Subgroups — C₄₃×#29797 #24949814

Order 11008.

918 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₃×#460	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2015	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1982	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
11	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₃	C₂²	1	4	yes	—
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#462	—	2	4	no	—
17	C₄₃×#460	—	2	4	no	—
18	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₃	C₂²	1	2	yes	—
21	C₂×#103×C₄₃	C₂²	1	4	yes	—
22	C₂×#102×C₄₃	C₂²	1	2	yes	—
23	C₂×#102×C₄₃	C₂²	1	4	yes	—
24	C₄₃×#391	C₂²	1	2	yes	—
25	C₄₃×#390	—	2	1	no	—
26	C₄₃×#390	—	2	1	no	—
27	C₄₃×#390	—	2	2	no	—
28	C₄₃×#389	C₂²	1	2	yes	—
29	C₄₃×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
31	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#376	—	2	1	no	—
33	C₄³×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#336	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
36	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	—	2	1	no	—
39	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
40	C₂×Q₁₆×C₄₃	—	2	4	no	—
41	C₂×Q₁₆×C₄₃	—	4	4	no	—
42	C₂×SD₁₆×C₄₃	—	2	4	no	—
43	C₂×SD₁₆×C₄₃	—	4	4	no	—
44	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₄₃	—	2	2	no	—
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	#127×C₄₃	—	2	2	no	—
49	#127×C₄₃	—	2	2	no	—
50	#124×C₄₃	—	4	4	no	—
51	#124×C₄₃	—	4	4	no	—
52	C₄×Q₈×C₄₃	—	2	2	no	—
53	C₄×Q₈×C₄₃	D₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
62	C₂×C₄²×C₄₃	—	2	1	no	—
63	C₂×C₄²×C₄₃	—	2	1	no	—
64	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	D₄	1	2	yes	—
67	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₃	—	2	2	no	—
70	C₄⋊C₈×C₄₃	—	2	2	no	—
71	#103×C₄₃	—	2	4	no	—
72	#103×C₄₃	—	4	4	no	—
73	#102×C₄₃	—	2	4	no	—
74	#102×C₄₃	—	4	4	no	—
75	#95×C₄₃	—	2	2	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	1	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂×Q₈×C₄₃	—	2	1	no	—
81	C₂×Q₈×C₄₃	—	2	2	no	—
82	C₂×Q₈×C₄₃	—	2	2	no	—
83	C₂×Q₈×C₄₃	—	2	2	no	—
84	C₂×Q₈×C₄₃	—	2	2	no	—
85	C₂×Q₈×C₄₃	—	2	4	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
88	C₂×D₄×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂×D₄×C₄₃	—	4	4	no	—
93	C₂×D₄×C₄₃	—	4	2	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂×D₄×C₄₃	—	4	2	no	—
96	C₂×D₄×C₄₃	—	4	2	no	—
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
106	Q₁₆×C₄₃	—	4	8	no	—
107	SD₁₆×C₄₃	—	4	8	no	—
108	C₂×C₈×C₄₃	—	2	2	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	4	no	—
111	C₂×C₈×C₄₃	—	2	4	no	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	4	4	no	—
117	C₄⋊C₄×C₄₃	—	4	2	no	—
118	C₄⋊C₄×C₄₃	—	4	2	no	—
119	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²⋊C₄×C₄₃	—	4	8	no	—
121	C₂²⋊C₄×C₄₃	—	4	8	no	—
122	C₄²×C₄₃	—	2	4	no	—
123	C₄²×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	2	2	no	—
127	C₄²×C₄₃	—	4	2	no	—
128	C₄²×C₄₃	—	4	2	no	—
129	C₄²×C₄₃	C₂×D₄	1	2	yes	—
130	C₄²×C₄₃	#41	1	2	yes	—
131	C₂³×C₄₃	—	4	2	no	—
132	C₂³×C₄₃	—	4	4	no	—
133	C₂³×C₄₃	—	4	2	no	—
134	C₂³×C₄₃	—	4	2	no	—
135	C₂³×C₄₃	—	4	4	no	—
136	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₄₃	—	2	2	no	—
