Subgroups — C₈×#13063311 #25104458

Order 11008.

974 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄×#13063311	C₂	1	1	yes	maximal, characteristic
4	#19135529	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135387	C₂	1	1	yes	maximal, characteristic
6	#19135203	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135202	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135199	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135198	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134710	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈×(C₂×D₄₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×C₂²⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
17	C₂×#13063311	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
20	C₈×Dic₈₆	—	2	4	no	—
21	C₈×C₂²⋊D₄₃	—	2	4	no	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	#14582803	C₄	1	1	yes	characteristic
38	#14582799	C₄	1	1	yes	characteristic
39	#14582792	C₄	1	1	yes	characteristic
40	#14582791	C₄	1	1	yes	characteristic
41	#14582788	C₄	1	1	yes	characteristic
42	#14582787	C₄	1	1	yes	characteristic
43	#14582763	C₄	1	1	yes	characteristic
44	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×(C₂×D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊Dic₄₃	C₂²	1	1	yes	characteristic
47	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
48	#14582654	C₂²	1	1	yes	characteristic
49	#14582654	C₂²	1	1	yes	characteristic
50	#14582653	C₂²	1	1	yes	characteristic
51	#14582653	C₂²	1	1	yes	characteristic
52	#14582653	C₂²	1	1	yes	characteristic
53	#14582653	C₂²	1	1	yes	characteristic
54	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
64	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₄₃	—	2	2	no	—
69	C₂×C₈×D₄₃	—	2	2	no	—
70	C₂×C₈×D₄₃	—	2	2	no	—
71	#13063311	C₈	1	8	yes	direct product factor
72	C₄×Dic₈₆	—	2	2	no	—
73	C₄×Dic₈₆	—	2	2	no	—
74	C₄×C₂²⋊D₄₃	—	2	2	no	—
75	C₄×C₂²⋊D₄₃	—	2	2	no	—
76	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
94	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
96	Dic₄₃⋊C₈	—	2	2	no	—
97	Dic₄₃⋊C₈	—	2	2	no	—
98	Dic₄₃⋊C₈	—	2	2	no	—
99	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
100	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
101	(C₂×D₄₃)⋊C₈	—	2	2	no	—
102	(C₂×D₄₃)⋊C₈	—	2	2	no	—
103	(C₂×D₄₃)⋊C₈	—	2	2	no	—
104	C₄×C₄₃⋊C₈	—	2	2	no	—
105	C₈×Dic₄₃	—	2	2	no	—
106	C₈×Dic₄₃	—	2	2	no	—
107	C₈×Dic₄₃	—	2	2	no	—
108	C₈×Dic₄₃	—	2	2	no	—
109	C₈×Dic₄₃	D₄	1	4	yes	—
110	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₃	—	2	2	no	—
118	C₂²×C₈×C₄₃	—	2	2	no	—
