Subgroups — C₂×C₄₃×#1488 #24937459

Order 11008.

1270 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1488	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄₃×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₃×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₃	C₄	1	1	yes	characteristic
8	C₄×#41×C₄₃	—	2	2	no	—
9	C₄×#41×C₄₃	—	2	2	no	—
10	C₄×#41×C₄₃	C₄	1	4	yes	—
11	C₄×#41×C₄₃	C₂²	1	4	yes	—
12	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₄₃	—	2	1	no	—
15	C₂×C₄×D₄×C₄₃	—	2	1	no	—
16	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₃	—	2	1	no	—
19	C₂×#117×C₄₃	C₄	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	—	2	1	no	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#432	—	2	2	no	—
23	C₄₃×#432	C₂²	1	4	yes	complemented
24	C₄₃×#431	—	2	2	no	—
25	C₄₃×#431	C₂²	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
27	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
29	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
30	C₂×#97×C₄₃	—	2	1	no	—
31	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
32	C₄₃×Q₈⋊C₈	C₂²	1	8	yes	complemented
33	C₄₃×D₄⋊C₈	C₂²	1	8	yes	complemented
34	C₂×#41×C₄₃	—	2	4	no	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂×#41×C₄₃	—	2	2	no	—
37	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
38	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
39	C₂²×D₄×C₄₃	—	2	1	no	—
40	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂³×C₄×C₄₃	—	2	1	no	—
43	C₂³×C₄×C₄₃	—	2	1	no	—
44	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₄₃	—	2	2	no	—
48	C₂²×C₈×C₄₃	—	2	2	no	—
49	C₄×Q₈×C₄₃	—	2	2	no	—
50	C₄×Q₈×C₄₃	—	2	1	no	—
51	C₄×Q₈×C₄₃	—	2	1	no	—
52	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
53	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
54	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
55	C₄×D₄×C₄₃	—	2	4	no	—
56	C₄×D₄×C₄₃	—	2	4	no	—
57	C₄×D₄×C₄₃	—	2	4	no	—
58	C₄×D₄×C₄₃	—	2	4	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	1	no	—
61	C₄×D₄×C₄₃	—	2	1	no	—
62	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
63	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
64	C₄×D₄×C₄₃	C₂³	1	2	yes	—
65	#117×C₄₃	—	2	2	no	—
66	#117×C₄₃	—	2	4	no	—
67	#117×C₄₃	—	2	4	no	—
68	#117×C₄₃	C₂×C₄	1	4	yes	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄²×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	1	no	—
78	C₂×C₄²×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	—	2	4	no	—
80	C₂×C₄²×C₄₃	—	2	4	no	—
81	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
83	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₃	D₄	1	2	yes	—
85	C₂×C₄²×C₄₃	D₄	1	2	yes	—
86	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₃	—	2	4	no	—
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
92	C₂²⋊C₈×C₄₃	—	2	4	no	—
93	C₂²⋊C₈×C₄₃	—	2	4	no	—
94	#97×C₄₃	—	2	4	no	—
95	C₄×C₈×C₄₃	—	2	2	no	—
96	C₄×C₈×C₄₃	C₂³	1	4	yes	—
97	C₂⁴×C₄₃	—	2	1	no	—
98	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
99	#41×C₄₃	—	2	16	no	—
100	#41×C₄₃	—	2	8	no	—
101	#41×C₄₃	—	2	8	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	M₁₆	1	4	yes	—
105	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₄₃	—	2	8	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	4	no	—
110	C₂×D₄×C₄₃	M₁₆	1	4	yes	—
111	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₃	—	2	8	no	—
113	C₂²×C₄×C₄₃	—	2	4	no	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	4	no	—
117	C₂²×C₄×C₄₃	—	2	4	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	2	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	—	2	1	no	—
123	C₂²×C₄×C₄₃	—	4	2	no	—
124	C₂²×C₄×C₄₃	—	4	4	no	—
125	C₂²×C₄×C₄₃	—	4	4	no	—
126	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
130	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
131	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
132	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	—	2	4	no	—
139	C₂×C₈×C₄₃	—	2	4	no	—
140	C₂×C₈×C₄₃	—	4	4	no	—
141	C₂×C₈×C₄₃	—	4	4	no	—
142	C₄⋊C₄×C₄₃	—	2	4	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₄⋊C₄×C₄₃	—	2	1	no	—
145	C₄⋊C₄×C₄₃	—	2	1	no	—
146	C₄⋊C₄×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
148	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
149	C₂²⋊C₄×C₄₃	—	2	4	no	—
150	C₂²⋊C₄×C₄₃	—	2	2	no	—
151	C₂²⋊C₄×C₄₃	—	2	2	no	—
152	C₂²⋊C₄×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	4	no	—
154	C₄²×C₄₃	—	2	4	no	—
155	C₄²×C₄₃	—	2	2	no	—
156	C₄²×C₄₃	—	2	2	no	—
157	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
158	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
159	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
