Subgroups — C₂×C₄₃×#1654 #24938513

Order 11008.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#1654	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₃×#332	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	—	2	1	no	—
10	C₂²×SD₁₆×C₄₃	—	2	1	no	—
11	C₄₃×#547	—	2	2	no	—
12	C₄₃×#547	—	2	2	no	—
13	C₄₃×#547	—	2	2	no	—
14	C₄₃×#547	C₂²	1	4	yes	—
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#123×C₄₃	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
19	C₂×#121×C₄₃	—	2	1	no	—
20	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
23	C₄₃×#498	—	2	2	no	—
24	C₄₃×#498	C₂²	1	4	yes	complemented
25	C₄₃×#474	—	2	2	no	—
26	C₄₃×#474	C₂²	1	4	yes	complemented
27	C₄₃×#461	—	2	2	no	—
28	C₄₃×#461	C₂²	1	4	yes	complemented
29	C₂×#107×C₄₃	—	2	1	no	—
30	C₂×#106×C₄₃	—	2	2	no	—
31	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
33	C₂×#103×C₄₃	—	2	1	no	—
34	C₂×#102×C₄₃	—	2	1	no	—
35	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#332	C₂²	1	4	yes	complemented
37	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
38	C₄₃×D₄⋊C₈	C₂²	1	4	yes	complemented
39	C₂×#41×C₄₃	—	2	4	no	—
40	C₂×#41×C₄₃	—	2	4	no	—
41	C₂×#41×C₄₃	—	4	4	no	—
42	C₂×#41×C₄₃	—	4	4	no	—
43	C₂²×Q₈×C₄₃	—	2	1	no	—
44	C₂²×Q₈×C₄₃	—	2	1	no	—
45	C₂²×D₄×C₄₃	—	2	2	no	—
46	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₃	—	2	2	no	—
49	C₂³×C₄×C₄₃	—	2	1	no	—
50	C₂³×C₄×C₄₃	—	2	1	no	—
51	C₂×SD₁₆×C₄₃	—	2	4	no	—
52	C₂×SD₁₆×C₄₃	—	4	4	no	—
53	C₂²×C₈×C₄₃	—	2	1	no	—
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₄⋊Q₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	—	2	1	no	—
60	C₄⋊Q₈×C₄₃	—	2	1	no	—
61	C₄⋊Q₈×C₄₃	D₄	1	2	yes	—
62	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
64	#123×C₄₃	—	2	8	no	—
65	#123×C₄₃	—	2	8	no	—
66	C₂²⋊Q₈×C₄₃	—	2	4	no	—
67	C₂²⋊Q₈×C₄₃	—	2	4	no	—
68	#121×C₄₃	—	2	4	no	—
69	#121×C₄₃	—	2	4	no	—
70	C₄×D₄×C₄₃	—	2	1	no	—
71	C₄×D₄×C₄₃	—	2	1	no	—
72	C₄×D₄×C₄₃	—	2	1	no	—
73	C₄×D₄×C₄₃	—	2	1	no	—
74	C₄×D₄×C₄₃	D₄	1	2	yes	—
75	C₄×D₄×C₄₃	D₄	1	2	yes	—
76	C₄×D₄×C₄₃	C₂³	1	2	yes	—
77	C₄×D₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
82	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	#107×C₄₃	—	2	4	no	—
92	#106×C₄₃	—	2	8	no	—
93	C₄⋊C₈×C₄₃	—	2	1	no	—
94	C₄⋊C₈×C₄₃	—	2	1	no	—
95	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	#103×C₄₃	—	2	4	no	—
98	#102×C₄₃	—	2	4	no	—
99	C₄×C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₂⁴×C₄₃	—	2	1	no	—
102	C₂⁴×C₄₃	—	2	1	no	—
103	#41×C₄₃	—	4	8	no	—
104	#41×C₄₃	—	4	16	no	—
105	#41×C₄₃	—	4	8	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	2	2	no	—
108	C₂×Q₈×C₄₃	—	2	2	no	—
109	C₂×Q₈×C₄₃	—	4	1	no	—
110	C₂×Q₈×C₄₃	—	4	2	no	—
111	C₂×Q₈×C₄₃	—	4	2	no	—
112	C₂×Q₈×C₄₃	—	4	2	no	—
113	C₂×Q₈×C₄₃	—	4	2	no	—
114	C₂×D₄×C₄₃	—	2	8	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	2	2	no	—
118	C₂×D₄×C₄₃	—	2	2	no	—
119	C₂×D₄×C₄₃	—	2	2	no	—
120	C₂×D₄×C₄₃	—	4	8	no	—
121	C₂×D₄×C₄₃	SD₁₆	1	4	yes	complemented
122	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₃	—	2	8	no	—
125	C₂²×C₄×C₄₃	—	2	2	no	—
126	C₂²×C₄×C₄₃	—	2	2	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	—	2	2	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	4	8	no	—
133	C₂²×C₄×C₄₃	—	4	2	no	—
134	C₂²×C₄×C₄₃	—	4	2	no	—
135	C₂²×C₄×C₄₃	—	4	2	no	—
