Subgroups — C₂×#19143339 #25960507

Order 11008.

2850 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	C₂²×#13063332	C₂	1	2	yes	maximal, complemented
2	#19143339	C₂	1	16	yes	maximal, direct product factor
3	C₂×#14582977	C₂	1	2	yes	maximal, complemented
4	C₂×#14582971	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14582866	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic
10	C₂×#13063332	—	2	16	no	—
11	C₂×#13063332	C₂²	1	16	yes	complemented
12	C₂²×#10621877	C₂²	1	1	yes	characteristic
13	C₂²×#10621877	C₂²	1	4	yes	—
14	C₂²×#10621877	C₂²	1	1	yes	characteristic
15	C₂³×C₄₃⋊C₈	C₂²	1	4	yes	—
16	C₂³×C₄₃⋊C₈	C₂²	1	2	yes	—
17	#14582977	C₂²	1	16	yes	complemented
18	#14582971	C₂²	1	32	yes	complemented
19	D₄×C₄₃⋊C₈	C₂²	1	16	yes	complemented
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	8	yes	complemented
24	#14582866	C₂²	1	16	yes	complemented
25	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
26	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	4	yes	—
27	C₄×#10621877	C₂²	1	8	yes	complemented
28	C₂×#13063236	C₂²	1	2	yes	—
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
30	C₂²×#41×C₄₃	C₂²	1	2	yes	—
31	C₄₃×#532	C₄	1	8	yes	—
32	C₄₃×#532	C₂²	1	8	yes	—
33	C₂×C₄⋊Q₈×C₄₃	C₄	1	1	yes	characteristic
34	C₂×#127×C₄₃	C₄	1	1	yes	characteristic
35	C₂×#124×C₄₃	C₄	1	2	yes	—
36	C₂×#121×C₄₃	C₄	1	2	yes	—
37	C₂×#121×C₄₃	C₄	1	2	yes	—
38	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
40	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
41	#13063332	—	2	64	no	—
42	C₂×#10621877	—	2	4	no	—
43	C₂×#10621877	—	2	16	no	—
44	C₂×#10621877	D₄	1	8	yes	complemented
45	C₂×#10621877	C₂³	1	4	yes	—
46	C₂×#10621877	C₂³	1	16	yes	—
47	C₂×#10621877	C₂³	1	4	yes	—
48	C₂²×C₄₃⋊C₈	—	2	8	no	—
49	C₂²×C₄₃⋊C₈	—	2	16	no	—
50	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
52	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
53	C₂²×C₄₃⋊C₈	C₂³	1	8	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	16	yes	—
55	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
56	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
57	C₄⋊(C₄₃⋊C₈)	C₂³	1	8	yes	—
58	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
59	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
60	C₂²⋊(C₄₃⋊C₈)	C₂³	1	16	yes	—
61	#13063236	C₂³	1	8	yes	—
62	C₄×C₄₃⋊C₈	C₂³	1	8	yes	—
63	C₂×#41×C₄₃	—	2	8	no	—
64	C₂×#41×C₄₃	—	2	8	no	—
65	C₂×#41×C₄₃	C₂×C₄	1	8	yes	—
66	C₂×#41×C₄₃	C₂³	1	8	yes	—
67	C₂²×Q₈×C₄₃	C₂×C₄	1	2	yes	—
68	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
69	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
70	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
71	C₂²×D₄×C₄₃	C₂×C₄	1	2	yes	—
72	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
75	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₄₃	C₂×C₄	1	8	yes	—
77	#127×C₄₃	C₂×C₄	1	8	yes	—
78	#124×C₄₃	C₂×C₄	1	16	yes	—
79	#121×C₄₃	C₂×C₄	1	16	yes	—
80	#121×C₄₃	C₂×C₄	1	16	yes	—
81	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
