Subgroups — #25964978

Order 11008.

2570 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144729	C₂	1	4	yes	maximal, complemented
3	#19144690	C₂	1	2	yes	maximal, complemented
4	#19144682	C₂	1	2	yes	maximal, complemented
5	#19144638	C₂	1	4	yes	maximal, complemented
6	#19144599	C₂	1	2	yes	maximal, complemented
7	#19144591	C₂	1	2	yes	maximal, complemented
8	#19144515	C₂	1	2	yes	maximal, complemented
9	#19144388	C₂	1	2	yes	maximal, complemented
10	#19144055	C₂	1	2	yes	maximal, complemented
11	#19143821	C₂	1	2	yes	maximal, complemented
12	C₄×#13063350	C₂	1	4	yes	maximal, complemented
13	#19143228	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
16	C₂³×C₄×D₄₃	—	2	1	no	—
17	C₂×#13063350	C₂²	1	4	yes	—
18	C₂×C₄×D₁₇₂	—	2	1	no	—
19	C₂×C₄×D₁₇₂	—	2	1	no	—
20	C₂×C₄×D₁₇₂	—	2	1	no	—
21	C₂×C₄×D₁₇₂	—	2	1	no	—
22	C₂×C₄×D₁₇₂	—	2	1	no	—
23	C₂×C₄×D₁₇₂	—	2	1	no	—
24	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
25	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
26	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
27	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
28	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
29	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
30	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
31	C₂²×(C₂×D₄₃)⋊C₄	—	2	1	no	—
32	#14583232	C₂²	1	4	yes	complemented
33	#14583227	C₂²	1	4	yes	complemented
34	#14583215	C₂²	1	4	yes	complemented
35	#14583210	C₂²	1	4	yes	complemented
36	#14583196	C₂²	1	8	yes	complemented
37	#14583186	C₂²	1	4	yes	complemented
38	#14583176	C₂²	1	4	yes	complemented
39	#14583111	C₂²	1	8	yes	complemented
40	#14583101	C₂²	1	4	yes	complemented
41	#14583091	C₂²	1	4	yes	complemented
42	#14583049	C₂²	1	4	yes	—
43	#14583049	C₂²	1	4	yes	—
44	#14583032	C₂²	1	4	yes	—
45	#14583032	C₂²	1	4	yes	—
46	#14583009	C₂²	1	8	yes	complemented
47	#14582997	C₂²	1	8	yes	complemented
48	C₄×#10621884	C₂²	1	8	yes	complemented
49	C₄×#10621882	C₂²	1	8	yes	complemented
50	#14582956	C₂²	1	2	yes	complemented
51	#14582956	C₂²	1	2	yes	complemented
52	#14582952	C₂²	1	2	yes	complemented
53	#14582952	C₂²	1	2	yes	complemented
54	#14582942	C₂²	1	4	yes	complemented
55	#14582923	C₂²	1	2	yes	complemented
56	#14582903	C₂²	1	4	yes	—
57	#14582900	C₂²	1	4	yes	complemented
58	#14582863	C₂²	1	2	yes	—
59	C₄×#10621877	C₂²	1	2	yes	complemented
60	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
61	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
62	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
63	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
64	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
65	C₄₃×#532	C₂²	1	1	yes	characteristic, complemented
66	C₄₃×#529	—	2	1	no	—
67	C₄₃×#529	—	2	1	no	—
68	C₄₃×#529	—	2	1	no	—
69	C₄₃×#529	—	2	1	no	—
70	C₄₃×#529	C₂²	1	2	yes	complemented
71	C₄₃×#529	C₂²	1	2	yes	complemented
72	C₄₃×#525	—	2	1	no	—
73	C₄₃×#525	—	2	1	no	—
74	C₄₃×#525	C₂²	1	2	yes	—
75	C₄×#41×C₄₃	—	2	1	no	—
76	C₄×#41×C₄₃	—	2	1	no	—
77	C₄×#41×C₄₃	C₂²	1	2	yes	complemented
78	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
79	C₂⁴×D₄₃	—	2	1	no	—
80	C₂²×D₁₇₂	—	2	1	no	—
81	C₂²×D₁₇₂	—	2	1	no	—
82	C₂²×D₁₇₂	—	2	1	no	—
83	C₂²×D₁₇₂	—	2	8	no	—
84	C₂²×D₁₇₂	C₂³	1	2	yes	—
85	C₂²×D₁₇₂	C₂³	1	2	yes	—
86	C₂²×D₁₇₂	C₂³	1	2	yes	—
87	C₂³×Dic₄₃	—	2	1	no	—
88	C₂²×C₄×D₄₃	—	2	2	no	—
89	C₂²×C₄×D₄₃	—	2	2	no	—
90	C₂²×C₄×D₄₃	—	2	2	no	—
91	C₂²×C₄×D₄₃	—	2	2	no	—
92	C₂²×C₄×D₄₃	—	2	2	no	—
93	C₂²×C₄×D₄₃	—	2	2	no	—
94	C₂²×C₄×D₄₃	—	4	8	no	—
95	#13063350	—	2	16	no	—
96	C₂×#10621884	C₂³	1	8	yes	—
97	C₂×#10621882	C₂³	1	8	yes	—
98	C₂×#10621877	C₂³	1	4	yes	—
99	C₄×D₁₇₂	—	2	2	no	—
100	C₄×D₁₇₂	—	2	2	no	—
101	C₄×D₁₇₂	—	2	2	no	—
102	C₄×D₁₇₂	—	2	2	no	—
103	C₄×D₁₇₂	—	2	2	no	—
