Subgroups — #24992821

Order 11008.

562 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583180	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582976	C₂	1	1	yes	maximal, characteristic
3	#19135396	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134592	C₂	1	1	yes	maximal, characteristic
5	C₂×#14582646	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132429	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621872	—	2	1	no	—
9	C₂×#13063325	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
11	#14583180	—	2	2	no	—
12	#14583180	C₄	1	4	yes	complemented
13	#14582976	—	2	2	no	—
14	#14582976	—	2	2	no	—
15	C₂×#13063259	—	2	1	no	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13063248	—	2	1	no	—
18	C₂×#13063248	—	2	1	no	—
19	C₂×#13063247	—	2	1	no	—
20	C₂×#13063245	—	2	1	no	—
21	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	#14582661	—	2	1	no	—
24	#14582646	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#384	C₂²	1	1	yes	characteristic
28	C₂²×Dic₈₆	—	2	1	no	—
29	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₃	—	2	1	no	—
31	C₂×#10621872	—	2	4	no	—
32	C₂×#10621872	—	4	2	no	—
33	C₂×#10621872	—	4	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
36	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
37	#13063325	—	2	1	no	—
38	#13063325	—	2	1	no	—
39	#13063325	—	2	1	no	—
40	#13063325	C₂×C₄	1	2	yes	—
41	C₄×D₁₇₂	—	2	1	no	—
42	C₄×D₁₇₂	—	2	1	no	—
43	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
44	C₄×D₁₇₂	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₄₃	—	2	1	no	—
46	C₂×C₄⋊Dic₄₃	—	2	1	no	—
47	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
48	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
49	#13063259	—	2	4	no	—
50	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
51	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
52	#13063248	—	4	2	no	—
53	#13063248	—	4	2	no	—
54	#13063247	—	2	4	no	—
55	#13063245	—	4	2	no	—
56	(C₂×D₄₃)⋊C₈	—	2	4	no	—
57	C₄×C₄₃⋊C₈	—	2	1	no	—
58	C₄×C₄₃⋊C₈	—	2	1	no	—
59	C₂²×C₈×C₄₃	—	2	1	no	—
60	C₂²×C₈×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₄₃	—	2	1	no	—
66	C₄⋊C₈×C₄₃	—	2	1	no	—
67	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
68	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
69	C₂³×D₄₃	—	2	1	no	—
70	C₂²×C₄×C₄₃	—	4	1	no	—
71	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
74	C₂²×Dic₄₃	—	2	1	no	—
75	C₂²×Dic₄₃	—	4	1	no	—
76	C₂×D₁₇₂	—	2	1	no	—
77	C₂×D₁₇₂	—	2	1	no	—
78	C₂×D₁₇₂	—	2	1	no	—
79	C₂×D₁₇₂	—	2	1	no	—
80	C₂×D₁₇₂	—	2	1	no	—
81	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
82	C₂×C₄×D₄₃	—	2	2	no	—
83	C₂×C₄×D₄₃	—	2	2	no	—
84	C₂×C₄×D₄₃	—	4	1	no	—
85	C₂×C₄×D₄₃	—	4	1	no	—
86	C₂×C₄×D₄₃	—	4	1	no	—
87	C₂×C₄×D₄₃	—	4	1	no	—
88	C₂×Dic₈₆	—	2	2	no	—
89	C₂×Dic₈₆	—	4	1	no	—
90	C₂×Dic₈₆	—	4	1	no	—
91	C₂×Dic₈₆	—	4	1	no	—
92	C₂×Dic₈₆	—	4	1	no	—
93	C₂×Dic₈₆	—	4	1	no	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₂×C₈×C₄₃	—	4	1	no	—
99	C₂×C₈×C₄₃	—	4	1	no	—
100	C₄⋊C₄×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	4	1	no	—
