Subgroups — C₄×2₋¹⁺⁴×D₄₃ #26003202

Order 11008.

11210 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×2₋¹⁺⁴×D₄₃	C₂	1	1	yes	maximal, characteristic
2	2₋¹⁺⁴×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063373	C₂	1	5	yes	maximal, complemented
4	#19147806	C₂	1	10	yes	maximal, complemented
5	C₄×#13063372	C₂	1	10	yes	maximal, complemented
6	#19147804	C₂	1	5	yes	maximal, complemented
7	#520×D₄₃	C₂	1	10	yes	maximal, complemented
8	#519×D₄₃	C₂	1	5	yes	maximal, complemented
9	C₄×#41×D₄₃	C₂	1	10	yes	maximal, complemented
10	C₂×C₄×Q₈×D₄₃	C₂	1	5	yes	maximal, complemented
11	C₄×2₋¹⁺⁴×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063373	C₂²	1	5	yes	—
13	C₂×#13063372	C₂²	1	10	yes	—
14	2₋¹⁺⁴×D₄₃	C₄	1	32	yes	direct product factor
15	C₂×#41×D₄₃	C₂²	1	10	yes	—
16	C₂²×Q₈×D₄₃	C₂²	1	5	yes	—
17	#14583382	C₂²	1	10	yes	complemented
18	#14583381	C₂²	1	20	yes	complemented
19	#14583380	C₂²	1	30	yes	complemented
20	#14583379	C₂²	1	30	yes	complemented
21	#14583378	C₂²	1	60	yes	complemented
22	#14583377	C₂²	1	5	yes	complemented
23	#14583376	C₂²	1	30	yes	complemented
24	#14583375	C₂²	1	20	yes	complemented
25	#14583375	C₂²	1	20	yes	complemented
26	#41×Dic₄₃	C₂²	1	10	yes	complemented
27	C₄×#10621902	C₂²	1	10	yes	complemented
28	C₄×#10621902	C₂²	1	10	yes	complemented
29	C₄×#10621898	C₂²	1	30	yes	complemented
30	#14583367	C₂²	1	30	yes	complemented
31	C₄×#10621900	C₂²	1	30	yes	complemented
32	C₄×#10621900	C₂²	1	30	yes	complemented
33	C₂×Q₈×Dic₄₃	C₂²	1	5	yes	complemented
34	C₂×C₄×Dic₈₆	C₂²	1	15	yes	complemented
35	C₂×#13063290	C₂²	1	15	yes	complemented
36	C₄×Q₈×D₄₃	C₂²	1	10	yes	—
37	C₄×Q₈×D₄₃	C₂²	1	20	yes	—
38	C₄×Q₈×D₄₃	C₂²	1	10	yes	—
39	C₄×Q₈×D₄₃	C₂²	1	20	yes	complemented
40	C₄×Q₈×D₄₃	C₂²	1	20	yes	complemented
41	C₄×D₄×D₄₃	C₂²	1	30	yes	—
42	C₄×D₄×D₄₃	C₂²	1	10	yes	—
43	#117×D₄₃	C₂²	1	30	yes	—
44	C₂×C₄⋊C₄×D₄₃	C₂²	1	15	yes	—
45	C₂×C₄²×D₄₃	C₂²	1	15	yes	—
46	C₂×2₋¹⁺⁴×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#520	C₂²	1	10	yes	complemented
