Subgroups — #19149039

Order 5504.

1004 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583653	C₂	1	2	yes	maximal, complemented
2	#14583651	C₂	1	2	yes	maximal, complemented
3	#14583627	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583621	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583605	C₂	1	2	yes	maximal, complemented
6	#14583600	C₂	1	2	yes	maximal, complemented
7	Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583562	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583562	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583561	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583559	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583551	C₂	1	1	yes	maximal, characteristic, complemented
13	#14583529	C₂	1	2	yes	maximal, complemented
14	#14583515	C₂	1	2	yes	maximal, complemented
15	#14583512	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583497	C₂	1	2	yes	maximal, complemented
17	#14583490	C₂	1	2	yes	maximal, complemented
18	#14583475	C₂	1	1	yes	maximal, characteristic, complemented
19	#14583474	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#14583434	C₂	1	1	yes	maximal, characteristic, complemented
22	#14583427	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10621902	C₂²	1	1	yes	characteristic
25	C₂×#10621898	C₂²	1	1	yes	characteristic
26	C₂²×Dic₈₆	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
29	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
30	#13063325	C₂²	1	1	yes	characteristic
31	#13063325	C₂²	1	2	yes	—
32	#13063325	C₂²	1	1	yes	characteristic
33	#13063324	C₂²	1	2	yes	—
34	#13063324	C₂²	1	2	yes	—
35	#13063324	C₂²	1	2	yes	—
36	#13063324	C₂²	1	2	yes	—
37	#13063323	C₂²	1	1	yes	characteristic
38	#13063323	C₂²	1	1	yes	characteristic
39	#13063323	C₂²	1	1	yes	characteristic
40	#13063320	C₂²	1	2	yes	—
41	#13063320	C₂²	1	2	yes	—
42	#13063320	C₂²	1	2	yes	—
43	#13063320	C₂²	1	1	yes	characteristic
44	#13063320	C₂²	1	2	yes	—
45	#13063319	C₂²	1	2	yes	—
46	#13063318	C₂²	1	1	yes	characteristic
47	#13063317	C₂²	1	2	yes	—
48	#13063316	C₂²	1	2	yes	—
49	#13063316	C₂²	1	2	yes	—
50	#13063315	C₂²	1	2	yes	—
51	#13063315	C₂²	1	2	yes	—
52	#13063315	C₂²	1	1	yes	characteristic
53	#13063314	C₂²	1	1	yes	characteristic
54	#13063313	C₂²	1	1	yes	characteristic
55	#13063313	C₂²	1	2	yes	—
56	#13063313	C₂²	1	1	yes	characteristic
57	#13063311	C₂²	1	2	yes	—
58	#13063311	C₂²	1	1	yes	characteristic
59	#13063310	C₂²	1	2	yes	—
60	#13063310	C₂²	1	2	yes	—
61	#13063310	C₂²	1	1	yes	characteristic
62	#13063310	C₂²	1	2	yes	—
63	#13063310	C₂²	1	2	yes	—