82	C₄×D₄×C₄₃	C₂×C₄	1	8	yes	—
83	C₄×D₄×C₄₃	C₂³	1	8	yes	—
84	C₄×D₄×C₄₃	C₂³	1	8	yes	—
85	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
87	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
88	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	4	yes	—
89	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	4	yes	—
95	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
96	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
97	#41×C₄₃	—	2	32	no	—
98	#41×C₄₃	—	2	16	no	—
99	#41×C₄₃	—	2	16	no	—
100	C₂×Q₈×C₄₃	—	2	8	no	—
101	C₂×Q₈×C₄₃	C₂²×C₄	1	8	yes	—
102	C₂×D₄×C₄₃	—	2	8	no	—
103	C₂×D₄×C₄₃	—	2	8	no	—
104	C₂×D₄×C₄₃	—	2	16	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	16	yes	—
108	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
109	C₂×D₄×C₄₃	C₂²×C₄	1	8	yes	—
110	C₂²×C₄×C₄₃	—	2	4	no	—
111	C₂²×C₄×C₄₃	—	2	8	no	—
112	C₂²×C₄×C₄₃	—	2	8	no	—
113	C₂²×C₄×C₄₃	—	4	2	no	—
114	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
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	4	yes	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₄₃	#41	1	4	yes	—
126	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
127	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
130	C₄⋊C₄×C₄₃	C₂²×C₄	1	8	yes	—
131	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
132	C₂²⋊C₄×C₄₃	C₂²×C₄	1	16	yes	—
133	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
134	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
136	C₄²×C₄₃	C₂²×C₄	1	4	yes	—
137	C₄²×C₄₃	C₂⁴	1	2	yes	—
138	C₄²×C₄₃	C₂⁴	1	2	yes	—
139	#10621877	—	2	8	no	—
140	#10621877	—	2	32	no	—
141	#10621877	C₂×D₄	1	16	yes	complemented
142	C₂×C₄₃⋊C₈	—	2	4	no	—
143	C₂×C₄₃⋊C₈	—	2	4	no	—
144	C₂×C₄₃⋊C₈	—	2	16	no	—
145	C₂×C₄₃⋊C₈	—	2	4	no	—
146	C₂×C₄₃⋊C₈	—	2	32	no	—
147	C₂×C₄₃⋊C₈	C₂×D₄	1	8	yes	—
148	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
149	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
150	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
151	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	—	2	2	no	—
154	C₂³×C₄₃	—	2	8	no	—
155	C₂³×C₄₃	—	2	8	no	—
156	C₂³×C₄₃	—	2	8	no	—
157	C₂³×C₄₃	C₄×D₄	1	4	yes	—
158	C₂³×C₄₃	C₂³×C₄	1	8	yes	—
159	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
160	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
161	Q₈×C₄₃	—	2	16	no	—
162	D₄×C₄₃	—	2	32	no	—
163	D₄×C₄₃	—	2	16	no	—
164	D₄×C₄₃	—	2	16	no	—
165	D₄×C₄₃	—	4	8	no	—
166	C₂×C₄×C₄₃	—	2	8	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	16	no	—
171	C₂×C₄×C₄₃	—	2	8	no	—
172	C₂×C₄×C₄₃	—	2	8	no	—
173	C₂×C₄×C₄₃	—	2	8	no	—
174	C₂×C₄×C₄₃	—	4	4	no	—
175	C₂×C₄×C₄₃	C₄×D₄	1	4	yes	—
176	C₂×C₄×C₄₃	C₄×D₄	1	8	yes	—
177	C₂×C₄×C₄₃	#131	1	4	yes	complemented
178	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
180	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
181	C₂×C₄×C₄₃	C₂³×C₄	1	8	yes	—
182	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
184	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
