Subgroups — #25965607

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144879	C₂	1	2	yes	maximal, complemented
4	#19144864	C₂	1	2	yes	maximal, complemented
5	#19144786	C₂	1	2	yes	maximal, complemented
6	#19144784	C₂	1	2	yes	maximal, complemented
7	#19144738	C₂	1	2	yes	maximal, complemented
8	#19144711	C₂	1	2	yes	maximal, complemented
9	#19144647	C₂	1	2	yes	maximal, complemented
10	#19144620	C₂	1	2	yes	maximal, complemented
11	#19144567	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144556	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144388	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144089	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#14583115	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143875	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143866	C₂	1	1	yes	maximal, characteristic
18	#19143453	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143446	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143441	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143430	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143260	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063371	C₂²	1	1	yes	characteristic
25	C₂×#13063355	C₂²	1	1	yes	characteristic
26	C₂×#13063350	C₂²	1	1	yes	characteristic
27	C₂²×#10621873	C₂²	1	1	yes	characteristic
28	C₂²×D₃₄₄	C₂²	1	1	yes	characteristic
29	#14583634	—	2	1	no	—
30	#14583634	—	2	1	no	—
31	#14583622	—	2	1	no	—
32	#14583622	—	2	1	no	—
33	#14583576	—	2	2	no	—
34	#14583576	—	2	2	no	—
35	#14583523	C₂²	1	2	yes	complemented
36	#14583523	C₂²	1	2	yes	complemented
37	#14583475	C₂²	1	1	yes	characteristic
38	#14583468	C₂²	1	1	yes	characteristic
39	#14583434	C₂²	1	2	yes	complemented
40	#14583434	C₂²	1	2	yes	complemented
41	C₂×#13063313	C₂²	1	1	yes	characteristic, complemented
42	#14583382	C₂²	1	1	yes	characteristic
43	#14583381	C₂²	1	2	yes	complemented
44	#14583379	—	2	1	no	—
45	#14583379	C₂²	1	1	yes	characteristic
46	#14583376	C₂²	1	1	yes	characteristic, complemented
47	#14583373	—	2	1	no	—
48	#14583373	C₂²	1	1	yes	characteristic
49	#14583373	C₂²	1	1	yes	characteristic, complemented
50	#14583371	—	2	2	no	—
51	#14583371	C₂²	1	2	yes	complemented
52	C₄×#10621902	C₂²	1	2	yes	complemented
53	C₄×#10621898	—	2	1	no	—
54	C₄×#10621898	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₁₇₂	—	2	1	no	—
56	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
57	C₄×D₄×D₄₃	—	2	2	no	—
58	C₄×D₄×D₄₃	C₂²	1	2	yes	complemented
59	#14583243	C₂²	1	2	yes	complemented
60	#14583242	C₂²	1	2	yes	complemented
61	#14583236	C₂²	1	2	yes	complemented
62	#14583231	C₂²	1	2	yes	complemented
63	#14583226	C₂²	1	2	yes	complemented
64	#14583225	C₂²	1	2	yes	complemented
65	#14583219	C₂²	1	2	yes	complemented
66	#14583214	C₂²	1	2	yes	complemented
67	#14583196	C₂²	1	2	yes	complemented
68	#14583196	C₂²	1	2	yes	complemented
69	#14583186	C₂²	1	2	yes	complemented
70	#14583176	C₂²	1	2	yes	complemented
71	#14583121	C₂²	1	2	yes	complemented
72	#14583121	C₂²	1	2	yes	complemented
73	#14583115	C₂²	1	2	yes	complemented
74	#14583115	C₂²	1	2	yes	complemented
75	#14583115	C₂²	1	2	yes	complemented
76	#14583115	C₂²	1	2	yes	complemented
77	#14583114	C₂²	1	2	yes	complemented
78	#14583114	C₂²	1	2	yes	complemented
79	#14583064	C₂²	1	2	yes	complemented
80	#14583064	C₂²	1	2	yes	complemented
81	#14583051	C₂²	1	2	yes	complemented
82	#14583051	C₂²	1	2	yes	complemented
83	#14583047	C₂²	1	2	yes	—
84	#14583047	C₂²	1	2	yes	—
85	#14583034	C₂²	1	2	yes	—
86	#14583034	C₂²	1	2	yes	—
87	#14583010	C₂²	1	2	yes	complemented
88	#14583010	C₂²	1	2	yes	complemented
89	#14583008	C₂²	1	2	yes	complemented
90	#14583003	C₂²	1	2	yes	complemented
91	#14583002	C₂²	1	2	yes	complemented
92	#14582998	C₂²	1	2	yes	complemented
93	#14582998	C₂²	1	2	yes	complemented
94	#14582996	C₂²	1	2	yes	complemented
95	#14582991	C₂²	1	2	yes	complemented
96	#14582990	C₂²	1	2	yes	complemented
97	#14582986	C₂²	1	2	yes	complemented
98	#14582986	C₂²	1	2	yes	complemented
99	#14582984	C₂²	1	2	yes	complemented
100	#14582981	C₂²	1	2	yes	complemented
101	#14582981	C₂²	1	2	yes	complemented
102	#14582979	C₂²	1	2	yes	complemented
103	#14582959	C₂²	1	2	yes	complemented
104	#14582959	C₂²	1	2	yes	complemented
105	#14582955	C₂²	1	2	yes	complemented
106	#14582951	C₂²	1	2	yes	complemented
107	#14582942	C₂²	1	1	yes	characteristic, complemented
108	#14582942	C₂²	1	1	yes	characteristic, complemented
109	#14582923	C₂²	1	1	yes	characteristic, complemented