64	#13063309	C₂²	1	2	yes	—
65	#13063309	C₂²	1	2	yes	—
66	#13063307	C₂²	1	2	yes	—
67	#13063307	C₂²	1	1	yes	characteristic
68	#13063305	C₂²	1	1	yes	characteristic
69	#13063305	C₂²	1	2	yes	—
70	#13063305	C₂²	1	1	yes	characteristic
71	#13063305	C₂²	1	2	yes	—
72	#13063305	C₂²	1	2	yes	—
73	#13063305	C₂²	1	1	yes	characteristic
74	#13063305	C₂²	1	2	yes	—
75	#13063305	C₂²	1	2	yes	—
76	#13063303	C₂²	1	2	yes	—
77	#13063303	C₂²	1	2	yes	—
78	#13063303	C₂²	1	2	yes	—
79	#13063303	C₂²	1	1	yes	characteristic
80	#13063303	C₂²	1	2	yes	—
81	#13063303	C₂²	1	2	yes	—
82	#13063303	C₂²	1	2	yes	—
83	#13063302	C₂²	1	2	yes	—
84	#13063302	C₂²	1	2	yes	—
85	#13063300	C₂²	1	1	yes	characteristic
86	#13063300	C₂²	1	2	yes	—
87	#13063298	C₂²	1	2	yes	—
88	#13063298	C₂²	1	1	yes	characteristic
89	#13063298	C₂²	1	2	yes	—
90	C₄×Dic₈₆	C₂²	1	2	yes	—
91	C₄×Dic₈₆	C₂²	1	1	yes	characteristic
92	#13063290	C₂²	1	1	yes	characteristic
93	#13063290	C₂²	1	1	yes	characteristic
94	#13063290	C₂²	1	1	yes	characteristic
95	C₄×D₁₇₂	C₂²	1	1	yes	characteristic
96	C₄×D₁₇₂	C₂²	1	2	yes	—
97	C₄×D₁₇₂	C₂²	1	2	yes	—
98	#13063287	C₂²	1	2	yes	—
99	#13063287	C₂²	1	2	yes	—
100	#13063287	C₂²	1	1	yes	characteristic
101	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
102	C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
103	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
104	(C₂²⋊D₄₃)⋊C₄	C₂²	1	2	yes	—
105	#13063283	C₂²	1	2	yes	—
106	#13063282	C₂²	1	2	yes	—
107	#13063282	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
109	C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
110	C₄⋊C₄×D₄₃	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	#125×C₄₃	C₂²	1	2	yes	—
116	#125×C₄₃	C₂²	1	1	yes	characteristic
117	#125×C₄₃	C₂²	1	2	yes	—
118	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
119	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
120	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
122	#117×C₄₃	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₄₃	C₂³	1	2	yes	—
129	C₂²×Dic₄₃	C₂³	1	2	yes	—
130	#10621902	—	4	2	no	—
131	Q₈×D₄₃	—	4	2	no	—
132	Q₈×D₄₃	—	4	2	no	—
133	Q₈×D₄₃	—	4	2	no	—
134	#10621898	—	4	2	no	—
135	C₂×D₁₇₂	C₂³	1	2	yes	—
136	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×D₁₇₂	C₂³	1	2	yes	—
139	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₄₃	C₂³	1	2	yes	—
143	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₄₃	C₂³	1	2	yes	—
145	C₂×C₄×D₄₃	C₂³	1	2	yes	—
146	C₂×C₄×D₄₃	C₂³	1	2	yes	—
147	C₂×C₄×D₄₃	C₂³	1	2	yes	—
148	C₂×C₄×D₄₃	C₂³	1	2	yes	—
149	C₂×Dic₈₆	—	4	2	no	—
