Subgroups — #25960272

Order 11008.

2666 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063331	C₂	1	1	yes	maximal, characteristic
2	#19147796	C₂	1	2	yes	maximal
3	#19143192	C₂	1	4	yes	maximal, complemented
4	#19143191	C₂	1	4	yes	maximal, complemented
5	#19143187	C₂	1	4	yes	maximal, complemented
6	#19143186	C₂	1	4	yes	maximal, complemented
7	#19143184	C₂	1	2	yes	maximal, complemented
8	#19143183	C₂	1	4	yes	maximal, complemented
9	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
10	#427×D₄₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621898	C₂²	1	1	yes	characteristic
13	C₂×#13063331	C₄	1	16	yes	complemented
14	C₂×#13063331	C₂²	1	2	yes	—
15	C₂×#13063331	C₂²	1	2	yes	—
16	C₂×#13063331	C₂²	1	2	yes	—
17	C₂×#13063331	C₂²	1	2	yes	—
18	C₂²×#10621877	C₂²	1	1	yes	characteristic
19	C₂²×#10621872	C₂²	1	2	yes	—
20	C₂²×C₈×D₄₃	C₂²	1	2	yes	—
21	#14583380	C₂²	1	8	yes	—
22	#14583379	C₂²	1	8	yes	—
23	#14583376	—	2	2	no	—
24	#14583373	—	2	2	no	—
25	#14583372	—	2	4	no	—
26	C₄×#10621898	—	2	4	no	—
27	#14583367	—	2	4	no	—
28	C₂×#13063284	C₂²	1	2	yes	—
29	#117×D₄₃	C₂²	1	8	yes	—
30	#14582942	C₂²	1	8	yes	complemented
31	#14582940	C₂²	1	16	yes	complemented
32	#14582939	C₂²	1	8	yes	complemented
33	#14582938	C₂²	1	16	yes	complemented
34	#14582937	C₂²	1	2	yes	—
35	#14582937	C₂²	1	2	yes	—
36	#14582937	C₂²	1	2	yes	complemented
37	#14582937	C₂²	1	2	yes	complemented
38	#14582936	C₂²	1	8	yes	complemented
39	#14582935	C₂²	1	8	yes	—
40	#14582934	C₂²	1	8	yes	complemented
41	C₂×#13063259	C₂²	1	2	yes	complemented
42	#107×D₄₃	C₂²	1	8	yes	complemented
43	C₂×#13063257	C₂²	1	2	yes	complemented
44	#106×D₄₃	C₂²	1	8	yes	complemented
45	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#117×C₄₃	C₂²	1	2	yes	—
47	C₄₃×#427	C₂²	1	2	yes	—
48	C₄₃×#427	C₂²	1	2	yes	—
49	C₄₃×#427	C₂²	1	2	yes	complemented
50	C₄₃×#427	C₂²	1	2	yes	complemented
51	C₂×#107×C₄₃	C₂²	1	2	yes	complemented
52	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
53	C₂×#10621898	C₂×C₄	1	8	yes	—
54	C₂×#10621898	D₄	1	2	yes	—
55	C₂×#10621898	D₄	1	2	yes	—
56	C₂×#10621898	Q₈	1	8	yes	—
57	C₂×#10621898	C₂³	1	2	yes	—
58	C₂×#10621898	C₂³	1	2	yes	—
59	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
60	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
61	C₂²×C₂²⋊D₄₃	D₄	1	2	yes	—
62	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
63	#13063331	C₂×C₄	1	16	yes	complemented
64	#13063331	C₂×C₄	1	16	yes	complemented
65	#13063331	C₂×C₄	1	16	yes	complemented
66	#13063331	C₂×C₄	1	16	yes	complemented
67	C₂×#10621877	C₂×C₄	1	8	yes	complemented
68	C₂×#10621877	C₂³	1	2	yes	—
69	C₂×#10621877	C₂³	1	2	yes	—
70	C₂×#10621872	C₂×C₄	1	16	yes	complemented
71	C₂×#10621872	C₂³	1	4	yes	—
72	C₂×#10621872	C₂³	1	4	yes	—
73	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
74	C₂×C₈×D₄₃	C₂×C₄	1	16	yes	complemented
75	C₂×C₈×D₄₃	C₂³	1	4	yes	—
76	C₂×C₈×D₄₃	C₂³	1	4	yes	—
77	C₄×Dic₈₆	—	2	8	no	—
78	#13063290	—	2	8	no	—
79	C₄×D₁₇₂	—	2	8	no	—
