Subgroups — #25014770

Order 11008.

466 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582975	C₂	1	1	yes	maximal, characteristic
2	#19136350	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14582681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582680	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582680	C₂	1	1	yes	maximal, characteristic, complemented
6	M₃₂×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#349	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621872	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₂²⋊D₄₃	C₄	1	1	yes	characteristic
10	C₂×#13063265	C₂²	1	1	yes	characteristic
11	C₂×#13063265	C₂²	1	1	yes	characteristic
12	#14582975	—	2	1	no	—
13	#14582975	—	2	1	no	—
14	#14582975	—	2	1	no	—
15	#14582975	—	2	1	no	—
16	C₂×Dic₄₃⋊C₈	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₃⋊C₈)	C₄	1	1	yes	characteristic
18	C₂×(C₂×D₄₃)⋊C₈	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
20	Dic₄₃⋊C₁₆	—	2	1	no	—
21	Dic₄₃⋊C₁₆	—	2	1	no	—
22	#14582681	—	2	2	no	—
23	#14582680	—	2	2	no	—
24	#14582680	—	2	2	no	—
25	#14582674	—	2	1	no	—
26	C₁₆×Dic₄₃	—	2	1	no	—
27	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#349	—	2	2	no	—
31	C₂²×C₂²⋊D₄₃	C₈	1	1	yes	characteristic
32	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
33	C₂×#10621872	—	2	1	no	—
34	C₂×#10621872	—	2	1	no	—
35	C₂×#10621872	—	2	1	no	—
36	C₂×#10621872	—	2	1	no	—
37	C₂×#10621872	—	2	1	no	—
38	C₂×#10621872	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₄×C₂²⋊D₄₃	—	2	1	no	—
42	C₄×C₂²⋊D₄₃	—	2	1	no	—
43	C₄×C₂²⋊D₄₃	—	2	1	no	—
44	C₄×C₂²⋊D₄₃	—	2	1	no	—
45	C₂×Dic₄₃⋊C₄	C₈	1	1	yes	characteristic
46	C₂×C₂²⋊Dic₄₃	C₈	1	1	yes	characteristic
47	C₂×(C₂×D₄₃)⋊C₄	C₈	1	1	yes	characteristic
48	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
49	#13063265	—	2	1	no	—
50	#13063265	—	2	1	no	—
51	#13063265	—	2	1	no	—
52	#13063265	D₄	1	2	yes	complemented
53	C₂×C₄₃⋊C₁₆	—	2	1	no	—
54	C₂×C₄₃⋊C₁₆	—	2	1	no	—
55	Dic₄₃⋊C₈	—	2	1	no	—
56	Dic₄₃⋊C₈	—	2	1	no	—
57	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
58	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
59	(C₂×D₄₃)⋊C₈	—	2	1	no	—
60	(C₂×D₄₃)⋊C₈	—	2	1	no	—
61	C₈×Dic₄₃	D₄	1	1	yes	characteristic
62	C₈×Dic₄₃	D₄	1	1	yes	characteristic
63	C₈×Dic₄₃	D₄	1	1	yes	characteristic
64	C₈×Dic₄₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₄₃	—	2	1	no	—
67	C₂×M₁₆×C₄₃	—	2	1	no	—
68	C₂×M₁₆×C₄₃	—	2	1	no	—
69	C₂×M₁₆×C₄₃	—	2	1	no	—
70	C₂×M₁₆×C₄₃	—	2	1	no	—
71	C₂×M₁₆×C₄₃	—	2	1	no	—
72	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	M₃₂×C₄₃	—	2	1	no	—
75	M₃₂×C₄₃	—	2	1	no	—
76	M₃₂×C₄₃	—	2	1	no	—
77	M₃₂×C₄₃	D₄	1	2	yes	complemented
78	C₂×C₁₆×C₄₃	—	2	1	no	—
79	C₂×C₁₆×C₄₃	—	2	1	no	—
80	C₂⁴×C₄₃	C₂×C₈	1	1	yes	characteristic
81	C₂³×D₄₃	C₂×C₈	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	—	2	1	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	1	no	—
87	C₂²×C₄×C₄₃	—	2	1	no	—
88	C₂²×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊D₄₃	—	2	1	no	—
