Subgroups — C₄₃×#17602 #24937619

Order 11008.

938 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3522	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2320	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1521	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1517	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1514	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1512	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1509	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1505	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1502	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1500	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₃×#559	C₄	1	2	yes	complemented
13	C₄₃×#559	C₄	1	1	yes	characteristic, complemented
14	Q₈²×C₄₃	C₄	1	1	yes	characteristic, complemented
15	C₄₃×#554	C₄	1	1	yes	characteristic, complemented
16	C₄₃×#554	C₄	1	2	yes	complemented
17	C₄₃×#550	C₄	1	1	yes	characteristic, complemented
18	C₄₃×#548	—	2	1	no	—
19	C₄₃×#547	—	2	2	no	—
20	C₄₃×#547	—	2	1	no	—
21	C₄₃×#542	—	2	1	no	—
22	C₄₃×#542	—	2	2	no	—
23	C₄₃×#532	C₂²	1	1	yes	characteristic
24	C₄₃×#532	C₂²	1	2	yes	—
25	C₄₃×#529	C₂²	1	1	yes	characteristic
26	C₄₃×#529	C₂²	1	2	yes	—
27	C₄₃×#520	—	2	1	no	—
28	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#446	—	2	1	no	—
30	C₄₃×#446	—	2	2	no	—
31	C₈×Q₈×C₄₃	—	2	1	no	—
32	C₄₃×#432	C₂²	1	1	yes	characteristic
33	C₄₃×#432	C₂²	1	2	yes	—
34	C₄₃×#431	C₂²	1	1	yes	characteristic
35	C₄₃×#431	C₂²	1	2	yes	—
36	C₄₃×#391	—	2	1	no	—
37	C₄₃×#389	—	2	1	no	—
38	C₄₃×#387	—	2	2	no	—
39	C₄₃×#383	C₂²	1	2	yes	—
40	C₄₃×#382	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#376	C₂²	1	1	yes	characteristic
43	C₄₃×#328	C₂²	1	1	yes	characteristic
44	C₄₃×#328	C₂²	1	1	yes	characteristic
45	C₄₃×#328	C₂²	1	2	yes	—
46	C₄₃×#327	C₂²	1	1	yes	characteristic
47	C₄₃×#327	C₂²	1	1	yes	characteristic
48	C₄₃×#327	C₂²	1	2	yes	—
49	C₄₃×#327	C₂²	1	2	yes	—
50	C₄₃×#327	C₂²	1	2	yes	—
51	C₄₃×#327	C₂²	1	2	yes	—
52	C₄₃×#327	C₂²	1	2	yes	—
53	C₂×#41×C₄₃	—	2	1	no	—
54	C₂×#41×C₄₃	—	2	1	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₃	—	2	2	no	—
58	C₄⋊Q₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
61	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
62	#127×C₄₃	C₂×C₄	1	2	yes	—
63	#126×C₄₃	—	2	2	no	—
64	#126×C₄₃	—	2	1	no	—
65	#125×C₄₃	C₂×C₄	1	1	yes	characteristic
66	#125×C₄₃	C₂×C₄	1	2	yes	—
67	#124×C₄₃	—	2	1	no	—
68	#124×C₄₃	—	2	2	no	—
69	#124×C₄₃	—	2	2	no	—
70	#124×C₄₃	—	2	1	no	—
71	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
72	#124×C₄₃	C₂×C₄	1	2	yes	—
73	#123×C₄₃	—	2	1	no	—
74	#123×C₄₃	—	2	2	no	—
75	#123×C₄₃	—	2	2	no	—
76	#123×C₄₃	—	2	2	no	—
77	#123×C₄₃	—	2	2	no	—
78	C₂²⋊Q₈×C₄₃	—	2	1	no	—
79	C₂²⋊Q₈×C₄₃	—	2	2	no	—
80	C₂²⋊Q₈×C₄₃	—	2	2	no	—
81	C₂²⋊Q₈×C₄₃	—	2	2	no	—
82	C₂²⋊Q₈×C₄₃	—	2	2	no	—
83	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	#121×C₄₃	—	2	1	no	—
85	#121×C₄₃	—	2	2	no	—
86	#121×C₄₃	—	2	2	no	—
87	#121×C₄₃	—	2	1	no	—
88	#121×C₄₃	C₂³	1	1	yes	characteristic
89	#121×C₄₃	C₂³	1	2	yes	—
90	C₄×Q₈×C₄₃	—	2	1	no	—
91	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