138	Q₈×C₄₃	—	2	2	no	—
139	Q₈×C₄₃	—	4	2	no	—
140	Q₈×C₄₃	—	4	2	no	—
141	Q₈×C₄₃	—	4	2	no	—
142	Q₈×C₄₃	—	4	4	no	—
143	D₄×C₄₃	—	4	2	no	—
144	D₄×C₄₃	—	4	2	no	—
145	D₄×C₄₃	—	4	4	no	—
146	D₄×C₄₃	—	8	4	no	—
147	D₄×C₄₃	—	8	4	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	#121	1	2	yes	—
165	C₂×C₄×C₄₃	#121	1	2	yes	—
166	C₂×C₄×C₄₃	#135	1	2	yes	—
167	C₂×C₄×C₄₃	#137	1	2	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₄₃	—	4	2	no	—
173	C₈×C₄₃	—	4	2	no	—
174	#29797	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₄₃	—	8	2	no	—
176	C₂²×C₄₃	—	8	4	no	—
177	C₂²×C₄₃	—	8	4	no	—
178	C₂²×C₄₃	—	8	2	no	—
179	C₂²×C₄₃	—	8	2	no	—
180	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
181	C₂²×C₄₃	#535	1	2	yes	—
182	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
183	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
184	C₂²×C₄₃	#575	1	2	yes	—
185	C₄×C₄₃	—	2	2	no	—
186	C₄×C₄₃	—	4	2	no	—
187	C₄×C₄₃	—	4	2	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	4	2	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	#464	1	4	yes	—
193	C₄×C₄₃	#535	1	1	yes	characteristic
194	C₄×C₄₃	#535	1	1	yes	characteristic
195	C₄×C₄₃	#540	1	2	yes	—
196	C₂×#462	C₂×C₄₃	1	1	yes	characteristic, complemented
197	C₂×#460	C₂×C₄₃	1	1	yes	characteristic
198	#2858	C₂×C₄₃	1	1	yes	characteristic
199	#2295	C₂×C₄₃	1	1	yes	characteristic, complemented
200	#2042	C₂×C₄₃	1	4	yes	complemented
201	#2015	C₂×C₄₃	1	4	yes	complemented
202	#1982	C₂×C₄₃	1	1	yes	characteristic
203	#1981	C₂×C₄₃	1	1	yes	characteristic, complemented
204	#1831	C₂×C₄₃	1	1	yes	characteristic, complemented
205	C₂×C₄₃	—	16	2	no	—
206	C₂×C₄₃	#2619	1	1	yes	characteristic
207	C₂×C₄₃	C₂×#464	1	1	yes	characteristic
208	C₂×C₄₃	#3040	1	1	yes	characteristic
209	C₂×C₄₃	#3212	1	2	yes	—
210	C₂×C₄₃	#3216	1	2	yes	—
211	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
212	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
213	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
214	C₂×#127	C₂²×C₄₃	1	1	yes	characteristic
215	C₂×#124	C₂²×C₄₃	1	4	yes	—
216	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
217	#462	—	2	4	no	—
218	#460	—	2	4	no	—
219	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
221	C₂×#103	C₂²×C₄₃	1	2	yes	—
222	C₂×#103	C₂²×C₄₃	1	4	yes	—
223	C₂×#102	C₂²×C₄₃	1	2	yes	—
224	C₂×#102	C₂²×C₄₃	1	4	yes	—
225	#391	C₂²×C₄₃	1	2	yes	—
226	#390	—	2	1	no	—
227	#390	—	2	1	no	—
228	#390	—	2	2	no	—
229	#389	C₂²×C₄₃	1	2	yes	—
230	#387	—	2	2	no	—
231	C₄×C₄⋊C₄	—	2	1	no	—
232	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
233	#376	—	2	1	no	—
234	C₄³	C₂²×C₄₃	1	1	yes	characteristic
235	#336	C₂²×C₄₃	1	4	yes	—
236	C₄₃	#29797	1	1	yes	characteristic, direct product factor, Sylow
237	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
238	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
242	C₂×Q₁₆	—	2	4	no	—
243	C₂×Q₁₆	—	4	4	no	—
244	C₂×SD₁₆	—	2	4	no	—
245	C₂×SD₁₆	—	4	4	no	—
246	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
247	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
248	C₄⋊Q₈	—	2	2	no	—
249	C₄⋊Q₈	—	2	2	no	—
250	#127	—	2	2	no	—
251	#127	—	2	2	no	—
252	#124	—	4	4	no	—