136	C₂²×C₄×C₄₃	—	4	2	no	—
137	C₂²×C₄×C₄₃	—	4	1	no	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	SD₁₆×C₄₃	—	4	8	no	—
142	C₂×C₈×C₄₃	—	2	4	no	—
143	C₂×C₈×C₄₃	—	2	2	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	4	2	no	—
147	C₂×C₈×C₄₃	—	4	2	no	—
148	C₄⋊C₄×C₄₃	—	2	8	no	—
149	C₄⋊C₄×C₄₃	—	2	1	no	—
150	C₄⋊C₄×C₄₃	—	2	2	no	—
151	C₄⋊C₄×C₄₃	—	2	1	no	—
152	C₄⋊C₄×C₄₃	—	2	2	no	—
153	C₄⋊C₄×C₄₃	—	2	2	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	2	no	—
156	C₄⋊C₄×C₄₃	—	4	1	no	—
157	C₄⋊C₄×C₄₃	—	4	1	no	—
158	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
160	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
161	C₂²⋊C₄×C₄₃	—	2	8	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	2	no	—
166	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
170	C₂³×C₄₃	—	2	2	no	—
171	C₂³×C₄₃	—	2	4	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	—	4	2	no	—
174	C₂³×C₄₃	—	4	2	no	—
175	C₂³×C₄₃	—	4	2	no	—
176	C₂³×C₄₃	—	4	2	no	—
177	C₂³×C₄₃	—	4	2	no	—
178	C₂³×C₄₃	#120	1	1	yes	characteristic
179	Q₈×C₄₃	—	4	2	no	—
180	Q₈×C₄₃	—	4	2	no	—
181	Q₈×C₄₃	—	4	4	no	—
182	Q₈×C₄₃	—	4	2	no	—
183	Q₈×C₄₃	—	4	2	no	—
184	Q₈×C₄₃	—	8	2	no	—
185	D₄×C₄₃	—	2	2	no	—
186	D₄×C₄₃	—	2	2	no	—
187	D₄×C₄₃	—	2	2	no	—
188	D₄×C₄₃	—	2	4	no	—
189	D₄×C₄₃	—	4	16	no	—
190	D₄×C₄₃	—	4	2	no	—
191	D₄×C₄₃	C₂×SD₁₆	1	4	yes	complemented
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	—	2	4	no	—
196	C₂×C₄×C₄₃	—	4	16	no	—
197	C₂×C₄×C₄₃	—	4	2	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	4	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	4	no	—
205	C₂×C₄×C₄₃	—	4	4	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	8	2	no	—
208	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
209	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
210	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₄₃	#135	1	2	yes	—
213	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
215	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
218	C₈×C₄₃	—	2	4	no	—
219	C₈×C₄₃	—	4	2	no	—
220	C₈×C₄₃	—	4	2	no	—
221	C₂×#1654	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂²×C₄₃	—	2	4	no	—
223	C₂²×C₄₃	—	4	8	no	—
224	C₂²×C₄₃	—	4	2	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	4	2	no	—
227	C₂²×C₄₃	—	4	2	no	—
228	C₂²×C₄₃	—	4	2	no	—
229	C₂²×C₄₃	—	8	4	no	—
230	C₂²×C₄₃	#449	1	2	yes	—
231	C₂²×C₄₃	#450	1	2	yes	—
232	C₂²×C₄₃	#456	1	2	yes	—
233	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	4	2	no	—
237	C₄×C₄₃	—	4	4	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	—	8	2	no	—
240	C₄×C₄₃	#449	1	2	yes	—
241	C₄×C₄₃	#450	1	2	yes	—
242	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
243	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
244	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂×#547	C₂×C₄₃	1	1	yes	characteristic
247	C₂×#498	C₂×C₄₃	1	1	yes	characteristic, complemented
248	C₂×#474	C₂×C₄₃	1	1	yes	characteristic, complemented
249	C₂×#461	C₂×C₄₃	1	1	yes	characteristic, complemented
250	#1654	C₂×C₄₃	1	8	yes	direct product factor
251	C₂×#332	C₂×C₄₃	1	1	yes	characteristic, complemented
252	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
253	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
254	C₂×C₄₃	—	4	4	no	—
255	C₂×C₄₃	—	8	2	no	—
256	C₂×C₄₃	#1654	1	4	yes	direct product factor
