Subgroups — C₄₃×#21865 #24941882

Order 11008.

1394 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1993	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1961	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1874	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1804	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₃	—	2	1	no	—
9	C₄₃×#532	—	2	4	no	—
10	C₄₃×#532	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₃	—	2	1	no	—
14	C₂×#121×C₄₃	—	2	1	no	—
15	C₂×#121×C₄₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₃	—	2	1	no	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#432	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×#97×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#382	—	2	1	no	—
26	C₄₃×#382	—	2	1	no	—
27	C₄₃×#382	C₂²	1	2	yes	—
28	C₄₃×#382	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	—	2	1	no	—
30	C₂×#95×C₄₃	—	2	1	no	—
31	C₄₃×#340	C₂²	1	8	yes	—
32	C₂×#41×C₄₃	—	2	8	no	—
33	C₂×#41×C₄₃	—	4	8	no	—
34	C₂²×Q₈×C₄₃	—	2	1	no	—
35	C₂²×D₄×C₄₃	—	2	2	no	—
36	C₂²×D₄×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	—	2	2	no	—
40	C₂³×C₄×C₄₃	—	2	2	no	—
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₄₃	—	2	2	no	—
46	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
47	#127×C₄₃	—	2	2	no	—
48	#127×C₄₃	C₂×C₄	1	4	yes	complemented
49	#124×C₄₃	—	2	8	no	—
50	#121×C₄₃	—	2	8	no	—
51	#121×C₄₃	—	2	4	no	—
52	#121×C₄₃	C₂×C₄	1	8	yes	—
53	C₄×D₄×C₄₃	—	2	8	no	—
54	C₄×D₄×C₄₃	—	2	4	no	—
55	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	complemented
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	D₄	1	4	yes	—
67	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₃	—	2	4	no	—
70	#102×C₄₃	—	4	8	no	—
71	C₂²⋊C₈×C₄₃	—	2	4	no	—
72	#97×C₄₃	—	2	4	no	—
73	#95×C₄₃	—	2	2	no	—
74	#95×C₄₃	—	2	2	no	—
75	#95×C₄₃	—	2	2	no	—
76	#95×C₄₃	—	2	2	no	—
77	C₂⁴×C₄₃	—	2	2	no	—
78	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
79	#41×C₄₃	—	4	32	no	—
80	C₂×Q₈×C₄₃	—	2	4	no	—
81	C₂×Q₈×C₄₃	—	4	4	no	—
82	C₂×D₄×C₄₃	—	2	4	no	—
83	C₂×D₄×C₄₃	—	2	4	no	—
84	C₂×D₄×C₄₃	—	2	2	no	—
85	C₂×D₄×C₄₃	—	2	8	no	—
86	C₂×D₄×C₄₃	—	2	4	no	—
87	C₂×D₄×C₄₃	—	2	4	no	—
88	C₂×D₄×C₄₃	—	4	4	no	—
89	C₂×D₄×C₄₃	—	4	4	no	—
90	C₂×D₄×C₄₃	—	4	8	no	—
91	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	8	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	4	2	no	—
99	C₂²×C₄×C₄₃	—	4	4	no	—
100	C₂²×C₄×C₄₃	—	4	4	no	—
101	C₂²×C₄×C₄₃	—	4	8	no	—
102	C₂²×C₄×C₄₃	—	4	4	no	—
103	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₃	—	2	4	no	—
114	C₂×C₈×C₄₃	—	2	4	no	—
115	C₂×C₈×C₄₃	—	2	4	no	—
116	C₄⋊C₄×C₄₃	—	2	4	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	8	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂²⋊C₄×C₄₃	—	2	8	no	—
122	C₂²⋊C₄×C₄₃	—	2	8	no	—
123	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₄₃	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₃	C₂×D₄	1	2	yes	—
128	C₄²×C₄₃	C₂×D₄	1	2	yes	—
129	C₂³×C₄₃	—	2	1	no	—
130	C₂³×C₄₃	—	2	1	no	—
131	C₂³×C₄₃	—	2	2	no	—
132	C₂³×C₄₃	—	2	4	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	4	no	—
136	C₂³×C₄₃	—	4	4	no	—
137	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
138	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
139	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₃	—	4	8	no	—
141	D₄×C₄₃	—	2	8	no	—
142	D₄×C₄₃	—	4	8	no	—
143	D₄×C₄₃	—	4	8	no	—
144	D₄×C₄₃	—	4	16	no	—
145	D₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	8	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	16	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	8	8	no	—
163	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
168	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
172	C₈×C₄₃	—	4	4	no	—
173	#21865	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₃	—	2	2	no	—
175	C₂²×C₄₃	—	2	2	no	—
176	C₂²×C₄₃	—	2	4	no	—
177	C₂²×C₄₃	—	2	4	no	—
178	C₂²×C₄₃	—	4	4	no	—
179	C₂²×C₄₃	—	4	4	no	—
180	C₂²×C₄₃	—	4	4	no	—
181	C₂²×C₄₃	—	8	4	no	—
182	C₂²×C₄₃	—	8	4	no	—
183	C₂²×C₄₃	#418	1	4	yes	—
184	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₃	#535	1	1	yes	characteristic
186	C₂²×C₄₃	#536	1	1	yes	characteristic
187	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₂²×C₄₃	#575	1	2	yes	—
189	C₄×C₄₃	—	2	2	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	4	4	no	—
195	C₄×C₄₃	—	8	4	no	—
196	C₄×C₄₃	#520	1	2	yes	—
197	C₄×C₄₃	#537	1	2	yes	—
198	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
199	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
200	C₂×#382	C₂×C₄₃	1	1	yes	characteristic, complemented
201	#1993	C₂×C₄₃	1	2	yes	complemented
202	#1961	C₂×C₄₃	1	2	yes	complemented
203	#1874	C₂×C₄₃	1	4	yes	complemented
204	#1804	C₂×C₄₃	1	4	yes	complemented
205	C₂×C₄₃	—	2	4	no	—
206	C₂×C₄₃	—	8	4	no	—
207	C₂×C₄₃	#2311	1	1	yes	characteristic
208	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
209	C₂×C₄₃	#2896	1	1	yes	characteristic
