Subgroups — C₄₃×#22964 #24942981

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#475	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2365	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1990	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1948	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1941	C₂	1	2	yes	maximal
7	C₄₃×#1920	C₂	1	2	yes	maximal
8	C₄₃×#1865	C₂	1	2	yes	maximal
9	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₄×#103×C₄₃	C₂	1	2	yes	maximal
11	C₄×#103×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
14	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#475	C₄	1	8	yes	complemented
17	C₂×#106×C₄₃	C₂²	1	2	yes	—
18	C₂×#106×C₄₃	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#103×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#391	—	2	1	no	—
26	C₄₃×#389	—	2	2	no	—
27	C₄₃×#389	C₂²	1	2	yes	—
28	C₄₃×#389	C₂²	1	2	yes	—
29	C₄₃×#387	—	2	2	no	—
30	C₄₃×#384	—	2	1	no	—
31	C₄₃×#384	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
33	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	1	yes	characteristic
38	C₄₃×#340	C₂²	1	2	yes	—
39	C₄₃×#340	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₃	—	2	1	no	—
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₄₃	—	2	2	no	—
48	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₄₃	—	2	2	no	—
50	C₄×Q₈×C₄₃	—	2	4	no	—
51	C₄×Q₈×C₄₃	—	4	2	no	—
52	C₄×Q₈×C₄₃	—	4	4	no	—
53	C₄×Q₈×C₄₃	C₂×C₄	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	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₃	—	2	1	no	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	1	no	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	#106×C₄₃	—	4	2	no	—
75	#106×C₄₃	C₂×C₄	1	8	yes	—
76	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
77	#103×C₄₃	—	2	2	no	—
78	#103×C₄₃	C₂×C₄	1	8	yes	—
79	#103×C₄₃	Q₈	1	4	yes	complemented
80	C₄×C₈×C₄₃	—	2	2	no	—
81	C₄×C₈×C₄₃	—	4	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	#95×C₄₃	—	2	1	no	—
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	D₄	1	2	yes	—
87	C₂×Q₈×C₄₃	—	2	4	no	—
88	C₂×Q₈×C₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	—	2	1	no	—
90	C₂×Q₈×C₄₃	—	2	1	no	—
91	C₂×Q₈×C₄₃	—	4	2	no	—
92	C₂×Q₈×C₄₃	—	4	2	no	—
93	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
95	C₂×Q₈×C₄₃	#41	1	2	yes	—
96	C₂²×C₄×C₄₃	—	2	1	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	1	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
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	2	yes	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	1	no	—
112	C₂×C₈×C₄₃	—	2	1	no	—
113	C₂×C₈×C₄₃	—	2	1	no	—
114	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
116	C₄⋊C₄×C₄₃	—	2	4	no	—
117	C₄⋊C₄×C₄₃	—	2	4	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	4	4	no	—
127	C₄⋊C₄×C₄₃	—	4	4	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	8	1	no	—
130	C₄⋊C₄×C₄₃	—	8	2	no	—
131	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
135	C₄²×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	4	4	no	—
139	C₄²×C₄₃	—	4	4	no	—
140	C₄²×C₄₃	—	4	2	no	—
141	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
142	C₄²×C₄₃	#41	1	2	yes	—
143	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₃	—	2	2	no	—
145	Q₈×C₄₃	—	2	2	no	—
146	Q₈×C₄₃	—	2	2	no	—
147	Q₈×C₄₃	—	4	8	no	—
148	Q₈×C₄₃	C₄×Q₈	1	4	yes	complemented
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	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
177	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
178	C₂×C₄×C₄₃	#135	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₈×C₄₃	—	2	4	no	—
186	C₈×C₄₃	—	2	2	no	—
187	C₈×C₄₃	—	4	1	no	—
188	#22964	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
190	C₂²×C₄₃	#546	1	1	yes	characteristic
191	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
192	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
194	C₂²×C₄₃	#577	1	1	yes	characteristic
195	C₂²×C₄₃	#578	1	1	yes	characteristic
196	C₄×C₄₃	—	2	4	no	—
197	C₄×C₄₃	—	2	2	no	—
198	C₄×C₄₃	—	2	4	no	—
199	C₄×C₄₃	—	4	2	no	—
200	C₄×C₄₃	—	4	4	no	—
201	C₄×C₄₃	—	4	2	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	C₄×SD₁₆	1	4	yes	—
206	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
207	C₄×C₄₃	#520	1	1	yes	characteristic
208	C₄×C₄₃	#552	1	1	yes	characteristic
209	C₄×C₄₃	#554	1	1	yes	characteristic
210	C₂×#475	C₂×C₄₃	1	1	yes	characteristic
211	#2365	C₂×C₄₃	1	1	yes	characteristic
212	Q₈×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
213	#1990	C₂×C₄₃	1	1	yes	characteristic
214	#1948	C₂×C₄₃	1	1	yes	characteristic
215	#1941	C₂×C₄₃	1	2	yes	—
216	#1920	C₂×C₄₃	1	2	yes	—
217	#1865	C₂×C₄₃	1	2	yes	—
