Subgroups — #25110517

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145089	C₂	1	1	yes	maximal, characteristic
2	#19143513	C₂	1	1	yes	maximal, characteristic
3	#19143464	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135510	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135493	C₂	1	1	yes	maximal, characteristic
6	#19135131	C₂	1	2	yes	maximal, complemented
7	#19135116	C₂	1	2	yes	maximal, complemented
8	#19135090	C₂	1	2	yes	maximal, complemented
9	#19135069	C₂	1	2	yes	maximal, complemented
10	#19134719	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	C₂²	1	2	yes	—
13	C₂×#13063347	C₂²	1	1	yes	characteristic
14	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
15	#14583665	C₂²	1	2	yes	—
16	#14583475	C₂²	1	2	yes	—
17	#14583376	C₂²	1	2	yes	—
18	#14583293	C₄	1	4	yes	complemented
19	#14583283	C₄	1	2	yes	complemented
20	#14583279	C₄	1	2	yes	complemented
21	#14583022	—	2	2	no	—
22	#14583017	—	2	2	no	—
23	#14583007	—	2	2	no	—
24	C₄×Dic₁₇₂	—	2	2	no	—
25	C₂×#13063261	C₂²	1	1	yes	characteristic
26	#14582937	C₂²	1	1	yes	characteristic
27	#14582917	C₂²	1	2	yes	—
28	#14582915	C₂²	1	2	yes	—
29	#14582909	C₂²	1	2	yes	—
30	#14582907	C₂²	1	2	yes	—
31	C₂×#13063243	C₂²	1	2	yes	—
32	#14582872	C₂²	1	2	yes	—
33	#14582670	C₂²	1	2	yes	—
34	#14582655	C₂²	1	2	yes	—
35	C₄₃×#405	C₂²	1	1	yes	characteristic
36	C₄₃×#405	C₂²	1	1	yes	characteristic
37	C₄₃×#405	C₂²	1	1	yes	characteristic
38	C₄₃×#338	C₂²	1	1	yes	characteristic
39	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
40	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
41	C₄₃×H(3,ℤ/4)	C₂²	1	1	yes	characteristic
42	C₂×#10621898	C₂³	1	2	yes	—
43	C₂²×Dic₈₆	C₂³	1	2	yes	—
44	#13063358	—	4	2	no	—
45	#13063358	—	4	2	no	—
46	#13063347	—	2	1	no	—
47	#13063347	—	2	1	no	—
48	#13063347	—	2	1	no	—
49	#13063347	—	2	1	no	—
50	C₂×Dic₁₇₂	—	2	1	no	—
51	C₂×Dic₁₇₂	—	2	1	no	—
52	C₂×Dic₁₇₂	—	2	1	no	—
53	C₂×Dic₁₇₂	—	2	1	no	—
54	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
55	C₂×Dic₁₇₂	C₂×C₄	1	2	yes	—
56	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
57	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	—
58	C₂×#10621873	C₂×C₄	1	2	yes	—
59	C₂×#10621873	C₂×C₄	1	4	yes	—
60	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
61	#13063333	—	4	2	no	—
62	#13063331	—	2	4	no	—
63	C₂×#10621877	C₂³	1	2	yes	—
64	M₁₆×D₄₃	—	4	2	no	—
65	#13063325	C₂×C₄	1	4	yes	—
66	#13063313	C₂×C₄	1	4	yes	—
67	#13063309	—	4	2	no	—
68	#13063305	—	4	2	no	—
69	C₄×Dic₈₆	—	2	4	no	—
70	#13063290	—	4	2	no	—
71	#13063284	C₂³	1	2	yes	—
72	#13063281	—	4	2	no	—
73	#13063261	—	2	1	no	—
74	#13063261	—	2	1	no	—
75	#13063259	—	2	1	no	—
76	#13063257	—	2	1	no	—
77	#13063253	—	2	4	no	—
78	#13063251	—	4	2	no	—
79	#13063250	—	2	4	no	—
80	#13063248	—	4	2	no	—
81	#13063243	—	4	2	no	—
82	#13063239	—	4	2	no	—
83	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
85	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	#117×C₄₃	C₂³	1	1	yes	characteristic
88	#117×C₄₃	C₂³	1	1	yes	characteristic
89	#117×C₄₃	C₂³	1	1	yes	characteristic
90	#97×C₄₃	—	2	1	no	—
91	#97×C₄₃	C₂×C₄	1	2	yes	—
92	#97×C₄₃	D₄	1	2	yes	—
93	C₄×C₈×C₄₃	—	2	1	no	—
