Subgroups — C₂×#19143600 #25961082

Order 11008.

2014 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143600	C₂	1	16	yes	maximal, direct product factor
2	C₂×#14583030	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582977	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582977	C₂	1	2	yes	maximal, complemented
6	C₂×#14582971	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14582960	C₂	1	2	yes	maximal, complemented
9	C₂×#14582952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582855	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
13	C₂²×#10621877	C₂²	1	1	yes	characteristic
14	C₂²×#10621877	C₂²	1	1	yes	characteristic
15	C₂²×#10621877	C₂²	1	2	yes	—
16	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
17	#14583030	C₂²	1	8	yes	complemented
18	Q₈×C₄₃⋊C₈	C₂²	1	8	yes	complemented
19	#14582977	C₂²	1	8	yes	complemented
20	#14582977	C₂²	1	16	yes	complemented
21	#14582971	C₂²	1	16	yes	complemented
22	D₄×C₄₃⋊C₈	C₂²	1	8	yes	complemented
23	#14582960	C₂²	1	16	yes	complemented
24	#14582952	C₂²	1	8	yes	complemented
25	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
29	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
30	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
31	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
32	#14582855	C₂²	1	16	yes	complemented
33	C₄×#10621877	C₂²	1	8	yes	complemented
34	C₂×#13063236	C₂²	1	1	yes	characteristic
35	C₂×#13063236	C₂²	1	1	yes	characteristic
36	C₂×#13063236	C₂²	1	2	yes	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
41	C₄₃×#529	C₄	1	8	yes	—
42	C₄₃×#529	C₂²	1	8	yes	—
43	C₂×#126×C₄₃	C₄	1	2	yes	—
44	C₂×#125×C₄₃	C₄	1	1	yes	characteristic
45	C₂×#124×C₄₃	C₄	1	1	yes	characteristic
46	C₂×#123×C₄₃	C₄	1	2	yes	—
47	C₂×C₂²⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
48	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
52	C₂×#117×C₄₃	C₂²	1	2	yes	—
53	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
54	C₂×#10621877	—	2	4	no	—
55	C₂×#10621877	—	2	4	no	—
56	C₂×#10621877	—	2	8	no	—
57	C₂×#10621877	C₂³	1	4	yes	—
58	C₂×#10621877	C₂³	1	4	yes	—
59	C₂×#10621877	C₂³	1	8	yes	—
60	C₂²×C₄₃⋊C₈	—	2	8	no	—
61	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
62	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
63	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
72	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
73	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
74	C₂²⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
75	#13063236	C₂³	1	4	yes	—
76	#13063236	C₂³	1	4	yes	—
77	#13063236	C₂³	1	8	yes	—
78	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
79	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
80	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
81	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
82	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
85	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
86	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
89	#126×C₄₃	C₂×C₄	1	16	yes	—
90	#125×C₄₃	C₂×C₄	1	8	yes	—
91	#124×C₄₃	C₂×C₄	1	8	yes	—
92	#123×C₄₃	C₂×C₄	1	16	yes	—
93	C₂²⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
94	#121×C₄₃	C₂×C₄	1	8	yes	—
95	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
96	C₄×Q₈×C₄₃	C₂³	1	4	yes	—
97	C₄×D₄×C₄₃	C₂×C₄	1	4	yes	—
98	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
99	C₄×D₄×C₄₃	C₂³	1	4	yes	—
100	C₄×D₄×C₄₃	C₂³	1	8	yes	—
101	#117×C₄₃	C₂×C₄	1	8	yes	—
102	#117×C₄₃	C₂³	1	8	yes	—
103	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
104	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
113	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
114	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
117	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
120	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
121	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
122	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×Q₈×C₄₃	—	2	4	no	—
124	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
125	C₂×D₄×C₄₃	—	2	4	no	—
126	C₂×D₄×C₄₃	—	4	4	no	—
127	C₂×D₄×C₄₃	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
129	C₂²×C₄×C₄₃	—	2	4	no	—
130	C₂²×C₄×C₄₃	—	2	4	no	—
