Subgroups — C₄×C₄₃×#387 #24933782

Order 11008.

1742 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#387	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#1436	C₂	1	2	yes	maximal
6	C₄₃×#1436	C₂	1	2	yes	maximal
7	C₄₃×#1434	C₂	1	2	yes	maximal
8	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄×#95×C₄₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#387	C₄	1	16	yes	direct product factor
25	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
26	C₄×C₄⋊C₄×C₄₃	C₄	1	8	yes	complemented
27	C₂×#95×C₄₃	C₂²	1	2	yes	—
28	C₂×#95×C₄₃	C₂²	1	2	yes	—
29	C₂×#95×C₄₃	C₂²	1	2	yes	—
30	C₂×#95×C₄₃	C₂²	1	2	yes	—
31	C₂×#95×C₄₃	C₂²	1	2	yes	—
32	C₂×#95×C₄₃	C₂²	1	2	yes	—
33	C₂×#95×C₄₃	C₂²	1	2	yes	—
34	C₂×#95×C₄₃	C₂²	1	2	yes	—
35	C₂×#95×C₄₃	C₂²	1	2	yes	—
36	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#95×C₄₃	C₂²	1	1	yes	characteristic
38	C₄³×C₄₃	—	2	4	no	—
39	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
51	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
55	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₂×C₄²×C₄₃	—	2	4	no	—
58	C₂×C₄²×C₄₃	—	2	4	no	—
59	C₂×C₄²×C₄₃	—	2	2	no	—
60	C₂×C₄²×C₄₃	—	2	2	no	—
61	C₂×C₄²×C₄₃	—	2	2	no	—
62	C₂×C₄²×C₄₃	—	2	4	no	—
63	C₂×C₄²×C₄₃	—	2	4	no	—
64	C₂×C₄²×C₄₃	—	2	2	no	—
65	C₂×C₄²×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	4	no	—
67	C₂×C₄²×C₄₃	—	2	2	no	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	—	2	2	no	—
70	C₂×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	—	2	2	no	—
73	C₂×C₄²×C₄₃	—	2	2	no	—
74	C₂×C₄²×C₄₃	—	2	2	no	—
75	C₂×C₄²×C₄₃	—	2	2	no	—
76	C₂×C₄²×C₄₃	—	2	2	no	—
77	C₂×C₄²×C₄₃	—	2	2	no	—
78	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
81	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	—
82	C₂×C₄²×C₄₃	D₄	1	4	yes	—
83	C₂×C₄²×C₄₃	Q₈	1	4	yes	—
84	#95×C₄₃	—	2	4	no	—
85	#95×C₄₃	—	2	4	no	—
86	#95×C₄₃	—	2	4	no	—
87	#95×C₄₃	—	2	4	no	—
88	#95×C₄₃	—	2	4	no	—
89	#95×C₄₃	C₂×C₄	1	4	yes	—
90	#95×C₄₃	C₂×C₄	1	4	yes	—
91	#95×C₄₃	C₂×C₄	1	8	yes	—
92	#95×C₄₃	C₂×C₄	1	8	yes	—
93	#95×C₄₃	C₂×C₄	1	8	yes	—
94	#95×C₄₃	C₂×C₄	1	8	yes	—
95	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	1	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	2	no	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	—	2	2	no	—
123	C₂²×C₄×C₄₃	—	2	2	no	—
124	C₂²×C₄×C₄₃	—	2	2	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	2	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	2	no	—
134	C₂²×C₄×C₄₃	—	2	2	no	—
135	C₂²×C₄×C₄₃	—	2	2	no	—
136	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
139	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
144	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
148	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
149	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
153	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
154	C₂²×C₄×C₄₃	#41	1	4	yes	—
155	C₂²×C₄×C₄₃	#41	1	4	yes	—
156	C₂²×C₄×C₄₃	#41	1	4	yes	—
157	C₂²×C₄×C₄₃	#41	1	2	yes	—
158	C₂²×C₄×C₄₃	#41	1	2	yes	—
159	C₂²×C₄×C₄₃	#41	1	2	yes	—
160	C₂²×C₄×C₄₃	#41	1	2	yes	—
161	C₄⋊C₄×C₄₃	—	2	8	no	—
162	C₄⋊C₄×C₄₃	—	2	16	no	—
163	C₄⋊C₄×C₄₃	C₄²	1	16	yes	complemented
164	C₄²×C₄₃	—	2	16	no	—
165	C₄²×C₄₃	—	2	8	no	—
166	C₄²×C₄₃	—	2	16	no	—
167	C₄²×C₄₃	—	2	8	no	—
168	C₄²×C₄₃	—	2	8	no	—
169	C₄²×C₄₃	—	2	8	no	—
170	C₄²×C₄₃	—	2	8	no	—
171	C₄²×C₄₃	—	4	4	no	—
172	C₄²×C₄₃	—	4	4	no	—
173	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
174	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
175	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂³×C₄₃	C₂²×Q₈	1	1	yes	characteristic
177	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂³×C₄₃	C₂×#41	1	2	yes	—
180	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂³×C₄₃	C₂×#41	1	2	yes	—
