Subgroups — C₄₃×#29694 #24949711

Order 11008.

1304 conjugacy classes of subgroups.

The subgroup lattice has 562 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×#478	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#2034	C₂	1	2	yes	maximal, complemented
9	C₄₃×#2033	C₂	1	2	yes	maximal, complemented
10	C₄₃×#1804	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	—	2	1	no	—
13	C₄₃×#532	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#121×C₄₃	—	2	1	no	—
19	C₂×#121×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₄₃	—	2	1	no	—
21	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#478	—	2	8	no	—
24	C₂×#107×C₄₃	C₂²	1	2	yes	—
25	C₂×#106×C₄₃	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₂×#102×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
32	C₄₃×#389	C₂²	1	1	yes	characteristic
33	C₄₃×#389	C₂²	1	1	yes	characteristic
34	C₄₃×#387	—	2	1	no	—
35	C₄₃×#387	—	2	1	no	—
36	C₄₃×#385	—	2	1	no	—
37	C₄₃×#385	—	2	1	no	—
38	C₄₃×#382	C₂²	1	1	yes	characteristic
39	C₄₃×#380	C₂²	1	1	yes	characteristic
40	C₄₃×#380	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₄₃×#336	C₂²	1	1	yes	characteristic
44	C₄₃×#336	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₃	—	2	8	no	—
46	C₂×#41×C₄₃	—	4	4	no	—
47	C₂×#41×C₄₃	—	4	4	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×D₄×C₄₃	—	2	2	no	—
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	—	2	1	no	—
52	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₃	—	2	2	no	—
54	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
58	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₃	—	2	4	no	—
60	#127×C₄₃	—	2	4	no	—
61	#125×C₄₃	—	2	4	no	—
62	#124×C₄₃	—	2	8	no	—
63	#121×C₄₃	—	2	8	no	—
64	#121×C₄₃	—	2	4	no	—
65	#121×C₄₃	—	2	4	no	—
66	C₄×D₄×C₄₃	—	2	8	no	—
67	C₄×D₄×C₄₃	—	2	4	no	—
68	C₄×D₄×C₄₃	D₄	1	8	yes	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄²×C₄₃	—	2	4	no	—
84	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	#107×C₄₃	—	2	4	no	—
89	#106×C₄₃	—	2	4	no	—
90	C₄⋊C₈×C₄₃	—	2	4	no	—
91	#102×C₄₃	—	2	4	no	—
92	#102×C₄₃	—	2	4	no	—
93	#102×C₄₃	—	4	2	no	—
94	#102×C₄₃	—	4	2	no	—
95	C₂²⋊C₈×C₄₃	—	4	2	no	—
96	#95×C₄₃	—	2	1	no	—
97	#95×C₄₃	—	2	1	no	—
98	#95×C₄₃	—	2	1	no	—
99	#95×C₄₃	—	2	1	no	—
100	#95×C₄₃	—	2	1	no	—
101	#95×C₄₃	—	2	1	no	—
102	C₂⁴×C₄₃	—	2	2	no	—
103	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
104	#41×C₄₃	—	4	32	no	—
105	C₂×Q₈×C₄₃	—	2	4	no	—
106	C₂×Q₈×C₄₃	—	4	2	no	—
107	C₂×Q₈×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	2	4	no	—
109	C₂×D₄×C₄₃	—	2	8	no	—
110	C₂×D₄×C₄₃	—	2	4	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	—	2	2	no	—
116	C₂×D₄×C₄₃	—	4	4	no	—
117	C₂×D₄×C₄₃	—	4	2	no	—
118	C₂×D₄×C₄₃	—	4	2	no	—
119	C₂×D₄×C₄₃	—	4	2	no	—
120	C₂×D₄×C₄₃	—	4	2	no	—
121	C₂×D₄×C₄₃	—	4	4	no	—
122	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	8	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	4	1	no	—
139	C₂²×C₄×C₄₃	—	4	4	no	—
