Subgroups — #19149082

Order 5504.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583651	C₂	1	2	yes	maximal, complemented
2	#14583650	C₂	1	2	yes	maximal, complemented
3	Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583627	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583625	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583624	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583618	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583618	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583616	C₂	1	2	yes	maximal, complemented
10	#14583608	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583582	C₂	1	2	yes	maximal, complemented
12	#14583528	C₂	1	2	yes	maximal, complemented
13	#14583518	C₂	1	1	yes	maximal, characteristic
14	#14583514	C₂	1	1	yes	maximal, characteristic
15	#14583511	C₂	1	2	yes	maximal, complemented
16	#14583510	C₂	1	1	yes	maximal, characteristic, complemented
17	#14583507	C₂	1	1	yes	maximal, characteristic, complemented
18	#14583506	C₂	1	2	yes	maximal, complemented
19	#14583506	C₂	1	2	yes	maximal, complemented
20	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
21	#14583453	C₂	1	1	yes	maximal, characteristic, complemented
22	#14583428	C₂	1	1	yes	maximal, characteristic
23	C₄₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
24	#13063325	C₂²	1	1	yes	characteristic
25	#13063325	C₂²	1	2	yes	—
26	#13063324	C₂²	1	1	yes	characteristic
27	#13063324	C₂²	1	2	yes	—
28	#13063324	C₂²	1	1	yes	characteristic
29	#13063324	C₂²	1	2	yes	—
30	#13063324	C₂²	1	2	yes	—
31	#13063324	C₂²	1	1	yes	characteristic
32	#13063323	C₂²	1	1	yes	characteristic
33	#13063323	C₂²	1	1	yes	characteristic
34	#13063323	C₂²	1	2	yes	—
35	#13063323	C₂²	1	1	yes	characteristic
36	#13063320	C₂²	1	2	yes	—
37	#13063320	C₂²	1	2	yes	—
38	#13063320	C₂²	1	2	yes	—
39	#13063319	C₂²	1	2	yes	—
40	#13063318	C₂²	1	2	yes	—
41	#13063318	C₂²	1	2	yes	—
42	#13063318	C₂²	1	2	yes	—
43	#13063318	C₂²	1	2	yes	—
44	#13063318	C₂²	1	2	yes	—
45	#13063318	C₂²	1	2	yes	—
46	#13063318	C₂²	1	2	yes	—
47	#13063317	C₂²	1	2	yes	—
48	#13063317	C₂²	1	1	yes	characteristic
49	#13063317	C₂²	1	1	yes	characteristic
50	#13063317	C₂²	1	2	yes	—
51	#13063316	C₂²	1	1	yes	characteristic
52	#13063316	C₂²	1	2	yes	—
53	#13063316	C₂²	1	2	yes	—
54	#13063315	C₂²	1	2	yes	—
55	#13063315	C₂²	1	2	yes	—
56	#13063315	C₂²	1	2	yes	—
57	#13063315	C₂²	1	2	yes	—
58	#13063315	C₂²	1	1	yes	characteristic
59	#13063315	C₂²	1	2	yes	—
60	#13063315	C₂²	1	1	yes	characteristic
61	#13063315	C₂²	1	2	yes	—
62	#13063315	C₂²	1	2	yes	—
63	#13063315	C₂²	1	2	yes	—
64	#13063312	C₂²	1	1	yes	characteristic
65	#13063311	C₂²	1	2	yes	—
66	#13063311	C₂²	1	2	yes	—
67	#13063309	C₂²	1	2	yes	—
68	#13063308	C₂²	1	2	yes	—
69	#13063307	C₂²	1	2	yes	—
70	#13063305	C₂²	1	1	yes	characteristic
71	#13063305	C₂²	1	1	yes	characteristic
72	#13063304	C₂²	1	2	yes	—
73	#13063304	C₂²	1	2	yes	—
74	#13063303	C₂²	1	1	yes	characteristic
