Subgroups — #25115189

Order 11008.

916 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582975	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19137054	C₂	1	1	yes	maximal, characteristic
4	#19135312	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135312	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134779	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134778	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134774	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134773	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134710	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134579	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134578	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134443	C₂	1	1	yes	maximal, characteristic, complemented
14	#19134290	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10621872	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
19	C₂×#13063282	C₂²	1	1	yes	characteristic
20	#14582975	—	2	4	no	—
21	C₈×C₂²⋊D₄₃	—	2	4	no	—
22	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₃⋊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×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	#14582799	C₄	1	1	yes	characteristic
37	#14582799	C₄	1	1	yes	characteristic
38	#14582794	C₄	1	1	yes	characteristic
39	#14582794	C₄	1	1	yes	characteristic
40	#14582793	C₄	1	1	yes	characteristic
41	#14582793	C₄	1	1	yes	characteristic
42	#14582789	C₄	1	1	yes	characteristic
43	#14582789	C₄	1	1	yes	characteristic
44	C₄×Dic₄₃⋊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	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
55	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
56	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#336	C₂²	1	1	yes	characteristic
58	C₄₃×#336	C₂²	1	1	yes	characteristic
59	C₄₃×#336	C₂²	1	1	yes	characteristic
60	C₄₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
63	C₂×#10621872	—	2	2	no	—
64	C₂×#10621872	—	2	2	no	—
65	C₂×#10621872	—	4	1	no	—
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₄₃	—	2	2	no	—
71	C₂×C₈×D₄₃	—	2	2	no	—
72	C₂×C₈×D₄₃	—	4	1	no	—
73	C₄×C₂²⋊D₄₃	D₄	1	4	yes	—
74	C₄×C₂²⋊D₄₃	Q₈	1	4	yes	—
75	#13063282	—	4	1	no	—
76	#13063282	—	4	1	no	—
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×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊Dic₄₃	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×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×(C₂×D₄₃)⋊C₄	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	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
95	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
98	C₄⋊(C₄₃⋊C₈)	—	4	1	no	—
99	Dic₄₃⋊C₈	—	2	2	no	—
100	Dic₄₃⋊C₈	—	2	2	no	—
101	Dic₄₃⋊C₈	—	2	2	no	—
102	Dic₄₃⋊C₈	—	2	2	no	—
103	Dic₄₃⋊C₈	—	4	1	no	—
104	Dic₄₃⋊C₈	—	4	1	no	—
105	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
