Subgroups — #26005179

Order 11008.

7210 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148515	C₂	1	4	yes	maximal, complemented
2	#19148502	C₂	1	4	yes	maximal, complemented
3	#19148489	C₂	1	4	yes	maximal, complemented
4	#19148479	C₂	1	2	yes	maximal, complemented
5	#19148469	C₂	1	2	yes	maximal, complemented
6	#19148457	C₂	1	4	yes	maximal, complemented
7	#19148444	C₂	1	4	yes	maximal, complemented
8	#19148429	C₂	1	8	yes	maximal, complemented
9	#19148192	C₂	1	8	yes	maximal, complemented
10	#19148153	C₂	1	8	yes	maximal, complemented
11	#19147984	C₂	1	4	yes	maximal, complemented
12	#19147924	C₂	1	2	yes	maximal, complemented
13	#19147890	C₂	1	4	yes	maximal, complemented
14	C₂×#14583456	C₂	1	1	yes	maximal, characteristic, complemented
15	#19147798	C₂	1	2	yes	maximal, complemented
16	C₂×C₄×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#10621898	C₂²	1	1	yes	characteristic
19	#14583635	C₂²	1	8	yes	complemented
20	#14583631	C₂²	1	16	yes	complemented
21	#14583624	C₂²	1	8	yes	complemented
22	#14583623	C₂²	1	8	yes	complemented
23	#14583619	C₂²	1	8	yes	complemented
24	#14583618	C₂²	1	16	yes	complemented
25	#14583614	C₂²	1	8	yes	complemented
26	#14583606	C₂²	1	8	yes	complemented
27	#14583601	C₂²	1	16	yes	complemented
28	#14583595	C₂²	1	16	yes	complemented
29	#14583592	C₂²	1	32	yes	complemented
30	#14583589	C₂²	1	16	yes	complemented
31	#14583584	C₂²	1	16	yes	complemented
32	#14583575	C₂²	1	32	yes	complemented
33	#14583569	C₂²	1	8	yes	complemented
34	#14583555	C₂²	1	16	yes	complemented
35	#14583553	C₂²	1	8	yes	complemented
36	#14583543	C₂²	1	16	yes	complemented
37	#14583518	C₂²	1	16	yes	complemented
38	#14583510	C₂²	1	8	yes	complemented
39	#14583503	C₂²	1	8	yes	complemented
40	#14583494	C₂²	1	16	yes	complemented
41	#14583486	C₂²	1	16	yes	complemented
42	#14583477	C₂²	1	8	yes	complemented
43	#14583473	C₂²	1	4	yes	—
44	#14583470	C₂²	1	4	yes	complemented
45	#14583466	C₂²	1	4	yes	—
46	#14583463	C₂²	1	4	yes	complemented
47	#14583458	C₂²	1	8	yes	—
48	#14583456	C₂²	1	2	yes	complemented
49	#14583456	C₂²	1	4	yes	complemented
50	#14583456	C₂²	1	4	yes	complemented
51	#14583456	C₂²	1	2	yes	complemented
52	#14583456	C₂²	1	2	yes	complemented
53	#14583456	C₂²	1	2	yes	complemented
54	#14583454	C₂²	1	8	yes	complemented
55	#14583447	C₂²	1	8	yes	complemented
56	#14583445	C₂²	1	8	yes	complemented
57	C₂×#13063325	C₂²	1	2	yes	complemented
58	#14583431	C₂²	1	16	yes	complemented
59	#14583430	C₂²	1	16	yes	complemented
60	#14583429	C₂²	1	32	yes	complemented
61	#14583428	C₂²	1	16	yes	complemented
62	C₂×#13063317	C₂²	1	2	yes	complemented
63	#14583410	C₂²	1	8	yes	—
64	#14583409	C₂²	1	16	yes	complemented
65	#14583406	C₂²	1	8	yes	complemented
66	C₂×#13063304	C₂²	1	4	yes	—
67	#14583382	C₂²	1	8	yes	complemented
68	#14583382	C₂²	1	8	yes	complemented
69	#14583377	C₂²	1	4	yes	complemented
70	#14583374	C₂²	1	8	yes	—
71	#14583374	C₂²	1	4	yes	complemented
72	#41×Dic₄₃	C₂²	1	8	yes	complemented
73	#41×Dic₄₃	C₂²	1	8	yes	complemented
74	C₄×#10621898	C₂²	1	4	yes	—
75	C₄×#10621898	C₂²	1	2	yes	—
76	C₄×#10621898	C₂²	1	2	yes	—
77	C₄×#10621898	C₂²	1	4	yes	complemented
78	C₄×#10621898	C₂²	1	2	yes	complemented
79	C₄×#10621898	C₂²	1	2	yes	complemented
80	C₄×#10621900	C₂²	1	16	yes	complemented
81	C₂×C₄×Dic₈₆	C₂²	1	4	yes	complemented
82	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
83	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
84	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	—
85	C₂×#13063284	C₂²	1	1	yes	characteristic
86	C₂×#13063284	C₂²	1	2	yes	—
87	C₂×#13063284	C₂²	1	8	yes	complemented
88	C₂×#13063282	C₂²	1	2	yes	complemented
89	C₂×C₄²×D₄₃	C₂²	1	2	yes	complemented
90	C₂²×#41×C₄₃	C₂²	1	2	yes	—
91	C₄₃×#532	C₂²	1	2	yes	—
92	C₄₃×#532	C₂²	1	4	yes	—
93	C₄₃×#532	C₂²	1	2	yes	—
94	C₄₃×#532	C₂²	1	4	yes	complemented
95	C₄₃×#532	C₂²	1	2	yes	complemented
96	C₄₃×#532	C₂²	1	2	yes	complemented
97	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×#127×C₄₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×#124×C₄₃	C₂²	1	2	yes	complemented
100	C₂×#121×C₄₃	C₂²	1	4	yes	—
