Subgroups — #25080431

Order 11008.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145154	C₂	1	1	yes	maximal, characteristic
2	#19144402	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144069	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134026	C₂	1	2	yes	maximal, complemented
6	#19134012	C₂	1	2	yes	maximal, complemented
7	#19133978	C₂	1	2	yes	maximal, complemented
8	#19133944	C₂	1	2	yes	maximal, complemented
9	#19133286	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133273	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
16	#14583297	C₂²	1	1	yes	characteristic
17	#14583272	C₂²	1	1	yes	characteristic
18	#14583250	C₂²	1	1	yes	characteristic
19	#14583246	C₂²	1	1	yes	characteristic
20	#14583207	—	2	2	no	—
21	#14583195	C₂²	1	2	yes	—
22	#14583185	C₂²	1	2	yes	—
23	#14583128	—	2	1	no	—
24	#14583128	—	2	1	no	—
25	#14583122	—	2	2	no	—
26	#14583110	C₂²	1	2	yes	—
27	#14583100	C₂²	1	2	yes	—
28	C₈×Dic₈₆	—	2	1	no	—
29	C₈×Dic₈₆	—	2	1	no	—
30	C₈×Dic₈₆	C₂²	1	2	yes	—
31	C₈×Dic₈₆	C₂²	1	2	yes	—
32	C₄×#10621873	—	2	1	no	—
33	C₄×#10621873	—	2	1	no	—
34	#14582941	—	2	1	no	—
35	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×Dic₄₃⋊C₈	—	2	1	no	—
37	#14582909	—	2	1	no	—
38	#14582901	—	2	1	no	—
39	C₂×C₈×Dic₄₃	—	2	1	no	—
40	#14582647	C₂²	1	2	yes	—
41	#14582646	C₂²	1	2	yes	—
42	#14582644	C₂²	1	2	yes	—
43	#14582642	C₂²	1	2	yes	—
44	C₄₃×#423	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#334	C₂²	1	2	yes	—
48	C₄₃×#334	C₂²	1	2	yes	—
49	C₂×#10621898	—	2	1	no	—
50	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
51	#13063358	—	4	4	no	—
52	C₂×Dic₁₇₂	—	2	2	no	—
53	C₂×#10621873	—	2	2	no	—
54	C₂×#10621873	—	2	1	no	—
55	C₂×#10621873	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	#13063325	C₂³	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063322	C₂³	1	1	yes	characteristic
61	#13063317	—	2	1	no	—
62	#13063313	—	2	1	no	—
63	#13063304	—	2	1	no	—
64	#13063304	—	2	1	no	—
65	#13063299	—	2	1	no	—
66	#13063299	—	2	1	no	—
67	C₄×Dic₈₆	—	2	1	no	—
68	C₄×Dic₈₆	—	2	1	no	—
69	C₄×Dic₈₆	—	2	1	no	—
70	C₄×Dic₈₆	—	2	1	no	—
71	C₄×Dic₈₆	D₄	1	2	yes	—
72	C₄×Dic₈₆	C₂³	1	2	yes	—
73	C₄×D₁₇₂	—	2	1	no	—
74	C₄×D₁₇₂	—	2	1	no	—
75	#13063284	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
77	C₂×Dic₄₃⋊C₄	—	2	1	no	—
78	C₂×C₄×Dic₄₃	—	2	1	no	—
79	#13063259	—	2	2	no	—
80	#13063257	—	2	1	no	—
81	#13063257	—	2	1	no	—
82	#13063257	—	2	2	no	—
83	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
84	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
85	Dic₄₃⋊C₈	—	2	2	no	—
86	Dic₄₃⋊C₈	—	2	2	no	—
87	#13063250	—	2	2	no	—
88	#13063250	—	2	2	no	—
89	#13063250	—	2	1	no	—
90	#13063250	—	2	1	no	—
91	#13063250	—	2	2	no	—
92	#13063247	—	2	1	no	—
93	#13063247	—	2	1	no	—
94	#13063247	—	2	2	no	—
95	C₈×Dic₄₃	—	2	2	no	—
96	C₈×Dic₄₃	—	2	2	no	—
97	C₂×M₁₆×C₄₃	—	2	1	no	—
98	C₂×M₁₆×C₄₃	—	2	1	no	—
99	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₃	—	2	1	no	—
103	C₄⋊C₈×C₄₃	—	2	1	no	—
104	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
105	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
106	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₄₃	—	4	1	no	—
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂²×Dic₄₃	—	2	1	no	—
116	#10621898	—	4	2	no	—
