Subgroups — #19146071

Order 5504.

568 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	C₂×#13063351	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#10621882	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583545	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583286	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583150	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583126	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583114	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583091	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583050	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583042	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583033	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583032	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583009	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582971	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄²×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621898	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
18	#13063351	—	2	4	no	—
19	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
20	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
21	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
22	C₂×#10621882	—	2	4	no	—
23	C₂×#10621882	C₂²	1	1	yes	characteristic
24	C₂×#10621882	C₂²	1	1	yes	characteristic
25	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
26	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
27	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
28	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
29	C₂×#10621877	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
31	#13063313	C₂²	1	1	yes	characteristic, complemented
32	#13063310	—	2	1	no	—
33	#13063304	C₂²	1	1	yes	characteristic, complemented
34	#13063299	C₂²	1	1	yes	characteristic, complemented
35	#13063298	—	2	1	no	—
36	#13063293	—	2	1	no	—
37	C₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
38	C₂²⋊C₄×D₄₃	—	2	1	no	—
39	#13063256	C₂²	1	1	yes	characteristic, complemented
40	C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
41	#13063248	C₂²	1	1	yes	characteristic, complemented
42	#13063246	C₂²	1	1	yes	characteristic, complemented
43	#13063246	C₂²	1	1	yes	characteristic, complemented
44	#13063246	C₂²	1	1	yes	characteristic, complemented
45	#13063245	C₂²	1	1	yes	characteristic, complemented
46	#13063245	C₂²	1	1	yes	characteristic, complemented
47	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
48	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
49	#13063236	C₂²	1	1	yes	characteristic, complemented
50	C₂²×D₄×C₄₃	—	2	1	no	—
51	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic
52	C₂²×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
53	#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
54	#121×C₄₃	—	2	1	no	—
55	#121×C₄₃	C₂²	1	1	yes	characteristic
56	#121×C₄₃	C₂²	1	1	yes	characteristic, complemented
57	#120×C₄₃	—	2	1	no	—
58	#120×C₄₃	—	2	1	no	—
59	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
60	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₄₃	—	2	1	no	—
62	C₂⁴×C₄₃	—	2	1	no	—
63	C₂³×D₄₃	—	2	1	no	—
64	C₂×D₄×C₄₃	—	2	1	no	—
65	C₂×D₄×C₄₃	—	2	1	no	—
66	C₂×D₄×C₄₃	—	2	1	no	—
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	—	2	1	no	—
69	C₂×D₄×C₄₃	—	2	1	no	—
70	C₂×D₄×C₄₃	—	2	2	no	—
71	C₂×D₄×C₄₃	—	2	2	no	—
72	C₂×D₄×C₄₃	—	4	1	no	—
73	C₂×D₄×C₄₃	—	4	1	no	—