93	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
96	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₄₃	D₄	1	2	yes	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₄×D₄×C₄₃	—	2	2	no	—
101	C₄×D₄×C₄₃	—	2	2	no	—
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	—	2	1	no	—
104	C₄×D₄×C₄₃	—	2	2	no	—
105	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
107	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
108	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
109	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
110	#117×C₄₃	—	2	1	no	—
111	#117×C₄₃	—	2	2	no	—
112	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
114	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
115	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
117	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	—	2	1	no	—
119	C₂×C₄²×C₄₃	—	2	1	no	—
120	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
122	C₄⋊C₈×C₄₃	—	2	2	no	—
123	C₄⋊C₈×C₄₃	—	2	1	no	—
124	C₄⋊C₈×C₄₃	—	2	1	no	—
125	C₄⋊C₈×C₄₃	—	2	2	no	—
126	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
128	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
129	#97×C₄₃	—	2	2	no	—
130	#97×C₄₃	—	2	1	no	—
131	C₄×C₈×C₄₃	—	2	1	no	—
132	C₄×C₈×C₄₃	—	2	2	no	—
133	#95×C₄₃	—	2	1	no	—
134	#95×C₄₃	—	2	2	no	—
135	#95×C₄₃	—	2	2	no	—
136	#95×C₄₃	—	2	2	no	—
137	#95×C₄₃	C₂³	1	1	yes	characteristic
138	#95×C₄₃	C₂³	1	1	yes	characteristic
139	#95×C₄₃	C₂³	1	2	yes	—
140	#41×C₄₃	—	4	4	no	—
141	#41×C₄₃	—	8	1	no	—
142	#41×C₄₃	—	8	2	no	—
143	#41×C₄₃	—	8	1	no	—
144	#41×C₄₃	—	8	2	no	—
145	C₂×Q₈×C₄₃	—	2	2	no	—
146	C₂×Q₈×C₄₃	—	2	1	no	—
147	C₂×Q₈×C₄₃	—	4	2	no	—
148	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
151	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₄₃	—	2	2	no	—
153	C₂×D₄×C₄₃	—	2	1	no	—
154	C₂×D₄×C₄₃	—	2	2	no	—
155	C₂×D₄×C₄₃	—	2	1	no	—
156	C₂×D₄×C₄₃	—	2	1	no	—
157	C₂×D₄×C₄₃	—	2	2	no	—
158	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₄₃	—	2	2	no	—
161	C₂²×C₄×C₄₃	—	2	1	no	—
162	C₂²×C₄×C₄₃	—	2	2	no	—
163	C₂²×C₄×C₄₃	—	2	2	no	—
164	C₂²×C₄×C₄₃	—	2	2	no	—
165	C₂²×C₄×C₄₃	—	2	1	no	—
166	C₂²×C₄×C₄₃	—	2	1	no	—
167	C₂²×C₄×C₄₃	—	2	2	no	—
168	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	2	1	no	—
175	C₂×C₈×C₄₃	—	2	2	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	—	2	1	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	—	2	2	no	—
182	C₄⋊C₄×C₄₃	—	2	2	no	—
183	C₄⋊C₄×C₄₃	—	2	1	no	—
184	C₄⋊C₄×C₄₃	—	2	1	no	—
185	C₄⋊C₄×C₄₃	—	4	2	no	—
186	C₄⋊C₄×C₄₃	—	8	2	no	—
187	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
188	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
189	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
190	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
191	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
192	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
193	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
194	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
196	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
201	C₂²⋊C₄×C₄₃	—	2	2	no	—
202	C₂²⋊C₄×C₄₃	—	2	1	no	—
203	C₂²⋊C₄×C₄₃	—	2	2	no	—
