Subgroups — C₄₃×#13806 #24933823

Order 11008.

1486 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#383	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#376	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#1436	C₂	1	4	yes	maximal
5	C₄₃×#1434	C₂	1	2	yes	maximal
6	C₄₃×#1434	C₂	1	2	yes	maximal
7	C₄×#95×C₄₃	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	2	yes	maximal
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	4	yes	—
11	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
12	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#383	C₄	1	8	yes	complemented
15	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
16	C₄₃×#376	C₄	1	8	yes	complemented
17	C₂×#95×C₄₃	C₂²	1	4	yes	—
18	C₂×#95×C₄₃	C₂²	1	4	yes	—
19	C₂×#95×C₄₃	C₂²	1	4	yes	—
20	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
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	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	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
31	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
32	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
34	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
36	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
39	C₂×C₄²×C₄₃	—	2	8	no	—
40	C₂×C₄²×C₄₃	—	2	8	no	—
41	C₂×C₄²×C₄₃	—	2	8	no	—
42	C₂×C₄²×C₄₃	—	4	4	no	—
43	C₂×C₄²×C₄₃	—	4	4	no	—
44	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
45	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
46	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
49	#95×C₄₃	—	2	8	no	—
50	#95×C₄₃	—	2	8	no	—
51	#95×C₄₃	—	4	4	no	—
52	#95×C₄₃	C₂×C₄	1	4	yes	—
53	#95×C₄₃	C₂×C₄	1	8	yes	—
54	#95×C₄₃	C₂×C₄	1	4	yes	—
55	#95×C₄₃	C₂×C₄	1	4	yes	—
56	#95×C₄₃	C₂×C₄	1	4	yes	—
57	#95×C₄₃	C₂×C₄	1	8	yes	—
58	#95×C₄₃	C₂×C₄	1	8	yes	—
59	#95×C₄₃	C₂×C₄	1	8	yes	—
60	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
61	C₂²×C₄×C₄₃	—	2	4	no	—
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	4	no	—
64	C₂²×C₄×C₄₃	—	2	2	no	—
65	C₂²×C₄×C₄₃	—	2	2	no	—
66	C₂²×C₄×C₄₃	—	2	4	no	—
67	C₂²×C₄×C₄₃	—	2	4	no	—
68	C₂²×C₄×C₄₃	—	2	4	no	—
69	C₂²×C₄×C₄₃	—	2	4	no	—
70	C₂²×C₄×C₄₃	—	2	4	no	—
71	C₂²×C₄×C₄₃	—	2	4	no	—
72	C₂²×C₄×C₄₃	—	2	4	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
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	2	no	—
79	C₂²×C₄×C₄₃	—	2	4	no	—
80	C₂²×C₄×C₄₃	—	2	4	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	4	no	—
84	C₂²×C₄×C₄₃	—	2	2	no	—
85	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
86	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
87	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₄₃	#41	1	4	yes	—
100	C₂²×C₄×C₄₃	#41	1	8	yes	—
101	C₂²×C₄×C₄₃	#41	1	4	yes	—
102	C₄⋊C₄×C₄₃	—	2	16	no	—
103	C₄²×C₄₃	—	2	16	no	—
104	C₄²×C₄₃	—	4	8	no	—
105	C₄²×C₄₃	—	4	16	no	—
106	C₄²×C₄₃	C₄²	1	16	yes	complemented
107	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
108	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
109	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
110	C₂³×C₄₃	C₂×#41	1	2	yes	—
111	C₂³×C₄₃	C₂×#41	1	4	yes	—
112	C₂³×C₄₃	C₂×#41	1	2	yes	—
113	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
114	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
115	C₂×C₄×C₄₃	—	2	4	no	—
116	C₂×C₄×C₄₃	—	2	4	no	—
117	C₂×C₄×C₄₃	—	2	4	no	—
118	C₂×C₄×C₄₃	—	2	4	no	—
119	C₂×C₄×C₄₃	—	2	2	no	—
120	C₂×C₄×C₄₃	—	2	2	no	—
121	C₂×C₄×C₄₃	—	2	4	no	—
122	C₂×C₄×C₄₃	—	2	4	no	—
123	C₂×C₄×C₄₃	—	2	4	no	—
124	C₂×C₄×C₄₃	—	2	2	no	—
125	C₂×C₄×C₄₃	—	2	4	no	—
126	C₂×C₄×C₄₃	—	2	2	no	—
127	C₂×C₄×C₄₃	—	2	4	no	—
128	C₂×C₄×C₄₃	—	2	4	no	—
129	C₂×C₄×C₄₃	—	2	4	no	—
130	C₂×C₄×C₄₃	—	2	8	no	—
