Subgroups — #25081800

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144682	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144591	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143618	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134043	C₂	1	2	yes	maximal, complemented
5	#19134001	C₂	1	2	yes	maximal, complemented
6	#19133947	C₂	1	2	yes	maximal, complemented
7	#19133933	C₂	1	2	yes	maximal, complemented
8	#19133375	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133300	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133257	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
13	#14583215	—	2	1	no	—
14	#14583210	—	2	1	no	—
15	#14583186	C₂²	1	2	yes	—
16	#14583176	C₂²	1	2	yes	—
17	#14583091	C₂²	1	2	yes	—
18	#14583091	C₂²	1	2	yes	—
19	#14583032	—	2	1	no	—
20	#14583032	—	2	1	no	—
21	#14583009	—	2	2	no	—
22	C₄×#10621882	—	2	2	no	—
23	C₈×D₁₇₂	C₂²	1	2	yes	—
24	C₈×D₁₇₂	C₂²	1	2	yes	—
25	#14582964	—	2	2	no	—
26	#14582956	C₂²	1	1	yes	characteristic
27	#14582952	C₂²	1	1	yes	characteristic
28	#14582952	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₄₃	—	2	2	no	—
30	#14582652	C₂²	1	2	yes	complemented
31	#14582650	C₂²	1	2	yes	complemented
32	#14582648	C₂²	1	2	yes	complemented
33	#14582645	C₂²	1	2	yes	complemented
34	#14582643	C₂²	1	2	yes	complemented
35	#14582643	C₂²	1	2	yes	complemented
36	C₄₃×#532	C₂²	1	1	yes	characteristic
37	C₄₃×#532	C₂²	1	1	yes	characteristic
38	C₄₃×#493	C₂²	1	1	yes	characteristic, complemented
39	C₄₃×#492	C₂²	1	1	yes	characteristic, complemented
40	C₄₃×#487	C₂²	1	1	yes	characteristic, complemented
41	C₄₃×#486	C₂²	1	1	yes	characteristic, complemented
42	C₄₃×#463	—	2	2	no	—
43	C₄₃×#449	—	2	2	no	—
44	C₄₃×#431	C₂²	1	1	yes	characteristic
45	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₃	—	2	1	no	—
47	C₂×#10621882	—	2	2	no	—
48	C₂×#10621882	—	2	2	no	—
49	C₂×C₈×D₄₃	—	2	2	no	—
50	C₂×C₈×D₄₃	—	2	2	no	—
51	C₄×D₁₇₂	—	2	1	no	—
52	C₄×D₁₇₂	—	2	1	no	—
53	C₄×D₁₇₂	D₄	1	2	yes	—
54	C₄×D₁₇₂	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
57	#13063258	—	2	2	no	—
58	#13063256	—	2	2	no	—
59	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
62	#13063246	—	2	2	no	—
63	#13063246	—	2	2	no	—
64	#13063245	—	2	2	no	—
65	#13063245	—	2	2	no	—
66	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
67	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
69	(C₂×D₄₃)⋊C₈	—	2	2	no	—
70	(C₂×D₄₃)⋊C₈	—	2	2	no	—
71	#13063236	—	2	1	no	—
72	C₄×C₄₃⋊C₈	—	2	1	no	—
73	C₄×C₄₃⋊C₈	—	2	1	no	—
74	C₂×#41×C₄₃	—	2	1	no	—
75	C₂×#41×C₄₃	—	2	1	no	—
76	C₂×SD₁₆×C₄₃	—	2	2	no	—
77	C₂×D₈×C₄₃	—	2	2	no	—
78	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
80	#127×C₄₃	C₂³	1	1	yes	characteristic
81	#127×C₄₃	C₂³	1	1	yes	characteristic
82	#124×C₄₃	—	2	1	no	—
83	#124×C₄₃	—	2	1	no	—
84	#121×C₄₃	—	2	1	no	—
85	#121×C₄₃	—	2	1	no	—
86	#121×C₄₃	—	2	1	no	—
87	#121×C₄₃	—	2	1	no	—
88	C₄×D₄×C₄₃	—	2	1	no	—
89	C₄×D₄×C₄₃	—	2	1	no	—
90	C₄×D₄×C₄₃	—	2	1	no	—
91	C₄×D₄×C₄₃	—	2	1	no	—
92	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
94	#103×C₄₃	—	2	2	no	—
95	#102×C₄₃	—	2	2	no	—
96	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂³×D₄₃	—	2	1	no	—
100	#41×C₄₃	—	8	2	no	—
101	#41×C₄₃	—	8	2	no	—
102	C₂×Q₈×C₄₃	—	2	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	4	1	no	—
111	C₂×D₄×C₄₃	—	4	1	no	—
112	C₂²×C₄×C₄₃	—	4	1	no	—
113	C₂²×C₄×C₄₃	—	4	1	no	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂²×Dic₄₃	—	2	1	no	—
118	C₂×D₁₇₂	—	2	1	no	—
119	C₂×D₁₇₂	—	2	4	no	—
120	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
121	C₂×C₄×D₄₃	—	2	2	no	—
122	C₂×C₄×D₄₃	—	2	2	no	—
123	C₂×C₄×D₄₃	—	8	2	no	—
