Subgroups — #25080479

Order 11008.

786 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144404	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144071	C₂	1	1	yes	maximal, characteristic
3	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133940	C₂	1	4	yes	maximal, complemented
5	#19133933	C₂	1	4	yes	maximal, complemented
6	#19133351	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133280	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133263	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₄₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13063351	—	2	1	no	—
11	C₄×#10621898	C₂²	1	1	yes	characteristic
12	#14583191	—	2	1	no	—
13	#14583186	—	2	1	no	—
14	#14583181	C₂²	1	2	yes	complemented
15	#14583176	C₂²	1	2	yes	complemented
16	#14583096	—	2	1	no	—
17	#14583096	C₂²	1	2	yes	—
18	#14583091	—	2	1	no	—
19	#14583091	C₂²	1	2	yes	—
20	C₈×Dic₈₆	C₂²	1	2	yes	complemented
21	C₈×D₁₇₂	C₂²	1	2	yes	complemented
22	C₈×C₂²⋊D₄₃	—	2	2	no	—
23	#14582952	C₂²	1	1	yes	characteristic
24	#14582950	—	2	1	no	—
25	#14582939	—	2	1	no	—
26	#14582923	C₂²	1	1	yes	characteristic
27	#14582923	C₂²	1	1	yes	characteristic
28	#14582904	—	2	1	no	—
29	#14582898	—	2	1	no	—
30	C₄×C₈×D₄₃	—	2	1	no	—
31	#14582650	C₂²	1	4	yes	complemented
32	#14582645	C₂²	1	4	yes	complemented
33	#14582643	C₂²	1	4	yes	—
34	C₂²×SD₁₆×C₄₃	—	2	2	no	—
35	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#492	—	2	1	no	—
38	C₄₃×#492	—	2	1	no	—
39	C₄₃×#492	C₂²	1	4	yes	—
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#10621898	D₄	1	1	yes	characteristic
42	#13063351	—	4	4	no	—
43	C₂×#10621883	—	2	2	no	—
44	C₂×#10621882	—	2	2	no	—
45	C₂×#10621877	—	2	1	no	—
46	C₂×#10621877	—	2	1	no	—
47	C₂×C₈×D₄₃	—	2	2	no	—
48	C₄×Dic₈₆	D₄	1	1	yes	characteristic
49	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
50	C₄×D₁₇₂	D₄	1	1	yes	characteristic
51	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₄₃	—	2	1	no	—
53	C₄×C₂²⋊D₄₃	—	2	1	no	—
54	#13063284	D₄	1	1	yes	characteristic
55	#13063282	—	2	1	no	—
56	C₄²×D₄₃	—	2	1	no	—
57	#13063258	—	2	2	no	—
58	#13063256	—	2	2	no	—
59	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
61	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
62	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
64	Dic₄₃⋊C₈	—	2	2	no	—
65	#13063248	—	2	2	no	—
66	#13063246	—	2	2	no	—
67	#13063246	—	2	2	no	—
68	#13063245	—	2	2	no	—
69	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
70	(C₂×D₄₃)⋊C₈	—	2	2	no	—
71	C₄×C₄₃⋊C₈	—	2	1	no	—
72	C₈×Dic₄₃	—	2	2	no	—
73	C₂²×Q₈×C₄₃	—	2	1	no	—
74	C₂²×D₄×C₄₃	—	2	1	no	—
75	C₂²×D₄×C₄₃	—	2	1	no	—
76	C₂²×D₄×C₄₃	—	2	1	no	—
77	C₂×SD₁₆×C₄₃	—	2	4	no	—
78	C₂×SD₁₆×C₄₃	—	2	4	no	—
79	C₂×SD₁₆×C₄₃	—	4	8	no	—
80	C₂²×C₈×C₄₃	D₄	1	2	yes	—
81	C₄⋊Q₈×C₄₃	—	2	1	no	—
82	C₄⋊Q₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
85	#127×C₄₃	—	2	1	no	—
86	#127×C₄₃	—	2	1	no	—
87	#127×C₄₃	—	2	1	no	—
88	#127×C₄₃	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₄×C₈×C₄₃	C₂³	1	2	yes	—
95	C₂⁴×C₄₃	—	4	1	no	—
