Subgroups — C₂×#19148646 #26004612

Order 11008.

7910 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148646	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583622	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583606	C₂	1	2	yes	maximal, complemented
4	C₂×#14583587	C₂	1	2	yes	maximal, complemented
5	C₂×#14583572	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14583557	C₂	1	2	yes	maximal, complemented
8	C₂×#14583554	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14583553	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14583545	C₂	1	2	yes	maximal, complemented
11	C₂×#14583520	C₂	1	2	yes	maximal, complemented
12	C₂×#14583490	C₂	1	4	yes	maximal, complemented
13	C₂×#14583456	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14583409	C₂	1	2	yes	maximal, complemented
15	C₂×C₂²⋊Q₈×D₄₃	C₂	1	2	yes	maximal, complemented
16	C₂×#14583379	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#10621898	C₂²	1	2	yes	—
20	C₂²×#10621900	C₂²	1	2	yes	complemented
21	C₂²×Q₈×D₄₃	C₂²	1	2	yes	complemented
22	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic
23	C₂³×C₄×D₄₃	C₂²	1	2	yes	—
24	#14583622	C₂²	1	16	yes	complemented
25	#14583606	C₂²	1	32	yes	complemented
26	#14583587	C₂²	1	32	yes	complemented
27	#14583572	C₂²	1	64	yes	complemented
28	Q₈×D₁₇₂	C₂²	1	16	yes	complemented
29	#14583557	C₂²	1	32	yes	complemented
30	#14583554	C₂²	1	16	yes	complemented
31	#14583553	C₂²	1	16	yes	complemented
32	#14583545	C₂²	1	32	yes	complemented
33	#14583520	C₂²	1	32	yes	complemented
34	#14583490	C₂²	1	64	yes	complemented
35	#14583456	C₂²	1	16	yes	complemented
36	C₂×#13063325	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13063325	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13063325	C₂²	1	2	yes	complemented
39	C₂×#13063320	C₂²	1	4	yes	complemented
40	C₂×#13063320	C₂²	1	4	yes	complemented
41	C₂×#13063317	C₂²	1	2	yes	complemented
42	C₂×#13063316	C₂²	1	4	yes	complemented
43	C₂×#13063313	C₂²	1	2	yes	—
44	C₂×#13063311	C₂²	1	4	yes	complemented
45	#14583409	C₂²	1	32	yes	complemented
46	C₂×#13063310	C₂²	1	4	yes	—
47	C₂×#13063309	C₂²	1	4	yes	complemented
48	C₂×#13063307	C₂²	1	4	yes	complemented
49	C₂×#13063307	C₂²	1	4	yes	complemented
50	C₂×#13063305	C₂²	1	2	yes	complemented
51	C₂×#13063305	C₂²	1	4	yes	complemented
52	C₂×#13063305	C₂²	1	2	yes	complemented
53	C₂×#13063304	C₂²	1	2	yes	—
54	C₂×#13063304	C₂²	1	2	yes	—
55	C₂×#13063304	C₂²	1	2	yes	complemented
56	C₂×#13063303	C₂²	1	4	yes	complemented
57	C₂×#13063302	C₂²	1	4	yes	—
58	C₂×#13063302	C₂²	1	4	yes	complemented
59	C₂×#13063301	C₂²	1	2	yes	complemented
60	C₂²⋊Q₈×D₄₃	C₂²	1	32	yes	complemented
61	C₂×#13063299	C₂²	1	2	yes	—
62	C₂×#13063298	C₂²	1	4	yes	—
63	C₂×#13063296	C₂²	1	2	yes	complemented
64	C₂×#13063293	C₂²	1	4	yes	—
65	#14583379	C₂²	1	32	yes	complemented
66	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
67	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
69	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
70	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
71	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
73	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
74	C₂×C₄×D₁₇₂	C₂²	1	2	yes	—
75	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₁₇₂	C₂²	1	16	yes	complemented
77	C₂×D₄×Dic₄₃	C₂²	1	4	yes	—
78	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
79	C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	1	4	yes	complemented
80	C₂×#13063284	C₂²	1	2	yes	—
81	C₂×#13063283	C₂²	1	4	yes	complemented
82	C₂×#13063283	C₂²	1	2	yes	complemented
83	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
84	C₂²×C₄⋊Dic₄₃	C₂²	1	2	yes	complemented
85	C₂×C₄⋊C₄×D₄₃	C₂²	1	4	yes	complemented
86	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	complemented
87	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	—
88	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	—
89	C₄₃×#529	C₂²	1	16	yes	complemented
90	C₂×#126×C₄₃	C₂²	1	2	yes	complemented
91	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic, complemented
92	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
93	C₂×#123×C₄₃	C₂²	1	2	yes	—
94	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
95	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
96	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
97	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
98	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
99	C₂×#117×C₄₃	C₂²	1	2	yes	complemented
