Subgroups — C₄₃×#17061 #24937078

Order 11008.

1230 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#398	C₂	1	2	yes	maximal
2	C₂×C₄₃×#387	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#384	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1445	C₂	1	2	yes	maximal
5	C₄₃×#1444	C₂	1	2	yes	maximal
6	C₄₃×#1444	C₂	1	2	yes	maximal
7	C₄₃×#1442	C₂	1	2	yes	maximal
8	C₄₃×#1441	C₂	1	2	yes	maximal
9	C₄₃×#1434	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#398	—	2	8	no	—
18	C₄₃×#387	—	2	4	no	—
19	C₄₃×#384	—	2	4	no	—
20	C₂×#95×C₄₃	C₂²	1	2	yes	—
21	C₂×#95×C₄₃	C₂²	1	4	yes	—
22	C₂×#95×C₄₃	C₂²	1	2	yes	—
23	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	4	yes	—
29	C₂×#95×C₄₃	C₂²	1	2	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
50	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
51	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
53	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
54	C₂×C₄²×C₄₃	—	2	4	no	—
55	C₂×C₄²×C₄₃	D₄	1	4	yes	—
56	#95×C₄₃	—	2	2	no	—
57	#95×C₄₃	—	2	2	no	—
58	#95×C₄₃	—	2	2	no	—
59	#95×C₄₃	—	2	2	no	—
60	#95×C₄₃	—	2	4	no	—
61	#95×C₄₃	—	2	8	no	—
62	#95×C₄₃	—	2	4	no	—
63	#95×C₄₃	—	4	4	no	—
64	#95×C₄₃	—	4	4	no	—
65	#95×C₄₃	Q₈	1	8	yes	—
66	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
67	C₂²×C₄×C₄₃	—	2	1	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	2	1	no	—
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	4	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	4	no	—
77	C₂²×C₄×C₄₃	—	2	1	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	4	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
109	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₄₃	#41	1	2	yes	—
111	C₂²×C₄×C₄₃	#41	1	4	yes	—
112	C₄⋊C₄×C₄₃	—	2	8	no	—
113	C₄⋊C₄×C₄₃	—	4	8	no	—
114	C₄⋊C₄×C₄₃	—	4	8	no	—
115	C₄⋊C₄×C₄₃	—	4	16	no	—
116	C₄⋊C₄×C₄₃	—	4	8	no	—
117	C₄⋊C₄×C₄₃	—	4	4	no	—
118	C₄²×C₄₃	—	2	8	no	—
119	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
120	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
121	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
122	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
123	C₂³×C₄₃	C₂×#41	1	2	yes	—
124	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
125	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
126	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
127	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
128	C₂×C₄×C₄₃	—	2	2	no	—
129	C₂×C₄×C₄₃	—	2	2	no	—
130	C₂×C₄×C₄₃	—	2	2	no	—
131	C₂×C₄×C₄₃	—	2	2	no	—
132	C₂×C₄×C₄₃	—	2	2	no	—
133	C₂×C₄×C₄₃	—	2	2	no	—
134	C₂×C₄×C₄₃	—	2	8	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	8	no	—
138	C₂×C₄×C₄₃	—	2	2	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	8	no	—
142	C₂×C₄×C₄₃	—	2	4	no	—
143	C₂×C₄×C₄₃	—	2	8	no	—
144	C₂×C₄×C₄₃	—	2	8	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	4	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	4	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	4	no	—
155	C₂×C₄×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	4	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	4	no	—
167	C₂×C₄×C₄₃	—	4	4	no	—
168	C₂×C₄×C₄₃	—	4	4	no	—
169	C₂×C₄×C₄₃	—	4	4	no	—
170	C₂×C₄×C₄₃	#121	1	4	yes	—
171	C₂×C₄×C₄₃	#123	1	4	yes	—
172	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
173	#17061	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
175	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
176	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₂²×C₄₃	#535	1	1	yes	characteristic
178	C₂²×C₄₃	#535	1	1	yes	characteristic
179	C₂²×C₄₃	#535	1	2	yes	—
180	C₂²×C₄₃	#536	1	1	yes	characteristic
181	C₂²×C₄₃	#536	1	1	yes	characteristic
182	C₂²×C₄₃	#539	1	4	yes	—
183	C₂²×C₄₃	#540	1	2	yes	—
184	C₂²×C₄₃	#544	1	4	yes	—
185	C₂²×C₄₃	#547	1	2	yes	—
186	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
187	C₂²×C₄₃	#552	1	2	yes	—
188	C₂²×C₄₃	#554	1	4	yes	—
189	C₂²×C₄₃	#557	1	2	yes	—
190	C₂²×C₄₃	#563	1	4	yes	—
191	C₄×C₄₃	—	2	4	no	—
192	C₄×C₄₃	—	2	4	no	—
193	C₄×C₄₃	—	2	4	no	—
194	C₄×C₄₃	—	4	2	no	—
195	C₄×C₄₃	—	4	8	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	8	1	no	—
198	C₄×C₄₃	—	8	4	no	—
199	C₄×C₄₃	—	8	1	no	—
200	C₂×#398	C₂×C₄₃	1	2	yes	—
201	C₂×#387	C₂×C₄₃	1	1	yes	characteristic
202	C₂×#384	C₂×C₄₃	1	1	yes	characteristic
203	#1445	C₂×C₄₃	1	2	yes	—