110	#14582907	C₂²	1	1	yes	characteristic, complemented
111	#14582903	C₂²	1	1	yes	characteristic
112	#14582903	C₂²	1	1	yes	characteristic
113	#14582903	C₂²	1	1	yes	characteristic, complemented
114	C₂×#13063250	C₂²	1	1	yes	characteristic, complemented
115	C₂×#13063247	C₂²	1	1	yes	characteristic, complemented
116	#14582865	C₂²	1	1	yes	characteristic
117	#14582865	C₂²	1	1	yes	characteristic
118	#14582854	C₂²	1	1	yes	characteristic, complemented
119	#14582854	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₄₃×#416	C₂²	1	1	yes	characteristic
135	#13063371	—	2	4	no	—
136	#13063371	—	2	4	no	—
137	C₂×#10621902	C₂³	1	2	yes	—
138	C₂×#10621898	—	2	1	no	—
139	C₂×#10621898	C₂³	1	1	yes	characteristic
140	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
141	C₂²×D₁₇₂	—	2	1	no	—
142	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
143	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
144	C₂×D₄×D₄₃	—	2	2	no	—
145	C₂×D₄×D₄₃	C₂³	1	2	yes	—
146	C₂²×C₄×D₄₃	—	2	1	no	—
147	C₂²×C₄×D₄₃	—	2	2	no	—
148	#13063355	—	2	4	no	—
149	#13063350	—	2	4	no	—
150	C₂×#10621885	C₂³	1	2	yes	—
151	C₂×#10621873	—	2	4	no	—
152	C₂×#10621873	C₂³	1	2	yes	—
153	C₂×#10621873	C₂³	1	2	yes	—
154	C₂×#10621883	C₂³	1	2	yes	—
155	C₂×#10621884	C₂³	1	2	yes	—
156	C₂×D₃₄₄	—	2	4	no	—
157	C₂×D₃₄₄	C₂³	1	2	yes	—
158	C₂×D₃₄₄	C₂³	1	2	yes	—
159	C₂×#10621882	C₂³	1	2	yes	—
160	C₂×#10621877	C₂³	1	1	yes	characteristic
161	C₂×#10621877	C₂³	1	1	yes	characteristic
162	#13063325	—	2	1	no	—
163	#13063322	—	2	1	no	—
164	#13063320	—	2	2	no	—
165	#13063320	—	2	2	no	—
166	#13063320	—	2	2	no	—
167	#13063320	—	2	2	no	—
168	#13063314	—	2	2	no	—
169	#13063314	—	2	2	no	—
170	#13063313	—	2	1	no	—
171	#13063313	—	2	1	no	—
172	#13063313	—	2	1	no	—
173	#13063313	—	2	1	no	—
174	#13063313	C₂³	1	2	yes	—
175	#13063313	C₂³	1	2	yes	—
176	#13063310	—	2	2	no	—
177	#13063310	—	2	2	no	—
178	#13063310	—	2	2	no	—
179	#13063310	—	2	2	no	—
180	#13063309	—	2	2	no	—
181	#13063305	C₂³	1	2	yes	—
182	#13063305	C₂³	1	2	yes	—
183	#13063301	—	2	2	no	—
184	#13063301	—	2	2	no	—
185	#13063300	C₂³	1	2	yes	—
186	#13063300	C₂³	1	2	yes	—
187	#13063295	—	2	2	no	—
188	Q₈×Dic₄₃	C₂³	1	2	yes	—
189	C₄×Dic₈₆	—	2	1	no	—
190	C₄×Dic₈₆	—	2	1	no	—
191	C₄×Dic₈₆	—	2	1	no	—
192	C₄×Dic₈₆	D₄	1	1	yes	characteristic
193	C₄×Dic₈₆	D₄	1	1	yes	characteristic
194	#13063290	C₂³	1	2	yes	—
195	#13063290	C₂³	1	2	yes	—
196	C₄×D₁₇₂	—	2	1	no	—
197	C₄×D₁₇₂	—	2	2	no	—
198	C₄×D₁₇₂	—	2	1	no	—
199	C₄×D₁₇₂	—	2	1	no	—
200	C₄×D₁₇₂	—	2	2	no	—
201	C₄×D₁₇₂	—	2	1	no	—
202	C₄×D₁₇₂	—	2	1	no	—
203	C₄×D₁₇₂	—	2	1	no	—
204	C₄×D₁₇₂	—	2	1	no	—
205	C₄×D₁₇₂	D₄	1	1	yes	characteristic
206	C₄×D₁₇₂	D₄	1	1	yes	characteristic
207	C₄×D₁₇₂	C₂³	1	2	yes	—
208	C₄×D₁₇₂	C₂³	1	2	yes	—
209	D₄×Dic₄₃	—	2	2	no	—
210	D₄×Dic₄₃	C₂³	1	2	yes	—
211	#13063287	—	2	2	no	—
212	#13063287	—	2	2	no	—
213	#13063287	—	2	2	no	—
214	#13063287	—	2	2	no	—
215	#13063287	C₂³	1	2	yes	—
216	#13063287	C₂³	1	2	yes	—
217	#13063287	C₂³	1	2	yes	—
218	#13063287	C₂³	1	2	yes	—
219	C₄×C₂²⋊D₄₃	—	2	2	no	—
220	C₄×C₂²⋊D₄₃	—	2	2	no	—
221	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
222	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
223	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
224	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
225	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
226	#13063284	—	2	1	no	—
227	#13063284	C₂³	1	1	yes	characteristic
228	#13063283	—	2	2	no	—
229	#13063283	—	2	2	no	—
230	#13063283	—	2	2	no	—
231	#13063283	C₂³	1	2	yes	—
232	#13063282	—	2	2	no	—
233	#13063282	C₂³	1	2	yes	—
234	#13063281	—	2	2	no	—
235	C₂×C₄⋊Dic₄₃	—	2	1	no	—
236	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×D₄₃	—	2	2	no	—
238	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
239	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
240	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
241	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
242	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
243	C₂²⋊C₄×D₄₃	—	2	2	no	—
244	C₂²⋊C₄×D₄₃	—	2	2	no	—
245	C₂²⋊C₄×D₄₃	—	2	2	no	—
246	C₂²⋊C₄×D₄₃	—	2	2	no	—
247	C₄²×D₄₃	—	2	2	no	—
248	C₄²×D₄₃	C₂³	1	2	yes	—
249	#13063258	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063256	C₂³	1	2	yes	—
252	#13063256	C₂³	1	2	yes	—
253	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
254	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
255	#13063250	C₂³	1	2	yes	—
256	#13063250	C₂³	1	2	yes	—
257	#13063248	C₂³	1	2	yes	—
258	#13063248	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063247	C₂³	1	2	yes	—
