Subgroups — C₄₃×#21858 #24941875

Order 11008.

1038 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3455	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1995	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1994	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1871	C₂	1	4	yes	maximal, complemented
9	C₄₃×#1806	C₂	1	4	yes	maximal, complemented
10	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
11	C₄₃×#542	C₄	1	4	yes	complemented
12	C₄₃×#541	C₄	1	2	yes	complemented
13	C₄₃×#540	C₄	1	2	yes	complemented
14	C₄₃×#539	—	2	2	no	—
15	C₄₃×#538	—	2	2	no	—
16	C₄₃×#533	C₂²	1	1	yes	characteristic
17	C₄₃×#532	C₂²	1	1	yes	characteristic
18	C₄₃×#529	—	2	4	no	—
19	C₄₃×#525	C₂²	1	2	yes	—
20	C₄×#41×C₄₃	C₂²	1	2	yes	—
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#424	—	2	4	no	—
23	C₄₃×#423	C₂²	1	1	yes	characteristic
24	C₄₃×#423	C₂²	1	1	yes	characteristic
25	C₄₃×#423	C₂²	1	2	yes	—
26	C₂×#104×C₄₃	C₂²	1	4	yes	—
27	C₂×#104×C₄₃	C₂²	1	4	yes	—
28	C₄₃×#388	—	2	2	no	—
29	C₄₃×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
32	C₄₃×#376	C₂²	1	1	yes	characteristic
33	C₄³×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#339	C₂²	1	4	yes	—
35	C₄₃×#339	C₂²	1	4	yes	—
36	C₂×#41×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
38	C₂×M₁₆×C₄₃	—	2	2	no	—
39	C₂×M₁₆×C₄₃	—	4	4	no	—
40	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
41	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₄₃	—	2	2	no	—
43	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
45	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
46	#126×C₄₃	—	2	4	no	—
47	#126×C₄₃	—	2	4	no	—
48	#125×C₄₃	—	2	4	no	—
49	#125×C₄₃	C₂×C₄	1	2	yes	—
50	#124×C₄₃	—	2	4	no	—
51	#124×C₄₃	C₂×C₄	1	2	yes	—
52	#123×C₄₃	—	2	2	no	—
53	#123×C₄₃	—	2	4	no	—
54	#123×C₄₃	—	2	4	no	—
55	C₂²⋊Q₈×C₄₃	—	2	2	no	—
56	C₂²⋊Q₈×C₄₃	—	2	4	no	—
57	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
58	#121×C₄₃	—	2	2	no	—
59	#121×C₄₃	—	2	4	no	—
60	#121×C₄₃	C₂×C₄	1	4	yes	—
61	#120×C₄₃	—	2	2	no	—
62	C₄×Q₈×C₄₃	—	2	2	no	—
63	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
64	C₄×D₄×C₄₃	—	2	4	no	—
65	C₄×D₄×C₄₃	—	2	4	no	—
66	C₄×D₄×C₄₃	—	2	2	no	—
67	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
68	#117×C₄₃	—	2	2	no	—
69	#117×C₄₃	C₂×C₄	1	2	yes	—
70	#117×C₄₃	C₂×C₄	1	2	yes	—
71	#117×C₄₃	D₄	1	4	yes	—
72	#117×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
74	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₃	—	2	4	no	—
84	C₄⋊C₈×C₄₃	—	2	2	no	—
85	C₄⋊C₈×C₄₃	—	2	2	no	—
86	#104×C₄₃	—	4	4	no	—
87	#104×C₄₃	—	4	4	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	—	2	2	no	—
90	#95×C₄₃	—	2	2	no	—
91	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
92	#41×C₄₃	—	2	4	no	—
93	#41×C₄₃	—	2	4	no	—
94	C₂×Q₈×C₄₃	—	2	2	no	—
95	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	4	no	—
98	C₂×D₄×C₄₃	—	2	2	no	—
99	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	4	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	M₁₆×C₄₃	—	2	4	no	—
113	M₁₆×C₄₃	—	2	4	no	—
114	M₁₆×C₄₃	—	4	4	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	4	4	no	—
118	C₄⋊C₄×C₄₃	—	2	4	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	4	4	no	—
124	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
125	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
126	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
127	C₂²⋊C₄×C₄₃	—	2	4	no	—
128	C₂²⋊C₄×C₄₃	—	2	4	no	—
129	C₂²⋊C₄×C₄₃	—	2	4	no	—
130	C₂²⋊C₄×C₄₃	—	2	4	no	—
131	C₂²⋊C₄×C₄₃	—	2	2	no	—
132	C₂²⋊C₄×C₄₃	—	4	4	no	—
133	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
