Subgroups — #25080171

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145533	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145048	C₂	1	1	yes	maximal, characteristic
3	#19143544	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134077	C₂	1	2	yes	maximal, complemented
5	#19134069	C₂	1	2	yes	maximal, complemented
6	#19133953	C₂	1	2	yes	maximal, complemented
7	#19133945	C₂	1	2	yes	maximal, complemented
8	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133244	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063350	—	2	1	no	—
13	C₂×#13063350	—	2	1	no	—
14	C₂×#13063322	C₂²	1	1	yes	characteristic
15	#14583289	—	2	2	no	—
16	#14583275	C₂²	1	2	yes	—
17	#14583273	—	2	1	no	—
18	#14583273	C₂²	1	2	yes	—
19	#14583247	—	2	1	no	—
20	#14583099	C₂²	1	2	yes	—
21	#14583099	C₂²	1	2	yes	—
22	#14583049	—	2	2	no	—
23	#14583030	—	2	2	no	—
24	#14583030	C₂²	1	2	yes	complemented
25	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	complemented
26	#14582952	C₂²	1	1	yes	characteristic
27	#14582926	—	2	1	no	—
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	#14582855	—	2	1	no	—
30	C₄×#10621877	C₂²	1	1	yes	characteristic
31	#14582651	C₂²	1	2	yes	complemented
32	#14582649	C₂²	1	2	yes	complemented
33	#14582645	C₂²	1	1	yes	characteristic, complemented
34	#14582645	C₂²	1	1	yes	characteristic, complemented
35	#14582643	C₂²	1	1	yes	characteristic, complemented
36	#14582643	C₂²	1	1	yes	characteristic, complemented
37	#14582642	C₂²	1	2	yes	—
38	#14582642	C₂²	1	2	yes	—
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#476	—	2	1	no	—
42	C₄₃×#475	C₂²	1	2	yes	complemented
43	C₄₃×#465	—	2	2	no	—
44	C₄₃×#461	—	2	1	no	—
45	C₄₃×#460	C₂²	1	2	yes	complemented
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×D₁₇₂	—	2	1	no	—
48	C₂²×D₁₇₂	—	2	1	no	—
49	C₂²×D₁₇₂	—	2	1	no	—
50	#13063350	—	4	4	no	—
51	#13063350	—	4	4	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	2	2	no	—
54	C₂×#10621884	—	2	2	no	—
55	C₂×#10621884	—	2	2	no	—
56	C₂×#10621882	—	2	2	no	—
57	C₂×#10621882	—	2	2	no	—
58	C₂×#10621877	D₄	1	1	yes	characteristic
59	C₂×#10621877	D₄	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	—	2	1	no	—
61	#13063322	—	2	1	no	—
62	#13063322	—	2	1	no	—
63	#13063322	—	2	1	no	—
64	#13063322	C₂³	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
67	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
72	#13063245	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
75	#13063236	—	2	2	no	—
76	#13063236	D₄	1	2	yes	—
77	C₄×C₄₃⋊C₈	—	2	1	no	—
78	C₄×C₄₃⋊C₈	—	2	2	no	—
79	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
80	C₂×#41×C₄₃	—	2	1	no	—
81	C₂×SD₁₆×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	#127×C₄₃	C₂³	1	1	yes	characteristic
87	#125×C₄₃	—	2	1	no	—
88	#124×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
91	#121×C₄₃	—	2	1	no	—
92	#121×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
95	C₄×D₄×C₄₃	—	2	1	no	—
96	C₄×D₄×C₄₃	—	2	1	no	—
97	#117×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	#106×C₄₃	—	2	2	no	—
100	C₄⋊C₈×C₄₃	—	2	1	no	—
101	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
102	#103×C₄₃	—	2	2	no	—
103	#102×C₄₃	—	2	2	no	—
104	C₂³×D₄₃	—	4	1	no	—
105	#41×C₄₃	—	4	2	no	—
106	#41×C₄₃	—	4	2	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	4	1	no	—
114	C₂²×C₄×C₄₃	—	4	1	no	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	—	2	2	no	—
120	C₂×D₁₇₂	—	2	2	no	—
121	C₂×D₁₇₂	—	4	1	no	—
122	C₂×D₁₇₂	—	4	1	no	—
123	C₂×D₁₇₂	—	4	1	no	—
124	C₂×D₁₇₂	—	4	2	no	—
125	C₂×D₁₇₂	—	4	2	no	—
126	C₂×D₁₇₂	—	8	1	no	—
127	C₂×D₁₇₂	—	8	1	no	—
128	C₂×D₁₇₂	—	8	2	no	—
129	SD₁₆×C₄₃	—	8	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₂×C₈×C₄₃	—	8	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	2	no	—
136	C₄⋊C₄×C₄₃	—	2	2	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₂²⋊C₄×C₄₃	—	4	1	no	—
