Subgroups — C₄₃×#29632 #24949649

Order 11008.

1452 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2625	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2041	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2014	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1788	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₄₃×#535	—	2	4	no	—
18	C₄₃×#535	—	2	4	no	—
19	C₂×#127×C₄₃	C₂²	1	2	yes	—
20	C₂×#124×C₄₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₃	—	2	1	no	—
23	C₂×#121×C₄₃	—	2	1	no	—
24	C₂×#120×C₄₃	—	2	2	no	—
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#452	—	2	4	no	—
27	C₄₃×#450	—	2	4	no	—
28	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#103×C₄₃	C₂²	1	2	yes	complemented
30	C₂×#102×C₄₃	C₂²	1	2	yes	—
31	C₂×#102×C₄₃	C₂²	1	2	yes	—
32	C₂×#102×C₄₃	C₂²	1	2	yes	—
33	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#102×C₄₃	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#400	—	2	1	no	—
38	C₄₃×#398	—	2	1	no	—
39	C₄₃×#397	—	2	2	no	—
40	C₄₃×#391	C₂²	1	2	yes	complemented
41	C₄₃×#389	C₂²	1	2	yes	complemented
42	C₄₃×#380	C₂²	1	1	yes	characteristic
43	C₄₃×#336	C₂²	1	2	yes	complemented
44	C₄₃×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₃	—	2	1	no	—
46	C₂×#41×C₄₃	—	2	2	no	—
47	C₂×#41×C₄₃	—	4	2	no	—
48	C₂×#41×C₄₃	—	4	2	no	—
49	C₂×#41×C₄₃	D₄	1	4	yes	—
50	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₃	—	2	1	no	—
53	C₂²×D₄×C₄₃	—	2	1	no	—
54	C₂²×D₄×C₄₃	—	2	2	no	—
55	C₂²×D₄×C₄₃	—	2	2	no	—
56	C₂²×D₄×C₄₃	—	2	2	no	—
57	C₂²×D₄×C₄₃	—	4	2	no	—
58	C₂²×D₄×C₄₃	—	4	2	no	—
59	C₂²×D₄×C₄₃	D₄	1	4	yes	—
60	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
61	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×Q₁₆×C₄₃	—	2	2	no	—
65	C₂×Q₁₆×C₄₃	—	4	2	no	—
66	C₂×SD₁₆×C₄₃	—	2	4	no	—
67	C₂×SD₁₆×C₄₃	—	2	2	no	—
68	C₂×SD₁₆×C₄₃	—	4	2	no	—
69	C₂×SD₁₆×C₄₃	—	4	2	no	—
70	C₂×SD₁₆×C₄₃	—	4	2	no	—
71	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
74	#127×C₄₃	—	2	4	no	—
75	#127×C₄₃	—	2	4	no	—
76	#124×C₄₃	—	2	4	no	—
77	#124×C₄₃	—	2	4	no	—
78	C₂²⋊Q₈×C₄₃	—	2	2	no	—
79	C₂²⋊Q₈×C₄₃	—	2	2	no	—
80	#121×C₄₃	—	2	8	no	—
81	#121×C₄₃	—	2	8	no	—
82	#120×C₄₃	—	2	16	no	—
83	#117×C₄₃	—	2	2	no	—
84	#117×C₄₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
96	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
97	#103×C₄₃	—	2	2	no	—
98	#103×C₄₃	—	4	2	no	—
99	#102×C₄₃	—	2	4	no	—
100	#102×C₄₃	—	2	2	no	—
101	#102×C₄₃	—	4	2	no	—
102	#102×C₄₃	—	4	2	no	—
103	#102×C₄₃	—	4	2	no	—
104	C₂²⋊C₈×C₄₃	—	2	2	no	—
105	C₂²⋊C₈×C₄₃	—	2	2	no	—
106	#95×C₄₃	—	2	1	no	—
107	#95×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	2	no	—
109	#95×C₄₃	—	2	2	no	—
110	C₂⁴×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	—	2	4	no	—
113	C₂⁴×C₄₃	—	4	4	no	—
114	C₂⁴×C₄₃	—	8	1	no	—
115	C₂⁴×C₄₃	—	8	2	no	—
116	C₂⁴×C₄₃	—	8	1	no	—
117	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
118	#41×C₄₃	—	4	4	no	—
119	#41×C₄₃	—	4	4	no	—
120	#41×C₄₃	—	4	8	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	1	no	—
