Subgroups — #25066237

Order 11008.

648 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	#19143708	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063356	C₂	1	1	yes	maximal, characteristic
3	#19133473	C₂	1	2	yes	maximal, complemented
4	#19133466	C₂	1	2	yes	maximal, complemented
5	#19133445	C₂	1	2	yes	maximal, complemented
6	#19133438	C₂	1	2	yes	maximal, complemented
7	#19133348	C₂	1	1	yes	maximal, characteristic, complemented
8	#19132975	C₂	1	1	yes	maximal, characteristic
9	C₂×Q₈⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#2982	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	C₄	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583029	C₂²	1	2	yes	—
15	#14583004	C₄	1	2	yes	—
16	#14582997	C₄	1	2	yes	—
17	C₄×#10621885	C₂²	1	2	yes	—
18	C₄×#10621884	C₂²	1	2	yes	—
19	#14582978	C₂²	1	2	yes	—
20	#14582967	—	2	2	no	—
21	#14582955	—	2	1	no	—
22	#14582939	C₄	1	1	yes	characteristic
23	#14582921	—	2	1	no	—
24	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
25	#14582908	C₄	1	1	yes	characteristic
26	#14582898	C₄	1	1	yes	characteristic
27	C₄×#10621877	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	#14582651	C₂²	1	2	yes	—
30	#14582649	C₂²	1	2	yes	—
31	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
32	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
33	#14582629	C₂²	1	1	yes	characteristic
34	#14582629	C₂²	1	1	yes	characteristic
35	#14582626	C₂²	1	1	yes	characteristic
36	#14582626	C₂²	1	1	yes	characteristic
37	#14582621	C₂²	1	2	yes	—
38	#14582620	C₂²	1	2	yes	—
39	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₄₃	—	2	1	no	—
41	C₈×Q₈×C₄₃	—	2	1	no	—
42	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
43	C₈×Q₈×C₄₃	C₂²	1	2	yes	—
44	C₄₃×#431	—	2	2	no	—
45	C₄₃×#431	C₂²	1	1	yes	characteristic
46	C₄₃×#431	C₂²	1	1	yes	characteristic
47	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
48	#13063356	—	2	4	no	—
49	C₂×#10621885	C₂×C₄	1	2	yes	—
50	C₂×#10621884	C₂×C₄	1	2	yes	—
51	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621872	—	2	2	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	1	no	—
56	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
57	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
58	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
59	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₄₃	—	2	1	no	—
61	C₄×C₂²⋊D₄₃	—	2	1	no	—
62	#13063284	C₂×C₄	1	1	yes	characteristic
63	#13063282	—	2	1	no	—
64	C₄²×D₄₃	—	2	1	no	—
65	#13063258	C₂×C₄	1	2	yes	—
66	#13063256	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
69	Dic₄₃⋊C₈	—	2	2	no	—
70	#13063249	C₂×C₄	1	2	yes	—
71	#13063249	C₂×C₄	1	2	yes	—
72	#13063248	C₂×C₄	1	2	yes	—
73	#13063245	C₂×C₄	1	2	yes	—
74	(C₂×D₄₃)⋊C₈	—	2	2	no	—
75	#13063236	C₂×C₄	1	2	yes	—
76	#13063235	—	2	2	no	—
77	C₄×C₄₃⋊C₈	—	2	1	no	—
78	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
81	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₄×Q₈×C₄₃	—	2	1	no	—
83	C₄×Q₈×C₄₃	—	2	1	no	—
84	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	—	2	2	no	—
92	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₄₃	—	2	1	no	—
97	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
98	C₄×C₈×C₄₃	—	2	2	no	—
99	C₄×C₈×C₄₃	—	2	2	no	—
100	C₄×C₈×C₄₃	—	2	1	no	—
101	C₄×C₈×C₄₃	C₂³	1	2	yes	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	M₁₆	1	4	yes	complemented
105	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₃	—	2	1	no	—
112	#10621898	—	2	2	no	—
113	#10621898	—	2	2	no	—
114	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	2	1	no	—
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	—	2	2	no	—
129	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₃	#41	1	1	yes	characteristic
132	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₄₃	—	2	1	no	—
134	#10621885	—	2	4	no	—
135	#10621884	—	2	4	no	—
136	(C₂×D₄₃)⋊C₄	—	2	1	no	—
137	(C₂×D₄₃)⋊C₄	—	2	1	no	—
138	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
140	Dic₄₃⋊C₄	—	2	1	no	—
141	Dic₄₃⋊C₄	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	#10621877	—	2	2	no	—
