Subgroups — #19148496

Order 5504.

1104 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583618	C₂	1	2	yes	maximal, complemented
2	#14583613	C₂	1	2	yes	maximal, complemented
3	#14583608	C₂	1	2	yes	maximal, complemented
4	#14583599	C₂	1	2	yes	maximal, complemented
5	#14583596	C₂	1	2	yes	maximal, complemented
6	#14583557	C₂	1	2	yes	maximal, complemented
7	#14583556	C₂	1	2	yes	maximal, complemented
8	#14583548	C₂	1	2	yes	maximal, complemented
9	#14583516	C₂	1	2	yes	maximal, complemented
10	#14583514	C₂	1	2	yes	maximal, complemented
11	#14583478	C₂	1	2	yes	maximal, complemented
12	#14583456	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583454	C₂	1	1	yes	maximal, characteristic, complemented
14	#14583447	C₂	1	1	yes	maximal, characteristic, complemented
15	#14583447	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583378	C₂	1	2	yes	maximal, complemented
18	C₄×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#10621898	C₂²	1	1	yes	characteristic
21	C₂×#10621900	C₂²	1	2	yes	—
22	C₂×#10621900	C₂²	1	2	yes	—
23	C₂×Q₈×D₄₃	C₂²	1	2	yes	—
24	#13063325	C₂²	1	1	yes	characteristic
25	#13063325	C₂²	1	1	yes	characteristic
26	#13063324	C₂²	1	2	yes	—
27	#13063324	C₂²	1	2	yes	—
28	#13063323	C₂²	1	2	yes	—
29	#13063318	C₂²	1	4	yes	—
30	#13063318	C₂²	1	4	yes	—
31	#13063317	C₂²	1	2	yes	—
32	#13063316	C₂²	1	2	yes	—
33	#13063312	C₂²	1	4	yes	—
34	#13063312	C₂²	1	2	yes	—
35	#13063312	C₂²	1	2	yes	—
36	#13063311	C₂²	1	4	yes	—
37	#13063308	C₂²	1	4	yes	—
38	#13063306	C₂²	1	4	yes	—
39	#13063305	C₂²	1	2	yes	—
40	#13063304	C₂²	1	4	yes	—
41	#13063304	C₂²	1	2	yes	—
42	#13063304	C₂²	1	2	yes	—
43	#13063302	C₂²	1	4	yes	—
44	#13063302	C₂²	1	4	yes	—
45	#13063301	C₂²	1	2	yes	—
46	#13063298	C₂²	1	4	yes	—
47	#13063297	C₂²	1	4	yes	—
48	#13063296	C₂²	1	2	yes	—
49	#13063296	C₂²	1	4	yes	—
50	#13063296	C₂²	1	2	yes	—
51	#13063296	C₂²	1	2	yes	—
52	#13063296	C₂²	1	2	yes	—
53	Q₈×Dic₄₃	C₂²	1	2	yes	—
54	C₄×Dic₈₆	C₂²	1	2	yes	—
55	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
56	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
57	C₄×Dic₈₆	C₂²	1	2	yes	—
58	#13063290	C₂²	1	2	yes	—
59	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
60	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
61	D₄×Dic₄₃	C₂²	1	2	yes	—
62	D₄×Dic₄₃	C₂²	1	2	yes	—
63	D₄×Dic₄₃	C₂²	1	2	yes	—
64	D₄×Dic₄₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
67	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
70	(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	—
71	#13063284	C₂²	1	2	yes	—
72	#13063284	C₂²	1	1	yes	characteristic
73	#13063283	C₂²	1	2	yes	—
74	#13063282	C₂²	1	1	yes	characteristic
75	#13063282	C₂²	1	1	yes	characteristic
76	#13063281	C₂²	1	4	yes	—
77	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
78	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
79	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
80	C₄²×D₄₃	C₂²	1	1	yes	characteristic
81	C₄²×D₄₃	C₂²	1	1	yes	characteristic
82	C₂×#41×C₄₃	C₂²	1	2	yes	—