142	C₂²⋊C₄×C₄₃	—	4	1	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	#41	1	1	yes	characteristic
147	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
148	#10621884	—	4	4	no	—
149	#10621884	—	4	4	no	—
150	#10621884	—	8	2	no	—
151	#10621884	—	8	2	no	—
152	#10621882	—	4	4	no	—
153	#10621882	—	4	4	no	—
154	#10621877	—	2	2	no	—
155	#10621877	SD₁₆	1	4	yes	complemented
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	—	2	1	no	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	4	2	no	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
162	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
163	C₂³×C₄₃	—	4	1	no	—
164	C₂³×C₄₃	#121	1	1	yes	characteristic
165	C₂²×D₄₃	—	4	2	no	—
166	C₂²×D₄₃	—	8	2	no	—
167	C₂²×D₄₃	—	8	2	no	—
168	C₂²×D₄₃	—	8	2	no	—
169	Q₈×C₄₃	—	2	2	no	—
170	Q₈×C₄₃	—	2	2	no	—
171	Q₈×C₄₃	—	4	1	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	Q₈×C₄₃	—	8	1	no	—
174	D₄×C₄₃	—	4	1	no	—
175	D₄×C₄₃	—	4	1	no	—
176	D₄×C₄₃	—	4	1	no	—
177	D₄×C₄₃	—	4	1	no	—
178	D₄×C₄₃	—	8	1	no	—
179	D₄×C₄₃	—	8	2	no	—
180	C₂×C₄×C₄₃	—	2	1	no	—
181	C₂×C₄×C₄₃	—	2	1	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	—	8	2	no	—
187	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
191	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
195	D₁₇₂	—	4	2	no	—
196	D₁₇₂	—	4	2	no	—
197	D₁₇₂	—	4	2	no	—
198	D₁₇₂	—	4	2	no	—
199	D₁₇₂	—	8	2	no	—
200	D₁₇₂	—	8	2	no	—
201	D₁₇₂	—	8	2	no	—
202	D₁₇₂	—	8	2	no	—
203	C₈×C₄₃	—	4	2	no	—
204	C₄₃⋊C₈	—	2	2	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	C₄₃⋊C₈	—	4	1	no	—
207	C₄₃⋊C₈	—	4	1	no	—
208	C₄₃⋊C₈	—	4	1	no	—
209	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
210	#19238	—	43	1	no	maximal, Sylow
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	8	1	no	—
214	C₂²×C₄₃	—	8	1	no	—
215	C₂²×C₄₃	—	8	1	no	—
216	C₂²×C₄₃	#460	1	2	yes	—
217	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
218	C₂×D₄₃	—	8	2	no	—
219	C₂×D₄₃	—	8	2	no	—
220	C₂×D₄₃	—	8	2	no	—
221	C₂×D₄₃	—	16	4	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	8	1	no	—
228	C₄×C₄₃	#460	1	2	yes	—
229	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
230	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₄₃	#576	1	1	yes	characteristic
232	C₄×C₄₃	#577	1	1	yes	characteristic
233	#3246	D₄₃	1	1	yes	characteristic, complemented
234	#3208	—	43	1	no	—
235	#3151	—	43	1	no	—
236	#2962	—	43	1	no	—
237	#1688	—	43	2	no	—
238	#1686	—	43	2	no	—
239	#1668	—	43	2	no	—
240	#1666	—	43	2	no	—
241	#1565	—	43	1	no	—
242	#1540	—	43	1	no	—
243	C₂×#331	—	43	1	no	—
244	C₂×C₄₃	—	2	2	no	—
245	C₂×C₄₃	—	16	1	no	—
246	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
247	C₂×C₄₃	#3062	1	1	yes	characteristic
248	C₂×C₄₃	#3068	1	1	yes	characteristic
249	D₄₃	—	16	2	no	—
250	C₂×AGL(1,ℤ/8)	—	86	1	no	—
251	C₂×AGL(1,ℤ/8)	—	86	1	no	—
252	#533	C₂×D₄₃	1	1	yes	characteristic
253	#532	C₂×D₄₃	1	1	yes	characteristic
254	C₂×#127	—	43	1	no	—
255	#496	—	86	2	no	—
256	#493	—	43	2	no	—
257	#492	—	43	2	no	—
258	#492	—	86	1	no	—
259	#486	—	86	1	no	—
260	#476	—	2	1	no	—
261	#475	C₂×D₄₃	1	2	yes	complemented
262	#465	—	2	2	no	—
263	#461	—	2	1	no	—
264	#460	—	43	2	no	—
265	#460	—	43	2	no	—
266	#460	C₂×D₄₃	1	2	yes	complemented
267	#450	—	86	2	no	—
268	#446	—	43	2	no	—
269	#446	—	86	2	no	—
270	C₈×Q₈	—	43	2	no	—
271	#431	—	43	1	no	—
272	#424	—	86	1	no	—
273	C₂×C₄⋊C₈	—	43	1	no	—
274	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
275	#405	—	86	1	no	—
276	C₄×M₁₆	—	43	1	no	—
277	#335	—	43	2	no	—
278	#334	—	43	2	no	—
279	#332	—	43	1	no	—
280	#332	—	43	1	no	—
281	#331	—	43	1	no	—
282	#331	—	43	1	no	—
283	#331	—	43	2	no	—
284	#331	—	43	2	no	—
285	C₄₃	#19238	1	1	yes	characteristic, complemented, Sylow
286	C₂×#41	—	2	1	no	—
287	C₂²×D₄	—	86	1	no	—
288	C₂²×D₄	—	86	1	no	—
289	C₂²×D₄	—	86	1	no	—
290	AGL(1,ℤ/8)	—	172	4	no	—
291	AGL(1,ℤ/8)	—	172	4	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	86	2	no	—