134	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	4	yes	—
135	C₄²×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	2	no	—
139	C₄²×C₄₃	—	2	2	no	—
140	C₄²×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	4	4	no	—
142	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
143	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₄²×C₄₃	C₂×D₄	1	2	yes	—
146	C₄²×C₄₃	C₂×D₄	1	2	yes	—
147	C₂³×C₄₃	—	2	2	no	—
148	C₂³×C₄₃	—	2	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
152	Q₈×C₄₃	—	2	4	no	—
153	Q₈×C₄₃	—	8	2	no	—
154	D₄×C₄₃	—	2	4	no	—
155	D₄×C₄₃	—	4	4	no	—
156	D₄×C₄₃	—	8	2	no	—
157	D₄×C₄₃	—	8	4	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	8	4	no	—
175	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
176	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
183	C₈×C₄₃	—	4	2	no	—
184	C₈×C₄₃	—	4	2	no	—
185	#21858	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₃	—	2	2	no	—
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	4	2	no	—
190	C₂²×C₄₃	—	4	4	no	—
191	C₂²×C₄₃	—	8	2	no	—
192	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₃	#537	1	2	yes	—
194	C₄×C₄₃	—	2	2	no	—
195	C₄×C₄₃	—	2	4	no	—
196	C₄×C₄₃	—	2	2	no	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	4	4	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	4	no	—
201	C₄×C₄₃	—	8	2	no	—
202	C₄×C₄₃	#520	1	2	yes	—
203	C₄×C₄₃	#535	1	1	yes	characteristic
204	C₄×C₄₃	#536	1	1	yes	characteristic
205	#3455	C₂×C₄₃	1	1	yes	characteristic
206	#2905	C₂×C₄₃	1	1	yes	characteristic, complemented
207	#2298	C₂×C₄₃	1	1	yes	characteristic, complemented
208	#1995	C₂×C₄₃	1	1	yes	characteristic, complemented
209	#1994	C₂×C₄₃	1	1	yes	characteristic, complemented
210	#1963	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#1962	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#1871	C₂×C₄₃	1	4	yes	complemented
213	#1806	C₂×C₄₃	1	4	yes	complemented
214	C₂×C₄₃	—	2	2	no	—
215	C₂×C₄₃	—	4	2	no	—
216	C₂×C₄₃	—	8	2	no	—
217	C₂×C₄₃	#2311	1	1	yes	characteristic
218	C₂×C₄₃	#2901	1	2	yes	—
219	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
220	#542	C₄×C₄₃	1	4	yes	complemented
221	#541	C₄×C₄₃	1	2	yes	complemented
222	#540	C₄×C₄₃	1	2	yes	complemented
223	#539	—	2	2	no	—
224	#538	—	2	2	no	—
225	#533	C₂²×C₄₃	1	1	yes	characteristic
226	#532	C₂²×C₄₃	1	1	yes	characteristic
227	#529	—	2	4	no	—
228	#525	C₂²×C₄₃	1	2	yes	—
229	C₄×#41	C₂²×C₄₃	1	2	yes	—
230	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
231	#424	—	2	4	no	—
232	#423	C₂²×C₄₃	1	2	yes	—
233	#423	C₂²×C₄₃	1	1	yes	characteristic
234	#423	C₂²×C₄₃	1	1	yes	characteristic
235	C₂×#104	C₂²×C₄₃	1	4	yes	—
236	C₂×#104	C₂²×C₄₃	1	4	yes	—
237	#388	—	2	2	no	—
238	#387	—	2	2	no	—
239	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
241	#376	C₂²×C₄₃	1	1	yes	characteristic
242	C₄³	C₂²×C₄₃	1	1	yes	characteristic
243	#339	C₂²×C₄₃	1	4	yes	—
244	#339	C₂²×C₄₃	1	4	yes	—
245	C₄₃	#21858	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#41	C₂³×C₄₃	1	2	yes	—
247	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	—	4	4	no	—
250	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
251	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
252	C₂²×C₈	—	2	2	no	—
253	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
254	C₄⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
255	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
256	#126	—	2	4	no	—
257	#126	—	2	4	no	—
258	#125	—	2	4	no	—
259	#125	C₂×C₄×C₄₃	1	2	yes	—
260	#124	—	2	4	no	—
261	#124	C₂×C₄×C₄₃	1	2	yes	—
262	#123	—	2	2	no	—
263	#123	—	2	4	no	—
264	#123	—	2	4	no	—
265	C₂²⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	2	4	no	—
