Subgroups — C₄₃×#60754 #24980771

Order 11008.

2130 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3202	C₂	1	4	yes	maximal, complemented
4	C₄₃×#3201	C₂	1	8	yes	maximal, complemented
5	C₄₃×#3200	C₂	1	4	yes	maximal, complemented
6	C₄₃×#3095	C₂	1	2	yes	maximal, complemented
7	C₄₃×#3093	C₂	1	2	yes	maximal, complemented
8	C₄₃×#3056	C₂	1	4	yes	maximal, complemented
9	C₄₃×#3007	C₂	1	2	yes	maximal, complemented
10	C₄₃×#3004	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
15	C₂×#137×C₄₃	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	complemented
17	C₄₃×#537	C₂²	1	4	yes	—
18	C₄₃×#536	—	2	2	no	—
19	C₄₃×#536	—	2	2	no	—
20	C₄₃×#536	—	2	1	no	—
21	C₄₃×#536	C₂²	1	4	yes	—
22	C₄₃×#536	C₂²	1	2	yes	—
23	C₄₃×#536	C₂²	1	4	yes	complemented
24	C₄₃×#535	—	2	1	no	—
25	C₄₃×#535	C₂²	1	2	yes	—
26	C₄₃×#534	—	2	1	no	—
27	C₄₃×#534	—	2	1	no	—
28	C₄₃×#532	—	2	2	no	—
29	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
30	C₂×#124×C₄₃	—	2	1	no	—
31	C₄₃×#525	—	2	2	no	—
32	C₄₃×#525	C₂²	1	2	yes	—
33	C₄₃×#525	C₂²	1	2	yes	—
34	C₂×#123×C₄₃	—	2	1	no	—
35	C₂×#123×C₄₃	—	2	1	no	—
36	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
38	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×#485	C₂²	1	8	yes	complemented
41	C₄₃×#485	C₂²	1	8	yes	complemented
42	C₄₃×#484	C₂²	1	4	yes	complemented
43	C₄₃×#483	C₂²	1	4	yes	complemented
44	C₄₃×#482	C₂²	1	8	yes	complemented
45	C₄₃×#470	C₂²	1	8	yes	complemented
46	C₄₃×#468	C₂²	1	8	yes	complemented
47	C₄₃×#467	C₂²	1	8	yes	complemented
48	C₄₃×#465	C₂²	1	8	yes	complemented
49	C₄₃×#452	C₂²	1	8	yes	complemented
50	C₄₃×#451	C₂²	1	8	yes	complemented
51	C₄₃×#451	C₂²	1	4	yes	complemented
52	C₄₃×#450	C₂²	1	4	yes	complemented
53	C₄₃×#448	C₂²	1	8	yes	complemented
54	C₄₃×#428	C₂²	1	4	yes	complemented
55	C₄₃×#419	C₂²	1	4	yes	complemented
56	C₄₃×#417	C₂²	1	4	yes	—
57	C₄₃×#408	C₂²	1	4	yes	—
58	C₄₃×#408	C₂²	1	4	yes	complemented
59	C₄₃×#407	C₂²	1	2	yes	—
60	C₄₃×#407	C₂²	1	2	yes	complemented
61	C₂×#41×C₄₃	—	2	1	no	—
62	C₂×#41×C₄₃	—	2	1	no	—
63	C₂×#41×C₄₃	—	4	4	no	—
64	C₂×#41×C₄₃	—	4	4	no	—
65	C₂×#41×C₄₃	D₄	1	2	yes	—
66	C₂×#41×C₄₃	D₄	1	2	yes	—
67	C₂×#41×C₄₃	C₂³	1	2	yes	—
68	C₂×#41×C₄₃	C₂³	1	2	yes	—
69	C₂×#41×C₄₃	C₂³	1	2	yes	—
70	C₂×#41×C₄₃	C₂³	1	2	yes	—
71	C₂²×Q₈×C₄₃	—	2	1	no	—
72	C₂²×Q₈×C₄₃	—	2	2	no	—
73	C₂²×Q₈×C₄₃	—	4	4	no	—
74	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
76	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
78	C₂²×D₄×C₄₃	—	2	1	no	—
79	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
80	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
81	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₄₃	—	2	1	no	—
84	C₂³×C₄×C₄₃	—	2	1	no	—
85	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	#137×C₄₃	—	4	8	no	—
89	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	—