131	C₂²×C₄×C₄₃	—	2	2	no	—
132	C₂²×C₄×C₄₃	—	2	2	no	—
133	C₂²×C₄×C₄₃	—	2	4	no	—
134	C₂²×C₄×C₄₃	—	4	2	no	—
135	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
145	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
150	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
151	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
152	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
153	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
154	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
155	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
156	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
157	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
158	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
159	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
160	C₂²⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
161	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
162	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
163	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
164	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
165	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
166	C₄²×C₄₃	C₂⁴	1	2	yes	—
167	C₄²×C₄₃	C₂⁴	1	2	yes	—
168	C₄²×C₄₃	C₂⁴	1	4	yes	—
169	#10621877	—	2	8	no	—
170	#10621877	—	2	8	no	—
171	#10621877	—	2	16	no	—
172	C₂×C₄₃⋊C₈	—	2	4	no	—
173	C₂×C₄₃⋊C₈	—	2	2	no	—
174	C₂×C₄₃⋊C₈	—	2	4	no	—
175	C₂×C₄₃⋊C₈	—	2	2	no	—
176	C₂×C₄₃⋊C₈	—	2	16	no	—
177	C₂×C₄₃⋊C₈	#41	1	4	yes	—
178	C₂×C₄₃⋊C₈	#41	1	4	yes	—
179	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
180	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
181	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
182	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
183	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
184	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
185	C₂³×C₄₃	—	2	4	no	—
186	C₂³×C₄₃	—	2	2	no	—
187	C₂³×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	4	no	—
189	C₂³×C₄₃	—	2	2	no	—
190	C₂³×C₄₃	—	2	4	no	—
191	C₂³×C₄₃	C₂³×C₄	1	4	yes	—
192	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
193	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
194	Q₈×C₄₃	—	2	8	no	—
195	D₄×C₄₃	—	2	8	no	—
196	D₄×C₄₃	—	4	8	no	—
197	C₂×C₄×C₄₃	—	2	4	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	4	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	8	no	—
205	C₂×C₄×C₄₃	—	2	4	no	—
206	C₂×C₄×C₄₃	—	2	8	no	—
207	C₂×C₄×C₄₃	—	2	4	no	—
208	C₂×C₄×C₄₃	—	2	2	no	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	4	4	no	—
212	C₂×C₄×C₄₃	#131	1	4	yes	—
213	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
220	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
225	C₄₃⋊C₈	—	2	4	no	—
226	C₄₃⋊C₈	—	2	2	no	—
227	C₄₃⋊C₈	—	2	2	no	—
228	C₄₃⋊C₈	—	2	4	no	—
229	C₄₃⋊C₈	C₂×#41	1	4	yes	—
230	C₄₃⋊C₈	C₂×#41	1	4	yes	—
231	C₂×#2969	—	43	1	no	maximal, Sylow
232	C₂²×C₄₃	—	2	4	no	—
233	C₂²×C₄₃	—	2	2	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	2	4	no	—
236	C₂²×C₄₃	—	2	2	no	—
237	C₂²×C₄₃	—	2	4	no	—
238	C₂²×C₄₃	—	4	4	no	—
239	C₂²×C₄₃	—	4	8	no	—
240	C₂²×C₄₃	C₄×#41	1	2	yes	—
241	C₂²×C₄₃	C₂×#131	1	2	yes	—
242	C₂²×C₄₃	#568	1	2	yes	—
243	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
244	C₄×C₄₃	—	2	4	no	—
245	C₄×C₄₃	—	2	2	no	—
246	C₄×C₄₃	—	2	2	no	—
247	C₄×C₄₃	—	2	4	no	—
248	C₄×C₄₃	—	2	2	no	—
249	C₄×C₄₃	—	2	2	no	—
250	C₄×C₄₃	—	2	4	no	—
251	C₄×C₄₃	C₄×#41	1	2	yes	—
252	C₄×C₄₃	C₂×#131	1	4	yes	—
253	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
254	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
255	C₂×#529	D₄₃	1	1	yes	characteristic
256	#2969	—	43	16	no	—
257	C₂×#446	—	43	1	no	—
258	C₂×C₈×Q₈	—	43	1	no	—
259	C₂×#436	—	43	1	no	—
260	C₂×#436	—	43	2	no	—
261	C₂×#435	—	43	2	no	—
262	C₂×C₈×D₄	—	43	1	no	—
263	C₂×#433	—	43	2	no	—
264	C₂×#431	—	43	1	no	—
265	C₂×#405	—	43	2	no	—
266	C₂×C₄×M₁₆	—	43	1	no	—
267	C₂×C₄₃	—	4	2	no	—
268	C₂×C₄₃	—	4	4	no	—
269	C₂×C₄₃	#2969	1	4	yes	complemented
270	C₂×C₄₃	C₂×C₄×#41	1	1	yes	characteristic
271	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
272	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
273	C₂²×M₁₆	—	43	1	no	—
274	C₂²×M₁₆	—	43	1	no	—
275	C₂²×M₁₆	—	43	2	no	—
276	C₂³×C₈	—	43	2	no	—
277	#529	Dic₄₃	1	8	yes	—
