Subgroups — #24991348

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583186	C₂	1	1	yes	maximal, characteristic
2	#19137546	C₂	1	1	yes	maximal, characteristic
3	#19135544	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582628	C₂	1	1	yes	maximal, characteristic
5	#19132478	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132435	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063283	—	2	1	no	—
10	#14583186	—	2	2	no	—
11	#14583186	C₄	1	4	yes	complemented
12	C₂×#13063256	—	2	1	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#13063245	—	2	1	no	—
16	#14582800	—	2	1	no	—
17	#14582789	—	2	2	no	—
18	#14582756	—	2	1	no	—
19	C₄⋊C₄×Dic₄₃	—	2	1	no	—
20	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
21	#14582661	—	2	1	no	—
22	#14582661	—	2	1	no	—
23	#14582628	—	2	2	no	—
24	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₃	—	2	2	no	—
26	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
27	C₄₃×#384	C₂²	1	1	yes	characteristic
28	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₄₃	—	2	1	no	—
30	C₂²×C₄₃⋊C₈	—	2	1	no	—
31	C₂²×C₄₃⋊C₈	—	2	1	no	—
32	C₄×D₁₇₂	—	2	1	no	—
33	C₄×D₁₇₂	—	2	1	no	—
34	C₄×D₁₇₂	C₂×C₄	1	2	yes	—
35	C₄×D₁₇₂	D₄	1	2	yes	—
36	#13063283	—	4	2	no	—
37	#13063283	—	4	2	no	—
38	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
41	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
43	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
44	C₂×C₄×Dic₄₃	—	2	2	no	—
45	C₂×C₄×Dic₄₃	—	2	1	no	—
46	#13063256	—	2	4	no	—
47	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
48	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
51	#13063245	—	2	4	no	—
52	C₄₃⋊#95	—	2	2	no	—
53	C₄₃⋊#95	—	2	1	no	—
54	C₂²×Q₈×C₄₃	—	2	1	no	—
55	C₂²×C₈×C₄₃	—	2	1	no	—
56	C₄⋊Q₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	—	2	1	no	—
59	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×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×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
65	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
66	#103×C₄₃	—	4	4	no	—
67	C₄×C₈×C₄₃	—	2	1	no	—
68	C₄×C₈×C₄₃	—	2	1	no	—
69	C₂³×D₄₃	—	2	1	no	—
70	C₂×Q₈×C₄₃	—	2	2	no	—
71	C₂×Q₈×C₄₃	—	4	2	no	—
72	C₂×Q₈×C₄₃	—	4	2	no	—
73	C₂×Q₈×C₄₃	—	4	1	no	—
74	C₂²×C₄×C₄₃	—	2	2	no	—
75	C₂²×C₄×C₄₃	—	4	1	no	—
76	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₄₃	—	2	1	no	—
80	C₂²×Dic₄₃	—	2	1	no	—
81	C₂²×Dic₄₃	—	2	1	no	—
82	C₂×D₁₇₂	—	2	1	no	—
83	C₂×D₁₇₂	—	2	1	no	—
84	C₂×D₁₇₂	—	2	1	no	—
85	C₂×D₁₇₂	—	2	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
88	C₂×C₄×D₄₃	—	2	2	no	—
89	C₂×C₄×D₄₃	—	2	2	no	—
90	C₂×C₄×D₄₃	—	4	1	no	—
91	C₂×C₄×D₄₃	—	4	1	no	—
92	C₂×C₄×D₄₃	—	4	1	no	—
93	C₂×C₄×D₄₃	—	4	1	no	—
94	C₂×C₈×C₄₃	—	2	2	no	—
95	C₂×C₈×C₄₃	—	4	1	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₄⋊C₄×C₄₃	—	2	2	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	4	2	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	—	4	1	no	—
105	C₄⋊C₄×C₄₃	—	4	1	no	—
