Subgroups — C₄₃×#13820 #24933837

Order 11008.

2666 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#390	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1437	C₂	1	4	yes	maximal, complemented
6	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×C₂²⋊#95	C₂	1	2	yes	maximal, complemented
8	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
11	C₂×C₄×D₄×C₄₃	—	2	8	no	—
12	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
21	C₄₃×#390	C₄	1	16	yes	complemented
22	C₄×C₄⋊C₄×C₄₃	—	2	8	no	—
23	C₄×C₂²⋊C₄×C₄₃	—	2	8	no	—
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	2	yes	—
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₂×#95×C₄₃	C₂²	1	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
30	C₂⁵×C₄₃	C₂³	1	2	yes	—
31	C₂²×D₄×C₄₃	—	2	4	no	—
32	C₂²×D₄×C₄₃	—	2	2	no	—
33	C₂²×D₄×C₄₃	—	2	2	no	—
34	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
35	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
36	C₂³×C₄×C₄₃	—	2	8	no	—
37	C₂³×C₄×C₄₃	—	2	4	no	—
38	C₂³×C₄×C₄₃	—	2	4	no	—
39	C₂³×C₄×C₄₃	—	4	4	no	—
40	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₄×D₄×C₄₃	—	2	32	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
53	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
54	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
55	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
56	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
57	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
58	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
59	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
60	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	complemented
61	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	complemented
62	C₂×C₄²×C₄₃	—	2	4	no	—
63	C₂×C₄²×C₄₃	—	2	4	no	—
64	C₂×C₄²×C₄₃	—	2	4	no	—
65	C₂×C₄²×C₄₃	—	2	8	no	—
66	C₂×C₄²×C₄₃	—	2	8	no	—
67	C₂×C₄²×C₄₃	—	4	4	no	—
68	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
69	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
70	#95×C₄₃	—	2	4	no	—
71	#95×C₄₃	—	2	8	no	—
72	#95×C₄₃	—	2	2	no	—
73	#95×C₄₃	—	2	4	no	—
74	#95×C₄₃	—	4	2	no	—
75	#95×C₄₃	D₄	1	4	yes	complemented
76	C₂⁴×C₄₃	—	2	2	no	—
77	C₂⁴×C₄₃	—	2	4	no	—
78	C₂⁴×C₄₃	—	2	4	no	—
79	C₂⁴×C₄₃	—	2	2	no	—
80	C₂⁴×C₄₃	—	2	2	no	—
81	C₂⁴×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	4	no	—
84	C₂⁴×C₄₃	—	2	2	no	—
85	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
86	C₂⁴×C₄₃	C₂²×C₄	1	8	yes	—
87	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
88	C₂×D₄×C₄₃	—	2	8	no	—
89	C₂×D₄×C₄₃	—	2	8	no	—
90	C₂×D₄×C₄₃	—	2	16	no	—
91	C₂×D₄×C₄₃	—	2	16	no	—
92	C₂×D₄×C₄₃	C₄²	1	16	yes	complemented
93	C₂²×C₄×C₄₃	—	2	16	no	—
94	C₂²×C₄×C₄₃	—	2	16	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	4	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	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	4	no	—
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	—	2	2	no	—
111	C₂²×C₄×C₄₃	—	2	4	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	2	4	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	4	8	no	—
121	C₂²×C₄×C₄₃	—	4	16	no	—
122	C₂²×C₄×C₄₃	—	4	16	no	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₄₃	#41	1	2	yes	—
136	C₂²×C₄×C₄₃	#41	1	4	yes	—
137	C₂²×C₄×C₄₃	#41	1	2	yes	—
138	C₂²×C₄×C₄₃	#41	1	2	yes	—
139	C₄⋊C₄×C₄₃	—	2	16	no	—
140	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	16	yes	complemented
141	C₂²⋊C₄×C₄₃	—	2	16	no	—
142	C₂²⋊C₄×C₄₃	—	2	32	no	—
143	C₂²⋊C₄×C₄₃	—	4	16	no	—
144	C₄²×C₄₃	—	2	8	no	—
145	C₄²×C₄₃	—	2	16	no	—
146	C₄²×C₄₃	—	4	16	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	—	2	4	no	—
149	C₂³×C₄₃	—	2	8	no	—
150	C₂³×C₄₃	—	2	4	no	—
151	C₂³×C₄₃	—	2	8	no	—
152	C₂³×C₄₃	—	2	8	no	—
153	C₂³×C₄₃	—	2	4	no	—
154	C₂³×C₄₃	—	2	8	no	—
155	C₂³×C₄₃	—	2	8	no	—
156	C₂³×C₄₃	—	2	4	no	—
157	C₂³×C₄₃	—	2	4	no	—
158	C₂³×C₄₃	—	2	8	no	—
159	C₂³×C₄₃	—	4	4	no	—
160	C₂³×C₄₃	—	4	4	no	—
161	C₂³×C₄₃	—	4	2	no	—
162	C₂³×C₄₃	—	4	4	no	—
163	C₂³×C₄₃	—	4	4	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	—	4	4	no	—
166	C₂³×C₄₃	—	4	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	4	no	—
169	C₂³×C₄₃	C₂×C₄²	1	8	yes	—