150	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
152	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₈₆	C₂³	1	2	yes	—
155	C₂×Dic₈₆	C₂³	1	2	yes	—
156	C₂×Dic₈₆	C₂³	1	2	yes	—
157	C₂×Dic₈₆	C₂³	1	2	yes	—
158	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
161	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
162	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
163	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
164	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
165	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
167	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
168	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
169	C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
171	C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
173	C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
174	C₄²×C₄₃	C₂³	1	1	yes	characteristic
175	C₄²×C₄₃	C₂³	1	1	yes	characteristic
176	C₄²×C₄₃	C₂³	1	2	yes	—
177	C₄²×C₄₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₄₃	C₂³	1	1	yes	characteristic
180	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
189	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
190	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
191	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
192	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
194	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₄₃)⋊C₄	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₄₃	C₂³	1	2	yes	—
198	C₄⋊Dic₄₃	C₂³	1	2	yes	—
199	C₄⋊Dic₄₃	C₂³	1	2	yes	—
200	C₄⋊Dic₄₃	C₂³	1	2	yes	—
201	C₄⋊Dic₄₃	C₂³	1	2	yes	—
202	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₄₃	C₂³	1	2	yes	—
204	C₄⋊Dic₄₃	C₂³	1	2	yes	—
205	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
206	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
207	Dic₄₃⋊C₄	C₂³	1	2	yes	—
208	Dic₄₃⋊C₄	C₂³	1	2	yes	—
209	Dic₄₃⋊C₄	C₂³	1	2	yes	—
210	Dic₄₃⋊C₄	C₂³	1	2	yes	—
211	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
212	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
213	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
214	Dic₄₃⋊C₄	C₂³	1	2	yes	—
215	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
216	Dic₄₃⋊C₄	C₂³	1	2	yes	—
217	Dic₄₃⋊C₄	C₂³	1	2	yes	—
218	Dic₄₃⋊C₄	C₂³	1	2	yes	—
219	Dic₄₃⋊C₄	C₂³	1	2	yes	—
220	Dic₄₃⋊C₄	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₄₃	C₂³	1	2	yes	—
225	C₄×Dic₄₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₃	C₂³	1	2	yes	—
227	C₄×Dic₄₃	C₂³	1	2	yes	—
228	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
230	C₂²×D₄₃	C₂⁴	1	2	yes	—
