Subgroups — #25250260

Order 11008.

444 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143524	C₂	1	1	yes	maximal, characteristic
2	#19136504	C₂	1	1	yes	maximal, characteristic, complemented
3	#19136503	C₂	1	1	yes	maximal, characteristic, complemented
4	#19136502	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136502	C₂	1	1	yes	maximal, characteristic, complemented
6	#19136501	C₂	1	1	yes	maximal, characteristic, complemented
7	#19136501	C₂	1	1	yes	maximal, characteristic, complemented
8	#19136500	C₂	1	1	yes	maximal, characteristic, complemented
9	#19136403	C₂	1	1	yes	maximal, characteristic
10	#19136401	C₂	1	1	yes	maximal, characteristic
11	#19136401	C₂	1	1	yes	maximal, characteristic
12	#19136400	C₂	1	1	yes	maximal, characteristic
13	#19136397	C₂	1	1	yes	maximal, characteristic
14	#19136396	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#2183	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583453	C₄	1	1	yes	characteristic
17	#14583030	C₄	1	1	yes	characteristic
18	#14583028	C₄	1	1	yes	characteristic
19	#14583028	C₄	1	1	yes	characteristic
20	#14583026	C₄	1	1	yes	characteristic
21	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
22	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
23	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
24	#14582924	C₄	1	1	yes	characteristic
25	#14582924	C₄	1	1	yes	characteristic
26	#14582921	C₄	1	1	yes	characteristic
27	#14582853	C₂²	1	1	yes	characteristic
28	#14582853	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
30	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	1	yes	characteristic
31	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	1	yes	characteristic
32	C₄⋊(C₄₃⋊C₁₆)	C₂²	1	1	yes	characteristic
33	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
34	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
35	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
36	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
37	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
38	Dic₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
39	(C₂×D₄₃)⋊C₁₆	C₂²	1	1	yes	characteristic
40	(C₂×D₄₃)⋊C₁₆	C₂²	1	1	yes	characteristic
41	(C₂×D₄₃)⋊C₁₆	C₂²	1	1	yes	characteristic
42	(C₂×D₄₃)⋊C₁₆	C₂²	1	1	yes	characteristic
43	#14582675	C₂²	1	1	yes	characteristic
44	#14582675	C₂²	1	1	yes	characteristic
45	#14582674	C₂²	1	1	yes	characteristic
46	#14582674	C₂²	1	1	yes	characteristic
47	#14582674	C₂²	1	1	yes	characteristic
48	#14582674	C₂²	1	1	yes	characteristic
49	C₄×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
52	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
54	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
55	C₄₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₄₃×#346	C₂²	1	1	yes	characteristic
57	C₄₃×#346	C₂²	1	1	yes	characteristic
58	C₄×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
59	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
60	C₂×#10621872	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
63	#13063324	C₈	1	1	yes	characteristic
64	#13063323	C₈	1	1	yes	characteristic
65	#13063315	C₈	1	1	yes	characteristic
66	#13063315	C₈	1	1	yes	characteristic
67	#13063305	C₈	1	1	yes	characteristic
68	#13063303	C₈	1	1	yes	characteristic
69	#13063303	C₈	1	1	yes	characteristic
70	#13063301	C₈	1	1	yes	characteristic
71	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
