Subgroups — #25080022

Order 11008.

630 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145567	C₂	1	2	yes	maximal, complemented
2	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
3	#19134113	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134108	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134079	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134074	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134039	C₂	1	2	yes	maximal, complemented
8	#19134032	C₂	1	2	yes	maximal, complemented
9	#19133343	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133301	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	2	yes	—
13	#14583304	C₂²	1	1	yes	characteristic
14	#14583281	—	2	2	no	—
15	#14583276	C₂²	1	1	yes	characteristic
16	#14583256	—	2	2	no	—
17	#14583246	C₂²	1	2	yes	—
18	#14583135	—	2	1	no	—
19	#14583135	—	2	1	no	—
20	#14583109	C₂²	1	2	yes	—
21	#14583104	C₂²	1	2	yes	—
22	#14583099	C₂²	1	2	yes	—
23	#14583094	C₂²	1	2	yes	—
24	#14583059	—	2	2	no	—
25	#14583042	—	2	2	no	—
26	C₄×D₃₄₄	—	2	1	no	—
27	C₄×D₃₄₄	—	2	1	no	—
28	#14582952	C₂²	1	2	yes	—
29	#14582652	C₂²	1	2	yes	—
30	#14582650	C₂²	1	1	yes	characteristic
31	#14582650	C₂²	1	1	yes	characteristic
32	#14582644	C₂²	1	2	yes	—
33	#14582644	C₂²	1	2	yes	—
34	#14582642	C₂²	1	2	yes	—
35	#14582642	C₂²	1	2	yes	—
36	C₄₃×#529	C₂²	1	1	yes	characteristic
37	C₄₃×#446	C₂²	1	1	yes	characteristic
38	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#436	C₂²	1	1	yes	characteristic
40	C₄₃×#435	—	2	1	no	—
41	C₈×D₄×C₄₃	—	2	1	no	—
42	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#433	—	2	1	no	—
44	C₄₃×#432	C₂²	1	1	yes	characteristic
45	C₄₃×#405	—	2	1	no	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	2	no	—
48	C₂×#10621885	—	2	2	no	—
49	C₂×#10621883	—	2	2	no	—
50	C₂×#10621884	—	2	2	no	—
51	C₂×D₃₄₄	—	2	1	no	—
52	C₂×D₃₄₄	—	2	1	no	—
53	C₂×#10621882	—	2	2	no	—
54	#13063325	C₂³	1	2	yes	—
55	#13063322	C₂³	1	2	yes	—
56	#13063313	—	2	2	no	—
57	#13063299	—	2	2	no	—
58	#13063299	—	2	2	no	—
59	C₄×D₁₇₂	—	2	2	no	—
60	C₄×D₁₇₂	—	2	2	no	—
61	#13063259	—	2	1	no	—
62	#13063259	—	2	1	no	—
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
65	#13063248	—	2	2	no	—
66	#13063248	—	2	2	no	—
67	#13063247	—	2	2	no	—
68	#13063247	—	2	2	no	—
69	#13063245	—	2	2	no	—
70	#13063245	—	2	2	no	—
71	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
72	C₄×C₄₃⋊C₈	—	2	2	no	—
73	C₂×M₁₆×C₄₃	—	2	1	no	—
74	C₂²×C₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
77	#126×C₄₃	—	2	1	no	—
78	#125×C₄₃	D₄	1	1	yes	characteristic
79	#124×C₄₃	D₄	1	1	yes	characteristic
80	#123×C₄₃	—	2	1	no	—
81	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
82	#121×C₄₃	D₄	1	1	yes	characteristic
83	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×D₄×C₄₃	—	2	1	no	—
85	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
86	#117×C₄₃	—	2	1	no	—
87	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₃	—	2	1	no	—
89	C₄⋊C₈×C₄₃	—	2	1	no	—
90	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²⋊C₈×C₄₃	—	2	1	no	—
93	C₂²⋊C₈×C₄₃	—	2	1	no	—
94	C₂²⋊C₈×C₄₃	—	2	1	no	—
95	#97×C₄₃	—	2	1	no	—
96	#97×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	—	2	1	no	—
98	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₃	—	4	2	no	—
110	#10621898	—	8	2	no	—
111	#10621898	—	8	2	no	—
112	C₂×D₁₇₂	—	2	2	no	—
113	C₂×D₁₇₂	—	2	2	no	—
114	C₂×D₁₇₂	—	2	2	no	—
115	C₂×C₄×D₄₃	—	4	2	no	—
116	C₂×Dic₈₆	—	2	2	no	—
117	M₁₆×C₄₃	—	4	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	4	1	no	—
122	C₂×C₈×C₄₃	—	4	2	no	—
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₄₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₄₃	—	2	1	no	—
134	C₂²⋊C₄×C₄₃	—	2	1	no	—
135	C₂²⋊C₄×C₄₃	—	2	1	no	—
136	C₂²⋊C₄×C₄₃	—	2	1	no	—
137	C₂²⋊C₄×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	—	2	1	no	—