90	C₂×SD₁₆×C₄₃	C₂³	1	8	yes	—
91	C₂×M₁₆×C₄₃	—	4	4	no	—
92	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
93	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
95	C₄⋊Q₈×C₄₃	—	2	4	no	—
96	C₄⋊Q₈×C₄₃	—	2	4	no	—
97	C₄⋊Q₈×C₄₃	—	2	2	no	—
98	#127×C₄₃	—	2	2	no	—
99	#124×C₄₃	—	2	2	no	—
100	#124×C₄₃	—	2	4	no	—
101	#124×C₄₃	—	2	4	no	—
102	#124×C₄₃	—	2	2	no	—
103	#123×C₄₃	—	2	4	no	—
104	#123×C₄₃	—	2	4	no	—
105	#123×C₄₃	—	2	4	no	—
106	#123×C₄₃	—	2	4	no	—
107	#123×C₄₃	—	2	2	no	—
108	#123×C₄₃	—	2	2	no	—
109	#123×C₄₃	—	2	2	no	—
110	#123×C₄₃	—	2	2	no	—
111	C₂²⋊Q₈×C₄₃	—	2	4	no	—
112	C₂²⋊Q₈×C₄₃	—	2	2	no	—
113	C₂²⋊Q₈×C₄₃	—	2	2	no	—
114	C₂²⋊Q₈×C₄₃	—	2	4	no	—
115	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
116	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
117	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	—
118	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
119	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
120	#121×C₄₃	—	2	4	no	—
121	#121×C₄₃	—	2	4	no	—
122	#121×C₄₃	—	2	4	no	—
123	#121×C₄₃	C₂³	1	4	yes	—
124	#121×C₄₃	C₂³	1	4	yes	—
125	#120×C₄₃	—	2	2	no	—
126	#120×C₄₃	—	2	2	no	—
127	#120×C₄₃	—	2	2	no	—
128	#120×C₄₃	—	2	2	no	—
129	C₄×D₄×C₄₃	—	2	4	no	—
130	C₄×D₄×C₄₃	—	2	4	no	—
131	#117×C₄₃	—	2	1	no	—
132	#117×C₄₃	—	2	1	no	—
133	#117×C₄₃	—	2	2	no	—
134	#117×C₄₃	C₂³	1	2	yes	—
135	#117×C₄₃	C₂³	1	2	yes	—
136	#117×C₄₃	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
138	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂×C₄²×C₄₃	—	2	1	no	—
146	C₂×C₄²×C₄₃	—	2	1	no	—
147	#107×C₄₃	C₂³	1	8	yes	—
148	#106×C₄₃	C₂³	1	8	yes	—
149	#103×C₄₃	C₂³	1	8	yes	—
150	#103×C₄₃	C₂³	1	8	yes	—
151	#103×C₄₃	C₂³	1	8	yes	—
152	#102×C₄₃	C₂³	1	8	yes	—
153	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
154	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
155	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
156	C₂⁴×C₄₃	—	2	1	no	—
157	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
160	#41×C₄₃	—	2	8	no	—
161	#41×C₄₃	—	4	4	no	—
162	#41×C₄₃	—	4	4	no	—
163	#41×C₄₃	—	4	2	no	—
164	#41×C₄₃	—	4	2	no	—
165	#41×C₄₃	—	4	2	no	—
166	#41×C₄₃	—	4	2	no	—
167	#41×C₄₃	—	4	4	no	—
168	#41×C₄₃	—	4	4	no	—
169	#41×C₄₃	—	4	4	no	—
170	C₂×Q₈×C₄₃	—	2	2	no	—
171	C₂×Q₈×C₄₃	—	2	4	no	—
172	C₂×Q₈×C₄₃	—	2	1	no	—
173	C₂×Q₈×C₄₃	—	2	8	no	—
174	C₂×Q₈×C₄₃	—	4	2	no	—
175	C₂×Q₈×C₄₃	—	4	4	no	—
176	C₂×Q₈×C₄₃	—	4	4	no	—
177	C₂×Q₈×C₄₃	—	4	2	no	—
178	C₂×Q₈×C₄₃	—	4	4	no	—
179	C₂×Q₈×C₄₃	—	4	8	no	—
180	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
181	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
182	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
183	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
184	C₂×D₄×C₄₃	—	2	1	no	—
185	C₂×D₄×C₄₃	—	2	2	no	—
186	C₂×D₄×C₄₃	—	2	2	no	—
187	C₂×D₄×C₄₃	—	2	4	no	—
188	C₂×D₄×C₄₃	—	2	4	no	—