96	C₂×Q₈×C₄₃	—	2	2	no	—
97	C₂×Q₈×C₄₃	—	4	4	no	—
98	C₂×Q₈×C₄₃	—	4	1	no	—
99	C₂×D₄×C₄₃	—	2	2	no	—
100	C₂×D₄×C₄₃	—	2	2	no	—
101	C₂×D₄×C₄₃	—	2	2	no	—
102	C₂×D₄×C₄₃	—	4	1	no	—
103	C₂×D₄×C₄₃	—	4	1	no	—
104	C₂×D₄×C₄₃	—	4	1	no	—
105	C₂×D₄×C₄₃	—	4	4	no	—
106	C₂×D₄×C₄₃	—	4	2	no	—
107	C₂×D₄×C₄₃	—	4	2	no	—
108	C₂×D₄×C₄₃	—	8	2	no	—
109	C₂²×C₄×C₄₃	—	4	1	no	—
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	—	2	1	no	—
114	#10621898	—	2	2	no	—
115	#10621898	SD₁₆	1	4	yes	complemented
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×Dic₈₆	C₂×D₄	1	1	yes	characteristic
121	SD₁₆×C₄₃	—	4	8	no	—
122	SD₁₆×C₄₃	—	4	8	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	4	1	no	—
129	C₄⋊C₄×C₄₃	—	4	1	no	—
130	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	#41	1	1	yes	characteristic
133	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₄₃	—	2	1	no	—
135	#10621883	—	4	4	no	—
136	#10621882	—	4	4	no	—
137	(C₂×D₄₃)⋊C₄	—	2	1	no	—
138	(C₂×D₄₃)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	Dic₄₃⋊C₄	—	2	1	no	—
142	Dic₄₃⋊C₄	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	#10621877	—	4	2	no	—
147	#10621877	—	4	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₈×D₄₃	—	4	4	no	—
152	C₂³×C₄₃	—	4	2	no	—
153	C₂³×C₄₃	—	8	2	no	—
154	C₂³×C₄₃	—	8	2	no	—
155	C₂³×C₄₃	—	8	2	no	—
156	C₂³×C₄₃	#121	1	1	yes	characteristic
157	C₂²×D₄₃	—	2	1	no	—
158	Q₈×C₄₃	—	4	4	no	—
159	Q₈×C₄₃	—	8	2	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	4	4	no	—
163	D₄×C₄₃	—	8	2	no	—
164	D₄×C₄₃	—	8	2	no	—
165	D₄×C₄₃	—	8	2	no	—
166	D₄×C₄₃	—	8	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	8	2	no	—
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₄₃	—	2	4	no	—
180	C₂×Dic₄₃	—	2	1	no	—
181	C₂×Dic₄₃	—	2	1	no	—
182	C₂×Dic₄₃	—	2	1	no	—
183	D₁₇₂	—	2	1	no	—
184	D₁₇₂	C₂×SD₁₆	1	2	yes	complemented
185	C₄×D₄₃	—	2	4	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	Dic₈₆	—	2	1	no	—
189	Dic₈₆	C₂×SD₁₆	1	2	yes	complemented
190	C₈×C₄₃	—	2	2	no	—
191	C₈×C₄₃	AGL(1,ℤ/8)	1	4	yes	complemented
192	C₄₃⋊C₈	—	4	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	C₄₃⋊C₈	—	4	2	no	—
195	#19266	—	43	1	no	maximal, Sylow
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	8	2	no	—
199	C₂²×C₄₃	—	8	2	no	—
200	C₂²×C₄₃	—	8	2	no	—
201	C₂²×C₄₃	—	16	4	no	—
202	C₂²×C₄₃	#465	1	2	yes	—
203	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₂×D₄₃	—	2	2	no	—
205	C₂×D₄₃	—	4	1	no	—
206	C₂×D₄₃	—	4	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	#465	1	2	yes	—
211	C₄×C₄₃	#471	1	2	yes	—
212	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
214	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
215	Dic₄₃	—	2	2	no	—
216	Dic₄₃	—	4	1	no	—
217	Dic₄₃	—	4	1	no	—
218	C₂×#492	D₄₃	1	1	yes	characteristic, complemented
219	#3079	—	43	1	no	—
220	#3038	—	43	1	no	—
221	C₈×#41	—	43	1	no	—
222	#1666	—	43	4	no	—
223	#1665	—	43	4	no	—
224	#1566	—	43	1	no	—
225	#1549	—	43	1	no	—
226	#1545	—	43	1	no	—
227	C₂×C₄₃	—	2	2	no	—
228	C₂×C₄₃	—	16	2	no	—
