Subgroups — #25080097

Order 11008.

652 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145907	C₂	1	1	yes	maximal, characteristic
2	#19145520	C₂	1	1	yes	maximal, characteristic
3	#19143341	C₂	1	1	yes	maximal, characteristic
4	#19134105	C₂	1	2	yes	maximal, complemented
5	#19134091	C₂	1	2	yes	maximal, complemented
6	#19133981	C₂	1	2	yes	maximal, complemented
7	#19133967	C₂	1	2	yes	maximal, complemented
8	#19133347	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133252	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583273	—	2	1	no	—
15	#14583249	—	2	1	no	—
16	#14583186	C₂²	1	2	yes	—
17	#14583184	—	2	1	no	—
18	#14583130	—	2	2	no	—
19	#14583101	C₂²	1	2	yes	—
20	#14583101	C₂²	1	2	yes	—
21	#14583101	C₂²	1	2	yes	—
22	#14583099	—	2	1	no	—
23	#14583038	—	2	2	no	—
24	#14582978	C₂²	1	2	yes	—
25	#14582972	—	2	2	no	—
26	C₈×D₁₇₂	C₂²	1	2	yes	—
27	#14582952	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582867	—	2	1	no	—
31	#14582652	C₂²	1	2	yes	—
32	#14582650	C₂²	1	2	yes	—
33	#14582648	C₂²	1	1	yes	characteristic
34	#14582648	C₂²	1	1	yes	characteristic
35	#14582645	C₂²	1	2	yes	—
36	#14582645	C₂²	1	1	yes	characteristic
37	#14582645	C₂²	1	2	yes	—
38	#14582645	C₂²	1	1	yes	characteristic
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#501	—	2	2	no	—
42	C₄₃×#500	C₂²	1	2	yes	—
43	C₄₃×#498	C₂²	1	2	yes	—
44	C₄₃×#428	—	2	1	no	—
45	C₄₃×#428	—	2	1	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621884	—	2	2	no	—
49	C₂×#10621884	—	2	2	no	—
50	C₂×#10621884	—	2	2	no	—
51	#13063333	—	4	4	no	—
52	C₂×#10621872	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂×C₈×D₄₃	—	2	2	no	—
56	#13063325	D₄	1	1	yes	characteristic
57	#13063322	D₄	1	1	yes	characteristic
58	#13063313	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	#13063299	D₄	1	2	yes	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	C₂³	1	2	yes	—
63	#13063256	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
69	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	#13063249	—	2	2	no	—
72	#13063249	—	2	2	no	—
73	#13063249	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
76	(C₂×D₄₃)⋊C₈	—	2	2	no	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	C₄×C₄₃⋊C₈	—	2	1	no	—
79	C₂²×Q₈×C₄₃	—	2	1	no	—
80	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₃	—	2	1	no	—
83	C₄⋊Q₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	—	2	1	no	—
85	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
87	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	#125×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	C₂²⋊Q₈×C₄₃	—	2	1	no	—
91	C₄×Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	#117×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#107×C₄₃	—	2	2	no	—
98	#107×C₄₃	—	2	2	no	—
99	#106×C₄₃	—	2	2	no	—
100	#106×C₄₃	—	2	2	no	—
101	#97×C₄₃	D₄	1	2	yes	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	4	1	no	—
107	C₂×Q₈×C₄₃	—	8	1	no	—
108	C₂×Q₈×C₄₃	—	8	1	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	2	no	—
114	#10621898	—	4	2	no	—
115	#10621898	—	4	2	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
119	C₂×C₄×D₄₃	—	2	2	no	—
120	C₂×Dic₈₆	—	2	1	no	—
121	M₁₆×C₄₃	—	2	2	no	—
122	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
123	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	4	1	no	—
132	C₄⋊C₄×C₄₃	—	4	1	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₂²⋊C₄×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	#41	1	1	yes	characteristic
140	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
141	#10621884	—	8	2	no	—
142	#10621884	—	8	2	no	—
143	#10621884	—	8	2	no	—
144	(C₂×D₄₃)⋊C₄	—	2	2	no	—
145	(C₂×D₄₃)⋊C₄	—	2	2	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	C₂×C₄₃⋊C₈	—	4	2	no	—
154	C₂×C₄₃⋊C₈	—	8	1	no	—
