₃⋊#95	—	2	1	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	D₄	1	1	yes	characteristic
71	C₄₃⋊#95	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	—	2	1	no	—
75	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
76	C₂×SD₁₆×C₄₃	D₄	1	4	yes	—
77	C₂×SD₁₆×C₄₃	Q₈	1	4	yes	—
78	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₄₃	—	2	2	no	—
81	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
82	C₄×D₄×C₄₃	—	2	2	no	—
83	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	#106×C₄₃	C₂×C₄	1	4	yes	complemented
91	#103×C₄₃	C₂×C₄	1	4	yes	complemented
92	#102×C₄₃	C₂×C₄	1	4	yes	—
93	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
94	C₂⁴×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
100	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	1	no	—
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	8	2	no	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	—	2	2	no	—
117	C₂²×Dic₄₃	—	4	4	no	—
118	C₂²×Dic₄₃	—	4	4	no	—
119	C₂²×Dic₄₃	—	8	2	no	—
120	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
121	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
122	SD₁₆×C₄₃	C₄⋊C₄	1	16	yes	complemented
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₄₃	—	2	4	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₃	#41	1	2	yes	—
138	C₂²⋊Dic₄₃	—	4	4	no	—
139	C₄⋊Dic₄₃	—	2	4	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	2	2	no	—
144	C₄⋊Dic₄₃	—	4	4	no	—
145	C₄⋊Dic₄₃	—	4	4	no	—
146	C₄⋊Dic₄₃	—	8	2	no	—
147	C₄×Dic₄₃	—	2	2	no	—
148	C₄×Dic₄₃	—	2	2	no	—
149	C₄×Dic₄₃	—	4	4	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	2	no	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	2	2	no	—
160	Q₈×C₄₃	—	2	2	no	—
161	Q₈×C₄₃	—	2	2	no	—
162	Q₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
163	D₄×C₄₃	—	2	2	no	—
164	D₄×C₄₃	—	2	2	no	—
165	D₄×C₄₃	—	2	2	no	—
166	D₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	2	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	8	4	no	—
177	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂×Dic₄₃	—	2	2	no	—
186	C₂×Dic₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	2	no	—
196	C₂×Dic₄₃	—	8	8	no	—
197	C₂×Dic₄₃	#135	1	4	yes	—
198	C₈×C₄₃	—	2	2	no	—
199	C₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
200	C₄₃⋊C₈	—	4	2	no	—
201	#22683	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	4	no	—
203	C₂²×C₄₃	—	4	4	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	4	no	—
207	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₃	D₄²	1	1	yes	characteristic
209	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
210	C₂²×C₄₃	C₂×#135	1	2	yes	—
211	C₂²×C₄₃	#577	1	2	yes	—
212	C₄×C₄₃	—	2	4	no	—
213	C₄×C₄₃	—	2	2	no	—
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
218	C₄×C₄₃	#520	1	1	yes	characteristic
219	C₄×C₄₃	#547	1	1	yes	characteristic
220	C₄×C₄₃	#554	1	1	yes	characteristic
221	Dic₄₃	—	2	4	no	—
222	Dic₄₃	—	4	2	no	—
223	Dic₄₃	—	8	2	no	—
224	Dic₄₃	—	8	2	no	—
225	C₂×C₄×SD₁₆	—	43	2	no	—
226	C₂×C₄×SD₁₆	D₄₃	1	1	yes	characteristic
227	#2351	—	43	1	no	—
228	#2349	—	43	1	no	—
229	#1941	—	43	2	no	—
230	#1863	—	43	2	no	—
231	#1862	—	43	2	no	—
232	#1846	—	43	1	no	—
233	#1805	—	43	1	no	—
234	#1804	—	43	1	no	—
235	C₈×C₄⋊C₄	—	43	1	no	—
236	C₂×C₄₃	—	4	4	no	—
237	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₄₃	C₄×#135	1	1	yes	characteristic
