Subgroups — C₄₃×#20903 #24940920

Order 11008.

1782 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#421	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1871	C₂	1	8	yes	maximal, complemented
7	C₄₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#568	—	2	4	no	—
12	C₄₃×#568	—	2	4	no	—
13	C₂×#131×C₄₃	—	2	2	no	—
14	C₂×#131×C₄₃	—	2	2	no	—
15	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₃	C₂²	1	4	yes	complemented
18	C₄₃×#537	C₄	1	4	yes	complemented
19	C₄₃×#536	—	2	1	no	—
20	C₄₃×#536	C₄	1	2	yes	complemented
21	C₄₃×#535	—	2	1	no	—
22	C₄₃×#535	C₄	1	2	yes	complemented
23	C₄₃×#534	—	2	2	no	—
24	C₄₃×#532	—	2	2	no	—
25	C₄₃×#525	—	2	2	no	—
26	C₄₃×#525	C₂²	1	4	yes	—
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#421	—	2	4	no	—
31	C₂×#104×C₄₃	—	2	4	no	—
32	C₂×#104×C₄₃	C₂²	1	4	yes	—
33	C₂×#104×C₄₃	C₂²	1	4	yes	—
34	C₄₃×#391	—	2	1	no	—
35	C₄₃×#390	—	2	1	no	—
36	C₄₃×#386	—	2	2	no	—
37	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	complemented
38	C₄₃×#339	C₂²	1	4	yes	complemented
39	C₄₃×#339	C₂²	1	4	yes	complemented
40	C₂×#41×C₄₃	—	2	2	no	—
41	C₂×#41×C₄₃	—	2	2	no	—
42	C₂×#41×C₄₃	—	2	1	no	—
43	C₂×#41×C₄₃	—	2	1	no	—
44	C₂×#41×C₄₃	—	2	2	no	—
45	C₂×#41×C₄₃	—	2	2	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	2	2	no	—
48	C₂×#41×C₄₃	—	2	2	no	—
49	C₂×#41×C₄₃	—	2	2	no	—
50	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
51	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
52	C₂×#41×C₄₃	C₂×C₄	1	2	yes	—
53	C₂×#41×C₄₃	D₄	1	2	yes	—
54	C₂×#41×C₄₃	D₄	1	2	yes	—
55	C₂×#41×C₄₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₃	—	2	1	no	—
59	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₃	D₄	1	2	yes	—
61	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	—	2	1	no	—
64	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	#131×C₄₃	—	2	16	no	—
67	#131×C₄₃	—	2	16	no	—
68	C₂×M₁₆×C₄₃	—	2	1	no	—
69	C₂×M₁₆×C₄₃	—	2	1	no	—
70	C₂×M₁₆×C₄₃	—	2	2	no	—
71	C₂×M₁₆×C₄₃	—	2	2	no	—
72	C₂×M₁₆×C₄₃	—	2	4	no	—
73	C₂×M₁₆×C₄₃	—	2	8	no	—
74	C₂×M₁₆×C₄₃	—	2	8	no	—
75	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
76	C₂×M₁₆×C₄₃	D₄	1	4	yes	complemented
77	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₄₃	—	2	1	no	—
80	C₂²×C₈×C₄₃	—	2	1	no	—
81	C₂²×C₈×C₄₃	—	2	4	no	—
82	C₄⋊Q₈×C₄₃	—	2	2	no	—
83	#127×C₄₃	—	2	2	no	—
84	#124×C₄₃	—	2	2	no	—
85	#124×C₄₃	—	2	2	no	—
86	#123×C₄₃	—	2	4	no	—
87	#123×C₄₃	—	2	4	no	—
88	C₂²⋊Q₈×C₄₃	—	2	4	no	—
89	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
90	#121×C₄₃	—	2	4	no	—
91	#121×C₄₃	—	2	8	no	—
92	#121×C₄₃	C₂×C₄	1	8	yes	complemented
93	#120×C₄₃	—	2	4	no	—
94	#120×C₄₃	—	2	4	no	—
95	C₄×D₄×C₄₃	—	2	8	no	—
96	#117×C₄₃	—	2	1	no	—
97	#117×C₄₃	—	2	1	no	—
98	#117×C₄₃	—	2	2	no	—
99	#117×C₄₃	—	2	2	no	—
100	#117×C₄₃	C₂×C₄	1	2	yes	—
101	#117×C₄₃	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
104	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
107	C₂×C₄²×C₄₃	—	2	1	no	—
108	C₂×C₄²×C₄₃	—	2	2	no	—
109	C₂×C₄²×C₄₃	—	2	2	no	—
110	C₂×C₄²×C₄₃	—	2	1	no	—
111	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
112	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
113	#104×C₄₃	—	2	8	no	—
114	#104×C₄₃	—	2	8	no	—
