Subgroups — C₄₃×#61665 #24981682

Order 11008.

2008 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3499	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#3328	C₂	1	4	yes	maximal, complemented
4	C₄₃×#3302	C₂	1	4	yes	maximal, complemented
5	D₄×Q₁₆×C₄₃	C₂	1	4	yes	maximal, complemented
6	C₄₃×#3276	C₂	1	4	yes	maximal, complemented
7	C₄₃×#3209	C₂	1	2	yes	maximal, complemented
8	C₄₃×#3202	C₂	1	4	yes	maximal, complemented
9	C₄₃×#3107	C₂	1	2	yes	maximal, complemented
10	C₄₃×#3011	C₂	1	4	yes	maximal, complemented
11	C₄₃×#2979	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	2	yes	—
13	C₂×#137×C₄₃	C₂²	1	4	yes	—
14	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
15	C₄₃×#563	—	2	2	no	—
16	C₄₃×#559	—	2	1	no	—
17	Q₈²×C₄₃	—	2	1	no	—
18	C₄₃×#556	C₂²	1	4	yes	—
19	D₄×Q₈×C₄₃	C₂²	1	4	yes	—
20	D₄×Q₈×C₄₃	C₂²	1	4	yes	—
21	C₄₃×#547	—	2	4	no	—
22	C₄₃×#547	C₂²	1	4	yes	—
23	C₄₃×#542	—	2	4	no	—
24	C₄₃×#536	—	2	2	no	—
25	C₄₃×#536	C₂²	1	2	yes	—
26	C₄₃×#536	C₂²	1	4	yes	—
27	C₄₃×#533	C₂²	1	2	yes	—
28	C₄₃×#532	—	2	1	no	—
29	C₄₃×#532	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
31	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
33	C₄₃×#494	C₂²	1	4	yes	—
34	C₄₃×#487	C₂²	1	4	yes	—
35	C₄₃×#485	C₂²	1	4	yes	—
36	C₄₃×#485	C₂²	1	8	yes	—
37	C₄₃×#475	C₂²	1	2	yes	—
38	C₄₃×#474	C₂²	1	2	yes	—
39	C₄₃×#470	C₂²	1	8	yes	—
40	C₄₃×#467	C₂²	1	8	yes	—
41	C₄₃×#462	C₂²	1	2	yes	—
42	C₄₃×#462	C₂²	1	4	yes	—
43	C₄₃×#462	C₂²	1	4	yes	—
44	C₄₃×#461	C₂²	1	2	yes	—
45	C₄₃×#452	C₂²	1	4	yes	—
46	C₄₃×#452	C₂²	1	8	yes	—
47	C₄₃×#451	C₂²	1	8	yes	—
48	C₄₃×#451	C₂²	1	8	yes	—
49	C₄₃×#451	C₂²	1	8	yes	—
50	C₄×Q₁₆×C₄₃	C₂²	1	4	yes	—
51	C₄×SD₁₆×C₄₃	C₂²	1	4	yes	—
52	C₄₃×#436	C₂²	1	4	yes	—
53	C₈×D₄×C₄₃	C₂²	1	4	yes	—
54	C₄₃×#431	C₂²	1	2	yes	—
55	C₄₃×#419	C₂²	1	4	yes	—
56	C₄₃×#416	C₂²	1	4	yes	—
57	C₄₃×#408	C₂²	1	4	yes	—
58	2₋¹⁺⁴×C₄₃	—	4	4	no	—
59	2₋¹⁺⁴×C₄₃	—	4	4	no	—
60	C₂×#41×C₄₃	—	2	2	no	—
61	C₂×#41×C₄₃	—	2	4	no	—
62	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
63	C₂×#41×C₄₃	C₂³	1	4	yes	—
64	C₂×#41×C₄₃	C₂³	1	2	yes	—
65	C₂²×Q₈×C₄₃	—	2	2	no	—
66	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
67	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
68	C₂²×Q₈×C₄₃	C₂³	1	4	yes	—
69	#137×C₄₃	—	4	8	no	—
70	C₂×Q₁₆×C₄₃	—	4	8	no	—
71	C₂×Q₁₆×C₄₃	C₂³	1	4	yes	—
72	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	—
73	C₂×Q₁₆×C₄₃	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₄₃	C₂³	1	4	yes	—
75	C₂×M₁₆×C₄₃	C₂³	1	4	yes	—
76	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
77	C₄⋊Q₈×C₄₃	—	2	2	no	—
78	C₄⋊Q₈×C₄₃	—	2	4	no	—
79	C₄⋊Q₈×C₄₃	—	2	4	no	—
80	C₄⋊Q₈×C₄₃	—	2	4	no	—
81	C₄⋊Q₈×C₄₃	—	2	1	no	—
82	C₄⋊Q₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₃	C₂³	1	4	yes	—
