Subgroups — #25096284

Order 11008.

1330 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063261	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14582937	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143114	C₂	1	2	yes	maximal
4	#19134659	C₂	1	4	yes	maximal, complemented
5	#19134654	C₂	1	4	yes	maximal, complemented
6	#19134333	C₂	1	2	yes	maximal, complemented
7	C₂²×#131×C₄₃	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	2	yes	—
9	C₂×#13063284	C₂²	1	2	yes	—
10	C₂×#13063261	—	2	4	no	—
11	C₂×#13063261	C₂²	1	2	yes	complemented
12	C₂×#13063261	C₂²	1	2	yes	complemented
13	#14582937	—	2	1	no	—
14	#14582937	—	2	1	no	—
15	#14582937	—	2	1	no	—
16	#14582937	—	2	1	no	—
17	C₂×#13063259	C₂²	1	2	yes	complemented
18	C₂×#13063257	C₂²	1	2	yes	complemented
19	#14582908	—	2	2	no	—
20	#14582904	—	2	2	no	—
21	#14582900	C₂²	1	8	yes	—
22	#14582895	—	2	4	no	—
23	#14582667	C₂²	1	8	yes	complemented
24	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#131×C₄₃	—	2	4	no	—
26	C₂×#131×C₄₃	—	2	1	no	—
27	C₂×#131×C₄₃	—	2	1	no	—
28	C₂×#131×C₄₃	C₄	1	8	yes	complemented
29	C₂×#131×C₄₃	C₂²	1	2	yes	—
30	C₂×#131×C₄₃	C₂²	1	2	yes	—
31	C₂²×M₁₆×C₄₃	—	2	1	no	—
32	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₄₃	—	2	1	no	—
34	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
35	C₂×#10621877	—	2	2	no	—
36	C₂×#10621877	—	2	4	no	—
37	C₂×#10621877	—	2	4	no	—
38	C₂×#10621877	C₂³	1	4	yes	—
39	C₂²×C₄₃⋊C₈	—	2	2	no	—
40	#13063284	—	2	2	no	—
41	#13063284	—	2	2	no	—
42	#13063284	—	2	2	no	—
43	#13063284	—	2	2	no	—
44	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
45	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
46	C₂×C₄×Dic₄₃	—	2	2	no	—
47	#13063261	—	2	4	no	—
48	#13063261	—	2	4	no	—
49	#13063259	—	2	2	no	—
50	#13063259	—	2	2	no	—
51	#13063257	—	2	2	no	—
52	#13063257	—	2	2	no	—
53	#13063249	—	2	8	no	—
54	#13063246	—	2	8	no	—
55	C₂×#41×C₄₃	—	2	2	no	—
56	C₂×#41×C₄₃	—	2	1	no	—
57	C₂×#41×C₄₃	—	2	1	no	—
58	C₂×#41×C₄₃	—	2	2	no	—
59	C₂×#41×C₄₃	C₂×C₄	1	4	yes	—
60	C₂×#41×C₄₃	D₄	1	2	yes	—
61	C₂×#41×C₄₃	Q₈	1	4	yes	—
62	C₂×#41×C₄₃	C₂³	1	2	yes	—
63	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
64	C₂²×D₄×C₄₃	—	2	1	no	—
65	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
68	#131×C₄₃	—	2	8	no	—
69	#131×C₄₃	—	2	8	no	—
70	#131×C₄₃	—	2	4	no	—
71	#131×C₄₃	—	2	4	no	—
72	#131×C₄₃	C₂×C₄	1	8	yes	—
73	#131×C₄₃	C₂×C₄	1	8	yes	—
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	—	2	1	no	—
76	C₂×M₁₆×C₄₃	—	2	8	no	—
77	C₂×M₁₆×C₄₃	—	2	2	no	—
78	C₂×M₁₆×C₄₃	—	2	2	no	—
79	C₂×M₁₆×C₄₃	C₂×C₄	1	4	yes	—
80	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₃	—	2	1	no	—
82	C₂²×C₈×C₄₃	—	2	8	no	—
83	C₂²×C₈×C₄₃	—	2	2	no	—
84	C₂²×C₈×C₄₃	—	2	2	no	—
85	C₂²×C₈×C₄₃	C₂×C₄	1	4	yes	—
86	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	D₄	1	4	yes	—
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
93	C₂⁴×C₄₃	—	2	1	no	—
94	C₂⁴×C₄₃	#41	1	1	yes	characteristic
95	#41×C₄₃	—	2	4	no	—
96	#41×C₄₃	—	2	4	no	—
97	#41×C₄₃	—	2	4	no	—
98	#41×C₄₃	—	2	4	no	—
99	#41×C₄₃	—	2	4	no	—
100	#41×C₄₃	—	2	2	no	—
101	#41×C₄₃	—	2	2	no	—
102	#41×C₄₃	C₄⋊C₄	1	8	yes	—
103	#41×C₄₃	C₂²×C₄	1	4	yes	—
104	#41×C₄₃	C₂×Q₈	1	4	yes	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	C₄⋊C₄	1	4	yes	—
108	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	2	no	—
111	C₂×D₄×C₄₃	—	2	4	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	—	2	4	no	—
114	C₂×D₄×C₄₃	—	2	2	no	—
115	C₂×D₄×C₄₃	C₄⋊C₄	1	4	yes	—
116	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₃	—	2	4	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	4	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	—	2	1	no	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
