Subgroups — #25103385

Order 11008.

906 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	#19144176	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583017	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143298	C₂	1	2	yes	maximal, complemented
4	#19135483	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135343	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135306	C₂	1	2	yes	maximal, complemented
7	#19135043	C₂	1	2	yes	maximal, complemented
8	#19134633	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134474	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134439	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063331	C₂²	1	2	yes	—
14	#14583410	C₂²	1	2	yes	—
15	#14583140	C₄	1	2	yes	complemented
16	#14583135	C₄	1	2	yes	complemented
17	#14583128	C₄	1	4	yes	complemented
18	#14583017	—	2	4	no	—
19	#14582975	—	2	4	no	—
20	#14582968	—	2	4	no	—
21	C₂×#13063261	C₂²	1	1	yes	characteristic
22	C₂×#13063261	C₂²	1	1	yes	characteristic
23	#14582937	C₂²	1	1	yes	characteristic
24	#14582925	C₂²	1	2	yes	—
25	C₂×#13063253	C₂²	1	2	yes	—
26	C₂×#13063253	C₂²	1	2	yes	—
27	#14582896	C₂²	1	2	yes	—
28	#14582865	C₂²	1	2	yes	—
29	#14582863	C₂²	1	2	yes	—
30	#14582854	C₂²	1	2	yes	—
31	#14582664	C₂²	1	2	yes	—
32	#14582659	C₂²	1	2	yes	—
33	#14582659	C₂²	1	2	yes	—
34	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
35	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
37	C₄₃×#405	—	2	4	no	—
38	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₂×#10621898	C₂³	1	2	yes	—
43	#13063347	—	2	2	no	—
44	#13063347	—	2	2	no	—
45	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
46	C₂×#10621873	C₂×C₄	1	2	yes	—
47	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
48	#13063331	—	2	4	no	—
49	#13063331	—	2	4	no	—
50	C₂×#10621877	C₂³	1	2	yes	—
51	C₂×#10621877	C₂³	1	2	yes	—
52	C₂×#10621872	—	2	2	no	—
53	C₂×C₈×D₄₃	—	2	2	no	—
54	#13063308	—	2	2	no	—
55	#13063304	C₂×C₄	1	4	yes	—
56	#13063299	C₂×C₄	1	4	yes	—
57	#13063294	—	2	2	no	—
58	C₄×C₂²⋊D₄₃	—	2	4	no	—
59	#13063284	C₂³	1	2	yes	—
60	#13063261	—	2	2	no	—
61	#13063261	—	2	2	no	—
62	#13063259	C₂×C₄	1	2	yes	—
63	#13063257	C₂×C₄	1	2	yes	—
64	Dic₄₃⋊C₈	—	2	4	no	—
65	#13063253	—	2	4	no	—
66	#13063253	—	2	4	no	—
67	#13063250	C₂×C₄	1	4	yes	—
68	#13063247	C₂×C₄	1	4	yes	—
69	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
70	(C₂×D₄₃)⋊C₈	—	2	4	no	—
71	#13063235	—	2	2	no	—
72	C₈×Dic₄₃	—	2	2	no	—
73	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₃	—	2	2	no	—
75	C₂×M₁₆×C₄₃	—	2	2	no	—
76	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
77	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
78	C₂²×C₈×C₄₃	—	2	2	no	—
79	C₂²×C₈×C₄₃	—	2	2	no	—
80	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₄₃	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
86	#117×C₄₃	—	2	2	no	—
87	#117×C₄₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
92	#97×C₄₃	—	2	2	no	—
93	#97×C₄₃	—	2	2	no	—
94	C₄×C₈×C₄₃	—	2	2	no	—
95	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
96	C₂⁴×C₄₃	#41	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	—	2	1	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	1	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₃	—	2	4	no	—
108	C₂×C₂²⋊D₄₃	—	2	2	no	—
109	#10621898	—	2	2	no	—
110	#10621898	—	2	2	no	—
111	#10621898	—	2	2	no	—
112	#10621898	—	2	2	no	—
113	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
114	C₂×C₄×D₄₃	—	2	2	no	—
115	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
116	M₁₆×C₄₃	—	2	4	no	—
117	M₁₆×C₄₃	—	2	4	no	—
118	C₂×C₈×C₄₃	—	2	1	no	—
119	C₂×C₈×C₄₃	—	2	1	no	—
120	C₂×C₈×C₄₃	—	2	1	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	4	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₃	#41	1	2	yes	—
133	C₂×C₈×C₄₃	#41	1	2	yes	—
134	C₄⋊C₄×C₄₃	—	2	4	no	—
135	C₂²⋊C₄×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	C₂×D₄	1	2	yes	—
139	C₄²×C₄₃	#41	1	2	yes	—
140	C₂²⋊Dic₄₃	—	2	4	no	—
141	C₂²⋊Dic₄₃	—	2	2	no	—
142	(C₂×D₄₃)⋊C₄	—	2	4	no	—
143	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
144	Dic₄₃⋊C₄	—	2	4	no	—
145	C₄×Dic₄₃	—	2	2	no	—
146	#10621877	—	2	2	no	—
