Subgroups — C₄₃×#13817 #24933834

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#391	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	2	yes	maximal
4	C₄₃×#1436	C₂	1	4	yes	maximal
5	C₄₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1434	C₂	1	2	yes	maximal
7	C₄×#95×C₄₃	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₄₃	—	2	8	no	—
11	C₂×C₄×Q₈×C₄₃	C₄	1	8	yes	complemented
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#391	C₄	1	16	yes	complemented
20	C₄×C₄⋊C₄×C₄₃	—	2	8	no	—
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	4	yes	—
28	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₄₃	—	2	4	no	—
30	C₂²×Q₈×C₄₃	—	2	2	no	—
31	C₂²×Q₈×C₄₃	—	2	2	no	—
32	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
33	C₂²×Q₈×C₄₃	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
36	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₄×Q₈×C₄₃	—	2	32	no	—
43	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
44	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
49	C₂×C₄⋊C₄×C₄₃	D₄	1	8	yes	—
50	C₂×C₄²×C₄₃	—	2	8	no	—
51	C₂×C₄²×C₄₃	—	2	4	no	—
52	C₂×C₄²×C₄₃	—	2	4	no	—
53	C₂×C₄²×C₄₃	—	2	4	no	—
54	C₂×C₄²×C₄₃	—	2	8	no	—
55	C₂×C₄²×C₄₃	—	2	8	no	—
56	C₂×C₄²×C₄₃	—	4	4	no	—
57	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
59	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
60	#95×C₄₃	—	2	8	no	—
61	#95×C₄₃	—	2	2	no	—
62	#95×C₄₃	—	2	4	no	—
63	#95×C₄₃	—	2	4	no	—
64	#95×C₄₃	—	4	2	no	—
65	#95×C₄₃	C₂×C₄	1	16	yes	—
66	#95×C₄₃	C₂×C₄	1	16	yes	—
67	#95×C₄₃	Q₈	1	4	yes	complemented
68	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
69	C₂×Q₈×C₄₃	—	2	8	no	—
70	C₂×Q₈×C₄₃	—	2	8	no	—
71	C₂×Q₈×C₄₃	—	2	16	no	—
72	C₂×Q₈×C₄₃	—	2	16	no	—
73	C₂×Q₈×C₄₃	C₄²	1	16	yes	complemented
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	4	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	4	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	4	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	2	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	1	no	—
94	C₂²×C₄×C₄₃	—	2	4	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	1	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
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	4	yes	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₄₃	#41	1	2	yes	—
117	C₂²×C₄×C₄₃	#41	1	4	yes	—
118	C₂²×C₄×C₄₃	#41	1	2	yes	—
119	C₂²×C₄×C₄₃	#41	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	16	no	—
121	C₄⋊C₄×C₄₃	—	2	16	no	—
122	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	16	yes	—
123	C₄²×C₄₃	—	2	16	no	—
124	C₄²×C₄₃	—	2	8	no	—
125	C₄²×C₄₃	—	2	16	no	—
126	C₄²×C₄₃	—	4	16	no	—
127	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
128	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
129	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
130	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
131	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
132	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
133	C₂³×C₄₃	C₂×#41	1	2	yes	—
134	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
135	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
136	C₂³×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
137	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
138	Q₈×C₄₃	—	2	32	no	—
139	C₂×C₄×C₄₃	—	2	2	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	4	no	—
142	C₂×C₄×C₄₃	—	2	4	no	—
143	C₂×C₄×C₄₃	—	2	8	no	—
144	C₂×C₄×C₄₃	—	2	8	no	—
145	C₂×C₄×C₄₃	—	2	4	no	—
146	C₂×C₄×C₄₃	—	2	2	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	8	no	—
151	C₂×C₄×C₄₃	—	2	8	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	4	no	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	4	4	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	4	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	—	4	4	no	—
176	C₂×C₄×C₄₃	C₂×C₄²	1	8	yes	—
177	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
179	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₃	#117	1	4	yes	—
181	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
182	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
183	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
184	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	complemented
