Subgroups — C₄₃×#28383 #24948400

Order 11008.

1058 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#459	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#124×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2092	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2012	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1973	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1972	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	—	2	2	no	—
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#475	—	2	4	no	—
21	C₄₃×#474	—	2	4	no	—
22	C₄₃×#460	—	2	4	no	—
23	C₄₃×#459	—	2	4	no	—
24	C₂×#107×C₄₃	C₂²	1	2	yes	—
25	C₂×#106×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#103×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#97×C₄₃	C₂²	1	2	yes	—
33	C₄₃×#391	C₂²	1	1	yes	characteristic
34	C₄₃×#390	—	2	2	no	—
35	C₄₃×#390	C₂²	1	2	yes	—
36	C₄₃×#390	C₂²	1	2	yes	—
37	C₄₃×#390	C₂²	1	1	yes	characteristic
38	C₄₃×#388	—	2	2	no	—
39	C₄₃×#382	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
41	C₄³×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	—	2	1	no	—
46	C₂²×D₄×C₄₃	—	2	1	no	—
47	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	—	2	1	no	—
50	C₂×SD₁₆×C₄₃	—	2	4	no	—
51	C₂×SD₁₆×C₄₃	—	2	4	no	—
52	C₂×SD₁₆×C₄₃	—	4	2	no	—
53	C₂×D₈×C₄₃	—	2	4	no	—
54	C₂×D₈×C₄₃	—	2	4	no	—
55	C₂×D₈×C₄₃	—	4	2	no	—
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	#127×C₄₃	—	2	2	no	—
61	#127×C₄₃	—	2	2	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	2	2	no	—
64	#124×C₄₃	—	4	8	no	—
65	C₄×Q₈×C₄₃	—	2	2	no	—
66	C₄×Q₈×C₄₃	—	2	2	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₄×D₄×C₄₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	D₄	1	2	yes	—
81	C₂×C₄²×C₄₃	D₄	1	2	yes	—
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	#107×C₄₃	—	2	4	no	—
86	#106×C₄₃	—	2	4	no	—
87	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
88	C₄⋊C₈×C₄₃	D₄	1	4	yes	—
89	#103×C₄₃	—	2	4	no	—
90	#102×C₄₃	—	2	4	no	—
91	#102×C₄₃	—	2	4	no	—
92	#102×C₄₃	—	2	4	no	—
93	#97×C₄₃	—	4	2	no	—
94	#95×C₄₃	—	2	2	no	—
95	#95×C₄₃	—	2	2	no	—
96	C₂⁴×C₄₃	—	2	1	no	—
97	C₂⁴×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	1	no	—
100	C₂×Q₈×C₄₃	—	2	1	no	—
101	C₂×Q₈×C₄₃	—	2	1	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	—	4	4	no	—
105	C₂×Q₈×C₄₃	#41	1	2	yes	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	2	no	—
117	C₂×D₄×C₄₃	—	4	4	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	4	4	no	—
121	C₂×D₄×C₄₃	#41	1	2	yes	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	2	1	no	—
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	4	2	no	—
127	C₂²×C₄×C₄₃	—	4	4	no	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	SD₁₆×C₄₃	—	4	8	no	—
134	D₈×C₄₃	—	4	8	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
140	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	—	2	1	no	—
147	C₄⋊C₄×C₄₃	—	4	2	no	—
148	C₄⋊C₄×C₄₃	—	4	2	no	—
149	C₂²⋊C₄×C₄₃	—	2	8	no	—
150	C₂²⋊C₄×C₄₃	—	4	4	no	—
151	C₂²⋊C₄×C₄₃	—	4	8	no	—
152	C₂²⋊C₄×C₄₃	—	4	8	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₄²×C₄₃	—	2	4	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₄²×C₄₃	—	2	1	no	—
158	C₄²×C₄₃	—	2	1	no	—
159	C₄²×C₄₃	—	4	2	no	—
160	C₄²×C₄₃	—	4	2	no	—
161	C₄²×C₄₃	C₂×D₄	1	2	yes	—
162	C₄²×C₄₃	C₂×D₄	1	2	yes	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	—	4	1	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	4	no	—
172	C₂³×C₄₃	—	4	4	no	—
173	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	2	no	—
176	Q₈×C₄₃	—	4	1	no	—
177	Q₈×C₄₃	—	4	1	no	—
178	Q₈×C₄₃	—	8	4	no	—
179	D₄×C₄₃	—	2	2	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	4	1	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	4	2	no	—
184	D₄×C₄₃	—	4	1	no	—
185	D₄×C₄₃	—	4	2	no	—
186	D₄×C₄₃	—	4	2	no	—
