Subgroups — #25080509

Order 11008.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145023	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144747	C₂	1	2	yes	maximal, complemented
3	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133966	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133961	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133956	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133951	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133944	C₂	1	2	yes	maximal, complemented
9	#19133937	C₂	1	2	yes	maximal, complemented
10	#19133301	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	—	2	1	no	—
13	C₂×#13063347	—	2	1	no	—
14	#14583449	C₂²	1	2	yes	—
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	#14583283	—	2	1	no	—
17	#14583283	—	2	1	no	—
18	#14583279	C₂²	1	1	yes	characteristic
19	#14583276	C₂²	1	1	yes	characteristic
20	#14583272	C₂²	1	2	yes	—
21	#14583224	—	2	2	no	—
22	#14583185	C₂²	1	2	yes	—
23	#14583180	C₂²	1	2	yes	—
24	#14583100	C₂²	1	2	yes	—
25	#14583095	C₂²	1	2	yes	—
26	#14583046	—	2	2	no	—
27	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
28	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
29	#14583012	—	2	2	no	—
30	#14583001	—	2	2	no	—
31	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
32	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₄₃	—	2	1	no	—
34	C₈×C₂²⋊D₄₃	—	2	1	no	—
35	#14582952	C₂²	1	1	yes	characteristic
36	#14582950	—	2	1	no	—
37	C₄×C₈×D₄₃	—	2	1	no	—
38	#14582644	C₂²	1	2	yes	—
39	#14582644	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	#14582642	C₂²	1	2	yes	—
42	C₄₃×#432	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#335	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	1	yes	characteristic
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	2	no	—
48	C₂×#10621898	D₄	1	1	yes	characteristic
49	#13063347	—	4	4	no	—
50	#13063347	—	4	4	no	—
51	C₂×Dic₁₇₂	—	2	1	no	—
52	C₂×Dic₁₇₂	—	2	1	no	—
53	C₂×#10621873	—	2	2	no	—
54	C₂×#10621873	—	2	2	no	—
55	C₂×#10621873	—	2	2	no	—
56	C₂×D₃₄₄	—	2	2	no	—
57	C₂×D₃₄₄	—	2	1	no	—
58	C₂×D₃₄₄	—	2	1	no	—
59	C₂×C₈×D₄₃	—	2	1	no	—
60	C₂×C₈×D₄₃	—	2	1	no	—
61	#13063325	C₂³	1	2	yes	—
62	#13063322	C₂³	1	2	yes	—
63	#13063313	—	2	2	no	—
64	#13063299	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	C₄×Dic₈₆	D₄	1	1	yes	characteristic
67	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
68	C₄×D₁₇₂	—	2	2	no	—
69	C₄×D₁₇₂	—	2	2	no	—
70	C₄×D₁₇₂	D₄	1	1	yes	characteristic
71	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
72	C₄×C₂²⋊D₄₃	—	2	1	no	—
73	C₄×C₂²⋊D₄₃	—	2	1	no	—
74	#13063284	D₄	1	1	yes	characteristic
75	#13063282	—	2	1	no	—
76	C₄²×D₄₃	—	2	1	no	—
77	#13063259	—	2	2	no	—
78	#13063257	—	2	2	no	—
79	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
81	Dic₄₃⋊C₈	—	2	1	no	—
82	Dic₄₃⋊C₈	—	2	1	no	—
83	#13063250	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	#13063247	—	2	2	no	—
86	#13063247	—	2	2	no	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
88	(C₂×D₄₃)⋊C₈	—	2	1	no	—
89	(C₂×D₄₃)⋊C₈	—	2	1	no	—
90	C₄×C₄₃⋊C₈	—	2	1	no	—
91	C₈×Dic₄₃	—	2	1	no	—
92	C₈×Dic₄₃	—	2	1	no	—
