Subgroups — C₂×C₄₃×#1679 #24939124

Order 11008.

758 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1679	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₄₃	—	2	1	no	—
10	C₂³×C₈×C₄₃	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#487	—	2	2	no	—
15	C₄₃×#487	C₂²	1	4	yes	complemented
16	C₄₃×#474	—	2	2	no	—
17	C₄₃×#474	C₂²	1	4	yes	—
18	C₄₃×#461	—	2	2	no	—
19	C₄₃×#461	C₂²	1	4	yes	—
20	C₈×D₄×C₄₃	—	2	2	no	—
21	C₈×D₄×C₄₃	C₂²	1	4	yes	—
22	C₂×#107×C₄₃	—	2	1	no	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₄₃	—	2	1	no	—
27	C₂×#103×C₄₃	—	2	1	no	—
28	C₂×#103×C₄₃	—	2	1	no	—
29	C₂×#102×C₄₃	—	2	1	no	—
30	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
31	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#334	C₂²	1	4	yes	complemented
33	C₄₃×#332	C₂²	1	4	yes	complemented
34	C₄₃×#332	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₄₃	—	2	1	no	—
36	C₂²×Q₈×C₄₃	—	2	1	no	—
37	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	—	2	1	no	—
39	C₂×SD₁₆×C₄₃	—	2	4	no	—
40	C₂×SD₁₆×C₄₃	—	4	4	no	—
41	C₂²×C₈×C₄₃	—	2	1	no	—
42	C₂²×C₈×C₄₃	—	2	1	no	—
43	C₂²×C₈×C₄₃	—	2	1	no	—
44	C₂²×C₈×C₄₃	—	2	4	no	—
45	C₂²×C₈×C₄₃	—	4	4	no	—
46	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
48	C₄⋊Q₈×C₄₃	—	2	1	no	—
49	C₄⋊Q₈×C₄₃	—	2	1	no	—
50	C₄⋊Q₈×C₄₃	—	2	1	no	—
51	C₄⋊Q₈×C₄₃	—	2	1	no	—
52	C₄⋊Q₈×C₄₃	—	2	1	no	—
53	C₄⋊Q₈×C₄₃	—	2	1	no	—
54	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
56	C₄×D₄×C₄₃	—	2	1	no	—
57	C₄×D₄×C₄₃	—	2	1	no	—
58	C₄×D₄×C₄₃	D₄	1	2	yes	—
59	C₄×D₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
67	#107×C₄₃	—	2	4	no	—
68	C₄⋊C₈×C₄₃	—	2	1	no	—
69	C₄⋊C₈×C₄₃	—	2	1	no	—
70	C₄⋊C₈×C₄₃	—	2	1	no	—
71	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
72	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
74	#103×C₄₃	—	2	4	no	—
75	#103×C₄₃	—	2	4	no	—
76	#103×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	2	4	no	—
78	C₂²⋊C₈×C₄₃	—	2	4	no	—
79	C₄×C₈×C₄₃	D₄	1	2	yes	—
80	C₄×C₈×C₄₃	C₂³	1	2	yes	—
81	C₂⁴×C₄₃	—	2	1	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	2	no	—
84	C₂×Q₈×C₄₃	—	4	1	no	—
85	C₂×Q₈×C₄₃	—	4	1	no	—
86	C₂×Q₈×C₄₃	—	4	2	no	—
87	C₂×Q₈×C₄₃	—	4	2	no	—
88	C₂×Q₈×C₄₃	—	4	2	no	—
89	C₂×Q₈×C₄₃	—	4	2	no	—
90	C₂×D₄×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	—	2	2	no	—
92	C₂×D₄×C₄₃	SD₁₆	1	4	yes	—
93	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	4	2	no	—
98	C₂²×C₄×C₄₃	—	4	2	no	—
99	C₂²×C₄×C₄₃	—	4	1	no	—
100	C₂²×C₄×C₄₃	—	4	1	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	SD₁₆×C₄₃	—	4	8	no	—
105	C₂×C₈×C₄₃	—	2	2	no	—
106	C₂×C₈×C₄₃	—	2	2	no	—
107	C₂×C₈×C₄₃	—	2	2	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	4	8	no	—
111	C₂×C₈×C₄₃	—	4	2	no	—
112	C₂×C₈×C₄₃	—	4	2	no	—
113	C₂×C₈×C₄₃	—	4	2	no	—
114	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	4	1	no	—
122	C₄⋊C₄×C₄₃	—	4	1	no	—
123	C₄⋊C₄×C₄₃	—	4	1	no	—
124	C₄⋊C₄×C₄₃	—	4	1	no	—
125	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
126	C₂²⋊C₄×C₄₃	—	2	2	no	—
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₃	#41	1	1	yes	characteristic
131	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂³×C₄₃	—	2	2	no	—
133	C₂³×C₄₃	—	2	4	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	2	no	—