189	C₂×D₄×C₄₃	—	4	2	no	—
190	C₂×D₄×C₄₃	—	4	2	no	—
191	C₂×D₄×C₄₃	—	4	2	no	—
192	C₂×D₄×C₄₃	—	4	4	no	—
193	C₂×D₄×C₄₃	—	4	2	no	—
194	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
195	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
196	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
198	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
199	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
200	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
201	C₂²×C₄×C₄₃	—	2	4	no	—
202	C₂²×C₄×C₄₃	—	2	4	no	—
203	C₂²×C₄×C₄₃	—	2	4	no	—
204	C₂²×C₄×C₄₃	—	2	2	no	—
205	C₂²×C₄×C₄₃	—	2	2	no	—
206	C₂²×C₄×C₄₃	—	2	2	no	—
207	C₂²×C₄×C₄₃	—	2	2	no	—
208	C₂²×C₄×C₄₃	—	2	1	no	—
209	C₂²×C₄×C₄₃	—	2	4	no	—
210	C₂²×C₄×C₄₃	—	2	2	no	—
211	C₂²×C₄×C₄₃	—	4	4	no	—
212	C₂²×C₄×C₄₃	—	4	4	no	—
213	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
225	Q₁₆×C₄₃	—	4	8	no	—
226	SD₁₆×C₄₃	—	4	8	no	—
227	M₁₆×C₄₃	—	2	8	no	—
228	M₁₆×C₄₃	—	4	4	no	—
229	C₂×C₈×C₄₃	—	4	4	no	—
230	C₂×C₈×C₄₃	C₂⁴	1	8	yes	—
231	C₄⋊C₄×C₄₃	—	2	4	no	—
232	C₄⋊C₄×C₄₃	—	2	8	no	—
233	C₄⋊C₄×C₄₃	—	2	4	no	—
234	C₄⋊C₄×C₄₃	—	2	2	no	—
235	C₄⋊C₄×C₄₃	—	2	2	no	—
236	C₄⋊C₄×C₄₃	—	2	4	no	—
237	C₄⋊C₄×C₄₃	—	2	4	no	—
238	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
239	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
240	C₂²⋊C₄×C₄₃	—	2	4	no	—
241	C₂²⋊C₄×C₄₃	—	2	4	no	—
242	C₂²⋊C₄×C₄₃	—	2	2	no	—
243	C₂²⋊C₄×C₄₃	—	2	2	no	—
244	C₂²⋊C₄×C₄₃	—	2	4	no	—
245	C₂²⋊C₄×C₄₃	—	2	4	no	—
246	C₂²⋊C₄×C₄₃	—	2	8	no	—
247	C₂²⋊C₄×C₄₃	—	2	4	no	—
248	C₂²⋊C₄×C₄₃	—	2	4	no	—
249	C₂²⋊C₄×C₄₃	—	2	4	no	—
250	C₄²×C₄₃	—	2	2	no	—
251	C₄²×C₄₃	—	2	2	no	—
252	C₄²×C₄₃	—	2	4	no	—
253	C₂³×C₄₃	—	2	2	no	—
254	C₂³×C₄₃	—	2	2	no	—
255	C₂³×C₄₃	—	2	2	no	—
256	C₂³×C₄₃	—	2	2	no	—
257	C₂³×C₄₃	—	4	2	no	—
258	C₂³×C₄₃	—	4	2	no	—
259	C₂³×C₄₃	—	4	2	no	—
260	C₂³×C₄₃	—	4	2	no	—
261	C₂³×C₄₃	—	8	2	no	—
262	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
263	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
264	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
265	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
266	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₄₃	—	2	8	no	—
268	Q₈×C₄₃	—	2	4	no	—
269	Q₈×C₄₃	—	4	2	no	—
270	Q₈×C₄₃	—	4	2	no	—
271	Q₈×C₄₃	—	4	8	no	—
272	Q₈×C₄₃	—	4	2	no	—
273	Q₈×C₄₃	—	4	4	no	—
274	D₄×C₄₃	—	2	4	no	—
275	D₄×C₄₃	—	4	2	no	—
276	D₄×C₄₃	—	4	2	no	—
277	D₄×C₄₃	—	4	2	no	—
278	D₄×C₄₃	—	4	2	no	—
279	D₄×C₄₃	—	4	2	no	—
280	D₄×C₄₃	—	4	2	no	—
281	D₄×C₄₃	—	4	2	no	—
282	D₄×C₄₃	—	4	4	no	—
283	D₄×C₄₃	—	4	4	no	—
284	D₄×C₄₃	—	8	4	no	—
285	D₄×C₄₃	—	8	4	no	—
286	C₂×C₄×C₄₃	—	2	2	no	—
287	C₂×C₄×C₄₃	—	2	2	no	—
288	C₂×C₄×C₄₃	—	2	2	no	—
289	C₂×C₄×C₄₃	—	2	2	no	—
290	C₂×C₄×C₄₃	—	2	4	no	—
291	C₂×C₄×C₄₃	—	2	4	no	—
292	C₂×C₄×C₄₃	—	2	2	no	—
293	C₂×C₄×C₄₃	—	2	2	no	—
294	C₂×C₄×C₄₃	—	2	2	no	—
295	C₂×C₄×C₄₃	—	2	2	no	—