104	C₄×D₁₇₂	—	2	2	no	—
105	C₄×D₁₇₂	—	2	2	no	—
106	C₄×D₁₇₂	—	2	2	no	—
107	C₄×D₁₇₂	—	2	2	no	—
108	C₄×D₁₇₂	—	2	2	no	—
109	C₄×D₁₇₂	—	2	2	no	—
110	C₄×D₁₇₂	—	2	2	no	—
111	C₄×D₁₇₂	C₂³	1	4	yes	—
112	C₄×D₁₇₂	C₂³	1	4	yes	—
113	C₄×D₁₇₂	C₂³	1	4	yes	—
114	C₄×D₁₇₂	C₂³	1	4	yes	—
115	C₂×C₄⋊Dic₄₃	—	2	1	no	—
116	C₂×C₄⋊Dic₄₃	—	2	1	no	—
117	C₂×C₄⋊Dic₄₃	—	2	1	no	—
118	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
119	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
120	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
121	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
122	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
123	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
124	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
125	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
126	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
127	#13063258	C₂³	1	8	yes	complemented
128	#13063256	C₂³	1	8	yes	complemented
129	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	complemented
130	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	complemented
131	#13063249	C₂³	1	8	yes	complemented
132	#13063246	C₂³	1	8	yes	complemented
133	#13063245	C₂³	1	8	yes	—
134	#13063245	C₂³	1	8	yes	—
135	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
136	C₂²⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
137	#13063236	C₂³	1	4	yes	complemented
138	C₄×C₄₃⋊C₈	C₂³	1	4	yes	complemented
139	C₂×#41×C₄₃	—	2	1	no	—
140	C₂×#41×C₄₃	—	2	1	no	—
141	C₂×#41×C₄₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
143	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
144	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
145	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
146	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
147	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic, complemented
148	#127×C₄₃	C₂³	1	1	yes	characteristic, complemented
149	#126×C₄₃	—	2	2	no	—
150	#126×C₄₃	—	2	2	no	—
151	#125×C₄₃	—	2	1	no	—
152	#125×C₄₃	—	2	1	no	—
153	#125×C₄₃	C₂³	1	2	yes	complemented
154	#124×C₄₃	—	2	1	no	—
155	#124×C₄₃	—	2	1	no	—
156	#124×C₄₃	C₂³	1	2	yes	complemented
157	#123×C₄₃	—	2	2	no	—
158	#123×C₄₃	—	2	2	no	—
159	#123×C₄₃	—	2	2	no	—
160	C₂²⋊Q₈×C₄₃	—	2	1	no	—
161	C₂²⋊Q₈×C₄₃	—	2	1	no	—
162	C₂²⋊Q₈×C₄₃	—	2	1	no	—
163	C₂²⋊Q₈×C₄₃	—	2	1	no	—
164	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
165	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
166	#121×C₄₃	—	2	1	no	—
167	#121×C₄₃	—	2	1	no	—
168	#121×C₄₃	—	2	1	no	—
169	#121×C₄₃	—	2	1	no	—
170	#121×C₄₃	C₂³	1	2	yes	—
171	#121×C₄₃	C₂³	1	2	yes	—
172	#120×C₄₃	—	2	2	no	—
173	C₄×Q₈×C₄₃	—	2	1	no	—
174	C₄×Q₈×C₄₃	—	2	1	no	—
175	C₄×Q₈×C₄₃	—	2	1	no	—
176	C₄×Q₈×C₄₃	—	2	1	no	—
177	C₄×Q₈×C₄₃	C₂³	1	2	yes	complemented
178	C₄×Q₈×C₄₃	C₂³	1	2	yes	complemented
179	C₄×D₄×C₄₃	—	2	2	no	—
180	C₄×D₄×C₄₃	—	2	2	no	—
181	C₄×D₄×C₄₃	—	2	2	no	—
182	C₄×D₄×C₄₃	—	2	2	no	—
183	C₄×D₄×C₄₃	—	2	2	no	—
184	C₄×D₄×C₄₃	—	2	2	no	—
185	C₄×D₄×C₄₃	—	2	1	no	—
186	C₄×D₄×C₄₃	—	2	1	no	—
187	C₄×D₄×C₄₃	—	2	1	no	—
188	C₄×D₄×C₄₃	—	2	1	no	—
189	C₄×D₄×C₄₃	C₂³	1	2	yes	complemented
190	C₄×D₄×C₄₃	C₂³	1	2	yes	complemented
191	#117×C₄₃	—	2	1	no	—
192	#117×C₄₃	—	2	1	no	—
193	#117×C₄₃	—	2	2	no	—
194	#117×C₄₃	—	2	2	no	—
195	#117×C₄₃	—	2	2	no	—
196	#117×C₄₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₄₃	—	2	2	no	—
198	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
199	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
200	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
201	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
202	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
203	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
