Subgroups — #25116062

Order 11008.

752 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063347	C₂	1	1	yes	maximal, characteristic
2	#19143260	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143160	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135299	C₂	1	2	yes	maximal, complemented
5	#19135195	C₂	1	2	yes	maximal, complemented
6	#19134921	C₂	1	2	yes	maximal
7	#19134733	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134616	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134616	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134432	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063331	C₂²	1	2	yes	—
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	C₄×#10621898	C₂²	1	1	yes	characteristic
16	C₄×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
17	C₄×Dic₁₇₂	C₄	1	1	yes	characteristic, complemented
18	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
19	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
20	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
21	C₄×#10621873	C₄	1	1	yes	characteristic, complemented
22	C₄×D₃₄₄	C₄	1	1	yes	characteristic, complemented
23	C₄×D₃₄₄	C₄	1	1	yes	characteristic, complemented
24	#14582959	—	2	2	no	—
25	#14582955	—	2	1	no	—
26	#14582951	—	2	1	no	—
27	#14582937	C₂²	1	1	yes	characteristic
28	#14582925	C₂²	1	2	yes	—
29	#14582924	—	2	2	no	—
30	#14582923	C₂²	1	1	yes	characteristic
31	#14582923	C₂²	1	1	yes	characteristic
32	#14582921	—	2	1	no	—
33	C₄⋊C₈×D₄₃	—	2	1	no	—
34	C₂×#13063253	C₂²	1	2	yes	—
35	C₂×#13063253	C₂²	1	2	yes	—
36	#14582896	C₂²	1	1	yes	characteristic
37	#14582896	C₂²	1	1	yes	characteristic
38	#14582865	C₂²	1	2	yes	—
39	#14582854	C₂²	1	2	yes	—
40	#14582664	C₂²	1	2	yes	—
41	#14582664	C₂²	1	2	yes	—
42	#14582659	C₂²	1	2	yes	—
43	#14582659	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
46	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
48	C₄₃×#336	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	C₂×#10621898	C₂³	1	1	yes	characteristic
51	#13063347	—	2	2	no	—
52	#13063347	—	2	2	no	—
53	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
55	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
56	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
57	#13063331	—	2	4	no	—
58	#13063331	—	4	2	no	—
59	C₂×#10621877	C₂³	1	2	yes	—
60	C₂×#10621877	C₂³	1	2	yes	—
61	C₂×#10621872	—	2	2	no	—
62	C₂×C₈×D₄₃	—	2	2	no	—
63	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
66	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
67	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
68	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
69	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
70	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₄₃	—	2	1	no	—
72	C₄×C₂²⋊D₄₃	—	2	1	no	—
73	C₄×C₂²⋊D₄₃	—	2	1	no	—
74	C₄×C₂²⋊D₄₃	—	2	1	no	—
75	#13063284	C₂³	1	1	yes	characteristic
76	#13063284	C₂³	1	1	yes	characteristic
77	#13063282	—	2	1	no	—
78	#13063282	—	2	1	no	—
79	C₄²×D₄₃	—	2	1	no	—
80	C₄²×D₄₃	—	2	1	no	—
81	#13063259	C₂×C₄	1	1	yes	characteristic
82	#13063259	C₂×C₄	1	1	yes	characteristic
83	#13063257	C₂×C₄	1	1	yes	characteristic
84	#13063257	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
86	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
87	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