101	C₂×C₄×D₄×C₄₃	C₂²	1	4	yes	complemented
102	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
103	C₂×#10621898	—	2	8	no	—
104	C₂×#10621898	C₂³	1	2	yes	—
105	C₂×#10621898	C₂³	1	2	yes	—
106	C₂×#10621898	C₂³	1	2	yes	—
107	C₂×#10621898	C₂³	1	2	yes	—
108	C₂×#10621900	C₂³	1	16	yes	—
109	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
110	C₂²×Dic₈₆	C₂³	1	4	yes	—
111	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
112	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
113	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
114	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
115	#13063325	C₂³	1	4	yes	—
116	#13063325	C₂³	1	4	yes	—
117	#13063325	C₂³	1	4	yes	—
118	#13063325	C₂³	1	4	yes	—
119	#13063323	C₂³	1	8	yes	—
120	#13063321	C₂³	1	8	yes	—
121	#13063320	C₂³	1	32	yes	—
122	#13063318	C₂³	1	32	yes	—
123	#13063318	C₂³	1	32	yes	—
124	#13063317	C₂³	1	8	yes	—
125	#13063317	C₂³	1	4	yes	—
126	#13063317	C₂³	1	4	yes	—
127	#13063316	C₂³	1	16	yes	—
128	#13063315	C₂³	1	32	yes	—
129	#13063314	C₂³	1	8	yes	—
130	#13063312	C₂³	1	16	yes	—
131	#13063312	C₂³	1	8	yes	—
132	#13063311	C₂³	1	32	yes	—
133	#13063309	C₂³	1	32	yes	—
134	#13063308	C₂³	1	16	yes	—
135	#13063307	C₂³	1	32	yes	—
136	#13063306	C₂³	1	32	yes	—
137	#13063306	C₂³	1	16	yes	—
138	#13063305	C₂³	1	16	yes	—
139	#13063304	C₂³	1	8	yes	—
140	#13063304	C₂³	1	8	yes	—
141	#13063304	C₂³	1	16	yes	—
142	#13063304	C₂³	1	8	yes	—
143	#13063304	C₂³	1	8	yes	—
144	#13063302	C₂³	1	32	yes	—
145	#13063301	C₂³	1	16	yes	—
146	#13063299	C₂³	1	16	yes	—
147	#13063297	C₂³	1	32	yes	—
148	#13063297	C₂³	1	32	yes	—
149	#13063296	C₂³	1	16	yes	—
150	#13063296	C₂³	1	16	yes	—
151	#13063294	C₂³	1	16	yes	—
152	#13063293	C₂³	1	16	yes	—
153	Q₈×Dic₄₃	C₂³	1	16	yes	—
154	Q₈×Dic₄₃	C₂³	1	16	yes	—
155	C₄×Dic₈₆	C₂³	1	8	yes	—
156	C₄×Dic₈₆	C₂³	1	4	yes	—
157	C₄×Dic₈₆	C₂³	1	4	yes	—
158	C₄×Dic₈₆	C₂³	1	4	yes	—
159	C₄×Dic₈₆	C₂³	1	8	yes	—
160	C₄×Dic₈₆	C₂³	1	8	yes	—
161	C₄×Dic₈₆	C₂³	1	4	yes	—
162	C₄×Dic₈₆	C₂³	1	8	yes	—
163	#13063290	C₂³	1	16	yes	—
164	C₄×D₁₇₂	C₂³	1	4	yes	—
165	C₄×D₁₇₂	C₂³	1	4	yes	—
166	C₄×D₁₇₂	C₂³	1	4	yes	—
167	C₄×D₁₇₂	C₂³	1	4	yes	—
168	D₄×Dic₄₃	C₂³	1	32	yes	—
169	D₄×Dic₄₃	C₂³	1	16	yes	—
170	D₄×Dic₄₃	C₂³	1	16	yes	—
171	D₄×Dic₄₃	C₂³	1	32	yes	—
172	D₄×Dic₄₃	C₂³	1	16	yes	—
173	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
174	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
175	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
176	C₄×C₂²⋊D₄₃	C₂³	1	8	yes	—
177	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	—
178	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	—
179	#13063284	C₂³	1	16	yes	—
180	#13063284	C₂³	1	16	yes	—
181	#13063284	C₂³	1	2	yes	—
182	#13063284	C₂³	1	4	yes	—
183	#13063284	C₂³	1	2	yes	—
184	#13063284	C₂³	1	2	yes	—
185	#13063284	C₂³	1	2	yes	—
186	#13063284	C₂³	1	4	yes	—
187	#13063284	C₂³	1	4	yes	—
188	#13063284	C₂³	1	4	yes	—
189	#13063284	C₂³	1	16	yes	—
190	#13063283	C₂³	1	16	yes	—
191	#13063282	C₂³	1	8	yes	—
192	#13063282	C₂³	1	4	yes	—
193	#13063282	C₂³	1	4	yes	—
194	#13063281	C₂³	1	32	yes	—
195	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	—
196	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
197	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
198	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
199	C₂×Dic₄₃⋊C₄	C₂³	1	8	yes	—
200	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
201	C₂×C₂²⋊Dic₄₃	C₂³	1	16	yes	—
202	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
204	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
205	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
206	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
207	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
208	C₂×C₄×Dic₄₃	C₂³	1	16	yes	—
209	C₄²×D₄₃	C₂³	1	8	yes	—
210	C₄²×D₄₃	C₂³	1	4	yes	—
211	C₄²×D₄₃	C₂³	1	4	yes	—
212	C₂×#41×C₄₃	—	2	16	no	—
213	C₂×#41×C₄₃	C₂³	1	4	yes	—
214	C₂×#41×C₄₃	C₂³	1	4	yes	—
215	C₂×#41×C₄₃	C₂³	1	4	yes	—
216	C₂×#41×C₄₃	C₂³	1	4	yes	—
217	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
218	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
