Subgroups — C₄₃×#29696 #24949713

Order 11008.

1012 conjugacy classes of subgroups.

The subgroup lattice has 560 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×#477	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2036	C₂	1	2	yes	maximal, complemented
8	C₄₃×#2033	C₂	1	2	yes	maximal
9	C₄₃×#1805	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#542	—	2	4	no	—
13	C₄₃×#542	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#126×C₄₃	—	2	1	no	—
17	C₂×#124×C₄₃	—	2	1	no	—
18	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×#123×C₄₃	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
21	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#477	—	2	4	no	—
27	C₄₃×#474	—	2	4	no	—
28	C₂×#107×C₄₃	C₂²	1	2	yes	—
29	C₂×#107×C₄₃	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
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×#102×C₄₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
37	C₄₃×#400	—	2	1	no	—
38	C₄₃×#399	—	2	1	no	—
39	C₄₃×#395	—	2	1	no	—
40	C₄₃×#393	—	2	1	no	—
41	C₄₃×#389	C₂²	1	2	yes	—
42	C₄₃×#382	C₂²	1	1	yes	characteristic
43	C₄₃×#380	C₂²	1	2	yes	—
44	C₄₃×#340	C₂²	1	2	yes	—
45	C₄₃×#340	C₂²	1	2	yes	—
46	C₄₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₃	—	2	1	no	—
48	C₂²×Q₈×C₄₃	—	2	1	no	—
49	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₃	—	2	1	no	—
53	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₄₃	—	2	2	no	—
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	2	no	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	#126×C₄₃	—	2	8	no	—
61	#124×C₄₃	—	2	8	no	—
62	#124×C₄₃	—	2	2	no	—
63	#124×C₄₃	—	2	2	no	—
64	#123×C₄₃	—	2	8	no	—
65	C₂²⋊Q₈×C₄₃	—	2	8	no	—
66	C₂²⋊Q₈×C₄₃	—	2	2	no	—
67	C₂²⋊Q₈×C₄₃	—	2	2	no	—
68	#121×C₄₃	—	2	2	no	—
69	#121×C₄₃	—	2	2	no	—
70	C₄×Q₈×C₄₃	—	2	2	no	—
71	C₄×Q₈×C₄₃	D₄	1	4	yes	—
72	C₄×D₄×C₄₃	—	2	2	no	—
73	C₄×D₄×C₄₃	D₄	1	4	yes	—
74	#117×C₄₃	—	2	2	no	—
75	#117×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#107×C₄₃	—	2	4	no	—
99	#107×C₄₃	—	2	4	no	—
100	C₄⋊C₈×C₄₃	—	2	2	no	—
101	C₄⋊C₈×C₄₃	—	2	2	no	—
102	#103×C₄₃	—	2	4	no	—
103	#103×C₄₃	—	4	2	no	—
104	#102×C₄₃	—	2	4	no	—
105	#102×C₄₃	—	4	2	no	—
106	C₂²⋊C₈×C₄₃	—	4	2	no	—
107	#95×C₄₃	—	2	2	no	—
108	#95×C₄₃	—	2	1	no	—
109	#95×C₄₃	—	2	1	no	—
110	#95×C₄₃	—	2	2	no	—
111	C₂⁴×C₄₃	—	2	1	no	—
112	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₄₃	—	2	4	no	—
114	C₂×Q₈×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂×Q₈×C₄₃	—	2	1	no	—
118	C₂×Q₈×C₄₃	—	2	1	no	—
119	C₂×Q₈×C₄₃	—	4	2	no	—
120	C₂×Q₈×C₄₃	—	8	2	no	—
121	C₂×Q₈×C₄₃	—	8	2	no	—
122	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₃	—	2	4	no	—
124	C₂×D₄×C₄₃	—	2	1	no	—
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	—	2	1	no	—
127	C₂×D₄×C₄₃	—	2	1	no	—
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	—	8	2	no	—
130	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	—	2	1	no	—
133	C₂²×C₄×C₄₃	—	2	1	no	—
134	C₂²×C₄×C₄₃	—	2	1	no	—