204	#1444	C₂×C₄₃	1	2	yes	—
205	#1444	C₂×C₄₃	1	2	yes	—
206	#1442	C₂×C₄₃	1	2	yes	—
207	#1441	C₂×C₄₃	1	2	yes	—
208	#1434	C₂×C₄₃	1	1	yes	characteristic
209	C₂×C₄₃	#2486	1	1	yes	characteristic
210	C₂×C₄₃	#2502	1	1	yes	characteristic
211	C₂×C₄₃	#2546	1	1	yes	characteristic
212	C₂×C₄₃	#2619	1	1	yes	characteristic
213	C₂×C₄₃	#2623	1	1	yes	characteristic
214	C₂×C₄₃	#2660	1	1	yes	characteristic
215	C₂×C₄₃	#2720	1	4	yes	—
216	C₂×C₄₃	#2791	1	4	yes	—
217	C₂×C₄₃	#2821	1	1	yes	characteristic
218	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
219	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
220	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
224	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
225	#398	—	2	8	no	—
226	#387	—	2	4	no	—
227	#384	—	2	4	no	—
228	C₂×#95	C₂²×C₄₃	1	2	yes	—
229	C₂×#95	C₂²×C₄₃	1	4	yes	—
230	C₂×#95	C₂²×C₄₃	1	2	yes	—
231	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
234	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
235	C₂×#95	C₂²×C₄₃	1	4	yes	—
236	C₂×#95	C₂²×C₄₃	1	4	yes	—
237	C₂×#95	C₂²×C₄₃	1	2	yes	—
238	C₄₃	#17061	1	1	yes	characteristic, direct product factor, Sylow
239	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
240	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
243	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
245	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	8	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	4	no	—
257	C₂×C₄⋊C₄	—	2	4	no	—
258	C₂×C₄⋊C₄	—	4	4	no	—
259	C₂×C₄⋊C₄	—	4	4	no	—
260	C₂×C₄⋊C₄	—	4	4	no	—
261	C₂×C₄⋊C₄	—	4	4	no	—
262	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	D₄×C₄₃	1	4	yes	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	4	no	—
270	#95	—	2	8	no	—
271	#95	—	2	4	no	—
272	#95	—	4	4	no	—
273	#95	—	4	4	no	—
274	#95	Q₈×C₄₃	1	8	yes	—
275	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
316	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
318	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
319	C₂²×C₄	#41×C₄₃	1	2	yes	—
320	C₂²×C₄	#41×C₄₃	1	4	yes	—
321	C₄⋊C₄	—	2	8	no	—
322	C₄⋊C₄	—	4	8	no	—
323	C₄⋊C₄	—	4	8	no	—
324	C₄⋊C₄	—	4	16	no	—
325	C₄⋊C₄	—	4	8	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄²	—	2	8	no	—
328	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
329	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
330	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
331	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
332	C₂³	C₂×#41×C₄₃	1	2	yes	—
333	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
334	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
335	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
336	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	#121×C₄₃	1	4	yes	—
380	C₂×C₄	#123×C₄₃	1	4	yes	—
381	C₂×C₄	C₄⋊Q₈×C₄₃	1	4	yes	—
382	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
383	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
384	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
385	C₂²	C₄₃×#535	1	1	yes	characteristic
386	C₂²	C₄₃×#535	1	2	yes	—
387	C₂²	C₄₃×#535	1	1	yes	characteristic
388	C₂²	C₄₃×#536	1	1	yes	characteristic
389	C₂²	C₄₃×#536	1	1	yes	characteristic
390	C₂²	C₄₃×#539	1	4	yes	—
391	C₂²	C₄₃×#540	1	2	yes	—
392	C₂²	C₄₃×#544	1	4	yes	—
393	C₂²	C₄₃×#547	1	2	yes	—
394	C₂²	D₄×Q₈×C₄₃	1	2	yes	—
395	C₂²	C₄₃×#552	1	2	yes	—
396	C₂²	C₄₃×#554	1	4	yes	—
397	C₂²	C₄₃×#557	1	2	yes	—
398	C₂²	C₄₃×#563	1	4	yes	—
399	C₄	—	2	4	no	—
400	C₄	—	2	4	no	—
401	C₄	—	2	4	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	8	no	—
404	C₄	—	4	2	no	—
405	C₄	—	8	4	no	—
406	C₄	—	8	1	no	—
407	C₄	—	8	1	no	—
408	C₂	C₄₃×#2486	1	1	yes	characteristic
409	C₂	C₄₃×#2502	1	1	yes	characteristic
410	C₂	C₄₃×#2546	1	1	yes	characteristic
411	C₂	C₄₃×#2619	1	1	yes	characteristic
412	C₂	C₄₃×#2623	1	1	yes	characteristic
413	C₂	C₄₃×#2660	1	1	yes	characteristic
414	C₂	C₄₃×#2720	1	4	yes	—
415	C₂	C₄₃×#2791	1	4	yes	—
416	C₂	C₄₃×#2821	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
173. #17061	C₄₃	direct (N × H)
238. C₄₃	#17061	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×#398	2
C₂×C₄₃×#387	2
C₂×C₄₃×#384	2
C₄₃×#1445	2
C₄₃×#1444	2
C₄₃×#1442	2
C₄₃×#1441	2
C₄₃×#1434	2
#17061	43

Subgroups — C43×#17061 #24937078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17061 #24937078