Subgroups — C₄₃×#29234 #24949251

Order 11008.

926 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2086	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2067	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1918	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1874	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1874	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₃	—	2	1	no	—
14	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₃	C₂²	1	2	yes	—
20	C₂×#107×C₄₃	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#390	C₂²	1	1	yes	characteristic
27	C₄₃×#389	—	2	1	no	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	C₂²	1	2	yes	—
30	C₄₃×#389	C₂²	1	1	yes	characteristic
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#388	—	2	1	no	—
33	C₄₃×#386	—	2	1	no	—
34	C₄₃×#380	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
37	C₂×#95×C₄₃	—	2	1	no	—
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	2	yes	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₃	—	2	1	no	—
44	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	—	2	1	no	—
46	C₂³×C₄×C₄₃	—	2	1	no	—
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
53	#121×C₄₃	—	2	2	no	—
54	#121×C₄₃	Q₈	1	4	yes	—
55	C₄×D₄×C₄₃	—	4	2	no	—
56	C₄×D₄×C₄₃	—	4	4	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
64	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	—	4	2	no	—
77	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#107×C₄₃	—	2	4	no	—
82	#107×C₄₃	—	4	2	no	—
83	C₄⋊C₈×C₄₃	—	4	2	no	—
84	#102×C₄₃	—	2	4	no	—
85	#102×C₄₃	—	4	2	no	—
86	C₂²⋊C₈×C₄₃	—	2	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	1	no	—
91	#95×C₄₃	—	2	1	no	—
92	#95×C₄₃	—	2	1	no	—
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₄₃	—	2	1	no	—
96	C₂×D₄×C₄₃	—	2	4	no	—
97	C₂×D₄×C₄₃	—	2	2	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	—	4	2	no	—
100	C₂×D₄×C₄₃	—	4	2	no	—
101	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	4	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	4	1	no	—
112	C₂²×C₄×C₄₃	—	4	1	no	—
113	C₂²×C₄×C₄₃	—	4	1	no	—
114	C₂²×C₄×C₄₃	—	4	1	no	—
115	C₂²×C₄×C₄₃	—	4	2	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	—	4	2	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	—	4	2	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	D₈	1	4	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₄₃	#41	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	2	no	—
137	C₂×C₈×C₄₃	—	2	2	no	—
138	C₄⋊C₄×C₄₃	—	2	4	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	2	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	4	4	no	—
147	C₄⋊C₄×C₄₃	—	4	4	no	—
148	C₄⋊C₄×C₄₃	—	4	2	no	—
149	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
150	C₄⋊C₄×C₄₃	#41	1	4	yes	—
151	C₂²⋊C₄×C₄₃	—	2	4	no	—
152	C₂²⋊C₄×C₄₃	—	4	2	no	—
153	C₂²⋊C₄×C₄₃	—	4	2	no	—
154	C₂²⋊C₄×C₄₃	—	4	2	no	—
155	C₂²⋊C₄×C₄₃	—	4	2	no	—
156	C₄²×C₄₃	—	2	2	no	—
157	C₄²×C₄₃	—	2	2	no	—
158	C₄²×C₄₃	—	4	1	no	—
159	C₄²×C₄₃	—	4	1	no	—
160	C₄²×C₄₃	—	4	2	no	—
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	—	2	1	no	—
163	C₂³×C₄₃	—	2	1	no	—
164	C₂³×C₄₃	—	2	1	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	—	4	1	no	—
170	C₂³×C₄₃	—	4	1	no	—
171	C₂³×C₄₃	—	4	1	no	—
172	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
173	C₂³×C₄₃	C₂×D₈	1	2	yes	—
174	C₂³×C₄₃	#137	1	2	yes	—
175	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	D₄×C₄₃	—	2	4	no	—
177	D₄×C₄₃	—	4	8	no	—
178	D₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	1	no	—
183	C₂×C₄×C₄₃	—	2	1	no	—
184	C₂×C₄×C₄₃	—	2	1	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	1	no	—
193	C₂×C₄×C₄₃	—	2	1	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	4	4	no	—
