Subgroups — C₄₃×#17780 #24937797

Order 11008.

870 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3509	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2990	C₂	1	2	yes	maximal
3	C₄₃×#1559	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1558	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1554	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1552	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1550	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1542	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#557	—	2	2	no	—
11	C₄₃×#556	—	2	2	no	—
12	C₄₃×#552	—	2	2	no	—
13	C₄₃×#552	—	2	2	no	—
14	C₄₃×#541	C₄	1	4	yes	—
15	C₄₃×#536	C₄	1	2	yes	—
16	C₄₃×#533	C₂²	1	2	yes	—
17	C₄₃×#533	C₂²	1	2	yes	—
18	C₄₃×#533	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#519	C₄	1	2	yes	—
21	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#446	—	2	2	no	—
23	C₄₃×#435	—	2	2	no	—
24	C₄₃×#435	—	2	2	no	—
25	C₈×D₄×C₄₃	—	2	2	no	—
26	C₄₃×#432	C₂²	1	2	yes	—
27	C₄₃×#432	C₂²	1	2	yes	—
28	C₄₃×#431	C₂²	1	2	yes	—
29	C₄₃×#423	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
32	C₄₃×#333	C₂²	1	1	yes	characteristic
33	C₄₃×#333	C₂²	1	2	yes	—
34	C₄₃×#333	C₂²	1	2	yes	—
35	C₄₃×#333	C₂²	1	1	yes	characteristic
36	C₄₃×#333	C₂²	1	1	yes	characteristic
37	C₄₃×#333	C₂²	1	1	yes	characteristic
38	C₄₃×#332	C₂²	1	2	yes	—
39	C₄₃×#332	C₂²	1	2	yes	—
40	C₄₃×#332	C₂²	1	2	yes	—
41	C₄₃×#332	C₂²	1	2	yes	—
42	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
44	C₂×M₁₆×C₄₃	—	2	2	no	—
45	C₂²×C₈×C₄₃	—	2	2	no	—
46	C₂²×C₈×C₄₃	—	2	2	no	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
50	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
53	#126×C₄₃	—	2	4	no	—
54	#126×C₄₃	—	2	4	no	—
55	#125×C₄₃	—	2	4	no	—
56	#125×C₄₃	—	2	4	no	—
57	#125×C₄₃	—	2	2	no	—
58	#125×C₄₃	—	2	2	no	—
59	#125×C₄₃	C₂×C₄	1	2	yes	—
60	#124×C₄₃	—	2	2	no	—
61	#123×C₄₃	—	2	4	no	—
62	C₂²⋊Q₈×C₄₃	—	2	2	no	—
63	C₂²⋊Q₈×C₄₃	—	2	2	no	—
64	C₂²⋊Q₈×C₄₃	—	2	2	no	—
65	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
66	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
67	C₄×Q₈×C₄₃	—	2	4	no	—
68	C₄×Q₈×C₄₃	—	2	2	no	—
69	C₄×Q₈×C₄₃	—	2	2	no	—
70	C₄×Q₈×C₄₃	—	2	2	no	—
71	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
72	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
73	C₄×Q₈×C₄₃	D₄	1	2	yes	—
74	C₄×D₄×C₄₃	D₄	1	2	yes	—
75	C₄×D₄×C₄₃	D₄	1	2	yes	—
76	C₄×D₄×C₄₃	D₄	1	2	yes	—
77	#117×C₄₃	—	2	2	no	—
78	#117×C₄₃	—	2	2	no	—
79	#117×C₄₃	—	2	2	no	—
80	#117×C₄₃	—	2	2	no	—
81	#117×C₄₃	C₂×C₄	1	2	yes	—
82	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
83	#117×C₄₃	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
87	C₄⋊C₈×C₄₃	—	2	2	no	—
88	C₄⋊C₈×C₄₃	—	2	2	no	—
89	C₄⋊C₈×C₄₃	—	2	2	no	—
90	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
91	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
92	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
94	C₂²⋊C₈×C₄₃	—	2	2	no	—
95	C₂²⋊C₈×C₄₃	—	2	2	no	—
96	C₂²⋊C₈×C₄₃	—	2	2	no	—
97	#97×C₄₃	—	2	2	no	—
98	#97×C₄₃	—	2	2	no	—
99	C₄×C₈×C₄₃	—	2	2	no	—
100	#41×C₄₃	—	4	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	4	4	no	—
104	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
108	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
115	M₁₆×C₄₃	—	8	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	8	2	no	—
121	C₂×C₈×C₄₃	—	8	2	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	4	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	4	no	—
126	C₄⋊C₄×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
132	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
