Subgroups — C₄₃×#23946 #24943963

Order 11008.

1222 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#542	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#451	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#448	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2310	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2024	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2015	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1878	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1877	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1875	C₂	1	1	yes	maximal, characteristic
10	C₄₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1818	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₃	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₃	C₂²	1	2	yes	—
15	C₄₃×#542	—	2	4	no	—
16	C₄₃×#542	—	2	4	no	—
17	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#126×C₄₃	—	2	1	no	—
19	C₂×#124×C₄₃	—	2	1	no	—
20	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#123×C₄₃	—	2	1	no	—
22	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
23	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
27	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#451	—	2	4	no	—
30	C₄₃×#448	—	2	4	no	—
31	C₂×#103×C₄₃	C₂²	1	2	yes	—
32	C₂×#103×C₄₃	C₂²	1	2	yes	—
33	C₂×#103×C₄₃	C₂²	1	2	yes	—
34	C₂×#102×C₄₃	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#391	—	2	1	no	—
38	C₄₃×#391	—	2	1	no	—
39	C₄₃×#391	C₂²	1	2	yes	—
40	C₄₃×#391	C₂²	1	2	yes	—
41	C₄₃×#381	—	2	1	no	—
42	C₄₃×#381	—	2	1	no	—
43	C₄₃×#340	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#336	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₃	—	2	4	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×Q₈×C₄₃	—	2	1	no	—
50	C₂²×Q₈×C₄₃	—	2	2	no	—
51	C₂²×Q₈×C₄₃	—	2	2	no	—
52	C₂²×Q₈×C₄₃	—	4	2	no	—
53	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×D₄×C₄₃	—	2	1	no	—
56	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₄₃	—	2	1	no	—
58	C₂³×C₄×C₄₃	—	2	1	no	—
59	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
60	C₂×Q₁₆×C₄₃	—	2	4	no	—
61	C₂×Q₁₆×C₄₃	—	2	4	no	—
62	C₂×Q₁₆×C₄₃	—	4	2	no	—
63	C₂×SD₁₆×C₄₃	—	2	4	no	—
64	C₂×SD₁₆×C₄₃	—	2	4	no	—
65	C₂×SD₁₆×C₄₃	—	4	2	no	—
66	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
67	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₄₃	—	2	2	no	—
69	C₄⋊Q₈×C₄₃	—	2	2	no	—
70	#126×C₄₃	—	2	8	no	—
71	#124×C₄₃	—	2	8	no	—
72	#124×C₄₃	—	2	2	no	—
73	#124×C₄₃	—	2	2	no	—
74	#123×C₄₃	—	2	8	no	—
75	C₂²⋊Q₈×C₄₃	—	2	8	no	—
76	C₂²⋊Q₈×C₄₃	—	2	2	no	—
77	C₂²⋊Q₈×C₄₃	D₄	1	4	yes	—
78	#121×C₄₃	—	2	2	no	—
79	#121×C₄₃	D₄	1	4	yes	—
80	C₄×Q₈×C₄₃	—	2	2	no	—
81	C₄×Q₈×C₄₃	—	2	2	no	—
82	C₄×D₄×C₄₃	—	2	2	no	—
83	C₄×D₄×C₄₃	—	2	2	no	—
84	#117×C₄₃	—	2	2	no	—
85	#117×C₄₃	—	2	2	no	—
86	#117×C₄₃	—	4	2	no	—
87	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	—	2	1	no	—
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	#103×C₄₃	—	2	4	no	—
108	#103×C₄₃	—	2	4	no	—
109	#103×C₄₃	—	4	2	no	—
110	#102×C₄₃	—	4	2	no	—
111	C₂²⋊C₈×C₄₃	—	2	2	no	—
112	C₂²⋊C₈×C₄₃	—	2	2	no	—
113	#95×C₄₃	—	2	2	no	—
114	#95×C₄₃	—	2	2	no	—
115	#95×C₄₃	—	2	2	no	—
116	#95×C₄₃	—	2	2	no	—
117	C₂⁴×C₄₃	—	2	1	no	—
118	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₄₃	—	2	4	no	—
120	C₂×Q₈×C₄₃	—	2	4	no	—