257	C₂×C₄₃	C₂×#450	1	1	yes	characteristic
258	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
259	C₂×C₄₃	C₂×#456	1	1	yes	characteristic
260	C₂²×#41	—	2	1	no	—
261	C₂²×SD₁₆	—	2	1	no	—
262	#547	—	2	2	no	—
263	#547	—	2	2	no	—
264	#547	—	2	2	no	—
265	#547	C₂²×C₄₃	1	4	yes	—
266	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#123	—	2	2	no	—
269	C₂×C₂²⋊Q₈	—	2	1	no	—
270	C₂×#121	—	2	1	no	—
271	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
272	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
273	C₂²×C₄⋊C₄	—	2	1	no	—
274	#498	—	2	2	no	—
275	#498	C₂²×C₄₃	1	4	yes	complemented
276	#474	—	2	2	no	—
277	#474	C₂²×C₄₃	1	4	yes	complemented
278	#461	—	2	2	no	—
279	#461	C₂²×C₄₃	1	4	yes	complemented
280	C₂×#107	—	2	1	no	—
281	C₂×#106	—	2	2	no	—
282	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
284	C₂×#103	—	2	1	no	—
285	C₂×#102	—	2	1	no	—
286	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
287	#332	C₂²×C₄₃	1	4	yes	complemented
288	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
289	D₄⋊C₈	C₂²×C₄₃	1	4	yes	complemented
290	C₄₃	C₂×#1654	1	1	yes	characteristic, direct product factor, Sylow
291	C₂×#41	—	2	4	no	—
292	C₂×#41	—	2	4	no	—
293	C₂×#41	—	4	4	no	—
294	C₂×#41	—	4	4	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
299	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
300	C₂³×C₄	—	2	2	no	—
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂×SD₁₆	—	2	4	no	—
304	C₂×SD₁₆	—	4	4	no	—
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₄⋊Q₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	D₄×C₄₃	1	2	yes	—
314	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
316	#123	—	2	8	no	—
317	#123	—	2	8	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	#121	—	2	4	no	—
321	#121	—	2	4	no	—
322	C₄×D₄	—	2	1	no	—
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	D₄×C₄₃	1	2	yes	—
327	C₄×D₄	D₄×C₄₃	1	2	yes	—
328	C₄×D₄	C₂³×C₄₃	1	2	yes	—
329	C₄×D₄	C₂³×C₄₃	1	2	yes	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
337	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
338	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
343	#107	—	2	4	no	—
344	#106	—	2	8	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
348	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
349	#103	—	2	4	no	—
350	#102	—	2	4	no	—
351	C₄×C₈	—	2	1	no	—
352	C₄×C₈	C₂³×C₄₃	1	2	yes	—
353	C₂⁴	—	2	1	no	—
354	C₂⁴	—	2	1	no	—
355	#41	—	4	8	no	—
356	#41	—	4	16	no	—
357	#41	—	4	8	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	4	1	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	4	8	no	—
373	C₂×D₄	SD₁₆×C₄₃	1	4	yes	complemented
374	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
375	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	8	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	4	2	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
393	SD₁₆	—	4	8	no	—
394	C₂×C₈	—	2	4	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	4	2	no	—
399	C₂×C₈	—	4	2	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
411	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
412	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
413	C₂²⋊C₄	—	2	8	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	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
