Subgroups — C₄₃×#20888 #24940905

Order 11008.

1502 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#410	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2297	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2296	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1867	C₂	1	8	yes	maximal, complemented
6	C₄₃×#1740	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
8	C₄₃×#520	—	2	4	no	—
9	C₄₃×#519	—	2	1	no	—
10	C₄₃×#518	—	2	1	no	—
11	C₄₃×#518	C₂²	1	4	yes	—
12	C₄×#41×C₄₃	—	2	4	no	—
13	C₂×#117×C₄₃	—	2	2	no	—
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	C₂²	1	2	yes	—
16	C₂×#117×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#410	C₄	1	8	yes	complemented
19	C₂×#99×C₄₃	C₂²	1	4	yes	—
20	C₄₃×#391	—	2	1	no	—
21	C₄₃×#390	—	2	1	no	—
22	C₄₃×#389	—	2	4	no	—
23	C₄₃×#386	C₂²	1	4	yes	—
24	C₄₃×#385	C₂²	1	8	yes	—
25	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₄×C₂²⋊C₄×C₄₃	—	2	2	no	—
27	C₄₃×#342	C₂²	1	8	yes	—
28	C₂×#41×C₄₃	—	2	2	no	—
29	C₂×#41×C₄₃	—	2	2	no	—
30	C₂×#41×C₄₃	—	2	4	no	—
31	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
32	C₂×#41×C₄₃	Q₈	1	4	yes	—
33	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
35	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₄₃	D₄	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₄×Q₈×C₄₃	—	2	8	no	—
40	C₄×D₄×C₄₃	—	2	8	no	—
41	C₄×D₄×C₄₃	—	2	16	no	—
42	#117×C₄₃	—	2	4	no	—
43	#117×C₄₃	—	2	4	no	—
44	#117×C₄₃	—	2	2	no	—
45	#117×C₄₃	—	2	4	no	—
46	#117×C₄₃	—	2	2	no	—
47	#117×C₄₃	—	2	2	no	—
48	#117×C₄₃	—	2	2	no	—
49	#117×C₄₃	—	2	4	no	—
50	#117×C₄₃	—	2	4	no	—
51	#117×C₄₃	C₂×C₄	1	8	yes	complemented
52	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
57	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
62	C₂×C₄²×C₄₃	—	2	4	no	—
63	C₂×C₄²×C₄₃	—	2	2	no	—
64	C₂×C₄²×C₄₃	—	2	1	no	—
65	C₂×C₄²×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	2	no	—
67	C₂×C₄²×C₄₃	—	2	1	no	—
68	C₂×C₄²×C₄₃	—	2	1	no	—
69	C₂×C₄²×C₄₃	D₄	1	4	yes	—
70	#99×C₄₃	C₂×C₄	1	16	yes	complemented
71	#95×C₄₃	—	2	4	no	—
72	#95×C₄₃	—	2	8	no	—
73	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
75	#41×C₄₃	—	2	8	no	—
76	#41×C₄₃	—	2	8	no	—
77	#41×C₄₃	—	2	8	no	—
78	#41×C₄₃	—	2	8	no	—
79	C₂×Q₈×C₄₃	—	2	2	no	—
80	C₂×Q₈×C₄₃	—	2	2	no	—
81	C₂×Q₈×C₄₃	C₄⋊C₄	1	4	yes	complemented
82	C₂×D₄×C₄₃	—	2	2	no	—
83	C₂×D₄×C₄₃	—	2	2	no	—
84	C₂×D₄×C₄₃	—	2	4	no	—
85	C₂×D₄×C₄₃	—	2	4	no	—
86	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	complemented
87	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
88	C₂×D₄×C₄₃	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	8	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	4	4	no	—
98	C₂²×C₄×C₄₃	C₄⋊C₄	1	8	yes	complemented
99	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₄₃	#41	1	4	yes	—
108	C₄⋊C₄×C₄₃	—	2	8	no	—
109	C₄⋊C₄×C₄₃	—	2	8	no	—
110	C₄⋊C₄×C₄₃	—	2	4	no	—
111	C₄⋊C₄×C₄₃	—	2	4	no	—
112	C₄⋊C₄×C₄₃	—	4	16	no	—
113	C₄⋊C₄×C₄₃	—	4	2	no	—
114	C₂²⋊C₄×C₄₃	—	2	8	no	—
115	C₂²⋊C₄×C₄₃	—	2	4	no	—
116	C₂²⋊C₄×C₄₃	—	2	4	no	—
117	C₂²⋊C₄×C₄₃	—	2	4	no	—
118	C₂²⋊C₄×C₄₃	—	2	4	no	—
119	C₂²⋊C₄×C₄₃	—	4	8	no	—
120	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
121	C₄²×C₄₃	—	2	8	no	—
122	C₄²×C₄₃	—	2	8	no	—
123	C₄²×C₄₃	—	2	4	no	—
124	C₄²×C₄₃	—	2	4	no	—
125	C₄²×C₄₃	—	4	2	no	—
126	C₄²×C₄₃	—	4	1	no	—
127	C₄²×C₄₃	—	4	1	no	—
128	C₄²×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	2	2	no	—
130	C₂³×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	4	2	no	—
132	C₂³×C₄₃	—	4	4	no	—
133	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
134	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
135	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
136	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
