Subgroups — C₄₃×#20728 #24940745

Order 11008.

1294 conjugacy classes of subgroups.

The subgroup lattice has 498 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	C₄₃×#2920	C₂	1	2	yes	maximal, complemented
3	C₄₃×#1822	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1801	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1800	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1785	C₂	1	2	yes	maximal
7	C₄×#101×C₄₃	C₂	1	2	yes	maximal, complemented
8	C₄×#100×C₄₃	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₄×#41×C₄₃	—	2	2	no	—
11	C₄×#41×C₄₃	—	2	2	no	—
12	C₄×#41×C₄₃	—	2	2	no	—
13	C₄×#41×C₄₃	—	2	2	no	—
14	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
17	C₂×C₄×D₄×C₄₃	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₃	C₄	1	2	yes	—
21	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₃	C₄	1	2	yes	—
23	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
24	C₄₃×#432	—	2	2	no	—
25	C₄₃×#432	—	2	2	no	—
26	C₄₃×#431	—	2	2	no	—
27	C₄₃×#431	—	2	2	no	—
28	C₄₃×#423	C₂²	1	4	yes	—
29	C₂×#101×C₄₃	C₂²	1	4	yes	—
30	C₂×#100×C₄₃	C₂²	1	4	yes	—
31	C₄₃×#407	C₂²	1	4	yes	—
32	C₄×M₁₆×C₄₃	C₂²	1	4	yes	—
33	C₄₃×#343	C₂²	1	4	yes	—
34	C₄₃×#343	C₂²	1	4	yes	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂×#41×C₄₃	—	2	4	no	—
37	C₂×#41×C₄₃	—	2	2	no	—
38	C₂×#41×C₄₃	—	2	2	no	—
39	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
41	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
43	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₄₃	C₂³	1	8	yes	—
49	C₄×Q₈×C₄₃	—	2	2	no	—
50	C₄×Q₈×C₄₃	—	2	2	no	—
51	C₄×Q₈×C₄₃	—	2	2	no	—
52	C₄×Q₈×C₄₃	—	2	2	no	—
53	C₄×D₄×C₄₃	—	2	4	no	—
54	C₄×D₄×C₄₃	—	2	4	no	—
55	C₄×D₄×C₄₃	—	2	4	no	—
56	C₄×D₄×C₄₃	—	2	4	no	—
57	C₄×D₄×C₄₃	—	2	2	no	—
58	C₄×D₄×C₄₃	—	2	2	no	—
59	C₄×D₄×C₄₃	—	2	2	no	—
60	C₄×D₄×C₄₃	—	2	2	no	—
61	#117×C₄₃	—	2	2	no	—
62	#117×C₄₃	—	2	2	no	—
63	#117×C₄₃	—	2	4	no	—
64	#117×C₄₃	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₃	D₄	1	2	yes	—
82	C₂×C₄²×C₄₃	D₄	1	2	yes	—
83	C₂×C₄²×C₄₃	D₄	1	2	yes	—
84	C₂×C₄²×C₄₃	D₄	1	2	yes	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₃	—	2	4	no	—
88	C₄⋊C₈×C₄₃	—	2	4	no	—
89	#101×C₄₃	—	2	8	no	—
90	#100×C₄₃	—	2	8	no	—
91	C₂²⋊C₈×C₄₃	—	2	4	no	—
92	C₂²⋊C₈×C₄₃	—	2	4	no	—
93	#97×C₄₃	—	2	4	no	—
94	C₄×C₈×C₄₃	—	2	4	no	—
95	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
96	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
97	#41×C₄₃	—	2	16	no	—
98	#41×C₄₃	—	2	16	no	—
99	C₂×Q₈×C₄₃	—	2	2	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	#41	1	4	yes	—
102	C₂×D₄×C₄₃	—	2	4	no	—
103	C₂×D₄×C₄₃	—	2	2	no	—
104	C₂×D₄×C₄₃	—	2	2	no	—
105	C₂×D₄×C₄₃	—	2	4	no	—
106	C₂×D₄×C₄₃	—	2	4	no	—
107	C₂×D₄×C₄₃	#41	1	4	yes	—
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	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	4	no	—
118	C₂²×C₄×C₄₃	—	4	2	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	—	4	4	no	—
121	C₂²×C₄×C₄₃	—	4	4	no	—
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
125	C₂²×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
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	2	yes	—
136	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
137	M₁₆×C₄₃	—	2	8	no	—
138	M₁₆×C₄₃	—	2	8	no	—
139	C₂×C₈×C₄₃	—	2	8	no	—
140	C₄⋊C₄×C₄₃	—	2	4	no	—
141	C₄⋊C₄×C₄₃	—	2	4	no	—
142	C₄⋊C₄×C₄₃	—	2	2	no	—
143	C₄⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	2	4	no	—
145	C₂²⋊C₄×C₄₃	—	2	4	no	—
146	C₂²⋊C₄×C₄₃	—	2	4	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₄²×C₄₃	—	2	2	no	—
151	C₄²×C₄₃	—	2	2	no	—
152	C₄²×C₄₃	—	2	2	no	—
153	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
156	C₄²×C₄₃	C₂²⋊C₄	1	2	yes	—
157	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
159	C₄²×C₄₃	C₂×D₄	1	2	yes	—
160	C₄²×C₄₃	C₂×D₄	1	2	yes	—
161	C₄²×C₄₃	C₂×D₄	1	2	yes	—
162	C₄²×C₄₃	C₂×D₄	1	2	yes	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	2	1	no	—
165	C₂³×C₄₃	—	2	1	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	4	1	no	—
