Subgroups — C₂×#19148830 #26003834

Order 11008.

8890 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148830	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583637	C₂	1	4	yes	maximal, complemented
3	C₂×#14583601	C₂	1	2	yes	maximal, complemented
4	C₂×#14583597	C₂	1	2	yes	maximal, complemented
5	C₂×#14583533	C₂	1	2	yes	maximal, complemented
6	C₂×D₄×C₂²⋊D₄₃	C₂	1	2	yes	maximal, complemented
7	C₂×D₄×C₂²⋊D₄₃	C₂	1	4	yes	maximal, complemented
8	C₂×#14583502	C₂	1	2	yes	maximal, complemented
9	C₂×#14583487	C₂	1	2	yes	maximal, complemented
10	C₂×#14583486	C₂	1	2	yes	maximal, complemented
11	C₂×#14583465	C₂	1	2	yes	maximal, complemented
12	C₂×#14583461	C₂	1	2	yes	maximal, complemented
13	C₂×#14583457	C₂	1	2	yes	maximal, complemented
14	C₂×#14583410	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#13063299	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#121×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10621898	C₂²	1	1	yes	characteristic, complemented
18	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
19	C₂³×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
20	C₂³×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
21	C₂²×D₄×D₄₃	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₄₃	C₂²	1	2	yes	complemented
23	#14583637	C₂²	1	64	yes	complemented
24	#14583601	C₂²	1	32	yes	complemented
25	#14583597	C₂²	1	32	yes	complemented
26	#14583533	C₂²	1	32	yes	complemented
27	D₄×C₂²⋊D₄₃	C₂²	1	32	yes	complemented
28	D₄×C₂²⋊D₄₃	C₂²	1	64	yes	complemented
29	#14583502	C₂²	1	32	yes	complemented
30	#14583487	C₂²	1	32	yes	complemented
31	#14583486	C₂²	1	32	yes	complemented
32	#14583465	C₂²	1	32	yes	complemented
33	#14583461	C₂²	1	32	yes	complemented
34	#14583457	C₂²	1	32	yes	complemented
35	C₂×#13063321	C₂²	1	2	yes	complemented
36	C₂×#13063321	C₂²	1	4	yes	complemented
37	C₂×#13063320	C₂²	1	4	yes	complemented
38	C₂×#13063318	C₂²	1	4	yes	complemented
39	C₂×#13063316	C₂²	1	2	yes	complemented
40	C₂×#13063311	C₂²	1	4	yes	complemented
41	#14583410	C₂²	1	16	yes	complemented
42	C₂×#13063310	C₂²	1	4	yes	complemented
43	C₂×#13063309	C₂²	1	4	yes	complemented
44	C₂×#13063309	C₂²	1	4	yes	complemented
45	C₂×#13063308	C₂²	1	2	yes	complemented
46	C₂×#13063307	C₂²	1	4	yes	complemented
47	C₂×#13063304	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13063304	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13063300	C₂²	1	2	yes	complemented
50	C₂×#13063299	C₂²	1	2	yes	complemented
51	C₂×#13063299	C₂²	1	4	yes	complemented
52	C₂×#13063299	C₂²	1	2	yes	complemented
53	C₂×#13063299	C₂²	1	2	yes	complemented
54	C₂×#13063299	C₂²	1	2	yes	complemented
55	C₂×#13063299	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13063299	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13063299	C₂²	1	16	yes	complemented
58	C₂×#13063298	C₂²	1	4	yes	complemented
59	C₂×#13063297	C₂²	1	4	yes	complemented
60	C₂×#13063297	C₂²	1	4	yes	complemented
61	C₂×#13063297	C₂²	1	4	yes	complemented
62	C₂×#13063296	C₂²	1	2	yes	complemented
63	C₂×#13063296	C₂²	1	4	yes	complemented
64	C₂×#13063295	C₂²	1	4	yes	complemented
65	C₂×#13063295	C₂²	1	4	yes	complemented
66	C₂×#13063294	C₂²	1	2	yes	complemented
67	C₂×#13063294	C₂²	1	4	yes	complemented
68	C₂×#13063293	C₂²	1	4	yes	complemented
69	C₂×#13063293	C₂²	1	4	yes	complemented
70	C₂×#13063293	C₂²	1	4	yes	complemented
71	C₂×D₄×Dic₄₃	C₂²	1	4	yes	complemented
72	C₂×D₄×Dic₄₃	C₂²	1	2	yes	complemented
73	C₂×#13063287	C₂²	1	2	yes	complemented
74	C₂×C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
75	C₂×C₄×C₂²⋊D₄₃	C₂²	1	4	yes	complemented
76	C₂×C₄×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
77	C₂×#13063284	C₂²	1	1	yes	characteristic, complemented
78	C₂×#13063283	C₂²	1	2	yes	complemented
79	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic, complemented
80	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	2	yes	complemented
81	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
82	C₂³×D₄×C₄₃	C₂²	1	2	yes	complemented
83	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×#121×C₄₃	C₂²	1	2	yes	complemented
85	C₂×#121×C₄₃	C₂²	1	2	yes	complemented
86	C₂×#121×C₄₃	C₂²	1	2	yes	complemented
87	C₂×#121×C₄₃	C₂²	1	2	yes	complemented
88	C₂×#121×C₄₃	C₂²	1	16	yes	complemented
89	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
90	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	complemented
91	C₂⁴×D₄₃	C₂³	1	2	yes	—
92	C₂⁴×D₄₃	C₂³	1	4	yes	—
93	C₂×#10621898	—	4	4	no	—
94	C₂×#10621898	C₂³	1	8	yes	complemented
95	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
96	C₂²×D₁₇₂	—	4	4	no	—
97	C₂²×D₁₇₂	C₂³	1	2	yes	—