80	#13063287	—	2	8	no	—
81	C₄×C₂²⋊D₄₃	—	2	16	no	—
82	(C₂²⋊D₄₃)⋊C₄	—	2	16	no	—
83	#13063284	—	2	2	no	—
84	#13063284	—	2	2	no	—
85	#13063284	C₂³	1	4	yes	—
86	#13063284	C₂³	1	4	yes	—
87	#13063283	C₂³	1	16	yes	—
88	#13063282	—	2	8	no	—
89	#13063281	—	2	8	no	—
90	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
91	C₄⋊C₄×D₄₃	C₂³	1	16	yes	—
92	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
93	C₂²⋊C₄×D₄₃	—	2	8	no	—
94	C₂×C₄×Dic₄₃	—	2	2	no	—
95	C₄²×D₄₃	—	2	8	no	—
96	#13063259	C₂³	1	4	yes	—
97	#13063259	C₂³	1	4	yes	—
98	#13063258	C₂³	1	16	yes	—
99	#13063257	C₂³	1	4	yes	—
100	#13063257	C₂³	1	4	yes	—
101	#13063256	C₂³	1	16	yes	—
102	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	C₂×C₄	1	8	yes	complemented
104	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	#117×C₄₃	—	2	2	no	—
111	#117×C₄₃	—	2	2	no	—
112	#117×C₄₃	C₂³	1	4	yes	—
113	#117×C₄₃	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
116	C₂×C₄²×C₄₃	—	2	2	no	—
117	#107×C₄₃	C₂³	1	4	yes	—
118	#107×C₄₃	C₂³	1	4	yes	—
119	#106×C₄₃	C₂³	1	4	yes	—
120	#106×C₄₃	C₂³	1	4	yes	—
121	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂³×D₄₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₃	—	2	4	no	—
124	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	16	yes	—
133	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
134	C₂×C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
135	C₂²×Dic₄₃	—	2	4	no	—
136	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
137	#10621898	C₄⋊C₄	1	16	yes	—
138	#10621898	C₄⋊C₄	1	16	yes	—
139	#10621898	C₂²×C₄	1	8	yes	—
140	#10621898	C₂²×C₄	1	8	yes	—
141	#10621898	C₂×Q₈	1	8	yes	—
142	#10621898	C₂×Q₈	1	8	yes	—
143	C₂×D₁₇₂	C₄⋊C₄	1	8	yes	—
144	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
145	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
146	C₂×C₄×D₄₃	—	2	16	no	—
147	C₂×C₄×D₄₃	C₂²×C₄	1	8	yes	—
148	C₂×C₄×D₄₃	C₂×D₄	1	4	yes	—
149	C₂×C₄×D₄₃	C₂×Q₈	1	8	yes	—
150	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
151	C₂×Dic₈₆	C₄⋊C₄	1	8	yes	—
152	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
153	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
155	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
156	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
158	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
159	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
160	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₄₃	—	2	4	no	—
165	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
166	C₂²⋊C₄×C₄₃	—	2	4	no	—
167	C₂²⋊C₄×C₄₃	—	2	4	no	—
168	C₄²×C₄₃	—	2	4	no	—
169	C₄²×C₄₃	—	2	4	no	—
170	C₂²⋊Dic₄₃	—	2	4	no	—
171	C₂²⋊Dic₄₃	—	2	4	no	—
172	(C₂×D₄₃)⋊C₄	—	2	16	no	—
173	C₄⋊Dic₄₃	—	2	4	no	—
174	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
175	Dic₄₃⋊C₄	—	2	16	no	—
176	C₄×Dic₄₃	—	2	4	no	—
177	C₄×Dic₄₃	—	2	4	no	—
178	C₄×Dic₄₃	—	2	16	no	—
179	#10621877	C₂²×C₄	1	8	yes	—
180	#10621877	C₂²×C₄	1	8	yes	—
181	C₂×C₄₃⋊C₈	C₂²×C₄	1	8	yes	—
