Subgroups — C₄₃×#20955 #24940972

Order 11008.

1710 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#536	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3428	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#419	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#413	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1886	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1885	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1733	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
11	C₄₃×#536	—	2	4	no	—
12	C₄₃×#536	C₄	1	8	yes	complemented
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#124×C₄₃	C₂²	1	2	yes	—
15	C₂×#123×C₄₃	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₄₃	—	2	2	no	—
17	C₄₃×#520	—	2	4	no	—
18	C₄₃×#519	C₂²	1	2	yes	—
19	C₄₃×#518	—	2	2	no	—
20	C₄₃×#518	C₂²	1	2	yes	—
21	C₄×#41×C₄₃	—	2	4	no	—
22	C₂×#117×C₄₃	—	2	2	no	—
23	C₂×#117×C₄₃	C₂²	1	2	yes	—
24	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
25	C₄₃×#419	—	2	4	no	—
26	C₄₃×#419	C₂²	1	8	yes	—
27	C₂×#103×C₄₃	—	2	4	no	—
28	C₄₃×#413	—	2	4	no	—
29	C₂×#101×C₄₃	C₂²	1	2	yes	—
30	C₂×#100×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#339	C₂²	1	8	yes	—
32	C₂×#41×C₄₃	—	2	2	no	—
33	C₂×#41×C₄₃	—	2	2	no	—
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
36	C₂×#41×C₄₃	D₄	1	4	yes	—
37	C₂²×Q₈×C₄₃	—	2	1	no	—
38	C₂²×Q₈×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	—	2	2	no	—
40	C₂²×Q₈×C₄₃	—	2	2	no	—
41	C₂²×Q₈×C₄₃	—	2	4	no	—
42	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	complemented
43	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	D₄	1	2	yes	—
46	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	—	2	1	no	—
48	C₂³×C₄×C₄₃	D₄	1	2	yes	—
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₃	—	2	2	no	—
51	C₂×M₁₆×C₄₃	—	2	4	no	—
52	C₂×M₁₆×C₄₃	—	2	4	no	—
53	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
54	C₂²×C₈×C₄₃	—	2	2	no	—
55	C₄⋊Q₈×C₄₃	—	2	4	no	—
56	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	complemented
57	#124×C₄₃	—	2	4	no	—
58	#124×C₄₃	C₂×C₄	1	8	yes	complemented
59	#123×C₄₃	—	2	16	no	—
60	C₂²⋊Q₈×C₄₃	—	2	16	no	—
61	C₄×Q₈×C₄₃	—	2	8	no	—
62	C₄×D₄×C₄₃	—	2	16	no	—
63	C₄×D₄×C₄₃	—	2	8	no	—
64	#117×C₄₃	—	2	4	no	—
65	#117×C₄₃	—	2	4	no	—
66	#117×C₄₃	—	2	2	no	—
67	#117×C₄₃	—	2	4	no	—
68	#117×C₄₃	—	2	2	no	—
69	#117×C₄₃	—	2	2	no	—
70	#117×C₄₃	C₂×C₄	1	4	yes	complemented
71	#117×C₄₃	D₄	1	4	yes	—
72	#117×C₄₃	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
76	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
81	C₂×C₄²×C₄₃	—	2	4	no	—
82	C₂×C₄²×C₄₃	—	2	2	no	—
83	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
84	#103×C₄₃	—	2	16	no	—
85	#101×C₄₃	—	2	4	no	—
86	#100×C₄₃	—	2	4	no	—
87	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
88	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
89	#41×C₄₃	—	2	8	no	—
90	#41×C₄₃	—	2	8	no	—
91	#41×C₄₃	—	2	8	no	—
92	#41×C₄₃	—	2	8	no	—
93	C₂×Q₈×C₄₃	—	2	4	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	8	no	—
98	C₂×Q₈×C₄₃	—	2	8	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	—	2	4	no	—
101	C₂×Q₈×C₄₃	—	4	1	no	—
102	C₂×Q₈×C₄₃	—	4	1	no	—
103	C₂×Q₈×C₄₃	—	4	4	no	—
104	C₂×Q₈×C₄₃	—	4	4	no	—
105	C₂×Q₈×C₄₃	—	4	2	no	—
106	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
107	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	4	no	—
112	C₂×D₄×C₄₃	—	2	4	no	—
113	C₂×D₄×C₄₃	C₂²⋊C₄	1	8	yes	—
114	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	4	no	—
119	C₂²×C₄×C₄₃	—	2	8	no	—
120	C₂²×C₄×C₄₃	—	2	4	no	—
121	C₂²×C₄×C₄₃	—	2	4	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	4	2	no	—
125	C₂²×C₄×C₄₃	—	4	2	no	—
126	C₂²×C₄×C₄₃	C₂²⋊C₄	1	8	yes	—
127	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	#41	1	4	yes	—
134	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
135	M₁₆×C₄₃	—	2	4	no	—
136	M₁₆×C₄₃	—	2	4	no	—
137	M₁₆×C₄₃	—	4	4	no	—
138	C₂×C₈×C₄₃	—	2	4	no	—
139	C₂×C₈×C₄₃	—	4	4	no	—
140	C₄⋊C₄×C₄₃	—	2	8	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	16	no	—
143	C₄⋊C₄×C₄₃	—	2	4	no	—
144	C₄⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
145	C₂²⋊C₄×C₄₃	—	2	8	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₂²⋊C₄×C₄₃	—	2	16	no	—