119	C₂²×C₈×C₄₃	—	2	2	no	—
120	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
128	C₂²⋊C₈×C₄₃	—	2	2	no	—
129	C₄×C₈×C₄₃	—	2	2	no	—
130	C₄×C₈×C₄₃	—	2	2	no	—
131	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
132	#95×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	—	2	1	no	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	—	2	1	no	—
139	C₂²×C₄×C₄₃	—	2	1	no	—
140	C₂²×C₄×C₄₃	—	2	1	no	—
141	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₂²⋊D₄₃	—	2	2	no	—
148	C₂×C₂²⋊D₄₃	—	2	2	no	—
149	C₂×C₂²⋊D₄₃	C₂×C₈	1	4	yes	—
150	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₄₃	—	2	1	no	—
158	C₂×C₄×D₄₃	—	2	1	no	—
159	C₂×C₄×D₄₃	—	2	1	no	—
160	C₂×C₄×D₄₃	—	2	1	no	—
161	C₂×C₄×D₄₃	—	2	1	no	—
162	C₂×C₄×D₄₃	—	2	1	no	—
163	C₂×Dic₈₆	—	2	2	no	—
164	C₂×Dic₈₆	—	2	2	no	—
165	C₂×Dic₈₆	C₂×C₈	1	4	yes	complemented
166	C₂×C₈×C₄₃	—	2	1	no	—
167	C₂×C₈×C₄₃	—	2	1	no	—
168	C₂×C₈×C₄₃	—	2	1	no	—
169	C₂×C₈×C₄₃	—	2	1	no	—
170	C₂×C₈×C₄₃	—	2	1	no	—
171	C₂×C₈×C₄₃	—	2	1	no	—
172	C₂×C₈×C₄₃	—	2	1	no	—
173	C₂×C₈×C₄₃	—	2	1	no	—
174	C₂×C₈×C₄₃	—	4	4	no	—
175	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
176	C₂×C₈×C₄₃	#41	1	2	yes	—
177	C₂×C₈×C₄₃	#41	1	2	yes	—
178	C₂×C₈×C₄₃	#41	1	2	yes	—
179	C₂²⋊C₄×C₄₃	—	2	2	no	—
180	C₂²⋊C₄×C₄₃	C₂×C₈	1	4	yes	complemented
181	C₄²×C₄₃	—	2	1	no	—
182	C₄²×C₄₃	—	2	1	no	—
183	C₄²×C₄₃	—	2	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₂²⋊Dic₄₃	—	2	2	no	—
186	C₂²⋊Dic₄₃	—	2	2	no	—
187	C₂²⋊Dic₄₃	C₂×C₈	1	4	yes	complemented
188	(C₂×D₄₃)⋊C₄	—	2	2	no	—
189	(C₂×D₄₃)⋊C₄	—	2	2	no	—
190	(C₂×D₄₃)⋊C₄	—	2	2	no	—
191	(C₂×D₄₃)⋊C₄	C₂×C₈	1	4	yes	complemented
192	(C₂×D₄₃)⋊C₄	C₂×C₈	1	4	yes	complemented
193	C₄⋊Dic₄₃	—	2	2	no	—
194	Dic₄₃⋊C₄	—	2	2	no	—
195	Dic₄₃⋊C₄	—	2	2	no	—
196	Dic₄₃⋊C₄	—	2	2	no	—
197	C₄×Dic₄₃	—	2	2	no	—
198	C₄×Dic₄₃	—	2	1	no	—
199	C₄×Dic₄₃	—	2	1	no	—
200	C₄×Dic₄₃	—	2	1	no	—
201	C₄×Dic₄₃	—	2	1	no	—
202	C₄×Dic₄₃	—	2	2	no	—
203	C₄×Dic₄₃	—	2	2	no	—
204	C₄×Dic₄₃	C₂×C₈	1	4	yes	complemented
205	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
206	C₄×Dic₄₃	#41	1	2	yes	—
207	C₂×C₄₃⋊C₈	—	2	1	no	—
208	C₂×C₄₃⋊C₈	—	2	1	no	—
209	C₂×C₄₃⋊C₈	—	2	1	no	—
210	C₂×C₄₃⋊C₈	—	2	1	no	—
211	C₂×C₄₃⋊C₈	—	2	1	no	—
212	C₂×C₄₃⋊C₈	—	2	1	no	—
213	C₂×C₄₃⋊C₈	—	2	1	no	—
214	C₂×C₄₃⋊C₈	—	2	1	no	—
215	C₂×C₄₃⋊C₈	—	2	1	no	—
216	C₂×C₄₃⋊C₈	—	2	1	no	—
217	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
218	C₂×C₄₃⋊C₈	#41	1	2	yes	—
219	C₈×D₄₃	—	4	4	no	—
220	C₂³×C₄₃	—	2	1	no	—
221	C₂³×C₄₃	—	2	1	no	—
222	C₂³×C₄₃	—	2	1	no	—
223	C₂³×C₄₃	—	2	1	no	—
224	C₂³×C₄₃	—	2	1	no	—
225	C₂³×C₄₃	—	2	1	no	—
