Subgroups — C₄×C₄₃×#390 #24933783

Order 11008.

2894 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#390	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊C₄×C₄₃	C₂	1	4	yes	maximal, complemented
5	C₂×C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₃×#1437	C₂	1	4	yes	maximal, complemented
7	C₄₃×C₄⋊#95	C₂	1	2	yes	maximal, complemented
8	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂×C₄×D₄×C₄₃	—	2	4	no	—
11	C₂×C₄×D₄×C₄₃	—	2	4	no	—
12	C₂×C₄×D₄×C₄₃	C₄	1	8	yes	complemented
13	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
16	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	8	yes	—
17	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₄₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#390	C₄	1	16	yes	direct product factor
23	C₄×C₄⋊C₄×C₄₃	—	2	4	no	—
24	C₄×C₂²⋊C₄×C₄₃	—	2	16	no	—
25	C₂×#95×C₄₃	C₂²	1	8	yes	—
26	C₂×#95×C₄₃	C₂²	1	2	yes	—
27	C₄³×C₄₃	—	2	4	no	—
28	C₂⁵×C₄₃	C₂³	1	2	yes	—
29	C₂²×D₄×C₄₃	—	2	2	no	—
30	C₂²×D₄×C₄₃	—	2	2	no	—
31	C₂²×D₄×C₄₃	—	2	4	no	—
32	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
33	C₂²×D₄×C₄₃	C₂×C₄	1	8	yes	—
34	C₂³×C₄×C₄₃	—	2	4	no	—
35	C₂³×C₄×C₄₃	—	2	4	no	—
36	C₂³×C₄×C₄₃	—	2	8	no	—
37	C₂³×C₄×C₄₃	—	2	8	no	—
38	C₂³×C₄×C₄₃	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
40	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
45	C₄×D₄×C₄₃	—	2	32	no	—
46	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
50	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	complemented
52	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
53	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
54	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
55	C₂×C₂²⋊C₄×C₄₃	—	2	16	no	—
56	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
57	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	32	yes	complemented
58	C₂×C₄²×C₄₃	—	2	4	no	—
59	C₂×C₄²×C₄₃	—	2	4	no	—
60	C₂×C₄²×C₄₃	—	2	4	no	—
61	C₂×C₄²×C₄₃	—	2	8	no	—
62	C₂×C₄²×C₄₃	—	2	4	no	—
63	C₂×C₄²×C₄₃	—	2	4	no	—
64	C₂×C₄²×C₄₃	—	2	8	no	—
65	C₂×C₄²×C₄₃	—	2	4	no	—
66	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₄₃	C₂×C₄	1	8	yes	complemented
68	C₂×C₄²×C₄₃	D₄	1	4	yes	—
69	C₂×C₄²×C₄₃	D₄	1	4	yes	—
70	C₂×C₄²×C₄₃	D₄	1	8	yes	complemented
71	#95×C₄₃	—	2	16	no	—
72	#95×C₄₃	—	2	4	no	—
73	C₂⁴×C₄₃	—	2	4	no	—
74	C₂⁴×C₄₃	—	2	2	no	—
75	C₂⁴×C₄₃	—	2	2	no	—
76	C₂⁴×C₄₃	—	2	8	no	—
77	C₂⁴×C₄₃	—	2	4	no	—
78	C₂⁴×C₄₃	—	2	4	no	—
79	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
80	C₂⁴×C₄₃	C₂²×C₄	1	8	yes	—
81	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
82	C₂×D₄×C₄₃	—	2	8	no	—
83	C₂×D₄×C₄₃	—	2	8	no	—
84	C₂×D₄×C₄₃	—	2	16	no	—
85	C₂×D₄×C₄₃	—	2	16	no	—
86	C₂×D₄×C₄₃	C₄²	1	16	yes	complemented
87	C₂²×C₄×C₄₃	—	2	16	no	—
88	C₂²×C₄×C₄₃	—	2	32	no	—
89	C₂²×C₄×C₄₃	—	2	4	no	—
90	C₂²×C₄×C₄₃	—	2	4	no	—
91	C₂²×C₄×C₄₃	—	2	8	no	—
92	C₂²×C₄×C₄₃	—	2	4	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	4	no	—
97	C₂²×C₄×C₄₃	—	2	4	no	—
98	C₂²×C₄×C₄₃	—	2	4	no	—
99	C₂²×C₄×C₄₃	—	2	8	no	—
100	C₂²×C₄×C₄₃	—	2	4	no	—