296	C₂×C₄×C₄₃	—	2	2	no	—
297	C₂×C₄×C₄₃	—	2	2	no	—
298	C₂×C₄×C₄₃	—	2	2	no	—
299	C₂×C₄×C₄₃	—	2	4	no	—
300	C₂×C₄×C₄₃	—	2	4	no	—
301	C₂×C₄×C₄₃	—	2	2	no	—
302	C₂×C₄×C₄₃	—	2	4	no	—
303	C₂×C₄×C₄₃	—	4	4	no	—
304	C₂×C₄×C₄₃	—	4	4	no	—
305	C₂×C₄×C₄₃	—	4	2	no	—
306	C₂×C₄×C₄₃	—	4	8	no	—
307	C₂×C₄×C₄₃	—	4	4	no	—
308	C₂×C₄×C₄₃	—	4	4	no	—
309	C₂×C₄×C₄₃	—	8	2	no	—
310	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
312	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
316	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
317	C₈×C₄₃	—	2	8	no	—
318	#60754	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂²×C₄₃	—	2	2	no	—
320	C₂²×C₄₃	—	2	2	no	—
321	C₂²×C₄₃	—	2	2	no	—
322	C₂²×C₄₃	—	2	4	no	—
323	C₂²×C₄₃	—	2	4	no	—
324	C₂²×C₄₃	—	2	1	no	—
325	C₂²×C₄₃	—	2	2	no	—
326	C₂²×C₄₃	—	2	2	no	—
327	C₂²×C₄₃	—	2	1	no	—
328	C₂²×C₄₃	—	4	4	no	—
329	C₂²×C₄₃	—	4	4	no	—
330	C₂²×C₄₃	—	4	2	no	—
331	C₂²×C₄₃	—	8	2	no	—
332	C₂²×C₄₃	—	8	2	no	—
333	C₂²×C₄₃	—	8	4	no	—
334	C₂²×C₄₃	#534	1	2	yes	—
335	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
336	C₄×C₄₃	—	2	1	no	—
337	C₄×C₄₃	—	2	1	no	—
338	C₄×C₄₃	—	2	2	no	—
339	C₄×C₄₃	—	2	2	no	—
340	C₄×C₄₃	—	4	4	no	—
341	C₄×C₄₃	—	4	4	no	—
342	C₄×C₄₃	—	4	2	no	—
343	C₄×C₄₃	—	4	4	no	—
344	C₄×C₄₃	#534	1	2	yes	—
345	C₄×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
346	#3449	C₂×C₄₃	1	1	yes	characteristic
347	C₂×#536	C₂×C₄₃	1	1	yes	characteristic, complemented
348	#3202	C₂×C₄₃	1	4	yes	complemented
349	#3201	C₂×C₄₃	1	8	yes	complemented
350	#3200	C₂×C₄₃	1	4	yes	complemented
351	#3095	C₂×C₄₃	1	2	yes	complemented
352	#3093	C₂×C₄₃	1	2	yes	complemented
353	#3056	C₂×C₄₃	1	4	yes	complemented
354	#3007	C₂×C₄₃	1	2	yes	complemented
355	#3004	C₂×C₄₃	1	2	yes	complemented
356	#2879	C₂×C₄₃	1	1	yes	characteristic, complemented
357	C₂×C₄₃	—	2	2	no	—
358	C₂×C₄₃	—	4	2	no	—
359	C₂×C₄₃	—	4	1	no	—
360	C₂×C₄₃	—	4	2	no	—
361	C₂×C₄₃	—	4	1	no	—
362	C₂×C₄₃	—	8	2	no	—
363	C₂×C₄₃	C₂×#534	1	1	yes	characteristic
364	C₂×C₄₃	#3586	1	2	yes	—
365	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
366	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
367	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic, complemented
368	C₂×#137	C₂²×C₄₃	1	4	yes	—
369	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	complemented
370	#537	C₂²×C₄₃	1	4	yes	—
371	#536	—	2	2	no	—
372	#536	—	2	2	no	—
373	#536	—	2	1	no	—
374	#536	C₂²×C₄₃	1	4	yes	—
375	#536	C₂²×C₄₃	1	2	yes	—
376	#536	C₂²×C₄₃	1	4	yes	complemented
377	#535	—	2	1	no	—
378	#535	C₂²×C₄₃	1	2	yes	—
379	#534	—	2	1	no	—
380	#534	—	2	1	no	—
381	#532	—	2	2	no	—
382	C₂×C₄⋊Q₈	—	2	1	no	—
383	C₂×#124	—	2	1	no	—
384	#525	—	2	2	no	—
385	#525	C₂²×C₄₃	1	2	yes	—
386	#525	C₂²×C₄₃	1	2	yes	—
387	C₂×#123	—	2	1	no	—
388	C₂×#123	—	2	1	no	—
389	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