148	C₂²⋊C₄×C₄₃	—	2	4	no	—
149	C₂²⋊C₄×C₄₃	—	2	4	no	—
150	C₄²×C₄₃	—	2	8	no	—
151	C₄²×C₄₃	—	2	4	no	—
152	C₄²×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
155	C₂³×C₄₃	—	2	2	no	—
156	C₂³×C₄₃	—	2	2	no	—
157	C₂³×C₄₃	—	4	2	no	—
158	C₂³×C₄₃	—	4	4	no	—
159	C₂³×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂³×C₄₃	#120	1	2	yes	—
162	C₂³×C₄₃	#123	1	2	yes	—
163	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₄₃	—	2	4	no	—
165	Q₈×C₄₃	—	2	4	no	—
166	Q₈×C₄₃	—	2	8	no	—
167	Q₈×C₄₃	—	4	4	no	—
168	Q₈×C₄₃	—	4	4	no	—
169	Q₈×C₄₃	—	4	4	no	—
170	D₄×C₄₃	—	2	16	no	—
171	D₄×C₄₃	—	2	4	no	—
172	D₄×C₄₃	—	2	4	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	8	no	—
176	C₂×C₄×C₄₃	—	2	8	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	2	8	no	—
180	C₂×C₄×C₄₃	—	4	4	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	8	no	—
184	C₂×C₄×C₄₃	—	8	4	no	—
185	C₂×C₄×C₄₃	—	8	8	no	—
186	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
187	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
189	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
190	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
191	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
192	C₂×C₄×C₄₃	#121	1	4	yes	—
193	C₂×C₄×C₄₃	#121	1	4	yes	—
194	C₂×C₄×C₄₃	#123	1	2	yes	—
195	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
199	C₈×C₄₃	—	4	4	no	—
200	#20955	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	4	no	—
203	C₂²×C₄₃	—	2	4	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	—	4	4	no	—
207	C₂²×C₄₃	—	4	4	no	—
208	C₂²×C₄₃	—	8	2	no	—
209	C₂²×C₄₃	#386	1	4	yes	—
210	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
212	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
213	C₄×C₄₃	—	2	4	no	—
214	C₄×C₄₃	—	4	4	no	—
215	C₄×C₄₃	—	4	8	no	—
216	C₄×C₄₃	—	4	4	no	—
217	C₄×C₄₃	#386	1	2	yes	—
218	C₄×C₄₃	#386	1	2	yes	—
219	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
220	C₄×C₄₃	C₂×#121	1	2	yes	—
221	C₂×#536	C₂×C₄₃	1	1	yes	characteristic
222	#3428	C₂×C₄₃	1	1	yes	characteristic
223	C₂×#419	C₂×C₄₃	1	2	yes	complemented
224	C₂×#413	C₂×C₄₃	1	1	yes	characteristic
225	#1886	C₂×C₄₃	1	4	yes	complemented
226	#1885	C₂×C₄₃	1	4	yes	complemented
227	#1733	C₂×C₄₃	1	2	yes	complemented
228	C₂×C₄₃	—	2	1	no	—
229	C₂×C₄₃	—	2	1	no	—
230	C₂×C₄₃	—	2	4	no	—
231	C₂×C₄₃	—	4	4	no	—
232	C₂×C₄₃	C₂×#386	1	1	yes	characteristic
233	C₂×C₄₃	#3022	1	2	yes	—
234	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
235	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
237	#536	—	2	4	no	—
238	#536	C₄×C₄₃	1	8	yes	complemented
239	C₂×C₄⋊Q₈	C₂²×C₄₃	1	2	yes	—
240	C₂×#124	C₂²×C₄₃	1	2	yes	—
241	C₂×#123	—	2	2	no	—
242	C₂×C₂²⋊Q₈	—	2	2	no	—
243	#520	—	2	4	no	—
244	#519	C₂²×C₄₃	1	2	yes	—
245	#518	—	2	2	no	—
246	#518	C₂²×C₄₃	1	2	yes	—
247	C₄×#41	—	2	4	no	—
248	C₂×#117	—	2	2	no	—
249	C₂×#117	C₂²×C₄₃	1	2	yes	—
250	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
251	#419	—	2	4	no	—
252	#419	C₂²×C₄₃	1	8	yes	—
253	C₂×#103	—	2	4	no	—
254	#413	—	2	4	no	—
255	C₂×#101	C₂²×C₄₃	1	2	yes	—
256	C₂×#100	C₂²×C₄₃	1	2	yes	—
257	#339	C₂²×C₄₃	1	8	yes	—
258	C₄₃	#20955	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#41	—	2	2	no	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	4	no	—
262	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
263	C₂×#41	D₄×C₄₃	1	4	yes	—
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	2	2	no	—
266	C₂²×Q₈	—	2	2	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	4	no	—
269	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	complemented
270	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
271	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
272	C₂²×D₄	D₄×C₄₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₄₃	1	2	yes	—
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	4	no	—
279	C₂×M₁₆	—	2	4	no	—
280	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
281	C₂²×C₈	—	2	2	no	—
282	C₄⋊Q₈	—	2	4	no	—
283	C₄⋊Q₈	C₂×C₄×C₄₃	1	8	yes	complemented
284	#124	—	2	4	no	—
285	#124	C₂×C₄×C₄₃	1	8	yes	complemented
286	#123	—	2	16	no	—
287	C₂²⋊Q₈	—	2	16	no	—
288	C₄×Q₈	—	2	8	no	—
289	C₄×D₄	—	2	16	no	—
290	C₄×D₄	—	2	8	no	—
