Subgroups — C₄₃×#13821 #24933838

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#389	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal
4	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1436	C₂	1	4	yes	maximal
6	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1434	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
14	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#389	C₄	1	16	yes	complemented
18	C₄×C₄⋊C₄×C₄₃	—	2	8	no	—
19	C₄×C₄⋊C₄×C₄₃	—	2	8	no	—
20	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
21	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#95×C₄₃	C₂²	1	2	yes	—
23	C₂×#95×C₄₃	C₂²	1	2	yes	—
24	C₂×#95×C₄₃	C₂²	1	4	yes	—
25	C₂×#95×C₄₃	C₂²	1	2	yes	—
26	C₂×#95×C₄₃	C₂²	1	4	yes	—
27	C₂×#95×C₄₃	C₂²	1	2	yes	—
28	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
42	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
43	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
44	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
45	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₃	Q₈	1	4	yes	—
48	C₂×C₄²×C₄₃	—	2	4	no	—
49	C₂×C₄²×C₄₃	—	2	4	no	—
50	C₂×C₄²×C₄₃	—	2	4	no	—
51	C₂×C₄²×C₄₃	—	2	4	no	—
52	C₂×C₄²×C₄₃	—	2	4	no	—
53	C₂×C₄²×C₄₃	—	2	8	no	—
54	C₂×C₄²×C₄₃	—	2	8	no	—
55	C₂×C₄²×C₄₃	—	4	4	no	—
56	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
57	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
58	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
59	#95×C₄₃	—	2	8	no	—
60	#95×C₄₃	—	2	4	no	—
61	#95×C₄₃	—	2	2	no	—
62	#95×C₄₃	—	2	4	no	—
63	#95×C₄₃	—	4	2	no	—
64	#95×C₄₃	C₂×C₄	1	8	yes	—
65	#95×C₄₃	C₂×C₄	1	16	yes	—
66	#95×C₄₃	D₄	1	4	yes	—
67	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
68	C₂²×C₄×C₄₃	—	2	2	no	—
69	C₂²×C₄×C₄₃	—	2	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	4	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	2	2	no	—
78	C₂²×C₄×C₄₃	—	2	4	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	4	no	—
85	C₂²×C₄×C₄₃	—	2	4	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	1	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
100	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
113	C₂²×C₄×C₄₃	#41	1	2	yes	—
114	C₂²×C₄×C₄₃	#41	1	4	yes	—
115	C₂²×C₄×C₄₃	#41	1	4	yes	—
116	C₄⋊C₄×C₄₃	—	2	32	no	—
117	C₄⋊C₄×C₄₃	—	2	16	no	—
118	C₄⋊C₄×C₄₃	C₄²	1	16	yes	complemented
119	C₄⋊C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
120	C₄²×C₄₃	—	2	8	no	—
121	C₄²×C₄₃	—	2	16	no	—
122	C₄²×C₄₃	—	2	16	no	—
123	C₄²×C₄₃	—	4	16	no	—
124	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
125	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
126	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
127	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
128	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
129	C₂³×C₄₃	C₂×#41	1	2	yes	—
130	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
131	C₂³×C₄₃	C₂×#41	1	2	yes	—
132	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
133	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
134	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
135	C₂×C₄×C₄₃	—	2	2	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	2	4	no	—
139	C₂×C₄×C₄₃	—	2	8	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	8	no	—
142	C₂×C₄×C₄₃	—	2	2	no	—
143	C₂×C₄×C₄₃	—	2	4	no	—
144	C₂×C₄×C₄₃	—	2	4	no	—
145	C₂×C₄×C₄₃	—	2	4	no	—
146	C₂×C₄×C₄₃	—	2	4	no	—
147	C₂×C₄×C₄₃	—	2	4	no	—
148	C₂×C₄×C₄₃	—	2	4	no	—
149	C₂×C₄×C₄₃	—	2	4	no	—
150	C₂×C₄×C₄₃	—	2	4	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	4	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	8	no	—
158	C₂×C₄×C₄₃	—	2	8	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	4	4	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	4	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
175	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
177	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
178	C₂×C₄×C₄₃	#117	1	4	yes	—
179	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