219	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
220	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
221	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
222	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
223	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
224	C₄⋊Q₈×C₄₃	C₂³	1	4	yes	—
225	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
226	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
227	#127×C₄₃	C₂³	1	4	yes	—
228	#127×C₄₃	C₂³	1	2	yes	—
229	#127×C₄₃	C₂³	1	2	yes	—
230	#124×C₄₃	C₂³	1	8	yes	—
231	#124×C₄₃	C₂³	1	4	yes	—
232	#124×C₄₃	C₂³	1	4	yes	—
233	#121×C₄₃	C₂³	1	8	yes	—
234	#121×C₄₃	C₂³	1	8	yes	—
235	#121×C₄₃	C₂³	1	8	yes	—
236	#121×C₄₃	C₂³	1	8	yes	—
237	C₄×D₄×C₄₃	C₂³	1	8	yes	—
238	C₄×D₄×C₄₃	C₂³	1	8	yes	—
239	C₄×D₄×C₄₃	C₂³	1	8	yes	—
240	C₄×D₄×C₄₃	C₂³	1	8	yes	—
241	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
242	C₂×C₂²⋊C₄×C₄₃	C₂³	1	8	yes	—
243	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
244	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
245	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
246	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
247	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
248	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
249	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
250	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
251	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
252	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
253	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
254	C₂³×D₄₃	C₂⁴	1	2	yes	—
255	#41×C₄₃	—	2	16	no	—
256	#41×C₄₃	—	2	16	no	—
257	#41×C₄₃	—	2	16	no	—
258	#41×C₄₃	—	2	16	no	—
259	C₂×Q₈×C₄₃	—	2	8	no	—
260	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
261	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
262	C₂×D₄×C₄₃	—	2	8	no	—
263	C₂×D₄×C₄₃	—	2	16	no	—
264	C₂×D₄×C₄₃	—	4	8	no	—
265	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
266	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
267	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
268	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
269	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
270	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₄₃	—	2	16	no	—
272	C₂²×C₄×C₄₃	—	4	4	no	—
273	C₂²×C₄×C₄₃	#41	1	8	yes	complemented
274	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
278	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
279	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
280	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
289	C₂×C₂²⋊D₄₃	—	2	8	no	—
290	C₂×C₂²⋊D₄₃	C₂⁴	1	4	yes	—
291	C₂×C₂²⋊D₄₃	C₂⁴	1	4	yes	—
292	C₂×C₂²⋊D₄₃	C₂⁴	1	32	yes	—
293	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
294	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
295	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
296	C₂²×Dic₄₃	C₂⁴	1	32	yes	—
297	#10621900	—	4	32	no	—
298	#10621898	—	2	8	no	—
299	#10621898	—	2	8	no	—
300	#10621898	—	2	8	no	—
301	#10621898	—	2	8	no	—
302	C₂×D₁₇₂	—	2	4	no	—
303	C₂×D₁₇₂	C₂⁴	1	2	yes	—
304	C₂×D₁₇₂	C₂⁴	1	2	yes	—
305	C₂×C₄×D₄₃	—	2	8	no	—
306	C₂×C₄×D₄₃	—	4	8	no	—
307	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
308	C₂×C₄×D₄₃	C₂⁴	1	4	yes	—
309	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
310	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
311	C₂×Dic₈₆	—	2	4	no	—
312	C₂×Dic₈₆	—	4	8	no	—
313	C₂×Dic₈₆	C₂⁴	1	8	yes	—
314	C₂×Dic₈₆	C₂⁴	1	2	yes	—
315	C₂×Dic₈₆	C₂⁴	1	2	yes	—
316	C₂×Dic₈₆	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
318	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
319	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
320	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
321	C₄²×C₄₃	C₂⁴	1	2	yes	—
322	C₄²×C₄₃	C₂⁴	1	2	yes	—
323	C₄²×C₄₃	C₂⁴	1	2	yes	—
324	C₄²×C₄₃	C₂⁴	1	2	yes	—
325	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₄₃	C₂⁴	1	2	yes	—
328	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
330	C₄²×C₄₃	C₂⁴	1	2	yes	—
331	C₂²⋊Dic₄₃	C₂⁴	1	4	yes	—