121	C₂×Q₈×C₄₃	—	2	1	no	—
122	C₂×Q₈×C₄₃	—	2	2	no	—
123	C₂×Q₈×C₄₃	—	2	2	no	—
124	C₂×Q₈×C₄₃	—	2	2	no	—
125	C₂×Q₈×C₄₃	—	2	2	no	—
126	C₂×Q₈×C₄₃	—	2	2	no	—
127	C₂×Q₈×C₄₃	—	2	2	no	—
128	C₂×Q₈×C₄₃	—	2	2	no	—
129	C₂×Q₈×C₄₃	—	4	8	no	—
130	C₂×Q₈×C₄₃	—	4	8	no	—
131	C₂×Q₈×C₄₃	—	4	2	no	—
132	C₂×Q₈×C₄₃	—	4	2	no	—
133	C₂×Q₈×C₄₃	—	8	2	no	—
134	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₄₃	#41	1	4	yes	—
136	C₂×D₄×C₄₃	—	2	1	no	—
137	C₂×D₄×C₄₃	—	2	4	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	2	no	—
140	C₂×D₄×C₄₃	—	8	2	no	—
141	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	4	no	—
145	C₂²×C₄×C₄₃	—	2	4	no	—
146	C₂²×C₄×C₄₃	—	2	2	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂²×C₄×C₄₃	—	2	1	no	—
149	C₂²×C₄×C₄₃	—	2	1	no	—
150	C₂²×C₄×C₄₃	—	2	2	no	—
151	C₂²×C₄×C₄₃	—	4	2	no	—
152	C₂²×C₄×C₄₃	—	4	2	no	—
153	C₂²×C₄×C₄₃	—	8	2	no	—
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
162	Q₁₆×C₄₃	—	4	8	no	—
163	SD₁₆×C₄₃	—	4	8	no	—
164	C₂×C₈×C₄₃	—	2	2	no	—
165	C₂×C₈×C₄₃	—	2	2	no	—
166	C₂×C₈×C₄₃	—	2	2	no	—
167	C₂×C₈×C₄₃	—	2	2	no	—
168	C₂×C₈×C₄₃	—	2	2	no	—
169	C₂×C₈×C₄₃	—	2	2	no	—
170	C₄⋊C₄×C₄₃	—	2	4	no	—
171	C₄⋊C₄×C₄₃	—	2	4	no	—
172	C₄⋊C₄×C₄₃	—	2	4	no	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	2	2	no	—
179	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₄₃	—	2	4	no	—
182	C₂²⋊C₄×C₄₃	—	2	4	no	—
183	C₂²⋊C₄×C₄₃	—	2	4	no	—
184	C₂²⋊C₄×C₄₃	—	2	4	no	—
185	C₂²⋊C₄×C₄₃	—	2	4	no	—
186	C₂²⋊C₄×C₄₃	—	2	2	no	—
187	C₂²⋊C₄×C₄₃	—	2	2	no	—
188	C₂²⋊C₄×C₄₃	—	4	2	no	—
189	C₄²×C₄₃	—	2	4	no	—
190	C₄²×C₄₃	—	2	1	no	—
191	C₄²×C₄₃	—	2	1	no	—
192	C₄²×C₄₃	—	2	1	no	—
193	C₄²×C₄₃	—	2	1	no	—
194	C₄²×C₄₃	—	4	2	no	—
195	C₂³×C₄₃	—	2	1	no	—
196	C₂³×C₄₃	—	2	1	no	—
197	C₂³×C₄₃	—	2	2	no	—
198	C₂³×C₄₃	—	2	2	no	—
199	C₂³×C₄₃	—	2	2	no	—
200	C₂³×C₄₃	—	4	1	no	—
201	C₂³×C₄₃	—	4	1	no	—
202	C₂³×C₄₃	—	4	2	no	—
203	C₂³×C₄₃	—	4	2	no	—
204	C₂³×C₄₃	#120	1	2	yes	—
205	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₃	—	2	4	no	—
207	Q₈×C₄₃	—	2	4	no	—
208	Q₈×C₄₃	—	2	4	no	—
209	Q₈×C₄₃	—	4	8	no	—
210	Q₈×C₄₃	—	4	2	no	—
211	Q₈×C₄₃	—	4	2	no	—
212	Q₈×C₄₃	—	4	2	no	—
213	Q₈×C₄₃	—	8	4	no	—
214	D₄×C₄₃	—	2	4	no	—
215	D₄×C₄₃	—	4	2	no	—
216	D₄×C₄₃	—	8	4	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	4	no	—
220	C₂×C₄×C₄₃	—	2	4	no	—
221	C₂×C₄×C₄₃	—	2	1	no	—
222	C₂×C₄×C₄₃	—	2	1	no	—
223	C₂×C₄×C₄₃	—	2	2	no	—
224	C₂×C₄×C₄₃	—	2	1	no	—
225	C₂×C₄×C₄₃	—	2	1	no	—
226	C₂×C₄×C₄₃	—	2	2	no	—
227	C₂×C₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	2	4	no	—
229	C₂×C₄×C₄₃	—	2	2	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	2	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	4	8	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	1	no	—
236	C₂×C₄×C₄₃	—	4	2	no	—
237	C₂×C₄×C₄₃	—	4	1	no	—
238	C₂×C₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	2	no	—
241	C₂×C₄×C₄₃	—	4	2	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	—	8	4	no	—
244	C₂×C₄×C₄₃	#120	1	2	yes	—
245	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
248	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
249	C₈×C₄₃	—	4	2	no	—
250	C₈×C₄₃	—	4	2	no	—
251	#23946	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂²×C₄₃	—	2	2	no	—
253	C₂²×C₄₃	—	2	2	no	—
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	4	2	no	—
256	C₂²×C₄₃	—	4	2	no	—