88	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
89	Dic₄₃⋊C₈	—	2	2	no	—
90	Dic₄₃⋊C₈	—	2	2	no	—
91	#13063253	—	2	4	no	—
92	#13063253	—	4	2	no	—
93	#13063250	C₂×C₄	1	1	yes	characteristic
94	#13063250	C₂×C₄	1	1	yes	characteristic
95	#13063250	C₂×C₄	1	1	yes	characteristic
96	#13063250	C₂×C₄	1	1	yes	characteristic
97	#13063247	C₂×C₄	1	1	yes	characteristic
98	#13063247	C₂×C₄	1	1	yes	characteristic
99	#13063247	C₂×C₄	1	1	yes	characteristic
100	#13063247	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₄₃)⋊C₈	—	2	2	no	—
102	(C₂×D₄₃)⋊C₈	—	2	2	no	—
103	#13063235	—	2	2	no	—
104	C₈×Dic₄₃	—	2	2	no	—
105	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
107	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
109	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
112	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
113	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
114	C₄×C₈×C₄₃	—	4	2	no	—
115	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
117	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
118	C₄×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
119	#95×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	2	no	—
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	—	2	1	no	—
125	C₂×C₂²⋊D₄₃	—	2	1	no	—
126	#10621898	—	2	1	no	—
127	#10621898	—	2	1	no	—
128	#10621898	—	2	1	no	—
129	#10621898	—	2	1	no	—
130	#10621898	—	2	1	no	—
131	#10621898	—	2	1	no	—
132	#10621898	#41	1	2	yes	—
133	#10621898	#41	1	2	yes	—
134	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
135	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×C₄×D₄₃	—	2	1	no	—
138	C₂×C₄×D₄₃	—	2	1	no	—
139	C₂×C₄×D₄₃	—	2	1	no	—
140	C₂×C₄×D₄₃	—	2	1	no	—
141	C₂×C₄×D₄₃	—	2	1	no	—
142	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
143	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	—	2	1	no	—
146	C₂×C₈×C₄₃	—	2	1	no	—
147	C₂×C₈×C₄₃	—	2	1	no	—
148	C₂×C₈×C₄₃	—	2	2	no	—
149	C₂×C₈×C₄₃	—	2	1	no	—
150	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₄₃	—	2	4	no	—
157	C₄²×C₄₃	—	2	2	no	—
158	C₄²×C₄₃	—	2	2	no	—
159	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
160	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊Dic₄₃	—	2	1	no	—
164	C₂²⋊Dic₄₃	—	2	1	no	—
165	(C₂×D₄₃)⋊C₄	—	2	1	no	—
166	(C₂×D₄₃)⋊C₄	—	2	1	no	—
167	(C₂×D₄₃)⋊C₄	—	2	1	no	—
168	(C₂×D₄₃)⋊C₄	—	2	1	no	—
169	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
173	Dic₄₃⋊C₄	—	2	1	no	—
174	Dic₄₃⋊C₄	—	2	1	no	—
175	Dic₄₃⋊C₄	—	2	1	no	—
176	Dic₄₃⋊C₄	—	2	1	no	—
177	C₄×Dic₄₃	—	2	1	no	—
178	C₄×Dic₄₃	—	2	1	no	—
179	C₄×Dic₄₃	—	2	1	no	—
180	C₄×Dic₄₃	—	2	1	no	—
181	C₄×Dic₄₃	—	2	1	no	—
182	C₄×Dic₄₃	—	2	1	no	—
183	#10621877	—	2	2	no	—
184	#10621877	—	2	2	no	—
185	#10621877	—	2	2	no	—
186	#10621877	—	2	2	no	—
187	C₂×C₄₃⋊C₈	—	2	2	no	—
188	C₂×C₄₃⋊C₈	—	2	2	no	—
189	Dic₁₇₂	—	2	2	no	—
190	D₃₄₄	—	2	2	no	—
191	#10621873	—	2	2	no	—
192	#10621873	—	2	2	no	—
193	#10621872	—	4	4	no	—
194	C₈×D₄₃	—	4	4	no	—
195	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂²×D₄₃	—	2	1	no	—
197	C₂²×D₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	4	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	4	2	no	—
203	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂²⋊D₄₃	—	2	2	no	—
214	C₂²⋊D₄₃	—	2	2	no	—
215	C₂²⋊D₄₃	—	4	1	no	—
216	C₂²⋊D₄₃	—	4	1	no	—