420	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
421	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	#120×C₄₃	1	1	yes	characteristic
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	2	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	—	2	4	no	—
441	D₄	—	4	16	no	—
442	D₄	—	4	2	no	—
443	D₄	C₂×SD₁₆×C₄₃	1	4	yes	complemented
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	16	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	4	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	8	2	no	—
460	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
461	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
462	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
463	C₂×C₄	C₂×SD₁₆×C₄₃	1	2	yes	—
464	C₂×C₄	#135×C₄₃	1	2	yes	—
465	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
466	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
467	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
470	C₈	—	2	4	no	—
471	C₈	—	4	2	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	4	no	—
474	C₂²	—	4	8	no	—
475	C₂²	—	4	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	8	4	no	—
481	C₂²	C₄₃×#449	1	2	yes	—
482	C₂²	C₄₃×#450	1	2	yes	—
483	C₂²	C₄₃×#456	1	2	yes	—
484	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	8	2	no	—
491	C₄	C₄₃×#449	1	2	yes	—
492	C₄	C₄₃×#450	1	2	yes	—
493	C₄	C₂²×SD₁₆×C₄₃	1	1	yes	characteristic
494	C₄	C₂×#135×C₄₃	1	1	yes	characteristic
495	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
496	C₄	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
497	C₂	—	4	4	no	—
498	C₂	—	8	2	no	—
499	C₂	C₄₃×#1654	1	4	yes	direct product factor
500	C₂	C₂×C₄₃×#450	1	1	yes	characteristic
501	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
502	C₂	C₂×C₄₃×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#547	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#498	C₂	semidirect
3. C₂×C₄₃×#474	C₂	semidirect
4. C₂×C₄₃×#461	C₂	semidirect
5. C₄₃×#1654	C₂	direct (N × H)
6. C₂×C₄₃×#332	C₂	semidirect
7. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
8. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
24. C₄₃×#498	C₂²	semidirect
26. C₄₃×#474	C₂²	semidirect
28. C₄₃×#461	C₂²	semidirect
36. C₄₃×#332	C₂²	semidirect
37. C₄₃×D₄⋊C₈	C₂²	semidirect
38. C₄₃×D₄⋊C₈	C₂²	semidirect
121. C₂×D₄×C₄₃	SD₁₆	semidirect
191. D₄×C₄₃	C₂×SD₁₆	semidirect
221. C₂×#1654	C₄₃	direct (N × H)
247. C₂×#498	C₂×C₄₃	semidirect
248. C₂×#474	C₂×C₄₃	semidirect
249. C₂×#461	C₂×C₄₃	semidirect
250. #1654	C₂×C₄₃	direct (N × H)
251. C₂×#332	C₂×C₄₃	semidirect
252. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
253. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
256. C₂×C₄₃	#1654	direct (N × H)
275. #498	C₂²×C₄₃	semidirect
277. #474	C₂²×C₄₃	semidirect
279. #461	C₂²×C₄₃	semidirect
287. #332	C₂²×C₄₃	semidirect
288. D₄⋊C₈	C₂²×C₄₃	semidirect
289. D₄⋊C₈	C₂²×C₄₃	semidirect
290. C₄₃	C₂×#1654	direct (N × H)
373. C₂×D₄	SD₁₆×C₄₃	semidirect
443. D₄	C₂×SD₁₆×C₄₃	semidirect
499. C₂	C₄₃×#1654	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×#547	2
C₂×C₄₃×#498	2
C₂×C₄₃×#474	2
C₂×C₄₃×#461	2
C₄₃×#1654	2
C₂×C₄₃×#332	2
C₂×C₄₃×D₄⋊C₈	2
C₂×#1654	43

Subgroups — C2×C43×#1654 #24938513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₃×#1654 #24938513