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	4	no	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	—	2	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	8	2	no	—
144	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₄₃	—	2	2	no	—
151	C₂×C₈×C₄₃	—	2	2	no	—
152	C₂×C₈×C₄₃	—	2	2	no	—
153	C₂×C₈×C₄₃	—	2	2	no	—
154	C₂×C₈×C₄₃	—	2	2	no	—
155	C₂×C₈×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	2	4	no	—
157	C₄⋊C₄×C₄₃	—	2	4	no	—
158	C₄⋊C₄×C₄₃	—	2	4	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	2	2	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	—	4	2	no	—
168	C₄⋊C₄×C₄₃	—	8	2	no	—
169	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₄₃	—	2	4	no	—
172	C₂²⋊C₄×C₄₃	—	2	4	no	—
173	C₂²⋊C₄×C₄₃	—	2	4	no	—
174	C₂²⋊C₄×C₄₃	—	2	4	no	—
175	C₂²⋊C₄×C₄₃	—	2	4	no	—
176	C₂²⋊C₄×C₄₃	—	2	2	no	—
177	C₂²⋊C₄×C₄₃	—	2	2	no	—
178	C₂²⋊C₄×C₄₃	—	8	2	no	—
179	C₄²×C₄₃	—	2	4	no	—
180	C₄²×C₄₃	—	2	1	no	—
181	C₄²×C₄₃	—	2	1	no	—
182	C₄²×C₄₃	C₂×D₄	1	2	yes	—
183	C₄²×C₄₃	C₂×D₄	1	2	yes	—
184	C₂³×C₄₃	—	2	1	no	—
185	C₂³×C₄₃	—	2	2	no	—
186	C₂³×C₄₃	—	2	1	no	—
187	C₂³×C₄₃	—	2	1	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	4	1	no	—
191	C₂³×C₄₃	—	4	1	no	—
192	C₂³×C₄₃	—	4	2	no	—
193	C₂³×C₄₃	—	4	2	no	—
194	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₄₃	—	2	2	no	—
196	Q₈×C₄₃	—	2	2	no	—
197	Q₈×C₄₃	—	4	1	no	—
198	Q₈×C₄₃	—	4	1	no	—
199	Q₈×C₄₃	—	8	4	no	—
200	Q₈×C₄₃	—	8	4	no	—
201	D₄×C₄₃	—	2	2	no	—
202	D₄×C₄₃	—	2	2	no	—
203	D₄×C₄₃	—	4	1	no	—
204	D₄×C₄₃	—	4	1	no	—
205	D₄×C₄₃	—	8	4	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	2	2	no	—
208	C₂×C₄×C₄₃	—	2	1	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	1	no	—
211	C₂×C₄×C₄₃	—	2	2	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	1	no	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	2	no	—
221	C₂×C₄×C₄₃	—	4	2	no	—
222	C₂×C₄×C₄₃	—	4	1	no	—
223	C₂×C₄×C₄₃	—	4	1	no	—
224	C₂×C₄×C₄₃	—	4	1	no	—
225	C₂×C₄×C₄₃	—	4	1	no	—
226	C₂×C₄×C₄₃	—	4	2	no	—
227	C₂×C₄×C₄₃	—	4	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	—	4	2	no	—
230	C₂×C₄×C₄₃	—	4	2	no	—
231	C₂×C₄×C₄₃	—	4	2	no	—
232	C₂×C₄×C₄₃	—	8	4	no	—
233	C₂×C₄×C₄₃	#120	1	2	yes	—
234	C₂×C₄×C₄₃	#120	1	2	yes	—
235	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
241	C₈×C₄₃	—	4	2	no	—
242	C₈×C₄₃	—	4	2	no	—
243	#29696	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	—	4	2	no	—
246	C₂²×C₄₃	—	4	2	no	—
247	C₂²×C₄₃	—	4	2	no	—
248	C₂²×C₄₃	—	4	1	no	—
249	C₂²×C₄₃	—	4	2	no	—
250	C₂²×C₄₃	—	4	1	no	—
251	C₂²×C₄₃	—	4	2	no	—
252	C₂²×C₄₃	—	8	2	no	—
253	C₂²×C₄₃	—	8	2	no	—
254	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
255	C₂²×C₄₃	#536	1	1	yes	characteristic
256	C₂²×C₄₃	#537	1	1	yes	characteristic
257	C₂²×C₄₃	#576	1	2	yes	—
258	C₂²×C₄₃	#578	1	2	yes	—
259	C₄×C₄₃	—	2	2	no	—
260	C₄×C₄₃	—	2	2	no	—
261	C₄×C₄₃	—	4	1	no	—
262	C₄×C₄₃	—	4	2	no	—
263	C₄×C₄₃	—	4	1	no	—
264	C₄×C₄₃	—	4	2	no	—
265	C₄×C₄₃	—	4	2	no	—
266	C₄×C₄₃	—	4	1	no	—
267	C₄×C₄₃	—	8	2	no	—
268	C₄×C₄₃	—	8	2	no	—
269	C₄×C₄₃	#536	1	1	yes	characteristic
270	C₄×C₄₃	#536	1	1	yes	characteristic