155	#10621872	—	4	4	no	—
156	C₈×D₄₃	—	4	4	no	—
157	C₂³×C₄₃	#121	1	1	yes	characteristic
158	C₂²×D₄₃	—	2	2	no	—
159	Q₈×C₄₃	—	4	1	no	—
160	Q₈×C₄₃	—	4	2	no	—
161	Q₈×C₄₃	—	4	2	no	—
162	Q₈×C₄₃	—	4	1	no	—
163	Q₈×C₄₃	—	8	1	no	—
164	Q₈×C₄₃	—	8	2	no	—
165	C₂×C₄×C₄₃	—	2	1	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	8	2	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	#137	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	—	4	4	no	—
181	C₂×Dic₄₃	—	2	2	no	—
182	D₁₇₂	—	2	2	no	—
183	D₁₇₂	—	2	2	no	—
184	D₁₇₂	—	4	2	no	—
185	D₁₇₂	—	8	1	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	Dic₈₆	—	4	2	no	—
189	C₈×C₄₃	—	2	2	no	—
190	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
191	C₄₃⋊C₈	—	4	1	no	—
192	C₄₃⋊C₈	—	4	1	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	C₄₃⋊C₈	—	4	1	no	—
195	C₄₃⋊C₈	—	4	1	no	—
196	#19232	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	#461	1	2	yes	—
200	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
201	C₂×D₄₃	—	4	2	no	—
202	C₂×D₄₃	—	4	2	no	—
203	C₂×D₄₃	—	4	2	no	—
204	C₄×C₄₃	—	2	1	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	8	2	no	—
208	C₄×C₄₃	—	8	1	no	—
209	C₄×C₄₃	—	8	1	no	—
210	C₄×C₄₃	#461	1	2	yes	—
211	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
212	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
213	C₄×C₄₃	#576	1	1	yes	characteristic
214	C₄×C₄₃	#577	1	1	yes	characteristic
215	Dic₄₃	—	4	2	no	—
216	#3246	—	43	1	no	—
217	#3206	—	43	1	no	—
218	#3165	D₄₃	1	1	yes	characteristic, complemented
219	#2935	—	43	1	no	—
220	#1693	—	43	2	no	—
221	#1691	—	43	2	no	—
222	#1673	—	43	2	no	—
223	#1671	—	43	2	no	—
224	#1565	—	43	1	no	—
225	#1542	—	43	1	no	—
226	C₂×#332	—	43	1	no	—
227	C₂×C₄₃	—	2	2	no	—
228	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
229	C₂×C₄₃	#3062	1	1	yes	characteristic
230	C₂×C₄₃	#3069	1	1	yes	characteristic
231	D₄₃	—	8	2	no	—
232	C₂×#131	—	86	1	no	—
233	#533	C₂×D₄₃	1	1	yes	characteristic
234	#532	—	43	1	no	—
235	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
236	#501	—	2	2	no	—
237	#500	C₂×D₄₃	1	2	yes	—
238	#498	C₂×D₄₃	1	2	yes	—
239	#492	—	86	1	no	—
240	#487	—	86	1	no	—
241	#476	—	43	2	no	—
242	#475	—	86	1	no	—
243	#465	—	86	2	no	—
244	#461	—	43	2	no	—
245	#461	—	43	2	no	—
246	#461	—	43	2	no	—
247	#460	—	86	1	no	—
248	#448	—	86	2	no	—
249	#436	—	43	2	no	—
250	#435	—	86	2	no	—
251	C₈×D₄	—	43	2	no	—
252	#431	—	43	1	no	—
253	#428	—	2	1	no	—
254	#428	—	2	1	no	—
255	C₂×C₄⋊C₈	—	43	1	no	—
256	C₂×C₄⋊C₈	—	43	1	no	—
257	#408	—	86	1	no	—
258	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
259	#335	—	43	2	no	—
260	#334	—	43	2	no	—
261	#333	—	43	1	no	—
262	#333	—	43	1	no	—
263	#332	—	43	2	no	—
264	#332	—	43	2	no	—
265	#332	—	43	1	no	—
266	#332	—	43	1	no	—
267	C₄₃	#19232	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	86	1	no	—
269	C₂²×Q₈	—	2	1	no	—
270	C₂×SD₁₆	—	86	2	no	—
271	C₂×SD₁₆	—	86	2	no	—
272	C₂×SD₁₆	—	86	2	no	—
273	#131	—	172	4	no	—
274	C₂×M₁₆	—	86	2	no	—
275	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
276	C₂×M₁₆	C₂²⋊D₄₃	1	1	yes	characteristic
277	C₂²×C₈	—	86	1	no	—
278	C₂²×C₈	—	86	1	no	—
279	C₂²×C₈	—	86	2	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	1	no	—
283	C₄⋊Q₈	—	43	1	no	—
284	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
285	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
286	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
287	#127	—	43	1	no	—
288	#125	—	2	1	no	—
289	#124	—	86	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	43	2	no	—
293	#121	—	86	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	43	2	no	—
297	C₄×D₄	—	86	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#107	—	2	2	no	—
304	#106	—	2	2	no	—
305	#106	—	2	2	no	—
306	#106	—	86	2	no	—