93	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₂²⋊C₈×C₄₃	—	2	2	no	—
99	#97×C₄₃	—	2	2	no	—
100	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₃	—	2	1	no	—
108	C₂×C₂²⋊D₄₃	—	4	2	no	—
109	#10621898	—	2	2	no	—
110	#10621898	—	2	2	no	—
111	#10621898	—	4	4	no	—
112	#10621898	—	4	4	no	—
113	C₂×D₁₇₂	—	2	2	no	—
114	C₂×D₁₇₂	—	2	2	no	—
115	C₂×D₁₇₂	—	2	2	no	—
116	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×C₄×D₄₃	—	2	1	no	—
119	C₂×C₄×D₄₃	—	2	1	no	—
120	C₂×C₄×D₄₃	—	4	2	no	—
121	C₂×Dic₈₆	—	2	2	no	—
122	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₃	#41	1	1	yes	characteristic
134	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₃	—	2	1	no	—
136	(C₂×D₄₃)⋊C₄	—	2	1	no	—
137	(C₂×D₄₃)⋊C₄	—	2	1	no	—
138	(C₂×D₄₃)⋊C₄	—	4	2	no	—
139	(C₂×D₄₃)⋊C₄	—	4	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
143	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
144	Dic₄₃⋊C₄	—	2	1	no	—
145	Dic₄₃⋊C₄	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₄×Dic₄₃	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	Dic₁₇₂	—	4	2	no	—
152	Dic₁₇₂	—	4	2	no	—
153	D₃₄₄	—	4	2	no	—
154	D₃₄₄	—	4	4	no	—
155	D₃₄₄	—	4	2	no	—
156	#10621873	—	4	4	no	—
157	#10621873	—	4	4	no	—
158	#10621873	—	4	4	no	—
159	C₈×D₄₃	—	4	2	no	—
160	C₈×D₄₃	—	4	2	no	—
161	C₂³×C₄₃	#121	1	1	yes	characteristic
162	C₂²×D₄₃	—	2	1	no	—
163	C₂²×D₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	2	4	no	—
176	C₂²⋊D₄₃	—	8	4	no	—
177	C₂×Dic₄₃	—	2	1	no	—
178	C₂×Dic₄₃	—	2	1	no	—
179	C₂×Dic₄₃	—	2	1	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	D₁₇₂	—	2	1	no	—
182	D₁₇₂	—	4	2	no	—
183	D₁₇₂	—	4	2	no	—
184	D₁₇₂	—	4	2	no	—
185	D₁₇₂	—	4	2	no	—
186	D₁₇₂	—	8	2	no	—
187	D₁₇₂	#135	1	2	yes	complemented
188	C₄×D₄₃	—	2	4	no	—
189	C₄×D₄₃	—	4	2	no	—
190	C₄×D₄₃	—	4	1	no	—
191	C₄×D₄₃	—	4	1	no	—
192	C₄×D₄₃	—	8	4	no	—
193	Dic₈₆	—	2	1	no	—
194	Dic₈₆	—	4	2	no	—
195	Dic₈₆	—	4	2	no	—
196	Dic₈₆	#135	1	2	yes	complemented
197	C₈×C₄₃	—	2	1	no	—
198	C₈×C₄₃	—	2	1	no	—
199	C₈×C₄₃	—	4	2	no	—
200	C₈×C₄₃	—	4	2	no	—
201	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
202	C₈×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
203	C₄₃⋊C₈	—	4	1	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	#19269	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
210	C₂×D₄₃	—	2	2	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	—	4	1	no	—
213	C₂×D₄₃	—	8	2	no	—
214	C₂×D₄₃	—	8	2	no	—
215	C₂×D₄₃	—	8	2	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
221	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
222	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	Dic₄₃	—	2	2	no	—
225	Dic₄₃	—	4	1	no	—
226	Dic₄₃	—	4	1	no	—
227	Dic₄₃	—	8	2	no	—
228	#3147	—	43	1	no	—
229	#3115	—	43	2	no	—
230	C₈×#41	—	43	1	no	—
231	#1670	—	43	1	no	—
232	#1669	—	43	1	no	—
233	#1668	—	43	1	no	—
234	#1667	—	43	1	no	—
235	#1666	—	43	2	no	—
236	#1665	—	43	2	no	—
237	#1568	D₄₃	1	1	yes	characteristic, complemented
238	#1553	—	43	2	no	—
239	C₂×C₄₃	—	4	1	no	—
240	C₂×C₄₃	#3038	1	1	yes	characteristic
241	C₂×C₄₃	#3050	1	1	yes	characteristic
242	C₂×C₄₃	#3067	1	1	yes	characteristic
243	D₄₃	—	4	2	no	—
244	D₄₃	—	16	2	no	—