115	#95×C₄₃	—	2	4	no	—
116	C₂⁴×C₄₃	—	2	1	no	—
117	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
118	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
119	#41×C₄₃	—	2	4	no	—
120	#41×C₄₃	—	2	4	no	—
121	#41×C₄₃	—	2	4	no	—
122	#41×C₄₃	—	2	4	no	—
123	#41×C₄₃	—	2	4	no	—
124	#41×C₄₃	—	2	4	no	—
125	#41×C₄₃	—	2	4	no	—
126	#41×C₄₃	—	2	4	no	—
127	#41×C₄₃	—	2	4	no	—
128	#41×C₄₃	—	2	4	no	—
129	#41×C₄₃	—	2	2	no	—
130	#41×C₄₃	—	2	2	no	—
131	#41×C₄₃	—	2	2	no	—
132	#41×C₄₃	—	2	2	no	—
133	#41×C₄₃	—	4	2	no	—
134	#41×C₄₃	—	4	2	no	—
135	#41×C₄₃	—	4	2	no	—
136	#41×C₄₃	—	4	2	no	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×Q₈×C₄₃	—	2	2	no	—
139	C₂×Q₈×C₄₃	—	2	2	no	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
143	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
144	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
145	C₂×D₄×C₄₃	—	2	1	no	—
146	C₂×D₄×C₄₃	—	2	2	no	—
147	C₂×D₄×C₄₃	—	2	2	no	—
148	C₂×D₄×C₄₃	—	2	2	no	—
149	C₂×D₄×C₄₃	—	2	8	no	—
150	C₂×D₄×C₄₃	—	2	4	no	—
151	C₂×D₄×C₄₃	—	2	4	no	—
152	C₂×D₄×C₄₃	—	2	2	no	—
153	C₂×D₄×C₄₃	—	2	2	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	4	2	no	—
156	C₂×D₄×C₄₃	—	4	2	no	—
157	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
158	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
159	C₂×D₄×C₄₃	C₂²⋊C₄	1	4	yes	—
160	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
161	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	2	2	no	—
164	C₂²×C₄×C₄₃	—	2	2	no	—
165	C₂²×C₄×C₄₃	—	2	2	no	—
166	C₂²×C₄×C₄₃	—	2	2	no	—
167	C₂²×C₄×C₄₃	—	2	2	no	—
168	C₂²×C₄×C₄₃	—	2	1	no	—
169	C₂²×C₄×C₄₃	—	2	2	no	—
170	C₂²×C₄×C₄₃	—	2	2	no	—
171	C₂²×C₄×C₄₃	—	2	2	no	—
172	C₂²×C₄×C₄₃	—	4	4	no	—
173	C₂²×C₄×C₄₃	—	4	2	no	—
174	C₂²×C₄×C₄₃	—	4	2	no	—
175	C₂²×C₄×C₄₃	—	4	2	no	—
176	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
185	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₃	#41	1	2	yes	—
187	C₂²×C₄×C₄₃	#41	1	2	yes	—
188	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
189	M₁₆×C₄₃	—	2	16	no	—
190	M₁₆×C₄₃	—	2	4	no	—
191	M₁₆×C₄₃	—	2	4	no	—
192	M₁₆×C₄₃	—	2	2	no	—
193	M₁₆×C₄₃	—	2	2	no	—
194	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
195	M₁₆×C₄₃	C₂×D₄	1	4	yes	—
196	C₂×C₈×C₄₃	—	2	16	no	—
197	C₂×C₈×C₄₃	—	2	4	no	—
198	C₂×C₈×C₄₃	—	2	4	no	—
199	C₂×C₈×C₄₃	—	2	2	no	—
200	C₂×C₈×C₄₃	—	2	2	no	—
201	C₄⋊C₄×C₄₃	—	2	2	no	—
202	C₄⋊C₄×C₄₃	—	2	8	no	—
203	C₄⋊C₄×C₄₃	—	4	2	no	—
204	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
205	C₂²⋊C₄×C₄₃	—	2	8	no	—
206	C₂²⋊C₄×C₄₃	—	2	2	no	—
207	C₂²⋊C₄×C₄₃	—	2	8	no	—
208	C₂²⋊C₄×C₄₃	—	2	2	no	—
209	C₂²⋊C₄×C₄₃	—	4	8	no	—
210	C₂²⋊C₄×C₄₃	—	4	2	no	—
211	C₄²×C₄₃	—	2	2	no	—
212	C₄²×C₄₃	—	2	2	no	—
213	C₄²×C₄₃	—	2	2	no	—
214	C₄²×C₄₃	—	2	2	no	—
215	C₄²×C₄₃	—	2	2	no	—
216	C₄²×C₄₃	—	2	2	no	—
217	C₄²×C₄₃	—	4	2	no	—
218	C₂³×C₄₃	—	2	2	no	—
219	C₂³×C₄₃	—	2	2	no	—
220	C₂³×C₄₃	—	2	2	no	—
221	C₂³×C₄₃	—	4	2	no	—
222	C₂³×C₄₃	—	4	4	no	—
223	C₂³×C₄₃	—	4	2	no	—
224	C₂³×C₄₃	—	8	2	no	—
225	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
226	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
227	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂³×C₄₃	#121	1	2	yes	—
229	C₂³×C₄₃	#121	1	2	yes	—