307	C₄⋊C₈	—	43	1	no	—
308	C₄⋊C₈	—	43	1	no	—
309	C₄⋊C₈	—	43	2	no	—
310	C₄⋊C₈	—	43	1	no	—
311	C₄⋊C₈	—	43	1	no	—
312	C₄⋊C₈	—	86	1	no	—
313	C₄⋊C₈	—	86	1	no	—
314	#103	—	86	2	no	—
315	#103	—	86	2	no	—
316	#103	—	86	2	no	—
317	#102	—	86	2	no	—
318	C₂²⋊C₈	—	86	1	no	—
319	C₂²⋊C₈	—	86	2	no	—
320	C₂²⋊C₈	—	86	2	no	—
321	#97	C₂²⋊D₄₃	1	2	yes	—
322	C₄×C₈	—	86	1	no	—
323	C₄×C₈	C₂²×D₄₃	1	2	yes	—
324	#41	—	172	2	no	—
325	#41	—	172	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	4	1	no	—
330	C₂×Q₈	—	8	1	no	—
331	C₂×Q₈	—	8	1	no	—
332	C₂×Q₈	—	86	1	no	—
333	C₂×D₄	—	43	2	no	—
334	C₂×D₄	—	86	2	no	—
335	C₂×D₄	—	86	1	no	—
336	C₂×D₄	—	86	1	no	—
337	C₂²×C₄	—	4	1	no	—
338	C₂²×C₄	—	86	2	no	—
339	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	#10621900	1	1	yes	characteristic
341	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
342	SD₁₆	—	344	2	no	—
343	SD₁₆	—	344	2	no	—
344	SD₁₆	—	344	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	172	4	no	—
347	M₁₆	#10621884	1	4	yes	complemented
348	C₂×C₈	—	86	1	no	—
349	C₂×C₈	—	86	1	no	—
350	C₂×C₈	—	86	2	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	—	86	1	no	—
353	C₂×C₈	—	344	1	no	—
354	C₂×C₈	—	172	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	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	4	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	43	2	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	86	2	no	—
372	C₂²⋊C₄	—	86	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	D₄×D₄₃	1	1	yes	characteristic
375	C₄²	#10621900	1	1	yes	characteristic
376	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
377	C₄²	C₂³×D₄₃	1	1	yes	characteristic
378	C₂³	—	86	2	no	—
379	C₂³	#13063296	1	1	yes	characteristic
380	Q₈	—	4	1	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	8	1	no	—
385	Q₈	—	8	2	no	—
386	Q₈	—	172	2	no	—
387	D₄	—	86	2	no	—
388	D₄	—	86	2	no	—
389	D₄	—	344	1	no	—
390	D₄	—	172	4	no	—
391	D₄	—	172	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	86	2	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	#13063296	1	1	yes	characteristic
403	C₂×C₄	#13063296	1	1	yes	characteristic
404	C₂×C₄	#13063296	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621884	1	2	yes	—
406	C₂×C₄	#13063356	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	172	1	no	—
412	C₈	—	172	1	no	—
413	C₈	—	172	2	no	—
414	C₈	—	172	1	no	—
415	C₈	—	172	1	no	—
416	C₈	C₂×#10621884	1	4	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	172	2	no	—
420	C₂²	—	172	2	no	—
421	C₂²	—	172	2	no	—
422	C₂²	#14583101	1	2	yes	—
423	C₂²	C₂×#13063296	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	2	no	—
428	C₄	—	8	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	172	2	no	—
431	C₄	#14583101	1	2	yes	—
432	C₄	C₂²×#10621884	1	1	yes	characteristic
433	C₄	C₂×#13063356	1	1	yes	characteristic
434	C₄	#14583703	1	1	yes	characteristic
435	C₄	#14583709	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	344	2	no	—
438	C₂	C₂×#14583101	1	1	yes	characteristic
439	C₂	#19144269	1	1	yes	characteristic
440	C₂	#19144328	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3165	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#3165	D₄₃
hypocenter	C₄₃	#19232
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
4. #19134105	C₂	semidirect
5. #19134091	C₂	semidirect
6. #19133981	C₂	semidirect
7. #19133967	C₂	semidirect
8. #19133347	C₂	semidirect
9. #19133252	C₂	semidirect
10. C₂×#14582645	C₂	semidirect
11. C₄₃×#3165	C₂	semidirect
122. M₁₆×C₄₃	SD₁₆	semidirect
218. #3165	D₄₃	semidirect
267. C₄₃	#19232	semidirect
347. M₁₆	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145907	2
#19145520	2
#19143341	2
#19134105	2
#19134091	2
#19133981	2
#19133967	2
#19133347	2
#19133252	2
C₂×#14582645	2
C₄₃×#3165	2
#19232	43