98	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
99	C₂²×D₁₇₂	C₂³	1	2	yes	—
100	C₂²×D₁₇₂	C₂³	1	4	yes	—
101	C₂²×D₁₇₂	C₂³	1	8	yes	complemented
102	C₂²×C₂²⋊D₄₃	—	4	8	no	—
103	C₂²×C₂²⋊D₄₃	—	4	16	no	—
104	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₄₃	C₂³	1	2	yes	—
108	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
109	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
110	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
111	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
112	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
113	C₂²×C₂²⋊D₄₃	C₂³	1	16	yes	complemented
114	C₂²×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
115	C₂×D₄×D₄₃	—	4	8	no	—
116	C₂×D₄×D₄₃	—	4	16	no	—
117	C₂×D₄×D₄₃	C₂³	1	32	yes	complemented
118	C₂×D₄×D₄₃	C₂³	1	16	yes	complemented
119	C₂³×Dic₄₃	C₂³	1	2	yes	—
120	C₂³×Dic₄₃	C₂³	1	4	yes	—
121	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
122	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
123	#13063321	C₂³	1	32	yes	complemented
124	#13063321	C₂³	1	16	yes	complemented
125	#13063320	C₂³	1	32	yes	complemented
126	#13063318	C₂³	1	32	yes	complemented
127	#13063316	C₂³	1	16	yes	complemented
128	#13063311	C₂³	1	32	yes	complemented
129	#13063310	C₂³	1	32	yes	complemented
130	#13063309	C₂³	1	32	yes	complemented
131	#13063309	C₂³	1	32	yes	complemented
132	#13063308	C₂³	1	16	yes	complemented
133	#13063307	C₂³	1	32	yes	complemented
134	#13063304	C₂³	1	8	yes	complemented
135	#13063304	C₂³	1	8	yes	complemented
136	#13063300	C₂³	1	16	yes	complemented
137	#13063299	C₂³	1	16	yes	complemented
138	#13063299	C₂³	1	32	yes	complemented
139	#13063299	C₂³	1	16	yes	complemented
140	#13063299	C₂³	1	16	yes	complemented
141	#13063299	C₂³	1	16	yes	complemented
142	#13063299	C₂³	1	8	yes	complemented
143	#13063299	C₂³	1	8	yes	complemented
144	#13063298	C₂³	1	32	yes	complemented
145	#13063297	C₂³	1	32	yes	complemented
146	#13063297	C₂³	1	32	yes	complemented
147	#13063297	C₂³	1	32	yes	complemented
148	#13063296	C₂³	1	16	yes	complemented
149	#13063296	C₂³	1	32	yes	complemented
150	#13063295	C₂³	1	32	yes	complemented
151	#13063295	C₂³	1	32	yes	complemented
152	#13063294	C₂³	1	16	yes	complemented
153	#13063294	C₂³	1	32	yes	complemented
154	#13063293	C₂³	1	32	yes	complemented
155	#13063293	C₂³	1	32	yes	complemented
156	#13063293	C₂³	1	32	yes	complemented
157	D₄×Dic₄₃	C₂³	1	32	yes	complemented
158	D₄×Dic₄₃	C₂³	1	16	yes	complemented
159	#13063287	C₂³	1	16	yes	complemented
160	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	complemented
161	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
162	C₄×C₂²⋊D₄₃	C₂³	1	16	yes	complemented
163	#13063284	C₂³	1	8	yes	complemented
164	#13063283	C₂³	1	16	yes	complemented
165	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
166	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
167	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
170	C₂×C₄⋊Dic₄₃	C₂³	1	8	yes	complemented
171	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
172	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
173	C₂×Dic₄₃⋊C₄	C₂³	1	2	yes	—
174	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
178	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
179	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
180	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
181	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
182	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
183	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
184	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	2	yes	—
185	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
186	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	16	yes	complemented
187	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
188	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
189	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
190	C₂⁵×C₄₃	C₂³	1	2	yes	—
191	C₂²×D₄×C₄₃	—	4	4	no	—
192	C₂²×D₄×C₄₃	—	4	8	no	—
193	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
194	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
195	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
196	C₂²×D₄×C₄₃	C₂³	1	4	yes	—
197	C₂²×D₄×C₄₃	C₂³	1	8	yes	complemented
198	C₂²×D₄×C₄₃	C₂³	1	16	yes	complemented
199	C₂³×C₄×C₄₃	—	4	4	no	—
200	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
205	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₄₃	C₂³	1	8	yes	complemented
208	#121×C₄₃	C₂³	1	16	yes	complemented
209	#121×C₄₃	C₂³	1	16	yes	complemented
210	#121×C₄₃	C₂³	1	16	yes	complemented
211	#121×C₄₃	C₂³	1	16	yes	complemented
