Subgroups — #19148146

Order 5504.

1132 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583618	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583613	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583608	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583592	C₂	1	2	yes	maximal, complemented
5	#14583591	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583589	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583586	C₂	1	2	yes	maximal, complemented
8	#14583580	C₂	1	2	yes	maximal, complemented
9	#14583575	C₂	1	2	yes	maximal, complemented
10	#14583548	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583543	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583451	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583430	C₂	1	2	yes	maximal, complemented
14	#14583430	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583428	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583426	C₂	1	2	yes	maximal, complemented
17	#14583405	C₂	1	2	yes	maximal, complemented
18	#41×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#10621900	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#10621900	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×D₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#13063281	C₂	1	2	yes	maximal, complemented
23	C₄₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10621900	C₂²	1	1	yes	characteristic
25	C₂×#10621900	C₂²	1	1	yes	characteristic
26	C₂³×Dic₄₃	C₂²	1	2	yes	—
27	#13063324	C₂²	1	1	yes	characteristic, complemented
28	#13063323	C₂²	1	1	yes	characteristic, complemented
29	#13063320	C₂²	1	2	yes	complemented
30	#13063318	C₂²	1	2	yes	complemented
31	#13063318	C₂²	1	2	yes	complemented
32	#13063318	C₂²	1	2	yes	complemented
33	#13063318	C₂²	1	2	yes	complemented
34	#13063318	C₂²	1	2	yes	complemented
35	#13063317	C₂²	1	1	yes	characteristic, complemented
36	#13063316	C₂²	1	2	yes	complemented
37	#13063316	C₂²	1	1	yes	characteristic, complemented
38	#13063315	C₂²	1	2	yes	complemented
39	#13063315	C₂²	1	2	yes	complemented
40	#13063312	C₂²	1	1	yes	characteristic
41	#13063312	C₂²	1	2	yes	complemented
42	#13063311	C₂²	1	2	yes	complemented
43	#13063309	C₂²	1	2	yes	—
44	#13063308	C₂²	1	2	yes	complemented
45	#13063307	C₂²	1	2	yes	complemented
46	#13063306	C₂²	1	2	yes	—
47	#13063306	C₂²	1	2	yes	—
48	#13063306	C₂²	1	2	yes	complemented
49	#13063306	C₂²	1	2	yes	complemented
50	#13063304	C₂²	1	1	yes	characteristic
51	#13063304	C₂²	1	2	yes	complemented
52	#13063304	C₂²	1	1	yes	characteristic, complemented
53	#13063302	C₂²	1	2	yes	—
54	#13063302	C₂²	1	2	yes	complemented
55	#13063302	C₂²	1	2	yes	complemented
56	#13063302	C₂²	1	2	yes	complemented
57	#13063301	C₂²	1	1	yes	characteristic, complemented
58	#13063297	C₂²	1	2	yes	—
59	#13063297	C₂²	1	2	yes	complemented
60	#13063297	C₂²	1	2	yes	complemented
61	#13063296	C₂²	1	1	yes	characteristic
62	#13063294	C₂²	1	2	yes	—
63	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
64	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
