Subgroups — C₄₃×#13802 #24933819

Order 11008.

2182 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#380	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	2	yes	maximal
3	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1436	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1434	C₂	1	2	yes	maximal, complemented
7	C₄₃×C₂²⋊#95	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
17	C₄₃×#380	C₄	1	8	yes	complemented
18	C₄×C₂²⋊C₄×C₄₃	—	2	8	no	—
19	C₄×C₂²⋊C₄×C₄₃	C₄	1	8	yes	complemented
20	C₂×#95×C₄₃	C₄	1	8	yes	complemented
21	C₂×#95×C₄₃	C₂²	1	4	yes	—
22	C₂×#95×C₄₃	C₂²	1	4	yes	—
23	C₂×#95×C₄₃	C₂²	1	4	yes	—
24	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₂×#95×C₄₃	C₂²	1	2	yes	—
28	C₂×#95×C₄₃	C₂²	1	2	yes	—
29	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	—	2	4	no	—
31	C₂³×C₄×C₄₃	—	2	4	no	—
32	C₂³×C₄×C₄₃	—	2	8	no	—
33	C₂³×C₄×C₄₃	—	4	4	no	—
34	C₂³×C₄×C₄₃	—	4	4	no	—
35	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
36	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
37	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
38	C₂³×C₄×C₄₃	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊C₄×C₄₃	—	4	4	no	—
47	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
48	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
51	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
53	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
54	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
55	C₂×C₂²⋊C₄×C₄₃	D₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₄₃	Q₈	1	4	yes	—
57	C₂×C₄²×C₄₃	—	2	8	no	—
58	C₂×C₄²×C₄₃	—	2	8	no	—
59	C₂×C₄²×C₄₃	—	4	4	no	—
60	C₂×C₄²×C₄₃	—	4	4	no	—
61	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
62	#95×C₄₃	—	2	8	no	—
63	#95×C₄₃	—	2	8	no	—
64	#95×C₄₃	—	4	4	no	—
65	#95×C₄₃	C₂×C₄	1	4	yes	—
66	#95×C₄₃	C₂×C₄	1	8	yes	—
67	#95×C₄₃	C₂×C₄	1	4	yes	—
68	#95×C₄₃	C₂×C₄	1	8	yes	complemented
69	#95×C₄₃	C₂×C₄	1	8	yes	complemented
70	C₂⁴×C₄₃	—	2	4	no	—
71	C₂⁴×C₄₃	—	2	4	no	—
72	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
73	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
74	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
75	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
76	C₂⁴×C₄₃	C₂×Q₈	1	2	yes	—
77	C₂⁴×C₄₃	#41	1	2	yes	—
78	C₂⁴×C₄₃	#41	1	2	yes	—
79	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
80	C₂²×C₄×C₄₃	—	2	16	no	—
81	C₂²×C₄×C₄₃	—	2	16	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	4	no	—
88	C₂²×C₄×C₄₃	—	2	4	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	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	4	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	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	2	4	no	—
103	C₂²×C₄×C₄₃	—	4	8	no	—
104	C₂²×C₄×C₄₃	—	4	8	no	—
105	C₂²×C₄×C₄₃	—	4	8	no	—
106	C₂²×C₄×C₄₃	—	4	8	no	—
107	C₂²×C₄×C₄₃	—	4	16	no	—
108	C₂²×C₄×C₄₃	—	4	16	no	—
109	C₂²×C₄×C₄₃	C₄²	1	16	yes	complemented
110	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
113	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
123	C₂²×C₄×C₄₃	#41	1	8	yes	—
124	C₄⋊C₄×C₄₃	—	4	8	no	—
125	C₂²⋊C₄×C₄₃	—	2	8	no	—
126	C₂²⋊C₄×C₄₃	—	2	16	no	—
127	C₂²⋊C₄×C₄₃	C₄⋊C₄	1	16	yes	complemented
128	C₄²×C₄₃	—	4	8	no	—
129	C₄²×C₄₃	—	4	16	no	—
130	C₂³×C₄₃	—	2	4	no	—
131	C₂³×C₄₃	—	2	4	no	—
132	C₂³×C₄₃	—	2	4	no	—
133	C₂³×C₄₃	—	2	4	no	—
134	C₂³×C₄₃	—	2	4	no	—
135	C₂³×C₄₃	—	2	4	no	—
136	C₂³×C₄₃	—	2	8	no	—
137	C₂³×C₄₃	—	2	8	no	—
138	C₂³×C₄₃	—	2	8	no	—
139	C₂³×C₄₃	—	2	8	no	—
140	C₂³×C₄₃	C₂×C₄²	1	4	yes	—