75	#13063303	C₂²	1	1	yes	characteristic
76	#13063303	C₂²	1	2	yes	—
77	#13063302	C₂²	1	2	yes	—
78	#13063302	C₂²	1	2	yes	—
79	#13063302	C₂²	1	2	yes	—
80	#13063302	C₂²	1	2	yes	—
81	#13063302	C₂²	1	2	yes	—
82	#13063301	C₂²	1	1	yes	characteristic
83	#13063301	C₂²	1	1	yes	characteristic
84	#13063301	C₂²	1	1	yes	characteristic
85	#13063296	C₂²	1	1	yes	characteristic
86	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
87	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
88	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
89	Q₈×Dic₄₃	C₂²	1	1	yes	characteristic
90	C₄×Dic₈₆	C₂²	1	2	yes	—
91	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
92	C₄×Dic₈₆	C₂²	1	2	yes	—
93	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
94	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
95	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
96	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
97	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
98	C₄×Dic₈₆	C₂²	1	2	yes	—
99	#13063290	C₂²	1	2	yes	—
100	#13063290	C₂²	1	2	yes	—
101	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
102	D₄×Dic₄₃	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
104	#13063282	C₂²	1	2	yes	—
105	#13063282	C₂²	1	1	yes	characteristic
106	#13063282	C₂²	1	1	yes	characteristic
107	#13063281	C₂²	1	2	yes	—
108	#13063281	C₂²	1	2	yes	—
109	#13063281	C₂²	1	2	yes	—
110	C₂×Dic₄₃⋊C₄	C₂²	1	2	yes	—
111	C₄²×D₄₃	C₂²	1	1	yes	characteristic
112	C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
113	#126×C₄₃	C₂²	1	2	yes	—
114	#126×C₄₃	C₂²	1	2	yes	—
115	#124×C₄₃	C₂²	1	1	yes	characteristic
116	#124×C₄₃	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
118	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
119	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
122	#117×C₄₃	C₂²	1	2	yes	—
123	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
129	C₂²×Dic₄₃	C₂³	1	2	yes	—
130	C₂²×Dic₄₃	C₂³	1	2	yes	—
131	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
135	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
136	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
137	C₂×Dic₈₆	C₂³	1	2	yes	—
138	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
139	C₂×Dic₈₆	C₂³	1	2	yes	—
140	C₂×Dic₈₆	C₂³	1	2	yes	—
141	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
142	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
143	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
144	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
145	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
147	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
148	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
149	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
151	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
152	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
153	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