182	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
183	#10621872	C₂²×C₄	1	16	yes	—
184	#10621872	C₂²×C₄	1	16	yes	—
185	C₈×D₄₃	C₂²×C₄	1	16	yes	—
186	C₈×D₄₃	C₂²×C₄	1	16	yes	—
187	C₂³×C₄₃	—	4	2	no	—
188	C₂³×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
189	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂²×D₄₃	—	4	4	no	—
193	C₂²×D₄₃	C₂×C₄⋊C₄	1	8	yes	—
194	C₂²×D₄₃	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₄₃	—	2	8	no	—
196	C₂×C₄×C₄₃	—	8	4	no	—
197	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
198	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
199	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
200	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
202	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
207	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
208	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
209	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
210	C₂²⋊D₄₃	C₂×C₄⋊C₄	1	16	yes	—
211	C₂²⋊D₄₃	C₂×C₄⋊C₄	1	16	yes	—
212	C₂×Dic₄₃	—	2	8	no	—
213	C₂×Dic₄₃	—	8	4	no	—
214	C₂×Dic₄₃	C₂×C₄⋊C₄	1	8	yes	—
215	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
216	D₁₇₂	C₂×C₄⋊C₄	1	8	yes	—
217	D₁₇₂	C₂×C₄⋊C₄	1	8	yes	—
218	C₄×D₄₃	—	8	16	no	—
219	C₄×D₄₃	C₂×C₄⋊C₄	1	16	yes	—
220	C₄×D₄₃	C₂³×C₄	1	8	yes	—
221	C₄×D₄₃	C₂²×Q₈	1	8	yes	—
222	Dic₈₆	C₂×C₄⋊C₄	1	8	yes	—
223	Dic₈₆	C₂×C₄⋊C₄	1	8	yes	—
224	C₈×C₄₃	C₂³×C₄	1	2	yes	—
225	C₈×C₄₃	C₂³×C₄	1	2	yes	—
226	C₈×C₄₃	C₂³×C₄	1	2	yes	—
227	C₈×C₄₃	C₂³×C₄	1	2	yes	—
228	C₄₃⋊C₈	C₂³×C₄	1	8	yes	—
229	#60108	—	43	1	no	maximal, Sylow
230	C₂²×C₄₃	—	2	2	no	—
231	C₂²×C₄₃	—	2	2	no	—
232	C₂²×C₄₃	—	2	2	no	—
233	C₂²×C₄₃	—	4	4	no	—
234	C₂²×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
235	C₂²×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
236	C₂²×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
237	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
238	C₂×D₄₃	—	2	8	no	—
239	C₂×D₄₃	—	4	8	no	—
240	C₂×D₄₃	C₂²×C₄⋊C₄	1	8	yes	—
241	C₄×C₄₃	—	4	8	no	—
242	C₄×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
243	C₄×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
244	C₄×C₄₃	C₂²×C₄⋊C₄	1	2	yes	—
245	C₄×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
246	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
247	Dic₄₃	—	4	8	no	—
248	Dic₄₃	C₂²×C₄⋊C₄	1	8	yes	—
249	C₂²×#131	—	43	1	no	—
250	#3428	—	43	2	no	—
251	#2913	—	43	4	no	—
252	#2913	—	43	4	no	—
253	#2912	—	43	4	no	—
254	#2912	—	43	4	no	—
255	#2911	—	43	4	no	—
256	#2911	—	43	2	no	—
257	C₂×#427	—	43	4	no	—
258	C₂×#427	—	43	1	no	—
259	C₂×#427	D₄₃	1	1	yes	characteristic, complemented
260	C₂×C₄₃	—	2	2	no	—
261	C₂×C₄₃	—	2	2	no	—
262	C₂×C₄₃	—	2	2	no	—
263	C₂×C₄₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
264	C₂×C₄₃	#3584	1	2	yes	—
265	D₄₃	—	2	8	no	—
266	C₂²×#41	—	43	1	no	—
267	C₂×#131	—	43	2	no	—
268	C₂×#131	—	43	2	no	—
269	C₂×#131	—	43	2	no	—
270	C₂×#131	—	43	2	no	—