85	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
87	#127×C₄₃	D₄	1	1	yes	characteristic
88	#126×C₄₃	—	2	8	no	—
89	#125×C₄₃	—	2	2	no	—
90	#124×C₄₃	—	2	2	no	—
91	#124×C₄₃	—	2	4	no	—
92	#124×C₄₃	—	2	4	no	—
93	#124×C₄₃	D₄	1	2	yes	—
94	#123×C₄₃	—	2	4	no	—
95	#123×C₄₃	—	2	4	no	—
96	#123×C₄₃	—	2	4	no	—
97	#123×C₄₃	—	2	8	no	—
98	C₂²⋊Q₈×C₄₃	—	2	2	no	—
99	C₂²⋊Q₈×C₄₃	—	2	8	no	—
100	C₂²⋊Q₈×C₄₃	—	2	8	no	—
101	C₂²⋊Q₈×C₄₃	C₂³	1	4	yes	—
102	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	—
103	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	—
104	#121×C₄₃	—	2	4	no	—
105	#121×C₄₃	D₄	1	4	yes	—
106	C₄×Q₈×C₄₃	—	2	4	no	—
107	C₄×Q₈×C₄₃	—	2	2	no	—
108	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
109	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
110	C₄×D₄×C₄₃	—	2	4	no	—
111	C₄×D₄×C₄₃	—	2	4	no	—
112	C₄×D₄×C₄₃	—	2	2	no	—
113	C₄×D₄×C₄₃	C₂³	1	2	yes	—
114	C₄×D₄×C₄₃	C₂³	1	4	yes	—
115	#117×C₄₃	—	2	2	no	—
116	#117×C₄₃	—	2	1	no	—
117	#117×C₄₃	C₂³	1	1	yes	characteristic
118	#117×C₄₃	C₂³	1	4	yes	—
119	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₂×C₄²×C₄₃	—	2	1	no	—
122	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
123	#107×C₄₃	C₂³	1	4	yes	—
124	#106×C₄₃	C₂³	1	4	yes	—
125	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
126	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
127	#103×C₄₃	C₂³	1	8	yes	—
128	#103×C₄₃	C₂³	1	4	yes	—
129	#103×C₄₃	C₂³	1	8	yes	—
130	#103×C₄₃	C₂³	1	4	yes	—
131	#103×C₄₃	C₂³	1	4	yes	—
132	#102×C₄₃	C₂³	1	4	yes	—
133	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	—
134	C₂²⋊C₈×C₄₃	C₂³	1	8	yes	—
135	C₄×C₈×C₄₃	C₂³	1	4	yes	—
136	#41×C₄₃	—	2	2	no	—
137	#41×C₄₃	—	2	2	no	—
138	#41×C₄₃	—	2	8	no	—
139	#41×C₄₃	—	4	2	no	—
140	#41×C₄₃	—	4	2	no	—
141	#41×C₄₃	—	4	4	no	—
142	#41×C₄₃	—	4	8	no	—
143	#41×C₄₃	—	4	16	no	—
144	C₂×Q₈×C₄₃	—	2	2	no	—
145	C₂×Q₈×C₄₃	—	2	4	no	—
146	C₂×Q₈×C₄₃	—	2	2	no	—
147	C₂×Q₈×C₄₃	—	2	4	no	—
148	C₂×Q₈×C₄₃	—	2	8	no	—
149	C₂×Q₈×C₄₃	—	4	4	no	—
150	C₂×Q₈×C₄₃	—	4	2	no	—
151	C₂×Q₈×C₄₃	—	4	2	no	—
152	C₂×Q₈×C₄₃	—	4	8	no	—
153	C₂×Q₈×C₄₃	—	4	4	no	—
154	C₂×Q₈×C₄₃	—	4	4	no	—
155	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
157	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
158	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂×D₄×C₄₃	—	2	1	no	—
160	C₂×D₄×C₄₃	—	2	4	no	—
161	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
162	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
164	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	2	no	—
167	C₂²×C₄×C₄₃	—	2	4	no	—
168	C₂²×C₄×C₄₃	—	2	2	no	—
169	C₂²×C₄×C₄₃	—	2	4	no	—
170	C₂²×C₄×C₄₃	—	2	4	no	—
171	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
174	Q₁₆×C₄₃	—	2	8	no	—
175	Q₁₆×C₄₃	—	4	8	no	—
176	Q₁₆×C₄₃	—	4	8	no	—
