Subgroups — C₄₃×#29759 #24949776

Order 11008.

812 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#485	C₂	1	2	yes	maximal
2	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2296	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2066	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1873	C₂	1	2	yes	maximal
11	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₄₃×#485	—	2	8	no	—
18	C₂×#107×C₄₃	C₂²	1	2	yes	—
19	C₂×#106×C₄₃	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
21	C₂×#103×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₄₃×#391	C₂²	1	2	yes	—
27	C₄₃×#389	—	2	1	no	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	C₂²	1	1	yes	characteristic
30	C₄₃×#389	C₂²	1	1	yes	characteristic
31	C₄₃×#389	C₂²	1	1	yes	characteristic
32	C₄₃×#389	C₂²	1	1	yes	characteristic
33	C₄₃×#385	—	2	1	no	—
34	C₄₃×#385	—	2	1	no	—
35	C₄₃×#384	C₂²	1	1	yes	characteristic
36	C₄₃×#380	—	2	1	no	—
37	C₄₃×#380	—	2	1	no	—
38	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#336	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	1	yes	characteristic
44	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₄₃	—	4	2	no	—
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	2	4	no	—
53	#117×C₄₃	—	2	2	no	—
54	#117×C₄₃	—	4	2	no	—
55	#117×C₄₃	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	—	2	1	no	—
74	C₂×C₄²×C₄₃	—	2	1	no	—
75	C₂×C₄²×C₄₃	—	4	2	no	—
76	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#107×C₄₃	—	2	4	no	—
81	#106×C₄₃	—	2	4	no	—
82	C₄⋊C₈×C₄₃	—	4	2	no	—
83	#103×C₄₃	—	2	4	no	—
84	#103×C₄₃	—	2	4	no	—
85	#103×C₄₃	—	4	2	no	—
86	#103×C₄₃	—	4	2	no	—
87	C₂²⋊C₈×C₄₃	—	2	4	no	—
88	#95×C₄₃	—	2	1	no	—
89	#95×C₄₃	—	2	1	no	—
90	#95×C₄₃	—	2	1	no	—
91	#95×C₄₃	—	2	1	no	—
92	#95×C₄₃	—	2	2	no	—
93	#95×C₄₃	—	2	2	no	—
94	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₃	—	2	2	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	2	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	2	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	1	no	—
107	C₂²×C₄×C₄₃	—	2	1	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	4	1	no	—
113	C₂²×C₄×C₄₃	—	4	1	no	—
114	C₂²×C₄×C₄₃	—	4	1	no	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	2	no	—
135	C₄⋊C₄×C₄₃	—	4	2	no	—
136	C₄⋊C₄×C₄₃	—	4	2	no	—
137	C₄⋊C₄×C₄₃	—	4	2	no	—
138	C₄⋊C₄×C₄₃	—	4	2	no	—
139	C₄⋊C₄×C₄₃	—	4	4	no	—
140	C₄⋊C₄×C₄₃	—	4	2	no	—
141	C₄⋊C₄×C₄₃	—	4	2	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₄⋊C₄×C₄₃	—	4	2	no	—
144	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₂²⋊C₄×C₄₃	—	4	2	no	—
148	C₂²⋊C₄×C₄₃	—	4	4	no	—
149	C₄²×C₄₃	—	2	4	no	—
150	C₄²×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	4	1	no	—
153	C₄²×C₄₃	—	4	1	no	—
154	C₄²×C₄₃	—	4	2	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	—	2	1	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	2	1	no	—
160	C₂³×C₄₃	—	2	1	no	—
161	C₂³×C₄₃	#121	1	2	yes	—
162	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	4	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	4	1	no	—
191	C₂×C₄×C₄₃	—	4	1	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	2	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	4	2	no	—
196	C₂×C₄×C₄₃	—	4	1	no	—
197	C₂×C₄×C₄₃	—	4	1	no	—
198	C₂×C₄×C₄₃	—	4	1	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	#121	1	2	yes	—
201	C₂×C₄×C₄₃	#135	1	2	yes	—
202	C₂×C₄×C₄₃	#137	1	2	yes	—
203	C₂×C₄×C₄₃	#137	1	2	yes	—
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	—	4	2	no	—
210	#29759	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₄₃	—	2	2	no	—
212	C₂²×C₄₃	—	2	2	no	—
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	—	4	1	no	—
215	C₂²×C₄₃	—	4	1	no	—
216	C₂²×C₄₃	—	4	1	no	—
217	C₂²×C₄₃	—	4	1	no	—
218	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₃	#534	1	1	yes	characteristic
220	C₂²×C₄₃	#536	1	1	yes	characteristic
221	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
222	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
223	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
224	C₂²×C₄₃	#575	1	1	yes	characteristic
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	2	2	no	—
227	C₄×C₄₃	—	2	2	no	—
228	C₄×C₄₃	—	2	2	no	—
229	C₄×C₄₃	—	4	1	no	—
230	C₄×C₄₃	—	4	2	no	—
231	C₄×C₄₃	—	4	2	no	—
232	C₄×C₄₃	—	8	2	no	—
233	C₄×C₄₃	—	8	1	no	—
234	C₄×C₄₃	—	8	1	no	—
235	C₄×C₄₃	—	8	2	no	—
236	C₄×C₄₃	#537	1	2	yes	—
237	C₄×C₄₃	#539	1	2	yes	—
238	C₂×#485	C₂×C₄₃	1	2	yes	—
239	#2857	C₂×C₄₃	1	1	yes	characteristic
240	#2296	C₂×C₄₃	1	1	yes	characteristic
241	#2084	C₂×C₄₃	1	1	yes	characteristic, complemented
242	#2083	C₂×C₄₃	1	1	yes	characteristic, complemented
243	#2068	C₂×C₄₃	1	2	yes	complemented
244	#2066	C₂×C₄₃	1	2	yes	complemented
245	#2043	C₂×C₄₃	1	1	yes	characteristic, complemented
246	#2043	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#1873	C₂×C₄₃	1	2	yes	—