101	C₂²×C₄×C₄₃	—	2	4	no	—
102	C₂²×C₄×C₄₃	—	4	16	no	—
103	C₂²×C₄×C₄₃	—	4	8	no	—
104	C₂²×C₄×C₄₃	—	4	8	no	—
105	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
106	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
107	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
111	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	8	yes	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₄₃	#41	1	8	yes	—
121	C₂²×C₄×C₄₃	#41	1	4	yes	—
122	C₂²×C₄×C₄₃	#41	1	4	yes	—
123	C₄⋊C₄×C₄₃	—	2	8	no	—
124	C₄⋊C₄×C₄₃	—	2	16	no	—
125	C₂²⋊C₄×C₄₃	—	2	16	no	—
126	C₂²⋊C₄×C₄₃	—	2	64	no	—
127	C₄²×C₄₃	—	2	16	no	—
128	C₄²×C₄₃	—	2	16	no	—
129	C₄²×C₄₃	—	2	16	no	—
130	C₄²×C₄₃	—	4	8	no	—
131	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	complemented
132	C₂³×C₄₃	—	2	4	no	—
133	C₂³×C₄₃	—	2	4	no	—
134	C₂³×C₄₃	—	2	16	no	—
135	C₂³×C₄₃	—	2	8	no	—
136	C₂³×C₄₃	—	2	8	no	—
137	C₂³×C₄₃	—	2	8	no	—
138	C₂³×C₄₃	—	2	8	no	—
139	C₂³×C₄₃	—	2	16	no	—
140	C₂³×C₄₃	—	4	4	no	—
141	C₂³×C₄₃	—	4	4	no	—
142	C₂³×C₄₃	—	4	2	no	—
143	C₂³×C₄₃	—	4	8	no	—
144	C₂³×C₄₃	—	4	2	no	—
145	C₂³×C₄₃	—	4	8	no	—
146	C₂³×C₄₃	—	4	4	no	—
147	C₂³×C₄₃	C₂×C₄²	1	8	yes	—
148	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
149	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
150	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
151	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
152	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
153	C₂³×C₄₃	C₂×#41	1	2	yes	—
154	C₂³×C₄₃	C₂×#41	1	2	yes	—
155	C₂³×C₄₃	C₂×#41	1	4	yes	—
156	D₄×C₄₃	—	2	32	no	—
157	C₂×C₄×C₄₃	—	2	8	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	8	no	—
160	C₂×C₄×C₄₃	—	2	8	no	—
161	C₂×C₄×C₄₃	—	2	4	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	8	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	8	no	—
166	C₂×C₄×C₄₃	—	2	4	no	—
167	C₂×C₄×C₄₃	—	2	16	no	—
168	C₂×C₄×C₄₃	—	2	8	no	—
169	C₂×C₄×C₄₃	—	2	8	no	—
170	C₂×C₄×C₄₃	—	4	4	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	4	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	8	no	—
175	C₂×C₄×C₄₃	—	4	4	no	—
176	C₂×C₄×C₄₃	—	4	32	no	—
177	C₂×C₄×C₄₃	C₂×C₄²	1	4	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
179	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
180	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₄₃	#117	1	4	yes	—
182	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
183	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
184	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
185	C₂×C₄×C₄₃	C₄×D₄	1	16	yes	complemented
186	C₂×C₄×C₄₃	#121	1	8	yes	—
187	C₂×C₄×C₄₃	#124	1	4	yes	—
188	C₂×C₄×C₄₃	#127	1	4	yes	—
189	C₄×#390	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂²×C₄₃	—	2	8	no	—
191	C₂²×C₄₃	—	2	16	no	—
192	C₂²×C₄₃	—	4	8	no	—
193	C₂²×C₄₃	—	4	4	no	—
194	C₂²×C₄₃	—	4	8	no	—
195	C₂²×C₄₃	—	4	4	no	—
196	C₂²×C₄₃	—	4	16	no	—
197	C₂²×C₄₃	—	4	8	no	—
198	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
199	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