261	#13063245	C₂³	1	2	yes	—
262	#13063245	C₂³	1	2	yes	—
263	#13063245	C₂³	1	2	yes	—
264	#13063245	C₂³	1	2	yes	—
265	#13063245	C₂³	1	2	yes	—
266	#13063245	C₂³	1	2	yes	—
267	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
271	#13063235	C₂³	1	2	yes	—
272	#13063235	C₂³	1	2	yes	—
273	C₈×Dic₄₃	C₂³	1	2	yes	—
274	C₈×Dic₄₃	C₂³	1	2	yes	—
275	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
280	#125×C₄₃	C₂³	1	1	yes	characteristic
281	#125×C₄₃	C₂³	1	1	yes	characteristic
282	C₂²⋊Q₈×C₄₃	—	2	1	no	—
283	C₂²⋊Q₈×C₄₃	—	2	1	no	—
284	C₄×Q₈×C₄₃	—	2	1	no	—
285	C₄×Q₈×C₄₃	—	2	1	no	—
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	—	2	1	no	—
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	#117×C₄₃	—	2	1	no	—
293	#117×C₄₃	C₂³	1	1	yes	characteristic
294	#117×C₄₃	C₂³	1	1	yes	characteristic
295	#117×C₄₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#107×C₄₃	C₂³	1	1	yes	characteristic
301	#107×C₄₃	C₂³	1	1	yes	characteristic
302	#106×C₄₃	C₂³	1	1	yes	characteristic
303	#106×C₄₃	C₂³	1	1	yes	characteristic
304	#106×C₄₃	C₂³	1	1	yes	characteristic
305	#106×C₄₃	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#103×C₄₃	C₂³	1	1	yes	characteristic
312	#103×C₄₃	C₂³	1	1	yes	characteristic
313	#103×C₄₃	C₂³	1	1	yes	characteristic
314	#102×C₄₃	C₂³	1	1	yes	characteristic
315	#102×C₄₃	C₂³	1	1	yes	characteristic
316	#102×C₄₃	C₂³	1	1	yes	characteristic
317	#102×C₄₃	C₂³	1	1	yes	characteristic
318	C₂³×D₄₃	—	2	1	no	—
319	C₂³×D₄₃	—	2	2	no	—
320	C₂³×D₄₃	—	2	1	no	—
321	#41×C₄₃	—	2	2	no	—
322	#41×C₄₃	#41	1	4	yes	—
323	C₂×Q₈×C₄₃	—	2	1	no	—
324	C₂×Q₈×C₄₃	—	2	1	no	—
325	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
336	C₂²×Dic₄₃	—	2	2	no	—
337	C₂²×Dic₄₃	—	2	1	no	—
338	C₂²×Dic₄₃	—	2	1	no	—
339	#10621902	—	2	4	no	—
340	#10621902	—	2	4	no	—
341	D₄×D₄₃	—	2	16	no	—
342	D₄×D₄₃	—	2	4	no	—
343	D₄×D₄₃	—	2	4	no	—
344	#10621898	—	2	8	no	—
345	#10621898	—	2	2	no	—
346	#10621898	—	2	2	no	—
347	C₂×D₁₇₂	—	2	8	no	—
348	C₂×D₁₇₂	—	2	1	no	—
349	C₂×D₁₇₂	—	2	2	no	—
350	C₂×D₁₇₂	—	2	1	no	—
351	C₂×D₁₇₂	—	2	2	no	—
352	C₂×D₁₇₂	—	2	2	no	—
353	C₂×D₁₇₂	—	2	2	no	—
354	C₂×D₁₇₂	—	2	2	no	—
355	C₂×D₁₇₂	—	2	2	no	—
356	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
357	C₂×D₁₇₂	#41	1	4	yes	—
358	C₂×D₁₇₂	C₂⁴	1	2	yes	—
359	C₂×D₁₇₂	C₂⁴	1	2	yes	—
360	C₂×C₄×D₄₃	—	2	2	no	—
361	C₂×C₄×D₄₃	—	2	2	no	—
362	C₂×C₄×D₄₃	—	2	2	no	—
363	C₂×C₄×D₄₃	—	2	2	no	—
364	C₂×C₄×D₄₃	—	2	2	no	—
365	C₂×C₄×D₄₃	—	2	2	no	—
366	C₂×C₄×D₄₃	—	2	2	no	—
367	C₂×C₄×D₄₃	—	2	2	no	—
368	C₂×C₄×D₄₃	—	8	4	no	—
369	C₂×C₄×D₄₃	—	8	2	no	—
370	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
371	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
372	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
373	C₂×Dic₈₆	—	2	2	no	—
374	C₂×Dic₈₆	—	2	2	no	—
375	C₂×Dic₈₆	—	2	1	no	—
376	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
377	C₂×Dic₈₆	C₂⁴	1	2	yes	—
378	C₂×C₈×C₄₃	—	2	2	no	—
379	C₂×C₈×C₄₃	—	2	2	no	—
380	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	—	2	1	no	—
385	C₄⋊C₄×C₄₃	—	2	1	no	—
386	C₄⋊C₄×C₄₃	—	2	1	no	—
387	C₄⋊C₄×C₄₃	—	2	1	no	—
388	C₄⋊C₄×C₄₃	—	2	1	no	—
389	C₄⋊C₄×C₄₃	—	2	1	no	—
390	C₄⋊C₄×C₄₃	—	2	1	no	—
391	C₄⋊C₄×C₄₃	—	2	1	no	—
392	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
398	C₂²⋊C₄×C₄₃	—	2	1	no	—
399	C₂²⋊C₄×C₄₃	—	2	1	no	—
400	C₂²⋊C₄×C₄₃	—	2	1	no	—
401	C₂²⋊C₄×C₄₃	—	2	1	no	—
402	C₂²⋊C₄×C₄₃	—	2	1	no	—
403	C₄²×C₄₃	—	2	1	no	—
404	C₄²×C₄₃	—	2	1	no	—
405	C₄²×C₄₃	—	2	1	no	—
406	C₄²×C₄₃	—	2	1	no	—
407	C₄²×C₄₃	—	2	1	no	—
408	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
409	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
410	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
411	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
412	C₂²⋊Dic₄₃	—	2	2	no	—
413	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
414	#10621885	—	2	4	no	—
415	#10621884	—	2	4	no	—
416	#10621883	—	2	4	no	—
417	#10621882	—	2	4	no	—
418	(C₂×D₄₃)⋊C₄	—	2	2	no	—
419	(C₂×D₄₃)⋊C₄	—	2	2	no	—
420	(C₂×D₄₃)⋊C₄	—	2	2	no	—
421	(C₂×D₄₃)⋊C₄	—	2	2	no	—
422	(C₂×D₄₃)⋊C₄	—	2	2	no	—
423	(C₂×D₄₃)⋊C₄	—	2	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	2	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	2	no	—
431	(C₂×D₄₃)⋊C₄	—	2	2	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
434	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
435	C₄⋊Dic₄₃	—	2	1	no	—
436	C₄⋊Dic₄₃	—	2	2	no	—
437	C₄⋊Dic₄₃	—	2	2	no	—
438	C₄⋊Dic₄₃	—	2	2	no	—
439	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
