Subgroups — C₄₃×#8558 #24928575

Order 11008.

682 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	2	yes	maximal
3	C₂×C₄₃×#324	C₂	1	2	yes	maximal
4	C₄₃×#1280	C₂	1	2	yes	maximal
5	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄²×C₄₃	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₄₃	C₄	1	1	yes	characteristic
9	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₄₃	—	2	2	no	—
11	C₂×C₂²⋊C₈×C₄₃	C₂²	1	4	yes	—
12	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
13	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
14	C₂×#95×C₄₃	C₄	1	1	yes	characteristic
15	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#336	—	2	2	no	—
17	C₄₃×#324	—	2	4	no	—
18	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₄₃	—	2	4	no	—
26	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
27	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
28	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
29	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
31	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₄₃	Q₈	1	2	yes	—
33	C₂×C₄²×C₄₃	—	2	1	no	—
34	C₂×C₄²×C₄₃	—	2	1	no	—
35	C₂×C₄²×C₄₃	—	2	2	no	—
36	C₂×C₄²×C₄₃	—	2	1	no	—
37	C₂×C₄²×C₄₃	—	2	1	no	—
38	C₂×C₄²×C₄₃	—	4	2	no	—
39	C₂×C₄²×C₄₃	—	4	2	no	—
40	C₂×C₄²×C₄₃	C₈	1	4	yes	complemented
41	C₂×C₄²×C₄₃	D₄	1	2	yes	—
42	C₂×C₄²×C₄₃	D₄	1	2	yes	—
43	C₄⋊C₈×C₄₃	—	4	4	no	—
44	C₂²⋊C₈×C₄₃	—	2	4	no	—
45	C₂²⋊C₈×C₄₃	—	2	4	no	—
46	#95×C₄₃	—	2	2	no	—
47	#95×C₄₃	—	2	2	no	—
48	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₄₃	—	2	2	no	—
50	C₂²×C₄×C₄₃	—	2	2	no	—
51	C₂²×C₄×C₄₃	—	2	1	no	—
52	C₂²×C₄×C₄₃	—	2	1	no	—
53	C₂²×C₄×C₄₃	—	2	1	no	—
54	C₂²×C₄×C₄₃	—	2	1	no	—
55	C₂²×C₄×C₄₃	—	2	1	no	—
56	C₂²×C₄×C₄₃	—	2	1	no	—
57	C₂²×C₄×C₄₃	—	2	1	no	—
58	C₂²×C₄×C₄₃	—	2	1	no	—
59	C₂²×C₄×C₄₃	—	2	1	no	—
60	C₂²×C₄×C₄₃	—	2	1	no	—
61	C₂²×C₄×C₄₃	—	2	1	no	—
62	C₂²×C₄×C₄₃	—	2	1	no	—
63	C₂²×C₄×C₄₃	—	4	1	no	—
64	C₂²×C₄×C₄₃	—	4	1	no	—
65	C₂²×C₄×C₄₃	—	4	1	no	—
66	C₂²×C₄×C₄₃	—	4	1	no	—
67	C₂²×C₄×C₄₃	—	4	1	no	—
68	C₂²×C₄×C₄₃	—	4	1	no	—
69	C₂²×C₄×C₄₃	—	4	1	no	—
70	C₂²×C₄×C₄₃	—	4	1	no	—
71	C₂²×C₄×C₄₃	—	4	1	no	—
72	C₂²×C₄×C₄₃	—	4	1	no	—
73	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
78	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
79	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
80	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
82	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
83	C₂²×C₄×C₄₃	M₁₆	1	2	yes	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	#41	1	2	yes	—
88	C₂×C₈×C₄₃	—	4	4	no	—
89	C₂×C₈×C₄₃	—	4	4	no	—
90	C₂×C₈×C₄₃	—	4	4	no	—
91	C₄⋊C₄×C₄₃	—	2	8	no	—
92	C₄⋊C₄×C₄₃	—	2	4	no	—