48	C₄₃×#519	C₂²	1	5	yes	complemented
49	C₄×#41×C₄₃	C₂²	1	10	yes	complemented
50	C₂×C₄×Q₈×C₄₃	C₂²	1	5	yes	complemented
51	#13063373	C₂×C₄	1	80	yes	complemented
52	#13063372	C₂×C₄	1	160	yes	complemented
53	C₂×#10621902	C₂³	1	10	yes	—
54	C₂×#10621898	C₂³	1	30	yes	—
55	C₂×#10621900	C₂³	1	30	yes	—
56	#41×D₄₃	C₂×C₄	1	160	yes	complemented
57	C₂²×Dic₈₆	C₂³	1	15	yes	—
58	C₂×Q₈×D₄₃	C₂×C₄	1	80	yes	complemented
59	C₂×Q₈×D₄₃	C₂³	1	10	yes	—
60	C₂×Q₈×D₄₃	C₂³	1	20	yes	—
61	C₂×D₄×D₄₃	C₂³	1	10	yes	—
62	C₂²×C₄×D₄₃	C₂³	1	5	yes	—
63	C₂²×C₄×D₄₃	C₂³	1	15	yes	—
64	C₂²×C₄×D₄₃	C₂³	1	15	yes	—
65	Q₈×Dic₄₃	C₂³	1	10	yes	—
66	Q₈×Dic₄₃	C₂³	1	20	yes	—
67	Q₈×Dic₄₃	C₂³	1	10	yes	—
68	C₄×Dic₈₆	C₂³	1	30	yes	—
69	C₄×Dic₈₆	C₂³	1	60	yes	—
70	C₄×Dic₈₆	C₂³	1	30	yes	—
71	#13063290	C₂³	1	30	yes	—
72	#13063290	C₂³	1	60	yes	—
73	#13063290	C₂³	1	30	yes	—
74	C₄×D₁₇₂	C₂³	1	10	yes	—
75	C₄×D₁₇₂	C₂³	1	30	yes	—
76	D₄×Dic₄₃	C₂³	1	10	yes	—
77	D₄×Dic₄₃	C₂³	1	30	yes	—
78	#13063287	C₂³	1	10	yes	—
79	#13063287	C₂³	1	30	yes	—
80	C₄×C₂²⋊D₄₃	C₂³	1	20	yes	—
81	C₄×C₂²⋊D₄₃	C₂³	1	60	yes	—
82	(C₂²⋊D₄₃)⋊C₄	C₂³	1	20	yes	—
83	(C₂²⋊D₄₃)⋊C₄	C₂³	1	60	yes	—
84	#13063284	C₂³	1	30	yes	—
85	#13063283	C₂³	1	30	yes	—
86	#13063283	C₂³	1	30	yes	—
87	#13063282	C₂³	1	60	yes	—
88	#13063281	C₂³	1	60	yes	—
89	C₂×C₄⋊Dic₄₃	C₂³	1	15	yes	—
90	C₂×Dic₄₃⋊C₄	C₂³	1	30	yes	—
91	C₄⋊C₄×D₄₃	C₂³	1	30	yes	—
92	C₄⋊C₄×D₄₃	C₂³	1	60	yes	—
93	C₄⋊C₄×D₄₃	C₂³	1	10	yes	—
94	C₂²⋊C₄×D₄₃	C₂³	1	20	yes	—
95	C₂×C₄×Dic₄₃	C₂³	1	15	yes	—
96	C₂×C₄×Dic₄₃	C₂³	1	15	yes	—
97	C₂×C₄×Dic₄₃	C₂³	1	15	yes	—
98	C₄²×D₄₃	C₂³	1	10	yes	—
99	C₄²×D₄₃	C₂³	1	30	yes	—
100	C₄²×D₄₃	C₂³	1	30	yes	—
101	C₄²×D₄₃	C₂³	1	30	yes	—
102	2₋¹⁺⁴×C₄₃	C₂×C₄	1	16	yes	complemented
103	C₂×#41×C₄₃	C₂³	1	10	yes	—
104	C₂²×Q₈×C₄₃	C₂³	1	5	yes	—
105	C₄×Q₈×C₄₃	C₂³	1	10	yes	—
106	C₄×Q₈×C₄₃	C₂³	1	20	yes	—
107	C₄×Q₈×C₄₃	C₂³	1	10	yes	—
108	C₄×D₄×C₄₃	C₂³	1	10	yes	—
109	C₄×D₄×C₄₃	C₂³	1	30	yes	—
110	#117×C₄₃	C₂³	1	30	yes	—
111	C₂×C₄⋊C₄×C₄₃	C₂³	1	15	yes	—
112	C₂×C₄²×C₄₃	C₂³	1	15	yes	—