231	C₂²×D₄₃	C₂⁴	1	1	yes	characteristic
232	Q₈×C₄₃	—	2	2	no	—
233	Q₈×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₄₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₄₃	—	2	2	no	—
246	C₂²⋊D₄₃	—	2	2	no	—
247	C₂²⋊D₄₃	—	4	2	no	—
248	C₂×Dic₄₃	—	4	2	no	—
249	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₄₃	C₂⁴	1	2	yes	—
254	C₂×Dic₄₃	C₂⁴	1	2	yes	—
255	C₂×Dic₄₃	C₂⁴	1	2	yes	—
256	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₄₃	C₂⁴	1	1	yes	characteristic
258	D₁₇₂	—	2	4	no	—
259	D₁₇₂	—	2	2	no	—
260	D₁₇₂	—	2	2	no	—
261	D₁₇₂	—	4	2	no	—
262	C₄×D₄₃	—	2	2	no	—
263	C₄×D₄₃	—	2	2	no	—
264	C₄×D₄₃	—	2	2	no	—
265	C₄×D₄₃	—	2	2	no	—
266	C₄×D₄₃	—	2	4	no	—
267	C₄×D₄₃	—	4	2	no	—
268	C₄×D₄₃	—	4	2	no	—
269	C₄×D₄₃	—	4	2	no	—
270	C₄×D₄₃	—	4	2	no	—
271	C₄×D₄₃	—	4	2	no	—
272	Dic₈₆	—	2	2	no	—
273	Dic₈₆	—	2	2	no	—
274	Dic₈₆	—	2	2	no	—
275	Dic₈₆	—	2	2	no	—
276	Dic₈₆	—	4	2	no	—
277	Dic₈₆	—	4	2	no	—
278	Dic₈₆	—	4	2	no	—
279	Dic₈₆	—	4	2	no	—
280	C₂²×C₄₃	—	2	1	no	—
281	C₂²×C₄₃	—	2	1	no	—
282	C₂²×C₄₃	—	2	1	no	—
283	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
284	C₂×D₄₃	—	2	1	no	—
285	C₂×D₄₃	—	2	1	no	—
286	C₂×D₄₃	—	2	1	no	—
287	C₂×D₄₃	—	2	2	no	—
288	C₂×D₄₃	—	2	2	no	—
289	C₂×D₄₃	—	2	1	no	—
290	C₂×D₄₃	—	2	2	no	—
291	C₂×D₄₃	—	2	1	no	—
292	C₂×D₄₃	2₋¹⁺⁴	1	2	yes	—
293	C₄×C₄₃	—	2	1	no	—
294	C₄×C₄₃	—	2	2	no	—
295	C₄×C₄₃	—	2	2	no	—
296	C₄×C₄₃	—	2	1	no	—
297	C₄×C₄₃	—	2	1	no	—
298	C₄×C₄₃	—	2	1	no	—
299	C₄×C₄₃	—	2	2	no	—
300	C₄×C₄₃	—	2	2	no	—
301	C₄×C₄₃	—	2	1	no	—
302	C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
303	Dic₄₃	—	2	2	no	—
304	Dic₄₃	—	2	2	no	—
305	Dic₄₃	—	2	2	no	—
306	Dic₄₃	—	2	1	no	—
307	Dic₄₃	—	2	1	no	—
308	Dic₄₃	—	2	1	no	—
309	Dic₄₃	—	2	1	no	—
310	Dic₄₃	—	2	1	no	—
311	Dic₄₃	2₋¹⁺⁴	1	2	yes	—
312	#3552	—	43	1	no	maximal, Sylow
313	C₂×C₄₃	—	4	1	no	—
314	C₂×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
316	C₂×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	D₄₃	—	2	2	no	—
318	D₄₃	—	4	1	no	—
319	D₄₃	—	4	2	no	—
320	#563	—	43	2	no	—
321	#563	—	43	2	no	—
322	#557	—	43	1	no	—
323	#556	—	43	1	no	—
324	#554	—	43	2	no	—
325	#553	—	43	2	no	—
326	D₄×Q₈	—	43	1	no	—
327	D₄×Q₈	—	43	1	no	—
328	D₄×Q₈	—	43	1	no	—
329	#548	—	43	1	no	—
330	#548	—	43	1	no	—
331	#547	—	43	1	no	—
332	#544	—	43	2	no	—
333	#542	—	43	2	no	—
334	#541	—	43	1	no	—
335	#541	D₄₃	1	1	yes	characteristic, complemented
336	#539	—	43	2	no	—
337	#539	—	43	2	no	—
338	#536	—	43	1	no	—
339	#536	—	43	1	no	—
340	C₂×C₄⋊Q₈	—	43	1	no	—
341	#529	—	43	1	no	—
342	#529	—	43	1	no	—
343	C₄₃	#3552	1	1	yes	characteristic, complemented, Sylow