226	C₂³×C₄₃	C₂²×C₈	1	2	yes	—
227	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
228	C₂²×D₄₃	—	2	1	no	—
229	C₂²×D₄₃	—	2	1	no	—
230	C₂²×D₄₃	—	2	1	no	—
231	C₂²×D₄₃	—	2	1	no	—
232	C₂²×D₄₃	—	2	1	no	—
233	C₂²×D₄₃	—	2	1	no	—
234	C₂²×D₄₃	C₂²×C₈	1	2	yes	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	1	no	—
238	C₂×C₄×C₄₃	—	2	1	no	—
239	C₂×C₄×C₄₃	—	2	1	no	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	1	no	—
245	C₂×C₄×C₄₃	—	2	1	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	—	4	1	no	—
248	C₂×C₄×C₄₃	—	4	1	no	—
249	C₂×C₄×C₄₃	—	4	1	no	—
250	C₂×C₄×C₄₃	—	4	1	no	—
251	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
252	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
253	C₂×C₄×C₄₃	#131	1	2	yes	—
254	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
260	C₂²⋊D₄₃	—	2	8	no	—
261	C₂×Dic₄₃	—	2	1	no	—
262	C₂×Dic₄₃	—	2	1	no	—
263	C₂×Dic₄₃	—	2	1	no	—
264	C₂×Dic₄₃	—	2	1	no	—
265	C₂×Dic₄₃	—	2	1	no	—
266	C₂×Dic₄₃	—	2	1	no	—
267	C₂×Dic₄₃	—	2	1	no	—
268	C₂×Dic₄₃	—	2	1	no	—
269	C₂×Dic₄₃	—	2	1	no	—
270	C₂×Dic₄₃	—	2	1	no	—
271	C₂×Dic₄₃	—	2	1	no	—
272	C₂×Dic₄₃	—	2	1	no	—
273	C₂×Dic₄₃	—	2	1	no	—
274	C₂×Dic₄₃	—	2	1	no	—
275	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
276	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
277	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
278	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
279	C₂×Dic₄₃	C₂²×C₈	1	2	yes	—
280	C₂×Dic₄₃	#131	1	2	yes	—
281	C₂×Dic₄₃	#131	1	2	yes	—
282	C₄×D₄₃	—	4	1	no	—
283	C₄×D₄₃	—	4	1	no	—
284	C₄×D₄₃	—	4	1	no	—
285	C₄×D₄₃	—	4	1	no	—
286	Dic₈₆	—	2	8	no	—
287	C₈×C₄₃	—	2	2	no	—
288	C₈×C₄₃	—	4	1	no	—
289	C₈×C₄₃	—	4	1	no	—
290	C₈×C₄₃	#124	1	4	yes	complemented
291	C₄₃⋊C₈	—	2	2	no	—
292	C₄₃⋊C₈	—	2	2	no	—
293	C₄₃⋊C₈	—	4	1	no	—
294	C₄₃⋊C₈	—	4	1	no	—
295	C₈×#124	—	43	1	no	maximal, Sylow
296	C₂²×C₄₃	—	2	2	no	—
297	C₂²×C₄₃	—	2	2	no	—
298	C₂²×C₄₃	—	2	2	no	—
299	C₂²×C₄₃	—	4	1	no	—
300	C₂²×C₄₃	—	4	1	no	—
301	C₂²×C₄₃	—	4	1	no	—
302	C₂²×C₄₃	—	4	1	no	—
303	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
305	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
306	C₂²×C₄₃	C₂³×C₈	1	1	yes	characteristic
307	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
308	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
309	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
310	C₂×D₄₃	—	2	2	no	—
311	C₂×D₄₃	—	2	2	no	—
312	C₂×D₄₃	—	2	2	no	—
313	C₂×D₄₃	—	4	1	no	—
314	C₂×D₄₃	—	4	1	no	—
315	C₂×D₄₃	—	4	1	no	—
316	C₂×D₄₃	—	4	1	no	—
317	C₄×C₄₃	—	2	2	no	—
318	C₄×C₄₃	—	2	2	no	—
319	C₄×C₄₃	—	2	2	no	—