212	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
213	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
214	C₂×C₄⋊C₄×C₄₃	C₂³	1	8	yes	complemented
215	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄×C₄₃	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄×C₄₃	C₂³	1	16	yes	complemented
218	C₂⁴×C₄₃	—	2	4	no	—
219	C₂⁴×C₄₃	—	2	4	no	—
220	C₂⁴×C₄₃	—	2	8	no	—
221	C₂⁴×C₄₃	—	4	2	no	—
222	C₂⁴×C₄₃	—	4	4	no	—
223	C₂⁴×C₄₃	—	4	4	no	—
224	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
225	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
226	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
227	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
228	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
229	C₂⁴×C₄₃	C₂⁴	1	8	yes	—
230	C₂³×D₄₃	—	2	8	no	—
231	C₂³×D₄₃	—	4	8	no	—
232	C₂³×D₄₃	—	4	8	no	—
233	C₂³×D₄₃	—	4	4	no	—
234	C₂³×D₄₃	—	4	8	no	—
235	C₂³×D₄₃	—	4	4	no	—
236	C₂³×D₄₃	C₂⁴	1	2	yes	—
237	C₂³×D₄₃	C₂⁴	1	4	yes	—
238	C₂³×D₄₃	C₂⁴	1	8	yes	—
239	C₂³×D₄₃	C₂⁴	1	16	yes	—
240	C₂×D₄×C₄₃	—	2	8	no	—
241	C₂×D₄×C₄₃	—	2	16	no	—
242	C₂×D₄×C₄₃	—	4	4	no	—
243	C₂×D₄×C₄₃	—	4	8	no	—
244	C₂×D₄×C₄₃	—	4	32	no	—
245	C₂×D₄×C₄₃	—	4	16	no	—
246	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
247	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
248	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
249	C₂×D₄×C₄₃	C₂⁴	1	16	yes	—
250	C₂²×C₄×C₄₃	—	2	4	no	—
251	C₂²×C₄×C₄₃	—	2	4	no	—
252	C₂²×C₄×C₄₃	—	2	4	no	—
253	C₂²×C₄×C₄₃	—	4	2	no	—
254	C₂²×C₄×C₄₃	—	4	2	no	—
255	C₂²×C₄×C₄₃	—	4	2	no	—
256	C₂²×C₄×C₄₃	—	4	4	no	—
257	C₂²×C₄×C₄₃	—	4	16	no	—
258	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
261	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
264	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
265	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
266	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
267	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
270	C₂×C₂²⋊D₄₃	—	2	8	no	—
271	C₂×C₂²⋊D₄₃	—	2	16	no	—
272	C₂×C₂²⋊D₄₃	—	2	8	no	—
273	C₂×C₂²⋊D₄₃	—	4	8	no	—
274	C₂×C₂²⋊D₄₃	—	4	8	no	—
275	C₂×C₂²⋊D₄₃	—	4	8	no	—
276	C₂×C₂²⋊D₄₃	—	4	8	no	—
277	C₂×C₂²⋊D₄₃	—	4	8	no	—
278	C₂×C₂²⋊D₄₃	—	4	4	no	—
279	C₂×C₂²⋊D₄₃	—	4	32	no	—
280	C₂×C₂²⋊D₄₃	—	4	64	no	—
281	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
282	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
283	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
284	C₂×C₂²⋊D₄₃	C₂⁴	1	8	yes	—
285	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
286	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
287	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
288	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
289	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
290	C₂²×Dic₄₃	—	4	4	no	—
291	C₂²×Dic₄₃	—	4	8	no	—
292	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
293	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
294	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
295	C₂²×Dic₄₃	C₂⁴	1	2	yes	—
296	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
297	C₂²×Dic₄₃	C₂⁴	1	16	yes	—
298	D₄×D₄₃	—	4	64	no	—
299	D₄×D₄₃	—	4	32	no	—
300	#10621898	—	4	16	no	—
301	C₂×D₁₇₂	—	2	8	no	—
302	C₂×D₁₇₂	—	4	8	no	—
303	C₂×D₁₇₂	—	4	4	no	—
304	C₂×D₁₇₂	—	4	2	no	—
305	C₂×D₁₇₂	—	4	16	no	—
306	C₂×D₁₇₂	C₂⁴	1	8	yes	—
307	C₂×D₁₇₂	C₂⁴	1	4	yes	—
308	C₂×D₁₇₂	C₂⁴	1	8	yes	—
309	C₂×D₁₇₂	C₂⁴	1	16	yes	—
310	C₂×C₄×D₄₃	—	2	8	no	—
311	C₂×C₄×D₄₃	—	4	8	no	—
312	C₂×C₄×D₄₃	C₂⁴	1	8	yes	—
313	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
314	C₂×Dic₈₆	—	4	2	no	—
315	C₂×Dic₈₆	C₂⁴	1	4	yes	—
316	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
317	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₄₃	C₂⁴	1	16	yes	—
320	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
321	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
322	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
323	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
324	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
325	(C₂×D₄₃)⋊C₄	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	16	yes	—
329	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
330	(C₂×D₄₃)⋊C₄	C₂⁴	1	8	yes	—
331	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
332	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
333	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
334	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
335	C₄⋊Dic₄₃	C₂⁴	1	4	yes	—
336	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
337	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
338	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