113	C₂³×D₄₃	C₂⁴	1	5	yes	—
114	#41×C₄₃	C₂²×C₄	1	80	yes	complemented
115	C₂×Q₈×C₄₃	C₂²×C₄	1	40	yes	complemented
116	C₂×Q₈×C₄₃	C₂⁴	1	10	yes	—
117	C₂×D₄×C₄₃	C₂⁴	1	10	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	5	yes	—
119	C₂²×C₄×C₄₃	C₂⁴	1	15	yes	—
120	C₂²×C₄×C₄₃	C₂⁴	1	15	yes	—
121	C₂×C₂²⋊D₄₃	C₂⁴	1	20	yes	—
122	C₂²×Dic₄₃	C₂⁴	1	5	yes	—
123	C₂²×Dic₄₃	C₂⁴	1	15	yes	—
124	C₂²×Dic₄₃	C₂⁴	1	15	yes	—
125	#10621902	C₂²×C₄	1	80	yes	complemented
126	Q₈×D₄₃	C₂²×C₄	1	80	yes	—
127	Q₈×D₄₃	C₂²×C₄	1	160	yes	complemented
128	#10621900	C₂²×C₄	1	240	yes	complemented
129	D₄×D₄₃	C₂²×C₄	1	80	yes	—
130	#10621898	C₂²×C₄	1	240	yes	complemented
131	C₂×D₁₇₂	C₂⁴	1	10	yes	—
132	C₂×C₄×D₄₃	—	2	20	no	—
133	C₂×C₄×D₄₃	—	4	30	no	—
134	C₂×C₄×D₄₃	C₂²×C₄	1	120	yes	—
135	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
136	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
137	C₂×C₄×D₄₃	C₂⁴	1	5	yes	—
138	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
139	C₂×C₄×D₄₃	C₂⁴	1	30	yes	—
140	C₂×C₄×D₄₃	C₂⁴	1	10	yes	—
141	C₂×C₄×D₄₃	C₂⁴	1	30	yes	—
142	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
143	C₂×Dic₈₆	C₂²×C₄	1	120	yes	complemented
144	C₂×Dic₈₆	C₂⁴	1	30	yes	—
145	C₄⋊C₄×C₄₃	C₂⁴	1	30	yes	—
146	C₄⋊C₄×C₄₃	C₂⁴	1	10	yes	—
147	C₂²⋊C₄×C₄₃	C₂⁴	1	20	yes	—
148	C₄²×C₄₃	C₂⁴	1	10	yes	—
149	C₄²×C₄₃	C₂⁴	1	30	yes	—
150	C₂²⋊Dic₄₃	C₂⁴	1	20	yes	—
151	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
152	(C₂×D₄₃)⋊C₄	C₂⁴	1	20	yes	—
153	C₄⋊Dic₄₃	C₂⁴	1	30	yes	—
154	C₄⋊Dic₄₃	C₂⁴	1	10	yes	—
155	Dic₄₃⋊C₄	C₂⁴	1	60	yes	—
156	Dic₄₃⋊C₄	C₂⁴	1	20	yes	—
157	C₄×Dic₄₃	C₂⁴	1	10	yes	—
158	C₄×Dic₄₃	C₂⁴	1	10	yes	—
159	C₄×Dic₄₃	C₂⁴	1	10	yes	—
160	C₄×Dic₄₃	C₂⁴	1	30	yes	—
161	C₄×Dic₄₃	C₂⁴	1	30	yes	—
162	C₄×Dic₄₃	C₂⁴	1	30	yes	—
163	C₂³×C₄₃	C₂⁵	1	5	yes	—
164	C₂²×D₄₃	—	2	10	no	—
165	C₂²×D₄₃	—	2	10	no	—
166	C₂²×D₄₃	C₂³×C₄	1	20	yes	—
167	C₂²×D₄₃	C₂⁵	1	5	yes	—
168	C₂²×D₄₃	C₂⁵	1	1	yes	characteristic
169	Q₈×C₄₃	C₂³×C₄	1	40	yes	—
170	D₄×C₄₃	C₂³×C₄	1	40	yes	—
171	C₂×C₄×C₄₃	—	2	10	no	—
