Subgroups — #25979057

Order 11008.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148610	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148558	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147593	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147411	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147315	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147009	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147009	C₂	1	2	yes	maximal, complemented
9	#19146879	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146838	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146783	C₂	1	2	yes	maximal, complemented
12	#19146633	C₂	1	2	yes	maximal, complemented
13	#19146307	C₂	1	2	yes	maximal, complemented
14	D₄×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145212	C₂	1	2	yes	maximal, complemented
16	#19145154	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144826	C₂	1	2	yes	maximal, complemented
18	#19144781	C₂	1	2	yes	maximal, complemented
19	#19144758	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144747	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143456	C₂	1	2	yes	maximal, complemented
22	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063347	C₂²	1	1	yes	characteristic
25	C₂²×#10621873	C₂²	1	2	yes	—
26	#14583634	C₂²	1	1	yes	characteristic
27	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
28	#14583622	C₂²	1	1	yes	characteristic, complemented
29	#14583620	—	2	1	no	—
30	#14583619	C₂²	1	1	yes	characteristic
31	#14583619	C₂²	1	2	yes	complemented
32	#14583616	—	2	2	no	—
33	#14583614	C₂²	1	2	yes	—
34	#14583614	C₂²	1	1	yes	characteristic
35	#14583613	—	2	1	no	—
36	#14583574	—	2	2	no	—
37	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
38	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
39	#14583559	—	2	1	no	—
40	#14583558	C₂²	1	2	yes	complemented
41	#14583546	—	2	1	no	—
42	#14583545	C₂²	1	2	yes	—
43	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
44	#14583520	C₂²	1	2	yes	—
45	#14583520	C₂²	1	2	yes	complemented
46	#14583517	—	2	2	no	—
47	#14583485	—	2	2	no	—
48	#14583456	C₂²	1	1	yes	characteristic, complemented
49	#14583455	—	2	1	no	—
50	#14583449	C₂²	1	1	yes	characteristic
51	#14583434	—	2	1	no	—
52	#14583428	—	2	1	no	—
53	#124×D₄₃	—	2	1	no	—
54	#14583376	C₂²	1	2	yes	complemented
55	#14583373	C₂²	1	2	yes	—
56	C₄×#10621898	C₂²	1	1	yes	characteristic
57	C₄×#10621898	C₂²	1	1	yes	characteristic, complemented
58	#14583297	C₂²	1	1	yes	characteristic, complemented
59	#14583297	C₂²	1	2	yes	complemented
60	#14583283	C₂²	1	2	yes	complemented
61	#14583272	C₂²	1	1	yes	characteristic
62	#14583259	C₂²	1	2	yes	complemented
63	#14583259	C₂²	1	2	yes	complemented
64	#14583250	C₂²	1	1	yes	characteristic, complemented
65	#14583246	C₂²	1	1	yes	characteristic
66	#14583241	C₂²	1	2	yes	complemented
67	#14583241	C₂²	1	2	yes	complemented
68	#14583241	C₂²	1	2	yes	complemented
69	#14583224	C₂²	1	2	yes	—
70	#14583224	C₂²	1	2	yes	complemented
71	#14583224	C₂²	1	2	yes	complemented
72	#14583195	C₂²	1	2	yes	complemented
73	#14583195	C₂²	1	1	yes	characteristic, complemented
74	#14583190	C₂²	1	1	yes	characteristic
75	#14583190	C₂²	1	2	yes	—
76	#14583185	C₂²	1	2	yes	complemented
77	#14583185	C₂²	1	1	yes	characteristic, complemented
78	#14583180	C₂²	1	1	yes	characteristic, complemented
79	#14583180	C₂²	1	2	yes	complemented
80	#14583157	C₂²	1	2	yes	complemented
81	#14583152	C₂²	1	2	yes	—
82	#14583128	C₂²	1	2	yes	—
83	#14583128	C₂²	1	2	yes	complemented
84	#14583128	C₂²	1	2	yes	complemented
85	#14583128	C₂²	1	2	yes	complemented
86	#14583122	C₂²	1	2	yes	complemented
87	#14583122	C₂²	1	2	yes	complemented
88	#14583115	C₂²	1	2	yes	—
89	#14583115	C₂²	1	2	yes	complemented
90	#14583110	C₂²	1	1	yes	characteristic, complemented
91	#14583105	C₂²	1	1	yes	characteristic
92	#14583100	C₂²	1	1	yes	characteristic
93	#14583095	C₂²	1	1	yes	characteristic
94	#14583063	C₂²	1	2	yes	—
95	#14583057	C₂²	1	2	yes	complemented
96	#14583052	C₂²	1	2	yes	—
97	#14583046	C₂²	1	2	yes	complemented
98	#14583040	C₂²	1	2	yes	—
99	#14583035	C₂²	1	2	yes	—
100	#14583012	C₂²	1	2	yes	complemented
101	#14583007	C₂²	1	2	yes	complemented
102	#14583001	C₂²	1	2	yes	—
103	#14583001	C₂²	1	2	yes	—
104	#14583001	C₂²	1	2	yes	complemented
105	#14583001	C₂²	1	2	yes	complemented
106	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
107	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