141	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
142	C₂³×C₄₃	#117	1	4	yes	—
143	C₂³×C₄₃	C₄×D₄	1	4	yes	—
144	C₂³×C₄₃	C₄×D₄	1	4	yes	—
145	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
146	C₂³×C₄₃	C₄×Q₈	1	4	yes	—
147	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
148	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
149	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
150	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
151	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
152	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
153	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
154	C₂³×C₄₃	C₂×#41	1	4	yes	—
155	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
156	C₂×C₄×C₄₃	—	2	4	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	4	no	—
163	C₂×C₄×C₄₃	—	2	4	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	8	no	—
167	C₂×C₄×C₄₃	—	2	8	no	—
168	C₂×C₄×C₄₃	—	2	8	no	—
169	C₂×C₄×C₄₃	—	2	8	no	—
170	C₂×C₄×C₄₃	—	2	4	no	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	2	8	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	4	no	—
175	C₂×C₄×C₄₃	—	2	8	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	8	no	—
178	C₂×C₄×C₄₃	—	2	4	no	—
179	C₂×C₄×C₄₃	—	4	16	no	—
180	C₂×C₄×C₄₃	—	4	32	no	—
181	C₂×C₄×C₄₃	—	4	4	no	—
182	C₂×C₄×C₄₃	—	4	4	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	4	no	—
185	C₂×C₄×C₄₃	—	4	4	no	—
186	C₂×C₄×C₄₃	—	4	4	no	—
187	C₂×C₄×C₄₃	—	4	4	no	—
188	C₂×C₄×C₄₃	—	4	4	no	—
189	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
190	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
191	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
192	C₂×C₄×C₄₃	#117	1	8	yes	—
193	#13802	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₃	—	2	8	no	—
195	C₂²×C₄₃	—	2	8	no	—
196	C₂²×C₄₃	—	2	8	no	—
197	C₂²×C₄₃	—	2	8	no	—
198	C₂²×C₄₃	—	2	8	no	—
199	C₂²×C₄₃	—	2	8	no	—
200	C₂²×C₄₃	—	2	4	no	—
201	C₂²×C₄₃	—	2	4	no	—
202	C₂²×C₄₃	C₄×C₄⋊C₄	1	8	yes	—
203	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
204	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×#117	1	2	yes	—
206	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
207	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
210	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
211	C₂²×C₄₃	C₄×#41	1	2	yes	—
212	C₂²×C₄₃	C₄×#41	1	2	yes	—
213	C₂²×C₄₃	#518	1	2	yes	—
214	C₂²×C₄₃	#518	1	2	yes	—
215	C₂²×C₄₃	#518	1	2	yes	—
216	C₂²×C₄₃	#546	1	4	yes	—
217	C₂²×C₄₃	#551	1	4	yes	—
218	C₂²×C₄₃	#553	1	4	yes	—
219	C₂²×C₄₃	#554	1	4	yes	—
220	C₄×C₄₃	—	2	8	no	—
221	C₄×C₄₃	—	2	8	no	—
222	C₄×C₄₃	—	2	4	no	—
223	C₄×C₄₃	—	2	4	no	—
224	C₄×C₄₃	—	4	4	no	—
225	C₄×C₄₃	—	4	4	no	—
226	C₄×C₄₃	—	4	8	no	—
227	C₂×#380	C₂×C₄₃	1	1	yes	characteristic
228	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	2	yes	—
229	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	1	yes	characteristic
230	C₂²×#95	C₂×C₄₃	1	1	yes	characteristic
231	#1436	C₂×C₄₃	1	4	yes	complemented
232	#1434	C₂×C₄₃	1	2	yes	complemented
233	C₂²⋊#95	C₂×C₄₃	1	2	yes	—
234	C₄×#95	C₂×C₄₃	1	2	yes	complemented
235	C₂×C₄₃	—	2	8	no	—
236	C₂×C₄₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₂×C₄₃	C₄×#117	1	1	yes	characteristic
238	C₂×C₄₃	#2273	1	1	yes	characteristic
239	C₂×C₄₃	#2342	1	2	yes	—
240	C₂×C₄₃	#2345	1	2	yes	—
241	C₂×C₄₃	#2349	1	2	yes	—
242	C₂×C₄₃	#2353	1	2	yes	—
243	C₂×C₄₃	#2364	1	2	yes	—
244	C₂×C₄₃	#2368	1	2	yes	—
245	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
246	C₂⁴×C₄	C₂²×C₄₃	1	1	yes	characteristic
247	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