332	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
333	C₂²⋊Dic₄₃	C₂⁴	1	4	yes	—
334	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
335	C₂²⋊Dic₄₃	C₂⁴	1	32	yes	—
336	C₂²⋊Dic₄₃	C₂⁴	1	32	yes	—
337	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
338	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
339	(C₂×D₄₃)⋊C₄	C₂⁴	1	32	yes	—
340	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
341	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
342	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
343	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
344	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
345	C₄⋊Dic₄₃	C₂⁴	1	32	yes	—
346	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
347	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
348	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
349	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
350	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
351	Dic₄₃⋊C₄	C₂⁴	1	32	yes	—
352	C₄×Dic₄₃	C₂⁴	1	4	yes	—
353	C₄×Dic₄₃	C₂⁴	1	8	yes	—
354	C₄×Dic₄₃	C₂⁴	1	4	yes	—
355	C₄×Dic₄₃	C₂⁴	1	8	yes	—
356	C₄×Dic₄₃	C₂⁴	1	8	yes	—
357	C₄×Dic₄₃	C₂⁴	1	32	yes	—
358	C₄×Dic₄₃	C₂⁴	1	8	yes	—
359	C₂³×C₄₃	—	2	8	no	—
360	C₂³×C₄₃	—	4	2	no	—
361	C₂³×C₄₃	—	4	8	no	—
362	C₂³×C₄₃	C₂×#41	1	4	yes	—
363	C₂³×C₄₃	C₂⁵	1	8	yes	—
364	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
365	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
366	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
367	C₂²×D₄₃	—	2	4	no	—
368	C₂²×D₄₃	—	4	4	no	—
369	C₂²×D₄₃	C₂⁵	1	4	yes	—
370	Q₈×C₄₃	—	2	8	no	—
371	Q₈×C₄₃	—	2	8	no	—
372	D₄×C₄₃	—	2	16	no	—
373	D₄×C₄₃	—	2	16	no	—
374	D₄×C₄₃	—	2	8	no	—
375	D₄×C₄₃	—	2	8	no	—
376	D₄×C₄₃	—	2	16	no	—
377	D₄×C₄₃	—	4	8	no	—
378	C₂×C₄×C₄₃	—	2	8	no	—
379	C₂×C₄×C₄₃	—	2	16	no	—
380	C₂×C₄×C₄₃	—	2	16	no	—
381	C₂×C₄×C₄₃	—	2	4	no	—
382	C₂×C₄×C₄₃	—	2	4	no	—
383	C₂×C₄×C₄₃	—	2	4	no	—
384	C₂×C₄×C₄₃	—	4	2	no	—
385	C₂×C₄×C₄₃	—	4	2	no	—
386	C₂×C₄×C₄₃	—	4	2	no	—
387	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
388	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
389	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
390	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
391	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
392	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
393	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
394	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
395	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
396	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
397	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
398	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
399	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
400	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
401	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
402	C₂²⋊D₄₃	—	2	8	no	—
403	C₂²⋊D₄₃	—	2	8	no	—
404	C₂²⋊D₄₃	—	4	32	no	—
405	C₂×Dic₄₃	—	2	4	no	—
406	C₂×Dic₄₃	—	4	8	no	—
407	C₂×Dic₄₃	—	4	4	no	—
408	C₂×Dic₄₃	—	4	32	no	—
409	C₂×Dic₄₃	C₂⁵	1	8	yes	—
410	C₂×Dic₄₃	C₂⁵	1	4	yes	—
411	C₂×Dic₄₃	C₂⁵	1	16	yes	—
412	D₁₇₂	—	2	4	no	—
413	D₁₇₂	—	2	4	no	—
414	C₄×D₄₃	—	2	8	no	—
415	C₄×D₄₃	—	2	8	no	—
416	C₄×D₄₃	—	2	16	no	—
417	C₄×D₄₃	—	4	8	no	—
418	Dic₈₆	—	2	4	no	—
419	Dic₈₆	—	2	4	no	—
420	Dic₈₆	—	2	16	no	—
421	Dic₈₆	—	4	8	no	—
422	#62815	—	43	1	no	maximal, Sylow
423	C₂²×C₄₃	—	2	2	no	—
424	C₂²×C₄₃	—	2	2	no	—
425	C₂²×C₄₃	—	2	2	no	—
426	C₂²×C₄₃	—	2	8	no	—
427	C₂²×C₄₃	—	2	16	no	—
428	C₂²×C₄₃	—	4	4	no	—
429	C₂²×C₄₃	—	8	8	no	—
430	C₂²×C₄₃	C₂²×#41	1	2	yes	—
431	C₂²×C₄₃	C₂²×#41	1	2	yes	—
432	C₂²×C₄₃	C₂²×#41	1	2	yes	—
433	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
434	C₂×D₄₃	—	2	4	no	—
435	C₂×D₄₃	—	2	8	no	—
436	C₂×D₄₃	—	4	8	no	—
437	C₄×C₄₃	—	2	8	no	—
438	C₄×C₄₃	—	2	2	no	—
439	C₄×C₄₃	—	2	2	no	—
440	C₄×C₄₃	—	2	2	no	—
441	C₄×C₄₃	C₂²×#41	1	2	yes	—
442	C₄×C₄₃	C₂²×#41	1	2	yes	—
443	C₄×C₄₃	C₂²×#41	1	2	yes	—
444	C₄×C₄₃	C₂²×#41	1	2	yes	—
445	C₄×C₄₃	#585	1	4	yes	—
446	Dic₄₃	—	2	4	no	—
447	Dic₄₃	—	2	16	no	—
448	Dic₄₃	—	2	8	no	—
