Subgroups — #25115774

Order 11008.

858 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137560	C₂	1	1	yes	maximal, characteristic, complemented
2	#19137505	C₂	1	1	yes	maximal, characteristic
3	#19135287	C₂	1	2	yes	maximal, complemented
4	#19135175	C₂	1	2	yes	maximal, complemented
5	#19134931	C₂	1	2	yes	maximal
6	#19134726	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134610	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134605	C₂	1	1	yes	maximal, characteristic
9	#19134462	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134422	C₂	1	2	yes	maximal
11	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₃	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063249	C₂²	1	2	yes	—
15	C₂×#13063246	C₂²	1	2	yes	—
16	C₂×#13063235	C₂²	1	2	yes	—
17	#14582806	C₂²	1	2	yes	—
18	#14582798	C₂²	1	2	yes	—
19	#14582785	—	2	2	no	—
20	#14582774	—	2	2	no	—
21	#14582767	—	2	1	no	—
22	#14582765	C₂²	1	1	yes	characteristic
23	#14582765	C₂²	1	1	yes	characteristic
24	#14582759	—	2	1	no	—
25	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
26	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
27	#14582745	—	2	1	no	—
28	C₂×C₄₃⋊#95	—	2	1	no	—
29	#14582662	C₂²	1	2	yes	—
30	#14582662	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582661	C₂²	1	2	yes	—
33	#14582653	C₂²	1	2	yes	—
34	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
37	C₄×SD₁₆×C₄₃	C₄	1	8	yes	complemented
38	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₃	—	2	2	no	—
43	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
44	D₄×Dic₄₃	—	2	4	no	—
45	D₄×Dic₄₃	—	4	2	no	—
46	C₂×C₄⋊Dic₄₃	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
48	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
51	C₂×C₄×Dic₄₃	—	2	2	no	—
52	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
53	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
54	#13063249	—	4	2	no	—
55	#13063246	—	2	4	no	—
56	#13063235	—	4	2	no	—
57	C₄₃⋊#95	—	2	1	no	—
58	C₄₃⋊#95	—	2	1	no	—
59	C₄₃⋊#95	—	2	1	no	—
60	C₄₃⋊#95	—	2	1	no	—
61	C₄₃⋊#95	—	2	2	no	—
62	C₄₃⋊#95	—	2	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	C₄₃⋊#95	—	2	2	no	—
65	C₄₃⋊#95	D₄	1	1	yes	characteristic
66	C₄₃⋊#95	D₄	1	1	yes	characteristic
67	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₄₃	—	2	1	no	—
70	C₂×SD₁₆×C₄₃	—	2	2	no	—
71	C₂×SD₁₆×C₄₃	—	2	2	no	—
72	C₂×SD₁₆×C₄₃	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₃	—	2	2	no	—
76	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
77	C₄×D₄×C₄₃	—	2	2	no	—
78	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	#106×C₄₃	C₂×C₄	1	4	yes	complemented
86	#103×C₄₃	C₂×C₄	1	4	yes	complemented
87	#102×C₄₃	C₂×C₄	1	4	yes	—
88	C₄×C₈×C₄₃	C₂×C₄	1	4	yes	complemented
89	C₂⁴×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	—	2	1	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₄₃	—	2	1	no	—
97	C₂×D₄×C₄₃	—	2	1	no	—
98	C₂×D₄×C₄₃	—	2	1	no	—
99	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₄₃	#41	1	2	yes	—
101	C₂×D₄×C₄₃	#41	1	2	yes	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	—	8	2	no	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂²×Dic₄₃	—	2	2	no	—
112	C₂²×Dic₄₃	—	4	4	no	—
113	C₂²×Dic₄₃	—	4	4	no	—
114	C₂²×Dic₄₃	—	8	2	no	—
115	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
116	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
117	SD₁₆×C₄₃	—	2	8	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₄²×C₄₃	—	2	4	no	—
131	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
132	C₄²×C₄₃	#41	1	2	yes	—
133	C₂²⋊Dic₄₃	—	4	4	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	—	4	2	no	—
139	C₄⋊Dic₄₃	—	8	2	no	—
140	C₄×Dic₄₃	—	2	2	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	4	4	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₄₃	—	2	2	no	—