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	#10621885	—	8	2	no	—
144	#10621884	—	8	2	no	—
145	#10621883	—	8	2	no	—
146	#10621882	—	8	2	no	—
147	(C₂×D₄₃)⋊C₄	—	4	2	no	—
148	(C₂×D₄₃)⋊C₄	—	4	2	no	—
149	C₄⋊Dic₄₃	—	2	2	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	—	2	2	no	—
153	D₃₄₄	—	4	2	no	—
154	D₃₄₄	—	4	2	no	—
155	C₂³×C₄₃	—	2	1	no	—
156	C₂³×C₄₃	#121	1	1	yes	characteristic
157	C₂²×D₄₃	—	4	2	no	—
158	Q₈×C₄₃	—	2	2	no	—
159	D₄×C₄₃	—	2	2	no	—
160	D₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	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	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₄₃	—	8	4	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	4	2	no	—
182	D₁₇₂	—	8	2	no	—
183	C₄×D₄₃	—	8	4	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	4	2	no	—
186	C₈×C₄₃	—	2	1	no	—
187	C₈×C₄₃	—	2	1	no	—
188	C₈×C₄₃	—	2	1	no	—
189	C₈×C₄₃	—	4	1	no	—
190	C₈×C₄₃	—	4	1	no	—
191	C₈×C₄₃	#135	1	2	yes	—
192	C₄₃⋊C₈	—	4	2	no	—
193	C₄₃⋊C₈	—	4	2	no	—
194	#19225	—	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	—	4	1	no	—
199	C₂²×C₄₃	—	4	1	no	—
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
202	C₂×D₄₃	—	8	2	no	—
203	C₂×D₄₃	—	8	2	no	—
204	C₂×D₄₃	—	8	2	no	—
205	C₄×C₄₃	—	2	1	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	4	1	no	—
210	C₄×C₄₃	—	4	1	no	—
211	C₄×C₄₃	—	4	1	no	—
212	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
213	C₄×C₄₃	#575	1	1	yes	characteristic
214	C₄×C₄₃	#576	1	2	yes	—
215	Dic₄₃	—	8	2	no	—
216	#3212	—	43	2	no	—
217	#3169	—	43	1	no	—
218	#2966	D₄₃	1	1	yes	characteristic, complemented
219	#1694	—	43	1	no	—
220	#1693	—	43	1	no	—
221	#1688	—	43	1	no	—
222	#1687	—	43	1	no	—
223	#1682	—	43	2	no	—
224	#1681	—	43	2	no	—
225	#1564	—	43	1	no	—
226	#1553	—	43	2	no	—
227	C₂×C₄₃	—	4	1	no	—
228	C₂×C₄₃	—	8	1	no	—
229	C₂×C₄₃	#3035	1	1	yes	characteristic
230	C₂×C₄₃	#3058	1	1	yes	characteristic
231	C₂×C₄₃	#3067	1	1	yes	characteristic
232	D₄₃	—	16	2	no	—
233	#532	—	43	2	no	—
234	#529	C₂×D₄₃	1	1	yes	characteristic
235	#500	—	43	1	no	—
236	#495	—	86	2	no	—
237	#493	—	43	1	no	—
238	#488	—	86	2	no	—
239	#486	—	43	2	no	—
240	#466	—	86	1	no	—
241	#466	—	86	1	no	—
242	#462	—	43	2	no	—
243	#461	—	43	2	no	—
244	#460	—	43	2	no	—
245	#459	—	43	2	no	—
246	#452	—	86	2	no	—
247	#449	—	86	2	no	—
248	#446	C₂×D₄₃	1	1	yes	characteristic
249	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
250	C₄×D₈	—	86	1	no	—
251	C₄×D₈	—	86	1	no	—
252	#436	C₂×D₄₃	1	1	yes	characteristic
253	#435	—	2	1	no	—
254	C₈×D₄	—	2	1	no	—
255	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
256	#433	—	2	1	no	—
257	#432	C₂×D₄₃	1	1	yes	characteristic
258	#431	—	43	2	no	—
259	#405	—	2	1	no	—
260	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
261	#335	—	43	2	no	—
262	#334	—	43	1	no	—
263	#334	—	43	1	no	—
264	#332	—	43	2	no	—
265	#332	—	43	2	no	—
266	#331	—	43	2	no	—
267	#331	—	43	2	no	—
268	C₄₃	#19225	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	86	2	no	—
270	C₂×Q₁₆	—	86	2	no	—
271	C₂×SD₁₆	—	86	2	no	—
272	C₂×SD₁₆	—	86	2	no	—
273	C₂×D₈	—	86	2	no	—
274	C₂×D₈	—	86	1	no	—
275	C₂×D₈	—	86	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
279	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
280	C₄⋊Q₈	—	43	2	no	—
281	#127	—	43	2	no	—
282	#126	—	2	1	no	—
283	#125	D₁₇₂	1	1	yes	characteristic
284	#124	—	86	2	no	—
285	#124	D₁₇₂	1	1	yes	characteristic
286	#123	—	2	1	no	—
287	C₂²⋊Q₈	D₁₇₂	1	1	yes	characteristic
288	#121	—	86	2	no	—
289	#121	—	86	2	no	—
290	#121	D₁₇₂	1	1	yes	characteristic
291	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	—	86	2	no	—
294	C₄×D₄	—	86	2	no	—
295	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
298	#107	—	86	1	no	—
299	#107	—	86	1	no	—
300	C₄⋊C₈	—	2	1	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	43	2	no	—
303	C₄⋊C₈	—	43	2	no	—