154	C₄²×C₄₃	C₂³	1	2	yes	—
155	C₄²×C₄₃	C₂³	1	2	yes	—
156	C₄²×C₄₃	C₂³	1	1	yes	characteristic
157	C₄²×C₄₃	C₂³	1	1	yes	characteristic
158	C₄²×C₄₃	C₂³	1	1	yes	characteristic
159	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₄₃	C₂³	1	2	yes	—
164	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
165	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
166	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
167	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
168	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
169	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
170	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
171	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₄₃	C₂³	1	2	yes	—
177	C₄⋊Dic₄₃	C₂³	1	2	yes	—
178	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₄⋊Dic₄₃	C₂³	1	2	yes	—
181	C₄⋊Dic₄₃	C₂³	1	2	yes	—
182	C₄⋊Dic₄₃	C₂³	1	2	yes	—
183	C₄⋊Dic₄₃	C₂³	1	2	yes	—
184	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
185	Dic₄₃⋊C₄	C₂³	1	2	yes	—
186	Dic₄₃⋊C₄	C₂³	1	2	yes	—
187	Dic₄₃⋊C₄	C₂³	1	2	yes	—
188	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
189	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
190	Dic₄₃⋊C₄	C₂³	1	2	yes	—
191	Dic₄₃⋊C₄	C₂³	1	2	yes	—
192	Dic₄₃⋊C₄	C₂³	1	2	yes	—
193	Dic₄₃⋊C₄	C₂³	1	2	yes	—
194	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
195	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
196	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
197	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
198	Dic₄₃⋊C₄	C₂³	1	2	yes	—
199	Dic₄₃⋊C₄	C₂³	1	2	yes	—
200	Dic₄₃⋊C₄	C₂³	1	2	yes	—
201	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₄₃⋊C₄	C₂³	1	2	yes	—
203	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₄₃⋊C₄	C₂³	1	2	yes	—
206	Dic₄₃⋊C₄	C₂³	1	2	yes	—
207	Dic₄₃⋊C₄	C₂³	1	2	yes	—
208	Dic₄₃⋊C₄	C₂³	1	2	yes	—
209	Dic₄₃⋊C₄	C₂³	1	2	yes	—
210	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
211	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₄₃	C₂³	1	2	yes	—
214	C₄×Dic₄₃	C₂³	1	2	yes	—
215	C₄×Dic₄₃	C₂³	1	2	yes	—
216	C₄×Dic₄₃	C₂³	1	2	yes	—
217	C₄×Dic₄₃	C₂³	1	2	yes	—
218	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₄₃	C₂³	1	2	yes	—
221	C₄×Dic₄₃	C₂³	1	2	yes	—
222	C₂³×C₄₃	C₂⁴	1	2	yes	—
223	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
224	Q₈×C₄₃	—	2	2	no	—
225	Q₈×C₄₃	—	2	2	no	—
226	Q₈×C₄₃	—	4	1	no	—
227	D₄×C₄₃	—	2	2	no	—
228	C₂×C₄×C₄₃	—	4	2	no	—
229	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
230	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
231	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
239	C₂²⋊D₄₃	—	4	2	no	—
240	C₂×Dic₄₃	—	2	4	no	—
241	C₂×Dic₄₃	—	4	2	no	—
242	C₂×Dic₄₃	C₂⁴	1	2	yes	—
243	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
244	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₄₃	C₂⁴	1	2	yes	—
246	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