140	C₂²×C₄×C₄₃	—	4	4	no	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₄₃	—	2	2	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	2	no	—
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	4	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	2	2	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	4	2	no	—
162	C₄⋊C₄×C₄₃	—	4	2	no	—
163	C₄⋊C₄×C₄₃	—	4	2	no	—
164	C₄⋊C₄×C₄₃	—	4	2	no	—
165	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
166	C₂²⋊C₄×C₄₃	—	2	8	no	—
167	C₂²⋊C₄×C₄₃	—	2	8	no	—
168	C₂²⋊C₄×C₄₃	—	4	2	no	—
169	C₂²⋊C₄×C₄₃	—	4	2	no	—
170	C₄²×C₄₃	—	2	2	no	—
171	C₄²×C₄₃	—	2	2	no	—
172	C₄²×C₄₃	—	2	2	no	—
173	C₄²×C₄₃	C₂×D₄	1	4	yes	—
174	C₂³×C₄₃	—	2	1	no	—
175	C₂³×C₄₃	—	2	1	no	—
176	C₂³×C₄₃	—	2	1	no	—
177	C₂³×C₄₃	—	2	1	no	—
178	C₂³×C₄₃	—	2	1	no	—
179	C₂³×C₄₃	—	2	1	no	—
180	C₂³×C₄₃	—	2	4	no	—
181	C₂³×C₄₃	—	4	2	no	—
182	C₂³×C₄₃	—	4	2	no	—
183	C₂³×C₄₃	—	4	2	no	—
184	C₂³×C₄₃	—	4	2	no	—
185	C₂³×C₄₃	—	4	2	no	—
186	C₂³×C₄₃	—	4	2	no	—
187	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
188	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₄₃	—	4	8	no	—
190	D₄×C₄₃	—	2	4	no	—
191	D₄×C₄₃	—	2	4	no	—
192	D₄×C₄₃	—	4	8	no	—
193	D₄×C₄₃	—	4	8	no	—
194	D₄×C₄₃	—	4	16	no	—
195	D₄×C₄₃	—	4	2	no	—
196	D₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	2	8	no	—
198	C₂×C₄×C₄₃	—	2	1	no	—
199	C₂×C₄×C₄₃	—	2	1	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	1	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	1	no	—
210	C₂×C₄×C₄₃	—	4	4	no	—
211	C₂×C₄×C₄₃	—	4	16	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	1	no	—
227	C₂×C₄×C₄₃	—	4	1	no	—
228	C₂×C₄×C₄₃	#120	1	2	yes	—
229	C₂×C₄×C₄₃	#120	1	2	yes	—
230	C₂×C₄×C₄₃	#135	1	2	yes	—
231	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
236	C₈×C₄₃	—	4	2	no	—
237	C₈×C₄₃	—	4	2	no	—
238	#29694	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂²×C₄₃	—	2	2	no	—
240	C₂²×C₄₃	—	2	2	no	—
241	C₂²×C₄₃	—	2	2	no	—
242	C₂²×C₄₃	—	4	1	no	—
243	C₂²×C₄₃	—	4	1	no	—
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	—	4	1	no	—
246	C₂²×C₄₃	—	4	4	no	—
247	C₂²×C₄₃	—	4	4	no	—
248	C₂²×C₄₃	—	4	4	no	—
249	C₂²×C₄₃	—	8	2	no	—
250	C₂²×C₄₃	—	8	2	no	—
251	C₂²×C₄₃	—	8	2	no	—
252	C₂²×C₄₃	—	8	2	no	—
253	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
254	C₂²×C₄₃	#536	1	1	yes	characteristic
255	C₂²×C₄₃	#537	1	1	yes	characteristic
256	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
257	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂²×C₄₃	#575	1	1	yes	characteristic
260	C₄×C₄₃	—	2	2	no	—
261	C₄×C₄₃	—	2	2	no	—
262	C₄×C₄₃	—	2	2	no	—
263	C₄×C₄₃	—	2	2	no	—
264	C₄×C₄₃	—	4	1	no	—
265	C₄×C₄₃	—	4	4	no	—
266	C₄×C₄₃	—	8	1	no	—
267	C₄×C₄₃	—	8	1	no	—
268	C₄×C₄₃	—	8	1	no	—
269	C₄×C₄₃	—	8	1	no	—
270	C₄×C₄₃	#536	1	2	yes	—
271	C₄×C₄₃	#537	1	2	yes	—
272	C₂×#532	C₂×C₄₃	1	1	yes	characteristic
273	C₂×#478	C₂×C₄₃	1	2	yes	complemented
274	#2851	C₂×C₄₃	1	1	yes	characteristic, complemented
275	#2058	C₂×C₄₃	1	1	yes	characteristic, complemented
276	#2057	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#2041	C₂×C₄₃	1	1	yes	characteristic, complemented