390	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	complemented
391	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
392	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic, complemented
393	#485	C₂²×C₄₃	1	8	yes	complemented
394	#485	C₂²×C₄₃	1	8	yes	complemented
395	#484	C₂²×C₄₃	1	4	yes	complemented
396	#483	C₂²×C₄₃	1	4	yes	complemented
397	#482	C₂²×C₄₃	1	8	yes	complemented
398	#470	C₂²×C₄₃	1	8	yes	complemented
399	#468	C₂²×C₄₃	1	8	yes	complemented
400	#467	C₂²×C₄₃	1	8	yes	complemented
401	#465	C₂²×C₄₃	1	8	yes	complemented
402	#452	C₂²×C₄₃	1	8	yes	complemented
403	#451	C₂²×C₄₃	1	8	yes	complemented
404	#451	C₂²×C₄₃	1	4	yes	complemented
405	#450	C₂²×C₄₃	1	4	yes	complemented
406	#448	C₂²×C₄₃	1	8	yes	complemented
407	#428	C₂²×C₄₃	1	4	yes	complemented
408	#419	C₂²×C₄₃	1	4	yes	complemented
409	#417	C₂²×C₄₃	1	4	yes	—
410	#408	C₂²×C₄₃	1	4	yes	—
411	#408	C₂²×C₄₃	1	4	yes	complemented
412	#407	C₂²×C₄₃	1	2	yes	—
413	#407	C₂²×C₄₃	1	2	yes	complemented
414	C₄₃	#60754	1	1	yes	characteristic, direct product factor, Sylow
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	1	no	—
417	C₂×#41	—	4	4	no	—
418	C₂×#41	—	4	4	no	—
419	C₂×#41	D₄×C₄₃	1	2	yes	—
420	C₂×#41	D₄×C₄₃	1	2	yes	—
421	C₂×#41	C₂³×C₄₃	1	2	yes	—
422	C₂×#41	C₂³×C₄₃	1	2	yes	—
423	C₂×#41	C₂³×C₄₃	1	2	yes	—
424	C₂×#41	C₂³×C₄₃	1	2	yes	—
425	C₂²×Q₈	—	2	1	no	—
426	C₂²×Q₈	—	2	2	no	—
427	C₂²×Q₈	—	4	4	no	—
428	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
429	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
430	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
431	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
432	C₂²×D₄	—	2	1	no	—
433	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
434	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
435	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
436	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
437	C₂³×C₄	—	2	1	no	—
438	C₂³×C₄	—	2	1	no	—
439	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
440	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
441	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
442	#137	—	4	8	no	—
443	C₂×Q₁₆	C₂³×C₄₃	1	8	yes	—
444	C₂×SD₁₆	C₂³×C₄₃	1	8	yes	—
445	C₂×M₁₆	—	4	4	no	—
446	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
447	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
448	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
449	C₄⋊Q₈	—	2	4	no	—
450	C₄⋊Q₈	—	2	4	no	—
451	C₄⋊Q₈	—	2	2	no	—
452	#127	—	2	2	no	—
453	#124	—	2	2	no	—
454	#124	—	2	4	no	—
455	#124	—	2	4	no	—
456	#124	—	2	2	no	—
457	#123	—	2	4	no	—
458	#123	—	2	4	no	—
459	#123	—	2	4	no	—
460	#123	—	2	4	no	—
461	#123	—	2	2	no	—
462	#123	—	2	2	no	—
463	#123	—	2	2	no	—
464	#123	—	2	2	no	—
465	C₂²⋊Q₈	—	2	4	no	—
466	C₂²⋊Q₈	—	2	2	no	—
467	C₂²⋊Q₈	—	2	2	no	—
468	C₂²⋊Q₈	—	2	4	no	—