339	Dic₄₃⋊C₄	C₂⁴	1	8	yes	—
340	C₄×Dic₄₃	C₂⁴	1	16	yes	—
341	C₄×Dic₄₃	C₂⁴	1	8	yes	—
342	C₂³×C₄₃	—	2	2	no	—
343	C₂³×C₄₃	—	2	2	no	—
344	C₂³×C₄₃	—	2	2	no	—
345	C₂³×C₄₃	—	2	2	no	—
346	C₂³×C₄₃	—	2	8	no	—
347	C₂³×C₄₃	—	2	8	no	—
348	C₂³×C₄₃	—	2	2	no	—
349	C₂³×C₄₃	—	2	2	no	—
350	C₂³×C₄₃	—	2	8	no	—
351	C₂³×C₄₃	—	2	8	no	—
352	C₂³×C₄₃	—	2	8	no	—
353	C₂³×C₄₃	—	2	2	no	—
354	C₂³×C₄₃	—	2	16	no	—
355	C₂³×C₄₃	—	4	4	no	—
356	C₂³×C₄₃	—	4	8	no	—
357	C₂³×C₄₃	—	4	8	no	—
358	C₂³×C₄₃	—	4	16	no	—
359	C₂³×C₄₃	—	8	16	no	—
360	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
361	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
362	C₂³×C₄₃	C₂⁵	1	8	yes	—
363	C₂³×C₄₃	C₂⁵	1	2	yes	—
364	C₂³×C₄₃	C₂⁵	1	2	yes	—
365	C₂³×C₄₃	C₂⁵	1	2	yes	—
366	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
367	C₂²×D₄₃	—	2	4	no	—
368	C₂²×D₄₃	—	2	8	no	—
369	C₂²×D₄₃	—	2	8	no	—
370	C₂²×D₄₃	—	2	4	no	—
371	C₂²×D₄₃	—	2	4	no	—
372	C₂²×D₄₃	—	2	8	no	—
373	C₂²×D₄₃	—	2	16	no	—
374	C₂²×D₄₃	—	4	8	no	—
375	C₂²×D₄₃	—	4	16	no	—
376	C₂²×D₄₃	—	4	16	no	—
377	C₂²×D₄₃	—	4	8	no	—
378	C₂²×D₄₃	—	4	16	no	—
379	C₂²×D₄₃	—	8	16	no	—
380	C₂²×D₄₃	—	8	32	no	—
381	C₂²×D₄₃	C₂⁵	1	8	yes	—
382	C₂²×D₄₃	C₂⁵	1	4	yes	—
383	D₄×C₄₃	—	2	32	no	—
384	D₄×C₄₃	—	2	16	no	—
385	D₄×C₄₃	—	4	16	no	—
386	D₄×C₄₃	—	4	8	no	—
387	C₂×C₄×C₄₃	—	2	2	no	—
388	C₂×C₄×C₄₃	—	2	8	no	—
389	C₂×C₄×C₄₃	—	2	2	no	—
390	C₂×C₄×C₄₃	—	2	2	no	—
391	C₂×C₄×C₄₃	—	2	8	no	—
392	C₂×C₄×C₄₃	—	2	8	no	—
393	C₂×C₄×C₄₃	—	2	8	no	—
394	C₂×C₄×C₄₃	—	4	4	no	—
395	C₂×C₄×C₄₃	—	4	4	no	—
396	C₂×C₄×C₄₃	—	4	4	no	—
397	C₂×C₄×C₄₃	—	4	8	no	—
398	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
399	C₂×C₄×C₄₃	C₂⁵	1	8	yes	—
400	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
401	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
402	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
403	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
404	C₂²⋊D₄₃	—	2	16	no	—
405	C₂²⋊D₄₃	—	2	32	no	—
406	C₂²⋊D₄₃	—	2	16	no	—
407	C₂²⋊D₄₃	—	4	8	no	—
408	C₂²⋊D₄₃	—	4	16	no	—
409	C₂²⋊D₄₃	—	4	16	no	—
410	C₂²⋊D₄₃	—	4	16	no	—
411	C₂²⋊D₄₃	—	4	16	no	—
412	C₂²⋊D₄₃	—	4	16	no	—
413	C₂×Dic₄₃	—	2	4	no	—
414	C₂×Dic₄₃	—	2	4	no	—
415	C₂×Dic₄₃	—	2	8	no	—
416	C₂×Dic₄₃	—	2	4	no	—
417	C₂×Dic₄₃	—	4	8	no	—
418	C₂×Dic₄₃	—	4	16	no	—
419	C₂×Dic₄₃	C₂⁵	1	4	yes	—
420	C₂×Dic₄₃	C₂⁵	1	4	yes	—
421	C₂×Dic₄₃	C₂⁵	1	8	yes	—
422	C₂×Dic₄₃	C₂⁵	1	4	yes	—
423	D₁₇₂	—	2	16	no	—
424	D₁₇₂	—	4	8	no	—
425	D₁₇₂	—	4	4	no	—
426	D₁₇₂	—	4	16	no	—
427	C₄×D₄₃	—	2	16	no	—
428	C₄×D₄₃	—	4	16	no	—
429	Dic₈₆	—	4	4	no	—
430	C₂×#3537	—	43	1	no	maximal, Sylow
431	C₂²×C₄₃	—	2	2	no	—
432	C₂²×C₄₃	—	2	2	no	—
433	C₂²×C₄₃	—	2	2	no	—
434	C₂²×C₄₃	—	2	2	no	—
435	C₂²×C₄₃	—	2	8	no	—
436	C₂²×C₄₃	—	2	8	no	—
437	C₂²×C₄₃	—	2	8	no	—
438	C₂²×C₄₃	—	2	8	no	—
439	C₂²×C₄₃	—	2	8	no	—
440	C₂²×C₄₃	—	2	2	no	—
441	C₂²×C₄₃	—	2	2	no	—
442	C₂²×C₄₃	—	2	2	no	—
443	C₂²×C₄₃	—	4	16	no	—
444	C₂²×C₄₃	—	4	16	no	—
445	C₂²×C₄₃	—	4	4	no	—
446	C₂²×C₄₃	—	8	16	no	—
447	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
448	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
449	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
450	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
451	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
452	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
453	C₂×D₄₃	—	2	8	no	—
454	C₂×D₄₃	—	2	4	no	—
455	C₂×D₄₃	—	2	8	no	—
456	C₂×D₄₃	—	2	4	no	—
457	C₂×D₄₃	—	2	8	no	—
458	C₂×D₄₃	—	2	4	no	—
459	C₂×D₄₃	—	4	8	no	—
460	C₂×D₄₃	—	4	16	no	—
461	C₂×D₄₃	—	8	16	no	—
462	C₂×D₄₃	—	8	32	no	—
463	C₄×C₄₃	—	2	2	no	—
464	C₄×C₄₃	—	2	8	no	—
465	C₄×C₄₃	—	2	2	no	—
466	C₄×C₄₃	—	2	2	no	—
467	C₄×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
468	Dic₄₃	—	2	4	no	—
469	Dic₄₃	—	2	4	no	—
470	Dic₄₃	—	2	8	no	—
471	Dic₄₃	—	2	4	no	—
472	#3537	—	43	32	no	—
473	C₂×#560	—	43	4	no	—
474	C₂×#553	—	43	2	no	—
475	C₂×#553	—	43	2	no	—
476	C₂×D₄²	—	43	4	no	—
477	C₂×D₄²	—	43	2	no	—
478	C₂×D₄²	—	43	2	no	—
479	C₂×#540	—	43	2	no	—
480	C₂×#538	—	43	2	no	—
481	C₂×#538	—	43	2	no	—
482	C₂×#535	—	43	2	no	—
483	C₂×#534	—	43	2	no	—
484	C₂×#534	—	43	2	no	—
485	C₂×#525	—	43	1	no	—
486	C₂²×#121	—	43	1	no	—
487	C₂²×#121	D₄₃	1	1	yes	characteristic, complemented
488	C₂×C₄₃	—	2	4	no	—
489	C₂×C₄₃	—	2	4	no	—
490	C₂×C₄₃	—	4	8	no	—
491	C₂×C₄₃	—	4	2	no	—
492	C₂×C₄₃	#3537	1	4	yes	complemented
493	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
496	D₄₃	—	4	8	no	—
497	D₄₃	—	4	4	no	—
498	C₂²×#41	—	43	1	no	—
499	C₂³×D₄	—	43	2	no	—
500	C₂³×D₄	—	43	4	no	—
501	C₂³×D₄	—	43	4	no	—
502	C₂³×D₄	—	43	2	no	—
503	C₂³×D₄	—	43	1	no	—
504	C₂³×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