94	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₄₃	D₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₂²⋊D₄₃	—	2	2	no	—
98	C₂²×Dic₄₃	—	2	2	no	—
99	#10621898	—	2	2	no	—
100	#10621898	—	2	2	no	—
101	#10621898	—	2	2	no	—
102	#10621898	—	2	2	no	—
103	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₃	—	2	2	no	—
105	C₂×Dic₈₆	—	2	2	no	—
106	C₂×Dic₈₆	—	2	2	no	—
107	C₂×Dic₈₆	—	2	2	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	2	no	—
110	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
111	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
112	M₁₆×C₄₃	—	2	1	no	—
113	M₁₆×C₄₃	—	2	1	no	—
114	M₁₆×C₄₃	—	2	1	no	—
115	M₁₆×C₄₃	—	2	1	no	—
116	M₁₆×C₄₃	—	2	1	no	—
117	M₁₆×C₄₃	—	2	1	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
126	C₂×C₈×C₄₃	#41	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	C₂²⋊C₄×C₄₃	—	2	1	no	—
131	C₂²⋊C₄×C₄₃	—	2	1	no	—
132	C₂²⋊C₄×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
135	C₄²×C₄₃	C₂×D₄	1	2	yes	—
136	C₂²⋊Dic₄₃	—	2	2	no	—
137	(C₂×D₄₃)⋊C₄	—	4	4	no	—
138	C₄⋊Dic₄₃	—	2	2	no	—
139	C₄⋊Dic₄₃	—	4	4	no	—
140	Dic₄₃⋊C₄	—	4	4	no	—
141	C₄×Dic₄₃	—	2	2	no	—
142	C₄×Dic₄₃	—	4	4	no	—
143	#10621877	—	2	2	no	—
144	#10621877	—	2	2	no	—
145	C₂×C₄₃⋊C₈	—	2	2	no	—
146	Dic₁₇₂	—	2	2	no	—
147	Dic₁₇₂	—	2	2	no	—
148	Dic₁₇₂	—	2	2	no	—
149	Dic₁₇₂	—	2	2	no	—
150	Dic₁₇₂	—	2	1	no	—
151	Dic₁₇₂	—	2	1	no	—
152	Dic₁₇₂	—	4	4	no	—
153	D₃₄₄	—	2	1	no	—
154	D₃₄₄	—	2	1	no	—
155	#10621873	—	2	2	no	—
156	#10621873	—	2	2	no	—
157	#10621873	—	4	4	no	—
158	#10621872	—	4	4	no	—
159	C₈×D₄₃	—	4	4	no	—
160	C₂³×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×D₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²⋊D₄₃	—	4	2	no	—
172	C₂²⋊D₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	2	2	no	—
174	C₂×Dic₄₃	—	2	4	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	2	no	—
178	D₁₇₂	—	2	2	no	—
179	D₁₇₂	—	2	2	no	—
180	C₄×D₄₃	—	4	2	no	—
181	C₄×D₄₃	—	4	2	no	—
182	Dic₈₆	—	2	2	no	—
183	Dic₈₆	—	2	4	no	—
184	Dic₈₆	—	2	4	no	—
185	Dic₈₆	—	2	2	no	—
186	Dic₈₆	—	4	2	no	—
187	Dic₈₆	—	4	2	no	—
188	C₈×C₄₃	—	2	2	no	—
189	C₈×C₄₃	—	2	2	no	—
190	C₈×C₄₃	—	4	1	no	—
191	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
192	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
193	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₈×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₄₃⋊C₈	—	4	2	no	—
196	#22285	—	43	1	no	maximal, Sylow
197	C₂²×C₄₃	—	4	1	no	—
198	C₂²×C₄₃	#518	1	1	yes	characteristic
199	C₂²×C₄₃	#535	1	1	yes	characteristic
200	C₂²×C₄₃	#540	1	1	yes	characteristic
201	C₂×D₄₃	—	4	2	no	—
202	C₂×D₄₃	—	8	2	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	8	1	no	—
206	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₄×C₄₃	#518	1	1	yes	characteristic
208	C₄×C₄₃	#535	1	1	yes	characteristic
209	C₄×C₄₃	#540	1	1	yes	characteristic
210	Dic₄₃	—	4	4	no	—
211	Dic₄₃	—	4	2	no	—
212	Dic₄₃	—	8	2	no	—
213	#3156	—	43	1	no	—
214	#2957	—	43	1	no	—
215	#2950	—	43	1	no	—
216	#1979	—	43	1	no	—
217	#1976	—	43	1	no	—
218	#1912	—	43	2	no	—
219	#1909	—	43	2	no	—
220	#1905	—	43	2	no	—
221	#1902	—	43	2	no	—
222	#1833	—	43	1	no	—
223	#1747	D₄₃	1	1	yes	characteristic, complemented
224	C₂×C₄₃	—	2	1	no	—
225	C₂×C₄₃	—	2	1	no	—