271	C₂×#131	—	43	16	no	—
272	C₂²×M₁₆	—	43	1	no	—
273	C₂²×M₁₆	—	43	2	no	—
274	C₂³×C₈	—	43	2	no	—
275	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
276	#520	—	43	8	no	—
277	#520	—	43	8	no	—
278	#519	—	86	2	no	—
279	#518	—	86	4	no	—
280	#518	—	86	2	no	—
281	C₄×#41	—	86	4	no	—
282	C₄×#41	—	86	4	no	—
283	C₂×#117	—	43	2	no	—
284	C₂×#117	—	43	8	no	—
285	C₂×#117	C₂×D₄₃	1	2	yes	—
286	#428	—	43	8	no	—
287	#428	—	43	8	no	—
288	#428	—	43	16	no	—
289	#428	—	43	16	no	—
290	#427	—	43	2	no	—
291	#427	—	43	2	no	—
292	#427	—	43	2	no	—
293	#427	—	43	2	no	—
294	#427	—	43	8	no	—
295	#427	—	43	8	no	—
296	#427	—	43	8	no	—
297	#427	C₂×D₄₃	1	2	yes	—
298	#427	C₂×D₄₃	1	2	yes	—
299	#427	C₂×D₄₃	1	2	yes	complemented
300	#427	C₂×D₄₃	1	2	yes	complemented
301	C₂×#107	—	43	2	no	—
302	C₂×#107	—	43	8	no	—
303	C₂×#107	C₂×D₄₃	1	2	yes	complemented
304	C₂×#106	—	43	2	no	—
305	C₂×#106	—	43	8	no	—
306	C₂×#106	C₂×D₄₃	1	2	yes	complemented
307	C₄₃	#60108	1	1	yes	characteristic, complemented, Sylow
308	C₂×#41	—	43	8	no	—
309	C₂×#41	—	43	2	no	—
310	C₂×#41	—	43	2	no	—
311	C₂×#41	—	43	8	no	—
312	C₂×#41	—	43	2	no	—
313	C₂×#41	—	43	2	no	—
314	C₂²×Q₈	—	43	1	no	—
315	C₂²×D₄	—	43	2	no	—
316	C₂²×D₄	—	43	1	no	—
317	C₂³×C₄	—	43	2	no	—
318	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
319	#131	—	43	16	no	—
320	#131	—	43	16	no	—
321	#131	—	43	16	no	—
322	#131	—	43	16	no	—
323	C₂×M₁₆	—	43	8	no	—
324	C₂×M₁₆	—	43	2	no	—
325	C₂×M₁₆	—	43	2	no	—
326	C₂×M₁₆	—	43	16	no	—
327	C₂×M₁₆	—	43	4	no	—
328	C₂×M₁₆	—	43	4	no	—
329	C₂²×C₈	—	43	2	no	—
330	C₂²×C₈	—	43	16	no	—
331	C₂²×C₈	—	43	4	no	—
332	C₂²×C₈	—	43	4	no	—
333	C₂²×C₈	C₄×D₄₃	1	8	yes	complemented
334	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
335	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
336	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
337	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
338	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
339	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
340	C₄×Q₈	—	86	8	no	—
341	C₄×Q₈	—	86	8	no	—
342	C₄×D₄	—	86	8	no	—
343	C₄×D₄	—	86	16	no	—
344	C₄×D₄	—	86	8	no	—
345	C₄×D₄	—	86	16	no	—
346	#117	—	2	2	no	—
347	#117	—	2	2	no	—
348	#117	—	43	4	no	—
349	#117	—	43	4	no	—
350	#117	—	43	16	no	—
351	#117	—	86	8	no	—
352	#117	—	86	8	no	—
353	#117	—	86	2	no	—
354	#117	—	86	2	no	—
355	#117	C₂²×D₄₃	1	4	yes	—
356	#117	C₂²×D₄₃	1	4	yes	—
357	C₂×C₄⋊C₄	—	43	4	no	—
358	C₂×C₄⋊C₄	—	43	16	no	—
359	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	86	8	no	—
362	C₂×C₂²⋊C₄	—	86	2	no	—
363	C₂×C₄²	—	2	2	no	—
364	C₂×C₄²	—	86	8	no	—
365	C₂×C₄²	—	86	2	no	—
366	#107	—	43	4	no	—
367	#107	—	43	4	no	—
368	#107	—	43	16	no	—
369	#107	C₂²×D₄₃	1	4	yes	—
370	#107	C₂²×D₄₃	1	4	yes	—
371	#106	—	43	4	no	—
372	#106	—	43	4	no	—
373	#106	—	43	16	no	—
374	#106	C₂²×D₄₃	1	4	yes	—
375	#106	C₂²×D₄₃	1	4	yes	—
376	C₂⁴	—	43	2	no	—
377	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
378	#41	—	43	16	no	—
379	#41	—	43	16	no	—