160	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
161	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂×D₄	1	2	yes	—
164	C₄²×C₄₃	C₂×D₄	1	2	yes	—
165	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂³×C₄₃	—	2	2	no	—
168	C₂³×C₄₃	—	2	2	no	—
169	C₂³×C₄₃	—	2	4	no	—
170	C₂³×C₄₃	—	2	2	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	—	4	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
175	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	Q₈×C₄₃	—	2	2	no	—
177	Q₈×C₄₃	—	2	4	no	—
178	Q₈×C₄₃	C₂×M₁₆	1	4	yes	—
179	D₄×C₄₃	—	2	16	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	C₂×M₁₆	1	4	yes	—
183	C₂×C₄×C₄₃	—	2	16	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	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	2	no	—
196	C₂×C₄×C₄₃	—	2	2	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	8	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	4	no	—
203	C₂×C₄×C₄₃	—	4	4	no	—
204	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
205	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
207	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
211	C₂×C₄×C₄₃	C₂×M₁₆	1	2	yes	—
212	C₂×C₄×C₄₃	#135	1	4	yes	—
213	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₄₃	—	4	4	no	—
217	C₈×C₄₃	—	4	4	no	—
218	C₂×#1488	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₃	—	2	4	no	—
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	2	2	no	—
222	C₂²×C₄₃	—	2	2	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	4	no	—
226	C₂²×C₄₃	—	4	8	no	—
227	C₂²×C₄₃	#407	1	2	yes	—
228	C₂²×C₄₃	#416	1	2	yes	—
229	C₂²×C₄₃	#421	1	2	yes	—
230	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
231	C₄×C₄₃	—	2	2	no	—
232	C₄×C₄₃	—	2	4	no	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	2	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	#407	1	2	yes	—
240	C₄×C₄₃	#416	1	2	yes	—
241	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
242	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
243	C₄×C₄₃	C₂×#135	1	2	yes	—
244	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic
245	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
246	C₂×#431	C₂×C₄₃	1	1	yes	characteristic, complemented
247	#1488	C₂×C₄₃	1	8	yes	direct product factor
248	C₂×Q₈⋊C₈	C₂×C₄₃	1	2	yes	complemented
249	C₂×D₄⋊C₈	C₂×C₄₃	1	2	yes	complemented
250	C₂×C₄₃	—	4	2	no	—
251	C₂×C₄₃	—	4	4	no	—
252	C₂×C₄₃	#1488	1	4	yes	direct product factor
253	C₂×C₄₃	C₂×#407	1	1	yes	characteristic
254	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
255	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
256	C₂²×#41	C₄×C₄₃	1	1	yes	characteristic
257	C₄×#41	—	2	2	no	—
258	C₄×#41	—	2	2	no	—
259	C₄×#41	C₄×C₄₃	1	4	yes	—
260	C₄×#41	C₂²×C₄₃	1	4	yes	—
261	C₂×C₄×Q₈	C₄×C₄₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂×C₄×D₄	—	2	1	no	—
265	C₂×C₄×D₄	C₄×C₄₃	1	1	yes	characteristic
266	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×#117	—	2	1	no	—
268	C₂×#117	C₄×C₄₃	1	1	yes	characteristic
269	C₂²×C₄²	—	2	1	no	—
270	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
271	#432	—	2	2	no	—
272	#432	C₂²×C₄₃	1	4	yes	complemented
273	#431	—	2	2	no	—
274	#431	C₂²×C₄₃	1	4	yes	complemented
275	C₂×C₄⋊C₈	—	2	1	no	—
276	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
277	C₂×C₂²⋊C₈	—	2	1	no	—
278	C₂×C₂²⋊C₈	—	2	1	no	—
279	C₂×#97	—	2	1	no	—
280	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
281	Q₈⋊C₈	C₂²×C₄₃	1	8	yes	complemented
282	D₄⋊C₈	C₂²×C₄₃	1	8	yes	complemented
283	C₄₃	C₂×#1488	1	1	yes	characteristic, direct product factor, Sylow
284	C₂×#41	—	2	4	no	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	C₂×C₄×C₄₃	1	4	yes	—
288	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
289	C₂²×D₄	—	2	1	no	—
290	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
295	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
296	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	1	no	—
301	C₄×Q₈	—	2	1	no	—
302	C₄×Q₈	C₂×C₄×C₄₃	1	4	yes	—
303	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
304	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	4	no	—
307	C₄×D₄	—	2	4	no	—
308	C₄×D₄	—	2	4	no	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	C₂×C₄×C₄₃	1	4	yes	—
313	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
314	C₄×D₄	C₂³×C₄₃	1	2	yes	—
315	#117	—	2	2	no	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	#117	C₂×C₄×C₄₃	1	4	yes	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	—	2	1	no	—
329	C₂×C₄²	—	2	4	no	—
330	C₂×C₄²	—	2	4	no	—
331	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
332	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