102	C₄⋊C₄×C₄₃	—	4	1	no	—
103	C₄⋊C₄×C₄₃	—	4	1	no	—
104	C₄⋊C₄×C₄₃	—	8	1	no	—
105	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
106	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	(C₂×D₄₃)⋊C₄	—	2	2	no	—
110	(C₂×D₄₃)⋊C₄	—	2	2	no	—
111	C₄⋊Dic₄₃	—	2	1	no	—
112	C₄⋊Dic₄₃	—	2	2	no	—
113	C₄⋊Dic₄₃	—	2	2	no	—
114	C₄⋊Dic₄₃	—	4	1	no	—
115	C₄⋊Dic₄₃	—	4	1	no	—
116	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
117	C₂×C₄₃⋊C₈	—	2	1	no	—
118	C₂×C₄₃⋊C₈	—	2	1	no	—
119	C₂×C₄₃⋊C₈	—	2	1	no	—
120	C₂×C₄₃⋊C₈	—	2	1	no	—
121	C₂×C₄₃⋊C₈	—	2	1	no	—
122	C₂×C₄₃⋊C₈	—	4	1	no	—
123	C₂×C₄₃⋊C₈	—	4	1	no	—
124	C₂×C₄₃⋊C₈	—	4	1	no	—
125	C₂×C₄₃⋊C₈	D₈	1	2	yes	—
126	#10621872	—	4	8	no	—
127	C₂³×C₄₃	#121	1	1	yes	characteristic
128	C₂²×D₄₃	—	2	2	no	—
129	C₂²×D₄₃	—	4	1	no	—
130	C₂²×D₄₃	—	4	1	no	—
131	C₂²×D₄₃	—	4	1	no	—
132	C₂²×D₄₃	—	4	1	no	—
133	C₂²×D₄₃	—	4	1	no	—
134	C₂²×D₄₃	—	4	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	8	1	no	—
138	C₂×C₄×C₄₃	—	8	1	no	—
139	C₂×C₄×C₄₃	—	8	1	no	—
140	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
145	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
153	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
154	C₂×Dic₄₃	—	2	2	no	—
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	1	no	—
157	C₂×Dic₄₃	—	4	2	no	—
158	C₂×Dic₄₃	—	8	1	no	—
159	C₂×Dic₄₃	—	8	1	no	—
160	D₁₇₂	—	2	2	no	—
161	D₁₇₂	—	2	2	no	—
162	D₁₇₂	—	4	1	no	—
163	D₁₇₂	—	4	1	no	—
164	C₄×D₄₃	—	4	2	no	—
165	C₄×D₄₃	—	4	2	no	—
166	C₄×D₄₃	—	4	2	no	—
167	C₄×D₄₃	—	4	2	no	—
168	Dic₈₆	—	4	2	no	—
169	Dic₈₆	—	4	2	no	—
170	Dic₈₆	—	8	1	no	—
171	Dic₈₆	—	8	1	no	—
172	C₈×C₄₃	—	4	2	no	—
173	C₈×C₄₃	—	4	2	no	—
174	C₄₃⋊C₈	—	2	2	no	—
175	C₄₃⋊C₈	—	4	1	no	—
176	C₄₃⋊C₈	—	8	1	no	—
177	#9227	—	43	1	no	maximal, Sylow
178	C₂²×C₄₃	#386	1	1	yes	characteristic
179	C₂²×C₄₃	#459	1	1	yes	characteristic
180	C₂²×C₄₃	#463	1	1	yes	characteristic
181	C₂²×C₄₃	#468	1	1	yes	characteristic
182	C₂²×C₄₃	#470	1	1	yes	characteristic
183	C₂²×C₄₃	#471	1	1	yes	characteristic
184	C₂²×C₄₃	#473	1	1	yes	characteristic
185	C₂×D₄₃	—	4	2	no	—
186	C₂×D₄₃	—	4	2	no	—
187	C₂×D₄₃	—	4	2	no	—
188	C₂×D₄₃	—	8	1	no	—
189	C₂×D₄₃	—	8	1	no	—
190	C₂×D₄₃	—	8	1	no	—
191	C₂×D₄₃	—	8	1	no	—
192	C₄×C₄₃	—	2	1	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	16	1	no	—
195	C₄×C₄₃	#417	1	1	yes	characteristic
196	C₄×C₄₃	#419	1	1	yes	characteristic
197	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
198	C₄×C₄₃	#442	1	1	yes	characteristic
199	C₄×C₄₃	#447	1	1	yes	characteristic
200	C₄×C₄₃	#449	1	1	yes	characteristic
201	C₄×C₄₃	#468	1	1	yes	characteristic
202	C₄×C₄₃	#470	1	1	yes	characteristic
203	Dic₄₃	—	4	2	no	—
204	Dic₄₃	—	8	2	no	—
205	C₂×#474	—	43	1	no	—
206	C₂×#436	—	43	1	no	—
207	#1956	—	43	1	no	—
208	#1802	—	43	1	no	—
209	C₂×#332	—	43	1	no	—
210	#1296	D₄₃	1	1	yes	characteristic, complemented
211	#1277	—	43	1	no	—
212	C₂×C₄₃	#1685	1	1	yes	characteristic
213	C₂×C₄₃	#1689	1	1	yes	characteristic
214	C₂×C₄₃	#1699	1	1	yes	characteristic
215	C₂×C₄₃	#1703	1	1	yes	characteristic