108	C₄×#10621873	C₂²	1	1	yes	characteristic
109	C₄×#10621873	C₂²	1	2	yes	—
110	C₄×#10621873	C₂²	1	1	yes	characteristic
111	C₄×#10621873	C₂²	1	2	yes	complemented
112	C₄×#10621873	C₂²	1	1	yes	characteristic, complemented
113	C₄×#10621873	C₂²	1	2	yes	complemented
114	C₄×#10621873	C₂²	1	2	yes	complemented
115	C₄×#10621873	C₂²	1	1	yes	characteristic, complemented
116	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
117	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
118	#14582937	C₂²	1	2	yes	complemented
119	#14582937	C₂²	1	1	yes	characteristic, complemented
120	#14582909	C₂²	1	2	yes	complemented
121	#14582905	C₂²	1	2	yes	—
122	#14582896	C₂²	1	1	yes	characteristic
123	#14582896	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#529	C₂²	1	1	yes	characteristic
125	C₄₃×#446	C₂²	1	1	yes	characteristic, complemented
126	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#436	C₂²	1	1	yes	characteristic
128	C₄₃×#435	C₂²	1	2	yes	complemented
129	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
130	C₈×D₄×C₄₃	C₂²	1	2	yes	complemented
131	C₄₃×#433	C₂²	1	2	yes	complemented
132	C₄₃×#432	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#405	C₂²	1	2	yes	complemented
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂×#10621898	C₂³	1	1	yes	characteristic
138	C₂²×Dic₈₆	C₂³	1	2	yes	—
139	C₂×Q₈×D₄₃	—	2	1	no	—
140	C₂²×D₁₇₂	C₂³	1	2	yes	—
141	C₂×D₄×D₄₃	—	2	1	no	—
142	#13063347	—	2	4	no	—
143	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₂	C₂³	1	2	yes	—
145	C₂×#10621873	—	2	8	no	—
146	C₂×#10621873	C₂³	1	2	yes	—
147	C₂×#10621873	C₂³	1	2	yes	—
148	C₂×#10621873	C₂³	1	2	yes	—
149	C₂×#10621873	C₂³	1	1	yes	characteristic
150	C₂×#10621873	C₂³	1	2	yes	—
151	C₂×#10621873	C₂³	1	1	yes	characteristic
152	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
153	C₂×D₃₄₄	C₂³	1	2	yes	—
154	#13063325	C₂³	1	1	yes	characteristic
155	#13063325	C₂³	1	2	yes	—
156	#13063325	C₂³	1	1	yes	characteristic
157	#13063325	C₂³	1	1	yes	characteristic
158	#13063325	C₂³	1	2	yes	—
159	#13063324	—	2	1	no	—
160	#13063324	—	2	1	no	—
161	#13063324	—	2	2	no	—
162	#13063322	C₂³	1	1	yes	characteristic
163	#13063320	—	2	2	no	—
164	#13063320	—	2	2	no	—
165	#13063320	—	2	2	no	—
166	#13063318	—	2	2	no	—
167	#13063318	—	2	2	no	—
168	#13063318	—	2	2	no	—
169	#13063317	—	2	1	no	—
170	#13063314	—	2	1	no	—
171	#13063313	—	2	1	no	—
172	#13063313	C₂³	1	2	yes	—
173	#13063313	C₂³	1	2	yes	—
174	#13063312	—	2	2	no	—
175	#13063312	—	2	1	no	—
176	#13063311	—	2	2	no	—
177	#13063311	—	2	2	no	—
178	#13063311	—	2	2	no	—
179	#13063311	—	2	2	no	—
180	#13063311	—	2	2	no	—
181	#13063311	—	2	2	no	—
182	#13063310	—	2	2	no	—
183	#13063310	—	2	2	no	—
184	#13063307	—	2	2	no	—
185	#13063307	—	2	2	no	—
186	#13063305	—	2	2	no	—
187	#13063305	—	2	1	no	—
188	#13063304	—	2	1	no	—
189	#13063304	C₂³	1	2	yes	—
190	#13063304	C₂³	1	2	yes	—
191	#13063304	C₂³	1	2	yes	—
192	#13063303	—	2	2	no	—
193	#13063303	—	2	2	no	—
194	#13063303	—	2	2	no	—
195	#13063302	—	2	2	no	—
196	#13063301	—	2	1	no	—
197	#13063300	—	2	1	no	—
198	#13063299	—	2	1	no	—
199	#13063299	C₂³	1	2	yes	—
200	#13063299	C₂³	1	2	yes	—
201	#13063299	C₂³	1	2	yes	—
202	#13063298	—	2	2	no	—
203	#13063297	—	2	2	no	—
204	#13063296	—	2	1	no	—
205	#13063296	—	2	2	no	—
206	#13063295	—	2	2	no	—
207	#13063293	—	2	2	no	—
208	Q₈×Dic₄₃	—	2	1	no	—
209	C₄×Dic₈₆	—	2	1	no	—
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
212	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
213	C₄×Dic₈₆	C₂³	1	2	yes	—
214	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
215	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
216	C₄×Dic₈₆	C₂³	1	2	yes	—
217	#13063290	—	2	1	no	—
218	#13063290	—	2	2	no	—
219	#13063290	—	2	2	no	—
220	#13063290	—	2	2	no	—
221	C₄×D₁₇₂	—	2	1	no	—
222	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
223	C₄×D₁₇₂	C₂³	1	2	yes	—
224	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
225	C₄×D₁₇₂	C₂³	1	2	yes	—
226	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
227	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
228	C₄×D₁₇₂	C₂³	1	2	yes	—
229	D₄×Dic₄₃	—	2	1	no	—
230	#13063287	—	2	2	no	—
231	#13063287	—	2	2	no	—
232	#13063287	—	2	1	no	—
233	C₄×C₂²⋊D₄₃	—	2	1	no	—
234	C₄×C₂²⋊D₄₃	—	2	1	no	—
235	C₄×C₂²⋊D₄₃	—	2	1	no	—
236	C₄×C₂²⋊D₄₃	—	2	1	no	—
237	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
238	#13063284	—	2	1	no	—
239	#13063284	C₂³	1	1	yes	characteristic
