Subgroups — C₄₃×#34575 #24954592

Order 11008.

2794 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#525	C₂	1	2	yes	maximal, complemented
2	C₄₃×#2663	C₂	1	4	yes	maximal, complemented
3	C₄₃×#2661	C₂	1	4	yes	maximal, complemented
4	C₄₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2656	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#2639	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2617	C₂	1	4	yes	maximal, complemented
8	C₄₃×#2395	C₂	1	4	yes	maximal, complemented
9	C₄₃×#2388	C₂	1	4	yes	maximal, complemented
10	C₄×#121×C₄₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₄₃	C₂²	1	2	yes	—
13	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#525	—	2	16	no	—
15	C₂×#123×C₄₃	C₂²	1	4	yes	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×#121×C₄₃	C₂²	1	4	yes	—
19	C₂×#121×C₄₃	C₂²	1	2	yes	—
20	C₂×#121×C₄₃	C₂²	1	2	yes	—
21	C₂×#120×C₄₃	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	—
24	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	complemented
25	C₂×#117×C₄₃	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
27	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
28	C₄₃×#400	C₂²	1	4	yes	complemented
29	C₄₃×#399	C₂²	1	4	yes	complemented
30	C₄₃×#398	C₂²	1	4	yes	complemented
31	C₄₃×#397	C₂²	1	8	yes	—
32	C₄₃×#397	C₂²	1	4	yes	complemented
33	C₄₃×#395	C₂²	1	4	yes	complemented
34	C₄₃×#394	C₂²	1	8	yes	—
35	C₄₃×#394	C₂²	1	8	yes	—
36	C₄₃×#394	C₂²	1	4	yes	complemented
37	C₄₃×#393	C₂²	1	4	yes	complemented
38	C₄₃×#392	C₂²	1	8	yes	—
39	C₄₃×#392	C₂²	1	4	yes	complemented
40	C₄₃×#390	C₂²	1	4	yes	complemented
41	C₄₃×#389	C₂²	1	4	yes	complemented
42	C₄₃×#388	C₂²	1	8	yes	complemented
43	C₄₃×#386	C₂²	1	8	yes	—
44	C₄₃×#380	C₂²	1	4	yes	—
45	C₄×C₄⋊C₄×C₄₃	C₂²	1	4	yes	complemented
46	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
47	C₄×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
48	C₄×C₂²⋊C₄×C₄₃	C₂²	1	8	yes	complemented
49	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
50	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
51	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
52	C₂×#41×C₄₃	—	2	8	no	—
53	C₂×#41×C₄₃	—	4	8	no	—
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
58	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₄₃	—	4	4	no	—
61	C₂³×C₄×C₄₃	D₄	1	8	yes	complemented
62	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
69	#123×C₄₃	—	2	16	no	—
70	C₂²⋊Q₈×C₄₃	—	2	8	no	—
71	C₂²⋊Q₈×C₄₃	—	2	8	no	—
72	#121×C₄₃	—	2	8	no	—
73	#121×C₄₃	—	2	8	no	—
74	#121×C₄₃	—	2	16	no	—
75	#120×C₄₃	—	2	16	no	—
76	C₄×D₄×C₄₃	—	2	16	no	—
77	C₄×D₄×C₄₃	—	2	16	no	—
78	C₄×D₄×C₄₃	—	4	8	no	—
79	#117×C₄₃	—	2	8	no	—
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
96	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
97	C₂×C₄²×C₄₃	—	4	4	no	—
98	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
99	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
101	#95×C₄₃	C₂³	1	4	yes	—
102	#95×C₄₃	C₂³	1	4	yes	—
103	#95×C₄₃	C₂³	1	8	yes	—
104	#95×C₄₃	C₂³	1	8	yes	—
105	#95×C₄₃	C₂³	1	8	yes	—
106	C₂⁴×C₄₃	—	2	4	no	—
107	C₂⁴×C₄₃	—	4	2	no	—
108	C₂⁴×C₄₃	—	4	1	no	—
109	C₂⁴×C₄₃	—	4	1	no	—
110	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
111	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
112	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