123	C₂×Q₈×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	2	2	no	—
128	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₄₃	—	2	8	no	—
130	C₂×D₄×C₄₃	—	2	8	no	—
131	C₂×D₄×C₄₃	—	2	4	no	—
132	C₂×D₄×C₄₃	—	2	2	no	—
133	C₂×D₄×C₄₃	—	2	1	no	—
134	C₂×D₄×C₄₃	—	2	4	no	—
135	C₂×D₄×C₄₃	—	2	2	no	—
136	C₂×D₄×C₄₃	—	2	2	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	2	2	no	—
141	C₂×D₄×C₄₃	—	4	4	no	—
142	C₂×D₄×C₄₃	—	4	8	no	—
143	C₂×D₄×C₄₃	—	4	4	no	—
144	C₂×D₄×C₄₃	—	4	4	no	—
145	C₂×D₄×C₄₃	—	4	4	no	—
146	C₂×D₄×C₄₃	—	8	2	no	—
147	C₂×D₄×C₄₃	—	8	2	no	—
148	C₂×D₄×C₄₃	—	8	2	no	—
149	C₂×D₄×C₄₃	—	8	2	no	—
150	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	—	2	2	no	—
153	C₂²×C₄×C₄₃	—	2	2	no	—
154	C₂²×C₄×C₄₃	—	2	4	no	—
155	C₂²×C₄×C₄₃	—	2	1	no	—
156	C₂²×C₄×C₄₃	—	2	2	no	—
157	C₂²×C₄×C₄₃	—	2	1	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	4	4	no	—
160	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
166	Q₁₆×C₄₃	—	4	4	no	—
167	SD₁₆×C₄₃	—	4	8	no	—
168	SD₁₆×C₄₃	—	4	4	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	1	no	—
172	C₂×C₈×C₄₃	—	2	2	no	—
173	C₂×C₈×C₄₃	—	2	2	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	2	2	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	2	1	no	—
179	C₄⋊C₄×C₄₃	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	4	2	no	—
183	C₄⋊C₄×C₄₃	—	8	2	no	—
184	C₂²⋊C₄×C₄₃	—	2	8	no	—
185	C₂²⋊C₄×C₄₃	—	2	8	no	—
186	C₂²⋊C₄×C₄₃	—	2	4	no	—
187	C₂²⋊C₄×C₄₃	—	4	2	no	—
188	C₂²⋊C₄×C₄₃	—	8	1	no	—
189	C₄²×C₄₃	—	2	2	no	—
190	C₄²×C₄₃	—	2	2	no	—
191	C₂³×C₄₃	—	2	2	no	—
192	C₂³×C₄₃	—	2	1	no	—
193	C₂³×C₄₃	—	2	2	no	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	—	2	4	no	—
196	C₂³×C₄₃	—	2	2	no	—
197	C₂³×C₄₃	—	4	8	no	—
198	C₂³×C₄₃	—	4	2	no	—
199	C₂³×C₄₃	—	4	2	no	—
200	C₂³×C₄₃	—	4	2	no	—
201	C₂³×C₄₃	—	4	1	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	—	4	1	no	—
205	C₂³×C₄₃	—	4	2	no	—
206	C₂³×C₄₃	—	4	2	no	—
207	C₂³×C₄₃	—	4	2	no	—
208	C₂³×C₄₃	—	8	4	no	—
209	C₂³×C₄₃	—	8	4	no	—
210	C₂³×C₄₃	—	8	8	no	—
211	C₂³×C₄₃	—	8	8	no	—
212	C₂³×C₄₃	#120	1	2	yes	—
213	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₄₃	—	2	2	no	—
215	Q₈×C₄₃	—	2	2	no	—
216	Q₈×C₄₃	—	4	2	no	—
217	Q₈×C₄₃	—	4	2	no	—
218	Q₈×C₄₃	—	4	1	no	—
219	Q₈×C₄₃	—	4	1	no	—
220	D₄×C₄₃	—	2	4	no	—
221	D₄×C₄₃	—	2	2	no	—
222	D₄×C₄₃	—	2	4	no	—
223	D₄×C₄₃	—	2	2	no	—
224	D₄×C₄₃	—	4	8	no	—
225	D₄×C₄₃	—	4	8	no	—
226	D₄×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	4	2	no	—
228	D₄×C₄₃	—	4	2	no	—
229	D₄×C₄₃	—	8	8	no	—
230	D₄×C₄₃	—	8	8	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	4	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	2	2	no	—
236	C₂×C₄×C₄₃	—	2	2	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	4	8	no	—
243	C₂×C₄×C₄₃	—	4	2	no	—
244	C₂×C₄×C₄₃	—	4	1	no	—
245	C₂×C₄×C₄₃	—	4	1	no	—
246	C₂×C₄×C₄₃	—	4	2	no	—
247	C₂×C₄×C₄₃	—	4	2	no	—
248	C₂×C₄×C₄₃	—	4	2	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	#120	1	2	yes	—
253	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
256	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