100	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
101	C₂⁴×D₄₃	C₂³	1	2	yes	—
102	C₂×#10621898	—	2	16	no	—
103	C₂×#10621898	C₂³	1	16	yes	—
104	C₂×#10621900	—	4	8	no	—
105	C₂×#10621900	C₂³	1	16	yes	complemented
106	C₂²×Dic₈₆	C₂³	1	2	yes	—
107	C₂²×Dic₈₆	C₂³	1	2	yes	—
108	C₂²×Dic₈₆	C₂³	1	4	yes	—
109	C₂×Q₈×D₄₃	—	4	8	no	—
110	C₂×Q₈×D₄₃	C₂³	1	16	yes	complemented
111	C₂²×D₁₇₂	—	2	8	no	—
112	C₂²×D₁₇₂	C₂³	1	2	yes	—
113	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
114	C₂²×D₁₇₂	C₂³	1	8	yes	—
115	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
116	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
117	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
118	C₂³×Dic₄₃	C₂³	1	2	yes	—
119	C₂³×Dic₄₃	C₂³	1	4	yes	—
120	C₂²×C₄×D₄₃	—	4	8	no	—
121	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
122	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
123	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
124	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
125	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
126	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
127	C₂²×C₄×D₄₃	C₂³	1	16	yes	—
128	#13063325	C₂³	1	8	yes	complemented
129	#13063325	C₂³	1	8	yes	complemented
130	#13063325	C₂³	1	16	yes	complemented
131	#13063320	C₂³	1	32	yes	complemented
132	#13063320	C₂³	1	32	yes	complemented
133	#13063317	C₂³	1	16	yes	complemented
134	#13063316	C₂³	1	32	yes	complemented
135	#13063313	C₂³	1	16	yes	—
136	#13063311	C₂³	1	32	yes	complemented
137	#13063310	C₂³	1	32	yes	—
138	#13063309	C₂³	1	32	yes	complemented
139	#13063307	C₂³	1	32	yes	complemented
140	#13063307	C₂³	1	32	yes	complemented
141	#13063305	C₂³	1	16	yes	complemented
142	#13063305	C₂³	1	32	yes	complemented
143	#13063305	C₂³	1	16	yes	complemented
144	#13063304	C₂³	1	16	yes	—
145	#13063304	C₂³	1	16	yes	—
146	#13063304	C₂³	1	16	yes	complemented
147	#13063303	C₂³	1	32	yes	complemented
148	#13063302	C₂³	1	32	yes	—
149	#13063302	C₂³	1	32	yes	complemented
150	#13063301	C₂³	1	16	yes	complemented
151	#13063299	C₂³	1	16	yes	—
152	#13063298	C₂³	1	32	yes	—
153	#13063296	C₂³	1	16	yes	complemented
154	#13063293	C₂³	1	32	yes	—
155	C₄×Dic₈₆	C₂³	1	16	yes	complemented
156	C₄×Dic₈₆	C₂³	1	16	yes	complemented
157	C₄×Dic₈₆	C₂³	1	16	yes	complemented
158	C₄×D₁₇₂	C₂³	1	8	yes	—
159	C₄×D₁₇₂	C₂³	1	8	yes	—
160	C₄×D₁₇₂	C₂³	1	16	yes	—
161	C₄×D₁₇₂	C₂³	1	16	yes	—
162	C₄×D₁₇₂	C₂³	1	8	yes	—
163	C₄×D₁₇₂	C₂³	1	16	yes	—
164	C₄×D₁₇₂	C₂³	1	8	yes	—
165	D₄×Dic₄₃	C₂³	1	32	yes	—
166	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	complemented
167	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	complemented
168	#13063284	C₂³	1	16	yes	—
169	#13063283	C₂³	1	32	yes	complemented
170	#13063283	C₂³	1	16	yes	complemented
171	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
172	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	—
175	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
176	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
177	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
178	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
179	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
180	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
181	C₂×C₄⋊Dic₄₃	C₂³	1	16	yes	complemented
182	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
183	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
184	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
185	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
186	C₄⋊C₄×D₄₃	C₂³	1	16	yes	complemented
187	C₄⋊C₄×D₄₃	C₂³	1	32	yes	complemented
188	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
189	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
190	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	—
191	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
192	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
193	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
194	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
195	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
196	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
197	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
198	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
199	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	—
200	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
201	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
202	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