344	C₂×#41	—	43	1	no	—
345	C₂×#41	—	43	1	no	—
346	C₂²×Q₈	—	43	1	no	—
347	C₂²×Q₈	—	43	1	no	—
348	C₂²×Q₈	—	43	1	no	—
349	C₂²×Q₈	—	43	1	no	—
350	C₄⋊Q₈	—	43	1	no	—
351	C₄⋊Q₈	—	43	1	no	—
352	C₄⋊Q₈	—	43	1	no	—
353	C₄⋊Q₈	—	43	2	no	—
354	C₄⋊Q₈	—	43	2	no	—
355	C₄⋊Q₈	—	43	2	no	—
356	C₄⋊Q₈	—	43	2	no	—
357	C₄⋊Q₈	—	43	1	no	—
358	C₄⋊Q₈	—	43	1	no	—
359	C₄⋊Q₈	—	43	2	no	—
360	C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
361	#126	—	43	2	no	—
362	#126	—	43	1	no	—
363	#126	—	43	2	no	—
364	#126	—	43	2	no	—
365	#126	—	43	2	no	—
366	#126	—	43	1	no	—
367	#126	—	43	2	no	—
368	#126	C₂×D₄₃	1	2	yes	—
369	#126	C₂×D₄₃	1	2	yes	—
370	#125	—	43	1	no	—
371	#125	—	43	2	no	—
372	#125	—	43	2	no	—
373	#125	—	43	2	no	—
374	#125	—	43	2	no	—
375	#125	—	43	2	no	—
376	#125	C₂×D₄₃	1	1	yes	characteristic
377	#125	C₂×D₄₃	1	2	yes	—
378	#125	C₂×D₄₃	1	2	yes	—
379	#124	—	43	1	no	—
380	#124	—	43	1	no	—
381	#124	—	43	2	no	—
382	#124	—	43	1	no	—
383	#124	—	43	1	no	—
384	#124	—	43	2	no	—
385	#123	—	43	2	no	—
386	#123	—	43	1	no	—
387	#123	—	43	2	no	—
388	#123	—	43	2	no	—
389	#123	—	43	2	no	—
390	#123	—	43	1	no	—
391	#123	—	43	2	no	—
392	#123	—	43	2	no	—
393	#123	—	43	2	no	—
394	C₂²⋊Q₈	—	43	1	no	—
395	C₂²⋊Q₈	—	43	1	no	—
396	C₂²⋊Q₈	—	43	2	no	—
397	C₂²⋊Q₈	—	43	2	no	—
398	C₂²⋊Q₈	—	43	2	no	—
399	C₂²⋊Q₈	—	43	2	no	—
400	C₂²⋊Q₈	—	43	2	no	—
401	C₂²⋊Q₈	—	43	2	no	—
402	C₂²⋊Q₈	—	43	2	no	—
403	C₂²⋊Q₈	—	43	1	no	—
404	C₂²⋊Q₈	—	43	1	no	—
405	C₂²⋊Q₈	—	43	2	no	—
406	C₂²⋊Q₈	—	43	2	no	—
407	C₂²⋊Q₈	—	43	2	no	—
408	C₂²⋊Q₈	—	43	2	no	—
409	C₂²⋊Q₈	—	43	2	no	—
410	C₂²⋊Q₈	—	43	2	no	—
411	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
413	#121	—	43	1	no	—
414	#121	—	43	2	no	—
415	#121	—	43	1	no	—
416	#121	—	43	2	no	—
417	#121	—	43	2	no	—
418	C₄×Q₈	—	43	1	no	—
419	C₄×Q₈	—	43	1	no	—
420	C₄×Q₈	—	43	1	no	—
421	C₄×Q₈	—	43	1	no	—
422	C₄×Q₈	—	43	2	no	—
423	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
424	C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
425	C₄×D₄	—	43	1	no	—
426	C₄×D₄	—	43	1	no	—
427	C₄×D₄	—	43	1	no	—
428	C₄×D₄	—	43	2	no	—
429	C₄×D₄	—	43	2	no	—
430	C₄×D₄	—	43	2	no	—
431	C₄×D₄	—	43	2	no	—
432	C₄×D₄	—	43	1	no	—
433	C₄×D₄	—	43	2	no	—
434	C₄×D₄	—	43	2	no	—
435	#117	—	43	2	no	—
436	#117	—	43	1	no	—
437	#117	—	43	2	no	—
438	#117	C₂×D₄₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	—	43	2	no	—
440	C₂×C₄⋊C₄	—	43	2	no	—
441	C₂×C₄⋊C₄	—	43	2	no	—
442	C₂×C₄²	—	43	1	no	—
443	#41	—	172	2	no	—
444	#41	—	172	2	no	—
445	C₂×Q₈	—	43	1	no	—
446	C₂×Q₈	—	43	1	no	—
447	C₂×Q₈	—	43	1	no	—
448	C₂×Q₈	—	43	1	no	—