133	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
135	C₂²⋊C₄×C₄₃	—	2	2	no	—
136	C₂²⋊C₄×C₄₃	—	2	4	no	—
137	C₂²⋊C₄×C₄₃	—	2	4	no	—
138	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
141	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
142	C₄²×C₄₃	—	2	4	no	—
143	C₄²×C₄₃	—	2	4	no	—
144	C₄²×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₄²×C₄₃	C₂×D₄	1	2	yes	—
149	C₄²×C₄₃	C₂×D₄	1	2	yes	—
150	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	Q₈×C₄₃	—	4	1	no	—
154	Q₈×C₄₃	—	4	2	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	4	no	—
157	Q₈×C₄₃	—	4	2	no	—
158	Q₈×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	2	4	no	—
160	D₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	4	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
180	C₈×C₄₃	—	4	2	no	—
181	C₈×C₄₃	—	4	2	no	—
182	C₈×C₄₃	—	4	2	no	—
183	C₈×C₄₃	—	4	2	no	—
184	#17780	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₃	—	2	2	no	—
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	#413	1	2	yes	—
190	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₄₃	—	2	1	no	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	—	2	2	no	—
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	—	4	2	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	#577	1	2	yes	—
201	C₄×C₄₃	#578	1	2	yes	—
202	#3509	C₂×C₄₃	1	1	yes	characteristic
203	#2990	C₂×C₄₃	1	2	yes	—
204	#1559	C₂×C₄₃	1	2	yes	complemented
205	#1558	C₂×C₄₃	1	1	yes	characteristic, complemented
206	#1554	C₂×C₄₃	1	2	yes	complemented
207	#1552	C₂×C₄₃	1	2	yes	complemented
208	#1550	C₂×C₄₃	1	2	yes	complemented
209	#1542	C₂×C₄₃	1	2	yes	complemented
210	C₂×#333	C₂×C₄₃	1	1	yes	characteristic, complemented
211	C₂×C₄₃	—	2	2	no	—
212	C₂×C₄₃	—	4	2	no	—
213	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
214	C₂×C₄₃	#2898	1	2	yes	—
215	#557	—	2	2	no	—
216	#556	—	2	2	no	—
217	#552	—	2	2	no	—
218	#552	—	2	2	no	—
219	#541	C₄×C₄₃	1	4	yes	—
220	#536	C₄×C₄₃	1	2	yes	—
221	#533	C₂²×C₄₃	1	2	yes	—
222	#533	C₂²×C₄₃	1	2	yes	—
223	#533	C₂²×C₄₃	1	1	yes	characteristic
224	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
225	#519	C₄×C₄₃	1	2	yes	—
226	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
227	#446	—	2	2	no	—
228	#435	—	2	2	no	—
229	#435	—	2	2	no	—
230	C₈×D₄	—	2	2	no	—
231	#432	C₂²×C₄₃	1	2	yes	—
232	#432	C₂²×C₄₃	1	2	yes	—
233	#431	C₂²×C₄₃	1	2	yes	—
234	#423	C₂²×C₄₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
237	#333	C₂²×C₄₃	1	1	yes	characteristic
238	#333	C₂²×C₄₃	1	2	yes	—
239	#333	C₂²×C₄₃	1	1	yes	characteristic
240	#333	C₂²×C₄₃	1	2	yes	—
241	#333	C₂²×C₄₃	1	1	yes	characteristic
242	#333	C₂²×C₄₃	1	1	yes	characteristic
243	#332	C₂²×C₄₃	1	2	yes	—
244	#332	C₂²×C₄₃	1	2	yes	—
245	#332	C₂²×C₄₃	1	2	yes	—
246	#332	C₂²×C₄₃	1	2	yes	—
247	C₄₃	#17780	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×#41	C₂×C₄×C₄₃	1	1	yes	characteristic
249	C₂²×Q₈	C₂×C₄×C₄₃	1	2	yes	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	—	2	2	no	—
253	C₄⋊Q₈	—	2	2	no	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
257	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
258	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
259	#126	—	2	4	no	—
260	#126	—	2	4	no	—
261	#125	—	2	4	no	—
262	#125	—	2	4	no	—
263	#125	—	2	2	no	—
264	#125	—	2	2	no	—
265	#125	C₂×C₄×C₄₃	1	2	yes	—
266	#124	—	2	2	no	—
267	#123	—	2	4	no	—
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	—	2	2	no	—
270	C₂²⋊Q₈	—	2	2	no	—
271	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
272	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
273	C₄×Q₈	—	2	4	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	2	2	no	—