74	C₂×D₄×C₄₃	—	4	4	no	—
75	C₂×D₄×C₄₃	D₄	1	1	yes	characteristic
76	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₄₃	—	2	1	no	—
80	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₂²⋊D₄₃	—	2	1	no	—
83	C₂×C₂²⋊D₄₃	—	2	1	no	—
84	#10621898	—	2	2	no	—
85	#10621898	—	4	1	no	—
86	C₂×D₁₇₂	—	2	1	no	—
87	C₂×D₁₇₂	—	2	2	no	—
88	C₂×D₁₇₂	—	4	1	no	—
89	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
90	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
91	C₂×C₄×D₄₃	—	2	1	no	—
92	C₂×C₄×D₄₃	—	2	1	no	—
93	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
94	C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
95	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²⋊C₄×C₄₃	—	2	1	no	—
97	C₂²⋊C₄×C₄₃	—	2	1	no	—
98	C₂²⋊C₄×C₄₃	—	2	1	no	—
99	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
100	C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
101	C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²⋊Dic₄₃	—	2	1	no	—
103	#10621883	—	2	2	no	—
104	#10621883	—	2	2	no	—
105	#10621883	—	4	1	no	—
106	#10621882	—	2	2	no	—
107	#10621882	—	2	2	no	—
108	#10621882	—	2	2	no	—
109	#10621882	—	2	2	no	—
110	#10621882	—	4	1	no	—
111	#10621882	D₄	1	4	yes	complemented
112	(C₂×D₄₃)⋊C₄	—	2	1	no	—
113	(C₂×D₄₃)⋊C₄	—	2	1	no	—
114	(C₂×D₄₃)⋊C₄	—	2	1	no	—
115	(C₂×D₄₃)⋊C₄	—	2	1	no	—
116	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
117	Dic₄₃⋊C₄	—	2	1	no	—
118	#10621877	—	2	2	no	—
119	C₂×C₄₃⋊C₈	—	2	2	no	—
120	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₂³×C₄₃	—	2	1	no	—
125	C₂³×C₄₃	—	2	1	no	—
126	C₂³×C₄₃	—	2	1	no	—
127	C₂³×C₄₃	—	4	2	no	—
128	C₂³×C₄₃	—	4	2	no	—
129	C₂³×C₄₃	—	4	2	no	—
130	C₂³×C₄₃	—	4	2	no	—
131	C₂³×C₄₃	—	8	1	no	—
132	C₂³×C₄₃	—	8	1	no	—
133	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×D₄₃	—	2	1	no	—
136	C₂²×D₄₃	—	2	1	no	—
137	C₂²×D₄₃	—	4	2	no	—
138	C₂²×D₄₃	—	4	2	no	—
139	C₂²×D₄₃	—	8	1	no	—
140	D₄×C₄₃	—	2	2	no	—
141	D₄×C₄₃	—	2	1	no	—
142	D₄×C₄₃	—	2	1	no	—
143	D₄×C₄₃	—	2	1	no	—
144	D₄×C₄₃	—	2	1	no	—
145	D₄×C₄₃	—	2	1	no	—
146	D₄×C₄₃	—	4	2	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	4	2	no	—
149	D₄×C₄₃	—	4	2	no	—
150	D₄×C₄₃	—	4	2	no	—
151	D₄×C₄₃	—	8	1	no	—
152	D₄×C₄₃	C₂×D₄	1	2	yes	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	1	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
164	C₂²⋊D₄₃	—	4	2	no	—
165	C₂²⋊D₄₃	—	8	1	no	—
166	C₂×Dic₄₃	—	2	1	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	D₁₇₂	—	2	1	no	—
169	D₁₇₂	—	2	1	no	—
170	D₁₇₂	—	2	1	no	—
171	D₁₇₂	—	4	2	no	—
172	D₁₇₂	C₂×D₄	1	2	yes	complemented
173	C₄×D₄₃	—	4	2	no	—
174	C₄×D₄₃	—	8	1	no	—
175	Dic₈₆	—	2	1	no	—
176	Dic₈₆	—	2	1	no	—
177	C₄₃⋊C₈	—	2	1	no	—
178	C₄₃⋊C₈	—	2	1	no	—
179	C₄₃⋊C₈	—	2	1	no	—
180	C₄₃⋊C₈	C₂×D₄	1	2	yes	complemented
181	C₂²×C₄₃	—	2	1	no	—
182	C₂²×C₄₃	—	2	1	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	2	1	no	—
185	C₂²×C₄₃	—	2	1	no	—
186	C₂²×C₄₃	—	2	1	no	—
187	C₂²×C₄₃	—	4	1	no	—
188	C₂²×C₄₃	—	4	1	no	—
189	C₂²×C₄₃	—	4	1	no	—
190	C₂²×C₄₃	—	4	1	no	—
191	C₂²×C₄₃	—	4	1	no	—
192	C₂²×C₄₃	—	4	1	no	—
193	C₂²×C₄₃	—	4	1	no	—
194	C₂²×C₄₃	—	4	1	no	—
195	C₂²×C₄₃	—	8	4	no	—
196	C₂²×C₄₃	—	8	4	no	—
197	C₂²×C₄₃	AGL(1,ℤ/8)	1	2	yes	complemented
198	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×D₄₃	—	2	2	no	—
200	C₂×D₄₃	—	4	1	no	—
201	C₂×D₄₃	—	4	1	no	—
202	C₂×D₄₃	—	4	1	no	—
203	C₂×D₄₃	—	4	1	no	—
204	C₂×D₄₃	—	4	1	no	—
205	C₂×D₄₃	—	8	4	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	4	1	no	—