229	C₂×C₄₃	#3038	1	1	yes	characteristic
230	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
231	C₂×C₄₃	C₂×#471	1	1	yes	characteristic
232	D₄₃	—	4	2	no	—
233	C₂×AGL(1,ℤ/8)	—	86	1	no	—
234	C₂²×SD₁₆	—	2	2	no	—
235	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
236	C₂×#127	C₂×D₄₃	1	1	yes	characteristic
237	C₄×#41	—	43	1	no	—
238	#492	—	2	1	no	—
239	#492	—	2	1	no	—
240	#492	C₂×D₄₃	1	4	yes	—
241	#477	—	86	1	no	—
242	#476	—	86	1	no	—
243	#475	—	43	2	no	—
244	#474	—	43	2	no	—
245	#460	—	43	2	no	—
246	#460	—	86	1	no	—
247	#459	—	43	2	no	—
248	#459	—	86	1	no	—
249	C₈×Q₈	—	43	2	no	—
250	C₈×D₄	—	43	2	no	—
251	C₈×D₄	—	86	2	no	—
252	#431	—	43	1	no	—
253	#431	—	86	1	no	—
254	#428	—	86	1	no	—
255	#423	—	43	1	no	—
256	#423	—	43	1	no	—
257	#418	—	86	1	no	—
258	#417	—	86	1	no	—
259	C₂×C₄×C₈	—	86	1	no	—
260	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
261	#334	—	43	4	no	—
262	#332	—	43	4	no	—
263	#331	—	43	4	no	—
264	C₄₃	#19266	1	1	yes	characteristic, complemented, Sylow
265	C₂×#41	—	43	1	no	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	AGL(1,ℤ/8)	—	172	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	4	8	no	—
274	C₂×SD₁₆	—	86	2	no	—
275	C₂×D₈	—	86	2	no	—
276	C₂×M₁₆	—	86	1	no	—
277	C₂×M₁₆	—	86	1	no	—
278	C₂²×C₈	—	86	2	no	—
279	C₂²×C₈	C₂²⋊D₄₃	1	2	yes	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	C₂²×D₄₃	1	2	yes	—
288	C₄×Q₈	—	43	1	no	—
289	C₄×Q₈	—	43	1	no	—
290	C₄×D₄	—	43	1	no	—
291	C₄×D₄	—	43	1	no	—
292	C₄×D₄	—	86	1	no	—
293	C₄×D₄	—	86	1	no	—
294	#117	—	43	1	no	—
295	#117	—	86	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄²	—	86	1	no	—
299	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
300	#107	—	86	2	no	—
301	#106	—	86	2	no	—
302	C₄⋊C₈	—	43	2	no	—
303	C₄⋊C₈	—	43	2	no	—
304	C₄⋊C₈	—	43	2	no	—
305	C₄⋊C₈	—	86	2	no	—
306	C₄⋊C₈	—	86	1	no	—
307	C₄⋊C₈	—	86	1	no	—
308	#103	—	86	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	#102	—	86	2	no	—
312	C₂²⋊C₈	—	86	1	no	—
313	C₂²⋊C₈	—	86	2	no	—
314	C₄×C₈	—	86	2	no	—
315	C₄×C₈	—	86	1	no	—
316	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
317	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
318	C₄×C₈	C₂²×D₄₃	1	2	yes	—
319	C₂⁴	—	4	1	no	—
320	#41	—	43	4	no	—
321	#41	—	86	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	4	4	no	—
324	C₂×Q₈	—	4	1	no	—
325	C₂×Q₈	—	43	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	8	2	no	—
336	C₂×D₄	—	43	1	no	—
337	C₂×D₄	—	86	1	no	—
338	C₂²×C₄	—	4	1	no	—
339	C₂²×C₄	—	86	1	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
343	C₂²×C₄	#10621900	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
345	SD₁₆	—	4	8	no	—
346	SD₁₆	—	4	8	no	—
347	SD₁₆	—	172	4	no	—
348	D₈	—	172	4	no	—
349	M₁₆	—	172	2	no	—
350	M₁₆	—	172	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	86	2	no	—
353	C₂×C₈	—	86	2	no	—
354	C₂×C₈	—	86	2	no	—
355	C₂×C₈	—	172	4	no	—
356	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
357	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	43	1	no	—