172	C₂×C₄×C₄₃	—	4	15	no	—
173	C₂×C₄×C₄₃	C₂³×C₄	1	60	yes	—
174	C₂×C₄×C₄₃	C₂⁵	1	5	yes	—
175	C₂×C₄×C₄₃	C₂⁵	1	10	yes	—
176	C₂×C₄×C₄₃	C₂⁵	1	10	yes	—
177	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
178	C₂²⋊D₄₃	C₂³×C₄	1	80	yes	—
179	C₂×Dic₄₃	—	2	10	no	—
180	C₂×Dic₄₃	—	4	15	no	—
181	C₂×Dic₄₃	C₂³×C₄	1	60	yes	—
182	C₂×Dic₄₃	C₂⁵	1	5	yes	—
183	C₂×Dic₄₃	C₂⁵	1	10	yes	—
184	C₂×Dic₄₃	C₂⁵	1	10	yes	—
185	C₂×Dic₄₃	C₂⁵	1	1	yes	characteristic
186	D₁₇₂	C₂³×C₄	1	40	yes	—
187	C₄×D₄₃	—	2	10	no	—
188	C₄×D₄₃	—	2	20	no	—
189	C₄×D₄₃	—	2	10	no	—
190	C₄×D₄₃	—	2	10	no	—
191	C₄×D₄₃	—	4	30	no	—
192	C₄×D₄₃	C₂³×C₄	1	40	yes	—
193	C₄×D₄₃	C₂³×C₄	1	120	yes	—
194	C₄×D₄₃	2₋¹⁺⁴	1	4	yes	direct product factor
195	Dic₈₆	C₂³×C₄	1	120	yes	—
196	C₂×C₄×2₋¹⁺⁴	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	5	no	—
198	C₂²×C₄₃	—	2	5	no	—
199	C₂²×C₄₃	C₂⁴×C₄	1	10	yes	—
200	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
201	C₂×D₄₃	—	2	5	no	—
202	C₂×D₄₃	—	2	5	no	—
203	C₂×D₄₃	—	2	40	no	—
204	C₂×D₄₃	C₂⁴×C₄	1	10	yes	—
205	C₂×D₄₃	C₂⁴×C₄	1	2	yes	—
206	C₂×D₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
207	C₂×D₄₃	#585	1	2	yes	—
208	C₄×C₄₃	—	2	5	no	—
209	C₄×C₄₃	—	2	10	no	—
210	C₄×C₄₃	C₂⁴×C₄	1	20	yes	—
211	C₄×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	complemented
212	Dic₄₃	—	2	5	no	—
213	Dic₄₃	—	2	10	no	—
214	Dic₄₃	C₂⁴×C₄	1	20	yes	—
215	Dic₄₃	C₂×2₋¹⁺⁴	1	2	yes	complemented
216	C₂²×2₋¹⁺⁴	—	43	1	no	—
217	C₄×2₋¹⁺⁴	—	43	1	no	—
218	C₄×2₋¹⁺⁴	—	43	10	no	—
219	C₄×2₋¹⁺⁴	—	43	5	no	—
220	C₄×2₋¹⁺⁴	—	43	10	no	—
221	C₄×2₋¹⁺⁴	—	43	5	no	—
222	C₄×2₋¹⁺⁴	D₄₃	1	1	yes	characteristic, direct product factor
223	C₂×#520	—	43	10	no	—
224	C₂×#519	—	43	5	no	—
225	C₂×C₄×#41	—	43	10	no	—
226	C₂²×C₄×Q₈	—	43	5	no	—
227	C₂×C₄₃	—	2	10	no	—
228	C₂×C₄₃	C₂⁵×C₄	1	1	yes	characteristic
229	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#585	1	1	yes	characteristic
231	D₄₃	—	2	10	no	—
232	D₄₃	C₄×2₋¹⁺⁴	1	4	yes	direct product factor
233	C₂×2₋¹⁺⁴	—	43	32	no	—
