Subgroups — #25973572

Order 11008.

2572 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#19146831	C₂	1	2	yes	maximal, complemented
3	#19146820	C₂	1	2	yes	maximal, complemented
4	#19146730	C₂	1	4	yes	maximal, complemented
5	#19146610	C₂	1	4	yes	maximal, complemented
6	#19146413	C₂	1	2	yes	maximal, complemented
7	#19146402	C₂	1	2	yes	maximal, complemented
8	#19144971	C₂	1	1	yes	maximal, characteristic, complemented
9	#19144535	C₂	1	2	yes	maximal, complemented
10	#19144388	C₂	1	1	yes	maximal, characteristic, complemented
11	#19144216	C₂	1	2	yes	maximal, complemented
12	#19144075	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143821	C₂	1	2	yes	maximal, complemented
14	C₄×#13063350	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×#10621877	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14582903	C₂	1	2	yes	maximal, complemented
17	C₄₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂³×D₁₇₂	C₂²	1	2	yes	—
19	C₂²×D₄×D₄₃	—	2	1	no	—
20	C₂×#13063350	C₂²	1	1	yes	characteristic
21	C₂×#13063350	C₂²	1	2	yes	complemented
22	C₂²×#10621877	C₂²	1	2	yes	complemented
23	D₄×D₁₇₂	—	2	1	no	—
24	D₄×D₁₇₂	—	2	1	no	—
25	D₄×D₁₇₂	—	2	2	no	—
26	D₄×D₁₇₂	C₂²	1	2	yes	—
27	D₄×D₁₇₂	C₂²	1	4	yes	—
28	D₄×D₁₇₂	C₂²	1	2	yes	—
29	C₂×#13063322	C₂²	1	1	yes	characteristic
30	C₂×#13063300	—	2	1	no	—
31	C₂×#13063299	C₂²	1	2	yes	—
32	C₂×#13063295	—	2	2	no	—
33	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
34	#14583265	C₂²	1	4	yes	complemented
35	#14583247	C₂²	1	2	yes	complemented
36	#14583247	C₂²	1	2	yes	complemented
37	#14583223	C₂²	1	4	yes	complemented
38	#14583223	C₂²	1	4	yes	complemented
39	#14583217	C₂²	1	4	yes	complemented
40	#14583212	C₂²	1	4	yes	complemented
41	#14583196	C₂²	1	4	yes	complemented
42	#14583186	C₂²	1	2	yes	complemented
43	#14583176	C₂²	1	2	yes	complemented
44	#14583150	C₂²	1	4	yes	complemented
45	#14583147	C₂²	1	4	yes	complemented
46	#14583133	C₂²	1	4	yes	complemented
47	#14583130	C₂²	1	4	yes	complemented
48	#14583099	C₂²	1	2	yes	complemented
49	#14583099	C₂²	1	2	yes	complemented
50	#14583094	C₂²	1	2	yes	complemented
51	#14583094	C₂²	1	2	yes	complemented
52	#14583049	C₂²	1	4	yes	complemented
53	#14583049	C₂²	1	4	yes	complemented
54	#14583032	C₂²	1	4	yes	complemented
55	#14583032	C₂²	1	4	yes	complemented
56	#14583009	C₂²	1	2	yes	complemented
57	#14582997	C₂²	1	2	yes	complemented
58	C₄×#10621884	C₂²	1	2	yes	complemented
59	C₄×#10621882	C₂²	1	2	yes	complemented
60	#14582977	C₂²	1	2	yes	complemented
61	#14582971	C₂²	1	4	yes	complemented
62	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
63	#14582942	C₂²	1	2	yes	complemented
64	#14582942	C₂²	1	1	yes	characteristic, complemented
65	#14582923	C₂²	1	1	yes	characteristic, complemented
66	#14582903	C₂²	1	2	yes	—
67	#14582903	C₂²	1	1	yes	characteristic
68	#14582903	C₂²	1	2	yes	complemented
69	#14582903	C₂²	1	2	yes	complemented
70	#14582903	C₂²	1	2	yes	complemented
71	#14582903	C₂²	1	4	yes	complemented
72	#14582903	C₂²	1	4	yes	complemented
73	#14582900	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13063245	C₂²	1	4	yes	complemented
75	C₂×#13063245	C₂²	1	4	yes	complemented
76	#14582863	C₂²	1	2	yes	complemented
77	C₄×#10621877	C₂²	1	1	yes	characteristic, complemented
78	C₄₃×#556	C₂²	1	1	yes	characteristic, complemented
79	C₄₃×#555	C₂²	1	1	yes	characteristic, complemented
80	C₄₃×#554	C₂²	1	1	yes	characteristic, complemented
81	C₄₃×#553	C₂²	1	2	yes	complemented
82	C₄₃×#552	—	2	1	no	—
83	C₄₃×#552	C₂²	1	2	yes	complemented
84	C₄₃×#551	—	2	2	no	—
85	C₄₃×#547	C₂²	1	1	yes	characteristic, complemented
86	C₄₃×#546	—	2	1	no	—
87	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
88	C₄₃×#529	—	2	2	no	—
89	C₄₃×#529	—	2	1	no	—
90	C₄₃×#525	C₂²	1	2	yes	complemented
91	C₄×#41×C₄₃	—	2	1	no	—
92	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
94	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
95	C₂⁴×D₄₃	—	2	2	no	—
96	C₂²×D₁₇₂	—	2	8	no	—
97	C₂²×D₁₇₂	—	2	2	no	—
98	C₂²×D₁₇₂	—	2	1	no	—
99	C₂²×D₁₇₂	—	2	2	no	—
100	C₂²×D₁₇₂	—	2	2	no	—
101	C₂²×D₁₇₂	—	2	1	no	—
102	C₂²×D₁₇₂	—	4	4	no	—
103	C₂²×D₁₇₂	C₂³	1	2	yes	—
104	C₂²×D₁₇₂	C₂³	1	4	yes	—
105	C₂²×D₁₇₂	C₂³	1	4	yes	—
106	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