106	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
107	(C₂×D₄₃)⋊C₈	—	2	2	no	—
108	(C₂×D₄₃)⋊C₈	—	2	2	no	—
109	C₈×Dic₄₃	—	2	2	no	—
110	C₈×Dic₄₃	—	2	2	no	—
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	C₄₃⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₄₃	—	2	2	no	—
119	C₂×M₁₆×C₄₃	—	2	2	no	—
120	C₂×M₁₆×C₄₃	—	4	1	no	—
121	C₂²×C₈×C₄₃	—	2	2	no	—
122	C₂²×C₈×C₄₃	—	2	2	no	—
123	C₂²×C₈×C₄₃	—	4	1	no	—
124	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
128	#117×C₄₃	—	4	1	no	—
129	#117×C₄₃	—	4	1	no	—
130	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
136	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₂²⋊D₄₃	—	2	2	no	—
151	C₂×C₂²⋊D₄₃	—	2	2	no	—
152	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	4	yes	—
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	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄×D₄₃	—	2	1	no	—
161	C₂×C₄×D₄₃	—	2	1	no	—
162	C₂×C₄×D₄₃	—	2	1	no	—
163	C₂×C₄×D₄₃	—	2	1	no	—
164	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
165	C₂×C₄×D₄₃	C₂×Q₈	1	2	yes	—
166	M₁₆×C₄₃	—	4	4	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	—	2	1	no	—
175	C₂×C₈×C₄₃	—	2	1	no	—
176	C₂×C₈×C₄₃	—	2	1	no	—
177	C₂×C₈×C₄₃	—	4	4	no	—
178	C₂×C₈×C₄₃	#41	1	2	yes	—
179	C₂×C₈×C₄₃	#41	1	2	yes	—
180	C₄⋊C₄×C₄₃	—	4	1	no	—
181	C₄⋊C₄×C₄₃	—	4	1	no	—
182	C₂²⋊C₄×C₄₃	—	4	1	no	—
183	C₂²⋊C₄×C₄₃	—	4	1	no	—
184	C₄²×C₄₃	—	2	1	no	—
185	C₄²×C₄₃	—	2	1	no	—
186	C₄²×C₄₃	—	2	1	no	—
187	C₄²×C₄₃	—	2	1	no	—
188	C₂²⋊Dic₄₃	—	2	2	no	—
189	C₂²⋊Dic₄₃	—	4	1	no	—
190	C₂²⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
191	(C₂×D₄₃)⋊C₄	—	2	2	no	—
192	(C₂×D₄₃)⋊C₄	—	4	1	no	—
193	(C₂×D₄₃)⋊C₄	—	4	1	no	—
194	(C₂×D₄₃)⋊C₄	—	4	1	no	—
195	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	4	yes	—
196	Dic₄₃⋊C₄	—	2	2	no	—
197	Dic₄₃⋊C₄	—	2	2	no	—
198	Dic₄₃⋊C₄	—	4	1	no	—
199	Dic₄₃⋊C₄	—	4	1	no	—
200	Dic₄₃⋊C₄	C₄⋊C₄	1	4	yes	—
201	C₄×Dic₄₃	—	2	1	no	—
202	C₄×Dic₄₃	—	2	1	no	—
203	C₄×Dic₄₃	—	2	1	no	—
204	C₄×Dic₄₃	—	2	1	no	—
205	C₄×Dic₄₃	—	2	2	no	—
206	C₄×Dic₄₃	—	2	2	no	—
207	C₄×Dic₄₃	—	2	2	no	—
208	C₄×Dic₄₃	—	4	1	no	—
209	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
210	C₄×Dic₄₃	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
218	C₂×C₄₃⋊C₈	—	2	1	no	—
219	C₂×C₄₃⋊C₈	—	2	1	no	—
220	C₂×C₄₃⋊C₈	—	2	1	no	—
221	C₂×C₄₃⋊C₈	—	2	1	no	—
222	C₂×C₄₃⋊C₈	—	2	1	no	—
223	#10621872	—	4	4	no	—
224	C₈×D₄₃	—	4	4	no	—
225	C₂³×C₄₃	—	2	1	no	—
226	C₂³×C₄₃	—	2	1	no	—
227	C₂³×C₄₃	—	2	1	no	—
228	C₂³×C₄₃	—	2	1	no	—
229	C₂³×C₄₃	—	2	1	no	—
230	C₂³×C₄₃	—	2	1	no	—
231	C₂³×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
232	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
233	C₂²×D₄₃	—	2	1	no	—
234	C₂²×D₄₃	—	2	1	no	—
235	C₂²×D₄₃	—	2	1	no	—
236	C₂²×D₄₃	—	2	1	no	—
237	C₂²×D₄₃	—	2	1	no	—
238	C₂²×D₄₃	—	2	1	no	—
239	C₂²×D₄₃	C₂×C₄⋊C₄	1	2	yes	—
240	C₂×C₄×C₄₃	—	2	1	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	2	no	—