91	C₂×C₂²⋊D₄₃	—	2	1	no	—
92	C₂×C₂²⋊D₄₃	—	4	2	no	—
93	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
94	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
95	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
98	C₂×C₄×D₄₃	—	2	1	no	—
99	C₂×C₄×D₄₃	—	2	1	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	M₁₆×C₄₃	—	4	1	no	—
103	M₁₆×C₄₃	—	4	1	no	—
104	M₁₆×C₄₃	—	4	1	no	—
105	M₁₆×C₄₃	—	4	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
114	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
115	C₂²⋊Dic₄₃	—	2	1	no	—
116	C₂²⋊Dic₄₃	—	2	1	no	—
117	(C₂×D₄₃)⋊C₄	—	2	1	no	—
118	(C₂×D₄₃)⋊C₄	—	2	1	no	—
119	Dic₄₃⋊C₄	—	2	1	no	—
120	Dic₄₃⋊C₄	—	2	1	no	—
121	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₃	M₁₆	1	1	yes	characteristic
124	C₄×Dic₄₃	M₁₆	1	1	yes	characteristic
125	C₂×C₄₃⋊C₈	—	2	1	no	—
126	C₂×C₄₃⋊C₈	—	2	1	no	—
127	C₂×C₄₃⋊C₈	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
132	#10621872	—	4	1	no	—
133	#10621872	—	4	1	no	—
134	#10621872	—	4	1	no	—
135	#10621872	—	4	1	no	—
136	C₁₆×C₄₃	—	2	2	no	—
137	C₁₆×C₄₃	—	4	1	no	—
138	C₄₃⋊C₁₆	—	2	2	no	—
139	C₄₃⋊C₁₆	—	4	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
146	C₂²×D₄₃	—	2	1	no	—
147	C₂²×D₄₃	—	2	1	no	—
148	C₂²×D₄₃	—	2	1	no	—
149	C₂²×D₄₃	—	4	1	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	4	1	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
164	C₂²⋊D₄₃	—	4	2	no	—
165	C₂²⋊D₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
172	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
173	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
174	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
175	C₄×D₄₃	—	4	1	no	—
176	C₄×D₄₃	—	4	1	no	—
177	C₄×D₄₃	—	4	1	no	—
178	C₄×D₄₃	—	4	1	no	—
179	C₈×C₄₃	—	4	1	no	—
180	C₈×C₄₃	#121	1	1	yes	characteristic
181	C₈×C₄₃	#121	1	1	yes	characteristic
182	C₈×C₄₃	#124	1	1	yes	characteristic
183	C₈×C₄₃	#127	1	1	yes	characteristic
184	C₄₃⋊C₈	—	2	1	no	—
185	C₄₃⋊C₈	—	2	1	no	—
186	C₄₃⋊C₈	—	4	1	no	—
187	#13194	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	1	no	—
190	C₂²×C₄₃	—	4	1	no	—
191	C₂²×C₄₃	—	4	1	no	—
192	C₂²×C₄₃	—	4	1	no	—
193	C₂²×C₄₃	—	8	1	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
196	C₂²×C₄₃	C₈×D₄	1	1	yes	characteristic
197	C₂²×C₄₃	C₈×D₄	1	1	yes	characteristic
198	C₂×D₄₃	—	4	1	no	—
199	C₂×D₄₃	—	4	1	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	8	1	no	—
202	C₂×D₄₃	—	8	1	no	—
203	C₄×C₄₃	—	4	1	no	—
204	C₄×C₄₃	#390	1	1	yes	characteristic
205	C₄×C₄₃	#408	1	1	yes	characteristic
206	C₄×C₄₃	#436	1	1	yes	characteristic
207	C₄×C₄₃	#436	1	1	yes	characteristic
208	Dic₄₃	—	2	1	no	—
209	Dic₄₃	—	2	1	no	—
210	Dic₄₃	—	2	1	no	—
211	Dic₄₃	—	4	1	no	—
212	Dic₄₃	#349	1	2	yes	complemented
213	C₂×#436	—	43	1	no	—
214	#2150	—	43	1	no	—
215	C₂×#349	—	43	1	no	—
216	C₂×#349	—	43	1	no	—
217	C₂×#349	—	43	1	no	—
218	C₂×#349	D₄₃	1	1	yes	characteristic, complemented
219	C₄×M₃₂	—	43	1	no	—
220	C₂×C₄₃	—	2	1	no	—
221	C₂×C₄₃	—	2	1	no	—