65	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
66	C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
67	#13063290	C₂²	1	1	yes	characteristic, complemented
68	#13063290	C₂²	1	1	yes	characteristic, complemented
69	#13063290	C₂²	1	2	yes	complemented
70	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
71	D₄×Dic₄₃	C₂²	1	2	yes	—
72	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
73	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
74	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
75	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
76	D₄×Dic₄₃	C₂²	1	2	yes	—
77	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
78	D₄×Dic₄₃	C₂²	1	2	yes	complemented
79	D₄×Dic₄₃	C₂²	1	2	yes	complemented
80	D₄×Dic₄₃	C₂²	1	2	yes	complemented
81	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
82	C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
83	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
84	(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic
85	(C₂²⋊D₄₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
86	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
87	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	complemented
88	#13063284	C₂²	1	2	yes	complemented
89	#13063284	C₂²	1	1	yes	characteristic, complemented
90	#13063283	C₂²	1	1	yes	characteristic, complemented
91	#13063283	C₂²	1	1	yes	characteristic, complemented
92	#13063281	C₂²	1	2	yes	—
93	#13063281	C₂²	1	2	yes	—
94	#13063281	C₂²	1	1	yes	characteristic
95	#13063281	C₂²	1	2	yes	—
96	#13063281	C₂²	1	2	yes	complemented
97	#13063281	C₂²	1	2	yes	complemented
98	#13063281	C₂²	1	2	yes	complemented
99	#13063281	C₂²	1	2	yes	complemented
100	#13063281	C₂²	1	2	yes	complemented
101	#13063281	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
103	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	complemented
104	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	complemented
105	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
106	C₂×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
107	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic
108	C₂×C₄×Dic₄₃	C₂²	1	2	yes	complemented
109	C₂×C₄×Dic₄₃	C₂²	1	2	yes	complemented
110	C₂×C₄×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
111	C₄²×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
113	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
114	#124×C₄₃	C₂²	1	1	yes	characteristic
115	#123×C₄₃	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
117	#121×C₄₃	C₂²	1	2	yes	—
118	#121×C₄₃	C₂²	1	1	yes	characteristic
119	#120×C₄₃	C₂²	1	2	yes	—
120	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
123	C₂⁴×C₄₃	C₂³	1	2	yes	—
124	#41×C₄₃	—	2	4	no	—
125	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₄₃	—	2	4	no	—
127	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₄₃	C₂³	1	2	yes	—
129	C₂×D₄×C₄₃	C₂³	1	2	yes	—
130	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₄₃	C₂³	1	2	yes	—
132	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
