Subgroups — #25960882

Order 11008.

2818 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	H(5,𝔽₂)×Dic₄₃	C₂	1	2	yes	maximal, complemented
2	#19143479	C₂	1	3	yes	maximal, complemented
3	#19143447	C₂	1	3	yes	maximal, complemented
4	#19143428	C₂	1	6	yes	maximal, complemented
5	AGL(1,ℤ/8)×Dic₄₃	C₂	1	6	yes	maximal, complemented
6	#19143396	C₂	1	3	yes	maximal, complemented
7	C₂×#14583011	C₂	1	3	yes	maximal, complemented
8	#19143190	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143121	C₂	1	2	yes	maximal, complemented
10	#19143021	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#576	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063332	C₂²	1	1	yes	characteristic
13	#14583382	—	2	2	no	—
14	#14583382	C₂²	1	2	yes	—
15	#14583382	C₂²	1	6	yes	complemented
16	#14583374	—	2	6	no	—
17	#14583374	C₂²	1	6	yes	complemented
18	#41×Dic₄₃	—	2	2	no	—
19	#41×Dic₄₃	C₂²	1	1	yes	characteristic
20	#41×Dic₄₃	C₂²	1	6	yes	complemented
21	C₂×D₄×Dic₄₃	—	2	6	no	—
22	C₂×D₄×Dic₄₃	C₂²	1	6	yes	complemented
23	#14583011	C₂²	1	6	yes	complemented
24	#14583011	C₂²	1	3	yes	complemented
25	#14583011	C₂²	1	6	yes	complemented
26	#14583011	C₂²	1	3	yes	complemented
27	#14583011	C₂²	1	6	yes	complemented
28	#14583006	C₂²	1	3	yes	complemented
29	#14583006	C₂²	1	1	yes	characteristic, complemented
30	#14583000	C₂²	1	6	yes	complemented
31	#14583000	C₂²	1	6	yes	complemented
32	SD₁₆×Dic₄₃	C₂²	1	12	yes	complemented
33	D₈×Dic₄₃	C₂²	1	12	yes	complemented
34	#14582941	C₂²	1	6	yes	complemented
35	#14582937	C₂²	1	3	yes	complemented
36	C₂×#13063257	C₂²	1	3	yes	complemented
37	#14582904	C₂²	1	6	yes	complemented
38	#14582900	C₂²	1	6	yes	complemented
39	#14582895	C₂²	1	6	yes	complemented
40	C₂×#13063246	C₂²	1	6	yes	complemented
41	#14582857	C₂²	1	3	yes	complemented
42	#14582854	C₂²	1	3	yes	complemented
43	M₁₆×Dic₄₃	C₂²	1	3	yes	complemented
44	C₂×#13063235	C₂²	1	3	yes	complemented
45	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	2	yes	—
46	C₄₃×#576	C₄	1	16	yes	complemented
47	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	6	yes	—
48	C₂×#135×C₄₃	C₂²	1	3	yes	—
49	C₂²×D₈×C₄₃	C₂²	1	3	yes	—
50	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
51	C₂³×Dic₄₃	—	2	6	no	—