196	C₂×C₄×C₄₃	—	4	8	no	—
197	C₂×C₄×C₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	4	1	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	1	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	8	4	no	—
212	C₂×C₄×C₄₃	—	8	4	no	—
213	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
214	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
216	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
219	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
220	C₈×C₄₃	—	4	2	no	—
221	C₈×C₄₃	—	4	2	no	—
222	#29234	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂²×C₄₃	—	2	2	no	—
224	C₂²×C₄₃	—	2	2	no	—
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	2	no	—
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	—	2	2	no	—
229	C₂²×C₄₃	—	4	2	no	—
230	C₂²×C₄₃	—	4	2	no	—
231	C₂²×C₄₃	—	4	2	no	—
232	C₂²×C₄₃	—	8	1	no	—
233	C₂²×C₄₃	—	8	1	no	—
234	C₂²×C₄₃	—	8	1	no	—
235	C₂²×C₄₃	—	8	1	no	—
236	C₂²×C₄₃	#474	1	4	yes	—
237	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
238	C₂²×C₄₃	#525	1	1	yes	characteristic
239	C₂²×C₄₃	#534	1	1	yes	characteristic
240	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
241	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
242	C₂²×C₄₃	#575	1	1	yes	characteristic
243	C₂²×C₄₃	#575	1	1	yes	characteristic
244	C₄×C₄₃	—	2	2	no	—
245	C₄×C₄₃	—	2	2	no	—
246	C₄×C₄₃	—	2	2	no	—
247	C₄×C₄₃	—	4	4	no	—
248	C₄×C₄₃	—	4	1	no	—
249	C₄×C₄₃	—	4	1	no	—
250	C₄×C₄₃	—	4	2	no	—
251	C₄×C₄₃	—	8	1	no	—
252	C₄×C₄₃	—	8	1	no	—
253	C₄×C₄₃	—	8	2	no	—
254	C₄×C₄₃	#553	1	2	yes	—
255	C₄×C₄₃	#554	1	2	yes	—
256	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
257	C₂×#389	C₂×C₄₃	1	1	yes	characteristic, complemented
258	#2086	C₂×C₄₃	1	2	yes	complemented
259	#2067	C₂×C₄₃	1	2	yes	complemented
260	#1918	C₂×C₄₃	1	2	yes	complemented
261	#1874	C₂×C₄₃	1	1	yes	characteristic
262	#1874	C₂×C₄₃	1	1	yes	characteristic
263	#1862	C₂×C₄₃	1	2	yes	complemented
264	#1852	C₂×C₄₃	1	1	yes	characteristic, complemented
265	#1852	C₂×C₄₃	1	1	yes	characteristic, complemented
266	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
267	C₂×C₄₃	—	2	4	no	—
268	C₂×C₄₃	—	8	2	no	—
269	C₂×C₄₃	#2579	1	1	yes	characteristic
270	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
271	C₂×C₄₃	#3080	1	1	yes	characteristic
272	C₂×C₄₃	#3100	1	1	yes	characteristic
273	C₂×C₄₃	#3117	1	1	yes	characteristic
274	C₂×C₄₃	#3186	1	1	yes	characteristic
275	C₂×C₄₃	#3196	1	1	yes	characteristic
276	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
279	C₂²×C₄⋊C₄	—	2	1	no	—
280	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
282	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×#107	C₂²×C₄₃	1	2	yes	—
284	C₂×#107	C₂²×C₄₃	1	2	yes	—
285	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
286	C₂×#102	C₂²×C₄₃	1	2	yes	—
287	C₂×#102	C₂²×C₄₃	1	2	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
290	#390	C₂²×C₄₃	1	1	yes	characteristic
291	#389	—	2	1	no	—
292	#389	—	2	1	no	—
293	#389	C₂²×C₄₃	1	2	yes	—
294	#389	C₂²×C₄₃	1	1	yes	characteristic
295	#389	C₂²×C₄₃	1	2	yes	—
296	#388	—	2	1	no	—
297	#386	—	2	1	no	—
298	#380	C₂²×C₄₃	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
300	C₄×C₂²⋊C₄	—	2	1	no	—
301	C₂×#95	—	2	1	no	—
302	#340	C₂²×C₄₃	1	2	yes	—
303	#340	C₂²×C₄₃	1	2	yes	—
304	#340	C₂²×C₄₃	1	2	yes	—
305	#340	C₂²×C₄₃	1	2	yes	—
306	#336	C₂²×C₄₃	1	2	yes	—
307	C₄₃	#29234	1	1	yes	characteristic, direct product factor, Sylow
308	C₂²×D₄	—	2	1	no	—
309	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	—	2	1	no	—
313	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
317	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
318	#121	—	2	2	no	—
319	#121	Q₈×C₄₃	1	4	yes	—
320	C₄×D₄	—	4	2	no	—
