Subgroups — #19149371

Order 5504.

1464 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583735	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063370	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583709	C₂	1	4	yes	maximal, complemented
4	#14583705	C₂	1	4	yes	maximal, complemented
5	#14583703	C₂	1	4	yes	maximal, complemented
6	#14583700	C₂	1	4	yes	maximal, complemented
7	#14583699	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583697	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583695	C₂	1	4	yes	maximal, complemented
10	C₂×#13063351	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₄₃	C₂	1	4	yes	maximal, complemented
12	#14583665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×AGL(1,ℤ/8)×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#13063373	C₂²	1	2	yes	complemented
15	#13063372	—	2	1	no	—
16	#13063372	C₂²	1	2	yes	complemented
17	#13063371	—	2	1	no	—
18	#13063371	C₂²	1	2	yes	complemented
19	#13063370	—	2	2	no	—
20	#13063370	—	2	2	no	—
21	#13063370	—	2	2	no	—
22	#13063370	C₂²	1	4	yes	complemented
23	#13063370	C₂²	1	4	yes	complemented
24	#13063370	C₂²	1	2	yes	complemented
25	C₂×#10621898	—	2	2	no	—
26	C₂×#10621898	C₂²	1	1	yes	characteristic
27	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
28	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
29	C₂×#10621900	—	2	1	no	—
30	C₂×#10621900	C₂²	1	2	yes	complemented
31	#41×D₄₃	—	2	2	no	—
32	#41×D₄₃	C₂²	1	4	yes	complemented
33	C₂²×C₂²⋊D₄₃	—	2	2	no	—
34	C₂×D₄×D₄₃	—	2	1	no	—
35	C₂×D₄×D₄₃	C₂²	1	2	yes	complemented
36	#13063358	C₂²	1	2	yes	complemented
37	#13063358	C₂²	1	2	yes	complemented
38	#13063356	C₂²	1	2	yes	complemented
39	#13063355	C₂²	1	2	yes	complemented
40	#13063354	C₂²	1	8	yes	complemented
41	#13063353	C₂²	1	2	yes	complemented
42	#13063353	C₂²	1	2	yes	complemented
43	#13063352	C₂²	1	8	yes	complemented
44	#13063351	C₂²	1	4	yes	complemented
45	#13063351	C₂²	1	2	yes	complemented
46	#13063351	C₂²	1	4	yes	complemented
47	#13063350	C₂²	1	2	yes	complemented
48	#13063349	C₂²	1	8	yes	complemented
49	#13063349	C₂²	1	8	yes	complemented
50	#13063347	C₂²	1	4	yes	complemented
51	#13063346	C₂²	1	8	yes	complemented
52	#13063345	C₂²	1	4	yes	complemented
53	#13063344	C₂²	1	8	yes	complemented
54	C₂×#10621883	C₂²	1	2	yes	complemented
55	SD₁₆×D₄₃	C₂²	1	8	yes	complemented
56	C₂×#10621882	C₂²	1	2	yes	complemented
57	D₈×D₄₃	C₂²	1	8	yes	complemented
58	#13063333	C₂²	1	4	yes	complemented
59	#13063331	C₂²	1	4	yes	complemented
60	C₂×#10621877	C₂²	1	1	yes	characteristic, complemented
61	M₁₆×D₄₃	C₂²	1	4	yes	complemented
62	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