83	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
84	#127×C₄₃	C₂²	1	1	yes	characteristic
85	#124×C₄₃	C₂²	1	2	yes	—
86	#121×C₄₃	C₂²	1	2	yes	—
87	#121×C₄₃	C₂²	1	2	yes	—
88	C₄×D₄×C₄₃	C₂²	1	2	yes	—
89	C₄×D₄×C₄₃	C₂²	1	2	yes	—
90	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
91	#41×C₄₃	—	4	4	no	—
92	C₂×Q₈×C₄₃	C₂³	1	2	yes	—
93	C₂×D₄×C₄₃	C₂³	1	2	yes	—
94	C₂×D₄×C₄₃	C₂³	1	2	yes	—
95	C₂×D₄×C₄₃	C₂³	1	2	yes	—
96	C₂×D₄×C₄₃	C₂³	1	4	yes	—
97	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₃	C₂³	1	4	yes	—
105	C₂²×Dic₄₃	C₂³	1	4	yes	—
106	C₂²×Dic₄₃	C₂³	1	4	yes	—
107	Q₈×D₄₃	—	4	4	no	—
108	#10621900	—	2	8	no	—
109	#10621900	—	4	4	no	—
110	#10621898	—	2	4	no	—
111	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
116	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₄₃	C₂³	1	4	yes	—
118	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
119	C₂×Dic₈₆	C₂³	1	2	yes	—
120	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
121	C₂×Dic₈₆	C₂³	1	2	yes	—
122	C₂×Dic₈₆	C₂³	1	4	yes	—
123	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
124	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
125	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
126	C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
127	C₄²×C₄₃	C₂³	1	1	yes	characteristic
128	C₄²×C₄₃	C₂³	1	1	yes	characteristic
129	C₄²×C₄₃	C₂³	1	1	yes	characteristic
130	C₄²×C₄₃	C₂³	1	1	yes	characteristic
131	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
132	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
133	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
134	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
135	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
136	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
137	C₂²⋊Dic₄₃	C₂³	1	4	yes	—
138	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
139	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
140	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
141	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
142	(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
143	C₄⋊Dic₄₃	C₂³	1	2	yes	—
144	C₄⋊Dic₄₃	C₂³	1	2	yes	—
145	C₄⋊Dic₄₃	C₂³	1	2	yes	—
146	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
147	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
148	C₄⋊Dic₄₃	C₂³	1	2	yes	—
149	C₄⋊Dic₄₃	C₂³	1	4	yes	—
150	Dic₄₃⋊C₄	C₂³	1	4	yes	—
151	Dic₄₃⋊C₄	C₂³	1	4	yes	—
152	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
153	Dic₄₃⋊C₄	C₂³	1	4	yes	—
154	Dic₄₃⋊C₄	C₂³	1	4	yes	—
155	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
156	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
157	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
158	Dic₄₃⋊C₄	C₂³	1	4	yes	—
159	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
160	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
161	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
162	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
163	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