106	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	C₄²×C₄₃	#41	1	1	yes	characteristic
110	(C₂×D₄₃)⋊C₄	—	2	2	no	—
111	(C₂×D₄₃)⋊C₄	—	2	2	no	—
112	(C₂×D₄₃)⋊C₄	—	4	4	no	—
113	(C₂×D₄₃)⋊C₄	—	8	2	no	—
114	C₄⋊Dic₄₃	—	2	1	no	—
115	C₄⋊Dic₄₃	—	2	1	no	—
116	C₄⋊Dic₄₃	—	2	1	no	—
117	C₄⋊Dic₄₃	—	2	1	no	—
118	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
119	C₄⋊Dic₄₃	SD₁₆	1	2	yes	—
120	C₄×Dic₄₃	—	4	4	no	—
121	C₄×Dic₄₃	—	4	1	no	—
122	C₄×Dic₄₃	—	4	1	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	4	1	no	—
125	C₂×C₄₃⋊C₈	—	4	1	no	—
126	C₂×C₄₃⋊C₈	—	4	1	no	—
127	C₂×C₄₃⋊C₈	—	4	1	no	—
128	C₂×C₄₃⋊C₈	—	4	1	no	—
129	C₂³×C₄₃	#120	1	1	yes	characteristic
130	C₂²×D₄₃	—	2	2	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	C₂²×D₄₃	—	4	1	no	—
136	C₂²×D₄₃	—	4	1	no	—
137	Q₈×C₄₃	—	4	4	no	—
138	Q₈×C₄₃	—	8	2	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	—	8	1	no	—
146	C₂×C₄×C₄₃	—	8	1	no	—
147	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
153	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
155	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
156	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
157	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	1	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	1	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	D₁₇₂	—	2	2	no	—
171	D₁₇₂	—	2	2	no	—
172	D₁₇₂	—	4	1	no	—
173	D₁₇₂	—	4	1	no	—
174	C₄×D₄₃	—	4	2	no	—
175	C₄×D₄₃	—	4	2	no	—
176	C₄×D₄₃	—	4	2	no	—
177	C₄×D₄₃	—	4	2	no	—
178	C₈×C₄₃	—	4	2	no	—
179	C₄₃⋊C₈	—	4	2	no	—
180	C₄₃⋊C₈	—	8	1	no	—
181	#8976	—	43	1	no	maximal, Sylow
182	C₂²×C₄₃	#386	1	1	yes	characteristic
183	C₂²×C₄₃	#450	1	1	yes	characteristic
184	C₂²×C₄₃	#452	1	1	yes	characteristic
185	C₂²×C₄₃	#452	1	1	yes	characteristic
186	C₂²×C₄₃	#452	1	1	yes	characteristic
187	C₂²×C₄₃	#453	1	1	yes	characteristic
188	C₂²×C₄₃	#454	1	1	yes	characteristic
189	C₂×D₄₃	—	4	2	no	—
190	C₂×D₄₃	—	4	2	no	—
191	C₂×D₄₃	—	4	2	no	—
192	C₂×D₄₃	—	8	1	no	—
193	C₂×D₄₃	—	8	1	no	—
194	C₂×D₄₃	—	8	1	no	—
195	C₂×D₄₃	—	8	1	no	—
196	C₄×C₄₃	—	2	1	no	—
197	C₄×C₄₃	—	2	1	no	—
198	C₄×C₄₃	—	8	2	no	—
199	C₄×C₄₃	—	8	2	no	—
200	C₄×C₄₃	#416	1	1	yes	characteristic
201	C₄×C₄₃	#419	1	1	yes	characteristic
202	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
203	C₄×C₄₃	#440	1	1	yes	characteristic
204	C₄×C₄₃	#461	1	1	yes	characteristic
205	C₄×C₄₃	#463	1	1	yes	characteristic
206	C₄×C₄₃	#485	1	1	yes	characteristic
207	C₄×C₄₃	#485	1	1	yes	characteristic
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	4	2	no	—
210	Dic₄₃	—	8	1	no	—
211	C₂×#476	—	43	1	no	—
212	#2354	—	43	1	no	—
213	#1987	—	43	1	no	—
214	#1956	D₄₃	1	1	yes	characteristic, complemented
215	C₂×D₄⋊C₈	—	43	1	no	—
216	#1296	—	43	1	no	—
217	#1279	—	43	1	no	—
218	C₂×C₄₃	#1631	1	1	yes	characteristic
219	C₂×C₄₃	#1634	1	1	yes	characteristic
220	C₂×C₄₃	#1635	1	1	yes	characteristic
221	C₂×C₄₃	#1638	1	1	yes	characteristic
222	C₂×C₄₃	#1873	1	1	yes	characteristic
223	C₂×C₄₃	#1877	1	1	yes	characteristic
224	C₂×C₄₃	#1883	1	1	yes	characteristic