243	C₂×C₄×C₄₃	—	2	2	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	2	2	no	—
246	C₂×C₄×C₄₃	—	2	1	no	—
247	C₂×C₄×C₄₃	—	2	1	no	—
248	C₂×C₄×C₄₃	—	2	1	no	—
249	C₂×C₄×C₄₃	—	2	1	no	—
250	C₂×C₄×C₄₃	—	2	1	no	—
251	C₂×C₄×C₄₃	—	2	1	no	—
252	C₂×C₄×C₄₃	—	2	1	no	—
253	C₂×C₄×C₄₃	—	2	1	no	—
254	C₂×C₄×C₄₃	—	2	1	no	—
255	C₂×C₄×C₄₃	—	2	1	no	—
256	C₂×C₄×C₄₃	—	2	1	no	—
257	C₂×C₄×C₄₃	—	2	1	no	—
258	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
259	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
261	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
264	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²⋊D₄₃	—	2	8	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	—	2	1	no	—
276	C₂×Dic₄₃	—	2	1	no	—
277	C₂×Dic₄₃	—	2	1	no	—
278	C₂×Dic₄₃	—	2	1	no	—
279	C₂×Dic₄₃	—	2	1	no	—
280	C₂×Dic₄₃	—	2	1	no	—
281	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
282	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
283	C₂×Dic₄₃	C₂×C₄⋊C₄	1	2	yes	—
284	C₂×Dic₄₃	#131	1	2	yes	—
285	C₂×Dic₄₃	#131	1	2	yes	—
286	C₂×Dic₄₃	#131	1	2	yes	—
287	C₄×D₄₃	—	2	2	no	—
288	C₄×D₄₃	—	2	2	no	—
289	C₄×D₄₃	—	2	2	no	—
290	C₄×D₄₃	—	2	2	no	—
291	C₈×C₄₃	—	2	2	no	—
292	C₈×C₄₃	—	2	2	no	—
293	C₈×C₄₃	—	4	1	no	—
294	C₈×C₄₃	—	4	1	no	—
295	C₄₃⋊C₈	—	4	1	no	—
296	C₄₃⋊C₈	—	4	1	no	—
297	C₄₃⋊C₈	—	4	1	no	—
298	C₄₃⋊C₈	—	4	1	no	—
299	#22701	—	43	1	no	maximal, Sylow
300	C₂²×C₄₃	—	2	2	no	—
301	C₂²×C₄₃	—	2	2	no	—
302	C₂²×C₄₃	—	2	2	no	—
303	C₂²×C₄₃	—	4	1	no	—
304	C₂²×C₄₃	—	4	1	no	—
305	C₂²×C₄₃	—	4	1	no	—
306	C₂²×C₄₃	—	4	1	no	—
307	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
308	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
309	C₂²×C₄₃	#518	1	1	yes	characteristic
310	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
311	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
312	C₂²×C₄₃	C₂×#131	1	1	yes	characteristic
313	C₂²×C₄₃	#568	1	1	yes	characteristic
314	C₂×D₄₃	—	2	2	no	—
315	C₂×D₄₃	—	2	2	no	—
316	C₂×D₄₃	—	2	2	no	—
317	C₂×D₄₃	—	4	1	no	—
318	C₂×D₄₃	—	4	1	no	—
319	C₂×D₄₃	—	4	1	no	—
320	C₂×D₄₃	—	4	1	no	—
321	C₄×C₄₃	—	2	2	no	—
322	C₄×C₄₃	—	4	1	no	—
323	C₄×C₄₃	—	4	1	no	—
324	C₄×C₄₃	—	4	1	no	—
325	C₄×C₄₃	—	4	1	no	—
326	C₄×C₄₃	#546	1	1	yes	characteristic
327	C₄×C₄₃	#546	1	1	yes	characteristic
328	C₄×C₄₃	#554	1	1	yes	characteristic
329	C₄×C₄₃	#554	1	1	yes	characteristic
330	Dic₄₃	—	2	2	no	—
331	Dic₄₃	—	2	2	no	—
332	Dic₄₃	—	2	2	no	—
333	Dic₄₃	—	4	1	no	—
334	Dic₄₃	—	4	1	no	—
335	Dic₄₃	—	4	1	no	—
336	Dic₄₃	#424	1	4	yes	—
337	C₂×#436	—	43	1	no	—
338	C₂×C₈×D₄	—	43	1	no	—
339	#2293	—	43	1	no	—
340	#1939	—	43	1	no	—
341	#1939	—	43	1	no	—
342	#1851	—	43	1	no	—
343	#1851	—	43	1	no	—
344	#1850	—	43	1	no	—
345	#1850	—	43	1	no	—
346	#1831	—	43	1	no	—
347	#1798	—	43	1	no	—
348	#1798	—	43	1	no	—
349	C₄×C₄⋊C₈	—	43	1	no	—
350	#1729	—	43	1	no	—
351	#1729	D₄₃	1	1	yes	characteristic, complemented
352	C₂×C₄₃	—	4	2	no	—
353	C₂×C₄₃	#2349	1	1	yes	characteristic