204	C₂²⋊C₄×C₄₃	—	2	2	no	—
205	C₂²⋊C₄×C₄₃	—	2	2	no	—
206	C₂²⋊C₄×C₄₃	—	2	1	no	—
207	C₂²⋊C₄×C₄₃	—	2	2	no	—
208	C₂²⋊C₄×C₄₃	—	2	1	no	—
209	C₄²×C₄₃	—	2	2	no	—
210	C₄²×C₄₃	—	2	1	no	—
211	C₄²×C₄₃	—	4	2	no	—
212	C₄²×C₄₃	—	8	1	no	—
213	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
215	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
216	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₄₃	C₂×D₄	1	2	yes	—
219	C₄²×C₄₃	C₂×D₄	1	2	yes	—
220	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₄₃	—	2	2	no	—
222	C₂³×C₄₃	—	2	1	no	—
223	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	Q₈×C₄₃	—	2	2	no	—
225	Q₈×C₄₃	—	2	2	no	—
226	Q₈×C₄₃	—	4	2	no	—
227	Q₈×C₄₃	—	4	1	no	—
228	Q₈×C₄₃	—	8	1	no	—
229	Q₈×C₄₃	—	8	2	no	—
230	D₄×C₄₃	—	4	1	no	—
231	D₄×C₄₃	—	4	2	no	—
232	D₄×C₄₃	—	4	4	no	—
233	D₄×C₄₃	—	4	2	no	—
234	D₄×C₄₃	—	4	1	no	—
235	D₄×C₄₃	—	4	1	no	—
236	D₄×C₄₃	—	4	2	no	—
237	D₄×C₄₃	—	4	2	no	—
238	D₄×C₄₃	—	8	1	no	—
239	D₄×C₄₃	—	8	2	no	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	2	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	2	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	2	1	no	—
246	C₂×C₄×C₄₃	—	2	2	no	—
247	C₂×C₄×C₄₃	—	2	1	no	—
248	C₂×C₄×C₄₃	—	2	1	no	—
249	C₂×C₄×C₄₃	—	4	2	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	—	4	4	no	—
252	C₂×C₄×C₄₃	—	4	2	no	—
253	C₂×C₄×C₄₃	—	4	1	no	—
254	C₂×C₄×C₄₃	—	4	1	no	—
255	C₂×C₄×C₄₃	—	4	2	no	—
256	C₂×C₄×C₄₃	—	4	1	no	—
257	C₂×C₄×C₄₃	—	4	1	no	—
258	C₂×C₄×C₄₃	—	4	2	no	—
259	C₂×C₄×C₄₃	—	4	2	no	—
260	C₂×C₄×C₄₃	—	4	1	no	—
261	C₂×C₄×C₄₃	—	4	1	no	—
262	C₂×C₄×C₄₃	—	8	2	no	—
263	C₂×C₄×C₄₃	—	8	2	no	—
264	C₂×C₄×C₄₃	—	8	2	no	—
265	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
268	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
270	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
271	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
275	C₈×C₄₃	—	4	1	no	—
276	C₈×C₄₃	—	4	1	no	—
277	C₈×C₄₃	—	4	2	no	—
278	#17602	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂²×C₄₃	—	2	1	no	—
280	C₂²×C₄₃	—	2	1	no	—
281	C₂²×C₄₃	—	4	2	no	—
282	C₂²×C₄₃	—	4	1	no	—
283	C₂²×C₄₃	—	4	2	no	—
284	C₂²×C₄₃	—	4	1	no	—
285	C₂²×C₄₃	—	4	2	no	—
286	C₂²×C₄₃	—	4	1	no	—
287	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
288	C₂²×C₄₃	#576	1	1	yes	characteristic
289	C₂²×C₄₃	#577	1	1	yes	characteristic
290	C₄×C₄₃	—	2	1	no	—
291	C₄×C₄₃	—	2	1	no	—
292	C₄×C₄₃	—	2	1	no	—
293	C₄×C₄₃	—	2	2	no	—
294	C₄×C₄₃	—	2	1	no	—
295	C₄×C₄₃	—	2	2	no	—
296	C₄×C₄₃	—	2	1	no	—
297	C₄×C₄₃	—	2	2	no	—
298	C₄×C₄₃	—	2	2	no	—
299	C₄×C₄₃	—	4	1	no	—
300	C₄×C₄₃	—	4	2	no	—
301	C₄×C₄₃	—	4	1	no	—
302	C₄×C₄₃	—	4	1	no	—
303	C₄×C₄₃	—	8	1	no	—
304	C₄×C₄₃	—	8	2	no	—
305	C₄×C₄₃	—	8	1	no	—
306	C₄×C₄₃	#421	1	2	yes	—
307	#3522	C₂×C₄₃	1	1	yes	characteristic
308	#2984	C₂×C₄₃	1	1	yes	characteristic, complemented
309	#2320	C₂×C₄₃	1	1	yes	characteristic, complemented
310	#1521	C₂×C₄₃	1	2	yes	complemented
311	#1517	C₂×C₄₃	1	2	yes	complemented
312	#1514	C₂×C₄₃	1	2	yes	complemented
313	#1512	C₂×C₄₃	1	2	yes	complemented
314	#1509	C₂×C₄₃	1	1	yes	characteristic, complemented
315	#1505	C₂×C₄₃	1	1	yes	characteristic, complemented