201	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
202	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
203	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
204	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
205	C₂²×C₄₃	C₄×#41	1	2	yes	—
206	C₂²×C₄₃	C₄×#41	1	4	yes	—
207	C₂²×C₄₃	C₂×#121	1	2	yes	—
208	C₂²×C₄₃	#525	1	2	yes	—
209	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
210	C₂²×C₄₃	#529	1	4	yes	—
211	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
212	C₂²×C₄₃	#532	1	4	yes	—
213	C₂²×C₄₃	#532	1	2	yes	—
214	C₄×C₄₃	—	2	4	no	—
215	C₄×C₄₃	—	2	16	no	—
216	C₄×C₄₃	—	4	8	no	—
217	C₄×C₄₃	—	4	4	no	—
218	C₄×C₄₃	C₄×C₂²⋊C₄	1	8	yes	complemented
219	C₄×C₄₃	#390	1	8	yes	direct product factor
220	C₂²×C₄×D₄	C₂×C₄₃	1	1	yes	characteristic
221	C₂×#390	C₂×C₄₃	1	2	yes	—
222	C₂×C₄×C₄⋊C₄	C₂×C₄₃	1	1	yes	characteristic, complemented
223	C₂×C₄×C₂²⋊C₄	C₂×C₄₃	1	4	yes	complemented
224	C₂×C₄³	C₂×C₄₃	1	1	yes	characteristic, complemented
225	#1437	C₂×C₄₃	1	4	yes	complemented
226	C₄⋊#95	C₂×C₄₃	1	2	yes	complemented
227	C₂×C₄₃	—	4	8	no	—
228	C₂×C₄₃	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄₃	C₄²×D₄	1	2	yes	—
230	C₂×C₄₃	C₂×#390	1	1	yes	characteristic
231	C₂×C₄₃	#2293	1	2	yes	—
232	C₂×C₄₃	#2297	1	1	yes	characteristic
233	C₂×C₄₃	C₄×#121	1	4	yes	—
234	C₂×C₄₃	C₄×#124	1	2	yes	—
235	C₂×C₄₃	C₄×#127	1	2	yes	—
236	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
237	C₂⁴×C₄	C₂²×C₄₃	1	2	yes	—
238	C₂×C₄×D₄	—	2	4	no	—
239	C₂×C₄×D₄	—	2	4	no	—
240	C₂×C₄×D₄	C₄×C₄₃	1	8	yes	complemented
241	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
243	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
244	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	8	yes	—
245	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
246	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
247	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
248	C₂²×C₄²	C₂²×C₄₃	1	2	yes	—
249	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
250	#390	C₄×C₄₃	1	16	yes	direct product factor
251	C₄×C₄⋊C₄	—	2	4	no	—
252	C₄×C₂²⋊C₄	—	2	16	no	—
253	C₂×#95	C₂²×C₄₃	1	8	yes	—
254	C₂×#95	C₂²×C₄₃	1	2	yes	—
255	C₄³	—	2	4	no	—
256	C₄₃	C₄×#390	1	1	yes	characteristic, direct product factor, Sylow
257	C₂⁵	C₂³×C₄₃	1	2	yes	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
262	C₂²×D₄	C₂×C₄×C₄₃	1	8	yes	—
263	C₂³×C₄	—	2	4	no	—
264	C₂³×C₄	—	2	4	no	—
265	C₂³×C₄	—	2	8	no	—
266	C₂³×C₄	—	2	8	no	—
267	C₂³×C₄	C₂×C₄×C₄₃	1	8	yes	—
268	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
269	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
270	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
272	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
273	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
274	C₄×D₄	—	2	32	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	complemented
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	—	2	4	no	—
283	C₂×C₂²⋊C₄	—	2	16	no	—
284	C₂×C₂²⋊C₄	—	2	16	no	—
285	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	32	yes	complemented