449	#3512	—	43	4	no	—
450	#3511	—	43	4	no	—
451	#3510	—	43	4	no	—
452	#3509	—	43	2	no	—
453	#3508	—	43	2	no	—
454	#3507	—	43	4	no	—
455	#3506	—	43	4	no	—
456	#3505	—	43	8	no	—
457	#3480	—	43	8	no	—
458	#3475	—	43	8	no	—
459	#3455	—	43	4	no	—
460	#3449	—	43	2	no	—
461	#3444	—	43	4	no	—
462	C₂×#533	—	43	1	no	—
463	C₂×#532	D₄₃	1	1	yes	characteristic, complemented
464	#3428	—	43	2	no	—
465	C₂×C₄×#41	—	43	1	no	—
466	C₂×C₄₃	—	2	2	no	—
467	C₂×C₄₃	—	2	2	no	—
468	C₂×C₄₃	—	2	2	no	—
469	C₂×C₄₃	—	4	8	no	—
470	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
471	C₂×C₄₃	C₂×#585	1	2	yes	—
472	D₄₃	—	4	4	no	—
473	C₂²×#41	—	43	1	no	—
474	C₂²×#41	C₂×D₄₃	1	2	yes	—
475	#559	—	43	8	no	—
476	#559	—	43	16	no	—
477	#557	—	43	8	no	—
478	#556	—	43	8	no	—
479	#556	—	43	16	no	—
480	#556	—	43	8	no	—
481	#555	—	43	8	no	—
482	#554	—	43	8	no	—
483	#553	—	43	32	no	—
484	#553	—	43	16	no	—
485	#553	—	43	16	no	—
486	#552	—	43	16	no	—
487	#552	—	43	16	no	—
488	#551	—	43	32	no	—
489	#550	—	43	8	no	—
490	#548	—	43	16	no	—
491	#547	—	43	8	no	—
492	#546	—	43	16	no	—
493	#542	—	43	16	no	—
494	#541	—	43	8	no	—
495	#540	—	43	8	no	—
496	#539	—	43	16	no	—
497	#538	—	43	16	no	—
498	#537	—	43	8	no	—
499	#536	—	43	4	no	—
500	#536	—	43	4	no	—
501	#535	—	43	4	no	—
502	#535	—	43	4	no	—
503	#534	—	43	8	no	—
504	#533	—	43	8	no	—
505	#533	—	43	2	no	—
506	#533	—	43	2	no	—
507	#533	—	43	4	no	—
508	#533	—	43	4	no	—
509	#533	—	43	2	no	—
510	#533	—	43	2	no	—
511	#532	—	43	8	no	—
512	#532	—	43	8	no	—
513	#532	C₂×D₄₃	1	2	yes	—
514	#532	C₂×D₄₃	1	2	yes	—
515	#532	C₂×D₄₃	1	4	yes	—
516	#532	C₂×D₄₃	1	4	yes	complemented
517	#532	C₂×D₄₃	1	2	yes	complemented
518	#532	C₂×D₄₃	1	2	yes	complemented
519	C₂×C₄⋊Q₈	—	43	2	no	—
520	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
521	C₂×#127	C₂×D₄₃	1	1	yes	characteristic, complemented
522	#529	—	43	16	no	—
523	#529	—	43	16	no	—
524	#529	—	43	16	no	—
525	#529	—	43	32	no	—
526	C₂×#125	—	43	2	no	—
527	C₂×#124	C₂×D₄₃	1	2	yes	complemented
528	#525	—	43	8	no	—
529	#525	—	43	8	no	—
530	#525	—	43	16	no	—
531	C₂×C₂²⋊Q₈	—	43	4	no	—
532	C₂×#121	C₂×D₄₃	1	4	yes	—
533	#520	—	43	8	no	—
534	#520	—	43	8	no	—
535	#519	—	43	4	no	—
536	#518	—	43	8	no	—
537	#518	—	43	4	no	—
538	C₄×#41	—	43	8	no	—
539	C₄×#41	—	43	8	no	—
540	C₄×#41	—	43	16	no	—
541	C₄×#41	—	43	4	no	—
542	C₄×#41	—	43	2	no	—
543	C₄×#41	—	43	2	no	—
544	C₄×#41	—	43	4	no	—
545	C₄×#41	—	43	2	no	—
546	C₄×#41	—	43	2	no	—
547	C₂×C₄×Q₈	—	43	2	no	—
548	C₂×C₄×Q₈	—	43	4	no	—
549	C₂×C₄×D₄	—	43	4	no	—
550	C₂×C₄×D₄	—	43	2	no	—
551	C₂×C₄×D₄	C₂×D₄₃	1	4	yes	complemented
552	C₂×#117	—	43	1	no	—
553	C₂×#117	—	43	2	no	—
554	C₂×#117	—	43	8	no	—
555	C₂×#117	—	43	2	no	—
556	C₂²×C₄²	—	43	2	no	—
557	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
558	C₄₃	#62815	1	1	yes	characteristic, complemented, Sylow
559	C₂×#41	—	2	16	no	—
560	C₂×#41	—	43	16	no	—
561	C₂×#41	—	43	2	no	—
562	C₂×#41	—	43	2	no	—
563	C₂×#41	—	43	2	no	—
564	C₂×#41	—	43	2	no	—
565	C₂×#41	—	86	8	no	—
566	C₂×#41	C₂²×D₄₃	1	4	yes	—
567	C₂×#41	C₂²×D₄₃	1	4	yes	—
568	C₂×#41	C₂²×D₄₃	1	4	yes	—
569	C₂×#41	C₂²×D₄₃	1	4	yes	—
570	C₂²×Q₈	—	43	1	no	—
571	C₂²×Q₈	—	43	4	no	—
572	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
573	C₂²×D₄	—	43	2	no	—
574	C₂²×D₄	—	43	1	no	—
575	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
576	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
577	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
578	C₂³×C₄	—	43	2	no	—
579	C₂³×C₄	—	43	4	no	—
580	C₂³×C₄	C₂²×D₄₃	1	4	yes	—
581	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
582	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
583	C₄⋊Q₈	—	43	8	no	—
584	C₄⋊Q₈	—	43	4	no	—
585	C₄⋊Q₈	—	43	4	no	—
586	C₄⋊Q₈	—	43	4	no	—
587	C₄⋊Q₈	—	43	4	no	—
588	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
589	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
590	C₄⋊Q₈	C₂²×D₄₃	1	4	yes	—
591	#127	—	43	8	no	—
592	#127	C₂²×D₄₃	1	2	yes	—
593	#127	C₂²×D₄₃	1	2	yes	—
594	#127	C₂²×D₄₃	1	4	yes	—
595	#126	—	43	32	no	—
596	#126	—	43	32	no	—
597	#126	—	43	32	no	—
598	#125	—	43	16	no	—