204	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
210	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
211	C₂³×D₄₃	—	2	8	no	—
212	C₂³×D₄₃	—	2	2	no	—
213	C₂³×D₄₃	—	2	2	no	—
214	C₂³×D₄₃	—	2	2	no	—
215	C₂³×D₄₃	—	4	4	no	—
216	C₂³×D₄₃	—	4	4	no	—
217	#41×C₄₃	—	2	8	no	—
218	#41×C₄₃	—	4	4	no	—
219	#41×C₄₃	—	4	4	no	—
220	C₂×Q₈×C₄₃	—	2	1	no	—
221	C₂×Q₈×C₄₃	—	2	1	no	—
222	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
223	C₂×D₄×C₄₃	—	2	1	no	—
224	C₂×D₄×C₄₃	—	2	1	no	—
225	C₂×D₄×C₄₃	—	2	2	no	—
226	C₂×D₄×C₄₃	—	2	2	no	—
227	C₂×D₄×C₄₃	—	2	2	no	—
228	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₄₃	—	2	4	no	—
230	C₂²×C₄×C₄₃	—	2	4	no	—
231	C₂²×C₄×C₄₃	—	2	2	no	—
232	C₂²×C₄×C₄₃	—	2	2	no	—
233	C₂²×C₄×C₄₃	—	2	2	no	—
234	C₂²×C₄×C₄₃	—	4	2	no	—
235	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
236	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
237	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
238	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
239	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
240	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
241	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
242	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
248	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
253	C₂²×Dic₄₃	—	2	2	no	—
254	C₂²×Dic₄₃	—	2	2	no	—
255	C₂²×Dic₄₃	—	2	2	no	—
256	C₂²×Dic₄₃	—	4	4	no	—
257	C₂×D₁₇₂	—	2	8	no	—
258	C₂×D₁₇₂	—	2	8	no	—
259	C₂×D₁₇₂	—	2	8	no	—
260	C₂×D₁₇₂	—	2	2	no	—
261	C₂×D₁₇₂	—	2	2	no	—
262	C₂×D₁₇₂	—	2	2	no	—
263	C₂×D₁₇₂	—	2	4	no	—
264	C₂×D₁₇₂	—	2	8	no	—
265	C₂×D₁₇₂	—	2	8	no	—
266	C₂×D₁₇₂	#41	1	8	yes	complemented
267	C₂×D₁₇₂	C₂⁴	1	4	yes	—
268	C₂×C₄×D₄₃	—	2	4	no	—
269	C₂×C₄×D₄₃	—	2	4	no	—
270	C₂×C₄×D₄₃	—	2	4	no	—
271	C₂×C₄×D₄₃	—	2	4	no	—
272	C₂×C₄×D₄₃	—	4	8	no	—
273	C₂×C₄×D₄₃	—	4	8	no	—
274	C₂×C₄×D₄₃	—	4	8	no	—
275	C₂×C₄×D₄₃	—	4	8	no	—
276	C₂×C₄×D₄₃	—	4	8	no	—
277	C₂×C₄×D₄₃	—	4	8	no	—
278	C₄⋊C₄×C₄₃	—	2	1	no	—
279	C₄⋊C₄×C₄₃	—	2	1	no	—
280	C₄⋊C₄×C₄₃	—	2	1	no	—
281	C₄⋊C₄×C₄₃	—	2	1	no	—
282	C₄⋊C₄×C₄₃	—	2	2	no	—
283	C₄⋊C₄×C₄₃	—	2	2	no	—
284	C₄⋊C₄×C₄₃	—	2	2	no	—
285	C₄⋊C₄×C₄₃	—	2	2	no	—
286	C₄⋊C₄×C₄₃	—	2	2	no	—
287	C₄⋊C₄×C₄₃	—	2	2	no	—
288	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
290	C₂²⋊C₄×C₄₃	—	2	2	no	—
291	C₂²⋊C₄×C₄₃	—	2	2	no	—
292	C₂²⋊C₄×C₄₃	—	2	2	no	—
293	C₂²⋊C₄×C₄₃	—	2	2	no	—
294	C₂²⋊C₄×C₄₃	—	2	2	no	—
295	C₂²⋊C₄×C₄₃	—	2	2	no	—
296	C₂²⋊C₄×C₄₃	—	2	2	no	—
297	C₂²⋊C₄×C₄₃	—	2	2	no	—
298	C₂²⋊C₄×C₄₃	—	2	2	no	—
299	C₄²×C₄₃	—	2	2	no	—
300	C₄²×C₄₃	—	2	2	no	—
301	C₄²×C₄₃	—	2	2	no	—
302	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
303	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
304	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
305	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
306	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
307	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
308	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
309	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
310	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
311	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
312	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
313	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
314	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
315	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
316	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
317	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
318	#10621884	—	2	16	no	—
319	#10621882	—	2	16	no	—
320	(C₂×D₄₃)⋊C₄	—	2	4	no	—
321	(C₂×D₄₃)⋊C₄	—	2	4	no	—
322	(C₂×D₄₃)⋊C₄	—	2	4	no	—
323	(C₂×D₄₃)⋊C₄	—	2	4	no	—
324	C₄⋊Dic₄₃	—	2	2	no	—
325	C₄⋊Dic₄₃	—	2	2	no	—