113	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
114	#41×C₄₃	—	4	32	no	—
115	C₂×Q₈×C₄₃	—	2	4	no	—
116	C₂×Q₈×C₄₃	—	4	4	no	—
117	C₂×D₄×C₄₃	—	2	4	no	—
118	C₂×D₄×C₄₃	—	2	8	no	—
119	C₂×D₄×C₄₃	—	2	8	no	—
120	C₂×D₄×C₄₃	—	2	8	no	—
121	C₂×D₄×C₄₃	—	2	8	no	—
122	C₂×D₄×C₄₃	—	2	16	no	—
123	C₂×D₄×C₄₃	—	4	4	no	—
124	C₂×D₄×C₄₃	—	4	4	no	—
125	C₂×D₄×C₄₃	—	4	4	no	—
126	C₂×D₄×C₄₃	—	4	4	no	—
127	C₂×D₄×C₄₃	—	4	8	no	—
128	C₂×D₄×C₄₃	—	4	4	no	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	8	no	—
131	C₂²×C₄×C₄₃	—	2	8	no	—
132	C₂²×C₄×C₄₃	—	2	16	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	4	2	no	—
135	C₂²×C₄×C₄₃	—	4	2	no	—
136	C₂²×C₄×C₄₃	—	4	2	no	—
137	C₂²×C₄×C₄₃	—	4	4	no	—
138	C₂²×C₄×C₄₃	—	4	2	no	—
139	C₂²×C₄×C₄₃	—	4	2	no	—
140	C₂²×C₄×C₄₃	—	4	16	no	—
141	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
142	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
145	C₂²×C₄×C₄₃	#41	1	8	yes	complemented
146	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₄₃	—	2	4	no	—
155	C₄⋊C₄×C₄₃	—	2	4	no	—
156	C₄⋊C₄×C₄₃	—	2	8	no	—
157	C₄⋊C₄×C₄₃	—	2	8	no	—
158	C₄⋊C₄×C₄₃	—	2	8	no	—
159	C₄⋊C₄×C₄₃	—	4	4	no	—
160	C₄⋊C₄×C₄₃	—	4	4	no	—
161	C₂²⋊C₄×C₄₃	—	2	8	no	—
162	C₂²⋊C₄×C₄₃	—	2	8	no	—
163	C₂²⋊C₄×C₄₃	—	2	16	no	—
164	C₂²⋊C₄×C₄₃	—	2	16	no	—
165	C₂²⋊C₄×C₄₃	—	2	8	no	—
166	C₂²⋊C₄×C₄₃	—	2	8	no	—
167	C₂²⋊C₄×C₄₃	—	2	8	no	—
168	C₂²⋊C₄×C₄₃	—	4	8	no	—
169	C₂²⋊C₄×C₄₃	—	4	8	no	—
170	C₄²×C₄₃	—	2	8	no	—
171	C₄²×C₄₃	—	2	8	no	—
172	C₄²×C₄₃	—	4	4	no	—
173	C₂³×C₄₃	—	2	2	no	—
174	C₂³×C₄₃	—	2	1	no	—
175	C₂³×C₄₃	—	2	1	no	—
176	C₂³×C₄₃	—	2	8	no	—
177	C₂³×C₄₃	—	2	4	no	—
178	C₂³×C₄₃	—	2	4	no	—
179	C₂³×C₄₃	—	2	2	no	—
180	C₂³×C₄₃	—	2	2	no	—
181	C₂³×C₄₃	—	2	4	no	—
182	C₂³×C₄₃	—	2	8	no	—
183	C₂³×C₄₃	—	2	8	no	—
184	C₂³×C₄₃	—	2	4	no	—
185	C₂³×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	4	4	no	—
187	C₂³×C₄₃	—	4	4	no	—
188	C₂³×C₄₃	—	4	8	no	—
189	C₂³×C₄₃	—	4	8	no	—
190	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
191	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
192	C₂³×C₄₃	C₂×#41	1	4	yes	—
193	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
194	Q₈×C₄₃	—	4	8	no	—
195	D₄×C₄₃	—	4	16	no	—
196	D₄×C₄₃	—	4	8	no	—
197	D₄×C₄₃	—	4	16	no	—
198	D₄×C₄₃	—	4	16	no	—
199	D₄×C₄₃	—	4	16	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	8	no	—
205	C₂×C₄×C₄₃	—	2	16	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	8	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	8	no	—
213	C₂×C₄×C₄₃	—	2	4	no	—
214	C₂×C₄×C₄₃	—	2	4	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	4	8	no	—
217	C₂×C₄×C₄₃	—	4	4	no	—
218	C₂×C₄×C₄₃	—	4	8	no	—
219	C₂×C₄×C₄₃	—	4	8	no	—
220	C₂×C₄×C₄₃	—	4	16	no	—
221	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₄₃	C₂×#41	1	8	yes	—
225	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
226	#34575	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₄₃	—	2	2	no	—
228	C₂²×C₄₃	—	2	2	no	—
229	C₂²×C₄₃	—	2	4	no	—
230	C₂²×C₄₃	—	2	4	no	—
231	C₂²×C₄₃	—	2	4	no	—
232	C₂²×C₄₃	—	2	4	no	—
233	C₂²×C₄₃	—	2	4	no	—
234	C₂²×C₄₃	—	4	16	no	—
235	C₂²×C₄₃	—	4	4	no	—
236	C₂²×C₄₃	—	4	4	no	—
237	C₂²×C₄₃	—	4	4	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	4	no	—
240	C₂²×C₄₃	—	4	8	no	—
241	C₂²×C₄₃	—	4	8	no	—
242	C₂²×C₄₃	#532	1	4	yes	—