177	SD₁₆×C₄₃	—	2	8	no	—
178	M₁₆×C₄₃	—	4	4	no	—
179	C₂×C₈×C₄₃	—	4	4	no	—
180	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
181	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
182	C₄⋊C₄×C₄₃	—	2	4	no	—
183	C₄⋊C₄×C₄₃	—	2	4	no	—
184	C₄⋊C₄×C₄₃	—	2	8	no	—
185	C₄⋊C₄×C₄₃	—	2	2	no	—
186	C₄⋊C₄×C₄₃	—	2	2	no	—
187	C₄⋊C₄×C₄₃	—	2	2	no	—
188	C₄⋊C₄×C₄₃	—	2	2	no	—
189	C₄⋊C₄×C₄₃	—	2	8	no	—
190	C₄⋊C₄×C₄₃	—	2	4	no	—
191	C₄⋊C₄×C₄₃	—	2	4	no	—
192	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
193	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
194	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
195	C₂²⋊C₄×C₄₃	—	2	2	no	—
196	C₂²⋊C₄×C₄₃	—	2	4	no	—
197	C₂²⋊C₄×C₄₃	—	2	1	no	—
198	C₂²⋊C₄×C₄₃	—	2	4	no	—
199	C₂²⋊C₄×C₄₃	—	2	8	no	—
200	C₂²⋊C₄×C₄₃	—	2	8	no	—
201	C₂²⋊C₄×C₄₃	C₂×D₄	1	8	yes	—
202	C₄²×C₄₃	—	2	1	no	—
203	C₄²×C₄₃	—	2	2	no	—
204	C₄²×C₄₃	—	2	4	no	—
205	C₄²×C₄₃	—	2	4	no	—
206	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₃	C₂⁴	1	2	yes	—
209	C₂³×C₄₃	—	2	1	no	—
210	C₂³×C₄₃	C₂²×D₄	1	4	yes	—
211	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₄₃	—	2	1	no	—
213	Q₈×C₄₃	—	2	4	no	—
214	Q₈×C₄₃	—	2	4	no	—
215	Q₈×C₄₃	—	2	4	no	—
216	Q₈×C₄₃	—	2	4	no	—
217	Q₈×C₄₃	—	4	2	no	—
218	Q₈×C₄₃	—	4	8	no	—
219	Q₈×C₄₃	—	4	4	no	—
220	Q₈×C₄₃	—	4	4	no	—
221	Q₈×C₄₃	—	8	4	no	—
222	Q₈×C₄₃	H(5,𝔽₂)	1	2	yes	—
223	D₄×C₄₃	—	2	4	no	—
224	D₄×C₄₃	—	2	8	no	—
225	D₄×C₄₃	—	2	1	no	—
226	D₄×C₄₃	—	4	2	no	—
227	D₄×C₄₃	—	4	4	no	—
228	D₄×C₄₃	—	4	8	no	—
229	D₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
230	C₂×C₄×C₄₃	—	2	4	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	2	4	no	—
233	C₂×C₄×C₄₃	—	2	4	no	—
234	C₂×C₄×C₄₃	—	2	4	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	4	no	—
238	C₂×C₄×C₄₃	—	2	2	no	—
239	C₂×C₄×C₄₃	—	2	4	no	—
240	C₂×C₄×C₄₃	—	2	4	no	—
241	C₂×C₄×C₄₃	—	4	8	no	—
242	C₂×C₄×C₄₃	—	4	8	no	—
243	C₂×C₄×C₄₃	—	4	4	no	—
244	C₂×C₄×C₄₃	—	4	4	no	—
245	C₂×C₄×C₄₃	—	8	4	no	—
246	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
248	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
251	C₈×C₄₃	—	2	4	no	—
252	C₈×C₄₃	—	2	4	no	—
253	#61665	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂²×C₄₃	—	2	2	no	—
255	C₂²×C₄₃	—	2	1	no	—
256	C₂²×C₄₃	—	2	4	no	—
257	C₂²×C₄₃	—	2	2	no	—
258	C₂²×C₄₃	—	2	8	no	—
259	C₂²×C₄₃	—	4	2	no	—
260	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
261	C₄×C₄₃	—	2	1	no	—
262	C₄×C₄₃	—	2	2	no	—
263	C₄×C₄₃	—	2	4	no	—
264	C₄×C₄₃	—	2	2	no	—
265	C₄×C₄₃	—	4	4	no	—
266	C₄×C₄₃	—	4	4	no	—
267	C₄×C₄₃	—	4	2	no	—
268	C₄×C₄₃	—	4	4	no	—
269	C₄×C₄₃	#578	1	4	yes	—
270	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
271	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
272	#3550	C₂×C₄₃	1	1	yes	characteristic, complemented