218	C₈×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
219	C₄×#103	C₂×C₄₃	1	2	yes	—
220	C₄×#103	C₂×C₄₃	1	1	yes	characteristic
221	C₂×C₄₃	#2360	1	1	yes	characteristic
222	C₂×C₄₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
223	C₂×C₄₃	#2947	1	1	yes	characteristic
224	C₂×C₄₃	#3298	1	1	yes	characteristic
225	C₂×C₄₃	#3304	1	1	yes	characteristic
226	C₂×C₄₃	Q₈×SD₁₆	1	1	yes	characteristic
227	C₂×C₄₃	#3383	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	—	2	1	no	—
230	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
231	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
232	#475	C₄×C₄₃	1	8	yes	complemented
233	C₂×#106	C₂²×C₄₃	1	2	yes	—
234	C₂×#106	C₂²×C₄₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×#103	C₂²×C₄₃	1	2	yes	—
238	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
241	#391	—	2	1	no	—
242	#389	—	2	2	no	—
243	#389	C₂²×C₄₃	1	2	yes	—
244	#389	C₂²×C₄₃	1	2	yes	—
245	#387	—	2	2	no	—
246	#384	—	2	1	no	—
247	#384	C₂²×C₄₃	1	1	yes	characteristic
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
252	#340	C₂²×C₄₃	1	2	yes	—
253	#340	C₂²×C₄₃	1	1	yes	characteristic
254	#340	C₂²×C₄₃	1	2	yes	—
255	#340	C₂²×C₄₃	1	1	yes	characteristic
256	#340	C₂²×C₄₃	1	2	yes	—
257	#336	C₂²×C₄₃	1	2	yes	—
258	C₄₃	#22964	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×Q₈	—	2	4	no	—
268	C₄×Q₈	—	4	2	no	—
269	C₄×Q₈	—	4	4	no	—
270	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
290	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
291	#106	—	4	2	no	—
292	#106	C₂×C₄×C₄₃	1	8	yes	—
293	C₄⋊C₈	C₂×C₄×C₄₃	1	4	yes	—
294	#103	—	2	2	no	—
295	#103	C₂×C₄×C₄₃	1	8	yes	—
296	#103	Q₈×C₄₃	1	4	yes	complemented
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	4	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	D₄×C₄₃	1	2	yes	—
304	C₂×Q₈	—	2	4	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	—	4	2	no	—
310	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
311	C₂×Q₈	C₂×Q₈×C₄₃	1	2	yes	—
312	C₂×Q₈	#41×C₄₃	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	C₂²×C₄×C₄₃	1	4	yes	—
332	C₂×C₈	C₂×Q₈×C₄₃	1	2	yes	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	8	1	no	—
347	C₄⋊C₄	—	8	2	no	—
348	C₄⋊C₄	SD₁₆×C₄₃	1	4	yes	—
349	C₄⋊C₄	C₂²×C₄×C₄₃	1	4	yes	—
350	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
351	C₄⋊C₄	C₂×Q₈×C₄₃	1	2	yes	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	4	4	no	—
356	C₄²	—	4	4	no	—
357	C₄²	—	4	2	no	—
358	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
359	C₄²	#41×C₄₃	1	2	yes	—
360	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	2	2	no	—
364	Q₈	—	4	8	no	—
365	Q₈	C₄×Q₈×C₄₃	1	4	yes	complemented
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
392	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
393	C₂×C₄	C₂×SD₁₆×C₄₃	1	4	yes	—
394	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
395	C₂×C₄	#135×C₄₃	1	2	yes	—
396	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×Q₈×C₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
400	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
401	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
402	C₈	—	2	4	no	—
403	C₈	—	2	2	no	—
404	C₈	—	4	1	no	—
405	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
406	C₂²	C₄₃×#546	1	1	yes	characteristic
407	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
408	C₂²	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
409	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
410	C₂²	C₄₃×#577	1	1	yes	characteristic
411	C₂²	C₄₃×#578	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	4	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	C₄×SD₁₆×C₄₃	1	4	yes	—
422	C₄	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
423	C₄	C₄₃×#520	1	1	yes	characteristic
424	C₄	C₄₃×#552	1	1	yes	characteristic
425	C₄	C₄₃×#554	1	1	yes	characteristic
426	C₂	C₄₃×#2360	1	1	yes	characteristic
427	C₂	C₂×C₄×SD₁₆×C₄₃	1	1	yes	characteristic
428	C₂	C₄₃×#2947	1	1	yes	characteristic
429	C₂	C₄₃×#3298	1	1	yes	characteristic
430	C₂	C₄₃×#3304	1	1	yes	characteristic
431	C₂	Q₈×SD₁₆×C₄₃	1	1	yes	characteristic
432	C₂	C₄₃×#3383	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
16. C₄₃×#475	C₄	semidirect
79. #103×C₄₃	Q₈	semidirect
148. Q₈×C₄₃	C₄×Q₈	semidirect
188. #22964	C₄₃	direct (N × H)
232. #475	C₄×C₄₃	semidirect
258. C₄₃	#22964	direct (N × H)
296. #103	Q₈×C₄₃	semidirect
365. Q₈	C₄×Q₈×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#475	2
C₄₃×#2365	2
Q₈×C₄⋊C₄×C₄₃	2
C₄₃×#1990	2
C₄₃×#1948	2
C₄₃×#1941	2
C₄₃×#1920	2
C₄₃×#1865	2
C₈×C₄⋊C₄×C₄₃	2
C₄×#103×C₄₃	2
#22964	43

Subgroups — C43×#22964 #24942981

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#22964 #24942981