Subgroups — C₄₃×#8953 #24928970

Order 11008.

514 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2988	C₂	1	1	yes	maximal, characteristic
2	C₄×#137×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1476	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1283	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#137×C₄₃	C₄	1	1	yes	characteristic
9	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
11	C₈×Q₈×C₄₃	—	2	1	no	—
12	C₄₃×#441	—	2	1	no	—
13	C₄₃×#440	—	2	1	no	—
14	C₄×Q₁₆×C₄₃	—	2	1	no	—
15	C₄×SD₁₆×C₄₃	—	2	1	no	—
16	C₈×D₄×C₄₃	—	2	2	no	—
17	C₈×D₄×C₄₃	—	2	1	no	—
18	C₄₃×#431	—	2	1	no	—
19	C₄₃×#431	C₂²	1	1	yes	characteristic
20	C₄₃×#431	C₂²	1	1	yes	characteristic
21	C₄₃×#428	C₄	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#419	C₄	1	1	yes	characteristic
25	C₄₃×#417	C₄	1	1	yes	characteristic
26	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#336	—	2	2	no	—
29	C₄₃×Q₈⋊C₈	—	2	1	no	—
30	C₄₃×Q₈⋊C₈	—	2	1	no	—
31	C₄₃×Q₈⋊C₈	—	2	1	no	—
32	C₄₃×D₄⋊C₈	—	2	1	no	—
33	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
35	#137×C₄₃	—	2	2	no	—
36	#137×C₄₃	C₈	1	4	yes	complemented
37	C₂×Q₁₆×C₄₃	—	2	1	no	—
38	C₂×SD₁₆×C₄₃	—	2	1	no	—
39	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	—	2	1	no	—
42	C₂²×C₈×C₄₃	—	2	2	no	—
43	C₂²×C₈×C₄₃	D₄	1	2	yes	—
44	C₄×Q₈×C₄₃	—	2	1	no	—
45	C₄×Q₈×C₄₃	—	2	1	no	—
46	C₄×Q₈×C₄₃	—	2	1	no	—
47	C₄×Q₈×C₄₃	—	2	1	no	—
48	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
49	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
50	C₄×D₄×C₄₃	—	2	1	no	—
51	C₄×D₄×C₄₃	—	2	1	no	—
52	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
53	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
54	#117×C₄₃	—	2	1	no	—
55	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₃	—	2	1	no	—
59	C₂×C₄²×C₄₃	—	2	1	no	—
60	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
61	#107×C₄₃	—	2	1	no	—
62	#106×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	2	no	—
64	C₄⋊C₈×C₄₃	—	2	1	no	—
65	C₄⋊C₈×C₄₃	—	2	1	no	—
66	C₄⋊C₈×C₄₃	—	2	1	no	—
67	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
68	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
69	#103×C₄₃	—	2	1	no	—
70	#103×C₄₃	—	2	1	no	—
71	#103×C₄₃	—	2	1	no	—
72	#102×C₄₃	—	2	1	no	—
73	C₂²⋊C₈×C₄₃	—	2	2	no	—
74	C₂²⋊C₈×C₄₃	—	2	1	no	—
75	C₂²⋊C₈×C₄₃	—	2	1	no	—
76	#97×C₄₃	—	2	1	no	—
77	C₄×C₈×C₄₃	—	2	2	no	—
78	C₄×C₈×C₄₃	—	2	1	no	—
79	C₄×C₈×C₄₃	—	2	1	no	—
80	C₄×C₈×C₄₃	—	2	1	no	—
81	C₄×C₈×C₄₃	—	2	1	no	—
82	C₄×C₈×C₄₃	—	2	1	no	—
83	#41×C₄₃	—	2	1	no	—
84	#41×C₄₃	—	2	1	no	—
85	#41×C₄₃	C₂×C₈	1	2	yes	—
86	#41×C₄₃	M₁₆	1	2	yes	—
87	C₂×Q₈×C₄₃	—	2	1	no	—
88	C₂×Q₈×C₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×Q₈×C₄₃	C₂×C₈	1	2	yes	complemented
94	C₂×D₄×C₄₃	—	2	1	no	—
95	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	Q₁₆×C₄₃	—	2	4	no	—
105	SD₁₆×C₄₃	—	2	4	no	—
106	M₁₆×C₄₃	—	2	1	no	—
107	M₁₆×C₄₃	—	2	1	no	—
108	M₁₆×C₄₃	—	2	1	no	—
109	M₁₆×C₄₃	C₂×C₈	1	2	yes	complemented
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	1	no	—
116	C₂×C₈×C₄₃	—	4	1	no	—
117	C₂×C₈×C₄₃	—	4	1	no	—
118	C₂×C₈×C₄₃	—	4	2	no	—
119	C₂×C₈×C₄₃	—	4	1	no	—
120	C₂×C₈×C₄₃	—	8	2	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	4	1	no	—
126	C₄⋊C₄×C₄₃	—	4	1	no	—
127	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²⋊C₄×C₄₃	—	2	1	no	—
130	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	#41	1	1	yes	characteristic
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	2	1	no	—
144	Q₈×C₄₃	—	2	2	no	—
145	Q₈×C₄₃	—	2	2	no	—
146	Q₈×C₄₃	—	4	1	no	—
147	Q₈×C₄₃	—	4	1	no	—
148	Q₈×C₄₃	C₂²⋊C₈	1	2	yes	—
149	D₄×C₄₃	—	2	2	no	—