93	C₄⋊C₄×C₄₃	—	2	4	no	—
94	C₄²×C₄₃	—	2	4	no	—
95	C₄²×C₄₃	—	2	4	no	—
96	C₄²×C₄₃	—	2	4	no	—
97	C₄²×C₄₃	—	4	2	no	—
98	C₄²×C₄₃	—	4	2	no	—
99	C₄²×C₄₃	—	4	2	no	—
100	C₂³×C₄₃	—	2	1	no	—
101	C₂³×C₄₃	—	2	1	no	—
102	C₂³×C₄₃	—	2	1	no	—
103	C₂³×C₄₃	—	2	1	no	—
104	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂³×C₄₃	#117	1	1	yes	characteristic
107	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
108	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
109	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
110	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
111	C₂×C₄×C₄₃	—	2	2	no	—
112	C₂×C₄×C₄₃	—	2	2	no	—
113	C₂×C₄×C₄₃	—	2	2	no	—
114	C₂×C₄×C₄₃	—	2	2	no	—
115	C₂×C₄×C₄₃	—	2	1	no	—
116	C₂×C₄×C₄₃	—	2	2	no	—
117	C₂×C₄×C₄₃	—	2	1	no	—
118	C₂×C₄×C₄₃	—	2	2	no	—
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	2	4	no	—
122	C₂×C₄×C₄₃	—	2	4	no	—
123	C₂×C₄×C₄₃	—	2	2	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	2	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	2	no	—
128	C₂×C₄×C₄₃	—	2	2	no	—
129	C₂×C₄×C₄₃	—	4	1	no	—
130	C₂×C₄×C₄₃	—	4	1	no	—
131	C₂×C₄×C₄₃	—	4	2	no	—
132	C₂×C₄×C₄₃	—	4	2	no	—
133	C₂×C₄×C₄₃	—	4	2	no	—
134	C₂×C₄×C₄₃	—	4	2	no	—
135	C₂×C₄×C₄₃	—	4	2	no	—
136	C₂×C₄×C₄₃	—	4	2	no	—
137	C₂×C₄×C₄₃	—	4	1	no	—
138	C₂×C₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	4	1	no	—
140	C₂×C₄×C₄₃	—	4	1	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
147	C₂×C₄×C₄₃	C₂²⋊C₈	1	2	yes	—
148	C₂×C₄×C₄₃	#99	1	2	yes	—
149	C₂×C₄×C₄₃	#101	1	2	yes	—
150	C₂×C₄×C₄₃	C₄⋊C₈	1	4	yes	complemented
151	C₂×C₄×C₄₃	#121	1	2	yes	—
152	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
153	C₈×C₄₃	—	8	4	no	—
154	#8558	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
155	C₂²×C₄₃	—	2	1	no	—
156	C₂²×C₄₃	—	2	1	no	—
157	C₂²×C₄₃	—	2	1	no	—
158	C₂²×C₄₃	—	2	1	no	—
159	C₂²×C₄₃	—	2	1	no	—
160	C₂²×C₄₃	—	2	1	no	—
161	C₂²×C₄₃	—	2	1	no	—
162	C₂²×C₄₃	—	2	1	no	—
163	C₂²×C₄₃	—	2	1	no	—
164	C₂²×C₄₃	—	2	1	no	—
165	C₂²×C₄₃	—	2	1	no	—
166	C₂²×C₄₃	—	2	1	no	—
167	C₂²×C₄₃	#380	1	1	yes	characteristic
168	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
169	C₂²×C₄₃	#407	1	1	yes	characteristic
170	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
171	C₂²×C₄₃	#410	1	1	yes	characteristic
172	C₂²×C₄₃	C₂×#101	1	1	yes	characteristic
173	C₂²×C₄₃	#413	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
175	C₂²×C₄₃	#423	1	1	yes	characteristic
176	C₂²×C₄₃	#431	1	1	yes	characteristic
177	C₂²×C₄₃	#432	1	1	yes	characteristic
178	C₄×C₄₃	—	2	4	no	—
179	C₄×C₄₃	—	2	2	no	—
180	C₄×C₄₃	—	2	2	no	—
181	C₄×C₄₃	—	2	2	no	—
182	C₄×C₄₃	—	4	2	no	—
183	C₄×C₄₃	—	4	2	no	—