505	C₂³×D₄	C₂×D₄₃	1	2	yes	complemented
506	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
507	#560	—	43	64	no	—
508	#553	—	43	32	no	—
509	#553	—	43	32	no	—
510	D₄²	—	43	64	no	—
511	D₄²	—	43	32	no	—
512	D₄²	—	43	32	no	—
513	#540	—	43	32	no	—
514	#538	—	43	32	no	—
515	#538	—	43	32	no	—
516	#535	—	43	32	no	—
517	#534	—	43	32	no	—
518	#534	—	43	32	no	—
519	C₂×#127	—	43	4	no	—
520	C₂×#127	—	43	2	no	—
521	C₂×#126	—	43	4	no	—
522	C₂×#126	—	43	4	no	—
523	C₂×#125	—	43	2	no	—
524	C₂×#124	—	43	4	no	—
525	#525	—	43	16	no	—
526	C₂×#123	—	43	2	no	—
527	C₂×#123	—	43	4	no	—
528	C₂×#123	—	43	4	no	—
529	C₂×#123	—	43	4	no	—
530	C₂×#123	—	43	4	no	—
531	C₂×C₂²⋊Q₈	—	43	1	no	—
532	C₂×C₂²⋊Q₈	—	43	1	no	—
533	C₂×#121	—	43	2	no	—
534	C₂×#121	—	43	4	no	—
535	C₂×#121	—	43	4	no	—
536	C₂×#121	—	43	4	no	—
537	C₂×#121	—	43	4	no	—
538	C₂×#121	—	43	2	no	—
539	C₂×#121	—	43	2	no	—
540	C₂×#121	—	43	2	no	—
541	C₂×#121	—	43	2	no	—
542	C₂×#121	—	43	1	no	—
543	C₂×#121	—	43	1	no	—
544	C₂×#121	—	43	4	no	—
545	C₂×#121	—	43	16	no	—
546	C₂×#121	—	43	2	no	—
547	C₂×#121	—	43	4	no	—
548	C₂×#121	C₂×D₄₃	1	2	yes	complemented
549	C₂×#121	C₂×D₄₃	1	2	yes	complemented
550	C₂×#121	C₂×D₄₃	1	2	yes	complemented
551	C₂×#121	C₂×D₄₃	1	2	yes	complemented
552	C₂×#121	C₂×D₄₃	1	16	yes	complemented
553	C₂×#120	—	43	2	no	—
554	C₂×#120	—	43	4	no	—
555	C₂×#120	—	43	4	no	—
556	C₂×#120	—	43	4	no	—
557	C₂×#120	—	43	4	no	—
558	C₂×#120	—	43	4	no	—
559	C₂×#120	—	43	4	no	—
560	C₂×C₄×D₄	—	43	4	no	—
561	C₂×C₄×D₄	—	43	2	no	—
562	C₂×C₄×D₄	—	43	2	no	—
563	C₂×C₄×D₄	—	43	2	no	—
564	C₂×C₄×D₄	—	43	4	no	—
565	C₂×C₄×D₄	—	43	2	no	—
566	C₂×#117	—	43	1	no	—
567	C₂×#117	—	43	2	no	—
568	C₂²×C₄⋊C₄	—	43	1	no	—
569	C₂²×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
570	C₂²×C₂²⋊C₄	—	43	2	no	—
571	C₂²×C₂²⋊C₄	C₂×D₄₃	1	2	yes	complemented
572	C₄₃	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
573	C₂⁵	—	43	2	no	—
574	C₂⁵	—	43	4	no	—
575	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
576	C₂⁵	C₂²×D₄₃	1	2	yes	—
577	C₂×#41	—	43	8	no	—
578	C₂×#41	—	172	4	no	—
579	C₂²×Q₈	—	43	1	no	—
580	C₂²×D₄	—	4	4	no	—
581	C₂²×D₄	—	4	8	no	—
582	C₂²×D₄	—	43	2	no	—
583	C₂²×D₄	—	43	2	no	—
584	C₂²×D₄	—	43	4	no	—
585	C₂²×D₄	—	43	2	no	—
586	C₂²×D₄	—	43	4	no	—
587	C₂²×D₄	—	43	4	no	—
588	C₂²×D₄	—	43	4	no	—
589	C₂²×D₄	—	43	4	no	—
590	C₂²×D₄	—	43	4	no	—
591	C₂²×D₄	—	43	16	no	—
592	C₂²×D₄	—	43	32	no	—
593	C₂²×D₄	—	43	32	no	—
594	C₂²×D₄	—	43	16	no	—
595	C₂²×D₄	—	43	2	no	—
596	C₂²×D₄	—	43	1	no	—
597	C₂²×D₄	—	43	2	no	—
598	C₂²×D₄	—	43	4	no	—
599	C₂²×D₄	—	43	8	no	—
600	C₂²×D₄	—	172	4	no	—
601	C₂²×D₄	—	172	8	no	—
602	C₂²×D₄	—	172	16	no	—
603	C₂²×D₄	—	172	8	no	—
604	C₂²×D₄	—	172	16	no	—
605	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
606	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
607	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
608	C₂²×D₄	C₂²×D₄₃	1	4	yes	—
609	C₂²×D₄	C₂²×D₄₃	1	8	yes	complemented
610	C₂²×D₄	C₂²×D₄₃	1	16	yes	complemented
611	C₂³×C₄	—	4	4	no	—
612	C₂³×C₄	—	43	2	no	—
613	C₂³×C₄	—	43	4	no	—
614	C₂³×C₄	—	43	2	no	—
615	C₂³×C₄	—	43	4	no	—
616	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
617	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
618	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
619	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
620	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
621	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
622	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
623	C₂³×C₄	C₂²×D₄₃	1	8	yes	complemented
624	#127	—	43	32	no	—
625	#127	—	43	16	no	—
626	#126	—	43	32	no	—
627	#126	—	43	32	no	—
628	#125	—	43	16	no	—
629	#124	—	43	32	no	—
630	#123	—	43	16	no	—
631	#123	—	43	32	no	—
632	#123	—	43	32	no	—
633	#123	—	43	32	no	—
634	#123	—	43	32	no	—
635	C₂²⋊Q₈	—	43	8	no	—
636	C₂²⋊Q₈	—	43	8	no	—
637	#121	—	43	32	no	—
638	#121	—	43	16	no	—
639	#121	—	43	32	no	—
640	#121	—	43	32	no	—
641	#121	—	43	32	no	—
642	#121	—	43	16	no	—
643	#121	—	43	16	no	—
644	#121	—	43	16	no	—
645	#121	—	43	16	no	—
646	#121	—	43	8	no	—
647	#121	—	43	8	no	—
648	#121	—	43	32	no	—
649	#121	—	43	16	no	—
650	#121	—	43	32	no	—
651	#121	C₂²×D₄₃	1	16	yes	complemented
652	#121	C₂²×D₄₃	1	16	yes	complemented
653	#121	C₂²×D₄₃	1	16	yes	complemented
654	#121	C₂²×D₄₃	1	16	yes	complemented
655	#120	—	43	16	no	—
656	#120	—	43	32	no	—
657	#120	—	43	32	no	—
658	#120	—	43	32	no	—
659	#120	—	43	32	no	—
660	#120	—	43	32	no	—
661	#120	—	43	32	no	—
662	C₄×D₄	—	43	32	no	—
663	C₄×D₄	—	43	16	no	—
664	C₄×D₄	—	43	16	no	—
665	C₄×D₄	—	43	16	no	—
666	C₄×D₄	—	43	32	no	—
667	C₄×D₄	—	43	16	no	—
668	#117	—	43	8	no	—
