Subgroups — C₂×C₄₃×#1494 #24937489

Order 11008.

1138 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1494	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	C₂³×C₈×C₄₃	—	2	1	no	—
8	C₄₃×#529	—	2	2	no	—
9	C₄₃×#529	—	2	2	no	—
10	C₄₃×#529	C₄	1	4	yes	—
11	C₄₃×#529	C₂²	1	4	yes	—
12	C₂×#126×C₄₃	—	2	1	no	—
13	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
14	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
15	C₂×#123×C₄₃	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
17	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	—	2	1	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₄₃	—	2	1	no	—
22	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#432	—	2	2	no	—
24	C₄₃×#432	C₂²	1	4	yes	complemented
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
27	C₂×#97×C₄₃	—	2	1	no	—
28	C₂×C₄×C₈×C₄₃	—	2	2	no	—
29	C₂×C₄×C₈×C₄₃	—	2	1	no	—
30	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₄₃	C₂²	1	4	yes	complemented
32	C₄₃×Q₈⋊C₈	C₂²	1	8	yes	complemented
33	C₄₃×D₄⋊C₈	C₂²	1	8	yes	complemented
34	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×D₄×C₄₃	—	2	1	no	—
36	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₃	—	2	1	no	—
38	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₄₃	—	2	8	no	—
42	C₂²×C₈×C₄₃	—	2	2	no	—
43	C₂²×C₈×C₄₃	—	2	4	no	—
44	C₂²×C₈×C₄₃	—	2	2	no	—
45	#126×C₄₃	—	2	4	no	—
46	#126×C₄₃	—	2	4	no	—
47	#125×C₄₃	—	2	2	no	—
48	#125×C₄₃	C₂×C₄	1	4	yes	—
49	#124×C₄₃	—	2	2	no	—
50	#124×C₄₃	C₂×C₄	1	4	yes	—
51	#123×C₄₃	—	2	4	no	—
52	#123×C₄₃	—	2	4	no	—
53	C₂²⋊Q₈×C₄₃	—	2	2	no	—
54	C₂²⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
55	#121×C₄₃	—	2	2	no	—
56	#121×C₄₃	C₂×C₄	1	4	yes	—
57	C₄×Q₈×C₄₃	—	2	1	no	—
58	C₄×Q₈×C₄₃	—	2	1	no	—
59	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
61	C₄×D₄×C₄₃	—	2	4	no	—
62	C₄×D₄×C₄₃	—	2	4	no	—
63	C₄×D₄×C₄₃	—	2	1	no	—
64	C₄×D₄×C₄₃	—	2	1	no	—
65	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₄₃	C₂³	1	2	yes	—
67	#117×C₄₃	—	2	4	no	—
68	#117×C₄₃	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	—	2	1	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	2	no	—
90	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
91	C₂²⋊C₈×C₄₃	—	2	4	no	—
92	#97×C₄₃	—	2	4	no	—
93	C₄×C₈×C₄₃	—	2	2	no	—
94	C₄×C₈×C₄₃	—	2	4	no	—
95	C₄×C₈×C₄₃	C₂³	1	4	yes	—
96	C₂⁴×C₄₃	—	2	1	no	—
97	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	4	no	—
100	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₃	—	2	1	no	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	4	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₃	—	2	4	no	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	1	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	4	4	no	—
115	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	—	2	8	no	—
128	C₂×C₈×C₄₃	—	2	16	no	—
129	C₂×C₈×C₄₃	—	2	4	no	—
130	C₂×C₈×C₄₃	—	2	4	no	—
131	C₂×C₈×C₄₃	—	4	4	no	—
132	C₄⋊C₄×C₄₃	—	2	4	no	—
133	C₄⋊C₄×C₄₃	—	2	4	no	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
140	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
141	C₂²⋊C₄×C₄₃	—	2	4	no	—
142	C₂²⋊C₄×C₄₃	—	2	4	no	—
143	C₂²⋊C₄×C₄₃	—	2	4	no	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₂²⋊C₄×C₄₃	—	2	2	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
150	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
151	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
152	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
154	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂×D₄	1	2	yes	—
156	C₄²×C₄₃	C₂×D₄	1	2	yes	—
157	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	—	2	2	no	—
162	C₂³×C₄₃	—	4	2	no	—
163	C₂³×C₄₃	—	4	2	no	—
164	C₂³×C₄₃	—	4	2	no	—
165	C₂³×C₄₃	#104	1	4	yes	—
166	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	Q₈×C₄₃	—	2	4	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	2	4	no	—
171	D₄×C₄₃	—	4	8	no	—
172	D₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	4	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	2	4	no	—