321	C₄×D₄	—	4	4	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	2	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	4	2	no	—
329	C₂×C₄⋊C₄	—	4	4	no	—
330	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
334	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₄²	—	2	1	no	—
341	C₂×C₄²	—	4	2	no	—
342	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
343	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
345	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
346	#107	—	2	4	no	—
347	#107	—	4	2	no	—
348	C₄⋊C₈	—	4	2	no	—
349	#102	—	2	4	no	—
350	#102	—	4	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	C₂²⋊C₈	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	1	no	—
356	#95	—	2	1	no	—
357	#95	—	2	1	no	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	C₂×Q₈×C₄₃	1	2	yes	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	4	2	no	—
382	C₂²×C₄	—	4	2	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	D₈×C₄₃	1	4	yes	—
389	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
395	C₂²×C₄	#41×C₄₃	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
415	C₄⋊C₄	#41×C₄₃	1	4	yes	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	—	4	2	no	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
438	C₂³	C₂×D₈×C₄₃	1	2	yes	—
439	C₂³	#137×C₄₃	1	2	yes	—
440	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
441	D₄	—	2	4	no	—
442	D₄	—	4	8	no	—
443	D₄	—	4	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	4	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	8	4	no	—
477	C₂×C₄	—	8	4	no	—
478	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
479	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
480	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
481	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
482	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
484	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	—	8	1	no	—
500	C₂²	C₄₃×#474	1	4	yes	—
501	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
502	C₂²	C₄₃×#525	1	1	yes	characteristic
503	C₂²	C₄₃×#534	1	1	yes	characteristic
504	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
505	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
506	C₂²	C₄₃×#575	1	1	yes	characteristic
507	C₂²	C₄₃×#575	1	1	yes	characteristic
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	1	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	2	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	C₄₃×#553	1	2	yes	—
519	C₄	C₄₃×#554	1	2	yes	—
520	C₂	—	2	4	no	—
521	C₂	—	8	2	no	—
522	C₂	C₄₃×#2579	1	1	yes	characteristic
523	C₂	C₂×C₄₃×#474	1	1	yes	characteristic
524	C₂	C₄₃×#3080	1	1	yes	characteristic
525	C₂	C₄₃×#3100	1	1	yes	characteristic
526	C₂	C₄₃×#3117	1	1	yes	characteristic
527	C₂	C₄₃×#3186	1	1	yes	characteristic
528	C₂	C₄₃×#3196	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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×#389	C₂	semidirect
3. C₄₃×#2086	C₂	semidirect
4. C₄₃×#2067	C₂	semidirect
5. C₄₃×#1918	C₂	semidirect
8. C₄₃×#1862	C₂	semidirect
9. C₄₃×#1852	C₂	semidirect
10. C₄₃×#1852	C₂	semidirect
11. C₄₃×#1797	C₂	semidirect
222. #29234	C₄₃	direct (N × H)
257. C₂×#389	C₂×C₄₃	semidirect
258. #2086	C₂×C₄₃	semidirect
259. #2067	C₂×C₄₃	semidirect
260. #1918	C₂×C₄₃	semidirect
263. #1862	C₂×C₄₃	semidirect
264. #1852	C₂×C₄₃	semidirect
265. #1852	C₂×C₄₃	semidirect
266. #1797	C₂×C₄₃	semidirect
307. C₄₃	#29234	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#121×C₄₃	2
C₂×C₄₃×#389	2
C₄₃×#2086	2
C₄₃×#2067	2
C₄₃×#1918	2
C₄₃×#1874	2
C₄₃×#1862	2
C₄₃×#1852	2
C₄₃×#1797	2
#29234	43

Subgroups — C43×#29234 #24949251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29234 #24949251