226	C₂×C₄₃	—	2	1	no	—
227	C₂×C₄₃	#2328	1	1	yes	characteristic
228	D₄₃	—	8	2	no	—
229	C₂×#137	—	43	2	no	—
230	C₂×#135	—	43	1	no	—
231	C₂²×Q₁₆	—	43	1	no	—
232	#568	—	43	2	no	—
233	#536	—	43	2	no	—
234	#519	—	43	2	no	—
235	#497	—	43	4	no	—
236	#495	—	43	2	no	—
237	#494	—	43	2	no	—
238	#444	—	86	2	no	—
239	#443	—	86	2	no	—
240	#441	—	86	2	no	—
241	C₄×Q₁₆	—	86	2	no	—
242	C₂×#108	—	43	1	no	—
243	#427	—	43	1	no	—
244	#421	—	43	2	no	—
245	#421	—	43	2	no	—
246	#419	—	43	2	no	—
247	#419	—	43	2	no	—
248	C₂×#101	—	43	2	no	—
249	#410	—	43	2	no	—
250	#405	C₂×D₄₃	1	1	yes	characteristic
251	#405	C₂×D₄₃	1	1	yes	characteristic
252	#405	C₂×D₄₃	1	1	yes	characteristic
253	#344	—	43	2	no	—
254	#338	C₂×D₄₃	1	1	yes	characteristic
255	H(3,ℤ/4)	—	43	2	no	—
256	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
257	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
258	H(3,ℤ/4)	C₂×D₄₃	1	1	yes	characteristic
259	C₄₃	#22285	1	1	yes	characteristic, complemented, Sylow
260	C₂×#41	—	43	2	no	—
261	C₂²×Q₈	—	43	2	no	—
262	#137	—	172	2	no	—
263	#137	—	172	2	no	—
264	#135	—	86	1	no	—
265	#135	—	86	1	no	—
266	#135	—	86	1	no	—
267	#135	—	86	1	no	—
268	C₂×Q₁₆	—	43	2	no	—
269	C₂×Q₁₆	—	43	2	no	—
270	C₂×Q₁₆	—	43	1	no	—
271	C₂×Q₁₆	—	43	4	no	—
272	C₂×Q₁₆	—	86	1	no	—
273	C₂×Q₁₆	—	86	1	no	—
274	C₂×Q₁₆	—	86	1	no	—
275	C₂×Q₁₆	—	86	1	no	—
276	C₂×SD₁₆	—	43	2	no	—
277	C₂×SD₁₆	—	43	4	no	—
278	C₂×D₈	—	43	1	no	—
279	#131	—	86	4	no	—
280	#131	—	172	2	no	—
281	C₂×M₁₆	—	43	2	no	—
282	C₂×M₁₆	—	172	2	no	—
283	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
284	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
285	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
287	C₄⋊Q₈	—	43	4	no	—
288	#124	—	43	4	no	—
289	#123	—	172	2	no	—
290	C₂²⋊Q₈	—	172	2	no	—
291	C₄×Q₈	—	86	4	no	—
292	C₄×Q₈	—	172	2	no	—
293	#117	—	43	2	no	—
294	#117	—	172	2	no	—
295	#117	C₂²×D₄₃	1	1	yes	characteristic
296	#117	C₂²×D₄₃	1	1	yes	characteristic
297	#117	C₂²×D₄₃	1	1	yes	characteristic
298	#108	—	86	1	no	—
299	#108	—	86	1	no	—
300	#107	—	86	1	no	—
301	#106	—	86	1	no	—
302	#104	—	86	4	no	—
303	#104	—	172	2	no	—
304	#103	—	86	4	no	—
305	#103	—	172	2	no	—
306	#101	—	172	2	no	—
307	#99	—	172	2	no	—
308	#97	—	2	1	no	—
309	#97	C₄×D₄₃	1	2	yes	—
310	#97	D₁₇₂	1	2	yes	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	C₄×D₄₃	1	2	yes	—
313	C₄×C₈	D₁₇₂	1	2	yes	—
314	#41	—	86	2	no	—
315	#41	—	86	2	no	—
316	#41	—	86	2	no	—
317	#41	—	86	2	no	—
318	C₂×Q₈	—	43	4	no	—
319	C₂×Q₈	—	43	2	no	—
320	C₂×Q₈	—	86	2	no	—
321	C₂×Q₈	—	86	2	no	—
322	C₂×Q₈	—	86	2	no	—
323	C₂×Q₈	—	86	2	no	—
324	C₂×Q₈	—	86	2	no	—
325	C₂×D₄	—	43	2	no	—
326	C₂×D₄	—	86	2	no	—
327	C₂²×C₄	—	86	2	no	—
328	C₂²×C₄	—	86	2	no	—
329	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
330	Q₁₆	—	86	2	no	—
331	Q₁₆	—	86	2	no	—
332	Q₁₆	—	86	2	no	—
333	Q₁₆	—	86	2	no	—
334	Q₁₆	—	86	1	no	—
335	Q₁₆	—	86	1	no	—
336	Q₁₆	—	172	4	no	—
337	SD₁₆	—	86	2	no	—
338	SD₁₆	—	86	2	no	—
339	SD₁₆	—	172	4	no	—
340	D₈	—	86	1	no	—
341	D₈	—	86	1	no	—
342	M₁₆	—	2	1	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	1	no	—
345	M₁₆	—	2	1	no	—
346	M₁₆	—	2	1	no	—
347	M₁₆	—	2	1	no	—
348	M₁₆	—	86	2	no	—
349	M₁₆	—	86	2	no	—
