Subgroups — #24991410

Order 11008.

592 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583176	C₂	1	1	yes	maximal, characteristic
2	#19137542	C₂	1	1	yes	maximal, characteristic
3	#19135557	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
5	#19132479	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
9	C₂×#13063283	—	2	1	no	—
10	#14583176	—	2	2	no	—
11	#14583176	C₄	1	4	yes	complemented
12	C₂×#13063258	—	2	1	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063245	—	2	1	no	—
15	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	#14582801	—	2	1	no	—
17	#14582791	—	2	2	no	—
18	#14582769	C₂²	1	1	yes	characteristic
19	#14582756	—	2	1	no	—
20	C₄×C₄⋊Dic₄₃	—	2	1	no	—
21	#14582661	—	2	2	no	—
22	#14582626	—	2	2	no	—
23	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×#103×C₄₃	—	2	1	no	—
26	C₂×#103×C₄₃	—	2	1	no	—
27	C₄×C₄⋊C₄×C₄₃	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	—	2	1	no	—
39	C₂×C₄⋊Dic₄₃	—	2	1	no	—
40	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
42	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
43	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
44	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
45	C₂×C₄×Dic₄₃	—	2	2	no	—
46	#13063258	—	2	4	no	—
47	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
48	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
49	#13063245	—	2	4	no	—
50	C₄×C₄₃⋊C₈	—	2	1	no	—
51	C₄×C₄₃⋊C₈	—	2	1	no	—
52	C₄₃⋊#95	—	2	2	no	—
53	C₂²×Q₈×C₄₃	—	2	1	no	—
54	C₂²×C₈×C₄₃	—	2	1	no	—
55	C₄⋊Q₈×C₄₃	—	2	1	no	—
56	C₄⋊Q₈×C₄₃	—	2	1	no	—
57	C₄⋊Q₈×C₄₃	—	2	1	no	—
58	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×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	#103×C₄₃	—	4	2	no	—
68	#103×C₄₃	—	4	2	no	—
69	#95×C₄₃	—	2	1	no	—
70	C₂³×D₄₃	—	2	1	no	—
71	C₂×Q₈×C₄₃	—	2	2	no	—
72	C₂×Q₈×C₄₃	—	4	1	no	—
73	C₂×Q₈×C₄₃	—	4	1	no	—
74	C₂×Q₈×C₄₃	—	4	1	no	—
75	C₂×Q₈×C₄₃	—	4	1	no	—
76	C₂×Q₈×C₄₃	—	4	1	no	—
77	C₂²×C₄×C₄₃	—	2	1	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	4	1	no	—
80	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₄₃	—	2	1	no	—
84	C₂²×Dic₄₃	—	2	2	no	—
85	C₂×D₁₇₂	—	2	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	—	2	1	no	—
88	C₂×D₁₇₂	—	2	1	no	—
89	C₂×D₁₇₂	—	2	1	no	—
90	C₂×D₁₇₂	C₂²⋊C₄	1	2	yes	—
91	C₂×C₄×D₄₃	—	2	2	no	—
92	C₂×C₄×D₄₃	—	2	2	no	—
93	C₂×C₄×D₄₃	—	4	1	no	—
94	C₂×C₄×D₄₃	—	4	1	no	—
95	C₂×C₄×D₄₃	—	4	1	no	—
96	C₂×C₄×D₄₃	—	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	—	2	1	no	—
101	C₄⋊C₄×C₄₃	—	2	2	no	—
102	C₄⋊C₄×C₄₃	—	2	2	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	4	1	no	—
106	C₄⋊C₄×C₄₃	—	4	1	no	—
107	C₄⋊C₄×C₄₃	D₈	1	2	yes	—
108	C₄²×C₄₃	—	4	1	no	—
109	C₄²×C₄₃	—	4	1	no	—
110	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₄₃	#41	1	1	yes	characteristic
113	C₄²×C₄₃	#41	1	1	yes	characteristic
114	(C₂×D₄₃)⋊C₄	—	2	2	no	—
115	(C₂×D₄₃)⋊C₄	—	2	2	no	—
116	(C₂×D₄₃)⋊C₄	—	4	4	no	—