150	D₄×C₄₃	—	2	2	no	—
151	D₄×C₄₃	—	2	1	no	—
152	D₄×C₄₃	C₂²⋊C₈	1	2	yes	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	8	1	no	—
169	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
178	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
179	C₈×C₄₃	—	2	2	no	—
180	C₈×C₄₃	—	4	2	no	—
181	C₈×C₄₃	—	4	1	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	—	4	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	—	8	1	no	—
186	#8953	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	2	1	no	—
188	C₂²×C₄₃	—	2	1	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	4	1	no	—
191	C₂²×C₄₃	—	4	1	no	—
192	C₂²×C₄₃	#386	1	1	yes	characteristic
193	C₂²×C₄₃	C₈×D₄	1	1	yes	characteristic
194	C₂²×C₄₃	#435	1	1	yes	characteristic
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	1	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	—	8	1	no	—
203	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
204	C₄×C₄₃	#408	1	1	yes	characteristic
205	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
206	C₄×C₄₃	#435	1	1	yes	characteristic
207	C₄×C₄₃	#455	1	1	yes	characteristic
208	C₄×C₄₃	#456	1	1	yes	characteristic
209	#2988	C₂×C₄₃	1	1	yes	characteristic
210	C₄×#137	C₂×C₄₃	1	1	yes	characteristic
211	#1984	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#1479	C₂×C₄₃	1	1	yes	characteristic, complemented
213	#1476	C₂×C₄₃	1	1	yes	characteristic
214	#1283	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#1278	C₂×C₄₃	1	1	yes	characteristic, complemented
216	C₂×C₄₃	—	2	1	no	—
217	C₂×C₄₃	—	2	1	no	—
218	C₂×C₄₃	—	4	2	no	—
219	C₂×C₄₃	#1869	1	1	yes	characteristic
220	C₂×C₄₃	#1881	1	1	yes	characteristic
221	C₂×C₄₃	#1882	1	1	yes	characteristic
222	C₂×#137	C₄×C₄₃	1	1	yes	characteristic
223	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
224	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
225	C₈×Q₈	—	2	1	no	—
226	#441	—	2	1	no	—
227	#440	—	2	1	no	—
228	C₄×Q₁₆	—	2	1	no	—
229	C₄×SD₁₆	—	2	1	no	—
230	C₈×D₄	—	2	2	no	—
231	C₈×D₄	—	2	1	no	—
232	#431	—	2	1	no	—
233	#431	C₂²×C₄₃	1	1	yes	characteristic
234	#431	C₂²×C₄₃	1	1	yes	characteristic
235	#428	C₄×C₄₃	1	1	yes	characteristic
236	C₂×C₄⋊C₈	—	2	1	no	—
237	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
238	#419	C₄×C₄₃	1	1	yes	characteristic
239	#417	C₄×C₄₃	1	1	yes	characteristic
240	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
241	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
242	#336	—	2	2	no	—
243	Q₈⋊C₈	—	2	1	no	—
244	Q₈⋊C₈	—	2	1	no	—
245	Q₈⋊C₈	—	2	1	no	—
246	D₄⋊C₈	—	2	1	no	—
247	C₄₃	#8953	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#41	C₂×C₄×C₄₃	1	1	yes	characteristic
249	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
250	#137	—	2	2	no	—
251	#137	C₈×C₄₃	1	4	yes	complemented
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×M₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
255	C₂×M₁₆	C₂×C₄×C₄₃	1	1	yes	characteristic
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	D₄×C₄₃	1	2	yes	—
259	C₄×Q₈	—	2	1	no	—
260	C₄×Q₈	—	2	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
264	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
268	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
269	#117	—	2	1	no	—
270	#117	C₂×C₄×C₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
276	#107	—	2	1	no	—
277	#106	—	2	1	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	D₄×C₄₃	1	1	yes	characteristic
283	C₄⋊C₈	D₄×C₄₃	1	1	yes	characteristic
284	#103	—	2	1	no	—
285	#103	—	2	1	no	—
286	#103	—	2	1	no	—
287	#102	—	2	1	no	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	1	no	—