117	#10621898	—	4	2	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×D₁₇₂	—	2	1	no	—
120	C₂×D₁₇₂	—	2	1	no	—
121	C₂×C₄×D₄₃	—	4	1	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	C₂×Dic₈₆	—	2	2	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	C₂×Dic₈₆	—	2	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	C₂×Dic₈₆	SD₁₆	1	4	yes	complemented
128	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
129	M₁₆×C₄₃	—	4	2	no	—
130	M₁₆×C₄₃	—	4	2	no	—
131	C₂×C₈×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	4	1	no	—
135	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	#41	1	1	yes	characteristic
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₃	—	4	1	no	—
144	(C₂×D₄₃)⋊C₄	—	4	1	no	—
145	(C₂×D₄₃)⋊C₄	—	4	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	C₄⋊Dic₄₃	—	2	1	no	—
153	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
154	Dic₄₃⋊C₄	—	2	2	no	—
155	Dic₄₃⋊C₄	—	2	2	no	—
156	Dic₄₃⋊C₄	—	4	1	no	—
157	Dic₄₃⋊C₄	—	4	1	no	—
158	C₄×Dic₄₃	—	2	2	no	—
159	C₄×Dic₄₃	—	2	2	no	—
160	C₄×Dic₄₃	—	4	1	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	4	2	no	—
163	Dic₁₇₂	—	4	4	no	—
164	#10621873	—	4	2	no	—
165	#10621873	—	4	4	no	—
166	#10621873	—	4	2	no	—
167	C₂³×C₄₃	#121	1	1	yes	characteristic
168	C₂²×D₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	2	1	no	—
170	C₂×C₄×C₄₃	—	2	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
176	C₂×C₄×C₄₃	#135	1	2	yes	—
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₃	—	8	2	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	2	4	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₂×Dic₄₃	—	4	1	no	—
188	D₁₇₂	—	4	1	no	—
189	D₁₇₂	—	4	1	no	—
190	D₁₇₂	—	4	1	no	—
191	D₁₇₂	—	4	1	no	—
192	D₁₇₂	—	8	1	no	—
193	C₄×D₄₃	—	8	2	no	—
194	Dic₈₆	—	2	2	no	—
195	Dic₈₆	—	2	4	no	—
196	Dic₈₆	—	4	1	no	—
197	Dic₈₆	—	4	1	no	—
198	Dic₈₆	—	4	1	no	—
199	Dic₈₆	—	4	1	no	—
200	Dic₈₆	—	8	1	no	—
201	Dic₈₆	C₂×SD₁₆	1	4	yes	—
202	C₈×C₄₃	—	2	1	no	—
203	C₈×C₄₃	—	2	1	no	—
204	C₈×C₄₃	—	2	1	no	—
205	C₈×C₄₃	—	4	2	no	—
206	C₈×C₄₃	—	4	2	no	—
207	C₈×C₄₃	#137	1	2	yes	complemented
208	C₄₃⋊C₈	—	4	2	no	—
209	#19260	—	43	1	no	maximal, Sylow
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	#465	1	2	yes	—
213	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
214	C₂×D₄₃	—	8	1	no	—
215	C₂×D₄₃	—	8	1	no	—
216	C₂×D₄₃	—	8	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	#465	1	2	yes	—
221	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
222	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
223	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
224	C₄×C₄₃	#575	1	1	yes	characteristic
225	Dic₄₃	—	2	4	no	—
226	Dic₄₃	—	4	2	no	—
227	Dic₄₃	—	8	1	no	—
228	Dic₄₃	—	8	1	no	—
229	Dic₄₃	—	8	1	no	—
230	#3167	—	43	1	no	—
231	#3078	—	43	1	no	—
232	#3037	—	43	1	no	—
233	C₂×C₈×Q₈	—	43	1	no	—
234	#1680	—	43	2	no	—
235	#1678	—	43	2	no	—
236	#1672	—	43	2	no	—
237	#1666	—	43	2	no	—
238	#1566	D₄₃	1	1	yes	characteristic, complemented
239	#1550	—	43	1	no	—
240	#1547	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	#3037	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
244	C₂×C₄₃	#3067	1	1	yes	characteristic
245	D₄₃	—	16	1	no	—
246	C₂×#137	—	86	1	no	—
247	#533	—	43	1	no	—
248	#532	—	43	1	no	—
249	C₂×C₄×Q₈	—	43	1	no	—
250	#498	—	43	1	no	—
251	#492	—	43	1	no	—