146	#10621877	—	2	2	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	4	2	no	—
151	C₂×C₄₃⋊C₈	—	8	1	no	—
152	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
154	#10621872	—	8	2	no	—
155	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₄₃	—	2	1	no	—
157	Q₈×C₄₃	—	2	2	no	—
158	Q₈×C₄₃	—	2	4	no	—
159	Q₈×C₄₃	C₂×M₁₆	1	4	yes	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	8	1	no	—
167	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
171	C₂×C₄×C₄₃	#131	1	2	yes	—
172	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	2	1	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	2	1	no	—
179	D₁₇₂	—	2	1	no	—
180	D₁₇₂	—	2	1	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	—	4	1	no	—
183	C₄×D₄₃	—	4	2	no	—
184	C₄×D₄₃	—	8	1	no	—
185	Dic₈₆	—	2	1	no	—
186	Dic₈₆	—	2	1	no	—
187	C₈×C₄₃	—	2	2	no	—
188	C₈×C₄₃	—	2	2	no	—
189	C₈×C₄₃	—	4	1	no	—
190	C₈×C₄₃	—	4	1	no	—
191	C₄₃⋊C₈	—	2	2	no	—
192	C₄₃⋊C₈	—	2	2	no	—
193	C₄₃⋊C₈	—	2	2	no	—
194	C₄₃⋊C₈	—	4	1	no	—
195	C₄₃⋊C₈	—	4	2	no	—
196	#17874	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	#435	1	2	yes	—
200	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₄₃	—	4	1	no	—
202	C₂×D₄₃	—	4	1	no	—
203	C₂×D₄₃	—	4	1	no	—
204	C₄×C₄₃	—	2	4	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	#435	1	2	yes	—
210	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
211	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
212	C₄×C₄₃	#577	1	1	yes	characteristic
213	C₄×C₄₃	#578	1	1	yes	characteristic
214	Dic₄₃	—	4	1	no	—
215	Dic₄₃	—	4	1	no	—
216	Dic₄₃	—	4	1	no	—
217	#2989	—	43	1	no	—
218	#2982	D₄₃	1	1	yes	characteristic, complemented
219	C₄×#137	—	43	1	no	—
220	#1588	—	43	2	no	—
221	#1587	—	43	2	no	—
222	#1584	—	43	2	no	—
223	#1583	—	43	2	no	—
224	#1565	—	43	1	no	—
225	#1476	—	43	1	no	—
226	C₂×Q₈⋊C₈	—	43	1	no	—
227	#1451	—	43	1	no	—
228	C₂×C₄₃	—	2	2	no	—
229	C₂×C₄₃	C₂×#435	1	1	yes	characteristic
230	C₂×C₄₃	#2947	1	1	yes	characteristic
231	C₂×C₄₃	#2956	1	1	yes	characteristic
232	D₄₃	—	8	1	no	—
233	C₂×#137	—	43	1	no	—
234	C₄×#41	—	43	1	no	—
235	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
236	#446	—	43	2	no	—
237	C₈×Q₈	—	2	1	no	—
238	C₈×Q₈	—	2	1	no	—
239	C₈×Q₈	C₂×D₄₃	1	2	yes	—
240	C₈×Q₈	C₂×D₄₃	1	2	yes	—
241	#441	—	43	2	no	—
242	#440	—	43	2	no	—
243	C₄×Q₁₆	—	43	2	no	—
244	C₄×SD₁₆	—	43	2	no	—
245	#436	—	43	2	no	—
246	#435	—	86	2	no	—
247	#432	—	86	1	no	—
248	#431	—	2	2	no	—
249	#431	C₂×D₄₃	1	1	yes	characteristic
250	#431	C₂×D₄₃	1	1	yes	characteristic
251	#428	—	43	1	no	—
252	#423	—	86	1	no	—
253	C₂×C₄⋊C₈	—	43	1	no	—
254	#419	—	43	1	no	—
255	#417	—	43	1	no	—
256	C₄×M₁₆	—	43	1	no	—
257	C₂×C₄×C₈	—	43	1	no	—
258	#335	—	43	2	no	—
259	#334	—	43	2	no	—
260	Q₈⋊C₈	—	43	2	no	—
261	Q₈⋊C₈	—	43	2	no	—
262	Q₈⋊C₈	—	43	1	no	—
263	Q₈⋊C₈	—	43	1	no	—
264	D₄⋊C₈	—	43	1	no	—
265	D₄⋊C₈	—	43	1	no	—
266	#322	—	43	2	no	—
267	#322	—	43	2	no	—
268	C₄₃	#17874	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	43	1	no	—
270	C₂²×Q₈	C₄×D₄₃	1	1	yes	characteristic
271	#137	—	86	4	no	—
272	C₂×Q₁₆	—	43	2	no	—
273	C₂×SD₁₆	—	43	2	no	—
274	C₂×M₁₆	—	43	1	no	—
275	C₂×M₁₆	—	43	1	no	—
276	C₂×M₁₆	—	86	2	no	—
277	C₂²×C₈	—	86	1	no	—
278	C₂²×C₈	—	86	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×Q₈	—	2	1	no	—
281	C₄×Q₈	—	43	1	no	—
282	C₄×Q₈	—	43	1	no	—
283	C₄×Q₈	C₄×D₄₃	1	2	yes	—
284	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
285	C₄×D₄	—	43	1	no	—
286	C₄×D₄	—	43	1	no	—
287	C₄×D₄	—	86	1	no	—
288	C₄×D₄	—	86	1	no	—
289	#117	—	43	1	no	—
290	#117	—	86	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	86	1	no	—
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	#107	—	43	2	no	—
297	#106	—	43	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	43	2	no	—
301	C₄⋊C₈	—	86	2	no	—
302	C₄⋊C₈	—	86	1	no	—
303	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
304	C₄⋊C₈	C₂²⋊D₄₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
307	#103	—	43	2	no	—
308	#103	—	43	2	no	—
309	#103	—	43	2	no	—
310	#102	—	43	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	86	2	no	—