186	C₂×C₄×C₄₃	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
188	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
189	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
190	C₄₃⋊C₈	—	2	4	no	—
191	C₄₃⋊C₈	—	2	4	no	—
192	C₄₃⋊C₈	—	2	4	no	—
193	C₄₃⋊C₈	C₂²×D₄	1	8	yes	—
194	C₂×#2935	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	8	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	8	no	—
199	C₂²×C₄₃	—	2	8	no	—
200	C₂²×C₄₃	—	2	8	no	—
201	C₂²×C₄₃	—	4	16	no	—
202	C₂²×C₄₃	C₂×C₄×D₄	1	4	yes	—
203	C₂²×C₄₃	C₂×C₄×D₄	1	2	yes	—
204	C₂²×C₄₃	C₂×#131	1	2	yes	—
205	C₂²×C₄₃	#568	1	2	yes	—
206	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
207	C₄×C₄₃	—	2	8	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	C₂×C₄×D₄	1	2	yes	—
212	C₄×C₄₃	C₂×C₄×D₄	1	4	yes	—
213	C₄×C₄₃	C₂×#131	1	4	yes	complemented
214	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
215	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
216	C₂²×#131	—	43	2	no	—
217	C₂×#532	D₄₃	1	1	yes	characteristic
218	#2935	—	43	16	no	—
219	C₂×#436	—	43	2	no	—
220	C₂×#435	—	43	4	no	—
221	C₂×C₈×D₄	—	43	2	no	—
222	C₂²×C₄⋊C₈	—	43	1	no	—
223	C₂×#408	—	43	2	no	—
224	C₂×C₄×M₁₆	—	43	1	no	—
225	C₂×C₄₃	—	2	4	no	—
226	C₂×C₄₃	—	4	8	no	—
227	C₂×C₄₃	#2935	1	4	yes	complemented
228	C₂×C₄₃	C₂²×C₄×D₄	1	1	yes	characteristic
229	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
231	C₂²×#41	C₂×D₄₃	1	2	yes	—
232	C₂×#131	—	43	16	no	—
233	C₂×#131	—	86	16	no	—
234	C₂²×M₁₆	—	43	1	no	—
235	C₂²×M₁₆	—	43	1	no	—
236	C₂²×M₁₆	—	43	4	no	—
237	C₂³×C₈	—	43	2	no	—
238	C₂³×C₈	—	43	4	no	—
239	#532	Dic₄₃	1	8	yes	—
240	#532	C₂×D₄₃	1	8	yes	—
241	C₂×C₄⋊Q₈	Dic₄₃	1	1	yes	characteristic
242	C₂×#127	Dic₄₃	1	1	yes	characteristic
243	C₂×#124	Dic₄₃	1	2	yes	—
244	C₂×#121	Dic₄₃	1	2	yes	—
245	C₂×#121	Dic₄₃	1	2	yes	—
246	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
247	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
248	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
249	#436	—	43	16	no	—
250	#435	—	43	32	no	—
251	C₈×D₄	—	43	16	no	—
252	C₂×C₄⋊C₈	—	43	1	no	—
253	C₂×C₄⋊C₈	—	43	2	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×C₄⋊C₈	—	43	8	no	—
256	#408	—	43	16	no	—
257	C₂×C₂²⋊C₈	—	43	4	no	—
258	C₂×C₂²⋊C₈	—	43	4	no	—
259	C₄×M₁₆	—	43	8	no	—
260	C₂×#97	—	43	2	no	—
261	C₂×C₄×C₈	—	43	2	no	—
262	C₄₃	C₂×#2935	1	1	yes	characteristic, complemented, Sylow
263	C₂×#41	—	2	8	no	—
264	C₂×#41	—	2	8	no	—
265	C₂×#41	C₂×Dic₄₃	1	8	yes	—
266	C₂×#41	C₂²×D₄₃	1	8	yes	—
267	C₂²×Q₈	C₂×Dic₄₃	1	2	yes	—
268	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
269	C₂²×D₄	C₂×Dic₄₃	1	4	yes	—
270	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
271	C₂²×D₄	C₂×Dic₄₃	1	2	yes	—
272	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
273	C₂³×C₄	C₂×Dic₄₃	1	1	yes	characteristic
274	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
275	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
276	#131	—	86	64	no	—
277	C₂×M₁₆	—	43	8	no	—
278	C₂×M₁₆	—	43	4	no	—