64	AGL(1,ℤ/8)×C₄₃	C₂²	1	4	yes	complemented
65	AGL(1,ℤ/8)×C₄₃	C₂²	1	4	yes	complemented
66	C₂×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
67	C₂×D₈×C₄₃	C₂²	1	2	yes	complemented
68	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
69	C₂⁴×C₄₃	—	2	1	no	—
70	C₂³×D₄₃	—	2	2	no	—
71	#41×C₄₃	—	2	1	no	—
72	#41×C₄₃	—	2	1	no	—
73	#41×C₄₃	C₂³	1	2	yes	—
74	#41×C₄₃	C₂³	1	2	yes	complemented
75	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
76	C₂×D₄×C₄₃	—	2	1	no	—
77	C₂×D₄×C₄₃	—	2	1	no	—
78	C₂×D₄×C₄₃	—	2	1	no	—
79	C₂×D₄×C₄₃	—	2	1	no	—
80	C₂×D₄×C₄₃	C₂³	1	2	yes	—
81	C₂×D₄×C₄₃	C₂³	1	2	yes	—
82	C₂×D₄×C₄₃	C₂³	1	2	yes	—
83	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊D₄₃	—	2	8	no	—
87	C₂×C₂²⋊D₄₃	—	2	8	no	—
88	C₂×C₂²⋊D₄₃	—	2	4	no	—
89	C₂×C₂²⋊D₄₃	—	2	2	no	—
90	C₂×C₂²⋊D₄₃	—	2	1	no	—
91	C₂×C₂²⋊D₄₃	—	2	1	no	—
92	C₂×C₂²⋊D₄₃	—	2	2	no	—
93	C₂×C₂²⋊D₄₃	D₄	1	2	yes	—
94	C₂²×Dic₄₃	—	2	2	no	—
95	#10621902	—	2	2	no	—
96	#10621902	C₂³	1	4	yes	complemented
97	Q₈×D₄₃	—	2	2	no	—
98	Q₈×D₄₃	C₂³	1	4	yes	complemented
99	#10621900	—	2	4	no	—
100	#10621900	—	2	4	no	—
101	#10621900	—	2	4	no	—
102	#10621900	—	2	2	no	—
103	#10621900	—	2	4	no	—
104	#10621900	—	2	4	no	—
105	#10621900	C₂³	1	8	yes	—
106	#10621900	C₂³	1	4	yes	complemented
107	D₄×D₄₃	—	2	4	no	—
108	D₄×D₄₃	—	2	4	no	—
109	D₄×D₄₃	—	2	4	no	—
110	D₄×D₄₃	—	2	2	no	—
111	D₄×D₄₃	—	2	4	no	—
112	D₄×D₄₃	—	2	4	no	—
113	D₄×D₄₃	C₂³	1	8	yes	—
114	D₄×D₄₃	C₂³	1	4	yes	complemented
115	#10621898	—	2	1	no	—
116	#10621898	—	2	1	no	—
117	#10621898	—	2	1	no	—
118	#10621898	—	2	1	no	—
119	#10621898	—	2	4	no	—
120	#10621898	—	2	2	no	—
121	#10621898	—	2	4	no	—
122	#10621898	—	2	2	no	—
123	#10621898	D₄	1	2	yes	—
124	#10621898	D₄	1	2	yes	—
125	#10621898	C₂³	1	2	yes	—
126	#10621898	C₂³	1	2	yes	—
127	#10621898	C₂³	1	2	yes	—
128	#10621898	C₂³	1	2	yes	—
129	#10621898	C₂³	1	2	yes	—
130	#10621898	C₂³	1	2	yes	complemented
131	C₂×D₁₇₂	—	2	2	no	—
132	C₂×D₁₇₂	D₄	1	1	yes	characteristic
133	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
134	C₂×D₁₇₂	C₂³	1	1	yes	characteristic, complemented
135	C₂×C₄×D₄₃	—	2	1	no	—
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×C₄×D₄₃	—	2	4	no	—
138	C₂×C₄×D₄₃	C₂³	1	2	yes	—
139	C₂×Dic₈₆	—	2	2	no	—
140	C₂×Dic₈₆	D₄	1	1	yes	characteristic
141	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₈₆	C₂³	1	1	yes	characteristic, complemented
143	SD₁₆×C₄₃	C₂³	1	8	yes	complemented
144	D₈×C₄₃	C₂³	1	8	yes	complemented
145	M₁₆×C₄₃	C₂³	1	2	yes	—
146	M₁₆×C₄₃	C₂³	1	2	yes	complemented
147	C₂×C₈×C₄₃	C₂³	1	2	yes	complemented
148	#10621885	C₂³	1	4	yes	complemented
149	#10621884	C₂³	1	4	yes	complemented