230	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₄₃	—	2	4	no	—
232	Q₈×C₄₃	—	2	4	no	—
233	Q₈×C₄₃	—	2	2	no	—
234	Q₈×C₄₃	—	2	2	no	—
235	Q₈×C₄₃	—	4	2	no	—
236	D₄×C₄₃	—	2	8	no	—
237	D₄×C₄₃	—	2	8	no	—
238	D₄×C₄₃	—	2	2	no	—
239	D₄×C₄₃	—	2	2	no	—
240	D₄×C₄₃	—	2	4	no	—
241	D₄×C₄₃	—	2	4	no	—
242	D₄×C₄₃	—	4	2	no	—
243	D₄×C₄₃	—	4	2	no	—
244	D₄×C₄₃	—	4	4	no	—
245	D₄×C₄₃	—	4	2	no	—
246	D₄×C₄₃	—	8	8	no	—
247	C₂×C₄×C₄₃	—	2	2	no	—
248	C₂×C₄×C₄₃	—	2	2	no	—
249	C₂×C₄×C₄₃	—	2	4	no	—
250	C₂×C₄×C₄₃	—	2	4	no	—
251	C₂×C₄×C₄₃	—	2	4	no	—
252	C₂×C₄×C₄₃	—	2	4	no	—
253	C₂×C₄×C₄₃	—	2	4	no	—
254	C₂×C₄×C₄₃	—	2	4	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	4	2	no	—
257	C₂×C₄×C₄₃	—	4	8	no	—
258	C₂×C₄×C₄₃	—	4	2	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	2	no	—
261	C₂×C₄×C₄₃	—	4	2	no	—
262	C₂×C₄×C₄₃	—	4	4	no	—
263	C₂×C₄×C₄₃	—	4	4	no	—
264	C₂×C₄×C₄₃	—	4	2	no	—
265	C₂×C₄×C₄₃	—	8	2	no	—
266	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
267	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
270	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
272	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₄₃	#120	1	2	yes	—
274	C₂×C₄×C₄₃	#120	1	2	yes	—
275	C₂×C₄×C₄₃	#121	1	2	yes	—
276	C₂×C₄×C₄₃	#121	1	2	yes	—
277	C₂×C₄×C₄₃	#123	1	2	yes	—
278	C₂×C₄×C₄₃	#123	1	2	yes	—
279	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
285	C₈×C₄₃	—	2	4	no	—
286	C₈×C₄₃	—	2	4	no	—
287	#20903	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
288	C₂²×C₄₃	—	2	2	no	—
289	C₂²×C₄₃	—	2	2	no	—
290	C₂²×C₄₃	—	2	2	no	—
291	C₂²×C₄₃	—	2	8	no	—
292	C₂²×C₄₃	—	2	4	no	—
293	C₂²×C₄₃	—	4	2	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	4	4	no	—
296	C₂²×C₄₃	—	4	2	no	—
297	C₂²×C₄₃	—	8	2	no	—
298	C₂²×C₄₃	—	8	2	no	—
299	C₂²×C₄₃	—	8	4	no	—
300	C₂²×C₄₃	#386	1	2	yes	—
301	C₂²×C₄₃	#386	1	2	yes	—
302	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
303	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
304	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
305	C₄×C₄₃	—	2	4	no	—
306	C₄×C₄₃	—	4	4	no	—
307	C₄×C₄₃	—	4	4	no	—
308	C₄×C₄₃	—	4	2	no	—
309	C₄×C₄₃	—	8	2	no	—
310	C₄×C₄₃	#386	1	2	yes	—
311	C₄×C₄₃	#386	1	2	yes	—
312	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
313	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
314	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
315	C₄×C₄₃	C₂×#123	1	1	yes	characteristic
316	C₂×#568	C₂×C₄₃	1	1	yes	characteristic, complemented
317	#3449	C₂×C₄₃	1	1	yes	characteristic
318	C₂×#421	C₂×C₄₃	1	1	yes	characteristic, complemented
319	C₂²×#104	C₂×C₄₃	1	1	yes	characteristic, complemented
320	#2297	C₂×C₄₃	1	1	yes	characteristic, complemented
321	#1871	C₂×C₄₃	1	8	yes	complemented
322	#1733	C₂×C₄₃	1	1	yes	characteristic, complemented
323	C₂×#339	C₂×C₄₃	1	1	yes	characteristic, complemented
324	C₂×C₄₃	—	2	1	no	—
325	C₂×C₄₃	—	2	1	no	—
326	C₂×C₄₃	—	2	2	no	—
327	C₂×C₄₃	—	2	2	no	—
328	C₂×C₄₃	—	4	4	no	—
329	C₂×C₄₃	—	8	2	no	—
330	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
331	C₂×C₄₃	#2901	1	2	yes	—
332	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
333	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
334	#568	—	2	4	no	—