107	C₂²×C₂²⋊D₄₃	—	2	2	no	—
108	C₂×D₄×D₄₃	—	2	4	no	—
109	C₂×D₄×D₄₃	—	2	2	no	—
110	C₂×D₄×D₄₃	—	2	2	no	—
111	C₂×D₄×D₄₃	—	4	8	no	—
112	C₂²×C₄×D₄₃	—	2	1	no	—
113	#13063350	—	2	4	no	—
114	#13063350	—	4	4	no	—
115	C₂×#10621884	C₂³	1	2	yes	—
116	C₂×#10621884	C₂³	1	4	yes	complemented
117	C₂×#10621882	C₂³	1	2	yes	—
118	C₂×#10621882	C₂³	1	4	yes	complemented
119	C₂×#10621877	—	4	4	no	—
120	C₂×#10621877	C₂³	1	1	yes	characteristic
121	C₂×#10621877	C₂³	1	1	yes	characteristic
122	C₂×#10621877	C₂³	1	2	yes	—
123	C₂×#10621877	C₂³	1	4	yes	complemented
124	C₂²×C₄₃⋊C₈	C₂³	1	4	yes	complemented
125	#13063322	—	2	1	no	—
126	#13063322	—	2	1	no	—
127	#13063322	C₂³	1	2	yes	—
128	#13063322	C₂³	1	2	yes	—
129	#13063300	—	2	2	no	—
130	#13063300	—	2	2	no	—
131	#13063300	—	2	4	no	—
132	#13063299	—	2	2	no	—
133	#13063299	—	2	2	no	—
134	#13063299	C₂³	1	4	yes	—
135	#13063299	C₂³	1	4	yes	—
136	#13063295	—	2	4	no	—
137	#13063295	—	2	4	no	—
138	#13063295	—	2	4	no	—
139	#13063295	—	2	4	no	—
140	C₄×D₁₇₂	—	2	1	no	—
141	C₄×D₁₇₂	—	2	1	no	—
142	C₄×D₁₇₂	C₂³	1	2	yes	—
143	C₄×D₁₇₂	C₂³	1	2	yes	—
144	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
145	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
146	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
147	#13063258	C₂³	1	4	yes	complemented
148	#13063258	C₂³	1	2	yes	complemented
149	#13063256	C₂³	1	4	yes	complemented
150	#13063256	C₂³	1	2	yes	complemented
151	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	complemented
152	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	complemented
153	#13063249	C₂³	1	2	yes	complemented
154	#13063246	C₂³	1	2	yes	complemented
155	#13063245	C₂³	1	4	yes	—
156	#13063245	C₂³	1	4	yes	—
157	#13063245	C₂³	1	2	yes	—
158	#13063245	C₂³	1	2	yes	—
159	#13063245	C₂³	1	4	yes	complemented
160	#13063245	C₂³	1	4	yes	complemented
161	#13063245	C₂³	1	4	yes	complemented
162	#13063245	C₂³	1	4	yes	complemented
163	#13063245	C₂³	1	4	yes	complemented
164	#13063245	C₂³	1	4	yes	complemented
165	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	complemented
166	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	complemented
167	#13063236	C₂³	1	2	yes	complemented
168	C₄×C₄₃⋊C₈	C₂³	1	2	yes	complemented
169	C₂×#41×C₄₃	—	2	1	no	—
170	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
171	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
172	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
173	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
174	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
175	#126×C₄₃	—	2	2	no	—
176	#126×C₄₃	—	2	2	no	—
177	#126×C₄₃	—	2	2	no	—
178	#125×C₄₃	—	2	2	no	—
179	#125×C₄₃	—	2	1	no	—
180	#125×C₄₃	C₂³	1	2	yes	complemented
181	#124×C₄₃	—	2	1	no	—
182	#124×C₄₃	—	2	2	no	—
183	#123×C₄₃	—	2	2	no	—
184	#123×C₄₃	—	2	2	no	—
185	#123×C₄₃	—	2	2	no	—
186	#123×C₄₃	—	2	2	no	—
187	C₂²⋊Q₈×C₄₃	—	2	1	no	—
188	C₂²⋊Q₈×C₄₃	—	2	1	no	—
189	C₂²⋊Q₈×C₄₃	—	2	1	no	—
190	C₂²⋊Q₈×C₄₃	—	2	2	no	—
191	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	complemented
192	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	complemented
193	#121×C₄₃	—	2	2	no	—
194	#121×C₄₃	—	2	1	no	—
195	#121×C₄₃	C₂³	1	2	yes	complemented
196	#121×C₄₃	C₂³	1	2	yes	complemented
197	#120×C₄₃	—	2	2	no	—
198	C₄×Q₈×C₄₃	—	2	1	no	—
199	C₄×Q₈×C₄₃	—	2	1	no	—
200	C₄×Q₈×C₄₃	—	2	1	no	—
201	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
202	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
203	C₄×D₄×C₄₃	—	2	1	no	—
204	C₄×D₄×C₄₃	—	2	2	no	—
205	C₄×D₄×C₄₃	—	2	1	no	—
206	C₄×D₄×C₄₃	—	2	1	no	—
207	C₄×D₄×C₄₃	—	2	2	no	—
208	C₄×D₄×C₄₃	—	2	2	no	—
209	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
210	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
211	C₄×D₄×C₄₃	D₄	1	2	yes	—
212	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₄₃	C₂³	1	2	yes	—
214	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
216	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
217	#117×C₄₃	—	2	2	no	—
218	#117×C₄₃	—	2	2	no	—
219	#117×C₄₃	—	2	1	no	—
220	#117×C₄₃	—	2	2	no	—
221	#117×C₄₃	—	2	1	no	—
222	#117×C₄₃	C₂³	1	1	yes	characteristic
223	#117×C₄₃	C₂³	1	2	yes	—
224	#117×C₄₃	C₂³	1	2	yes	complemented
225	#117×C₄₃	C₂³	1	2	yes	complemented