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	—	2	4	no	—
289	C₂×C₄²	—	2	4	no	—
290	C₂×C₄²	—	2	8	no	—
291	C₂×C₄²	—	2	4	no	—
292	C₂×C₄²	—	2	4	no	—
293	C₂×C₄²	—	2	8	no	—
294	C₂×C₄²	—	2	4	no	—
295	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
296	C₂×C₄²	C₂×C₄×C₄₃	1	8	yes	complemented
297	C₂×C₄²	D₄×C₄₃	1	4	yes	—
298	C₂×C₄²	D₄×C₄₃	1	4	yes	—
299	C₂×C₄²	D₄×C₄₃	1	8	yes	complemented
300	#95	—	2	16	no	—
301	#95	—	2	4	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	2	2	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	2	4	no	—
308	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
309	C₂⁴	C₂²×C₄×C₄₃	1	8	yes	—
310	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	2	16	no	—
314	C₂×D₄	—	2	16	no	—
315	C₂×D₄	C₄²×C₄₃	1	16	yes	complemented
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	4	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	4	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	2	32	no	—
331	C₂²×C₄	—	4	16	no	—
332	C₂²×C₄	—	4	8	no	—
333	C₂²×C₄	—	4	8	no	—
334	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
335	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
336	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
337	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
338	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₄₃	1	8	yes	—
344	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
346	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
349	C₂²×C₄	#41×C₄₃	1	8	yes	—
350	C₂²×C₄	#41×C₄₃	1	4	yes	—
351	C₂²×C₄	#41×C₄₃	1	4	yes	—
352	C₄⋊C₄	—	2	8	no	—
353	C₄⋊C₄	—	2	16	no	—
354	C₂²⋊C₄	—	2	16	no	—
355	C₂²⋊C₄	—	2	64	no	—
356	C₄²	—	2	16	no	—
357	C₄²	—	2	16	no	—
358	C₄²	—	2	16	no	—
359	C₄²	—	4	8	no	—
360	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	complemented
361	C₂³	—	2	4	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	16	no	—
364	C₂³	—	2	8	no	—
365	C₂³	—	2	8	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	2	8	no	—
368	C₂³	—	2	16	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	4	4	no	—
376	C₂³	C₂×C₄²×C₄₃	1	8	yes	—
377	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
378	C₂³	C₂³×C₄×C₄₃	1	2	yes	—
379	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
380	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
381	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
382	C₂³	C₂×#41×C₄₃	1	2	yes	—
383	C₂³	C₂×#41×C₄₃	1	2	yes	—
384	C₂³	C₂×#41×C₄₃	1	4	yes	—
385	D₄	—	2	32	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	8	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	8	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	32	no	—
406	C₂×C₄	C₂×C₄²×C₄₃	1	4	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
409	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
410	C₂×C₄	#117×C₄₃	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
412	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
413	C₂×C₄	C₄×D₄×C₄₃	1	8	yes	—
414	C₂×C₄	C₄×D₄×C₄₃	1	16	yes	complemented