247	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₄₃	C₂⁴	1	2	yes	—
249	C₂×Dic₄₃	C₂⁴	1	2	yes	—
250	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
253	C₄×D₄₃	—	2	2	no	—
254	C₄×D₄₃	—	2	2	no	—
255	C₄×D₄₃	—	4	1	no	—
256	Dic₈₆	—	2	2	no	—
257	Dic₈₆	—	2	2	no	—
258	Dic₈₆	—	2	2	no	—
259	Dic₈₆	—	4	2	no	—
260	Dic₈₆	—	4	1	no	—
261	Dic₈₆	—	4	2	no	—
262	Dic₈₆	—	4	2	no	—
263	C₂²×C₄₃	—	2	2	no	—
264	C₂²×C₄₃	—	2	2	no	—
265	C₂²×C₄₃	—	2	2	no	—
266	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
267	C₂×D₄₃	—	2	1	no	—
268	C₂×D₄₃	—	2	1	no	—
269	C₂×D₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	2	1	no	—
272	C₄×C₄₃	—	2	1	no	—
273	C₄×C₄₃	—	2	2	no	—
274	C₄×C₄₃	—	2	2	no	—
275	C₄×C₄₃	—	2	2	no	—
276	C₄×C₄₃	—	2	1	no	—
277	C₄×C₄₃	—	2	1	no	—
278	C₄×C₄₃	—	2	1	no	—
279	C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
280	Dic₄₃	—	2	1	no	—
281	Dic₄₃	—	2	1	no	—
282	Dic₄₃	—	2	2	no	—
283	Dic₄₃	—	2	1	no	—
284	Dic₄₃	—	2	2	no	—
285	Dic₄₃	—	2	1	no	—
286	Dic₄₃	—	2	1	no	—
287	Dic₄₃	—	2	2	no	—
288	Dic₄₃	—	2	2	no	—
289	Dic₄₃	—	2	1	no	—
290	Dic₄₃	2₋¹⁺⁴	1	2	yes	—
291	#3555	—	43	1	no	maximal, Sylow
292	C₂×C₄₃	—	4	2	no	—
293	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
294	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
295	C₂×C₄₃	#585	1	1	yes	characteristic
296	D₄₃	—	4	1	no	—
297	#563	—	43	2	no	—
298	#563	—	43	2	no	—
299	Q₈²	—	43	1	no	—
300	#557	—	43	1	no	—
301	#557	—	43	1	no	—
302	#557	—	43	1	no	—
303	#556	—	43	2	no	—
304	#556	—	43	1	no	—
305	#556	—	43	1	no	—
306	#556	D₄₃	1	1	yes	characteristic, complemented
307	#554	—	43	1	no	—
308	#552	—	43	2	no	—
309	#544	—	43	2	no	—
310	#542	—	43	1	no	—
311	#542	—	43	1	no	—
312	#541	—	43	1	no	—
313	#541	—	43	2	no	—
314	#541	—	43	2	no	—
315	#541	—	43	1	no	—
316	#541	—	43	2	no	—
317	#533	—	43	1	no	—
318	#533	—	43	1	no	—
319	#529	—	43	1	no	—
320	C₄₃	#3555	1	1	yes	characteristic, complemented, Sylow
321	C₄⋊Q₈	—	43	1	no	—
322	C₄⋊Q₈	—	43	1	no	—
323	C₄⋊Q₈	—	43	1	no	—
324	C₄⋊Q₈	—	43	2	no	—
325	C₄⋊Q₈	—	43	1	no	—
326	C₄⋊Q₈	—	43	1	no	—
327	C₄⋊Q₈	—	43	2	no	—
328	C₄⋊Q₈	—	43	1	no	—
329	C₄⋊Q₈	—	43	2	no	—
330	C₄⋊Q₈	—	43	2	no	—
331	C₄⋊Q₈	—	43	2	no	—
332	C₄⋊Q₈	—	43	1	no	—
333	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
334	#126	—	43	2	no	—
335	#126	—	43	2	no	—
336	#126	—	43	2	no	—
337	#126	—	43	2	no	—
338	#126	—	43	2	no	—
339	#126	—	43	2	no	—
340	#126	—	43	2	no	—
341	#126	—	43	2	no	—
342	#126	—	43	2	no	—
343	#126	—	43	2	no	—
344	#126	—	43	2	no	—
345	#126	C₂×D₄₃	1	2	yes	—
346	#126	C₂×D₄₃	1	2	yes	—
347	#125	—	43	1	no	—
348	#125	—	43	1	no	—
349	#125	—	43	2	no	—
350	#125	—	43	2	no	—
351	#125	—	43	2	no	—
352	#125	—	43	2	no	—
353	#125	—	43	2	no	—
354	#125	—	43	1	no	—
355	#125	—	43	2	no	—
356	#125	—	43	2	no	—
357	#125	—	43	2	no	—
358	#125	—	43	2	no	—
359	#125	—	43	2	no	—
360	#125	—	43	1	no	—
361	#125	—	43	2	no	—
362	#125	—	43	2	no	—
363	#125	—	43	1	no	—
364	#124	—	43	1	no	—
365	#124	—	43	2	no	—
366	#124	—	43	2	no	—