273	#3499	C₂×C₄₃	1	1	yes	characteristic
274	#3328	C₂×C₄₃	1	4	yes	complemented
275	#3302	C₂×C₄₃	1	4	yes	complemented
276	D₄×Q₁₆	C₂×C₄₃	1	4	yes	complemented
277	#3276	C₂×C₄₃	1	4	yes	complemented
278	#3209	C₂×C₄₃	1	2	yes	complemented
279	#3202	C₂×C₄₃	1	4	yes	complemented
280	#3107	C₂×C₄₃	1	2	yes	complemented
281	#3011	C₂×C₄₃	1	4	yes	complemented
282	#2979	C₂×C₄₃	1	1	yes	characteristic, complemented
283	C₂×C₄₃	—	4	1	no	—
284	C₂×C₄₃	—	4	4	no	—
285	C₂×C₄₃	—	4	2	no	—
286	C₂×C₄₃	#3484	1	1	yes	characteristic
287	C₂×C₄₃	C₂×#578	1	2	yes	—
288	C₂×2₋¹⁺⁴	C₂²×C₄₃	1	2	yes	—
289	C₂×#137	C₂²×C₄₃	1	4	yes	—
290	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
291	#563	—	2	2	no	—
292	#559	—	2	1	no	—
293	Q₈²	—	2	1	no	—
294	#556	C₂²×C₄₃	1	4	yes	—
295	D₄×Q₈	C₂²×C₄₃	1	4	yes	—
296	D₄×Q₈	C₂²×C₄₃	1	4	yes	—
297	#547	—	2	4	no	—
298	#547	C₂²×C₄₃	1	4	yes	—
299	#542	—	2	4	no	—
300	#536	—	2	2	no	—
301	#536	C₂²×C₄₃	1	2	yes	—
302	#536	C₂²×C₄₃	1	4	yes	—
303	#533	C₂²×C₄₃	1	2	yes	—
304	#532	—	2	1	no	—
305	#532	C₂²×C₄₃	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	—	2	1	no	—
307	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
308	C₄×#41	C₂²×C₄₃	1	1	yes	characteristic
309	#494	C₂²×C₄₃	1	4	yes	—
310	#487	C₂²×C₄₃	1	4	yes	—
311	#485	C₂²×C₄₃	1	8	yes	—
312	#485	C₂²×C₄₃	1	4	yes	—
313	#475	C₂²×C₄₃	1	2	yes	—
314	#474	C₂²×C₄₃	1	2	yes	—
315	#470	C₂²×C₄₃	1	8	yes	—
316	#467	C₂²×C₄₃	1	8	yes	—
317	#462	C₂²×C₄₃	1	4	yes	—
318	#462	C₂²×C₄₃	1	2	yes	—
319	#462	C₂²×C₄₃	1	4	yes	—
320	#461	C₂²×C₄₃	1	2	yes	—
321	#452	C₂²×C₄₃	1	4	yes	—
322	#452	C₂²×C₄₃	1	8	yes	—
323	#451	C₂²×C₄₃	1	8	yes	—
324	#451	C₂²×C₄₃	1	8	yes	—
325	#451	C₂²×C₄₃	1	8	yes	—
326	C₄×Q₁₆	C₂²×C₄₃	1	4	yes	—
327	C₄×SD₁₆	C₂²×C₄₃	1	4	yes	—
328	#436	C₂²×C₄₃	1	4	yes	—
329	C₈×D₄	C₂²×C₄₃	1	4	yes	—
330	#431	C₂²×C₄₃	1	2	yes	—
331	#419	C₂²×C₄₃	1	4	yes	—
332	#416	C₂²×C₄₃	1	4	yes	—
333	#408	C₂²×C₄₃	1	4	yes	—
334	C₄₃	#61665	1	1	yes	characteristic, direct product factor, Sylow
335	2₋¹⁺⁴	—	4	4	no	—
336	2₋¹⁺⁴	—	4	4	no	—
337	C₂×#41	—	2	2	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	C₂³×C₄₃	1	1	yes	characteristic
340	C₂×#41	C₂³×C₄₃	1	4	yes	—
341	C₂×#41	C₂³×C₄₃	1	2	yes	—
342	C₂²×Q₈	—	2	2	no	—
343	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
344	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
345	C₂²×Q₈	C₂³×C₄₃	1	4	yes	—
346	#137	—	4	8	no	—
347	C₂×Q₁₆	—	4	8	no	—
348	C₂×Q₁₆	C₂³×C₄₃	1	4	yes	—
349	C₂×Q₁₆	C₂³×C₄₃	1	8	yes	—
350	C₂×Q₁₆	C₂³×C₄₃	1	8	yes	—
351	C₂×SD₁₆	C₂³×C₄₃	1	4	yes	—
352	C₂×M₁₆	C₂³×C₄₃	1	4	yes	—
353	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	—	2	4	no	—
356	C₄⋊Q₈	—	2	4	no	—
357	C₄⋊Q₈	—	2	4	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	—	2	1	no	—