204	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
209	#126×C₄₃	C₂³	1	16	yes	complemented
210	#125×C₄₃	C₂³	1	8	yes	complemented
211	#124×C₄₃	C₂³	1	8	yes	complemented
212	#123×C₄₃	C₂³	1	16	yes	—
213	C₂²⋊Q₈×C₄₃	C₂³	1	8	yes	—
214	#121×C₄₃	C₂³	1	8	yes	—
215	C₄×Q₈×C₄₃	C₂³	1	8	yes	complemented
216	C₄×D₄×C₄₃	C₂³	1	16	yes	—
217	C₄×D₄×C₄₃	C₂³	1	8	yes	complemented
218	#117×C₄₃	C₂³	1	16	yes	complemented
219	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
221	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
222	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
225	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
226	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
227	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
228	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
229	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
230	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
233	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
234	C₂×C₄²×C₄₃	C₂³	1	8	yes	—
235	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
236	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
237	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
238	C₂³×D₄₃	—	2	8	no	—
239	C₂³×D₄₃	—	2	8	no	—
240	C₂³×D₄₃	—	4	4	no	—
241	C₂³×D₄₃	C₂⁴	1	2	yes	—
242	C₂³×D₄₃	C₂⁴	1	8	yes	—
243	C₂³×D₄₃	C₂⁴	1	2	yes	—
244	C₂×Q₈×C₄₃	—	2	4	no	—
245	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
246	C₂×D₄×C₄₃	—	2	4	no	—
247	C₂×D₄×C₄₃	—	2	8	no	—
248	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
249	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₄₃	—	2	4	no	—
251	C₂²×C₄×C₄₃	—	2	8	no	—
252	C₂²×C₄×C₄₃	—	2	4	no	—
253	C₂²×C₄×C₄₃	—	2	4	no	—
254	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
258	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
265	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
267	C₂×C₂²⋊D₄₃	—	2	16	no	—
268	C₂×C₂²⋊D₄₃	—	4	8	no	—
269	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
270	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
271	C₂²×Dic₄₃	—	4	4	no	—
272	C₂²×Dic₄₃	—	4	8	no	—
273	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
274	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
275	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
276	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
277	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
278	C₂²×Dic₄₃	C₂⁴	1	16	yes	—
279	Q₈×D₄₃	—	4	32	no	—
280	#10621900	—	4	32	no	—
281	#10621898	—	2	64	no	—
282	C₂×D₁₇₂	—	2	4	no	—
283	C₂×D₁₇₂	—	2	32	no	—
284	C₂×D₁₇₂	—	2	8	no	—
285	C₂×D₁₇₂	#41	1	8	yes	complemented
286	C₂×D₁₇₂	C₂⁴	1	8	yes	—
287	C₂×D₁₇₂	C₂⁴	1	4	yes	—
288	C₂×D₁₇₂	C₂⁴	1	4	yes	—
289	C₂×C₄×D₄₃	—	2	8	no	—
290	C₂×C₄×D₄₃	—	2	8	no	—
291	C₂×C₄×D₄₃	—	2	16	no	—
292	C₂×C₄×D₄₃	—	4	4	no	—
293	C₂×C₄×D₄₃	—	4	4	no	—
294	C₂×C₄×D₄₃	—	4	8	no	—
295	C₂×C₄×D₄₃	—	4	32	no	—
296	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
297	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
298	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
299	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
300	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
301	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
302	C₂×Dic₈₆	—	2	8	no	—
303	C₂×Dic₈₆	—	2	8	no	—
304	C₂×Dic₈₆	—	4	8	no	—
305	C₂×Dic₈₆	C₂⁴	1	8	yes	—
306	C₂×Dic₈₆	C₂⁴	1	8	yes	—
307	C₂×Dic₈₆	C₂⁴	1	16	yes	—
308	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
310	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
311	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₄₃	C₂⁴	1	4	yes	—
313	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
314	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
315	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
317	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
319	C₄²×C₄₃	C₂⁴	1	4	yes	—
320	C₄²×C₄₃	C₂⁴	1	4	yes	—
321	C₄²×C₄₃	C₂⁴	1	4	yes	—
322	C₄²×C₄₃	C₂⁴	1	4	yes	—
323	C₄²×C₄₃	C₂⁴	1	8	yes	—
324	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
325	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
326	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
327	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
328	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
329	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
330	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
331	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
332	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