669	#117	—	43	16	no	—
670	C₂×C₄⋊C₄	—	43	2	no	—
671	C₂×C₄⋊C₄	—	43	2	no	—
672	C₂×C₄⋊C₄	—	43	8	no	—
673	C₂×C₄⋊C₄	—	43	1	no	—
674	C₂×C₄⋊C₄	—	43	1	no	—
675	C₂×C₄⋊C₄	—	43	2	no	—
676	C₂×C₄⋊C₄	—	43	2	no	—
677	C₂×C₄⋊C₄	—	43	4	no	—
678	C₂×C₄⋊C₄	—	43	4	no	—
679	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
681	C₂×C₄⋊C₄	C₂²×D₄₃	1	8	yes	complemented
682	C₂×C₂²⋊C₄	—	43	2	no	—
683	C₂×C₂²⋊C₄	—	43	2	no	—
684	C₂×C₂²⋊C₄	—	43	2	no	—
685	C₂×C₂²⋊C₄	—	43	4	no	—
686	C₂×C₂²⋊C₄	—	43	4	no	—
687	C₂×C₂²⋊C₄	—	43	4	no	—
688	C₂×C₂²⋊C₄	—	43	4	no	—
689	C₂×C₂²⋊C₄	—	43	16	no	—
690	C₂×C₂²⋊C₄	—	43	4	no	—
691	C₂×C₂²⋊C₄	—	43	4	no	—
692	C₂×C₂²⋊C₄	—	43	4	no	—
693	C₂×C₂²⋊C₄	—	43	2	no	—
694	C₂×C₂²⋊C₄	—	43	2	no	—
695	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
696	C₂×C₂²⋊C₄	C₂²×D₄₃	1	4	yes	—
697	C₂×C₂²⋊C₄	C₂²×D₄₃	1	16	yes	complemented
698	C₂×C₄²	—	43	2	no	—
699	C₂×C₄²	—	43	4	no	—
700	C₂⁴	—	2	4	no	—
701	C₂⁴	—	2	4	no	—
702	C₂⁴	—	2	8	no	—
703	C₂⁴	—	4	2	no	—
704	C₂⁴	—	4	4	no	—
705	C₂⁴	—	4	4	no	—
706	C₂⁴	—	43	2	no	—
707	C₂⁴	—	43	4	no	—
708	C₂⁴	—	43	8	no	—
709	C₂⁴	—	43	16	no	—
710	C₂⁴	—	86	8	no	—
711	C₂⁴	—	172	4	no	—
712	C₂⁴	—	172	4	no	—
713	C₂⁴	—	172	8	no	—
714	C₂⁴	—	172	8	no	—
715	C₂⁴	—	172	8	no	—
716	C₂⁴	C₂³×D₄₃	1	4	yes	—
717	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
718	C₂⁴	C₂³×D₄₃	1	4	yes	—
719	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
720	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
721	C₂⁴	C₂³×D₄₃	1	8	yes	—
722	#41	—	172	16	no	—
723	C₂×Q₈	—	43	4	no	—
724	C₂×Q₈	—	172	2	no	—
725	C₂×D₄	—	2	16	no	—
726	C₂×D₄	—	2	8	no	—
727	C₂×D₄	—	4	16	no	—
728	C₂×D₄	—	4	4	no	—
729	C₂×D₄	—	4	8	no	—
730	C₂×D₄	—	4	32	no	—
731	C₂×D₄	—	43	8	no	—
732	C₂×D₄	—	43	8	no	—
733	C₂×D₄	—	43	16	no	—
734	C₂×D₄	—	43	8	no	—
735	C₂×D₄	—	43	16	no	—
736	C₂×D₄	—	43	16	no	—
737	C₂×D₄	—	43	16	no	—
738	C₂×D₄	—	43	16	no	—
739	C₂×D₄	—	43	16	no	—
740	C₂×D₄	—	43	8	no	—
741	C₂×D₄	—	43	4	no	—
742	C₂×D₄	—	43	8	no	—
743	C₂×D₄	—	43	16	no	—
744	C₂×D₄	—	86	8	no	—
745	C₂×D₄	—	86	8	no	—
746	C₂×D₄	—	86	16	no	—
747	C₂×D₄	—	86	8	no	—
748	C₂×D₄	—	172	16	no	—
749	C₂×D₄	—	172	4	no	—
750	C₂×D₄	—	172	8	no	—
751	C₂×D₄	—	172	2	no	—
752	C₂×D₄	—	172	32	no	—
753	C₂×D₄	—	172	8	no	—
754	C₂×D₄	—	172	8	no	—
755	C₂×D₄	—	172	8	no	—
756	C₂×D₄	—	172	8	no	—
757	C₂×D₄	—	172	8	no	—
758	C₂×D₄	—	172	4	no	—
759	C₂×D₄	—	172	64	no	—
760	C₂×D₄	—	172	32	no	—
761	C₂×D₄	—	172	64	no	—
762	C₂×D₄	C₂³×D₄₃	1	16	yes	—
763	C₂×D₄	C₂³×D₄₃	1	8	yes	—
764	C₂×D₄	C₂³×D₄₃	1	8	yes	—
765	C₂×D₄	C₂³×D₄₃	1	16	yes	—
766	C₂²×C₄	—	2	4	no	—
767	C₂²×C₄	—	2	4	no	—
768	C₂²×C₄	—	2	4	no	—
769	C₂²×C₄	—	4	16	no	—
770	C₂²×C₄	—	4	2	no	—
771	C₂²×C₄	—	4	2	no	—
772	C₂²×C₄	—	4	2	no	—
773	C₂²×C₄	—	4	4	no	—
774	C₂²×C₄	—	43	2	no	—
775	C₂²×C₄	—	43	2	no	—
776	C₂²×C₄	—	43	2	no	—
777	C₂²×C₄	—	43	4	no	—
778	C₂²×C₄	—	43	8	no	—
779	C₂²×C₄	—	43	16	no	—
780	C₂²×C₄	—	43	8	no	—
781	C₂²×C₄	—	43	16	no	—
782	C₂²×C₄	—	86	8	no	—
783	C₂²×C₄	—	172	8	no	—
784	C₂²×C₄	—	172	4	no	—
785	C₂²×C₄	—	172	8	no	—
786	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
787	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
788	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
789	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
790	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
791	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
792	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
793	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
794	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
795	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
796	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
797	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
798	C₄⋊C₄	—	43	8	no	—
799	C₄⋊C₄	—	43	8	no	—
800	C₄⋊C₄	—	43	4	no	—
801	C₄⋊C₄	—	43	4	no	—
802	C₄⋊C₄	—	43	8	no	—
803	C₄⋊C₄	—	43	8	no	—
804	C₄⋊C₄	—	43	16	no	—
805	C₄⋊C₄	—	43	16	no	—
806	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
807	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
808	C₂²⋊C₄	—	43	8	no	—
809	C₂²⋊C₄	—	43	8	no	—
810	C₂²⋊C₄	—	43	8	no	—
811	C₂²⋊C₄	—	43	16	no	—
812	C₂²⋊C₄	—	43	16	no	—
813	C₂²⋊C₄	—	43	16	no	—
814	C₂²⋊C₄	—	43	16	no	—
815	C₂²⋊C₄	—	43	16	no	—
816	C₂²⋊C₄	—	43	16	no	—
817	C₂²⋊C₄	—	43	16	no	—
818	C₂²⋊C₄	—	43	8	no	—
819	C₂²⋊C₄	—	43	8	no	—
820	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
821	C₂²⋊C₄	C₂³×D₄₃	1	16	yes	—
822	C₄²	—	43	8	no	—
823	C₄²	—	43	16	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	2	8	no	—
830	C₂³	—	2	8	no	—
831	C₂³	—	2	8	no	—
832	C₂³	—	2	2	no	—
833	C₂³	—	2	8	no	—
834	C₂³	—	2	8	no	—
835	C₂³	—	2	2	no	—
836	C₂³	—	2	16	no	—
837	C₂³	—	4	4	no	—