164	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
165	C₄×Dic₄₃	C₂³	1	4	yes	—
166	C₄×Dic₄₃	C₂³	1	4	yes	—
167	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
168	C₂³×C₄₃	C₂⁴	1	4	yes	—
169	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
170	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
171	Q₈×C₄₃	—	2	4	no	—
172	D₄×C₄₃	—	2	4	no	—
173	D₄×C₄₃	—	2	4	no	—
174	D₄×C₄₃	—	2	4	no	—
175	D₄×C₄₃	—	4	4	no	—
176	C₂×C₄×C₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
182	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
187	C₂²⋊D₄₃	—	2	2	no	—
188	C₂²⋊D₄₃	—	2	8	no	—
189	C₂²⋊D₄₃	—	2	2	no	—
190	C₂²⋊D₄₃	—	4	4	no	—
191	C₂×Dic₄₃	—	2	8	no	—
192	C₂×Dic₄₃	—	4	4	no	—
193	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
194	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
195	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
196	C₂×Dic₄₃	C₂⁴	1	4	yes	—
197	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
198	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
199	C₂×Dic₄₃	C₂⁴	1	4	yes	—
200	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
201	D₁₇₂	—	2	2	no	—
202	C₄×D₄₃	—	2	2	no	—
203	C₄×D₄₃	—	2	2	no	—
204	C₄×D₄₃	—	2	2	no	—
205	C₄×D₄₃	—	2	2	no	—
206	C₄×D₄₃	—	2	2	no	—
207	C₄×D₄₃	—	4	4	no	—
208	C₄×D₄₃	#41	1	4	yes	complemented
209	Dic₈₆	—	2	4	no	—
210	Dic₈₆	—	2	4	no	—
211	Dic₈₆	—	2	2	no	—
212	Dic₈₆	—	4	4	no	—
213	C₂²×C₄₃	—	2	4	no	—
214	C₂²×C₄₃	—	2	1	no	—
215	C₂²×C₄₃	—	2	4	no	—
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	1	no	—
218	C₂²×C₄₃	—	2	4	no	—
219	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
220	C₂×D₄₃	—	2	1	no	—
221	C₂×D₄₃	—	2	1	no	—
222	C₂×D₄₃	—	2	1	no	—
223	C₂×D₄₃	—	2	1	no	—
224	C₂×D₄₃	—	2	1	no	—
225	C₂×D₄₃	C₂×#41	1	2	yes	—
226	C₄×C₄₃	—	2	1	no	—
227	C₄×C₄₃	—	2	4	no	—
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	C₂×#41	1	2	yes	—
231	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
232	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
233	Dic₄₃	—	2	1	no	—
234	Dic₄₃	—	2	4	no	—
235	Dic₄₃	—	2	4	no	—
236	Dic₄₃	—	2	1	no	—
237	Dic₄₃	—	2	1	no	—
238	Dic₄₃	—	2	1	no	—
239	Dic₄₃	—	2	1	no	—
240	Dic₄₃	C₂×#41	1	2	yes	—
241	#3511	—	43	1	no	maximal, Sylow
242	C₂×C₄₃	—	4	4	no	—
243	C₂×C₄₃	—	4	1	no	—
244	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
245	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
247	D₄₃	—	2	2	no	—
248	D₄₃	—	4	1	no	—
249	#556	—	43	2	no	—
250	#555	—	43	2	no	—
251	#554	—	43	2	no	—
252	#553	—	43	2	no	—
253	#553	—	43	2	no	—
254	#548	—	43	2	no	—
255	#548	—	43	2	no	—
256	#547	—	43	2	no	—
257	#542	—	43	2	no	—
258	#542	—	43	2	no	—
259	#537	—	43	2	no	—
260	#533	—	43	1	no	—
261	#533	—	43	1	no	—
262	#532	—	43	1	no	—
263	#532	—	43	1	no	—
264	#532	D₄₃	1	1	yes	characteristic, complemented
265	C₂×C₄⋊Q₈	—	43	1	no	—
266	#520	—	43	2	no	—
267	C₄×#41	—	43	1	no	—
268	C₄₃	#3511	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	43	2	no	—
270	C₂×#41	—	43	2	no	—
271	C₂×#41	—	43	1	no	—
272	C₂×#41	C₂×D₄₃	1	2	yes	—
273	C₂²×Q₈	—	43	2	no	—
274	C₄⋊Q₈	—	43	2	no	—