217	C₂×Dic₄₃	—	2	1	no	—
218	C₂×Dic₄₃	—	2	1	no	—
219	C₂×Dic₄₃	—	2	1	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	1	no	—
222	C₂×Dic₄₃	—	2	1	no	—
223	D₁₇₂	—	2	1	no	—
224	D₁₇₂	—	2	1	no	—
225	D₁₇₂	—	2	1	no	—
226	D₁₇₂	#117	1	2	yes	—
227	C₄×D₄₃	—	2	2	no	—
228	C₄×D₄₃	—	2	2	no	—
229	C₄×D₄₃	—	4	1	no	—
230	C₄×D₄₃	—	4	1	no	—
231	C₄×D₄₃	—	4	2	no	—
232	C₄×D₄₃	—	4	2	no	—
233	C₄×D₄₃	—	8	1	no	—
234	C₄×D₄₃	—	8	1	no	—
235	Dic₈₆	—	2	1	no	—
236	Dic₈₆	—	2	1	no	—
237	Dic₈₆	—	2	1	no	—
238	Dic₈₆	#117	1	2	yes	—
239	C₈×C₄₃	—	2	1	no	—
240	C₈×C₄₃	—	2	1	no	—
241	C₈×C₄₃	—	2	1	no	—
242	C₈×C₄₃	—	2	1	no	—
243	C₈×C₄₃	—	2	2	no	—
244	C₈×C₄₃	—	2	2	no	—
245	C₄₃⋊C₈	—	4	2	no	—
246	C₄₃⋊C₈	—	4	2	no	—
247	#22783	—	43	1	no	maximal, Sylow
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	—	2	1	no	—
250	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
251	C₂²×C₄₃	#552	1	1	yes	characteristic
252	C₂²×C₄₃	#553	1	1	yes	characteristic
253	C₂×D₄₃	—	2	2	no	—
254	C₂×D₄₃	—	4	1	no	—
255	C₂×D₄₃	—	4	1	no	—
256	C₂×D₄₃	—	4	1	no	—
257	C₂×D₄₃	—	4	1	no	—
258	C₂×D₄₃	—	4	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	2	1	no	—
261	C₄×C₄₃	—	2	1	no	—
262	C₄×C₄₃	—	4	4	no	—
263	C₄×C₄₃	#443	1	2	yes	—
264	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
265	C₄×C₄₃	#520	1	1	yes	characteristic
266	C₄×C₄₃	#546	1	1	yes	characteristic
267	C₄×C₄₃	#548	1	1	yes	characteristic
268	Dic₄₃	—	2	2	no	—
269	Dic₄₃	—	4	1	no	—
270	Dic₄₃	—	4	1	no	—
271	Dic₄₃	—	4	1	no	—
272	Dic₄₃	—	4	1	no	—
273	Dic₄₃	—	4	1	no	—
274	C₄×#135	—	43	1	no	—
275	#2925	—	43	1	no	—
276	#2906	—	43	1	no	—
277	#1937	—	43	2	no	—
278	#1922	—	43	2	no	—
279	#1876	—	43	2	no	—
280	#1837	—	43	1	no	—
281	#1806	—	43	1	no	—
282	#1806	—	43	1	no	—
283	C₈×C₄⋊C₄	D₄₃	1	1	yes	characteristic, complemented
284	#1764	—	43	2	no	—
285	C₂×C₄₃	—	2	1	no	—
286	C₂×C₄₃	—	2	1	no	—
287	C₂×C₄₃	#2352	1	1	yes	characteristic
288	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
289	C₂×C₄₃	#2957	1	1	yes	characteristic
290	D₄₃	—	4	2	no	—
291	D₄₃	—	8	1	no	—
292	C₂×#135	—	43	1	no	—
293	C₂×#131	—	43	2	no	—
294	C₄×#41	—	43	1	no	—
295	C₄×#41	—	43	1	no	—
296	C₄×Q₁₆	—	43	1	no	—
297	C₄×Q₁₆	—	43	1	no	—
298	C₄×SD₁₆	—	43	1	no	—
299	C₄×SD₁₆	—	43	1	no	—
300	C₄×SD₁₆	—	43	1	no	—
301	C₄×SD₁₆	—	43	1	no	—
302	C₄×D₈	—	43	1	no	—
303	C₄×D₈	—	43	1	no	—
304	#433	—	86	2	no	—
305	#432	—	86	1	no	—
306	#431	—	86	1	no	—
307	#427	—	43	1	no	—
308	#424	—	43	2	no	—
309	#424	—	86	2	no	—
310	#423	—	43	1	no	—
311	#423	—	43	1	no	—
312	#423	—	86	1	no	—
313	C₂×C₄⋊C₈	—	86	1	no	—
314	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
315	C₂×#104	—	43	2	no	—
316	C₂×#104	—	43	2	no	—
317	#416	—	43	1	no	—
318	#416	—	43	1	no	—
319	#408	—	43	2	no	—
320	#405	—	43	2	no	—
321	C₂×C₄×C₈	C₂×D₄₃	1	2	yes	—
322	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
323	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
324	#341	—	43	2	no	—
325	#341	—	43	2	no	—
326	#339	—	43	2	no	—
327	#339	—	43	2	no	—
328	#336	C₂×D₄₃	1	2	yes	—
329	C₄₃	#22783	1	1	yes	characteristic, complemented, Sylow
330	C₂×#41	—	43	1	no	—
331	C₂×#41	—	43	1	no	—
332	#135	—	86	2	no	—
333	#135	—	86	2	no	—
334	C₂×Q₁₆	—	43	1	no	—
335	C₂×SD₁₆	—	43	1	no	—
336	C₂×SD₁₆	—	43	1	no	—
337	C₂×D₈	—	43	1	no	—
338	#131	—	86	4	no	—
339	#131	—	172	2	no	—
340	C₂×M₁₆	—	43	2	no	—
341	C₂×M₁₆	—	43	2	no	—