72	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
73	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
74	#13063282	C₂×C₄	1	1	yes	characteristic
75	#13063282	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₄₃⋊C₁₆	C₂³	1	1	yes	characteristic
81	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
84	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
85	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
86	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
87	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
88	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
90	#13063236	C₂×C₄	1	1	yes	characteristic
91	#13063236	C₂×C₄	1	1	yes	characteristic
92	#13063235	C₂×C₄	1	1	yes	characteristic
93	#13063235	C₂×C₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
97	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
98	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
99	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₁₆×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	C₂×Q₈×C₄₃	C₂×C₈	1	1	yes	characteristic
111	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×Dic₈₆	C₂×C₈	1	1	yes	characteristic
115	C₂×Dic₈₆	C₂×C₈	1	1	yes	characteristic
116	C₂×Dic₈₆	C₂×C₈	1	1	yes	characteristic
117	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
121	C₄⋊C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
122	C₄⋊C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
123	C₄⋊C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
124	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	(C₂×D₄₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
128	(C₂×D₄₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
129	(C₂×D₄₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
130	(C₂×D₄₃)⋊C₄	C₂×C₈	1	1	yes	characteristic
131	C₄⋊Dic₄₃	C₂×C₈	1	1	yes	characteristic
132	C₄⋊Dic₄₃	C₂×C₈	1	1	yes	characteristic
133	C₄⋊Dic₄₃	C₂×C₈	1	1	yes	characteristic
134	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
135	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
136	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
137	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
138	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
142	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
143	Dic₄₃⋊C₄	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₄₃	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	#10621872	—	4	1	no	—
154	#10621872	—	4	1	no	—
155	C₈×D₄₃	—	2	1	no	—
156	C₈×D₄₃	—	2	1	no	—
157	C₈×D₄₃	—	4	1	no	—
158	C₁₆×C₄₃	—	2	1	no	—
159	C₁₆×C₄₃	—	2	1	no	—
160	C₁₆×C₄₃	—	2	1	no	—
161	C₁₆×C₄₃	—	2	1	no	—
162	C₄₃⋊C₁₆	—	2	1	no	—
163	C₄₃⋊C₁₆	—	2	1	no	—
164	C₄₃⋊C₁₆	—	2	1	no	—
165	C₄₃⋊C₁₆	—	2	1	no	—
166	C₂²×D₄₃	C₂²×C₈	1	1	yes	characteristic
167	Q₈×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
177	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
178	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
179	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
180	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
181	C₂×Dic₄₃	C₂²×C₈	1	1	yes	characteristic
182	C₄×D₄₃	—	2	1	no	—
183	C₄×D₄₃	—	2	1	no	—
184	C₄×D₄₃	—	4	1	no	—
185	C₄×D₄₃	—	4	1	no	—
186	Dic₈₆	—	4	1	no	—
187	Dic₈₆	—	4	1	no	—
188	Dic₈₆	—	4	1	no	—
189	C₈×C₄₃	—	2	1	no	—
190	C₈×C₄₃	—	2	1	no	—
191	C₈×C₄₃	—	2	1	no	—
192	C₈×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
193	C₈×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
