Subgroups — C₄₃×#13880 #24933897

Order 11008.

2510 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#385	C₂	1	4	yes	maximal
3	C₂×C₄₃×#384	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1444	C₂	1	4	yes	maximal, complemented
7	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
9	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊C₄×C₄₃	—	2	4	no	—
11	C₂²×C₄⋊C₄×C₄₃	—	2	8	no	—
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₃	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₄₃×#385	—	2	16	no	—
21	C₄₃×#384	—	2	8	no	—
22	C₄₃×#380	—	2	4	no	—
23	C₄×C₂²⋊C₄×C₄₃	C₄	1	8	yes	complemented
24	C₂×#95×C₄₃	C₂²	1	8	yes	—
25	C₂×#95×C₄₃	C₂²	1	2	yes	—
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	—	2	4	no	—
29	C₂³×C₄×C₄₃	—	2	4	no	—
30	C₂³×C₄×C₄₃	—	2	4	no	—
31	C₂³×C₄×C₄₃	—	2	8	no	—
32	C₂³×C₄×C₄₃	—	2	8	no	—
33	C₂³×C₄×C₄₃	—	4	4	no	—
34	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
35	C₂³×C₄×C₄₃	D₄	1	4	yes	—
36	C₂³×C₄×C₄₃	Q₈	1	4	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₃	—	2	32	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	16	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₃	—	4	8	no	—
55	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
56	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
59	C₂×C₂²⋊C₄×C₄₃	D₄	1	8	yes	—
60	C₂×C₂²⋊C₄×C₄₃	Q₈	1	8	yes	—
61	C₂×C₄²×C₄₃	—	2	4	no	—
62	C₂×C₄²×C₄₃	—	2	4	no	—
63	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
64	#95×C₄₃	—	2	4	no	—
65	#95×C₄₃	—	2	16	no	—
66	#95×C₄₃	C₂×C₄	1	8	yes	complemented
67	C₂⁴×C₄₃	—	2	2	no	—
68	C₂⁴×C₄₃	—	2	2	no	—
69	C₂⁴×C₄₃	—	2	2	no	—
70	C₂⁴×C₄₃	—	2	2	no	—
71	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
72	C₂⁴×C₄₃	C₂×D₄	1	4	yes	—
73	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
74	C₂⁴×C₄₃	C₂×Q₈	1	4	yes	—
75	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
76	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	—	2	16	no	—
78	C₂²×C₄×C₄₃	—	2	8	no	—
79	C₂²×C₄×C₄₃	—	2	16	no	—
80	C₂²×C₄×C₄₃	—	2	8	no	—
81	C₂²×C₄×C₄₃	—	2	16	no	—
82	C₂²×C₄×C₄₃	—	2	4	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	8	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	4	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	8	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	4	32	no	—
101	C₂²×C₄×C₄₃	—	4	8	no	—
102	C₂²×C₄×C₄₃	—	4	8	no	—
103	C₂²×C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
104	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×Q₈	1	8	yes	—
114	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₄₃	#41	1	4	yes	—
116	C₄⋊C₄×C₄₃	—	2	16	no	—
117	C₄⋊C₄×C₄₃	—	2	16	no	—
118	C₄⋊C₄×C₄₃	—	4	32	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₄⋊C₄×C₄₃	—	4	4	no	—
121	C₂²⋊C₄×C₄₃	—	4	8	no	—
122	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	32	yes	complemented
123	C₄²×C₄₃	—	2	16	no	—
124	C₂³×C₄₃	—	2	4	no	—
125	C₂³×C₄₃	—	2	4	no	—
126	C₂³×C₄₃	—	2	2	no	—
127	C₂³×C₄₃	—	2	4	no	—
128	C₂³×C₄₃	—	2	2	no	—
129	C₂³×C₄₃	—	2	2	no	—
130	C₂³×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	2	4	no	—
132	C₂³×C₄₃	—	2	8	no	—
133	C₂³×C₄₃	—	2	8	no	—
134	C₂³×C₄₃	—	2	8	no	—
135	C₂³×C₄₃	—	2	8	no	—
136	C₂³×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
137	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
138	C₂³×C₄₃	#127	1	4	yes	—
139	C₂³×C₄₃	C₄⋊Q₈	1	4	yes	—
140	C₂³×C₄₃	C₄⋊Q₈	1	8	yes	—
141	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
142	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
144	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
145	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
146	C₂³×C₄₃	C₂²×Q₈	1	2	yes	—
147	C₂³×C₄₃	C₂×#41	1	2	yes	—
148	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
149	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
150	C₂×C₄×C₄₃	—	2	8	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	8	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	8	no	—
157	C₂×C₄×C₄₃	—	2	8	no	—
158	C₂×C₄×C₄₃	—	2	8	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	2	32	no	—
161	C₂×C₄×C₄₃	—	2	8	no	—
162	C₂×C₄×C₄₃	—	2	16	no	—
163	C₂×C₄×C₄₃	—	4	32	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	8	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	8	no	—
174	C₂×C₄×C₄₃	—	4	8	no	—
175	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