304	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
306	#103	—	86	2	no	—
307	#103	—	86	2	no	—
308	#102	—	86	2	no	—
309	#102	—	86	2	no	—
310	#102	—	86	2	no	—
311	#102	—	86	2	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	86	2	no	—
316	#97	—	2	1	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	86	2	no	—
320	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
321	C₄×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
324	#41	—	344	2	no	—
325	#41	—	344	2	no	—
326	C₂×Q₈	—	86	2	no	—
327	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	86	2	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂×D₄	—	86	2	no	—
332	C₂×D₄	—	172	2	no	—
333	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	172	2	no	—
336	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
337	C₂²×C₄	#10621898	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
339	Q₁₆	—	344	2	no	—
340	SD₁₆	—	344	2	no	—
341	SD₁₆	—	344	2	no	—
342	D₈	—	344	2	no	—
343	D₈	—	172	2	no	—
344	D₈	—	172	2	no	—
345	M₁₆	—	4	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	86	2	no	—
352	C₂×C₈	—	86	2	no	—
353	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
354	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
355	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	86	2	no	—
362	C₄⋊C₄	—	86	2	no	—
363	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
364	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	2	1	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	172	2	no	—
371	C₂²⋊C₄	—	172	2	no	—
372	C₄²	—	2	1	no	—
373	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
374	C₄²	#10621898	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
376	C₄²	C₂³×D₄₃	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	—	172	2	no	—
379	C₂³	#13063299	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	172	2	no	—
382	Q₈	—	172	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	344	2	no	—
386	D₄	—	344	4	no	—
387	D₄	—	172	2	no	—
388	D₄	—	172	2	no	—
389	D₄	—	172	2	no	—
390	D₄	—	172	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	344	4	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	#13063299	1	1	yes	characteristic
403	C₂×C₄	#13063299	1	1	yes	characteristic
404	C₂×C₄	#13063299	1	1	yes	characteristic
405	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
407	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
408	C₈	—	2	1	no	—
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	172	2	no	—
414	C₈	—	172	2	no	—
415	C₈	#13063345	1	2	yes	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	344	2	no	—
423	C₂²	—	344	2	no	—
424	C₂²	—	344	2	no	—
425	C₂²	C₂×#13063299	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	344	2	no	—
434	C₄	C₂×#13063345	1	1	yes	characteristic
435	C₄	#14583697	1	1	yes	characteristic
436	C₄	#14583704	1	2	yes	—
437	C₂	—	4	1	no	—
438	C₂	—	8	1	no	—
439	C₂	—	688	2	no	—
440	C₂	#19144050	1	1	yes	characteristic
441	C₂	#19144243	1	1	yes	characteristic
442	C₂	#19144315	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063299
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2966	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	#2966	D₄₃
hypocenter	C₄₃	#19225
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #19145567	C₂	semidirect
2. #19145174	C₂	semidirect
3. #19134113	C₂	semidirect
4. #19134108	C₂	semidirect
5. #19134079	C₂	semidirect
6. #19134074	C₂	semidirect
7. #19134039	C₂	semidirect
8. #19134032	C₂	semidirect
9. #19133343	C₂	semidirect
10. #19133301	C₂	semidirect
11. C₄₃×#2966	C₂	semidirect
218. #2966	D₄₃	semidirect
268. C₄₃	#19225	semidirect

Maximal subgroups

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

subgroup	index
#19145567	2
#19145174	2
#19134113	2
#19134108	2
#19134079	2
#19134074	2
#19134039	2
#19134032	2
#19133343	2
#19133301	2
C₄₃×#2966	2
#19225	43