316	#1502	C₂×C₄₃	1	1	yes	characteristic, complemented
317	#1500	C₂×C₄₃	1	1	yes	characteristic, complemented
318	C₂×C₄₃	—	2	1	no	—
319	C₂×C₄₃	—	2	1	no	—
320	C₂×C₄₃	—	8	2	no	—
321	C₂×C₄₃	—	8	1	no	—
322	C₂×C₄₃	#2884	1	1	yes	characteristic
323	C₂×C₄₃	#2897	1	1	yes	characteristic
324	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
325	#559	C₄×C₄₃	1	2	yes	complemented
326	#559	C₄×C₄₃	1	1	yes	characteristic, complemented
327	Q₈²	C₄×C₄₃	1	1	yes	characteristic, complemented
328	#554	C₄×C₄₃	1	1	yes	characteristic, complemented
329	#554	C₄×C₄₃	1	2	yes	complemented
330	#550	C₄×C₄₃	1	1	yes	characteristic, complemented
331	#548	—	2	1	no	—
332	#547	—	2	2	no	—
333	#547	—	2	1	no	—
334	#542	—	2	1	no	—
335	#542	—	2	2	no	—
336	#532	C₂²×C₄₃	1	1	yes	characteristic
337	#532	C₂²×C₄₃	1	2	yes	—
338	#529	C₂²×C₄₃	1	1	yes	characteristic
339	#529	C₂²×C₄₃	1	2	yes	—
340	#520	—	2	1	no	—
341	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
342	#446	—	2	1	no	—
343	#446	—	2	2	no	—
344	C₈×Q₈	—	2	1	no	—
345	#432	C₂²×C₄₃	1	1	yes	characteristic
346	#432	C₂²×C₄₃	1	2	yes	—
347	#431	C₂²×C₄₃	1	1	yes	characteristic
348	#431	C₂²×C₄₃	1	2	yes	—
349	#391	—	2	1	no	—
350	#389	—	2	1	no	—
351	#387	—	2	2	no	—
352	#383	C₂²×C₄₃	1	2	yes	—
353	#382	C₂²×C₄₃	1	2	yes	—
354	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
355	#376	C₂²×C₄₃	1	1	yes	characteristic
356	#328	C₂²×C₄₃	1	1	yes	characteristic
357	#328	C₂²×C₄₃	1	1	yes	characteristic
358	#328	C₂²×C₄₃	1	2	yes	—
359	#327	C₂²×C₄₃	1	1	yes	characteristic
360	#327	C₂²×C₄₃	1	1	yes	characteristic
361	#327	C₂²×C₄₃	1	2	yes	—
362	#327	C₂²×C₄₃	1	2	yes	—
363	#327	C₂²×C₄₃	1	2	yes	—
364	#327	C₂²×C₄₃	1	2	yes	—
365	#327	C₂²×C₄₃	1	2	yes	—
366	C₄₃	#17602	1	1	yes	characteristic, direct product factor, Sylow
367	C₂×#41	—	2	1	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	2	no	—
370	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	2	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
374	C₄⋊Q₈	C₂×C₄×C₄₃	1	2	yes	—
375	#127	C₂×C₄×C₄₃	1	1	yes	characteristic
376	#127	C₂×C₄×C₄₃	1	2	yes	—
377	#126	—	2	2	no	—
378	#126	—	2	1	no	—
379	#125	C₂×C₄×C₄₃	1	1	yes	characteristic
380	#125	C₂×C₄×C₄₃	1	2	yes	—
381	#124	—	2	1	no	—
382	#124	—	2	2	no	—
383	#124	—	2	2	no	—
384	#124	—	2	1	no	—
385	#124	C₂×C₄×C₄₃	1	1	yes	characteristic
386	#124	C₂×C₄×C₄₃	1	2	yes	—
387	#123	—	2	1	no	—
388	#123	—	2	2	no	—
389	#123	—	2	2	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	1	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	2	no	—
395	C₂²⋊Q₈	—	2	2	no	—
396	C₂²⋊Q₈	—	2	2	no	—
397	C₂²⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
398	#121	—	2	1	no	—
399	#121	—	2	2	no	—
400	#121	—	2	2	no	—
401	#121	—	2	1	no	—
402	#121	C₂³×C₄₃	1	1	yes	characteristic
403	#121	C₂³×C₄₃	1	2	yes	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
406	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
407	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
408	C₄×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
409	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
410	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