225	D₄₃	—	8	2	no	—
226	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
227	C₂×C₄×D₄	—	43	1	no	—
228	C₂×#117	—	86	1	no	—
229	#476	—	43	4	no	—
230	#476	—	86	2	no	—
231	C₂×#106	—	86	1	no	—
232	C₂×C₄⋊C₈	—	43	1	no	—
233	C₂×C₄⋊C₈	—	43	1	no	—
234	C₂×#103	—	2	2	no	—
235	C₂×#102	—	86	1	no	—
236	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
237	#390	—	86	1	no	—
238	#388	—	86	2	no	—
239	#384	C₂×D₄₃	1	1	yes	characteristic
240	#380	—	86	1	no	—
241	C₄×C₄⋊C₄	—	43	1	no	—
242	C₄×C₄⋊C₄	—	86	1	no	—
243	#340	—	86	1	no	—
244	#340	—	86	1	no	—
245	D₄⋊C₈	—	86	2	no	—
246	C₄₃	#8976	1	1	yes	characteristic, complemented, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×D₄	—	43	1	no	—
249	C₂³×C₄	—	86	1	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	86	1	no	—
252	C₂²×C₈	—	86	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
257	C₄×D₄	—	43	2	no	—
258	C₄×D₄	—	43	2	no	—
259	C₄×D₄	—	86	1	no	—
260	C₄×D₄	—	86	1	no	—
261	#117	—	172	2	no	—
262	#117	—	172	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	43	1	no	—
268	C₂×C₄⋊C₄	—	43	1	no	—
269	C₂×C₄⋊C₄	—	43	1	no	—
270	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	86	1	no	—
272	C₂×C₂²⋊C₄	—	86	2	no	—
273	C₂×C₂²⋊C₄	—	86	2	no	—
274	C₂×C₄²	—	86	2	no	—
275	C₂×C₄²	—	86	1	no	—
276	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
277	#106	—	86	4	no	—
278	C₄⋊C₈	—	43	2	no	—
279	C₄⋊C₈	—	86	1	no	—
280	C₄⋊C₈	—	86	1	no	—
281	C₄⋊C₈	—	86	1	no	—
282	#103	—	4	4	no	—
283	#102	—	86	4	no	—
284	C₄×C₈	—	2	1	no	—
285	C₄×C₈	—	2	1	no	—
286	#95	—	86	2	no	—
287	#95	—	86	1	no	—
288	C₂⁴	—	86	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×D₄	—	43	2	no	—
294	C₂×D₄	—	86	1	no	—
295	C₂×D₄	—	86	1	no	—
296	C₂×D₄	—	86	1	no	—
297	C₂×D₄	—	86	1	no	—
298	C₂×D₄	—	86	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	1	no	—
301	C₂²×C₄	—	86	1	no	—
302	C₂²×C₄	—	86	1	no	—
303	C₂²×C₄	—	86	2	no	—
304	C₂²×C₄	—	86	2	no	—
305	C₂²×C₄	—	86	1	no	—
306	C₂²×C₄	—	172	1	no	—
307	C₂²×C₄	—	172	1	no	—
308	C₂²×C₄	—	172	1	no	—
309	C₂²×C₄	—	172	1	no	—
310	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	86	2	no	—
317	C₂×C₈	—	172	1	no	—
318	C₂×C₈	—	172	1	no	—
319	C₂×C₈	—	172	1	no	—
320	C₂×C₈	—	172	1	no	—
321	C₂×C₈	—	172	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	43	2	no	—
332	C₄⋊C₄	—	43	2	no	—
333	C₄⋊C₄	—	86	1	no	—
334	C₄⋊C₄	—	86	1	no	—
335	C₄⋊C₄	—	86	1	no	—
336	C₄⋊C₄	—	86	1	no	—
337	C₂²⋊C₄	—	86	2	no	—
338	C₂²⋊C₄	—	86	2	no	—
339	C₂²⋊C₄	—	344	2	no	—
340	C₂²⋊C₄	—	172	4	no	—
341	C₄²	—	172	4	no	—
342	C₄²	—	172	1	no	—
343	C₄²	—	172	1	no	—
344	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
345	C₄²	#10621898	1	1	yes	characteristic
346	C₄²	D₄×D₄₃	1	1	yes	characteristic
347	C₄²	#10621900	1	1	yes	characteristic
348	C₂³	—	86	2	no	—
349	C₂³	—	172	1	no	—
350	C₂³	—	172	1	no	—
351	C₂³	—	172	1	no	—
352	C₂³	—	172	1	no	—
353	C₂³	—	172	1	no	—
354	C₂³	—	172	1	no	—
355	C₂³	#13063293	1	1	yes	characteristic
356	Q₈	—	4	4	no	—
357	Q₈	—	8	2	no	—
358	D₄	—	86	2	no	—