226	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	complemented
228	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	complemented
229	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
230	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
231	C₂×C₄²×C₄₃	—	2	2	no	—
232	C₂×C₄²×C₄₃	—	2	1	no	—
233	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
234	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
235	C₂³×D₄₃	—	2	1	no	—
236	C₂³×D₄₃	—	2	2	no	—
237	C₂³×D₄₃	—	2	4	no	—
238	C₂³×D₄₃	—	2	4	no	—
239	C₂³×D₄₃	—	4	8	no	—
240	C₂³×D₄₃	—	4	8	no	—
241	C₂³×D₄₃	—	8	4	no	—
242	#41×C₄₃	—	2	2	no	—
243	#41×C₄₃	—	2	2	no	—
244	#41×C₄₃	—	4	4	no	—
245	C₂×Q₈×C₄₃	—	2	1	no	—
246	C₂×Q₈×C₄₃	—	2	1	no	—
247	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₄₃	—	2	4	no	—
249	C₂×D₄×C₄₃	—	2	1	no	—
250	C₂×D₄×C₄₃	—	2	2	no	—
251	C₂×D₄×C₄₃	—	2	2	no	—
252	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
253	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
254	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
255	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₄₃	—	2	4	no	—
257	C₂²×C₄×C₄₃	—	2	4	no	—
258	C₂²×C₄×C₄₃	—	2	1	no	—
259	C₂²×C₄×C₄₃	—	2	1	no	—
260	C₂²×C₄×C₄₃	—	2	1	no	—
261	C₂²×C₄×C₄₃	—	2	2	no	—
262	C₂²×C₄×C₄₃	—	2	2	no	—
263	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
267	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
271	C₂×C₂²⋊D₄₃	—	2	4	no	—
272	C₂×C₂²⋊D₄₃	—	2	4	no	—
273	C₂×C₂²⋊D₄₃	—	4	8	no	—
274	C₂²×Dic₄₃	—	2	1	no	—
275	D₄×D₄₃	—	4	8	no	—
276	D₄×D₄₃	—	4	16	no	—
277	D₄×D₄₃	—	4	8	no	—
278	C₂×D₁₇₂	—	2	1	no	—
279	C₂×D₁₇₂	—	2	2	no	—
280	C₂×D₁₇₂	—	2	4	no	—
281	C₂×D₁₇₂	—	2	4	no	—
282	C₂×D₁₇₂	—	2	2	no	—
283	C₂×D₁₇₂	—	2	2	no	—
284	C₂×D₁₇₂	—	2	2	no	—
285	C₂×D₁₇₂	—	2	2	no	—
286	C₂×D₁₇₂	—	2	2	no	—
287	C₂×D₁₇₂	—	2	4	no	—
288	C₂×D₁₇₂	—	2	4	no	—
289	C₂×D₁₇₂	—	2	8	no	—
290	C₂×D₁₇₂	—	2	8	no	—
291	C₂×D₁₇₂	—	4	8	no	—
292	C₂×D₁₇₂	—	4	4	no	—
293	C₂×D₁₇₂	—	4	4	no	—
294	C₂×D₁₇₂	—	4	8	no	—
295	C₂×D₁₇₂	—	4	8	no	—
296	C₂×D₁₇₂	—	4	4	no	—
297	C₂×D₁₇₂	—	8	2	no	—
298	C₂×D₁₇₂	#41	1	4	yes	complemented
299	C₂×D₁₇₂	C₂⁴	1	4	yes	—
300	C₂×D₁₇₂	C₂⁴	1	2	yes	—
301	C₂×C₄×D₄₃	—	2	2	no	—
302	C₂×C₄×D₄₃	—	2	2	no	—
303	C₂×C₄×D₄₃	—	4	4	no	—
304	C₄⋊C₄×C₄₃	—	2	2	no	—
305	C₄⋊C₄×C₄₃	—	2	2	no	—
306	C₄⋊C₄×C₄₃	—	2	1	no	—
307	C₄⋊C₄×C₄₃	—	2	2	no	—
308	C₄⋊C₄×C₄₃	—	2	2	no	—
309	C₄⋊C₄×C₄₃	—	2	1	no	—
310	C₄⋊C₄×C₄₃	—	2	1	no	—
311	C₄⋊C₄×C₄₃	—	2	2	no	—
312	C₄⋊C₄×C₄₃	—	2	2	no	—
313	C₄⋊C₄×C₄₃	—	2	1	no	—
314	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
316	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
317	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
320	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
321	C₂²⋊C₄×C₄₃	—	2	2	no	—
322	C₂²⋊C₄×C₄₃	—	2	1	no	—
323	C₂²⋊C₄×C₄₃	—	2	1	no	—
324	C₂²⋊C₄×C₄₃	—	2	2	no	—
325	C₂²⋊C₄×C₄₃	—	2	1	no	—
326	C₂²⋊C₄×C₄₃	—	2	2	no	—
327	C₂²⋊C₄×C₄₃	—	2	2	no	—
328	C₂²⋊C₄×C₄₃	—	2	2	no	—
329	C₂²⋊C₄×C₄₃	—	2	2	no	—
330	C₂²⋊C₄×C₄₃	—	2	2	no	—
331	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
335	C₄²×C₄₃	—	2	1	no	—
336	C₄²×C₄₃	—	2	2	no	—
337	C₄²×C₄₃	—	2	1	no	—
338	C₄²×C₄₃	—	2	2	no	—
339	C₄²×C₄₃	—	2	2	no	—
340	C₄²×C₄₃	—	2	1	no	—
341	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
344	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
345	#10621884	—	2	4	no	—
346	#10621884	—	4	4	no	—
347	#10621882	—	2	4	no	—
348	#10621882	—	4	4	no	—
349	(C₂×D₄₃)⋊C₄	—	2	2	no	—
350	(C₂×D₄₃)⋊C₄	—	2	2	no	—
351	(C₂×D₄₃)⋊C₄	—	2	4	no	—
352	(C₂×D₄₃)⋊C₄	—	2	4	no	—
353	C₄⋊Dic₄₃	—	2	1	no	—
354	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
355	#10621877	—	2	2	no	—
356	#10621877	—	2	2	no	—
357	#10621877	—	2	4	no	—
358	#10621877	—	4	4	no	—
359	C₂×C₄₃⋊C₈	—	4	4	no	—
360	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
361	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
362	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
363	C₂³×C₄₃	—	2	4	no	—
364	C₂³×C₄₃	—	2	4	no	—
365	C₂³×C₄₃	—	2	1	no	—
366	C₂³×C₄₃	—	4	2	no	—
367	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
368	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
369	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
370	C₂²×D₄₃	—	2	4	no	—
371	C₂²×D₄₃	—	2	2	no	—
372	C₂²×D₄₃	—	2	4	no	—
373	C₂²×D₄₃	—	4	8	no	—
