Subgroups — #25065851

Order 11008.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143561	C₂	1	1	yes	maximal, characteristic
2	#19143263	C₂	1	1	yes	maximal, characteristic
3	#19143164	C₂	1	1	yes	maximal, characteristic
4	#19133385	C₂	1	2	yes	maximal, complemented
5	#19133379	C₂	1	2	yes	maximal, complemented
6	#19133371	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133367	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133361	C₂	1	2	yes	maximal, complemented
9	#19133346	C₂	1	2	yes	maximal, complemented
10	C₂×#14582650	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583029	C₄	1	1	yes	characteristic
15	#14583029	C₄	1	1	yes	characteristic
16	#14582978	C₄	1	1	yes	characteristic
17	#14582978	C₄	1	1	yes	characteristic
18	#14582970	C₄	1	2	yes	—
19	#14582970	C₄	1	2	yes	—
20	#14582959	—	2	2	no	—
21	#14582955	C₂²	1	2	yes	—
22	#14582952	C₂²	1	1	yes	characteristic
23	#14582951	C₂²	1	2	yes	—
24	#14582950	C₂²	1	2	yes	—
25	#14582927	—	2	1	no	—
26	#14582924	—	2	2	no	—
27	#14582921	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
31	#14582867	—	2	1	no	—
32	#14582857	—	2	1	no	—
33	C₄×#10621872	C₂²	1	2	yes	—
34	#14582651	C₂²	1	2	yes	—
35	#14582651	C₂²	1	2	yes	—
36	#14582650	C₂²	1	1	yes	characteristic
37	#14582650	C₂²	1	1	yes	characteristic
38	#14582650	C₂²	1	1	yes	characteristic
39	#14582650	C₂²	1	1	yes	characteristic
40	#14582649	C₂²	1	2	yes	—
41	#14582649	C₂²	1	2	yes	—
42	C₄₃×#423	C₂²	1	1	yes	characteristic
43	C₄₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	—
46	C₄₃×#335	C₂²	1	2	yes	—
47	C₂×#10621898	D₄	1	1	yes	characteristic
48	#13063333	—	4	4	no	—
49	C₂×#10621872	—	2	2	no	—
50	C₂×#10621872	C₂×C₄	1	2	yes	—
51	C₂×#10621872	C₂×C₄	1	2	yes	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂×C₈×D₄₃	—	2	2	no	—
55	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₈₆	Q₈	1	1	yes	characteristic
57	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
58	C₄×D₁₇₂	Q₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₄₃	Q₈	1	2	yes	—
61	#13063284	D₄	1	1	yes	characteristic
62	#13063282	D₄	1	2	yes	—
63	C₄²×D₄₃	C₂³	1	2	yes	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
72	Dic₄₃⋊C₈	—	2	2	no	—
73	Dic₄₃⋊C₈	—	2	2	no	—
74	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
75	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	(C₂×D₄₃)⋊C₈	—	2	2	no	—
79	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
80	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
81	#13063235	—	2	2	no	—
82	#13063235	C₂×C₄	1	2	yes	—
83	#13063235	C₂×C₄	1	2	yes	—
84	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₃	—	2	2	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	—	2	1	no	—
92	C₄⋊C₈×C₄₃	—	2	1	no	—
93	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
94	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
95	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
102	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	2	yes	—
103	#10621898	—	2	2	no	—
104	#10621898	—	2	2	no	—
105	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
107	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
108	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
109	C₂×Dic₈₆	C₄⋊C₄	1	1	yes	characteristic
110	M₁₆×C₄₃	—	4	2	no	—
111	M₁₆×C₄₃	—	4	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	4	1	no	—
116	C₂×C₈×C₄₃	C₂²×C₄	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	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
123	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₃	C₄⋊C₄	1	2	yes	—
125	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
126	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	2	yes	—
127	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