449	C₂×Q₈	—	43	2	no	—
450	C₂×Q₈	—	43	2	no	—
451	C₂×Q₈	—	43	2	no	—
452	C₂×Q₈	—	43	2	no	—
453	C₂×Q₈	—	172	2	no	—
454	C₂×Q₈	—	172	2	no	—
455	C₂×Q₈	—	172	2	no	—
456	C₂×Q₈	—	172	2	no	—
457	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
458	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
459	C₂×D₄	—	43	1	no	—
460	C₂×D₄	—	43	1	no	—
461	C₂×D₄	—	43	2	no	—
462	C₂×D₄	—	43	2	no	—
463	C₂×D₄	—	43	1	no	—
464	C₂×D₄	—	43	1	no	—
465	C₂×D₄	—	43	2	no	—
466	C₂²×C₄	—	43	2	no	—
467	C₂²×C₄	—	43	1	no	—
468	C₂²×C₄	—	43	1	no	—
469	C₂²×C₄	—	43	1	no	—
470	C₂²×C₄	—	43	2	no	—
471	C₂²×C₄	—	43	1	no	—
472	C₂²×C₄	—	43	2	no	—
473	C₂²×C₄	—	43	2	no	—
474	C₂²×C₄	—	43	2	no	—
475	C₂²×C₄	—	43	2	no	—
476	C₂²×C₄	—	43	2	no	—
477	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
478	C₄⋊C₄	—	43	1	no	—
479	C₄⋊C₄	—	43	2	no	—
480	C₄⋊C₄	—	43	2	no	—
481	C₄⋊C₄	—	43	2	no	—
482	C₄⋊C₄	—	43	2	no	—
483	C₄⋊C₄	—	43	2	no	—
484	C₄⋊C₄	—	43	2	no	—
485	C₄⋊C₄	—	43	2	no	—
486	C₄⋊C₄	—	43	1	no	—
487	C₄⋊C₄	—	43	1	no	—
488	C₄⋊C₄	—	43	2	no	—
489	C₄⋊C₄	—	43	1	no	—
490	C₄⋊C₄	—	43	2	no	—
491	C₄⋊C₄	—	43	1	no	—
492	C₄⋊C₄	—	43	1	no	—
493	C₄⋊C₄	—	43	2	no	—
494	C₄⋊C₄	—	43	2	no	—
495	C₄⋊C₄	—	43	2	no	—
496	C₄⋊C₄	—	43	2	no	—
497	C₄⋊C₄	—	43	2	no	—
498	C₄⋊C₄	—	43	2	no	—
499	C₄⋊C₄	—	43	2	no	—
500	C₄⋊C₄	—	43	1	no	—
501	C₄⋊C₄	—	43	1	no	—
502	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
506	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
510	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
514	C₂²⋊C₄	—	43	1	no	—
515	C₂²⋊C₄	—	43	1	no	—
516	C₂²⋊C₄	—	43	2	no	—
517	C₂²⋊C₄	—	43	2	no	—
518	C₂²⋊C₄	—	43	2	no	—
519	C₂²⋊C₄	—	43	1	no	—
520	C₂²⋊C₄	—	43	2	no	—
521	C₂²⋊C₄	—	43	1	no	—
522	C₂²⋊C₄	—	43	1	no	—
523	C₂²⋊C₄	—	43	2	no	—
524	C₂²⋊C₄	—	43	1	no	—
525	C₂²⋊C₄	—	43	2	no	—
526	C₂²⋊C₄	—	43	2	no	—
527	C₂²⋊C₄	—	43	1	no	—
528	C₂²⋊C₄	—	43	2	no	—
529	C₂²⋊C₄	—	43	2	no	—
530	C₂²⋊C₄	—	43	2	no	—
531	C₂²⋊C₄	—	43	1	no	—
532	C₂²⋊C₄	—	43	2	no	—
533	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
534	C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
535	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
536	C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
537	C₄²	—	43	1	no	—
538	C₄²	—	43	1	no	—
539	C₄²	—	43	1	no	—
540	C₄²	—	43	2	no	—
541	C₄²	—	43	1	no	—
542	C₄²	—	43	2	no	—
543	C₄²	—	43	2	no	—
544	C₄²	C₂²×D₄₃	1	1	yes	characteristic
545	C₄²	C₂²×D₄₃	1	2	yes	—
546	C₄²	C₂²×D₄₃	1	1	yes	characteristic
547	C₄²	C₂²×D₄₃	1	2	yes	—
548	C₂³	—	43	1	no	—
549	C₂³	—	43	1	no	—
550	C₂³	—	43	2	no	—
551	C₂³	C₂³×D₄₃	1	1	yes	characteristic
