Subgroups — C₄₃×#18569 #24938586

Order 11008.

1002 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1634	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1632	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1624	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1622	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₄₃	—	2	2	no	—
13	C₄₃×#556	—	2	1	no	—
14	C₄₃×#555	C₂²	1	2	yes	—
15	C₄₃×#554	C₂²	1	2	yes	—
16	C₄₃×#553	—	2	2	no	—
17	C₄₃×#548	—	2	2	no	—
18	C₄₃×#547	—	2	1	no	—
19	C₄₃×#542	—	2	2	no	—
20	C₄₃×#537	—	2	1	no	—
21	C₄₃×#533	—	2	1	no	—
22	C₄₃×#532	—	2	1	no	—
23	C₄₃×#532	C₂²	1	1	yes	characteristic
24	C₄₃×#532	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#520	—	2	1	no	—
27	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#497	—	2	2	no	—
29	C₄₃×#494	C₂²	1	2	yes	—
30	C₄₃×#492	C₂²	1	2	yes	—
31	C₄₃×#482	—	2	1	no	—
32	C₄₃×#477	C₂²	1	1	yes	characteristic
33	C₄₃×#476	—	2	1	no	—
34	C₄₃×#476	C₂²	1	1	yes	characteristic
35	C₄₃×#476	C₂²	1	2	yes	—
36	C₄₃×#469	—	2	2	no	—
37	C₄₃×#460	C₂²	1	1	yes	characteristic
38	C₄₃×#459	—	2	1	no	—
39	C₄₃×#459	C₂²	1	1	yes	characteristic
40	C₄₃×#459	C₂²	1	2	yes	—
41	C₄₃×#449	—	2	1	no	—
42	C₄×SD₁₆×C₄₃	—	2	1	no	—
43	C₄×D₈×C₄₃	—	2	1	no	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#333	C₂²	1	2	yes	—
48	C₄₃×#333	C₂²	1	2	yes	—
49	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
51	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
52	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₄₃	—	2	2	no	—
54	C₂×#41×C₄₃	—	2	1	no	—
55	C₂×#41×C₄₃	—	2	1	no	—
56	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₄₃	D₄	1	2	yes	—
58	#137×C₄₃	—	4	8	no	—
59	C₂×Q₁₆×C₄₃	—	2	4	no	—
60	C₂×SD₁₆×C₄₃	—	2	4	no	—
61	C₂×SD₁₆×C₄₃	—	2	1	no	—
62	C₂×D₈×C₄₃	—	2	1	no	—
63	C₂×D₈×C₄₃	—	2	2	no	—
64	C₂×M₁₆×C₄₃	—	2	1	no	—
65	C₂×M₁₆×C₄₃	—	2	1	no	—
66	C₄⋊Q₈×C₄₃	—	2	1	no	—
67	C₄⋊Q₈×C₄₃	—	2	1	no	—
68	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
69	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
71	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
72	#127×C₄₃	D₄	1	1	yes	characteristic
73	#127×C₄₃	C₂³	1	1	yes	characteristic
74	#126×C₄₃	—	2	4	no	—
75	#125×C₄₃	—	2	2	no	—
76	#124×C₄₃	—	2	2	no	—
77	#124×C₄₃	—	2	4	no	—
78	#124×C₄₃	—	2	1	no	—
79	#124×C₄₃	—	2	1	no	—
80	#123×C₄₃	—	2	4	no	—
81	C₂²⋊Q₈×C₄₃	—	2	2	no	—
82	C₂²⋊Q₈×C₄₃	—	2	2	no	—
83	C₂²⋊Q₈×C₄₃	—	2	2	no	—
84	C₂²⋊Q₈×C₄₃	—	2	4	no	—
85	#121×C₄₃	—	2	2	no	—
86	#121×C₄₃	—	2	4	no	—
87	#121×C₄₃	—	2	2	no	—
88	#121×C₄₃	—	2	2	no	—
89	#121×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	—	2	1	no	—
92	#121×C₄₃	D₄	1	2	yes	—
93	C₄×Q₈×C₄₃	—	2	2	no	—
94	C₄×Q₈×C₄₃	—	2	2	no	—
95	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
96	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₃	—	2	2	no	—
98	C₄×D₄×C₄₃	—	2	4	no	—
99	C₄×D₄×C₄₃	—	2	2	no	—
100	C₄×D₄×C₄₃	—	2	1	no	—
101	C₄×D₄×C₄₃	—	2	1	no	—
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	—	2	1	no	—
104	C₄×D₄×C₄₃	—	2	1	no	—
105	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