320	C₄×C₄₃	—	4	1	no	—
321	C₄×C₄₃	—	4	1	no	—
322	C₄×C₄₃	C₂×#124	1	1	yes	characteristic
323	C₄×C₄₃	#529	1	1	yes	characteristic
324	C₄×C₄₃	#529	1	1	yes	characteristic
325	C₄×C₄₃	#532	1	1	yes	characteristic
326	Dic₄₃	—	2	2	no	—
327	Dic₄₃	—	2	2	no	—
328	Dic₄₃	—	2	2	no	—
329	Dic₄₃	—	2	2	no	—
330	Dic₄₃	—	4	1	no	—
331	Dic₄₃	—	4	1	no	—
332	Dic₄₃	C₈×D₄	1	4	yes	—
333	C₂×C₈×Q₈	—	43	1	no	—
334	C₂×C₈×D₄	—	43	1	no	—
335	C₄×#124	—	43	1	no	—
336	#1984	—	43	1	no	—
337	#1954	—	43	1	no	—
338	#1923	—	43	1	no	—
339	#1923	—	43	1	no	—
340	#1923	—	43	1	no	—
341	#1923	—	43	1	no	—
342	#1831	—	43	1	no	—
343	C₈×C₂²⋊C₄	—	43	1	no	—
344	C₈×C₂²⋊C₄	—	43	1	no	—
345	C₈×C₂²⋊C₄	—	43	1	no	—
346	C₈×C₂²⋊C₄	D₄₃	1	1	yes	characteristic, complemented
347	C₄²×C₈	—	43	1	no	—
348	C₂×C₄₃	—	4	2	no	—
349	C₂×C₄₃	C₄×#124	1	1	yes	characteristic
350	C₂×C₄₃	C₂×C₈×D₄	1	1	yes	characteristic
351	C₂×C₄₃	#2931	1	1	yes	characteristic
352	C₂×C₄₃	C₈×#41	1	1	yes	characteristic
353	C₂×C₄₃	C₈×#41	1	1	yes	characteristic
354	C₂×C₄₃	#2966	1	1	yes	characteristic
355	C₂×C₄₃	#2966	1	1	yes	characteristic
356	D₄₃	—	4	2	no	—
357	C₂³×C₈	—	43	1	no	—
358	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
359	C₂×#124	—	43	1	no	—
360	C₂×C₄×Q₈	—	43	1	no	—
361	C₂×C₄×D₄	—	43	1	no	—
362	C₈×Q₈	—	86	4	no	—
363	C₈×D₄	—	86	4	no	—
364	C₂×C₄⋊C₈	—	43	1	no	—
365	C₂×C₄⋊C₈	—	43	1	no	—
366	C₂×C₄⋊C₈	—	43	1	no	—
367	C₂×C₄⋊C₈	—	43	1	no	—
368	C₂×C₂²⋊C₈	—	43	1	no	—
369	C₂×C₂²⋊C₈	—	43	1	no	—
370	C₂×C₂²⋊C₈	—	43	1	no	—
371	C₂×C₂²⋊C₈	—	43	1	no	—
372	C₂×C₂²⋊C₈	—	43	1	no	—
373	C₂×C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic
374	C₂×C₄×C₈	—	43	1	no	—
375	C₂×C₄×C₈	—	43	1	no	—
376	C₂×C₄×C₈	—	43	1	no	—
377	C₂×C₄×C₈	—	43	1	no	—
378	C₂×C₄×C₈	—	43	1	no	—
379	C₂×C₄×C₈	—	43	1	no	—
380	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
381	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
382	#391	—	43	1	no	—
383	#390	—	43	1	no	—
384	#388	—	43	1	no	—
385	#388	—	43	1	no	—
386	#388	—	43	1	no	—
387	#388	—	43	1	no	—
388	#382	—	43	1	no	—
389	C₄×C₂²⋊C₄	—	43	1	no	—
390	C₄×C₂²⋊C₄	—	43	1	no	—
391	C₄×C₂²⋊C₄	—	43	1	no	—
392	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
393	C₄³	—	43	1	no	—
394	#336	—	43	1	no	—
395	#336	—	43	1	no	—
396	#336	—	43	1	no	—
397	#336	—	43	1	no	—
398	#336	—	43	1	no	—
399	#336	—	43	1	no	—
400	#336	C₂×D₄₃	1	1	yes	characteristic
401	#336	C₂×D₄₃	1	1	yes	characteristic
402	C₄₃	C₈×#124	1	1	yes	characteristic, complemented, Sylow
403	C₂²×Q₈	—	43	1	no	—
404	C₂²×D₄	—	43	1	no	—
405	C₂³×C₄	—	43	1	no	—
406	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