374	C₂²×D₄₃	—	4	8	no	—
375	C₂²×D₄₃	—	4	2	no	—
376	C₂²×D₄₃	—	4	2	no	—
377	C₂²×D₄₃	—	4	4	no	—
378	C₂²×D₄₃	—	4	4	no	—
379	C₂²×D₄₃	—	4	8	no	—
380	C₂²×D₄₃	—	4	4	no	—
381	C₂²×D₄₃	—	4	8	no	—
382	C₂²×D₄₃	—	8	4	no	—
383	C₂²×D₄₃	—	8	4	no	—
384	C₂²×D₄₃	—	8	32	no	—
385	Q₈×C₄₃	—	2	1	no	—
386	Q₈×C₄₃	—	2	1	no	—
387	Q₈×C₄₃	—	4	2	no	—
388	Q₈×C₄₃	—	8	1	no	—
389	D₄×C₄₃	—	2	4	no	—
390	D₄×C₄₃	—	2	2	no	—
391	D₄×C₄₃	—	2	1	no	—
392	D₄×C₄₃	—	2	1	no	—
393	D₄×C₄₃	—	4	2	no	—
394	D₄×C₄₃	—	4	4	no	—
395	D₄×C₄₃	—	8	2	no	—
396	D₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	complemented
397	C₂×C₄×C₄₃	—	2	4	no	—
398	C₂×C₄×C₄₃	—	2	4	no	—
399	C₂×C₄×C₄₃	—	2	4	no	—
400	C₂×C₄×C₄₃	—	2	2	no	—
401	C₂×C₄×C₄₃	—	2	2	no	—
402	C₂×C₄×C₄₃	—	2	2	no	—
403	C₂×C₄×C₄₃	—	2	2	no	—
404	C₂×C₄×C₄₃	—	2	2	no	—
405	C₂×C₄×C₄₃	—	2	1	no	—
406	C₂×C₄×C₄₃	—	2	1	no	—
407	C₂×C₄×C₄₃	—	2	1	no	—
408	C₂×C₄×C₄₃	—	2	2	no	—
409	C₂×C₄×C₄₃	—	2	2	no	—
410	C₂×C₄×C₄₃	—	4	1	no	—
411	C₂×C₄×C₄₃	—	4	4	no	—
412	C₂×C₄×C₄₃	—	4	2	no	—
413	C₂×C₄×C₄₃	—	4	2	no	—
414	C₂×C₄×C₄₃	—	8	1	no	—
415	C₂×C₄×C₄₃	—	8	2	no	—
416	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
417	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
420	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
424	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
425	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
426	C₂²⋊D₄₃	—	4	8	no	—
427	C₂²⋊D₄₃	—	4	8	no	—
428	C₂×Dic₄₃	—	2	2	no	—
429	C₂×Dic₄₃	—	4	2	no	—
430	D₁₇₂	—	2	4	no	—
431	D₁₇₂	—	2	4	no	—
432	D₁₇₂	—	2	2	no	—
433	D₁₇₂	—	2	4	no	—
434	D₁₇₂	—	4	8	no	—
435	D₁₇₂	—	4	8	no	—
436	D₁₇₂	—	4	4	no	—
437	D₁₇₂	—	4	4	no	—
438	D₁₇₂	—	4	4	no	—
439	D₁₇₂	—	8	2	no	—
440	D₁₇₂	—	8	2	no	—
441	D₁₇₂	C₂×#41	1	4	yes	—
442	C₄×D₄₃	—	4	4	no	—
443	C₄×D₄₃	—	4	4	no	—
444	C₄₃⋊C₈	—	2	2	no	—
445	C₄₃⋊C₈	—	2	2	no	—
446	C₄₃⋊C₈	—	2	4	no	—
447	#61155	—	43	1	no	maximal, Sylow
448	C₂²×C₄₃	—	2	1	no	—
449	C₂²×C₄₃	—	2	2	no	—
450	C₂²×C₄₃	—	2	2	no	—
451	C₂²×C₄₃	—	2	1	no	—
452	C₂²×C₄₃	—	2	2	no	—
453	C₂²×C₄₃	—	2	2	no	—
454	C₂²×C₄₃	—	2	2	no	—
455	C₂²×C₄₃	—	4	8	no	—
456	C₂²×C₄₃	—	4	1	no	—
457	C₂²×C₄₃	—	4	1	no	—
458	C₂²×C₄₃	—	4	1	no	—
459	C₂²×C₄₃	#546	1	2	yes	—
460	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
461	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
462	C₂×D₄₃	—	2	4	no	—
463	C₂×D₄₃	—	4	8	no	—
464	C₂×D₄₃	—	4	2	no	—
465	C₂×D₄₃	—	4	2	no	—
466	C₂×D₄₃	—	4	4	no	—
467	C₂×D₄₃	—	4	4	no	—
468	C₂×D₄₃	—	4	4	no	—
469	C₂×D₄₃	—	8	16	no	—
470	C₂×D₄₃	—	8	16	no	—
471	C₂×D₄₃	—	8	8	no	—
472	C₄×C₄₃	—	2	1	no	—
473	C₄×C₄₃	—	2	1	no	—
474	C₄×C₄₃	—	2	2	no	—
475	C₄×C₄₃	—	2	2	no	—
476	C₄×C₄₃	—	2	1	no	—
477	C₄×C₄₃	—	4	1	no	—
478	C₄×C₄₃	—	4	2	no	—
479	C₄×C₄₃	—	4	1	no	—
480	C₄×C₄₃	—	4	1	no	—
481	C₄×C₄₃	—	4	2	no	—
482	C₄×C₄₃	#546	1	2	yes	—
483	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
484	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
485	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
486	Dic₄₃	—	4	2	no	—
487	#3475	D₄₃	1	1	yes	characteristic, complemented
488	C₂×D₄²	—	43	1	no	—
489	#3325	—	43	2	no	—
490	#3324	—	43	2	no	—
491	#3318	—	43	4	no	—
492	#3310	—	43	4	no	—
493	#3295	—	43	2	no	—
494	#3294	—	43	2	no	—
495	#3138	—	43	1	no	—
496	#3094	—	43	2	no	—
497	#3077	—	43	1	no	—
498	#3055	—	43	2	no	—
499	#3038	—	43	1	no	—
500	#3003	—	43	2	no	—
501	C₄×AGL(1,ℤ/8)	—	43	1	no	—
502	D₄×M₁₆	—	43	1	no	—
503	C₂×#418	—	43	2	no	—
504	C₂×C₄₃	—	2	2	no	—
505	C₂×C₄₃	—	2	4	no	—
506	C₂×C₄₃	—	4	2	no	—
507	C₂×C₄₃	—	8	1	no	—
508	C₂×C₄₃	C₂×#546	1	1	yes	characteristic
509	C₂×C₄₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
510	C₂×C₄₃	#3585	1	1	yes	characteristic
511	D₄₃	—	4	4	no	—
512	D₄₃	—	8	4	no	—
513	C₂³×D₄	—	43	2	no	—
514	C₂³×D₄	—	86	1	no	—
515	C₂×AGL(1,ℤ/8)	—	43	1	no	—
516	C₂×AGL(1,ℤ/8)	—	43	2	no	—
517	C₂²×M₁₆	—	43	2	no	—
518	#556	C₂×D₄₃	1	1	yes	characteristic, complemented
519	#555	C₂×D₄₃	1	1	yes	characteristic, complemented
520	#554	C₂×D₄₃	1	1	yes	characteristic, complemented
521	#553	C₂×D₄₃	1	2	yes	complemented
522	#552	—	2	1	no	—
523	#552	C₂×D₄₃	1	2	yes	complemented
524	#551	—	2	2	no	—
525	#547	C₂×D₄₃	1	1	yes	characteristic, complemented
526	#546	—	2	1	no	—
527	D₄²	—	43	2	no	—
528	D₄²	—	43	4	no	—
529	D₄²	—	43	2	no	—
530	D₄²	—	86	1	no	—
