Subgroups — #25079987

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145922	C₂	1	2	yes	maximal, complemented
2	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134136	C₂	1	2	yes	maximal, complemented
5	#19134129	C₂	1	2	yes	maximal, complemented
6	#19134000	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133995	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133956	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133951	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133288	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#335	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	2	yes	—
13	#14583433	C₂²	1	1	yes	characteristic
14	#14583304	C₂²	1	1	yes	characteristic
15	#14583276	C₂²	1	1	yes	characteristic
16	#14583246	C₂²	1	2	yes	—
17	#14583200	—	2	2	no	—
18	#14583195	C₂²	1	2	yes	—
19	#14583190	C₂²	1	2	yes	—
20	#14583135	—	2	2	no	—
21	#14583135	—	2	1	no	—
22	#14583135	—	2	1	no	—
23	#14583128	—	2	2	no	—
24	#14583115	—	2	2	no	—
25	#14583100	C₂²	1	2	yes	—
26	#14583095	C₂²	1	2	yes	—
27	#14583029	C₂²	1	1	yes	characteristic
28	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
29	C₄×D₃₄₄	—	2	1	no	—
30	C₄×D₃₄₄	—	2	1	no	—
31	#14582978	C₂²	1	1	yes	characteristic
32	#14582970	—	2	1	no	—
33	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₄₃	—	2	1	no	—
35	#14582958	—	2	1	no	—
36	#14582956	C₂²	1	1	yes	characteristic
37	#14582853	—	2	1	no	—
38	#14582647	C₂²	1	2	yes	—
39	#14582647	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	#14582642	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₃	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×#335	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	2	no	—
48	C₂×#10621873	—	2	2	no	—
49	C₂×D₃₄₄	—	2	1	no	—
50	C₂×D₃₄₄	—	2	1	no	—
51	C₂×D₃₄₄	—	2	2	no	—
52	C₂×#10621872	—	2	1	no	—
53	C₂×C₈×D₄₃	—	2	1	no	—
54	#13063325	C₂³	1	2	yes	—
55	#13063322	C₂³	1	2	yes	—
56	#13063319	—	2	1	no	—
57	#13063317	D₄	1	1	yes	characteristic
58	#13063313	—	2	2	no	—
59	#13063313	D₄	1	1	yes	characteristic
60	#13063308	—	2	1	no	—
61	#13063304	D₄	1	1	yes	characteristic
62	#13063299	—	2	2	no	—
63	#13063299	—	2	2	no	—
64	#13063299	D₄	1	1	yes	characteristic
65	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
66	C₄×D₁₇₂	—	2	2	no	—
67	C₄×D₁₇₂	—	2	2	no	—
68	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	—	2	1	no	—
70	#13063282	—	2	1	no	—
71	#13063259	—	2	1	no	—
72	#13063259	—	2	1	no	—
73	#13063259	—	2	2	no	—
74	#13063257	—	2	2	no	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₃⋊C₈	—	2	1	no	—
78	Dic₄₃⋊C₈	—	2	1	no	—
79	#13063250	—	2	2	no	—
80	#13063247	—	2	2	no	—
81	#13063247	—	2	2	no	—
82	#13063247	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
86	(C₂×D₄₃)⋊C₈	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	1	no	—
88	#13063236	—	2	1	no	—
89	#13063235	—	2	1	no	—
90	C₈×Dic₄₃	—	2	1	no	—
91	C₂²×C₈×C₄₃	—	2	2	no	—
92	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	2	no	—
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