170	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
171	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
172	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
173	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂³×C₄₃	C₂×#41	1	2	yes	—
178	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
179	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
181	D₄×C₄₃	—	2	32	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	4	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	8	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	8	no	—
193	C₂×C₄×C₄₃	—	2	4	no	—
194	C₂×C₄×C₄₃	—	2	4	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	8	no	—
199	C₂×C₄×C₄₃	—	2	8	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	8	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	4	32	no	—
206	C₂×C₄×C₄₃	—	4	4	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	—	4	2	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	4	no	—
212	C₂×C₄×C₄₃	—	4	4	no	—
213	C₂×C₄×C₄₃	—	4	2	no	—
214	C₂×C₄×C₄₃	—	4	2	no	—
215	C₂×C₄×C₄₃	—	4	4	no	—
216	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
217	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
219	C₂×C₄×C₄₃	#117	1	4	yes	—
220	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
221	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
222	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
223	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	complemented
224	#13820	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₄₃	—	2	8	no	—
226	C₂²×C₄₃	—	2	8	no	—
227	C₂²×C₄₃	—	2	8	no	—
228	C₂²×C₄₃	—	4	4	no	—
229	C₂²×C₄₃	—	4	4	no	—
230	C₂²×C₄₃	—	4	4	no	—
231	C₂²×C₄₃	—	4	4	no	—
232	C₂²×C₄₃	—	4	8	no	—
233	C₂²×C₄₃	—	4	8	no	—
234	C₂²×C₄₃	—	4	8	no	—
235	C₂²×C₄₃	—	4	8	no	—
236	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
237	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
238	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
239	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
241	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
242	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
243	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
244	C₂²×C₄₃	C₄×#41	1	2	yes	—
245	C₂²×C₄₃	#518	1	1	yes	characteristic
246	C₂²×C₄₃	#518	1	2	yes	—
247	C₂²×C₄₃	#520	1	1	yes	characteristic
248	C₂²×C₄₃	#520	1	2	yes	—
249	C₂²×C₄₃	D₄²	1	2	yes	—
250	C₂²×C₄₃	#546	1	2	yes	—
251	C₂²×C₄₃	#547	1	1	yes	characteristic
252	C₂²×C₄₃	#548	1	2	yes	—
253	C₂²×C₄₃	#550	1	2	yes	—
254	C₂²×C₄₃	#550	1	1	yes	characteristic
255	C₂²×C₄₃	#553	1	2	yes	—
256	C₂²×C₄₃	#555	1	1	yes	characteristic
257	C₂²×C₄₃	#556	1	1	yes	characteristic
258	C₂²×C₄₃	#559	1	2	yes	—
259	C₄×C₄₃	—	2	4	no	—
260	C₄×C₄₃	—	2	8	no	—
261	C₄×C₄₃	—	2	8	no	—
262	C₄×C₄₃	—	4	2	no	—
263	C₄×C₄₃	—	4	4	no	—
264	C₄×C₄₃	—	4	8	no	—
265	C₄×C₄₃	C₄×C₂²⋊C₄	1	8	yes	complemented
266	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
267	C₂×#390	C₂×C₄₃	1	2	yes	—
268	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	2	yes	complemented
269	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	2	yes	complemented
270	#1437	C₂×C₄₃	1	4	yes	complemented
271	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic, complemented
272	C₂²⋊#95	C₂×C₄₃	1	2	yes	complemented
273	C₄×#95	C₂×C₄₃	1	1	yes	characteristic, complemented
274	C₂×C₄₃	—	4	8	no	—
275	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
277	C₂×C₄₃	#2275	1	1	yes	characteristic
278	C₂×C₄₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×C₄₃	#2341	1	1	yes	characteristic
280	C₂×C₄₃	#2354	1	1	yes	characteristic
281	C₂×C₄₃	#2357	1	1	yes	characteristic
282	C₂×C₄₃	#2361	1	2	yes	—
283	C₂×C₄₃	#2363	1	2	yes	—
284	C₂×C₄₃	#2366	1	2	yes	—
285	C₂×C₄₃	#2367	1	2	yes	—
286	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
287	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
288	C₂×C₄×D₄	—	2	8	no	—
289	C₂×C₄×D₄	C₄×C₄₃	1	8	yes	complemented
290	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
291	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
292	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
293	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