182	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂³×C₄₃	C₂×#41	1	2	yes	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	4	no	—
191	C₂×C₄×C₄₃	—	2	4	no	—
192	C₂×C₄×C₄₃	—	2	4	no	—
193	C₂×C₄×C₄₃	—	2	4	no	—
194	C₂×C₄×C₄₃	—	2	4	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	4	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	4	no	—
202	C₂×C₄×C₄₃	—	2	4	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	4	no	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	4	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	4	no	—
209	C₂×C₄×C₄₃	—	2	4	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	4	no	—
212	C₂×C₄×C₄₃	—	2	2	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	4	no	—
216	C₂×C₄×C₄₃	—	2	4	no	—
217	C₂×C₄×C₄₃	—	2	4	no	—
218	C₂×C₄×C₄₃	—	2	4	no	—
219	C₂×C₄×C₄₃	—	2	2	no	—
220	C₂×C₄×C₄₃	—	2	2	no	—
221	C₂×C₄×C₄₃	—	2	2	no	—
222	C₂×C₄×C₄₃	—	2	4	no	—
223	C₂×C₄×C₄₃	—	2	4	no	—
224	C₂×C₄×C₄₃	—	4	2	no	—
225	C₂×C₄×C₄₃	—	4	2	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	—	4	2	no	—
233	C₂×C₄×C₄₃	—	4	2	no	—
234	C₂×C₄×C₄₃	—	4	2	no	—
235	C₂×C₄×C₄₃	—	4	2	no	—
236	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
237	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
238	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
239	C₂×C₄×C₄₃	#117	1	4	yes	—
240	C₂×C₄×C₄₃	#117	1	4	yes	—
241	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
242	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
243	C₂×C₄×C₄₃	C₄×Q₈	1	8	yes	—
244	C₂×C₄×C₄₃	C₄×Q₈	1	4	yes	—
245	C₂×C₄×C₄₃	C₂²⋊Q₈	1	4	yes	—
246	C₂×C₄×C₄₃	#123	1	4	yes	—
247	C₂×C₄×C₄₃	#125	1	4	yes	—
248	C₂×C₄×C₄₃	#126	1	4	yes	—
249	C₄×#387	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
251	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
252	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
253	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
255	C₂²×C₄₃	C₂×C₄×Q₈	1	2	yes	—
256	C₂²×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
257	C₂²×C₄₃	C₄×#41	1	2	yes	—
258	C₂²×C₄₃	C₄×#41	1	2	yes	—
259	C₂²×C₄₃	C₄×#41	1	2	yes	—
260	C₂²×C₄₃	C₄×#41	1	2	yes	—
261	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
262	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
263	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂²×C₄₃	C₂×#123	1	1	yes	characteristic
265	C₂²×C₄₃	#525	1	2	yes	—
266	C₂²×C₄₃	C₂×#125	1	1	yes	characteristic
267	C₂²×C₄₃	C₂×#126	1	1	yes	characteristic
268	C₂²×C₄₃	#529	1	2	yes	—
269	C₂²×C₄₃	#529	1	2	yes	—
270	C₂²×C₄₃	#529	1	2	yes	—
271	C₂²×C₄₃	#529	1	2	yes	—
272	C₂²×C₄₃	#533	1	2	yes	—
273	C₄×C₄₃	—	2	4	no	—
274	C₄×C₄₃	—	2	4	no	—
275	C₄×C₄₃	—	2	4	no	—
276	C₄×C₄₃	—	2	4	no	—
277	C₄×C₄₃	—	2	8	no	—
278	C₄×C₄₃	—	2	8	no	—
279	C₄×C₄₃	—	4	4	no	—
280	C₄×C₄₃	—	4	2	no	—
281	C₄×C₄₃	—	4	2	no	—
282	C₄×C₄₃	—	4	4	no	—
283	C₄×C₄₃	#387	1	8	yes	direct product factor
284	C₂×#387	C₂×C₄₃	1	2	yes	—
285	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
286	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic
287	C₂×C₄³	C₂×C₄₃	1	1	yes	characteristic
288	#1436	C₂×C₄₃	1	2	yes	—
289	#1436	C₂×C₄₃	1	2	yes	—
290	#1434	C₂×C₄₃	1	2	yes	—
291	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
292	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
293	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
294	C₄×#95	C₂×C₄₃	1	1	yes	characteristic
295	C₂×C₄₃	C₄×#117	1	1	yes	characteristic
296	C₂×C₄₃	C₄²×D₄	1	1	yes	characteristic
297	C₂×C₄₃	C₄²×Q₈	1	1	yes	characteristic
298	C₂×C₄₃	C₂×#387	1	1	yes	characteristic
299	C₂×C₄₃	#2290	1	1	yes	characteristic
300	C₂×C₄₃	#2295	1	1	yes	characteristic
301	C₂×C₄₃	#2298	1	1	yes	characteristic
302	C₂×C₄₃	C₄×#123	1	2	yes	—
303	C₂×C₄₃	C₄×C₂²⋊Q₈	1	2	yes	—
304	C₂×C₄₃	C₄×#126	1	2	yes	—
305	C₂×C₄₃	C₄×#125	1	2	yes	—