342	C₂×M₁₆	—	86	2	no	—
343	C₂²×C₈	—	86	2	no	—
344	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
346	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
347	C₄×Q₈	—	43	1	no	—
348	C₄×Q₈	—	43	1	no	—
349	C₄×Q₈	—	43	1	no	—
350	C₄×Q₈	—	43	1	no	—
351	C₄×D₄	—	43	1	no	—
352	C₄×D₄	—	43	1	no	—
353	C₄×D₄	—	43	1	no	—
354	C₄×D₄	—	43	1	no	—
355	C₄×D₄	—	86	1	no	—
356	C₄×D₄	—	86	1	no	—
357	C₄×D₄	—	86	1	no	—
358	C₄×D₄	—	86	1	no	—
359	#117	—	43	1	no	—
360	#117	—	43	1	no	—
361	#117	—	86	1	no	—
362	#117	—	86	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄²	—	86	1	no	—
365	C₂×C₄²	—	86	1	no	—
366	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
367	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
368	#107	—	43	1	no	—
369	#107	—	43	1	no	—
370	#106	—	43	1	no	—
371	#106	—	43	1	no	—
372	C₄⋊C₈	—	86	2	no	—
373	C₄⋊C₈	—	86	2	no	—
374	C₄⋊C₈	—	86	1	no	—
375	C₄⋊C₈	—	86	1	no	—
376	C₄⋊C₈	—	86	1	no	—
377	C₄⋊C₈	—	86	1	no	—
378	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
379	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
380	C₄⋊C₈	D₁₇₂	1	2	yes	—
381	#104	—	86	4	no	—
382	#104	—	172	2	no	—
383	#103	—	43	1	no	—
384	#103	—	43	1	no	—
385	#103	—	43	1	no	—
386	#103	—	43	1	no	—
387	#102	—	43	1	no	—
388	#102	—	43	1	no	—
389	#102	—	43	1	no	—
390	#102	—	43	1	no	—
391	C₂²⋊C₈	—	86	2	no	—
392	C₂²⋊C₈	—	86	2	no	—
393	#97	—	86	2	no	—
394	C₄×C₈	—	4	2	no	—
395	C₄×C₈	—	86	2	no	—
396	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
397	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
398	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
399	C₄×C₈	C₄×D₄₃	1	1	yes	characteristic
400	#95	—	2	1	no	—
401	#41	—	43	2	no	—
402	#41	—	43	2	no	—
403	#41	—	86	1	no	—
404	#41	—	86	1	no	—
405	#41	—	86	1	no	—
406	#41	—	86	1	no	—
407	#41	—	86	1	no	—
408	#41	—	86	1	no	—
409	C₂×Q₈	—	43	1	no	—
410	C₂×Q₈	—	43	1	no	—
411	C₂×D₄	—	43	1	no	—
412	C₂×D₄	—	43	1	no	—
413	C₂×D₄	—	86	1	no	—
414	C₂×D₄	—	86	1	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	86	1	no	—
417	C₂²×C₄	—	86	1	no	—
418	C₂²×C₄	—	86	1	no	—
419	C₂²×C₄	—	86	1	no	—
420	C₂²×C₄	—	86	1	no	—
421	C₂²×C₄	—	86	1	no	—
422	C₂²×C₄	#10621898	1	1	yes	characteristic
423	C₂²×C₄	#10621898	1	1	yes	characteristic
424	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
425	Q₁₆	—	86	2	no	—
426	SD₁₆	—	86	2	no	—
427	SD₁₆	—	86	2	no	—
428	D₈	—	86	2	no	—
429	M₁₆	—	86	2	no	—
430	M₁₆	—	86	2	no	—
431	M₁₆	—	86	2	no	—
432	M₁₆	—	86	2	no	—
433	M₁₆	—	172	4	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	86	2	no	—
441	C₂×C₈	—	86	2	no	—
442	C₂×C₈	—	172	4	no	—
443	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
445	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
446	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
448	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	43	1	no	—
451	C₄⋊C₄	—	43	1	no	—
452	C₄⋊C₄	—	43	1	no	—
453	C₄⋊C₄	—	43	1	no	—
454	C₄⋊C₄	—	86	1	no	—
455	C₄⋊C₄	—	86	1	no	—
456	C₄⋊C₄	—	86	1	no	—
457	C₄⋊C₄	—	86	1	no	—
458	C₂²⋊C₄	—	86	1	no	—
459	C₂²⋊C₄	—	86	1	no	—
460	C₂²⋊C₄	—	86	1	no	—
461	C₂²⋊C₄	—	86	1	no	—
462	C₂²⋊C₄	—	86	1	no	—
463	C₂²⋊C₄	—	86	1	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	86	1	no	—
467	C₄²	—	86	1	no	—
468	C₄²	—	86	1	no	—
469	C₄²	—	86	1	no	—
470	C₄²	—	86	1	no	—
471	C₄²	—	86	1	no	—
472	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