257	C₈×C₄₃	—	4	2	no	—
258	C₈×C₄₃	—	4	1	no	—
259	C₈×C₄₃	—	4	1	no	—
260	#29632	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₃	—	2	2	no	—
262	C₂²×C₄₃	—	2	2	no	—
263	C₂²×C₄₃	—	2	2	no	—
264	C₂²×C₄₃	—	4	2	no	—
265	C₂²×C₄₃	—	4	2	no	—
266	C₂²×C₄₃	—	4	4	no	—
267	C₂²×C₄₃	—	4	2	no	—
268	C₂²×C₄₃	—	4	4	no	—
269	C₂²×C₄₃	—	4	2	no	—
270	C₂²×C₄₃	—	4	4	no	—
271	C₂²×C₄₃	—	4	2	no	—
272	C₂²×C₄₃	—	8	16	no	—
273	C₂²×C₄₃	—	8	2	no	—
274	C₂²×C₄₃	—	8	2	no	—
275	C₂²×C₄₃	—	8	2	no	—
276	C₂²×C₄₃	—	8	2	no	—
277	C₂²×C₄₃	—	8	2	no	—
278	C₂²×C₄₃	—	8	2	no	—
279	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
280	C₂²×C₄₃	#535	1	2	yes	—
281	C₂²×C₄₃	#576	1	1	yes	characteristic
282	C₂²×C₄₃	#577	1	1	yes	characteristic
283	C₂²×C₄₃	#577	1	2	yes	—
284	C₄×C₄₃	—	2	2	no	—
285	C₄×C₄₃	—	4	2	no	—
286	C₄×C₄₃	—	4	2	no	—
287	C₄×C₄₃	—	4	2	no	—
288	C₄×C₄₃	—	8	1	no	—
289	C₄×C₄₃	—	8	2	no	—
290	C₄×C₄₃	—	8	1	no	—
291	C₄×C₄₃	#534	1	2	yes	—
292	C₄×C₄₃	#534	1	1	yes	characteristic
293	C₄×C₄₃	#534	1	1	yes	characteristic
294	C₂×#535	C₂×C₄₃	1	1	yes	characteristic
295	C₂×#452	C₂×C₄₃	1	1	yes	characteristic, complemented
296	C₂×#450	C₂×C₄₃	1	1	yes	characteristic, complemented
297	#2625	C₂×C₄₃	1	1	yes	characteristic, complemented
298	#2042	C₂×C₄₃	1	2	yes	complemented
299	#2041	C₂×C₄₃	1	2	yes	complemented
300	#2015	C₂×C₄₃	1	2	yes	complemented
301	#2014	C₂×C₄₃	1	2	yes	complemented
302	#1818	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#1788	C₂×C₄₃	1	1	yes	characteristic, complemented
304	#1786	C₂×C₄₃	1	1	yes	characteristic, complemented
305	C₂×C₄₃	—	4	2	no	—
306	C₂×C₄₃	—	8	2	no	—
307	C₂×C₄₃	—	8	4	no	—
308	C₂×C₄₃	#2613	1	1	yes	characteristic
309	C₂×C₄₃	#3009	1	1	yes	characteristic
310	C₂×C₄₃	#3012	1	1	yes	characteristic
311	C₂×C₄₃	#3222	1	2	yes	—
312	C₂×C₄₃	#3224	1	2	yes	—
313	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
314	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
315	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
316	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
317	C₂²×SD₁₆	C₂²×C₄₃	1	1	yes	characteristic, complemented
318	#535	—	2	4	no	—
319	#535	—	2	4	no	—
320	C₂×#127	C₂²×C₄₃	1	2	yes	—
321	C₂×#124	C₂²×C₄₃	1	2	yes	—
322	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
323	C₂×#121	—	2	1	no	—
324	C₂×#121	—	2	1	no	—
325	C₂×#120	—	2	2	no	—
326	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
327	#452	—	2	4	no	—
328	#450	—	2	4	no	—
329	C₂×#103	C₂²×C₄₃	1	1	yes	characteristic, complemented
330	C₂×#103	C₂²×C₄₃	1	2	yes	complemented
331	C₂×#102	C₂²×C₄₃	1	2	yes	—
332	C₂×#102	C₂²×C₄₃	1	2	yes	—
333	C₂×#102	C₂²×C₄₃	1	2	yes	—
334	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic, complemented
335	C₂×#102	C₂²×C₄₃	1	2	yes	complemented
336	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
337	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
338	#400	—	2	1	no	—
339	#398	—	2	1	no	—
340	#397	—	2	2	no	—
341	#391	C₂²×C₄₃	1	2	yes	complemented
342	#389	C₂²×C₄₃	1	2	yes	complemented
343	#380	C₂²×C₄₃	1	1	yes	characteristic