240	#13063284	C₂³	1	2	yes	—
241	#13063284	C₂³	1	2	yes	—
242	#13063284	C₂³	1	1	yes	characteristic
243	#13063283	—	2	2	no	—
244	#13063283	—	2	1	no	—
245	#13063283	—	2	1	no	—
246	#13063282	—	2	1	no	—
247	#13063282	—	2	1	no	—
248	#13063281	—	2	2	no	—
249	#13063281	—	2	2	no	—
250	C₂²⋊C₄×D₄₃	—	2	2	no	—
251	C₂²⋊C₄×D₄₃	—	2	2	no	—
252	C₂²⋊C₄×D₄₃	—	2	2	no	—
253	C₄²×D₄₃	—	2	1	no	—
254	C₄²×D₄₃	—	2	1	no	—
255	#13063259	C₂³	1	1	yes	characteristic
256	#13063259	C₂³	1	2	yes	—
257	#13063259	C₂³	1	2	yes	—
258	#13063259	C₂³	1	1	yes	characteristic
259	#13063257	C₂³	1	1	yes	characteristic
260	#13063257	C₂³	1	2	yes	—
261	#13063257	C₂³	1	2	yes	—
262	#13063257	C₂³	1	2	yes	—
263	#13063257	C₂³	1	2	yes	—
264	#13063257	C₂³	1	1	yes	characteristic
265	#13063250	C₂³	1	1	yes	characteristic
266	#13063250	C₂³	1	2	yes	—
267	#13063250	C₂³	1	2	yes	—
268	#13063250	C₂³	1	2	yes	—
269	#13063250	C₂³	1	2	yes	—
270	#13063250	C₂³	1	2	yes	—
271	#13063250	C₂³	1	1	yes	characteristic
272	#13063250	C₂³	1	2	yes	—
273	#13063250	C₂³	1	1	yes	characteristic
274	#13063250	C₂³	1	1	yes	characteristic
275	#13063247	C₂³	1	2	yes	—
276	#13063247	C₂³	1	1	yes	characteristic
277	#13063247	C₂³	1	2	yes	—
278	#13063247	C₂³	1	2	yes	—
279	#13063247	C₂³	1	2	yes	—
280	#13063247	C₂³	1	1	yes	characteristic
281	#13063247	C₂³	1	2	yes	—
282	#13063247	C₂³	1	2	yes	—
283	#13063247	C₂³	1	1	yes	characteristic
284	#13063247	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
286	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
287	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
289	#126×C₄₃	D₄	1	2	yes	—
290	#125×C₄₃	D₄	1	1	yes	characteristic
291	#124×C₄₃	D₄	1	1	yes	characteristic
292	#123×C₄₃	D₄	1	2	yes	—
293	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
294	#121×C₄₃	D₄	1	1	yes	characteristic
295	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₄₃	C₂³	1	2	yes	—
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	C₂³	1	2	yes	—
299	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
303	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
304	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
306	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
307	#97×C₄₃	C₂³	1	2	yes	—
308	#97×C₄₃	C₂³	1	2	yes	—
309	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	2	yes	—
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	2	no	—
315	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
316	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
318	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
322	C₂×C₂²⋊D₄₃	—	2	1	no	—
323	C₂×C₂²⋊D₄₃	—	2	1	no	—
324	C₂×C₂²⋊D₄₃	—	2	2	no	—
325	C₂×C₂²⋊D₄₃	—	2	2	no	—
326	C₂×C₂²⋊D₄₃	—	2	2	no	—
327	C₂²×Dic₄₃	—	2	2	no	—
328	Q₈×D₄₃	—	8	2	no	—
329	D₄×D₄₃	—	8	2	no	—
330	#10621898	—	2	2	no	—
331	#10621898	—	2	2	no	—
332	#10621898	—	4	1	no	—
333	#10621898	—	4	1	no	—
334	#10621898	—	8	2	no	—
335	C₂×D₁₇₂	—	2	2	no	—
336	C₂×D₁₇₂	—	2	1	no	—
337	C₂×D₁₇₂	—	2	1	no	—
338	C₂×D₁₇₂	—	2	4	no	—
339	C₂×D₁₇₂	—	4	2	no	—
340	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
341	C₂×D₁₇₂	C₂⁴	1	2	yes	—
342	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
343	C₂×C₄×D₄₃	—	2	1	no	—
344	C₂×C₄×D₄₃	—	2	1	no	—
345	C₂×C₄×D₄₃	—	2	1	no	—
346	C₂×C₄×D₄₃	—	2	1	no	—
347	C₂×C₄×D₄₃	—	2	1	no	—
348	C₂×C₄×D₄₃	—	2	1	no	—
349	C₂×C₄×D₄₃	—	2	2	no	—
350	C₂×C₄×D₄₃	—	2	2	no	—
351	C₂×C₄×D₄₃	—	2	2	no	—
352	C₂×Dic₈₆	—	2	4	no	—
353	C₂×Dic₈₆	—	2	2	no	—
354	C₂×Dic₈₆	—	2	1	no	—
355	C₂×Dic₈₆	—	2	2	no	—
356	C₂×Dic₈₆	—	2	1	no	—
357	C₂×Dic₈₆	—	2	2	no	—
358	C₂×Dic₈₆	—	4	2	no	—
359	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
360	C₂×Dic₈₆	C₂⁴	1	2	yes	—
361	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
362	M₁₆×C₄₃	—	4	2	no	—
363	C₂×C₈×C₄₃	—	2	4	no	—
364	C₂×C₈×C₄₃	—	2	2	no	—
365	C₂×C₈×C₄₃	—	4	1	no	—
366	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
370	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
371	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
378	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
380	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
381	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
382	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
383	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
384	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
385	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₄²×C₄₃	C₂⁴	1	2	yes	—
388	C₂²⋊Dic₄₃	—	2	2	no	—
389	C₂²⋊Dic₄₃	—	2	2	no	—