354	C₂×C₄₃	C₂×#424	1	1	yes	characteristic
355	C₂×C₄₃	#2906	1	1	yes	characteristic
356	C₂×C₄₃	#2966	1	1	yes	characteristic
357	C₂×C₄₃	#2969	1	1	yes	characteristic
358	C₂×C₄₃	#2979	1	1	yes	characteristic
359	C₂×C₄₃	#2981	1	1	yes	characteristic
360	D₄₃	—	4	2	no	—
361	C₂²×M₁₆	—	43	1	no	—
362	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
363	C₂³×C₈	—	43	1	no	—
364	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
365	C₂×C₄×D₄	—	43	1	no	—
366	C₂×#117	—	43	1	no	—
367	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
368	#436	—	86	4	no	—
369	C₈×D₄	—	86	4	no	—
370	C₂×C₄⋊C₈	—	43	1	no	—
371	C₂×C₄⋊C₈	—	43	1	no	—
372	C₂×C₄⋊C₈	—	43	1	no	—
373	C₂×C₄⋊C₈	—	43	1	no	—
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×C₂²⋊C₈	—	43	1	no	—
379	C₂×C₂²⋊C₈	—	43	1	no	—
380	C₂×C₂²⋊C₈	—	43	1	no	—
381	C₂×C₂²⋊C₈	—	43	1	no	—
382	C₂×C₄×C₈	—	43	1	no	—
383	C₂×C₄×C₈	—	43	1	no	—
384	#390	—	43	1	no	—
385	#390	—	43	1	no	—
386	#389	—	43	1	no	—
387	#389	—	43	1	no	—
388	#388	—	43	1	no	—
389	#388	—	43	1	no	—
390	#388	—	43	1	no	—
391	#388	—	43	1	no	—
392	C₄×C₄⋊C₄	—	43	1	no	—
393	C₄×C₂²⋊C₄	—	43	1	no	—
394	C₄×C₂²⋊C₄	—	43	1	no	—
395	C₄³	—	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	—	43	1	no	—
401	#336	—	43	1	no	—
402	#336	C₂×D₄₃	1	1	yes	characteristic
403	#336	C₂×D₄₃	1	1	yes	characteristic
404	#336	C₂×D₄₃	1	1	yes	characteristic
405	#336	C₂×D₄₃	1	1	yes	characteristic
406	C₄₃	#22701	1	1	yes	characteristic, complemented, Sylow
407	C₂²×D₄	—	43	1	no	—
408	C₂³×C₄	—	43	1	no	—
409	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	—	2	2	no	—
412	C₂×M₁₆	—	4	1	no	—
413	C₂×M₁₆	—	86	2	no	—
414	C₂×M₁₆	—	86	2	no	—
415	C₂×M₁₆	—	172	1	no	—
416	C₂²×C₈	—	2	2	no	—
417	C₂²×C₈	—	2	2	no	—
418	C₂²×C₈	—	4	1	no	—
419	C₂²×C₈	—	43	1	no	—
420	C₂²×C₈	—	43	1	no	—
421	C₂²×C₈	—	43	1	no	—
422	C₂²×C₈	—	43	1	no	—
423	C₂²×C₈	—	86	2	no	—
424	C₂²×C₈	—	86	2	no	—
425	C₂²×C₈	—	172	1	no	—
426	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
427	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
428	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
429	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
430	C₄×D₄	—	43	4	no	—
431	C₄×D₄	—	43	4	no	—
432	#117	—	4	1	no	—
433	#117	—	4	1	no	—
434	#117	—	172	1	no	—
435	#117	—	172	1	no	—
436	C₂×C₄⋊C₄	—	43	1	no	—
437	C₂×C₄⋊C₄	—	43	1	no	—
438	C₂×C₄⋊C₄	—	43	1	no	—
439	C₂×C₄⋊C₄	—	43	1	no	—
440	C₂×C₄⋊C₄	—	43	1	no	—
441	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	—	43	1	no	—
444	C₂×C₂²⋊C₄	—	43	1	no	—
445	C₂×C₂²⋊C₄	—	43	1	no	—
446	C₂×C₂²⋊C₄	—	43	1	no	—
447	C₂×C₂²⋊C₄	—	43	1	no	—
448	C₂×C₂²⋊C₄	—	43	1	no	—
449	C₂×C₂²⋊C₄	—	43	1	no	—
450	C₂×C₂²⋊C₄	—	43	1	no	—
451	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₄×D₄₃	1	1	yes	characteristic
453	C₂×C₄²	—	43	1	no	—
454	C₂×C₄²	—	43	1	no	—
455	C₂×C₄²	—	43	1	no	—
456	C₂×C₄²	—	43	1	no	—
457	C₂×C₄²	—	43	1	no	—
458	C₂×C₄²	—	43	1	no	—