147	#10621877	—	2	2	no	—
148	#10621877	—	2	2	no	—
149	#10621877	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	Dic₁₇₂	—	2	2	no	—
153	D₃₄₄	—	2	2	no	—
154	#10621873	—	2	4	no	—
155	#10621872	—	4	4	no	—
156	C₈×D₄₃	—	4	4	no	—
157	C₂³×C₄₃	—	2	1	no	—
158	C₂³×C₄₃	—	2	1	no	—
159	C₂³×C₄₃	—	4	2	no	—
160	C₂³×C₄₃	C₄×D₄	1	2	yes	—
161	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
162	C₂²×D₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₃	—	4	2	no	—
181	C₂²⋊D₄₃	—	4	2	no	—
182	C₂²⋊D₄₃	—	8	4	no	—
183	C₂×Dic₄₃	—	2	4	no	—
184	C₂×Dic₄₃	—	2	2	no	—
185	D₁₇₂	—	2	2	no	—
186	D₁₇₂	—	2	2	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	4	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	2	2	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₈×C₄₃	C₄×D₄	1	2	yes	—
194	C₈×C₄₃	C₄×D₄	1	2	yes	—
195	C₈×C₄₃	#121	1	2	yes	—
196	C₈×C₄₃	#121	1	2	yes	—
197	C₄₃⋊C₈	—	4	2	no	—
198	C₄₃⋊C₈	—	4	2	no	—
199	#21545	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	2	2	no	—
201	C₂²×C₄₃	—	2	2	no	—
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	4	2	no	—
205	C₂²×C₄₃	—	4	2	no	—
206	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₃	#525	1	1	yes	characteristic
208	C₂²×C₄₃	#529	1	1	yes	characteristic
209	C₂×D₄₃	—	4	4	no	—
210	C₂×D₄₃	—	4	2	no	—
211	C₄×C₄₃	—	2	2	no	—
212	C₄×C₄₃	—	4	2	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
216	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₄×C₄₃	#532	1	1	yes	characteristic
218	Dic₄₃	—	4	4	no	—
219	Dic₄₃	—	4	2	no	—
220	#3050	—	43	1	no	—
221	C₂×#443	—	43	1	no	—
222	#2930	—	43	2	no	—
223	C₂×#405	D₄₃	1	1	yes	characteristic, complemented
224	#1974	—	43	1	no	—
225	#1945	—	43	1	no	—
226	#1938	—	43	2	no	—
227	#1897	—	43	2	no	—
228	#1810	—	43	1	no	—
229	#1772	—	43	1	no	—
230	#1765	—	43	2	no	—
231	C₂×C₄₃	—	2	1	no	—
232	C₂×C₄₃	—	2	1	no	—
233	C₂×C₄₃	—	4	2	no	—
234	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
235	C₂×C₄₃	#2957	1	2	yes	—
236	D₄₃	—	8	2	no	—
237	C₂×#135	—	43	1	no	—
238	C₂×#131	—	43	2	no	—
239	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
240	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
241	#525	—	43	2	no	—
242	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
243	#467	—	43	2	no	—
244	#466	—	43	2	no	—
245	#465	—	43	4	no	—
246	#443	—	86	4	no	—
247	#436	—	86	4	no	—
248	#435	—	86	4	no	—
249	C₂×#108	—	43	1	no	—
250	C₂×#108	—	43	1	no	—
251	#427	—	43	1	no	—
252	#424	—	43	2	no	—
253	C₂×#104	—	43	2	no	—
254	C₂×#104	—	43	2	no	—
255	#416	—	43	2	no	—
256	#408	—	43	2	no	—
257	#407	—	43	2	no	—
258	#405	—	2	4	no	—
259	#405	—	43	2	no	—
260	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
261	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
264	#341	—	43	2	no	—
265	#339	—	43	2	no	—
266	#339	—	43	2	no	—
267	C₄₃	#21545	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	43	2	no	—
269	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
270	#135	—	86	2	no	—
271	#135	—	86	2	no	—
272	C₂×Q₁₆	—	43	1	no	—
273	C₂×SD₁₆	—	43	2	no	—
274	C₂×D₈	—	43	1	no	—
275	#131	—	86	4	no	—
276	#131	—	86	4	no	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	—	43	2	no	—
280	C₂×M₁₆	—	43	2	no	—
281	C₂×M₁₆	—	86	2	no	—
282	C₂×M₁₆	D₁₇₂	1	2	yes	—
283	C₂×M₁₆	D₁₇₂	1	2	yes	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	86	2	no	—
287	C₂²×C₈	C₄×D₄₃	1	2	yes	—
288	C₂²×C₈	C₄×D₄₃	1	2	yes	—
289	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
290	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
291	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
292	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
293	#123	—	86	2	no	—
294	C₂²⋊Q₈	—	43	4	no	—
295	#121	—	43	4	no	—
296	#120	—	86	2	no	—
297	C₄×D₄	—	86	4	no	—
298	#117	—	2	2	no	—
299	#117	—	2	2	no	—
300	#117	—	43	2	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₂²⋊C₄	—	2	1	no	—
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#108	—	86	2	no	—
306	#108	—	86	2	no	—
307	#107	—	43	2	no	—
308	#106	—	43	2	no	—
309	C₄⋊C₈	—	86	4	no	—
310	#104	—	86	4	no	—
311	#104	—	86	4	no	—
312	#103	—	43	4	no	—
313	#102	—	43	4	no	—
314	C₂²⋊C₈	—	86	4	no	—
315	C₂²⋊C₈	—	86	4	no	—
316	#97	—	2	2	no	—