106	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
107	C₄×D₄×C₄₃	C₂³	1	2	yes	—
108	#117×C₄₃	—	2	2	no	—
109	#117×C₄₃	—	2	2	no	—
110	#117×C₄₃	—	2	1	no	—
111	#117×C₄₃	D₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₂×C₄²×C₄₃	—	2	1	no	—
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	#107×C₄₃	—	2	1	no	—
118	#106×C₄₃	—	2	1	no	—
119	#106×C₄₃	—	2	2	no	—
120	C₄⋊C₈×C₄₃	—	2	1	no	—
121	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
124	#103×C₄₃	—	2	1	no	—
125	#102×C₄₃	—	2	1	no	—
126	#102×C₄₃	—	2	2	no	—
127	#102×C₄₃	—	2	1	no	—
128	#102×C₄₃	—	2	1	no	—
129	#102×C₄₃	—	2	2	no	—
130	C₂²⋊C₈×C₄₃	—	2	1	no	—
131	#97×C₄₃	—	2	1	no	—
132	C₄×C₈×C₄₃	—	2	1	no	—
133	C₄×C₈×C₄₃	C₂³	1	2	yes	—
134	#41×C₄₃	—	4	1	no	—
135	#41×C₄₃	—	4	1	no	—
136	#41×C₄₃	—	4	2	no	—
137	#41×C₄₃	—	4	2	no	—
138	#41×C₄₃	—	4	4	no	—
139	#41×C₄₃	—	8	4	no	—
140	C₂×Q₈×C₄₃	—	2	1	no	—
141	C₂×Q₈×C₄₃	—	2	2	no	—
142	C₂×Q₈×C₄₃	—	2	1	no	—
143	C₂×Q₈×C₄₃	—	4	4	no	—
144	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₄₃	—	2	4	no	—
147	C₂×D₄×C₄₃	—	2	1	no	—
148	C₂×D₄×C₄₃	—	2	1	no	—
149	C₂×D₄×C₄₃	—	2	1	no	—
150	C₂×D₄×C₄₃	—	2	2	no	—
151	C₂×D₄×C₄₃	—	2	1	no	—
152	C₂×D₄×C₄₃	—	2	1	no	—
153	C₂×D₄×C₄₃	—	2	1	no	—
154	C₂×D₄×C₄₃	—	4	1	no	—
155	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	—	2	4	no	—
158	C₂²×C₄×C₄₃	—	2	1	no	—
159	C₂²×C₄×C₄₃	—	2	1	no	—
160	C₂²×C₄×C₄₃	—	2	1	no	—
161	C₂²×C₄×C₄₃	—	2	2	no	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	4	1	no	—
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	Q₁₆×C₄₃	—	4	8	no	—
168	SD₁₆×C₄₃	—	4	8	no	—
169	SD₁₆×C₄₃	—	4	2	no	—
170	D₈×C₄₃	—	4	2	no	—
171	D₈×C₄₃	—	8	2	no	—
172	M₁₆×C₄₃	—	2	4	no	—
173	M₁₆×C₄₃	—	8	1	no	—
174	C₂×C₈×C₄₃	—	2	2	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	—	2	4	no	—
179	C₄⋊C₄×C₄₃	—	2	4	no	—
180	C₄⋊C₄×C₄₃	—	2	2	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	2	1	no	—
183	C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₄⋊C₄×C₄₃	—	2	2	no	—
185	C₄⋊C₄×C₄₃	—	2	2	no	—
186	C₄⋊C₄×C₄₃	—	2	1	no	—
187	C₄⋊C₄×C₄₃	—	2	1	no	—
188	C₄⋊C₄×C₄₃	—	2	1	no	—
189	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
191	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₄₃	—	2	4	no	—
193	C₂²⋊C₄×C₄₃	—	2	4	no	—
194	C₂²⋊C₄×C₄₃	—	2	4	no	—
195	C₂²⋊C₄×C₄₃	—	2	1	no	—
196	C₂²⋊C₄×C₄₃	—	2	2	no	—
197	C₂²⋊C₄×C₄₃	—	2	1	no	—
198	C₂²⋊C₄×C₄₃	—	2	2	no	—
199	C₂²⋊C₄×C₄₃	—	2	1	no	—
200	C₂²⋊C₄×C₄₃	—	4	1	no	—
201	C₂²⋊C₄×C₄₃	—	4	1	no	—
202	C₄²×C₄₃	—	2	4	no	—
203	C₄²×C₄₃	—	2	1	no	—
204	C₄²×C₄₃	—	2	1	no	—
205	C₄²×C₄₃	—	2	1	no	—
206	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₄₃	—	2	1	no	—
211	C₂³×C₄₃	—	2	2	no	—
212	C₂³×C₄₃	—	4	1	no	—
213	C₂³×C₄₃	#120	1	1	yes	characteristic
214	Q₈×C₄₃	—	2	1	no	—
215	Q₈×C₄₃	—	2	1	no	—
216	Q₈×C₄₃	—	4	4	no	—
217	Q₈×C₄₃	—	4	2	no	—
218	Q₈×C₄₃	—	4	2	no	—
219	Q₈×C₄₃	—	4	4	no	—
220	D₄×C₄₃	—	2	1	no	—
221	D₄×C₄₃	—	2	1	no	—
222	D₄×C₄₃	—	2	2	no	—
223	D₄×C₄₃	—	2	2	no	—
224	D₄×C₄₃	—	4	2	no	—
225	D₄×C₄₃	—	4	2	no	—
226	D₄×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	4	4	no	—