124	SD₁₆×C₄₃	—	8	2	no	—
125	D₈×C₄₃	—	8	2	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₂²⋊C₄×C₄₃	—	4	1	no	—
133	C₂²⋊C₄×C₄₃	—	4	1	no	—
134	C₂²⋊C₄×C₄₃	—	4	1	no	—
135	C₂²⋊C₄×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	#41	1	1	yes	characteristic
139	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
140	#10621882	—	4	4	no	—
141	#10621882	—	4	4	no	—
142	(C₂×D₄₃)⋊C₄	—	2	2	no	—
143	(C₂×D₄₃)⋊C₄	—	2	2	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	—	2	2	no	—
147	C₂×C₄₃⋊C₈	—	2	2	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	C₈×D₄₃	—	8	2	no	—
150	C₈×D₄₃	—	8	2	no	—
151	C₂³×C₄₃	—	4	1	no	—
152	C₂³×C₄₃	—	4	1	no	—
153	C₂³×C₄₃	#121	1	1	yes	characteristic
154	C₂²×D₄₃	—	2	2	no	—
155	C₂²×D₄₃	—	2	4	no	—
156	C₂²×D₄₃	—	8	1	no	—
157	C₂²×D₄₃	—	8	1	no	—
158	Q₈×C₄₃	—	4	2	no	—
159	Q₈×C₄₃	—	8	1	no	—
160	D₄×C₄₃	—	4	2	no	—
161	D₄×C₄₃	—	4	2	no	—
162	D₄×C₄₃	—	4	2	no	—
163	D₄×C₄₃	—	4	2	no	—
164	D₄×C₄₃	—	8	1	no	—
165	D₄×C₄₃	—	8	1	no	—
166	D₄×C₄₃	—	8	2	no	—
167	D₄×C₄₃	—	8	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	8	2	no	—
174	C₂×C₄×C₄₃	—	8	2	no	—
175	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₃	—	2	2	no	—
182	C₂×Dic₄₃	—	8	1	no	—
183	D₁₇₂	—	2	4	no	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	#135	1	4	yes	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	8	2	no	—
189	C₈×C₄₃	—	2	2	no	—
190	C₈×C₄₃	—	2	2	no	—
191	C₄₃⋊C₈	—	4	2	no	—
192	C₄₃⋊C₈	—	4	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	#19389	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	8	1	no	—
199	C₂²×C₄₃	—	8	1	no	—
200	C₂²×C₄₃	—	8	1	no	—
201	C₂²×C₄₃	—	8	1	no	—
202	C₂²×C₄₃	—	8	1	no	—
203	C₂²×C₄₃	—	8	1	no	—
204	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
205	C₂×D₄₃	—	2	4	no	—
206	C₂×D₄₃	—	4	2	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₂×D₄₃	—	8	4	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	8	1	no	—
214	C₄×C₄₃	—	8	1	no	—
215	C₄×C₄₃	C₂×#135	1	2	yes	—
216	C₄×C₄₃	#576	1	2	yes	—
217	Dic₄₃	—	4	2	no	—
218	#3207	D₄₃	1	1	yes	characteristic, complemented
219	#3109	—	43	1	no	—
220	#3100	—	43	1	no	—
221	#2972	—	43	1	no	—
222	#1683	—	43	2	no	—
223	#1677	—	43	2	no	—
224	#1667	—	43	2	no	—
225	#1665	—	43	2	no	—
226	#1572	—	43	1	no	—
227	#1553	—	43	1	no	—
228	#1543	—	43	1	no	—
229	C₂×C₄₃	—	4	1	no	—
230	C₂×C₄₃	—	16	1	no	—
231	C₂×C₄₃	—	16	1	no	—
232	C₂×C₄₃	#3041	1	1	yes	characteristic
233	C₂×C₄₃	#3050	1	1	yes	characteristic
234	C₂×C₄₃	#3068	1	1	yes	characteristic
235	D₄₃	—	4	4	no	—
236	#532	C₂×D₄₃	1	1	yes	characteristic
237	#532	C₂×D₄₃	1	1	yes	characteristic
238	C₂×C₄×D₄	—	43	1	no	—
239	#493	C₂×D₄₃	1	1	yes	characteristic, complemented
240	#492	C₂×D₄₃	1	1	yes	characteristic, complemented
241	#487	C₂×D₄₃	1	1	yes	characteristic, complemented
242	#486	C₂×D₄₃	1	1	yes	characteristic, complemented
243	#481	—	86	1	no	—
244	#480	—	86	1	no	—
245	#476	—	43	2	no	—
246	#474	—	43	2	no	—
247	#463	—	2	2	no	—
248	#459	—	43	2	no	—
249	#459	—	43	2	no	—
250	#449	—	2	2	no	—
251	#447	—	86	1	no	—
252	#447	—	86	1	no	—
253	#442	—	86	2	no	—
254	C₄×D₈	—	86	2	no	—
255	C₈×D₄	—	43	2	no	—
256	C₈×D₄	—	43	2	no	—
257	C₈×D₄	—	86	2	no	—
258	#432	—	43	1	no	—
259	#431	—	43	1	no	—
260	#431	—	43	1	no	—
261	#431	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₂²⋊C₈	—	86	2	no	—
263	#335	—	43	2	no	—
264	#334	—	43	2	no	—
265	#333	—	43	2	no	—
266	#332	—	43	2	no	—
267	#331	—	43	2	no	—
268	#331	—	43	2	no	—
269	C₄₃	#19389	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	2	1	no	—
271	C₂×#41	—	2	1	no	—
272	C₂²×D₄	—	43	1	no	—
273	C₂³×C₄	—	86	1	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×D₈	—	2	2	no	—