390	C₂²⋊Dic₄₃	—	2	2	no	—
391	C₂²⋊Dic₄₃	—	2	2	no	—
392	C₂²⋊Dic₄₃	—	2	1	no	—
393	C₂²⋊Dic₄₃	—	2	1	no	—
394	C₂²⋊Dic₄₃	—	2	2	no	—
395	(C₂×D₄₃)⋊C₄	—	2	1	no	—
396	(C₂×D₄₃)⋊C₄	—	2	2	no	—
397	(C₂×D₄₃)⋊C₄	—	2	2	no	—
398	(C₂×D₄₃)⋊C₄	—	2	2	no	—
399	(C₂×D₄₃)⋊C₄	—	2	2	no	—
400	(C₂×D₄₃)⋊C₄	—	2	2	no	—
401	(C₂×D₄₃)⋊C₄	—	2	1	no	—
402	(C₂×D₄₃)⋊C₄	—	2	1	no	—
403	(C₂×D₄₃)⋊C₄	—	2	1	no	—
404	(C₂×D₄₃)⋊C₄	—	2	2	no	—
405	(C₂×D₄₃)⋊C₄	—	2	2	no	—
406	(C₂×D₄₃)⋊C₄	—	2	2	no	—
407	(C₂×D₄₃)⋊C₄	—	2	2	no	—
408	(C₂×D₄₃)⋊C₄	—	2	2	no	—
409	C₄⋊Dic₄₃	—	2	1	no	—
410	C₄⋊Dic₄₃	—	2	1	no	—
411	C₄⋊Dic₄₃	—	2	2	no	—
412	C₄⋊Dic₄₃	—	2	1	no	—
413	C₄⋊Dic₄₃	—	2	1	no	—
414	C₄⋊Dic₄₃	—	2	2	no	—
415	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
417	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
419	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
421	Dic₄₃⋊C₄	—	2	1	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	—	2	1	no	—
426	Dic₄₃⋊C₄	—	2	1	no	—
427	Dic₄₃⋊C₄	—	2	1	no	—
428	Dic₄₃⋊C₄	—	2	2	no	—
429	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	C₄×Dic₄₃	—	2	1	no	—
432	C₄×Dic₄₃	—	2	1	no	—
433	C₄×Dic₄₃	—	2	1	no	—
434	C₄×Dic₄₃	—	2	1	no	—
435	C₄×Dic₄₃	—	2	1	no	—
436	C₄×Dic₄₃	—	2	1	no	—
437	C₄×Dic₄₃	—	2	2	no	—
438	C₄×Dic₄₃	—	2	2	no	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	—	2	2	no	—
441	C₄×Dic₄₃	—	2	2	no	—
442	Dic₁₇₂	—	2	2	no	—
443	Dic₁₇₂	—	4	2	no	—
444	D₃₄₄	—	2	2	no	—
445	D₃₄₄	—	4	2	no	—
446	#10621873	—	2	4	no	—
447	#10621873	—	2	4	no	—
448	#10621873	—	2	4	no	—
449	#10621873	—	2	2	no	—
450	#10621873	—	4	2	no	—
451	#10621873	#41	1	4	yes	complemented
452	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
453	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
454	C₂²×D₄₃	—	2	1	no	—
455	C₂²×D₄₃	—	2	1	no	—
456	C₂²×D₄₃	—	2	2	no	—
457	C₂²×D₄₃	—	4	4	no	—
458	C₂²×D₄₃	—	8	2	no	—
459	C₂²×D₄₃	—	8	2	no	—
460	Q₈×C₄₃	—	2	2	no	—
461	D₄×C₄₃	—	2	2	no	—
462	D₄×C₄₃	—	4	2	no	—
463	C₂×C₄×C₄₃	—	2	2	no	—
464	C₂×C₄×C₄₃	—	2	2	no	—
465	C₂×C₄×C₄₃	—	2	1	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	2	no	—
468	C₂×C₄×C₄₃	—	4	1	no	—
469	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
478	C₂²⋊D₄₃	—	4	2	no	—
479	C₂²⋊D₄₃	—	4	2	no	—
480	C₂²⋊D₄₃	—	8	2	no	—
481	C₂²⋊D₄₃	—	8	2	no	—
482	C₂²⋊D₄₃	—	8	2	no	—
483	C₂×Dic₄₃	—	2	1	no	—
484	C₂×Dic₄₃	—	2	1	no	—
485	C₂×Dic₄₃	—	2	1	no	—
486	C₂×Dic₄₃	—	2	2	no	—
487	C₂×Dic₄₃	—	2	2	no	—
488	C₂×Dic₄₃	—	2	1	no	—
489	C₂×Dic₄₃	—	2	1	no	—
490	C₂×Dic₄₃	—	2	1	no	—
491	C₂×Dic₄₃	—	2	2	no	—
492	C₂×Dic₄₃	—	4	4	no	—
493	D₁₇₂	—	2	2	no	—
494	D₁₇₂	—	2	1	no	—
495	D₁₇₂	—	2	1	no	—
496	D₁₇₂	—	2	2	no	—
497	D₁₇₂	—	2	1	no	—
498	D₁₇₂	—	4	4	no	—
499	D₁₇₂	—	4	2	no	—
500	D₁₇₂	—	8	1	no	—
501	D₁₇₂	C₂×#41	1	2	yes	—
502	C₄×D₄₃	—	4	2	no	—
503	C₄×D₄₃	—	4	2	no	—
504	C₄×D₄₃	—	4	2	no	—
505	C₄×D₄₃	—	4	2	no	—
506	C₄×D₄₃	—	8	1	no	—
507	C₄×D₄₃	—	8	2	no	—
508	C₄×D₄₃	—	8	1	no	—
509	C₄×D₄₃	—	8	2	no	—
510	C₄×D₄₃	—	8	2	no	—
511	Dic₈₆	—	2	1	no	—
512	Dic₈₆	—	2	2	no	—
513	Dic₈₆	—	2	1	no	—
514	Dic₈₆	—	2	2	no	—
515	Dic₈₆	—	2	1	no	—
516	Dic₈₆	—	4	4	no	—
517	Dic₈₆	—	4	2	no	—
518	Dic₈₆	—	8	2	no	—
519	Dic₈₆	—	8	1	no	—
520	Dic₈₆	—	8	2	no	—
521	Dic₈₆	C₂×#41	1	2	yes	—
522	C₈×C₄₃	—	2	2	no	—
523	C₈×C₄₃	—	2	1	no	—
524	C₈×C₄₃	—	2	1	no	—
525	C₈×C₄₃	—	2	2	no	—
526	C₈×C₄₃	—	2	1	no	—
527	C₈×C₄₃	C₂×#41	1	2	yes	—
528	#61474	—	43	1	no	maximal, Sylow
529	C₂²×C₄₃	—	2	2	no	—
530	C₂²×C₄₃	—	2	1	no	—
531	C₂²×C₄₃	—	2	2	no	—
532	C₂²×C₄₃	—	2	1	no	—
533	C₂²×C₄₃	—	2	2	no	—
534	C₂²×C₄₃	—	2	1	no	—
535	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
536	C₂×D₄₃	—	2	2	no	—
537	C₂×D₄₃	—	4	1	no	—
538	C₂×D₄₃	—	4	1	no	—
539	C₂×D₄₃	—	4	2	no	—
540	C₂×D₄₃	—	4	1	no	—
541	C₂×D₄₃	—	4	2	no	—
542	C₂×D₄₃	—	4	1	no	—
543	C₂×D₄₃	—	4	2	no	—
544	C₂×D₄₃	—	4	1	no	—
545	C₂×D₄₃	—	16	4	no	—
546	C₄×C₄₃	—	2	2	no	—
547	C₄×C₄₃	—	2	1	no	—
548	C₄×C₄₃	—	2	1	no	—
549	C₄×C₄₃	—	2	2	no	—
550	C₄×C₄₃	—	2	1	no	—
551	C₄×C₄₃	—	2	2	no	—
552	C₄×C₄₃	—	2	1	no	—
553	C₄×C₄₃	#577	1	2	yes	—
554	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
555	C₄×C₄₃	#585	1	1	yes	characteristic
556	Dic₄₃	—	2	2	no	—
557	Dic₄₃	—	4	1	no	—
558	Dic₄₃	—	4	2	no	—
559	Dic₄₃	—	4	1	no	—
560	Dic₄₃	—	4	2	no	—
561	Dic₄₃	—	4	1	no	—
562	Dic₄₃	—	4	2	no	—
563	Dic₄₃	—	4	1	no	—
564	Dic₄₃	—	4	1	no	—
565	#3518	—	43	1	no	—
566	#3514	—	43	1	no	—
567	#3394	—	43	1	no	—
568	Q₈×SD₁₆	—	43	1	no	—
569	#3375	—	43	1	no	—
570	#3367	—	43	1	no	—
571	#3340	—	43	1	no	—
572	#3340	—	43	2	no	—
573	#3328	—	43	1	no	—
574	#3325	—	43	1	no	—