294	C₂×SD₁₆	—	86	2	no	—
295	C₂×SD₁₆	—	86	2	no	—
296	C₂×SD₁₆	—	86	2	no	—
297	C₂×D₈	—	86	2	no	—
298	C₂×D₈	—	86	2	no	—
299	C₂×M₁₆	—	43	1	no	—
300	C₂×M₁₆	—	43	1	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	86	1	no	—
303	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
304	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
305	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
306	#127	—	43	2	no	—
307	#127	—	86	1	no	—
308	#127	—	86	1	no	—
309	#127	—	86	1	no	—
310	#127	C₂²×D₄₃	1	1	yes	characteristic
311	#125	—	2	1	no	—
312	#124	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	—	2	1	no	—
322	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
323	#106	—	2	2	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	43	1	no	—
326	C₄⋊C₈	—	43	1	no	—
327	C₄⋊C₈	—	43	1	no	—
328	C₄⋊C₈	—	43	1	no	—
329	C₄⋊C₈	—	86	2	no	—
330	C₄⋊C₈	—	86	2	no	—
331	C₄⋊C₈	—	86	1	no	—
332	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
333	#103	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	86	2	no	—
336	#102	—	86	2	no	—
337	C₂²⋊C₈	—	86	1	no	—
338	#97	—	43	2	no	—
339	#97	—	86	2	no	—
340	C₄×C₈	—	43	2	no	—
341	C₄×C₈	—	86	2	no	—
342	C₄×C₈	—	86	1	no	—
343	C₂⁴	—	172	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	4	1	no	—
353	C₂×D₄	—	86	2	no	—
354	C₂×D₄	—	86	2	no	—
355	C₂×D₄	—	86	2	no	—
356	C₂×D₄	—	344	1	no	—
357	C₂×D₄	—	344	1	no	—
358	C₂×D₄	—	344	2	no	—
359	C₂×D₄	—	172	1	no	—
360	C₂×D₄	—	172	1	no	—
361	C₂×D₄	—	172	1	no	—
362	C₂×D₄	—	172	2	no	—
363	C₂×D₄	—	172	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
366	C₂²×C₄	#10621900	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
368	SD₁₆	—	8	2	no	—
369	SD₁₆	—	344	2	no	—
370	SD₁₆	—	344	2	no	—
371	SD₁₆	—	172	4	no	—
372	SD₁₆	—	172	4	no	—
373	D₈	—	172	4	no	—
374	D₈	—	172	4	no	—
375	M₁₆	—	43	4	no	—
376	M₁₆	—	86	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	8	1	no	—
379	C₂×C₈	—	43	2	no	—
380	C₂×C₈	—	43	2	no	—
381	C₂×C₈	—	86	1	no	—
382	C₂×C₈	—	86	1	no	—
383	C₂×C₈	—	86	1	no	—
384	C₂×C₈	—	86	1	no	—
385	C₂×C₈	—	172	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	D₄×D₄₃	1	1	yes	characteristic
399	C₄²	#10621900	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	—	344	2	no	—
404	C₂³	—	344	2	no	—
405	C₂³	—	344	2	no	—
406	C₂³	—	172	2	no	—
407	C₂³	#13063297	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	1	no	—
412	Q₈	—	8	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	8	1	no	—
418	D₄	—	8	2	no	—
419	D₄	—	344	2	no	—
420	D₄	—	344	2	no	—
421	D₄	—	344	2	no	—
422	D₄	—	344	2	no	—
423	D₄	—	172	2	no	—
424	D₄	—	172	2	no	—
425	D₄	—	172	2	no	—
426	D₄	—	172	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#13063297	1	1	yes	characteristic
435	C₂×C₄	#13063297	1	1	yes	characteristic
436	C₂×C₄	#13063297	1	1	yes	characteristic
437	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
438	C₂×C₄	#13063352	1	2	yes	—
439	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	43	4	no	—
444	C₈	—	86	2	no	—
445	C₈	—	172	1	no	—
446	C₈	—	172	1	no	—
447	C₈	—	172	1	no	—
448	C₈	—	172	1	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	344	2	no	—
455	C₂²	—	344	2	no	—
456	C₂²	—	344	2	no	—
457	C₂²	—	688	4	no	—
458	C₂²	#14583097	1	2	yes	—
459	C₂²	C₂×#13063297	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	#14583097	1	2	yes	—
467	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
468	C₄	C₂×#13063352	1	1	yes	characteristic
469	C₄	#14583702	1	1	yes	characteristic
470	C₄	#14583707	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	16	1	no	—
473	C₂	—	688	2	no	—
474	C₂	C₂×#14583097	1	1	yes	characteristic
475	C₂	#19144277	1	1	yes	characteristic
476	C₂	#19144325	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3246	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145048	C₂
hypercenter	#3246	D₄₃
hypocenter	C₄₃	#19238
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3246

