Subgroups — C₄₃×#32953 #24952970

Order 11008.

1764 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#474	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1862	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1852	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1802	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1786	C₂	1	2	yes	maximal
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₃	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
13	C₂×C₄×D₄×C₄₃	—	2	8	no	—
14	C₂×C₄×D₄×C₄₃	—	2	1	no	—
15	C₂×C₄×D₄×C₄₃	—	2	1	no	—
16	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊C₄×C₄₃	—	2	1	no	—
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#474	—	2	8	no	—
22	C₂×#107×C₄₃	C₂²	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
24	C₂×#102×C₄₃	C₂²	1	4	yes	—
25	C₂×#102×C₄₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#391	—	2	1	no	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	C₂²	1	2	yes	complemented
30	C₄₃×#384	C₂²	1	1	yes	characteristic, complemented
31	C₄₃×#380	—	2	1	no	—
32	C₄₃×#380	C₂²	1	2	yes	—
33	C₄₃×#340	C₂²	1	4	yes	complemented
34	C₄₃×#336	C₂²	1	2	yes	complemented
35	C₂⁵×C₄₃	—	2	1	no	—
36	C₂²×Q₈×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	—	2	4	no	—
38	C₂²×D₄×C₄₃	—	2	4	no	—
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	—	2	2	no	—
41	C₂²×D₄×C₄₃	Q₈	1	4	yes	complemented
42	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	—	2	8	no	—
44	C₂³×C₄×C₄₃	—	2	1	no	—
45	C₂³×C₄×C₄₃	—	2	2	no	—
46	C₂³×C₄×C₄₃	—	2	2	no	—
47	C₂³×C₄×C₄₃	—	4	4	no	—
48	C₂³×C₄×C₄₃	—	4	4	no	—
49	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
53	C₄⋊Q₈×C₄₃	—	2	4	no	—
54	C₂²⋊Q₈×C₄₃	—	4	4	no	—
55	C₄×D₄×C₄₃	—	2	8	no	—
56	C₄×D₄×C₄₃	—	2	8	no	—
57	C₄×D₄×C₄₃	—	2	4	no	—
58	C₄×D₄×C₄₃	—	2	4	no	—
59	C₄×D₄×C₄₃	—	2	4	no	—
60	C₄×D₄×C₄₃	D₄	1	8	yes	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₄²×C₄₃	—	2	4	no	—
75	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	#107×C₄₃	—	2	8	no	—
80	C₄⋊C₈×C₄₃	—	2	4	no	—
81	#102×C₄₃	—	2	8	no	—
82	#102×C₄₃	—	2	8	no	—
83	C₂²⋊C₈×C₄₃	—	2	4	no	—
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	C₂⁴×C₄₃	—	2	4	no	—
87	C₂⁴×C₄₃	—	2	4	no	—
88	C₂⁴×C₄₃	—	2	4	no	—
89	C₂⁴×C₄₃	—	2	2	no	—
90	C₂⁴×C₄₃	—	4	2	no	—
91	C₂⁴×C₄₃	—	4	2	no	—
92	C₂⁴×C₄₃	—	4	2	no	—
93	C₂⁴×C₄₃	—	4	2	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	—	4	2	no	—
97	C₂×Q₈×C₄₃	—	4	2	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	2	16	no	—
100	C₂×D₄×C₄₃	—	2	4	no	—
101	C₂×D₄×C₄₃	—	2	16	no	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	2	no	—
106	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
107	C₂×D₄×C₄₃	C₂×Q₈	1	4	yes	—
108	C₂×D₄×C₄₃	#41	1	4	yes	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	8	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	8	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	4	1	no	—
122	C₂²×C₄×C₄₃	—	4	2	no	—
123	C₂²×C₄×C₄₃	—	4	32	no	—
124	C₂²×C₄×C₄₃	—	4	4	no	—
125	C₂²×C₄×C₄₃	—	4	4	no	—
126	C₂²×C₄×C₄₃	—	4	4	no	—
127	C₂²×C₄×C₄₃	—	4	4	no	—
128	C₂²×C₄×C₄₃	—	4	2	no	—
129	C₂²×C₄×C₄₃	D₈	1	4	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	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
136	C₂²×C₄×C₄₃	#41	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
138	C₂×C₈×C₄₃	—	2	4	no	—
139	C₂×C₈×C₄₃	—	2	4	no	—
140	C₂×C₈×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	4	no	—