411	C₄×Q₈	D₄×C₄₃	1	1	yes	characteristic
412	C₄×Q₈	D₄×C₄₃	1	2	yes	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	2	1	no	—
417	C₄×D₄	—	2	1	no	—
418	C₄×D₄	—	2	2	no	—
419	C₄×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
420	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
421	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
422	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
423	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
424	#117	—	2	1	no	—
425	#117	—	2	2	no	—
426	C₂×C₄⋊C₄	—	2	2	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	2	no	—
430	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
431	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
432	C₂×C₄²	—	2	1	no	—
433	C₂×C₄²	—	2	1	no	—
434	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
436	C₄⋊C₈	—	2	2	no	—
437	C₄⋊C₈	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	2	no	—
440	C₂²⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
441	C₂²⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
442	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
443	#97	—	2	2	no	—
444	#97	—	2	1	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	—	2	2	no	—
447	#95	—	2	1	no	—
448	#95	—	2	2	no	—
449	#95	—	2	2	no	—
450	#95	—	2	2	no	—
451	#95	C₂³×C₄₃	1	1	yes	characteristic
452	#95	C₂³×C₄₃	1	1	yes	characteristic
453	#95	C₂³×C₄₃	1	2	yes	—
454	#41	—	4	4	no	—
455	#41	—	8	1	no	—
456	#41	—	8	2	no	—
457	#41	—	8	1	no	—
458	#41	—	8	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	4	2	no	—
462	C₂×Q₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
463	C₂×Q₈	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
464	C₂×Q₈	C₂²⋊C₄×C₄₃	1	2	yes	—
465	C₂×Q₈	C₂²×C₄×C₄₃	1	1	yes	characteristic
466	C₂×D₄	—	2	1	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
473	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	2	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
484	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	2	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	8	2	no	—
501	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
502	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
504	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
506	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
507	C₄⋊C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
508	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
510	C₄⋊C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
511	C₂²⋊C₄	—	2	1	no	—
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	2	no	—
514	C₂²⋊C₄	—	2	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	1	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	4	2	no	—
526	C₄²	—	8	1	no	—
527	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
528	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
529	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
530	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
531	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
532	C₄²	C₂×D₄×C₄₃	1	2	yes	—
533	C₄²	C₂×D₄×C₄₃	1	2	yes	—
534	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