415	C₂×C₄	#121×C₄₃	1	8	yes	—
416	C₂×C₄	#124×C₄₃	1	4	yes	—
417	C₂×C₄	#127×C₄₃	1	4	yes	—
418	C₂²	—	2	8	no	—
419	C₂²	—	2	16	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	8	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	16	no	—
424	C₂²	—	4	8	no	—
425	C₂²	—	4	8	no	—
426	C₂²	C₂²×C₄²×C₄₃	1	1	yes	characteristic
427	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
428	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
429	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
430	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
431	C₂²	C₂×C₄×D₄×C₄₃	1	2	yes	—
432	C₂²	C₂×C₄×D₄×C₄₃	1	4	yes	—
433	C₂²	C₄×#41×C₄₃	1	2	yes	—
434	C₂²	C₄×#41×C₄₃	1	4	yes	—
435	C₂²	C₂×#121×C₄₃	1	2	yes	—
436	C₂²	C₄₃×#525	1	2	yes	—
437	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
438	C₂²	C₄₃×#529	1	4	yes	—
439	C₂²	C₂×#127×C₄₃	1	1	yes	characteristic
440	C₂²	C₄₃×#532	1	4	yes	—
441	C₂²	C₄₃×#532	1	2	yes	—
442	C₄	—	2	4	no	—
443	C₄	—	2	16	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	8	no	—
446	C₄	C₄×C₂²⋊C₄×C₄₃	1	8	yes	complemented
447	C₄	C₄₃×#390	1	8	yes	direct product factor
448	C₂	—	4	8	no	—
449	C₂	C₂×C₄×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
450	C₂	C₄²×D₄×C₄₃	1	2	yes	—
451	C₂	C₂×C₄₃×#390	1	1	yes	characteristic
452	C₂	C₄₃×#2293	1	2	yes	—
453	C₂	C₄₃×#2297	1	1	yes	characteristic
454	C₂	C₄×#121×C₄₃	1	4	yes	—
455	C₂	C₄×#124×C₄₃	1	2	yes	—
456	C₂	C₄×#127×C₄₃	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₃	C₂³
commutator	C₂²	C₂²×C₄²×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
socle	C₂⁴×C₄₃	C₂⁴
prime radical	C₂³×D₄×C₄₃	C₂²
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
3. C₂×C₄×C₄⋊C₄×C₄₃	C₂	semidirect
4. C₂×C₄×C₂²⋊C₄×C₄₃	C₂	semidirect
5. C₂×C₄³×C₄₃	C₂	semidirect
6. C₄₃×#1437	C₂	semidirect
7. C₄₃×C₄⋊#95	C₂	semidirect
12. C₂×C₄×D₄×C₄₃	C₄	semidirect
22. C₄₃×#390	C₄	direct (N × H)
51. C₂×C₄⋊C₄×C₄₃	C₂×C₄	semidirect
57. C₂×C₂²⋊C₄×C₄₃	C₂×C₄	semidirect
67. C₂×C₄²×C₄₃	C₂×C₄	semidirect
70. C₂×C₄²×C₄₃	D₄	semidirect
86. C₂×D₄×C₄₃	C₄²	semidirect
131. C₄²×C₄₃	C₂²⋊C₄	semidirect
185. C₂×C₄×C₄₃	C₄×D₄	semidirect
189. C₄×#390	C₄₃	direct (N × H)
218. C₄×C₄₃	C₄×C₂²⋊C₄	semidirect
219. C₄×C₄₃	#390	direct (N × H)
222. C₂×C₄×C₄⋊C₄	C₂×C₄₃	semidirect
223. C₂×C₄×C₂²⋊C₄	C₂×C₄₃	semidirect
224. C₂×C₄³	C₂×C₄₃	semidirect
225. #1437	C₂×C₄₃	semidirect
226. C₄⋊#95	C₂×C₄₃	semidirect
240. C₂×C₄×D₄	C₄×C₄₃	semidirect
250. #390	C₄×C₄₃	direct (N × H)
256. C₄₃	C₄×#390	direct (N × H)
280. C₂×C₄⋊C₄	C₂×C₄×C₄₃	semidirect
286. C₂×C₂²⋊C₄	C₂×C₄×C₄₃	semidirect
296. C₂×C₄²	C₂×C₄×C₄₃	semidirect
299. C₂×C₄²	D₄×C₄₃	semidirect
315. C₂×D₄	C₄²×C₄₃	semidirect
360. C₄²	C₂²⋊C₄×C₄₃	semidirect
414. C₂×C₄	C₄×D₄×C₄₃	semidirect
446. C₄	C₄×C₂²⋊C₄×C₄₃	semidirect
447. C₄	C₄₃×#390	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₃	2
C₂×C₄₃×#390	2
C₂×C₄×C₄⋊C₄×C₄₃	2
C₂×C₄×C₂²⋊C₄×C₄₃	2
C₂×C₄³×C₄₃	2
C₄₃×#1437	2
C₄₃×C₄⋊#95	2
C₄×#390	43

Subgroups — C4×C43×#390 #24933783

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄₃×#390 #24933783