Subgroups — #25251081

Order 11008.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583340	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13063265	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144176	C₂	1	1	yes	maximal, characteristic
4	#19136710	C₂	1	2	yes	maximal, complemented
5	#19136701	C₂	1	2	yes	maximal, complemented
6	#19136693	C₂	1	2	yes	maximal, complemented
7	#19136684	C₂	1	2	yes	maximal, complemented
8	#19136381	C₂	1	1	yes	maximal, characteristic, complemented
9	#19136315	C₂	1	1	yes	maximal, characteristic, complemented
10	#19136305	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	#14583410	—	2	1	no	—
14	#14583340	—	2	4	no	—
15	C₂×#13063271	C₂²	1	2	yes	complemented
16	C₂×#13063268	C₂²	1	2	yes	complemented
17	C₂×#13063265	—	2	4	no	—
18	C₂×#13063265	C₂²	1	1	yes	characteristic
19	C₂×#13063265	C₂²	1	2	yes	—
20	C₂×#13063265	C₂²	1	1	yes	characteristic
21	C₂²×C₄₃⋊C₁₆	C₂²	1	2	yes	—
22	#14583140	C₂²	1	1	yes	characteristic
23	#14583140	C₂²	1	1	yes	characteristic
24	#14583135	C₂²	1	1	yes	characteristic
25	#14583135	C₂²	1	1	yes	characteristic
26	#14583128	—	2	1	no	—
27	#14583128	—	2	1	no	—
28	#14582937	C₂²	1	1	yes	characteristic
29	#14582896	—	2	1	no	—
30	#14582726	C₂²	1	2	yes	complemented
31	#14582724	C₂²	1	2	yes	complemented
32	#14582703	C₂²	1	2	yes	complemented
33	#14582703	C₂²	1	2	yes	complemented
34	#14582702	C₂²	1	2	yes	complemented
35	#14582699	C₂²	1	2	yes	complemented
36	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
37	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
39	C₄₃×#467	—	2	1	no	—
40	C₄₃×#467	—	2	1	no	—
41	C₄₃×#467	C₂²	1	2	yes	—
42	C₄₃×#467	C₂²	1	2	yes	—
43	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#103×C₄₃	—	2	1	no	—
45	C₂×#10621898	—	2	1	no	—
46	#13063347	—	2	2	no	—
47	#13063347	—	2	2	no	—
48	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
49	C₂×#10621873	—	2	1	no	—
50	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
51	#13063308	—	4	1	no	—
52	#13063304	—	2	1	no	—
53	#13063304	—	2	1	no	—
54	#13063299	—	2	1	no	—
55	#13063299	—	2	1	no	—
56	#13063294	—	4	1	no	—
57	C₄×C₂²⋊D₄₃	—	4	1	no	—
58	C₄×C₂²⋊D₄₃	—	4	1	no	—
59	#13063284	—	2	1	no	—
60	#13063271	—	2	4	no	—
61	#13063268	—	2	4	no	—
62	#13063265	—	2	2	no	—
63	#13063265	—	2	4	no	—
64	#13063265	D₄	1	4	yes	complemented
65	C₂×C₄₃⋊C₁₆	—	2	4	no	—
66	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₄₃⋊C₁₆	C₂³	1	2	yes	—
68	#13063259	C₂³	1	1	yes	characteristic
69	#13063259	C₂³	1	1	yes	characteristic
70	#13063257	—	2	1	no	—
71	#13063250	—	2	1	no	—
72	#13063250	—	2	1	no	—
73	#13063247	—	2	1	no	—
74	#13063247	—	2	1	no	—
75	C₂²×Q₈×C₄₃	—	2	1	no	—
76	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
77	C₂×Q₁₆×C₄₃	—	2	2	no	—
78	C₂×Q₁₆×C₄₃	—	2	1	no	—
79	C₂×Q₁₆×C₄₃	—	2	2	no	—
80	C₂×Q₁₆×C₄₃	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₃	—	2	2	no	—
82	C₂²×C₈×C₄₃	—	2	2	no	—
83	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₂²⋊Q₈×C₄₃	—	2	2	no	—
90	C₂²⋊Q₈×C₄₃	—	2	2	no	—
91	C₂²⋊Q₈×C₄₃	—	4	1	no	—
92	C₂²⋊Q₈×C₄₃	—	4	1	no	—
93	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₄₃	—	4	1	no	—
95	C₂×C₂²⋊C₄×C₄₃	—	4	1	no	—
96	#107×C₄₃	—	2	1	no	—
97	#107×C₄₃	C₂³	1	2	yes	—