326	C₄⋊Dic₄₃	—	2	2	no	—
327	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
328	#10621877	—	2	8	no	—
329	C₂×C₄₃⋊C₈	C₂⁴	1	8	yes	—
330	C₂³×C₄₃	—	2	2	no	—
331	C₂³×C₄₃	—	2	2	no	—
332	C₂³×C₄₃	—	2	2	no	—
333	C₂³×C₄₃	—	2	2	no	—
334	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
335	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
336	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
337	C₂²×D₄₃	—	2	8	no	—
338	C₂²×D₄₃	—	2	8	no	—
339	C₂²×D₄₃	—	2	8	no	—
340	C₂²×D₄₃	—	2	4	no	—
341	C₂²×D₄₃	—	4	4	no	—
342	C₂²×D₄₃	—	4	4	no	—
343	C₂²×D₄₃	—	4	32	no	—
344	C₂²×D₄₃	—	4	4	no	—
345	C₂²×D₄₃	—	4	4	no	—
346	C₂²×D₄₃	—	4	4	no	—
347	C₂²×D₄₃	—	4	4	no	—
348	Q₈×C₄₃	—	2	4	no	—
349	Q₈×C₄₃	—	4	2	no	—
350	Q₈×C₄₃	—	4	2	no	—
351	D₄×C₄₃	—	2	4	no	—
352	D₄×C₄₃	—	4	2	no	—
353	D₄×C₄₃	—	4	4	no	—
354	D₄×C₄₃	—	4	4	no	—
355	D₄×C₄₃	—	4	4	no	—
356	D₄×C₄₃	—	4	2	no	—
357	C₂×C₄×C₄₃	—	2	2	no	—
358	C₂×C₄×C₄₃	—	2	2	no	—
359	C₂×C₄×C₄₃	—	2	2	no	—
360	C₂×C₄×C₄₃	—	2	2	no	—
361	C₂×C₄×C₄₃	—	2	2	no	—
362	C₂×C₄×C₄₃	—	2	2	no	—
363	C₂×C₄×C₄₃	—	2	2	no	—
364	C₂×C₄×C₄₃	—	2	2	no	—
365	C₂×C₄×C₄₃	—	2	2	no	—
366	C₂×C₄×C₄₃	—	2	2	no	—
367	C₂×C₄×C₄₃	—	2	2	no	—
368	C₂×C₄×C₄₃	—	2	2	no	—
369	C₂×C₄×C₄₃	—	2	2	no	—
370	C₂×C₄×C₄₃	—	2	2	no	—
371	C₂×C₄×C₄₃	—	2	2	no	—
372	C₂×C₄×C₄₃	—	4	1	no	—
373	C₂×C₄×C₄₃	—	4	1	no	—
374	C₂×C₄×C₄₃	—	4	1	no	—
375	C₂×C₄×C₄₃	—	4	1	no	—
376	C₂×C₄×C₄₃	—	4	4	no	—
377	C₂×C₄×C₄₃	—	4	4	no	—
378	C₂×C₄×C₄₃	—	4	4	no	—
379	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	complemented
380	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
386	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
392	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
393	C₂×Dic₄₃	—	2	4	no	—
394	C₂×Dic₄₃	—	4	4	no	—
395	C₂×Dic₄₃	—	4	4	no	—
396	C₂×Dic₄₃	—	4	4	no	—
397	D₁₇₂	—	2	8	no	—
398	D₁₇₂	—	2	8	no	—
399	D₁₇₂	—	2	8	no	—
400	D₁₇₂	—	2	4	no	—
401	D₁₇₂	C₂×#41	1	8	yes	—
402	C₄×D₄₃	—	4	8	no	—
403	C₄×D₄₃	—	4	8	no	—
404	C₄×D₄₃	—	4	8	no	—
405	C₄×D₄₃	—	4	8	no	—
406	C₄₃⋊C₈	—	2	8	no	—
407	#60558	—	43	1	no	maximal, Sylow
408	C₂²×C₄₃	—	2	8	no	—
409	C₂²×C₄₃	—	2	1	no	—
410	C₂²×C₄₃	—	2	1	no	—
411	C₂²×C₄₃	—	2	1	no	—
412	C₂²×C₄₃	—	2	1	no	—
413	C₂²×C₄₃	—	2	1	no	—
414	C₂²×C₄₃	—	2	1	no	—
415	C₂²×C₄₃	—	4	2	no	—
416	C₂²×C₄₃	—	4	2	no	—
417	C₂²×C₄₃	—	4	2	no	—
418	C₂²×C₄₃	#525	1	2	yes	—
419	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
420	C₂²×C₄₃	#575	1	2	yes	—
421	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
422	C₂×D₄₃	—	2	8	no	—
423	C₂×D₄₃	—	4	16	no	—
424	C₂×D₄₃	—	4	16	no	—
425	C₂×D₄₃	—	4	16	no	—
426	C₂×D₄₃	—	4	4	no	—
427	C₂×D₄₃	—	4	4	no	—
428	C₄×C₄₃	—	2	1	no	—
429	C₄×C₄₃	—	2	1	no	—
430	C₄×C₄₃	—	2	1	no	—
431	C₄×C₄₃	—	2	1	no	—
432	C₄×C₄₃	—	2	1	no	—
433	C₄×C₄₃	—	2	1	no	—
434	C₄×C₄₃	—	2	1	no	—
435	C₄×C₄₃	—	2	1	no	—
436	C₄×C₄₃	—	4	2	no	—
437	C₄×C₄₃	—	4	2	no	—
438	C₄×C₄₃	—	4	2	no	—
439	C₄×C₄₃	#525	1	2	yes	—
440	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
441	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
442	C₄×C₄₃	C₂²×#41	1	2	yes	—
443	Dic₄₃	—	4	4	no	—
444	#3444	D₄₃	1	1	yes	characteristic, complemented
445	C₂²×C₄×D₄	—	43	1	no	—
446	#3114	—	43	4	no	—
447	#3110	—	43	2	no	—
448	#3109	—	43	2	no	—
449	#3105	—	43	4	no	—
450	#3101	—	43	2	no	—
451	#3100	—	43	2	no	—
452	#3092	—	43	2	no	—
453	#3077	—	43	2	no	—
454	#3036	—	43	2	no	—
455	#3003	—	43	2	no	—
456	C₄×AGL(1,ℤ/8)	—	43	4	no	—
457	#2920	—	43	1	no	—
458	C₂×C₄₃	—	2	2	no	—
459	C₂×C₄₃	—	2	2	no	—
460	C₂×C₄₃	—	2	2	no	—
461	C₂×C₄₃	—	8	2	no	—
462	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
463	C₂×C₄₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
464	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
465	D₄₃	—	4	8	no	—
466	C₂³×D₄	—	43	1	no	—
467	C₂⁴×C₄	—	86	1	no	—