575	#3321	—	43	2	no	—
576	#3311	—	43	2	no	—
577	#3282	—	43	2	no	—
578	D₄×SD₁₆	—	43	1	no	—
579	#3173	—	43	2	no	—
580	#3167	—	43	1	no	—
581	#3121	—	43	2	no	—
582	#3118	—	43	2	no	—
583	#3116	—	43	1	no	—
584	#3115	—	43	1	no	—
585	#2966	D₄₃	1	1	yes	characteristic, complemented
586	#2949	—	43	2	no	—
587	C₄×#135	—	43	1	no	—
588	C₂×C₄₃	—	4	2	no	—
589	C₂×C₄₃	—	4	1	no	—
590	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
591	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
592	C₂×C₄₃	#3584	1	1	yes	characteristic
593	D₄₃	—	4	2	no	—
594	D₄₃	—	8	1	no	—
595	D₄₃	—	8	2	no	—
596	C₂×#135	—	43	1	no	—
597	C₂²×SD₁₆	—	43	2	no	—
598	#559	—	43	1	no	—
599	Q₈²	—	43	1	no	—
600	#556	—	43	1	no	—
601	#556	—	43	2	no	—
602	#556	—	43	1	no	—
603	#556	—	86	2	no	—
604	#556	—	86	1	no	—
605	#555	—	43	2	no	—
606	#555	—	43	1	no	—
607	#555	—	86	1	no	—
608	#551	—	86	2	no	—
609	D₄×Q₈	—	43	1	no	—
610	D₄×Q₈	—	43	1	no	—
611	#548	—	43	2	no	—
612	#548	—	86	1	no	—
613	#546	—	43	2	no	—
614	#546	—	86	1	no	—
615	D₄²	—	43	1	no	—
616	#542	—	43	2	no	—
617	#542	—	43	2	no	—
618	#542	—	86	2	no	—
619	#538	—	86	2	no	—
620	#533	—	43	1	no	—
621	#533	—	86	1	no	—
622	#532	—	43	1	no	—
623	#529	—	86	1	no	—
624	#529	—	86	1	no	—
625	#529	C₂×D₄₃	1	1	yes	characteristic
626	C₂×#124	—	86	1	no	—
627	#519	—	43	2	no	—
628	#518	—	43	2	no	—
629	C₄×#41	—	43	1	no	—
630	C₄×#41	—	43	1	no	—
631	#498	—	43	1	no	—
632	#498	—	43	2	no	—
633	#495	—	43	2	no	—
634	#492	—	43	1	no	—
635	#489	—	43	2	no	—
636	#489	—	43	2	no	—
637	#487	—	43	1	no	—
638	#486	—	43	1	no	—
639	#485	—	43	2	no	—
640	#485	—	43	2	no	—
641	#485	—	43	2	no	—
642	#482	—	43	2	no	—
643	#482	—	43	2	no	—
644	#482	—	43	2	no	—
645	#477	—	43	2	no	—
646	#477	—	43	1	no	—
647	#476	—	43	1	no	—
648	#476	—	43	2	no	—
649	#475	—	43	1	no	—
650	#475	—	43	2	no	—
651	#474	—	43	1	no	—
652	#474	—	43	2	no	—
653	#470	—	43	2	no	—
654	#469	—	43	2	no	—
655	#465	—	43	2	no	—
656	#465	—	43	2	no	—
657	#465	—	43	2	no	—
658	#465	—	43	2	no	—
659	#464	—	43	2	no	—
660	#464	—	43	2	no	—
661	#463	—	43	2	no	—
662	#463	—	43	2	no	—
663	#462	—	43	1	no	—
664	#461	—	43	1	no	—
665	#460	—	43	1	no	—
666	#459	—	43	1	no	—
667	#452	—	43	2	no	—
668	#451	—	43	2	no	—
669	#450	—	43	2	no	—
670	#449	—	43	2	no	—
671	#448	—	43	2	no	—
672	#447	—	43	2	no	—
673	#446	C₂×D₄₃	1	1	yes	characteristic, complemented
674	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
675	#442	—	43	2	no	—
676	#441	—	43	2	no	—
677	#440	—	43	2	no	—
678	#440	—	43	2	no	—
679	#440	—	43	2	no	—
680	#440	—	43	2	no	—
681	C₄×Q₁₆	—	43	1	no	—
682	C₄×Q₁₆	—	43	1	no	—
683	C₄×SD₁₆	—	43	1	no	—
684	C₄×SD₁₆	—	43	2	no	—
685	C₄×SD₁₆	—	43	2	no	—
686	C₄×SD₁₆	—	43	1	no	—
687	C₄×SD₁₆	—	43	2	no	—
688	C₄×SD₁₆	—	43	2	no	—
689	C₄×SD₁₆	—	43	1	no	—
690	C₄×SD₁₆	—	43	1	no	—
691	C₄×D₈	—	43	1	no	—
692	C₄×D₈	—	43	1	no	—
693	#436	C₂×D₄₃	1	1	yes	characteristic
694	#435	C₂×D₄₃	1	2	yes	complemented
695	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
696	C₈×D₄	C₂×D₄₃	1	2	yes	complemented
697	#433	C₂×D₄₃	1	2	yes	complemented
698	#432	C₂×D₄₃	1	1	yes	characteristic, complemented
699	#427	—	43	1	no	—
700	#427	—	43	2	no	—
701	#419	—	43	2	no	—
702	#418	—	43	2	no	—
703	#416	—	43	1	no	—
704	#416	—	43	1	no	—
705	#405	C₂×D₄₃	1	2	yes	complemented
706	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
707	C₄₃	#61474	1	1	yes	characteristic, complemented, Sylow
708	C₂×#41	—	43	1	no	—
709	C₂×#41	—	43	1	no	—
710	C₂×#41	—	86	1	no	—
711	C₂²×Q₈	—	43	2	no	—
712	C₂²×Q₈	—	86	1	no	—
713	C₂²×D₄	—	43	2	no	—
714	C₂²×D₄	—	86	1	no	—
715	#135	—	86	4	no	—
716	C₂×Q₁₆	—	43	1	no	—
717	C₂×Q₁₆	—	43	2	no	—
718	C₂×SD₁₆	—	43	1	no	—
719	C₂×SD₁₆	—	43	2	no	—
720	C₂×SD₁₆	—	43	2	no	—
721	C₂×SD₁₆	—	43	2	no	—
722	C₂×SD₁₆	—	43	1	no	—
723	C₂×SD₁₆	—	43	2	no	—
724	C₂×SD₁₆	—	86	8	no	—
725	C₂×D₈	—	43	1	no	—
726	C₂×D₈	—	43	2	no	—
727	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
728	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
729	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
730	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
731	C₄⋊Q₈	—	43	1	no	—
732	C₄⋊Q₈	—	43	1	no	—
733	C₄⋊Q₈	—	43	2	no	—
734	C₄⋊Q₈	—	43	2	no	—
735	C₄⋊Q₈	—	43	1	no	—
736	C₄⋊Q₈	—	86	1	no	—
737	C₄⋊Q₈	—	86	1	no	—
738	C₄⋊Q₈	—	86	2	no	—
739	#127	—	43	1	no	—
740	#126	—	86	2	no	—
741	#126	—	86	2	no	—
742	#126	—	86	2	no	—
743	#126	—	86	2	no	—
744	#126	—	86	2	no	—
745	#126	—	86	2	no	—
746	#126	D₁₇₂	1	2	yes	—
747	#125	—	86	1	no	—
748	#125	D₁₇₂	1	1	yes	characteristic