211	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
213	Dic₄₃	—	4	1	no	—
214	Dic₄₃	—	4	1	no	—
215	#3264	—	43	1	no	maximal, Sylow
216	C₂×C₄₃	—	2	2	no	—
217	C₂×C₄₃	—	4	1	no	—
218	C₂×C₄₃	—	4	2	no	—
219	C₂×C₄₃	—	8	1	no	—
220	C₂×C₄₃	—	8	1	no	—
221	C₂×C₄₃	D₄²	1	1	yes	characteristic
222	C₂×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₂×C₄₃	#576	1	1	yes	characteristic
224	D₄₃	—	4	2	no	—
225	D₄₃	—	8	1	no	—
226	C₂×AGL(1,ℤ/8)	—	43	1	no	—
227	C₂²×D₈	—	43	1	no	—
228	#546	—	43	1	no	—
229	D₄²	D₄₃	1	1	yes	characteristic, complemented
230	#496	—	43	1	no	—
231	#469	—	43	1	no	—
232	#465	—	43	1	no	—
233	#463	—	43	1	no	—
234	#459	—	43	1	no	—
235	#450	—	43	1	no	—
236	#449	—	43	1	no	—
237	#447	—	43	1	no	—
238	#447	—	43	1	no	—
239	#442	—	43	1	no	—
240	#435	—	43	1	no	—
241	C₄₃	#3264	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	43	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	43	1	no	—
245	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic
246	C₂²×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
247	AGL(1,ℤ/8)	—	86	4	no	—
248	C₂×SD₁₆	—	43	1	no	—
249	C₂×SD₁₆	—	43	1	no	—
250	C₂×SD₁₆	—	43	1	no	—
251	C₂×D₈	—	43	1	no	—
252	C₂×D₈	—	43	1	no	—
253	C₂×D₈	—	43	1	no	—
254	C₂×D₈	—	43	1	no	—
255	C₂×D₈	—	43	1	no	—
256	C₂×D₈	—	43	1	no	—
257	C₂×D₈	—	86	4	no	—
258	C₂×M₁₆	—	43	1	no	—
259	C₂²×C₈	—	43	1	no	—
260	#127	C₂×D₄₃	1	1	yes	characteristic, complemented
261	#124	—	43	1	no	—
262	#123	—	86	1	no	—
263	C₂²⋊Q₈	—	43	1	no	—
264	#121	—	2	1	no	—
265	#121	—	43	1	no	—
266	#121	—	86	1	no	—
267	#121	C₂×D₄₃	1	1	yes	characteristic
268	#121	C₂×D₄₃	1	1	yes	characteristic, complemented
269	#120	—	2	1	no	—
270	#120	—	2	1	no	—
271	#120	—	86	1	no	—
272	C₄×D₄	—	43	1	no	—
273	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
274	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	86	1	no	—
276	#106	—	43	1	no	—
277	C₄⋊C₈	—	43	1	no	—
278	#103	—	43	1	no	—
279	#102	—	43	1	no	—
280	#102	—	43	1	no	—
281	#102	—	43	1	no	—
282	#102	—	43	1	no	—
283	#102	—	43	1	no	—
284	C₂²⋊C₈	—	43	1	no	—
285	C₂²⋊C₈	—	43	1	no	—
286	#97	—	43	1	no	—
287	C₂⁴	—	2	1	no	—
288	C₂⁴	—	2	1	no	—
289	C₂⁴	—	86	1	no	—
290	#41	—	86	2	no	—
291	#41	—	172	1	no	—
292	C₂×Q₈	—	43	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	4	no	—
304	C₂×D₄	—	43	1	no	—
305	C₂×D₄	—	43	1	no	—
306	C₂×D₄	—	86	2	no	—
307	C₂×D₄	—	86	1	no	—
308	C₂×D₄	—	86	1	no	—
309	C₂×D₄	—	86	1	no	—
310	C₂×D₄	—	172	1	no	—
311	C₂×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
312	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
320	SD₁₆	—	86	2	no	—
321	SD₁₆	—	86	2	no	—
322	SD₁₆	—	172	1	no	—
323	D₈	—	43	4	no	—
324	D₈	—	86	2	no	—
325	D₈	—	86	2	no	—
326	D₈	—	86	2	no	—
327	D₈	—	86	2	no	—
328	D₈	—	172	1	no	—
329	M₁₆	—	86	2	no	—
330	C₂×C₈	—	43	1	no	—
331	C₂×C₈	—	43	1	no	—
332	C₂×C₈	—	43	1	no	—
333	C₂×C₈	—	43	1	no	—
334	C₂×C₈	—	86	2	no	—
335	C₄⋊C₄	—	43	1	no	—
336	C₄⋊C₄	—	86	1	no	—
337	C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
338	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	1	no	—
342	C₂²⋊C₄	—	86	1	no	—
343	C₂²⋊C₄	—	86	1	no	—
344	C₂²⋊C₄	—	86	1	no	—
345	C₂²⋊C₄	—	86	1	no	—
346	C₂²⋊C₄	—	86	1	no	—
347	C₂²⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
348	C₂²⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
349	C₄²	C₂²×D₄₃	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	8	1	no	—
358	C₂³	—	8	1	no	—
359	C₂³	—	86	1	no	—
360	C₂³	—	86	1	no	—
361	C₂³	—	344	1	no	—
362	C₂³	—	172	2	no	—
363	C₂³	—	172	2	no	—