531	D₄²	—	86	1	no	—
532	D₄²	—	86	2	no	—
533	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
534	C₂×#127	—	43	1	no	—
535	#529	—	2	2	no	—
536	#529	—	2	1	no	—
537	#525	C₂×D₄₃	1	2	yes	complemented
538	C₂×#121	—	43	2	no	—
539	C₂×#121	—	86	1	no	—
540	C₂×#120	—	86	2	no	—
541	C₄×#41	—	2	1	no	—
542	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
543	C₂×C₄×D₄	—	43	1	no	—
544	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
545	C₂×#117	C₂×D₄₃	1	2	yes	complemented
546	#490	—	43	4	no	—
547	#486	—	43	2	no	—
548	#486	—	43	2	no	—
549	#482	—	43	4	no	—
550	#482	—	43	4	no	—
551	#481	—	43	4	no	—
552	#480	—	43	4	no	—
553	#478	—	43	4	no	—
554	#476	—	43	2	no	—
555	#474	—	43	2	no	—
556	#469	—	43	4	no	—
557	#468	—	43	4	no	—
558	#466	—	43	4	no	—
559	#465	—	43	4	no	—
560	#460	—	43	2	no	—
561	#460	—	43	2	no	—
562	#459	—	43	2	no	—
563	#459	—	43	2	no	—
564	#450	—	43	4	no	—
565	#450	—	43	4	no	—
566	#447	—	43	4	no	—
567	#447	—	43	4	no	—
568	#442	—	43	2	no	—
569	#440	—	43	2	no	—
570	C₄×SD₁₆	—	43	2	no	—
571	C₄×D₈	—	43	2	no	—
572	#436	—	43	2	no	—
573	#435	—	43	4	no	—
574	C₈×D₄	—	43	2	no	—
575	#428	—	43	2	no	—
576	#428	—	43	1	no	—
577	#423	—	43	1	no	—
578	#418	—	43	2	no	—
579	#418	—	43	2	no	—
580	#418	—	43	2	no	—
581	#418	—	43	2	no	—
582	#418	—	43	1	no	—
583	#418	—	43	4	no	—
584	#418	—	43	4	no	—
585	#417	—	43	1	no	—
586	C₂×#102	—	43	4	no	—
587	C₂×#102	—	43	4	no	—
588	#407	—	43	2	no	—
589	C₄×M₁₆	—	43	1	no	—
590	C₄₃	#61155	1	1	yes	characteristic, complemented, Sylow
591	C₂⁵	—	86	2	no	—
592	C₂×#41	—	2	1	no	—
593	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
594	C₂²×D₄	—	43	1	no	—
595	C₂²×D₄	—	43	2	no	—
596	C₂²×D₄	—	43	4	no	—
597	C₂²×D₄	—	43	4	no	—
598	C₂²×D₄	—	86	8	no	—
599	C₂²×D₄	—	86	2	no	—
600	C₂²×D₄	—	86	4	no	—
601	C₂²×D₄	—	86	2	no	—
602	C₂²×D₄	—	86	2	no	—
603	C₂²×D₄	—	86	1	no	—
604	C₂²×D₄	—	86	2	no	—
605	C₂²×D₄	—	86	1	no	—
606	C₂²×D₄	—	86	2	no	—
607	C₂²×D₄	—	86	2	no	—
608	C₂²×D₄	—	172	4	no	—
609	C₂²×D₄	—	172	8	no	—
610	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
611	C₂³×C₄	—	86	1	no	—
612	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
613	AGL(1,ℤ/8)	—	86	4	no	—
614	AGL(1,ℤ/8)	—	172	4	no	—
615	C₂×SD₁₆	—	43	2	no	—
616	C₂×SD₁₆	—	43	4	no	—
617	C₂×D₈	—	43	2	no	—
618	C₂×D₈	—	43	4	no	—
619	C₂×M₁₆	—	43	1	no	—
620	C₂×M₁₆	—	43	2	no	—
621	C₂×M₁₆	—	43	1	no	—
622	C₂×M₁₆	—	43	4	no	—
623	C₂×M₁₆	—	172	4	no	—
624	C₂²×C₈	—	43	4	no	—
625	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
626	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
627	#127	—	43	2	no	—
628	#127	—	43	2	no	—
629	#127	—	86	1	no	—
630	#127	—	86	1	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	—	2	1	no	—
636	#125	C₂²×D₄₃	1	2	yes	complemented
637	#124	—	2	1	no	—
638	#124	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	#123	—	2	2	no	—
642	#123	—	2	2	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	2	no	—
647	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	complemented
648	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	complemented
649	#121	—	2	2	no	—
650	#121	—	2	1	no	—
651	#121	—	43	4	no	—
652	#121	—	43	4	no	—
653	#121	—	86	2	no	—
654	#121	—	86	2	no	—
655	#121	—	86	2	no	—
656	#121	—	86	2	no	—
657	#121	—	86	4	no	—
658	#121	C₂²×D₄₃	1	2	yes	complemented
659	#121	C₂²×D₄₃	1	2	yes	complemented
660	#120	—	2	2	no	—
661	#120	—	86	4	no	—
662	#120	—	86	4	no	—
663	#120	—	86	4	no	—
664	#120	—	86	4	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	—	2	1	no	—
667	C₄×Q₈	—	2	1	no	—
668	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
669	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
670	C₄×D₄	—	2	1	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	1	no	—
673	C₄×D₄	—	2	1	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	43	2	no	—
677	C₄×D₄	—	43	2	no	—
678	C₄×D₄	—	86	1	no	—
679	C₄×D₄	—	86	1	no	—
680	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
681	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
682	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
683	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
684	C₄×D₄	C₂²×D₄₃	1	2	yes	—
685	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
686	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic, complemented