335	#568	—	2	4	no	—
336	C₂×#131	—	2	2	no	—
337	C₂×#131	—	2	2	no	—
338	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
339	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
340	C₂²×M₁₆	C₂²×C₄₃	1	4	yes	complemented
341	#537	C₄×C₄₃	1	4	yes	complemented
342	#536	—	2	1	no	—
343	#536	C₄×C₄₃	1	2	yes	complemented
344	#535	—	2	1	no	—
345	#535	C₄×C₄₃	1	2	yes	complemented
346	#534	—	2	2	no	—
347	#532	—	2	2	no	—
348	#525	—	2	2	no	—
349	#525	C₂²×C₄₃	1	4	yes	—
350	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
351	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
352	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
353	#421	—	2	4	no	—
354	C₂×#104	—	2	4	no	—
355	C₂×#104	C₂²×C₄₃	1	4	yes	—
356	C₂×#104	C₂²×C₄₃	1	4	yes	—
357	#391	—	2	1	no	—
358	#390	—	2	1	no	—
359	#386	—	2	2	no	—
360	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	complemented
361	#339	C₂²×C₄₃	1	4	yes	complemented
362	#339	C₂²×C₄₃	1	4	yes	complemented
363	C₄₃	#20903	1	1	yes	characteristic, direct product factor, Sylow
364	C₂×#41	—	2	2	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	1	no	—
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	2	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	2	no	—
371	C₂×#41	—	2	2	no	—
372	C₂×#41	—	2	2	no	—
373	C₂×#41	—	2	2	no	—
374	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
375	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
376	C₂×#41	C₂×C₄×C₄₃	1	2	yes	—
377	C₂×#41	D₄×C₄₃	1	2	yes	—
378	C₂×#41	D₄×C₄₃	1	2	yes	—
379	C₂×#41	C₂³×C₄₃	1	2	yes	—
380	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
381	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
384	C₂²×D₄	D₄×C₄₃	1	2	yes	—
385	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
389	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
390	#131	—	2	16	no	—
391	#131	—	2	16	no	—
392	C₂×M₁₆	—	2	1	no	—
393	C₂×M₁₆	—	2	1	no	—
394	C₂×M₁₆	—	2	2	no	—
395	C₂×M₁₆	—	2	2	no	—
396	C₂×M₁₆	—	2	4	no	—
397	C₂×M₁₆	—	2	8	no	—
398	C₂×M₁₆	—	2	8	no	—
399	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
400	C₂×M₁₆	D₄×C₄₃	1	4	yes	complemented
401	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
402	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
403	C₂²×C₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	2	4	no	—
406	C₄⋊Q₈	—	2	2	no	—
407	#127	—	2	2	no	—
408	#124	—	2	2	no	—
409	#124	—	2	2	no	—
410	#123	—	2	4	no	—
411	#123	—	2	4	no	—
412	C₂²⋊Q₈	—	2	4	no	—
413	C₂²⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
414	#121	—	2	4	no	—
415	#121	—	2	8	no	—
416	#121	C₂×C₄×C₄₃	1	8	yes	complemented
417	#120	—	2	4	no	—
418	#120	—	2	4	no	—
419	C₄×D₄	—	2	8	no	—
420	#117	—	2	1	no	—
421	#117	—	2	1	no	—
422	#117	—	2	2	no	—
423	#117	—	2	2	no	—
424	#117	C₂×C₄×C₄₃	1	2	yes	—
425	#117	C₂³×C₄₃	1	2	yes	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₂²⋊C₄	—	2	1	no	—
430	C₂×C₂²⋊C₄	—	2	4	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	2	2	no	—
433	C₂×C₄²	—	2	2	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
436	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
437	#104	—	2	8	no	—
438	#104	—	2	8	no	—
439	#95	—	2	4	no	—
440	C₂⁴	—	2	1	no	—