344	#336	C₂²×C₄₃	1	2	yes	complemented
345	#336	C₂²×C₄₃	1	2	yes	complemented
346	C₄₃	#29632	1	1	yes	characteristic, direct product factor, Sylow
347	C₂⁵	—	2	1	no	—
348	C₂×#41	—	2	2	no	—
349	C₂×#41	—	4	2	no	—
350	C₂×#41	—	4	2	no	—
351	C₂×#41	D₄×C₄₃	1	4	yes	—
352	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
353	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	2	no	—
357	C₂²×D₄	—	2	2	no	—
358	C₂²×D₄	—	2	2	no	—
359	C₂²×D₄	—	4	2	no	—
360	C₂²×D₄	—	4	2	no	—
361	C₂²×D₄	D₄×C₄₃	1	4	yes	—
362	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
363	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	4	2	no	—
368	C₂×SD₁₆	—	2	4	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	4	2	no	—
371	C₂×SD₁₆	—	4	2	no	—
372	C₂×SD₁₆	—	4	2	no	—
373	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
374	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
376	#127	—	2	4	no	—
377	#127	—	2	4	no	—
378	#124	—	2	4	no	—
379	#124	—	2	4	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	#121	—	2	8	no	—
383	#121	—	2	8	no	—
384	#120	—	2	16	no	—
385	#117	—	2	2	no	—
386	#117	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
393	C₂×C₂²⋊C₄	—	2	2	no	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
398	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
399	#103	—	2	2	no	—
400	#103	—	4	2	no	—
401	#102	—	2	4	no	—
402	#102	—	2	2	no	—
403	#102	—	4	2	no	—
404	#102	—	4	2	no	—
405	#102	—	4	2	no	—
406	C₂²⋊C₈	—	2	2	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	#95	—	2	1	no	—
409	#95	—	2	2	no	—
410	#95	—	2	2	no	—
411	#95	—	2	2	no	—
412	C₂⁴	—	2	2	no	—
413	C₂⁴	—	2	1	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	4	4	no	—
416	C₂⁴	—	8	1	no	—
417	C₂⁴	—	8	2	no	—
418	C₂⁴	—	8	1	no	—
419	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
420	#41	—	4	4	no	—
421	#41	—	4	4	no	—
422	#41	—	4	8	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	2	2	no	—
428	C₂×Q₈	—	2	2	no	—
429	C₂×Q₈	—	2	2	no	—
430	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
431	C₂×D₄	—	2	4	no	—
432	C₂×D₄	—	2	8	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	4	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	8	2	no	—
449	C₂×D₄	—	8	2	no	—
450	C₂×D₄	—	8	2	no	—
451	C₂×D₄	—	8	2	no	—
452	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
453	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
463	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
464	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
466	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
468	Q₁₆	—	4	4	no	—
469	SD₁₆	—	4	8	no	—
470	SD₁₆	—	4	4	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	—	8	2	no	—
486	C₂²⋊C₄	—	2	8	no	—
487	C₂²⋊C₄	—	2	8	no	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	4	2	no	—
490	C₂²⋊C₄	—	8	1	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	4	8	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	4	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	8	4	no	—
511	C₂³	—	8	4	no	—
512	C₂³	—	8	8	no	—
513	C₂³	—	8	8	no	—