168	C₂³×C₄₃	—	4	1	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	—	4	2	no	—
171	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
172	C₂³×C₄₃	#117	1	4	yes	—
173	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
174	Q₈×C₄₃	—	2	8	no	—
175	D₄×C₄₃	—	2	16	no	—
176	D₄×C₄₃	—	2	8	no	—
177	C₂×C₄×C₄₃	—	2	8	no	—
178	C₂×C₄×C₄₃	—	2	8	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	4	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	4	no	—
188	C₂×C₄×C₄₃	—	2	4	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	—	4	2	no	—
193	C₂×C₄×C₄₃	—	4	1	no	—
194	C₂×C₄×C₄₃	—	4	1	no	—
195	C₂×C₄×C₄₃	—	4	4	no	—
196	C₂×C₄×C₄₃	—	4	4	no	—
197	C₂×C₄×C₄₃	—	4	4	no	—
198	C₂×C₄×C₄₃	—	4	4	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	#117	1	4	yes	—
210	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
212	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
213	C₈×C₄₃	—	4	8	no	—
214	#20728	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₃	—	2	1	no	—
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	2	2	no	—
219	C₂²×C₄₃	—	2	2	no	—
220	C₂²×C₄₃	—	2	4	no	—
221	C₂²×C₄₃	—	4	4	no	—
222	C₂²×C₄₃	—	4	2	no	—
223	C₂²×C₄₃	—	4	2	no	—
224	C₂²×C₄₃	—	4	4	no	—
225	C₂²×C₄₃	—	4	2	no	—
226	C₂²×C₄₃	—	4	2	no	—
227	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
229	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	2	no	—
233	C₄×C₄₃	—	2	2	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	4	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	#413	1	2	yes	—
240	C₄×C₄₃	#413	1	2	yes	—
241	C₄×C₄₃	#525	1	4	yes	—
242	C₂×C₄×#41	C₂×C₄₃	1	1	yes	characteristic
243	#2920	C₂×C₄₃	1	2	yes	complemented
244	#1822	C₂×C₄₃	1	2	yes	complemented
245	#1801	C₂×C₄₃	1	2	yes	complemented
246	#1800	C₂×C₄₃	1	2	yes	complemented
247	#1785	C₂×C₄₃	1	2	yes	—
248	C₄×#101	C₂×C₄₃	1	2	yes	complemented
249	C₄×#100	C₂×C₄₃	1	2	yes	complemented
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	2	1	no	—
252	C₂×C₄₃	—	4	2	no	—
253	C₂×C₄₃	—	4	4	no	—
254	C₂×C₄₃	#2280	1	1	yes	characteristic
255	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
256	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
257	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
258	C₄×#41	—	2	2	no	—
259	C₄×#41	—	2	2	no	—
260	C₄×#41	—	2	2	no	—
261	C₄×#41	—	2	2	no	—
262	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
264	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
265	C₂×C₄×D₄	C₄×C₄₃	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
267	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
268	C₂×#117	C₄×C₄₃	1	2	yes	—
269	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
270	C₂²×C₄²	C₄×C₄₃	1	2	yes	—
271	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
272	#432	—	2	2	no	—
273	#432	—	2	2	no	—
274	#431	—	2	2	no	—
275	#431	—	2	2	no	—
276	#423	C₂²×C₄₃	1	4	yes	—
277	C₂×#101	C₂²×C₄₃	1	4	yes	—
278	C₂×#100	C₂²×C₄₃	1	4	yes	—
279	#407	C₂²×C₄₃	1	4	yes	—
280	C₄×M₁₆	C₂²×C₄₃	1	4	yes	—
281	#343	C₂²×C₄₃	1	4	yes	—
282	#343	C₂²×C₄₃	1	4	yes	—
283	C₄₃	#20728	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	—	2	2	no	—
288	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
289	C₂²×D₄	C₂×C₄×C₄₃	1	2	yes	—
290	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
291	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
292	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
293	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
294	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
295	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
296	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
297	C₂×M₁₆	C₂³×C₄₃	1	8	yes	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	2	2	no	—
300	C₄×Q₈	—	2	2	no	—
301	C₄×Q₈	—	2	2	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	—	2	4	no	—
304	C₄×D₄	—	2	4	no	—
305	C₄×D₄	—	2	4	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	—	2	2	no	—
309	C₄×D₄	—	2	2	no	—
310	#117	—	2	2	no	—