144	C₄⋊C₄×C₄₃	—	2	4	no	—
145	C₄⋊C₄×C₄₃	—	4	2	no	—
146	C₄⋊C₄×C₄₃	—	4	2	no	—
147	C₄⋊C₄×C₄₃	—	4	2	no	—
148	C₄⋊C₄×C₄₃	—	4	4	no	—
149	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
150	C₂²⋊C₄×C₄₃	—	2	8	no	—
151	C₂²⋊C₄×C₄₃	—	2	8	no	—
152	C₂²⋊C₄×C₄₃	—	4	4	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	C₂×D₄	1	4	yes	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	—	2	16	no	—
162	C₂³×C₄₃	—	2	4	no	—
163	C₂³×C₄₃	—	2	4	no	—
164	C₂³×C₄₃	—	2	4	no	—
165	C₂³×C₄₃	—	4	8	no	—
166	C₂³×C₄₃	—	4	8	no	—
167	C₂³×C₄₃	—	4	8	no	—
168	C₂³×C₄₃	—	4	8	no	—
169	C₂³×C₄₃	—	4	8	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	—	4	2	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	—	4	8	no	—
175	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
176	C₂³×C₄₃	C₂×D₈	1	2	yes	—
177	C₂³×C₄₃	#137	1	2	yes	—
178	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₄₃	—	8	4	no	—
180	D₄×C₄₃	—	2	16	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	—	2	4	no	—
183	D₄×C₄₃	—	2	4	no	—
184	D₄×C₄₃	C₂²⋊Q₈	1	8	yes	complemented
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	4	no	—
193	C₂×C₄×C₄₃	—	2	8	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	4	4	no	—
199	C₂×C₄×C₄₃	—	4	16	no	—
200	C₂×C₄×C₄₃	—	4	8	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	16	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	#120	1	2	yes	—
211	C₂×C₄×C₄₃	#120	1	2	yes	—
212	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
213	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
215	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
219	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
220	C₈×C₄₃	—	4	4	no	—
221	#32953	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₃	—	2	2	no	—
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	8	no	—
229	C₂²×C₄₃	—	4	32	no	—
230	C₂²×C₄₃	—	4	4	no	—
231	C₂²×C₄₃	—	4	4	no	—
232	C₂²×C₄₃	—	4	4	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	—	4	4	no	—
235	C₂²×C₄₃	—	4	4	no	—
236	C₂²×C₄₃	#474	1	4	yes	complemented
237	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
238	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
239	C₂²×C₄₃	#525	1	1	yes	characteristic
240	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
241	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂²×C₄₃	C₂×#137	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	—	8	2	no	—
250	C₄×C₄₃	—	8	2	no	—
251	C₄×C₄₃	#447	1	4	yes	—
252	C₄×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
253	C₄×C₄₃	#525	1	2	yes	—
254	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
255	C₂×#474	C₂×C₄₃	1	2	yes	complemented
256	#2857	C₂×C₄₃	1	1	yes	characteristic, complemented
257	#1862	C₂×C₄₃	1	4	yes	complemented
258	#1852	C₂×C₄₃	1	2	yes	complemented
259	#1802	C₂×C₄₃	1	2	yes	complemented
260	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
261	#1786	C₂×C₄₃	1	2	yes	—
262	C₂×C₄₃	—	2	4	no	—
263	C₂×C₄₃	—	4	8	no	—
264	C₂×C₄₃	#2848	1	1	yes	characteristic
265	C₂×C₄₃	C₂×#447	1	1	yes	characteristic
266	C₂×C₄₃	#3007	1	1	yes	characteristic
267	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
268	C₂×C₄₃	#3077	1	1	yes	characteristic
269	C₂×C₄₃	#3100	1	1	yes	characteristic
270	C₂×C₄₃	#3110	1	1	yes	characteristic
271	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
272	C₂⁴×C₄	—	2	1	no	—
273	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
274	C₂×C₂²⋊Q₈	—	2	1	no	—