187	D₄×C₄₃	—	8	4	no	—
188	D₄×C₄₃	—	8	4	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	4	1	no	—
199	C₂×C₄×C₄₃	—	4	1	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	4	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	8	4	no	—
206	C₂×C₄×C₄₃	#127	1	2	yes	—
207	C₂×C₄×C₄₃	#127	1	2	yes	—
208	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
215	C₈×C₄₃	—	2	4	no	—
216	C₈×C₄₃	—	2	4	no	—
217	#28383	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	—	4	2	no	—
220	C₂²×C₄₃	—	8	1	no	—
221	C₂²×C₄₃	—	8	1	no	—
222	C₂²×C₄₃	—	8	2	no	—
223	C₂²×C₄₃	—	8	4	no	—
224	C₂²×C₄₃	—	8	2	no	—
225	C₂²×C₄₃	—	8	2	no	—
226	C₂²×C₄₃	—	8	4	no	—
227	C₂²×C₄₃	—	8	2	no	—
228	C₂²×C₄₃	#525	1	1	yes	characteristic
229	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
230	C₂²×C₄₃	#537	1	1	yes	characteristic
231	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
232	C₂²×C₄₃	#575	1	2	yes	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	4	2	no	—
235	C₄×C₄₃	—	4	2	no	—
236	C₄×C₄₃	—	4	2	no	—
237	C₄×C₄₃	—	8	1	no	—
238	C₄×C₄₃	—	8	2	no	—
239	C₄×C₄₃	—	8	1	no	—
240	C₄×C₄₃	#496	1	4	yes	—
241	C₄×C₄₃	#546	1	1	yes	characteristic
242	C₄×C₄₃	#546	1	1	yes	characteristic
243	C₄×C₄₃	#548	1	1	yes	characteristic
244	C₄×C₄₃	#548	1	1	yes	characteristic
245	C₂×#475	C₂×C₄₃	1	1	yes	characteristic, complemented
246	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
247	C₂×#460	C₂×C₄₃	1	1	yes	characteristic, complemented
248	C₂×#459	C₂×C₄₃	1	1	yes	characteristic
249	#2858	C₂×C₄₃	1	1	yes	characteristic, complemented
250	C₄×#124	C₂×C₄₃	1	1	yes	characteristic, complemented
251	#2092	C₂×C₄₃	1	2	yes	complemented
252	#2012	C₂×C₄₃	1	2	yes	complemented
253	#1973	C₂×C₄₃	1	2	yes	complemented
254	#1972	C₂×C₄₃	1	2	yes	complemented
255	#1767	C₂×C₄₃	1	1	yes	characteristic, complemented
256	C₂×C₄₃	—	8	2	no	—
257	C₂×C₄₃	—	16	2	no	—
258	C₂×C₄₃	#2540	1	1	yes	characteristic
259	C₂×C₄₃	#3115	1	2	yes	—
260	C₂×C₄₃	C₂×#496	1	1	yes	characteristic
261	C₂×C₄₃	#3153	1	1	yes	characteristic
262	C₂×C₄₃	#3251	1	2	yes	—
263	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
264	C₂²×D₈	C₂²×C₄₃	1	2	yes	—
265	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
266	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×#124	—	2	2	no	—
268	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
270	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
271	#475	—	2	4	no	—
272	#474	—	2	4	no	—
273	#460	—	2	4	no	—
274	#459	—	2	4	no	—
275	C₂×#107	C₂²×C₄₃	1	2	yes	—
276	C₂×#106	C₂²×C₄₃	1	2	yes	—
277	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
279	C₂×#103	C₂²×C₄₃	1	2	yes	—
280	C₂×#102	C₂²×C₄₃	1	2	yes	—
281	C₂×#102	C₂²×C₄₃	1	2	yes	—
282	C₂×#102	C₂²×C₄₃	1	2	yes	—
283	C₂×#97	C₂²×C₄₃	1	2	yes	—
284	#391	C₂²×C₄₃	1	1	yes	characteristic
285	#390	—	2	2	no	—
286	#390	C₂²×C₄₃	1	2	yes	—
287	#390	C₂²×C₄₃	1	2	yes	—
288	#390	C₂²×C₄₃	1	1	yes	characteristic
289	#388	—	2	2	no	—
290	#382	C₂²×C₄₃	1	1	yes	characteristic
291	C₄×C₂²⋊C₄	—	2	2	no	—
292	C₄³	C₂²×C₄₃	1	1	yes	characteristic
293	#336	C₂²×C₄₃	1	2	yes	—
294	C₄₃	#28383	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
297	C₂²×D₄	—	2	1	no	—
298	C₂²×D₄	—	2	1	no	—
299	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
300	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂×SD₁₆	—	2	4	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×SD₁₆	—	4	2	no	—
305	C₂×D₈	—	2	4	no	—
306	C₂×D₈	—	2	4	no	—
307	C₂×D₈	—	4	2	no	—
308	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
309	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	#127	—	2	2	no	—
313	#127	—	2	2	no	—
314	#124	—	2	2	no	—
315	#124	—	2	2	no	—
316	#124	—	4	8	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	4	no	—
329	C₂×C₂²⋊C₄	—	2	4	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	D₄×C₄₃	1	2	yes	—