228	D₄×C₄₃	—	4	1	no	—
229	D₄×C₄₃	—	4	1	no	—
230	D₄×C₄₃	—	4	1	no	—
231	D₄×C₄₃	—	4	1	no	—
232	D₄×C₄₃	—	4	2	no	—
233	D₄×C₄₃	—	8	4	no	—
234	D₄×C₄₃	—	8	2	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	1	no	—
238	C₂×C₄×C₄₃	—	2	1	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	4	no	—
245	C₂×C₄×C₄₃	—	4	2	no	—
246	C₂×C₄×C₄₃	—	4	2	no	—
247	C₂×C₄×C₄₃	—	4	2	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	2	no	—
251	C₂×C₄×C₄₃	—	4	1	no	—
252	C₂×C₄×C₄₃	—	8	2	no	—
253	C₂×C₄×C₄₃	—	8	4	no	—
254	C₂×C₄×C₄₃	—	8	2	no	—
255	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
256	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
257	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
261	C₈×C₄₃	—	2	4	no	—
262	C₈×C₄₃	—	4	1	no	—
263	C₈×C₄₃	—	4	1	no	—
264	C₈×C₄₃	—	4	2	no	—
265	#18569	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₄₃	—	2	1	no	—
267	C₂²×C₄₃	—	2	1	no	—
268	C₂²×C₄₃	—	2	1	no	—
269	C₂²×C₄₃	—	4	1	no	—
270	C₂²×C₄₃	—	4	2	no	—
271	C₂²×C₄₃	—	4	1	no	—
272	C₂²×C₄₃	—	4	2	no	—
273	C₂²×C₄₃	—	4	1	no	—
274	C₂²×C₄₃	—	4	2	no	—
275	C₂²×C₄₃	—	8	1	no	—
276	C₂²×C₄₃	—	8	1	no	—
277	C₂²×C₄₃	—	8	1	no	—
278	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
279	C₄×C₄₃	—	2	1	no	—
280	C₄×C₄₃	—	2	1	no	—
281	C₄×C₄₃	—	2	1	no	—
282	C₄×C₄₃	—	4	1	no	—
283	C₄×C₄₃	—	4	2	no	—
284	C₄×C₄₃	—	4	1	no	—
285	C₄×C₄₃	—	4	1	no	—
286	C₄×C₄₃	—	4	4	no	—
287	C₄×C₄₃	—	8	1	no	—
288	C₄×C₄₃	#453	1	2	yes	—
289	C₄×C₄₃	#575	1	1	yes	characteristic
290	C₄×C₄₃	#575	1	1	yes	characteristic
291	C₄×C₄₃	#577	1	1	yes	characteristic
292	C₄×C₄₃	#578	1	1	yes	characteristic
293	#3511	C₂×C₄₃	1	1	yes	characteristic, complemented
294	#3253	C₂×C₄₃	1	1	yes	characteristic, complemented
295	#3152	C₂×C₄₃	1	1	yes	characteristic, complemented
296	#3106	C₂×C₄₃	1	1	yes	characteristic, complemented
297	#1634	C₂×C₄₃	1	2	yes	complemented
298	#1632	C₂×C₄₃	1	2	yes	complemented
299	#1624	C₂×C₄₃	1	2	yes	complemented
300	#1622	C₂×C₄₃	1	2	yes	complemented
301	#1548	C₂×C₄₃	1	1	yes	characteristic, complemented
302	#1489	C₂×C₄₃	1	1	yes	characteristic, complemented
303	#1484	C₂×C₄₃	1	1	yes	characteristic, complemented
304	C₂×C₄₃	—	4	1	no	—
305	C₂×C₄₃	—	8	1	no	—
306	C₂×C₄₃	—	8	2	no	—
307	C₂×C₄₃	—	16	1	no	—
308	C₂×C₄₃	#3005	1	1	yes	characteristic
309	C₂×C₄₃	#3013	1	1	yes	characteristic
310	C₂×C₄₃	C₂×#453	1	1	yes	characteristic
311	C₂×#137	—	2	2	no	—
312	#556	—	2	1	no	—
313	#555	C₂²×C₄₃	1	2	yes	—
314	#554	C₂²×C₄₃	1	2	yes	—
315	#553	—	2	2	no	—
316	#548	—	2	2	no	—
317	#547	—	2	1	no	—
318	#542	—	2	2	no	—
319	#537	—	2	1	no	—
320	#533	—	2	1	no	—
321	#532	—	2	1	no	—
322	#532	C₂²×C₄₃	1	1	yes	characteristic
323	#532	C₂²×C₄₃	1	1	yes	characteristic
324	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
325	#520	—	2	1	no	—
326	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
327	#497	—	2	2	no	—
328	#494	C₂²×C₄₃	1	2	yes	—
329	#492	C₂²×C₄₃	1	2	yes	—
330	#482	—	2	1	no	—
331	#477	C₂²×C₄₃	1	1	yes	characteristic
332	#476	—	2	1	no	—
333	#476	C₂²×C₄₃	1	1	yes	characteristic