441	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
442	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
443	#41	—	2	4	no	—
444	#41	—	2	4	no	—
445	#41	—	2	4	no	—
446	#41	—	2	4	no	—
447	#41	—	2	4	no	—
448	#41	—	2	4	no	—
449	#41	—	2	4	no	—
450	#41	—	2	4	no	—
451	#41	—	2	4	no	—
452	#41	—	2	4	no	—
453	#41	—	2	2	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	2	no	—
457	#41	—	4	2	no	—
458	#41	—	4	2	no	—
459	#41	—	4	2	no	—
460	#41	—	4	2	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
467	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
468	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
469	C₂×D₄	—	2	4	no	—
470	C₂×D₄	—	2	4	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	4	2	no	—
480	C₂×D₄	—	4	2	no	—
481	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
482	C₂×D₄	C₂²⋊C₄×C₄₃	1	4	yes	—
483	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
484	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
485	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
486	C₂²×C₄	—	2	2	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	2	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	4	4	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
501	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
502	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
504	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
505	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
510	C₂²×C₄	#41×C₄₃	1	2	yes	—
511	C₂²×C₄	#41×C₄₃	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
513	M₁₆	—	2	16	no	—
514	M₁₆	—	2	4	no	—
515	M₁₆	—	2	4	no	—
516	M₁₆	—	2	2	no	—
517	M₁₆	—	2	2	no	—
518	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
519	M₁₆	C₂×D₄×C₄₃	1	4	yes	—
520	C₂×C₈	—	2	16	no	—
521	C₂×C₈	—	2	4	no	—
522	C₂×C₈	—	2	4	no	—
523	C₂×C₈	—	2	2	no	—
524	C₂×C₈	—	2	2	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	4	2	no	—
528	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
529	C₂²⋊C₄	—	2	2	no	—
530	C₂²⋊C₄	—	2	8	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	4	8	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	2	no	—
537	C₄²	—	2	2	no	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	2	no	—
540	C₄²	—	2	2	no	—
541	C₄²	—	4	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	4	4	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	8	2	no	—
549	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
550	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
551	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
552	C₂³	#121×C₄₃	1	2	yes	—
553	C₂³	#121×C₄₃	1	2	yes	—
554	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
555	Q₈	—	2	4	no	—
556	Q₈	—	2	4	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	4	2	no	—
560	D₄	—	2	8	no	—
561	D₄	—	2	8	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	4	no	—
566	D₄	—	4	2	no	—
567	D₄	—	4	2	no	—
568	D₄	—	4	4	no	—
569	D₄	—	4	2	no	—
570	D₄	—	8	8	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	4	8	no	—
582	C₂×C₄	—	4	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	8	2	no	—
590	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
591	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