440	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
441	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
442	Dic₄₃⋊C₄	—	2	2	no	—
443	Dic₄₃⋊C₄	—	2	2	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
446	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₃	—	2	2	no	—
448	C₄×Dic₄₃	—	2	2	no	—
449	C₄×Dic₄₃	—	2	2	no	—
450	C₄×Dic₄₃	—	2	2	no	—
451	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
452	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
453	C₄×Dic₄₃	C₂⁴	1	2	yes	—
454	#10621877	—	2	2	no	—
455	#10621877	—	2	2	no	—
456	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
458	D₃₄₄	—	2	4	no	—
459	D₃₄₄	—	2	4	no	—
460	#10621873	—	2	4	no	—
461	#10621873	—	2	4	no	—
462	C₂³×C₄₃	—	2	1	no	—
463	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂²×D₄₃	—	2	2	no	—
465	C₂²×D₄₃	—	2	8	no	—
466	C₂²×D₄₃	—	2	4	no	—
467	C₂²×D₄₃	—	2	2	no	—
468	C₂²×D₄₃	—	4	2	no	—
469	C₂²×D₄₃	—	8	2	no	—
470	C₂²×D₄₃	—	8	2	no	—
471	C₂²×D₄₃	—	8	1	no	—
472	C₂²×D₄₃	—	8	1	no	—
473	C₂²×D₄₃	—	8	1	no	—
474	C₂²×D₄₃	—	8	1	no	—
475	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
476	Q₈×C₄₃	—	2	1	no	—
477	Q₈×C₄₃	—	8	1	no	—
478	Q₈×C₄₃	—	8	1	no	—
479	Q₈×C₄₃	C₂×#41	1	2	yes	—
480	D₄×C₄₃	—	2	4	no	—
481	D₄×C₄₃	—	2	1	no	—
482	D₄×C₄₃	C₂×#41	1	2	yes	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	2	4	no	—
485	C₂×C₄×C₄₃	—	2	1	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	2	1	no	—
489	C₂×C₄×C₄₃	—	2	1	no	—
490	C₂×C₄×C₄₃	—	2	1	no	—
491	C₂×C₄×C₄₃	—	4	1	no	—
492	C₂×C₄×C₄₃	—	4	1	no	—
493	C₂×C₄×C₄₃	—	4	2	no	—
494	C₂×C₄×C₄₃	—	8	1	no	—
495	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
501	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
502	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
503	C₂²⋊D₄₃	—	2	8	no	—
504	C₂²⋊D₄₃	—	2	4	no	—
505	C₂×Dic₄₃	—	2	2	no	—
506	C₂×Dic₄₃	—	2	2	no	—
507	C₂×Dic₄₃	—	4	2	no	—
508	C₂×Dic₄₃	—	8	2	no	—
509	C₂×Dic₄₃	—	8	1	no	—
510	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
511	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
512	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
513	D₁₇₂	—	2	8	no	—
514	D₁₇₂	—	2	2	no	—
515	D₁₇₂	—	2	4	no	—
516	D₁₇₂	—	2	2	no	—
517	D₁₇₂	—	2	2	no	—
518	D₁₇₂	—	2	2	no	—
519	D₁₇₂	—	4	2	no	—
520	D₁₇₂	—	8	2	no	—
521	D₁₇₂	—	8	2	no	—
522	D₁₇₂	C₂×#41	1	4	yes	—
523	C₄×D₄₃	—	2	8	no	—
524	C₄×D₄₃	—	2	2	no	—
525	C₄×D₄₃	—	2	2	no	—
526	C₄×D₄₃	—	4	2	no	—
527	C₄×D₄₃	—	4	2	no	—
528	C₄×D₄₃	—	4	4	no	—
529	C₄×D₄₃	—	8	2	no	—
530	C₄×D₄₃	—	8	2	no	—
531	C₄×D₄₃	—	8	2	no	—
532	C₄×D₄₃	—	8	2	no	—
533	C₄×D₄₃	—	8	2	no	—
534	C₄×D₄₃	—	8	2	no	—
535	Dic₈₆	—	2	2	no	—
536	Dic₈₆	—	2	2	no	—
537	Dic₈₆	—	2	2	no	—
538	Dic₈₆	—	4	2	no	—
539	C₈×C₄₃	—	2	1	no	—
540	C₈×C₄₃	—	2	1	no	—
541	C₈×C₄₃	—	2	1	no	—
542	C₈×C₄₃	—	2	1	no	—
543	C₄₃⋊C₈	—	2	2	no	—
544	C₄₃⋊C₈	—	2	2	no	—
545	#60592	—	43	1	no	maximal, Sylow
546	C₂²×C₄₃	—	2	1	no	—
547	C₂²×C₄₃	—	2	1	no	—
548	C₂²×C₄₃	—	2	2	no	—
549	C₂²×C₄₃	—	4	1	no	—
550	C₂²×C₄₃	—	4	1	no	—
551	C₂²×C₄₃	#525	1	2	yes	—
552	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
553	C₂×D₄₃	—	2	2	no	—
554	C₂×D₄₃	—	2	2	no	—
555	C₂×D₄₃	—	2	4	no	—
556	C₂×D₄₃	—	2	2	no	—
557	C₂×D₄₃	—	4	2	no	—
558	C₂×D₄₃	—	4	2	no	—
559	C₂×D₄₃	—	4	2	no	—
560	C₂×D₄₃	—	4	2	no	—
561	C₂×D₄₃	—	4	2	no	—
562	C₂×D₄₃	—	8	4	no	—
563	C₂×D₄₃	—	8	8	no	—
564	C₂×D₄₃	—	16	2	no	—
565	C₄×C₄₃	—	2	1	no	—
566	C₄×C₄₃	—	2	1	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	2	1	no	—
569	C₄×C₄₃	—	2	2	no	—
570	C₄×C₄₃	—	4	1	no	—
571	C₄×C₄₃	—	4	1	no	—
572	C₄×C₄₃	—	4	1	no	—
573	C₄×C₄₃	—	4	1	no	—
574	C₄×C₄₃	—	4	1	no	—
575	C₄×C₄₃	—	4	1	no	—
576	C₄×C₄₃	#525	1	2	yes	—
577	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
578	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
579	Dic₄₃	—	2	2	no	—
580	Dic₄₃	—	2	2	no	—
581	Dic₄₃	—	2	2	no	—
582	Dic₄₃	—	4	2	no	—
583	Dic₄₃	—	4	2	no	—
584	#3510	—	43	1	no	—
585	C₄×H(5,𝔽₂)	—	43	1	no	—
586	#3125	—	43	2	no	—
587	#3124	—	43	2	no	—
588	#3118	—	43	2	no	—
589	#3118	—	43	2	no	—
590	#3114	—	43	2	no	—
591	#3111	—	43	2	no	—
592	#3105	—	43	2	no	—
593	#3102	—	43	2	no	—
594	#3097	—	43	1	no	—
595	#3096	—	43	1	no	—
596	#3077	—	43	1	no	—
597	#3076	D₄₃	1	1	yes	characteristic, complemented
598	#3040	—	43	1	no	—
599	C₂×#463	—	43	1	no	—
600	#3009	—	43	1	no	—
601	#3008	—	43	1	no	—
602	#2949	—	43	1	no	—
603	#2948	—	43	1	no	—
604	#2947	—	43	1	no	—
605	#2946	—	43	1	no	—
606	#2925	—	43	1	no	—
607	C₂×C₄₃	—	2	2	no	—
608	C₂×C₄₃	—	4	2	no	—
609	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