749	#124	—	43	2	no	—
750	#124	—	43	2	no	—
751	#124	—	86	1	no	—
752	#124	—	86	1	no	—
753	#124	—	86	2	no	—
754	#124	—	86	2	no	—
755	#124	—	86	2	no	—
756	#124	—	86	2	no	—
757	#124	—	86	2	no	—
758	#124	—	86	2	no	—
759	#124	—	86	2	no	—
760	#124	—	86	1	no	—
761	#124	D₁₇₂	1	1	yes	characteristic
762	#123	—	86	2	no	—
763	#123	—	86	2	no	—
764	#123	—	86	2	no	—
765	#123	—	86	2	no	—
766	#123	D₁₇₂	1	2	yes	—
767	C₂²⋊Q₈	—	43	2	no	—
768	C₂²⋊Q₈	—	43	2	no	—
769	C₂²⋊Q₈	—	43	2	no	—
770	C₂²⋊Q₈	—	86	1	no	—
771	C₂²⋊Q₈	—	86	1	no	—
772	C₂²⋊Q₈	—	86	1	no	—
773	C₂²⋊Q₈	—	86	2	no	—
774	C₂²⋊Q₈	—	86	2	no	—
775	C₂²⋊Q₈	—	86	2	no	—
776	C₂²⋊Q₈	—	86	2	no	—
777	C₂²⋊Q₈	—	86	2	no	—
778	C₂²⋊Q₈	D₁₇₂	1	1	yes	characteristic
779	#121	—	43	2	no	—
780	#121	—	43	2	no	—
781	#121	—	43	2	no	—
782	#121	—	86	1	no	—
783	#121	—	86	2	no	—
784	#121	—	86	2	no	—
785	#121	—	86	1	no	—
786	#121	—	86	1	no	—
787	#121	—	86	2	no	—
788	#121	D₁₇₂	1	1	yes	characteristic
789	#120	—	86	2	no	—
790	#120	—	86	2	no	—
791	C₄×Q₈	—	43	1	no	—
792	C₄×Q₈	—	43	1	no	—
793	C₄×Q₈	—	43	1	no	—
794	C₄×Q₈	—	43	1	no	—
795	C₄×Q₈	—	43	2	no	—
796	C₄×Q₈	—	43	2	no	—
797	C₄×Q₈	—	43	2	no	—
798	C₄×Q₈	—	86	1	no	—
799	C₄×Q₈	—	86	2	no	—
800	C₄×Q₈	—	86	2	no	—
801	C₄×Q₈	—	86	1	no	—
802	C₄×Q₈	—	86	2	no	—
803	C₄×Q₈	—	86	1	no	—
804	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
805	C₄×D₄	—	43	1	no	—
806	C₄×D₄	—	43	1	no	—
807	C₄×D₄	—	43	1	no	—
808	C₄×D₄	—	43	1	no	—
809	C₄×D₄	—	43	2	no	—
810	C₄×D₄	—	43	2	no	—
811	C₄×D₄	—	43	2	no	—
812	C₄×D₄	—	86	1	no	—
813	C₄×D₄	—	86	1	no	—
814	C₄×D₄	—	86	1	no	—
815	C₄×D₄	—	86	1	no	—
816	C₄×D₄	—	86	1	no	—
817	C₄×D₄	—	86	2	no	—
818	C₄×D₄	—	86	2	no	—
819	C₄×D₄	—	86	1	no	—
820	C₄×D₄	—	86	2	no	—
821	C₄×D₄	—	86	1	no	—
822	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₄₃	1	2	yes	—
824	#117	—	43	1	no	—
825	#117	—	43	1	no	—
826	#117	—	43	2	no	—
827	#117	—	43	2	no	—
828	#117	—	86	1	no	—
829	#117	—	86	2	no	—
830	#117	—	86	1	no	—
831	#117	—	86	1	no	—
832	#117	—	86	2	no	—
833	#117	—	86	2	no	—
834	#117	—	86	1	no	—
835	#117	—	86	1	no	—
836	#117	C₂²×D₄₃	1	2	yes	—
837	C₂×C₂²⋊C₄	—	86	2	no	—
838	C₂×C₂²⋊C₄	—	86	2	no	—
839	C₂×C₂²⋊C₄	—	86	2	no	—
840	C₂×C₄²	—	86	1	no	—
841	C₂×C₄²	—	86	1	no	—
842	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
843	#107	—	43	1	no	—
844	#107	—	43	1	no	—
845	#107	—	43	2	no	—
846	#107	—	43	2	no	—
847	#106	—	43	1	no	—
848	#106	—	43	1	no	—
849	#106	—	43	2	no	—
850	#106	—	43	2	no	—
851	#106	—	43	2	no	—
852	#106	—	43	2	no	—
853	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
854	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
855	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
856	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
857	#103	—	43	1	no	—
858	#103	—	43	1	no	—
859	#103	—	43	1	no	—
860	#103	—	43	1	no	—
861	#103	—	43	2	no	—
862	#103	—	43	2	no	—
863	#103	—	43	2	no	—
864	#103	—	43	2	no	—
865	#103	—	43	2	no	—
866	#103	—	43	2	no	—
867	#102	—	43	1	no	—
868	#102	—	43	1	no	—
869	#102	—	43	1	no	—
870	#102	—	43	1	no	—
871	#102	—	43	2	no	—
872	#102	—	43	2	no	—
873	#102	—	43	2	no	—
874	#102	—	43	2	no	—
875	#102	—	43	2	no	—
876	#102	—	43	2	no	—
877	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
878	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
879	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
880	#97	C₂²×D₄₃	1	2	yes	—
881	#97	C₂²×D₄₃	1	2	yes	—
882	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
883	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₄₃	1	2	yes	—
887	C₂⁴	—	86	2	no	—
888	#41	—	86	2	no	—
889	#41	—	86	2	no	—
890	#41	—	344	2	no	—
891	#41	—	172	1	no	—
892	#41	—	172	1	no	—
893	C₂×Q₈	—	43	1	no	—
894	C₂×Q₈	—	43	1	no	—
895	C₂×Q₈	—	43	2	no	—
896	C₂×Q₈	—	86	4	no	—
897	C₂×Q₈	—	86	1	no	—
898	C₂×Q₈	—	86	2	no	—
899	C₂×Q₈	—	86	2	no	—
900	C₂×Q₈	—	86	2	no	—
901	C₂×Q₈	—	86	1	no	—
902	C₂×Q₈	—	344	2	no	—
903	C₂×Q₈	—	172	2	no	—
904	C₂×Q₈	C₂×D₁₇₂	1	1	yes	characteristic
905	C₂×D₄	—	43	1	no	—
906	C₂×D₄	—	43	1	no	—
907	C₂×D₄	—	43	2	no	—
908	C₂×D₄	—	86	4	no	—
909	C₂×D₄	—	86	2	no	—
910	C₂×D₄	—	86	2	no	—
911	C₂×D₄	—	86	2	no	—
912	C₂×D₄	—	86	1	no	—
913	C₂×D₄	—	86	1	no	—
914	C₂×D₄	—	86	1	no	—
915	C₂×D₄	—	86	2	no	—
916	C₂×D₄	—	86	1	no	—
917	C₂×D₄	—	344	2	no	—
918	C₂×D₄	—	172	2	no	—
919	C₂×D₄	C₂×D₁₇₂	1	1	yes	characteristic
920	C₂×D₄	C₂×D₁₇₂	1	2	yes	—
921	C₂²×C₄	—	86	2	no	—
922	C₂²×C₄	—	86	1	no	—
923	C₂²×C₄	—	86	1	no	—
924	C₂²×C₄	—	86	2	no	—
925	C₂²×C₄	—	86	2	no	—
926	C₂²×C₄	—	86	2	no	—