306	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
307	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
309	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
310	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
312	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
313	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
314	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
315	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
316	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
317	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
318	#387	C₄×C₄₃	1	16	yes	direct product factor
319	C₄×C₄⋊C₄	—	2	4	no	—
320	C₄×C₄⋊C₄	C₄×C₄₃	1	8	yes	complemented
321	C₂×#95	C₂²×C₄₃	1	2	yes	—
322	C₂×#95	C₂²×C₄₃	1	2	yes	—
323	C₂×#95	C₂²×C₄₃	1	2	yes	—
324	C₂×#95	C₂²×C₄₃	1	2	yes	—
325	C₂×#95	C₂²×C₄₃	1	2	yes	—
326	C₂×#95	C₂²×C₄₃	1	2	yes	—
327	C₂×#95	C₂²×C₄₃	1	2	yes	—
328	C₂×#95	C₂²×C₄₃	1	2	yes	—
329	C₂×#95	C₂²×C₄₃	1	2	yes	—
330	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
331	C₂×#95	C₂²×C₄₃	1	1	yes	characteristic
332	C₄³	—	2	4	no	—
333	C₄₃	C₄×#387	1	1	yes	characteristic, direct product factor, Sylow
334	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
336	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
338	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
342	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
343	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
349	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
350	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
351	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
352	C₂×C₄²	—	2	4	no	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	—	2	2	no	—
355	C₂×C₄²	—	2	2	no	—
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	—	2	4	no	—
358	C₂×C₄²	—	2	4	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	—	2	2	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	—	2	2	no	—
372	C₂×C₄²	—	2	2	no	—
373	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
374	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
375	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
376	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	—
377	C₂×C₄²	D₄×C₄₃	1	4	yes	—
378	C₂×C₄²	Q₈×C₄₃	1	4	yes	—
379	#95	—	2	4	no	—
380	#95	—	2	4	no	—
381	#95	—	2	4	no	—
382	#95	—	2	4	no	—
383	#95	—	2	4	no	—
384	#95	C₂×C₄×C₄₃	1	4	yes	—
385	#95	C₂×C₄×C₄₃	1	4	yes	—
386	#95	C₂×C₄×C₄₃	1	8	yes	—
387	#95	C₂×C₄×C₄₃	1	8	yes	—
388	#95	C₂×C₄×C₄₃	1	8	yes	—
389	#95	C₂×C₄×C₄₃	1	8	yes	—
390	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
432	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
433	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
434	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
435	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
436	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
437	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
438	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
439	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
440	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
441	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
442	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
443	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
444	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
445	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
447	C₂²×C₄	C₂×Q₈×C₄₃	1	4	yes	—
448	C₂²×C₄	C₂×Q₈×C₄₃	1	2	yes	—
449	C₂²×C₄	#41×C₄₃	1	4	yes	—
450	C₂²×C₄	#41×C₄₃	1	4	yes	—
451	C₂²×C₄	#41×C₄₃	1	4	yes	—
452	C₂²×C₄	#41×C₄₃	1	2	yes	—
453	C₂²×C₄	#41×C₄₃	1	2	yes	—
454	C₂²×C₄	#41×C₄₃	1	2	yes	—
455	C₂²×C₄	#41×C₄₃	1	2	yes	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	16	no	—