838	C₂³	—	4	8	no	—
839	C₂³	—	4	8	no	—
840	C₂³	—	4	16	no	—
841	C₂³	—	8	16	no	—
842	C₂³	—	43	4	no	—
843	C₂³	—	43	8	no	—
844	C₂³	—	86	16	no	—
845	C₂³	—	86	4	no	—
846	C₂³	—	86	8	no	—
847	C₂³	—	86	4	no	—
848	C₂³	—	86	8	no	—
849	C₂³	—	86	4	no	—
850	C₂³	—	86	8	no	—
851	C₂³	—	344	16	no	—
852	C₂³	—	344	32	no	—
853	C₂³	—	172	8	no	—
854	C₂³	—	172	8	no	—
855	C₂³	—	172	16	no	—
856	C₂³	—	172	16	no	—
857	C₂³	—	172	16	no	—
858	C₂³	#13063370	1	4	yes	—
859	C₂³	#13063371	1	4	yes	—
860	C₂³	C₂⁴×D₄₃	1	8	yes	—
861	C₂³	C₂⁴×D₄₃	1	2	yes	—
862	C₂³	C₂⁴×D₄₃	1	2	yes	—
863	C₂³	C₂⁴×D₄₃	1	2	yes	—
864	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
865	Q₈	—	172	4	no	—
866	D₄	—	2	32	no	—
867	D₄	—	2	16	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	16	no	—
870	D₄	—	86	16	no	—
871	D₄	—	86	16	no	—
872	D₄	—	86	32	no	—
873	D₄	—	86	16	no	—
874	D₄	—	172	8	no	—
875	D₄	—	172	16	no	—
876	D₄	—	172	4	no	—
877	D₄	—	172	16	no	—
878	D₄	—	172	16	no	—
879	D₄	—	172	16	no	—
880	D₄	—	172	16	no	—
881	D₄	—	172	16	no	—
882	D₄	—	172	8	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	8	no	—
887	C₂×C₄	—	2	8	no	—
888	C₂×C₄	—	2	8	no	—
889	C₂×C₄	—	2	8	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	8	no	—
894	C₂×C₄	—	43	4	no	—
895	C₂×C₄	—	43	4	no	—
896	C₂×C₄	—	43	4	no	—
897	C₂×C₄	—	43	8	no	—
898	C₂×C₄	—	86	4	no	—
899	C₂×C₄	—	86	4	no	—
900	C₂×C₄	—	86	4	no	—
901	C₂×C₄	—	86	8	no	—
902	C₂×C₄	—	86	16	no	—
903	C₂×C₄	—	172	16	no	—
904	C₂×C₄	—	172	8	no	—
905	C₂×C₄	—	172	16	no	—
906	C₂×C₄	#13063370	1	4	yes	—
907	C₂×C₄	C₂⁴×D₄₃	1	8	yes	—
908	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
909	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
910	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
911	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
912	C₂²	—	2	8	no	—
913	C₂²	—	2	8	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	8	no	—
920	C₂²	—	2	8	no	—
921	C₂²	—	2	2	no	—
922	C₂²	—	2	8	no	—
923	C₂²	—	2	2	no	—
924	C₂²	—	4	16	no	—
925	C₂²	—	4	4	no	—
926	C₂²	—	4	16	no	—
927	C₂²	—	8	16	no	—
928	C₂²	—	86	4	no	—
929	C₂²	—	86	8	no	—
930	C₂²	—	86	4	no	—
931	C₂²	—	86	8	no	—
932	C₂²	—	86	4	no	—
933	C₂²	—	86	8	no	—
934	C₂²	—	344	16	no	—
935	C₂²	—	344	32	no	—
936	C₂²	—	172	8	no	—
937	C₂²	—	172	16	no	—
938	C₂²	C₂×#13063370	1	4	yes	—
939	C₂²	C₂×#13063370	1	2	yes	—
940	C₂²	C₂×#13063370	1	2	yes	—
941	C₂²	C₂×#13063371	1	4	yes	—
942	C₂²	C₂×#13063371	1	2	yes	—
943	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
944	C₄	—	2	2	no	—
945	C₄	—	2	2	no	—
946	C₄	—	2	2	no	—
947	C₄	—	2	8	no	—
948	C₄	—	86	4	no	—
949	C₄	—	86	4	no	—
950	C₄	—	86	4	no	—
951	C₄	—	86	8	no	—
952	C₄	C₂×#13063370	1	4	yes	—
953	C₂	—	2	4	no	—
954	C₂	—	2	4	no	—
955	C₂	—	4	2	no	—
956	C₂	—	4	8	no	—
957	C₂	—	172	4	no	—
958	C₂	—	172	8	no	—
959	C₂	#19148830	1	4	yes	direct product factor
960	C₂	C₂²×#13063370	1	1	yes	characteristic
961	C₂	C₂²×#13063370	1	1	yes	characteristic
962	C₂	C₂²×#13063371	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×#121×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂²×#121	D₄₃
hypocenter	C₄₃	C₂×#3537
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#121

Complements

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

N	H ≅ G/N	type
1. #19148830	C₂	direct (N × H)
2. C₂×#14583637	C₂	semidirect
3. C₂×#14583601	C₂	semidirect
4. C₂×#14583597	C₂	semidirect
5. C₂×#14583533	C₂	semidirect
6. C₂×D₄×C₂²⋊D₄₃	C₂	semidirect
7. C₂×D₄×C₂²⋊D₄₃	C₂	semidirect
8. C₂×#14583502	C₂	semidirect
9. C₂×#14583487	C₂	semidirect
10. C₂×#14583486	C₂	semidirect
11. C₂×#14583465	C₂	semidirect
12. C₂×#14583461	C₂	semidirect
13. C₂×#14583457	C₂	semidirect
14. C₂×#14583410	C₂	semidirect
15. C₂²×#13063299	C₂	semidirect
16. C₂²×#121×C₄₃	C₂	semidirect
17. C₂²×#10621898	C₂²	semidirect
18. C₂³×D₁₇₂	C₂²	semidirect
19. C₂³×C₂²⋊D₄₃	C₂²	semidirect
20. C₂³×C₂²⋊D₄₃	C₂²	semidirect
21. C₂²×D₄×D₄₃	C₂²	semidirect
22. C₂²×D₄×D₄₃	C₂²	semidirect
23. #14583637	C₂²	semidirect
24. #14583601	C₂²	semidirect
25. #14583597	C₂²	semidirect
26. #14583533	C₂²	semidirect
27. D₄×C₂²⋊D₄₃	C₂²	semidirect
28. D₄×C₂²⋊D₄₃	C₂²	semidirect
29. #14583502	C₂²	semidirect
30. #14583487	C₂²	semidirect
31. #14583486	C₂²	semidirect
32. #14583465	C₂²	semidirect
33. #14583461	C₂²	semidirect
34. #14583457	C₂²	semidirect
35. C₂×#13063321	C₂²	semidirect
36. C₂×#13063321	C₂²	semidirect
37. C₂×#13063320	C₂²	semidirect
38. C₂×#13063318	C₂²	semidirect
39. C₂×#13063316	C₂²	semidirect
40. C₂×#13063311	C₂²	semidirect
41. #14583410	C₂²	semidirect
42. C₂×#13063310	C₂²	semidirect
43. C₂×#13063309	C₂²	semidirect
44. C₂×#13063309	C₂²	semidirect
45. C₂×#13063308	C₂²	semidirect