333	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
334	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
335	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
336	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
337	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
338	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
339	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
340	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
341	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
342	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
343	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
344	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
345	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
346	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
347	C₄×Dic₄₃	C₂⁴	1	16	yes	—
348	C₄×Dic₄₃	C₂⁴	1	16	yes	—
349	C₂³×C₄₃	—	2	2	no	—
350	C₂³×C₄₃	—	2	2	no	—
351	C₂³×C₄₃	—	2	4	no	—
352	C₂³×C₄₃	—	2	4	no	—
353	C₂³×C₄₃	—	2	4	no	—
354	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
355	C₂³×C₄₃	C₂⁵	1	4	yes	—
356	C₂³×C₄₃	C₂⁵	1	2	yes	—
357	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
358	C₂²×D₄₃	—	2	4	no	—
359	C₂²×D₄₃	—	2	4	no	—
360	C₂²×D₄₃	—	2	4	no	—
361	C₂²×D₄₃	—	2	4	no	—
362	C₂²×D₄₃	—	2	16	no	—
363	C₂²×D₄₃	—	2	4	no	—
364	C₂²×D₄₃	—	2	16	no	—
365	C₂²×D₄₃	—	4	8	no	—
366	C₂²×D₄₃	—	4	32	no	—
367	C₂²×D₄₃	C₂×#41	1	8	yes	—
368	C₂²×D₄₃	C₂⁵	1	4	yes	—
369	C₂²×D₄₃	C₂⁵	1	4	yes	—
370	Q₈×C₄₃	—	2	8	no	—
371	D₄×C₄₃	—	2	16	no	—
372	D₄×C₄₃	—	2	8	no	—
373	C₂×C₄×C₄₃	—	2	4	no	—
374	C₂×C₄×C₄₃	—	2	2	no	—
375	C₂×C₄×C₄₃	—	2	4	no	—
376	C₂×C₄×C₄₃	—	2	2	no	—
377	C₂×C₄×C₄₃	—	2	8	no	—
378	C₂×C₄×C₄₃	—	2	2	no	—
379	C₂×C₄×C₄₃	—	2	2	no	—
380	C₂×C₄×C₄₃	—	2	4	no	—
381	C₂×C₄×C₄₃	—	2	8	no	—
382	C₂×C₄×C₄₃	—	2	16	no	—
383	C₂×C₄×C₄₃	—	2	8	no	—
384	C₂×C₄×C₄₃	C₂×#41	1	4	yes	—
385	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
386	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
387	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
388	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
389	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
390	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
391	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
392	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
393	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
394	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
395	C₂²⋊D₄₃	—	2	32	no	—
396	C₂²⋊D₄₃	—	4	16	no	—
397	C₂×Dic₄₃	—	2	8	no	—
398	C₂×Dic₄₃	—	2	8	no	—
399	C₂×Dic₄₃	—	2	4	no	—
400	C₂×Dic₄₃	—	2	4	no	—
401	C₂×Dic₄₃	—	4	8	no	—
402	C₂×Dic₄₃	—	4	16	no	—
403	C₂×Dic₄₃	C₂⁵	1	8	yes	—
404	C₂×Dic₄₃	C₂⁵	1	4	yes	—
405	C₂×Dic₄₃	C₂⁵	1	8	yes	—
406	C₂×Dic₄₃	C₂⁵	1	4	yes	—
407	D₁₇₂	—	2	16	no	—
408	D₁₇₂	—	2	8	no	—
409	D₁₇₂	C₂×#41	1	16	yes	complemented
410	C₄×D₄₃	—	2	32	no	—
411	C₄×D₄₃	—	2	16	no	—
412	C₄×D₄₃	—	2	16	no	—
413	C₄×D₄₃	—	4	8	no	—
414	C₄×D₄₃	—	4	8	no	—
415	C₄×D₄₃	—	4	16	no	—
416	Dic₈₆	—	2	16	no	—
417	Dic₈₆	—	2	16	no	—
418	Dic₈₆	—	4	16	no	—
419	C₂×#3520	—	43	1	no	maximal, Sylow
420	C₂²×C₄₃	—	2	2	no	—
421	C₂²×C₄₃	—	2	2	no	—
422	C₂²×C₄₃	—	2	8	no	—
423	C₂²×C₄₃	—	2	4	no	—
424	C₂²×C₄₃	—	2	4	no	—
425	C₂²×C₄₃	—	2	4	no	—
426	C₂²×C₄₃	—	4	8	no	—
427	C₂²×C₄₃	C₂²×#41	1	2	yes	—
428	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	4	yes	—
430	C₂²×C₄₃	C₂×2₋¹⁺⁴	1	2	yes	—
431	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
432	C₂×D₄₃	—	2	4	no	—
433	C₂×D₄₃	—	2	4	no	—
434	C₂×D₄₃	—	2	16	no	—
435	C₂×D₄₃	—	2	4	no	—
436	C₂×D₄₃	—	2	4	no	—
437	C₂×D₄₃	—	2	4	no	—
438	C₂×D₄₃	—	4	32	no	—
439	C₂×D₄₃	—	4	8	no	—
440	C₂×D₄₃	C₂²×#41	1	8	yes	—
441	C₄×C₄₃	—	2	4	no	—
442	C₄×C₄₃	—	2	2	no	—
443	C₄×C₄₃	—	2	4	no	—
444	C₄×C₄₃	—	2	2	no	—
445	C₄×C₄₃	—	2	2	no	—
446	C₄×C₄₃	—	2	2	no	—
447	C₄×C₄₃	—	2	4	no	—
448	C₄×C₄₃	C₂²×#41	1	4	yes	—
449	C₄×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
450	Dic₄₃	—	2	8	no	—
451	Dic₄₃	—	2	8	no	—
452	Dic₄₃	—	2	4	no	—
453	Dic₄₃	—	2	4	no	—
454	#3520	—	43	32	no	—
455	C₂×#556	—	43	1	no	—
456	C₂×#554	—	43	2	no	—
457	C₂×#552	—	43	2	no	—
458	C₂×#551	—	43	4	no	—
459	C₂×D₄×Q₈	—	43	1	no	—
460	C₂×#548	—	43	2	no	—
461	C₂×#547	—	43	1	no	—
462	C₂×#547	—	43	1	no	—
463	C₂×#546	—	43	2	no	—
464	C₂×#542	—	43	2	no	—
465	C₂×#539	—	43	4	no	—
466	C₂×#533	—	43	1	no	—
467	C₂×#529	D₄₃	1	1	yes	characteristic, complemented
468	C₂×#525	—	43	2	no	—
469	C₂²×C₂²⋊Q₈	—	43	2	no	—
470	C₂×#520	—	43	2	no	—
471	C₂²×C₄×D₄	—	43	1	no	—