128	C₂²×C₄×C₄₃	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₄₃	#41	1	2	yes	—
130	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂²×Dic₄₃	—	2	4	no	—
133	M₁₆×C₄₃	—	2	4	no	—
134	M₁₆×C₄₃	—	2	2	no	—
135	M₁₆×C₄₃	—	2	8	no	—
136	M₁₆×C₄₃	—	2	8	no	—
137	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₄₃	—	2	4	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	8	no	—
141	C₂×C₈×C₄₃	—	2	8	no	—
142	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
143	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
144	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
145	C₂×C₈×C₄₃	C₂²⋊C₄	1	4	yes	—
146	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
154	C₂²⋊Dic₄₃	—	4	2	no	—
155	C₂²⋊Dic₄₃	—	4	2	no	—
156	C₄⋊Dic₄₃	—	2	4	no	—
157	C₄⋊Dic₄₃	—	2	4	no	—
158	C₄×Dic₄₃	—	4	2	no	—
159	C₄×Dic₄₃	—	4	2	no	—
160	#10621877	—	2	4	no	—
161	#10621877	—	2	4	no	—
162	#10621877	—	4	4	no	—
163	C₂×C₄₃⋊C₈	—	2	4	no	—
164	C₂×C₄₃⋊C₈	—	4	4	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	2	4	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	4	no	—
169	C₂³×C₄₃	#117	1	2	yes	—
170	C₂³×C₄₃	#121	1	1	yes	characteristic
171	C₂³×C₄₃	#121	1	1	yes	characteristic
172	C₂³×C₄₃	C₂²⋊Q₈	1	2	yes	—
173	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	4	no	—
176	Q₈×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
177	D₄×C₄₃	—	2	4	no	—
178	D₄×C₄₃	—	2	4	no	—
179	D₄×C₄₃	—	2	8	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	2	4	no	—
182	D₄×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	4	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	8	no	—
188	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
191	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
192	C₂×C₄×C₄₃	#117	1	2	yes	—
193	C₂×C₄×C₄₃	#121	1	2	yes	—
194	C₂×C₄×C₄₃	#121	1	2	yes	—
195	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
199	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
200	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
206	C₂×Dic₄₃	—	4	4	no	—
207	C₂×Dic₄₃	—	8	4	no	—
208	C₈×C₄₃	—	2	4	no	—
209	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
210	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
211	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
212	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₄₃⋊C₈	—	4	4	no	—
214	#20678	—	43	1	no	maximal, Sylow
215	C₂²×C₄₃	—	2	2	no	—
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	2	2	no	—
218	C₂²×C₄₃	—	2	4	no	—
219	C₂²×C₄₃	—	4	2	no	—
220	C₂²×C₄₃	—	4	2	no	—
221	C₂²×C₄₃	—	4	8	no	—
222	C₂²×C₄₃	—	4	4	no	—
223	C₂²×C₄₃	#380	1	2	yes	—
224	C₂²×C₄₃	#380	1	2	yes	—
225	C₂²×C₄₃	C₂×#117	1	1	yes	characteristic
226	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
227	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₄×C₄₃	—	2	4	no	—
229	C₄×C₄₃	#380	1	2	yes	—
230	C₄×C₄₃	#380	1	2	yes	—
231	C₄×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₄×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
233	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
234	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
235	Dic₄₃	—	8	4	no	—
236	C₂²×#131	D₄₃	1	1	yes	characteristic
237	C₂²×#108	—	43	1	no	—
238	C₂×#427	—	43	1	no	—
239	#2896	—	43	2	no	—
240	#1816	—	43	4	no	—
241	#1815	—	43	4	no	—
242	#1742	—	43	2	no	—
243	C₂×C₄₃	—	2	2	no	—
244	C₂×C₄₃	—	2	1	no	—
245	C₂×C₄₃	—	2	1	no	—
246	C₂×C₄₃	—	2	2	no	—
247	C₂×C₄₃	—	4	4	no	—
248	C₂×C₄₃	C₂×#380	1	1	yes	characteristic
249	C₂×C₄₃	#3067	1	2	yes	—
250	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
251	C₂×#131	—	2	4	no	—