407	C₂²×C₈	—	2	2	no	—
408	C₂²×C₈	—	2	2	no	—
409	C₂²×C₈	—	2	2	no	—
410	C₂²×C₈	—	43	1	no	—
411	C₂²×C₈	—	43	1	no	—
412	C₂²×C₈	—	43	1	no	—
413	C₂²×C₈	—	43	1	no	—
414	C₂²×C₈	—	86	2	no	—
415	C₂²×C₈	—	86	2	no	—
416	C₂²×C₈	—	86	2	no	—
417	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
418	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
419	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
420	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
421	#124	—	43	8	no	—
422	C₄×Q₈	—	86	2	no	—
423	C₄×Q₈	—	86	2	no	—
424	C₄×D₄	—	86	2	no	—
425	C₄×D₄	—	86	2	no	—
426	C₂×C₄⋊C₄	—	43	1	no	—
427	C₂×C₄⋊C₄	—	43	1	no	—
428	C₂×C₄⋊C₄	—	43	1	no	—
429	C₂×C₄⋊C₄	—	43	1	no	—
430	C₂×C₂²⋊C₄	—	43	1	no	—
431	C₂×C₂²⋊C₄	—	43	1	no	—
432	C₂×C₂²⋊C₄	—	43	1	no	—
433	C₂×C₂²⋊C₄	—	43	1	no	—
434	C₂×C₂²⋊C₄	—	43	1	no	—
435	C₂×C₂²⋊C₄	—	43	1	no	—
436	C₂×C₂²⋊C₄	—	43	1	no	—
437	C₂×C₂²⋊C₄	—	43	1	no	—
438	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄²	—	43	1	no	—
441	C₂×C₄²	—	43	1	no	—
442	C₂×C₄²	—	43	1	no	—
443	C₂×C₄²	—	43	1	no	—
444	C₂×C₄²	—	43	1	no	—
445	C₂×C₄²	—	43	1	no	—
446	C₂×C₄²	—	43	1	no	—
447	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
448	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
449	C₄⋊C₈	—	86	2	no	—
450	C₄⋊C₈	—	86	2	no	—
451	C₄⋊C₈	—	86	2	no	—
452	C₄⋊C₈	—	86	2	no	—
453	C₂²⋊C₈	—	2	2	no	—
454	C₂²⋊C₈	—	86	2	no	—
455	C₂²⋊C₈	—	86	2	no	—
456	C₂²⋊C₈	—	86	2	no	—
457	C₂²⋊C₈	—	86	2	no	—
458	C₂²⋊C₈	—	86	2	no	—
459	C₄×C₈	—	2	2	no	—
460	C₄×C₈	—	2	2	no	—
461	C₄×C₈	—	43	4	no	—
462	C₄×C₈	—	86	2	no	—
463	C₄×C₈	—	86	2	no	—
464	C₄×C₈	—	86	2	no	—
465	C₄×C₈	—	86	2	no	—
466	C₄×C₈	—	86	2	no	—
467	#95	—	43	1	no	—
468	#95	—	43	1	no	—
469	#95	—	43	1	no	—
470	#95	—	43	1	no	—
471	#95	—	43	1	no	—
472	#95	—	43	1	no	—
473	#95	C₄×D₄₃	1	1	yes	characteristic
474	#95	C₄×D₄₃	1	1	yes	characteristic
475	C₂⁴	—	43	1	no	—
476	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
477	C₂×Q₈	—	43	4	no	—
478	C₂×Q₈	—	86	2	no	—
479	C₂×Q₈	—	86	2	no	—
480	C₂×D₄	—	43	4	no	—
481	C₂×D₄	—	86	2	no	—
482	C₂×D₄	—	86	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	43	1	no	—
490	C₂²×C₄	—	43	1	no	—
491	C₂²×C₄	—	43	1	no	—
492	C₂²×C₄	—	43	1	no	—
493	C₂²×C₄	—	43	1	no	—
494	C₂²×C₄	—	43	1	no	—
495	C₂²×C₄	—	43	1	no	—
496	C₂²×C₄	—	86	1	no	—
497	C₂²×C₄	—	86	1	no	—
498	C₂²×C₄	—	86	1	no	—
499	C₂²×C₄	—	86	1	no	—
500	C₂²×C₄	—	86	1	no	—
501	C₂²×C₄	—	86	1	no	—
502	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
507	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	4	4	no	—
517	C₂×C₈	—	43	2	no	—