52	#13063332	—	2	4	no	—
53	C₂×#10621877	C₂³	1	3	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	—
55	Q₈×Dic₄₃	—	2	2	no	—
56	Q₈×Dic₄₃	D₄	1	2	yes	—
57	Q₈×Dic₄₃	C₂³	1	2	yes	—
58	Q₈×Dic₄₃	C₂³	1	6	yes	—
59	D₄×Dic₄₃	—	2	6	no	—
60	D₄×Dic₄₃	—	2	6	no	—
61	D₄×Dic₄₃	—	2	6	no	—
62	D₄×Dic₄₃	—	2	12	no	—
63	D₄×Dic₄₃	—	2	6	no	—
64	D₄×Dic₄₃	—	2	6	no	—
65	D₄×Dic₄₃	—	2	6	no	—
66	D₄×Dic₄₃	—	2	6	no	—
67	D₄×Dic₄₃	D₄	1	6	yes	—
68	D₄×Dic₄₃	C₂³	1	6	yes	—
69	D₄×Dic₄₃	C₂³	1	12	yes	—
70	D₄×Dic₄₃	C₂³	1	6	yes	—
71	#13063284	—	2	6	no	—
72	#13063284	—	2	6	no	—
73	#13063284	C₂³	1	6	yes	—
74	#13063284	C₂³	1	3	yes	—
75	C₂×C₄⋊Dic₄₃	—	2	6	no	—
76	C₂×C₄⋊Dic₄₃	C₂³	1	6	yes	—
77	C₂×C₂²⋊Dic₄₃	—	2	6	no	—
78	C₂×C₂²⋊Dic₄₃	—	2	12	no	—
79	C₂×C₄×Dic₄₃	—	2	6	no	—
80	C₂×C₄×Dic₄₃	C₂³	1	3	yes	—
81	#13063259	C₂³	1	6	yes	—
82	#13063257	C₂³	1	3	yes	—
83	#13063257	C₂³	1	6	yes	—
84	#13063257	C₂³	1	1	yes	characteristic
85	#13063249	C₂³	1	2	yes	—
86	#13063249	C₂³	1	6	yes	—
87	#13063246	C₂³	1	6	yes	—
88	#13063246	C₂³	1	12	yes	—
89	#13063246	C₂³	1	6	yes	—
90	#13063235	C₂³	1	1	yes	characteristic
91	#13063235	C₂³	1	3	yes	—
92	#13063235	C₂³	1	3	yes	—
93	#13063235	C₂³	1	3	yes	—
94	C₈×Dic₄₃	C₂³	1	6	yes	—
95	H(5,𝔽₂)×C₄₃	—	2	8	no	—
96	H(5,𝔽₂)×C₄₃	C₂×C₄	1	16	yes	complemented
97	C₂×#41×C₄₃	—	2	2	no	—
98	C₂×#41×C₄₃	C₂³	1	6	yes	—
99	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₄₃	—	2	6	no	—
101	C₂²×D₄×C₄₃	C₂³	1	6	yes	—
102	AGL(1,ℤ/8)×C₄₃	C₂×C₄	1	48	yes	complemented
103	#135×C₄₃	C₂×C₄	1	24	yes	complemented
104	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×SD₁₆×C₄₃	C₂³	1	6	yes	—
106	C₂×D₈×C₄₃	C₂×C₄	1	24	yes	complemented
107	C₂×D₈×C₄₃	C₂³	1	3	yes	—
108	C₂×D₈×C₄₃	C₂³	1	6	yes	—
109	#131×C₄₃	C₂×C₄	1	8	yes	complemented
110	C₂×M₁₆×C₄₃	C₂³	1	3	yes	—
111	C₂²×C₈×C₄₃	C₂³	1	3	yes	—
112	C₂⁴×C₄₃	—	2	6	no	—
113	#41×C₄₃	—	2	16	no	—
114	#41×C₄₃	—	2	12	no	—
115	#41×C₄₃	C₂²×C₄	1	4	yes	—
116	#41×C₄₃	C₂²×C₄	1	24	yes	complemented
117	#41×C₄₃	#41	1	4	yes	—
118	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
120	C₂×D₄×C₄₃	—	2	48	no	—
121	C₂×D₄×C₄₃	—	2	6	no	—
122	C₂×D₄×C₄₃	—	2	12	no	—
123	C₂×D₄×C₄₃	—	2	6	no	—
124	C₂×D₄×C₄₃	C₂²×C₄	1	24	yes	complemented
125	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