257	C₂²×C₄₃	—	4	2	no	—
258	C₂²×C₄₃	—	4	2	no	—
259	C₂²×C₄₃	—	4	2	no	—
260	C₂²×C₄₃	—	8	2	no	—
261	C₂²×C₄₃	—	8	2	no	—
262	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
263	C₂²×C₄₃	#525	1	1	yes	characteristic
264	C₂²×C₄₃	#535	1	1	yes	characteristic
265	C₂²×C₄₃	#577	1	2	yes	—
266	C₂²×C₄₃	#578	1	2	yes	—
267	C₄×C₄₃	—	2	2	no	—
268	C₄×C₄₃	—	4	4	no	—
269	C₄×C₄₃	—	4	2	no	—
270	C₄×C₄₃	—	4	1	no	—
271	C₄×C₄₃	—	4	1	no	—
272	C₄×C₄₃	—	4	2	no	—
273	C₄×C₄₃	—	4	2	no	—
274	C₄×C₄₃	—	4	1	no	—
275	C₄×C₄₃	—	4	1	no	—
276	C₄×C₄₃	—	8	2	no	—
277	C₄×C₄₃	#546	1	2	yes	—
278	C₄×C₄₃	#546	1	2	yes	—
279	C₂×#542	C₂×C₄₃	1	1	yes	characteristic
280	C₂×#451	C₂×C₄₃	1	1	yes	characteristic, complemented
281	C₂×#448	C₂×C₄₃	1	1	yes	characteristic
282	#2310	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#2024	C₂×C₄₃	1	2	yes	complemented
284	#2015	C₂×C₄₃	1	2	yes	complemented
285	#1878	C₂×C₄₃	1	2	yes	complemented
286	#1877	C₂×C₄₃	1	2	yes	complemented
287	#1875	C₂×C₄₃	1	1	yes	characteristic
288	#1873	C₂×C₄₃	1	1	yes	characteristic, complemented
289	#1818	C₂×C₄₃	1	1	yes	characteristic, complemented
290	C₂×C₄₃	—	4	2	no	—
291	C₂×C₄₃	—	8	2	no	—
292	C₂×C₄₃	#2404	1	1	yes	characteristic
293	C₂×C₄₃	#3009	1	1	yes	characteristic
294	C₂×C₄₃	#3011	1	1	yes	characteristic
295	C₂×C₄₃	#3121	1	2	yes	—
296	C₂×C₄₃	#3225	1	2	yes	—
297	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
298	C₂²×Q₁₆	C₂²×C₄₃	1	2	yes	—
299	C₂²×SD₁₆	C₂²×C₄₃	1	2	yes	—
300	#542	—	2	4	no	—
301	#542	—	2	4	no	—
302	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
303	C₂×#126	—	2	1	no	—
304	C₂×#124	—	2	1	no	—
305	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×#123	—	2	1	no	—
307	C₂×C₂²⋊Q₈	—	2	1	no	—
308	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
309	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
312	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
313	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
314	#451	—	2	4	no	—
315	#448	—	2	4	no	—
316	C₂×#103	C₂²×C₄₃	1	2	yes	—
317	C₂×#103	C₂²×C₄₃	1	2	yes	—
318	C₂×#103	C₂²×C₄₃	1	2	yes	—
319	C₂×#102	C₂²×C₄₃	1	2	yes	—
320	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
321	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
322	#391	—	2	1	no	—
323	#391	—	2	1	no	—
324	#391	C₂²×C₄₃	1	2	yes	—
325	#391	C₂²×C₄₃	1	2	yes	—
326	#381	—	2	1	no	—
327	#381	—	2	1	no	—
328	#340	C₂²×C₄₃	1	2	yes	—
329	#340	C₂²×C₄₃	1	2	yes	—
330	#336	C₂²×C₄₃	1	2	yes	—
331	#336	C₂²×C₄₃	1	2	yes	—
332	C₄₃	#23946	1	1	yes	characteristic, direct product factor, Sylow
333	C₂²×Q₈	—	2	4	no	—
334	C₂²×Q₈	—	2	1	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	2	2	no	—
338	C₂²×Q₈	—	4	2	no	—
339	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
340	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	—	2	1	no	—
345	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
346	C₂×Q₁₆	—	2	4	no	—
347	C₂×Q₁₆	—	2	4	no	—
348	C₂×Q₁₆	—	4	2	no	—
349	C₂×SD₁₆	—	2	4	no	—
350	C₂×SD₁₆	—	2	4	no	—
351	C₂×SD₁₆	—	4	2	no	—
352	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
353	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	—	2	2	no	—
356	#126	—	2	8	no	—
357	#124	—	2	8	no	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#123	—	2	8	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	D₄×C₄₃	1	4	yes	—