275	C₄⋊Q₈	—	43	2	no	—
276	C₄⋊Q₈	—	43	2	no	—
277	C₄⋊Q₈	—	43	1	no	—
278	C₄⋊Q₈	—	43	1	no	—
279	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
280	#127	C₂×D₄₃	1	1	yes	characteristic
281	#126	—	43	4	no	—
282	#126	—	43	4	no	—
283	#125	—	43	2	no	—
284	#125	—	43	2	no	—
285	#124	—	43	2	no	—
286	#124	—	43	2	no	—
287	#124	—	43	4	no	—
288	#124	—	43	4	no	—
289	#124	C₂×D₄₃	1	2	yes	—
290	#123	—	43	4	no	—
291	#123	—	43	4	no	—
292	C₂²⋊Q₈	—	43	2	no	—
293	C₂²⋊Q₈	—	43	2	no	—
294	C₂²⋊Q₈	—	43	2	no	—
295	C₂²⋊Q₈	—	43	4	no	—
296	C₂²⋊Q₈	—	43	2	no	—
297	C₂²⋊Q₈	—	43	4	no	—
298	C₂²⋊Q₈	—	43	4	no	—
299	#121	—	43	2	no	—
300	#121	—	43	2	no	—
301	#121	—	43	2	no	—
302	#121	—	43	2	no	—
303	#121	—	43	4	no	—
304	#121	—	43	4	no	—
305	#121	—	43	4	no	—
306	#121	C₂×D₄₃	1	2	yes	—
307	#121	C₂×D₄₃	1	2	yes	—
308	C₄×Q₈	—	43	2	no	—
309	C₄×Q₈	—	43	2	no	—
310	C₄×Q₈	—	43	1	no	—
311	C₄×Q₈	—	43	1	no	—
312	C₄×Q₈	—	43	2	no	—
313	C₄×Q₈	—	43	2	no	—
314	C₄×D₄	—	43	2	no	—
315	C₄×D₄	—	43	2	no	—
316	C₄×D₄	—	43	2	no	—
317	C₄×D₄	—	43	2	no	—
318	C₄×D₄	—	43	1	no	—
319	C₄×D₄	—	43	1	no	—
320	C₄×D₄	—	43	1	no	—
321	C₄×D₄	—	43	1	no	—
322	C₄×D₄	—	43	4	no	—
323	C₄×D₄	—	43	4	no	—
324	C₄×D₄	—	43	1	no	—
325	C₄×D₄	—	43	1	no	—
326	C₄×D₄	C₂×D₄₃	1	2	yes	—
327	C₄×D₄	C₂×D₄₃	1	2	yes	—
328	#117	—	43	1	no	—
329	#117	—	43	2	no	—
330	#117	—	43	2	no	—
331	#117	—	43	4	no	—
332	#117	—	43	1	no	—
333	#117	—	43	1	no	—
334	C₂×C₄⋊C₄	—	43	4	no	—
335	C₂×C₄⋊C₄	—	43	2	no	—
336	C₂×C₄⋊C₄	—	43	2	no	—
337	C₂×C₄²	—	43	1	no	—
338	C₂×C₄²	—	43	1	no	—
339	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
340	#41	—	4	4	no	—
341	#41	—	86	4	no	—
342	#41	—	86	8	no	—
343	#41	—	172	4	no	—
344	C₂×Q₈	—	43	1	no	—
345	C₂×Q₈	—	43	2	no	—
346	C₂×Q₈	—	43	2	no	—
347	C₂×Q₈	—	43	4	no	—
348	C₂×Q₈	—	172	4	no	—
349	C₂×Q₈	C₂²×D₄₃	1	2	yes	—
350	C₂×D₄	—	43	1	no	—
351	C₂×D₄	—	43	1	no	—
352	C₂×D₄	—	43	4	no	—
353	C₂×D₄	—	43	4	no	—
354	C₂×D₄	—	43	1	no	—
355	C₂×D₄	C₂²×D₄₃	1	2	yes	—
356	C₂×D₄	C₂²×D₄₃	1	2	yes	—
357	C₂×D₄	C₂²×D₄₃	1	2	yes	—
358	C₂×D₄	C₂²×D₄₃	1	4	yes	—
359	C₂²×C₄	—	43	1	no	—
360	C₂²×C₄	—	43	4	no	—
361	C₂²×C₄	—	43	4	no	—
362	C₂²×C₄	—	43	1	no	—
363	C₂²×C₄	—	43	1	no	—
364	C₂²×C₄	—	43	1	no	—
365	C₂²×C₄	—	43	1	no	—
366	C₂²×C₄	—	43	1	no	—
367	C₂²×C₄	—	43	4	no	—
368	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
369	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
371	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
372	C₄⋊C₄	—	43	1	no	—
373	C₄⋊C₄	—	43	4	no	—
374	C₄⋊C₄	—	43	2	no	—
375	C₄⋊C₄	—	43	2	no	—
376	C₄⋊C₄	—	43	4	no	—
377	C₄⋊C₄	—	43	4	no	—
378	C₄⋊C₄	—	43	4	no	—
379	C₄⋊C₄	—	43	1	no	—
380	C₄⋊C₄	—	43	2	no	—
381	C₄⋊C₄	—	43	1	no	—
382	C₄⋊C₄	—	43	1	no	—
383	C₄⋊C₄	—	43	1	no	—
384	C₄⋊C₄	—	43	1	no	—
385	C₄⋊C₄	—	43	2	no	—
386	C₄⋊C₄	—	43	4	no	—
387	C₄⋊C₄	—	43	4	no	—
388	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
389	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
390	C₂²⋊C₄	—	43	4	no	—
391	C₂²⋊C₄	—	43	1	no	—
392	C₂²⋊C₄	—	43	1	no	—
393	C₂²⋊C₄	—	43	4	no	—
394	C₂²⋊C₄	—	43	4	no	—
395	C₂²⋊C₄	—	43	4	no	—