610	C₂×C₄₃	#3584	1	1	yes	characteristic
611	C₂×C₄₃	#3585	1	1	yes	characteristic
612	D₄₃	—	4	2	no	—
613	D₄₃	—	4	4	no	—
614	D₄₃	—	8	2	no	—
615	C₂×H(5,𝔽₂)	—	43	1	no	—
616	C₂×#137	—	43	1	no	—
617	C₂×AGL(1,ℤ/8)	—	43	1	no	—
618	C₂²×SD₁₆	—	43	1	no	—
619	C₂²×D₈	—	43	1	no	—
620	#559	—	86	1	no	—
621	#559	—	86	1	no	—
622	#556	—	86	1	no	—
623	#556	—	86	1	no	—
624	#551	—	86	2	no	—
625	#551	—	86	2	no	—
626	#542	—	43	2	no	—
627	#542	—	43	2	no	—
628	#536	—	43	1	no	—
629	#535	—	43	1	no	—
630	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
631	#529	—	43	2	no	—
632	#529	—	43	2	no	—
633	C₂×#124	—	43	1	no	—
634	#520	—	43	1	no	—
635	#520	—	43	1	no	—
636	#520	—	43	2	no	—
637	#520	—	86	1	no	—
638	#519	—	43	1	no	—
639	#518	—	43	2	no	—
640	#518	—	43	1	no	—
641	#518	—	43	1	no	—
642	#518	—	86	1	no	—
643	#518	—	86	2	no	—
644	C₄×#41	—	43	1	no	—
645	C₄×#41	—	43	2	no	—
646	C₄×#41	—	86	1	no	—
647	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
648	C₂×C₄×D₄	—	43	2	no	—
649	C₂×C₄×D₄	—	43	1	no	—
650	C₂×C₄×D₄	—	86	1	no	—
651	C₂×C₄×D₄	—	86	2	no	—
652	#485	—	43	2	no	—
653	#485	—	43	2	no	—
654	#484	—	43	2	no	—
655	#483	—	43	2	no	—
656	#482	—	43	2	no	—
657	#482	—	43	2	no	—
658	#481	—	43	2	no	—
659	#480	—	43	2	no	—
660	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
661	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
662	#478	—	43	2	no	—
663	#478	—	43	2	no	—
664	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
665	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
666	#477	C₂×D₄₃	1	1	yes	characteristic, complemented
667	#476	—	43	2	no	—
668	#476	C₂×D₄₃	1	1	yes	characteristic, complemented
669	#475	C₂×D₄₃	1	1	yes	characteristic, complemented
670	#474	—	43	2	no	—
671	#474	C₂×D₄₃	1	1	yes	characteristic, complemented
672	#464	—	43	2	no	—
673	#464	—	43	2	no	—
674	#463	—	43	2	no	—
675	#463	—	43	2	no	—
676	#463	—	43	2	no	—
677	#463	—	43	2	no	—
678	#463	—	43	2	no	—
679	#463	—	43	2	no	—
680	#452	—	43	2	no	—
681	#452	—	43	2	no	—
682	#450	—	43	2	no	—
683	#450	—	43	2	no	—
684	#449	—	43	2	no	—
685	#449	—	43	2	no	—
686	#447	—	43	2	no	—
687	#447	—	43	2	no	—
688	#442	—	43	2	no	—
689	#442	—	43	2	no	—
690	#442	—	43	2	no	—
691	#441	—	43	2	no	—
692	#440	—	43	2	no	—
693	#440	—	43	2	no	—
694	#440	—	43	2	no	—
695	#440	—	43	2	no	—
696	C₄×Q₁₆	—	43	2	no	—
697	C₄×SD₁₆	—	43	2	no	—
698	C₄×SD₁₆	—	43	2	no	—
699	C₄×SD₁₆	—	43	2	no	—
700	C₄×SD₁₆	—	43	2	no	—
701	C₄×D₈	—	43	2	no	—
702	C₄×D₈	—	43	2	no	—
703	C₄×D₈	—	43	2	no	—
704	#433	—	43	2	no	—
705	#433	—	43	2	no	—
706	#432	—	43	2	no	—
707	#431	—	43	2	no	—
708	#428	—	43	1	no	—
709	#428	—	43	1	no	—
710	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
711	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
712	#423	—	43	1	no	—
713	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
714	#419	—	43	1	no	—
715	#418	—	43	1	no	—
716	#418	—	43	1	no	—
717	#418	—	43	1	no	—
718	#416	C₂×D₄₃	1	1	yes	characteristic
719	#416	C₂×D₄₃	1	1	yes	characteristic
720	C₂×#103	—	43	1	no	—
721	C₂×#102	—	43	1	no	—
722	#408	—	43	1	no	—
723	#408	—	43	1	no	—
724	#405	—	43	1	no	—
725	#405	—	43	1	no	—
726	C₄₃	#60592	1	1	yes	characteristic, complemented, Sylow
727	H(5,𝔽₂)	—	86	4	no	—
728	H(5,𝔽₂)	—	86	4	no	—
729	C₂×#41	—	43	1	no	—
730	C₂×#41	—	43	2	no	—
731	C₂×#41	—	86	1	no	—
732	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
733	C₂²×Q₈	—	43	1	no	—
734	C₂²×D₄	—	43	2	no	—
735	C₂²×D₄	—	43	1	no	—
736	C₂²×D₄	—	43	1	no	—
737	C₂²×D₄	—	86	1	no	—
738	C₂²×D₄	—	86	2	no	—
739	C₂³×C₄	—	86	2	no	—
740	C₂³×C₄	—	86	1	no	—
741	#137	—	86	4	no	—
742	AGL(1,ℤ/8)	—	86	4	no	—
743	C₂×Q₁₆	—	43	2	no	—
744	C₂×SD₁₆	—	43	2	no	—
745	C₂×SD₁₆	—	43	2	no	—
746	C₂×SD₁₆	—	43	2	no	—
747	C₂×SD₁₆	—	43	2	no	—
748	C₂×SD₁₆	—	86	4	no	—
749	C₂×D₈	—	43	2	no	—
750	C₂×D₈	—	43	2	no	—
751	C₂×D₈	—	43	2	no	—
752	C₂×D₈	—	86	4	no	—
753	C₂×M₁₆	—	43	1	no	—
754	C₂×M₁₆	—	43	1	no	—
755	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
756	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
757	C₄⋊Q₈	—	86	1	no	—
758	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
760	#127	—	86	1	no	—
761	#126	—	86	2	no	—
762	#126	—	86	2	no	—
763	#126	—	86	2	no	—
764	#126	—	86	2	no	—
765	#125	C₂²×D₄₃	1	1	yes	characteristic
766	#125	C₂²×D₄₃	1	1	yes	characteristic
767	#124	—	43	2	no	—
768	#124	—	43	2	no	—
769	#124	—	86	1	no	—
770	#124	—	86	1	no	—
771	#124	—	86	2	no	—
772	#124	—	86	2	no	—
773	#124	—	86	1	no	—
774	#124	—	86	1	no	—
775	#123	—	86	2	no	—
776	#123	—	86	2	no	—
777	#123	—	86	2	no	—
778	#123	—	86	2	no	—