518	C₂×C₈	—	43	2	no	—
519	C₂×C₈	—	86	1	no	—
520	C₂×C₈	—	86	1	no	—
521	C₂×C₈	—	86	1	no	—
522	C₂×C₈	—	86	1	no	—
523	C₂×C₈	—	86	1	no	—
524	C₂×C₈	—	86	1	no	—
525	C₂×C₈	—	86	1	no	—
526	C₂×C₈	—	86	1	no	—
527	C₂×C₈	—	86	1	no	—
528	C₂×C₈	—	86	1	no	—
529	C₂×C₈	—	172	4	no	—
530	C₂×C₈	#10621898	1	2	yes	—
531	C₂×C₈	#10621898	1	2	yes	—
532	C₂×C₈	D₄×D₄₃	1	2	yes	—
533	C₂×C₈	#10621900	1	2	yes	—
534	C₄⋊C₄	—	86	2	no	—
535	C₄⋊C₄	—	86	2	no	—
536	C₄⋊C₄	—	86	2	no	—
537	C₄⋊C₄	—	86	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	43	4	no	—
540	C₂²⋊C₄	—	43	4	no	—
541	C₂²⋊C₄	—	43	4	no	—
542	C₂²⋊C₄	—	86	2	no	—
543	C₂²⋊C₄	—	86	2	no	—
544	C₂²⋊C₄	—	86	2	no	—
545	C₂²⋊C₄	—	86	2	no	—
546	C₂²⋊C₄	—	86	2	no	—
547	C₂²⋊C₄	C₈×D₄₃	1	4	yes	complemented
548	C₄²	—	2	1	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	43	4	no	—
553	C₄²	—	43	2	no	—
554	C₄²	—	43	2	no	—
555	C₄²	—	86	2	no	—
556	C₄²	—	86	2	no	—
557	C₄²	—	86	2	no	—
558	C₄²	—	86	1	no	—
559	C₄²	—	86	1	no	—
560	C₄²	—	86	1	no	—
561	C₄²	—	86	1	no	—
562	C₂³	—	2	1	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	43	2	no	—
569	C₂³	—	86	1	no	—
570	C₂³	—	86	1	no	—
571	C₂³	—	86	1	no	—
572	C₂³	—	86	1	no	—
573	C₂³	—	86	1	no	—
574	C₂³	—	86	1	no	—
575	C₂³	C₂×C₈×D₄₃	1	2	yes	—
576	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
577	Q₈	—	86	8	no	—
578	D₄	—	86	8	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	43	2	no	—
596	C₂×C₄	—	43	2	no	—
597	C₂×C₄	—	43	2	no	—
598	C₂×C₄	—	43	2	no	—
599	C₂×C₄	—	43	2	no	—
600	C₂×C₄	—	43	2	no	—
601	C₂×C₄	—	43	2	no	—
602	C₂×C₄	—	86	1	no	—
603	C₂×C₄	—	86	1	no	—
604	C₂×C₄	—	86	1	no	—
605	C₂×C₄	—	86	1	no	—
606	C₂×C₄	—	86	1	no	—
607	C₂×C₄	—	86	1	no	—
608	C₂×C₄	—	86	1	no	—
609	C₂×C₄	—	86	1	no	—
610	C₂×C₄	—	86	1	no	—
611	C₂×C₄	—	86	1	no	—
612	C₂×C₄	—	86	1	no	—
613	C₂×C₄	—	86	1	no	—
614	C₂×C₄	—	86	1	no	—
615	C₂×C₄	—	86	1	no	—
616	C₂×C₄	—	172	1	no	—
617	C₂×C₄	—	172	1	no	—
618	C₂×C₄	—	172	1	no	—
619	C₂×C₄	—	172	1	no	—
620	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
621	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
622	C₂×C₄	#13063331	1	2	yes	—
623	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
624	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
625	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
626	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
627	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
628	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
629	C₈	—	2	2	no	—
630	C₈	—	4	1	no	—
631	C₈	—	4	1	no	—
632	C₈	—	86	2	no	—
633	C₈	—	86	2	no	—
634	C₈	—	172	1	no	—