275	C₂×C₄×D₄	—	2	8	no	—
276	C₂×C₄×D₄	—	2	1	no	—
277	C₂×C₄×D₄	—	2	1	no	—
278	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
279	C₂×C₄×D₄	C₂²×C₄₃	1	2	yes	—
280	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
281	C₂²×C₂²⋊C₄	—	2	1	no	—
282	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
283	#474	—	2	8	no	—
284	C₂×#107	C₂²×C₄₃	1	4	yes	complemented
285	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	complemented
286	C₂×#102	C₂²×C₄₃	1	4	yes	—
287	C₂×#102	C₂²×C₄₃	1	4	yes	—
288	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
289	#391	—	2	1	no	—
290	#389	—	2	1	no	—
291	#389	C₂²×C₄₃	1	2	yes	complemented
292	#384	C₂²×C₄₃	1	1	yes	characteristic, complemented
293	#380	—	2	1	no	—
294	#380	C₂²×C₄₃	1	2	yes	—
295	#340	C₂²×C₄₃	1	4	yes	complemented
296	#336	C₂²×C₄₃	1	2	yes	complemented
297	C₄₃	#32953	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁵	—	2	1	no	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	4	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	Q₈×C₄₃	1	4	yes	complemented
305	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
306	C₂³×C₄	—	2	8	no	—
307	C₂³×C₄	—	2	1	no	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	—	2	2	no	—
310	C₂³×C₄	—	4	4	no	—
311	C₂³×C₄	—	4	4	no	—
312	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
313	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
316	C₄⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	4	4	no	—
318	C₄×D₄	—	2	8	no	—
319	C₄×D₄	—	2	8	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	D₄×C₄₃	1	8	yes	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₄²	—	2	4	no	—
338	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
339	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
342	#107	—	2	8	no	—
343	C₄⋊C₈	—	2	4	no	—
344	#102	—	2	8	no	—
345	#102	—	2	8	no	—
346	C₂²⋊C₈	—	2	4	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	4	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	4	2	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	—	4	2	no	—
356	C₂⁴	—	4	2	no	—
357	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
358	C₂×Q₈	—	4	2	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	16	no	—
364	C₂×D₄	—	2	16	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
370	C₂×D₄	C₂×Q₈×C₄₃	1	4	yes	—
371	C₂×D₄	#41×C₄₃	1	4	yes	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	8	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	32	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	4	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	D₈×C₄₃	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
396	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
398	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
399	C₂²×C₄	#41×C₄₃	1	2	yes	—
400	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
401	C₂×C₈	—	2	4	no	—
402	C₂×C₈	—	2	4	no	—
403	C₂×C₈	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	—	4	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
413	C₂²⋊C₄	—	2	8	no	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	4	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₄²	C₂×D₄×C₄₃	1	4	yes	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	16	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	4	8	no	—
429	C₂³	—	4	8	no	—
430	C₂³	—	4	8	no	—
431	C₂³	—	4	8	no	—
432	C₂³	—	4	8	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	—	4	2	no	—