117	(C₂×D₄₃)⋊C₄	—	8	2	no	—
118	C₄⋊Dic₄₃	—	2	1	no	—
119	C₄⋊Dic₄₃	—	4	1	no	—
120	C₄⋊Dic₄₃	—	4	1	no	—
121	C₄⋊Dic₄₃	—	4	1	no	—
122	C₄⋊Dic₄₃	—	4	1	no	—
123	C₄⋊Dic₄₃	—	4	2	no	—
124	C₄⋊Dic₄₃	C₂²⋊C₄	1	2	yes	—
125	C₄×Dic₄₃	—	4	4	no	—
126	C₂×C₄₃⋊C₈	—	2	2	no	—
127	C₂×C₄₃⋊C₈	—	2	2	no	—
128	C₂×C₄₃⋊C₈	—	4	1	no	—
129	C₂×C₄₃⋊C₈	—	4	1	no	—
130	C₂×C₄₃⋊C₈	—	4	1	no	—
131	C₂×C₄₃⋊C₈	—	4	1	no	—
132	C₂³×C₄₃	#120	1	1	yes	characteristic
133	C₂²×D₄₃	—	2	2	no	—
134	C₂²×D₄₃	—	4	1	no	—
135	C₂²×D₄₃	—	4	1	no	—
136	C₂²×D₄₃	—	4	1	no	—
137	C₂²×D₄₃	—	4	1	no	—
138	C₂²×D₄₃	—	4	1	no	—
139	C₂²×D₄₃	—	4	1	no	—
140	Q₈×C₄₃	—	4	2	no	—
141	Q₈×C₄₃	—	4	2	no	—
142	Q₈×C₄₃	—	8	1	no	—
143	Q₈×C₄₃	—	8	1	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	8	1	no	—
154	C₂×C₄×C₄₃	—	8	1	no	—
155	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
163	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
164	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
165	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	2	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	D₁₇₂	—	2	2	no	—
176	D₁₇₂	—	2	2	no	—
177	D₁₇₂	—	4	1	no	—
178	D₁₇₂	—	4	1	no	—
179	C₄×D₄₃	—	4	2	no	—
180	C₄×D₄₃	—	4	2	no	—
181	C₄×D₄₃	—	4	2	no	—
182	C₄×D₄₃	—	4	2	no	—
183	C₈×C₄₃	—	8	1	no	—
184	C₄₃⋊C₈	—	4	2	no	—
185	C₄₃⋊C₈	—	4	2	no	—
186	#8984	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	#386	1	1	yes	characteristic
188	C₂²×C₄₃	#447	1	1	yes	characteristic
189	C₂²×C₄₃	#449	1	1	yes	characteristic
190	C₂²×C₄₃	#452	1	1	yes	characteristic
191	C₂²×C₄₃	#452	1	1	yes	characteristic
192	C₂²×C₄₃	#455	1	1	yes	characteristic
193	C₂²×C₄₃	#456	1	1	yes	characteristic
194	C₂×D₄₃	—	4	2	no	—
195	C₂×D₄₃	—	4	2	no	—
196	C₂×D₄₃	—	4	2	no	—
197	C₂×D₄₃	—	8	1	no	—
198	C₂×D₄₃	—	8	1	no	—
199	C₂×D₄₃	—	8	1	no	—
200	C₂×D₄₃	—	8	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	8	2	no	—
205	C₄×C₄₃	—	8	1	no	—
206	C₄×C₄₃	#416	1	1	yes	characteristic
207	C₄×C₄₃	#419	1	1	yes	characteristic
208	C₄×C₄₃	C₄×D₈	1	1	yes	characteristic
209	C₄×C₄₃	#442	1	1	yes	characteristic
210	C₄×C₄₃	#459	1	1	yes	characteristic
211	C₄×C₄₃	#463	1	1	yes	characteristic
212	C₄×C₄₃	#485	1	1	yes	characteristic
213	C₄×C₄₃	#485	1	1	yes	characteristic
214	Dic₄₃	—	4	2	no	—
215	Dic₄₃	—	8	2	no	—
216	C₂×#474	—	43	1	no	—
217	#2354	—	43	1	no	—
218	#1990	—	43	1	no	—
219	#1981	D₄₃	1	1	yes	characteristic, complemented
220	C₂×D₄⋊C₈	—	43	1	no	—
221	#1296	—	43	1	no	—
222	#1279	—	43	1	no	—
223	C₂×C₄₃	#1641	1	1	yes	characteristic
224	C₂×C₄₃	#1646	1	1	yes	characteristic
225	C₂×C₄₃	#1647	1	1	yes	characteristic
226	C₂×C₄₃	#1652	1	1	yes	characteristic
227	C₂×C₄₃	#1873	1	1	yes	characteristic
228	C₂×C₄₃	#1879	1	1	yes	characteristic
229	C₂×C₄₃	#1882	1	1	yes	characteristic
230	D₄₃	—	8	2	no	—
231	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
232	C₂×C₄×D₄	—	43	1	no	—
233	C₂×#117	—	86	1	no	—
234	#474	—	43	4	no	—
235	#474	—	86	2	no	—
236	C₂×#107	—	86	1	no	—