592	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
593	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
594	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
595	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
596	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
597	C₂×C₄	#120×C₄₃	1	2	yes	—
598	C₂×C₄	#120×C₄₃	1	2	yes	—
599	C₂×C₄	#121×C₄₃	1	2	yes	—
600	C₂×C₄	#121×C₄₃	1	2	yes	—
601	C₂×C₄	#123×C₄₃	1	2	yes	—
602	C₂×C₄	#123×C₄₃	1	2	yes	—
603	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
607	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
609	C₈	—	2	4	no	—
610	C₈	—	2	4	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	4	2	no	—
617	C₂²	—	4	2	no	—
618	C₂²	—	4	4	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	8	2	no	—
621	C₂²	—	8	2	no	—
622	C₂²	—	8	4	no	—
623	C₂²	C₄₃×#386	1	2	yes	—
624	C₂²	C₄₃×#386	1	2	yes	—
625	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
626	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
627	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
628	C₄	—	2	4	no	—
629	C₄	—	4	4	no	—
630	C₄	—	4	4	no	—
631	C₄	—	4	2	no	—
632	C₄	—	8	2	no	—
633	C₄	C₄₃×#386	1	2	yes	—
634	C₄	C₄₃×#386	1	2	yes	—
635	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
636	C₄	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
637	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
638	C₄	C₂×#123×C₄₃	1	1	yes	characteristic
639	C₂	—	2	1	no	—
640	C₂	—	2	1	no	—
641	C₂	—	2	2	no	—
642	C₂	—	2	2	no	—
643	C₂	—	4	4	no	—
644	C₂	—	8	2	no	—
645	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
646	C₂	C₄₃×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₄₃×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#568	C₂	semidirect
3. C₂×C₄₃×#421	C₂	semidirect
4. C₂²×#104×C₄₃	C₂	semidirect
5. C₄₃×#2297	C₂	semidirect
6. C₄₃×#1871	C₂	semidirect
7. C₄₃×#1733	C₂	semidirect
8. C₂×C₄₃×#339	C₂	semidirect
17. C₂²×M₁₆×C₄₃	C₂²	semidirect
18. C₄₃×#537	C₄	semidirect
20. C₄₃×#536	C₄	semidirect
22. C₄₃×#535	C₄	semidirect
37. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
38. C₄₃×#339	C₂²	semidirect
39. C₄₃×#339	C₂²	semidirect
75. C₂×M₁₆×C₄₃	D₄	semidirect
76. C₂×M₁₆×C₄₃	D₄	semidirect
89. C₂²⋊Q₈×C₄₃	C₂×C₄	semidirect
92. #121×C₄₃	C₂×C₄	semidirect
287. #20903	C₄₃	direct (N × H)
316. C₂×#568	C₂×C₄₃	semidirect
318. C₂×#421	C₂×C₄₃	semidirect
319. C₂²×#104	C₂×C₄₃	semidirect
320. #2297	C₂×C₄₃	semidirect
321. #1871	C₂×C₄₃	semidirect
322. #1733	C₂×C₄₃	semidirect
323. C₂×#339	C₂×C₄₃	semidirect
340. C₂²×M₁₆	C₂²×C₄₃	semidirect
341. #537	C₄×C₄₃	semidirect
343. #536	C₄×C₄₃	semidirect
345. #535	C₄×C₄₃	semidirect
360. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
361. #339	C₂²×C₄₃	semidirect
362. #339	C₂²×C₄₃	semidirect
363. C₄₃	#20903	direct (N × H)
399. C₂×M₁₆	D₄×C₄₃	semidirect
400. C₂×M₁₆	D₄×C₄₃	semidirect
413. C₂²⋊Q₈	C₂×C₄×C₄₃	semidirect
416. #121	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×#568	2
C₄₃×#3449	2
C₂×C₄₃×#421	2
C₂²×#104×C₄₃	2
C₄₃×#2297	2
C₄₃×#1871	2
C₄₃×#1733	2
C₂×C₄₃×#339	2
#20903	43

Subgroups — C43×#20903 #24940920

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20903 #24940920