253	#124	—	4	4	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	D₄×C₄₃	1	4	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	2	no	—
260	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
261	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₄	—	2	4	no	—
263	C₂×C₂²⋊C₄	—	2	4	no	—
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₄₃	1	2	yes	—
269	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
270	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	#103	—	2	4	no	—
274	#103	—	4	4	no	—
275	#102	—	2	4	no	—
276	#102	—	4	4	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	1	no	—
281	C₂⁴	—	2	2	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	4	4	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
305	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
308	Q₁₆	—	4	8	no	—
309	SD₁₆	—	4	8	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	2	4	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²⋊C₄	—	4	8	no	—
323	C₂²⋊C₄	—	4	8	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	4	2	no	—
330	C₄²	—	4	2	no	—
331	C₄²	C₂×D₄×C₄₃	1	2	yes	—
332	C₄²	#41×C₄₃	1	2	yes	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	4	no	—
338	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
339	Q₈	—	2	2	no	—
340	Q₈	—	2	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	4	no	—
345	D₄	—	4	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	4	no	—
349	D₄	—	8	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	#121×C₄₃	1	2	yes	—
367	C₂×C₄	#121×C₄₃	1	2	yes	—
368	C₂×C₄	#135×C₄₃	1	2	yes	—
369	C₂×C₄	#137×C₄₃	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
372	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
373	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	4	no	—
378	C₂²	—	8	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
382	C₂²	C₄₃×#535	1	2	yes	—
383	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
384	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
385	C₂²	C₄₃×#575	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	C₄₃×#464	1	4	yes	—
394	C₄	C₄₃×#535	1	1	yes	characteristic
395	C₄	C₄₃×#535	1	1	yes	characteristic
396	C₄	C₄₃×#540	1	2	yes	—
397	C₂	—	16	2	no	—
398	C₂	C₄₃×#2619	1	1	yes	characteristic
399	C₂	C₂×C₄₃×#464	1	1	yes	characteristic
400	C₂	C₄₃×#3040	1	1	yes	characteristic
401	C₂	C₄₃×#3212	1	2	yes	—
402	C₂	C₄₃×#3216	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#127×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄³×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#462	C₂	semidirect
4. C₄₃×#2295	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2015	C₂	semidirect
8. C₄₃×#1981	C₂	semidirect
9. C₄₃×#1831	C₂	semidirect
174. #29797	C₄₃	direct (N × H)
196. C₂×#462	C₂×C₄₃	semidirect
199. #2295	C₂×C₄₃	semidirect
200. #2042	C₂×C₄₃	semidirect
201. #2015	C₂×C₄₃	semidirect
203. #1981	C₂×C₄₃	semidirect
204. #1831	C₂×C₄₃	semidirect
236. C₄₃	#29797	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×#462	2
C₂×C₄₃×#460	2
C₄₃×#2858	2
C₄₃×#2295	2
C₄₃×#2042	2
C₄₃×#2015	2
C₄₃×#1982	2
C₄₃×#1981	2
C₄₃×#1831	2
#29797	43

Subgroups — C43×#29797 #24949814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29797 #24949814