98	#103×C₄₃	—	2	2	no	—
99	#103×C₄₃	—	2	2	no	—
100	C₂⁴×C₄₃	D₈	1	1	yes	characteristic
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	4	1	no	—
103	C₂×Q₈×C₄₃	—	4	2	no	—
104	C₂×Q₈×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	4	1	no	—
108	C₂²×C₄×C₄₃	—	4	1	no	—
109	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	D₈	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₄₃	—	4	1	no	—
116	C₂×C₂²⋊D₄₃	—	4	1	no	—
117	C₂×C₂²⋊D₄₃	—	4	1	no	—
118	#10621898	—	4	2	no	—
119	#10621898	—	4	2	no	—
120	C₂×D₁₇₂	—	2	1	no	—
121	C₂×C₄×D₄₃	—	4	1	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	Q₁₆×C₄₃	—	2	2	no	—
124	Q₁₆×C₄₃	—	2	2	no	—
125	Q₁₆×C₄₃	—	4	2	no	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	2	2	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	1	no	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₄₃	#41	1	2	yes	—
138	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	4	1	no	—
141	C₄⋊C₄×C₄₃	—	4	2	no	—
142	C₄⋊C₄×C₄₃	—	4	2	no	—
143	C₂²⋊C₄×C₄₃	—	4	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	2	no	—
145	C₂²⋊Dic₄₃	—	4	1	no	—
146	C₂²⋊Dic₄₃	—	4	1	no	—
147	C₂²⋊Dic₄₃	—	4	1	no	—
148	(C₂×D₄₃)⋊C₄	—	4	1	no	—
149	(C₂×D₄₃)⋊C₄	—	4	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	Dic₄₃⋊C₄	—	4	1	no	—
154	C₄×Dic₄₃	—	4	1	no	—
155	Dic₁₇₂	—	2	1	no	—
156	Dic₁₇₂	—	2	1	no	—
157	D₃₄₄	—	2	1	no	—
158	D₃₄₄	—	2	1	no	—
159	#10621873	—	4	2	no	—
160	C₄₃⋊C₁₆	—	2	2	no	—
161	C₄₃⋊C₁₆	C₂×D₄	1	4	yes	—
162	C₂³×C₄₃	—	2	2	no	—
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	4	1	no	—
165	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
166	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
167	C₂³×C₄₃	C₂×D₈	1	1	yes	characteristic
168	C₂²×D₄₃	—	4	1	no	—
169	Q₈×C₄₃	—	4	2	no	—
170	Q₈×C₄₃	—	4	2	no	—
171	Q₈×C₄₃	—	8	2	no	—
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	8	2	no	—
182	C₂×C₄×C₄₃	—	8	2	no	—
183	C₂×C₄×C₄₃	#121	1	2	yes	—
184	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#135	1	2	yes	—
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂²⋊D₄₃	—	8	2	no	—
190	C₂²⋊D₄₃	—	8	2	no	—
191	C₂²⋊D₄₃	—	8	2	no	—
192	C₂×Dic₄₃	—	4	1	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	C₂×Dic₄₃	—	4	1	no	—
195	D₁₇₂	—	4	1	no	—
196	D₁₇₂	—	4	1	no	—
197	C₄×D₄₃	—	8	2	no	—
198	Dic₈₆	—	4	1	no	—
199	Dic₈₆	—	4	1	no	—
200	C₈×C₄₃	—	2	1	no	—
201	C₈×C₄₃	—	2	1	no	—
202	C₈×C₄₃	#121	1	2	yes	—
203	C₈×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₄₃	C₂×#41	1	1	yes	characteristic
205	#33606	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	4	4	no	—
214	C₂²×C₄₃	#466	1	2	yes	—
215	C₂²×C₄₃	#510	1	2	yes	complemented
216	C₂²×C₄₃	C₂²×D₈	1	1	yes	characteristic
217	C₂×D₄₃	—	8	1	no	—
218	C₂×D₄₃	—	8	1	no	—
219	C₂×D₄₃	—	8	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	2	1	no	—
222	C₄×C₄₃	—	8	2	no	—
223	C₄×C₄₃	—	8	2	no	—
224	C₄×C₄₃	#466	1	2	yes	—
225	C₄×C₄₃	C₂×#121	1	1	yes	characteristic
226	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
227	Dic₄₃	—	8	1	no	—
228	Dic₄₃	—	8	1	no	—
229	Dic₄₃	—	8	1	no	—
230	C₂×#510	—	43	1	no	—
231	C₂²×M₃₂	—	43	1	no	—
232	#3050	—	43	1	no	—
233	C₂×#467	D₄₃	1	1	yes	characteristic, complemented
234	#2220	—	43	2	no	—
235	#2219	—	43	2	no	—
236	#2217	—	43	2	no	—