278	#529	C₂×D₄₃	1	8	yes	—
279	C₂×#126	Dic₄₃	1	2	yes	—
280	C₂×#125	Dic₄₃	1	1	yes	characteristic
281	C₂×#124	Dic₄₃	1	1	yes	characteristic
282	C₂×#123	Dic₄₃	1	2	yes	—
283	C₂×C₂²⋊Q₈	Dic₄₃	1	1	yes	characteristic
284	C₂×#121	Dic₄₃	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
288	C₂×#117	C₂×D₄₃	1	2	yes	—
289	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
290	#446	—	43	8	no	—
291	C₈×Q₈	—	43	8	no	—
292	#436	—	43	8	no	—
293	#436	—	43	16	no	—
294	#435	—	43	16	no	—
295	C₈×D₄	—	43	8	no	—
296	#433	—	43	16	no	—
297	#431	—	43	8	no	—
298	C₂×C₄⋊C₈	—	43	1	no	—
299	C₂×C₄⋊C₈	—	43	1	no	—
300	C₂×C₄⋊C₈	—	43	2	no	—
301	C₂×C₄⋊C₈	—	43	2	no	—
302	C₂×C₂²⋊C₈	—	43	2	no	—
303	C₂×C₂²⋊C₈	—	43	2	no	—
304	C₂×C₂²⋊C₈	—	43	2	no	—
305	#405	—	43	16	no	—
306	C₄×M₁₆	—	43	8	no	—
307	C₂×#97	—	43	1	no	—
308	C₂×#97	—	43	1	no	—
309	C₂×#97	—	43	2	no	—
310	C₂×C₄×C₈	—	43	1	no	—
311	C₂×C₄×C₈	—	43	1	no	—
312	C₂×C₄×C₈	—	43	2	no	—
313	C₂×C₄×C₈	—	43	2	no	—
314	C₄₃	C₂×#2969	1	1	yes	characteristic, complemented, Sylow
315	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
316	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
317	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
318	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
319	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
320	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
321	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
322	C₂×M₁₆	—	43	4	no	—
323	C₂×M₁₆	—	43	4	no	—
324	C₂×M₁₆	—	43	8	no	—
325	C₂×M₁₆	—	86	4	no	—
326	C₂×M₁₆	—	86	4	no	—
327	C₂×M₁₆	—	86	8	no	—
328	C₂²×C₈	—	43	1	no	—
329	C₂²×C₈	—	43	1	no	—
330	C₂²×C₈	—	43	8	no	—
331	C₂²×C₈	—	43	2	no	—
332	C₂²×C₈	—	43	1	no	—
333	C₂²×C₈	—	43	1	no	—
334	C₂²×C₈	—	43	2	no	—
335	C₂²×C₈	—	86	8	no	—
336	#126	C₂×Dic₄₃	1	16	yes	—
337	#125	C₂×Dic₄₃	1	8	yes	—
338	#124	C₂×Dic₄₃	1	8	yes	—
339	#123	C₂×Dic₄₃	1	16	yes	—
340	C₂²⋊Q₈	C₂×Dic₄₃	1	8	yes	—
341	#121	C₂×Dic₄₃	1	8	yes	—
342	C₄×Q₈	C₂×Dic₄₃	1	4	yes	—
343	C₄×Q₈	C₂²×D₄₃	1	4	yes	—
344	C₄×D₄	C₂×Dic₄₃	1	4	yes	—
345	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
346	C₄×D₄	C₂²×D₄₃	1	4	yes	—
347	C₄×D₄	C₂²×D₄₃	1	8	yes	—
348	#117	C₂×Dic₄₃	1	8	yes	—
349	#117	C₂²×D₄₃	1	8	yes	—
350	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
351	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
361	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
362	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
363	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
364	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
365	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
366	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
367	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
368	C₄⋊C₈	—	43	4	no	—
369	C₄⋊C₈	—	43	4	no	—
370	C₄⋊C₈	—	43	8	no	—
371	C₄⋊C₈	—	43	8	no	—
372	C₂²⋊C₈	—	43	8	no	—
373	C₂²⋊C₈	—	43	8	no	—
374	C₂²⋊C₈	—	43	8	no	—
375	#97	—	43	4	no	—
376	#97	—	43	4	no	—
377	#97	—	43	8	no	—
378	C₄×C₈	—	43	4	no	—
379	C₄×C₈	—	43	4	no	—
380	C₄×C₈	—	43	8	no	—
381	C₄×C₈	—	43	8	no	—
382	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
383	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	C₂²×Dic₄₃	1	4	yes	—
386	C₂×D₄	—	2	4	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	C₂²×Dic₄₃	1	4	yes	—
389	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
397	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
398	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
399	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
400	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
401	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
402	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
403	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
404	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
405	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
406	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
407	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
409	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
410	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
411	M₁₆	—	86	8	no	—
412	M₁₆	—	86	8	no	—
413	M₁₆	—	86	16	no	—
414	C₂×C₈	—	43	4	no	—
415	C₂×C₈	—	43	4	no	—
416	C₂×C₈	—	43	2	no	—