927	C₂²×C₄	—	86	1	no	—
928	C₂²×C₄	—	86	1	no	—
929	C₂²×C₄	—	86	1	no	—
930	C₂²×C₄	—	86	1	no	—
931	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
932	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
933	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
935	Q₁₆	—	86	2	no	—
936	Q₁₆	—	172	2	no	—
937	SD₁₆	—	43	4	no	—
938	SD₁₆	—	86	4	no	—
939	SD₁₆	—	86	4	no	—
940	SD₁₆	—	86	4	no	—
941	SD₁₆	—	86	2	no	—
942	SD₁₆	—	172	2	no	—
943	D₈	—	86	2	no	—
944	D₈	—	172	2	no	—
945	M₁₆	—	4	2	no	—
946	C₂×C₈	—	2	4	no	—
947	C₂×C₈	—	2	2	no	—
948	C₂×C₈	—	4	1	no	—
949	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
950	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
951	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₄₃	1	2	yes	—
953	C₂×C₈	C₂³×D₄₃	1	2	yes	—
954	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
955	C₄⋊C₄	—	43	1	no	—
956	C₄⋊C₄	—	43	2	no	—
957	C₄⋊C₄	—	43	1	no	—
958	C₄⋊C₄	—	43	2	no	—
959	C₄⋊C₄	—	43	1	no	—
960	C₄⋊C₄	—	43	1	no	—
961	C₄⋊C₄	—	86	1	no	—
962	C₄⋊C₄	—	86	1	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	—	86	1	no	—
966	C₄⋊C₄	—	86	1	no	—
967	C₄⋊C₄	—	86	2	no	—
968	C₄⋊C₄	—	86	2	no	—
969	C₄⋊C₄	—	86	2	no	—
970	C₄⋊C₄	—	86	2	no	—
971	C₄⋊C₄	—	86	2	no	—
972	C₄⋊C₄	—	86	1	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	—	86	2	no	—
975	C₄⋊C₄	—	86	1	no	—
976	C₄⋊C₄	—	86	2	no	—
977	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
978	C₄⋊C₄	C₂×D₁₇₂	1	1	yes	characteristic
979	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
980	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
981	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
982	C₄⋊C₄	C₂×D₁₇₂	1	2	yes	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	1	no	—
987	C₂²⋊C₄	—	86	1	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	—	86	1	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	2	no	—
994	C₂²⋊C₄	—	86	2	no	—
995	C₂²⋊C₄	—	86	2	no	—
996	C₂²⋊C₄	—	86	1	no	—
997	C₂²⋊C₄	—	86	1	no	—
998	C₂²⋊C₄	—	86	1	no	—
999	C₂²⋊C₄	—	86	2	no	—
1000	C₂²⋊C₄	—	86	2	no	—
1001	C₂²⋊C₄	—	86	2	no	—
1002	C₂²⋊C₄	—	86	2	no	—
1003	C₂²⋊C₄	—	86	2	no	—
1004	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
1005	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
1006	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
1007	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
1008	C₂²⋊C₄	C₂×D₁₇₂	1	2	yes	—
1009	C₄²	—	86	1	no	—
1010	C₄²	—	86	1	no	—
1011	C₄²	—	86	1	no	—
1012	C₄²	—	86	1	no	—
1013	C₄²	—	86	1	no	—
1014	C₄²	—	86	1	no	—
1015	C₄²	—	86	2	no	—
1016	C₄²	—	86	2	no	—
1017	C₄²	—	86	2	no	—
1018	C₄²	—	86	2	no	—
1019	C₄²	—	86	2	no	—
1020	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
1021	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
1022	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1024	C₄²	C₂³×D₄₃	1	2	yes	—
1025	C₂³	—	86	1	no	—
1026	C₂³	—	86	1	no	—
1027	C₂³	—	86	2	no	—
1028	C₂³	—	344	2	no	—
1029	C₂³	—	344	2	no	—
1030	C₂³	—	172	4	no	—
1031	C₂³	C₂²×D₁₇₂	1	2	yes	—
1032	C₂³	C₂²×D₁₇₂	1	1	yes	characteristic
1033	Q₈	—	2	2	no	—
1034	Q₈	—	43	2	no	—
1035	Q₈	—	86	1	no	—
1036	Q₈	—	86	2	no	—
1037	Q₈	—	86	1	no	—
1038	Q₈	—	86	2	no	—
1039	Q₈	—	86	1	no	—
1040	Q₈	—	344	2	no	—
1041	Q₈	—	344	1	no	—
1042	Q₈	—	344	2	no	—
1043	Q₈	—	172	4	no	—
1044	Q₈	—	172	2	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	43	2	no	—
1048	D₄	—	86	1	no	—
1049	D₄	—	86	2	no	—
1050	D₄	—	86	1	no	—
1051	D₄	—	86	1	no	—
1052	D₄	—	86	2	no	—
1053	D₄	—	344	1	no	—
1054	D₄	—	344	2	no	—
1055	D₄	—	344	2	no	—
1056	D₄	—	344	2	no	—
1057	D₄	—	172	4	no	—
1058	D₄	—	172	2	no	—
1059	D₄	—	172	2	no	—
1060	D₄	—	172	2	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	2	no	—
1066	C₂×C₄	—	4	1	no	—
1067	C₂×C₄	—	86	1	no	—
1068	C₂×C₄	—	86	1	no	—
1069	C₂×C₄	—	86	1	no	—
1070	C₂×C₄	—	86	2	no	—
1071	C₂×C₄	—	86	1	no	—
1072	C₂×C₄	—	86	1	no	—
1073	C₂×C₄	—	86	1	no	—
1074	C₂×C₄	—	86	2	no	—
1075	C₂×C₄	—	86	2	no	—
1076	C₂×C₄	—	344	2	no	—
1077	C₂×C₄	—	344	2	no	—
1078	C₂×C₄	—	344	1	no	—
1079	C₂×C₄	—	344	1	no	—
1080	C₂×C₄	—	344	2	no	—
1081	C₂×C₄	—	172	2	no	—
1082	C₂×C₄	—	172	2	no	—
1083	C₂×C₄	—	172	4	no	—
1084	C₂×C₄	—	172	2	no	—
1085	C₂×C₄	—	172	2	no	—
1086	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1087	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1088	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1089	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1090	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1091	C₂×C₄	C₂²×D₁₇₂	1	2	yes	—