150	#10621883	C₂³	1	8	yes	complemented
151	#10621883	C₂³	1	4	yes	complemented
152	#10621882	C₂³	1	4	yes	complemented
153	#10621882	C₂³	1	8	yes	complemented
154	#10621877	C₂³	1	2	yes	—
155	#10621877	C₂³	1	2	yes	complemented
156	C₂×C₄₃⋊C₈	C₂³	1	2	yes	complemented
157	Dic₁₇₂	C₂³	1	4	yes	complemented
158	D₃₄₄	C₂³	1	4	yes	complemented
159	#10621873	C₂³	1	4	yes	complemented
160	#10621873	C₂³	1	4	yes	complemented
161	#10621872	C₂³	1	8	yes	complemented
162	C₈×D₄₃	C₂³	1	8	yes	complemented
163	C₂³×C₄₃	—	2	2	no	—
164	C₂³×C₄₃	—	2	1	no	—
165	C₂³×C₄₃	—	2	2	no	—
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	8	2	no	—
168	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×D₄₃	—	2	1	no	—
170	C₂²×D₄₃	—	2	1	no	—
171	C₂²×D₄₃	—	2	4	no	—
172	C₂²×D₄₃	—	2	8	no	—
173	C₂²×D₄₃	—	8	4	no	—
174	C₂²×D₄₃	C₂×D₄	1	2	yes	—
175	Q₈×C₄₃	—	2	1	no	—
176	Q₈×C₄₃	C₂⁴	1	2	yes	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	2	2	no	—
179	D₄×C₄₃	—	2	2	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	2	2	no	—
182	D₄×C₄₃	—	2	1	no	—
183	D₄×C₄₃	C₂⁴	1	2	yes	—
184	D₄×C₄₃	C₂⁴	1	4	yes	—
185	C₂×C₄×C₄₃	—	2	1	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
194	C₂²⋊D₄₃	—	2	2	no	—
195	C₂²⋊D₄₃	—	2	2	no	—
196	C₂²⋊D₄₃	—	2	2	no	—
197	C₂²⋊D₄₃	—	2	2	no	—
198	C₂²⋊D₄₃	—	2	4	no	—
199	C₂²⋊D₄₃	—	2	8	no	—
200	C₂²⋊D₄₃	—	2	4	no	—
201	C₂²⋊D₄₃	—	2	8	no	—
202	C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
203	C₂²⋊D₄₃	C₂×D₄	1	4	yes	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	1	no	—
206	C₂×Dic₄₃	—	2	4	no	—
207	C₂×Dic₄₃	—	2	8	no	—
208	C₂×Dic₄₃	C₂×D₄	1	2	yes	—
209	D₁₇₂	—	2	4	no	—
210	D₁₇₂	—	2	1	no	—
211	D₁₇₂	—	2	1	no	—
212	D₁₇₂	C₂×D₄	1	2	yes	—
213	D₁₇₂	C₂×D₄	1	2	yes	—
214	D₁₇₂	C₂⁴	1	2	yes	—
215	D₁₇₂	C₂⁴	1	2	yes	—
216	C₄×D₄₃	—	2	4	no	—
217	C₄×D₄₃	—	2	2	no	—
218	C₄×D₄₃	—	2	2	no	—
219	C₄×D₄₃	—	2	2	no	—
220	C₄×D₄₃	—	2	2	no	—
221	C₄×D₄₃	—	2	4	no	—
222	C₄×D₄₃	C₂×D₄	1	4	yes	—
223	C₄×D₄₃	C₂⁴	1	4	yes	—
224	Dic₈₆	—	2	1	no	—
225	Dic₈₆	—	2	1	no	—
226	Dic₈₆	—	2	4	no	—
227	Dic₈₆	C₂×D₄	1	2	yes	—
228	Dic₈₆	C₂×D₄	1	2	yes	—
229	Dic₈₆	C₂⁴	1	2	yes	—
230	Dic₈₆	C₂⁴	1	2	yes	—
231	C₈×C₄₃	C₂⁴	1	4	yes	—
232	C₄₃⋊C₈	C₂⁴	1	4	yes	—
233	C₂²×C₄₃	—	2	4	no	—
234	C₂²×C₄₃	—	2	2	no	—
235	C₂²×C₄₃	—	4	1	no	—
236	C₂²×C₄₃	—	4	4	no	—
237	C₂²×C₄₃	—	8	1	no	—
238	C₂²×C₄₃	—	8	2	no	—
239	C₂²×C₄₃	—	8	2	no	—
240	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
241	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
242	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×D₄₃	—	2	2	no	—
244	C₂×D₄₃	—	2	2	no	—
245	C₂×D₄₃	—	4	2	no	—
246	C₂×D₄₃	—	4	2	no	—
247	C₂×D₄₃	—	8	4	no	—
248	C₂×D₄₃	—	8	8	no	—