237	C₂×C₄⋊C₈	—	43	1	no	—
238	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
239	C₂×#103	—	2	1	no	—
240	C₂×#103	—	2	1	no	—
241	C₂×#102	—	86	1	no	—
242	C₂×C₄×C₈	—	43	1	no	—
243	#390	—	86	1	no	—
244	#388	—	86	2	no	—
245	#384	—	43	1	no	—
246	#380	—	86	1	no	—
247	C₄×C₄⋊C₄	—	86	1	no	—
248	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
249	#340	—	86	2	no	—
250	D₄⋊C₈	—	86	2	no	—
251	C₄₃	#8984	1	1	yes	characteristic, complemented, Sylow
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×D₄	—	43	1	no	—
254	C₂³×C₄	—	86	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₂²×C₈	—	86	1	no	—
257	C₂²×C₈	—	86	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₄×D₄₃	1	2	yes	—
262	C₄×D₄	—	43	2	no	—
263	C₄×D₄	—	43	2	no	—
264	C₄×D₄	—	86	1	no	—
265	C₄×D₄	—	86	1	no	—
266	#117	—	172	2	no	—
267	#117	—	172	2	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	43	1	no	—
271	C₂×C₄⋊C₄	—	43	2	no	—
272	C₂×C₄⋊C₄	—	86	1	no	—
273	C₂×C₄⋊C₄	—	86	1	no	—
274	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	—	86	1	no	—
277	C₂×C₂²⋊C₄	—	86	2	no	—
278	C₂×C₂²⋊C₄	—	86	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	86	2	no	—
281	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
282	#107	—	86	4	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	43	2	no	—
286	C₄⋊C₈	—	86	1	no	—
287	#103	—	4	2	no	—
288	#103	—	4	2	no	—
289	#102	—	86	4	no	—
290	C₄×C₈	—	86	1	no	—
291	C₄×C₈	—	86	1	no	—
292	#95	—	2	1	no	—
293	#95	—	86	2	no	—
294	C₂⁴	—	86	1	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	—	4	1	no	—
301	C₂×D₄	—	43	2	no	—
302	C₂×D₄	—	86	1	no	—
303	C₂×D₄	—	86	1	no	—
304	C₂×D₄	—	86	1	no	—
305	C₂×D₄	—	86	1	no	—
306	C₂×D₄	—	86	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	86	1	no	—
311	C₂²×C₄	—	86	2	no	—
312	C₂²×C₄	—	86	2	no	—
313	C₂²×C₄	—	86	2	no	—
314	C₂²×C₄	—	172	1	no	—
315	C₂²×C₄	—	172	1	no	—
316	C₂²×C₄	—	172	1	no	—
317	C₂²×C₄	—	172	1	no	—
318	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	4	1	no	—
323	C₂×C₈	—	4	1	no	—
324	C₂×C₈	—	86	2	no	—
325	C₂×C₈	—	86	2	no	—
326	C₂×C₈	—	172	1	no	—
327	C₂×C₈	—	172	1	no	—
328	C₂×C₈	—	172	1	no	—
329	C₂×C₈	—	172	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	43	2	no	—
338	C₄⋊C₄	—	86	1	no	—
339	C₄⋊C₄	—	172	2	no	—
340	C₄⋊C₄	—	172	1	no	—
341	C₄⋊C₄	—	172	1	no	—
342	C₄⋊C₄	—	172	1	no	—
343	C₄⋊C₄	—	172	1	no	—
344	C₄⋊C₄	#10621882	1	2	yes	—
345	C₂²⋊C₄	—	86	2	no	—
346	C₂²⋊C₄	—	86	2	no	—
347	C₂²⋊C₄	—	344	2	no	—
348	C₂²⋊C₄	—	172	4	no	—
349	C₄²	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	172	4	no	—
352	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
353	C₄²	#10621898	1	1	yes	characteristic
354	C₄²	D₄×D₄₃	1	1	yes	characteristic
355	C₄²	#10621900	1	1	yes	characteristic
356	C₂³	—	86	2	no	—
357	C₂³	—	172	1	no	—
358	C₂³	—	172	1	no	—
359	C₂³	—	172	1	no	—
360	C₂³	—	172	1	no	—
361	C₂³	—	172	1	no	—
362	C₂³	—	172	1	no	—
363	C₂³	#13063293	1	1	yes	characteristic