333	C₂×C₄²	D₄×C₄₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
337	#107	—	2	4	no	—
338	#106	—	2	4	no	—
339	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
340	C₄⋊C₈	D₄×C₄₃	1	4	yes	—
341	#103	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	2	4	no	—
345	#97	—	4	2	no	—
346	#95	—	2	2	no	—
347	#95	—	2	2	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	2	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	#41×C₄₃	1	2	yes	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	#41×C₄₃	1	2	yes	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
385	SD₁₆	—	4	8	no	—
386	D₈	—	4	8	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
392	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₄⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	4	8	no	—
404	C₂²⋊C₄	—	4	4	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	2	1	no	—
408	C₄²	—	2	1	no	—
409	C₄²	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	4	2	no	—
412	C₄²	—	4	2	no	—
413	C₄²	C₂×D₄×C₄₃	1	2	yes	—
414	C₄²	C₂×D₄×C₄₃	1	2	yes	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	4	no	—
424	C₂³	—	4	4	no	—
425	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
426	Q₈	—	2	2	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	8	4	no	—
431	D₄	—	2	2	no	—
432	D₄	—	2	2	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	1	no	—
437	D₄	—	4	2	no	—
438	D₄	—	4	2	no	—
439	D₄	—	8	4	no	—
440	D₄	—	8	4	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	4	no	—
458	C₂×C₄	#127×C₄₃	1	2	yes	—
459	C₂×C₄	#127×C₄₃	1	2	yes	—
460	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
461	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
463	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
465	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
466	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
467	C₈	—	2	4	no	—
468	C₈	—	2	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	2	no	—
474	C₂²	—	8	4	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	8	4	no	—
478	C₂²	—	8	2	no	—
479	C₂²	C₄₃×#525	1	1	yes	characteristic
480	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
481	C₂²	C₄₃×#537	1	1	yes	characteristic
482	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
483	C₂²	C₄₃×#575	1	2	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	8	1	no	—
489	C₄	—	8	2	no	—
490	C₄	—	8	1	no	—
491	C₄	C₄₃×#496	1	4	yes	—
492	C₄	C₄₃×#546	1	1	yes	characteristic
493	C₄	C₄₃×#546	1	1	yes	characteristic
494	C₄	C₄₃×#548	1	1	yes	characteristic
495	C₄	C₄₃×#548	1	1	yes	characteristic
496	C₂	—	8	2	no	—
497	C₂	—	16	2	no	—
498	C₂	C₄₃×#2540	1	1	yes	characteristic
499	C₂	C₄₃×#3115	1	2	yes	—
500	C₂	C₂×C₄₃×#496	1	1	yes	characteristic
501	C₂	C₄₃×#3153	1	1	yes	characteristic
502	C₂	C₄₃×#3251	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#459	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#475	C₂	semidirect
2. C₂×C₄₃×#474	C₂	semidirect
3. C₂×C₄₃×#460	C₂	semidirect
5. C₄₃×#2858	C₂	semidirect
6. C₄×#124×C₄₃	C₂	semidirect
7. C₄₃×#2092	C₂	semidirect
8. C₄₃×#2012	C₂	semidirect
9. C₄₃×#1973	C₂	semidirect
10. C₄₃×#1972	C₂	semidirect
11. C₄₃×#1767	C₂	semidirect
217. #28383	C₄₃	direct (N × H)
245. C₂×#475	C₂×C₄₃	semidirect
246. C₂×#474	C₂×C₄₃	semidirect
247. C₂×#460	C₂×C₄₃	semidirect
249. #2858	C₂×C₄₃	semidirect
250. C₄×#124	C₂×C₄₃	semidirect
251. #2092	C₂×C₄₃	semidirect
252. #2012	C₂×C₄₃	semidirect
253. #1973	C₂×C₄₃	semidirect
254. #1972	C₂×C₄₃	semidirect
255. #1767	C₂×C₄₃	semidirect
294. C₄₃	#28383	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#475	2
C₂×C₄₃×#474	2
C₂×C₄₃×#460	2
C₂×C₄₃×#459	2
C₄₃×#2858	2
C₄×#124×C₄₃	2
C₄₃×#2092	2
C₄₃×#2012	2
C₄₃×#1973	2
C₄₃×#1972	2
C₄₃×#1767	2
#28383	43

Subgroups — C43×#28383 #24948400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28383 #24948400