234	C₂×2₋¹⁺⁴	—	43	10	no	—
235	C₂×2₋¹⁺⁴	—	43	5	no	—
236	C₂×2₋¹⁺⁴	C₂×D₄₃	1	1	yes	characteristic
237	C₂²×#41	—	43	10	no	—
238	C₂³×Q₈	—	43	5	no	—
239	#520	—	43	10	no	—
240	#520	—	43	20	no	—
241	#520	—	43	60	no	—
242	#520	—	43	30	no	—
243	#520	—	43	30	no	—
244	#520	C₂×D₄₃	1	10	yes	complemented
245	#519	—	43	5	no	—
246	#519	—	43	20	no	—
247	#519	—	43	20	no	—
248	#519	—	43	30	no	—
249	#519	C₂×D₄₃	1	5	yes	complemented
250	C₄×#41	—	43	10	no	—
251	C₄×#41	—	43	10	no	—
252	C₄×#41	—	43	10	no	—
253	C₄×#41	—	43	30	no	—
254	C₄×#41	—	43	30	no	—
255	C₄×#41	—	43	30	no	—
256	C₄×#41	—	43	30	no	—
257	C₄×#41	C₂×D₄₃	1	10	yes	complemented
258	C₂×C₄×Q₈	—	43	5	no	—
259	C₂×C₄×Q₈	—	43	10	no	—
260	C₂×C₄×Q₈	—	43	20	no	—
261	C₂×C₄×Q₈	—	43	10	no	—
262	C₂×C₄×Q₈	—	43	20	no	—
263	C₂×C₄×Q₈	—	43	20	no	—
264	C₂×C₄×Q₈	—	43	15	no	—
265	C₂×C₄×Q₈	—	43	15	no	—
266	C₂×C₄×Q₈	C₂×D₄₃	1	5	yes	complemented
267	C₂×C₄×D₄	—	43	10	no	—
268	C₂×C₄×D₄	—	43	30	no	—
269	C₂×#117	—	43	30	no	—
270	C₂²×C₄⋊C₄	—	43	15	no	—
271	C₂²×C₄²	—	43	15	no	—
272	C₄₃	C₂×C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
273	2₋¹⁺⁴	—	43	160	no	—
274	2₋¹⁺⁴	—	43	80	no	—
275	2₋¹⁺⁴	C₄×D₄₃	1	16	yes	direct product factor
276	C₂×#41	—	43	160	no	—
277	C₂×#41	—	43	10	no	—
278	C₂×#41	—	43	30	no	—
279	C₂×#41	—	43	30	no	—
280	C₂×#41	C₂²×D₄₃	1	10	yes	—
281	C₂²×Q₈	—	43	80	no	—
282	C₂²×Q₈	—	43	10	no	—
283	C₂²×Q₈	—	43	20	no	—
284	C₂²×Q₈	—	43	15	no	—
285	C₂²×Q₈	C₂²×D₄₃	1	5	yes	—
286	C₂²×D₄	—	43	10	no	—
287	C₂³×C₄	—	43	15	no	—
288	C₂³×C₄	—	43	5	no	—
289	C₂³×C₄	—	43	15	no	—
290	C₄×Q₈	—	43	10	no	—
291	C₄×Q₈	—	43	20	no	—
292	C₄×Q₈	—	43	10	no	—
293	C₄×Q₈	—	43	30	no	—
294	C₄×Q₈	—	43	60	no	—
295	C₄×Q₈	—	43	30	no	—
296	C₄×Q₈	—	43	30	no	—
297	C₄×Q₈	—	43	60	no	—
298	C₄×Q₈	—	43	30	no	—
299	C₄×Q₈	C₂²×D₄₃	1	10	yes	—
300	C₄×Q₈	C₂²×D₄₃	1	20	yes	—
301	C₄×Q₈	C₂²×D₄₃	1	10	yes	—
302	C₄×D₄	—	43	10	no	—
303	C₄×D₄	—	43	30	no	—
304	C₄×D₄	—	43	20	no	—
305	C₄×D₄	—	43	60	no	—
306	C₄×D₄	—	43	10	no	—
307	C₄×D₄	—	43	30	no	—
308	C₄×D₄	—	43	20	no	—