687	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic, complemented
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	1	no	—
691	#117	—	2	2	no	—
692	#117	—	2	1	no	—
693	#117	C₂²×D₄₃	1	1	yes	characteristic
694	#117	C₂²×D₄₃	1	2	yes	—
695	#117	C₂²×D₄₃	1	2	yes	complemented
696	#117	C₂²×D₄₃	1	2	yes	complemented
697	C₂×C₄⋊C₄	—	43	1	no	—
698	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
699	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	complemented
700	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	complemented
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₂²⋊C₄	—	86	1	no	—
703	C₂×C₂²⋊C₄	—	86	2	no	—
704	C₂×C₂²⋊C₄	C₂²⋊D₄₃	1	2	yes	—
705	C₂×C₄²	—	2	2	no	—
706	C₂×C₄²	—	2	1	no	—
707	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
708	#107	—	43	2	no	—
709	#107	—	43	4	no	—
710	#106	—	43	2	no	—
711	#106	—	43	4	no	—
712	C₄⋊C₈	—	43	2	no	—
713	C₄⋊C₈	—	43	2	no	—
714	#103	—	43	2	no	—
715	#102	—	43	2	no	—
716	#102	—	43	2	no	—
717	#102	—	43	2	no	—
718	#102	—	43	4	no	—
719	#102	—	43	4	no	—
720	#102	—	43	4	no	—
721	#102	—	43	4	no	—
722	#102	—	43	4	no	—
723	#102	—	43	4	no	—
724	#102	—	43	4	no	—
725	#102	—	43	4	no	—
726	C₂²⋊C₈	—	43	4	no	—
727	C₂²⋊C₈	—	43	4	no	—
728	#97	—	43	2	no	—
729	C₄×C₈	—	43	2	no	—
730	C₂⁴	—	86	1	no	—
731	C₂⁴	—	86	4	no	—
732	C₂⁴	—	86	4	no	—
733	C₂⁴	—	86	2	no	—
734	C₂⁴	—	344	4	no	—
735	C₂⁴	—	172	8	no	—
736	C₂⁴	—	172	8	no	—
737	C₂⁴	C₂×C₂²⋊D₄₃	1	2	yes	—
738	#41	—	2	2	no	—
739	#41	—	2	2	no	—
740	#41	—	4	4	no	—
741	C₂×Q₈	—	2	1	no	—
742	C₂×Q₈	—	2	1	no	—
743	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
744	C₂×D₄	—	2	4	no	—
745	C₂×D₄	—	2	1	no	—
746	C₂×D₄	—	2	2	no	—
747	C₂×D₄	—	2	2	no	—
748	C₂×D₄	—	43	4	no	—
749	C₂×D₄	—	43	2	no	—
750	C₂×D₄	—	43	4	no	—
751	C₂×D₄	—	86	8	no	—
752	C₂×D₄	—	86	8	no	—
753	C₂×D₄	—	86	4	no	—
754	C₂×D₄	—	86	4	no	—
755	C₂×D₄	—	86	1	no	—
756	C₂×D₄	—	86	2	no	—
757	C₂×D₄	—	86	2	no	—
758	C₂×D₄	—	86	4	no	—
759	C₂×D₄	—	86	4	no	—
760	C₂×D₄	—	86	2	no	—
761	C₂×D₄	—	86	2	no	—
762	C₂×D₄	—	86	2	no	—
763	C₂×D₄	—	86	4	no	—
764	C₂×D₄	—	86	2	no	—
765	C₂×D₄	—	86	4	no	—
766	C₂×D₄	—	344	2	no	—
767	C₂×D₄	—	172	4	no	—
768	C₂×D₄	—	172	4	no	—
769	C₂×D₄	—	172	8	no	—
770	C₂×D₄	—	172	8	no	—
771	C₂×D₄	—	172	8	no	—
772	C₂×D₄	—	172	4	no	—
773	C₂×D₄	—	172	16	no	—
774	C₂×D₄	—	172	8	no	—
775	C₂×D₄	—	172	8	no	—
776	C₂×D₄	—	172	8	no	—
777	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
778	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
779	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
780	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
781	C₂²×C₄	—	2	4	no	—
782	C₂²×C₄	—	2	4	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	1	no	—
786	C₂²×C₄	—	2	1	no	—
787	C₂²×C₄	—	2	1	no	—
788	C₂²×C₄	—	86	1	no	—
789	C₂²×C₄	—	86	2	no	—
790	C₂²×C₄	—	86	2	no	—
791	C₂²×C₄	—	172	4	no	—
792	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
793	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
795	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
796	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
797	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
798	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
799	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
800	SD₁₆	—	86	4	no	—
801	SD₁₆	—	172	4	no	—
802	D₈	—	86	4	no	—
803	D₈	—	172	4	no	—
804	M₁₆	—	86	2	no	—
805	M₁₆	—	86	2	no	—
806	M₁₆	—	86	4	no	—
807	M₁₆	—	172	4	no	—
808	C₂×C₈	—	43	2	no	—
809	C₂×C₈	—	43	2	no	—
810	C₂×C₈	—	43	4	no	—
811	C₂×C₈	—	172	4	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	1	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	1	no	—
822	C₄⋊C₄	—	43	2	no	—
823	C₄⋊C₄	—	86	1	no	—
824	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
825	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
826	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
827	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
828	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
829	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
830	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	1	no	—
839	C₂²⋊C₄	—	2	1	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	86	2	no	—
842	C₂²⋊C₄	—	86	2	no	—
843	C₂²⋊C₄	—	86	4	no	—