237	#2216	—	43	2	no	—
238	#2159	—	43	1	no	—
239	#2141	—	43	1	no	—
240	#2139	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	—	2	2	no	—
243	C₂×C₄₃	—	4	1	no	—
244	C₂×C₄₃	C₂×#466	1	1	yes	characteristic
245	C₂×C₄₃	C₂×#510	1	1	yes	characteristic
246	C₂×C₄₃	#3414	1	1	yes	characteristic
247	D₄₃	—	16	1	no	—
248	C₂×#135	—	43	1	no	—
249	C₂²×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
250	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
251	#525	—	86	1	no	—
252	C₂×C₂²⋊Q₈	—	2	1	no	—
253	#510	—	86	4	no	—
254	C₂×Q₃₂	—	43	2	no	—
255	C₂×SD₃₂	—	43	2	no	—
256	C₂×M₃₂	—	43	1	no	—
257	C₂×M₃₂	—	43	1	no	—
258	C₂×M₃₂	—	43	2	no	—
259	C₂×M₃₂	—	86	4	no	—
260	C₂²×C₁₆	—	43	2	no	—
261	#467	—	2	1	no	—
262	#467	—	2	1	no	—
263	#467	—	43	1	no	—
264	#467	—	43	1	no	—
265	#467	C₂×D₄₃	1	2	yes	—
266	#467	C₂×D₄₃	1	2	yes	—
267	#466	—	43	1	no	—
268	#466	—	43	1	no	—
269	#465	—	86	1	no	—
270	#465	—	86	1	no	—
271	#427	—	43	1	no	—
272	C₂×#107	C₂×D₄₃	1	1	yes	characteristic
273	#416	—	86	1	no	—
274	C₂×#103	—	2	1	no	—
275	#367	—	43	2	no	—
276	#366	—	43	2	no	—
277	#358	—	43	2	no	—
278	#358	—	43	2	no	—
279	#358	—	43	2	no	—
280	#357	—	43	2	no	—
281	C₄₃	#33606	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	86	1	no	—
283	C₂²×Q₈	—	2	1	no	—
284	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
285	#135	—	86	2	no	—
286	#135	—	86	2	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	2	2	no	—
289	C₂×Q₁₆	—	2	1	no	—
290	C₂×Q₁₆	—	43	1	no	—
291	C₂×Q₁₆	C₂²×D₄₃	1	2	yes	—
292	C₂×SD₁₆	—	86	1	no	—
293	C₂×D₈	—	43	1	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
298	C₂²×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
302	#123	—	172	1	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	C₂²⋊Q₈	—	4	1	no	—
306	C₂²⋊Q₈	—	4	1	no	—
307	C₂²⋊Q₈	—	86	1	no	—
308	C₂²⋊Q₈	—	86	1	no	—
309	#121	—	86	1	no	—
310	#121	—	86	1	no	—
311	#120	—	172	1	no	—
312	C₄×D₄	—	172	1	no	—
313	C₄×D₄	—	172	1	no	—
314	#117	—	86	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	4	1	no	—
317	C₂×C₂²⋊C₄	—	4	1	no	—
318	Q₃₂	—	86	4	no	—
319	SD₃₂	—	86	4	no	—
320	M₃₂	—	43	4	no	—
321	M₃₂	—	86	4	no	—
322	M₃₂	—	86	2	no	—
323	C₂×C₁₆	—	43	2	no	—
324	C₂×C₁₆	—	43	2	no	—
325	C₂×C₁₆	—	86	4	no	—
326	#107	—	2	1	no	—
327	#107	—	43	1	no	—
328	#107	—	43	1	no	—
329	#107	C₂²×D₄₃	1	2	yes	—
330	#106	—	86	1	no	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#102	—	86	1	no	—
336	#102	—	86	1	no	—
337	C₂⁴	#10621882	1	1	yes	characteristic
338	#41	—	172	2	no	—
339	#41	—	172	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	4	2	no	—
344	C₂×Q₈	—	86	1	no	—
345	C₂×D₄	—	86	1	no	—
346	C₂×D₄	—	172	1	no	—
347	C₂×D₄	—	172	1	no	—
348	C₂×D₄	—	172	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	172	1	no	—
354	C₂²×C₄	#10621882	1	1	yes	characteristic
355	C₂²×C₄	#10621882	1	1	yes	characteristic
356	C₂²×C₄	#10621882	1	1	yes	characteristic
357	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
360	Q₁₆	—	2	2	no	—
361	Q₁₆	—	2	2	no	—
362	Q₁₆	—	4	2	no	—
363	Q₁₆	—	86	1	no	—
364	Q₁₆	—	86	1	no	—
365	SD₁₆	—	172	2	no	—
366	D₈	—	86	1	no	—
367	D₈	—	86	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	D₄×D₄₃	1	2	yes	—
376	C₂×C₈	#10621900	1	2	yes	—
377	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