131	C₂×C₄×C₄₃	—	2	8	no	—
132	C₂×C₄×C₄₃	—	2	8	no	—
133	C₂×C₄×C₄₃	—	2	8	no	—
134	C₂×C₄×C₄₃	—	2	4	no	—
135	C₂×C₄×C₄₃	—	2	4	no	—
136	C₂×C₄×C₄₃	—	2	4	no	—
137	C₂×C₄×C₄₃	—	2	4	no	—
138	C₂×C₄×C₄₃	—	2	8	no	—
139	C₂×C₄×C₄₃	—	2	8	no	—
140	C₂×C₄×C₄₃	—	2	4	no	—
141	C₂×C₄×C₄₃	—	2	4	no	—
142	C₂×C₄×C₄₃	—	2	8	no	—
143	C₂×C₄×C₄₃	—	4	4	no	—
144	C₂×C₄×C₄₃	—	4	4	no	—
145	C₂×C₄×C₄₃	—	4	4	no	—
146	C₂×C₄×C₄₃	—	4	4	no	—
147	C₂×C₄×C₄₃	—	4	4	no	—
148	C₂×C₄×C₄₃	—	4	4	no	—
149	C₂×C₄×C₄₃	—	4	4	no	—
150	C₂×C₄×C₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
152	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
153	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
154	C₂×C₄×C₄₃	#117	1	8	yes	—
155	C₂×C₄×C₄₃	#117	1	8	yes	—
156	#13806	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
157	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
158	C₂²×C₄₃	C₂×#117	1	2	yes	—
159	C₂²×C₄₃	C₂×#117	1	2	yes	—
160	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
161	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
162	C₂²×C₄₃	C₄×#41	1	2	yes	—
163	C₂²×C₄₃	C₄×#41	1	2	yes	—
164	C₂²×C₄₃	C₄×#41	1	2	yes	—
165	C₂²×C₄₃	#518	1	1	yes	characteristic
166	C₂²×C₄₃	#519	1	1	yes	characteristic
167	C₂²×C₄₃	#520	1	2	yes	—
168	C₂²×C₄₃	#520	1	2	yes	—
169	C₂²×C₄₃	#551	1	4	yes	—
170	C₂²×C₄₃	#552	1	4	yes	—
171	C₂²×C₄₃	#553	1	4	yes	—
172	C₂²×C₄₃	#556	1	4	yes	—
173	C₄×C₄₃	—	2	8	no	—
174	C₄×C₄₃	—	2	8	no	—
175	C₄×C₄₃	—	2	4	no	—
176	C₄×C₄₃	—	2	4	no	—
177	C₄×C₄₃	—	2	4	no	—
178	C₄×C₄₃	—	4	4	no	—
179	C₄×C₄₃	—	4	4	no	—
180	C₄×C₄₃	—	4	8	no	—
181	C₂×#383	C₂×C₄₃	1	1	yes	characteristic
182	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
183	C₂×#376	C₂×C₄₃	1	1	yes	characteristic
184	#1436	C₂×C₄₃	1	4	yes	—
185	#1434	C₂×C₄₃	1	2	yes	—
186	#1434	C₂×C₄₃	1	2	yes	—
187	C₄×#95	C₂×C₄₃	1	2	yes	—
188	C₄×#95	C₂×C₄₃	1	2	yes	—
189	C₂×C₄₃	C₄×#117	1	1	yes	characteristic
190	C₂×C₄₃	C₄×#117	1	1	yes	characteristic
191	C₂×C₄₃	#2274	1	1	yes	characteristic
192	C₂×C₄₃	#2343	1	2	yes	—
193	C₂×C₄₃	#2347	1	2	yes	—
194	C₂×C₄₃	#2353	1	2	yes	—
195	C₂×C₄₃	#2356	1	2	yes	—
196	C₂×C₄₃	#2373	1	4	yes	—
197	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
198	C₂²×C₄²	C₂²×C₄₃	1	4	yes	—
199	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
200	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
201	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
202	#383	C₄×C₄₃	1	8	yes	complemented
203	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
204	#376	C₄×C₄₃	1	8	yes	complemented
205	C₂×#95	C₂²×C₄₃	1	4	yes	—
206	C₂×#95	C₂²×C₄₃	1	4	yes	—
207	C₂×#95	C₂²×C₄₃	1	4	yes	—
208	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
209	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
210	C₂×#95	C₂²×C₄₃	1	2	yes	—
211	C₂×#95	C₂²×C₄₃	1	2	yes	—
212	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
213	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
214	C₂×#95	C₂²×C₄₃	1	2	yes	—
215	C₂×#95	C₂²×C₄₃	1	2	yes	—
216	C₄₃	#13806	1	1	yes	characteristic, direct product factor, Sylow
217	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
218	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
219	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
220	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
221	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
224	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
225	C₂×C₄⋊C₄	—	2	4	no	—
226	C₂×C₄⋊C₄	—	2	4	no	—
227	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
228	C₂×C₄²	—	2	8	no	—
229	C₂×C₄²	—	2	8	no	—
230	C₂×C₄²	—	2	8	no	—
231	C₂×C₄²	—	4	4	no	—
232	C₂×C₄²	—	4	4	no	—
233	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