Complements

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

N	H ≅ G/N	type
1. #19145533	C₂	semidirect
3. #19143544	C₂	semidirect
4. #19134077	C₂	semidirect
5. #19134069	C₂	semidirect
6. #19133953	C₂	semidirect
7. #19133945	C₂	semidirect
8. #19133345	C₂	semidirect
9. #19133244	C₂	semidirect
10. C₂×#14582642	C₂	semidirect
11. C₄₃×#3246	C₂	semidirect
24. #14583030	C₂²	semidirect
25. Q₈×C₄₃⋊C₈	C₂²	semidirect
31. #14582651	C₂²	semidirect
32. #14582649	C₂²	semidirect
33. #14582645	C₂²	semidirect
34. #14582645	C₂²	semidirect
35. #14582643	C₂²	semidirect
36. #14582643	C₂²	semidirect
42. C₄₃×#475	C₂²	semidirect
45. C₄₃×#460	C₂²	semidirect
155. #10621877	SD₁₆	semidirect
233. #3246	D₄₃	semidirect
261. #475	C₂×D₄₃	semidirect
266. #460	C₂×D₄₃	semidirect
285. C₄₃	#19238	semidirect

Maximal subgroups

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

subgroup	index
#19145533	2
#19145048	2
#19143544	2
#19134077	2
#19134069	2
#19133953	2
#19133945	2
#19133345	2
#19133244	2
C₂×#14582642	2
C₄₃×#3246	2
#19238	43