458	C₄⋊C₄	C₄²×C₄₃	1	16	yes	complemented
459	C₄²	—	2	16	no	—
460	C₄²	—	2	8	no	—
461	C₄²	—	2	16	no	—
462	C₄²	—	2	8	no	—
463	C₄²	—	2	8	no	—
464	C₄²	—	2	8	no	—
465	C₄²	—	2	8	no	—
466	C₄²	—	4	4	no	—
467	C₄²	—	4	4	no	—
468	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
469	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
470	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
471	C₂³	C₂²×Q₈×C₄₃	1	1	yes	characteristic
472	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
473	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
474	C₂³	C₂×#41×C₄₃	1	2	yes	—
475	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
476	C₂³	C₂×#41×C₄₃	1	2	yes	—
477	C₂³	C₂×#41×C₄₃	1	1	yes	characteristic
478	C₂³	C₂×#41×C₄₃	1	2	yes	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	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	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
532	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
533	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
534	C₂×C₄	#117×C₄₃	1	4	yes	—
535	C₂×C₄	#117×C₄₃	1	4	yes	—
536	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
537	C₂×C₄	C₄×D₄×C₄₃	1	4	yes	—
538	C₂×C₄	C₄×Q₈×C₄₃	1	8	yes	—
539	C₂×C₄	C₄×Q₈×C₄₃	1	4	yes	—
540	C₂×C₄	C₂²⋊Q₈×C₄₃	1	4	yes	—
541	C₂×C₄	#123×C₄₃	1	4	yes	—
542	C₂×C₄	#125×C₄₃	1	4	yes	—
543	C₂×C₄	#126×C₄₃	1	4	yes	—
544	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
545	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
546	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
547	C₂²	C₂×C₄×D₄×C₄₃	1	1	yes	characteristic
548	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
549	C₂²	C₂×C₄×Q₈×C₄₃	1	1	yes	characteristic
550	C₂²	C₂×C₄×Q₈×C₄₃	1	2	yes	—
551	C₂²	C₄×#41×C₄₃	1	2	yes	—
552	C₂²	C₄×#41×C₄₃	1	2	yes	—
553	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
554	C₂²	C₄×#41×C₄₃	1	2	yes	—
555	C₂²	C₄×#41×C₄₃	1	1	yes	characteristic
556	C₂²	C₄×#41×C₄₃	1	2	yes	—
557	C₂²	C₂×C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
558	C₂²	C₂×#123×C₄₃	1	1	yes	characteristic
559	C₂²	C₄₃×#525	1	2	yes	—
560	C₂²	C₂×#125×C₄₃	1	1	yes	characteristic
561	C₂²	C₂×#126×C₄₃	1	1	yes	characteristic
562	C₂²	C₄₃×#529	1	2	yes	—
563	C₂²	C₄₃×#529	1	2	yes	—
564	C₂²	C₄₃×#529	1	2	yes	—
565	C₂²	C₄₃×#529	1	2	yes	—
566	C₂²	C₄₃×#533	1	2	yes	—
567	C₄	—	2	4	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	8	no	—
572	C₄	—	2	8	no	—
573	C₄	—	4	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	4	no	—
576	C₄	—	4	4	no	—
577	C₄	C₄₃×#387	1	8	yes	direct product factor
578	C₂	C₄×#117×C₄₃	1	1	yes	characteristic
579	C₂	C₄²×D₄×C₄₃	1	1	yes	characteristic
580	C₂	C₄²×Q₈×C₄₃	1	1	yes	characteristic
581	C₂	C₂×C₄₃×#387	1	1	yes	characteristic
582	C₂	C₄₃×#2290	1	1	yes	characteristic
583	C₂	C₄₃×#2295	1	1	yes	characteristic
584	C₂	C₄₃×#2298	1	1	yes	characteristic
585	C₂	C₄×#123×C₄₃	1	2	yes	—
586	C₂	C₄×C₂²⋊Q₈×C₄₃	1	2	yes	—
587	C₂	C₄×#126×C₄₃	1	2	yes	—
588	C₂	C₄×#125×C₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₃	C₂³
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
socle, prime radical	C₂⁴×C₄₃	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
24. C₄₃×#387	C₄	direct (N × H)
26. C₄×C₄⋊C₄×C₄₃	C₄	semidirect
163. C₄⋊C₄×C₄₃	C₄²	semidirect
249. C₄×#387	C₄₃	direct (N × H)
283. C₄×C₄₃	#387	direct (N × H)
318. #387	C₄×C₄₃	direct (N × H)
320. C₄×C₄⋊C₄	C₄×C₄₃	semidirect
333. C₄₃	C₄×#387	direct (N × H)
458. C₄⋊C₄	C₄²×C₄₃	semidirect
577. C₄	C₄₃×#387	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×#387	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄³×C₄₃	2
C₄₃×#1436	2
C₄₃×#1434	2
C₄×#95×C₄₃	2
C₄×#387	43

Subgroups — C4×C43×#387 #24933782

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×#387 #24933782