248	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
249	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
251	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
252	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
253	#380	C₄×C₄₃	1	8	yes	complemented
254	C₄×C₂²⋊C₄	—	2	8	no	—
255	C₄×C₂²⋊C₄	C₄×C₄₃	1	8	yes	complemented
256	C₂×#95	C₄×C₄₃	1	8	yes	complemented
257	C₂×#95	C₂²×C₄₃	1	4	yes	—
258	C₂×#95	C₂²×C₄₃	1	4	yes	—
259	C₂×#95	C₂²×C₄₃	1	4	yes	—
260	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
261	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
262	C₂×#95	C₂²×C₄₃	1	2	yes	—
263	C₂×#95	C₂²×C₄₃	1	2	yes	—
264	C₂×#95	C₂²×C₄₃	1	2	yes	—
265	C₄₃	#13802	1	1	yes	characteristic, direct product factor, Sylow
266	C₂⁵	C₂³×C₄₃	1	1	yes	characteristic
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	8	no	—
270	C₂³×C₄	—	4	4	no	—
271	C₂³×C₄	—	4	4	no	—
272	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	—
273	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
274	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
275	C₂³×C₄	C₂×C₄×C₄₃	1	4	yes	—
276	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
277	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
278	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
280	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
282	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
283	C₂×C₄⋊C₄	—	4	4	no	—
284	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
291	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
292	C₂×C₂²⋊C₄	D₄×C₄₃	1	4	yes	—
293	C₂×C₂²⋊C₄	Q₈×C₄₃	1	4	yes	—
294	C₂×C₄²	—	2	8	no	—
295	C₂×C₄²	—	2	8	no	—
296	C₂×C₄²	—	4	4	no	—
297	C₂×C₄²	—	4	4	no	—
298	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	complemented
299	#95	—	2	8	no	—
300	#95	—	2	8	no	—
301	#95	—	4	4	no	—
302	#95	C₂×C₄×C₄₃	1	4	yes	—
303	#95	C₂×C₄×C₄₃	1	8	yes	—
304	#95	C₂×C₄×C₄₃	1	4	yes	—
305	#95	C₂×C₄×C₄₃	1	8	yes	complemented
306	#95	C₂×C₄×C₄₃	1	8	yes	complemented
307	C₂⁴	—	2	4	no	—
308	C₂⁴	—	2	4	no	—
309	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
310	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
311	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
312	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
313	C₂⁴	C₂×Q₈×C₄₃	1	2	yes	—
314	C₂⁴	#41×C₄₃	1	2	yes	—
315	C₂⁴	#41×C₄₃	1	2	yes	—
316	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	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	16	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	4	8	no	—
341	C₂²×C₄	—	4	8	no	—
342	C₂²×C₄	—	4	8	no	—
343	C₂²×C₄	—	4	8	no	—
344	C₂²×C₄	—	4	16	no	—
345	C₂²×C₄	—	4	16	no	—
346	C₂²×C₄	C₄²×C₄₃	1	16	yes	complemented
347	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
348	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
349	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
350	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
351	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
353	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
355	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
359	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
360	C₂²×C₄	#41×C₄₃	1	8	yes	—
361	C₄⋊C₄	—	4	8	no	—
362	C₂²⋊C₄	—	2	8	no	—
363	C₂²⋊C₄	—	2	16	no	—
364	C₂²⋊C₄	C₄⋊C₄×C₄₃	1	16	yes	complemented
365	C₄²	—	4	8	no	—
366	C₄²	—	4	16	no	—
367	C₂³	—	2	4	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	2	4	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	2	4	no	—
373	C₂³	—	2	8	no	—
374	C₂³	—	2	8	no	—
375	C₂³	—	2	8	no	—