292	C₄×C₈	—	2	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	2	1	no	—
296	C₄×C₈	—	2	1	no	—
297	C₄×C₈	—	2	1	no	—
298	#41	—	2	1	no	—
299	#41	—	2	1	no	—
300	#41	C₂×C₈×C₄₃	1	2	yes	—
301	#41	M₁₆×C₄₃	1	2	yes	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
308	C₂×Q₈	C₂×C₈×C₄₃	1	2	yes	complemented
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
318	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
319	Q₁₆	—	2	4	no	—
320	SD₁₆	—	2	4	no	—
321	M₁₆	—	2	1	no	—
322	M₁₆	—	2	1	no	—
323	M₁₆	—	2	1	no	—
324	M₁₆	C₂×C₈×C₄₃	1	2	yes	complemented
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	4	1	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	8	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
343	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
344	C₂²⋊C₄	—	2	1	no	—
345	C₂²⋊C₄	—	2	1	no	—
346	C₂²⋊C₄	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	1	no	—
352	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
354	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
355	C₄²	#41×C₄₃	1	1	yes	characteristic
356	C₂³	—	2	1	no	—
357	C₂³	C₄×D₄×C₄₃	1	1	yes	characteristic
358	Q₈	—	2	1	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	Q₈	C₂²⋊C₈×C₄₃	1	2	yes	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	2	1	no	—
367	D₄	C₂²⋊C₈×C₄₃	1	2	yes	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	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	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	8	1	no	—
384	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
385	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
386	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
387	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
388	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
389	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×C₈×C₄₃	1	1	yes	characteristic
391	C₂×C₄	C₂×M₁₆×C₄₃	1	1	yes	characteristic
392	C₂×C₄	#131×C₄₃	1	1	yes	characteristic
393	C₂×C₄	#131×C₄₃	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	2	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	8	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	C₄₃×#386	1	1	yes	characteristic
407	C₂²	C₈×D₄×C₄₃	1	1	yes	characteristic
408	C₂²	C₄₃×#435	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	8	1	no	—
417	C₄	C₂×C₂²⋊C₈×C₄₃	1	1	yes	characteristic
418	C₄	C₄₃×#408	1	1	yes	characteristic
419	C₄	C₈×D₄×C₄₃	1	1	yes	characteristic
420	C₄	C₄₃×#435	1	1	yes	characteristic
421	C₄	C₄₃×#455	1	1	yes	characteristic
422	C₄	C₄₃×#456	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	C₄₃×#1869	1	1	yes	characteristic
427	C₂	C₄₃×#1881	1	1	yes	characteristic
428	C₂	C₄₃×#1882	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator	C₂×C₄	C₂²×C₈×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂²×C₄₃	#386
prime radical	C₂×#41×C₄₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#1984	C₂	semidirect
4. C₄₃×#1479	C₂	semidirect
6. C₄₃×#1283	C₂	semidirect
7. C₄₃×#1278	C₂	semidirect
36. #137×C₄₃	C₈	semidirect
93. C₂×Q₈×C₄₃	C₂×C₈	semidirect
109. M₁₆×C₄₃	C₂×C₈	semidirect
186. #8953	C₄₃	direct (N × H)
211. #1984	C₂×C₄₃	semidirect
212. #1479	C₂×C₄₃	semidirect
214. #1283	C₂×C₄₃	semidirect
215. #1278	C₂×C₄₃	semidirect
247. C₄₃	#8953	direct (N × H)
251. #137	C₈×C₄₃	semidirect
308. C₂×Q₈	C₂×C₈×C₄₃	semidirect
324. M₁₆	C₂×C₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#2988	2
C₄×#137×C₄₃	2
C₄₃×#1984	2
C₄₃×#1479	2
C₄₃×#1476	2
C₄₃×#1283	2
C₄₃×#1278	2
#8953	43

Subgroups — C43×#8953 #24928970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8953 #24928970