252	#487	—	43	1	no	—
253	#486	—	43	1	no	—
254	#479	—	86	2	no	—
255	#477	—	43	2	no	—
256	#475	—	43	2	no	—
257	#465	—	86	1	no	—
258	#465	—	86	1	no	—
259	#464	—	86	2	no	—
260	#462	—	43	2	no	—
261	#460	—	43	2	no	—
262	C₈×Q₈	—	43	2	no	—
263	C₈×Q₈	—	43	2	no	—
264	C₈×Q₈	—	86	1	no	—
265	C₈×Q₈	—	86	1	no	—
266	C₄×SD₁₆	—	86	1	no	—
267	C₄×SD₁₆	—	86	1	no	—
268	#428	—	86	1	no	—
269	#423	C₂×D₄₃	1	1	yes	characteristic
270	#423	C₂×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	—	43	1	no	—
272	C₂×C₄⋊C₈	—	86	1	no	—
273	#419	—	86	1	no	—
274	#417	—	86	1	no	—
275	C₂×C₄×C₈	—	86	1	no	—
276	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
277	#334	C₂×D₄₃	1	2	yes	—
278	#334	C₂×D₄₃	1	2	yes	—
279	#333	—	43	2	no	—
280	#332	—	43	2	no	—
281	#332	—	43	2	no	—
282	#331	—	43	2	no	—
283	C₄₃	#19260	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	86	1	no	—
285	C₂²×Q₈	—	43	1	no	—
286	#137	—	172	4	no	—
287	C₂×Q₁₆	—	86	2	no	—
288	C₂×SD₁₆	—	86	2	no	—
289	C₂×SD₁₆	—	86	1	no	—
290	C₂×SD₁₆	—	86	1	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	1	no	—
293	C₂²×C₈	—	86	1	no	—
294	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
295	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
296	C₄⋊Q₈	—	43	1	no	—
297	C₄⋊Q₈	—	43	1	no	—
298	C₄⋊Q₈	—	43	1	no	—
299	#127	—	43	1	no	—
300	#125	—	86	1	no	—
301	#124	—	86	1	no	—
302	C₂²⋊Q₈	—	86	1	no	—
303	C₂²⋊Q₈	—	86	1	no	—
304	#121	—	86	1	no	—
305	#121	—	86	1	no	—
306	C₄×Q₈	—	43	2	no	—
307	C₄×Q₈	—	43	2	no	—
308	C₄×Q₈	—	86	1	no	—
309	C₄×Q₈	—	86	1	no	—
310	C₄×Q₈	—	86	1	no	—
311	C₄×Q₈	—	86	1	no	—
312	C₄×D₄	—	86	1	no	—
313	C₄×D₄	—	86	1	no	—
314	#117	—	86	1	no	—
315	C₂×C₄⋊C₄	—	43	1	no	—
316	C₂×C₄⋊C₄	—	86	1	no	—
317	C₂×C₄²	—	86	1	no	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	#107	—	86	2	no	—
320	#106	—	86	2	no	—
321	#106	—	86	1	no	—
322	#106	—	86	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	43	2	no	—
326	C₄⋊C₈	—	86	2	no	—
327	C₄⋊C₈	—	86	2	no	—
328	C₄⋊C₈	—	86	1	no	—
329	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
330	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
331	#103	—	86	2	no	—
332	#103	—	86	2	no	—
333	#103	—	86	2	no	—
334	#103	—	86	1	no	—
335	#103	—	86	1	no	—
336	#102	—	86	2	no	—
337	#102	—	86	1	no	—
338	#102	—	86	1	no	—
339	C₄×C₈	—	86	2	no	—
340	C₄×C₈	—	86	2	no	—
341	C₄×C₈	D₁₇₂	1	1	yes	characteristic
342	C₄×C₈	D₁₇₂	1	1	yes	characteristic
343	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
344	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
345	#41	—	172	2	no	—
346	#41	—	172	2	no	—
347	C₂×Q₈	—	43	4	no	—
348	C₂×Q₈	—	43	2	no	—
349	C₂×Q₈	—	86	1	no	—
350	C₂×Q₈	—	86	2	no	—
351	C₂×Q₈	—	86	1	no	—
352	C₂×Q₈	—	86	1	no	—
353	C₂×Q₈	—	86	1	no	—
354	C₂×D₄	—	86	1	no	—
355	C₂×D₄	—	86	1	no	—
356	C₂×D₄	—	86	1	no	—
357	C₂×D₄	—	172	1	no	—
358	C₂²×C₄	—	86	1	no	—
359	C₂²×C₄	—	86	1	no	—
360	C₂²×C₄	—	172	1	no	—
361	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
362	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
363	C₂²×C₄	#10621902	1	1	yes	characteristic
364	Q₁₆	—	172	4	no	—
365	SD₁₆	—	172	2	no	—
366	SD₁₆	—	172	4	no	—
367	SD₁₆	—	172	2	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	4	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	86	2	no	—
375	C₂×C₈	—	172	2	no	—
376	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