295	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
296	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
298	#390	C₄×C₄₃	1	16	yes	complemented
299	C₄×C₄⋊C₄	—	2	8	no	—
300	C₄×C₂²⋊C₄	—	2	8	no	—
301	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
302	C₂×#95	C₂²×C₄₃	1	2	yes	—
303	C₂×#95	C₂²×C₄₃	1	2	yes	—
304	C₂×#95	C₂²×C₄₃	1	4	yes	—
305	C₂×#95	C₂²×C₄₃	1	2	yes	—
306	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
307	C₄₃	#13820	1	1	yes	characteristic, direct product factor, Sylow
308	C₂⁵	C₂³×C₄₃	1	2	yes	—
309	C₂²×D₄	—	2	4	no	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
313	C₂²×D₄	C₂×C₄×C₄₃	1	8	yes	—
314	C₂³×C₄	—	2	8	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	—	2	4	no	—
317	C₂³×C₄	—	4	4	no	—
318	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	—
319	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
320	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
323	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
324	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
326	C₄×D₄	—	2	32	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
330	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
331	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
332	C₂×C₂²⋊C₄	—	2	8	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	2	8	no	—
335	C₂×C₂²⋊C₄	—	4	4	no	—
336	C₂×C₂²⋊C₄	—	4	4	no	—
337	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
338	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	16	yes	complemented
339	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	16	yes	complemented
340	C₂×C₄²	—	2	4	no	—
341	C₂×C₄²	—	2	4	no	—
342	C₂×C₄²	—	2	4	no	—
343	C₂×C₄²	—	2	8	no	—
344	C₂×C₄²	—	2	8	no	—
345	C₂×C₄²	—	4	4	no	—
346	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
347	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	complemented
348	#95	—	2	4	no	—
349	#95	—	2	8	no	—
350	#95	—	2	2	no	—
351	#95	—	2	4	no	—
352	#95	—	4	2	no	—
353	#95	D₄×C₄₃	1	4	yes	complemented
354	C₂⁴	—	2	2	no	—
355	C₂⁴	—	2	4	no	—
356	C₂⁴	—	2	4	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	2	2	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	2	no	—
363	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
364	C₂⁴	C₂²×C₄×C₄₃	1	8	yes	—
365	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	8	no	—
368	C₂×D₄	—	2	16	no	—
369	C₂×D₄	—	2	16	no	—
370	C₂×D₄	C₄²×C₄₃	1	16	yes	complemented
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	16	no	—
397	C₂²×C₄	—	2	16	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	—	4	16	no	—
400	C₂²×C₄	—	4	16	no	—
401	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
402	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
403	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
404	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
405	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
408	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
409	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
410	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
412	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
413	C₂²×C₄	#41×C₄₃	1	2	yes	—
414	C₂²×C₄	#41×C₄₃	1	4	yes	—
415	C₂²×C₄	#41×C₄₃	1	2	yes	—
416	C₂²×C₄	#41×C₄₃	1	2	yes	—
417	C₄⋊C₄	—	2	16	no	—
418	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	16	yes	complemented
419	C₂²⋊C₄	—	2	16	no	—
420	C₂²⋊C₄	—	2	32	no	—
421	C₂²⋊C₄	—	4	16	no	—
422	C₄²	—	2	8	no	—
423	C₄²	—	2	16	no	—
424	C₄²	—	4	16	no	—
425	C₂³	—	2	4	no	—
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	8	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	4	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	4	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	4	no	—
447	C₂³	C₂×C₄²×C₄₃	1	8	yes	—
448	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
449	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
450	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
451	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
452	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
453	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
454	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