599	#125	—	43	32	no	—
600	#125	—	43	4	no	—
601	#125	—	43	4	no	—
602	#125	—	43	8	no	—
603	#124	—	43	8	no	—
604	#124	—	43	16	no	—
605	#124	—	43	8	no	—
606	#124	—	43	32	no	—
607	#124	C₂²×D₄₃	1	4	yes	—
608	#124	C₂²×D₄₃	1	4	yes	—
609	#124	C₂²×D₄₃	1	8	yes	—
610	#123	—	43	16	no	—
611	#123	—	43	32	no	—
612	#123	—	43	16	no	—
613	#123	—	43	32	no	—
614	#123	—	43	32	no	—
615	C₂²⋊Q₈	—	43	16	no	—
616	C₂²⋊Q₈	—	43	8	no	—
617	C₂²⋊Q₈	—	43	8	no	—
618	C₂²⋊Q₈	—	43	8	no	—
619	C₂²⋊Q₈	—	43	8	no	—
620	C₂²⋊Q₈	—	43	16	no	—
621	C₂²⋊Q₈	—	43	16	no	—
622	C₂²⋊Q₈	—	43	32	no	—
623	#121	—	43	16	no	—
624	#121	—	43	16	no	—
625	#121	—	43	32	no	—
626	#121	—	43	32	no	—
627	#121	—	43	16	no	—
628	#121	C₂²×D₄₃	1	8	yes	—
629	#121	C₂²×D₄₃	1	8	yes	—
630	#121	C₂²×D₄₃	1	8	yes	—
631	#121	C₂²×D₄₃	1	8	yes	—
632	#120	—	43	16	no	—
633	#120	—	43	16	no	—
634	C₄×Q₈	—	43	16	no	—
635	C₄×Q₈	—	43	16	no	—
636	C₄×Q₈	—	43	16	no	—
637	C₄×Q₈	—	43	8	no	—
638	C₄×Q₈	—	43	4	no	—
639	C₄×Q₈	—	43	4	no	—
640	C₄×Q₈	—	43	4	no	—
641	C₄×Q₈	—	43	4	no	—
642	C₄×Q₈	—	43	8	no	—
643	C₄×Q₈	—	43	8	no	—
644	C₄×Q₈	—	43	8	no	—
645	C₄×D₄	—	43	32	no	—
646	C₄×D₄	—	43	16	no	—
647	C₄×D₄	—	43	32	no	—
648	C₄×D₄	—	43	16	no	—
649	C₄×D₄	—	43	16	no	—
650	C₄×D₄	—	43	8	no	—
651	C₄×D₄	—	43	8	no	—
652	C₄×D₄	—	43	8	no	—
653	C₄×D₄	—	43	8	no	—
654	C₄×D₄	—	43	32	no	—
655	C₄×D₄	—	43	32	no	—
656	C₄×D₄	—	43	4	no	—
657	C₄×D₄	—	43	4	no	—
658	C₄×D₄	—	43	4	no	—
659	C₄×D₄	—	43	4	no	—
660	C₄×D₄	C₂²×D₄₃	1	8	yes	—
661	C₄×D₄	C₂²×D₄₃	1	8	yes	—
662	C₄×D₄	C₂²×D₄₃	1	8	yes	—
663	C₄×D₄	C₂²×D₄₃	1	8	yes	—
664	#117	—	43	2	no	—
665	#117	—	43	4	no	—
666	#117	—	43	2	no	—
667	#117	—	43	2	no	—
668	#117	—	43	2	no	—
669	#117	—	43	4	no	—
670	#117	—	43	16	no	—
671	#117	—	43	4	no	—
672	#117	—	43	16	no	—
673	#117	—	43	4	no	—
674	#117	—	43	16	no	—
675	#117	—	43	16	no	—
676	#117	—	43	32	no	—
677	#117	—	43	8	no	—
678	#117	—	43	4	no	—
679	#117	—	43	4	no	—
680	C₂×C₄⋊C₄	—	43	2	no	—
681	C₂×C₄⋊C₄	—	43	4	no	—
682	C₂×C₄⋊C₄	—	43	4	no	—
683	C₂×C₄⋊C₄	—	43	16	no	—
684	C₂×C₄⋊C₄	—	43	8	no	—
685	C₂×C₄⋊C₄	—	43	4	no	—
686	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
687	C₂×C₂²⋊C₄	—	43	2	no	—
688	C₂×C₂²⋊C₄	—	43	4	no	—
689	C₂×C₂²⋊C₄	—	43	16	no	—
690	C₂×C₂²⋊C₄	—	43	4	no	—
691	C₂×C₂²⋊C₄	C₂²×D₄₃	1	8	yes	—
692	C₂×C₄²	—	43	2	no	—
693	C₂×C₄²	—	43	4	no	—
694	C₂×C₄²	—	43	16	no	—
695	C₂×C₄²	—	43	4	no	—
696	C₂×C₄²	—	43	8	no	—
697	C₂×C₄²	—	43	4	no	—
698	C₂×C₄²	—	43	4	no	—
699	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
700	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
701	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
702	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
703	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
704	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
705	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
706	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
707	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
708	C₂⁴	—	43	2	no	—
709	C₂⁴	C₂³×D₄₃	1	4	yes	—
710	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
711	#41	—	2	16	no	—
712	#41	—	2	16	no	—
713	#41	—	2	16	no	—
714	#41	—	2	16	no	—
715	#41	—	86	8	no	—
716	#41	—	86	8	no	—
717	#41	—	86	8	no	—
718	#41	—	86	8	no	—
719	#41	—	172	32	no	—
720	C₂×Q₈	—	2	8	no	—
721	C₂×Q₈	—	43	2	no	—
722	C₂×Q₈	—	43	8	no	—
723	C₂×Q₈	—	43	2	no	—
724	C₂×Q₈	—	43	8	no	—
725	C₂×Q₈	—	86	4	no	—
726	C₂×Q₈	—	172	8	no	—
727	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
728	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
729	C₂×D₄	—	2	16	no	—
730	C₂×D₄	—	2	8	no	—
731	C₂×D₄	—	4	8	no	—
732	C₂×D₄	—	43	4	no	—
733	C₂×D₄	—	43	4	no	—
734	C₂×D₄	—	43	32	no	—
735	C₂×D₄	—	43	2	no	—
736	C₂×D₄	—	43	2	no	—
737	C₂×D₄	—	86	8	no	—
738	C₂×D₄	—	86	4	no	—
739	C₂×D₄	C₂³×D₄₃	1	8	yes	—
740	C₂×D₄	C₂³×D₄₃	1	8	yes	—
741	C₂×D₄	C₂³×D₄₃	1	4	yes	—
742	C₂×D₄	C₂³×D₄₃	1	4	yes	—
743	C₂×D₄	C₂³×D₄₃	1	8	yes	—
744	C₂×D₄	C₂³×D₄₃	1	8	yes	—
745	C₂²×C₄	—	2	16	no	—
746	C₂²×C₄	—	4	4	no	—
747	C₂²×C₄	—	43	2	no	—
748	C₂²×C₄	—	43	4	no	—
749	C₂²×C₄	—	43	8	no	—
750	C₂²×C₄	—	43	32	no	—
751	C₂²×C₄	—	43	8	no	—
752	C₂²×C₄	—	43	4	no	—
