Subgroups — #25155552

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19139626	C₂	1	1	yes	maximal, characteristic, complemented
2	#19136123	C₂	1	2	yes	maximal
3	#19135983	C₂	1	2	yes	maximal
4	#19135353	C₂	1	2	yes	maximal, complemented
5	#19135351	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135314	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135166	C₂	1	2	yes	maximal, complemented
8	#19134754	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134595	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063246	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2354	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063316	—	2	1	no	—
13	C₂×#13063258	C₂²	1	2	yes	—
14	C₂×#13063258	C₂²	1	2	yes	—
15	C₂×#13063258	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	C₂×#13063246	C₂²	1	1	yes	characteristic
19	C₂×#13063246	C₂²	1	1	yes	characteristic
20	C₂×#13063246	C₂²	1	2	yes	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582831	—	2	2	no	—
23	#14582798	—	2	1	no	—
24	#14582797	C₂²	1	2	yes	—
25	#14582769	C₂²	1	1	yes	characteristic
26	#14582769	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
28	#14582661	C₂²	1	2	yes	—
29	#14582661	C₂²	1	1	yes	characteristic
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	1	yes	characteristic
32	#14582654	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
34	C₂×#117×C₄₃	—	2	1	no	—
35	C₄₃×#390	C₂²	1	2	yes	—
36	C₄₃×#388	—	2	2	no	—
37	C₄₃×#384	C₂²	1	1	yes	characteristic
38	C₄₃×#380	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	#13063316	—	4	4	no	—
45	C₂×C₄⋊Dic₄₃	—	2	1	no	—
46	C₂×C₄⋊Dic₄₃	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	—	2	2	no	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×Dic₄₃⋊C₄	—	2	2	no	—
53	C₂×C₄×Dic₄₃	—	2	1	no	—
54	#13063258	—	2	4	no	—
55	#13063258	—	4	2	no	—
56	#13063258	—	4	2	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
59	#13063246	—	2	2	no	—
60	#13063246	—	2	2	no	—
61	#13063246	—	4	2	no	—
62	C₄×C₄₃⋊C₈	—	2	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	C₄₃⋊#95	—	2	1	no	—
65	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₄₃	—	2	1	no	—
67	C₄×D₄×C₄₃	—	2	2	no	—
68	C₄×D₄×C₄₃	Q₈	1	4	yes	—
69	#117×C₄₃	—	4	4	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
79	C₂×C₄²×C₄₃	—	2	2	no	—
80	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
82	#95×C₄₃	—	2	2	no	—
83	#95×C₄₃	D₄	1	2	yes	—
84	C₂⁴×C₄₃	—	2	1	no	—
85	C₂×D₄×C₄₃	—	2	1	no	—
86	C₂×D₄×C₄₃	—	2	1	no	—
87	C₂×D₄×C₄₃	—	2	1	no	—
88	C₂×D₄×C₄₃	—	2	1	no	—
89	C₂×D₄×C₄₃	—	2	1	no	—
90	C₂×D₄×C₄₃	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	4	2	no	—
95	C₂²×C₄×C₄₃	—	4	2	no	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₃	—	2	1	no	—
102	C₂²×Dic₄₃	—	2	1	no	—
103	C₂²×Dic₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	4	2	no	—
109	C₄⋊C₄×C₄₃	—	8	1	no	—
110	C₄⋊C₄×C₄₃	D₈	1	4	yes	—
111	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
112	C₂²⋊C₄×C₄₃	—	2	4	no	—
113	C₂²⋊C₄×C₄₃	—	4	4	no	—
114	C₂²⋊C₄×C₄₃	—	8	2	no	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	—	4	4	no	—
118	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
119	C₄²×C₄₃	#41	1	2	yes	—
120	C₄⋊Dic₄₃	—	2	1	no	—
121	C₄⋊Dic₄₃	—	2	1	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	C₄⋊Dic₄₃	—	2	2	no	—
124	C₄⋊Dic₄₃	—	2	1	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	4	4	no	—
127	C₄⋊Dic₄₃	—	4	2	no	—
128	C₄⋊Dic₄₃	—	8	1	no	—
129	C₄⋊Dic₄₃	—	8	2	no	—
130	Dic₄₃⋊C₄	—	4	4	no	—
131	C₄×Dic₄₃	—	4	2	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	—	2	1	no	—
136	C₂×C₄₃⋊C₈	—	2	2	no	—
137	C₂×C₄₃⋊C₈	—	2	2	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	#41	1	2	yes	—