844	C₂²⋊C₄	—	86	4	no	—
845	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
846	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
847	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
848	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
849	C₄²	—	2	1	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	1	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	1	no	—
855	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
856	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
857	C₄²	C₂³×D₄₃	1	1	yes	characteristic
858	C₄²	C₂³×D₄₃	1	1	yes	characteristic
859	C₂³	—	2	4	no	—
860	C₂³	—	2	4	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	4	2	no	—
863	C₂³	—	86	2	no	—
864	C₂³	—	86	4	no	—
865	C₂³	—	86	4	no	—
866	C₂³	—	344	4	no	—
867	C₂³	—	344	4	no	—
868	C₂³	—	344	32	no	—
869	C₂³	—	172	8	no	—
870	C₂³	—	172	8	no	—
871	C₂³	—	172	4	no	—
872	C₂³	—	172	4	no	—
873	C₂³	—	172	8	no	—
874	C₂³	—	172	2	no	—
875	C₂³	—	172	2	no	—
876	C₂³	—	172	8	no	—
877	C₂³	—	172	4	no	—
878	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
879	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
880	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
881	Q₈	—	2	1	no	—
882	Q₈	—	2	1	no	—
883	Q₈	—	4	2	no	—
884	Q₈	—	8	1	no	—
885	D₄	—	2	4	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	1	no	—
888	D₄	—	2	1	no	—
889	D₄	—	4	4	no	—
890	D₄	—	4	2	no	—
891	D₄	—	8	2	no	—
892	D₄	—	43	4	no	—
893	D₄	—	86	4	no	—
894	D₄	—	86	2	no	—
895	D₄	—	86	4	no	—
896	D₄	—	86	4	no	—
897	D₄	—	344	2	no	—
898	D₄	—	344	2	no	—
899	D₄	—	172	8	no	—
900	D₄	—	172	8	no	—
901	D₄	—	172	4	no	—
902	D₄	—	172	8	no	—
903	D₄	—	172	8	no	—
904	D₄	—	172	4	no	—
905	D₄	—	172	4	no	—
906	D₄	#13063350	1	4	yes	complemented
907	C₂×C₄	—	2	4	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	4	no	—
914	C₂×C₄	—	2	4	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	1	no	—
917	C₂×C₄	—	2	1	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	4	no	—
922	C₂×C₄	—	4	2	no	—
923	C₂×C₄	—	4	2	no	—
924	C₂×C₄	—	8	1	no	—
925	C₂×C₄	—	8	2	no	—
926	C₂×C₄	—	86	2	no	—
927	C₂×C₄	—	172	4	no	—
928	C₂×C₄	—	172	2	no	—
929	C₂×C₄	—	172	4	no	—
930	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
931	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
935	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
937	C₂×C₄	#41×D₄₃	1	2	yes	—
938	C₂×C₄	#13063371	1	2	yes	—
939	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
940	C₈	—	86	2	no	—
941	C₈	—	86	2	no	—
942	C₈	—	86	4	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	1	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	2	no	—
947	C₂²	—	2	2	no	—
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	4	8	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	86	4	no	—
955	C₂²	—	344	8	no	—
956	C₂²	—	344	16	no	—
957	C₂²	—	344	16	no	—
958	C₂²	—	172	8	no	—
959	C₂²	—	172	4	no	—
960	C₂²	—	172	4	no	—
961	C₂²	—	172	4	no	—
962	C₂²	—	172	2	no	—
963	C₂²	—	172	2	no	—
964	C₂²	#14583537	1	2	yes	—
965	C₂²	C₂×#13063350	1	4	yes	—
966	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
967	C₄	—	2	2	no	—
968	C₄	—	2	2	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	4	1	no	—
973	C₄	—	4	1	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	1	no	—
976	C₄	—	4	2	no	—
977	C₄	—	172	2	no	—
978	C₄	#14583537	1	2	yes	—
979	C₄	C₂×#13063350	1	2	yes	—
980	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
981	C₄	C₂×#13063371	1	1	yes	characteristic
982	C₂	—	2	2	no	—
983	C₂	—	2	4	no	—
984	C₂	—	4	2	no	—
985	C₂	—	8	1	no	—
986	C₂	—	344	4	no	—
987	C₂	—	172	4	no	—
988	C₂	C₂×#14583537	1	1	yes	characteristic
989	C₂	C₂²×#13063350	1	1	yes	characteristic
990	C₂	#19149374	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3475	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3475	D₄₃
hypocenter	C₄₃	#61155
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×D₁₇₂	C₂	semidirect
2. #19146831	C₂	semidirect
3. #19146820	C₂	semidirect
4. #19146730	C₂	semidirect
5. #19146610	C₂	semidirect
6. #19146413	C₂	semidirect
7. #19146402	C₂	semidirect
8. #19144971	C₂	semidirect
9. #19144535	C₂	semidirect
10. #19144388	C₂	semidirect
11. #19144216	C₂	semidirect
12. #19144075	C₂	semidirect
13. #19143821	C₂	semidirect