276	C₂×D₈	—	86	2	no	—
277	C₂×D₈	—	86	2	no	—
278	C₂²×C₈	—	86	2	no	—
279	C₂²×C₈	—	86	2	no	—
280	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
281	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
282	#127	C₂²×D₄₃	1	1	yes	characteristic
283	#127	C₂²×D₄₃	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#124	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	—	2	1	no	—
288	#121	—	2	1	no	—
289	#121	—	2	1	no	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	2	1	no	—
294	C₄×D₄	—	43	2	no	—
295	C₄×D₄	—	43	2	no	—
296	C₄×D₄	—	86	1	no	—
297	C₄×D₄	—	86	1	no	—
298	C₂×C₄⋊C₄	—	43	1	no	—
299	C₂×C₂²⋊C₄	—	86	1	no	—
300	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
301	#107	—	86	2	no	—
302	#106	—	86	2	no	—
303	C₄⋊C₈	—	43	2	no	—
304	C₄⋊C₈	—	43	2	no	—
305	C₄⋊C₈	—	43	2	no	—
306	C₄⋊C₈	C₂²⋊D₄₃	1	2	yes	—
307	#103	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	#102	—	86	2	no	—
312	#102	—	86	2	no	—
313	C₂²⋊C₈	—	86	1	no	—
314	C₂²⋊C₈	—	86	1	no	—
315	C₂²⋊C₈	—	86	1	no	—
316	C₂²⋊C₈	—	86	2	no	—
317	C₂²⋊C₈	—	86	2	no	—
318	C₂²⋊C₈	C₂²⋊D₄₃	1	2	yes	—
319	#97	—	86	1	no	—
320	C₄×C₈	—	86	1	no	—
321	C₄×C₈	—	86	1	no	—
322	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
324	C₂⁴	—	86	1	no	—
325	#41	—	8	2	no	—
326	#41	—	8	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	43	2	no	—
338	C₂×D₄	—	86	4	no	—
339	C₂×D₄	—	86	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	2	no	—
344	C₂²×C₄	—	86	2	no	—
345	C₂²×C₄	—	344	2	no	—
346	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	#10621900	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
349	SD₁₆	—	8	2	no	—
350	D₈	—	8	2	no	—
351	D₈	—	172	4	no	—
352	D₈	—	172	4	no	—
353	C₂×C₈	—	86	2	no	—
354	C₂×C₈	—	86	2	no	—
355	C₂×C₈	—	86	2	no	—
356	C₂×C₈	—	344	2	no	—
357	C₂×C₈	—	344	2	no	—
358	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
359	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	43	2	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	1	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	86	2	no	—
371	C₂²⋊C₄	—	86	2	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	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	86	4	no	—
379	C₂³	—	86	2	no	—
380	C₂³	—	344	1	no	—
381	C₂³	—	344	1	no	—
382	C₂³	#13063296	1	1	yes	characteristic
383	Q₈	—	4	2	no	—
384	Q₈	—	8	1	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	1	no	—
390	D₄	—	8	1	no	—
391	D₄	—	8	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	43	4	no	—
394	D₄	—	86	4	no	—
395	D₄	—	86	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	344	2	no	—
405	C₂×C₄	—	344	1	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	#13063296	1	1	yes	characteristic
409	C₂×C₄	#13063296	1	1	yes	characteristic
410	C₂×C₄	#13063296	1	1	yes	characteristic
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	—	2	2	no	—
416	C₈	—	172	2	no	—
417	C₈	—	172	2	no	—
418	C₈	—	172	2	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	86	4	no	—
429	C₂²	—	344	4	no	—
430	C₂²	—	172	2	no	—
431	C₂²	—	172	2	no	—
432	C₂²	C₂×#13063296	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	8	1	no	—
439	C₄	—	172	2	no	—
440	C₄	#135×D₄₃	1	2	yes	—
441	C₄	#14583702	1	2	yes	—
442	C₂	—	4	1	no	—
443	C₂	—	16	1	no	—
444	C₂	—	16	1	no	—
445	C₂	—	172	4	no	—
446	C₂	#19144094	1	1	yes	characteristic
447	C₂	#19144172	1	1	yes	characteristic
448	C₂	#19144319	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063296
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3207	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#3207	D₄₃
hypocenter	C₄₃	#19389
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3207