267	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
268	#121	—	2	2	no	—
269	#121	—	2	4	no	—
270	#121	C₂×C₄×C₄₃	1	4	yes	—
271	#120	—	2	2	no	—
272	C₄×Q₈	—	2	2	no	—
273	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
274	C₄×D₄	—	2	4	no	—
275	C₄×D₄	—	2	4	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
278	#117	—	2	2	no	—
279	#117	C₂×C₄×C₄₃	1	2	yes	—
280	#117	C₂×C₄×C₄₃	1	2	yes	—
281	#117	D₄×C₄₃	1	4	yes	—
282	#117	C₂³×C₄₃	1	2	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
287	C₂×C₄²	—	2	2	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	#104	—	4	4	no	—
297	#104	—	4	4	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
302	#41	—	2	4	no	—
303	#41	—	2	4	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
318	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	4	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	4	4	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
335	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
336	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	4	no	—
340	C₂²⋊C₄	—	2	4	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
344	C₂²⋊C₄	C₂²⋊C₄×C₄₃	1	4	yes	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	2	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
353	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
354	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
355	C₄²	C₂×D₄×C₄₃	1	2	yes	—
356	C₄²	C₂×D₄×C₄₃	1	2	yes	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
361	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
362	Q₈	—	2	4	no	—
363	Q₈	—	8	2	no	—
364	D₄	—	2	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	8	4	no	—
385	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
386	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
387	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
388	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
389	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
391	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
392	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
393	C₈	—	4	2	no	—
394	C₈	—	4	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
402	C₂²	C₄₃×#537	1	2	yes	—
403	C₄	—	2	4	no	—
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₄₃×#520	1	2	yes	—
412	C₄	C₄₃×#535	1	1	yes	characteristic
413	C₄	C₄₃×#536	1	1	yes	characteristic
414	C₂	—	2	2	no	—
415	C₂	—	4	2	no	—
416	C₂	—	8	2	no	—
417	C₂	C₄₃×#2311	1	1	yes	characteristic
418	C₂	C₄₃×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₄₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₄₃×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2905	C₂	semidirect
3. C₄₃×#2298	C₂	semidirect
4. C₄₃×#1995	C₂	semidirect
5. C₄₃×#1994	C₂	semidirect
6. C₄₃×#1963	C₂	semidirect
7. C₄₃×#1962	C₂	semidirect
8. C₄₃×#1871	C₂	semidirect
9. C₄₃×#1806	C₂	semidirect
11. C₄₃×#542	C₄	semidirect
12. C₄₃×#541	C₄	semidirect
13. C₄₃×#540	C₄	semidirect
185. #21858	C₄₃	direct (N × H)
206. #2905	C₂×C₄₃	semidirect
207. #2298	C₂×C₄₃	semidirect
208. #1995	C₂×C₄₃	semidirect
209. #1994	C₂×C₄₃	semidirect
210. #1963	C₂×C₄₃	semidirect
211. #1962	C₂×C₄₃	semidirect
212. #1871	C₂×C₄₃	semidirect
213. #1806	C₂×C₄₃	semidirect
220. #542	C₄×C₄₃	semidirect
221. #541	C₄×C₄₃	semidirect
222. #540	C₄×C₄₃	semidirect
245. C₄₃	#21858	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3455	2
C₄₃×#2905	2
C₄₃×#2298	2
C₄₃×#1995	2
C₄₃×#1994	2
C₄₃×#1963	2
C₄₃×#1962	2
C₄₃×#1871	2
C₄₃×#1806	2
#21858	43

Subgroups — C43×#21858 #24941875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#21858 #24941875