468	C₂×AGL(1,ℤ/8)	—	43	4	no	—
469	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
470	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
471	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
472	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
473	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
474	#532	C₂×D₄₃	1	1	yes	characteristic, complemented
475	#529	—	2	1	no	—
476	#529	—	2	1	no	—
477	#529	—	2	1	no	—
478	#529	—	2	1	no	—
479	#529	C₂×D₄₃	1	2	yes	complemented
480	#529	C₂×D₄₃	1	2	yes	complemented
481	#525	—	2	1	no	—
482	#525	—	2	1	no	—
483	#525	C₂×D₄₃	1	2	yes	—
484	C₄×#41	—	2	1	no	—
485	C₄×#41	—	2	1	no	—
486	C₄×#41	C₂×D₄₃	1	2	yes	complemented
487	C₂×C₄×D₄	—	43	2	no	—
488	C₂×C₄×D₄	—	43	2	no	—
489	C₂×C₄×D₄	—	43	2	no	—
490	C₂×C₄×D₄	—	43	2	no	—
491	C₂×C₄×D₄	—	43	2	no	—
492	C₂×C₄×D₄	—	43	2	no	—
493	C₂×C₄×D₄	—	86	1	no	—
494	C₂×C₄×D₄	—	86	1	no	—
495	C₂×C₄×D₄	—	86	1	no	—
496	C₂×C₄×D₄	—	86	1	no	—
497	C₂×C₄×D₄	—	86	1	no	—
498	C₂×C₄×D₄	—	86	1	no	—
499	C₂²×C₄⋊C₄	—	43	1	no	—
500	C₂²×C₂²⋊C₄	—	86	1	no	—
501	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
502	#484	—	43	4	no	—
503	#483	—	43	4	no	—
504	#481	—	43	4	no	—
505	#480	—	43	4	no	—
506	#478	—	43	8	no	—
507	#476	—	43	4	no	—
508	#474	—	43	4	no	—
509	#463	—	43	8	no	—
510	#461	—	43	4	no	—
511	#459	—	43	4	no	—
512	#450	—	43	4	no	—
513	#450	—	43	4	no	—
514	#447	—	43	4	no	—
515	#447	—	43	4	no	—
516	#442	—	43	8	no	—
517	#440	—	43	8	no	—
518	C₄×SD₁₆	—	43	8	no	—
519	C₄×D₈	—	43	8	no	—
520	#432	—	43	2	no	—
521	#432	—	43	2	no	—
522	#431	—	43	2	no	—
523	#431	—	43	2	no	—
524	#428	—	43	4	no	—
525	#423	—	43	2	no	—
526	#418	—	43	4	no	—
527	#417	—	43	4	no	—
528	#407	—	43	2	no	—
529	C₄×M₁₆	—	43	2	no	—
530	C₄₃	#60558	1	1	yes	characteristic, complemented, Sylow
531	C₂⁵	—	86	1	no	—
532	C₂×#41	—	2	1	no	—
533	C₂×#41	—	2	1	no	—
534	C₂×#41	C₂²×D₄₃	1	2	yes	—
535	C₂²×D₄	—	43	2	no	—
536	C₂²×D₄	—	43	2	no	—
537	C₂²×D₄	—	43	2	no	—
538	C₂²×D₄	—	86	8	no	—
539	C₂²×D₄	—	86	1	no	—
540	C₂²×D₄	—	86	1	no	—
541	C₂²×D₄	—	86	1	no	—
542	C₂³×C₄	—	86	1	no	—
543	C₂³×C₄	—	86	2	no	—
544	C₂³×C₄	—	86	2	no	—
545	C₂³×C₄	—	86	2	no	—
546	C₂³×C₄	—	86	2	no	—
547	C₂³×C₄	—	86	2	no	—
548	C₂³×C₄	—	86	2	no	—
549	C₂³×C₄	—	172	8	no	—
550	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
551	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
552	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
553	AGL(1,ℤ/8)	—	86	16	no	—
554	C₂×SD₁₆	—	43	8	no	—
555	C₂×D₈	—	43	8	no	—
556	C₂×M₁₆	—	43	4	no	—
557	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
558	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
559	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic, complemented
560	#127	C₂²×D₄₃	1	1	yes	characteristic, complemented
561	#126	—	2	2	no	—
562	#126	—	2	2	no	—
563	#125	—	2	1	no	—
564	#125	—	2	1	no	—
565	#125	C₂²×D₄₃	1	2	yes	complemented
566	#124	—	2	1	no	—
567	#124	—	2	1	no	—
568	#124	C₂²×D₄₃	1	2	yes	complemented
569	#123	—	2	2	no	—
570	#123	—	2	2	no	—
571	#123	—	2	2	no	—
572	C₂²⋊Q₈	—	2	1	no	—
573	C₂²⋊Q₈	—	2	1	no	—
574	C₂²⋊Q₈	—	2	1	no	—
575	C₂²⋊Q₈	—	2	1	no	—
576	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
577	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
578	#121	—	2	1	no	—
579	#121	—	2	1	no	—
580	#121	—	2	1	no	—
581	#121	—	2	1	no	—
582	#121	C₂²×D₄₃	1	2	yes	—
583	#121	C₂²×D₄₃	1	2	yes	—
584	#120	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	C₂²×D₄₃	1	2	yes	complemented
590	C₄×Q₈	C₂²×D₄₃	1	2	yes	complemented
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	1	no	—
599	C₄×D₄	—	2	1	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	43	4	no	—
602	C₄×D₄	—	43	4	no	—
603	C₄×D₄	—	43	4	no	—
604	C₄×D₄	—	43	4	no	—
605	C₄×D₄	—	86	2	no	—