210	C₂×C₄₃	#3213	1	2	yes	—
211	C₂×C₄₃	#3234	1	2	yes	—
212	C₂²×#41	—	2	1	no	—
213	#532	—	2	4	no	—
214	#532	C₄×C₄₃	1	8	yes	complemented
215	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
216	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
217	C₂×#124	—	2	1	no	—
218	C₂×#121	—	2	1	no	—
219	C₂×#121	C₂²×C₄₃	1	2	yes	—
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
223	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
224	#432	—	2	4	no	—
225	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
226	C₂×#102	C₂²×C₄₃	1	8	yes	—
227	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
228	C₂×#97	C₂²×C₄₃	1	2	yes	—
229	#382	—	2	1	no	—
230	#382	—	2	1	no	—
231	#382	C₂²×C₄₃	1	2	yes	—
232	#382	C₂²×C₄₃	1	2	yes	—
233	C₂×#95	—	2	1	no	—
234	C₂×#95	—	2	1	no	—
235	#340	C₂²×C₄₃	1	8	yes	—
236	C₄₃	#21865	1	1	yes	characteristic, direct product factor, Sylow
237	C₂×#41	—	2	8	no	—
238	C₂×#41	—	4	8	no	—
239	C₂²×Q₈	—	2	1	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
252	#127	—	2	2	no	—
253	#127	C₂×C₄×C₄₃	1	4	yes	complemented
254	#124	—	2	8	no	—
255	#121	—	2	8	no	—
256	#121	—	2	4	no	—
257	#121	C₂×C₄×C₄₃	1	8	yes	—
258	C₄×D₄	—	2	8	no	—
259	C₄×D₄	—	2	4	no	—
260	C₄×D₄	C₂×C₄×C₄₃	1	8	yes	complemented
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	4	4	no	—
264	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
269	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₄₃	1	4	yes	—
272	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
274	C₄⋊C₈	—	2	4	no	—
275	#102	—	4	8	no	—
276	C₂²⋊C₈	—	2	4	no	—
277	#97	—	2	4	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
284	#41	—	4	32	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	4	4	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	4	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	8	no	—
296	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	4	8	no	—
305	C₂²×C₄	—	4	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
309	C₂²×C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
310	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
311	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	4	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	8	no	—
328	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
329	C₄²	C₂²⋊C₄×C₄₃	1	4	yes	—
330	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
331	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
332	C₄²	C₂×D₄×C₄₃	1	2	yes	—
333	C₄²	C₂×D₄×C₄₃	1	2	yes	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	4	no	—
342	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
343	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
344	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
345	Q₈	—	4	8	no	—
346	D₄	—	2	8	no	—
347	D₄	—	4	8	no	—
348	D₄	—	4	8	no	—
349	D₄	—	4	16	no	—
350	D₄	—	4	4	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	16	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
370	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
371	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
372	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
373	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
375	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
376	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
377	C₈	—	4	4	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	4	no	—
386	C₂²	—	8	4	no	—
387	C₂²	C₄₃×#418	1	4	yes	—
388	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
389	C₂²	C₄₃×#535	1	1	yes	characteristic
390	C₂²	C₄₃×#536	1	1	yes	characteristic
391	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
392	C₂²	C₄₃×#575	1	2	yes	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₄₃×#520	1	2	yes	—
401	C₄	C₄₃×#537	1	2	yes	—
402	C₂	—	2	4	no	—
403	C₂	—	8	4	no	—
404	C₂	C₄₃×#2311	1	1	yes	characteristic
405	C₂	C₂×C₄₃×#418	1	1	yes	characteristic
406	C₂	C₄₃×#2896	1	1	yes	characteristic
407	C₂	C₄₃×#3213	1	2	yes	—
408	C₂	C₄₃×#3234	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#432	C₂	semidirect
3. C₂×C₄₃×#382	C₂	semidirect
4. C₄₃×#1993	C₂	semidirect
5. C₄₃×#1961	C₂	semidirect
6. C₄₃×#1874	C₂	semidirect
7. C₄₃×#1804	C₂	semidirect
10. C₄₃×#532	C₄	semidirect
46. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
48. #127×C₄₃	C₂×C₄	semidirect
55. C₄×D₄×C₄₃	C₂×C₄	semidirect
173. #21865	C₄₃	direct (N × H)
199. C₂×#432	C₂×C₄₃	semidirect
200. C₂×#382	C₂×C₄₃	semidirect
201. #1993	C₂×C₄₃	semidirect
202. #1961	C₂×C₄₃	semidirect
203. #1874	C₂×C₄₃	semidirect
204. #1804	C₂×C₄₃	semidirect
214. #532	C₄×C₄₃	semidirect
236. C₄₃	#21865	direct (N × H)
251. C₄⋊Q₈	C₂×C₄×C₄₃	semidirect
253. #127	C₂×C₄×C₄₃	semidirect
260. C₄×D₄	C₂×C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#532	2
C₂×C₄₃×#432	2
C₂×C₄₃×#382	2
C₄₃×#1993	2
C₄₃×#1961	2
C₄₃×#1874	2
C₄₃×#1804	2
#21865	43

Subgroups — C43×#21865 #24941882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#21865 #24941882