473	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
474	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
475	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
476	C₂³	—	86	1	no	—
477	C₂³	—	86	1	no	—
478	C₂³	C₂×#10621898	1	1	yes	characteristic
479	Q₈	—	43	2	no	—
480	Q₈	—	86	1	no	—
481	Q₈	—	86	1	no	—
482	Q₈	—	86	1	no	—
483	D₄	—	43	2	no	—
484	D₄	—	86	2	no	—
485	D₄	—	86	2	no	—
486	D₄	—	86	1	no	—
487	D₄	—	86	1	no	—
488	D₄	—	86	1	no	—
489	D₄	—	172	1	no	—
490	D₄	—	172	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	86	1	no	—
497	C₂×C₄	—	86	2	no	—
498	C₂×C₄	—	86	2	no	—
499	C₂×C₄	—	86	1	no	—
500	C₂×C₄	—	86	1	no	—
501	C₂×C₄	—	86	1	no	—
502	C₂×C₄	—	86	1	no	—
503	C₂×C₄	—	86	1	no	—
504	C₂×C₄	—	344	1	no	—
505	C₂×C₄	—	344	1	no	—
506	C₂×C₄	—	172	1	no	—
507	C₂×C₄	—	172	2	no	—
508	C₂×C₄	—	172	2	no	—
509	C₂×C₄	—	172	1	no	—
510	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
511	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
512	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
513	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
514	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
516	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
517	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
518	C₂×C₄	#13063370	1	1	yes	characteristic
519	C₂×C₄	#13063373	1	1	yes	characteristic
520	C₈	—	2	1	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	172	2	no	—
527	C₈	—	172	2	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	86	2	no	—
531	C₂²	—	172	1	no	—
532	C₂²	—	172	1	no	—
533	C₂²	—	172	1	no	—
534	C₂²	—	172	1	no	—
535	C₂²	—	172	1	no	—
536	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
537	C₂²	#14583590	1	1	yes	characteristic
538	C₂²	#14583599	1	1	yes	characteristic
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	4	4	no	—
543	C₄	—	86	2	no	—
544	C₄	—	172	1	no	—
545	C₄	—	172	1	no	—
546	C₄	—	172	1	no	—
547	C₄	—	172	1	no	—
548	C₄	—	172	1	no	—
549	C₄	#14583017	1	2	yes	—
550	C₄	#117×D₄₃	1	1	yes	characteristic
551	C₄	#14583380	1	1	yes	characteristic
552	C₄	#14583544	1	1	yes	characteristic
553	C₄	#14583561	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	344	1	no	—
557	C₂	—	172	2	no	—
558	C₂	#19137527	1	1	yes	characteristic
559	C₂	C₂×#14583017	1	1	yes	characteristic
560	C₂	#19143513	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₈×C₄⋊C₄×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063347	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₃
hypocenter	C₄₃	#22783
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #19143260	C₂	semidirect
3. #19143160	C₂	semidirect
4. #19135299	C₂	semidirect
5. #19135195	C₂	semidirect
7. #19134733	C₂	semidirect
8. #19134616	C₂	semidirect
9. #19134616	C₂	semidirect
10. #19134432	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₃	C₂	semidirect
16. C₄×Dic₁₇₂	C₄	semidirect
17. C₄×Dic₁₇₂	C₄	semidirect
18. C₄×#10621873	C₄	semidirect
19. C₄×#10621873	C₄	semidirect
20. C₄×#10621873	C₄	semidirect
21. C₄×#10621873	C₄	semidirect
22. C₄×D₃₄₄	C₄	semidirect
23. C₄×D₃₄₄	C₄	semidirect
283. C₈×C₄⋊C₄	D₄₃	semidirect
329. C₄₃	#22783	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063347	2
#19143260	2
#19143160	2
#19135299	2
#19135195	2
#19134921	2
#19134733	2
#19134616	2
#19134432	2
C₈×C₄⋊C₄×C₄₃	2
#22783	43