606	C₄×D₄	—	86	2	no	—
607	C₄×D₄	—	86	2	no	—
608	C₄×D₄	—	86	2	no	—
609	C₄×D₄	—	86	2	no	—
610	C₄×D₄	—	86	2	no	—
611	C₄×D₄	—	86	2	no	—
612	C₄×D₄	—	86	2	no	—
613	C₄×D₄	—	86	2	no	—
614	C₄×D₄	—	86	2	no	—
615	C₄×D₄	—	86	2	no	—
616	C₄×D₄	—	86	2	no	—
617	C₄×D₄	C₂²×D₄₃	1	2	yes	complemented
618	C₄×D₄	C₂²×D₄₃	1	2	yes	complemented
619	#117	—	2	1	no	—
620	#117	—	2	1	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	C₂²×D₄₃	1	2	yes	—
625	C₂×C₄⋊C₄	—	43	2	no	—
626	C₂×C₄⋊C₄	—	43	2	no	—
627	C₂×C₄⋊C₄	—	43	2	no	—
628	C₂×C₄⋊C₄	—	86	1	no	—
629	C₂×C₄⋊C₄	—	86	1	no	—
630	C₂×C₄⋊C₄	—	86	1	no	—
631	C₂×C₂²⋊C₄	—	86	2	no	—
632	C₂×C₂²⋊C₄	—	86	2	no	—
633	C₂×C₂²⋊C₄	—	86	2	no	—
634	C₂×C₂²⋊C₄	—	86	2	no	—
635	C₂×C₂²⋊C₄	—	86	2	no	—
636	C₂×C₂²⋊C₄	—	86	2	no	—
637	C₂×C₄²	—	2	2	no	—
638	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
639	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
640	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
641	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
642	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
643	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
644	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
645	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
646	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
647	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
648	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
649	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
650	#107	—	43	8	no	—
651	#106	—	43	8	no	—
652	C₄⋊C₈	—	43	4	no	—
653	C₄⋊C₈	—	43	4	no	—
654	#103	—	43	8	no	—
655	#102	—	43	8	no	—
656	#102	—	43	8	no	—
657	#102	—	43	8	no	—
658	C₂²⋊C₈	—	43	4	no	—
659	C₂²⋊C₈	—	43	4	no	—
660	#97	—	43	4	no	—
661	C₄×C₈	—	43	4	no	—
662	C₂⁴	—	86	8	no	—
663	C₂⁴	—	86	2	no	—
664	C₂⁴	—	86	2	no	—
665	C₂⁴	—	86	2	no	—
666	C₂⁴	—	172	4	no	—
667	C₂⁴	—	172	4	no	—
668	C₂⁴	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
669	#41	—	2	8	no	—
670	#41	—	4	4	no	—
671	#41	—	4	4	no	—
672	C₂×Q₈	—	2	1	no	—
673	C₂×Q₈	—	2	1	no	—
674	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	43	8	no	—
681	C₂×D₄	—	43	4	no	—
682	C₂×D₄	—	86	8	no	—
683	C₂×D₄	—	86	8	no	—
684	C₂×D₄	—	86	8	no	—
685	C₂×D₄	—	86	8	no	—
686	C₂×D₄	—	86	8	no	—
687	C₂×D₄	—	86	2	no	—
688	C₂×D₄	—	86	2	no	—
689	C₂×D₄	—	86	2	no	—
690	C₂×D₄	—	86	4	no	—
691	C₂×D₄	C₂³×D₄₃	1	2	yes	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	2	4	no	—
694	C₂²×C₄	—	2	2	no	—
695	C₂²×C₄	—	2	2	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	4	2	no	—
698	C₂²×C₄	—	86	2	no	—
699	C₂²×C₄	—	86	2	no	—
700	C₂²×C₄	—	86	2	no	—
701	C₂²×C₄	—	86	4	no	—
702	C₂²×C₄	—	86	4	no	—
703	C₂²×C₄	—	86	4	no	—
704	C₂²×C₄	—	86	4	no	—
705	C₂²×C₄	—	172	8	no	—
706	C₂²×C₄	—	172	8	no	—
707	C₂²×C₄	—	172	8	no	—
708	C₂²×C₄	—	172	8	no	—
709	C₂²×C₄	—	172	8	no	—
710	C₂²×C₄	—	172	4	no	—
711	C₂²×C₄	—	172	8	no	—
712	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
715	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
716	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
717	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
718	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
719	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
720	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
721	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
722	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
723	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
724	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
725	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
726	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
727	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
728	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