277	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
278	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
279	C₄×Q₈	D₄×C₄₃	1	2	yes	—
280	C₄×D₄	D₄×C₄₃	1	2	yes	—
281	C₄×D₄	D₄×C₄₃	1	2	yes	—
282	C₄×D₄	D₄×C₄₃	1	2	yes	—
283	#117	—	2	2	no	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	#117	—	2	2	no	—
287	#117	C₂×C₄×C₄₃	1	2	yes	—
288	#117	C₂×C₄×C₄₃	1	1	yes	characteristic
289	#117	C₂×C₄×C₄₃	1	2	yes	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
293	C₄⋊C₈	—	2	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
297	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
298	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
299	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	2	2	no	—
302	C₂²⋊C₈	—	2	2	no	—
303	#97	—	2	2	no	—
304	#97	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	#41	—	4	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	4	4	no	—
310	C₂×Q₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
311	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
312	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
313	C₂×D₄	C₂²⋊C₄×C₄₃	1	2	yes	—
314	C₂×D₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
321	M₁₆	—	8	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	8	2	no	—
327	C₂×C₈	—	8	2	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
338	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
339	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
340	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	2	4	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
345	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
346	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
347	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
352	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₄₃	1	2	yes	—
354	C₄²	C₂×D₄×C₄₃	1	2	yes	—
355	C₄²	C₂×D₄×C₄₃	1	2	yes	—
356	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
357	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
358	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
359	Q₈	—	4	1	no	—
360	Q₈	—	4	2	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
380	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
381	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
383	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
384	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
386	C₈	—	4	2	no	—
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	2	no	—
394	C₂²	C₄₃×#413	1	2	yes	—
395	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	C₄₃×#577	1	2	yes	—
406	C₄	C₄₃×#578	1	2	yes	—
407	C₂	—	2	2	no	—
408	C₂	—	4	2	no	—
409	C₂	C₂×C₄₃×#413	1	1	yes	characteristic
410	C₂	C₄₃×#2898	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
prime radical	C₂×#41×C₄₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₄×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄₃×#1559	C₂	semidirect
4. C₄₃×#1558	C₂	semidirect
5. C₄₃×#1554	C₂	semidirect
6. C₄₃×#1552	C₂	semidirect
7. C₄₃×#1550	C₂	semidirect
8. C₄₃×#1542	C₂	semidirect
9. C₂×C₄₃×#333	C₂	semidirect
184. #17780	C₄₃	direct (N × H)
204. #1559	C₂×C₄₃	semidirect
205. #1558	C₂×C₄₃	semidirect
206. #1554	C₂×C₄₃	semidirect
207. #1552	C₂×C₄₃	semidirect
208. #1550	C₂×C₄₃	semidirect
209. #1542	C₂×C₄₃	semidirect
210. C₂×#333	C₂×C₄₃	semidirect
247. C₄₃	#17780	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×#3509	2
C₄₃×#2990	2
C₄₃×#1559	2
C₄₃×#1558	2
C₄₃×#1554	2
C₄₃×#1552	2
C₄₃×#1550	2
C₄₃×#1542	2
C₂×C₄₃×#333	2
#17780	43

Subgroups — C43×#17780 #24937797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17780 #24937797