472	C₂×C₄₃	—	2	4	no	—
473	C₂×C₄₃	—	4	4	no	—
474	C₂×C₄₃	#3520	1	4	yes	complemented
475	C₂×C₄₃	C₂³×#41	1	1	yes	characteristic
476	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₄₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
478	D₄₃	—	2	8	no	—
479	D₄₃	—	4	4	no	—
480	C₂²×#41	—	43	2	no	—
481	C₂²×#41	—	43	2	no	—
482	C₂³×Q₈	—	43	2	no	—
483	C₂³×D₄	—	43	1	no	—
484	C₂⁴×C₄	—	43	2	no	—
485	#556	—	43	16	no	—
486	#554	—	43	32	no	—
487	#552	—	43	32	no	—
488	#551	—	43	64	no	—
489	D₄×Q₈	—	43	16	no	—
490	#548	—	43	32	no	—
491	#547	—	43	16	no	—
492	#547	—	43	16	no	—
493	#546	—	43	32	no	—
494	#542	—	43	32	no	—
495	#539	—	43	64	no	—
496	#533	—	43	16	no	—
497	C₂×C₄⋊Q₈	—	43	1	no	—
498	C₂×C₄⋊Q₈	—	43	1	no	—
499	C₂×C₄⋊Q₈	—	43	2	no	—
500	#529	C₂×D₄₃	1	16	yes	complemented
501	C₂×#126	—	43	4	no	—
502	C₂×#126	—	43	4	no	—
503	C₂×#126	C₂×D₄₃	1	2	yes	complemented
504	C₂×#125	—	43	4	no	—
505	C₂×#125	—	43	2	no	—
506	C₂×#125	C₂×D₄₃	1	1	yes	characteristic, complemented
507	C₂×#124	—	43	4	no	—
508	C₂×#124	—	43	2	no	—
509	C₂×#124	C₂×D₄₃	1	1	yes	characteristic, complemented
510	#525	—	43	32	no	—
511	C₂×#123	—	43	4	no	—
512	C₂×#123	—	43	4	no	—
513	C₂×#123	—	43	4	no	—
514	C₂×#123	—	43	4	no	—
515	C₂×#123	C₂×D₄₃	1	2	yes	—
516	C₂×C₂²⋊Q₈	—	43	2	no	—
517	C₂×C₂²⋊Q₈	—	43	2	no	—
518	C₂×C₂²⋊Q₈	—	43	2	no	—
519	C₂×C₂²⋊Q₈	—	43	2	no	—
520	C₂×C₂²⋊Q₈	—	43	32	no	—
521	C₂×C₂²⋊Q₈	—	43	4	no	—
522	C₂×C₂²⋊Q₈	—	43	2	no	—
523	C₂×C₂²⋊Q₈	—	43	2	no	—
524	C₂×C₂²⋊Q₈	—	43	4	no	—
525	C₂×C₂²⋊Q₈	—	43	4	no	—
526	C₂×C₂²⋊Q₈	—	43	4	no	—
527	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
528	C₂×#121	—	43	2	no	—
529	C₂×#121	—	43	2	no	—
530	C₂×#121	—	43	4	no	—
531	C₂×#121	C₂×D₄₃	1	1	yes	characteristic
532	C₂×#120	—	43	4	no	—
533	#520	—	43	32	no	—
534	C₂×C₄×Q₈	—	43	2	no	—
535	C₂×C₄×Q₈	—	43	2	no	—
536	C₂×C₄×Q₈	—	43	2	no	—
537	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
538	C₂×C₄×D₄	—	43	4	no	—
539	C₂×C₄×D₄	—	43	4	no	—
540	C₂×C₄×D₄	—	43	4	no	—
541	C₂×C₄×D₄	—	43	1	no	—
542	C₂×C₄×D₄	—	43	2	no	—
543	C₂×C₄×D₄	—	43	1	no	—
544	C₂×C₄×D₄	—	43	1	no	—
545	C₂×C₄×D₄	—	43	1	no	—
546	C₂×C₄×D₄	—	43	2	no	—
547	C₂×C₄×D₄	—	43	2	no	—
548	C₂×C₄×D₄	—	43	16	no	—
549	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
550	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
551	C₂×#117	—	43	2	no	—
552	C₂×#117	—	43	4	no	—
553	C₂×#117	—	43	2	no	—
554	C₂×#117	C₂×D₄₃	1	2	yes	complemented
555	C₂²×C₄⋊C₄	—	43	1	no	—
556	C₂²×C₄⋊C₄	—	43	2	no	—
557	C₂²×C₄⋊C₄	—	43	4	no	—
558	C₂²×C₄⋊C₄	—	43	2	no	—
559	C₂²×C₂²⋊C₄	—	43	2	no	—
560	C₂²×C₂²⋊C₄	—	43	4	no	—
561	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
562	C₄₃	C₂×#3520	1	1	yes	characteristic, complemented, Sylow
563	C₂⁵	—	43	2	no	—
564	C₂×#41	—	43	16	no	—
565	C₂×#41	—	43	16	no	—
566	C₂×#41	—	86	16	no	—
567	C₂×#41	—	172	8	no	—
568	C₂²×Q₈	—	43	16	no	—
569	C₂²×Q₈	—	43	2	no	—
570	C₂²×Q₈	—	43	2	no	—
571	C₂²×Q₈	—	43	4	no	—
572	C₂²×Q₈	—	172	8	no	—
573	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
574	C₂²×D₄	—	43	4	no	—
575	C₂²×D₄	—	43	4	no	—
576	C₂²×D₄	—	43	1	no	—
577	C₂²×D₄	—	43	2	no	—
578	C₂²×D₄	—	43	1	no	—
579	C₂²×D₄	—	43	8	no	—
580	C₂²×D₄	—	86	8	no	—
581	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
582	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
583	C₂³×C₄	—	43	2	no	—
584	C₂³×C₄	—	43	4	no	—
585	C₂³×C₄	—	43	4	no	—
586	C₂³×C₄	—	43	2	no	—
587	C₂³×C₄	—	43	2	no	—
588	C₂³×C₄	—	43	4	no	—
589	C₂³×C₄	—	43	2	no	—
590	C₂³×C₄	—	43	2	no	—
591	C₂³×C₄	—	43	16	no	—
592	C₂³×C₄	—	172	8	no	—
593	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
594	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
595	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
596	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
597	C₄⋊Q₈	—	43	8	no	—
598	C₄⋊Q₈	—	43	8	no	—
599	C₄⋊Q₈	—	43	16	no	—
600	#126	—	43	32	no	—
601	#126	—	43	32	no	—
602	#126	C₂²×D₄₃	1	16	yes	complemented
603	#125	—	43	32	no	—
604	#125	—	43	16	no	—
605	#125	C₂²×D₄₃	1	8	yes	complemented
606	#124	—	43	32	no	—
607	#124	—	43	16	no	—
608	#124	C₂²×D₄₃	1	8	yes	complemented
609	#123	—	43	32	no	—
610	#123	—	43	32	no	—
611	#123	—	43	32	no	—
612	#123	—	43	32	no	—
613	#123	C₂²×D₄₃	1	16	yes	—
614	C₂²⋊Q₈	—	43	16	no	—
615	C₂²⋊Q₈	—	43	16	no	—
616	C₂²⋊Q₈	—	43	16	no	—
617	C₂²⋊Q₈	—	43	16	no	—
618	C₂²⋊Q₈	—	43	32	no	—
619	C₂²⋊Q₈	—	43	16	no	—
620	C₂²⋊Q₈	—	43	16	no	—
621	C₂²⋊Q₈	—	43	32	no	—
622	C₂²⋊Q₈	—	43	32	no	—
623	C₂²⋊Q₈	—	43	32	no	—
624	C₂²⋊Q₈	C₂²×D₄₃	1	8	yes	—
625	#121	—	43	16	no	—