363	C₄⋊C₄	—	43	1	no	—
364	C₄⋊C₄	—	86	1	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₂²⋊C₄	—	86	1	no	—
367	C₂²⋊C₄	—	86	1	no	—
368	C₂²⋊C₄	—	86	1	no	—
369	C₄²	—	86	1	no	—
370	C₄²	—	86	1	no	—
371	C₄²	—	86	1	no	—
372	C₄²	D₄×D₄₃	1	1	yes	characteristic
373	C₄²	#10621900	1	1	yes	characteristic
374	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
375	C₄²	C₂³×D₄₃	1	1	yes	characteristic
376	C₂³	—	4	2	no	—
377	C₂³	—	8	2	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	86	1	no	—
381	C₂³	#13063296	1	1	yes	characteristic
382	Q₈	—	4	4	no	—
383	Q₈	—	8	2	no	—
384	Q₈	—	43	2	no	—
385	Q₈	—	86	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	4	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	43	2	no	—
394	D₄	—	86	4	no	—
395	D₄	—	86	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	4	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	1	no	—
404	C₂×C₄	—	172	2	no	—
405	C₂×C₄	—	172	2	no	—
406	C₂×C₄	#13063296	1	1	yes	characteristic
407	C₂×C₄	#13063296	1	1	yes	characteristic
408	C₂×C₄	#13063296	1	1	yes	characteristic
409	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
410	C₂×C₄	#13063346	1	2	yes	—
411	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	172	2	no	—
416	C₈	—	172	2	no	—
417	C₈	—	172	2	no	—
418	C₈	#13063351	1	4	yes	complemented
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	16	4	no	—
425	C₂²	—	86	2	no	—
426	C₂²	—	172	1	no	—
427	C₂²	—	172	1	no	—
428	C₂²	#14583125	1	2	yes	—
429	C₂²	C₂×#13063296	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	8	2	no	—
433	C₄	—	86	2	no	—
434	C₄	—	172	1	no	—
435	C₄	—	172	1	no	—
436	C₄	#14583125	1	2	yes	—
437	C₄	#14583159	1	2	yes	—
438	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
439	C₄	C₂×#13063346	1	1	yes	characteristic
440	C₄	C₂×#13063351	1	2	yes	—
441	C₂	—	2	2	no	—
442	C₂	—	16	2	no	—
443	C₂	—	172	2	no	—
444	C₂	#19144071	1	1	yes	characteristic
445	C₂	C₂×#14583125	1	1	yes	characteristic
446	C₂	C₂×#14583159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#492	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144071	C₂
hypercenter	C₂×#492	D₄₃
hypocenter	C₄₃	#19266
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. #19144404	C₂	semidirect
3. C₈×#10621898	C₂	semidirect
4. #19133940	C₂	semidirect
5. #19133933	C₂	semidirect
6. #19133351	C₂	semidirect
7. #19133280	C₂	semidirect
8. #19133263	C₂	semidirect
9. C₂×C₄₃×#492	C₂	semidirect
14. #14583181	C₂²	semidirect
15. #14583176	C₂²	semidirect
20. C₈×Dic₈₆	C₂²	semidirect
21. C₈×D₁₇₂	C₂²	semidirect
31. #14582650	C₂²	semidirect
32. #14582645	C₂²	semidirect
115. #10621898	SD₁₆	semidirect
184. D₁₇₂	C₂×SD₁₆	semidirect
189. Dic₈₆	C₂×SD₁₆	semidirect
191. C₈×C₄₃	AGL(1,ℤ/8)	semidirect
218. C₂×#492	D₄₃	semidirect
264. C₄₃	#19266	semidirect
418. C₈	#13063351	semidirect

Maximal subgroups

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

subgroup	index
#19144404	2
#19144071	2
C₈×#10621898	2
#19133940	2
#19133933	2
#19133351	2
#19133280	2
#19133263	2
C₂×C₄₃×#492	2
#19266	43