753	C₂²×C₄	—	43	4	no	—
754	C₂²×C₄	—	43	8	no	—
755	C₂²×C₄	—	86	8	no	—
756	C₂²×C₄	—	172	8	no	—
757	C₂²×C₄	#10621900	1	8	yes	complemented
758	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
759	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
760	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
761	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
762	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
763	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
764	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
765	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
766	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
767	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
768	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
770	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
771	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
772	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
773	C₄⋊C₄	—	43	4	no	—
774	C₄⋊C₄	—	43	8	no	—
775	C₄⋊C₄	—	43	4	no	—
776	C₄⋊C₄	—	43	8	no	—
777	C₄⋊C₄	—	43	8	no	—
778	C₄⋊C₄	—	43	8	no	—
779	C₄⋊C₄	—	43	16	no	—
780	C₄⋊C₄	—	43	32	no	—
781	C₄⋊C₄	—	43	8	no	—
782	C₄⋊C₄	—	43	16	no	—
783	C₄⋊C₄	—	43	8	no	—
784	C₄⋊C₄	—	43	32	no	—
785	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
786	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
787	C₂²⋊C₄	—	43	4	no	—
788	C₂²⋊C₄	—	43	8	no	—
789	C₂²⋊C₄	—	43	4	no	—
790	C₂²⋊C₄	—	43	8	no	—
791	C₂²⋊C₄	—	43	32	no	—
792	C₂²⋊C₄	—	43	32	no	—
793	C₂²⋊C₄	—	43	8	no	—
794	C₂²⋊C₄	—	43	8	no	—
795	C₂²⋊C₄	—	43	32	no	—
796	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
797	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
798	C₄²	—	43	4	no	—
799	C₄²	—	43	8	no	—
800	C₄²	—	43	8	no	—
801	C₄²	—	43	32	no	—
802	C₄²	—	43	8	no	—
803	C₄²	—	43	4	no	—
804	C₄²	—	43	8	no	—
805	C₄²	C₂³×D₄₃	1	1	yes	characteristic
806	C₄²	C₂³×D₄₃	1	1	yes	characteristic
807	C₄²	C₂³×D₄₃	1	1	yes	characteristic
808	C₄²	C₂³×D₄₃	1	1	yes	characteristic
809	C₄²	C₂³×D₄₃	1	2	yes	—
810	C₄²	C₂³×D₄₃	1	2	yes	—
811	C₄²	C₂³×D₄₃	1	2	yes	—
812	C₄²	C₂³×D₄₃	1	2	yes	—
813	C₄²	C₂³×D₄₃	1	2	yes	—
814	C₄²	C₂³×D₄₃	1	2	yes	—
815	C₂³	—	2	8	no	—
816	C₂³	—	4	2	no	—
817	C₂³	—	4	8	no	—
818	C₂³	—	43	4	no	—
819	C₂³	—	86	4	no	—
820	C₂³	—	172	4	no	—
821	C₂³	C₂×#10621900	1	4	yes	—
822	C₂³	C₂⁴×D₄₃	1	8	yes	—
823	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
824	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
825	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
826	Q₈	—	2	8	no	—
827	Q₈	—	2	8	no	—
828	Q₈	—	86	4	no	—
829	Q₈	—	86	4	no	—
830	Q₈	—	86	16	no	—
831	Q₈	—	172	8	no	—
832	D₄	—	2	16	no	—
833	D₄	—	2	16	no	—
834	D₄	—	2	8	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	16	no	—
837	D₄	—	4	8	no	—
838	D₄	—	86	8	no	—
839	D₄	—	86	8	no	—
840	D₄	—	86	4	no	—
841	D₄	—	86	4	no	—
842	D₄	—	172	32	no	—
843	C₂×C₄	—	2	8	no	—
844	C₂×C₄	—	2	16	no	—
845	C₂×C₄	—	2	16	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	4	no	—
848	C₂×C₄	—	2	4	no	—
849	C₂×C₄	—	4	2	no	—
850	C₂×C₄	—	4	2	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	43	8	no	—
853	C₂×C₄	—	43	4	no	—
854	C₂×C₄	—	43	16	no	—
855	C₂×C₄	—	86	4	no	—
856	C₂×C₄	—	86	8	no	—
857	C₂×C₄	—	86	8	no	—
858	C₂×C₄	—	86	16	no	—
859	C₂×C₄	—	172	8	no	—
860	C₂×C₄	—	172	4	no	—
861	C₂×C₄	—	172	8	no	—
862	C₂×C₄	—	172	32	no	—
863	C₂×C₄	C₂×#10621900	1	4	yes	—
864	C₂×C₄	C₂×#10621900	1	4	yes	—
865	C₂×C₄	C₂×#10621900	1	4	yes	—
866	C₂×C₄	C₂×#10621900	1	4	yes	—
867	C₂×C₄	C₂×#10621900	1	4	yes	—
868	C₂×C₄	C₂×#10621900	1	4	yes	—
869	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
870	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
871	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
872	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
873	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
874	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
875	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
876	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
877	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	8	no	—