222	C₂×C₄₃	—	8	1	no	—
223	C₂×C₄₃	#1954	1	1	yes	characteristic
224	C₂×C₄₃	C₂×#349	1	1	yes	characteristic
225	C₂×C₄₃	#2115	1	1	yes	characteristic
226	D₄₃	—	8	1	no	—
227	C₂²×M₁₆	—	43	1	no	—
228	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
229	C₂×C₄×D₄	—	43	1	no	—
230	C₂×M₃₂	—	43	1	no	—
231	C₂×M₃₂	—	43	1	no	—
232	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
233	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
234	#436	—	86	1	no	—
235	#436	—	86	1	no	—
236	#436	—	86	1	no	—
237	#436	—	86	1	no	—
238	C₂×C₄⋊C₈	—	43	1	no	—
239	C₂×C₂²⋊C₈	—	43	1	no	—
240	C₂×C₂²⋊C₈	—	43	1	no	—
241	C₂×C₄×C₈	—	43	1	no	—
242	C₄⋊C₁₆	—	86	1	no	—
243	C₄⋊C₁₆	—	86	1	no	—
244	#349	—	2	2	no	—
245	#349	—	86	2	no	—
246	#349	—	86	2	no	—
247	#349	—	86	2	no	—
248	#346	—	86	1	no	—
249	C₄×C₁₆	—	86	1	no	—
250	C₄₃	#13194	1	1	yes	characteristic, complemented, Sylow
251	C₂²×D₄	—	43	1	no	—
252	C₂³×C₄	—	43	1	no	—
253	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
254	C₂×M₁₆	—	2	1	no	—
255	C₂×M₁₆	—	2	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	86	1	no	—
261	C₂×M₁₆	—	86	1	no	—
262	C₂×M₁₆	—	86	1	no	—
263	C₂×M₁₆	—	86	1	no	—
264	C₂×M₁₆	—	86	1	no	—
265	C₂×M₁₆	—	86	1	no	—
266	C₂²×C₈	—	43	1	no	—
267	C₂²×C₈	—	43	1	no	—
268	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
270	C₄×D₄	—	86	1	no	—
271	C₄×D₄	—	86	1	no	—
272	C₄×D₄	—	86	1	no	—
273	C₄×D₄	—	86	1	no	—
274	C₂×C₄⋊C₄	—	43	1	no	—
275	C₂×C₂²⋊C₄	—	43	1	no	—
276	C₂×C₂²⋊C₄	—	43	1	no	—
277	C₂×C₄²	—	43	1	no	—
278	M₃₂	—	2	1	no	—
279	M₃₂	—	2	1	no	—
280	M₃₂	—	2	1	no	—
281	M₃₂	—	43	2	no	—
282	M₃₂	—	86	1	no	—
283	M₃₂	—	86	1	no	—
284	M₃₂	—	86	1	no	—
285	M₃₂	C₂²⋊D₄₃	1	2	yes	complemented
286	C₂×C₁₆	—	2	1	no	—
287	C₂×C₁₆	—	2	1	no	—
288	C₂×C₁₆	—	86	1	no	—
289	C₂×C₁₆	—	86	1	no	—
290	C₄⋊C₈	—	86	1	no	—
291	C₄⋊C₈	—	86	1	no	—
292	C₂²⋊C₈	—	86	1	no	—
293	C₂²⋊C₈	—	86	1	no	—
294	C₂²⋊C₈	—	86	1	no	—
295	C₂²⋊C₈	—	86	1	no	—
296	C₄×C₈	—	43	1	no	—
297	C₄×C₈	—	43	1	no	—
298	C₄×C₈	—	43	1	no	—
299	C₄×C₈	—	43	1	no	—
300	C₂⁴	—	43	1	no	—
301	C₂⁴	C₈×D₄₃	1	1	yes	characteristic
302	C₂×D₄	—	86	1	no	—
303	C₂×D₄	—	86	1	no	—
304	C₂×D₄	—	172	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	43	1	no	—
312	C₂²×C₄	—	43	1	no	—
313	C₂²×C₄	—	43	1	no	—
314	C₂²×C₄	—	86	1	no	—
315	C₂²×C₄	—	86	1	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	1	no	—
319	C₂²×C₄	—	86	1	no	—
320	C₂²×C₄	C₈×D₄₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
322	M₁₆	—	4	1	no	—
323	M₁₆	—	4	1	no	—
324	M₁₆	—	4	1	no	—
325	M₁₆	—	4	1	no	—
326	M₁₆	—	172	1	no	—
327	M₁₆	—	172	1	no	—
328	M₁₆	—	172	1	no	—
329	M₁₆	—	172	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	43	1	no	—
334	C₂×C₈	—	43	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	1	no	—
337	C₂×C₈	—	86	1	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	#10621898	1	1	yes	characteristic
341	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
342	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
343	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