364	#121	—	2	2	no	—
365	#121	D₄×C₄₃	1	4	yes	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	4	2	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
393	#103	—	2	4	no	—
394	#103	—	2	4	no	—
395	#103	—	4	2	no	—
396	#102	—	4	2	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	C₂²⋊C₈	—	2	2	no	—
399	#95	—	2	2	no	—
400	#95	—	2	2	no	—
401	#95	—	2	2	no	—
402	#95	—	2	2	no	—
403	C₂⁴	—	2	1	no	—
404	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	2	2	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	4	8	no	—
416	C₂×Q₈	—	4	8	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	8	2	no	—
420	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
421	C₂×Q₈	#41×C₄₃	1	4	yes	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	8	2	no	—
427	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	—	4	2	no	—
439	C₂²×C₄	—	8	2	no	—
440	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
448	Q₁₆	—	4	8	no	—
449	SD₁₆	—	4	8	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
466	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	4	2	no	—
481	C₂³	—	2	1	no	—
482	C₂³	—	2	1	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	#120×C₄₃	1	2	yes	—
491	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
492	Q₈	—	2	4	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	2	4	no	—
495	Q₈	—	4	8	no	—
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	8	4	no	—
500	D₄	—	2	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	8	4	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	8	4	no	—
530	C₂×C₄	#120×C₄₃	1	2	yes	—
531	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
534	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
535	C₈	—	4	2	no	—
536	C₈	—	4	2	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	8	2	no	—
546	C₂²	—	8	2	no	—
547	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
548	C₂²	C₄₃×#525	1	1	yes	characteristic
549	C₂²	C₄₃×#535	1	1	yes	characteristic
550	C₂²	C₄₃×#577	1	2	yes	—
551	C₂²	C₄₃×#578	1	2	yes	—
552	C₄	—	2	2	no	—
553	C₄	—	4	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	1	no	—
556	C₄	—	4	1	no	—
557	C₄	—	4	2	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	8	2	no	—
562	C₄	C₄₃×#546	1	2	yes	—
563	C₄	C₄₃×#546	1	2	yes	—
564	C₂	—	4	2	no	—
565	C₂	—	8	2	no	—
566	C₂	C₄₃×#2404	1	1	yes	characteristic
567	C₂	C₄₃×#3009	1	1	yes	characteristic
568	C₂	C₄₃×#3011	1	1	yes	characteristic
569	C₂	C₄₃×#3121	1	2	yes	—
570	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#451	C₂	semidirect
4. C₄₃×#2310	C₂	semidirect
5. C₄₃×#2024	C₂	semidirect
6. C₄₃×#2015	C₂	semidirect
7. C₄₃×#1878	C₂	semidirect
8. C₄₃×#1877	C₂	semidirect
10. C₄₃×#1873	C₂	semidirect
11. C₄₃×#1818	C₂	semidirect
251. #23946	C₄₃	direct (N × H)
280. C₂×#451	C₂×C₄₃	semidirect
282. #2310	C₂×C₄₃	semidirect
283. #2024	C₂×C₄₃	semidirect
284. #2015	C₂×C₄₃	semidirect
285. #1878	C₂×C₄₃	semidirect
286. #1877	C₂×C₄₃	semidirect
288. #1873	C₂×C₄₃	semidirect
289. #1818	C₂×C₄₃	semidirect
332. C₄₃	#23946	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#542	2
C₂×C₄₃×#451	2
C₂×C₄₃×#448	2
C₄₃×#2310	2
C₄₃×#2024	2
C₄₃×#2015	2
C₄₃×#1878	2
C₄₃×#1877	2
C₄₃×#1875	2
C₄₃×#1873	2
C₄₃×#1818	2
#23946	43

Subgroups — C43×#23946 #24943963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#23946 #24943963