141	C₂²×Dic₄₃	—	2	8	no	—
142	C₂²×Dic₄₃	C₂³	1	2	yes	—
143	C₂²×Dic₄₃	C₂³	1	2	yes	—
144	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
145	C₂²×Dic₄₃	C₂³	1	2	yes	—
146	C₂²×Dic₄₃	C₂³	1	2	yes	—
147	C₂²×Dic₄₃	C₂³	1	2	yes	—
148	C₂²×Dic₄₃	C₂³	1	2	yes	—
149	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₄₃	C₂³	1	2	yes	—
151	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
152	C₂²×Dic₄₃	C₂³	1	1	yes	characteristic
153	#10621900	—	2	4	no	—
154	#10621900	—	2	4	no	—
155	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
158	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
159	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
160	C₂×Dic₈₆	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
165	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
169	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
170	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
171	C₄²×C₄₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
185	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
186	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
187	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
189	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₄₃	C₂³	1	2	yes	—
192	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
194	C₄⋊Dic₄₃	C₂³	1	2	yes	—
195	C₄⋊Dic₄₃	C₂³	1	2	yes	—
196	C₄⋊Dic₄₃	C₂³	1	2	yes	—
197	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
198	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₄₃⋊C₄	C₂³	1	2	yes	—
200	Dic₄₃⋊C₄	C₂³	1	2	yes	—
201	Dic₄₃⋊C₄	C₂³	1	2	yes	—
202	Dic₄₃⋊C₄	C₂³	1	2	yes	—
203	Dic₄₃⋊C₄	C₂³	1	2	yes	—
204	Dic₄₃⋊C₄	C₂³	1	2	yes	—
205	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₄₃⋊C₄	C₂³	1	2	yes	—
207	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₄₃⋊C₄	C₂³	1	2	yes	—
209	Dic₄₃⋊C₄	C₂³	1	2	yes	—
210	Dic₄₃⋊C₄	C₂³	1	2	yes	—
211	Dic₄₃⋊C₄	C₂³	1	2	yes	—
212	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₃	C₂³	1	2	yes	—
220	C₄×Dic₄₃	C₂³	1	2	yes	—
221	C₄×Dic₄₃	C₂³	1	2	yes	—
222	C₄×Dic₄₃	C₂³	1	2	yes	—
223	C₄×Dic₄₃	C₂³	1	2	yes	—
224	C₄×Dic₄₃	C₂³	1	2	yes	—
225	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
227	C₂³×C₄₃	—	2	4	no	—
228	C₂³×C₄₃	—	2	4	no	—
229	C₂³×C₄₃	—	4	2	no	—
230	C₂³×C₄₃	C₂⁴	1	2	yes	—
231	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂³×C₄₃	C₂⁴	1	2	yes	—
234	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
235	Q₈×C₄₃	—	2	2	no	—
236	D₄×C₄₃	—	2	2	no	—
237	D₄×C₄₃	—	2	4	no	—
238	D₄×C₄₃	—	2	4	no	—
239	D₄×C₄₃	—	2	2	no	—
240	D₄×C₄₃	—	4	2	no	—
241	D₄×C₄₃	#41	1	4	yes	complemented
242	C₂×C₄×C₄₃	—	2	4	no	—
243	C₂×C₄×C₄₃	—	2	2	no	—
244	C₂×C₄×C₄₃	—	2	2	no	—
245	C₂×C₄×C₄₃	—	4	2	no	—
246	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
253	C₂²⋊D₄₃	—	2	2	no	—
254	C₂²⋊D₄₃	—	2	4	no	—
255	C₂²⋊D₄₃	—	2	2	no	—
256	C₂²⋊D₄₃	—	4	2	no	—
257	C₂×Dic₄₃	—	2	4	no	—
258	C₂×Dic₄₃	—	2	4	no	—
259	C₂×Dic₄₃	—	2	2	no	—
260	C₂×Dic₄₃	—	2	4	no	—
261	C₂×Dic₄₃	—	2	4	no	—
262	C₂×Dic₄₃	—	2	4	no	—
263	C₂×Dic₄₃	—	2	4	no	—
264	C₂×Dic₄₃	—	4	1	no	—
265	C₂×Dic₄₃	—	4	2	no	—