136	C₂³×C₄₃	#121	1	1	yes	characteristic
137	Q₈×C₄₃	—	4	2	no	—
138	Q₈×C₄₃	—	4	2	no	—
139	Q₈×C₄₃	—	4	2	no	—
140	Q₈×C₄₃	—	4	2	no	—
141	Q₈×C₄₃	—	8	2	no	—
142	Q₈×C₄₃	—	8	2	no	—
143	D₄×C₄₃	—	2	2	no	—
144	D₄×C₄₃	—	2	4	no	—
145	D₄×C₄₃	C₂×SD₁₆	1	4	yes	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	4	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	8	2	no	—
155	C₂×C₄×C₄₃	—	8	2	no	—
156	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₄₃	#135	1	2	yes	—
161	C₂×C₄×C₄₃	#135	1	2	yes	—
162	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
166	C₈×C₄₃	—	2	2	no	—
167	C₈×C₄₃	—	2	2	no	—
168	C₈×C₄₃	—	4	2	no	—
169	C₈×C₄₃	—	4	2	no	—
170	C₈×C₄₃	—	4	2	no	—
171	C₂×#1679	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₃	—	2	4	no	—
173	C₂²×C₄₃	—	4	8	no	—
174	C₂²×C₄₃	—	4	2	no	—
175	C₂²×C₄₃	—	4	2	no	—
176	C₂²×C₄₃	#463	1	2	yes	—
177	C₂²×C₄₃	#465	1	2	yes	—
178	C₂²×C₄₃	#473	1	2	yes	—
179	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
180	C₄×C₄₃	—	2	1	no	—
181	C₄×C₄₃	—	2	1	no	—
182	C₄×C₄₃	—	4	2	no	—
183	C₄×C₄₃	—	8	2	no	—
184	C₄×C₄₃	—	8	2	no	—
185	C₄×C₄₃	#463	1	2	yes	—
186	C₄×C₄₃	#465	1	2	yes	—
187	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
188	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
189	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
190	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×#487	C₂×C₄₃	1	1	yes	characteristic, complemented
192	C₂×#474	C₂×C₄₃	1	1	yes	characteristic
193	C₂×#461	C₂×C₄₃	1	1	yes	characteristic
194	C₂×C₈×D₄	C₂×C₄₃	1	1	yes	characteristic
195	#1679	C₂×C₄₃	1	8	yes	direct product factor
196	C₂×#334	C₂×C₄₃	1	1	yes	characteristic, complemented
197	C₂×#332	C₂×C₄₃	1	1	yes	characteristic, complemented
198	C₂×#332	C₂×C₄₃	1	1	yes	characteristic, complemented
199	C₂×C₄₃	—	4	4	no	—
200	C₂×C₄₃	#1679	1	4	yes	direct product factor
201	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
202	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
203	C₂×C₄₃	C₂×#473	1	1	yes	characteristic
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂³×C₈	—	2	1	no	—
206	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
208	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
209	#487	—	2	2	no	—
210	#487	C₂²×C₄₃	1	4	yes	complemented
211	#474	—	2	2	no	—
212	#474	C₂²×C₄₃	1	4	yes	—
213	#461	—	2	2	no	—
214	#461	C₂²×C₄₃	1	4	yes	—
215	C₈×D₄	—	2	2	no	—
216	C₈×D₄	C₂²×C₄₃	1	4	yes	—
217	C₂×#107	—	2	1	no	—
218	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
221	C₂×#103	—	2	1	no	—
222	C₂×#103	—	2	1	no	—
223	C₂×#103	—	2	1	no	—
224	C₂×#102	—	2	1	no	—
225	C₂×C₂²⋊C₈	—	2	1	no	—
226	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
227	#334	C₂²×C₄₃	1	4	yes	complemented
228	#332	C₂²×C₄₃	1	4	yes	complemented
229	#332	C₂²×C₄₃	1	4	yes	complemented
230	C₄₃	C₂×#1679	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	—	2	1	no	—
233	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	4	no	—
241	C₂²×C₈	—	4	4	no	—
242	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
243	C₂²×C₈	D₄×C₄₃	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	1	no	—
247	C₄⋊Q₈	—	2	1	no	—
248	C₄⋊Q₈	—	2	1	no	—
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
251	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₄×D₄	D₄×C₄₃	1	2	yes	—