243	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
244	C₂²×C₄₃	C₂²×#41	1	2	yes	—
245	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
246	C₂²×C₄₃	#585	1	1	yes	characteristic
247	C₂²×C₄₃	#585	1	1	yes	characteristic
248	C₄×C₄₃	—	2	2	no	—
249	C₄×C₄₃	—	2	4	no	—
250	C₄×C₄₃	—	2	8	no	—
251	C₄×C₄₃	—	4	4	no	—
252	C₄×C₄₃	—	4	4	no	—
253	C₄×C₄₃	—	4	4	no	—
254	C₄×C₄₃	—	4	4	no	—
255	C₄×C₄₃	#534	1	4	yes	—
256	C₂×#525	C₂×C₄₃	1	2	yes	complemented
257	#2663	C₂×C₄₃	1	4	yes	complemented
258	#2661	C₂×C₄₃	1	4	yes	complemented
259	#2659	C₂×C₄₃	1	1	yes	characteristic, complemented
260	#2656	C₂×C₄₃	1	1	yes	characteristic, complemented
261	#2639	C₂×C₄₃	1	2	yes	complemented
262	#2617	C₂×C₄₃	1	4	yes	complemented
263	#2395	C₂×C₄₃	1	4	yes	complemented
264	#2388	C₂×C₄₃	1	4	yes	complemented
265	C₄×#121	C₂×C₄₃	1	4	yes	complemented
266	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
267	C₂×C₄₃	—	2	4	no	—
268	C₂×C₄₃	—	4	4	no	—
269	C₂×C₄₃	—	8	4	no	—
270	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
271	C₂×C₄₃	C₂×#534	1	1	yes	characteristic
272	C₂×C₄₃	#3449	1	1	yes	characteristic
273	C₂×C₄₃	#3459	1	2	yes	—
274	C₂×C₄₃	#3460	1	2	yes	—
275	C₂²×#41	C₂²×C₄₃	1	2	yes	—
276	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
277	#525	—	2	16	no	—
278	C₂×#123	C₂²×C₄₃	1	4	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
280	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
281	C₂×#121	C₂²×C₄₃	1	4	yes	—
282	C₂×#121	C₂²×C₄₃	1	2	yes	—
283	C₂×#121	C₂²×C₄₃	1	2	yes	—
284	C₂×#120	C₂²×C₄₃	1	4	yes	—
285	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
286	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	—
287	C₂×C₄×D₄	C₂²×C₄₃	1	4	yes	complemented
288	C₂×#117	C₂²×C₄₃	1	2	yes	—
289	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
290	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
291	#400	C₂²×C₄₃	1	4	yes	complemented
292	#399	C₂²×C₄₃	1	4	yes	complemented
293	#398	C₂²×C₄₃	1	4	yes	complemented
294	#397	C₂²×C₄₃	1	8	yes	—
295	#397	C₂²×C₄₃	1	4	yes	complemented
296	#395	C₂²×C₄₃	1	4	yes	complemented
297	#394	C₂²×C₄₃	1	8	yes	—
298	#394	C₂²×C₄₃	1	8	yes	—
299	#394	C₂²×C₄₃	1	4	yes	complemented
300	#393	C₂²×C₄₃	1	4	yes	complemented
301	#392	C₂²×C₄₃	1	8	yes	—
302	#392	C₂²×C₄₃	1	4	yes	complemented
303	#390	C₂²×C₄₃	1	4	yes	complemented
304	#389	C₂²×C₄₃	1	4	yes	complemented
305	#388	C₂²×C₄₃	1	8	yes	complemented
306	#386	C₂²×C₄₃	1	8	yes	—
307	#380	C₂²×C₄₃	1	4	yes	—
308	C₄×C₄⋊C₄	C₂²×C₄₃	1	4	yes	complemented
309	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
311	C₄×C₂²⋊C₄	C₂²×C₄₃	1	8	yes	complemented
312	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
314	C₄₃	#34575	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
316	C₂×#41	—	2	8	no	—
317	C₂×#41	—	4	8	no	—
318	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
319	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
320	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
321	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
322	C₂²×D₄	C₂³×C₄₃	1	4	yes	—
323	C₂²×D₄	C₂³×C₄₃	1	2	yes	—
324	C₂³×C₄	—	4	4	no	—
325	C₂³×C₄	D₄×C₄₃	1	8	yes	complemented
326	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
327	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
328	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