266	C₂×Dic₄₃	—	4	1	no	—
267	C₂×Dic₄₃	#41	1	4	yes	complemented
268	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₄₃	C₂⁴	1	2	yes	—
272	C₂×Dic₄₃	C₂⁴	1	2	yes	—
273	C₂×Dic₄₃	C₂⁴	1	2	yes	—
274	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₄₃	C₂⁴	1	2	yes	—
277	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
279	C₄×D₄₃	—	2	2	no	—
280	C₄×D₄₃	—	2	2	no	—
281	C₄×D₄₃	—	4	1	no	—
282	Dic₈₆	—	2	2	no	—
283	Dic₈₆	—	2	2	no	—
284	Dic₈₆	—	4	2	no	—
285	C₂²×C₄₃	—	2	1	no	—
286	C₂²×C₄₃	—	2	2	no	—
287	C₂²×C₄₃	—	2	1	no	—
288	C₂²×C₄₃	—	2	2	no	—
289	C₂²×C₄₃	—	2	2	no	—
290	C₂²×C₄₃	—	2	2	no	—
291	C₂²×C₄₃	—	2	1	no	—
292	C₂²×C₄₃	—	2	1	no	—
293	C₂²×C₄₃	—	2	2	no	—
294	C₂²×C₄₃	—	2	1	no	—
295	C₂²×C₄₃	—	4	8	no	—
296	C₂²×C₄₃	C₂×#41	1	2	yes	—
297	C₂²×C₄₃	C₂×#41	1	4	yes	—
298	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
299	C₂×D₄₃	—	2	1	no	—
300	C₂×D₄₃	—	2	1	no	—
301	C₂×D₄₃	—	2	1	no	—
302	C₄×C₄₃	—	2	1	no	—
303	C₄×C₄₃	—	2	1	no	—
304	C₄×C₄₃	—	2	1	no	—
305	C₄×C₄₃	—	2	2	no	—
306	C₄×C₄₃	—	2	2	no	—
307	C₄×C₄₃	—	2	1	no	—
308	C₄×C₄₃	C₂×#41	1	2	yes	—
309	Dic₄₃	—	2	1	no	—
310	Dic₄₃	—	2	2	no	—
311	Dic₄₃	—	2	1	no	—
312	Dic₄₃	—	2	2	no	—
313	Dic₄₃	—	2	2	no	—
314	Dic₄₃	—	2	1	no	—
315	Dic₄₃	—	2	2	no	—
316	Dic₄₃	—	2	1	no	—
317	Dic₄₃	—	2	1	no	—
318	Dic₄₃	C₂×#41	1	2	yes	—
319	Dic₄₃	C₂×#41	1	2	yes	—
320	#3475	—	43	1	no	maximal, Sylow
321	C₂×C₄₃	—	2	2	no	—
322	C₂×C₄₃	—	2	4	no	—
323	C₂×C₄₃	—	4	1	no	—
324	C₂×C₄₃	—	4	2	no	—
325	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
326	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
327	C₂×C₄₃	#585	1	1	yes	characteristic
328	D₄₃	—	4	1	no	—
329	#556	—	43	1	no	—
330	#555	—	43	1	no	—
331	#554	—	43	1	no	—
332	#553	—	43	2	no	—
333	#552	—	43	2	no	—
334	#552	—	43	1	no	—
335	#552	—	43	1	no	—
336	#551	—	43	2	no	—
337	#551	—	43	2	no	—
338	#547	—	43	1	no	—
339	#546	—	43	1	no	—
340	#546	D₄₃	1	1	yes	characteristic, complemented
341	#533	—	43	1	no	—
342	#529	—	43	1	no	—
343	#529	—	43	2	no	—
344	#529	—	43	2	no	—
345	#529	—	43	1	no	—
346	#525	—	43	2	no	—
347	C₄×#41	—	43	1	no	—
348	C₄×#41	—	43	1	no	—
349	C₄×#41	—	43	1	no	—
350	C₂×C₄×D₄	—	43	1	no	—
351	C₂×#117	—	43	2	no	—
352	C₄₃	#3475	1	1	yes	characteristic, complemented, Sylow
353	C₂×#41	—	43	1	no	—
354	C₂×#41	—	43	1	no	—
355	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
356	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
357	C₂³×C₄	—	43	2	no	—
358	C₄⋊Q₈	—	43	1	no	—
359	C₄⋊Q₈	—	43	1	no	—
360	#126	—	43	2	no	—
361	#126	—	43	2	no	—
362	#126	—	43	2	no	—
363	#126	—	43	2	no	—
364	#126	—	43	2	no	—
365	#126	—	43	2	no	—
366	#125	—	43	2	no	—
367	#125	—	43	2	no	—
368	#125	—	43	1	no	—
369	#125	—	43	2	no	—
370	#125	—	43	1	no	—
371	#124	—	43	1	no	—
372	#124	—	43	2	no	—
373	#124	—	43	2	no	—
374	#124	C₂×D₄₃	1	1	yes	characteristic
375	#123	—	43	2	no	—
376	#123	—	43	2	no	—
377	#123	—	43	2	no	—
378	#123	—	43	2	no	—
379	#123	—	43	2	no	—
380	#123	—	43	2	no	—
381	#123	—	43	2	no	—
382	#123	C₂×D₄₃	1	2	yes	—
383	C₂²⋊Q₈	—	43	1	no	—
384	C₂²⋊Q₈	—	43	1	no	—
385	C₂²⋊Q₈	—	43	2	no	—