278	#2041	C₂×C₄₃	1	1	yes	characteristic, complemented
279	#2034	C₂×C₄₃	1	2	yes	complemented
280	#2033	C₂×C₄₃	1	2	yes	complemented
281	#1804	C₂×C₄₃	1	2	yes	complemented
282	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×C₄₃	—	4	2	no	—
284	C₂×C₄₃	—	8	4	no	—
285	C₂×C₄₃	#2616	1	1	yes	characteristic
286	C₂×C₄₃	#3002	1	1	yes	characteristic
287	C₂×C₄₃	#3003	1	1	yes	characteristic
288	C₂×C₄₃	#3228	1	1	yes	characteristic
289	C₂×C₄₃	#3234	1	1	yes	characteristic
290	C₂×C₄₃	#3247	1	1	yes	characteristic
291	C₂×C₄₃	#3251	1	1	yes	characteristic
292	C₂²×#41	—	2	1	no	—
293	#532	—	2	8	no	—
294	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
296	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
297	C₂×#124	—	2	1	no	—
298	C₂×#121	—	2	1	no	—
299	C₂×#121	C₂²×C₄₃	1	2	yes	—
300	C₂×C₄×D₄	—	2	1	no	—
301	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
302	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
303	#478	—	2	8	no	—
304	C₂×#107	C₂²×C₄₃	1	2	yes	—
305	C₂×#106	C₂²×C₄₃	1	2	yes	—
306	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
307	C₂×#102	C₂²×C₄₃	1	2	yes	—
308	C₂×#102	C₂²×C₄₃	1	2	yes	—
309	C₂×#102	C₂²×C₄₃	1	2	yes	—
310	C₂×#102	C₂²×C₄₃	1	2	yes	—
311	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
312	#389	C₂²×C₄₃	1	1	yes	characteristic
313	#389	C₂²×C₄₃	1	1	yes	characteristic
314	#387	—	2	1	no	—
315	#387	—	2	1	no	—
316	#385	—	2	1	no	—
317	#385	—	2	1	no	—
318	#382	C₂²×C₄₃	1	1	yes	characteristic
319	#380	C₂²×C₄₃	1	1	yes	characteristic
320	#380	C₂²×C₄₃	1	1	yes	characteristic
321	#340	C₂²×C₄₃	1	2	yes	—
322	#340	C₂²×C₄₃	1	2	yes	—
323	#336	C₂²×C₄₃	1	1	yes	characteristic
324	#336	C₂²×C₄₃	1	1	yes	characteristic
325	C₄₃	#29694	1	1	yes	characteristic, direct product factor, Sylow
326	C₂×#41	—	2	8	no	—
327	C₂×#41	—	4	4	no	—
328	C₂×#41	—	4	4	no	—
329	C₂²×Q₈	—	2	1	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
334	C₂³×C₄	—	2	2	no	—
335	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
339	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
340	C₄⋊Q₈	—	2	4	no	—
341	#127	—	2	4	no	—
342	#125	—	2	4	no	—
343	#124	—	2	8	no	—
344	#121	—	2	8	no	—
345	#121	—	2	4	no	—
346	#121	—	2	4	no	—
347	C₄×D₄	—	2	8	no	—
348	C₄×D₄	—	2	4	no	—
349	C₄×D₄	D₄×C₄₃	1	8	yes	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
366	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
369	#107	—	2	4	no	—
370	#106	—	2	4	no	—
371	C₄⋊C₈	—	2	4	no	—
372	#102	—	2	4	no	—
373	#102	—	2	4	no	—
374	#102	—	4	2	no	—
375	#102	—	4	2	no	—
376	C₂²⋊C₈	—	4	2	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	C₂⁴	—	2	2	no	—
384	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
385	#41	—	4	32	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	4	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	2	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	2	no	—
398	C₂×D₄	—	4	2	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	4	1	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	4	2	no	—