334	#476	C₂²×C₄₃	1	2	yes	—
335	#469	—	2	2	no	—
336	#460	C₂²×C₄₃	1	1	yes	characteristic
337	#459	—	2	1	no	—
338	#459	C₂²×C₄₃	1	1	yes	characteristic
339	#459	C₂²×C₄₃	1	2	yes	—
340	#449	—	2	1	no	—
341	C₄×SD₁₆	—	2	1	no	—
342	C₄×D₈	—	2	1	no	—
343	#431	C₂²×C₄₃	1	1	yes	characteristic
344	#423	C₂²×C₄₃	1	1	yes	characteristic
345	C₄×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
346	#333	C₂²×C₄₃	1	2	yes	—
347	#333	C₂²×C₄₃	1	2	yes	—
348	Q₈⋊C₈	C₂²×C₄₃	1	2	yes	—
349	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
350	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
351	D₄⋊C₈	C₂²×C₄₃	1	2	yes	—
352	C₄₃	#18569	1	1	yes	characteristic, direct product factor, Sylow
353	C₂×#41	—	2	2	no	—
354	C₂×#41	—	2	1	no	—
355	C₂×#41	—	2	1	no	—
356	C₂×#41	D₄×C₄₃	1	1	yes	characteristic
357	C₂²×Q₈	D₄×C₄₃	1	2	yes	—
358	#137	—	4	8	no	—
359	C₂×Q₁₆	—	2	4	no	—
360	C₂×SD₁₆	—	2	4	no	—
361	C₂×SD₁₆	—	2	1	no	—
362	C₂×D₈	—	2	1	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	—	2	1	no	—
366	C₄⋊Q₈	—	2	1	no	—
367	C₄⋊Q₈	—	2	1	no	—
368	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
369	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
370	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
372	#127	D₄×C₄₃	1	1	yes	characteristic
373	#127	C₂³×C₄₃	1	1	yes	characteristic
374	#126	—	2	4	no	—
375	#125	—	2	2	no	—
376	#124	—	2	2	no	—
377	#124	—	2	4	no	—
378	#124	—	2	1	no	—
379	#124	—	2	1	no	—
380	#123	—	2	4	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	2	no	—
383	C₂²⋊Q₈	—	2	2	no	—
384	C₂²⋊Q₈	—	2	4	no	—
385	#121	—	2	2	no	—
386	#121	—	2	4	no	—
387	#121	—	2	2	no	—
388	#121	—	2	2	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	D₄×C₄₃	1	2	yes	—
393	C₄×Q₈	—	2	2	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
397	C₄×D₄	—	2	2	no	—
398	C₄×D₄	—	2	4	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	1	no	—
404	C₄×D₄	—	2	1	no	—
405	C₄×D₄	D₄×C₄₃	1	1	yes	characteristic
406	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
407	C₄×D₄	C₂³×C₄₃	1	2	yes	—
408	#117	—	2	2	no	—
409	#117	—	2	2	no	—
410	#117	—	2	1	no	—
411	#117	D₄×C₄₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
417	#107	—	2	1	no	—
418	#106	—	2	1	no	—
419	#106	—	2	2	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
422	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
423	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
424	#103	—	2	1	no	—
425	#102	—	2	1	no	—
426	#102	—	2	2	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
429	#102	—	2	2	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	#97	—	2	1	no	—
432	C₄×C₈	—	2	1	no	—
433	C₄×C₈	C₂³×C₄₃	1	2	yes	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	#41	—	4	2	no	—
437	#41	—	4	2	no	—
438	#41	—	4	4	no	—
439	#41	—	8	4	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	4	4	no	—
444	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	4	1	no	—
455	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
456	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
467	Q₁₆	—	4	8	no	—