779	#123	—	86	2	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	43	2	no	—
783	C₂²⋊Q₈	—	43	2	no	—
784	C₂²⋊Q₈	—	86	2	no	—
785	C₂²⋊Q₈	—	86	2	no	—
786	#121	—	43	2	no	—
787	#121	—	43	2	no	—
788	#120	—	86	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	43	1	no	—
792	C₄×Q₈	—	43	1	no	—
793	C₄×Q₈	—	43	2	no	—
794	C₄×Q₈	—	43	2	no	—
795	C₄×Q₈	—	43	2	no	—
796	C₄×Q₈	—	86	1	no	—
797	C₄×Q₈	—	86	1	no	—
798	C₄×Q₈	—	86	1	no	—
799	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	43	2	no	—
804	C₄×D₄	—	43	2	no	—
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	2	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	43	2	no	—
809	C₄×D₄	—	43	2	no	—
810	C₄×D₄	—	43	1	no	—
811	C₄×D₄	—	43	1	no	—
812	C₄×D₄	—	43	2	no	—
813	C₄×D₄	—	43	2	no	—
814	C₄×D₄	—	86	2	no	—
815	C₄×D₄	—	86	1	no	—
816	C₄×D₄	—	86	1	no	—
817	C₄×D₄	—	86	1	no	—
818	C₄×D₄	—	86	1	no	—
819	C₄×D₄	—	86	2	no	—
820	C₄×D₄	—	86	1	no	—
821	C₄×D₄	—	86	2	no	—
822	C₄×D₄	—	86	2	no	—
823	C₄×D₄	—	86	2	no	—
824	C₄×D₄	—	86	2	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	2	no	—
827	C₄×D₄	—	86	2	no	—
828	C₄×D₄	—	86	2	no	—
829	C₄×D₄	—	86	2	no	—
830	C₄×D₄	—	86	2	no	—
831	C₄×D₄	—	86	1	no	—
832	C₄×D₄	—	86	1	no	—
833	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
835	#117	—	2	1	no	—
836	#117	—	43	1	no	—
837	#117	—	43	2	no	—
838	#117	—	43	2	no	—
839	#117	—	86	2	no	—
840	#117	—	86	2	no	—
841	#117	—	86	2	no	—
842	#117	—	86	2	no	—
843	#117	—	86	2	no	—
844	#117	—	86	1	no	—
845	#117	C₂²×D₄₃	1	1	yes	characteristic
846	#117	C₂²×D₄₃	1	1	yes	characteristic
847	#117	C₂²×D₄₃	1	1	yes	characteristic
848	C₂×C₄⋊C₄	—	43	1	no	—
849	C₂×C₄⋊C₄	—	43	2	no	—
850	C₂×C₄⋊C₄	—	86	2	no	—
851	C₂×C₄⋊C₄	—	86	1	no	—
852	C₂×C₂²⋊C₄	—	86	2	no	—
853	C₂×C₂²⋊C₄	—	86	2	no	—
854	C₂×C₂²⋊C₄	—	86	2	no	—
855	C₂×C₂²⋊C₄	—	86	2	no	—
856	C₂×C₂²⋊C₄	—	86	2	no	—
857	C₂×C₂²⋊C₄	—	86	1	no	—
858	C₂×C₂²⋊C₄	—	86	1	no	—
859	C₂×C₂²⋊C₄	—	86	1	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	43	2	no	—
862	C₂×C₄²	—	86	2	no	—
863	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
864	#107	—	43	2	no	—
865	#107	—	43	2	no	—
866	#107	C₂²×D₄₃	1	1	yes	characteristic
867	#107	C₂²×D₄₃	1	1	yes	characteristic
868	#107	C₂²×D₄₃	1	1	yes	characteristic
869	#107	C₂²×D₄₃	1	1	yes	characteristic
870	#106	—	43	2	no	—
871	#106	—	43	2	no	—
872	#106	C₂²×D₄₃	1	1	yes	characteristic
873	#106	C₂²×D₄₃	1	1	yes	characteristic
874	#106	C₂²×D₄₃	1	1	yes	characteristic
875	#106	C₂²×D₄₃	1	1	yes	characteristic
876	C₄⋊C₈	—	43	2	no	—
877	C₄⋊C₈	—	43	2	no	—
878	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
879	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
880	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
881	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
882	#103	—	43	2	no	—
883	#103	—	43	2	no	—
884	#103	—	43	2	no	—
885	#103	—	43	2	no	—
886	#103	C₂²×D₄₃	1	1	yes	characteristic
887	#103	C₂²×D₄₃	1	1	yes	characteristic
888	#103	C₂²×D₄₃	1	1	yes	characteristic
889	#103	C₂²×D₄₃	1	1	yes	characteristic
890	#102	—	43	2	no	—
891	#102	—	43	2	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	2	no	—
895	#102	—	43	2	no	—
896	#102	—	43	2	no	—
897	#102	—	43	2	no	—
898	#102	C₂²×D₄₃	1	1	yes	characteristic
899	#102	C₂²×D₄₃	1	1	yes	characteristic
900	#102	C₂²×D₄₃	1	1	yes	characteristic
901	#102	C₂²×D₄₃	1	1	yes	characteristic
902	C₂²⋊C₈	—	43	2	no	—
903	C₂²⋊C₈	—	43	2	no	—
904	C₂²⋊C₈	—	43	2	no	—
905	C₂²⋊C₈	—	43	2	no	—
906	#97	—	43	2	no	—
907	#97	—	43	2	no	—
908	C₄×C₈	—	43	2	no	—
909	C₄×C₈	—	43	2	no	—
910	C₂⁴	—	86	2	no	—
911	C₂⁴	—	86	1	no	—
912	C₂⁴	—	86	1	no	—
913	#41	—	2	2	no	—
914	#41	—	86	8	no	—
915	#41	—	86	4	no	—
916	#41	—	86	4	no	—
917	#41	—	86	2	no	—
918	#41	—	86	2	no	—
919	#41	#10621902	1	4	yes	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	43	1	no	—
923	C₂×Q₈	—	43	2	no	—
924	C₂×Q₈	—	86	1	no	—
925	C₂×Q₈	—	86	2	no	—
926	C₂×Q₈	—	86	2	no	—
927	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
928	C₂×D₄	—	2	1	no	—
929	C₂×D₄	—	43	2	no	—
930	C₂×D₄	—	43	1	no	—
931	C₂×D₄	—	43	4	no	—
932	C₂×D₄	—	43	2	no	—
933	C₂×D₄	—	43	2	no	—
934	C₂×D₄	—	86	2	no	—
935	C₂×D₄	—	86	8	no	—
936	C₂×D₄	—	86	2	no	—
937	C₂×D₄	—	86	2	no	—
938	C₂×D₄	—	86	2	no	—
939	C₂×D₄	—	86	4	no	—
940	C₂×D₄	—	86	16	no	—
941	C₂×D₄	—	86	4	no	—
942	C₂×D₄	—	86	1	no	—
943	C₂×D₄	—	86	1	no	—
944	C₂×D₄	—	86	2	no	—
945	C₂×D₄	—	86	2	no	—
946	C₂×D₄	—	86	2	no	—
947	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	43	2	no	—
952	C₂²×C₄	—	43	2	no	—
953	C₂²×C₄	—	43	2	no	—
954	C₂²×C₄	—	86	2	no	—
955	C₂²×C₄	—	86	2	no	—