313	C₂²⋊C₈	C₂²⋊D₄₃	1	2	yes	—
314	#97	—	43	2	no	—
315	#97	—	86	2	no	—
316	C₄×C₈	—	2	2	no	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	43	2	no	—
320	C₄×C₈	—	43	1	no	—
321	C₄×C₈	—	43	1	no	—
322	C₄×C₈	—	86	1	no	—
323	C₄×C₈	C₂²×D₄₃	1	2	yes	—
324	#41	—	86	2	no	—
325	#41	—	86	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	43	1	no	—
329	C₂×Q₈	#10621872	1	4	yes	complemented
330	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
331	C₂×D₄	—	43	1	no	—
332	C₂×D₄	—	86	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	86	1	no	—
336	C₂²×C₄	—	86	1	no	—
337	C₂²×C₄	—	86	1	no	—
338	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	#10621898	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
341	Q₁₆	—	86	4	no	—
342	SD₁₆	—	86	4	no	—
343	M₁₆	—	86	2	no	—
344	M₁₆	—	86	2	no	—
345	M₁₆	—	344	2	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	43	2	no	—
349	C₂×C₈	—	43	2	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	2	no	—
352	C₂×C₈	—	86	1	no	—
353	C₂×C₈	—	344	1	no	—
354	C₂×C₈	—	172	2	no	—
355	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
356	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	43	1	no	—
361	C₄⋊C₄	—	43	1	no	—
362	C₄⋊C₄	—	86	1	no	—
363	C₄⋊C₄	—	86	1	no	—
364	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
365	C₂²⋊C₄	—	86	1	no	—
366	C₂²⋊C₄	—	86	1	no	—
367	C₂²⋊C₄	—	86	1	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	86	1	no	—
371	C₄²	—	86	1	no	—
372	C₄²	—	86	1	no	—
373	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
374	C₄²	#10621898	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
376	C₄²	C₂³×D₄₃	1	1	yes	characteristic
377	C₂³	—	86	1	no	—
378	C₂³	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
379	Q₈	—	2	2	no	—
380	Q₈	—	2	4	no	—
381	Q₈	—	86	1	no	—
382	Q₈	—	86	1	no	—
383	Q₈	C₂×#10621872	1	4	yes	—
384	D₄	—	86	1	no	—
385	D₄	—	86	1	no	—
386	D₄	—	172	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	4	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	86	1	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	344	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	1	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
403	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂×#10621872	1	2	yes	—
405	C₂×C₄	#13063331	1	2	yes	—
406	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
409	C₈	—	2	2	no	—
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	86	2	no	—
414	C₈	—	86	2	no	—
415	C₈	—	86	2	no	—
416	C₈	—	172	1	no	—
417	C₈	—	172	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	172	1	no	—
421	C₂²	—	172	1	no	—
422	C₂²	—	172	1	no	—
423	C₂²	#14582970	1	2	yes	—
424	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	4	no	—
429	C₄	—	4	2	no	—
430	C₄	—	172	1	no	—
431	C₄	—	172	1	no	—
432	C₄	—	172	1	no	—
433	C₄	#14582970	1	2	yes	—
434	C₄	C₂²×#10621872	1	1	yes	characteristic
435	C₄	C₂×#13063331	1	1	yes	characteristic
436	C₄	#14583707	1	1	yes	characteristic
437	C₄	#14583714	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	344	1	no	—
440	C₂	C₂×#14582970	1	1	yes	characteristic
441	C₂	#19143438	1	1	yes	characteristic
442	C₂	#19143502	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2982	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2982	D₄₃
hypocenter	C₄₃	#17874
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2982

Complements

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

N	H ≅ G/N	type
3. #19133473	C₂	semidirect
4. #19133466	C₂	semidirect
5. #19133445	C₂	semidirect
6. #19133438	C₂	semidirect
7. #19133348	C₂	semidirect
9. C₂×Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
10. #19132885	C₂	semidirect
11. C₄₃×#2982	C₂	semidirect
104. C₂×Q₈×C₄₃	M₁₆	semidirect
218. #2982	D₄₃	semidirect
268. C₄₃	#17874	semidirect
329. C₂×Q₈	#10621872	semidirect

Maximal subgroups

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

subgroup	index
#19143708	2
C₄×#13063356	2
#19133473	2
#19133466	2
#19133445	2
#19133438	2
#19133348	2
#19132975	2
C₂×Q₈⋊(C₄₃⋊C₈)	2
#19132885	2
C₄₃×#2982	2
#17874	43