126	C₂×D₄×C₄₃	C₂⁴	1	6	yes	—
127	C₂²×C₄×C₄₃	—	2	6	no	—
128	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
129	C₂²×Dic₄₃	—	2	6	no	—
130	C₂²×Dic₄₃	—	2	6	no	—
131	C₂²×Dic₄₃	—	2	12	no	—
132	C₂²×Dic₄₃	—	2	6	no	—
133	C₂²×Dic₄₃	—	8	12	no	—
134	C₂²×Dic₄₃	C₂×D₄	1	6	yes	—
135	Q₁₆×C₄₃	C₂²×C₄	1	4	yes	complemented
136	SD₁₆×C₄₃	C₂²×C₄	1	24	yes	complemented
137	D₈×C₄₃	C₂²×C₄	1	12	yes	complemented
138	D₈×C₄₃	C₂²×C₄	1	24	yes	complemented
139	M₁₆×C₄₃	C₂²×C₄	1	12	yes	complemented
140	C₂×C₈×C₄₃	C₂²×C₄	1	12	yes	complemented
141	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂⁴	1	3	yes	—
143	C₂²⋊Dic₄₃	—	2	6	no	—
144	C₂²⋊Dic₄₃	—	2	6	no	—
145	C₂²⋊Dic₄₃	—	2	12	no	—
146	C₂²⋊Dic₄₃	—	2	6	no	—
147	C₂²⋊Dic₄₃	C₂×D₄	1	6	yes	—
148	C₄⋊Dic₄₃	—	2	6	no	—
149	C₄⋊Dic₄₃	—	2	6	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₄⋊Dic₄₃	C₂×D₄	1	6	yes	—
152	C₄⋊Dic₄₃	C₂⁴	1	6	yes	—
153	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
154	C₄×Dic₄₃	—	2	6	no	—
155	C₄×Dic₄₃	—	2	2	no	—
156	C₄×Dic₄₃	—	2	6	no	—
157	C₄×Dic₄₃	C₂×D₄	1	6	yes	—
158	C₄×Dic₄₃	C₂⁴	1	3	yes	—
159	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
160	#10621877	—	2	6	no	—
161	C₂×C₄₃⋊C₈	—	2	6	no	—
162	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
163	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
164	C₂³×C₄₃	—	2	6	no	—
165	C₂³×C₄₃	—	2	24	no	—
166	C₂³×C₄₃	—	8	6	no	—
167	C₂³×C₄₃	—	8	6	no	—
168	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
169	Q₈×C₄₃	—	2	2	no	—
170	Q₈×C₄₃	C₄×D₄	1	4	yes	—
171	Q₈×C₄₃	C₂³×C₄	1	4	yes	—
172	D₄×C₄₃	—	2	24	no	—
173	D₄×C₄₃	—	2	24	no	—
174	D₄×C₄₃	—	2	6	no	—
175	D₄×C₄₃	C₄×D₄	1	12	yes	—
176	D₄×C₄₃	C₂³×C₄	1	12	yes	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	24	no	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	6	yes	—
180	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
181	C₂×C₄×C₄₃	C₂×#41	1	6	yes	—
182	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	2	6	no	—
185	C₂×Dic₄₃	—	4	6	no	—
186	C₂×Dic₄₃	—	4	12	no	—
187	C₂×Dic₄₃	—	8	6	no	—
188	C₂×Dic₄₃	—	8	12	no	—
189	C₂×Dic₄₃	—	8	6	no	—
190	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
191	C₂×Dic₄₃	C₂²×D₄	1	6	yes	—
192	C₈×C₄₃	C₂³×C₄	1	2	yes	—
193	C₈×C₄₃	C₂³×C₄	1	6	yes	—
194	C₄₃⋊C₈	—	2	1	no	—