364	Q₈	—	4	2	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	8	1	no	—
367	Q₈	—	8	1	no	—
368	D₄	—	86	2	no	—
369	D₄	—	86	2	no	—
370	D₄	—	172	1	no	—
371	D₄	—	172	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	8	1	no	—
382	C₂×C₄	—	8	1	no	—
383	C₂×C₄	—	86	2	no	—
384	C₂×C₄	—	172	2	no	—
385	C₂×C₄	—	172	2	no	—
386	C₂×C₄	—	172	2	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	2	no	—
390	C₂×C₄	—	172	2	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
394	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
396	C₂×C₄	#13063296	1	1	yes	characteristic
397	C₂×C₄	#13063298	1	1	yes	characteristic
398	C₂×C₄	#13063307	1	1	yes	characteristic
399	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
400	C₂×C₄	#13063345	1	1	yes	characteristic
401	C₂×C₄	#13063346	1	1	yes	characteristic
402	C₂×C₄	#13063348	1	1	yes	characteristic
403	C₂×C₄	#13063350	1	1	yes	characteristic
404	C₂×C₄	#13063351	1	1	yes	characteristic
405	C₂×C₄	#13063354	1	1	yes	characteristic
406	C₂×C₄	#13063357	1	1	yes	characteristic
407	C₈	—	8	1	no	—
408	C₈	—	172	2	no	—
409	C₈	—	172	2	no	—
410	C₂²	—	344	1	no	—
411	C₂²	—	344	1	no	—
412	C₂²	—	344	1	no	—
413	C₂²	—	344	1	no	—
414	C₂²	—	172	2	no	—
415	C₂²	—	172	2	no	—
416	C₂²	—	172	2	no	—
417	C₂²	#14582775	1	1	yes	characteristic
418	C₂²	#14583032	1	1	yes	characteristic
419	C₂²	#14583042	1	1	yes	characteristic
420	C₂²	#14583058	1	1	yes	characteristic
421	C₂²	#14583060	1	1	yes	characteristic
422	C₂²	#14583075	1	1	yes	characteristic
423	C₂²	#14583080	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	344	2	no	—
430	C₄	—	172	2	no	—
431	C₄	#14582894	1	1	yes	characteristic
432	C₄	#14582906	1	1	yes	characteristic
433	C₄	C₄×#10621882	1	1	yes	characteristic
434	C₄	#14583009	1	1	yes	characteristic
435	C₄	#14583091	1	1	yes	characteristic
436	C₄	#14583111	1	1	yes	characteristic
437	C₄	#14583238	1	1	yes	characteristic
438	C₄	#14583239	1	1	yes	characteristic
439	C₂	—	344	2	no	—
440	C₂	#19133786	1	1	yes	characteristic
441	C₂	#19133821	1	1	yes	characteristic
442	C₂	#19133828	1	1	yes	characteristic
443	C₂	#19133863	1	1	yes	characteristic
444	C₂	#19134904	1	1	yes	characteristic
445	C₂	#19134946	1	1	yes	characteristic
446	C₂	#19134961	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063293
commutator	C₄²×C₄₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1981	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1981	D₄₃
hypocenter	C₄₃	#8984
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1981

Complements

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

N	H ≅ G/N	type
3. #19135557	C₂	semidirect
5. #19132479	C₂	semidirect
6. #19132436	C₂	semidirect
7. C₄₃×#1981	C₂	semidirect
11. #14583176	C₄	semidirect
219. #1981	D₄₃	semidirect
251. C₄₃	#8984	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583176	2
#19137542	2
#19135557	2
C₂×#14582626	2
#19132479	2
#19132436	2
C₄₃×#1981	2
#8984	43