181	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
182	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
183	#13821	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
185	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
187	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
189	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
190	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
191	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
192	C₂²×C₄₃	C₄×#41	1	2	yes	—
193	C₂²×C₄₃	#519	1	1	yes	characteristic
194	C₂²×C₄₃	#519	1	2	yes	—
195	C₂²×C₄₃	#520	1	1	yes	characteristic
196	C₂²×C₄₃	#520	1	2	yes	—
197	C₂²×C₄₃	D₄²	1	1	yes	characteristic
198	C₂²×C₄₃	#547	1	2	yes	—
199	C₂²×C₄₃	#547	1	1	yes	characteristic
200	C₂²×C₄₃	#548	1	2	yes	—
201	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₄₃	#552	1	2	yes	—
203	C₂²×C₄₃	#553	1	2	yes	—
204	C₂²×C₄₃	#554	1	1	yes	characteristic
205	C₂²×C₄₃	#556	1	2	yes	—
206	C₂²×C₄₃	#557	1	2	yes	—
207	C₄×C₄₃	—	2	4	no	—
208	C₄×C₄₃	—	2	8	no	—
209	C₄×C₄₃	—	2	8	no	—
210	C₄×C₄₃	—	2	8	no	—
211	C₄×C₄₃	—	4	2	no	—
212	C₄×C₄₃	—	4	8	no	—
213	C₄×C₄₃	—	4	4	no	—
214	C₄×C₄₃	C₄×C₄⋊C₄	1	8	yes	complemented
215	C₂×#389	C₂×C₄₃	1	2	yes	—
216	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	2	yes	—
217	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	2	yes	—
218	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
219	#1436	C₂×C₄₃	1	4	yes	—
220	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
221	#1434	C₂×C₄₃	1	2	yes	—
222	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
223	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
224	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
225	C₂×C₄₃	#2276	1	1	yes	characteristic
226	C₂×C₄₃	#2344	1	1	yes	characteristic
227	C₂×C₄₃	#2347	1	1	yes	characteristic
228	C₂×C₄₃	D₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₄₃	#2351	1	1	yes	characteristic
230	C₂×C₄₃	#2361	1	2	yes	—
231	C₂×C₄₃	#2362	1	2	yes	—
232	C₂×C₄₃	#2365	1	2	yes	—
233	C₂×C₄₃	#2370	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
236	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
239	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
240	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
241	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
242	#389	C₄×C₄₃	1	16	yes	complemented
243	C₄×C₄⋊C₄	—	2	8	no	—
244	C₄×C₄⋊C₄	—	2	8	no	—
245	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
246	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
247	C₂×#95	C₂²×C₄₃	1	2	yes	—
248	C₂×#95	C₂²×C₄₃	1	2	yes	—
249	C₂×#95	C₂²×C₄₃	1	4	yes	—
250	C₂×#95	C₂²×C₄₃	1	2	yes	—
251	C₂×#95	C₂²×C₄₃	1	4	yes	—
252	C₂×#95	C₂²×C₄₃	1	2	yes	—
253	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
254	C₄₃	#13821	1	1	yes	characteristic, direct product factor, Sylow
255	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
256	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	16	yes	—
269	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
270	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
271	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
272	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
273	C₂×C₄⋊C₄	Q₈×C₄₃	1	4	yes	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	—	2	4	no	—
276	C₂×C₄²	—	2	4	no	—
277	C₂×C₄²	—	2	4	no	—
278	C₂×C₄²	—	2	4	no	—
279	C₂×C₄²	—	2	8	no	—
280	C₂×C₄²	—	2	8	no	—
281	C₂×C₄²	—	4	4	no	—
282	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
283	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
284	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
285	#95	—	2	8	no	—
286	#95	—	2	4	no	—
287	#95	—	2	2	no	—
288	#95	—	2	4	no	—
289	#95	—	4	2	no	—
290	#95	C₂×C₄×C₄₃	1	8	yes	—
291	#95	C₂×C₄×C₄₃	1	16	yes	—
292	#95	D₄×C₄₃	1	4	yes	—
293	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
324	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
325	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
326	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
327	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