245	C₂×#135	—	86	1	no	—
246	C₂×#135	—	86	1	no	—
247	#532	—	43	2	no	—
248	C₄×#41	—	43	1	no	—
249	#495	—	86	1	no	—
250	#495	—	86	1	no	—
251	#494	—	43	1	no	—
252	#493	—	43	1	no	—
253	#492	—	43	2	no	—
254	#482	—	86	2	no	—
255	#475	—	43	2	no	—
256	#474	—	43	2	no	—
257	#460	—	43	2	no	—
258	#459	—	43	2	no	—
259	#449	—	86	2	no	—
260	C₈×Q₈	—	43	1	no	—
261	C₈×Q₈	—	43	1	no	—
262	#442	—	86	2	no	—
263	#440	—	86	2	no	—
264	C₈×D₄	—	43	1	no	—
265	C₈×D₄	—	43	1	no	—
266	C₈×D₄	—	86	1	no	—
267	C₈×D₄	—	86	1	no	—
268	#432	C₂×D₄₃	1	2	yes	—
269	#431	—	43	1	no	—
270	#431	—	86	1	no	—
271	C₂×C₄×C₈	—	86	1	no	—
272	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
273	#335	C₂×D₄₃	1	1	yes	characteristic
274	#335	C₂×D₄₃	1	1	yes	characteristic
275	#334	C₂×D₄₃	1	2	yes	—
276	#332	—	43	2	no	—
277	#332	—	43	2	no	—
278	#331	—	43	2	no	—
279	#331	—	43	2	no	—
280	C₄₃	#19269	1	1	yes	characteristic, complemented, Sylow
281	C₂×#41	—	43	1	no	—
282	C₂×#41	—	86	2	no	—
283	#135	—	172	4	no	—
284	#135	—	172	4	no	—
285	C₂×Q₁₆	—	86	1	no	—
286	C₂×Q₁₆	—	86	1	no	—
287	C₂×SD₁₆	—	86	2	no	—
288	C₂×SD₁₆	—	86	2	no	—
289	C₂×SD₁₆	—	86	2	no	—
290	C₂×D₈	—	86	2	no	—
291	C₂×D₈	—	86	1	no	—
292	C₂×D₈	—	86	1	no	—
293	C₂²×C₈	—	86	1	no	—
294	C₂²×C₈	—	86	1	no	—
295	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
296	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
297	C₄⋊Q₈	—	43	2	no	—
298	#127	—	43	2	no	—
299	#124	—	86	2	no	—
300	#121	—	86	2	no	—
301	#121	—	86	2	no	—
302	C₄×Q₈	—	43	1	no	—
303	C₄×Q₈	—	43	1	no	—
304	C₄×D₄	—	43	1	no	—
305	C₄×D₄	—	43	1	no	—
306	C₄×D₄	—	86	1	no	—
307	C₄×D₄	—	86	1	no	—
308	C₄×D₄	—	86	2	no	—
309	C₄×D₄	—	86	2	no	—
310	#117	—	43	1	no	—
311	#117	—	86	1	no	—
312	C₂×C₄²	—	86	1	no	—
313	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
314	#107	—	86	2	no	—
315	#106	—	86	2	no	—
316	C₄⋊C₈	—	43	1	no	—
317	C₄⋊C₈	—	43	1	no	—
318	C₄⋊C₈	—	86	1	no	—
319	C₄⋊C₈	—	86	1	no	—
320	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
321	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
322	#103	—	86	2	no	—
323	#102	—	86	2	no	—
324	#102	—	86	2	no	—
325	#102	—	86	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	86	1	no	—
328	C₂²⋊C₈	—	86	1	no	—
329	C₂²⋊C₈	—	86	1	no	—
330	#97	—	2	2	no	—
331	C₄×C₈	—	86	1	no	—
332	C₄×C₈	—	86	1	no	—
333	C₄×C₈	—	86	1	no	—
334	C₄×C₈	D₁₇₂	1	1	yes	characteristic
335	C₄×C₈	D₁₇₂	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
338	#41	—	86	2	no	—
339	#41	—	86	2	no	—
340	#41	—	172	4	no	—
341	#41	—	172	4	no	—
342	C₂×Q₈	—	43	1	no	—
343	C₂×Q₈	—	86	2	no	—
344	C₂×D₄	—	43	1	no	—
345	C₂×D₄	—	86	1	no	—
346	C₂×D₄	—	86	2	no	—
347	C₂×D₄	—	86	2	no	—
348	C₂×D₄	—	86	2	no	—
349	C₂×D₄	—	172	2	no	—
350	C₂²×C₄	—	86	1	no	—
351	C₂²×C₄	—	86	1	no	—
352	C₂²×C₄	—	86	1	no	—
353	C₂²×C₄	—	172	2	no	—
354	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
356	C₂²×C₄	#10621902	1	1	yes	characteristic
357	Q₁₆	—	172	2	no	—
358	Q₁₆	—	172	2	no	—
359	SD₁₆	—	172	4	no	—
360	SD₁₆	—	172	4	no	—
361	SD₁₆	—	172	4	no	—
362	D₈	—	172	2	no	—
363	D₈	—	172	4	no	—
364	D₈	—	172	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	1	no	—
371	C₂×C₈	—	172	2	no	—
372	C₂×C₈	—	172	2	no	—