129	Dic₄₃⋊C₄	C₄⋊C₄	1	2	yes	—
130	Dic₄₃⋊C₄	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
132	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
133	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	1	no	—
136	C₂×C₄₃⋊C₈	—	2	1	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	4	2	no	—
139	C₂×C₄₃⋊C₈	—	4	2	no	—
140	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
142	#10621872	—	2	4	no	—
143	#10621872	—	4	2	no	—
144	#10621872	—	4	4	no	—
145	C₈×D₄₃	—	4	4	no	—
146	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₄₃	#137	1	2	yes	—
156	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
159	C₂²⋊D₄₃	—	2	4	no	—
160	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
163	D₁₇₂	—	2	2	no	—
164	C₄×D₄₃	—	2	2	no	—
165	C₄×D₄₃	—	2	2	no	—
166	C₄×D₄₃	—	2	2	no	—
167	C₄×D₄₃	—	2	2	no	—
168	C₄×D₄₃	—	4	2	no	—
169	Dic₈₆	—	2	2	no	—
170	C₈×C₄₃	—	2	1	no	—
171	C₈×C₄₃	—	2	1	no	—
172	C₈×C₄₃	—	2	1	no	—
173	C₈×C₄₃	—	4	2	no	—
174	C₈×C₄₃	—	4	2	no	—
175	C₈×C₄₃	#131	1	2	yes	complemented
176	C₄₃⋊C₈	—	2	2	no	—
177	C₄₃⋊C₈	—	2	2	no	—
178	C₄₃⋊C₈	—	4	1	no	—
179	C₄₃⋊C₈	—	4	1	no	—
180	C₄₃⋊C₈	—	4	1	no	—
181	C₄₃⋊C₈	—	4	1	no	—
182	#17830	—	43	1	no	maximal, Sylow
183	C₂²×C₄₃	—	2	1	no	—
184	C₂²×C₄₃	—	2	1	no	—
185	C₂²×C₄₃	#428	1	2	yes	—
186	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₄₃	—	2	2	no	—
188	C₂×D₄₃	—	2	2	no	—
189	C₂×D₄₃	—	2	2	no	—
190	C₄×C₄₃	—	2	1	no	—
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	#428	1	2	yes	—
194	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
195	C₄×C₄₃	#568	1	1	yes	characteristic
196	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
198	Dic₄₃	—	2	2	no	—
199	Dic₄₃	—	2	2	no	—
200	Dic₄₃	—	2	2	no	—
201	#2965	—	43	1	no	—
202	#2925	—	43	1	no	—
203	#2906	—	43	1	no	—
204	#1574	—	43	2	no	—
205	#1573	—	43	2	no	—
206	#1571	—	43	1	no	—
207	#1570	—	43	1	no	—
208	#1569	—	43	2	no	—
209	#1567	D₄₃	1	1	yes	characteristic, complemented
210	#1565	—	43	2	no	—
211	C₂×#334	—	43	1	no	—
212	C₂×C₄₃	—	2	2	no	—
213	C₂×C₄₃	#2906	1	1	yes	characteristic
214	C₂×C₄₃	C₂×#428	1	1	yes	characteristic
215	C₂×C₄₃	#2916	1	1	yes	characteristic
216	D₄₃	—	4	2	no	—
217	C₂×#131	—	86	1	no	—
218	C₄×#41	—	43	1	no	—
219	#446	—	43	1	no	—
220	#446	—	43	1	no	—
221	#436	—	43	1	no	—
222	#436	—	43	1	no	—
223	#435	—	43	2	no	—
224	#435	—	43	2	no	—
225	#433	—	86	2	no	—
226	#432	—	43	2	no	—
227	#431	—	43	1	no	—
228	#431	—	43	2	no	—
229	#431	—	43	2	no	—
230	#424	—	86	2	no	—
231	#424	—	86	1	no	—
232	#423	—	43	2	no	—
233	#423	C₂×D₄₃	1	1	yes	characteristic
234	#423	C₂×D₄₃	1	1	yes	characteristic
235	C₂×C₄⋊C₈	—	43	1	no	—
236	C₂×C₄⋊C₈	—	43	1	no	—
237	C₂×C₄⋊C₈	—	43	2	no	—
238	#408	—	86	1	no	—
239	#405	—	86	1	no	—
240	C₄×M₁₆	—	43	2	no	—
241	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
242	#335	—	43	2	no	—
243	#335	—	43	2	no	—
244	#335	C₂×D₄₃	1	2	yes	—
245	#335	C₂×D₄₃	1	2	yes	—
246	#334	—	43	2	no	—
247	#334	—	43	2	no	—
248	#334	—	43	1	no	—
249	#334	—	43	1	no	—
250	#334	—	43	1	no	—
251	#334	—	43	1	no	—
252	C₄₃	#17830	1	1	yes	characteristic, complemented, Sylow
253	C₂×#41	—	43	1	no	—
254	#131	—	172	4	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	43	2	no	—
258	C₂×M₁₆	—	43	2	no	—
259	C₂×M₁₆	—	86	2	no	—
260	C₂²×C₈	—	86	2	no	—
261	C₂²×C₈	—	86	1	no	—
262	C₂²×C₈	—	86	1	no	—
263	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
265	C₄×Q₈	—	43	1	no	—
266	C₄×Q₈	—	43	1	no	—
267	C₄×D₄	—	43	2	no	—
268	C₄×D₄	—	43	2	no	—
269	C₄×D₄	—	43	1	no	—
270	C₄×D₄	—	43	1	no	—
271	#117	—	43	1	no	—
272	#117	—	43	2	no	—
273	C₂×C₄²	—	43	2	no	—
274	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	43	2	no	—
278	C₄⋊C₈	—	43	2	no	—
279	C₄⋊C₈	—	43	1	no	—
280	C₄⋊C₈	—	43	1	no	—
281	C₄⋊C₈	—	43	1	no	—
282	C₄⋊C₈	—	43	1	no	—
283	C₄⋊C₈	—	43	1	no	—