309	C₄×D₄	—	43	60	no	—
310	C₄×D₄	—	43	10	no	—
311	C₄×D₄	—	43	30	no	—
312	C₄×D₄	C₂²×D₄₃	1	10	yes	—
313	C₄×D₄	C₂²×D₄₃	1	30	yes	—
314	#117	—	43	30	no	—
315	#117	—	43	30	no	—
316	#117	—	43	30	no	—
317	#117	—	43	60	no	—
318	#117	—	43	60	no	—
319	#117	C₂²×D₄₃	1	30	yes	—
320	C₂×C₄⋊C₄	—	43	30	no	—
321	C₂×C₄⋊C₄	—	43	15	no	—
322	C₂×C₄⋊C₄	—	43	30	no	—
323	C₂×C₄⋊C₄	—	43	60	no	—
324	C₂×C₄⋊C₄	—	43	10	no	—
325	C₂×C₄⋊C₄	C₂²×D₄₃	1	15	yes	—
326	C₂×C₂²⋊C₄	—	43	20	no	—
327	C₂×C₄²	—	43	15	no	—
328	C₂×C₄²	—	43	15	no	—
329	C₂×C₄²	—	43	15	no	—
330	C₂×C₄²	—	43	30	no	—
331	C₂×C₄²	—	43	10	no	—
332	C₂×C₄²	—	43	30	no	—
333	C₂×C₄²	—	43	30	no	—
334	C₂×C₄²	C₂²×D₄₃	1	15	yes	—
335	C₂⁴	—	43	5	no	—
336	#41	—	43	80	no	—
337	#41	—	43	240	no	—
338	#41	—	43	240	no	—
339	#41	C₂×C₄×D₄₃	1	80	yes	complemented
340	C₂×Q₈	—	43	80	no	—
341	C₂×Q₈	—	43	160	no	—
342	C₂×Q₈	—	43	120	no	—
343	C₂×Q₈	—	43	30	no	—
344	C₂×Q₈	C₂×C₄×D₄₃	1	40	yes	complemented
345	C₂×Q₈	C₂³×D₄₃	1	10	yes	—
346	C₂×D₄	—	43	20	no	—
347	C₂×D₄	—	43	80	no	—
348	C₂×D₄	—	43	10	no	—
349	C₂×D₄	C₂³×D₄₃	1	10	yes	—
350	C₂²×C₄	—	43	15	no	—
351	C₂²×C₄	—	43	120	no	—
352	C₂²×C₄	—	43	10	no	—
353	C₂²×C₄	—	43	30	no	—
354	C₂²×C₄	—	43	1	no	—
355	C₂²×C₄	—	43	5	no	—
356	C₂²×C₄	—	43	15	no	—
357	C₂²×C₄	—	43	5	no	—
358	C₂²×C₄	—	43	5	no	—
359	C₂²×C₄	—	43	10	no	—
360	C₂²×C₄	—	43	5	no	—
361	C₂²×C₄	—	43	30	no	—
362	C₂²×C₄	—	86	20	no	—
363	C₂²×C₄	—	172	30	no	—
364	C₂²×C₄	C₂³×D₄₃	1	5	yes	—
365	C₂²×C₄	C₂³×D₄₃	1	15	yes	—
366	C₂²×C₄	C₂³×D₄₃	1	15	yes	—
367	C₄⋊C₄	—	43	60	no	—
368	C₄⋊C₄	—	43	30	no	—
369	C₄⋊C₄	—	43	20	no	—
370	C₄⋊C₄	—	43	10	no	—
371	C₄⋊C₄	C₂³×D₄₃	1	30	yes	—
372	C₄⋊C₄	C₂³×D₄₃	1	10	yes	—
373	C₂²⋊C₄	—	43	20	no	—
374	C₂²⋊C₄	—	43	20	no	—
375	C₂²⋊C₄	—	43	20	no	—
376	C₂²⋊C₄	C₂³×D₄₃	1	20	yes	—
377	C₄²	—	43	10	no	—
378	C₄²	—	43	10	no	—
379	C₄²	—	43	30	no	—
380	C₄²	—	43	30	no	—
381	C₄²	—	43	30	no	—
382	C₄²	—	43	10	no	—
383	C₄²	C₂³×D₄₃	1	30	yes	—
384	C₄²	C₂³×D₄₃	1	10	yes	—
385	C₂³	—	43	1	no	—
386	C₂³	—	43	20	no	—
387	C₂³	—	43	5	no	—