350	M₁₆	—	172	4	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	86	2	no	—
353	C₂×C₈	—	172	4	no	—
354	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
356	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
357	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
358	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
359	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
360	C₂×C₈	#10621898	1	1	yes	characteristic
361	C₂×C₈	#10621898	1	1	yes	characteristic
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	86	2	no	—
366	C₄⋊C₄	—	172	4	no	—
367	C₄⋊C₄	—	172	4	no	—
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	86	2	no	—
372	C₂²⋊C₄	—	172	4	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	86	2	no	—
375	C₄²	—	172	4	no	—
376	C₄²	C₂×C₄×D₄₃	1	2	yes	—
377	C₄²	C₂×D₁₇₂	1	2	yes	—
378	C₂³	—	86	2	no	—
379	C₂³	#13063371	1	1	yes	characteristic
380	Q₈	—	86	2	no	—
381	Q₈	—	86	4	no	—
382	Q₈	—	86	4	no	—
383	Q₈	—	86	2	no	—
384	Q₈	—	172	2	no	—
385	Q₈	—	172	2	no	—
386	D₄	—	86	2	no	—
387	D₄	—	86	2	no	—
388	D₄	—	172	2	no	—
389	D₄	—	172	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	86	4	no	—
394	C₂×C₄	—	86	2	no	—
395	C₂×C₄	—	172	2	no	—
396	C₂×C₄	—	172	2	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
402	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
403	C₂×C₄	#13063371	1	1	yes	characteristic
404	C₂×C₄	#13063371	1	1	yes	characteristic
405	C₂×C₄	#13063371	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	172	2	no	—
410	C₈	C₄×D₁₇₂	1	1	yes	characteristic
411	C₈	C₄×D₁₇₂	1	1	yes	characteristic
412	C₈	C₄×D₁₇₂	1	1	yes	characteristic
413	C₈	C₄×D₁₇₂	1	1	yes	characteristic
414	C₂²	—	4	1	no	—
415	C₂²	—	344	2	no	—
416	C₂²	—	172	2	no	—
417	C₂²	#14583373	1	1	yes	characteristic
418	C₂²	#14583468	1	1	yes	characteristic
419	C₂²	#14583504	1	1	yes	characteristic
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	344	2	no	—
424	C₄	—	172	2	no	—
425	C₄	—	172	4	no	—
426	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
427	C₄	#14583373	1	1	yes	characteristic
428	C₄	#14583468	1	1	yes	characteristic
429	C₄	#14583504	1	1	yes	characteristic
430	C₂	—	2	1	no	—
431	C₂	—	2	1	no	—
432	C₂	—	2	1	no	—
433	C₂	—	344	2	no	—
434	C₂	#19137320	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19137320
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1747	C₂
socle	C₂×C₄₃	#2328
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1747	D₄₃
hypocenter	C₄₃	#22285
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1747

Complements

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

N	H ≅ G/N	type
3. #19143464	C₂	semidirect
4. #19135510	C₂	semidirect
6. #19135131	C₂	semidirect
7. #19135116	C₂	semidirect
8. #19135090	C₂	semidirect
9. #19135069	C₂	semidirect
10. #19134719	C₂	semidirect
11. C₄₃×#1747	C₂	semidirect
18. #14583293	C₄	semidirect
19. #14583283	C₄	semidirect
20. #14583279	C₄	semidirect
223. #1747	D₄₃	semidirect
259. C₄₃	#22285	semidirect

Maximal subgroups

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

subgroup	index
#19145089	2
#19143513	2
#19143464	2
#19135510	2
#19135493	2
#19135131	2
#19135116	2
#19135090	2
#19135069	2
#19134719	2
C₄₃×#1747	2
#22285	43