417	C₂×C₈	—	43	2	no	—
418	C₂×C₈	—	43	4	no	—
419	C₂×C₈	—	43	2	no	—
420	C₂×C₈	—	43	2	no	—
421	C₂×C₈	—	43	4	no	—
422	C₂×C₈	—	86	16	no	—
423	C₂×C₈	—	86	4	no	—
424	C₂×C₈	—	86	2	no	—
425	C₂×C₈	—	86	2	no	—
426	C₂×C₈	—	86	4	no	—
427	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
428	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
429	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
430	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
431	C₄⋊C₄	C₂²×Dic₄₃	1	4	yes	—
432	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
433	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
434	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
435	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
436	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
437	C₂²⋊C₄	C₂²×Dic₄₃	1	8	yes	—
438	C₄²	C₂²×Dic₄₃	1	2	yes	—
439	C₄²	C₂²×Dic₄₃	1	2	yes	—
440	C₄²	C₂²×Dic₄₃	1	4	yes	—
441	C₄²	C₂²×Dic₄₃	1	4	yes	—
442	C₄²	C₂²×Dic₄₃	1	4	yes	—
443	C₄²	C₂³×D₄₃	1	2	yes	—
444	C₄²	C₂³×D₄₃	1	2	yes	—
445	C₄²	C₂³×D₄₃	1	4	yes	—
446	C₂³	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	4	no	—
452	C₂³	C₂³×Dic₄₃	1	4	yes	—
453	C₂³	C₂³×Dic₄₃	1	2	yes	—
454	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
455	Q₈	—	2	8	no	—
456	D₄	—	2	8	no	—
457	D₄	—	4	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	#13063332	1	4	yes	—
474	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
475	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
476	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
477	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
478	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
479	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
480	C₂×C₄	C₂³×Dic₄₃	1	4	yes	—
481	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
482	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
483	C₂×C₄	#41×D₄₃	1	2	yes	—
484	C₂×C₄	#41×D₄₃	1	2	yes	—
485	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
486	C₈	—	43	4	no	—
487	C₈	—	43	4	no	—
488	C₈	—	86	4	no	—
489	C₈	—	86	2	no	—
490	C₈	—	86	2	no	—
491	C₈	—	86	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	4	no	—
499	C₂²	—	4	8	no	—
500	C₂²	#41×Dic₄₃	1	2	yes	—
501	C₂²	C₂×#13063332	1	2	yes	—
502	C₂²	#14583666	1	2	yes	—
503	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
504	C₄	—	2	4	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	2	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	#41×Dic₄₃	1	2	yes	—
512	C₄	C₂×#13063332	1	4	yes	—
513	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
514	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
515	C₂	—	4	2	no	—
516	C₂	—	4	4	no	—
517	C₂	#19143600	1	4	yes	direct product factor
518	C₂	C₂×#41×Dic₄₃	1	1	yes	characteristic
519	C₂	C₂²×#13063332	1	1	yes	characteristic
520	C₂	C₂×#14583666	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#529	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂×#121×C₄₃	C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#529	D₄₃
hypocenter	C₄₃	C₂×#2969
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #19143600	C₂	direct (N × H)
2. C₂×#14583030	C₂	semidirect
3. C₂×Q₈×C₄₃⋊C₈	C₂	semidirect
4. C₂×#14582977	C₂	semidirect
5. C₂×#14582977	C₂	semidirect
6. C₂×#14582971	C₂	semidirect
7. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
8. C₂×#14582960	C₂	semidirect
9. C₂×#14582952	C₂	semidirect
10. C₂×#14582855	C₂	semidirect
11. C₂×C₄×#10621877	C₂	semidirect
17. #14583030	C₂²	semidirect
18. Q₈×C₄₃⋊C₈	C₂²	semidirect
19. #14582977	C₂²	semidirect
20. #14582977	C₂²	semidirect
21. #14582971	C₂²	semidirect
22. D₄×C₄₃⋊C₈	C₂²	semidirect
23. #14582960	C₂²	semidirect
24. #14582952	C₂²	semidirect
32. #14582855	C₂²	semidirect
33. C₄×#10621877	C₂²	semidirect
269. C₂×C₄₃	#2969	semidirect
314. C₄₃	C₂×#2969	semidirect
517. C₂	#19143600	direct (N × H)

Maximal subgroups

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

subgroup	index
#19143600	2
C₂×#14583030	2
C₂×Q₈×C₄₃⋊C₈	2
C₂×#14582977	2
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
C₂×#14582960	2
C₂×#14582952	2
C₂×#14582855	2
C₂×C₄×#10621877	2
C₂×C₄₃×#529	2
C₂×#2969	43

Subgroups — C2×#19143600 #25961082

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143600 #25961082