137	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
138	C₂³×C₄₃	C₂×#41	1	2	yes	—
139	Q₈×C₄₃	—	2	8	no	—
140	D₄×C₄₃	—	2	8	no	—
141	D₄×C₄₃	—	2	8	no	—
142	D₄×C₄₃	—	2	8	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	8	no	—
146	C₂×C₄×C₄₃	—	2	8	no	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	2	8	no	—
149	C₂×C₄×C₄₃	—	2	8	no	—
150	C₂×C₄×C₄₃	—	2	8	no	—
151	C₂×C₄×C₄₃	—	4	8	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	4	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	8	no	—
156	C₂×C₄×C₄₃	—	4	4	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	8	8	no	—
159	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
160	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
164	C₂×C₄×C₄₃	#120	1	2	yes	—
165	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
169	C₂×C₄×C₄₃	#123	1	2	yes	—
170	C₂×C₄×C₄₃	#123	1	2	yes	—
171	#20888	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₄₃	—	2	2	no	—
173	C₂²×C₄₃	—	2	4	no	—
174	C₂²×C₄₃	—	2	4	no	—
175	C₂²×C₄₃	—	4	1	no	—
176	C₂²×C₄₃	—	4	1	no	—
177	C₂²×C₄₃	—	4	2	no	—
178	C₂²×C₄₃	—	4	4	no	—
179	C₂²×C₄₃	—	4	4	no	—
180	C₂²×C₄₃	—	8	2	no	—
181	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
183	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
185	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
186	C₄×C₄₃	—	2	4	no	—
187	C₄×C₄₃	—	4	8	no	—
188	C₄×C₄₃	—	4	4	no	—
189	C₄×C₄₃	—	4	8	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	#385	1	2	yes	—
192	C₄×C₄₃	#385	1	2	yes	—
193	C₄×C₄₃	#385	1	4	yes	—
194	#3428	C₂×C₄₃	1	1	yes	characteristic
195	C₂×#410	C₂×C₄₃	1	1	yes	characteristic
196	#2297	C₂×C₄₃	1	1	yes	characteristic
197	#2296	C₂×C₄₃	1	2	yes	complemented
198	#1867	C₂×C₄₃	1	8	yes	complemented
199	#1740	C₂×C₄₃	1	2	yes	complemented
200	C₂×C₄₃	—	2	2	no	—
201	C₂×C₄₃	—	2	1	no	—
202	C₂×C₄₃	—	2	1	no	—
203	C₂×C₄₃	—	2	2	no	—
204	C₂×C₄₃	—	4	4	no	—
205	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
206	C₂×C₄₃	#3025	1	2	yes	—
207	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
208	#520	—	2	4	no	—
209	#519	—	2	1	no	—
210	#518	—	2	1	no	—
211	#518	C₂²×C₄₃	1	4	yes	—
212	C₄×#41	—	2	4	no	—
213	C₂×#117	—	2	2	no	—
214	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
215	C₂×#117	C₂²×C₄₃	1	2	yes	—
216	C₂×#117	C₂²×C₄₃	1	2	yes	—
217	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
218	#410	C₄×C₄₃	1	8	yes	complemented
219	C₂×#99	C₂²×C₄₃	1	4	yes	—
220	#391	—	2	1	no	—
221	#390	—	2	1	no	—
222	#389	—	2	4	no	—
223	#386	C₂²×C₄₃	1	4	yes	—
224	#385	C₂²×C₄₃	1	8	yes	—
225	C₄×C₄⋊C₄	—	2	4	no	—
226	C₄×C₂²⋊C₄	—	2	2	no	—
227	#342	C₂²×C₄₃	1	8	yes	—
228	C₄₃	#20888	1	1	yes	characteristic, direct product factor, Sylow
229	C₂×#41	—	2	2	no	—
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
233	C₂×#41	Q₈×C₄₃	1	4	yes	—
234	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
235	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
236	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
237	C₂³×C₄	D₄×C₄₃	1	2	yes	—
238	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
239	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
240	C₄×Q₈	—	2	8	no	—
241	C₄×D₄	—	2	8	no	—
242	C₄×D₄	—	2	16	no	—
243	#117	—	2	4	no	—
244	#117	—	2	4	no	—
245	#117	—	2	2	no	—
246	#117	—	2	4	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	#117	—	2	4	no	—
251	#117	—	2	4	no	—
252	#117	C₂×C₄×C₄₃	1	8	yes	complemented
253	C₂×C₄⋊C₄	—	2	4	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	8	no	—
257	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
262	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	2	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	D₄×C₄₃	1	4	yes	—
271	#99	C₂×C₄×C₄₃	1	16	yes	complemented
272	#95	—	2	4	no	—
273	#95	—	2	8	no	—