234	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
235	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
236	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
237	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
238	#95	—	2	8	no	—
239	#95	—	2	8	no	—
240	#95	—	4	4	no	—
241	#95	C₂×C₄×C₄₃	1	4	yes	—
242	#95	C₂×C₄×C₄₃	1	8	yes	—
243	#95	C₂×C₄×C₄₃	1	4	yes	—
244	#95	C₂×C₄×C₄₃	1	4	yes	—
245	#95	C₂×C₄×C₄₃	1	4	yes	—
246	#95	C₂×C₄×C₄₃	1	8	yes	—
247	#95	C₂×C₄×C₄₃	1	8	yes	—
248	#95	C₂×C₄×C₄₃	1	8	yes	—
249	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	4	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	4	no	—
262	C₂²×C₄	—	2	4	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
276	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
277	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
279	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
280	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
287	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
288	C₂²×C₄	#41×C₄₃	1	4	yes	—
289	C₂²×C₄	#41×C₄₃	1	8	yes	—
290	C₂²×C₄	#41×C₄₃	1	4	yes	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄²	—	2	16	no	—
293	C₄²	—	4	8	no	—
294	C₄²	—	4	16	no	—
295	C₄²	C₄²×C₄₃	1	16	yes	complemented
296	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
297	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
298	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
299	C₂³	C₂×#41×C₄₃	1	2	yes	—
300	C₂³	C₂×#41×C₄₃	1	4	yes	—
301	C₂³	C₂×#41×C₄₃	1	2	yes	—
302	C₂³	H(5,𝔽₂)×C₄₃	1	2	yes	—
303	C₂³	2₋¹⁺⁴×C₄₃	1	2	yes	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	4	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	4	no	—
337	C₂×C₄	—	4	4	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
341	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
342	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
343	C₂×C₄	#117×C₄₃	1	8	yes	—
344	C₂×C₄	#117×C₄₃	1	8	yes	—
345	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
346	C₂²	C₂×#117×C₄₃	1	2	yes	—
347	C₂²	C₂×#117×C₄₃	1	2	yes	—
348	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
349	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
350	C₂²	C₄×#41×C₄₃	1	2	yes	—
351	C₂²	C₄×#41×C₄₃	1	2	yes	—
352	C₂²	C₄×#41×C₄₃	1	2	yes	—
353	C₂²	C₄₃×#518	1	1	yes	characteristic
354	C₂²	C₄₃×#519	1	1	yes	characteristic
355	C₂²	C₄₃×#520	1	2	yes	—
356	C₂²	C₄₃×#520	1	2	yes	—
357	C₂²	C₄₃×#551	1	4	yes	—
358	C₂²	C₄₃×#552	1	4	yes	—
359	C₂²	C₄₃×#553	1	4	yes	—
360	C₂²	C₄₃×#556	1	4	yes	—
361	C₄	—	2	8	no	—
362	C₄	—	2	8	no	—
363	C₄	—	2	4	no	—
364	C₄	—	2	4	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	4	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	8	no	—
369	C₂	C₄×#117×C₄₃	1	1	yes	characteristic
370	C₂	C₄×#117×C₄₃	1	1	yes	characteristic
371	C₂	C₄₃×#2274	1	1	yes	characteristic
372	C₂	C₄₃×#2343	1	2	yes	—
373	C₂	C₄₃×#2347	1	2	yes	—
374	C₂	C₄₃×#2353	1	2	yes	—
375	C₂	C₄₃×#2356	1	2	yes	—
376	C₂	C₄₃×#2373	1	4	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
14. C₄₃×#383	C₄	semidirect
15. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
16. C₄₃×#376	C₄	semidirect
106. C₄²×C₄₃	C₄²	semidirect
156. #13806	C₄₃	direct (N × H)
202. #383	C₄×C₄₃	semidirect
203. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
204. #376	C₄×C₄₃	semidirect
216. C₄₃	#13806	direct (N × H)
295. C₄²	C₄²×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×#383	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄₃×#376	2
C₄₃×#1436	2
C₄₃×#1434	2
C₄×#95×C₄₃	2
#13806	43

Subgroups — C43×#13806 #24933823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#13806 #24933823