364	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
365	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
366	Q₈	—	86	1	no	—
367	Q₈	—	86	1	no	—
368	D₄	—	2	2	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	2	1	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	8	1	no	—
380	D₄	—	43	2	no	—
381	D₄	—	86	1	no	—
382	D₄	—	86	1	no	—
383	D₄	—	86	1	no	—
384	D₄	—	344	1	no	—
385	D₄	—	172	2	no	—
386	D₄	—	172	2	no	—
387	D₄	D₄×D₄₃	1	2	yes	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	86	1	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	344	1	no	—
397	C₂×C₄	—	172	2	no	—
398	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
403	C₈	—	43	2	no	—
404	C₈	—	86	1	no	—
405	C₈	—	86	1	no	—
406	C₈	—	86	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	—	4	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	8	4	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	86	2	no	—
424	C₂²	—	344	4	no	—
425	C₂²	—	172	1	no	—
426	C₂²	—	172	1	no	—
427	C₂²	—	172	1	no	—
428	C₂²	—	172	1	no	—
429	C₂²	—	172	1	no	—
430	C₂²	#13063351	1	2	yes	complemented
431	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	172	1	no	—
438	C₄	—	172	1	no	—
439	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₄	#13063370	1	1	yes	characteristic
441	C₂	—	2	2	no	—
442	C₂	—	4	1	no	—
443	C₂	—	4	2	no	—
444	C₂	—	8	1	no	—
445	C₂	—	8	1	no	—
446	C₂	—	344	1	no	—
447	C₂	—	172	2	no	—
448	C₂	D₄×C₂²⋊D₄₃	1	1	yes	characteristic
449	C₂	C₂×#13063351	1	1	yes	characteristic
450	C₂	#14583702	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	D₄²×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	D₄²	D₄₃
hypocenter	C₄₃	#3264
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. C₂×#13063351	C₂	semidirect
2. C₂²×#10621882	C₂	semidirect
3. #14583545	C₂	semidirect
4. #14583286	C₂	semidirect
5. #14583150	C₂	semidirect
6. #14583126	C₂	semidirect
7. #14583114	C₂	semidirect
8. #14583091	C₂	semidirect
9. #14583050	C₂	semidirect
10. #14583042	C₂	semidirect
11. #14583033	C₂	semidirect
12. #14583032	C₂	semidirect
13. #14583009	C₂	semidirect
14. #14582971	C₂	semidirect
15. D₄²×C₄₃	C₂	semidirect
16. C₂×#10621898	C₂²	semidirect
17. C₂²×D₁₇₂	C₂²	semidirect
19. C₂×#10621883	C₂²	semidirect
20. C₂×#10621883	C₂²	semidirect
21. C₂×#10621883	C₂²	semidirect
25. C₂×#10621882	C₂²	semidirect
26. C₂×#10621882	C₂²	semidirect
27. C₂×#10621882	C₂²	semidirect
28. C₂×#10621882	C₂²	semidirect
29. C₂×#10621877	C₂²	semidirect
30. C₂²×C₄₃⋊C₈	C₂²	semidirect
31. #13063313	C₂²	semidirect
33. #13063304	C₂²	semidirect
34. #13063299	C₂²	semidirect
37. C₄×D₁₇₂	C₂²	semidirect
39. #13063256	C₂²	semidirect
40. C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
41. #13063248	C₂²	semidirect
42. #13063246	C₂²	semidirect
43. #13063246	C₂²	semidirect
44. #13063246	C₂²	semidirect
45. #13063245	C₂²	semidirect
46. #13063245	C₂²	semidirect
47. C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
48. C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
49. #13063236	C₂²	semidirect
52. C₂²×D₄×C₄₃	C₂²	semidirect
53. #127×C₄₃	C₂²	semidirect
56. #121×C₄₃	C₂²	semidirect
60. C₄×D₄×C₄₃	C₂²	semidirect
111. #10621882	D₄	semidirect
172. D₁₇₂	C₂×D₄	semidirect
180. C₄₃⋊C₈	C₂×D₄	semidirect
197. C₂²×C₄₃	AGL(1,ℤ/8)	semidirect
229. D₄²	D₄₃	semidirect
241. C₄₃	#3264	semidirect
246. C₂²×D₄	C₂×D₄₃	semidirect
260. #127	C₂×D₄₃	semidirect
268. #121	C₂×D₄₃	semidirect
274. C₄×D₄	C₂×D₄₃	semidirect
430. C₂²	#13063351	semidirect