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	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₃	—	2	1	no	—
106	C₂×C₂²⋊D₄₃	—	4	2	no	—
107	#10621898	—	8	4	no	—
108	C₂×D₁₇₂	—	2	2	no	—
109	C₂×D₁₇₂	—	2	2	no	—
110	C₂×D₁₇₂	—	2	2	no	—
111	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₄₃	—	2	1	no	—
113	C₂×C₄×D₄₃	—	4	2	no	—
114	C₂×Dic₈₆	—	2	2	no	—
115	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₂×C₈×C₄₃	—	2	2	no	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	4	1	no	—
120	C₂×C₈×C₄₃	—	8	2	no	—
121	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₄₃	#41	1	1	yes	characteristic
128	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₂²⋊Dic₄₃	—	2	1	no	—
130	(C₂×D₄₃)⋊C₄	—	2	1	no	—
131	(C₂×D₄₃)⋊C₄	—	2	1	no	—
132	(C₂×D₄₃)⋊C₄	—	2	1	no	—
133	(C₂×D₄₃)⋊C₄	—	2	1	no	—
134	(C₂×D₄₃)⋊C₄	—	4	2	no	—
135	(C₂×D₄₃)⋊C₄	—	4	2	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	2	no	—
138	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
140	Dic₄₃⋊C₄	—	2	1	no	—
141	Dic₄₃⋊C₄	—	2	1	no	—
142	Dic₄₃⋊C₄	—	2	1	no	—
143	Dic₄₃⋊C₄	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	D₃₄₄	—	4	2	no	—
148	D₃₄₄	—	4	2	no	—
149	D₃₄₄	—	8	2	no	—
150	#10621873	—	8	2	no	—
151	#10621872	—	4	2	no	—
152	C₈×D₄₃	—	4	2	no	—
153	C₂³×C₄₃	#121	1	1	yes	characteristic
154	C₂²×D₄₃	—	2	1	no	—
155	C₂²×D₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₂²⋊D₄₃	—	4	2	no	—
168	C₂²⋊D₄₃	—	8	4	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	D₁₇₂	—	2	1	no	—
174	D₁₇₂	—	2	1	no	—
175	D₁₇₂	—	4	2	no	—
176	D₁₇₂	—	4	2	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	8	2	no	—
180	C₄×D₄₃	—	4	1	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	—	8	4	no	—
183	Dic₈₆	—	2	1	no	—
184	Dic₈₆	—	2	1	no	—
185	Dic₈₆	—	8	2	no	—
186	C₈×C₄₃	—	2	1	no	—
187	C₈×C₄₃	—	2	1	no	—
188	C₈×C₄₃	—	2	1	no	—
189	C₈×C₄₃	—	4	2	no	—
190	C₈×C₄₃	—	4	2	no	—
191	C₈×C₄₃	#135	1	2	yes	—
192	C₄₃⋊C₈	—	4	1	no	—
193	C₄₃⋊C₈	—	4	1	no	—
194	#19222	—	43	1	no	maximal, Sylow
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	#472	1	2	yes	—
198	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
199	C₂×D₄₃	—	4	1	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	4	1	no	—
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	C₂×#135	1	1	yes	characteristic
210	C₄×C₄₃	#575	1	1	yes	characteristic
211	C₄×C₄₃	#576	1	1	yes	characteristic
212	C₄×C₄₃	#578	1	1	yes	characteristic
213	Dic₄₃	—	4	1	no	—
214	Dic₄₃	—	4	1	no	—
215	Dic₄₃	—	4	1	no	—
216	Dic₄₃	—	8	2	no	—
217	#3247	—	43	2	no	—
218	#3169	—	43	1	no	—
219	#2966	—	43	1	no	—
220	#1698	—	43	2	no	—
221	#1697	—	43	2	no	—
222	#1676	—	43	1	no	—
223	#1675	—	43	1	no	—
224	#1668	—	43	1	no	—
225	#1667	—	43	1	no	—
226	C₂×#335	D₄₃	1	1	yes	characteristic, complemented
227	#1551	—	43	2	no	—
228	C₂×C₄₃	—	2	2	no	—
229	C₂×C₄₃	#3035	1	1	yes	characteristic
230	C₂×C₄₃	#3061	1	1	yes	characteristic
231	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
232	D₄₃	—	8	1	no	—
233	D₄₃	—	16	2	no	—
234	#532	—	43	2	no	—
235	#529	—	43	1	no	—
236	#500	—	43	1	no	—
237	#493	—	43	1	no	—
238	#486	—	43	2	no	—