1092	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1093	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	1	no	—
1099	C₈	—	2	2	no	—
1100	C₈	#41×D₄₃	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	86	2	no	—
1108	C₂²	—	172	2	no	—
1109	C₂²	—	172	1	no	—
1110	C₂²	—	172	1	no	—
1111	C₂²	—	172	2	no	—
1112	C₂²	—	172	1	no	—
1113	C₂²	—	172	2	no	—
1114	C₂²	—	172	1	no	—
1115	C₂²	—	172	1	no	—
1116	C₂²	—	688	4	no	—
1117	C₂²	C₂³×D₁₇₂	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	86	2	no	—
1126	C₄	—	172	2	no	—
1127	C₄	—	172	1	no	—
1128	C₄	—	172	1	no	—
1129	C₄	—	172	1	no	—
1130	C₄	—	172	2	no	—
1131	C₄	—	172	1	no	—
1132	C₄	—	172	1	no	—
1133	C₄	—	172	2	no	—
1134	C₄	#14583711	1	2	yes	—
1135	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1136	C₄	#14583735	1	1	yes	characteristic
1137	C₂	—	4	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	344	2	no	—
1140	C₂	—	344	1	no	—
1141	C₂	—	172	2	no	—
1142	C₂	#41×D₁₇₂	1	1	yes	characteristic
1143	C₂	C₂×#14583711	1	1	yes	characteristic
1144	C₂	#19149369	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₁₇₂
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#2966	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#2966	D₄₃
hypocenter	C₄₃	#61474
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #19148610	C₂	semidirect
2. #19148558	C₂	semidirect
3. #19147593	C₂	semidirect
4. Q₈×#10621873	C₂	semidirect
5. #19147411	C₂	semidirect
6. #19147315	C₂	semidirect
7. #19147009	C₂	semidirect
8. #19147009	C₂	semidirect
9. #19146879	C₂	semidirect
10. #19146838	C₂	semidirect
11. #19146783	C₂	semidirect
12. #19146633	C₂	semidirect
13. #19146307	C₂	semidirect
14. D₄×#10621873	C₂	semidirect
15. #19145212	C₂	semidirect
16. #19145154	C₂	semidirect
17. #19144826	C₂	semidirect
18. #19144781	C₂	semidirect
19. #19144758	C₂	semidirect
20. #19144747	C₂	semidirect
21. #19143456	C₂	semidirect
22. C₄×#13063347	C₂	semidirect
23. C₄₃×#2966	C₂	semidirect
27. Q₈×Dic₈₆	C₂²	semidirect
28. #14583622	C₂²	semidirect
31. #14583619	C₂²	semidirect
40. #14583558	C₂²	semidirect
45. #14583520	C₂²	semidirect
48. #14583456	C₂²	semidirect
54. #14583376	C₂²	semidirect
57. C₄×#10621898	C₂²	semidirect
58. #14583297	C₂²	semidirect
59. #14583297	C₂²	semidirect
60. #14583283	C₂²	semidirect
62. #14583259	C₂²	semidirect
63. #14583259	C₂²	semidirect
64. #14583250	C₂²	semidirect
66. #14583241	C₂²	semidirect
67. #14583241	C₂²	semidirect
68. #14583241	C₂²	semidirect
70. #14583224	C₂²	semidirect
71. #14583224	C₂²	semidirect
72. #14583195	C₂²	semidirect
73. #14583195	C₂²	semidirect
76. #14583185	C₂²	semidirect
77. #14583185	C₂²	semidirect
78. #14583180	C₂²	semidirect
79. #14583180	C₂²	semidirect
80. #14583157	C₂²	semidirect
83. #14583128	C₂²	semidirect
84. #14583128	C₂²	semidirect
85. #14583128	C₂²	semidirect
86. #14583122	C₂²	semidirect
87. #14583122	C₂²	semidirect
89. #14583115	C₂²	semidirect
90. #14583110	C₂²	semidirect
95. #14583057	C₂²	semidirect
97. #14583046	C₂²	semidirect
100. #14583012	C₂²	semidirect
101. #14583007	C₂²	semidirect
104. #14583001	C₂²	semidirect
105. #14583001	C₂²	semidirect
106. C₄×Dic₁₇₂	C₂²	semidirect
107. C₄×Dic₁₇₂	C₂²	semidirect
111. C₄×#10621873	C₂²	semidirect
112. C₄×#10621873	C₂²	semidirect
113. C₄×#10621873	C₂²	semidirect
114. C₄×#10621873	C₂²	semidirect
115. C₄×#10621873	C₂²	semidirect
118. #14582937	C₂²	semidirect
119. #14582937	C₂²	semidirect
120. #14582909	C₂²	semidirect
123. #14582896	C₂²	semidirect
125. C₄₃×#446	C₂²	semidirect
126. C₈×Q₈×C₄₃	C₂²	semidirect
128. C₄₃×#435	C₂²	semidirect
130. C₈×D₄×C₄₃	C₂²	semidirect
131. C₄₃×#433	C₂²	semidirect
132. C₄₃×#432	C₂²	semidirect
133. C₄₃×#405	C₂²	semidirect
134. C₂×C₄×C₈×C₄₃	C₂²	semidirect
451. #10621873	#41	semidirect
585. #2966	D₄₃	semidirect
673. #446	C₂×D₄₃	semidirect
674. C₈×Q₈	C₂×D₄₃	semidirect
694. #435	C₂×D₄₃	semidirect
696. C₈×D₄	C₂×D₄₃	semidirect
697. #433	C₂×D₄₃	semidirect
698. #432	C₂×D₄₃	semidirect
705. #405	C₂×D₄₃	semidirect
706. C₂×C₄×C₈	C₂×D₄₃	semidirect
707. C₄₃	#61474	semidirect

Maximal subgroups

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

subgroup	index
#19148610	2
#19148558	2
#19147593	2
Q₈×#10621873	2
#19147411	2
#19147315	2
#19147009	2
#19146879	2
#19146838	2
#19146783	2
#19146633	2
#19146307	2
D₄×#10621873	2
#19145212	2
#19145154	2
#19144826	2
#19144781	2
#19144758	2
#19144747	2
#19143456	2
C₄×#13063347	2
C₄₃×#2966	2
#61474	43