185	#13817	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
187	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
189	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
190	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
191	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
193	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
194	C₂²×C₄₃	C₄×#41	1	2	yes	—
195	C₂²×C₄₃	#519	1	1	yes	characteristic
196	C₂²×C₄₃	#519	1	2	yes	—
197	C₂²×C₄₃	#520	1	1	yes	characteristic
198	C₂²×C₄₃	#520	1	2	yes	—
199	C₂²×C₄₃	#546	1	2	yes	—
200	C₂²×C₄₃	#547	1	2	yes	—
201	C₂²×C₄₃	#548	1	2	yes	—
202	C₂²×C₄₃	D₄×Q₈	1	2	yes	—
203	C₂²×C₄₃	#552	1	2	yes	—
204	C₂²×C₄₃	#554	1	1	yes	characteristic
205	C₂²×C₄₃	#556	1	1	yes	characteristic
206	C₂²×C₄₃	#556	1	2	yes	—
207	C₂²×C₄₃	#557	1	1	yes	characteristic
208	C₂²×C₄₃	#559	1	1	yes	characteristic
209	C₄×C₄₃	—	2	8	no	—
210	C₄×C₄₃	—	2	4	no	—
211	C₄×C₄₃	—	2	8	no	—
212	C₄×C₄₃	—	2	8	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	—	4	4	no	—
215	C₄×C₄₃	—	4	8	no	—
216	C₄×C₄₃	C₄×C₂²⋊C₄	1	8	yes	—
217	C₂²×C₄×Q₈	C₂×C₄₃	1	1	yes	characteristic
218	C₂×#391	C₂×C₄₃	1	2	yes	—
219	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	2	yes	—
220	#1436	C₂×C₄₃	1	4	yes	—
221	C₄⋊#95	C₂×C₄₃	1	1	yes	characteristic
222	#1434	C₂×C₄₃	1	2	yes	—
223	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
224	C₄×#95	C₂×C₄₃	1	2	yes	—
225	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
226	C₂×C₄₃	C₄²×Q₈	1	1	yes	characteristic
227	C₂×C₄₃	#2276	1	1	yes	characteristic
228	C₂×C₄₃	#2339	1	1	yes	characteristic
229	C₂×C₄₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄₃	#2355	1	1	yes	characteristic
231	C₂×C₄₃	#2356	1	1	yes	characteristic
232	C₂×C₄₃	#2360	1	2	yes	—
233	C₂×C₄₃	#2362	1	2	yes	—
234	C₂×C₄₃	#2365	1	2	yes	—
235	C₂×C₄₃	#2367	1	2	yes	—
236	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×C₄×Q₈	—	2	8	no	—
238	C₂×C₄×Q₈	C₄×C₄₃	1	8	yes	complemented
239	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
240	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
243	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
244	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
246	#391	C₄×C₄₃	1	16	yes	complemented
247	C₄×C₄⋊C₄	—	2	8	no	—
248	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
249	C₂×#95	C₂²×C₄₃	1	2	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	4	yes	—
254	C₂×#95	C₂²×C₄₃	1	4	yes	—
255	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
256	C₄₃	#13817	1	1	yes	characteristic, direct product factor, Sylow
257	C₂²×Q₈	—	2	4	no	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
261	C₂²×Q₈	C₂×C₄×C₄₃	1	8	yes	—
262	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
263	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
264	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
266	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
267	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
269	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
270	C₄×Q₈	—	2	32	no	—
271	C₂×C₄⋊C₄	—	2	8	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
275	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
276	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
277	C₂×C₄⋊C₄	D₄×C₄₃	1	8	yes	—
278	C₂×C₄²	—	2	8	no	—
279	C₂×C₄²	—	2	4	no	—
280	C₂×C₄²	—	2	4	no	—
281	C₂×C₄²	—	2	4	no	—
282	C₂×C₄²	—	2	8	no	—
283	C₂×C₄²	—	2	8	no	—
284	C₂×C₄²	—	4	4	no	—
285	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
286	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
287	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
288	#95	—	2	8	no	—
289	#95	—	2	2	no	—
290	#95	—	2	4	no	—
291	#95	—	2	4	no	—
292	#95	—	4	2	no	—
293	#95	C₂×C₄×C₄₃	1	16	yes	—
294	#95	C₂×C₄×C₄₃	1	16	yes	—
295	#95	Q₈×C₄₃	1	4	yes	complemented
296	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	2	16	no	—
300	C₂×Q₈	—	2	16	no	—
301	C₂×Q₈	C₄²×C₄₃	1	16	yes	complemented
302	C₂²×C₄	—	2	2	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	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	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	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	4	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