239	#478	—	86	2	no	—
240	#477	—	43	2	no	—
241	#476	—	43	2	no	—
242	#466	—	86	2	no	—
243	#466	—	86	1	no	—
244	#466	—	86	1	no	—
245	#465	—	86	2	no	—
246	#463	—	86	2	no	—
247	#460	—	43	2	no	—
248	#459	—	43	2	no	—
249	#446	—	43	1	no	—
250	C₈×Q₈	—	43	1	no	—
251	C₄×D₈	—	86	1	no	—
252	C₄×D₈	—	86	1	no	—
253	#436	—	43	1	no	—
254	#435	—	86	1	no	—
255	C₈×D₄	—	43	1	no	—
256	C₈×D₄	—	86	1	no	—
257	#433	—	86	1	no	—
258	#432	—	43	1	no	—
259	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
260	#405	—	86	1	no	—
261	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
262	#335	C₂×D₄₃	1	1	yes	characteristic
263	#335	C₂×D₄₃	1	1	yes	characteristic
264	#335	C₂×D₄₃	1	2	yes	—
265	#333	—	43	2	no	—
266	#333	—	43	2	no	—
267	#331	—	43	2	no	—
268	#331	—	43	2	no	—
269	C₄₃	#19222	1	1	yes	characteristic, complemented, Sylow
270	C₂×#41	—	86	2	no	—
271	C₂×SD₁₆	—	86	2	no	—
272	C₂×D₈	—	86	2	no	—
273	C₂×D₈	—	86	1	no	—
274	C₂×D₈	—	86	1	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂²×C₈	—	2	2	no	—
277	C₂²×C₈	—	86	1	no	—
278	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
279	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
280	C₄⋊Q₈	—	43	2	no	—
281	#127	—	43	2	no	—
282	#126	—	86	1	no	—
283	#125	—	43	1	no	—
284	#124	—	43	1	no	—
285	#124	—	86	2	no	—
286	#123	—	86	1	no	—
287	C₂²⋊Q₈	—	43	1	no	—
288	#121	—	43	1	no	—
289	#121	—	86	2	no	—
290	#121	—	86	2	no	—
291	C₄×Q₈	—	43	1	no	—
292	C₄×D₄	—	43	1	no	—
293	C₄×D₄	—	86	1	no	—
294	C₄×D₄	—	86	2	no	—
295	C₄×D₄	—	86	2	no	—
296	#117	—	86	1	no	—
297	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
298	#107	—	86	2	no	—
299	#107	—	86	1	no	—
300	#107	—	86	1	no	—
301	#106	—	86	2	no	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	43	1	no	—
304	C₄⋊C₈	—	43	1	no	—
305	C₄⋊C₈	—	86	1	no	—
306	C₄⋊C₈	—	86	1	no	—
307	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
308	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
309	#103	—	86	2	no	—
310	#102	—	86	2	no	—
311	#102	—	86	2	no	—
312	#102	—	86	2	no	—
313	#102	—	86	2	no	—
314	#102	—	86	2	no	—
315	C₂²⋊C₈	—	86	1	no	—
316	C₂²⋊C₈	—	86	1	no	—
317	C₂²⋊C₈	—	86	1	no	—
318	#97	—	86	1	no	—
319	#97	—	86	1	no	—
320	C₄×C₈	—	86	1	no	—
321	C₄×C₈	D₁₇₂	1	1	yes	characteristic
322	C₄×C₈	D₁₇₂	1	1	yes	characteristic
323	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
324	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
325	#41	—	344	4	no	—
326	C₂×Q₈	—	43	1	no	—
327	C₂×Q₈	—	86	2	no	—
328	C₂×D₄	—	43	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂×D₄	—	86	2	no	—
332	C₂×D₄	—	86	2	no	—
333	C₂×D₄	—	172	2	no	—
334	C₂²×C₄	—	86	1	no	—
335	C₂²×C₄	—	172	2	no	—
336	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
337	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	#10621902	1	1	yes	characteristic
339	SD₁₆	—	344	2	no	—
340	D₈	—	344	2	no	—
341	D₈	—	172	2	no	—
342	D₈	—	172	2	no	—
343	M₁₆	—	172	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	4	1	no	—
348	C₂×C₈	—	8	2	no	—
349	C₂×C₈	—	86	1	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	172	2	no	—