195	C₄₃⋊C₈	—	2	3	no	—
196	#60176	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	6	no	—
198	C₂²×C₄₃	—	2	12	no	—
199	C₂²×C₄₃	—	4	6	no	—
200	C₂²×C₄₃	—	4	6	no	—
201	C₂²×C₄₃	—	8	24	no	—
202	C₂²×C₄₃	C₂×C₄×D₄	1	6	yes	—
203	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₄₃	—	2	4	no	—
205	C₄×C₄₃	C₂×C₄×D₄	1	6	yes	—
206	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
207	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
208	Dic₄₃	—	2	2	no	—
209	Dic₄₃	—	2	6	no	—
210	Dic₄₃	—	4	6	no	—
211	Dic₄₃	—	4	2	no	—
212	C₂×#576	D₄₃	1	1	yes	characteristic
213	C₄×H(5,𝔽₂)	—	43	2	no	—
214	#2952	—	43	3	no	—
215	#2948	—	43	3	no	—
216	#2946	—	43	6	no	—
217	C₄×AGL(1,ℤ/8)	—	43	6	no	—
218	#2943	—	43	3	no	—
219	C₂×#442	—	43	3	no	—
220	#2912	—	43	1	no	—
221	#2897	—	43	2	no	—
222	#2875	—	43	1	no	—
223	C₂×C₄₃	—	2	6	no	—
224	C₂×C₄₃	—	4	12	no	—
225	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
226	C₂×C₄₃	#3585	1	2	yes	—
227	C₂×H(5,𝔽₂)	C₂×D₄₃	1	2	yes	—
228	#576	Dic₄₃	1	16	yes	complemented
229	C₂×AGL(1,ℤ/8)	C₂×D₄₃	1	6	yes	—
230	C₂×#135	C₂×D₄₃	1	3	yes	—
231	C₂²×D₈	C₂×D₄₃	1	3	yes	—
232	C₂×#131	—	43	1	no	—
233	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
234	#520	—	43	2	no	—
235	#520	—	43	6	no	—
236	#520	—	86	2	no	—
237	#518	—	43	6	no	—
238	#518	—	86	6	no	—
239	C₄×#41	—	43	1	no	—
240	C₄×#41	—	43	6	no	—
241	C₄×#41	—	86	2	no	—
242	C₂×C₄×D₄	—	43	6	no	—
243	C₂×C₄×D₄	—	86	6	no	—
244	#442	—	43	3	no	—
245	#442	—	43	6	no	—
246	#442	—	43	6	no	—
247	#442	—	43	6	no	—
248	#442	—	43	3	no	—
249	#441	—	43	1	no	—
250	#441	—	43	3	no	—
251	#440	—	43	6	no	—
252	#440	—	43	6	no	—
253	C₄×SD₁₆	—	43	12	no	—
254	C₄×D₈	—	43	12	no	—
255	#428	—	43	6	no	—
256	#427	—	43	3	no	—
257	C₂×#106	—	43	3	no	—
258	#418	—	43	6	no	—
259	#417	—	43	6	no	—
260	#416	—	43	6	no	—
261	C₂×#102	—	43	6	no	—
262	#405	—	43	3	no	—
263	#405	—	43	3	no	—
264	C₄×M₁₆	—	43	3	no	—
265	C₂×#97	—	43	3	no	—
266	C₄₃	#60176	1	1	yes	characteristic, complemented, Sylow
267	H(5,𝔽₂)	—	2	8	no	—
268	H(5,𝔽₂)	C₂×Dic₄₃	1	16	yes	complemented
269	C₂×#41	—	2	2	no	—
270	C₂×#41	C₂²×D₄₃	1	6	yes	—
271	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
272	C₂²×D₄	—	2	6	no	—
273	C₂²×D₄	C₂²×D₄₃	1	6	yes	—
274	C₂³×C₄	—	86	6	no	—