177	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	16	yes	complemented
178	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
179	C₂×C₄×C₄₃	#120	1	4	yes	—
180	C₂×C₄×C₄₃	C₂²⋊Q₈	1	8	yes	—
181	C₂×C₄×C₄₃	#123	1	4	yes	—
182	#13880	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₄₃	—	2	4	no	—
184	C₂²×C₄₃	—	2	16	no	—
185	C₂²×C₄₃	—	2	4	no	—
186	C₂²×C₄₃	—	2	4	no	—
187	C₂²×C₄₃	—	2	16	no	—
188	C₂²×C₄₃	—	2	4	no	—
189	C₂²×C₄₃	—	2	4	no	—
190	C₂²×C₄₃	—	2	4	no	—
191	C₂²×C₄₃	#384	1	8	yes	complemented
192	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
194	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
195	C₂²×C₄₃	#520	1	2	yes	—
196	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
197	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	2	yes	—
198	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
199	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
202	C₂²×C₄₃	#535	1	1	yes	characteristic
203	C₂²×C₄₃	#536	1	1	yes	characteristic
204	C₂²×C₄₃	#544	1	2	yes	—
205	C₂²×C₄₃	D₄²	1	4	yes	—
206	C₂²×C₄₃	#547	1	4	yes	—
207	C₂²×C₄₃	D₄×Q₈	1	4	yes	—
208	C₂²×C₄₃	#554	1	4	yes	—
209	C₄×C₄₃	—	2	16	no	—
210	C₄×C₄₃	—	2	4	no	—
211	C₄×C₄₃	—	4	8	no	—
212	C₄×C₄₃	—	8	2	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	#385	1	8	yes	complemented
215	C₂³×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
216	C₂×#385	C₂×C₄₃	1	4	yes	—
217	C₂×#384	C₂×C₄₃	1	2	yes	complemented
218	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
219	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
220	#1444	C₂×C₄₃	1	4	yes	complemented
221	C₄⋊#95	C₂×C₄₃	1	2	yes	complemented
222	C₂×C₄₃	—	2	8	no	—
223	C₂×C₄₃	C₂×#384	1	1	yes	characteristic
224	C₂×C₄₃	C₂×#385	1	1	yes	characteristic
225	C₂×C₄₃	#2317	1	1	yes	characteristic
226	C₂×C₄₃	D₄×C₄⋊C₄	1	4	yes	—
227	C₂×C₄₃	#2433	1	1	yes	characteristic
228	C₂×C₄₃	#2434	1	1	yes	characteristic
229	C₂×C₄₃	#2440	1	4	yes	—
230	C₂×C₄₃	#2501	1	1	yes	characteristic
231	C₂×C₄₃	#2502	1	1	yes	characteristic
232	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
233	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	—	2	4	no	—
235	C₂²×C₄⋊C₄	—	2	8	no	—
236	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
238	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₄₃	1	8	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
241	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
243	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
244	#385	—	2	16	no	—
245	#384	—	2	8	no	—
246	#380	—	2	4	no	—
247	C₄×C₂²⋊C₄	C₄×C₄₃	1	8	yes	complemented
248	C₂×#95	C₂²×C₄₃	1	8	yes	—
249	C₂×#95	C₂²×C₄₃	1	2	yes	—
250	C₂×#95	C₂²×C₄₃	1	2	yes	—
251	C₄₃	#13880	1	1	yes	characteristic, direct product factor, Sylow
252	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
253	C₂³×C₄	—	2	4	no	—
254	C₂³×C₄	—	2	4	no	—
255	C₂³×C₄	—	2	4	no	—
256	C₂³×C₄	—	2	8	no	—
257	C₂³×C₄	—	2	8	no	—
258	C₂³×C₄	—	4	4	no	—
259	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
260	C₂³×C₄	D₄×C₄₃	1	4	yes	—
261	C₂³×C₄	Q₈×C₄₃	1	4	yes	—
262	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
265	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
268	C₂×C₄⋊C₄	—	2	32	no	—
269	C₂×C₄⋊C₄	—	2	8	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	—	2	4	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	16	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	16	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	4	8	no	—
280	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
284	C₂×C₂²⋊C₄	D₄×C₄₃	1	8	yes	—
285	C₂×C₂²⋊C₄	Q₈×C₄₃	1	8	yes	—
286	C₂×C₄²	—	2	4	no	—
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	complemented
289	#95	—	2	4	no	—
290	#95	—	2	16	no	—
291	#95	C₂×C₄×C₄₃	1	8	yes	complemented
292	C₂⁴	—	2	2	no	—
293	C₂⁴	—	2	2	no	—
294	C₂⁴	—	2	2	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
297	C₂⁴	C₂×D₄×C₄₃	1	4	yes	—
298	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
299	C₂⁴	C₂×Q₈×C₄₃	1	4	yes	—
300	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
301	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	16	no	—
309	C₂²×C₄	—	2	8	no	—
310	C₂²×C₄	—	2	16	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	16	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	4	32	no	—
326	C₂²×C₄	—	4	8	no	—