377	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
378	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
379	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
380	C₄⋊C₄	—	43	2	no	—
381	C₄⋊C₄	—	86	1	no	—
382	C₄⋊C₄	—	86	2	no	—
383	C₄⋊C₄	—	86	2	no	—
384	C₄⋊C₄	—	86	1	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	1	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	172	1	no	—
391	C₄⋊C₄	—	172	1	no	—
392	C₂²⋊C₄	—	172	1	no	—
393	C₂²⋊C₄	—	172	1	no	—
394	C₂²⋊C₄	—	172	1	no	—
395	C₄²	—	86	2	no	—
396	C₄²	—	86	2	no	—
397	C₄²	—	172	1	no	—
398	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
399	C₄²	D₄×D₄₃	1	1	yes	characteristic
400	C₄²	#10621902	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	172	1	no	—
403	C₂³	#13063300	1	1	yes	characteristic
404	Q₈	—	43	4	no	—
405	Q₈	—	86	4	no	—
406	Q₈	—	86	2	no	—
407	Q₈	—	344	1	no	—
408	Q₈	—	172	1	no	—
409	Q₈	—	172	1	no	—
410	Q₈	—	172	1	no	—
411	Q₈	—	172	1	no	—
412	D₄	—	344	1	no	—
413	D₄	—	344	2	no	—
414	D₄	—	172	1	no	—
415	D₄	—	172	1	no	—
416	D₄	—	172	1	no	—
417	D₄	—	172	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	86	4	no	—
422	C₂×C₄	—	86	2	no	—
423	C₂×C₄	—	86	2	no	—
424	C₂×C₄	—	344	2	no	—
425	C₂×C₄	—	172	1	no	—
426	C₂×C₄	—	172	1	no	—
427	C₂×C₄	—	172	1	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	#13063300	1	1	yes	characteristic
430	C₂×C₄	#13063300	1	1	yes	characteristic
431	C₂×C₄	#13063300	1	1	yes	characteristic
432	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
433	C₂×C₄	#13063346	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
436	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	2	no	—
442	C₈	—	172	2	no	—
443	C₈	#13063358	1	2	yes	complemented
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	344	1	no	—
447	C₂²	—	344	1	no	—
448	C₂²	—	344	1	no	—
449	C₂²	#14583129	1	2	yes	—
450	C₂²	C₂×#13063300	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	86	4	no	—
455	C₄	—	344	1	no	—
456	C₄	—	344	1	no	—
457	C₄	—	344	1	no	—
458	C₄	—	172	2	no	—
459	C₄	#14583129	1	2	yes	—
460	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
461	C₄	C₂×#13063346	1	1	yes	characteristic
462	C₄	C₂×#13063358	1	1	yes	characteristic
463	C₄	#14583699	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	688	1	no	—
466	C₂	#19144069	1	1	yes	characteristic
467	C₂	C₂×#14583129	1	1	yes	characteristic
468	C₂	#19144316	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1566	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1566	D₄₃
hypocenter	C₄₃	#19260
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

Complements

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

N	H ≅ G/N	type
2. #19144402	C₂	semidirect
4. C₂×C₈×Dic₈₆	C₂	semidirect
5. #19134026	C₂	semidirect
6. #19134012	C₂	semidirect
7. #19133978	C₂	semidirect
8. #19133944	C₂	semidirect
9. #19133286	C₂	semidirect
11. C₄₃×#1566	C₂	semidirect
127. C₂×Dic₈₆	SD₁₆	semidirect
207. C₈×C₄₃	#137	semidirect
238. #1566	D₄₃	semidirect
283. C₄₃	#19260	semidirect
443. C₈	#13063358	semidirect

Maximal subgroups

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

subgroup	index
#19145154	2
#19144402	2
#19144069	2
C₂×C₈×Dic₈₆	2
#19134026	2
#19134012	2
#19133978	2
#19133944	2
#19133286	2
#19133273	2
C₄₃×#1566	2
#19260	43