249	C₂×D₄₃	—	8	1	no	—
250	C₂×D₄₃	C₂²×D₄	1	4	yes	—
251	C₄×C₄₃	—	2	2	no	—
252	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
253	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
254	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
255	C₄×C₄₃	C₂⁵	1	1	yes	characteristic
256	Dic₄₃	—	2	2	no	—
257	Dic₄₃	—	2	2	no	—
258	Dic₄₃	C₂²×D₄	1	4	yes	—
259	#3585	—	43	1	no	maximal, Sylow
260	C₂×C₄₃	—	2	1	no	—
261	C₂×C₄₃	—	2	1	no	—
262	C₂×C₄₃	—	2	1	no	—
263	C₂×C₄₃	—	4	4	no	—
264	C₂×C₄₃	—	4	2	no	—
265	C₂×C₄₃	C₂³×D₄	1	1	yes	characteristic
266	D₄₃	—	2	4	no	—
267	D₄₃	—	4	2	no	—
268	D₄₃	—	4	2	no	—
269	#585	—	43	1	no	—
270	C₂×H(5,𝔽₂)	—	43	1	no	—
271	#577	—	43	4	no	—
272	#577	—	43	4	no	—
273	#576	—	43	4	no	—
274	#576	—	43	4	no	—
275	#575	—	43	1	no	—
276	#575	—	43	4	no	—
277	#575	—	43	1	no	—
278	C₂×AGL(1,ℤ/8)	—	43	1	no	—
279	C₂×AGL(1,ℤ/8)	—	43	4	no	—
280	C₂×AGL(1,ℤ/8)	D₄₃	1	1	yes	characteristic, complemented
281	#568	—	43	1	no	—
282	C₄₃	#3585	1	1	yes	characteristic, complemented, Sylow
283	2₋¹⁺⁴	—	43	2	no	—
284	2₋¹⁺⁴	—	43	2	no	—
285	2₋¹⁺⁴	—	86	1	no	—
286	H(5,𝔽₂)	—	43	2	no	—
287	H(5,𝔽₂)	—	43	4	no	—
288	H(5,𝔽₂)	—	43	4	no	—
289	H(5,𝔽₂)	—	43	2	no	—
290	H(5,𝔽₂)	—	86	2	no	—
291	H(5,𝔽₂)	—	86	2	no	—
292	H(5,𝔽₂)	—	86	2	no	—
293	H(5,𝔽₂)	—	86	1	no	—
294	C₂×#41	—	43	1	no	—
295	C₂×#41	—	43	4	no	—
296	C₂×#41	—	43	2	no	—
297	C₂×#41	—	43	1	no	—
298	C₂×#41	—	43	1	no	—
299	C₂×#41	—	86	2	no	—
300	C₂×#41	—	86	1	no	—
301	C₂×#41	—	86	2	no	—
302	C₂×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
303	C₂²×D₄	—	43	2	no	—
304	C₂²×D₄	—	86	1	no	—
305	C₂²×D₄	—	86	2	no	—
306	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
307	#137	—	43	2	no	—
308	#137	—	43	2	no	—
309	#137	—	43	8	no	—
310	#137	—	43	2	no	—
311	#137	—	43	2	no	—
312	AGL(1,ℤ/8)	—	43	2	no	—
313	AGL(1,ℤ/8)	—	43	4	no	—
314	AGL(1,ℤ/8)	—	43	4	no	—
315	AGL(1,ℤ/8)	—	43	2	no	—
316	AGL(1,ℤ/8)	—	43	8	no	—
317	AGL(1,ℤ/8)	—	43	8	no	—
318	AGL(1,ℤ/8)	—	43	8	no	—
319	AGL(1,ℤ/8)	—	43	2	no	—
320	AGL(1,ℤ/8)	—	43	2	no	—
321	AGL(1,ℤ/8)	C₂×D₄₃	1	4	yes	complemented
322	AGL(1,ℤ/8)	C₂×D₄₃	1	4	yes	complemented
323	#135	—	43	4	no	—
324	#135	—	43	8	no	—
325	#135	—	43	8	no	—
326	#135	—	43	4	no	—
327	C₂×SD₁₆	—	43	2	no	—
328	C₂×SD₁₆	—	43	8	no	—
329	C₂×SD₁₆	C₂×D₄₃	1	2	yes	complemented
330	C₂×D₈	—	43	2	no	—
331	C₂×D₈	—	43	8	no	—
332	C₂×D₈	C₂×D₄₃	1	2	yes	complemented
333	#131	—	43	4	no	—
334	#131	—	43	4	no	—
335	C₂×M₁₆	—	43	1	no	—
336	C₂×M₁₆	—	43	4	no	—
337	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
338	C₂⁴	—	2	1	no	—
339	C₂⁴	—	86	2	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	43	2	no	—
343	#41	—	43	2	no	—
344	#41	—	43	2	no	—
