Subgroups — C₂×#19148153 #26003634

Order 11008.

7954 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂²×C₄×D₄×C₄₃	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₃
hypocenter	C₄₃	C₂×#3475
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. #19148153	C₂	direct (N × H)
2. C₂×#14583619	C₂	semidirect
3. C₂×#14583614	C₂	semidirect
4. C₂×#14583606	C₂	semidirect
5. C₂×#14583595	C₂	semidirect
6. C₂×#14583589	C₂	semidirect
7. C₂×#14583584	C₂	semidirect
8. C₂×#14583575	C₂	semidirect
9. C₂×#14583553	C₂	semidirect
10. C₂×#14583543	C₂	semidirect
11. C₂×#14583456	C₂	semidirect
12. C₂×#14583431	C₂	semidirect
13. C₂×#14583429	C₂	semidirect
14. C₂×#14583410	C₂	semidirect
15. C₂×C₄×#10621898	C₂	semidirect
16. C₂×C₄×#10621900	C₂	semidirect
17. C₂²×#13063284	C₂	semidirect
18. C₂²×C₄×D₄×C₄₃	C₂	semidirect
21. #14583619	C₂²	semidirect
22. #14583614	C₂²	semidirect
23. #14583606	C₂²	semidirect
24. #14583595	C₂²	semidirect
25. #14583589	C₂²	semidirect
26. #14583584	C₂²	semidirect
27. #14583575	C₂²	semidirect
28. #14583553	C₂²	semidirect
29. #14583543	C₂²	semidirect
30. #14583456	C₂²	semidirect
31. C₂×#13063325	C₂²	semidirect
32. C₂×#13063325	C₂²	semidirect
33. #14583431	C₂²	semidirect
34. #14583429	C₂²	semidirect
35. C₂×#13063320	C₂²	semidirect
36. C₂×#13063318	C₂²	semidirect
37. C₂×#13063318	C₂²	semidirect
38. C₂×#13063317	C₂²	semidirect
39. C₂×#13063316	C₂²	semidirect
40. C₂×#13063315	C₂²	semidirect
42. C₂×#13063311	C₂²	semidirect
43. #14583410	C₂²	semidirect
44. C₂×#13063309	C₂²	semidirect
46. C₂×#13063307	C₂²	semidirect
48. C₂×#13063305	C₂²	semidirect
51. C₂×#13063304	C₂²	semidirect
52. C₂×#13063304	C₂²	semidirect
53. C₂×#13063302	C₂²	semidirect
54. C₂×#13063299	C₂²	semidirect
55. C₂×#13063299	C₂²	semidirect
59. C₄×#10621898	C₂²	semidirect
60. C₄×#10621900	C₂²	semidirect
61. C₂×C₄×Dic₈₆	C₂²	semidirect
62. C₂×C₄×Dic₈₆	C₂²	semidirect
63. C₂×C₄×Dic₈₆	C₂²	semidirect
64. C₂×C₄×Dic₈₆	C₂²	semidirect
65. C₂×#13063290	C₂²	semidirect
66. C₂×C₄×D₁₇₂	C₂²	semidirect
67. C₂×C₄×D₁₇₂	C₂²	semidirect
71. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
72. C₂×C₄×C₂²⋊D₄₃	C₂²	semidirect
73. C₂×(C₂²⋊D₄₃)⋊C₄	C₂²	semidirect
77. C₂×#13063284	C₂²	semidirect
78. C₂×#13063284	C₂²	semidirect
79. C₂×#13063284	C₂²	semidirect
80. C₂×#13063284	C₂²	semidirect
81. C₂×#13063283	C₂²	semidirect
82. C₂×#13063282	C₂²	semidirect
83. C₂×#13063281	C₂²	semidirect
84. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
85. C₂²×C₄⋊Dic₄₃	C₂²	semidirect
87. C₂²×C₄×Dic₄₃	C₂²	semidirect
88. C₂×C₄²×D₄₃	C₂²	semidirect
97. C₂×C₄×D₄×C₄₃	C₂²	semidirect
117. #13063325	C₂³	semidirect
118. #13063325	C₂³	semidirect
119. #13063320	C₂³	semidirect
120. #13063318	C₂³	semidirect
121. #13063318	C₂³	semidirect
122. #13063317	C₂³	semidirect
123. #13063316	C₂³	semidirect
124. #13063315	C₂³	semidirect
126. #13063311	C₂³	semidirect
127. #13063309	C₂³	semidirect
129. #13063307	C₂³	semidirect
131. #13063305	C₂³	semidirect
134. #13063304	C₂³	semidirect
135. #13063304	C₂³	semidirect
136. #13063302	C₂³	semidirect
137. #13063299	C₂³	semidirect
138. #13063299	C₂³	semidirect
142. C₄×Dic₈₆	C₂³	semidirect
143. C₄×Dic₈₆	C₂³	semidirect
144. C₄×Dic₈₆	C₂³	semidirect
145. C₄×Dic₈₆	C₂³	semidirect
146. #13063290	C₂³	semidirect
147. C₄×D₁₇₂	C₂³	semidirect
148. C₄×D₁₇₂	C₂³	semidirect
152. C₄×C₂²⋊D₄₃	C₂³	semidirect
153. C₄×C₂²⋊D₄₃	C₂³	semidirect
154. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
158. #13063284	C₂³	semidirect
159. #13063284	C₂³	semidirect
160. #13063284	C₂³	semidirect
161. #13063283	C₂³	semidirect
162. #13063282	C₂³	semidirect
163. #13063281	C₂³	semidirect
172. C₂×C₄⋊Dic₄₃	C₂³	semidirect
173. C₂×C₄⋊Dic₄₃	C₂³	semidirect
197. C₂×C₄×Dic₄₃	C₂³	semidirect
198. C₄²×D₄₃	C₂³	semidirect
246. C₂×D₄×C₄₃	#41	semidirect
258. C₂²×C₄×C₄₃	#41	semidirect
370. D₄×C₄₃	C₂×#41	semidirect
386. C₂×C₄×C₄₃	C₂×#41	semidirect
468. C₂²×C₄×D₄	D₄₃	semidirect
473. C₂×C₄₃	#3475	semidirect
541. C₂×C₄×D₄	C₂×D₄₃	semidirect
560. C₄₃	C₂×#3475	semidirect
722. C₂×D₄	#10621898	semidirect
749. C₂²×C₄	#10621900	semidirect
837. D₄	C₂×#10621898	semidirect
867. C₂×C₄	C₂×#10621900	semidirect
915. C₂	#19148153	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148153	2
C₂×#14583619	2
C₂×#14583614	2
C₂×#14583606	2
C₂×#14583595	2
C₂×#14583589	2
C₂×#14583584	2
C₂×#14583575	2
C₂×#14583553	2
C₂×#14583543	2
C₂×#14583456	2
C₂×#14583431	2
C₂×#14583429	2
C₂×#14583410	2
C₂×C₄×#10621898	2
C₂×C₄×#10621900	2
C₂²×#13063284	2
C₂²×C₄×D₄×C₄₃	2
C₂×#3475	43

Subgroups — C2×#19148153 #26003634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148153 #26003634