626	#121	—	43	16	no	—
627	#121	—	43	32	no	—
628	#121	C₂²×D₄₃	1	8	yes	—
629	#120	—	43	32	no	—
630	C₄×Q₈	—	43	16	no	—
631	C₄×Q₈	—	43	16	no	—
632	C₄×Q₈	—	43	16	no	—
633	C₄×Q₈	C₂²×D₄₃	1	8	yes	complemented
634	C₄×D₄	—	43	32	no	—
635	C₄×D₄	—	43	32	no	—
636	C₄×D₄	—	43	32	no	—
637	C₄×D₄	—	43	8	no	—
638	C₄×D₄	—	43	16	no	—
639	C₄×D₄	—	43	8	no	—
640	C₄×D₄	—	43	8	no	—
641	C₄×D₄	—	43	8	no	—
642	C₄×D₄	—	43	16	no	—
643	C₄×D₄	—	43	16	no	—
644	C₄×D₄	C₂²×D₄₃	1	16	yes	—
645	C₄×D₄	C₂²×D₄₃	1	8	yes	complemented
646	#117	—	43	16	no	—
647	#117	—	43	32	no	—
648	#117	—	43	16	no	—
649	#117	C₂²×D₄₃	1	16	yes	complemented
650	C₂×C₄⋊C₄	—	43	1	no	—
651	C₂×C₄⋊C₄	—	43	4	no	—
652	C₂×C₄⋊C₄	—	43	2	no	—
653	C₂×C₄⋊C₄	—	43	2	no	—
654	C₂×C₄⋊C₄	—	43	1	no	—
655	C₂×C₄⋊C₄	—	43	8	no	—
656	C₂×C₄⋊C₄	—	43	2	no	—
657	C₂×C₄⋊C₄	—	43	4	no	—
658	C₂×C₄⋊C₄	—	43	4	no	—
659	C₂×C₄⋊C₄	—	43	16	no	—
660	C₂×C₄⋊C₄	—	43	4	no	—
661	C₂×C₄⋊C₄	—	43	2	no	—
662	C₂×C₄⋊C₄	—	43	2	no	—
663	C₂×C₄⋊C₄	—	43	4	no	—
664	C₂×C₄⋊C₄	—	43	4	no	—
665	C₂×C₄⋊C₄	—	43	32	no	—
666	C₂×C₄⋊C₄	—	43	16	no	—
667	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
668	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
670	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
672	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
673	C₂×C₂²⋊C₄	—	43	4	no	—
674	C₂×C₂²⋊C₄	—	43	4	no	—
675	C₂×C₂²⋊C₄	—	43	2	no	—
676	C₂×C₂²⋊C₄	—	43	2	no	—
677	C₂×C₂²⋊C₄	—	43	2	no	—
678	C₂×C₂²⋊C₄	—	43	2	no	—
679	C₂×C₂²⋊C₄	—	43	16	no	—
680	C₂×C₂²⋊C₄	—	43	4	no	—
681	C₂×C₂²⋊C₄	—	43	4	no	—
682	C₂×C₂²⋊C₄	—	43	4	no	—
683	C₂×C₂²⋊C₄	—	43	4	no	—
684	C₂×C₂²⋊C₄	—	43	32	no	—
685	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
686	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
687	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
688	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
689	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
690	C₂×C₄²	—	43	4	no	—
691	C₂×C₄²	—	43	4	no	—
692	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
693	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
694	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
695	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
696	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×C₄²	C₂²×D₄₃	1	8	yes	—
698	C₂⁴	—	43	2	no	—
699	C₂⁴	—	43	2	no	—
700	C₂⁴	—	43	8	no	—
701	C₂⁴	—	86	8	no	—
702	C₂⁴	—	86	8	no	—
703	C₂⁴	—	172	4	no	—
704	C₂⁴	C₂³×D₄₃	1	2	yes	—
705	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
706	#41	—	86	64	no	—
707	#41	—	172	32	no	—
708	C₂×Q₈	—	2	4	no	—
709	C₂×Q₈	—	43	8	no	—
710	C₂×Q₈	—	43	8	no	—
711	C₂×Q₈	—	43	16	no	—
712	C₂×Q₈	—	86	8	no	—
713	C₂×Q₈	—	86	8	no	—
714	C₂×Q₈	—	172	8	no	—
715	C₂×Q₈	—	172	32	no	—
716	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
717	C₂×D₄	—	2	8	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	43	16	no	—
720	C₂×D₄	—	43	16	no	—
721	C₂×D₄	—	43	8	no	—
722	C₂×D₄	—	43	4	no	—
723	C₂×D₄	—	43	8	no	—
724	C₂×D₄	—	43	4	no	—
725	C₂×D₄	—	86	32	no	—
726	C₂×D₄	—	86	8	no	—
727	C₂×D₄	—	86	16	no	—
728	C₂×D₄	—	86	4	no	—
729	C₂×D₄	—	172	8	no	—
730	C₂×D₄	C₂³×D₄₃	1	8	yes	—
731	C₂×D₄	C₂³×D₄₃	1	4	yes	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	—	2	4	no	—
734	C₂²×C₄	—	2	8	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	43	4	no	—
737	C₂²×C₄	—	43	2	no	—
738	C₂²×C₄	—	43	4	no	—
739	C₂²×C₄	—	43	2	no	—
740	C₂²×C₄	—	43	8	no	—
741	C₂²×C₄	—	43	16	no	—
742	C₂²×C₄	—	43	16	no	—
743	C₂²×C₄	—	43	8	no	—
744	C₂²×C₄	—	43	8	no	—
745	C₂²×C₄	—	43	16	no	—
746	C₂²×C₄	—	43	8	no	—
747	C₂²×C₄	—	43	8	no	—
748	C₂²×C₄	—	86	16	no	—
749	C₂²×C₄	—	86	8	no	—
750	C₂²×C₄	—	86	8	no	—
751	C₂²×C₄	—	172	32	no	—
752	C₂²×C₄	—	172	4	no	—
753	C₂²×C₄	—	172	4	no	—
754	C₂²×C₄	—	172	8	no	—
755	C₂²×C₄	—	172	4	no	—
756	C₂²×C₄	—	172	8	no	—
757	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
758	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
759	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
760	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
761	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
762	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
763	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
764	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
765	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
766	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
767	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
768	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