194	C₄₃⋊C₈	—	2	1	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₄₃⋊C₈	—	2	1	no	—
198	#33501	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
200	C₂×D₄₃	—	2	1	no	—
201	C₂×D₄₃	—	2	1	no	—
202	C₂×D₄₃	—	2	1	no	—
203	C₄×C₄₃	—	2	1	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	#519	1	1	yes	characteristic
210	C₄×C₄₃	#568	1	1	yes	characteristic
211	Dic₄₃	—	2	1	no	—
212	Dic₄₃	—	2	1	no	—
213	Dic₄₃	—	2	1	no	—
214	Dic₄₃	—	2	1	no	—
215	Dic₄₃	—	2	1	no	—
216	Dic₄₃	—	2	1	no	—
217	Dic₄₃	—	2	1	no	—
218	#2960	—	43	1	no	—
219	#2183	—	43	1	no	—
220	#2183	—	43	1	no	—
221	#2183	—	43	1	no	—
222	#2183	—	43	1	no	—
223	#2183	—	43	1	no	—
224	#2183	—	43	1	no	—
225	#2183	—	43	1	no	—
226	#2183	D₄₃	1	1	yes	characteristic, complemented
227	#2164	—	43	1	no	—
228	#2164	—	43	1	no	—
229	#2164	—	43	1	no	—
230	#2164	—	43	1	no	—
231	#2163	—	43	1	no	—
232	#2163	—	43	1	no	—
233	C₂×C₄₃	#2982	1	1	yes	characteristic
234	C₂×C₄₃	#3407	1	1	yes	characteristic
235	C₂×C₄₃	#3407	1	1	yes	characteristic
236	D₄₃	—	4	1	no	—
237	#533	—	43	1	no	—
238	#446	—	43	1	no	—
239	#446	—	43	1	no	—
240	#446	—	43	1	no	—
241	#446	—	43	1	no	—
242	C₈×Q₈	—	43	1	no	—
243	C₈×Q₈	—	43	1	no	—
244	C₈×Q₈	—	43	1	no	—
245	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
246	#424	—	43	1	no	—
247	#424	—	43	1	no	—
248	#423	—	43	1	no	—
249	#405	—	43	1	no	—
250	#405	—	43	1	no	—
251	C₂×C₄×C₈	—	43	1	no	—
252	C₄⋊C₁₆	—	43	1	no	—
253	C₄⋊C₁₆	—	43	1	no	—
254	C₄⋊C₁₆	—	43	1	no	—
255	C₄⋊C₁₆	—	43	1	no	—
256	C₄⋊C₁₆	—	43	1	no	—
257	C₄⋊C₁₆	—	43	1	no	—
258	C₄⋊C₁₆	—	43	1	no	—
259	C₄⋊C₁₆	—	43	1	no	—
260	C₄⋊C₁₆	—	43	1	no	—
261	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
262	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
263	C₄⋊C₁₆	C₂×D₄₃	1	1	yes	characteristic
264	C₂²⋊C₁₆	—	43	1	no	—
265	C₂²⋊C₁₆	—	43	1	no	—
266	C₂²⋊C₁₆	—	43	1	no	—
267	C₂²⋊C₁₆	—	43	1	no	—
268	#346	—	43	1	no	—
269	#346	—	43	1	no	—
270	#346	—	43	1	no	—
271	#346	—	43	1	no	—
272	#346	—	43	1	no	—
273	#346	—	43	1	no	—
274	#346	C₂×D₄₃	1	1	yes	characteristic
275	#346	C₂×D₄₃	1	1	yes	characteristic
276	C₄×C₁₆	—	43	1	no	—
277	C₄×C₁₆	—	43	1	no	—
278	C₄×C₁₆	—	43	1	no	—
279	C₄×C₁₆	C₂×D₄₃	1	1	yes	characteristic
280	C₄₃	#33501	1	1	yes	characteristic, complemented, Sylow
281	C₂×M₁₆	—	43	1	no	—
282	C₂×M₁₆	—	43	1	no	—
283	C₂²×C₈	—	43	1	no	—
284	C₂²×C₈	—	43	1	no	—
285	C₄⋊Q₈	—	43	1	no	—
286	C₄⋊Q₈	—	43	1	no	—
287	#125	—	43	1	no	—
288	#125	—	43	1	no	—
289	C₂²⋊Q₈	—	43	1	no	—
290	C₂²⋊Q₈	—	43	1	no	—
291	C₂²⋊Q₈	—	43	1	no	—
292	C₂²⋊Q₈	—	43	1	no	—
293	C₄×Q₈	—	43	1	no	—
294	C₄×Q₈	—	43	1	no	—
295	C₄×Q₈	—	43	1	no	—
296	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
297	#117	—	43	1	no	—
298	#117	—	43	1	no	—
299	C₂×C₄²	—	43	1	no	—
300	C₂×C₁₆	—	43	1	no	—
301	C₂×C₁₆	—	43	1	no	—
302	C₂×C₁₆	—	43	1	no	—
303	C₂×C₁₆	—	43	1	no	—
304	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
306	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
307	C₂×C₁₆	C₂²×D₄₃	1	1	yes	characteristic
308	C₄⋊C₈	—	43	1	no	—
309	C₄⋊C₈	—	43	1	no	—
310	C₄⋊C₈	—	43	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	43	1	no	—
313	C₄⋊C₈	—	43	1	no	—
314	C₄⋊C₈	—	43	1	no	—
315	C₄⋊C₈	—	43	1	no	—
316	C₄⋊C₈	—	43	1	no	—
317	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
318	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
319	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
320	#97	—	43	1	no	—
321	#97	—	43	1	no	—