332	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
333	#123	—	2	16	no	—
334	C₂²⋊Q₈	—	2	8	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	#121	—	2	8	no	—
337	#121	—	2	8	no	—
338	#121	—	2	16	no	—
339	#120	—	2	16	no	—
340	C₄×D₄	—	2	16	no	—
341	C₄×D₄	—	2	16	no	—
342	C₄×D₄	—	4	8	no	—
343	#117	—	2	8	no	—
344	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
348	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
351	C₂×C₂²⋊C₄	—	2	8	no	—
352	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₄₃	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₄₃	1	8	yes	—
361	C₂×C₄²	—	4	4	no	—
362	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
363	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
364	C₂×C₄²	C₂³×C₄₃	1	4	yes	—
365	#95	C₂³×C₄₃	1	4	yes	—
366	#95	C₂³×C₄₃	1	4	yes	—
367	#95	C₂³×C₄₃	1	8	yes	—
368	#95	C₂³×C₄₃	1	8	yes	—
369	#95	C₂³×C₄₃	1	8	yes	—
370	C₂⁴	—	2	4	no	—
371	C₂⁴	—	4	2	no	—
372	C₂⁴	—	4	1	no	—
373	C₂⁴	—	4	1	no	—
374	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
375	C₂⁴	C₂⁴×C₄₃	1	4	yes	—
376	C₂⁴	C₂⁴×C₄₃	1	2	yes	—
377	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
378	#41	—	4	32	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	4	4	no	—
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	16	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	8	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	16	no	—
398	C₂²×C₄	—	4	16	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	4	2	no	—
401	C₂²×C₄	—	4	4	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
406	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
407	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
408	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
409	C₂²×C₄	#41×C₄₃	1	8	yes	complemented
410	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
411	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
412	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
413	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
416	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	4	4	no	—
424	C₄⋊C₄	—	4	4	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	8	no	—
428	C₂²⋊C₄	—	2	8	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	16	no	—
431	C₂²⋊C₄	—	2	16	no	—
432	C₂²⋊C₄	—	4	8	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₄²	—	2	8	no	—
435	C₄²	—	2	8	no	—
436	C₄²	—	4	4	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	8	no	—
441	C₂³	—	2	4	no	—
442	C₂³	—	2	4	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	4	no	—
446	C₂³	—	2	8	no	—
447	C₂³	—	2	8	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	4	4	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	8	no	—
453	C₂³	—	4	8	no	—
454	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
455	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
456	C₂³	C₂×#41×C₄₃	1	4	yes	—
457	C₂³	C₂⁵×C₄₃	1	1	yes	characteristic
458	Q₈	—	4	8	no	—
459	D₄	—	4	8	no	—
460	D₄	—	4	16	no	—
461	D₄	—	4	16	no	—
462	D₄	—	4	16	no	—
463	D₄	—	4	16	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	16	no	—
469	C₂×C₄	—	2	8	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	8	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	4	4	no	—
481	C₂×C₄	—	4	8	no	—
482	C₂×C₄	—	4	8	no	—