469	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
470	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
471	C₂²⋊Q₈	C₂³×C₄₃	1	8	yes	—
472	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
473	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
474	#121	—	2	4	no	—
475	#121	—	2	4	no	—
476	#121	—	2	4	no	—
477	#121	C₂³×C₄₃	1	4	yes	—
478	#121	C₂³×C₄₃	1	4	yes	—
479	#120	—	2	2	no	—
480	#120	—	2	2	no	—
481	#120	—	2	2	no	—
482	#120	—	2	2	no	—
483	C₄×D₄	—	2	4	no	—
484	C₄×D₄	—	2	4	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	2	no	—
488	#117	C₂³×C₄₃	1	2	yes	—
489	#117	C₂³×C₄₃	1	2	yes	—
490	#117	C₂³×C₄₃	1	4	yes	—
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	2	no	—
493	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
495	C₂×C₂²⋊C₄	—	2	1	no	—
496	C₂×C₂²⋊C₄	—	2	1	no	—
497	C₂×C₂²⋊C₄	—	2	2	no	—
498	C₂×C₂²⋊C₄	—	2	2	no	—
499	C₂×C₄²	—	2	1	no	—
500	C₂×C₄²	—	2	1	no	—
501	#107	C₂³×C₄₃	1	8	yes	—
502	#106	C₂³×C₄₃	1	8	yes	—
503	#103	C₂³×C₄₃	1	8	yes	—
504	#103	C₂³×C₄₃	1	8	yes	—
505	#103	C₂³×C₄₃	1	8	yes	—
506	#102	C₂³×C₄₃	1	8	yes	—
507	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
508	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
509	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
510	C₂⁴	—	2	1	no	—
511	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
512	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
513	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
514	#41	—	2	8	no	—
515	#41	—	4	2	no	—
516	#41	—	4	2	no	—
517	#41	—	4	2	no	—
518	#41	—	4	2	no	—
519	#41	—	4	4	no	—
520	#41	—	4	4	no	—
521	#41	—	4	4	no	—
522	#41	—	4	4	no	—
523	#41	—	4	4	no	—
524	C₂×Q₈	—	2	2	no	—
525	C₂×Q₈	—	2	4	no	—
526	C₂×Q₈	—	2	1	no	—
527	C₂×Q₈	—	2	8	no	—
528	C₂×Q₈	—	4	2	no	—
529	C₂×Q₈	—	4	4	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	2	no	—
532	C₂×Q₈	—	4	4	no	—
533	C₂×Q₈	—	4	8	no	—
534	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
535	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
536	C₂×Q₈	C₂⁴×C₄₃	1	4	yes	—
537	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	—	4	2	no	—
544	C₂×D₄	—	4	2	no	—
545	C₂×D₄	—	4	2	no	—
546	C₂×D₄	—	4	2	no	—
547	C₂×D₄	—	4	4	no	—
548	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
549	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
550	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
551	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
552	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
553	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
554	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	1	no	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	4	4	no	—
566	C₂²×C₄	—	4	4	no	—
567	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
568	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