322	#97	—	43	1	no	—
323	#97	—	43	1	no	—
324	C₄×C₈	—	43	1	no	—
325	C₄×C₈	—	43	1	no	—
326	C₄×C₈	—	43	1	no	—
327	C₄×C₈	—	43	1	no	—
328	C₄×C₈	—	43	1	no	—
329	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
332	C₂×Q₈	—	43	1	no	—
333	C₂×Q₈	—	43	1	no	—
334	C₂×Q₈	—	43	1	no	—
335	C₂×Q₈	C₈×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	1	no	—
339	M₁₆	—	172	1	no	—
340	M₁₆	—	172	1	no	—
341	C₂×C₈	—	43	1	no	—
342	C₂×C₈	—	43	1	no	—
343	C₂×C₈	—	43	1	no	—
344	C₂×C₈	—	43	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	86	1	no	—
347	C₂×C₈	—	172	1	no	—
348	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
352	C₄⋊C₄	—	43	1	no	—
353	C₄⋊C₄	—	43	1	no	—
354	C₄⋊C₄	—	43	1	no	—
355	C₄⋊C₄	—	43	1	no	—
356	C₄⋊C₄	—	43	1	no	—
357	C₄⋊C₄	—	43	1	no	—
358	C₄⋊C₄	—	43	1	no	—
359	C₄⋊C₄	—	43	1	no	—
360	C₄⋊C₄	—	43	1	no	—
361	C₄⋊C₄	—	43	1	no	—
362	C₄⋊C₄	—	43	1	no	—
363	C₄⋊C₄	—	43	1	no	—
364	C₄⋊C₄	—	43	1	no	—
365	C₄⋊C₄	C₈×D₄₃	1	1	yes	characteristic
366	C₄⋊C₄	C₈×D₄₃	1	1	yes	characteristic
367	C₄⋊C₄	C₈×D₄₃	1	1	yes	characteristic
368	C₂²⋊C₄	—	43	1	no	—
369	C₂²⋊C₄	—	43	1	no	—
370	C₂²⋊C₄	—	43	1	no	—
371	C₂²⋊C₄	—	43	1	no	—
372	C₄²	—	43	1	no	—
373	C₄²	—	43	1	no	—
374	C₄²	—	43	1	no	—
375	C₄²	—	43	1	no	—
376	C₄²	—	43	1	no	—
377	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
378	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
380	C₁₆	—	2	1	no	—
381	C₁₆	—	2	1	no	—
382	C₁₆	—	2	1	no	—
383	C₁₆	—	2	1	no	—
384	C₁₆	—	86	1	no	—
385	C₁₆	—	86	1	no	—
386	C₁₆	—	86	1	no	—
387	C₁₆	—	86	1	no	—
388	C₂³	—	43	1	no	—
389	Q₈	—	4	1	no	—
390	Q₈	—	172	1	no	—
391	Q₈	—	172	1	no	—
392	Q₈	—	172	1	no	—
393	C₂×C₄	—	43	1	no	—
394	C₂×C₄	—	43	1	no	—
395	C₂×C₄	—	43	1	no	—
396	C₂×C₄	—	43	1	no	—
397	C₂×C₄	—	43	1	no	—
398	C₂×C₄	—	43	1	no	—
399	C₂×C₄	—	43	1	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	1	no	—
402	C₂×C₄	—	172	1	no	—
403	C₂×C₄	—	172	1	no	—
404	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	86	1	no	—
415	C₈	—	86	1	no	—
416	C₈	—	86	1	no	—
417	C₈	—	86	1	no	—
418	C₈	#13063372	1	1	yes	characteristic
419	C₈	#13063373	1	1	yes	characteristic
420	C₂²	—	86	1	no	—
421	C₂²	—	86	1	no	—
422	C₂²	—	86	1	no	—
423	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	86	1	no	—
431	C₄	—	86	1	no	—
432	C₄	—	86	1	no	—
433	C₄	—	86	1	no	—
434	C₄	—	86	1	no	—
435	C₄	—	86	1	no	—
436	C₄	—	86	1	no	—
437	C₄	#14583375	1	1	yes	characteristic
438	C₄	#14583664	1	1	yes	characteristic
439	C₂	—	172	1	no	—
440	C₂	#19143674	1	1	yes	characteristic
441	C₂	#19147696	1	1	yes	characteristic
442	C₂	#19147697	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₃
commutator, socle	C₂²×C₄₃	C₂³×C₈
Fitting	C₄₃×#2183	C₂
prime radical	C₂²×D₄₃	C₂²×C₈
cosocle	C₂×C₈×C₄₃	C₂⁴
hypercenter	#2183	D₄₃
hypocenter	C₄₃	#33501
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ #2183

Complements

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

N	H ≅ G/N	type
2. #19136504	C₂	semidirect
3. #19136503	C₂	semidirect
4. #19136502	C₂	semidirect
5. #19136502	C₂	semidirect
6. #19136501	C₂	semidirect
7. #19136501	C₂	semidirect
8. #19136500	C₂	semidirect
15. C₄₃×#2183	C₂	semidirect
226. #2183	D₄₃	semidirect
280. C₄₃	#33501	semidirect

Maximal subgroups

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

subgroup	index
#19143524	2
#19136504	2
#19136503	2
#19136502	2
#19136501	2
#19136500	2
#19136403	2
#19136401	2
#19136400	2
#19136397	2
#19136396	2
C₄₃×#2183	2
#33501	43