514	C₂³	#120×C₄₃	1	2	yes	—
515	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	1	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	2	no	—
526	D₄	—	4	8	no	—
527	D₄	—	4	8	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	8	8	no	—
532	D₄	—	8	8	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	#120×C₄₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
557	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
558	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
559	C₈	—	4	2	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	2	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	8	16	no	—
574	C₂²	—	8	2	no	—
575	C₂²	—	8	2	no	—
576	C₂²	—	8	2	no	—
577	C₂²	—	8	2	no	—
578	C₂²	—	8	2	no	—
579	C₂²	—	8	2	no	—
580	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
581	C₂²	C₄₃×#535	1	2	yes	—
582	C₂²	C₄₃×#576	1	1	yes	characteristic
583	C₂²	C₄₃×#577	1	1	yes	characteristic
584	C₂²	C₄₃×#577	1	2	yes	—
585	C₄	—	2	2	no	—
586	C₄	—	4	2	no	—
587	C₄	—	4	2	no	—
588	C₄	—	4	2	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	2	no	—
591	C₄	—	8	1	no	—
592	C₄	C₄₃×#534	1	2	yes	—
593	C₄	C₄₃×#534	1	1	yes	characteristic
594	C₄	C₄₃×#534	1	1	yes	characteristic
595	C₂	—	4	2	no	—
596	C₂	—	8	4	no	—
597	C₂	—	8	2	no	—
598	C₂	C₄₃×#2613	1	1	yes	characteristic
599	C₂	C₄₃×#3009	1	1	yes	characteristic
600	C₂	C₄₃×#3012	1	1	yes	characteristic
601	C₂	C₄₃×#3222	1	2	yes	—
602	C₂	C₄₃×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#452	C₂	semidirect
3. C₂×C₄₃×#450	C₂	semidirect
4. C₄₃×#2625	C₂	semidirect
5. C₄₃×#2042	C₂	semidirect
6. C₄₃×#2041	C₂	semidirect
7. C₄₃×#2015	C₂	semidirect
8. C₄₃×#2014	C₂	semidirect
9. C₄₃×#1818	C₂	semidirect
10. C₄₃×#1788	C₂	semidirect
11. C₄₃×#1786	C₂	semidirect
14. C₂²×Q₁₆×C₄₃	C₂²	semidirect
16. C₂²×SD₁₆×C₄₃	C₂²	semidirect
28. C₂×#103×C₄₃	C₂²	semidirect
29. C₂×#103×C₄₃	C₂²	semidirect
33. C₂×#102×C₄₃	C₂²	semidirect
34. C₂×#102×C₄₃	C₂²	semidirect
40. C₄₃×#391	C₂²	semidirect
41. C₄₃×#389	C₂²	semidirect
43. C₄₃×#336	C₂²	semidirect
44. C₄₃×#336	C₂²	semidirect
260. #29632	C₄₃	direct (N × H)
295. C₂×#452	C₂×C₄₃	semidirect
296. C₂×#450	C₂×C₄₃	semidirect
297. #2625	C₂×C₄₃	semidirect
298. #2042	C₂×C₄₃	semidirect
299. #2041	C₂×C₄₃	semidirect
300. #2015	C₂×C₄₃	semidirect
301. #2014	C₂×C₄₃	semidirect
302. #1818	C₂×C₄₃	semidirect
303. #1788	C₂×C₄₃	semidirect
304. #1786	C₂×C₄₃	semidirect
315. C₂²×Q₁₆	C₂²×C₄₃	semidirect
317. C₂²×SD₁₆	C₂²×C₄₃	semidirect
329. C₂×#103	C₂²×C₄₃	semidirect
330. C₂×#103	C₂²×C₄₃	semidirect
334. C₂×#102	C₂²×C₄₃	semidirect
335. C₂×#102	C₂²×C₄₃	semidirect
341. #391	C₂²×C₄₃	semidirect
342. #389	C₂²×C₄₃	semidirect
344. #336	C₂²×C₄₃	semidirect
345. #336	C₂²×C₄₃	semidirect
346. C₄₃	#29632	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×#535	2
C₂×C₄₃×#452	2
C₂×C₄₃×#450	2
C₄₃×#2625	2
C₄₃×#2042	2
C₄₃×#2041	2
C₄₃×#2015	2
C₄₃×#2014	2
C₄₃×#1818	2
C₄₃×#1788	2
C₄₃×#1786	2
#29632	43

Subgroups — C43×#29632 #24949649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29632 #24949649