569	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
570	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
572	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
573	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
577	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
579	Q₁₆	—	4	8	no	—
580	SD₁₆	—	4	8	no	—
581	M₁₆	—	2	8	no	—
582	M₁₆	—	4	4	no	—
583	C₂×C₈	—	4	4	no	—
584	C₂×C₈	C₂⁴×C₄₃	1	8	yes	—
585	C₄⋊C₄	—	2	4	no	—
586	C₄⋊C₄	—	2	8	no	—
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
593	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
594	C₂²⋊C₄	—	2	2	no	—
595	C₂²⋊C₄	—	2	2	no	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	4	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	4	no	—
600	C₂²⋊C₄	—	2	4	no	—
601	C₂²⋊C₄	—	2	4	no	—
602	C₂²⋊C₄	—	2	4	no	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	2	no	—
606	C₄²	—	2	4	no	—
607	C₂³	—	2	2	no	—
608	C₂³	—	2	2	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	2	no	—
611	C₂³	—	4	2	no	—
612	C₂³	—	4	2	no	—
613	C₂³	—	4	2	no	—
614	C₂³	—	4	2	no	—
615	C₂³	—	8	2	no	—
616	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
617	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
618	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
619	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
620	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
621	Q₈	—	2	8	no	—
622	Q₈	—	2	4	no	—
623	Q₈	—	4	2	no	—
624	Q₈	—	4	2	no	—
625	Q₈	—	4	8	no	—
626	Q₈	—	4	2	no	—
627	Q₈	—	4	4	no	—
628	D₄	—	2	4	no	—
629	D₄	—	4	2	no	—
630	D₄	—	4	2	no	—
631	D₄	—	4	2	no	—
632	D₄	—	4	2	no	—
633	D₄	—	4	2	no	—
634	D₄	—	4	2	no	—
635	D₄	—	4	2	no	—
636	D₄	—	4	4	no	—
637	D₄	—	4	4	no	—
638	D₄	—	8	4	no	—
639	D₄	—	8	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	2	2	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	4	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	4	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	4	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	2	no	—
659	C₂×C₄	—	4	8	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	4	4	no	—
662	C₂×C₄	—	4	4	no	—
663	C₂×C₄	—	8	2	no	—
664	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
665	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
667	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
669	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
670	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
671	C₈	—	2	8	no	—
672	C₂²	—	2	2	no	—
673	C₂²	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	2	no	—
677	C₂²	—	2	2	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	4	no	—
680	C₂²	—	2	2	no	—
681	C₂²	—	4	4	no	—
682	C₂²	—	4	2	no	—
683	C₂²	—	4	4	no	—
684	C₂²	—	8	2	no	—
685	C₂²	—	8	2	no	—
686	C₂²	—	8	4	no	—
687	C₂²	C₄₃×#534	1	2	yes	—
688	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	2	no	—