331	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
332	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
334	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
335	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
336	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
338	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
340	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
341	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
342	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
343	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
344	C₂²×C₄	#41×C₄₃	1	2	yes	—
345	C₂²×C₄	#41×C₄₃	1	4	yes	—
346	C₂²×C₄	#41×C₄₃	1	2	yes	—
347	C₂²×C₄	#41×C₄₃	1	2	yes	—
348	C₄⋊C₄	—	2	16	no	—
349	C₄⋊C₄	—	2	16	no	—
350	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	16	yes	—
351	C₄²	—	2	16	no	—
352	C₄²	—	2	8	no	—
353	C₄²	—	2	16	no	—
354	C₄²	—	4	16	no	—
355	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
356	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
357	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
358	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
359	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
360	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
361	C₂³	C₂×#41×C₄₃	1	2	yes	—
362	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
363	C₂³	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
364	C₂³	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
365	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
366	Q₈	—	2	32	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	C₂×C₄²×C₄₃	1	8	yes	—
405	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
408	C₂×C₄	#117×C₄₃	1	4	yes	—
409	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
410	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
411	C₂×C₄	C₄×Q₈×C₄₃	1	4	yes	—
412	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	complemented
413	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
414	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
415	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
416	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
417	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
418	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
419	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
420	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
421	C₂²	C₄×#41×C₄₃	1	2	yes	—
422	C₂²	C₄₃×#519	1	1	yes	characteristic
423	C₂²	C₄₃×#519	1	2	yes	—
424	C₂²	C₄₃×#520	1	1	yes	characteristic
425	C₂²	C₄₃×#520	1	2	yes	—
426	C₂²	C₄₃×#546	1	2	yes	—
427	C₂²	C₄₃×#547	1	2	yes	—
428	C₂²	C₄₃×#548	1	2	yes	—
429	C₂²	D₄×Q₈×C₄₃	1	2	yes	—
430	C₂²	C₄₃×#552	1	2	yes	—
431	C₂²	C₄₃×#554	1	1	yes	characteristic
432	C₂²	C₄₃×#556	1	1	yes	characteristic
433	C₂²	C₄₃×#556	1	2	yes	—
434	C₂²	C₄₃×#557	1	1	yes	characteristic
435	C₂²	C₄₃×#559	1	1	yes	characteristic
436	C₄	—	2	8	no	—
437	C₄	—	2	4	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	8	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	4	no	—
442	C₄	—	4	8	no	—
443	C₄	C₄×C₂²⋊C₄×C₄₃	1	8	yes	—
444	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
445	C₂	C₄²×Q₈×C₄₃	1	1	yes	characteristic
446	C₂	C₄₃×#2276	1	1	yes	characteristic
447	C₂	C₄₃×#2339	1	1	yes	characteristic
448	C₂	Q₈×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
449	C₂	C₄₃×#2355	1	1	yes	characteristic
450	C₂	C₄₃×#2356	1	1	yes	characteristic
451	C₂	C₄₃×#2360	1	2	yes	—
452	C₂	C₄₃×#2362	1	2	yes	—
453	C₂	C₄₃×#2365	1	2	yes	—
454	C₂	C₄₃×#2367	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
11. C₂×C₄×Q₈×C₄₃	C₄	semidirect
19. C₄₃×#391	C₄	semidirect
67. #95×C₄₃	Q₈	semidirect
73. C₂×Q₈×C₄₃	C₄²	semidirect
184. C₂×C₄×C₄₃	C₄×Q₈	semidirect
185. #13817	C₄₃	direct (N × H)
238. C₂×C₄×Q₈	C₄×C₄₃	semidirect
246. #391	C₄×C₄₃	semidirect
256. C₄₃	#13817	direct (N × H)
295. #95	Q₈×C₄₃	semidirect
301. C₂×Q₈	C₄²×C₄₃	semidirect
412. C₂×C₄	C₄×Q₈×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×Q₈×C₄₃	2
C₂×C₄₃×#391	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₄₃×#1436	2
C₄₃×C₄⋊#95	2
C₄₃×#1434	2
C₄×#95×C₄₃	2
#13817	43

Subgroups — C43×#13817 #24933834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13817 #24933834