359	D₄	—	86	2	no	—
360	D₄	—	172	1	no	—
361	D₄	—	172	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	8	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	86	2	no	—
371	C₂×C₄	—	86	2	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	—	172	1	no	—
374	C₂×C₄	—	172	1	no	—
375	C₂×C₄	—	172	1	no	—
376	C₂×C₄	—	172	1	no	—
377	C₂×C₄	—	172	1	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	—	172	2	no	—
380	C₂×C₄	—	172	2	no	—
381	C₂×C₄	—	172	2	no	—
382	C₂×C₄	—	172	2	no	—
383	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
384	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
386	C₂×C₄	#13063296	1	1	yes	characteristic
387	C₂×C₄	#13063298	1	1	yes	characteristic
388	C₂×C₄	#13063307	1	1	yes	characteristic
389	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
390	C₂×C₄	#13063346	1	1	yes	characteristic
391	C₂×C₄	#13063348	1	1	yes	characteristic
392	C₂×C₄	#13063348	1	1	yes	characteristic
393	C₂×C₄	#13063352	1	1	yes	characteristic
394	C₂×C₄	#13063354	1	1	yes	characteristic
395	C₂×C₄	#13063357	1	1	yes	characteristic
396	C₂×C₄	#13063357	1	1	yes	characteristic
397	C₈	—	4	2	no	—
398	C₈	—	344	1	no	—
399	C₈	—	172	2	no	—
400	C₂²	—	344	1	no	—
401	C₂²	—	344	1	no	—
402	C₂²	—	344	1	no	—
403	C₂²	—	344	1	no	—
404	C₂²	—	172	2	no	—
405	C₂²	—	172	2	no	—
406	C₂²	—	172	2	no	—
407	C₂²	#14582775	1	1	yes	characteristic
408	C₂²	#14583048	1	1	yes	characteristic
409	C₂²	#14583058	1	1	yes	characteristic
410	C₂²	#14583060	1	1	yes	characteristic
411	C₂²	#14583060	1	1	yes	characteristic
412	C₂²	#14583066	1	1	yes	characteristic
413	C₂²	#14583071	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	2	no	—
418	C₄	—	344	1	no	—
419	C₄	—	172	2	no	—
420	C₄	—	172	2	no	—
421	C₄	#14582894	1	1	yes	characteristic
422	C₄	#14582906	1	1	yes	characteristic
423	C₄	#14582984	1	1	yes	characteristic
424	C₄	#14583002	1	1	yes	characteristic
425	C₄	#14583103	1	1	yes	characteristic
426	C₄	#14583117	1	1	yes	characteristic
427	C₄	#14583238	1	1	yes	characteristic
428	C₄	#14583239	1	1	yes	characteristic
429	C₂	—	344	2	no	—
430	C₂	#19133719	1	1	yes	characteristic
431	C₂	#19133738	1	1	yes	characteristic
432	C₂	#19133743	1	1	yes	characteristic
433	C₂	#19133764	1	1	yes	characteristic
434	C₂	#19134904	1	1	yes	characteristic
435	C₂	#19134926	1	1	yes	characteristic
436	C₂	#19134974	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063293
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1956	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1956	D₄₃
hypocenter	C₄₃	#8976
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

Complements

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

N	H ≅ G/N	type
3. #19135544	C₂	semidirect
5. #19132478	C₂	semidirect
6. #19132435	C₂	semidirect
7. C₄₃×#1956	C₂	semidirect
11. #14583186	C₄	semidirect
214. #1956	D₄₃	semidirect
246. C₄₃	#8976	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583186	2
#19137546	2
#19135544	2
C₂×#14582628	2
#19132478	2
#19132435	2
C₄₃×#1956	2
#8976	43