360	C₄⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₄₃	1	4	yes	—
362	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
363	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
364	#127	D₄×C₄₃	1	1	yes	characteristic
365	#126	—	2	8	no	—
366	#125	—	2	2	no	—
367	#124	—	2	2	no	—
368	#124	—	2	4	no	—
369	#124	—	2	4	no	—
370	#124	D₄×C₄₃	1	2	yes	—
371	#123	—	2	4	no	—
372	#123	—	2	4	no	—
373	#123	—	2	4	no	—
374	#123	—	2	8	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	8	no	—
377	C₂²⋊Q₈	—	2	8	no	—
378	C₂²⋊Q₈	C₂³×C₄₃	1	4	yes	—
379	C₂²⋊Q₈	C₂³×C₄₃	1	8	yes	—
380	C₂²⋊Q₈	C₂³×C₄₃	1	8	yes	—
381	#121	—	2	4	no	—
382	#121	D₄×C₄₃	1	4	yes	—
383	C₄×Q₈	—	2	4	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
386	C₄×Q₈	C₂³×C₄₃	1	4	yes	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	C₂³×C₄₃	1	2	yes	—
391	C₄×D₄	C₂³×C₄₃	1	4	yes	—
392	#117	—	2	2	no	—
393	#117	—	2	1	no	—
394	#117	C₂³×C₄₃	1	1	yes	characteristic
395	#117	C₂³×C₄₃	1	4	yes	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	4	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
400	#107	C₂³×C₄₃	1	4	yes	—
401	#106	C₂³×C₄₃	1	4	yes	—
402	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
403	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
404	#103	C₂³×C₄₃	1	8	yes	—
405	#103	C₂³×C₄₃	1	4	yes	—
406	#103	C₂³×C₄₃	1	8	yes	—
407	#103	C₂³×C₄₃	1	4	yes	—
408	#103	C₂³×C₄₃	1	4	yes	—
409	#102	C₂³×C₄₃	1	4	yes	—
410	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	—
411	C₂²⋊C₈	C₂³×C₄₃	1	8	yes	—
412	C₄×C₈	C₂³×C₄₃	1	4	yes	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	8	no	—
416	#41	—	4	2	no	—
417	#41	—	4	2	no	—
418	#41	—	4	4	no	—
419	#41	—	4	8	no	—
420	#41	—	4	16	no	—
421	C₂×Q₈	—	2	2	no	—
422	C₂×Q₈	—	2	4	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	4	no	—
425	C₂×Q₈	—	2	8	no	—
426	C₂×Q₈	—	4	4	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	8	no	—
430	C₂×Q₈	—	4	4	no	—
431	C₂×Q₈	—	4	4	no	—
432	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
433	C₂×Q₈	C₂⁴×C₄₃	1	4	yes	—
434	C₂×Q₈	C₂⁴×C₄₃	1	4	yes	—
435	C₂×Q₈	C₂⁴×C₄₃	1	1	yes	characteristic
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
439	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
440	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
441	C₂×D₄	C₂⁴×C₄₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
450	C₂²×C₄	C₂⁴×C₄₃	1	4	yes	—
451	Q₁₆	—	2	8	no	—
452	Q₁₆	—	4	8	no	—
453	Q₁₆	—	4	8	no	—
454	SD₁₆	—	2	8	no	—
455	M₁₆	—	4	4	no	—
456	C₂×C₈	—	4	4	no	—
457	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
458	C₂×C₈	C₂⁴×C₄₃	1	4	yes	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₄₃	1	4	yes	—
471	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