14. C₄×#13063350	C₂	semidirect
15. D₄×#10621877	C₂	semidirect
16. C₂×#14582903	C₂	semidirect
17. C₄₃×#3475	C₂	semidirect
21. C₂×#13063350	C₂²	semidirect
22. C₂²×#10621877	C₂²	semidirect
34. #14583265	C₂²	semidirect
35. #14583247	C₂²	semidirect
36. #14583247	C₂²	semidirect
37. #14583223	C₂²	semidirect
38. #14583223	C₂²	semidirect
39. #14583217	C₂²	semidirect
40. #14583212	C₂²	semidirect
41. #14583196	C₂²	semidirect
42. #14583186	C₂²	semidirect
43. #14583176	C₂²	semidirect
44. #14583150	C₂²	semidirect
45. #14583147	C₂²	semidirect
46. #14583133	C₂²	semidirect
47. #14583130	C₂²	semidirect
48. #14583099	C₂²	semidirect
49. #14583099	C₂²	semidirect
50. #14583094	C₂²	semidirect
51. #14583094	C₂²	semidirect
52. #14583049	C₂²	semidirect
53. #14583049	C₂²	semidirect
54. #14583032	C₂²	semidirect
55. #14583032	C₂²	semidirect
56. #14583009	C₂²	semidirect
57. #14582997	C₂²	semidirect
58. C₄×#10621884	C₂²	semidirect
59. C₄×#10621882	C₂²	semidirect
60. #14582977	C₂²	semidirect
61. #14582971	C₂²	semidirect
62. D₄×C₄₃⋊C₈	C₂²	semidirect
63. #14582942	C₂²	semidirect
64. #14582942	C₂²	semidirect
65. #14582923	C₂²	semidirect
68. #14582903	C₂²	semidirect
69. #14582903	C₂²	semidirect
70. #14582903	C₂²	semidirect
71. #14582903	C₂²	semidirect
72. #14582903	C₂²	semidirect
73. #14582900	C₂²	semidirect
74. C₂×#13063245	C₂²	semidirect
75. C₂×#13063245	C₂²	semidirect
76. #14582863	C₂²	semidirect
77. C₄×#10621877	C₂²	semidirect
78. C₄₃×#556	C₂²	semidirect
79. C₄₃×#555	C₂²	semidirect
80. C₄₃×#554	C₂²	semidirect
81. C₄₃×#553	C₂²	semidirect
83. C₄₃×#552	C₂²	semidirect
85. C₄₃×#547	C₂²	semidirect
87. C₄₃×#533	C₂²	semidirect
90. C₄₃×#525	C₂²	semidirect
92. C₄×#41×C₄₃	C₂²	semidirect
94. C₂×#117×C₄₃	C₂²	semidirect
116. C₂×#10621884	C₂³	semidirect
118. C₂×#10621882	C₂³	semidirect
123. C₂×#10621877	C₂³	semidirect
124. C₂²×C₄₃⋊C₈	C₂³	semidirect
147. #13063258	C₂³	semidirect
148. #13063258	C₂³	semidirect
149. #13063256	C₂³	semidirect
150. #13063256	C₂³	semidirect
151. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
152. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
153. #13063249	C₂³	semidirect
154. #13063246	C₂³	semidirect
159. #13063245	C₂³	semidirect
160. #13063245	C₂³	semidirect
161. #13063245	C₂³	semidirect
162. #13063245	C₂³	semidirect
163. #13063245	C₂³	semidirect
164. #13063245	C₂³	semidirect
165. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
166. C₂²⋊(C₄₃⋊C₈)	C₂³	semidirect
167. #13063236	C₂³	semidirect
168. C₄×C₄₃⋊C₈	C₂³	semidirect
173. C₄⋊Q₈×C₄₃	C₂³	semidirect
174. C₄⋊Q₈×C₄₃	C₂³	semidirect
180. #125×C₄₃	C₂³	semidirect
191. C₂²⋊Q₈×C₄₃	C₂³	semidirect
192. C₂²⋊Q₈×C₄₃	C₂³	semidirect
195. #121×C₄₃	C₂³	semidirect
196. #121×C₄₃	C₂³	semidirect
201. C₄×Q₈×C₄₃	C₂³	semidirect
202. C₄×Q₈×C₄₃	C₂³	semidirect
215. C₄×D₄×C₄₃	C₂³	semidirect
216. C₄×D₄×C₄₃	C₂³	semidirect
224. #117×C₄₃	C₂³	semidirect
225. #117×C₄₃	C₂³	semidirect
227. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
228. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
298. C₂×D₁₇₂	#41	semidirect
396. D₄×C₄₃	AGL(1,ℤ/8)	semidirect
487. #3475	D₄₃	semidirect
518. #556	C₂×D₄₃	semidirect
519. #555	C₂×D₄₃	semidirect
520. #554	C₂×D₄₃	semidirect
521. #553	C₂×D₄₃	semidirect
523. #552	C₂×D₄₃	semidirect
525. #547	C₂×D₄₃	semidirect
533. #533	C₂×D₄₃	semidirect
537. #525	C₂×D₄₃	semidirect
542. C₄×#41	C₂×D₄₃	semidirect
545. C₂×#117	C₂×D₄₃	semidirect
590. C₄₃	#61155	semidirect
625. C₄⋊Q₈	C₂²×D₄₃	semidirect
626. C₄⋊Q₈	C₂²×D₄₃	semidirect
636. #125	C₂²×D₄₃	semidirect
647. C₂²⋊Q₈	C₂²×D₄₃	semidirect
648. C₂²⋊Q₈	C₂²×D₄₃	semidirect
658. #121	C₂²×D₄₃	semidirect
659. #121	C₂²×D₄₃	semidirect
668. C₄×Q₈	C₂²×D₄₃	semidirect
669. C₄×Q₈	C₂²×D₄₃	semidirect
686. C₄×D₄	C₂²×D₄₃	semidirect
687. C₄×D₄	C₂²×D₄₃	semidirect
695. #117	C₂²×D₄₃	semidirect
696. #117	C₂²×D₄₃	semidirect
699. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
700. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
906. D₄	#13063350	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×D₁₇₂	2
#19146831	2
#19146820	2
#19146730	2
#19146610	2
#19146413	2
#19146402	2
#19144971	2
#19144535	2
#19144388	2
#19144216	2
#19144075	2
#19143821	2
C₄×#13063350	2
D₄×#10621877	2
C₂×#14582903	2
C₄₃×#3475	2
#61155	43