769	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
770	C₄⋊C₄	—	43	4	no	—
771	C₄⋊C₄	—	43	16	no	—
772	C₄⋊C₄	—	43	8	no	—
773	C₄⋊C₄	—	43	8	no	—
774	C₄⋊C₄	—	43	4	no	—
775	C₄⋊C₄	—	43	8	no	—
776	C₄⋊C₄	—	43	16	no	—
777	C₄⋊C₄	—	43	16	no	—
778	C₄⋊C₄	—	43	16	no	—
779	C₄⋊C₄	—	43	8	no	—
780	C₄⋊C₄	—	43	8	no	—
781	C₄⋊C₄	—	43	16	no	—
782	C₄⋊C₄	—	43	16	no	—
783	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
784	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
785	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
786	C₄⋊C₄	C₂³×D₄₃	1	4	yes	—
787	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
788	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
789	C₂²⋊C₄	—	43	16	no	—
790	C₂²⋊C₄	—	43	16	no	—
791	C₂²⋊C₄	—	43	8	no	—
792	C₂²⋊C₄	—	43	8	no	—
793	C₂²⋊C₄	—	43	8	no	—
794	C₂²⋊C₄	—	43	8	no	—
795	C₂²⋊C₄	—	43	16	no	—
796	C₂²⋊C₄	—	43	16	no	—
797	C₂²⋊C₄	—	43	16	no	—
798	C₂²⋊C₄	—	43	16	no	—
799	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
800	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
801	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
802	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
803	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
804	C₄²	—	43	16	no	—
805	C₄²	—	43	16	no	—
806	C₄²	C₂³×D₄₃	1	4	yes	—
807	C₄²	C₂³×D₄₃	1	4	yes	—
808	C₄²	C₂³×D₄₃	1	4	yes	—
809	C₄²	C₂³×D₄₃	1	4	yes	—
810	C₄²	C₂³×D₄₃	1	8	yes	—
811	C₂³	—	2	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	4	no	—
814	C₂³	—	2	4	no	—
815	C₂³	—	2	4	no	—
816	C₂³	—	43	8	no	—
817	C₂³	—	43	4	no	—
818	C₂³	—	43	4	no	—
819	C₂³	—	86	16	no	—
820	C₂³	—	86	4	no	—
821	C₂³	—	86	4	no	—
822	C₂³	—	86	4	no	—
823	C₂³	—	86	4	no	—
824	C₂³	—	86	16	no	—
825	C₂³	—	86	4	no	—
826	C₂³	—	172	8	no	—
827	C₂³	—	172	32	no	—
828	C₂³	#13063372	1	4	yes	—
829	C₂³	C₂⁴×D₄₃	1	4	yes	—
830	C₂³	C₂⁴×D₄₃	1	2	yes	—
831	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
832	Q₈	—	2	8	no	—
833	Q₈	—	86	16	no	—
834	Q₈	—	86	16	no	—
835	Q₈	—	172	16	no	—
836	D₄	—	2	16	no	—
837	D₄	—	2	8	no	—
838	D₄	—	43	16	no	—
839	D₄	—	86	16	no	—
840	D₄	—	86	32	no	—
841	D₄	—	86	8	no	—
842	D₄	—	172	16	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	4	no	—
847	C₂×C₄	—	2	8	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	16	no	—
853	C₂×C₄	—	2	8	no	—
854	C₂×C₄	—	43	8	no	—
855	C₂×C₄	—	43	4	no	—
856	C₂×C₄	—	43	8	no	—
857	C₂×C₄	—	43	4	no	—
858	C₂×C₄	—	86	32	no	—
859	C₂×C₄	—	86	8	no	—
860	C₂×C₄	—	86	4	no	—
861	C₂×C₄	—	86	4	no	—
862	C₂×C₄	—	86	8	no	—
863	C₂×C₄	—	86	16	no	—
864	C₂×C₄	—	86	16	no	—
865	C₂×C₄	—	172	8	no	—
866	C₂×C₄	—	172	8	no	—
867	C₂×C₄	—	172	16	no	—
868	C₂×C₄	—	172	8	no	—
869	C₂×C₄	—	172	16	no	—
870	C₂×C₄	#41×D₄₃	1	4	yes	—
871	C₂×C₄	#13063371	1	4	yes	—
872	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
873	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
874	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
875	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
876	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
877	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
878	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
879	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
880	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	8	no	—
884	C₂²	—	2	4	no	—
885	C₂²	—	2	4	no	—
886	C₂²	—	2	4	no	—
887	C₂²	—	4	8	no	—
888	C₂²	—	43	8	no	—
889	C₂²	—	86	4	no	—
890	C₂²	—	86	4	no	—
891	C₂²	—	86	16	no	—
892	C₂²	—	86	4	no	—
893	C₂²	—	86	4	no	—
894	C₂²	—	86	4	no	—
895	C₂²	—	172	32	no	—
896	C₂²	—	172	8	no	—
897	C₂²	C₂×#41×D₄₃	1	2	yes	—
898	C₂²	C₂×#13063371	1	2	yes	—
899	C₂²	C₂×#13063372	1	4	yes	—
900	C₂²	C₂×#13063372	1	2	yes	—
901	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
902	C₄	—	2	4	no	—
903	C₄	—	2	2	no	—
904	C₄	—	2	2	no	—
905	C₄	—	2	4	no	—
906	C₄	—	2	2	no	—
907	C₄	—	2	2	no	—
908	C₄	—	2	4	no	—
909	C₄	—	86	8	no	—
910	C₄	—	86	4	no	—
911	C₄	—	86	4	no	—
912	C₄	—	86	8	no	—
913	C₄	C₂×#41×D₄₃	1	4	yes	—
914	C₄	C₂×#13063371	1	4	yes	—
915	C₂	—	2	4	no	—
916	C₂	—	4	4	no	—
917	C₂	—	86	8	no	—
918	C₂	—	172	4	no	—
919	C₂	#19148646	1	4	yes	direct product factor
920	C₂	C₂²×#41×D₄₃	1	1	yes	characteristic
921	C₂	C₂²×#13063371	1	1	yes	characteristic
922	C₂	C₂²×#13063372	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#529	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#529	D₄₃
hypocenter	C₄₃	C₂×#3520
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #19148646	C₂	direct (N × H)
2. C₂×#14583622	C₂	semidirect
3. C₂×#14583606	C₂	semidirect