327	C₂²×C₄	—	4	8	no	—
328	C₂²×C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
329	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
333	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
337	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂×Q₈×C₄₃	1	8	yes	—
339	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
340	C₂²×C₄	#41×C₄₃	1	4	yes	—
341	C₄⋊C₄	—	2	16	no	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	4	32	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₂²⋊C₄	—	4	8	no	—
347	C₂²⋊C₄	C₄⋊C₄×C₄₃	1	32	yes	complemented
348	C₄²	—	2	16	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	2	2	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	2	8	no	—
361	C₂³	C₂×C₄⋊C₄×C₄₃	1	8	yes	—
362	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
363	C₂³	#127×C₄₃	1	4	yes	—
364	C₂³	C₄⋊Q₈×C₄₃	1	4	yes	—
365	C₂³	C₄⋊Q₈×C₄₃	1	8	yes	—
366	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
367	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
368	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
369	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
370	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
371	C₂³	C₂²×Q₈×C₄₃	1	2	yes	—
372	C₂³	C₂×#41×C₄₃	1	2	yes	—
373	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
374	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	32	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	16	no	—
388	C₂×C₄	—	4	32	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
401	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
402	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	16	yes	complemented
403	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
404	C₂×C₄	#120×C₄₃	1	4	yes	—
405	C₂×C₄	C₂²⋊Q₈×C₄₃	1	8	yes	—
406	C₂×C₄	#123×C₄₃	1	4	yes	—
407	C₂²	—	2	16	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	16	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	4	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	C₄₃×#384	1	8	yes	complemented
416	C₂²	C₂²×C₄⋊C₄×C₄₃	1	2	yes	—
417	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
418	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
419	C₂²	C₄₃×#520	1	2	yes	—
420	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
421	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	2	yes	—
422	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
423	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
424	C₂²	C₂×C₄⋊Q₈×C₄₃	1	1	yes	characteristic
425	C₂²	C₂×C₄⋊Q₈×C₄₃	1	2	yes	—
426	C₂²	C₄₃×#535	1	1	yes	characteristic
427	C₂²	C₄₃×#536	1	1	yes	characteristic
428	C₂²	C₄₃×#544	1	2	yes	—
429	C₂²	D₄²×C₄₃	1	4	yes	—
430	C₂²	C₄₃×#547	1	4	yes	—
431	C₂²	D₄×Q₈×C₄₃	1	4	yes	—
432	C₂²	C₄₃×#554	1	4	yes	—
433	C₄	—	2	16	no	—
434	C₄	—	2	4	no	—
435	C₄	—	4	8	no	—
436	C₄	—	8	2	no	—
437	C₄	—	8	2	no	—
438	C₄	C₄₃×#385	1	8	yes	complemented
439	C₂	—	2	8	no	—
440	C₂	C₂×C₄₃×#384	1	1	yes	characteristic
441	C₂	C₂×C₄₃×#385	1	1	yes	characteristic
442	C₂	C₄₃×#2317	1	1	yes	characteristic
443	C₂	D₄×C₄⋊C₄×C₄₃	1	4	yes	—
444	C₂	C₄₃×#2433	1	1	yes	characteristic
445	C₂	C₄₃×#2434	1	1	yes	characteristic
446	C₂	C₄₃×#2440	1	4	yes	—
447	C₂	C₄₃×#2501	1	1	yes	characteristic
448	C₂	C₄₃×#2502	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₃×#384	C₂	semidirect
6. C₄₃×#1444	C₂	semidirect
7. C₄₃×C₄⋊#95	C₂	semidirect
23. C₄×C₂²⋊C₄×C₄₃	C₄	semidirect
63. C₂×C₄²×C₄₃	C₂×C₄	semidirect
66. #95×C₄₃	C₂×C₄	semidirect
103. C₂²×C₄×C₄₃	C₄⋊C₄	semidirect
122. C₂²⋊C₄×C₄₃	C₄⋊C₄	semidirect
177. C₂×C₄×C₄₃	C₂×C₄⋊C₄	semidirect
182. #13880	C₄₃	direct (N × H)
191. C₂²×C₄₃	#384	semidirect
214. C₄×C₄₃	#385	semidirect
217. C₂×#384	C₂×C₄₃	semidirect
220. #1444	C₂×C₄₃	semidirect
221. C₄⋊#95	C₂×C₄₃	semidirect
247. C₄×C₂²⋊C₄	C₄×C₄₃	semidirect
251. C₄₃	#13880	direct (N × H)
288. C₂×C₄²	C₂×C₄×C₄₃	semidirect
291. #95	C₂×C₄×C₄₃	semidirect
328. C₂²×C₄	C₄⋊C₄×C₄₃	semidirect
347. C₂²⋊C₄	C₄⋊C₄×C₄₃	semidirect
402. C₂×C₄	C₂×C₄⋊C₄×C₄₃	semidirect
415. C₂²	C₄₃×#384	semidirect
438. C₄	C₄₃×#385	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊C₄×C₄₃	2
C₂×C₄₃×#385	2
C₂×C₄₃×#384	2
C₂×C₄₃×#380	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₄₃×#1444	2
C₄₃×C₄⋊#95	2
#13880	43

Subgroups — C43×#13880 #24933897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13880 #24933897