459	C₂×C₄²	—	43	1	no	—
460	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
461	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
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	—	172	1	no	—
467	C₄⋊C₈	—	172	1	no	—
468	C₄⋊C₈	—	172	1	no	—
469	C₄⋊C₈	—	172	1	no	—
470	C₂²⋊C₈	—	86	2	no	—
471	C₂²⋊C₈	—	86	2	no	—
472	C₂²⋊C₈	—	86	2	no	—
473	C₂²⋊C₈	—	86	2	no	—
474	C₄×C₈	—	86	2	no	—
475	C₄×C₈	—	86	2	no	—
476	#95	—	43	1	no	—
477	#95	—	43	1	no	—
478	#95	—	43	1	no	—
479	#95	—	43	1	no	—
480	#95	—	43	1	no	—
481	#95	—	43	1	no	—
482	C₂⁴	—	43	1	no	—
483	C₂⁴	C₂×C₄×D₄₃	1	1	yes	characteristic
484	C₂×D₄	—	43	4	no	—
485	C₂×D₄	—	86	2	no	—
486	C₂×D₄	—	86	2	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	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	2	no	—
496	C₂²×C₄	—	43	2	no	—
497	C₂²×C₄	—	43	1	no	—
498	C₂²×C₄	—	43	1	no	—
499	C₂²×C₄	—	43	1	no	—
500	C₂²×C₄	—	86	1	no	—
501	C₂²×C₄	—	86	1	no	—
502	C₂²×C₄	—	86	1	no	—
503	C₂²×C₄	—	86	1	no	—
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	C₂×C₄×D₄₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
509	C₂²×C₄	D₄×D₄₃	1	2	yes	—
510	C₂²×C₄	Q₈×D₄₃	1	2	yes	—
511	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
512	M₁₆	—	4	4	no	—
513	M₁₆	—	172	4	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	4	4	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	—	86	1	no	—
530	C₂×C₈	—	86	1	no	—
531	C₂×C₈	—	86	1	no	—
532	C₂×C₈	—	86	1	no	—
533	C₂×C₈	—	86	1	no	—
534	C₂×C₈	—	86	1	no	—
535	C₂×C₈	—	86	1	no	—
536	C₂×C₈	—	86	1	no	—
537	C₂×C₈	—	172	4	no	—
538	C₂×C₈	#10621898	1	2	yes	—
539	C₂×C₈	#10621898	1	2	yes	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	43	4	no	—
543	C₄⋊C₄	—	86	2	no	—
544	C₄⋊C₄	—	86	2	no	—
545	C₄⋊C₄	—	172	1	no	—
546	C₄⋊C₄	—	172	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	43	4	no	—
550	C₂²⋊C₄	—	43	4	no	—
551	C₂²⋊C₄	—	86	2	no	—
552	C₂²⋊C₄	—	86	2	no	—
553	C₂²⋊C₄	—	172	1	no	—
554	C₂²⋊C₄	—	172	1	no	—
555	C₂²⋊C₄	—	172	1	no	—
556	C₂²⋊C₄	—	172	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	43	2	no	—
562	C₄²	—	43	2	no	—
563	C₄²	—	86	2	no	—
564	C₄²	—	86	2	no	—
565	C₄²	—	86	2	no	—
566	C₄²	—	86	1	no	—
567	C₄²	—	86	1	no	—
568	C₄²	—	86	1	no	—
569	C₄²	—	86	1	no	—
570	C₄²	—	172	1	no	—
571	C₂³	—	2	1	no	—
572	C₂³	—	2	1	no	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	43	2	no	—
578	C₂³	—	86	1	no	—
579	C₂³	—	86	1	no	—
580	C₂³	—	86	1	no	—
581	C₂³	—	86	1	no	—
582	C₂³	—	86	1	no	—
583	C₂³	—	86	1	no	—
584	C₂³	C₄⋊C₄×D₄₃	1	2	yes	—
585	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
586	D₄	—	86	8	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	43	2	no	—
606	C₂×C₄	—	43	2	no	—
607	C₂×C₄	—	43	2	no	—
608	C₂×C₄	—	43	2	no	—
609	C₂×C₄	—	43	2	no	—
610	C₂×C₄	—	43	2	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	—	86	1	no	—
617	C₂×C₄	—	86	2	no	—
618	C₂×C₄	—	86	2	no	—
619	C₂×C₄	—	86	2	no	—
620	C₂×C₄	—	86	2	no	—