180	C₂×C₄×C₄₃	—	2	4	no	—
181	C₂×C₄×C₄₃	—	2	4	no	—
182	C₂×C₄×C₄₃	—	2	4	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	4	no	—
190	C₂×C₄×C₄₃	—	4	4	no	—
191	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
192	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
193	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	#131	1	4	yes	—
198	C₂×C₄×C₄₃	#135	1	4	yes	—
199	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₈×C₄₃	—	2	8	no	—
203	C₈×C₄₃	—	4	4	no	—
204	C₂×#1494	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	8	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	—	8	4	no	—
212	C₂²×C₄₃	#408	1	2	yes	—
213	C₂²×C₄₃	#416	1	2	yes	—
214	C₂²×C₄₃	C₂×#104	1	4	yes	—
215	C₂²×C₄₃	C₂×#104	1	2	yes	—
216	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
217	C₄×C₄₃	—	2	2	no	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	1	no	—
222	C₄×C₄₃	—	4	2	no	—
223	C₄×C₄₃	—	4	2	no	—
224	C₄×C₄₃	—	4	2	no	—
225	C₄×C₄₃	#408	1	2	yes	—
226	C₄×C₄₃	#416	1	2	yes	—
227	C₄×C₄₃	C₂×#131	1	2	yes	—
228	C₄×C₄₃	C₂×#135	1	2	yes	—
229	C₂×#529	C₂×C₄₃	1	1	yes	characteristic
230	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
231	C₂²×C₄×C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
232	#1494	C₂×C₄₃	1	8	yes	direct product factor
233	C₂×Q₈⋊C₈	C₂×C₄₃	1	2	yes	complemented
234	C₂×D₄⋊C₈	C₂×C₄₃	1	2	yes	complemented
235	C₂×C₄₃	—	2	4	no	—
236	C₂×C₄₃	—	8	2	no	—
237	C₂×C₄₃	#1494	1	4	yes	direct product factor
238	C₂×C₄₃	C₂×#408	1	1	yes	characteristic
239	C₂×C₄₃	C₂×#416	1	1	yes	characteristic
240	C₂×C₄₃	C₂²×#104	1	1	yes	characteristic
241	C₂³×C₈	—	2	1	no	—
242	#529	—	2	2	no	—
243	#529	—	2	2	no	—
244	#529	C₄×C₄₃	1	4	yes	—
245	#529	C₂²×C₄₃	1	4	yes	—
246	C₂×#126	—	2	1	no	—
247	C₂×#125	C₄×C₄₃	1	1	yes	characteristic
248	C₂×#124	C₄×C₄₃	1	1	yes	characteristic
249	C₂×#123	—	2	1	no	—
250	C₂×C₂²⋊Q₈	C₄×C₄₃	1	1	yes	characteristic
251	C₂×#121	C₄×C₄₃	1	1	yes	characteristic
252	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
253	C₂×C₄×D₄	—	2	1	no	—
254	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
255	C₂×#117	—	2	1	no	—
256	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
257	#432	—	2	2	no	—
258	#432	C₂²×C₄₃	1	4	yes	complemented
259	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
260	C₂×C₂²⋊C₈	—	2	1	no	—
261	C₂×#97	—	2	1	no	—
262	C₂×C₄×C₈	—	2	2	no	—
263	C₂×C₄×C₈	—	2	1	no	—
264	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
265	C₂×C₄×C₈	C₂²×C₄₃	1	4	yes	complemented
266	Q₈⋊C₈	C₂²×C₄₃	1	8	yes	complemented
267	D₄⋊C₈	C₂²×C₄₃	1	8	yes	complemented
268	C₄₃	C₂×#1494	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×Q₈	C₂×C₄×C₄₃	1	1	yes	characteristic
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
272	C₂³×C₄	—	2	1	no	—
273	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
274	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
275	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
276	C₂²×C₈	—	2	8	no	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	4	no	—
279	C₂²×C₈	—	2	2	no	—
280	#126	—	2	4	no	—
281	#126	—	2	4	no	—
282	#125	—	2	2	no	—
283	#125	C₂×C₄×C₄₃	1	4	yes	—
284	#124	—	2	2	no	—
285	#124	C₂×C₄×C₄₃	1	4	yes	—
286	#123	—	2	4	no	—
287	#123	—	2	4	no	—
288	C₂²⋊Q₈	—	2	2	no	—
289	C₂²⋊Q₈	C₂×C₄×C₄₃	1	4	yes	—
290	#121	—	2	2	no	—
291	#121	C₂×C₄×C₄₃	1	4	yes	—
292	C₄×Q₈	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	C₂×C₄×C₄₃	1	2	yes	—
295	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
296	C₄×D₄	—	2	4	no	—
297	C₄×D₄	—	2	4	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
301	C₄×D₄	C₂³×C₄₃	1	2	yes	—
302	#117	—	2	4	no	—
303	#117	—	2	4	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
317	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
318	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₄₃	1	2	yes	—
321	C₂×C₄²	D₄×C₄₃	1	2	yes	—
322	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	C₂³×C₄₃	1	4	yes	—