380	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	4	2	no	—
385	C₄⋊C₄	—	86	1	no	—
386	C₄⋊C₄	—	86	1	no	—
387	C₄⋊C₄	—	172	1	no	—
388	C₄⋊C₄	—	172	1	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	172	1	no	—
392	C₂²⋊C₄	—	172	1	no	—
393	C₂²⋊C₄	—	172	1	no	—
394	C₂²⋊C₄	—	172	1	no	—
395	C₂²⋊C₄	—	172	1	no	—
396	C₄²	—	172	1	no	—
397	C₁₆	—	43	4	no	—
398	C₁₆	—	86	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	4	1	no	—
402	C₂³	—	172	1	no	—
403	C₂³	C₂×#10621882	1	1	yes	characteristic
404	C₂³	C₂×#10621882	1	1	yes	characteristic
405	C₂³	C₂×#10621882	1	1	yes	characteristic
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	8	2	no	—
409	Q₈	—	172	1	no	—
410	Q₈	—	172	1	no	—
411	D₄	—	344	2	no	—
412	D₄	—	344	2	no	—
413	D₄	—	344	2	no	—
414	D₄	—	172	1	no	—
415	D₄	—	172	1	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	344	2	no	—
428	C₂×C₄	—	172	1	no	—
429	C₂×C₄	—	172	1	no	—
430	C₂×C₄	—	172	1	no	—
431	C₂×C₄	#13063297	1	2	yes	—
432	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
433	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
434	C₂×C₄	C₂×#10621882	1	1	yes	characteristic
435	C₂×C₄	#13063345	1	2	yes	—
436	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	#13063297	1	2	yes	—
440	C₈	C₂×D₄×D₄₃	1	1	yes	characteristic
441	C₈	C₂×#10621900	1	1	yes	characteristic
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	344	1	no	—
451	C₂²	—	344	1	no	—
452	C₂²	—	344	1	no	—
453	C₂²	#14583133	1	2	yes	—
454	C₂²	#14583340	1	2	yes	complemented
455	C₂²	C₂²×#10621882	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	344	1	no	—
461	C₄	—	344	1	no	—
462	C₄	—	344	1	no	—
463	C₄	#14583133	1	2	yes	—
464	C₄	C₂×#13063297	1	1	yes	characteristic
465	C₄	C₂×#13063345	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	1	no	—
469	C₂	—	688	1	no	—
470	C₂	C₂×#14583133	1	1	yes	characteristic
471	C₂	C₂×#14583340	1	1	yes	characteristic
472	C₂	#19147729	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#10621882
commutator, cosocle	C₂×C₈×C₄₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₃
Fitting	C₂×C₄₃×#467	C₂
socle	C₂²×C₄₃	C₂²×D₈
prime radical	#19144176	C₂
hypercenter	C₂×#467	D₄₃
hypocenter	C₄₃	#33606
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂×#467

Complements

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

N	H ≅ G/N	type
1. C₂×#14583340	C₂	semidirect
2. C₂²×#13063265	C₂	semidirect
4. #19136710	C₂	semidirect
5. #19136701	C₂	semidirect
6. #19136693	C₂	semidirect
7. #19136684	C₂	semidirect
8. #19136381	C₂	semidirect
9. #19136315	C₂	semidirect
10. #19136305	C₂	semidirect
11. C₂×C₄₃×#467	C₂	semidirect
15. C₂×#13063271	C₂²	semidirect
16. C₂×#13063268	C₂²	semidirect
30. #14582726	C₂²	semidirect
31. #14582724	C₂²	semidirect
32. #14582703	C₂²	semidirect
33. #14582703	C₂²	semidirect
34. #14582702	C₂²	semidirect
35. #14582699	C₂²	semidirect
64. #13063265	D₄	semidirect
215. C₂²×C₄₃	#510	semidirect
233. C₂×#467	D₄₃	semidirect
281. C₄₃	#33606	semidirect
454. C₂²	#14583340	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583340	2
C₂²×#13063265	2
#19144176	2
#19136710	2
#19136701	2
#19136693	2
#19136684	2
#19136381	2
#19136315	2
#19136305	2
C₂×C₄₃×#467	2
#33606	43