345	#41	—	43	2	no	—
346	#41	—	43	4	no	—
347	#41	—	43	4	no	—
348	#41	—	43	8	no	—
349	#41	—	43	2	no	—
350	#41	—	43	2	no	—
351	#41	—	43	2	no	—
352	#41	—	43	2	no	—
353	#41	—	86	4	no	—
354	#41	—	86	4	no	—
355	#41	—	86	2	no	—
356	#41	—	86	2	no	—
357	#41	—	86	4	no	—
358	#41	—	86	4	no	—
359	#41	—	86	4	no	—
360	#41	—	86	4	no	—
361	#41	—	86	4	no	—
362	#41	—	86	2	no	—
363	#41	—	86	2	no	—
364	#41	—	86	1	no	—
365	#41	—	86	1	no	—
366	#41	—	86	1	no	—
367	#41	—	86	1	no	—
368	#41	C₂²×D₄₃	1	2	yes	—
369	#41	C₂²×D₄₃	1	2	yes	complemented
370	C₂×Q₈	—	43	1	no	—
371	C₂×Q₈	—	43	4	no	—
372	C₂×Q₈	—	43	1	no	—
373	C₂×Q₈	—	43	1	no	—
374	C₂×Q₈	—	86	2	no	—
375	C₂×Q₈	—	86	2	no	—
376	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	1	no	—
380	C₂×D₄	—	2	1	no	—
381	C₂×D₄	—	43	2	no	—
382	C₂×D₄	—	43	4	no	—
383	C₂×D₄	—	43	8	no	—
384	C₂×D₄	—	43	1	no	—
385	C₂×D₄	—	43	1	no	—
386	C₂×D₄	—	43	1	no	—
387	C₂×D₄	—	86	2	no	—
388	C₂×D₄	—	86	4	no	—
389	C₂×D₄	—	86	2	no	—
390	C₂×D₄	—	86	4	no	—
391	C₂×D₄	—	86	4	no	—
392	C₂×D₄	—	86	4	no	—
393	C₂×D₄	—	86	2	no	—
394	C₂×D₄	—	86	4	no	—
395	C₂×D₄	—	86	8	no	—
396	C₂×D₄	—	86	8	no	—
397	C₂×D₄	—	86	4	no	—
398	C₂×D₄	—	86	2	no	—
399	C₂×D₄	—	86	1	no	—
400	C₂×D₄	—	86	1	no	—
401	C₂×D₄	C₂²×D₄₃	1	2	yes	—
402	C₂×D₄	C₂²×D₄₃	1	2	yes	—
403	C₂×D₄	C₂²×D₄₃	1	2	yes	—
404	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic, complemented
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	43	2	no	—
407	C₂²×C₄	—	86	4	no	—
408	C₂²×C₄	—	86	2	no	—
409	C₂²×C₄	—	86	1	no	—
410	C₂²×C₄	—	86	1	no	—
411	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
412	Q₁₆	—	43	4	no	—
413	Q₁₆	—	43	4	no	—
414	SD₁₆	—	43	4	no	—
415	SD₁₆	—	43	8	no	—
416	SD₁₆	—	43	4	no	—
417	SD₁₆	—	43	4	no	—
418	SD₁₆	—	43	4	no	—
419	SD₁₆	C₂²×D₄₃	1	8	yes	complemented
420	D₈	—	43	8	no	—
421	D₈	—	43	4	no	—
422	D₈	—	43	4	no	—
423	D₈	C₂²×D₄₃	1	8	yes	complemented
424	M₁₆	—	43	2	no	—
425	M₁₆	—	43	2	no	—
426	M₁₆	—	43	8	no	—
427	M₁₆	C₂²×D₄₃	1	2	yes	—
428	M₁₆	C₂²×D₄₃	1	2	yes	complemented
429	C₂×C₈	—	43	2	no	—
430	C₂×C₈	—	43	8	no	—
431	C₂×C₈	C₂²×D₄₃	1	2	yes	complemented
432	C₂³	—	2	2	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	8	2	no	—
437	C₂³	—	43	2	no	—
438	C₂³	—	86	4	no	—
439	C₂³	—	86	8	no	—
440	C₂³	—	86	1	no	—
441	C₂³	—	86	1	no	—
442	C₂³	—	344	4	no	—
443	C₂³	D₄×D₄₃	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	43	2	no	—
446	Q₈	—	43	2	no	—
447	Q₈	—	43	2	no	—
448	Q₈	—	43	2	no	—
449	Q₈	—	86	4	no	—
450	Q₈	—	86	1	no	—
451	Q₈	—	86	1	no	—
452	Q₈	C₂³×D₄₃	1	2	yes	—
453	D₄	—	2	2	no	—
454	D₄	—	2	2	no	—
455	D₄	—	2	2	no	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	43	4	no	—