380	#41	—	43	8	no	—
381	#41	—	43	8	no	—
382	#41	—	43	8	no	—
383	#41	—	43	8	no	—
384	C₂×Q₈	—	43	8	no	—
385	C₂×Q₈	—	43	2	no	—
386	C₂×Q₈	—	43	2	no	—
387	C₂×D₄	—	43	16	no	—
388	C₂×D₄	—	43	4	no	—
389	C₂×D₄	—	43	4	no	—
390	C₂×D₄	—	43	8	no	—
391	C₂×D₄	—	43	2	no	—
392	C₂×D₄	—	43	2	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	43	2	no	—
395	C₂²×C₄	—	43	8	no	—
396	C₂²×C₄	—	43	4	no	—
397	C₂²×C₄	—	43	8	no	—
398	C₂²×C₄	—	43	4	no	—
399	C₂²×C₄	—	86	16	no	—
400	C₂²×C₄	—	86	4	no	—
401	C₂²×C₄	C₂×C₄×D₄₃	1	4	yes	—
402	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
403	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
404	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
405	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
406	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
407	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
408	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
409	M₁₆	—	43	8	no	—
410	M₁₆	—	43	8	no	—
411	M₁₆	—	43	16	no	—
412	M₁₆	—	43	16	no	—
413	C₂×C₈	—	43	8	no	—
414	C₂×C₈	—	43	4	no	—
415	C₂×C₈	—	43	16	no	—
416	C₂×C₈	—	43	16	no	—
417	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
418	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
419	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
420	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
421	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
422	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
423	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
424	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
425	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
426	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	43	8	no	—
429	C₄⋊C₄	—	86	16	no	—
430	C₄⋊C₄	—	86	4	no	—
431	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	86	16	no	—
435	C₂²⋊C₄	—	86	4	no	—
436	C₂²⋊C₄	—	86	4	no	—
437	C₄²	—	2	4	no	—
438	C₄²	—	2	4	no	—
439	C₄²	—	86	16	no	—
440	C₄²	—	86	4	no	—
441	C₄²	—	86	4	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	43	4	no	—
444	C₂³	—	43	8	no	—
445	C₂³	—	172	4	no	—
446	C₂³	C₄⋊C₄×D₄₃	1	4	yes	—
447	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
448	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
449	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
450	Q₈	—	43	8	no	—
451	Q₈	—	43	8	no	—
452	D₄	—	43	16	no	—
453	D₄	—	43	16	no	—
454	D₄	—	43	8	no	—
455	D₄	—	43	8	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	8	4	no	—
458	C₂×C₄	—	43	8	no	—
459	C₂×C₄	—	43	4	no	—
460	C₂×C₄	—	43	16	no	—
461	C₂×C₄	—	43	8	no	—
462	C₂×C₄	—	43	8	no	—
463	C₂×C₄	—	86	8	no	—
464	C₂×C₄	—	344	16	no	—
465	C₂×C₄	—	344	4	no	—
466	C₂×C₄	C₄⋊C₄×D₄₃	1	4	yes	—
467	C₂×C₄	C₄⋊C₄×D₄₃	1	4	yes	—
468	C₂×C₄	C₄⋊C₄×D₄₃	1	4	yes	—
469	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
470	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
471	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
472	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