388	C₂³	—	86	10	no	—
389	C₂³	—	86	10	no	—
390	C₂³	C₂⁴×D₄₃	1	5	yes	—
391	Q₈	—	43	120	no	—
392	Q₈	C₂²×C₄×D₄₃	1	40	yes	—
393	D₄	—	43	80	no	—
394	D₄	—	43	40	no	—
395	D₄	C₂²×C₄×D₄₃	1	40	yes	—
396	C₂×C₄	—	2	10	no	—
397	C₂×C₄	—	4	15	no	—
398	C₂×C₄	—	43	60	no	—
399	C₂×C₄	—	43	1	no	—
400	C₂×C₄	—	43	10	no	—
401	C₂×C₄	—	43	40	no	—
402	C₂×C₄	—	43	120	no	—
403	C₂×C₄	—	43	4	no	—
404	C₂×C₄	—	43	5	no	—
405	C₂×C₄	—	43	10	no	—
406	C₂×C₄	—	86	10	no	—
407	C₂×C₄	—	86	10	no	—
408	C₂×C₄	—	86	20	no	—
409	C₂×C₄	—	86	10	no	—
410	C₂×C₄	—	86	10	no	—
411	C₂×C₄	—	172	30	no	—
412	C₂×C₄	—	172	15	no	—
413	C₂×C₄	C₂²×C₄×D₄₃	1	60	yes	—
414	C₂×C₄	C₂⁴×D₄₃	1	5	yes	—
415	C₂×C₄	C₂⁴×D₄₃	1	10	yes	—
416	C₂×C₄	C₂⁴×D₄₃	1	10	yes	—
417	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
418	C₂²	—	2	5	no	—
419	C₂²	—	2	5	no	—
420	C₂²	—	43	2	no	—
421	C₂²	—	43	2	no	—
422	C₂²	—	43	2	no	—
423	C₂²	—	43	10	no	—
424	C₂²	—	86	40	no	—
425	C₂²	—	86	5	no	—
426	C₂²	—	86	5	no	—
427	C₂²	C₂³×C₄×D₄₃	1	10	yes	—
428	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
429	C₄	—	2	5	no	—
430	C₄	—	2	10	no	—
431	C₄	—	43	20	no	—
432	C₄	—	43	2	no	—
433	C₄	—	86	5	no	—
434	C₄	—	86	10	no	—
435	C₄	C₂³×C₄×D₄₃	1	20	yes	—
436	C₄	2₋¹⁺⁴×D₄₃	1	2	yes	direct product factor
437	C₂	—	2	10	no	—
438	C₂	—	43	4	no	—
439	C₂	—	86	10	no	—
440	C₂	C₂⁴×C₄×D₄₃	1	1	yes	characteristic
441	C₂	C₂×2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
442	C₂	#585×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₃
commutator	C₂×C₄₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₄×2₋¹⁺⁴×C₄₃	C₂
socle, cosocle	C₂²×C₄₃	C₂⁶
prime radical	C₂×2₋¹⁺⁴×D₄₃	C₂
hypercenter	C₄×2₋¹⁺⁴	D₄₃
hypocenter	C₄₃	C₂×C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
2. 2₋¹⁺⁴×Dic₄₃	C₂	semidirect
3. C₄×#13063373	C₂	semidirect
4. #19147806	C₂	semidirect
5. C₄×#13063372	C₂	semidirect
6. #19147804	C₂	semidirect
7. #520×D₄₃	C₂	semidirect
8. #519×D₄₃	C₂	semidirect
9. C₄×#41×D₄₃	C₂	semidirect
10. C₂×C₄×Q₈×D₄₃	C₂	semidirect