153	Q₈×C₄₃	—	2	2	no	—
154	Q₈×C₄₃	—	4	1	no	—
155	Q₈×C₄₃	—	4	1	no	—
156	D₄×C₄₃	—	2	2	no	—
157	D₄×C₄₃	—	2	2	no	—
158	D₄×C₄₃	—	2	2	no	—
159	D₄×C₄₃	#117	1	4	yes	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	8	4	no	—
170	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	C₂×Dic₄₃	—	4	2	no	—
186	C₂×Dic₄₃	—	4	2	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	C₂×Dic₄₃	—	4	2	no	—
190	C₂×Dic₄₃	—	8	8	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	#22760	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	4	no	—
196	C₂²×C₄₃	—	4	4	no	—
197	C₂²×C₄₃	—	4	2	no	—
198	C₂²×C₄₃	—	4	2	no	—
199	C₂²×C₄₃	—	4	4	no	—
200	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂²×C₄₃	#546	1	1	yes	characteristic
202	C₂²×C₄₃	#548	1	1	yes	characteristic
203	C₂²×C₄₃	#575	1	2	yes	—
204	C₂²×C₄₃	#577	1	2	yes	—
205	C₄×C₄₃	—	2	2	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
211	C₄×C₄₃	#520	1	1	yes	characteristic
212	C₄×C₄₃	#552	1	1	yes	characteristic
213	C₄×C₄₃	#553	1	1	yes	characteristic
214	Dic₄₃	—	4	2	no	—
215	Dic₄₃	—	4	2	no	—
216	Dic₄₃	—	8	2	no	—
217	Dic₄₃	—	8	2	no	—
218	C₂×C₄×SD₁₆	D₄₃	1	1	yes	characteristic
219	#2356	—	43	1	no	—
220	#2349	—	43	1	no	—
221	#1935	—	43	2	no	—
222	#1919	—	43	2	no	—
223	#1877	—	43	2	no	—
224	#1835	—	43	1	no	—
225	#1805	—	43	1	no	—
226	#1804	—	43	1	no	—
227	#1770	—	43	1	no	—
228	#1762	—	43	2	no	—
229	C₂×C₄₃	—	4	4	no	—
230	C₂×C₄₃	#2352	1	1	yes	characteristic
231	C₂×C₄₃	#2943	1	1	yes	characteristic
232	C₂×C₄₃	#2949	1	1	yes	characteristic
233	C₂×C₄₃	#3323	1	2	yes	—
234	C₂×C₄₃	#3376	1	2	yes	—
235	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
236	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
237	C₂×C₄×D₄	—	43	2	no	—
238	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
239	C₄×SD₁₆	Dic₄₃	1	8	yes	complemented
240	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
241	C₂×C₄⋊C₈	—	43	1	no	—
242	C₂×#103	—	43	2	no	—
243	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
244	C₂×#102	—	43	2	no	—
245	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
246	C₂×#97	—	43	2	no	—
247	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
248	#391	—	43	2	no	—
249	#389	—	43	2	no	—
250	#387	—	86	2	no	—
251	#385	—	86	2	no	—
252	#383	—	86	1	no	—
253	#382	—	43	1	no	—
254	#382	—	43	1	no	—
255	#380	—	86	1	no	—
256	C₄×C₄⋊C₄	—	43	1	no	—
257	C₄×C₄⋊C₄	—	43	2	no	—
258	#376	—	86	1	no	—
259	C₂×#95	—	86	1	no	—
260	#340	—	43	2	no	—
261	#340	—	43	2	no	—
262	#340	—	43	2	no	—
263	#340	—	43	2	no	—
264	#336	—	43	2	no	—
265	C₄₃	#22760	1	1	yes	characteristic, complemented, Sylow
266	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	—	86	2	no	—
270	C₂×SD₁₆	—	2	2	no	—
271	C₂×SD₁₆	—	2	2	no	—
272	C₂×SD₁₆	C₂×Dic₄₃	1	4	yes	—
273	C₂²×C₈	—	43	2	no	—
274	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
275	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	C₂×Dic₄₃	1	4	yes	complemented
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	86	4	no	—
280	C₄×D₄	—	172	2	no	—
281	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	43	2	no	—
284	C₂×C₄⋊C₄	—	43	2	no	—
285	C₂×C₄⋊C₄	—	43	2	no	—
286	C₂×C₄⋊C₄	—	86	2	no	—
287	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	1	no	—
290	C₂×C₂²⋊C₄	—	86	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	43	2	no	—
293	C₂×C₄²	—	86	2	no	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	#106	C₂×Dic₄₃	1	4	yes	complemented
296	C₄⋊C₈	—	86	2	no	—
297	#103	—	172	2	no	—
298	#103	C₂×Dic₄₃	1	4	yes	complemented
299	#102	—	86	4	no	—
300	#102	C₂×Dic₄₃	1	4	yes	—
301	#97	—	172	2	no	—
302	C₄×C₈	C₂×Dic₄₃	1	4	yes	complemented
303	#95	—	43	1	no	—
304	#95	—	43	1	no	—
305	#95	—	86	2	no	—