311	#117	—	2	2	no	—
312	#117	—	2	4	no	—
313	#117	—	2	4	no	—
314	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
315	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	2	yes	—
321	C₂×C₄²	—	2	2	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
326	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
327	C₂×C₄²	C₂×C₄×C₄₃	1	2	yes	—
328	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
330	C₂×C₄²	D₄×C₄₃	1	2	yes	—
331	C₂×C₄²	D₄×C₄₃	1	2	yes	—
332	C₂×C₄²	D₄×C₄₃	1	2	yes	—
333	C₂×C₄²	D₄×C₄₃	1	2	yes	—
334	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
336	C₄⋊C₈	—	2	4	no	—
337	C₄⋊C₈	—	2	4	no	—
338	#101	—	2	8	no	—
339	#100	—	2	8	no	—
340	C₂²⋊C₈	—	2	4	no	—
341	C₂²⋊C₈	—	2	4	no	—
342	#97	—	2	4	no	—
343	C₄×C₈	—	2	4	no	—
344	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
345	C₂⁴	C₂²×C₄×C₄₃	1	2	yes	—
346	#41	—	2	16	no	—
347	#41	—	2	16	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	#41×C₄₃	1	4	yes	—
351	C₂×D₄	—	2	4	no	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	#41×C₄₃	1	4	yes	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	4	2	no	—
369	C₂²×C₄	—	4	4	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
372	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
373	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
374	C₂²×C₄	C₂²⋊C₄×C₄₃	1	2	yes	—
375	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
382	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
386	M₁₆	—	2	8	no	—
387	M₁₆	—	2	8	no	—
388	C₂×C₈	—	2	8	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	2	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	2	no	—
401	C₄²	—	2	2	no	—
402	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
403	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
404	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
405	C₄²	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
406	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
407	C₄²	C₂²⋊C₄×C₄₃	1	2	yes	—
408	C₄²	C₂×D₄×C₄₃	1	2	yes	—
409	C₄²	C₂×D₄×C₄₃	1	2	yes	—
410	C₄²	C₂×D₄×C₄₃	1	2	yes	—
411	C₄²	C₂×D₄×C₄₃	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	4	1	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	C₂×C₂²⋊C₄×C₄₃	1	2	yes	—
421	C₂³	#117×C₄₃	1	4	yes	—
422	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
423	Q₈	—	2	8	no	—
424	D₄	—	2	16	no	—
425	D₄	—	2	8	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
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	1	yes	characteristic
457	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
458	C₂×C₄	#117×C₄₃	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
460	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
461	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
462	C₈	—	4	8	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
476	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
477	C₂²	C₂×#117×C₄₃	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	2	4	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	C₄₃×#413	1	2	yes	—
488	C₄	C₄₃×#413	1	2	yes	—
489	C₄	C₄₃×#525	1	4	yes	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	4	4	no	—
494	C₂	C₄₃×#2280	1	1	yes	characteristic
495	C₂	C₂×C₄₃×#413	1	1	yes	characteristic
496	C₂	C₂×C₄₃×#413	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄₃×#2920	C₂	semidirect
3. C₄₃×#1822	C₂	semidirect
4. C₄₃×#1801	C₂	semidirect
5. C₄₃×#1800	C₂	semidirect
7. C₄×#101×C₄₃	C₂	semidirect
8. C₄×#100×C₄₃	C₂	semidirect
214. #20728	C₄₃	direct (N × H)
243. #2920	C₂×C₄₃	semidirect
244. #1822	C₂×C₄₃	semidirect
245. #1801	C₂×C₄₃	semidirect
246. #1800	C₂×C₄₃	semidirect
248. C₄×#101	C₂×C₄₃	semidirect
249. C₄×#100	C₂×C₄₃	semidirect
283. C₄₃	#20728	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
C₄₃×#2920	2
C₄₃×#1822	2
C₄₃×#1801	2
C₄₃×#1800	2
C₄₃×#1785	2
C₄×#101×C₄₃	2
C₄×#100×C₄₃	2
#20728	43

Subgroups — C43×#20728 #24940745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#20728 #24940745