274	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
275	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
276	#41	—	2	8	no	—
277	#41	—	2	8	no	—
278	#41	—	2	8	no	—
279	#41	—	2	8	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	C₄⋊C₄×C₄₃	1	4	yes	complemented
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	C₄⋊C₄×C₄₃	1	4	yes	complemented
288	C₂×D₄	C₂²×C₄×C₄₃	1	4	yes	—
289	C₂×D₄	C₂×Q₈×C₄₃	1	4	yes	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	C₄⋊C₄×C₄₃	1	8	yes	complemented
300	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
303	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
307	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
308	C₂²×C₄	#41×C₄₃	1	4	yes	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	2	8	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	4	16	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	2	8	no	—
316	C₂²⋊C₄	—	2	4	no	—
317	C₂²⋊C₄	—	2	4	no	—
318	C₂²⋊C₄	—	2	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	4	8	no	—
321	C₂²⋊C₄	C₂²×C₄×C₄₃	1	8	yes	—
322	C₄²	—	2	8	no	—
323	C₄²	—	2	8	no	—
324	C₄²	—	2	4	no	—
325	C₄²	—	2	4	no	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	4	no	—
334	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
335	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
336	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
337	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
338	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
339	C₂³	C₂×#41×C₄₃	1	2	yes	—
340	Q₈	—	2	8	no	—
341	D₄	—	2	8	no	—
342	D₄	—	2	8	no	—
343	D₄	—	2	8	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	8	8	no	—
360	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
361	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
362	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
364	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
365	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
366	C₂×C₄	#120×C₄₃	1	2	yes	—
367	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
370	C₂×C₄	#123×C₄₃	1	2	yes	—
371	C₂×C₄	#123×C₄₃	1	2	yes	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
382	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
383	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
384	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
385	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
386	C₄	—	2	4	no	—
387	C₄	—	4	8	no	—
388	C₄	—	4	4	no	—
389	C₄	—	4	8	no	—
390	C₄	—	8	2	no	—
391	C₄	C₄₃×#385	1	2	yes	—
392	C₄	C₄₃×#385	1	2	yes	—
393	C₄	C₄₃×#385	1	4	yes	—
394	C₂	—	2	2	no	—
395	C₂	—	2	1	no	—
396	C₂	—	2	1	no	—
397	C₂	—	2	2	no	—
398	C₂	—	4	4	no	—
399	C₂	C₂×C₄₃×#385	1	1	yes	characteristic
400	C₂	C₄₃×#3025	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	#120
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂×#120
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#2296	C₂	semidirect
5. C₄₃×#1867	C₂	semidirect
6. C₄₃×#1740	C₂	semidirect
18. C₄₃×#410	C₄	semidirect
51. #117×C₄₃	C₂×C₄	semidirect
70. #99×C₄₃	C₂×C₄	semidirect
81. C₂×Q₈×C₄₃	C₄⋊C₄	semidirect
86. C₂×D₄×C₄₃	C₄⋊C₄	semidirect
98. C₂²×C₄×C₄₃	C₄⋊C₄	semidirect
171. #20888	C₄₃	direct (N × H)
197. #2296	C₂×C₄₃	semidirect
198. #1867	C₂×C₄₃	semidirect
199. #1740	C₂×C₄₃	semidirect
218. #410	C₄×C₄₃	semidirect
228. C₄₃	#20888	direct (N × H)
252. #117	C₂×C₄×C₄₃	semidirect
271. #99	C₂×C₄×C₄₃	semidirect
282. C₂×Q₈	C₄⋊C₄×C₄₃	semidirect
287. C₂×D₄	C₄⋊C₄×C₄₃	semidirect
299. C₂²×C₄	C₄⋊C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₃×#3428	2
C₂×C₄₃×#410	2
C₄₃×#2297	2
C₄₃×#2296	2
C₄₃×#1867	2
C₄₃×#1740	2
#20888	43

Subgroups — C43×#20888 #24940905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20888 #24940905