460	D₄	—	43	4	no	—
461	D₄	—	43	2	no	—
462	D₄	—	43	2	no	—
463	D₄	—	43	2	no	—
464	D₄	—	43	2	no	—
465	D₄	—	86	4	no	—
466	D₄	—	86	8	no	—
467	D₄	—	86	4	no	—
468	D₄	—	86	8	no	—
469	D₄	—	86	4	no	—
470	D₄	—	86	2	no	—
471	D₄	—	86	2	no	—
472	D₄	—	86	2	no	—
473	D₄	—	86	2	no	—
474	D₄	—	86	1	no	—
475	D₄	—	86	1	no	—
476	D₄	C₂³×D₄₃	1	2	yes	—
477	D₄	C₂³×D₄₃	1	4	yes	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	43	2	no	—
482	C₂×C₄	—	43	4	no	—
483	C₂×C₄	—	43	4	no	—
484	C₂×C₄	—	86	4	no	—
485	C₂×C₄	—	86	4	no	—
486	C₂×C₄	—	86	8	no	—
487	C₂×C₄	—	86	4	no	—
488	C₂×C₄	—	86	1	no	—
489	C₂×C₄	—	86	1	no	—
490	C₂×C₄	—	86	2	no	—
491	C₂×C₄	—	86	2	no	—
492	C₂×C₄	—	86	2	no	—
493	C₂×C₄	—	86	2	no	—
494	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
495	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
496	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
497	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
498	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
499	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
500	C₈	—	43	4	no	—
501	C₈	C₂³×D₄₃	1	4	yes	—
502	C₂²	—	2	2	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	43	4	no	—
510	C₂²	—	86	2	no	—
511	C₂²	—	86	2	no	—
512	C₂²	—	344	1	no	—
513	C₂²	—	344	8	no	—
514	C₂²	—	344	4	no	—
515	C₂²	—	172	2	no	—
516	C₂²	—	172	2	no	—
517	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
518	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
519	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	43	4	no	—
522	C₄	—	86	2	no	—
523	C₄	—	86	2	no	—
524	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
525	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
526	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
527	C₄	C₂⁴×D₄₃	1	1	yes	characteristic
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	4	4	no	—
532	C₂	—	4	2	no	—
533	C₂	—	86	4	no	—
534	C₂	—	172	2	no	—
535	C₂	—	172	2	no	—
536	C₂	C₂²×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₄₃
commutator	C₄×C₄₃	C₂⁵
Frattini	C₄	C₂⁴×D₄₃
Fitting	C₂×AGL(1,ℤ/8)×C₄₃	C₂
socle	C₂×C₄₃	C₂³×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₄₃
hypocenter	C₄₃	#3585
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #14583735	C₂	semidirect
2. C₂×#13063370	C₂	semidirect
3. #14583709	C₂	semidirect
4. #14583705	C₂	semidirect
5. #14583703	C₂	semidirect
6. #14583700	C₂	semidirect
7. #14583699	C₂	semidirect
8. #14583697	C₂	semidirect
9. #14583695	C₂	semidirect
10. C₂×#13063351	C₂	semidirect
11. AGL(1,ℤ/8)×D₄₃	C₂	semidirect
12. #14583665	C₂	semidirect
13. C₂×AGL(1,ℤ/8)×C₄₃	C₂	semidirect
14. #13063373	C₂²	semidirect
16. #13063372	C₂²	semidirect