535	C₂³	—	2	2	no	—
536	C₂³	—	2	1	no	—
537	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
538	Q₈	—	2	2	no	—
539	Q₈	—	2	2	no	—
540	Q₈	—	4	2	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	8	1	no	—
543	Q₈	—	8	2	no	—
544	D₄	—	4	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	1	no	—
549	D₄	—	4	1	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	8	1	no	—
553	D₄	—	8	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	—	8	2	no	—
578	C₂×C₄	—	8	2	no	—
579	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
580	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
581	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
582	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
583	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
584	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
585	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
586	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
589	C₈	—	4	1	no	—
590	C₈	—	4	1	no	—
591	C₈	—	4	2	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	2	1	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	1	no	—
600	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
601	C₂²	C₄₃×#576	1	1	yes	characteristic
602	C₂²	C₄₃×#577	1	1	yes	characteristic
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	2	no	—
612	C₄	—	4	1	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	1	no	—
615	C₄	—	4	1	no	—
616	C₄	—	8	1	no	—
617	C₄	—	8	2	no	—
618	C₄	—	8	1	no	—
619	C₄	C₄₃×#421	1	2	yes	—
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	8	2	no	—
623	C₂	—	8	1	no	—
624	C₂	C₄₃×#2884	1	1	yes	characteristic
625	C₂	C₄₃×#2897	1	1	yes	characteristic
626	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₄₃×#3522	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂×C₄×Q₈×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2984	C₂	semidirect
3. C₄₃×#2320	C₂	semidirect
4. C₄₃×#1521	C₂	semidirect
5. C₄₃×#1517	C₂	semidirect
6. C₄₃×#1514	C₂	semidirect
7. C₄₃×#1512	C₂	semidirect
8. C₄₃×#1509	C₂	semidirect
9. C₄₃×#1505	C₂	semidirect
10. C₄₃×#1502	C₂	semidirect
11. C₄₃×#1500	C₂	semidirect
12. C₄₃×#559	C₄	semidirect
13. C₄₃×#559	C₄	semidirect
14. Q₈²×C₄₃	C₄	semidirect
15. C₄₃×#554	C₄	semidirect
16. C₄₃×#554	C₄	semidirect
17. C₄₃×#550	C₄	semidirect
278. #17602	C₄₃	direct (N × H)
308. #2984	C₂×C₄₃	semidirect
309. #2320	C₂×C₄₃	semidirect
310. #1521	C₂×C₄₃	semidirect
311. #1517	C₂×C₄₃	semidirect
312. #1514	C₂×C₄₃	semidirect
313. #1512	C₂×C₄₃	semidirect
314. #1509	C₂×C₄₃	semidirect
315. #1505	C₂×C₄₃	semidirect
316. #1502	C₂×C₄₃	semidirect
317. #1500	C₂×C₄₃	semidirect
325. #559	C₄×C₄₃	semidirect
326. #559	C₄×C₄₃	semidirect
327. Q₈²	C₄×C₄₃	semidirect
328. #554	C₄×C₄₃	semidirect
329. #554	C₄×C₄₃	semidirect
330. #550	C₄×C₄₃	semidirect
366. C₄₃	#17602	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×#3522	2
C₄₃×#2984	2
C₄₃×#2320	2
C₄₃×#1521	2
C₄₃×#1517	2
C₄₃×#1514	2
C₄₃×#1512	2
C₄₃×#1509	2
C₄₃×#1505	2
C₄₃×#1502	2
C₄₃×#1500	2
#17602	43

Subgroups — C43×#17602 #24937619

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#17602 #24937619