239	C₂×C₄₃	#2949	1	1	yes	characteristic
240	C₂×C₄₃	#3282	1	2	yes	—
241	C₂×C₄₃	#3381	1	2	yes	—
242	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	—	43	2	no	—
244	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
245	C₂×C₄×D₄	—	43	2	no	—
246	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
247	C₄×SD₁₆	—	86	8	no	—
248	C₄×SD₁₆	Dic₄₃	1	8	yes	complemented
249	C₂×#107	—	43	2	no	—
250	C₂×#106	—	43	2	no	—
251	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
252	C₂×C₄⋊C₈	—	43	1	no	—
253	C₂×#103	—	43	2	no	—
254	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
255	C₂×#102	—	43	2	no	—
256	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
257	C₂×C₄×C₈	—	43	2	no	—
258	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
259	#389	—	43	2	no	—
260	#389	—	43	2	no	—
261	#389	—	86	2	no	—
262	#385	—	86	2	no	—
263	#382	—	43	1	no	—
264	#382	—	43	1	no	—
265	#382	—	86	1	no	—
266	#380	—	86	1	no	—
267	C₄×C₄⋊C₄	—	43	1	no	—
268	C₄×C₄⋊C₄	—	86	1	no	—
269	C₂×#95	—	86	1	no	—
270	#340	—	43	2	no	—
271	#340	—	43	2	no	—
272	#336	—	43	2	no	—
273	C₄₃	#22683	1	1	yes	characteristic, complemented, Sylow
274	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
275	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	—	86	2	no	—
278	C₂×SD₁₆	Dic₈₆	1	4	yes	—
279	C₂×SD₁₆	D₁₇₂	1	4	yes	—
280	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
281	C₂²×C₈	—	43	2	no	—
282	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
283	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	86	4	no	—
286	C₄×Q₈	—	172	2	no	—
287	C₄×Q₈	C₂×Dic₄₃	1	4	yes	complemented
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	86	4	no	—
290	C₄×D₄	—	172	2	no	—
291	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	43	2	no	—
295	C₂×C₄⋊C₄	—	43	2	no	—
296	C₂×C₄⋊C₄	—	86	2	no	—
297	C₂×C₄⋊C₄	—	86	2	no	—
298	C₂×C₄⋊C₄	—	86	2	no	—
299	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
301	C₂×C₂²⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	86	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	43	2	no	—
305	C₂×C₄²	—	86	2	no	—
306	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
307	#107	—	172	2	no	—
308	#106	—	86	4	no	—
309	#106	C₂×Dic₄₃	1	4	yes	complemented
310	C₄⋊C₈	—	86	2	no	—
311	#103	—	86	4	no	—
312	#103	C₂×Dic₄₃	1	4	yes	complemented
313	#102	—	86	4	no	—
314	#102	C₂×Dic₄₃	1	4	yes	—
315	C₄×C₈	—	86	4	no	—
316	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
317	#95	—	43	1	no	—
318	#95	—	43	1	no	—
319	#95	—	86	2	no	—
320	#95	—	86	2	no	—
321	#95	—	86	1	no	—
322	#95	—	86	1	no	—
323	#95	—	86	1	no	—
324	#95	—	86	1	no	—
325	C₂⁴	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	C₂×Dic₈₆	1	2	yes	—
330	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
331	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	C₂×Dic₈₆	1	2	yes	—
336	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
337	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	8	2	no	—
343	C₂²×C₄	—	43	2	no	—
344	C₂²×C₄	—	43	2	no	—
345	C₂²×C₄	—	86	2	no	—
346	C₂²×C₄	—	86	2	no	—
347	C₂²×C₄	—	344	2	no	—
348	C₂²×C₄	—	172	4	no	—
349	C₂²×C₄	—	172	4	no	—
350	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
353	SD₁₆	C₄⋊Dic₄₃	1	16	yes	complemented
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	86	2	no	—