729	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
730	SD₁₆	—	86	16	no	—
731	D₈	—	86	16	no	—
732	M₁₆	—	86	8	no	—
733	C₂×C₈	—	43	8	no	—
734	C₄⋊C₄	—	2	1	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	2	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	43	4	no	—
745	C₄⋊C₄	—	86	2	no	—
746	C₄⋊C₄	—	86	2	no	—
747	C₄⋊C₄	—	86	2	no	—
748	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
749	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	2	no	—
753	C₂²⋊C₄	—	2	2	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	2	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	86	4	no	—
760	C₂²⋊C₄	—	86	4	no	—
761	C₂²⋊C₄	—	86	4	no	—
762	C₂²⋊C₄	—	86	4	no	—
763	C₄²	—	2	2	no	—
764	C₄²	—	2	2	no	—
765	C₄²	—	2	2	no	—
766	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
767	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
768	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
769	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
770	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
771	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
772	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
773	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
774	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
775	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
776	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
777	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
778	C₄²	C₂³×D₄₃	1	1	yes	characteristic
779	C₄²	C₂³×D₄₃	1	1	yes	characteristic
780	C₄²	C₂³×D₄₃	1	1	yes	characteristic
781	C₄²	C₂³×D₄₃	1	1	yes	characteristic
782	C₂³	—	2	2	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	86	8	no	—
787	C₂³	—	86	8	no	—
788	C₂³	—	86	8	no	—
789	C₂³	—	86	4	no	—
790	C₂³	—	172	4	no	—
791	C₂³	—	172	4	no	—
792	C₂³	—	172	32	no	—
793	C₂³	—	172	4	no	—
794	C₂³	—	172	4	no	—
795	C₂³	—	172	4	no	—
796	C₂³	—	172	4	no	—
797	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
798	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
799	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
800	Q₈	—	2	4	no	—
801	Q₈	—	4	2	no	—
802	Q₈	—	4	2	no	—
803	D₄	—	2	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	D₄	—	4	4	no	—
807	D₄	—	4	4	no	—
808	D₄	—	4	2	no	—
809	D₄	—	43	8	no	—
810	D₄	—	86	8	no	—
811	D₄	—	86	8	no	—
812	D₄	—	86	8	no	—
813	D₄	—	86	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	4	1	no	—
830	C₂×C₄	—	4	1	no	—
831	C₂×C₄	—	4	1	no	—
832	C₂×C₄	—	4	1	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	86	4	no	—
837	C₂×C₄	—	172	8	no	—
838	C₂×C₄	—	172	8	no	—
839	C₂×C₄	—	172	4	no	—
840	C₂×C₄	—	172	4	no	—
841	C₂×C₄	—	172	4	no	—
842	C₂×C₄	—	172	8	no	—
843	C₂×C₄	—	172	8	no	—
844	C₂×C₄	#13063350	1	4	yes	complemented
845	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
847	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
848	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
849	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
850	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
851	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
852	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
853	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
855	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
856	C₂×C₄	#41×D₄₃	1	4	yes	—
857	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
858	C₈	—	86	8	no	—
859	C₂²	—	2	8	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	4	2	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	86	8	no	—
870	C₂²	—	172	16	no	—
871	C₂²	—	172	16	no	—
872	C₂²	—	172	16	no	—
873	C₂²	—	172	4	no	—
874	C₂²	—	172	4	no	—
875	C₂²	#14583406	1	2	yes	—
876	C₂²	C₂×#13063350	1	2	yes	—