271	C₄×C₄₃	#537	1	1	yes	characteristic
272	C₄×C₄₃	#537	1	1	yes	characteristic
273	C₂×#542	C₂×C₄₃	1	1	yes	characteristic
274	C₂×#477	C₂×C₄₃	1	1	yes	characteristic, complemented
275	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
276	#2628	C₂×C₄₃	1	1	yes	characteristic, complemented
277	#2057	C₂×C₄₃	1	2	yes	complemented
278	#2042	C₂×C₄₃	1	2	yes	complemented
279	#2036	C₂×C₄₃	1	2	yes	complemented
280	#2033	C₂×C₄₃	1	2	yes	—
281	#1805	C₂×C₄₃	1	1	yes	characteristic, complemented
282	#1804	C₂×C₄₃	1	1	yes	characteristic, complemented
283	#1798	C₂×C₄₃	1	1	yes	characteristic, complemented
284	C₂×C₄₃	—	8	1	no	—
285	C₂×C₄₃	—	8	2	no	—
286	C₂×C₄₃	#2616	1	1	yes	characteristic
287	C₂×C₄₃	#3008	1	1	yes	characteristic
288	C₂×C₄₃	#3011	1	1	yes	characteristic
289	C₂×C₄₃	#3243	1	2	yes	—
290	C₂×C₄₃	#3262	1	2	yes	—
291	#542	—	2	4	no	—
292	#542	—	2	4	no	—
293	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
294	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
295	C₂×#126	—	2	1	no	—
296	C₂×#124	—	2	1	no	—
297	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
298	C₂×#123	—	2	1	no	—
299	C₂×C₂²⋊Q₈	—	2	1	no	—
300	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
301	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
302	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
304	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
305	#477	—	2	4	no	—
306	#474	—	2	4	no	—
307	C₂×#107	C₂²×C₄₃	1	2	yes	—
308	C₂×#107	C₂²×C₄₃	1	2	yes	—
309	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
311	C₂×#103	C₂²×C₄₃	1	2	yes	—
312	C₂×#103	C₂²×C₄₃	1	2	yes	—
313	C₂×#102	C₂²×C₄₃	1	2	yes	—
314	C₂×#102	C₂²×C₄₃	1	2	yes	—
315	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
316	#400	—	2	1	no	—
317	#399	—	2	1	no	—
318	#395	—	2	1	no	—
319	#393	—	2	1	no	—
320	#389	C₂²×C₄₃	1	2	yes	—
321	#382	C₂²×C₄₃	1	1	yes	characteristic
322	#380	C₂²×C₄₃	1	2	yes	—
323	#340	C₂²×C₄₃	1	2	yes	—
324	#340	C₂²×C₄₃	1	2	yes	—
325	#336	C₂²×C₄₃	1	2	yes	—
326	C₄₃	#29696	1	1	yes	characteristic, direct product factor, Sylow
327	C₂²×Q₈	—	2	1	no	—
328	C₂²×Q₈	—	2	1	no	—
329	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
330	C₂²×D₄	—	2	1	no	—
331	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
335	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	#126	—	2	8	no	—
341	#124	—	2	8	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#123	—	2	8	no	—
345	C₂²⋊Q₈	—	2	8	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	D₄×C₄₃	1	4	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	D₄×C₄₃	1	4	yes	—
354	#117	—	2	2	no	—
355	#117	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
362	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
378	#107	—	2	4	no	—
379	#107	—	2	4	no	—
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	2	2	no	—
382	#103	—	2	4	no	—
383	#103	—	4	2	no	—
384	#102	—	2	4	no	—
385	#102	—	4	2	no	—
386	C₂²⋊C₈	—	4	2	no	—
387	#95	—	2	2	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	2	no	—