4. C₂×#14583587	C₂	semidirect
5. C₂×#14583572	C₂	semidirect
6. C₂×Q₈×D₁₇₂	C₂	semidirect
7. C₂×#14583557	C₂	semidirect
8. C₂×#14583554	C₂	semidirect
9. C₂×#14583553	C₂	semidirect
10. C₂×#14583545	C₂	semidirect
11. C₂×#14583520	C₂	semidirect
12. C₂×#14583490	C₂	semidirect
13. C₂×#14583456	C₂	semidirect
14. C₂×#14583409	C₂	semidirect
15. C₂×C₂²⋊Q₈×D₄₃	C₂	semidirect
16. C₂×#14583379	C₂	semidirect
17. C₂²×C₄×D₁₇₂	C₂	semidirect
18. C₂×C₄₃×#529	C₂	semidirect
20. C₂²×#10621900	C₂²	semidirect
21. C₂²×Q₈×D₄₃	C₂²	semidirect
24. #14583622	C₂²	semidirect
25. #14583606	C₂²	semidirect
26. #14583587	C₂²	semidirect
27. #14583572	C₂²	semidirect
28. Q₈×D₁₇₂	C₂²	semidirect
29. #14583557	C₂²	semidirect
30. #14583554	C₂²	semidirect
31. #14583553	C₂²	semidirect
32. #14583545	C₂²	semidirect
33. #14583520	C₂²	semidirect
34. #14583490	C₂²	semidirect
35. #14583456	C₂²	semidirect
36. C₂×#13063325	C₂²	semidirect
37. C₂×#13063325	C₂²	semidirect
38. C₂×#13063325	C₂²	semidirect
39. C₂×#13063320	C₂²	semidirect
40. C₂×#13063320	C₂²	semidirect
41. C₂×#13063317	C₂²	semidirect
42. C₂×#13063316	C₂²	semidirect
44. C₂×#13063311	C₂²	semidirect
45. #14583409	C₂²	semidirect
47. C₂×#13063309	C₂²	semidirect
48. C₂×#13063307	C₂²	semidirect
49. C₂×#13063307	C₂²	semidirect
50. C₂×#13063305	C₂²	semidirect
51. C₂×#13063305	C₂²	semidirect
52. C₂×#13063305	C₂²	semidirect
55. C₂×#13063304	C₂²	semidirect
56. C₂×#13063303	C₂²	semidirect
58. C₂×#13063302	C₂²	semidirect
59. C₂×#13063301	C₂²	semidirect
60. C₂²⋊Q₈×D₄₃	C₂²	semidirect
63. C₂×#13063296	C₂²	semidirect
65. #14583379	C₂²	semidirect
66. C₂×C₄×Dic₈₆	C₂²	semidirect
67. C₂×C₄×Dic₈₆	C₂²	semidirect
68. C₂×C₄×Dic₈₆	C₂²	semidirect
76. C₂×C₄×D₁₇₂	C₂²	semidirect
78. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
79. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
81. C₂×#13063283	C₂²	semidirect
82. C₂×#13063283	C₂²	semidirect
84. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
85. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
86. C₂×C₄⋊C₄×D₄₃	C₂²	semidirect
89. C₄₃×#529	C₂²	semidirect
90. C₂×#126×C₄₃	C₂²	semidirect
91. C₂×#125×C₄₃	C₂²	semidirect
92. C₂×#124×C₄₃	C₂²	semidirect
96. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
98. C₂×C₄×D₄×C₄₃	C₂²	semidirect
99. C₂×#117×C₄₃	C₂²	semidirect
105. C₂×#10621900	C₂³	semidirect
110. C₂×Q₈×D₄₃	C₂³	semidirect
128. #13063325	C₂³	semidirect
129. #13063325	C₂³	semidirect
130. #13063325	C₂³	semidirect
131. #13063320	C₂³	semidirect
132. #13063320	C₂³	semidirect
133. #13063317	C₂³	semidirect
134. #13063316	C₂³	semidirect
136. #13063311	C₂³	semidirect
138. #13063309	C₂³	semidirect
139. #13063307	C₂³	semidirect
140. #13063307	C₂³	semidirect
141. #13063305	C₂³	semidirect
142. #13063305	C₂³	semidirect
143. #13063305	C₂³	semidirect
146. #13063304	C₂³	semidirect
147. #13063303	C₂³	semidirect
149. #13063302	C₂³	semidirect
150. #13063301	C₂³	semidirect
153. #13063296	C₂³	semidirect
155. C₄×Dic₈₆	C₂³	semidirect
156. C₄×Dic₈₆	C₂³	semidirect
157. C₄×Dic₈₆	C₂³	semidirect
166. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
167. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
169. #13063283	C₂³	semidirect
170. #13063283	C₂³	semidirect
181. C₂×C₄⋊Dic₄₃	C₂³	semidirect
186. C₄⋊C₄×D₄₃	C₂³	semidirect
187. C₄⋊C₄×D₄₃	C₂³	semidirect
209. #126×C₄₃	C₂³	semidirect
210. #125×C₄₃	C₂³	semidirect
211. #124×C₄₃	C₂³	semidirect
215. C₄×Q₈×C₄₃	C₂³	semidirect
217. C₄×D₄×C₄₃	C₂³	semidirect
218. #117×C₄₃	C₂³	semidirect
285. C₂×D₁₇₂	#41	semidirect
409. D₁₇₂	C₂×#41	semidirect
467. C₂×#529	D₄₃	semidirect
474. C₂×C₄₃	#3520	semidirect
500. #529	C₂×D₄₃	semidirect
503. C₂×#126	C₂×D₄₃	semidirect
506. C₂×#125	C₂×D₄₃	semidirect
509. C₂×#124	C₂×D₄₃	semidirect
537. C₂×C₄×Q₈	C₂×D₄₃	semidirect
550. C₂×C₄×D₄	C₂×D₄₃	semidirect
554. C₂×#117	C₂×D₄₃	semidirect
562. C₄₃	C₂×#3520	semidirect
602. #126	C₂²×D₄₃	semidirect
605. #125	C₂²×D₄₃	semidirect
608. #124	C₂²×D₄₃	semidirect
633. C₄×Q₈	C₂²×D₄₃	semidirect
645. C₄×D₄	C₂²×D₄₃	semidirect
649. #117	C₂²×D₄₃	semidirect
919. C₂	#19148646	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148646	2
C₂×#14583622	2
C₂×#14583606	2
C₂×#14583587	2
C₂×#14583572	2
C₂×Q₈×D₁₇₂	2
C₂×#14583557	2
C₂×#14583554	2
C₂×#14583553	2
C₂×#14583545	2
C₂×#14583520	2
C₂×#14583490	2
C₂×#14583456	2
C₂×#14583409	2
C₂×C₂²⋊Q₈×D₄₃	2
C₂×#14583379	2
C₂²×C₄×D₁₇₂	2
C₂×C₄₃×#529	2
C₂×#3520	43

Subgroups — C2×#19148646 #26004612

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148646 #26004612