275	AGL(1,ℤ/8)	C₂×Dic₄₃	1	48	yes	complemented
276	#135	C₂×Dic₄₃	1	24	yes	complemented
277	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
278	C₂×SD₁₆	C₂²×D₄₃	1	6	yes	—
279	C₂×D₈	C₂×Dic₄₃	1	24	yes	complemented
280	C₂×D₈	C₂²×D₄₃	1	3	yes	—
281	C₂×D₈	C₂²×D₄₃	1	6	yes	—
282	#131	—	86	4	no	—
283	#131	C₂×Dic₄₃	1	8	yes	complemented
284	C₂×M₁₆	—	43	3	no	—
285	C₂×M₁₆	C₂²×D₄₃	1	3	yes	—
286	C₂²×C₈	—	43	3	no	—
287	C₂²×C₈	C₂²×D₄₃	1	3	yes	—
288	C₄×Q₈	—	43	2	no	—
289	C₄×Q₈	—	43	2	no	—
290	C₄×Q₈	—	43	6	no	—
291	C₄×Q₈	—	86	2	no	—
292	C₄×D₄	—	43	6	no	—
293	C₄×D₄	—	43	6	no	—
294	C₄×D₄	—	43	12	no	—
295	C₄×D₄	—	43	6	no	—
296	C₄×D₄	—	86	6	no	—
297	C₄×D₄	—	86	6	no	—
298	C₄×D₄	—	86	12	no	—
299	C₄×D₄	—	86	6	no	—
300	C₄×D₄	—	86	6	no	—
301	C₄×D₄	—	86	6	no	—
302	C₄×D₄	—	86	6	no	—
303	C₄×D₄	—	86	6	no	—
304	#117	—	43	3	no	—
305	#117	—	43	6	no	—
306	#117	—	86	6	no	—
307	#117	—	86	6	no	—
308	C₂×C₄⋊C₄	—	43	6	no	—
309	C₂×C₄⋊C₄	—	86	6	no	—
310	C₂×C₂²⋊C₄	—	86	12	no	—
311	C₂×C₂²⋊C₄	—	86	6	no	—
312	C₂×C₄²	—	43	3	no	—
313	C₂×C₄²	—	86	6	no	—
314	#107	—	43	6	no	—
315	#106	—	43	3	no	—
316	#106	—	43	6	no	—
317	#106	—	43	1	no	—
318	#103	—	43	2	no	—
319	#103	—	43	6	no	—
320	#102	—	43	6	no	—
321	#102	—	43	12	no	—
322	#102	—	43	6	no	—
323	#97	—	43	1	no	—
324	#97	—	43	3	no	—
325	#97	—	43	3	no	—
326	#97	—	43	3	no	—
327	C₄×C₈	—	43	6	no	—
328	C₂⁴	—	2	6	no	—
329	#41	—	2	16	no	—
330	#41	—	2	12	no	—
331	#41	#10621900	1	4	yes	—
332	#41	C₂²×Dic₄₃	1	4	yes	—
333	#41	C₂²×Dic₄₃	1	24	yes	complemented
334	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
335	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
336	C₂×D₄	—	2	6	no	—
337	C₂×D₄	—	2	48	no	—
338	C₂×D₄	—	2	6	no	—
339	C₂×D₄	—	2	12	no	—
340	C₂×D₄	D₄×D₄₃	1	3	yes	—
341	C₂×D₄	C₂²×Dic₄₃	1	24	yes	complemented
342	C₂×D₄	C₂³×D₄₃	1	6	yes	—
343	C₂²×C₄	—	2	6	no	—
344	C₂²×C₄	—	43	6	no	—
345	C₂²×C₄	—	86	6	no	—
346	C₂²×C₄	—	86	12	no	—
347	C₂²×C₄	—	86	6	no	—
348	C₂²×C₄	—	86	6	no	—
349	C₂²×C₄	—	344	12	no	—
350	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
351	Q₁₆	C₂²×Dic₄₃	1	4	yes	complemented
352	SD₁₆	C₂²×Dic₄₃	1	24	yes	complemented
353	D₈	C₂²×Dic₄₃	1	12	yes	complemented
354	D₈	C₂²×Dic₄₃	1	24	yes	complemented
355	M₁₆	—	86	6	no	—
356	M₁₆	C₂²×Dic₄₃	1	12	yes	complemented