317	#97	—	2	2	no	—
318	#97	—	86	2	no	—
319	C₄×C₈	—	2	2	no	—
320	C₄×C₈	—	86	2	no	—
321	C₄×C₈	C₂²⋊D₄₃	1	4	yes	complemented
322	C₂⁴	#10621898	1	1	yes	characteristic
323	#41	—	86	2	no	—
324	#41	—	86	2	no	—
325	#41	—	86	2	no	—
326	#41	—	86	2	no	—
327	C₂×Q₈	—	43	2	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	—	86	4	no	—
330	C₂×D₄	—	86	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	86	2	no	—
338	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
339	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
340	C₂²×C₄	#10621898	1	1	yes	characteristic
341	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
342	Q₁₆	—	86	2	no	—
343	SD₁₆	—	86	4	no	—
344	D₈	—	86	2	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	M₁₆	—	86	2	no	—
348	M₁₆	—	86	2	no	—
349	M₁₆	—	86	2	no	—
350	M₁₆	—	86	2	no	—
351	M₁₆	—	172	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	2	4	no	—
358	C₂×C₈	—	86	2	no	—
359	C₂×C₈	—	86	2	no	—
360	C₂×C₈	—	172	4	no	—
361	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
362	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
363	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
364	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
365	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
366	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
367	C₂×C₈	#10621898	1	2	yes	—
368	C₂×C₈	#10621898	1	2	yes	—
369	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
370	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	43	4	no	—
373	C₄⋊C₄	—	86	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	86	4	no	—
376	C₂²⋊C₄	—	86	2	no	—
377	C₂²⋊C₄	—	86	4	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	86	2	no	—
381	C₄²	#10621898	1	2	yes	—
382	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	86	2	no	—
387	C₂³	C₄×D₁₇₂	1	2	yes	—
388	C₂³	C₂×#10621898	1	1	yes	characteristic
389	Q₈	—	86	2	no	—
390	Q₈	—	86	2	no	—
391	D₄	—	86	2	no	—
392	D₄	—	86	2	no	—
393	D₄	—	344	4	no	—
394	D₄	—	172	2	no	—
395	D₄	—	172	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	86	4	no	—
407	C₂×C₄	—	86	2	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
411	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
414	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
415	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
416	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	172	2	no	—
420	C₈	—	172	2	no	—
421	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
422	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
423	C₈	#13063299	1	2	yes	—
424	C₈	#13063299	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	172	2	no	—
432	C₂²	—	172	4	no	—
433	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
434	C₂²	#14583410	1	1	yes	characteristic
435	C₂²	#14583433	1	1	yes	characteristic
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	172	2	no	—
440	C₄	—	172	4	no	—
441	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
442	C₄	C₄×#10621898	1	1	yes	characteristic
443	C₄	C₂×#13063299	1	1	yes	characteristic
444	C₄	#14583449	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	4	2	no	—
448	C₂	—	344	2	no	—
449	C₂	C₄×#13063299	1	1	yes	characteristic
450	C₂	#19143513	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#405	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144176	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#405	D₄₃
hypocenter	C₄₃	#21545
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#14583017	C₂	semidirect
3. #19143298	C₂	semidirect
4. #19135483	C₂	semidirect
5. #19135343	C₂	semidirect
6. #19135306	C₂	semidirect
7. #19135043	C₂	semidirect
8. #19134633	C₂	semidirect
9. #19134474	C₂	semidirect
10. #19134439	C₂	semidirect
11. C₂×C₄₃×#405	C₂	semidirect
15. #14583140	C₄	semidirect
16. #14583135	C₄	semidirect
17. #14583128	C₄	semidirect
95. C₄×C₈×C₄₃	D₄	semidirect
223. C₂×#405	D₄₃	semidirect
267. C₄₃	#21545	semidirect
321. C₄×C₈	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19144176	2
C₂×#14583017	2
#19143298	2
#19135483	2
#19135343	2
#19135306	2
#19135043	2
#19134633	2
#19134474	2
#19134439	2
C₂×C₄₃×#405	2
#21545	43