367	#124	C₂×D₄₃	1	1	yes	characteristic
368	#124	C₂×D₄₃	1	1	yes	characteristic
369	#123	—	43	2	no	—
370	#123	—	43	2	no	—
371	#123	—	43	2	no	—
372	C₂²⋊Q₈	—	43	1	no	—
373	C₂²⋊Q₈	—	43	1	no	—
374	C₂²⋊Q₈	—	43	1	no	—
375	C₂²⋊Q₈	—	43	2	no	—
376	C₂²⋊Q₈	—	43	2	no	—
377	C₂²⋊Q₈	—	43	1	no	—
378	C₂²⋊Q₈	—	43	1	no	—
379	C₂²⋊Q₈	—	43	1	no	—
380	C₂²⋊Q₈	—	43	2	no	—
381	C₂²⋊Q₈	—	43	1	no	—
382	C₂²⋊Q₈	—	43	2	no	—
383	C₂²⋊Q₈	—	43	2	no	—
384	C₂²⋊Q₈	—	43	2	no	—
385	C₂²⋊Q₈	—	43	2	no	—
386	C₂²⋊Q₈	—	43	2	no	—
387	C₂²⋊Q₈	C₂×D₄₃	1	2	yes	—
388	#121	—	43	1	no	—
389	C₄×Q₈	—	43	1	no	—
390	C₄×Q₈	—	43	1	no	—
391	C₄×Q₈	—	43	1	no	—
392	C₄×Q₈	—	43	1	no	—
393	C₄×Q₈	—	43	2	no	—
394	C₄×Q₈	—	43	2	no	—
395	C₄×Q₈	—	43	2	no	—
396	C₄×Q₈	—	43	1	no	—
397	C₄×Q₈	—	43	1	no	—
398	C₄×Q₈	—	43	1	no	—
399	C₄×Q₈	—	43	1	no	—
400	C₄×Q₈	—	43	2	no	—
401	C₄×Q₈	—	43	1	no	—
402	C₄×Q₈	—	43	2	no	—
403	C₄×Q₈	—	43	1	no	—
404	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
405	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
406	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
407	C₄×D₄	—	43	1	no	—
408	C₄×D₄	—	43	1	no	—
409	C₄×D₄	—	43	2	no	—
410	C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
411	#117	—	43	2	no	—
412	#117	—	43	2	no	—
413	#117	—	43	2	no	—
414	#117	—	43	1	no	—
415	#117	—	43	1	no	—
416	#117	—	43	2	no	—
417	#117	C₂×D₄₃	1	2	yes	—
418	C₂×C₄⋊C₄	—	43	2	no	—
419	C₂×C₄²	—	43	1	no	—
420	C₂×Q₈	—	43	1	no	—
421	C₂×Q₈	—	43	1	no	—
422	C₂×Q₈	—	43	1	no	—
423	C₂×Q₈	—	43	1	no	—
424	C₂×Q₈	—	43	2	no	—
425	C₂×Q₈	—	43	2	no	—
426	C₂×Q₈	—	43	2	no	—
427	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
429	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
430	C₂×D₄	—	43	2	no	—
431	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
432	C₂²×C₄	—	43	2	no	—
433	C₂²×C₄	—	43	2	no	—
434	C₂²×C₄	—	43	1	no	—
435	C₂²×C₄	—	43	1	no	—
436	C₂²×C₄	—	43	1	no	—
437	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
438	C₄⋊C₄	—	43	1	no	—
439	C₄⋊C₄	—	43	2	no	—
440	C₄⋊C₄	—	43	2	no	—
441	C₄⋊C₄	—	43	2	no	—
442	C₄⋊C₄	—	43	1	no	—
443	C₄⋊C₄	—	43	2	no	—
444	C₄⋊C₄	—	43	1	no	—
445	C₄⋊C₄	—	43	1	no	—
446	C₄⋊C₄	—	43	1	no	—
447	C₄⋊C₄	—	43	2	no	—
448	C₄⋊C₄	—	43	2	no	—
449	C₄⋊C₄	—	43	2	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	—	43	2	no	—
455	C₄⋊C₄	—	43	1	no	—
456	C₄⋊C₄	—	43	1	no	—
457	C₄⋊C₄	—	43	1	no	—
458	C₄⋊C₄	—	43	1	no	—
459	C₄⋊C₄	—	43	2	no	—
460	C₄⋊C₄	—	43	2	no	—
461	C₄⋊C₄	—	43	2	no	—
462	C₄⋊C₄	—	43	2	no	—
463	C₄⋊C₄	—	43	2	no	—
464	C₄⋊C₄	—	43	2	no	—
465	C₄⋊C₄	—	43	2	no	—
466	C₄⋊C₄	—	43	2	no	—
467	C₄⋊C₄	—	43	2	no	—
468	C₄⋊C₄	—	43	2	no	—
469	C₄⋊C₄	—	43	1	no	—
470	C₄⋊C₄	—	43	1	no	—
471	C₄⋊C₄	—	43	2	no	—
472	C₄⋊C₄	—	43	1	no	—
473	C₄⋊C₄	—	43	2	no	—
474	C₄⋊C₄	—	43	2	no	—
475	C₄⋊C₄	—	43	2	no	—
476	C₄⋊C₄	—	43	2	no	—
477	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
479	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
483	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
485	C₂²⋊C₄	—	43	2	no	—