376	C₂³	—	2	8	no	—
377	C₂³	C₂×C₄²×C₄₃	1	4	yes	—
378	C₂³	C₂×C₄⋊C₄×C₄₃	1	4	yes	—
379	C₂³	#117×C₄₃	1	4	yes	—
380	C₂³	C₄×D₄×C₄₃	1	4	yes	—
381	C₂³	C₄×D₄×C₄₃	1	4	yes	—
382	C₂³	C₄×Q₈×C₄₃	1	4	yes	—
383	C₂³	C₄×Q₈×C₄₃	1	4	yes	—
384	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
385	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
386	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
387	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
388	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
389	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
390	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
391	C₂³	C₂×#41×C₄₃	1	4	yes	—
392	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	8	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	16	no	—
417	C₂×C₄	—	4	32	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
427	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
428	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	8	yes	—
429	C₂×C₄	#117×C₄₃	1	8	yes	—
430	C₂²	—	2	8	no	—
431	C₂²	—	2	8	no	—
432	C₂²	—	2	8	no	—
433	C₂²	—	2	8	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	C₄×C₄⋊C₄×C₄₃	1	8	yes	—
439	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
440	C₂²	C₂²×C₄⋊C₄×C₄₃	1	1	yes	characteristic
441	C₂²	C₂×#117×C₄₃	1	2	yes	—
442	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
443	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
444	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
445	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
446	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
447	C₂²	C₄×#41×C₄₃	1	2	yes	—
448	C₂²	C₄×#41×C₄₃	1	2	yes	—
449	C₂²	C₄₃×#518	1	2	yes	—
450	C₂²	C₄₃×#518	1	2	yes	—
451	C₂²	C₄₃×#518	1	2	yes	—
452	C₂²	C₄₃×#546	1	4	yes	—
453	C₂²	C₄₃×#551	1	4	yes	—
454	C₂²	C₄₃×#553	1	4	yes	—
455	C₂²	C₄₃×#554	1	4	yes	—
456	C₄	—	2	8	no	—
457	C₄	—	2	8	no	—
458	C₄	—	2	4	no	—
459	C₄	—	2	4	no	—
460	C₄	—	4	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	8	no	—
463	C₂	—	2	8	no	—
464	C₂	C₂×C₄×C₄⋊C₄×C₄₃	1	1	yes	characteristic
465	C₂	C₄×#117×C₄₃	1	1	yes	characteristic
466	C₂	C₄₃×#2273	1	1	yes	characteristic
467	C₂	C₄₃×#2342	1	2	yes	—
468	C₂	C₄₃×#2345	1	2	yes	—
469	C₂	C₄₃×#2349	1	2	yes	—
470	C₂	C₄₃×#2353	1	2	yes	—
471	C₂	C₄₃×#2364	1	2	yes	—
472	C₂	C₄₃×#2368	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂⁵×C₄₃	C₂³
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
5. C₄₃×#1436	C₂	semidirect
6. C₄₃×#1434	C₂	semidirect
8. C₄×#95×C₄₃	C₂	semidirect
17. C₄₃×#380	C₄	semidirect
19. C₄×C₂²⋊C₄×C₄₃	C₄	semidirect
20. C₂×#95×C₄₃	C₄	semidirect
47. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
61. C₂×C₄²×C₄₃	C₂×C₄	semidirect
68. #95×C₄₃	C₂×C₄	semidirect
69. #95×C₄₃	C₂×C₄	semidirect
109. C₂²×C₄×C₄₃	C₄²	semidirect
127. C₂²⋊C₄×C₄₃	C₄⋊C₄	semidirect
193. #13802	C₄₃	direct (N × H)
231. #1436	C₂×C₄₃	semidirect
232. #1434	C₂×C₄₃	semidirect
234. C₄×#95	C₂×C₄₃	semidirect
253. #380	C₄×C₄₃	semidirect
255. C₄×C₂²⋊C₄	C₄×C₄₃	semidirect
256. C₂×#95	C₄×C₄₃	semidirect
265. C₄₃	#13802	direct (N × H)
284. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
298. C₂×C₄²	C₂×C₄×C₄₃	semidirect
305. #95	C₂×C₄×C₄₃	semidirect
306. #95	C₂×C₄×C₄₃	semidirect
346. C₂²×C₄	C₄²×C₄₃	semidirect
364. C₂²⋊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×#380	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₂²×#95×C₄₃	2
C₄₃×#1436	2
C₄₃×#1434	2
C₄₃×C₂²⋊#95	2
C₄×#95×C₄₃	2
#13802	43

Subgroups — C43×#13802 #24933819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13802 #24933819