252	C₂×#131	—	2	1	no	—
253	C₂×#131	—	2	1	no	—
254	C₂×#131	Dic₄₃	1	8	yes	complemented
255	C₂×#131	C₂×D₄₃	1	2	yes	—
256	C₂×#131	C₂×D₄₃	1	2	yes	—
257	C₂²×M₁₆	—	2	1	no	—
258	C₂²×M₁₆	—	43	2	no	—
259	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
260	C₂³×C₈	—	2	1	no	—
261	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#117	—	43	2	no	—
263	C₂×#108	—	43	2	no	—
264	C₂×#108	—	43	2	no	—
265	C₂×#108	—	86	4	no	—
266	#427	—	86	1	no	—
267	#427	—	86	1	no	—
268	#427	—	86	1	no	—
269	#427	—	86	1	no	—
270	C₂×#107	—	43	2	no	—
271	C₂×#106	—	43	2	no	—
272	#419	—	86	2	no	—
273	#418	—	86	2	no	—
274	#417	—	43	8	no	—
275	#416	—	86	4	no	—
276	#343	—	43	8	no	—
277	C₄₃	#20678	1	1	yes	characteristic, complemented, Sylow
278	C₂×#41	—	2	1	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	1	no	—
282	C₂×#41	Dic₈₆	1	4	yes	—
283	C₂×#41	D₁₇₂	1	2	yes	—
284	C₂×#41	C₂×Dic₄₃	1	4	yes	—
285	C₂×#41	C₂²×D₄₃	1	2	yes	—
286	C₂²×Q₈	D₁₇₂	1	1	yes	characteristic
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	D₁₇₂	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
291	#131	—	2	8	no	—
292	#131	—	2	8	no	—
293	#131	—	2	4	no	—
294	#131	—	2	4	no	—
295	#131	C₂×Dic₄₃	1	8	yes	—
296	#131	C₂×Dic₄₃	1	8	yes	—
297	C₂×M₁₆	—	2	2	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	8	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	—	43	4	no	—
303	C₂×M₁₆	—	86	2	no	—
304	C₂×M₁₆	—	86	4	no	—
305	C₂×M₁₆	—	86	4	no	—
306	C₂×M₁₆	C₂×Dic₄₃	1	4	yes	—
307	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	8	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	86	2	no	—
313	C₂²×C₈	C₂×Dic₄₃	1	4	yes	—
314	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
315	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
316	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
318	C₂²×C₈	C₂²⋊D₄₃	1	4	yes	—
319	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
321	#117	—	86	2	no	—
322	#117	—	86	2	no	—
323	#117	—	86	2	no	—
324	#117	—	86	2	no	—
325	C₂×C₄⋊C₄	—	43	4	no	—
326	C₂×C₂²⋊C₄	—	86	2	no	—
327	C₂×C₄²	—	86	2	no	—
328	#108	—	86	4	no	—
329	#108	—	86	4	no	—
330	#107	—	86	2	no	—
331	#107	—	86	2	no	—
332	#106	—	86	2	no	—
333	#106	—	86	2	no	—
334	#103	—	86	8	no	—
335	#102	—	86	8	no	—
336	C₂⁴	—	2	1	no	—
337	C₂⁴	#10621898	1	1	yes	characteristic
338	#41	—	2	4	no	—
339	#41	—	2	4	no	—
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	C₄⋊Dic₄₃	1	8	yes	—
346	#41	C₂×Dic₈₆	1	4	yes	—
347	#41	C₂²×Dic₄₃	1	4	yes	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	C₄⋊Dic₄₃	1	4	yes	—
351	C₂×Q₈	C₂×D₁₇₂	1	2	yes	—
352	C₂×D₄	—	2	4	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	C₄⋊Dic₄₃	1	4	yes	—
359	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	86	4	no	—
366	C₂²×C₄	C₂×Dic₈₆	1	2	yes	—
367	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
369	C₂²×C₄	#10621898	1	1	yes	characteristic
370	C₂²×C₄	#10621898	1	2	yes	—
371	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
372	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
373	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
375	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
376	M₁₆	—	2	4	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	2	8	no	—
379	M₁₆	—	2	8	no	—
380	M₁₆	—	86	4	no	—
381	M₁₆	—	86	4	no	—
382	M₁₆	—	172	4	no	—
383	M₁₆	C₂²×Dic₄₃	1	4	yes	—
384	C₂×C₈	—	2	4	no	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	8	no	—
387	C₂×C₈	—	2	8	no	—
388	C₂×C₈	—	86	4	no	—
389	C₂×C₈	—	172	4	no	—
390	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
391	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
392	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