279	C₂×M₁₆	—	43	16	no	—
280	C₂×M₁₆	—	43	4	no	—
281	C₂×M₁₆	—	86	16	no	—
282	C₂×M₁₆	—	86	4	no	—
283	C₂²×C₈	—	43	2	no	—
284	C₂²×C₈	—	43	8	no	—
285	C₂²×C₈	—	43	16	no	—
286	C₂²×C₈	—	43	2	no	—
287	C₂²×C₈	—	43	2	no	—
288	C₂²×C₈	—	43	2	no	—
289	C₂²×C₈	—	86	16	no	—
290	C₂²×C₈	—	86	8	no	—
291	C₄⋊Q₈	C₂×Dic₄₃	1	8	yes	—
292	#127	C₂×Dic₄₃	1	8	yes	—
293	#124	C₂×Dic₄₃	1	16	yes	—
294	#121	C₂×Dic₄₃	1	16	yes	—
295	#121	C₂×Dic₄₃	1	16	yes	—
296	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
297	C₄×D₄	C₂×Dic₄₃	1	8	yes	—
298	C₄×D₄	C₂²×D₄₃	1	8	yes	—
299	C₄×D₄	C₂²×D₄₃	1	8	yes	—
300	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
302	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
303	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	4	yes	—
304	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
305	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
306	C₂×C₄²	C₂×Dic₄₃	1	4	yes	—
307	C₂×C₄²	C₂²×D₄₃	1	4	yes	—
308	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
309	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
310	C₄⋊C₈	—	43	4	no	—
311	C₄⋊C₈	—	43	8	no	—
312	C₄⋊C₈	—	43	4	no	—
313	C₂²⋊C₈	—	43	16	no	—
314	C₂²⋊C₈	—	43	16	no	—
315	#97	—	43	8	no	—
316	C₄×C₈	—	43	8	no	—
317	C₂⁴	C₂²×Dic₄₃	1	4	yes	—
318	C₂⁴	C₂²×Dic₄₃	1	1	yes	characteristic
319	#41	—	2	32	no	—
320	#41	—	2	16	no	—
321	#41	—	2	16	no	—
322	C₂×Q₈	—	2	8	no	—
323	C₂×Q₈	C₂²×Dic₄₃	1	8	yes	—
324	C₂×D₄	—	2	16	no	—
325	C₂×D₄	—	2	8	no	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
329	C₂×D₄	C₂²×Dic₄₃	1	16	yes	—
330	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
331	C₂×D₄	C₂²×Dic₄₃	1	8	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	D₄×D₄₃	1	4	yes	—
337	C₂²×C₄	#10621900	1	4	yes	—
338	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
342	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
343	C₂²×C₄	C₂²×Dic₄₃	1	8	yes	—
344	C₂²×C₄	C₂²×Dic₄₃	1	4	yes	—
345	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
347	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
348	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
349	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
350	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
351	M₁₆	—	43	16	no	—
352	M₁₆	—	86	32	no	—
353	M₁₆	—	86	8	no	—
354	C₂×C₈	—	43	8	no	—
355	C₂×C₈	—	43	4	no	—
356	C₂×C₈	—	43	4	no	—
357	C₂×C₈	—	43	4	no	—
358	C₂×C₈	—	43	4	no	—
359	C₂×C₈	—	86	32	no	—
360	C₂×C₈	—	86	4	no	—
361	C₂×C₈	—	86	4	no	—
362	C₂×C₈	—	86	16	no	—
363	C₂×C₈	—	86	4	no	—
364	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
365	C₄⋊C₄	C₂²×Dic₄₃	1	8	yes	—
366	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
367	C₂²⋊C₄	C₂²×Dic₄₃	1	16	yes	—
368	C₄²	C₂²×Dic₄₃	1	2	yes	—
369	C₄²	C₂²×Dic₄₃	1	2	yes	—
370	C₄²	C₂²×Dic₄₃	1	4	yes	—
371	C₄²	C₂²×Dic₄₃	1	4	yes	—
372	C₄²	C₂³×D₄₃	1	2	yes	—
373	C₄²	C₂³×D₄₃	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	2	8	no	—
378	C₂³	—	2	8	no	—
379	C₂³	D₄×Dic₄₃	1	4	yes	—
380	C₂³	C₂³×Dic₄₃	1	8	yes	—