692	C₄	—	2	2	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	4	no	—
695	C₄	—	4	4	no	—
696	C₄	—	4	4	no	—
697	C₄	C₄₃×#534	1	2	yes	—
698	C₄	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
699	C₂	—	2	2	no	—
700	C₂	—	4	2	no	—
701	C₂	—	4	1	no	—
702	C₂	—	4	1	no	—
703	C₂	—	4	2	no	—
704	C₂	—	8	2	no	—
705	C₂	C₂×C₄₃×#534	1	1	yes	characteristic
706	C₂	C₄₃×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
prime radical	C₄₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#536	C₂	semidirect
3. C₄₃×#3202	C₂	semidirect
4. C₄₃×#3201	C₂	semidirect
5. C₄₃×#3200	C₂	semidirect
6. C₄₃×#3095	C₂	semidirect
7. C₄₃×#3093	C₂	semidirect
8. C₄₃×#3056	C₂	semidirect
9. C₄₃×#3007	C₂	semidirect
10. C₄₃×#3004	C₂	semidirect
11. C₄₃×#2879	C₂	semidirect
14. C₂³×Q₈×C₄₃	C₂²	semidirect
16. C₂²×M₁₆×C₄₃	C₂²	semidirect
23. C₄₃×#536	C₂²	semidirect
37. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
39. C₂×#117×C₄₃	C₂²	semidirect
40. C₄₃×#485	C₂²	semidirect
41. C₄₃×#485	C₂²	semidirect
42. C₄₃×#484	C₂²	semidirect
43. C₄₃×#483	C₂²	semidirect
44. C₄₃×#482	C₂²	semidirect
45. C₄₃×#470	C₂²	semidirect
46. C₄₃×#468	C₂²	semidirect
47. C₄₃×#467	C₂²	semidirect
48. C₄₃×#465	C₂²	semidirect
49. C₄₃×#452	C₂²	semidirect
50. C₄₃×#451	C₂²	semidirect
51. C₄₃×#451	C₂²	semidirect
52. C₄₃×#450	C₂²	semidirect
53. C₄₃×#448	C₂²	semidirect
54. C₄₃×#428	C₂²	semidirect
55. C₄₃×#419	C₂²	semidirect
58. C₄₃×#408	C₂²	semidirect
60. C₄₃×#407	C₂²	semidirect
318. #60754	C₄₃	direct (N × H)
347. C₂×#536	C₂×C₄₃	semidirect
348. #3202	C₂×C₄₃	semidirect
349. #3201	C₂×C₄₃	semidirect
350. #3200	C₂×C₄₃	semidirect
351. #3095	C₂×C₄₃	semidirect
352. #3093	C₂×C₄₃	semidirect
353. #3056	C₂×C₄₃	semidirect
354. #3007	C₂×C₄₃	semidirect
355. #3004	C₂×C₄₃	semidirect
356. #2879	C₂×C₄₃	semidirect
367. C₂³×Q₈	C₂²×C₄₃	semidirect
369. C₂²×M₁₆	C₂²×C₄₃	semidirect
376. #536	C₂²×C₄₃	semidirect
390. C₂×C₂²⋊Q₈	C₂²×C₄₃	semidirect
392. C₂×#117	C₂²×C₄₃	semidirect
393. #485	C₂²×C₄₃	semidirect
394. #485	C₂²×C₄₃	semidirect
395. #484	C₂²×C₄₃	semidirect
396. #483	C₂²×C₄₃	semidirect
397. #482	C₂²×C₄₃	semidirect
398. #470	C₂²×C₄₃	semidirect
399. #468	C₂²×C₄₃	semidirect
400. #467	C₂²×C₄₃	semidirect
401. #465	C₂²×C₄₃	semidirect
402. #452	C₂²×C₄₃	semidirect
403. #451	C₂²×C₄₃	semidirect
404. #451	C₂²×C₄₃	semidirect
405. #450	C₂²×C₄₃	semidirect
406. #448	C₂²×C₄₃	semidirect
407. #428	C₂²×C₄₃	semidirect
408. #419	C₂²×C₄₃	semidirect
411. #408	C₂²×C₄₃	semidirect
413. #407	C₂²×C₄₃	semidirect
414. C₄₃	#60754	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3449	2
C₂×C₄₃×#536	2
C₄₃×#3202	2
C₄₃×#3201	2
C₄₃×#3200	2
C₄₃×#3095	2
C₄₃×#3093	2
C₄₃×#3056	2
C₄₃×#3007	2
C₄₃×#3004	2
C₄₃×#2879	2
#60754	43

Subgroups — C43×#60754 #24980771

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#60754 #24980771