386	C₂²⋊Q₈	—	43	1	no	—
387	C₂²⋊Q₈	—	43	2	no	—
388	C₂²⋊Q₈	—	43	2	no	—
389	C₂²⋊Q₈	—	43	2	no	—
390	C₂²⋊Q₈	—	43	2	no	—
391	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
392	#121	—	43	2	no	—
393	#121	—	43	2	no	—
394	#121	—	43	2	no	—
395	#121	—	43	1	no	—
396	#121	C₂×D₄₃	1	2	yes	—
397	#121	C₂×D₄₃	1	1	yes	characteristic
398	#120	—	43	2	no	—
399	#120	C₂×D₄₃	1	2	yes	—
400	C₄×Q₈	—	43	1	no	—
401	C₄×Q₈	—	43	1	no	—
402	C₄×Q₈	—	43	1	no	—
403	C₄×Q₈	—	43	1	no	—
404	C₄×Q₈	—	43	2	no	—
405	C₄×Q₈	—	43	1	no	—
406	C₄×Q₈	—	43	1	no	—
407	C₄×D₄	—	43	1	no	—
408	C₄×D₄	—	43	1	no	—
409	C₄×D₄	—	43	2	no	—
410	C₄×D₄	—	43	1	no	—
411	C₄×D₄	—	43	2	no	—
412	C₄×D₄	—	43	1	no	—
413	C₄×D₄	—	43	2	no	—
414	C₄×D₄	—	43	1	no	—
415	C₄×D₄	—	43	1	no	—
416	C₄×D₄	—	43	2	no	—
417	C₄×D₄	—	43	2	no	—
418	C₄×D₄	—	43	1	no	—
419	C₄×D₄	—	43	1	no	—
420	C₄×D₄	—	43	2	no	—
421	C₄×D₄	—	43	2	no	—
422	C₄×D₄	—	43	1	no	—
423	C₄×D₄	—	43	1	no	—
424	C₄×D₄	—	43	2	no	—
425	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
426	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
427	#117	—	43	2	no	—
428	#117	—	43	1	no	—
429	#117	—	43	1	no	—
430	#117	—	43	1	no	—
431	#117	—	43	1	no	—
432	#117	—	43	2	no	—
433	#117	—	43	2	no	—
434	#117	—	43	2	no	—
435	#117	—	43	2	no	—
436	#117	—	43	2	no	—
437	#117	—	43	2	no	—
438	#117	—	43	2	no	—
439	#117	—	43	1	no	—
440	#117	—	43	2	no	—
441	C₂×C₄⋊C₄	—	43	2	no	—
442	C₂×C₄⋊C₄	—	43	2	no	—
443	C₂×C₄⋊C₄	—	43	1	no	—
444	C₂×C₂²⋊C₄	—	43	2	no	—
445	C₂×C₂²⋊C₄	—	43	2	no	—
446	C₂×C₂²⋊C₄	C₂×D₄₃	1	2	yes	—
447	C₂×C₄²	—	43	2	no	—
448	C₂×C₄²	—	43	2	no	—
449	C₂×C₄²	—	43	1	no	—
450	C₂×C₄²	—	43	1	no	—
451	C₂×C₄²	—	43	1	no	—
452	C₂⁴	C₂²×D₄₃	1	2	yes	—
453	#41	—	2	4	no	—
454	#41	—	86	4	no	—
455	#41	—	86	4	no	—
456	C₂×Q₈	—	43	1	no	—
457	C₂×Q₈	—	43	1	no	—
458	C₂×Q₈	—	43	2	no	—
459	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	43	1	no	—
462	C₂×D₄	—	43	2	no	—
463	C₂×D₄	—	43	1	no	—
464	C₂×D₄	—	43	2	no	—
465	C₂×D₄	C₂²×D₄₃	1	2	yes	—
466	C₂×D₄	C₂²×D₄₃	1	2	yes	—
467	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
468	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
469	C₂×D₄	C₂²×D₄₃	1	2	yes	—
470	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
471	C₂²×C₄	—	43	1	no	—
472	C₂²×C₄	—	43	2	no	—
473	C₂²×C₄	—	43	2	no	—
474	C₂²×C₄	—	43	1	no	—
475	C₂²×C₄	—	43	2	no	—
476	C₂²×C₄	—	43	2	no	—
477	C₂²×C₄	—	43	2	no	—
478	C₂²×C₄	—	43	2	no	—
479	C₂²×C₄	—	43	1	no	—
480	C₂²×C₄	—	43	2	no	—
481	C₂²×C₄	—	43	1	no	—
482	C₂²×C₄	—	43	1	no	—
483	C₂²×C₄	—	43	1	no	—
484	C₂²×C₄	—	43	1	no	—
485	C₂²×C₄	—	86	8	no	—
486	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
487	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
488	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
489	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
490	C₄⋊C₄	—	43	1	no	—
491	C₄⋊C₄	—	43	1	no	—
492	C₄⋊C₄	—	43	1	no	—
493	C₄⋊C₄	—	43	2	no	—
494	C₄⋊C₄	—	43	2	no	—
495	C₄⋊C₄	—	43	2	no	—
496	C₄⋊C₄	—	43	2	no	—
497	C₄⋊C₄	—	43	2	no	—
498	C₄⋊C₄	—	43	2	no	—
499	C₄⋊C₄	—	43	1	no	—
500	C₄⋊C₄	—	43	2	no	—
501	C₄⋊C₄	—	43	1	no	—