306	#95	—	86	2	no	—
307	#95	—	86	2	no	—
308	#95	—	86	2	no	—
309	#95	—	86	1	no	—
310	#95	—	86	1	no	—
311	#95	—	86	1	no	—
312	#95	—	86	1	no	—
313	C₂⁴	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
320	C₂×D₄	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	#10621898	1	2	yes	—
324	C₂×D₄	#10621898	1	2	yes	—
325	C₂×D₄	C₂²×Dic₄₃	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	8	2	no	—
331	C₂²×C₄	—	43	2	no	—
332	C₂²×C₄	—	43	2	no	—
333	C₂²×C₄	—	86	2	no	—
334	C₂²×C₄	—	86	2	no	—
335	C₂²×C₄	—	344	2	no	—
336	C₂²×C₄	—	172	4	no	—
337	C₂²×C₄	—	172	4	no	—
338	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
341	SD₁₆	—	2	8	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	86	2	no	—
347	C₂×C₈	—	86	2	no	—
348	C₂×C₈	—	86	2	no	—
349	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
350	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	86	2	no	—
356	C₄⋊C₄	—	86	2	no	—
357	C₄⋊C₄	—	86	2	no	—
358	C₄⋊C₄	—	344	2	no	—
359	C₄⋊C₄	—	172	2	no	—
360	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
361	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	172	4	no	—
364	C₄²	—	2	4	no	—
365	C₄²	—	86	2	no	—
366	C₄²	—	86	2	no	—
367	C₄²	—	172	4	no	—
368	C₄²	#10621900	1	2	yes	—
369	C₄²	C₂²×Dic₄₃	1	2	yes	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	1	no	—
380	D₄	—	2	2	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	#13063284	1	4	yes	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	4	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	86	2	no	—
396	C₂×C₄	—	86	2	no	—
397	C₂×C₄	—	86	2	no	—
398	C₂×C₄	—	86	2	no	—
399	C₂×C₄	—	86	2	no	—
400	C₂×C₄	—	344	8	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	—	172	2	no	—
403	C₂×C₄	—	172	2	no	—
404	C₂×C₄	—	172	2	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
408	C₂×C₄	D₄×Dic₄₃	1	2	yes	—
409	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
411	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
412	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
413	C₂×C₄	#13063371	1	1	yes	characteristic
414	C₂×C₄	#13063372	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	172	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	2	no	—
423	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
424	C₂²	#14583545	1	1	yes	characteristic
425	C₂²	#14583558	1	1	yes	characteristic
426	C₂²	#14583696	1	2	yes	—
427	C₂²	#14583705	1	2	yes	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	2	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	344	2	no	—
434	C₄	—	344	2	no	—
435	C₄	—	172	2	no	—
436	C₄	—	172	2	no	—
437	C₄	C₂×#13063284	1	1	yes	characteristic
438	C₄	#14583382	1	1	yes	characteristic
439	C₄	#14583589	1	1	yes	characteristic
440	C₄	#14583595	1	1	yes	characteristic
441	C₂	—	4	4	no	—
442	C₂	#19137524	1	1	yes	characteristic
443	C₂	#19143396	1	1	yes	characteristic
444	C₂	#19143455	1	1	yes	characteristic
445	C₂	#19146816	1	2	yes	—
446	C₂	#19147418	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	#22760
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
1. #19137560	C₂	semidirect
3. #19135287	C₂	semidirect
4. #19135175	C₂	semidirect
6. #19134726	C₂	semidirect
7. #19134610	C₂	semidirect
9. #19134462	C₂	semidirect
37. C₄×SD₁₆×C₄₃	C₄	semidirect
76. C₄×Q₈×C₄₃	C₂×C₄	semidirect
85. #106×C₄₃	C₂×C₄	semidirect
86. #103×C₄₃	C₂×C₄	semidirect
88. C₄×C₈×C₄₃	C₂×C₄	semidirect
239. C₄×SD₁₆	Dic₄₃	semidirect
265. C₄₃	#22760	semidirect
277. C₄×Q₈	C₂×Dic₄₃	semidirect
295. #106	C₂×Dic₄₃	semidirect
298. #103	C₂×Dic₄₃	semidirect
302. C₄×C₈	C₂×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19137560	2
#19137505	2
#19135287	2
#19135175	2
#19134931	2
#19134726	2
#19134610	2
#19134605	2
#19134462	2
#19134422	2
C₂×C₄×SD₁₆×C₄₃	2
#22760	43