396	C₂²⋊C₄	—	43	4	no	—
397	C₂²⋊C₄	—	43	1	no	—
398	C₂²⋊C₄	—	43	1	no	—
399	C₂²⋊C₄	—	43	1	no	—
400	C₂²⋊C₄	—	43	1	no	—
401	C₂²⋊C₄	—	43	4	no	—
402	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
403	C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
404	C₄²	—	43	1	no	—
405	C₄²	—	43	1	no	—
406	C₄²	—	43	1	no	—
407	C₄²	—	43	1	no	—
408	C₄²	—	43	1	no	—
409	C₄²	—	43	1	no	—
410	C₄²	—	43	4	no	—
411	C₄²	—	43	4	no	—
412	C₄²	C₂²×D₄₃	1	1	yes	characteristic
413	C₄²	C₂²×D₄₃	1	1	yes	characteristic
414	C₄²	C₂²×D₄₃	1	1	yes	characteristic
415	C₄²	C₂²×D₄₃	1	1	yes	characteristic
416	C₂³	—	43	1	no	—
417	C₂³	—	43	1	no	—
418	C₂³	C₂³×D₄₃	1	1	yes	characteristic
419	C₂³	C₂³×D₄₃	1	4	yes	—
420	Q₈	—	2	4	no	—
421	Q₈	—	86	2	no	—
422	Q₈	—	86	4	no	—
423	Q₈	—	86	4	no	—
424	Q₈	—	172	4	no	—
425	D₄	—	2	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	4	no	—
429	D₄	—	86	2	no	—
430	D₄	—	86	2	no	—
431	D₄	—	86	2	no	—
432	D₄	—	86	8	no	—
433	D₄	—	172	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	43	1	no	—
439	C₂×C₄	—	43	4	no	—
440	C₂×C₄	—	43	1	no	—
441	C₂×C₄	—	43	1	no	—
442	C₂×C₄	—	43	1	no	—
443	C₂×C₄	—	43	1	no	—
444	C₂×C₄	—	43	4	no	—
445	C₂×C₄	—	43	1	no	—
446	C₂×C₄	—	43	4	no	—
447	C₂×C₄	—	86	8	no	—
448	C₂×C₄	—	86	2	no	—
449	C₂×C₄	—	86	2	no	—
450	C₂×C₄	—	86	2	no	—
451	C₂×C₄	—	86	2	no	—
452	C₂×C₄	—	86	2	no	—
453	C₂×C₄	—	172	4	no	—
454	C₂×C₄	—	172	4	no	—
455	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
456	C₂×C₄	C₂³×D₄₃	1	4	yes	—
457	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
458	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
462	C₂²	—	2	1	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	43	2	no	—
469	C₂²	—	86	1	no	—
470	C₂²	—	86	1	no	—
471	C₂²	—	86	1	no	—
472	C₂²	—	86	1	no	—
473	C₂²	—	86	1	no	—
474	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	1	no	—
479	C₄	—	43	2	no	—
480	C₄	—	86	4	no	—
481	C₄	—	86	1	no	—
482	C₄	—	86	1	no	—
483	C₄	—	86	1	no	—
484	C₄	—	86	4	no	—
485	C₄	—	86	1	no	—
486	C₄	—	86	1	no	—
487	C₄	#41×D₄₃	1	2	yes	—
488	C₄	#13063370	1	2	yes	—
489	C₄	#13063372	1	2	yes	—
490	C₂	—	4	1	no	—
491	C₂	—	4	4	no	—
492	C₂	—	86	2	no	—
493	C₂	—	172	1	no	—
494	C₂	C₂×#41×D₄₃	1	1	yes	characteristic
495	C₂	C₂×#13063370	1	1	yes	characteristic
496	C₂	C₂×#13063372	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#532	C₂
hypercenter	#532	D₄₃
hypocenter	C₄₃	#3511
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. #14583618	C₂	semidirect
2. #14583613	C₂	semidirect
3. #14583608	C₂	semidirect
4. #14583599	C₂	semidirect
5. #14583596	C₂	semidirect
6. #14583557	C₂	semidirect
7. #14583556	C₂	semidirect
8. #14583548	C₂	semidirect
9. #14583516	C₂	semidirect
10. #14583514	C₂	semidirect
11. #14583478	C₂	semidirect
12. #14583456	C₂	semidirect
13. #14583454	C₂	semidirect
14. #14583447	C₂	semidirect
15. #14583447	C₂	semidirect
16. C₄⋊Q₈×D₄₃	C₂	semidirect
17. #14583378	C₂	semidirect
18. C₄×#10621898	C₂	semidirect
19. C₄₃×#532	C₂	semidirect
208. C₄×D₄₃	#41	semidirect
264. #532	D₄₃	semidirect
268. C₄₃	#3511	semidirect