486	C₂²⋊C₄	—	43	2	no	—
487	C₂²⋊C₄	—	43	2	no	—
488	C₂²⋊C₄	—	43	2	no	—
489	C₂²⋊C₄	—	43	2	no	—
490	C₂²⋊C₄	—	43	1	no	—
491	C₂²⋊C₄	—	43	1	no	—
492	C₂²⋊C₄	—	43	2	no	—
493	C₂²⋊C₄	—	43	2	no	—
494	C₂²⋊C₄	—	43	1	no	—
495	C₂²⋊C₄	—	43	1	no	—
496	C₂²⋊C₄	—	43	2	no	—
497	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
502	C₄²	—	43	1	no	—
503	C₄²	—	43	1	no	—
504	C₄²	—	43	1	no	—
505	C₄²	—	43	2	no	—
506	C₄²	—	43	2	no	—
507	C₄²	—	43	1	no	—
508	C₄²	—	43	1	no	—
509	C₄²	—	43	2	no	—
510	C₄²	—	43	2	no	—
511	C₄²	—	43	2	no	—
512	C₄²	—	43	2	no	—
513	C₄²	—	43	2	no	—
514	C₄²	C₂²×D₄₃	1	1	yes	characteristic
515	C₄²	C₂²×D₄₃	1	2	yes	—
516	C₄²	C₂²×D₄₃	1	1	yes	characteristic
517	C₄²	C₂²×D₄₃	1	1	yes	characteristic
518	C₄²	C₂²×D₄₃	1	2	yes	—
519	C₂³	—	43	1	no	—
520	C₂³	C₂³×D₄₃	1	2	yes	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	86	2	no	—
525	Q₈	—	86	2	no	—
526	Q₈	—	86	2	no	—
527	Q₈	—	172	2	no	—
528	Q₈	—	172	2	no	—
529	Q₈	—	172	1	no	—
530	Q₈	—	172	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	172	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	43	1	no	—
535	C₂×C₄	—	43	1	no	—
536	C₂×C₄	—	43	1	no	—
537	C₂×C₄	—	43	2	no	—
538	C₂×C₄	—	43	1	no	—
539	C₂×C₄	—	43	2	no	—
540	C₂×C₄	—	43	2	no	—
541	C₂×C₄	—	43	1	no	—
542	C₂×C₄	—	43	1	no	—
543	C₂×C₄	—	43	2	no	—
544	C₂×C₄	—	43	1	no	—
545	C₂×C₄	—	86	2	no	—
546	C₂×C₄	—	86	4	no	—
547	C₂×C₄	—	86	2	no	—
548	C₂×C₄	—	172	1	no	—
549	C₂×C₄	—	172	2	no	—
550	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
551	C₂×C₄	C₂³×D₄₃	1	2	yes	—
552	C₂×C₄	C₂³×D₄₃	1	2	yes	—
553	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₄₃	1	2	yes	—
558	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	86	1	no	—
564	C₂²	—	86	1	no	—
565	C₂²	—	86	1	no	—
566	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	43	2	no	—
577	C₄	—	86	2	no	—
578	C₄	—	86	1	no	—
579	C₄	—	86	1	no	—
580	C₄	—	86	1	no	—
581	C₄	—	86	2	no	—
582	C₄	—	86	1	no	—
583	C₄	—	86	1	no	—
584	C₄	—	86	2	no	—
585	C₄	—	86	2	no	—
586	C₄	—	86	1	no	—
587	C₄	#13063372	1	2	yes	—
588	C₂	—	4	2	no	—
589	C₂	—	172	1	no	—
590	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
591	C₂	C₂×#13063372	1	1	yes	characteristic
592	C₂	#14583735	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#556	C₂
hypercenter	#556	D₄₃
hypocenter	C₄₃	#3555
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #14583651	C₂	semidirect
2. #14583650	C₂	semidirect
3. Q₈×Dic₈₆	C₂	semidirect
4. #14583627	C₂	semidirect
5. #14583625	C₂	semidirect
6. #14583624	C₂	semidirect
7. #14583618	C₂	semidirect
8. #14583618	C₂	semidirect
9. #14583616	C₂	semidirect
10. #14583608	C₂	semidirect
11. #14583582	C₂	semidirect
12. #14583528	C₂	semidirect
15. #14583511	C₂	semidirect
16. #14583510	C₂	semidirect
17. #14583507	C₂	semidirect
18. #14583506	C₂	semidirect
19. #14583506	C₂	semidirect
20. #14583453	C₂	semidirect
21. #14583453	C₂	semidirect
23. C₄₃×#556	C₂	semidirect
306. #556	D₄₃	semidirect
320. C₄₃	#3555	semidirect