472	C₂²⋊C₄	—	2	4	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	C₂×D₄×C₄₃	1	8	yes	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	4	no	—
482	C₄²	—	2	4	no	—
483	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
485	C₄²	C₂⁴×C₄₃	1	2	yes	—
486	C₂³	—	2	1	no	—
487	C₂³	C₂²×D₄×C₄₃	1	4	yes	—
488	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
489	Q₈	—	2	1	no	—
490	Q₈	—	2	4	no	—
491	Q₈	—	2	4	no	—
492	Q₈	—	2	4	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	8	no	—
496	Q₈	—	4	4	no	—
497	Q₈	—	4	4	no	—
498	Q₈	—	8	4	no	—
499	Q₈	H(5,𝔽₂)×C₄₃	1	2	yes	—
500	D₄	—	2	4	no	—
501	D₄	—	2	8	no	—
502	D₄	—	2	1	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	4	no	—
505	D₄	—	4	8	no	—
506	D₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	8	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	4	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
524	C₂×C₄	C₂²×D₄×C₄₃	1	4	yes	—
525	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
526	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
527	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
528	C₈	—	2	4	no	—
529	C₈	—	2	4	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	8	no	—
535	C₂²	—	4	2	no	—
536	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	2	no	—
539	C₄	—	2	4	no	—
540	C₄	—	2	2	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	4	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	4	no	—
545	C₄	C₄₃×#578	1	4	yes	—
546	C₄	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
547	C₄	C₂×H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
548	C₂	—	4	1	no	—
549	C₂	—	4	4	no	—
550	C₂	—	4	2	no	—
551	C₂	C₄₃×#3484	1	1	yes	characteristic
552	C₂	C₂×C₄₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
prime radical	C₄₃×#3499	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₄₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3550	C₂	semidirect
3. C₄₃×#3328	C₂	semidirect
4. C₄₃×#3302	C₂	semidirect
5. D₄×Q₁₆×C₄₃	C₂	semidirect
6. C₄₃×#3276	C₂	semidirect
7. C₄₃×#3209	C₂	semidirect
8. C₄₃×#3202	C₂	semidirect
9. C₄₃×#3107	C₂	semidirect
10. C₄₃×#3011	C₂	semidirect
11. C₄₃×#2979	C₂	semidirect
253. #61665	C₄₃	direct (N × H)
272. #3550	C₂×C₄₃	semidirect
274. #3328	C₂×C₄₃	semidirect
275. #3302	C₂×C₄₃	semidirect
276. D₄×Q₁₆	C₂×C₄₃	semidirect
277. #3276	C₂×C₄₃	semidirect
278. #3209	C₂×C₄₃	semidirect
279. #3202	C₂×C₄₃	semidirect
280. #3107	C₂×C₄₃	semidirect
281. #3011	C₂×C₄₃	semidirect
282. #2979	C₂×C₄₃	semidirect
334. C₄₃	#61665	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×#3550	2
C₄₃×#3499	2
C₄₃×#3328	2
C₄₃×#3302	2
D₄×Q₁₆×C₄₃	2
C₄₃×#3276	2
C₄₃×#3209	2
C₄₃×#3202	2
C₄₃×#3107	2
C₄₃×#3011	2
C₄₃×#2979	2
#61665	43

Subgroups — C43×#61665 #24981682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#61665 #24981682