373	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
374	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
375	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
376	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
377	C₄⋊C₄	—	43	1	no	—
378	C₄⋊C₄	—	43	1	no	—
379	C₄⋊C₄	—	86	1	no	—
380	C₄⋊C₄	—	86	1	no	—
381	C₄⋊C₄	—	86	2	no	—
382	C₄⋊C₄	—	86	2	no	—
383	C₂²⋊C₄	—	86	1	no	—
384	C₂²⋊C₄	—	86	1	no	—
385	C₂²⋊C₄	—	86	1	no	—
386	C₂²⋊C₄	—	172	2	no	—
387	C₂²⋊C₄	—	172	2	no	—
388	C₄²	—	86	1	no	—
389	C₄²	—	86	1	no	—
390	C₄²	—	86	1	no	—
391	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
392	C₄²	D₄×D₄₃	1	1	yes	characteristic
393	C₄²	#10621902	1	1	yes	characteristic
394	C₄²	C₂³×D₄₃	1	1	yes	characteristic
395	C₂³	—	86	1	no	—
396	C₂³	—	172	2	no	—
397	C₂³	#13063300	1	1	yes	characteristic
398	Q₈	—	43	2	no	—
399	Q₈	—	86	1	no	—
400	Q₈	—	172	2	no	—
401	Q₈	—	172	2	no	—
402	D₄	—	43	2	no	—
403	D₄	—	86	4	no	—
404	D₄	—	86	1	no	—
405	D₄	—	344	2	no	—
406	D₄	—	344	4	no	—
407	D₄	—	172	2	no	—
408	D₄	—	172	2	no	—
409	D₄	—	172	2	no	—
410	D₄	—	172	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	86	4	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	1	no	—
419	C₂×C₄	—	86	1	no	—
420	C₂×C₄	—	344	4	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	—	172	1	no	—
424	C₂×C₄	—	172	1	no	—
425	C₂×C₄	#13063300	1	1	yes	characteristic
426	C₂×C₄	#13063300	1	1	yes	characteristic
427	C₂×C₄	#13063300	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
430	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	172	1	no	—
436	C₈	—	172	1	no	—
437	C₈	#13063353	1	2	yes	—
438	C₈	#13063353	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	86	2	no	—
443	C₂²	—	344	2	no	—
444	C₂²	—	344	2	no	—
445	C₂²	—	344	2	no	—
446	C₂²	—	172	1	no	—
447	C₂²	—	172	1	no	—
448	C₂²	C₂×#13063300	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	86	2	no	—
454	C₄	—	344	2	no	—
455	C₄	—	172	1	no	—
456	C₄	—	172	1	no	—
457	C₄	#135×D₄₃	1	1	yes	characteristic
458	C₄	#135×D₄₃	1	1	yes	characteristic
459	C₄	C₂×#13063353	1	1	yes	characteristic
460	C₄	C₂×#13063353	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	172	2	no	—
463	C₂	—	688	2	no	—
464	C₂	#19144076	1	1	yes	characteristic
465	C₂	#19144177	1	1	yes	characteristic
466	C₂	#19144316	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1568	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#1568	D₄₃
hypocenter	C₄₃	#19269
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
1. #19145023	C₂	semidirect
2. #19144747	C₂	semidirect
3. C₈×#10621898	C₂	semidirect
4. #19133966	C₂	semidirect
5. #19133961	C₂	semidirect
6. #19133956	C₂	semidirect
7. #19133951	C₂	semidirect
8. #19133944	C₂	semidirect
9. #19133937	C₂	semidirect
10. #19133301	C₂	semidirect
11. C₄₃×#1568	C₂	semidirect
187. D₁₇₂	#135	semidirect
196. Dic₈₆	#135	semidirect
237. #1568	D₄₃	semidirect
280. C₄₃	#19269	semidirect

Maximal subgroups

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

subgroup	index
#19145023	2
#19144747	2
C₈×#10621898	2
#19133966	2
#19133961	2
#19133956	2
#19133951	2
#19133944	2
#19133937	2
#19133301	2
C₄₃×#1568	2
#19269	43