502	C₄⋊C₄	—	43	1	no	—
503	C₄⋊C₄	—	43	1	no	—
504	C₄⋊C₄	—	43	2	no	—
505	C₄⋊C₄	—	43	2	no	—
506	C₄⋊C₄	—	43	2	no	—
507	C₄⋊C₄	—	43	2	no	—
508	C₄⋊C₄	—	43	1	no	—
509	C₄⋊C₄	—	43	2	no	—
510	C₄⋊C₄	—	43	2	no	—
511	C₄⋊C₄	—	43	2	no	—
512	C₄⋊C₄	—	43	2	no	—
513	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
516	C₂²⋊C₄	—	43	1	no	—
517	C₂²⋊C₄	—	43	2	no	—
518	C₂²⋊C₄	—	43	2	no	—
519	C₂²⋊C₄	—	43	2	no	—
520	C₂²⋊C₄	—	43	2	no	—
521	C₂²⋊C₄	—	43	2	no	—
522	C₂²⋊C₄	—	43	2	no	—
523	C₂²⋊C₄	—	43	2	no	—
524	C₂²⋊C₄	—	43	2	no	—
525	C₂²⋊C₄	—	43	2	no	—
526	C₂²⋊C₄	—	43	1	no	—
527	C₂²⋊C₄	—	43	2	no	—
528	C₂²⋊C₄	—	43	2	no	—
529	C₂²⋊C₄	—	43	1	no	—
530	C₂²⋊C₄	—	43	2	no	—
531	C₂²⋊C₄	—	43	1	no	—
532	C₂²⋊C₄	—	43	2	no	—
533	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
535	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
537	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
539	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
540	C₄²	—	43	1	no	—
541	C₄²	—	43	1	no	—
542	C₄²	—	43	1	no	—
543	C₄²	—	43	2	no	—
544	C₄²	—	43	2	no	—
545	C₄²	—	43	1	no	—
546	C₄²	—	43	2	no	—
547	C₄²	—	43	2	no	—
548	C₄²	—	43	2	no	—
549	C₄²	—	43	1	no	—
550	C₄²	—	43	1	no	—
551	C₄²	—	43	2	no	—
552	C₄²	—	43	1	no	—
553	C₄²	—	43	1	no	—
554	C₄²	—	43	1	no	—
555	C₄²	C₂²×D₄₃	1	1	yes	characteristic
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	43	1	no	—
560	C₂³	C₂³×D₄₃	1	2	yes	—
561	C₂³	C₂³×D₄₃	1	1	yes	characteristic
562	C₂³	C₂³×D₄₃	1	1	yes	characteristic
563	C₂³	C₂³×D₄₃	1	2	yes	—
564	Q₈	—	2	2	no	—
565	Q₈	—	86	2	no	—
566	Q₈	—	86	2	no	—
567	Q₈	—	172	2	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	4	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	2	no	—
572	D₄	—	4	2	no	—
573	D₄	—	86	2	no	—
574	D₄	—	86	2	no	—
575	D₄	—	86	4	no	—
576	D₄	—	172	2	no	—
577	D₄	#10621900	1	4	yes	complemented
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	4	2	no	—
582	C₂×C₄	—	43	4	no	—
583	C₂×C₄	—	43	1	no	—
584	C₂×C₄	—	43	1	no	—
585	C₂×C₄	—	43	2	no	—
586	C₂×C₄	—	43	1	no	—
587	C₂×C₄	—	43	1	no	—
588	C₂×C₄	—	43	1	no	—
589	C₂×C₄	—	43	1	no	—
590	C₂×C₄	—	43	1	no	—
591	C₂×C₄	—	43	2	no	—
592	C₂×C₄	—	43	2	no	—
593	C₂×C₄	—	43	2	no	—
594	C₂×C₄	—	86	2	no	—
595	C₂×C₄	—	86	4	no	—
596	C₂×C₄	—	86	4	no	—
597	C₂×C₄	—	86	4	no	—
598	C₂×C₄	—	86	4	no	—
599	C₂×C₄	—	86	2	no	—
600	C₂×C₄	—	86	4	no	—
601	C₂×C₄	—	86	4	no	—
602	C₂×C₄	—	86	2	no	—
603	C₂×C₄	—	172	1	no	—
604	C₂×C₄	—	172	1	no	—
605	C₂×C₄	—	172	2	no	—
606	C₂×C₄	—	172	1	no	—
607	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₄₃	1	2	yes	—
610	C₂×C₄	C₂³×D₄₃	1	2	yes	—
611	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
613	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	4	8	no	—
625	C₂²	—	86	1	no	—
626	C₂²	—	86	1	no	—
627	C₂²	—	86	1	no	—
628	C₂²	#41×D₄₃	1	2	yes	—
629	C₂²	C₂×#10621900	1	4	yes	—
630	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	43	2	no	—
638	C₄	—	43	2	no	—
639	C₄	—	86	2	no	—
640	C₄	—	86	2	no	—
641	C₄	—	86	1	no	—
642	C₄	—	86	1	no	—
643	C₄	—	86	2	no	—
644	C₄	—	86	1	no	—
645	C₄	—	86	1	no	—
646	C₄	—	86	2	no	—