248	#1797	C₂×C₄₃	1	1	yes	characteristic
249	C₂×C₄₃	—	4	2	no	—
250	C₂×C₄₃	#2618	1	1	yes	characteristic
251	C₂×C₄₃	#3035	1	1	yes	characteristic
252	C₂×C₄₃	#3039	1	1	yes	characteristic
253	C₂×C₄₃	#3190	1	1	yes	characteristic
254	C₂×C₄₃	#3196	1	1	yes	characteristic
255	C₂×C₄₃	#3231	1	1	yes	characteristic
256	C₂×C₄₃	#3237	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
258	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
259	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
260	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
261	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
262	#485	—	2	8	no	—
263	C₂×#107	C₂²×C₄₃	1	2	yes	—
264	C₂×#106	C₂²×C₄₃	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
266	C₂×#103	C₂²×C₄₃	1	2	yes	—
267	C₂×#103	C₂²×C₄₃	1	2	yes	—
268	C₂×#103	C₂²×C₄₃	1	2	yes	—
269	C₂×#103	C₂²×C₄₃	1	2	yes	—
270	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
271	#391	C₂²×C₄₃	1	2	yes	—
272	#389	—	2	1	no	—
273	#389	—	2	1	no	—
274	#389	C₂²×C₄₃	1	1	yes	characteristic
275	#389	C₂²×C₄₃	1	1	yes	characteristic
276	#389	C₂²×C₄₃	1	1	yes	characteristic
277	#389	C₂²×C₄₃	1	1	yes	characteristic
278	#385	—	2	1	no	—
279	#385	—	2	1	no	—
280	#384	C₂²×C₄₃	1	1	yes	characteristic
281	#380	—	2	1	no	—
282	#380	—	2	1	no	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	—	2	1	no	—
285	#340	C₂²×C₄₃	1	2	yes	—
286	#340	C₂²×C₄₃	1	2	yes	—
287	#336	C₂²×C₄₃	1	1	yes	characteristic
288	#336	C₂²×C₄₃	1	1	yes	characteristic
289	C₄₃	#29759	1	1	yes	characteristic, direct product factor, Sylow
290	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
291	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
292	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
296	C₄⋊Q₈	—	4	2	no	—
297	C₂²⋊Q₈	—	2	4	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	#117	—	2	2	no	—
300	#117	—	4	2	no	—
301	#117	D₄×C₄₃	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
314	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	—	4	2	no	—
322	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
323	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
324	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
326	#107	—	2	4	no	—
327	#106	—	2	4	no	—
328	C₄⋊C₈	—	4	2	no	—
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#103	—	4	2	no	—
332	#103	—	4	2	no	—
333	C₂²⋊C₈	—	2	4	no	—
334	#95	—	2	1	no	—
335	#95	—	2	1	no	—
336	#95	—	2	1	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
367	C₂²×C₄	#41×C₄₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
391	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	4	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	1	no	—
399	C₄²	—	4	1	no	—
400	C₄²	—	4	2	no	—
401	C₂³	—	2	1	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	#121×C₄₃	1	2	yes	—
408	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	2	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	#121×C₄₃	1	2	yes	—
447	C₂×C₄	#135×C₄₃	1	2	yes	—
448	C₂×C₄	#137×C₄₃	1	2	yes	—
449	C₂×C₄	#137×C₄₃	1	2	yes	—
450	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
452	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
453	C₂×C₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	4	1	no	—
460	C₂²	—	4	1	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
464	C₂²	C₄₃×#534	1	1	yes	characteristic
465	C₂²	C₄₃×#536	1	1	yes	characteristic
466	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
467	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
468	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
469	C₂²	C₄₃×#575	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	8	2	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	2	no	—
481	C₄	C₄₃×#537	1	2	yes	—
482	C₄	C₄₃×#539	1	2	yes	—
483	C₂	—	4	2	no	—
484	C₂	C₄₃×#2618	1	1	yes	characteristic
485	C₂	C₄₃×#3035	1	1	yes	characteristic
486	C₂	C₄₃×#3039	1	1	yes	characteristic
487	C₂	C₄₃×#3190	1	1	yes	characteristic
488	C₂	C₄₃×#3196	1	1	yes	characteristic
489	C₂	C₄₃×#3231	1	1	yes	characteristic
490	C₂	C₄₃×#3237	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#2084	C₂	semidirect
5. C₄₃×#2083	C₂	semidirect
6. C₄₃×#2068	C₂	semidirect
7. C₄₃×#2066	C₂	semidirect
8. C₄₃×#2043	C₂	semidirect
9. C₄₃×#2043	C₂	semidirect
210. #29759	C₄₃	direct (N × H)
241. #2084	C₂×C₄₃	semidirect
242. #2083	C₂×C₄₃	semidirect
243. #2068	C₂×C₄₃	semidirect
244. #2066	C₂×C₄₃	semidirect
245. #2043	C₂×C₄₃	semidirect
246. #2043	C₂×C₄₃	semidirect
289. C₄₃	#29759	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×#485	2
C₄₃×#2857	2
C₄₃×#2296	2
C₄₃×#2084	2
C₄₃×#2083	2
C₄₃×#2068	2
C₄₃×#2066	2
C₄₃×#2043	2
C₄₃×#1873	2
C₄₃×#1797	2
#29759	43

Subgroups — C43×#29759 #24949776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29759 #24949776