291	#117	—	2	4	no	—
292	#117	—	2	4	no	—
293	#117	—	2	2	no	—
294	#117	—	2	4	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	C₂×C₄×C₄₃	1	4	yes	complemented
298	#117	D₄×C₄₃	1	4	yes	—
299	#117	C₂³×C₄₃	1	4	yes	—
300	C₂×C₄⋊C₄	—	2	4	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	4	no	—
303	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	4	no	—
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
311	#103	—	2	16	no	—
312	#101	—	2	4	no	—
313	#100	—	2	4	no	—
314	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
315	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
316	#41	—	2	8	no	—
317	#41	—	2	8	no	—
318	#41	—	2	8	no	—
319	#41	—	2	8	no	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	8	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	—	4	4	no	—
332	C₂×Q₈	—	4	2	no	—
333	C₂×Q₈	C₂²×C₄×C₄₃	1	4	yes	—
334	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
335	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	C₂²⋊C₄×C₄₃	1	8	yes	—
341	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
342	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	4	2	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	C₂²⋊C₄×C₄₃	1	8	yes	—
354	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
360	C₂²×C₄	#41×C₄₃	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	4	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	4	4	no	—
367	C₄⋊C₄	—	2	8	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	16	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₄²	—	2	8	no	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	C₂²×C₄×C₄₃	1	4	yes	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	4	no	—
386	C₂³	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
387	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
388	C₂³	#120×C₄₃	1	2	yes	—
389	C₂³	#123×C₄₃	1	2	yes	—
390	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
391	Q₈	—	2	4	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	2	8	no	—
394	Q₈	—	4	4	no	—
395	Q₈	—	4	4	no	—
396	Q₈	—	4	4	no	—
397	D₄	—	2	16	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	8	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	—	8	8	no	—
413	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
414	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
415	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
416	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
417	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
418	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
419	C₂×C₄	#121×C₄₃	1	4	yes	—
420	C₂×C₄	#121×C₄₃	1	4	yes	—
421	C₂×C₄	#123×C₄₃	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
426	C₈	—	4	4	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	8	2	no	—
435	C₂²	C₄₃×#386	1	4	yes	—
436	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
437	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
438	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
439	C₄	—	2	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	4	no	—
443	C₄	C₄₃×#386	1	2	yes	—
444	C₄	C₄₃×#386	1	2	yes	—
445	C₄	C₂×C₄×D₄×C₄₃	1	2	yes	—
446	C₄	C₂×#121×C₄₃	1	2	yes	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	2	4	no	—
450	C₂	—	4	4	no	—
451	C₂	C₂×C₄₃×#386	1	1	yes	characteristic
452	C₂	C₄₃×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₃×#419	C₂	semidirect
5. C₄₃×#1886	C₂	semidirect
6. C₄₃×#1885	C₂	semidirect
7. C₄₃×#1733	C₂	semidirect
12. C₄₃×#536	C₄	semidirect
42. C₂²×Q₈×C₄₃	C₂×C₄	semidirect
56. C₄⋊Q₈×C₄₃	C₂×C₄	semidirect
58. #124×C₄₃	C₂×C₄	semidirect
70. #117×C₄₃	C₂×C₄	semidirect
200. #20955	C₄₃	direct (N × H)
223. C₂×#419	C₂×C₄₃	semidirect
225. #1886	C₂×C₄₃	semidirect
226. #1885	C₂×C₄₃	semidirect
227. #1733	C₂×C₄₃	semidirect
238. #536	C₄×C₄₃	semidirect
258. C₄₃	#20955	direct (N × H)
269. C₂²×Q₈	C₂×C₄×C₄₃	semidirect
283. C₄⋊Q₈	C₂×C₄×C₄₃	semidirect
285. #124	C₂×C₄×C₄₃	semidirect
297. #117	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×#536	2
C₄₃×#3428	2
C₂×C₄₃×#419	2
C₂×C₄₃×#413	2
C₄₃×#1886	2
C₄₃×#1885	2
C₄₃×#1733	2
#20955	43

Subgroups — C43×#20955 #24940972

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20955 #24940972