483	C₂×C₄	—	4	8	no	—
484	C₂×C₄	—	4	16	no	—
485	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
487	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
488	C₂×C₄	C₂×#41×C₄₃	1	8	yes	—
489	C₂×C₄	H(5,𝔽₂)×C₄₃	1	4	yes	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	2	4	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	4	16	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	4	no	—
500	C₂²	—	4	4	no	—
501	C₂²	—	4	4	no	—
502	C₂²	—	4	4	no	—
503	C₂²	—	4	8	no	—
504	C₂²	—	4	8	no	—
505	C₂²	C₄₃×#532	1	4	yes	—
506	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
507	C₂²	C₂²×#41×C₄₃	1	2	yes	—
508	C₂²	C₂×H(5,𝔽₂)×C₄₃	1	2	yes	—
509	C₂²	C₄₃×#585	1	1	yes	characteristic
510	C₂²	C₄₃×#585	1	1	yes	characteristic
511	C₄	—	2	4	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	8	no	—
514	C₄	—	4	4	no	—
515	C₄	—	4	4	no	—
516	C₄	—	4	4	no	—
517	C₄	—	4	4	no	—
518	C₄	C₄₃×#534	1	4	yes	—
519	C₂	—	2	4	no	—
520	C₂	—	4	4	no	—
521	C₂	—	8	4	no	—
522	C₂	C₂×C₄₃×#532	1	1	yes	characteristic
523	C₂	C₂×C₄₃×#534	1	1	yes	characteristic
524	C₂	C₄₃×#3449	1	1	yes	characteristic
525	C₂	C₄₃×#3459	1	2	yes	—
526	C₂	C₄₃×#3460	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₃
socle	C₂³×C₄₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#525	C₂	semidirect
2. C₄₃×#2663	C₂	semidirect
3. C₄₃×#2661	C₂	semidirect
4. C₄₃×#2659	C₂	semidirect
5. C₄₃×#2656	C₂	semidirect
6. C₄₃×#2639	C₂	semidirect
7. C₄₃×#2617	C₂	semidirect
8. C₄₃×#2395	C₂	semidirect
9. C₄₃×#2388	C₂	semidirect
10. C₄×#121×C₄₃	C₂	semidirect
11. C₂×C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
24. C₂×C₄×D₄×C₄₃	C₂²	semidirect
28. C₄₃×#400	C₂²	semidirect
29. C₄₃×#399	C₂²	semidirect
30. C₄₃×#398	C₂²	semidirect
32. C₄₃×#397	C₂²	semidirect
33. C₄₃×#395	C₂²	semidirect
36. C₄₃×#394	C₂²	semidirect
37. C₄₃×#393	C₂²	semidirect
39. C₄₃×#392	C₂²	semidirect
40. C₄₃×#390	C₂²	semidirect
41. C₄₃×#389	C₂²	semidirect
42. C₄₃×#388	C₂²	semidirect
45. C₄×C₄⋊C₄×C₄₃	C₂²	semidirect
48. C₄×C₂²⋊C₄×C₄₃	C₂²	semidirect
61. C₂³×C₄×C₄₃	D₄	semidirect
145. C₂²×C₄×C₄₃	#41	semidirect
226. #34575	C₄₃	direct (N × H)
256. C₂×#525	C₂×C₄₃	semidirect
257. #2663	C₂×C₄₃	semidirect
258. #2661	C₂×C₄₃	semidirect
259. #2659	C₂×C₄₃	semidirect
260. #2656	C₂×C₄₃	semidirect
261. #2639	C₂×C₄₃	semidirect
262. #2617	C₂×C₄₃	semidirect
263. #2395	C₂×C₄₃	semidirect
264. #2388	C₂×C₄₃	semidirect
265. C₄×#121	C₂×C₄₃	semidirect
266. C₂×C₄×C₂²⋊C₄	C₂×C₄₃	semidirect
287. C₂×C₄×D₄	C₂²×C₄₃	semidirect
291. #400	C₂²×C₄₃	semidirect
292. #399	C₂²×C₄₃	semidirect
293. #398	C₂²×C₄₃	semidirect
295. #397	C₂²×C₄₃	semidirect
296. #395	C₂²×C₄₃	semidirect
299. #394	C₂²×C₄₃	semidirect
300. #393	C₂²×C₄₃	semidirect
302. #392	C₂²×C₄₃	semidirect
303. #390	C₂²×C₄₃	semidirect
304. #389	C₂²×C₄₃	semidirect
305. #388	C₂²×C₄₃	semidirect
308. C₄×C₄⋊C₄	C₂²×C₄₃	semidirect
311. C₄×C₂²⋊C₄	C₂²×C₄₃	semidirect
314. C₄₃	#34575	direct (N × H)
325. C₂³×C₄	D₄×C₄₃	semidirect
409. C₂²×C₄	#41×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×#525	2
C₄₃×#2663	2
C₄₃×#2661	2
C₄₃×#2659	2
C₄₃×#2656	2
C₄₃×#2639	2
C₄₃×#2617	2
C₄₃×#2395	2
C₄₃×#2388	2
C₄×#121×C₄₃	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
#34575	43

Subgroups — C43×#34575 #24954592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#34575 #24954592