216	C₂×C₄₃	#1879	1	1	yes	characteristic
217	C₂×C₄₃	#1894	1	1	yes	characteristic
218	C₂×C₄₃	#1908	1	1	yes	characteristic
219	D₄₃	—	8	2	no	—
220	C₂²×M₁₆	—	86	1	no	—
221	C₂×C₄⋊Q₈	—	43	1	no	—
222	C₂×C₄×D₄	—	43	1	no	—
223	#474	—	43	4	no	—
224	#474	—	86	2	no	—
225	#436	—	86	2	no	—
226	#436	—	86	2	no	—
227	C₂×#107	—	86	1	no	—
228	C₂×C₄⋊C₈	—	43	1	no	—
229	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
231	C₂×#103	—	86	1	no	—
232	C₂×#103	—	86	1	no	—
233	C₂×#102	—	86	1	no	—
234	C₂×#102	—	86	1	no	—
235	C₂×C₂²⋊C₈	—	86	1	no	—
236	C₂×C₄×C₈	—	43	1	no	—
237	#384	C₂×D₄₃	1	1	yes	characteristic
238	#340	—	86	1	no	—
239	#332	—	86	2	no	—
240	C₄₃	#9227	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	—	86	1	no	—
242	C₂²×D₄	—	43	1	no	—
243	C₂³×C₄	—	86	1	no	—
244	C₂×M₁₆	—	86	4	no	—
245	C₂×M₁₆	—	172	2	no	—
246	C₂×M₁₆	—	172	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	86	1	no	—
252	C₄⋊Q₈	—	43	2	no	—
253	C₄⋊Q₈	—	86	1	no	—
254	C₄⋊Q₈	—	86	1	no	—
255	C₄⋊Q₈	—	86	1	no	—
256	C₄×D₄	—	43	2	no	—
257	C₄×D₄	—	43	2	no	—
258	C₄×D₄	—	86	1	no	—
259	C₄×D₄	—	86	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	43	1	no	—
264	C₂×C₄⋊C₄	—	86	1	no	—
265	C₂×C₄⋊C₄	—	86	1	no	—
266	C₂×C₂²⋊C₄	—	86	1	no	—
267	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
268	#107	—	86	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	86	1	no	—
272	C₄⋊C₈	—	86	1	no	—
273	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
274	C₄⋊C₈	D₁₇₂	1	2	yes	—
275	#103	—	172	2	no	—
276	#103	—	172	2	no	—
277	#102	—	86	4	no	—
278	#102	—	172	2	no	—
279	C₂²⋊C₈	—	86	4	no	—
280	C₄×C₈	—	86	1	no	—
281	C₄×C₈	—	86	1	no	—
282	C₂⁴	—	86	1	no	—
283	C₂×Q₈	—	86	2	no	—
284	C₂×Q₈	—	172	1	no	—
285	C₂×Q₈	—	172	1	no	—
286	C₂×Q₈	—	172	1	no	—
287	C₂×Q₈	—	172	1	no	—
288	C₂×Q₈	—	172	1	no	—
289	C₂×D₄	—	43	2	no	—
290	C₂×D₄	—	86	1	no	—
291	C₂×D₄	—	86	1	no	—
292	C₂×D₄	—	86	1	no	—
293	C₂×D₄	—	86	1	no	—
294	C₂×D₄	—	86	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	86	1	no	—
297	C₂²×C₄	—	86	2	no	—
298	C₂²×C₄	—	86	2	no	—
299	C₂²×C₄	—	172	1	no	—
300	C₂²×C₄	—	172	1	no	—
301	C₂²×C₄	—	172	1	no	—
302	C₂²×C₄	—	172	1	no	—
303	C₂²×C₄	—	172	1	no	—
304	C₂²×C₄	#10621898	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
307	M₁₆	—	172	8	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	43	2	no	—
315	C₂×C₈	—	86	1	no	—
316	C₂×C₈	—	86	1	no	—
317	C₂×C₈	—	86	1	no	—
318	C₂×C₈	—	86	1	no	—
319	C₂×C₈	—	86	1	no	—
320	C₂×C₈	—	172	1	no	—
321	C₂×C₈	—	172	1	no	—
322	C₂×C₈	—	172	1	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	8	1	no	—
328	C₄⋊C₄	—	43	2	no	—
329	C₄⋊C₄	—	86	1	no	—
330	C₄⋊C₄	—	86	2	no	—
331	C₄⋊C₄	—	86	2	no	—
332	C₄⋊C₄	—	172	1	no	—
333	C₄⋊C₄	—	172	1	no	—
334	C₂²⋊C₄	—	86	2	no	—
335	C₂²⋊C₄	—	86	2	no	—
336	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
337	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
338	C₄²	D₄×D₄₃	1	1	yes	characteristic
339	C₄²	#10621902	1	1	yes	characteristic
340	C₂³	—	86	2	no	—
341	C₂³	—	172	1	no	—
342	C₂³	—	172	1	no	—
343	C₂³	—	172	1	no	—
344	C₂³	—	172	1	no	—