326	C₂²⋊C₈	—	2	4	no	—
327	#97	—	2	4	no	—
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	—	2	4	no	—
330	C₄×C₈	C₂³×C₄₃	1	4	yes	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	C₂²×C₄×C₄₃	1	2	yes	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	C₂²×C₄×C₄₃	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
352	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
353	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
354	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
355	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
356	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
362	C₂×C₈	—	2	8	no	—
363	C₂×C₈	—	2	16	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	4	4	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
375	C₄⋊C₄	C₂²×C₄×C₄₃	1	2	yes	—
376	C₂²⋊C₄	—	2	4	no	—
377	C₂²⋊C₄	—	2	4	no	—
378	C₂²⋊C₄	—	2	4	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	2	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
385	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
386	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
387	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
388	C₄²	C₂²×C₄×C₄₃	1	2	yes	—
389	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₄₃	1	2	yes	—
391	C₄²	C₂×D₄×C₄₃	1	2	yes	—
392	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
393	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	#104×C₄₃	1	4	yes	—
401	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
402	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	4	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	4	8	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
427	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
428	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
430	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
431	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
432	C₂×C₄	#131×C₄₃	1	4	yes	—
433	C₂×C₄	#135×C₄₃	1	4	yes	—
434	C₂×C₄	C₂³×C₄×C₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
437	C₈	—	2	8	no	—
438	C₈	—	4	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	8	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	4	no	—
446	C₂²	C₄₃×#408	1	2	yes	—
447	C₂²	C₄₃×#416	1	2	yes	—
448	C₂²	C₂×#104×C₄₃	1	4	yes	—
449	C₂²	C₂×#104×C₄₃	1	2	yes	—
450	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
451	C₄	—	2	2	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	1	no	—
456	C₄	—	4	2	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	C₄₃×#408	1	2	yes	—
460	C₄	C₄₃×#416	1	2	yes	—
461	C₄	C₂×#131×C₄₃	1	2	yes	—
462	C₄	C₂×#135×C₄₃	1	2	yes	—
463	C₂	—	2	4	no	—
464	C₂	—	8	2	no	—
465	C₂	C₄₃×#1494	1	4	yes	direct product factor
466	C₂	C₂×C₄₃×#408	1	1	yes	characteristic
467	C₂	C₂×C₄₃×#416	1	1	yes	characteristic
468	C₂	C₂²×#104×C₄₃	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	C₂×#121×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. C₂²×C₄×C₈×C₄₃	C₂	semidirect
4. C₄₃×#1494	C₂	direct (N × H)
5. C₂×C₄₃×Q₈⋊C₈	C₂	semidirect
6. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
24. C₄₃×#432	C₂²	semidirect
31. C₂×C₄×C₈×C₄₃	C₂²	semidirect
32. C₄₃×Q₈⋊C₈	C₂²	semidirect
33. C₄₃×D₄⋊C₈	C₂²	semidirect
204. C₂×#1494	C₄₃	direct (N × H)
230. C₂×#432	C₂×C₄₃	semidirect
231. C₂²×C₄×C₈	C₂×C₄₃	semidirect
232. #1494	C₂×C₄₃	direct (N × H)
233. C₂×Q₈⋊C₈	C₂×C₄₃	semidirect
234. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
237. C₂×C₄₃	#1494	direct (N × H)
258. #432	C₂²×C₄₃	semidirect
265. C₂×C₄×C₈	C₂²×C₄₃	semidirect
266. Q₈⋊C₈	C₂²×C₄₃	semidirect
267. D₄⋊C₈	C₂²×C₄₃	semidirect
268. C₄₃	C₂×#1494	direct (N × H)
465. C₂	C₄₃×#1494	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×#529	2
C₂×C₄₃×#432	2
C₂²×C₄×C₈×C₄₃	2
C₄₃×#1494	2
C₂×C₄₃×Q₈⋊C₈	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1494	43

Subgroups — C2×C43×#1494 #24937489

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1494 #24937489