468	SD₁₆	—	4	8	no	—
469	SD₁₆	—	4	2	no	—
470	D₈	—	4	2	no	—
471	D₈	—	8	2	no	—
472	M₁₆	—	2	4	no	—
473	M₁₆	—	8	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	2	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
491	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
492	C₂²⋊C₄	—	2	4	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	1	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	4	1	no	—
501	C₂²⋊C₄	—	4	1	no	—
502	C₄²	—	2	4	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
507	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
508	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
509	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
510	C₂³	—	2	1	no	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	#120×C₄₃	1	1	yes	characteristic
514	Q₈	—	2	1	no	—
515	Q₈	—	2	1	no	—
516	Q₈	—	4	4	no	—
517	Q₈	—	4	2	no	—
518	Q₈	—	4	2	no	—
519	Q₈	—	4	4	no	—
520	D₄	—	2	1	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	2	no	—
533	D₄	—	8	4	no	—
534	D₄	—	8	2	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	8	2	no	—
553	C₂×C₄	—	8	4	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
556	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
557	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
558	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
561	C₈	—	2	4	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₈	—	4	2	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	4	1	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	8	1	no	—
575	C₂²	—	8	1	no	—
576	C₂²	—	8	1	no	—
577	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	4	no	—
586	C₄	—	8	1	no	—
587	C₄	C₄₃×#453	1	2	yes	—
588	C₄	C₄₃×#575	1	1	yes	characteristic
589	C₄	C₄₃×#575	1	1	yes	characteristic
590	C₄	C₄₃×#577	1	1	yes	characteristic
591	C₄	C₄₃×#578	1	1	yes	characteristic
592	C₂	—	4	1	no	—
593	C₂	—	8	1	no	—
594	C₂	—	8	2	no	—
595	C₂	—	16	1	no	—
596	C₂	C₄₃×#3005	1	1	yes	characteristic
597	C₂	C₄₃×#3013	1	1	yes	characteristic
598	C₂	C₂×C₄₃×#453	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3511	C₂	semidirect
2. C₄₃×#3253	C₂	semidirect
3. C₄₃×#3152	C₂	semidirect
4. C₄₃×#3106	C₂	semidirect
5. C₄₃×#1634	C₂	semidirect
6. C₄₃×#1632	C₂	semidirect
7. C₄₃×#1624	C₂	semidirect
8. C₄₃×#1622	C₂	semidirect
9. C₄₃×#1548	C₂	semidirect
10. C₄₃×#1489	C₂	semidirect
11. C₄₃×#1484	C₂	semidirect
265. #18569	C₄₃	direct (N × H)
293. #3511	C₂×C₄₃	semidirect
294. #3253	C₂×C₄₃	semidirect
295. #3152	C₂×C₄₃	semidirect
296. #3106	C₂×C₄₃	semidirect
297. #1634	C₂×C₄₃	semidirect
298. #1632	C₂×C₄₃	semidirect
299. #1624	C₂×C₄₃	semidirect
300. #1622	C₂×C₄₃	semidirect
301. #1548	C₂×C₄₃	semidirect
302. #1489	C₂×C₄₃	semidirect
303. #1484	C₂×C₄₃	semidirect
352. C₄₃	#18569	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3511	2
C₄₃×#3253	2
C₄₃×#3152	2
C₄₃×#3106	2
C₄₃×#1634	2
C₄₃×#1632	2
C₄₃×#1624	2
C₄₃×#1622	2
C₄₃×#1548	2
C₄₃×#1489	2
C₄₃×#1484	2
#18569	43

Subgroups — C43×#18569 #24938586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18569 #24938586