352	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
353	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
354	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
355	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
356	C₄⋊C₄	—	43	1	no	—
357	C₄⋊C₄	—	43	1	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	86	1	no	—
361	C₄⋊C₄	—	86	1	no	—
362	C₄⋊C₄	—	86	2	no	—
363	C₄⋊C₄	—	86	2	no	—
364	C₂²⋊C₄	—	86	1	no	—
365	C₂²⋊C₄	—	86	1	no	—
366	C₂²⋊C₄	—	86	1	no	—
367	C₂²⋊C₄	—	86	1	no	—
368	C₂²⋊C₄	—	86	1	no	—
369	C₂²⋊C₄	—	172	2	no	—
370	C₂²⋊C₄	—	172	2	no	—
371	C₄²	—	86	1	no	—
372	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
373	C₄²	D₄×D₄₃	1	1	yes	characteristic
374	C₄²	#10621902	1	1	yes	characteristic
375	C₄²	C₂³×D₄₃	1	1	yes	characteristic
376	C₂³	—	86	1	no	—
377	C₂³	—	172	2	no	—
378	C₂³	#13063300	1	1	yes	characteristic
379	Q₈	—	86	1	no	—
380	Q₈	—	86	1	no	—
381	Q₈	—	344	2	no	—
382	D₄	—	86	1	no	—
383	D₄	—	86	1	no	—
384	D₄	—	344	2	no	—
385	D₄	—	344	4	no	—
386	D₄	—	172	2	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	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	86	1	no	—
398	C₂×C₄	—	86	1	no	—
399	C₂×C₄	—	344	4	no	—
400	C₂×C₄	—	172	2	no	—
401	C₂×C₄	—	172	1	no	—
402	C₂×C₄	—	172	1	no	—
403	C₂×C₄	#13063300	1	1	yes	characteristic
404	C₂×C₄	#13063300	1	1	yes	characteristic
405	C₂×C₄	#13063300	1	1	yes	characteristic
406	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
408	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	2	no	—
414	C₈	—	172	1	no	—
415	C₈	—	172	1	no	—
416	C₈	#13063347	1	2	yes	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	344	2	no	—
420	C₂²	—	344	2	no	—
421	C₂²	—	344	2	no	—
422	C₂²	—	172	1	no	—
423	C₂²	—	172	1	no	—
424	C₂²	—	172	1	no	—
425	C₂²	#14583170	1	2	yes	—
426	C₂²	C₂×#13063300	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	344	2	no	—
432	C₄	—	172	1	no	—
433	C₄	—	172	1	no	—
434	C₄	—	172	1	no	—
435	C₄	C₂×#13063347	1	1	yes	characteristic
436	C₄	#14583699	1	1	yes	characteristic
437	C₄	#14583700	1	1	yes	characteristic
438	C₄	#14583712	1	1	yes	characteristic
439	C₂	—	2	2	no	—
440	C₂	—	344	1	no	—
441	C₂	—	688	2	no	—
442	C₂	#19144052	1	1	yes	characteristic
443	C₂	#19144267	1	1	yes	characteristic
444	C₂	C₂×#14583170	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#335	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	C₂×#335	D₄₃
hypocenter	C₄₃	#19222
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
1. #19145922	C₂	semidirect
2. #19145174	C₂	semidirect
3. #19143570	C₂	semidirect
4. #19134136	C₂	semidirect
5. #19134129	C₂	semidirect
6. #19134000	C₂	semidirect
7. #19133995	C₂	semidirect
8. #19133956	C₂	semidirect
9. #19133951	C₂	semidirect
10. #19133288	C₂	semidirect
11. C₂×C₄₃×#335	C₂	semidirect
226. C₂×#335	D₄₃	semidirect
269. C₄₃	#19222	semidirect

Maximal subgroups

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

subgroup	index
#19145922	2
#19145174	2
#19143570	2
#19134136	2
#19134129	2
#19134000	2
#19133995	2
#19133956	2
#19133951	2
#19133288	2
C₂×C₄₃×#335	2
#19222	43