Complements

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

N	H ≅ G/N	type
1. #19144682	C₂	semidirect
2. #19144591	C₂	semidirect
3. #19143618	C₂	semidirect
4. #19134043	C₂	semidirect
5. #19134001	C₂	semidirect
6. #19133947	C₂	semidirect
7. #19133933	C₂	semidirect
8. #19133375	C₂	semidirect
9. #19133300	C₂	semidirect
10. #19133257	C₂	semidirect
11. C₄₃×#3207	C₂	semidirect
30. #14582652	C₂²	semidirect
31. #14582650	C₂²	semidirect
32. #14582648	C₂²	semidirect
33. #14582645	C₂²	semidirect
34. #14582643	C₂²	semidirect
35. #14582643	C₂²	semidirect
38. C₄₃×#493	C₂²	semidirect
39. C₄₃×#492	C₂²	semidirect
40. C₄₃×#487	C₂²	semidirect
41. C₄₃×#486	C₂²	semidirect
218. #3207	D₄₃	semidirect
239. #493	C₂×D₄₃	semidirect
240. #492	C₂×D₄₃	semidirect
241. #487	C₂×D₄₃	semidirect
242. #486	C₂×D₄₃	semidirect
269. C₄₃	#19389	semidirect

Maximal subgroups

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

subgroup	index
#19144682	2
#19144591	2
#19143618	2
#19134043	2
#19134001	2
#19133947	2
#19133933	2
#19133375	2
#19133300	2
#19133257	2
C₄₃×#3207	2
#19389	43