552	Q₈	—	2	2	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	86	2	no	—
555	Q₈	—	86	2	no	—
556	Q₈	—	86	2	no	—
557	Q₈	—	86	2	no	—
558	Q₈	—	172	2	no	—
559	Q₈	—	172	2	no	—
560	Q₈	—	172	2	no	—
561	Q₈	—	172	2	no	—
562	D₄	—	86	4	no	—
563	D₄	—	86	2	no	—
564	D₄	—	86	2	no	—
565	D₄	—	86	2	no	—
566	D₄	—	86	2	no	—
567	D₄	—	172	2	no	—
568	D₄	—	172	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	43	1	no	—
571	C₂×C₄	—	43	1	no	—
572	C₂×C₄	—	43	1	no	—
573	C₂×C₄	—	43	1	no	—
574	C₂×C₄	—	43	1	no	—
575	C₂×C₄	—	43	2	no	—
576	C₂×C₄	—	43	2	no	—
577	C₂×C₄	—	43	2	no	—
578	C₂×C₄	—	43	1	no	—
579	C₂×C₄	—	86	2	no	—
580	C₂×C₄	—	86	4	no	—
581	C₂×C₄	—	86	2	no	—
582	C₂×C₄	—	86	2	no	—
583	C₂×C₄	—	86	2	no	—
584	C₂×C₄	—	172	2	no	—
585	C₂×C₄	—	172	2	no	—
586	C₂×C₄	—	172	2	no	—
587	C₂×C₄	—	172	2	no	—
588	C₂×C₄	—	172	2	no	—
589	C₂×C₄	—	172	2	no	—
590	C₂×C₄	C₂³×D₄₃	1	2	yes	—
591	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₄₃	1	2	yes	—
594	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₄₃	1	2	yes	—
597	C₂×C₄	C₂³×D₄₃	1	2	yes	—
598	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	43	2	no	—
604	C₂²	—	86	1	no	—
605	C₂²	—	86	1	no	—
606	C₂²	—	86	1	no	—
607	C₂²	—	86	2	no	—
608	C₂²	—	86	2	no	—
609	C₂²	—	86	1	no	—
610	C₂²	—	86	1	no	—
611	C₂²	—	86	2	no	—
612	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	43	2	no	—
623	C₄	—	86	1	no	—
624	C₄	—	86	1	no	—
625	C₄	—	86	2	no	—
626	C₄	—	86	2	no	—
627	C₄	—	86	2	no	—
628	C₄	—	86	1	no	—
629	C₄	—	86	1	no	—
630	C₄	—	86	1	no	—
631	C₄	#13063371	1	2	yes	—
632	C₂	—	4	1	no	—
633	C₂	—	86	2	no	—
634	C₂	—	172	1	no	—
635	C₂	—	172	2	no	—
636	C₂	C₂×#13063371	1	1	yes	characteristic
637	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
638	C₂	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁵
Fitting	C₄₃×#541	C₂
hypercenter	#541	D₄₃
hypocenter	C₄₃	#3552
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. #14583653	C₂	semidirect
2. #14583651	C₂	semidirect
3. #14583627	C₂	semidirect
4. #14583621	C₂	semidirect
5. #14583605	C₂	semidirect
6. #14583600	C₂	semidirect
7. Q₈×D₁₇₂	C₂	semidirect
8. #14583562	C₂	semidirect
9. #14583562	C₂	semidirect
10. #14583561	C₂	semidirect
11. #14583559	C₂	semidirect
12. #14583551	C₂	semidirect
13. #14583529	C₂	semidirect
14. #14583515	C₂	semidirect
15. #14583512	C₂	semidirect
16. #14583497	C₂	semidirect
17. #14583490	C₂	semidirect
18. #14583475	C₂	semidirect
19. #14583474	C₂	semidirect
20. C₄⋊Q₈×D₄₃	C₂	semidirect
21. #14583434	C₂	semidirect
22. #14583427	C₂	semidirect
23. C₄₃×#541	C₂	semidirect
335. #541	D₄₃	semidirect
343. C₄₃	#3552	semidirect