956	C₂²×C₄	—	86	2	no	—
957	C₂²×C₄	—	86	2	no	—
958	C₂²×C₄	—	86	2	no	—
959	C₂²×C₄	—	86	2	no	—
960	C₂²×C₄	—	86	2	no	—
961	C₂²×C₄	—	86	1	no	—
962	C₂²×C₄	—	86	1	no	—
963	C₂²×C₄	—	86	2	no	—
964	C₂²×C₄	—	86	2	no	—
965	C₂²×C₄	—	344	2	no	—
966	C₂²×C₄	—	344	4	no	—
967	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
968	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
969	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
970	Q₁₆	—	86	4	no	—
971	SD₁₆	—	86	4	no	—
972	SD₁₆	—	86	4	no	—
973	SD₁₆	—	86	4	no	—
974	SD₁₆	—	86	4	no	—
975	D₈	—	86	4	no	—
976	D₈	—	86	4	no	—
977	D₈	—	86	4	no	—
978	M₁₆	—	86	2	no	—
979	M₁₆	—	86	2	no	—
980	C₂×C₈	—	2	2	no	—
981	C₂×C₈	—	2	2	no	—
982	C₂×C₈	—	43	2	no	—
983	C₂×C₈	—	43	2	no	—
984	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
985	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
986	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
987	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	43	1	no	—
997	C₄⋊C₄	—	43	2	no	—
998	C₄⋊C₄	—	43	1	no	—
999	C₄⋊C₄	—	43	2	no	—
1000	C₄⋊C₄	—	43	2	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	2	no	—
1003	C₄⋊C₄	—	86	2	no	—
1004	C₄⋊C₄	—	86	2	no	—
1005	C₄⋊C₄	—	86	2	no	—
1006	C₄⋊C₄	—	86	2	no	—
1007	C₄⋊C₄	—	86	1	no	—
1008	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	1	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	43	2	no	—
1020	C₂²⋊C₄	—	43	2	no	—
1021	C₂²⋊C₄	—	43	2	no	—
1022	C₂²⋊C₄	—	86	2	no	—
1023	C₂²⋊C₄	—	86	2	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	—	86	2	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	2	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	2	no	—
1030	C₂²⋊C₄	—	86	2	no	—
1031	C₂²⋊C₄	—	86	2	no	—
1032	C₂²⋊C₄	—	86	2	no	—
1033	C₂²⋊C₄	—	86	2	no	—
1034	C₂²⋊C₄	—	86	2	no	—
1035	C₂²⋊C₄	—	86	2	no	—
1036	C₂²⋊C₄	—	86	2	no	—
1037	C₂²⋊C₄	—	86	2	no	—
1038	C₄²	—	2	1	no	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	43	2	no	—
1044	C₄²	—	43	2	no	—
1045	C₄²	—	43	2	no	—
1046	C₄²	—	86	2	no	—
1047	C₄²	—	86	2	no	—
1048	C₄²	—	86	2	no	—
1049	C₄²	—	86	2	no	—
1050	C₄²	D₄×D₄₃	1	1	yes	characteristic
1051	C₄²	D₄×D₄₃	1	1	yes	characteristic
1052	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1053	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1054	C₂³	—	2	1	no	—
1055	C₂³	—	43	2	no	—
1056	C₂³	—	86	8	no	—
1057	C₂³	—	86	4	no	—
1058	C₂³	—	86	2	no	—
1059	C₂³	—	86	2	no	—
1060	C₂³	—	344	1	no	—
1061	C₂³	—	344	1	no	—
1062	C₂³	—	344	1	no	—
1063	C₂³	—	344	1	no	—
1064	C₂³	—	344	2	no	—
1065	C₂³	—	344	2	no	—
1066	C₂³	—	172	2	no	—
1067	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1068	Q₈	—	2	1	no	—
1069	Q₈	—	8	1	no	—
1070	Q₈	—	8	1	no	—
1071	Q₈	—	86	2	no	—
1072	Q₈	—	86	2	no	—
1073	Q₈	—	86	2	no	—
1074	Q₈	—	172	2	no	—
1075	Q₈	C₂×#10621902	1	2	yes	—
1076	D₄	—	2	4	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	43	4	no	—
1079	D₄	—	86	8	no	—
1080	D₄	—	86	8	no	—
1081	D₄	—	86	4	no	—
1082	D₄	—	86	4	no	—
1083	D₄	—	86	2	no	—
1084	D₄	—	86	2	no	—
1085	D₄	—	86	2	no	—
1086	D₄	—	86	2	no	—
1087	D₄	—	344	2	no	—
1088	D₄	—	344	2	no	—
1089	D₄	—	172	2	no	—
1090	D₄	C₂×#10621902	1	2	yes	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	8	1	no	—
1103	C₂×C₄	—	43	2	no	—
1104	C₂×C₄	—	43	2	no	—
1105	C₂×C₄	—	43	2	no	—
1106	C₂×C₄	—	86	8	no	—
1107	C₂×C₄	—	86	2	no	—
1108	C₂×C₄	—	86	2	no	—
1109	C₂×C₄	—	86	2	no	—
1110	C₂×C₄	—	86	2	no	—
1111	C₂×C₄	—	344	2	no	—
1112	C₂×C₄	—	344	2	no	—
1113	C₂×C₄	—	344	2	no	—
1114	C₂×C₄	—	344	2	no	—
1115	C₂×C₄	—	344	2	no	—
1116	C₂×C₄	—	344	2	no	—
1117	C₂×C₄	—	344	2	no	—
1118	C₂×C₄	—	344	1	no	—
1119	C₂×C₄	—	172	2	no	—
1120	C₂×C₄	—	172	2	no	—
1121	C₂×C₄	—	172	4	no	—
1122	C₂×C₄	—	172	2	no	—
1123	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1124	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1125	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1126	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1127	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1128	C₂×C₄	#41×D₄₃	1	2	yes	—
1129	C₂×C₄	C₂×#10621902	1	2	yes	—
1130	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1131	C₈	—	2	1	no	—
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	86	2	no	—
1136	C₈	—	86	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	4	1	no	—
1142	C₂²	—	86	2	no	—
1143	C₂²	—	86	2	no	—
1144	C₂²	—	86	4	no	—
1145	C₂²	—	86	2	no	—
1146	C₂²	—	344	4	no	—
1147	C₂²	—	344	8	no	—
1148	C₂²	—	172	2	no	—
1149	C₂²	—	172	2	no	—
1150	C₂²	—	172	2	no	—
1151	C₂²	—	172	2	no	—
1152	C₂²	—	172	2	no	—
1153	C₂²	—	688	2	no	—