344	C₂×C₈	#10621900	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	1	no	—
348	C₂²⋊C₄	—	86	1	no	—
349	C₂²⋊C₄	—	86	1	no	—
350	C₂²⋊C₄	—	86	1	no	—
351	C₂²⋊C₄	—	86	1	no	—
352	C₄²	—	43	1	no	—
353	C₄²	—	43	1	no	—
354	C₄²	—	43	1	no	—
355	C₄²	—	43	1	no	—
356	C₁₆	—	2	2	no	—
357	C₁₆	—	4	1	no	—
358	C₁₆	—	86	2	no	—
359	C₁₆	—	172	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	86	1	no	—
366	C₂³	—	86	1	no	—
367	C₂³	—	86	1	no	—
368	C₂³	—	172	1	no	—
369	C₂³	—	172	1	no	—
370	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
371	D₄	—	172	2	no	—
372	D₄	—	172	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	43	1	no	—
381	C₂×C₄	—	43	1	no	—
382	C₂×C₄	—	43	1	no	—
383	C₂×C₄	—	43	1	no	—
384	C₂×C₄	—	86	2	no	—
385	C₂×C₄	—	86	1	no	—
386	C₂×C₄	—	86	1	no	—
387	C₂×C₄	—	86	1	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	—	172	1	no	—
392	C₂×C₄	—	172	1	no	—
393	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
394	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
397	C₂×C₄	#13063331	1	1	yes	characteristic
398	C₂×C₄	#13063333	1	1	yes	characteristic
399	C₈	—	4	1	no	—
400	C₈	—	86	1	no	—
401	C₈	—	86	1	no	—
402	C₈	—	172	1	no	—
403	C₈	#13063297	1	1	yes	characteristic
404	C₈	#13063298	1	1	yes	characteristic
405	C₈	#13063311	1	1	yes	characteristic
406	C₈	#13063321	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	344	1	no	—
415	C₂²	—	344	1	no	—
416	C₂²	—	172	1	no	—
417	C₂²	—	172	1	no	—
418	C₂²	—	172	1	no	—
419	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
420	C₂²	(C₂²⋊D₄₃)⋊C₈	1	1	yes	characteristic
421	C₂²	C₈×C₂²⋊D₄₃	1	1	yes	characteristic
422	C₄	—	4	1	no	—
423	C₄	—	43	2	no	—
424	C₄	—	86	1	no	—
425	C₄	—	86	1	no	—
426	C₄	—	86	1	no	—
427	C₄	—	172	1	no	—
428	C₄	#14582799	1	1	yes	characteristic
429	C₄	#14582864	1	1	yes	characteristic
430	C₄	#14582974	1	1	yes	characteristic
431	C₄	#14582975	1	1	yes	characteristic
432	C₂	—	2	1	no	—
433	C₂	—	2	1	no	—
434	C₂	—	8	1	no	—
435	C₂	—	344	1	no	—
436	C₂	#19135387	1	1	yes	characteristic
437	C₂	#349×D₄₃	1	1	yes	characteristic
438	C₂	#19136214	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂³×C₄₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#349	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₈
prime radical	C₂²×C₂²⋊D₄₃	C₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#349	D₄₃
hypocenter	C₄₃	#13194
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#349

Complements

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

N	H ≅ G/N	type
2. #19136350	C₂	semidirect
3. C₂×#14582681	C₂	semidirect
4. C₂×#14582680	C₂	semidirect
5. C₂×#14582680	C₂	semidirect
6. M₃₂×Dic₄₃	C₂	semidirect
7. C₂×C₄₃×#349	C₂	semidirect
52. #13063265	D₄	semidirect
77. M₃₂×C₄₃	D₄	semidirect
212. Dic₄₃	#349	semidirect
218. C₂×#349	D₄₃	semidirect
250. C₄₃	#13194	semidirect
285. M₃₂	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582975	2
#19136350	2
C₂×#14582681	2
C₂×#14582680	2
M₃₂×Dic₄₃	2
C₂×C₄₃×#349	2
#13194	43