11. C₄×2₋¹⁺⁴×C₄₃	C₂	semidirect
14. 2₋¹⁺⁴×D₄₃	C₄	direct (N × H)
17. #14583382	C₂²	semidirect
18. #14583381	C₂²	semidirect
19. #14583380	C₂²	semidirect
20. #14583379	C₂²	semidirect
21. #14583378	C₂²	semidirect
22. #14583377	C₂²	semidirect
23. #14583376	C₂²	semidirect
24. #14583375	C₂²	semidirect
25. #14583375	C₂²	semidirect
26. #41×Dic₄₃	C₂²	semidirect
27. C₄×#10621902	C₂²	semidirect
28. C₄×#10621902	C₂²	semidirect
29. C₄×#10621898	C₂²	semidirect
30. #14583367	C₂²	semidirect
31. C₄×#10621900	C₂²	semidirect
32. C₄×#10621900	C₂²	semidirect
33. C₂×Q₈×Dic₄₃	C₂²	semidirect
34. C₂×C₄×Dic₈₆	C₂²	semidirect
35. C₂×#13063290	C₂²	semidirect
39. C₄×Q₈×D₄₃	C₂²	semidirect
40. C₄×Q₈×D₄₃	C₂²	semidirect
47. C₄₃×#520	C₂²	semidirect
48. C₄₃×#519	C₂²	semidirect
49. C₄×#41×C₄₃	C₂²	semidirect
50. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
51. #13063373	C₂×C₄	semidirect
52. #13063372	C₂×C₄	semidirect
56. #41×D₄₃	C₂×C₄	semidirect
58. C₂×Q₈×D₄₃	C₂×C₄	semidirect
102. 2₋¹⁺⁴×C₄₃	C₂×C₄	semidirect
114. #41×C₄₃	C₂²×C₄	semidirect
115. C₂×Q₈×C₄₃	C₂²×C₄	semidirect
125. #10621902	C₂²×C₄	semidirect
127. Q₈×D₄₃	C₂²×C₄	semidirect
128. #10621900	C₂²×C₄	semidirect
130. #10621898	C₂²×C₄	semidirect
143. C₂×Dic₈₆	C₂²×C₄	semidirect
194. C₄×D₄₃	2₋¹⁺⁴	direct (N × H)
211. C₄×C₄₃	C₂×2₋¹⁺⁴	semidirect
215. Dic₄₃	C₂×2₋¹⁺⁴	semidirect
222. C₄×2₋¹⁺⁴	D₄₃	direct (N × H)
232. D₄₃	C₄×2₋¹⁺⁴	direct (N × H)
244. #520	C₂×D₄₃	semidirect
249. #519	C₂×D₄₃	semidirect
257. C₄×#41	C₂×D₄₃	semidirect
266. C₂×C₄×Q₈	C₂×D₄₃	semidirect
272. C₄₃	C₂×C₄×2₋¹⁺⁴	semidirect
275. 2₋¹⁺⁴	C₄×D₄₃	direct (N × H)
339. #41	C₂×C₄×D₄₃	semidirect
344. C₂×Q₈	C₂×C₄×D₄₃	semidirect
436. C₄	2₋¹⁺⁴×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×2₋¹⁺⁴×D₄₃	2
2₋¹⁺⁴×Dic₄₃	2
C₄×#13063373	2
#19147806	2
C₄×#13063372	2
#19147804	2
#520×D₄₃	2
#519×D₄₃	2
C₄×#41×D₄₃	2
C₂×C₄×Q₈×D₄₃	2
C₄×2₋¹⁺⁴×C₄₃	2
C₂×C₄×2₋¹⁺⁴	43

Subgroups — C4×2−1+4×D43 #26003202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×2₋¹⁺⁴×D₄₃ #26003202