381	C₂³	C₂³×Dic₄₃	1	2	yes	—
382	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
383	Q₈	—	2	16	no	—
384	D₄	—	2	32	no	—
385	D₄	—	2	16	no	—
386	D₄	—	2	16	no	—
387	D₄	—	4	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	8	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	D₄×Dic₄₃	1	4	yes	—
398	C₂×C₄	D₄×Dic₄₃	1	8	yes	—
399	C₂×C₄	#13063332	1	4	yes	complemented
400	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
401	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
402	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
403	C₂×C₄	C₂³×Dic₄₃	1	8	yes	—
404	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
406	C₂×C₄	C₂³×Dic₄₃	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
408	C₂×C₄	C₂×D₄×D₄₃	1	4	yes	—
409	C₂×C₄	C₂×#10621900	1	2	yes	—
410	C₂×C₄	C₂×#10621900	1	4	yes	—
411	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
412	C₈	—	43	8	no	—
413	C₈	—	86	4	no	—
414	C₈	—	86	4	no	—
415	C₈	—	86	4	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	8	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	4	16	no	—
423	C₂²	C₂×D₄×Dic₄₃	1	4	yes	—
424	C₂²	C₂×D₄×Dic₄₃	1	2	yes	—
425	C₂²	C₂×#13063332	1	2	yes	—
426	C₂²	#14583666	1	2	yes	—
427	C₂²	C₂⁴×Dic₄₃	1	1	yes	characteristic
428	C₄	—	2	2	no	—
429	C₄	—	2	8	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	C₂×D₄×Dic₄₃	1	2	yes	—
433	C₄	C₂×D₄×Dic₄₃	1	4	yes	—
434	C₄	C₂×#13063332	1	4	yes	complemented
435	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
436	C₄	C₂²×#10621900	1	1	yes	characteristic
437	C₂	—	2	4	no	—
438	C₂	—	4	8	no	—
439	C₂	#19143339	1	4	yes	direct product factor
440	C₂	C₂²×D₄×Dic₄₃	1	1	yes	characteristic
441	C₂	C₂²×#13063332	1	1	yes	characteristic
442	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, prime radical	C₂×C₄₃×#532	C₂
socle	C₂³×C₄₃	C₂³×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	C₂×#2935
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063332	C₂	semidirect
2. #19143339	C₂	direct (N × H)
3. C₂×#14582977	C₂	semidirect
4. C₂×#14582971	C₂	semidirect
5. C₂×D₄×C₄₃⋊C₈	C₂	semidirect
6. C₂²×C₄⋊(C₄₃⋊C₈)	C₂	semidirect
7. C₂×#14582866	C₂	semidirect
8. C₂×C₄×#10621877	C₂	semidirect
11. C₂×#13063332	C₂²	semidirect
17. #14582977	C₂²	semidirect
18. #14582971	C₂²	semidirect
19. D₄×C₄₃⋊C₈	C₂²	semidirect
23. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
24. #14582866	C₂²	semidirect
27. C₄×#10621877	C₂²	semidirect
44. C₂×#10621877	D₄	semidirect
141. #10621877	C₂×D₄	semidirect
177. C₂×C₄×C₄₃	#131	semidirect
213. C₄×C₄₃	C₂×#131	semidirect
227. C₂×C₄₃	#2935	semidirect
262. C₄₃	C₂×#2935	semidirect
399. C₂×C₄	#13063332	semidirect
434. C₄	C₂×#13063332	semidirect
439. C₂	#19143339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13063332	2
#19143339	2
C₂×#14582977	2
C₂×#14582971	2
C₂×D₄×C₄₃⋊C₈	2
C₂²×C₄⋊(C₄₃⋊C₈)	2
C₂×#14582866	2
C₂×C₄×#10621877	2
C₂×C₄₃×#532	2
C₂×#2935	43

Subgroups — C2×#19143339 #25960507

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19143339 #25960507