455	C₂³	C₂×#41×C₄₃	1	2	yes	—
456	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
457	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
458	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
459	D₄	—	2	32	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	4	32	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	4	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
495	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
496	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
497	C₂×C₄	#117×C₄₃	1	4	yes	—
498	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
499	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
500	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
501	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	complemented
502	C₂²	—	2	8	no	—
503	C₂²	—	2	8	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	4	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	8	no	—
513	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
514	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
515	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
516	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
517	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
518	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
519	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
520	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
521	C₂²	C₄×#41×C₄₃	1	2	yes	—
522	C₂²	C₄₃×#518	1	1	yes	characteristic
523	C₂²	C₄₃×#518	1	2	yes	—
524	C₂²	C₄₃×#520	1	1	yes	characteristic
525	C₂²	C₄₃×#520	1	2	yes	—
526	C₂²	D₄²×C₄₃	1	2	yes	—
527	C₂²	C₄₃×#546	1	2	yes	—
528	C₂²	C₄₃×#547	1	1	yes	characteristic
529	C₂²	C₄₃×#548	1	2	yes	—
530	C₂²	C₄₃×#550	1	2	yes	—
531	C₂²	C₄₃×#550	1	1	yes	characteristic
532	C₂²	C₄₃×#553	1	2	yes	—
533	C₂²	C₄₃×#555	1	1	yes	characteristic
534	C₂²	C₄₃×#556	1	1	yes	characteristic
535	C₂²	C₄₃×#559	1	2	yes	—
536	C₄	—	2	4	no	—
537	C₄	—	2	8	no	—
538	C₄	—	2	8	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	4	no	—
541	C₄	—	4	8	no	—
542	C₄	C₄×C₂²⋊C₄×C₄₃	1	8	yes	complemented
543	C₂	—	4	8	no	—
544	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
545	C₂	C₄²×D₄×C₄₃	1	1	yes	characteristic
546	C₂	C₄₃×#2275	1	1	yes	characteristic
547	C₂	D₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
548	C₂	C₄₃×#2341	1	1	yes	characteristic
549	C₂	C₄₃×#2354	1	1	yes	characteristic
550	C₂	C₄₃×#2357	1	1	yes	characteristic
551	C₂	C₄₃×#2361	1	2	yes	—
552	C₂	C₄₃×#2363	1	2	yes	—
553	C₂	C₄₃×#2366	1	2	yes	—
554	C₂	C₄₃×#2367	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₄⋊C₄×C₄₃	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
5. C₄₃×#1437	C₂	semidirect
6. C₄₃×C₄⋊#95	C₂	semidirect
7. C₄₃×C₂²⋊#95	C₂	semidirect
8. C₄×#95×C₄₃	C₂	semidirect
12. C₂×C₄×D₄×C₄₃	C₄	semidirect
21. C₄₃×#390	C₄	semidirect
52. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
60. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
61. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
69. C₂×C₄²×C₄₃	C₂×C₄	semidirect
75. #95×C₄₃	D₄	semidirect
92. C₂×D₄×C₄₃	C₄²	semidirect
140. C₄⋊C₄×C₄₃	C₂²⋊C₄	semidirect
223. C₂×C₄×C₄₃	C₄×D₄	semidirect
224. #13820	C₄₃	direct (N × H)
265. C₄×C₄₃	C₄×C₂²⋊C₄	semidirect
268. C₂×C₄×C₄⋊C₄	C₂×C₄₃	semidirect
269. C₂×C₄×C₂²⋊C₄	C₂×C₄₃	semidirect
270. #1437	C₂×C₄₃	semidirect
271. C₄⋊#95	C₂×C₄₃	semidirect
272. C₂²⋊#95	C₂×C₄₃	semidirect
273. C₄×#95	C₂×C₄₃	semidirect
289. C₂×C₄×D₄	C₄×C₄₃	semidirect
298. #390	C₄×C₄₃	semidirect
307. C₄₃	#13820	direct (N × H)
330. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
338. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
339. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
347. C₂×C₄²	C₂×C₄×C₄₃	semidirect
353. #95	D₄×C₄₃	semidirect
370. C₂×D₄	C₄²×C₄₃	semidirect
418. C₄⋊C₄	C₂²⋊C₄×C₄₃	semidirect
501. C₂×C₄	C₄×D₄×C₄₃	semidirect
542. C₄	C₄×C₂²⋊C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#390	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1437	2
C₄₃×C₄⋊#95	2
C₄₃×C₂²⋊#95	2
C₄×#95×C₄₃	2
#13820	43

Subgroups — C43×#13820 #24933837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13820 #24933837