359	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
360	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
361	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
362	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	86	4	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	86	2	no	—
370	C₄⋊C₄	—	86	2	no	—
371	C₄⋊C₄	—	344	2	no	—
372	C₄⋊C₄	—	172	4	no	—
373	C₄⋊C₄	—	172	4	no	—
374	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
375	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	172	4	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	86	2	no	—
380	C₄²	—	86	2	no	—
381	C₄²	—	172	4	no	—
382	C₄²	#10621900	1	2	yes	—
383	C₄²	C₂²×Dic₄₃	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	C₂×C₄⋊Dic₄₃	1	4	yes	—
394	D₄	—	2	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	—	43	4	no	—
409	C₂×C₄	—	86	2	no	—
410	C₂×C₄	—	86	2	no	—
411	C₂×C₄	—	86	2	no	—
412	C₂×C₄	—	86	2	no	—
413	C₂×C₄	—	86	2	no	—
414	C₂×C₄	—	344	8	no	—
415	C₂×C₄	—	172	2	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	—	172	2	no	—
420	C₂×C₄	—	172	2	no	—
421	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
422	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
423	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
425	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
426	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
427	C₂×C₄	#13063371	1	1	yes	characteristic
428	C₂×C₄	#13063372	1	1	yes	characteristic
429	C₈	—	2	2	no	—
430	C₈	—	172	2	no	—
431	C₈	C₂×C₄⋊Dic₄₃	1	4	yes	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	4	no	—
437	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
438	C₂²	D₄×D₁₇₂	1	1	yes	characteristic
439	C₂²	D₄×Dic₈₆	1	1	yes	characteristic
440	C₂²	#135×D₄₃	1	2	yes	—
441	C₂²	#14583705	1	2	yes	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	4	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	2	no	—
447	C₄	—	86	4	no	—
448	C₄	—	344	2	no	—
449	C₄	—	344	2	no	—
450	C₄	—	172	2	no	—
451	C₄	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
452	C₄	#14583382	1	1	yes	characteristic
453	C₄	#14583553	1	1	yes	characteristic
454	C₄	#14583606	1	1	yes	characteristic
455	C₂	—	4	4	no	—
456	C₂	D₄×C₄⋊Dic₄₃	1	1	yes	characteristic
457	C₂	#135×Dic₄₃	1	1	yes	characteristic
458	C₂	#19143455	1	1	yes	characteristic
459	C₂	#19146304	1	2	yes	—
460	C₂	#19147471	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄×SD₁₆×C₄₃	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₄₃
hypocenter	C₄₃	#22683
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. #19137516	C₂	semidirect
4. #19135324	C₂	semidirect
5. #19134851	C₂	semidirect
7. #19134759	C₂	semidirect
8. #19134610	C₂	semidirect
10. C₈×C₄⋊Dic₄₃	C₂	semidirect
38. C₄×SD₁₆×C₄₃	C₄	semidirect
81. C₄×Q₈×C₄₃	C₂×C₄	semidirect
90. #106×C₄₃	C₂×C₄	semidirect
91. #103×C₄₃	C₂×C₄	semidirect
93. C₄×C₈×C₄₃	C₂×C₄	semidirect
122. SD₁₆×C₄₃	C₄⋊C₄	semidirect
248. C₄×SD₁₆	Dic₄₃	semidirect
273. C₄₃	#22683	semidirect
287. C₄×Q₈	C₂×Dic₄₃	semidirect
309. #106	C₂×Dic₄₃	semidirect
312. #103	C₂×Dic₄₃	semidirect
316. C₄×C₈	C₂×Dic₄₃	semidirect
353. SD₁₆	C₄⋊Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×Dic₄₃	2
#19137516	2
#19137505	2
#19135324	2
#19134851	2
#19134844	2
#19134759	2
#19134610	2
#19134605	2
C₈×C₄⋊Dic₄₃	2
C₂×C₄×SD₁₆×C₄₃	2
#22683	43