473	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
474	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
475	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
476	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
477	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
478	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
479	C₈	—	43	8	no	—
480	C₈	C₂²×C₄×D₄₃	1	2	yes	—
481	C₈	C₂²×C₄×D₄₃	1	2	yes	—
482	C₈	C₂²×C₄×D₄₃	1	2	yes	—
483	C₈	C₂²×C₄×D₄₃	1	2	yes	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	43	8	no	—
489	C₂²	—	86	8	no	—
490	C₂²	—	172	8	no	—
491	C₂²	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
492	C₂²	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
493	C₂²	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
494	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
495	C₄	—	4	8	no	—
496	C₄	—	43	8	no	—
497	C₄	—	172	8	no	—
498	C₄	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
499	C₄	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
500	C₄	C₂×C₄⋊C₄×D₄₃	1	2	yes	—
501	C₄	C₂³×C₄×D₄₃	1	1	yes	characteristic
502	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	2	2	no	—
506	C₂	—	86	8	no	—
507	C₂	C₂²×C₄⋊C₄×D₄₃	1	1	yes	characteristic
508	C₂	#19149364	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#427	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂²×#10621898	C₂²
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	C₂×#427	D₄₃
hypocenter	C₄₃	#60108
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
3. #19143192	C₂	semidirect
4. #19143191	C₂	semidirect
5. #19143187	C₂	semidirect
6. #19143186	C₂	semidirect
7. #19143184	C₂	semidirect
8. #19143183	C₂	semidirect
9. C₂×#14582937	C₂	semidirect
10. #427×D₄₃	C₂	semidirect
11. C₂×C₄₃×#427	C₂	semidirect
13. C₂×#13063331	C₄	semidirect
30. #14582942	C₂²	semidirect
31. #14582940	C₂²	semidirect
32. #14582939	C₂²	semidirect
33. #14582938	C₂²	semidirect
36. #14582937	C₂²	semidirect
37. #14582937	C₂²	semidirect
38. #14582936	C₂²	semidirect
40. #14582934	C₂²	semidirect
41. C₂×#13063259	C₂²	semidirect
42. #107×D₄₃	C₂²	semidirect
43. C₂×#13063257	C₂²	semidirect
44. #106×D₄₃	C₂²	semidirect
49. C₄₃×#427	C₂²	semidirect
50. C₄₃×#427	C₂²	semidirect
51. C₂×#107×C₄₃	C₂²	semidirect
52. C₂×#106×C₄₃	C₂²	semidirect
63. #13063331	C₂×C₄	semidirect
64. #13063331	C₂×C₄	semidirect
65. #13063331	C₂×C₄	semidirect
66. #13063331	C₂×C₄	semidirect
67. C₂×#10621877	C₂×C₄	semidirect
70. C₂×#10621872	C₂×C₄	semidirect
74. C₂×C₈×D₄₃	C₂×C₄	semidirect
103. C₂²×C₈×C₄₃	C₂×C₄	semidirect
259. C₂×#427	D₄₃	semidirect
299. #427	C₂×D₄₃	semidirect
300. #427	C₂×D₄₃	semidirect
303. C₂×#107	C₂×D₄₃	semidirect
306. C₂×#106	C₂×D₄₃	semidirect
307. C₄₃	#60108	semidirect
333. C₂²×C₈	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063331	2
#19147796	2
#19143192	2
#19143191	2
#19143187	2
#19143186	2
#19143184	2
#19143183	2
C₂×#14582937	2
#427×D₄₃	2
C₂×C₄₃×#427	2
#60108	43