877	C₂²	#14583697	1	2	yes	—
878	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
879	C₄	—	2	1	no	—
880	C₄	—	2	1	no	—
881	C₄	—	2	1	no	—
882	C₄	—	2	1	no	—
883	C₄	—	2	1	no	—
884	C₄	—	2	1	no	—
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	172	4	no	—
891	C₄	#14583406	1	2	yes	—
892	C₄	C₂×#13063350	1	2	yes	—
893	C₄	C₂×#13063350	1	2	yes	—
894	C₄	C₂×#41×D₄₃	1	2	yes	—
895	C₂	—	2	2	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	2	no	—
898	C₂	—	8	2	no	—
899	C₂	—	172	8	no	—
900	C₂	C₂×#14583406	1	1	yes	characteristic
901	C₂	C₂²×#13063350	1	1	yes	characteristic
902	C₂	C₂×#14583697	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3444	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3444	D₄₃
hypocenter	C₄₃	#60558
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ #3444

Complements

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

N	H ≅ G/N	type
1. C₂²×C₄×D₁₇₂	C₂	semidirect
2. #19144729	C₂	semidirect
3. #19144690	C₂	semidirect
4. #19144682	C₂	semidirect
5. #19144638	C₂	semidirect
6. #19144599	C₂	semidirect
7. #19144591	C₂	semidirect
8. #19144515	C₂	semidirect
9. #19144388	C₂	semidirect
10. #19144055	C₂	semidirect
11. #19143821	C₂	semidirect
12. C₄×#13063350	C₂	semidirect
13. #19143228	C₂	semidirect
14. C₄₃×#3444	C₂	semidirect
32. #14583232	C₂²	semidirect
33. #14583227	C₂²	semidirect
34. #14583215	C₂²	semidirect
35. #14583210	C₂²	semidirect
36. #14583196	C₂²	semidirect
37. #14583186	C₂²	semidirect
38. #14583176	C₂²	semidirect
39. #14583111	C₂²	semidirect
40. #14583101	C₂²	semidirect
41. #14583091	C₂²	semidirect
46. #14583009	C₂²	semidirect
47. #14582997	C₂²	semidirect
48. C₄×#10621884	C₂²	semidirect
49. C₄×#10621882	C₂²	semidirect
50. #14582956	C₂²	semidirect
51. #14582956	C₂²	semidirect
52. #14582952	C₂²	semidirect
53. #14582952	C₂²	semidirect
54. #14582942	C₂²	semidirect
55. #14582923	C₂²	semidirect
57. #14582900	C₂²	semidirect
59. C₄×#10621877	C₂²	semidirect
60. C₄₃×#533	C₂²	semidirect
61. C₄₃×#533	C₂²	semidirect
62. C₄₃×#533	C₂²	semidirect
63. C₄₃×#532	C₂²	semidirect
64. C₄₃×#532	C₂²	semidirect
65. C₄₃×#532	C₂²	semidirect
70. C₄₃×#529	C₂²	semidirect
71. C₄₃×#529	C₂²	semidirect
77. C₄×#41×C₄₃	C₂²	semidirect
127. #13063258	C₂³	semidirect
128. #13063256	C₂³	semidirect
129. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
130. C₄⋊(C₄₃⋊C₈)	C₂³	semidirect
131. #13063249	C₂³	semidirect
132. #13063246	C₂³	semidirect
137. #13063236	C₂³	semidirect
138. C₄×C₄₃⋊C₈	C₂³	semidirect
145. C₄⋊Q₈×C₄₃	C₂³	semidirect
146. C₄⋊Q₈×C₄₃	C₂³	semidirect
147. C₄⋊Q₈×C₄₃	C₂³	semidirect
148. #127×C₄₃	C₂³	semidirect
153. #125×C₄₃	C₂³	semidirect
156. #124×C₄₃	C₂³	semidirect
177. C₄×Q₈×C₄₃	C₂³	semidirect
178. C₄×Q₈×C₄₃	C₂³	semidirect
189. C₄×D₄×C₄₃	C₂³	semidirect
190. C₄×D₄×C₄₃	C₂³	semidirect
266. C₂×D₁₇₂	#41	semidirect
379. C₂×C₄×C₄₃	AGL(1,ℤ/8)	semidirect
444. #3444	D₄₃	semidirect
469. #533	C₂×D₄₃	semidirect
470. #533	C₂×D₄₃	semidirect
471. #533	C₂×D₄₃	semidirect
472. #532	C₂×D₄₃	semidirect
473. #532	C₂×D₄₃	semidirect
474. #532	C₂×D₄₃	semidirect
479. #529	C₂×D₄₃	semidirect
480. #529	C₂×D₄₃	semidirect
486. C₄×#41	C₂×D₄₃	semidirect
530. C₄₃	#60558	semidirect
557. C₄⋊Q₈	C₂²×D₄₃	semidirect
558. C₄⋊Q₈	C₂²×D₄₃	semidirect
559. C₄⋊Q₈	C₂²×D₄₃	semidirect
560. #127	C₂²×D₄₃	semidirect
565. #125	C₂²×D₄₃	semidirect
568. #124	C₂²×D₄₃	semidirect
589. C₄×Q₈	C₂²×D₄₃	semidirect
590. C₄×Q₈	C₂²×D₄₃	semidirect
617. C₄×D₄	C₂²×D₄₃	semidirect
618. C₄×D₄	C₂²×D₄₃	semidirect
844. C₂×C₄	#13063350	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₁₇₂	2
#19144729	2
#19144690	2
#19144682	2
#19144638	2
#19144599	2
#19144591	2
#19144515	2
#19144388	2
#19144055	2
#19143821	2
C₄×#13063350	2
#19143228	2
C₄₃×#3444	2
#60558	43