391	C₂⁴	—	2	1	no	—
392	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	1	no	—
396	C₂×Q₈	—	2	1	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	—	8	2	no	—
401	C₂×Q₈	—	8	2	no	—
402	C₂×Q₈	C₂×D₄×C₄₃	1	2	yes	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	8	2	no	—
410	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	8	2	no	—
424	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	8	2	no	—
449	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	—	2	2	no	—
457	C₂²⋊C₄	—	2	2	no	—
458	C₂²⋊C₄	—	8	2	no	—
459	C₄²	—	2	4	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	C₂×D₄×C₄₃	1	2	yes	—
463	C₄²	C₂×D₄×C₄₃	1	2	yes	—
464	C₂³	—	2	1	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	1	no	—
472	C₂³	—	4	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
475	Q₈	—	2	2	no	—
476	Q₈	—	2	2	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	4	1	no	—
479	Q₈	—	8	4	no	—
480	Q₈	—	8	4	no	—
481	D₄	—	2	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	8	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	8	4	no	—
513	C₂×C₄	#120×C₄₃	1	2	yes	—
514	C₂×C₄	#120×C₄₃	1	2	yes	—
515	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
517	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
518	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
519	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
520	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
521	C₈	—	4	2	no	—
522	C₈	—	4	2	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
534	C₂²	C₄₃×#536	1	1	yes	characteristic
535	C₂²	C₄₃×#537	1	1	yes	characteristic
536	C₂²	C₄₃×#576	1	2	yes	—
537	C₂²	C₄₃×#578	1	2	yes	—
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	8	2	no	—
547	C₄	—	8	2	no	—
548	C₄	C₄₃×#536	1	1	yes	characteristic
549	C₄	C₄₃×#536	1	1	yes	characteristic
550	C₄	C₄₃×#537	1	1	yes	characteristic
551	C₄	C₄₃×#537	1	1	yes	characteristic
552	C₂	—	8	1	no	—
553	C₂	—	8	2	no	—
554	C₂	C₄₃×#2616	1	1	yes	characteristic
555	C₂	C₄₃×#3008	1	1	yes	characteristic
556	C₂	C₄₃×#3011	1	1	yes	characteristic
557	C₂	C₄₃×#3243	1	2	yes	—
558	C₂	C₄₃×#3262	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×#477	C₂	semidirect
3. C₂×C₄₃×#474	C₂	semidirect
4. C₄₃×#2628	C₂	semidirect
5. C₄₃×#2057	C₂	semidirect
6. C₄₃×#2042	C₂	semidirect
7. C₄₃×#2036	C₂	semidirect
9. C₄₃×#1805	C₂	semidirect
10. C₄₃×#1804	C₂	semidirect
11. C₄₃×#1798	C₂	semidirect
243. #29696	C₄₃	direct (N × H)
274. C₂×#477	C₂×C₄₃	semidirect
275. C₂×#474	C₂×C₄₃	semidirect
276. #2628	C₂×C₄₃	semidirect
277. #2057	C₂×C₄₃	semidirect
278. #2042	C₂×C₄₃	semidirect
279. #2036	C₂×C₄₃	semidirect
281. #1805	C₂×C₄₃	semidirect
282. #1804	C₂×C₄₃	semidirect
283. #1798	C₂×C₄₃	semidirect
326. C₄₃	#29696	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×#477	2
C₂×C₄₃×#474	2
C₄₃×#2628	2
C₄₃×#2057	2
C₄₃×#2042	2
C₄₃×#2036	2
C₄₃×#2033	2
C₄₃×#1805	2
C₄₃×#1804	2
C₄₃×#1798	2
#29696	43

Subgroups — C43×#29696 #24949713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29696 #24949713