436	C₂³	—	4	2	no	—
437	C₂³	—	4	8	no	—
438	C₂³	C₂²⋊Q₈×C₄₃	1	2	yes	—
439	C₂³	C₂×D₈×C₄₃	1	2	yes	—
440	C₂³	#137×C₄₃	1	2	yes	—
441	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
442	Q₈	—	8	4	no	—
443	D₄	—	2	16	no	—
444	D₄	—	2	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	C₂²⋊Q₈×C₄₃	1	8	yes	complemented
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	16	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	16	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	#120×C₄₃	1	2	yes	—
474	C₂×C₄	#120×C₄₃	1	2	yes	—
475	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
476	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
477	C₂×C₄	C₂×D₈×C₄₃	1	2	yes	—
478	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
480	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
481	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
482	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
483	C₈	—	4	4	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	8	no	—
491	C₂²	—	4	32	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	4	4	no	—
497	C₂²	—	4	4	no	—
498	C₂²	C₄₃×#474	1	4	yes	complemented
499	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
500	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
501	C₂²	C₄₃×#525	1	1	yes	characteristic
502	C₂²	C₂²×D₈×C₄₃	1	1	yes	characteristic
503	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
504	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
505	C₂²	C₄₃×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	1	no	—
511	C₄	—	8	2	no	—
512	C₄	—	8	2	no	—
513	C₄	C₄₃×#447	1	4	yes	—
514	C₄	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
515	C₄	C₄₃×#525	1	2	yes	—
516	C₂	—	2	4	no	—
517	C₂	—	4	8	no	—
518	C₂	C₄₃×#2848	1	1	yes	characteristic
519	C₂	C₂×C₄₃×#447	1	1	yes	characteristic
520	C₂	C₄₃×#3007	1	1	yes	characteristic
521	C₂	C₂×C₄₃×#474	1	1	yes	characteristic
522	C₂	C₄₃×#3077	1	1	yes	characteristic
523	C₂	C₄₃×#3100	1	1	yes	characteristic
524	C₂	C₄₃×#3110	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂³×D₄×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×#474	C₂	semidirect
3. C₄₃×#2857	C₂	semidirect
4. C₄₃×#1862	C₂	semidirect
5. C₄₃×#1852	C₂	semidirect
6. C₄₃×#1802	C₂	semidirect
7. C₄₃×#1797	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
22. C₂×#107×C₄₃	C₂²	semidirect
23. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
29. C₄₃×#389	C₂²	semidirect
30. C₄₃×#384	C₂²	semidirect
33. C₄₃×#340	C₂²	semidirect
34. C₄₃×#336	C₂²	semidirect
41. C₂²×D₄×C₄₃	Q₈	semidirect
184. D₄×C₄₃	C₂²⋊Q₈	semidirect
221. #32953	C₄₃	direct (N × H)
236. C₂²×C₄₃	#474	semidirect
255. C₂×#474	C₂×C₄₃	semidirect
256. #2857	C₂×C₄₃	semidirect
257. #1862	C₂×C₄₃	semidirect
258. #1852	C₂×C₄₃	semidirect
259. #1802	C₂×C₄₃	semidirect
260. #1797	C₂×C₄₃	semidirect
273. C₂×C₄⋊Q₈	C₂²×C₄₃	semidirect
284. C₂×#107	C₂²×C₄₃	semidirect
285. C₂×C₄⋊C₈	C₂²×C₄₃	semidirect
291. #389	C₂²×C₄₃	semidirect
292. #384	C₂²×C₄₃	semidirect
295. #340	C₂²×C₄₃	semidirect
296. #336	C₂²×C₄₃	semidirect
297. C₄₃	#32953	direct (N × H)
304. C₂²×D₄	Q₈×C₄₃	semidirect
447. D₄	C₂²⋊Q₈×C₄₃	semidirect
498. C₂²	C₄₃×#474	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#474	2
C₄₃×#2857	2
C₄₃×#1862	2
C₄₃×#1852	2
C₄₃×#1802	2
C₄₃×#1797	2
C₄₃×#1786	2
#32953	43

Subgroups — C43×#32953 #24952970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32953 #24952970