357	C₂×C₈	—	43	3	no	—
358	C₂×C₈	—	43	1	no	—
359	C₂×C₈	—	86	6	no	—
360	C₂×C₈	C₂²×Dic₄₃	1	12	yes	complemented
361	C₂×C₈	C₂³×D₄₃	1	3	yes	—
362	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
363	C₄⋊C₄	—	43	6	no	—
364	C₄⋊C₄	—	43	6	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	—	86	6	no	—
367	C₄⋊C₄	—	86	2	no	—
368	C₄⋊C₄	—	86	6	no	—
369	C₂²⋊C₄	—	43	6	no	—
370	C₂²⋊C₄	—	86	6	no	—
371	C₂²⋊C₄	—	86	6	no	—
372	C₂²⋊C₄	—	86	12	no	—
373	C₂²⋊C₄	—	86	6	no	—
374	C₄²	—	43	6	no	—
375	C₄²	—	43	3	no	—
376	C₄²	—	43	1	no	—
377	C₄²	—	86	2	no	—
378	C₄²	—	86	6	no	—
379	C₄²	—	86	6	no	—
380	C₂³	—	2	6	no	—
381	C₂³	—	2	24	no	—
382	C₂³	—	8	6	no	—
383	C₂³	—	8	6	no	—
384	C₂³	C₂×D₄×D₄₃	1	3	yes	—
385	Q₈	—	2	2	no	—
386	Q₈	D₄×Dic₄₃	1	4	yes	—
387	Q₈	C₂³×Dic₄₃	1	4	yes	—
388	D₄	—	2	24	no	—
389	D₄	—	2	24	no	—
390	D₄	—	2	6	no	—
391	D₄	D₄×Dic₄₃	1	12	yes	—
392	D₄	C₂³×Dic₄₃	1	12	yes	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	24	no	—
395	C₂×C₄	—	43	2	no	—
396	C₂×C₄	—	43	6	no	—
397	C₂×C₄	—	86	2	no	—
398	C₂×C₄	—	86	6	no	—
399	C₂×C₄	—	344	12	no	—
400	C₂×C₄	—	344	6	no	—
401	C₂×C₄	—	344	6	no	—
402	C₂×C₄	—	172	6	no	—
403	C₂×C₄	—	172	12	no	—
404	C₂×C₄	C₂³×Dic₄₃	1	6	yes	—
405	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
406	C₂×C₄	C₂×#10621900	1	6	yes	—
407	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
408	C₈	—	86	1	no	—
409	C₈	—	86	3	no	—
410	C₈	C₂³×Dic₄₃	1	2	yes	—
411	C₈	C₂³×Dic₄₃	1	6	yes	—
412	C₂²	—	2	6	no	—
413	C₂²	—	2	12	no	—
414	C₂²	—	4	6	no	—
415	C₂²	—	4	6	no	—
416	C₂²	—	8	24	no	—
417	C₂²	C₂×D₄×Dic₄₃	1	6	yes	—
418	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
419	C₄	—	2	4	no	—
420	C₄	—	86	6	no	—
421	C₄	—	86	2	no	—
422	C₄	—	172	6	no	—
423	C₄	—	172	2	no	—
424	C₄	C₂×D₄×Dic₄₃	1	6	yes	—
425	C₄	C₂⁴×Dic₄₃	1	1	yes	characteristic
426	C₄	C₂²×#10621900	1	1	yes	characteristic
427	C₂	—	2	6	no	—
428	C₂	—	4	12	no	—
429	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
430	C₂	#19149370	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting, prime radical	C₂×C₄₃×#576	C₂
socle	C₂²×C₄₃	C₂³×D₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#576	D₄₃
hypocenter	C₄₃	#60176
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. H(5,𝔽₂)×Dic₄₃	C₂	semidirect