18. #13063371	C₂²	semidirect
22. #13063370	C₂²	semidirect
23. #13063370	C₂²	semidirect
24. #13063370	C₂²	semidirect
27. C₂×#10621898	C₂²	semidirect
28. C₂×#10621898	C₂²	semidirect
30. C₂×#10621900	C₂²	semidirect
32. #41×D₄₃	C₂²	semidirect
35. C₂×D₄×D₄₃	C₂²	semidirect
36. #13063358	C₂²	semidirect
37. #13063358	C₂²	semidirect
38. #13063356	C₂²	semidirect
39. #13063355	C₂²	semidirect
40. #13063354	C₂²	semidirect
41. #13063353	C₂²	semidirect
42. #13063353	C₂²	semidirect
43. #13063352	C₂²	semidirect
44. #13063351	C₂²	semidirect
45. #13063351	C₂²	semidirect
46. #13063351	C₂²	semidirect
47. #13063350	C₂²	semidirect
48. #13063349	C₂²	semidirect
49. #13063349	C₂²	semidirect
50. #13063347	C₂²	semidirect
51. #13063346	C₂²	semidirect
52. #13063345	C₂²	semidirect
53. #13063344	C₂²	semidirect
54. C₂×#10621883	C₂²	semidirect
55. SD₁₆×D₄₃	C₂²	semidirect
56. C₂×#10621882	C₂²	semidirect
57. D₈×D₄₃	C₂²	semidirect
58. #13063333	C₂²	semidirect
59. #13063331	C₂²	semidirect
60. C₂×#10621877	C₂²	semidirect
61. M₁₆×D₄₃	C₂²	semidirect
62. C₂×#41×C₄₃	C₂²	semidirect
63. C₂²×D₄×C₄₃	C₂²	semidirect
64. AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
65. AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
66. C₂×SD₁₆×C₄₃	C₂²	semidirect
67. C₂×D₈×C₄₃	C₂²	semidirect
68. C₂×M₁₆×C₄₃	C₂²	semidirect
74. #41×C₄₃	C₂³	semidirect
75. C₂×Q₈×C₄₃	C₂³	semidirect
83. C₂×D₄×C₄₃	C₂³	semidirect
96. #10621902	C₂³	semidirect
98. Q₈×D₄₃	C₂³	semidirect
106. #10621900	C₂³	semidirect
114. D₄×D₄₃	C₂³	semidirect
130. #10621898	C₂³	semidirect
134. C₂×D₁₇₂	C₂³	semidirect
142. C₂×Dic₈₆	C₂³	semidirect
143. SD₁₆×C₄₃	C₂³	semidirect
144. D₈×C₄₃	C₂³	semidirect
146. M₁₆×C₄₃	C₂³	semidirect
147. C₂×C₈×C₄₃	C₂³	semidirect
148. #10621885	C₂³	semidirect
149. #10621884	C₂³	semidirect
150. #10621883	C₂³	semidirect
151. #10621883	C₂³	semidirect
152. #10621882	C₂³	semidirect
153. #10621882	C₂³	semidirect
155. #10621877	C₂³	semidirect
156. C₂×C₄₃⋊C₈	C₂³	semidirect
157. Dic₁₇₂	C₂³	semidirect
158. D₃₄₄	C₂³	semidirect
159. #10621873	C₂³	semidirect
160. #10621873	C₂³	semidirect
161. #10621872	C₂³	semidirect
162. C₈×D₄₃	C₂³	semidirect
280. C₂×AGL(1,ℤ/8)	D₄₃	semidirect
282. C₄₃	#3585	semidirect
302. C₂×#41	C₂×D₄₃	semidirect
306. C₂²×D₄	C₂×D₄₃	semidirect
321. AGL(1,ℤ/8)	C₂×D₄₃	semidirect
322. AGL(1,ℤ/8)	C₂×D₄₃	semidirect
329. C₂×SD₁₆	C₂×D₄₃	semidirect
332. C₂×D₈	C₂×D₄₃	semidirect
337. C₂×M₁₆	C₂×D₄₃	semidirect
369. #41	C₂²×D₄₃	semidirect
376. C₂×Q₈	C₂²×D₄₃	semidirect
404. C₂×D₄	C₂²×D₄₃	semidirect
419. SD₁₆	C₂²×D₄₃	semidirect
423. D₈	C₂²×D₄₃	semidirect
428. M₁₆	C₂²×D₄₃	semidirect
431. C₂×C₈	C₂²×D₄₃	semidirect