328	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
329	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
336	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
338	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
339	C₂²×C₄	#41×C₄₃	1	2	yes	—
340	C₂²×C₄	#41×C₄₃	1	4	yes	—
341	C₂²×C₄	#41×C₄₃	1	4	yes	—
342	C₄⋊C₄	—	2	32	no	—
343	C₄⋊C₄	—	2	16	no	—
344	C₄⋊C₄	C₄²×C₄₃	1	16	yes	complemented
345	C₄⋊C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
346	C₄²	—	2	8	no	—
347	C₄²	—	2	16	no	—
348	C₄²	—	2	16	no	—
349	C₄²	—	4	16	no	—
350	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
351	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
352	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
353	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
354	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
355	C₂³	C₂×#41×C₄₃	1	2	yes	—
356	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
357	C₂³	C₂×#41×C₄₃	1	2	yes	—
358	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
359	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
360	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	C₂×C₄²×C₄₃	1	8	yes	—
401	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
402	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	8	yes	—
403	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
404	C₂×C₄	#117×C₄₃	1	4	yes	—
405	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
406	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
407	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
408	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
409	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
410	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
411	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
412	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
413	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
414	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
415	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
416	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
417	C₂²	C₄×#41×C₄₃	1	2	yes	—
418	C₂²	C₄₃×#519	1	1	yes	characteristic
419	C₂²	C₄₃×#519	1	2	yes	—
420	C₂²	C₄₃×#520	1	1	yes	characteristic
421	C₂²	C₄₃×#520	1	2	yes	—
422	C₂²	D₄²×C₄₃	1	1	yes	characteristic
423	C₂²	C₄₃×#547	1	2	yes	—
424	C₂²	C₄₃×#547	1	1	yes	characteristic
425	C₂²	C₄₃×#548	1	2	yes	—
426	C₂²	D₄×Q₈×C₄₃	1	1	yes	characteristic
427	C₂²	C₄₃×#552	1	2	yes	—
428	C₂²	C₄₃×#553	1	2	yes	—
429	C₂²	C₄₃×#554	1	1	yes	characteristic
430	C₂²	C₄₃×#556	1	2	yes	—
431	C₂²	C₄₃×#557	1	2	yes	—
432	C₄	—	2	4	no	—
433	C₄	—	2	8	no	—
434	C₄	—	2	8	no	—
435	C₄	—	2	8	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	8	no	—
438	C₄	—	4	4	no	—
439	C₄	C₄×C₄⋊C₄×C₄₃	1	8	yes	complemented
440	C₂	C₂×C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
441	C₂	C₄²×D₄×C₄₃	1	1	yes	characteristic
442	C₂	C₄₃×#2276	1	1	yes	characteristic
443	C₂	C₄₃×#2344	1	1	yes	characteristic
444	C₂	C₄₃×#2347	1	1	yes	characteristic
445	C₂	D₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
446	C₂	C₄₃×#2351	1	1	yes	characteristic
447	C₂	C₄₃×#2361	1	2	yes	—
448	C₂	C₄₃×#2362	1	2	yes	—
449	C₂	C₄₃×#2365	1	2	yes	—
450	C₂	C₄₃×#2370	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
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
17. C₄₃×#389	C₄	semidirect
20. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
118. C₄⋊C₄×C₄₃	C₄²	semidirect
119. C₄⋊C₄×C₄₃	C₄⋊C₄	semidirect
183. #13821	C₄₃	direct (N × H)
214. C₄×C₄₃	C₄×C₄⋊C₄	semidirect
242. #389	C₄×C₄₃	semidirect
245. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
254. C₄₃	#13821	direct (N × H)
344. C₄⋊C₄	C₄²×C₄₃	semidirect
345. C₄⋊C₄	C₄⋊C₄×C₄₃	semidirect
439. C₄	C₄×C₄⋊C₄×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×#389	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄₃×#1434	2
C₄×#95×C₄₃	2
#13821	43

Subgroups — C43×#13821 #24933838

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13821 #24933838