2. #19143479	C₂	semidirect
3. #19143447	C₂	semidirect
4. #19143428	C₂	semidirect
5. AGL(1,ℤ/8)×Dic₄₃	C₂	semidirect
6. #19143396	C₂	semidirect
7. C₂×#14583011	C₂	semidirect
8. #19143190	C₂	semidirect
9. #19143121	C₂	semidirect
10. #19143021	C₂	semidirect
15. #14583382	C₂²	semidirect
17. #14583374	C₂²	semidirect
20. #41×Dic₄₃	C₂²	semidirect
22. C₂×D₄×Dic₄₃	C₂²	semidirect
23. #14583011	C₂²	semidirect
24. #14583011	C₂²	semidirect
25. #14583011	C₂²	semidirect
26. #14583011	C₂²	semidirect
27. #14583011	C₂²	semidirect
28. #14583006	C₂²	semidirect
29. #14583006	C₂²	semidirect
30. #14583000	C₂²	semidirect
31. #14583000	C₂²	semidirect
32. SD₁₆×Dic₄₃	C₂²	semidirect
33. D₈×Dic₄₃	C₂²	semidirect
34. #14582941	C₂²	semidirect
35. #14582937	C₂²	semidirect
36. C₂×#13063257	C₂²	semidirect
37. #14582904	C₂²	semidirect
38. #14582900	C₂²	semidirect
39. #14582895	C₂²	semidirect
40. C₂×#13063246	C₂²	semidirect
41. #14582857	C₂²	semidirect
42. #14582854	C₂²	semidirect
43. M₁₆×Dic₄₃	C₂²	semidirect
44. C₂×#13063235	C₂²	semidirect
46. C₄₃×#576	C₄	semidirect
96. H(5,𝔽₂)×C₄₃	C₂×C₄	semidirect
102. AGL(1,ℤ/8)×C₄₃	C₂×C₄	semidirect
103. #135×C₄₃	C₂×C₄	semidirect
106. C₂×D₈×C₄₃	C₂×C₄	semidirect
109. #131×C₄₃	C₂×C₄	semidirect
116. #41×C₄₃	C₂²×C₄	semidirect
124. C₂×D₄×C₄₃	C₂²×C₄	semidirect
135. Q₁₆×C₄₃	C₂²×C₄	semidirect
136. SD₁₆×C₄₃	C₂²×C₄	semidirect
137. D₈×C₄₃	C₂²×C₄	semidirect
138. D₈×C₄₃	C₂²×C₄	semidirect
139. M₁₆×C₄₃	C₂²×C₄	semidirect
140. C₂×C₈×C₄₃	C₂²×C₄	semidirect
228. #576	Dic₄₃	semidirect
266. C₄₃	#60176	semidirect
268. H(5,𝔽₂)	C₂×Dic₄₃	semidirect
275. AGL(1,ℤ/8)	C₂×Dic₄₃	semidirect
276. #135	C₂×Dic₄₃	semidirect
279. C₂×D₈	C₂×Dic₄₃	semidirect
283. #131	C₂×Dic₄₃	semidirect
333. #41	C₂²×Dic₄₃	semidirect
341. C₂×D₄	C₂²×Dic₄₃	semidirect
351. Q₁₆	C₂²×Dic₄₃	semidirect
352. SD₁₆	C₂²×Dic₄₃	semidirect
353. D₈	C₂²×Dic₄₃	semidirect
354. D₈	C₂²×Dic₄₃	semidirect
356. M₁₆	C₂²×Dic₄₃	semidirect
360. C₂×C₈	C₂²×Dic₄₃	semidirect

Maximal subgroups

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

subgroup	index
H(5,𝔽₂)×Dic₄₃	2
#19143479	2
#19143447	2
#19143428	2
AGL(1,ℤ/8)×Dic₄₃	2
#19143396	2
C₂×#14583011	2
#19143190	2
#19143121	2
#19143021	2
C₂×C₄₃×#576	2
#60176	43