621	C₂×C₄	—	86	1	no	—
622	C₂×C₄	—	86	1	no	—
623	C₂×C₄	—	86	1	no	—
624	C₂×C₄	—	86	1	no	—
625	C₂×C₄	—	86	1	no	—
626	C₂×C₄	—	86	1	no	—
627	C₂×C₄	—	86	1	no	—
628	C₂×C₄	—	86	1	no	—
629	C₂×C₄	—	86	1	no	—
630	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
631	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
632	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
633	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
634	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
635	C₂×C₄	#13063370	1	1	yes	characteristic
636	C₂×C₄	#13063370	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	2	no	—
639	C₈	—	4	1	no	—
640	C₈	—	4	1	no	—
641	C₈	—	172	1	no	—
642	C₈	—	172	1	no	—
643	C₈	—	172	1	no	—
644	C₈	—	172	1	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	1	no	—
651	C₂²	—	4	1	no	—
652	C₂²	—	86	2	no	—
653	C₂²	—	86	2	no	—
654	C₂²	—	86	2	no	—
655	C₂²	—	172	1	no	—
656	C₂²	—	172	1	no	—
657	C₂²	—	172	1	no	—
658	C₂²	—	172	1	no	—
659	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
660	C₂²	C₄×#10621898	1	1	yes	characteristic
661	C₂²	#14583372	1	1	yes	characteristic
662	C₂²	#131×D₄₃	1	1	yes	characteristic
663	C₂²	#131×D₄₃	1	1	yes	characteristic
664	C₂²	#131×D₄₃	1	1	yes	characteristic
665	C₂²	#14583664	1	1	yes	characteristic
666	C₄	—	2	2	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	43	4	no	—
672	C₄	—	86	2	no	—
673	C₄	—	86	2	no	—
674	C₄	—	86	2	no	—
675	C₄	—	172	1	no	—
676	C₄	—	172	1	no	—
677	C₄	—	172	1	no	—
678	C₄	#14583539	1	1	yes	characteristic
679	C₄	#14583539	1	1	yes	characteristic
680	C₄	#14583604	1	1	yes	characteristic
681	C₄	#14583604	1	1	yes	characteristic
682	C₂	—	4	2	no	—
683	C₂	—	172	2	no	—
684	C₂	#19137502	1	1	yes	characteristic
685	C₂	#424×D₄₃	1	1	yes	characteristic
686	C₂	#19143162	1	1	yes	characteristic
687	C₂	#19143566	1	1	yes	characteristic
688	C₂	#19143595	1	1	yes	characteristic
689	C₂	#19143659	1	1	yes	characteristic
690	C₂	#19143668	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂³×C₄
Fitting	C₄₃×#1729	C₂
prime radical	C₂²×C₂²⋊D₄₃	C₂×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1729	D₄₃
hypocenter	C₄₃	#22701
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1729

Complements

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

N	H ≅ G/N	type
4. #19135312	C₂	semidirect
5. #19135312	C₂	semidirect
6. #19134779	C₂	semidirect
7. #19134778	C₂	semidirect
8. #19134774	C₂	semidirect
9. #19134773	C₂	semidirect
10. #19134710	C₂	semidirect
11. #19134579	C₂	semidirect
12. #19134578	C₂	semidirect
13. #19134443	C₂	semidirect
14. #19134290	C₂	semidirect
15. C₄₃×#1729	C₂	semidirect
351. #1729	D₄₃	semidirect
406. C₄₃	#22701	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582975	2
C₂×C₈×C₂²⋊D₄₃	2
#19137054	2
#19135312	2
#19134779	2
#19134778	2
#19134774	2
#19134773	2
#19134710	2
#19134579	2
#19134578	2
#19134443	2
#19134290	2
C₄₃×#1729	2
#22701	43