255	C₄×D₄	C₂³×C₄₃	1	2	yes	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
263	#107	—	2	4	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
268	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
269	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
270	#103	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	C₂²⋊C₈	—	2	4	no	—
275	C₄×C₈	D₄×C₄₃	1	2	yes	—
276	C₄×C₈	C₂³×C₄₃	1	2	yes	—
277	C₂⁴	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	SD₁₆×C₄₃	1	4	yes	—
289	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
299	C₂²×C₄	#41×C₄₃	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	8	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	2	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²⋊C₄	—	2	2	no	—
323	C₂²⋊C₄	—	2	2	no	—
324	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
325	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₄²	#41×C₄₃	1	1	yes	characteristic
327	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	#121×C₄₃	1	1	yes	characteristic
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	8	2	no	—
338	Q₈	—	8	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	4	no	—
341	D₄	C₂×SD₁₆×C₄₃	1	4	yes	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
353	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
354	C₂×C₄	#121×C₄₃	1	1	yes	characteristic
355	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
356	C₂×C₄	#135×C₄₃	1	2	yes	—
357	C₂×C₄	#135×C₄₃	1	2	yes	—
358	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
362	C₈	—	2	2	no	—
363	C₈	—	2	2	no	—
364	C₈	—	4	2	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	C₄₃×#463	1	2	yes	—
372	C₂²	C₄₃×#465	1	2	yes	—
373	C₂²	C₄₃×#473	1	2	yes	—
374	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₄₃×#463	1	2	yes	—
381	C₄	C₄₃×#465	1	2	yes	—
382	C₄	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
383	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
384	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
385	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
386	C₂	—	4	4	no	—
387	C₂	C₄₃×#1679	1	4	yes	direct product factor
388	C₂	C₂×C₄₃×#463	1	1	yes	characteristic
389	C₂	C₂×C₄₃×#465	1	1	yes	characteristic
390	C₂	C₂×C₄₃×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#487	C₂	semidirect
5. C₄₃×#1679	C₂	direct (N × H)
6. C₂×C₄₃×#334	C₂	semidirect
7. C₂×C₄₃×#332	C₂	semidirect
8. C₂×C₄₃×#332	C₂	semidirect
15. C₄₃×#487	C₂²	semidirect
32. C₄₃×#334	C₂²	semidirect
33. C₄₃×#332	C₂²	semidirect
34. C₄₃×#332	C₂²	semidirect
171. C₂×#1679	C₄₃	direct (N × H)
191. C₂×#487	C₂×C₄₃	semidirect
195. #1679	C₂×C₄₃	direct (N × H)
196. C₂×#334	C₂×C₄₃	semidirect
197. C₂×#332	C₂×C₄₃	semidirect
198. C₂×#332	C₂×C₄₃	semidirect
200. C₂×C₄₃	#1679	direct (N × H)
210. #487	C₂²×C₄₃	semidirect
227. #334	C₂²×C₄₃	semidirect
228. #332	C₂²×C₄₃	semidirect
229. #332	C₂²×C₄₃	semidirect
230. C₄₃	C₂×#1679	direct (N × H)
387. C₂	C₄₃×#1679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#487	2
C₂×C₄₃×#474	2
C₂×C₄₃×#461	2
C₂×C₈×D₄×C₄₃	2
C₄₃×#1679	2
C₂×C₄₃×#334	2
C₂×C₄₃×#332	2
C₂×#1679	43

Subgroups — C2×C43×#1679 #24939124

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1679 #24939124