647	C₄	—	86	1	no	—
648	C₄	C₂×#10621900	1	2	yes	—
649	C₂	—	2	2	no	—
650	C₂	—	2	4	no	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	172	1	no	—
654	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
655	C₂	C₂²×#10621900	1	1	yes	characteristic
656	C₂	#14583734	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#546	C₂
hypercenter	#546	D₄₃
hypocenter	C₄₃	#3475
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. #14583618	C₂	semidirect
2. #14583613	C₂	semidirect
3. #14583608	C₂	semidirect
4. #14583592	C₂	semidirect
5. #14583591	C₂	semidirect
6. #14583589	C₂	semidirect
7. #14583586	C₂	semidirect
8. #14583580	C₂	semidirect
9. #14583575	C₂	semidirect
10. #14583548	C₂	semidirect
11. #14583543	C₂	semidirect
12. #14583451	C₂	semidirect
13. #14583430	C₂	semidirect
14. #14583430	C₂	semidirect
15. #14583428	C₂	semidirect
16. #14583426	C₂	semidirect
17. #14583405	C₂	semidirect
18. #41×Dic₄₃	C₂	semidirect
19. C₄×#10621900	C₂	semidirect
20. C₄×#10621900	C₂	semidirect
21. C₂×D₄×Dic₄₃	C₂	semidirect
22. C₂×#13063281	C₂	semidirect
23. C₄₃×#546	C₂	semidirect
27. #13063324	C₂²	semidirect
28. #13063323	C₂²	semidirect
29. #13063320	C₂²	semidirect
30. #13063318	C₂²	semidirect
31. #13063318	C₂²	semidirect
32. #13063318	C₂²	semidirect
33. #13063318	C₂²	semidirect
34. #13063318	C₂²	semidirect
35. #13063317	C₂²	semidirect
36. #13063316	C₂²	semidirect
37. #13063316	C₂²	semidirect
38. #13063315	C₂²	semidirect
39. #13063315	C₂²	semidirect
41. #13063312	C₂²	semidirect
42. #13063311	C₂²	semidirect
44. #13063308	C₂²	semidirect
45. #13063307	C₂²	semidirect
48. #13063306	C₂²	semidirect
49. #13063306	C₂²	semidirect
51. #13063304	C₂²	semidirect
52. #13063304	C₂²	semidirect
54. #13063302	C₂²	semidirect
55. #13063302	C₂²	semidirect
56. #13063302	C₂²	semidirect
57. #13063301	C₂²	semidirect
59. #13063297	C₂²	semidirect
60. #13063297	C₂²	semidirect
63. Q₈×Dic₄₃	C₂²	semidirect
64. Q₈×Dic₄₃	C₂²	semidirect
65. C₄×Dic₈₆	C₂²	semidirect
66. C₄×Dic₈₆	C₂²	semidirect
67. #13063290	C₂²	semidirect
68. #13063290	C₂²	semidirect
69. #13063290	C₂²	semidirect
78. D₄×Dic₄₃	C₂²	semidirect
79. D₄×Dic₄₃	C₂²	semidirect
80. D₄×Dic₄₃	C₂²	semidirect
82. C₄×C₂²⋊D₄₃	C₂²	semidirect
83. C₄×C₂²⋊D₄₃	C₂²	semidirect
85. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
86. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
87. (C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
88. #13063284	C₂²	semidirect
89. #13063284	C₂²	semidirect
90. #13063283	C₂²	semidirect
91. #13063283	C₂²	semidirect
96. #13063281	C₂²	semidirect
97. #13063281	C₂²	semidirect
98. #13063281	C₂²	semidirect
99. #13063281	C₂²	semidirect
100. #13063281	C₂²	semidirect
101. #13063281	C₂²	semidirect
103. C₂×Dic₄₃⋊C₄	C₂²	semidirect
104. C₂×Dic₄₃⋊C₄	C₂²	semidirect
108. C₂×C₄×Dic₄₃	C₂²	semidirect
109. C₂×C₄×Dic₄₃	C₂²	semidirect
110. C₂×C₄×Dic₄₃	C₂²	semidirect
111. C₄²×D₄₃	C₂²	semidirect
241. D₄×C₄₃	#41	semidirect
267. C₂×Dic₄₃	#41	semidirect
340. #546	D₄₃	semidirect
352. C₄₃	#3475	semidirect
577. D₄	#10621900	semidirect