333	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
334	C₂×C₄²	D₄×C₄₃	1	2	yes	—
335	C₂×C₄²	D₄×C₄₃	1	2	yes	—
336	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
339	C₄⋊C₈	—	2	4	no	—
340	C₄⋊C₈	—	2	2	no	—
341	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
342	C₂²⋊C₈	—	2	4	no	—
343	C₂²⋊C₈	—	2	4	no	—
344	#97	—	2	4	no	—
345	C₄×C₈	—	2	2	no	—
346	C₄×C₈	C₂³×C₄₃	1	4	yes	—
347	C₂⁴	—	2	1	no	—
348	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
349	#41	—	2	16	no	—
350	#41	—	2	8	no	—
351	#41	—	2	8	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	M₁₆×C₄₃	1	4	yes	—
355	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	M₁₆×C₄₃	1	4	yes	—
361	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
377	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
379	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
380	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
381	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
382	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
383	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	4	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
398	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₂²⋊C₄	—	2	4	no	—
401	C₂²⋊C₄	—	2	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	2	no	—
407	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
408	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
409	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
410	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
411	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
412	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
413	C₄²	C₂×D₄×C₄₃	1	2	yes	—
414	C₄²	C₂×D₄×C₄₃	1	2	yes	—
415	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
416	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
425	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
426	Q₈	—	2	2	no	—
427	Q₈	—	2	4	no	—
428	Q₈	C₂×M₁₆×C₄₃	1	4	yes	—
429	D₄	—	2	16	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	4	no	—
432	D₄	C₂×M₁₆×C₄₃	1	4	yes	—
433	C₂×C₄	—	2	16	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	4	no	—
454	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
455	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
456	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
457	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
458	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂×M₁₆×C₄₃	1	2	yes	—
461	C₂×C₄	C₂×M₁₆×C₄₃	1	2	yes	—
462	C₂×C₄	#135×C₄₃	1	4	yes	—
463	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
466	C₈	—	4	4	no	—
467	C₈	—	4	4	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	2	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	4	no	—
475	C₂²	—	4	8	no	—
476	C₂²	C₄₃×#407	1	2	yes	—
477	C₂²	C₄₃×#416	1	2	yes	—
478	C₂²	C₄₃×#421	1	2	yes	—
479	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	4	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	2	no	—
485	C₄	—	2	1	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	C₄₃×#407	1	2	yes	—
489	C₄	C₄₃×#416	1	2	yes	—
490	C₄	C₂²×M₁₆×C₄₃	1	1	yes	characteristic
491	C₄	C₂²×M₁₆×C₄₃	1	1	yes	characteristic
492	C₄	C₂×#135×C₄₃	1	2	yes	—
493	C₂	—	4	2	no	—
494	C₂	—	4	4	no	—
495	C₂	C₄₃×#1488	1	4	yes	direct product factor
496	C₂	C₂×C₄₃×#407	1	1	yes	characteristic
497	C₂	C₂×C₄₃×#416	1	1	yes	characteristic
498	C₂	C₂×C₄₃×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₃
Frattini, cosocle	C₄²	C₂⁴×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₃	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#432	C₂	semidirect
3. C₂×C₄₃×#431	C₂	semidirect
4. C₄₃×#1488	C₂	direct (N × H)
5. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
6. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
23. C₄₃×#432	C₂²	semidirect
25. C₄₃×#431	C₂²	semidirect
32. C₄₃×Q₈⋊C₈	C₂²	semidirect
33. C₄₃×D₄⋊C₈	C₂²	semidirect
218. C₂×#1488	C₄₃	direct (N × H)
245. C₂×#432	C₂×C₄₃	semidirect
246. C₂×#431	C₂×C₄₃	semidirect
247. #1488	C₂×C₄₃	direct (N × H)
248. C₂×Q₈⋊C₈	C₂×C₄₃	semidirect
249. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
252. C₂×C₄₃	#1488	direct (N × H)
272. #432	C₂²×C₄₃	semidirect
274. #431	C₂²×C₄₃	semidirect
281. Q₈⋊C₈	C₂²×C₄₃	semidirect
282. D₄⋊C₈	C₂²×C₄₃	semidirect
283. C₄₃	C₂×#1488	direct (N × H)
495. C₂	C₄₃×#1488	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×C₄×#41×C₄₃	2
C₂×C₄₃×#432	2
C₂×C₄₃×#431	2
C₄₃×#1488	2
C₂×C₄₃×Q₈⋊C₈	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1488	43

Subgroups — C2×C43×#1488 #24937459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1488 #24937459