140	C₂×C₄₃⋊C₈	#41	1	2	yes	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	4	1	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	4	1	no	—
148	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
149	D₄×C₄₃	—	2	2	no	—
150	D₄×C₄₃	—	2	2	no	—
151	D₄×C₄₃	—	4	1	no	—
152	D₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	4	8	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	2	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
169	C₂×C₄×C₄₃	C₂×D₈	1	4	yes	—
170	C₂×C₄×C₄₃	C₂×D₈	1	2	yes	—
171	C₂×C₄×C₄₃	#137	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	—	4	2	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₄₃⋊C₈	—	2	2	no	—
188	C₄₃⋊C₈	—	2	2	no	—
189	C₄₃⋊C₈	—	4	2	no	—
190	#26086	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	4	2	no	—
192	C₂²×C₄₃	—	4	2	no	—
193	C₂²×C₄₃	—	4	2	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	—	8	1	no	—
196	C₂²×C₄₃	—	8	1	no	—
197	C₂²×C₄₃	—	8	1	no	—
198	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
199	C₂²×C₄₃	#547	1	1	yes	characteristic
200	C₂²×C₄₃	#550	1	1	yes	characteristic
201	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
203	C₂²×C₄₃	#576	1	1	yes	characteristic
204	C₂²×C₄₃	#578	1	1	yes	characteristic
205	C₄×C₄₃	—	2	4	no	—
206	C₄×C₄₃	—	2	2	no	—
207	C₄×C₄₃	—	4	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	#474	1	4	yes	—
211	C₄×C₄₃	#533	1	1	yes	characteristic
212	C₄×C₄₃	#544	1	1	yes	characteristic
213	C₄×C₄₃	#552	1	1	yes	characteristic
214	C₄×C₄₃	#553	1	1	yes	characteristic
215	Dic₄₃	—	8	1	no	—
216	Dic₄₃	—	8	1	no	—
217	Dic₄₃	—	8	2	no	—
218	#2552	—	43	1	no	—
219	#2354	D₄₃	1	1	yes	characteristic
220	#2093	—	43	2	no	—
221	#2067	—	43	2	no	—
222	#1947	—	43	1	no	—
223	#1947	—	43	2	no	—
224	#1939	—	43	1	no	—
225	#1918	—	43	2	no	—
226	#1845	—	43	1	no	—
227	#1802	—	43	1	no	—
228	C₄×#102	—	43	1	no	—
229	C₂×C₄₃	—	8	2	no	—
230	C₂×C₄₃	#2441	1	1	yes	characteristic
231	C₂×C₄₃	C₂×#474	1	1	yes	characteristic
232	C₂×C₄₃	#3083	1	1	yes	characteristic
233	C₂×C₄₃	#3334	1	1	yes	characteristic
234	C₂×C₄₃	#3357	1	1	yes	characteristic
235	C₂×C₄₃	#3391	1	1	yes	characteristic
236	C₂×C₄₃	#3398	1	1	yes	characteristic
237	C₂×#125	—	86	1	no	—
238	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
239	C₂×#117	—	2	1	no	—
240	C₂×#107	—	43	2	no	—
241	C₂×#107	—	43	2	no	—
242	C₂×#107	—	43	2	no	—
243	C₂×C₄⋊C₈	—	43	1	no	—
244	C₂×C₄⋊C₈	—	43	2	no	—
245	C₂×#102	—	43	1	no	—
246	C₂×#102	—	43	1	no	—
247	C₂×#102	—	43	2	no	—
248	C₂×C₄×C₈	—	43	1	no	—
249	#398	—	86	2	no	—
250	#390	C₂×D₄₃	1	2	yes	—
251	#389	—	43	2	no	—
252	#389	—	86	1	no	—
253	#388	—	2	2	no	—
254	#384	—	43	1	no	—
255	#384	—	43	2	no	—
256	#384	C₂×D₄₃	1	1	yes	characteristic
257	#380	—	2	1	no	—
258	C₄×C₄⋊C₄	—	43	1	no	—
259	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
260	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
261	#340	—	43	2	no	—
262	#340	—	43	2	no	—
263	#340	—	43	1	no	—
264	#340	—	43	1	no	—
265	#336	—	43	2	no	—
266	C₄₃	#26086	1	1	yes	characteristic, complemented, Sylow
267	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	—	43	1	no	—
271	C₂²×C₈	—	43	2	no	—
272	#125	—	172	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	Dic₈₆	1	4	yes	—
275	#117	—	4	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	43	1	no	—
279	C₂×C₄⋊C₄	—	43	1	no	—
280	C₂×C₄⋊C₄	—	43	2	no	—
281	C₂×C₄⋊C₄	—	86	2	no	—
282	C₂×C₄⋊C₄	—	86	1	no	—
283	C₂×C₄⋊C₄	—	86	2	no	—
284	C₂×C₄⋊C₄	—	86	1	no	—
285	C₂×C₄⋊C₄	—	86	2	no	—
286	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	86	1	no	—
295	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
296	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
297	#107	—	86	4	no	—
298	#107	—	172	2	no	—