284	C₄⋊C₈	—	43	1	no	—
285	C₄⋊C₈	—	86	2	no	—
286	C₄⋊C₈	—	86	2	no	—
287	C₄⋊C₈	—	86	1	no	—
288	C₄⋊C₈	—	86	1	no	—
289	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
290	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
291	C₂²⋊C₈	—	43	2	no	—
292	C₂²⋊C₈	—	43	2	no	—
293	C₂²⋊C₈	—	43	2	no	—
294	C₂²⋊C₈	—	86	2	no	—
295	C₂²⋊C₈	—	86	2	no	—
296	#97	—	43	2	no	—
297	#97	—	43	2	no	—
298	#97	—	86	2	no	—
299	C₄×C₈	—	43	2	no	—
300	C₄×C₈	—	86	2	no	—
301	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
302	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
305	#41	—	86	2	no	—
306	#41	—	86	2	no	—
307	C₂×Q₈	—	43	1	no	—
308	C₂×D₄	—	43	2	no	—
309	C₂×D₄	—	43	1	no	—
310	C₂²×C₄	—	43	2	no	—
311	C₂²×C₄	—	43	2	no	—
312	C₂²×C₄	—	43	2	no	—
313	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
316	M₁₆	—	4	2	no	—
317	M₁₆	—	4	2	no	—
318	M₁₆	—	86	4	no	—
319	M₁₆	—	172	2	no	—
320	M₁₆	—	172	4	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	43	2	no	—
326	C₂×C₈	—	43	2	no	—
327	C₂×C₈	—	86	1	no	—
328	C₂×C₈	—	86	1	no	—
329	C₂×C₈	—	86	1	no	—
330	C₂×C₈	—	86	1	no	—
331	C₂×C₈	—	172	4	no	—
332	C₂×C₈	—	172	2	no	—
333	C₂×C₈	—	172	2	no	—
334	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
338	C₄⋊C₄	—	43	2	no	—
339	C₄⋊C₄	—	43	2	no	—
340	C₄⋊C₄	—	43	1	no	—
341	C₄⋊C₄	—	43	1	no	—
342	C₂²⋊C₄	—	43	2	no	—
343	C₂²⋊C₄	—	43	2	no	—
344	C₂²⋊C₄	—	43	2	no	—
345	C₄²	—	43	2	no	—
346	C₄²	—	43	2	no	—
347	C₄²	—	43	2	no	—
348	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₄²	D₄×D₄₃	1	1	yes	characteristic
350	C₄²	Q₈×D₄₃	1	1	yes	characteristic
351	C₄²	C₂³×D₄₃	1	1	yes	characteristic
352	C₂³	—	43	2	no	—
353	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
354	Q₈	—	86	2	no	—
355	D₄	—	86	4	no	—
356	D₄	—	86	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	43	2	no	—
361	C₂×C₄	—	43	2	no	—
362	C₂×C₄	—	43	2	no	—
363	C₂×C₄	—	86	2	no	—
364	C₂×C₄	—	86	2	no	—
365	C₂×C₄	—	86	2	no	—
366	C₂×C₄	—	86	2	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
371	C₂×C₄	#13063349	1	2	yes	—
372	C₂×C₄	#13063357	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₈	—	86	2	no	—
382	C₈	—	86	2	no	—
383	C₈	—	172	1	no	—
384	C₈	—	172	1	no	—
385	C₈	—	172	1	no	—
386	C₈	—	172	1	no	—
387	C₈	#13063333	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	86	2	no	—
391	C₂²	—	86	2	no	—
392	C₂²	—	86	2	no	—
393	C₂²	#14582940	1	2	yes	—
394	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	86	2	no	—
399	C₄	—	86	2	no	—
400	C₄	—	86	2	no	—
401	C₄	#14582940	1	2	yes	—
402	C₄	C₂×#13063333	1	1	yes	characteristic
403	C₄	#14583665	1	1	yes	characteristic
404	C₄	C₂×#13063349	1	1	yes	characteristic
405	C₄	C₂×#13063357	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	172	2	no	—
408	C₂	#19143164	1	1	yes	characteristic
409	C₂	C₂×#14582940	1	1	yes	characteristic
410	C₂	#19143203	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×#1567	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#10621898	D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1567	D₄₃
hypocenter	C₄₃	#17830
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

Complements

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

N	H ≅ G/N	type
4. #19133385	C₂	semidirect
5. #19133379	C₂	semidirect
6. #19133371	C₂	semidirect
7. #19133367	C₂	semidirect
8. #19133361	C₂	semidirect
9. #19133346	C₂	semidirect
10. C₂×#14582650	C₂	semidirect
11. C₄₃×#1567	C₂	semidirect
175. C₈×C₄₃	#131	semidirect
209. #1567	D₄₃	semidirect
252. C₄₃	#17830	semidirect
387. C₈	#13063333	semidirect

Maximal subgroups

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

subgroup	index
#19143561	2
#19143263	2
#19143164	2
#19133385	2
#19133379	2
#19133371	2
#19133367	2
#19133361	2
#19133346	2
C₂×#14582650	2
C₄₃×#1567	2
#17830	43