635	C₈	—	172	1	no	—
636	C₈	#13063311	1	4	yes	direct product factor
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	86	2	no	—
645	C₂²	—	86	2	no	—
646	C₂²	—	86	2	no	—
647	C₂²	—	172	1	no	—
648	C₂²	—	172	1	no	—
649	C₂²	—	172	1	no	—
650	C₂²	—	172	1	no	—
651	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
652	C₂²	C₄×#10621900	1	1	yes	characteristic
653	C₂²	C₄×#10621898	1	1	yes	characteristic
654	C₂²	C₂²×C₈×D₄₃	1	1	yes	characteristic
655	C₂²	#131×D₄₃	1	1	yes	characteristic
656	C₂²	#131×D₄₃	1	1	yes	characteristic
657	C₂²	C₂×#13063331	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	1	no	—
663	C₄	—	43	4	no	—
664	C₄	—	86	2	no	—
665	C₄	—	86	2	no	—
666	C₄	—	86	2	no	—
667	C₄	—	86	2	no	—
668	C₄	—	172	1	no	—
669	C₄	—	172	1	no	—
670	C₄	C₂×#13063311	1	1	yes	characteristic
671	C₄	#14583427	1	1	yes	characteristic
672	C₄	#14583429	1	1	yes	characteristic
673	C₄	#14583446	1	1	yes	characteristic
674	C₂	—	4	2	no	—
675	C₂	—	172	2	no	—
676	C₂	C₄×#13063311	1	1	yes	characteristic
677	C₂	C₈×D₄×D₄₃	1	1	yes	characteristic
678	C₂	#19143302	1	1	yes	characteristic
679	C₂	C₈×#10621900	1	1	yes	characteristic
680	C₂	C₈×#10621898	1	1	yes	characteristic
681	C₂	#19143563	1	1	yes	characteristic
682	C₂	#19143566	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₈×C₂²⋊C₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₃	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₄₃
hypocenter	C₄₃	C₈×#124
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Dic₈₆	C₂	semidirect
4. #19135529	C₂	semidirect
6. #19135203	C₂	semidirect
7. #19135202	C₂	semidirect
8. #19135199	C₂	semidirect
9. #19135198	C₂	semidirect
10. #19134710	C₂	semidirect
11. C₈×(C₂×D₄₃)⋊C₄	C₂	semidirect
12. C₈×(C₂×D₄₃)⋊C₄	C₂	semidirect
13. C₈×C₂²⋊Dic₄₃	C₂	semidirect
14. C₄×C₈×Dic₄₃	C₂	semidirect
15. C₈×C₂²⋊C₄×C₄₃	C₂	semidirect
71. #13063311	C₈	direct (N × H)
165. C₂×Dic₈₆	C₂×C₈	semidirect
180. C₂²⋊C₄×C₄₃	C₂×C₈	semidirect
187. C₂²⋊Dic₄₃	C₂×C₈	semidirect
191. (C₂×D₄₃)⋊C₄	C₂×C₈	semidirect
192. (C₂×D₄₃)⋊C₄	C₂×C₈	semidirect
204. C₄×Dic₄₃	C₂×C₈	semidirect
290. C₈×C₄₃	#124	semidirect
346. C₈×C₂²⋊C₄	D₄₃	semidirect
402. C₄₃	C₈×#124	semidirect
547. C₂²⋊C₄	C₈×D₄₃	semidirect
636. C₈	#13063311	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×C₈×Dic₈₆	2
C₂×C₈×C₂²⋊D₄₃	2
C₄×#13063311	2
#19135529	2
#19135387	2
#19135203	2
#19135202	2
#19135199	2
#19135198	2
#19134710	2
C₈×(C₂×D₄₃)⋊C₄	2
C₈×C₂²⋊Dic₄₃	2
C₄×C₈×Dic₄₃	2
C₈×C₂²⋊C₄×C₄₃	2
C₈×#124	43

Subgroups — C8×#13063311 #25104458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13063311 #25104458