1154	C₂²	#14583412	1	2	yes	—
1155	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	2	no	—
1161	C₄	—	4	1	no	—
1162	C₄	—	4	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	86	2	no	—
1168	C₄	—	86	2	no	—
1169	C₄	—	86	2	no	—
1170	C₄	—	172	2	no	—
1171	C₄	—	172	2	no	—
1172	C₄	#14583412	1	2	yes	—
1173	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1174	C₄	C₂²×#10621902	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	344	2	no	—
1178	C₂	—	172	2	no	—
1179	C₂	—	172	4	no	—
1180	C₂	C₂×#14583412	1	1	yes	characteristic
1181	C₂	#19149364	1	1	yes	characteristic
1182	C₂	#19149372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3076	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19143866	C₂
hypercenter	#3076	D₄₃
hypocenter	C₄₃	#60592
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #19148493	C₂	semidirect
2. C₄×#13063371	C₂	semidirect
3. #19144879	C₂	semidirect
4. #19144864	C₂	semidirect
5. #19144786	C₂	semidirect
6. #19144784	C₂	semidirect
7. #19144738	C₂	semidirect
8. #19144711	C₂	semidirect
9. #19144647	C₂	semidirect
10. #19144620	C₂	semidirect
11. #19144567	C₂	semidirect
12. #19144556	C₂	semidirect
13. #19144388	C₂	semidirect
14. #19144089	C₂	semidirect
15. C₂×#14583115	C₂	semidirect
16. #19143875	C₂	semidirect
18. #19143453	C₂	semidirect
19. #19143446	C₂	semidirect
20. #19143441	C₂	semidirect
21. #19143430	C₂	semidirect
22. #19143260	C₂	semidirect
23. C₄₃×#3076	C₂	semidirect
35. #14583523	C₂²	semidirect
36. #14583523	C₂²	semidirect
39. #14583434	C₂²	semidirect
40. #14583434	C₂²	semidirect
41. C₂×#13063313	C₂²	semidirect
43. #14583381	C₂²	semidirect
46. #14583376	C₂²	semidirect
49. #14583373	C₂²	semidirect
51. #14583371	C₂²	semidirect
52. C₄×#10621902	C₂²	semidirect
58. C₄×D₄×D₄₃	C₂²	semidirect
59. #14583243	C₂²	semidirect
60. #14583242	C₂²	semidirect
61. #14583236	C₂²	semidirect
62. #14583231	C₂²	semidirect
63. #14583226	C₂²	semidirect
64. #14583225	C₂²	semidirect
65. #14583219	C₂²	semidirect
66. #14583214	C₂²	semidirect
67. #14583196	C₂²	semidirect
68. #14583196	C₂²	semidirect
69. #14583186	C₂²	semidirect
70. #14583176	C₂²	semidirect
71. #14583121	C₂²	semidirect
72. #14583121	C₂²	semidirect
73. #14583115	C₂²	semidirect
74. #14583115	C₂²	semidirect
75. #14583115	C₂²	semidirect
76. #14583115	C₂²	semidirect
77. #14583114	C₂²	semidirect
78. #14583114	C₂²	semidirect
79. #14583064	C₂²	semidirect
80. #14583064	C₂²	semidirect
81. #14583051	C₂²	semidirect
82. #14583051	C₂²	semidirect
87. #14583010	C₂²	semidirect
88. #14583010	C₂²	semidirect
89. #14583008	C₂²	semidirect
90. #14583003	C₂²	semidirect
91. #14583002	C₂²	semidirect
92. #14582998	C₂²	semidirect
93. #14582998	C₂²	semidirect
94. #14582996	C₂²	semidirect
95. #14582991	C₂²	semidirect
96. #14582990	C₂²	semidirect
97. #14582986	C₂²	semidirect
98. #14582986	C₂²	semidirect
99. #14582984	C₂²	semidirect
100. #14582981	C₂²	semidirect
101. #14582981	C₂²	semidirect
102. #14582979	C₂²	semidirect
103. #14582959	C₂²	semidirect
104. #14582959	C₂²	semidirect
105. #14582955	C₂²	semidirect
106. #14582951	C₂²	semidirect
107. #14582942	C₂²	semidirect
108. #14582942	C₂²	semidirect
109. #14582923	C₂²	semidirect
110. #14582907	C₂²	semidirect
113. #14582903	C₂²	semidirect
114. C₂×#13063250	C₂²	semidirect
115. C₂×#13063247	C₂²	semidirect
118. #14582854	C₂²	semidirect
119. #14582854	C₂²	semidirect
120. C₄₃×#533	C₂²	semidirect
122. C₄₃×#479	C₂²	semidirect
123. C₄₃×#479	C₂²	semidirect
124. C₄₃×#478	C₂²	semidirect
125. C₄₃×#478	C₂²	semidirect
126. C₄₃×#477	C₂²	semidirect
127. C₄₃×#476	C₂²	semidirect
128. C₄₃×#475	C₂²	semidirect
129. C₄₃×#474	C₂²	semidirect
130. C₄₃×#427	C₂²	semidirect
131. C₄₃×#427	C₂²	semidirect
132. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
597. #3076	D₄₃	semidirect
630. #533	C₂×D₄₃	semidirect
660. #479	C₂×D₄₃	semidirect
661. #479	C₂×D₄₃	semidirect
664. #478	C₂×D₄₃	semidirect
665. #478	C₂×D₄₃	semidirect
666. #477	C₂×D₄₃	semidirect
668. #476	C₂×D₄₃	semidirect
669. #475	C₂×D₄₃	semidirect
671. #474	C₂×D₄₃	semidirect
710. #427	C₂×D₄₃	semidirect
711. #427	C₂×D₄₃	semidirect
713. C₂×C₄⋊C₈	C₂×D₄₃	semidirect
726. C₄₃	#60592	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#19148493	2
C₄×#13063371	2
#19144879	2
#19144864	2
#19144786	2
#19144784	2
#19144738	2
#19144711	2
#19144647	2
#19144620	2
#19144567	2
#19144556	2
#19144388	2
#19144089	2
C₂×#14583115	2
#19143875	2
#19143866	2
#19143453	2
#19143446	2
#19143441	2
#19143430	2
#19143260	2
C₄₃×#3076	2
#60592	43