345	C₂³	—	172	1	no	—
346	C₂³	—	172	1	no	—
347	C₂³	#13063298	1	1	yes	characteristic
348	Q₈	—	344	1	no	—
349	Q₈	—	344	1	no	—
350	Q₈	—	172	2	no	—
351	Q₈	—	172	2	no	—
352	D₄	—	86	2	no	—
353	D₄	—	86	2	no	—
354	D₄	—	172	1	no	—
355	D₄	—	172	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	—	86	2	no	—
362	C₂×C₄	—	344	1	no	—
363	C₂×C₄	—	344	1	no	—
364	C₂×C₄	—	172	2	no	—
365	C₂×C₄	—	172	1	no	—
366	C₂×C₄	—	172	1	no	—
367	C₂×C₄	—	172	2	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	2	no	—
370	C₂×C₄	—	172	2	no	—
371	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
372	C₂×C₄	#13063287	1	1	yes	characteristic
373	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
374	C₂×C₄	#13063295	1	1	yes	characteristic
375	C₂×C₄	#13063300	1	1	yes	characteristic
376	C₂×C₄	#13063310	1	1	yes	characteristic
377	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
378	C₂×C₄	#13063348	1	1	yes	characteristic
379	C₂×C₄	#13063349	1	1	yes	characteristic
380	C₂×C₄	#13063352	1	1	yes	characteristic
381	C₂×C₄	#13063352	1	1	yes	characteristic
382	C₂×C₄	#13063354	1	1	yes	characteristic
383	C₂×C₄	#13063354	1	1	yes	characteristic
384	C₂×C₄	#13063357	1	1	yes	characteristic
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	86	2	no	—
388	C₈	—	344	1	no	—
389	C₈	—	172	1	no	—
390	C₂²	—	344	1	no	—
391	C₂²	—	344	1	no	—
392	C₂²	—	344	1	no	—
393	C₂²	—	344	1	no	—
394	C₂²	—	172	2	no	—
395	C₂²	—	172	2	no	—
396	C₂²	—	172	2	no	—
397	C₂²	#14582777	1	1	yes	characteristic
398	C₂²	#14583093	1	1	yes	characteristic
399	C₂²	#14583117	1	1	yes	characteristic
400	C₂²	#14583144	1	1	yes	characteristic
401	C₂²	#14583156	1	1	yes	characteristic
402	C₂²	#14583161	1	1	yes	characteristic
403	C₂²	#14583173	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	16	1	no	—
407	C₄	—	344	2	no	—
408	C₄	—	172	2	no	—
409	C₄	#14582897	1	1	yes	characteristic
410	C₄	#14582906	1	1	yes	characteristic
411	C₄	#14582981	1	1	yes	characteristic
412	C₄	#14583010	1	1	yes	characteristic
413	C₄	#14583034	1	1	yes	characteristic
414	C₄	#14583047	1	1	yes	characteristic
415	C₄	#14583146	1	1	yes	characteristic
416	C₄	#14583158	1	1	yes	characteristic
417	C₂	—	344	2	no	—
418	C₂	#19134059	1	1	yes	characteristic
419	C₂	#19134083	1	1	yes	characteristic
420	C₂	#19134145	1	1	yes	characteristic
421	C₂	#19134173	1	1	yes	characteristic
422	C₂	#19134944	1	1	yes	characteristic
423	C₂	#19135027	1	1	yes	characteristic
424	C₂	#19135111	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063298
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1296	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1296	D₄₃
hypocenter	C₄₃	#9227
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
3. #19135396	C₂	semidirect
5. C₂×#14582646	C₂	semidirect
6. #19132429	C₂	semidirect
7. C₄₃×#1296	C₂	semidirect
12. #14583180	C₄	semidirect
210. #1296	D₄₃	semidirect
240. C₄₃	#9227	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583180	2
C₂×#14582976	2
#19135396	2
#19134592	2
C₂×#14582646	2
#19132429	2
C₄₃×#1296	2
#9227	43