184	C₄×C₄₃	—	4	2	no	—
185	C₄×C₄₃	—	4	2	no	—
186	C₄×C₄₃	#324	1	4	yes	complemented
187	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
188	#1797	C₂×C₄₃	1	2	yes	—
189	C₂×#324	C₂×C₄₃	1	2	yes	—
190	#1280	C₂×C₄₃	1	2	yes	—
191	C₂×C₄₃	—	2	1	no	—
192	C₂×C₄₃	—	2	1	no	—
193	C₂×C₄₃	—	2	1	no	—
194	C₂×C₄₃	—	2	1	no	—
195	C₂×C₄₃	C₂×#324	1	1	yes	characteristic
196	C₂×C₄₃	#1458	1	1	yes	characteristic
197	C₂×C₄₃	#1465	1	1	yes	characteristic
198	C₂×C₄₃	#1467	1	1	yes	characteristic
199	C₂×C₄₃	#1797	1	1	yes	characteristic
200	C₂×C₄₃	#1799	1	1	yes	characteristic
201	C₂×C₄₃	#1801	1	1	yes	characteristic
202	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
203	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
204	C₂²×C₄²	C₄×C₄₃	1	1	yes	characteristic
205	C₂²×C₄²	C₄×C₄₃	1	1	yes	characteristic
206	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
207	C₂×C₄⋊C₈	—	2	2	no	—
208	C₂×C₂²⋊C₈	C₂²×C₄₃	1	4	yes	—
209	C₄×C₄⋊C₄	—	2	2	no	—
210	C₄×C₄⋊C₄	—	2	2	no	—
211	C₂×#95	C₄×C₄₃	1	1	yes	characteristic
212	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
213	#336	—	2	2	no	—
214	#324	—	2	4	no	—
215	C₄₃	#8558	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
218	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
220	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
221	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
223	C₂²×C₈	—	2	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
230	C₂×C₄⋊C₄	Q₈×C₄₃	1	2	yes	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	1	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	4	2	no	—
237	C₂×C₄²	—	4	2	no	—
238	C₂×C₄²	C₈×C₄₃	1	4	yes	complemented
239	C₂×C₄²	D₄×C₄₃	1	2	yes	—
240	C₂×C₄²	D₄×C₄₃	1	2	yes	—
241	C₄⋊C₈	—	4	4	no	—
242	C₂²⋊C₈	—	2	4	no	—
243	C₂²⋊C₈	—	2	4	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	1	no	—
249	C₂²×C₄	—	2	1	no	—
250	C₂²×C₄	—	2	1	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	1	no	—
254	C₂²×C₄	—	2	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	2	1	no	—
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	4	1	no	—
262	C₂²×C₄	—	4	1	no	—
263	C₂²×C₄	—	4	1	no	—
264	C₂²×C₄	—	4	1	no	—
265	C₂²×C₄	—	4	1	no	—
266	C₂²×C₄	—	4	1	no	—
267	C₂²×C₄	—	4	1	no	—
268	C₂²×C₄	—	4	1	no	—
269	C₂²×C₄	—	4	1	no	—
270	C₂²×C₄	—	4	1	no	—
271	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
272	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
274	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
275	C₂²×C₄	C₄⋊C₄×C₄₃	1	2	yes	—
276	C₂²×C₄	C₂×C₈×C₄₃	1	2	yes	—
277	C₂²×C₄	C₂×C₈×C₄₃	1	2	yes	—
278	C₂²×C₄	C₂×C₈×C₄₃	1	2	yes	—
279	C₂²×C₄	M₁₆×C₄₃	1	2	yes	—
280	C₂²×C₄	M₁₆×C₄₃	1	2	yes	—