882	C₂²	—	2	16	no	—
883	C₂²	—	4	4	no	—
884	C₂²	—	8	8	no	—
885	C₂²	—	86	4	no	—
886	C₂²	—	86	8	no	—
887	C₂²	—	172	8	no	—
888	C₂²	C₂²×#10621900	1	2	yes	—
889	C₂²	C₂²×#10621900	1	2	yes	—
890	C₂²	C₂²×#10621900	1	2	yes	—
891	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
892	C₄	—	2	8	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	86	4	no	—
897	C₄	—	86	8	no	—
898	C₄	—	86	16	no	—
899	C₄	C₂²×#10621900	1	2	yes	—
900	C₄	C₂²×#10621900	1	2	yes	—
901	C₄	C₂²×#10621900	1	2	yes	—
902	C₄	C₂²×#10621900	1	2	yes	—
903	C₄	#14583735	1	4	yes	—
904	C₂	—	2	2	no	—
905	C₂	—	2	2	no	—
906	C₂	—	2	2	no	—
907	C₂	—	4	8	no	—
908	C₂	—	172	4	no	—
909	C₂	C₂³×#10621900	1	1	yes	characteristic
910	C₂	C₂×#14583735	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₄₃
commutator, socle, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#532	C₂
hypercenter	C₂×#532	D₄₃
hypocenter	C₄₃	#62815
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #19148515	C₂	semidirect
2. #19148502	C₂	semidirect
3. #19148489	C₂	semidirect
4. #19148479	C₂	semidirect
5. #19148469	C₂	semidirect
6. #19148457	C₂	semidirect
7. #19148444	C₂	semidirect
8. #19148429	C₂	semidirect
9. #19148192	C₂	semidirect
10. #19148153	C₂	semidirect
11. #19147984	C₂	semidirect
12. #19147924	C₂	semidirect
13. #19147890	C₂	semidirect
14. C₂×#14583456	C₂	semidirect
15. #19147798	C₂	semidirect
16. C₂×C₄×#10621898	C₂	semidirect
17. C₂×C₄₃×#532	C₂	semidirect
19. #14583635	C₂²	semidirect
20. #14583631	C₂²	semidirect
21. #14583624	C₂²	semidirect
22. #14583623	C₂²	semidirect
23. #14583619	C₂²	semidirect
24. #14583618	C₂²	semidirect
25. #14583614	C₂²	semidirect
26. #14583606	C₂²	semidirect
27. #14583601	C₂²	semidirect
28. #14583595	C₂²	semidirect
29. #14583592	C₂²	semidirect
30. #14583589	C₂²	semidirect
31. #14583584	C₂²	semidirect
32. #14583575	C₂²	semidirect
33. #14583569	C₂²	semidirect
34. #14583555	C₂²	semidirect
35. #14583553	C₂²	semidirect
36. #14583543	C₂²	semidirect
37. #14583518	C₂²	semidirect
38. #14583510	C₂²	semidirect
39. #14583503	C₂²	semidirect
40. #14583494	C₂²	semidirect
41. #14583486	C₂²	semidirect
42. #14583477	C₂²	semidirect
44. #14583470	C₂²	semidirect
46. #14583463	C₂²	semidirect
48. #14583456	C₂²	semidirect
49. #14583456	C₂²	semidirect
50. #14583456	C₂²	semidirect
51. #14583456	C₂²	semidirect
52. #14583456	C₂²	semidirect
53. #14583456	C₂²	semidirect
54. #14583454	C₂²	semidirect
55. #14583447	C₂²	semidirect
56. #14583445	C₂²	semidirect
57. C₂×#13063325	C₂²	semidirect
58. #14583431	C₂²	semidirect
59. #14583430	C₂²	semidirect
60. #14583429	C₂²	semidirect
61. #14583428	C₂²	semidirect
62. C₂×#13063317	C₂²	semidirect
64. #14583409	C₂²	semidirect
65. #14583406	C₂²	semidirect
67. #14583382	C₂²	semidirect
68. #14583382	C₂²	semidirect
69. #14583377	C₂²	semidirect
71. #14583374	C₂²	semidirect
72. #41×Dic₄₃	C₂²	semidirect
73. #41×Dic₄₃	C₂²	semidirect
77. C₄×#10621898	C₂²	semidirect
78. C₄×#10621898	C₂²	semidirect
79. C₄×#10621898	C₂²	semidirect
80. C₄×#10621900	C₂²	semidirect
81. C₂×C₄×Dic₈₆	C₂²	semidirect
82. C₂×C₄×Dic₈₆	C₂²	semidirect
83. C₂×C₄×D₁₇₂	C₂²	semidirect
87. C₂×#13063284	C₂²	semidirect
88. C₂×#13063282	C₂²	semidirect
89. C₂×C₄²×D₄₃	C₂²	semidirect
94. C₄₃×#532	C₂²	semidirect
95. C₄₃×#532	C₂²	semidirect
96. C₄₃×#532	C₂²	semidirect
97. C₂×C₄⋊Q₈×C₄₃	C₂²	semidirect
98. C₂×#127×C₄₃	C₂²	semidirect
99. C₂×#124×C₄₃	C₂²	semidirect
101. C₂×C₄×D₄×C₄₃	C₂²	semidirect
273. C₂²×C₄×C₄₃	#41	semidirect
463. C₂×#532	D₄₃	semidirect
516. #532	C₂×D₄₃	semidirect
517. #532	C₂×D₄₃	semidirect
518. #532	C₂×D₄₃	semidirect
520. C₂×C₄⋊Q₈	C₂×D₄₃	semidirect
521. C₂×#127	C₂×D₄₃	semidirect
527. C₂×#124	C₂×D₄₃	semidirect
551. C₂×C₄×D₄	C₂×D₄₃	semidirect
558. C₄₃	#62815	semidirect
757. C₂²×C₄	#10621900	semidirect

Maximal subgroups

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

subgroup	index
#19148515	2
#19148502	2
#19148489	2
#19148479	2
#19148469	2
#19148457	2
#19148444	2
#19148429	2
#19148192	2
#19148153	2
#19147984	2
#19147924	2
#19147890	2
C₂×#14583456	2
#19147798	2
C₂×C₄×#10621898	2
C₂×C₄₃×#532	2
#62815	43