46. C₂×#13063307	C₂²	semidirect
47. C₂×#13063304	C₂²	semidirect
48. C₂×#13063304	C₂²	semidirect
49. C₂×#13063300	C₂²	semidirect
50. C₂×#13063299	C₂²	semidirect
51. C₂×#13063299	C₂²	semidirect
52. C₂×#13063299	C₂²	semidirect
53. C₂×#13063299	C₂²	semidirect
54. C₂×#13063299	C₂²	semidirect
55. C₂×#13063299	C₂²	semidirect
56. C₂×#13063299	C₂²	semidirect
57. C₂×#13063299	C₂²	semidirect
58. C₂×#13063298	C₂²	semidirect
59. C₂×#13063297	C₂²	semidirect
60. C₂×#13063297	C₂²	semidirect
61. C₂×#13063297	C₂²	semidirect
62. C₂×#13063296	C₂²	semidirect
63. C₂×#13063296	C₂²	semidirect
64. C₂×#13063295	C₂²	semidirect
65. C₂×#13063295	C₂²	semidirect
66. C₂×#13063294	C₂²	semidirect
67. C₂×#13063294	C₂²	semidirect
68. C₂×#13063293	C₂²	semidirect
69. C₂×#13063293	C₂²	semidirect
70. C₂×#13063293	C₂²	semidirect
71. C₂×D₄×Dic₄₃	C₂²	semidirect
72. C₂×D₄×Dic₄₃	C₂²	semidirect
73. C₂×#13063287	C₂²	semidirect
74. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
75. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
76. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
77. C₂×#13063284	C₂²	semidirect
78. C₂×#13063283	C₂²	semidirect
79. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
80. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
81. C₂³×D₄×C₄₃	C₂²	semidirect
82. C₂³×D₄×C₄₃	C₂²	semidirect
83. C₂⁴×C₄×C₄₃	C₂²	semidirect
84. C₂×#121×C₄₃	C₂²	semidirect
85. C₂×#121×C₄₃	C₂²	semidirect
86. C₂×#121×C₄₃	C₂²	semidirect
87. C₂×#121×C₄₃	C₂²	semidirect
88. C₂×#121×C₄₃	C₂²	semidirect
89. C₂²×C₄⋊C₄×C₄₃	C₂²	semidirect
90. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
94. C₂×#10621898	C₂³	semidirect
101. C₂²×D₁₇₂	C₂³	semidirect
113. C₂²×C₂²⋊D₄₃	C₂³	semidirect
114. C₂²×C₂²⋊D₄₃	C₂³	semidirect
117. C₂×D₄×D₄₃	C₂³	semidirect
118. C₂×D₄×D₄₃	C₂³	semidirect
123. #13063321	C₂³	semidirect
124. #13063321	C₂³	semidirect
125. #13063320	C₂³	semidirect
126. #13063318	C₂³	semidirect
127. #13063316	C₂³	semidirect
128. #13063311	C₂³	semidirect
129. #13063310	C₂³	semidirect
130. #13063309	C₂³	semidirect
131. #13063309	C₂³	semidirect
132. #13063308	C₂³	semidirect
133. #13063307	C₂³	semidirect
134. #13063304	C₂³	semidirect
135. #13063304	C₂³	semidirect
136. #13063300	C₂³	semidirect
137. #13063299	C₂³	semidirect
138. #13063299	C₂³	semidirect
139. #13063299	C₂³	semidirect
140. #13063299	C₂³	semidirect
141. #13063299	C₂³	semidirect
142. #13063299	C₂³	semidirect
143. #13063299	C₂³	semidirect
144. #13063298	C₂³	semidirect
145. #13063297	C₂³	semidirect
146. #13063297	C₂³	semidirect
147. #13063297	C₂³	semidirect
148. #13063296	C₂³	semidirect
149. #13063296	C₂³	semidirect
150. #13063295	C₂³	semidirect
151. #13063295	C₂³	semidirect
152. #13063294	C₂³	semidirect
153. #13063294	C₂³	semidirect
154. #13063293	C₂³	semidirect
155. #13063293	C₂³	semidirect
156. #13063293	C₂³	semidirect
157. D₄×Dic₄₃	C₂³	semidirect
158. D₄×Dic₄₃	C₂³	semidirect
159. #13063287	C₂³	semidirect
160. C₄×C₂²⋊D₄₃	C₂³	semidirect
161. C₄×C₂²⋊D₄₃	C₂³	semidirect
162. C₄×C₂²⋊D₄₃	C₂³	semidirect
163. #13063284	C₂³	semidirect
164. #13063283	C₂³	semidirect
170. C₂×C₄⋊Dic₄₃	C₂³	semidirect
186. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
197. C₂²×D₄×C₄₃	C₂³	semidirect
198. C₂²×D₄×C₄₃	C₂³	semidirect
207. C₂³×C₄×C₄₃	C₂³	semidirect
208. #121×C₄₃	C₂³	semidirect
209. #121×C₄₃	C₂³	semidirect
210. #121×C₄₃	C₂³	semidirect
211. #121×C₄₃	C₂³	semidirect
214. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
217. C₂×C₂²⋊C₄×C₄₃	C₂³	semidirect
487. C₂²×#121	D₄₃	semidirect
492. C₂×C₄₃	#3537	semidirect
504. C₂³×D₄	C₂×D₄₃	semidirect
505. C₂³×D₄	C₂×D₄₃	semidirect
506. C₂⁴×C₄	C₂×D₄₃	semidirect
548. C₂×#121	C₂×D₄₃	semidirect
549. C₂×#121	C₂×D₄₃	semidirect
550. C₂×#121	C₂×D₄₃	semidirect
551. C₂×#121	C₂×D₄₃	semidirect
552. C₂×#121	C₂×D₄₃	semidirect
569. C₂²×C₄⋊C₄	C₂×D₄₃	semidirect
571. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
572. C₄₃	C₂×#3537	semidirect
609. C₂²×D₄	C₂²×D₄₃	semidirect
610. C₂²×D₄	C₂²×D₄₃	semidirect
623. C₂³×C₄	C₂²×D₄₃	semidirect
651. #121	C₂²×D₄₃	semidirect
652. #121	C₂²×D₄₃	semidirect
653. #121	C₂²×D₄₃	semidirect
654. #121	C₂²×D₄₃	semidirect
681. C₂×C₄⋊C₄	C₂²×D₄₃	semidirect
697. C₂×C₂²⋊C₄	C₂²×D₄₃	semidirect
959. C₂	#19148830	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148830	2
C₂×#14583637	2
C₂×#14583601	2
C₂×#14583597	2
C₂×#14583533	2
C₂×D₄×C₂²⋊D₄₃	2
C₂×#14583502	2
C₂×#14583487	2
C₂×#14583486	2
C₂×#14583465	2
C₂×#14583461	2
C₂×#14583457	2
C₂×#14583410	2
C₂²×#13063299	2
C₂²×#121×C₄₃	2
C₂×#3537	43

Subgroups — C2×#19148830 #26003834

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148830 #26003834