281	C₂²×C₄	M₁₆×C₄₃	1	2	yes	—
282	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
284	C₂²×C₄	C₂×Q₈×C₄₃	1	1	yes	characteristic
285	C₂²×C₄	#41×C₄₃	1	2	yes	—
286	C₂×C₈	—	4	4	no	—
287	C₂×C₈	—	4	4	no	—
288	C₂×C₈	—	4	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄²	—	2	4	no	—
293	C₄²	—	2	4	no	—
294	C₄²	—	2	4	no	—
295	C₄²	—	4	2	no	—
296	C₄²	—	4	2	no	—
297	C₄²	—	4	2	no	—
298	C₂³	—	2	1	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
303	C₂³	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
304	C₂³	#117×C₄₃	1	1	yes	characteristic
305	C₂³	C₂²×C₈×C₄₃	1	1	yes	characteristic
306	C₂³	C₂×M₁₆×C₄₃	1	1	yes	characteristic
307	C₂³	C₂×M₁₆×C₄₃	1	1	yes	characteristic
308	C₂³	C₂×M₁₆×C₄₃	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	C₂²⋊C₈×C₄₃	1	2	yes	—
345	C₂×C₄	C₂²⋊C₈×C₄₃	1	2	yes	—
346	C₂×C₄	#99×C₄₃	1	2	yes	—
347	C₂×C₄	#101×C₄₃	1	2	yes	—
348	C₂×C₄	C₄⋊C₈×C₄₃	1	4	yes	complemented
349	C₂×C₄	#121×C₄₃	1	2	yes	—
350	C₂×C₄	C₂²⋊Q₈×C₄₃	1	2	yes	—
351	C₈	—	8	4	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	C₄₃×#380	1	1	yes	characteristic
365	C₂²	C₂×C₂²⋊C₈×C₄₃	1	1	yes	characteristic
366	C₂²	C₄₃×#407	1	1	yes	characteristic
367	C₂²	C₂×#99×C₄₃	1	1	yes	characteristic
368	C₂²	C₄₃×#410	1	1	yes	characteristic
369	C₂²	C₂×#101×C₄₃	1	1	yes	characteristic
370	C₂²	C₄₃×#413	1	1	yes	characteristic
371	C₂²	C₂×C₄⋊C₈×C₄₃	1	1	yes	characteristic
372	C₂²	C₄₃×#423	1	1	yes	characteristic
373	C₂²	C₄₃×#431	1	1	yes	characteristic
374	C₂²	C₄₃×#432	1	1	yes	characteristic
375	C₄	—	2	2	no	—
376	C₄	—	2	4	no	—
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	C₄₃×#324	1	4	yes	complemented
384	C₂	—	2	1	no	—
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	2	1	no	—
388	C₂	C₂×C₄₃×#324	1	1	yes	characteristic
389	C₂	C₄₃×#1458	1	1	yes	characteristic
390	C₂	C₄₃×#1465	1	1	yes	characteristic
391	C₂	C₄₃×#1467	1	1	yes	characteristic
392	C₂	C₄₃×#1797	1	1	yes	characteristic
393	C₂	C₄₃×#1799	1	1	yes	characteristic
394	C₂	C₄₃×#1801	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₈×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
prime radical	C₂⁴×C₄₃	C₂²×C₄
LCS	G ▷ C₂³ ▷ 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
40. C₂×C₄²×C₄₃	C₈	semidirect
150. C₂×C₄×C₄₃	C₄⋊C₈	semidirect
154. #8558	C₄₃	direct (N × H)
186. C₄×C₄₃	#324	semidirect
215. C₄₃	#8558	direct (N × H)
238. C₂×C₄²	C₈×C₄₃	semidirect
348. C₂×C₄	C₄⋊C₈×C₄₃	semidirect
383. C₄	C₄₃×#324	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1797	2
C₂×C₄₃×#324	2
C₄₃×#1280	2
#8558	43

Subgroups — C43×#8558 #24928575

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8558 #24928575