299	#107	—	172	2	no	—
300	C₄⋊C₈	—	86	4	no	—
301	C₄⋊C₈	—	86	2	no	—
302	#102	—	86	2	no	—
303	#102	—	86	2	no	—
304	#102	—	172	2	no	—
305	C₄×C₈	—	86	2	no	—
306	#95	—	2	2	no	—
307	#95	—	86	1	no	—
308	#95	—	86	2	no	—
309	#95	C₂²⋊D₄₃	1	2	yes	—
310	C₂⁴	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂×Dic₈₆	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	4	2	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	86	1	no	—
323	C₂²×C₄	—	86	1	no	—
324	C₂²×C₄	—	86	2	no	—
325	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
326	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
328	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
329	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
330	C₂×C₈	—	43	2	no	—
331	C₂×C₈	—	43	2	no	—
332	C₂×C₈	—	86	1	no	—
333	C₂×C₈	—	86	1	no	—
334	C₂×C₈	—	86	1	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	2	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	86	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	86	1	no	—
347	C₄⋊C₄	—	86	2	no	—
348	C₄⋊C₄	—	86	2	no	—
349	C₄⋊C₄	—	86	1	no	—
350	C₄⋊C₄	—	86	1	no	—
351	C₄⋊C₄	—	344	1	no	—
352	C₄⋊C₄	—	344	2	no	—
353	C₄⋊C₄	—	172	4	no	—
354	C₄⋊C₄	—	172	4	no	—
355	C₄⋊C₄	—	172	2	no	—
356	C₄⋊C₄	#10621882	1	4	yes	—
357	C₄⋊C₄	C₂×Dic₈₆	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	172	2	no	—
365	C₄²	C₂×Dic₈₆	1	2	yes	—
366	C₄²	#10621898	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	172	1	no	—
394	C₂×C₄	—	172	2	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	—	172	1	no	—
401	C₂×C₄	—	172	1	no	—
402	C₂×C₄	#13063304	1	2	yes	—
403	C₂×C₄	#13063304	1	2	yes	—
404	C₂×C₄	C₂×#10621882	1	4	yes	—
405	C₂×C₄	C₂×#10621882	1	2	yes	—
406	C₂×C₄	#13063355	1	2	yes	—
407	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
408	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
409	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
411	C₂×C₄	#13063371	1	1	yes	characteristic
412	C₂×C₄	#13063372	1	1	yes	characteristic
413	C₈	—	86	2	no	—
414	C₈	—	86	2	no	—
415	C₈	—	172	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	C₂×#13063304	1	1	yes	characteristic
424	C₂²	#14583548	1	1	yes	characteristic
425	C₂²	#14583568	1	1	yes	characteristic
426	C₂²	C₂²×#10621882	1	1	yes	characteristic
427	C₂²	C₂×#13063355	1	1	yes	characteristic
428	C₂²	#14583702	1	1	yes	characteristic
429	C₂²	#14583714	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	344	1	no	—
436	C₄	—	344	2	no	—
437	C₄	—	344	1	no	—
438	C₄	#14583179	1	4	yes	—
439	C₄	#14583452	1	1	yes	characteristic
440	C₄	#14583527	1	1	yes	characteristic
441	C₄	#14583588	1	1	yes	characteristic
442	C₄	#14583593	1	1	yes	characteristic
443	C₂	—	8	2	no	—
444	C₂	#19138302	1	1	yes	characteristic
445	C₂	C₂×#14583179	1	1	yes	characteristic
446	C₂	#19144446	1	1	yes	characteristic
447	C₂	#19146938	1	1	yes	characteristic
448	C₂	#19147215	1	1	yes	characteristic
449	C₂	#19147567	1	1	yes	characteristic
450	C₂	#19147626	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2354	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₄×C₄₃	C₂³
hypercenter	#2354	D₄₃
hypocenter	C₄₃	#26086
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2354

Complements

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

N	H ≅ G/N	type
1. #19139626	C₂	semidirect
4. #19135353	C₂	semidirect
5. #19135351	C₂	semidirect
6. #19135314	C₂	semidirect
7. #19135166	C₂	semidirect
8. #19134754	C₂	semidirect
266. C₄₃	#26086	semidirect

Maximal subgroups

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

subgroup	index
#19139626	2
#19136123	2
#19135983	2
#19135353	2
#19135351	2
#19135314	2
#19135166	2
#19134754	2
#19134595	2
C₄×#13063246	2
C₄₃×#2354	2
#26086	43