443	C₄⋊C₄	—	4	2	no	—
444	C₄⋊C₄	—	4	2	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	4	2	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	C₂×D₄×C₄₃	1	4	yes	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	4	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
469	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
470	Q₈	—	4	8	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	16	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	8	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	16	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	#120×C₄₃	1	2	yes	—
510	C₂×C₄	#120×C₄₃	1	2	yes	—
511	C₂×C₄	#135×C₄₃	1	2	yes	—
512	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
513	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
514	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
515	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
516	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
517	C₈	—	4	2	no	—
518	C₈	—	4	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	1	no	—
525	C₂²	—	4	1	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
534	C₂²	C₄₃×#536	1	1	yes	characteristic
535	C₂²	C₄₃×#537	1	1	yes	characteristic
536	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
537	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
538	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
539	C₂²	C₄₃×#575	1	1	yes	characteristic
540	C₄	—	2	2	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	2	2	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	4	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	C₄₃×#536	1	2	yes	—
551	C₄	C₄₃×#537	1	2	yes	—
552	C₂	—	4	2	no	—
553	C₂	—	8	4	no	—
554	C₂	C₄₃×#2616	1	1	yes	characteristic
555	C₂	C₄₃×#3002	1	1	yes	characteristic
556	C₂	C₄₃×#3003	1	1	yes	characteristic
557	C₂	C₄₃×#3228	1	1	yes	characteristic
558	C₂	C₄₃×#3234	1	1	yes	characteristic
559	C₂	C₄₃×#3247	1	1	yes	characteristic
560	C₂	C₄₃×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#532	C₂
LCS	G ▷ C₂²×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×#478	C₂	semidirect
3. C₄₃×#2851	C₂	semidirect
4. C₄₃×#2058	C₂	semidirect
5. C₄₃×#2057	C₂	semidirect
6. C₄₃×#2041	C₂	semidirect
7. C₄₃×#2041	C₂	semidirect
8. C₄₃×#2034	C₂	semidirect
9. C₄₃×#2033	C₂	semidirect
10. C₄₃×#1804	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
238. #29694	C₄₃	direct (N × H)
273. C₂×#478	C₂×C₄₃	semidirect
274. #2851	C₂×C₄₃	semidirect
275. #2058	C₂×C₄₃	semidirect
276. #2057	C₂×C₄₃	semidirect
277. #2041	C₂×C₄₃	semidirect
278. #2041	C₂×C₄₃	semidirect
279. #2034	C₂×C₄₃	semidirect
280. #2033	C₂×C₄₃	semidirect
281. #1804	C₂×C₄₃	semidirect
282. #1797	C₂×C₄₃	semidirect
325. C₄₃	#29694	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×#532	2
C₂×C₄₃×#478	2
C₄₃×#2851	2
C₄₃×#2058	2
C₄₃×#2057	2
C₄₃×#2041	2
C₄₃×#2034	2
C₄₃×#2033	2
C₄₃×#1804	2
C₄₃×#1797	2
#29694	43

Subgroups — C43×#29694 #24949711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29694 #24949711