393	C₂×C₈	C₂²⋊Dic₄₃	1	4	yes	—
394	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
395	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
396	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
397	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
399	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
400	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
401	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
402	C₄⋊C₄	—	86	4	no	—
403	C₄⋊C₄	—	86	4	no	—
404	C₂²⋊C₄	—	172	2	no	—
405	C₂²⋊C₄	—	172	2	no	—
406	C₄²	—	172	2	no	—
407	C₄²	—	172	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	#13063284	1	2	yes	—
413	C₂³	#13063299	1	1	yes	characteristic
414	C₂³	#13063299	1	1	yes	characteristic
415	C₂³	#13063304	1	2	yes	—
416	C₂³	C₂×#10621898	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	4	no	—
419	Q₈	C₂×C₄⋊Dic₄₃	1	4	yes	—
420	D₄	—	2	4	no	—
421	D₄	—	2	4	no	—
422	D₄	—	2	8	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	4	no	—
425	D₄	C₂×C₄⋊Dic₄₃	1	4	yes	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	344	4	no	—
432	C₂×C₄	—	172	4	no	—
433	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
434	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
435	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
436	C₂×C₄	C₂×C₄⋊Dic₄₃	1	2	yes	—
437	C₂×C₄	#13063284	1	2	yes	—
438	C₂×C₄	#13063299	1	2	yes	—
439	C₂×C₄	#13063299	1	2	yes	—
440	C₂×C₄	#13063299	1	1	yes	characteristic
441	C₂×C₄	#13063299	1	1	yes	characteristic
442	C₂×C₄	#13063304	1	2	yes	—
443	C₂×C₄	#13063304	1	2	yes	—
444	C₂×C₄	#13063304	1	2	yes	—
445	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
449	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
450	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
451	C₈	—	2	4	no	—
452	C₈	—	172	4	no	—
453	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
454	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
455	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
456	C₈	C₂×C₂²⋊Dic₄₃	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	8	no	—
464	C₂²	—	4	4	no	—
465	C₂²	#14582759	1	2	yes	—
466	C₂²	#14582759	1	2	yes	—
467	C₂²	C₂×#13063284	1	1	yes	characteristic
468	C₂²	C₂×#13063299	1	1	yes	characteristic
469	C₂²	C₂×#13063304	1	1	yes	characteristic
470	C₄	—	2	4	no	—
471	C₄	—	344	4	no	—
472	C₄	#14582759	1	2	yes	—
473	C₄	#14582759	1	2	yes	—
474	C₄	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
475	C₄	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
476	C₄	C₂×#13063299	1	1	yes	characteristic
477	C₄	C₂×#13063304	1	1	yes	characteristic
478	C₂	—	2	2	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	2	2	no	—
482	C₂	—	4	4	no	—
483	C₂	C₂×#14582759	1	1	yes	characteristic
484	C₂	#19144315	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13063299
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂²×#131×C₄₃	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂²×#41×C₄₃	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂²×#131	D₄₃
hypocenter	C₄₃	#20678
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#13063261	C₂	semidirect
2. C₂×#14582937	C₂	semidirect
4. #19134659	C₂	semidirect
5. #19134654	C₂	semidirect
6. #19134333	C₂	semidirect
11. C₂×#13063261	C₂²	semidirect
12. C₂×#13063261	C₂²	semidirect
17. C₂×#13063259	C₂²	semidirect
18. C₂×#13063257	C₂²	semidirect
23. #14582667	C₂²	semidirect
28. C₂×#131×C₄₃	C₄	semidirect
254. C₂×#131	Dic₄₃	semidirect
277. C₄₃	#20678	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063261	2
C₂×#14582937	2
#19143114	2
#19134659	2
#19134654	2
#19134333	2
C₂²×#131×C₄₃	2
#20678	43