Subgroups — C₂×#19148870 #26003888

Order 11008.

7418 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148870	C₂	1	32	yes	maximal, direct product factor
2	C₂×#14583642	C₂	1	2	yes	maximal, complemented
3	C₂×#14583638	C₂	1	2	yes	maximal, complemented
4	C₂×#14583633	C₂	1	2	yes	maximal, complemented
5	C₂×#14583619	C₂	1	2	yes	maximal, complemented
6	C₂×#14583614	C₂	1	2	yes	maximal, complemented
7	C₂×#14583577	C₂	1	2	yes	maximal, complemented
8	C₂×#14583558	C₂	1	2	yes	maximal, complemented
9	C₂×#14583545	C₂	1	2	yes	maximal, complemented
10	C₂×#14583520	C₂	1	2	yes	maximal, complemented
11	C₂×#14583519	C₂	1	4	yes	maximal, complemented
12	C₂×#14583481	C₂	1	4	yes	maximal, complemented
13	C₂×#14583470	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14583463	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#14583410	C₂	1	2	yes	maximal, complemented
16	C₂×C₄₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#10621898	C₂²	1	2	yes	—
18	C₂³×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
20	#14583642	C₂²	1	32	yes	complemented
21	#14583638	C₂²	1	32	yes	complemented
22	#14583633	C₂²	1	32	yes	complemented
23	#14583619	C₂²	1	32	yes	complemented
24	#14583614	C₂²	1	32	yes	complemented
25	#14583577	C₂²	1	32	yes	complemented
26	#14583558	C₂²	1	32	yes	complemented
27	#14583545	C₂²	1	32	yes	complemented
28	#14583520	C₂²	1	32	yes	complemented
29	#14583519	C₂²	1	64	yes	complemented
30	#14583481	C₂²	1	64	yes	complemented
31	#14583470	C₂²	1	16	yes	complemented
32	#14583463	C₂²	1	16	yes	complemented
33	C₂×#13063325	C₂²	1	2	yes	complemented
34	C₂×#13063323	C₂²	1	2	yes	complemented
35	C₂×#13063321	C₂²	1	2	yes	—
36	C₂×#13063320	C₂²	1	4	yes	complemented
37	C₂×#13063318	C₂²	1	4	yes	complemented
38	C₂×#13063318	C₂²	1	4	yes	complemented
39	C₂×#13063314	C₂²	1	2	yes	complemented
40	C₂×#13063313	C₂²	1	2	yes	complemented
41	C₂×#13063312	C₂²	1	2	yes	—
42	C₂×#13063312	C₂²	1	4	yes	—
43	C₂×#13063311	C₂²	1	4	yes	complemented
44	C₂×#13063311	C₂²	1	4	yes	complemented
45	C₂×#13063311	C₂²	1	4	yes	complemented
46	C₂×#13063311	C₂²	1	4	yes	complemented
47	#14583410	C₂²	1	32	yes	complemented
48	C₂×#13063310	C₂²	1	4	yes	complemented
49	C₂×#13063308	C₂²	1	4	yes	complemented
50	C₂×#13063307	C₂²	1	4	yes	complemented
51	C₂×#13063306	C₂²	1	2	yes	complemented
52	C₂×#13063306	C₂²	1	2	yes	complemented
53	C₂×#13063304	C₂²	1	2	yes	complemented
54	C₂×#13063304	C₂²	1	2	yes	complemented
55	C₂×#13063304	C₂²	1	2	yes	complemented
56	C₂×#13063303	C₂²	1	4	yes	complemented
57	C₂×#13063303	C₂²	1	4	yes	complemented
58	C₂×#13063299	C₂²	1	2	yes	—
59	C₂×#13063299	C₂²	1	2	yes	—
60	C₂×#13063299	C₂²	1	2	yes	complemented
61	C₂×#13063298	C₂²	1	4	yes	—
62	C₂×#13063297	C₂²	1	4	yes	complemented
63	C₂×#13063296	C₂²	1	4	yes	complemented
64	C₂×#13063294	C₂²	1	4	yes	complemented
65	C₂×#13063293	C₂²	1	4	yes	—
66	C₂×#13063293	C₂²	1	2	yes	—
67	C₂×#13063293	C₂²	1	2	yes	complemented
68	C₂×C₄×Dic₈₆	C₂²	1	2	yes	complemented
69	C₂×#13063290	C₂²	1	4	yes	complemented
70	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
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	2	yes	complemented
75	C₂×#13063284	C₂²	1	1	yes	characteristic, complemented
76	C₂×#13063284	C₂²	1	1	yes	characteristic, complemented
77	C₂×#13063283	C₂²	1	4	yes	complemented
78	C₂×C₂²⋊C₄×D₄₃	C₂²	1	4	yes	complemented
79	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
80	C₂⁴×C₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
81	C₄₃×#525	C₂²	1	16	yes	complemented
82	C₂×#123×C₄₃	C₂²	1	1	yes	characteristic
83	C₂×#123×C₄₃	C₂²	1	1	yes	characteristic, complemented
84	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	complemented
85	C₂×#121×C₄₃	C₂²	1	2	yes	—
86	C₂×#120×C₄₃	C₂²	1	1	yes	characteristic
87	C₂×#120×C₄₃	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
89	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	complemented
90	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
91	C₂⁴×D₄₃	C₂³	1	2	yes	—
92	C₂×#10621898	—	4	8	no	—
93	C₂×#10621898	C₂³	1	16	yes	—
94	C₂²×Dic₈₆	—	4	4	no	—
95	C₂²×Dic₈₆	C₂³	1	2	yes	—
96	C₂²×Dic₈₆	C₂³	1	4	yes	—
97	C₂²×Dic₈₆	C₂³	1	2	yes	—
98	C₂²×Dic₈₆	C₂³	1	8	yes	complemented
99	C₂²×D₁₇₂	—	4	4	no	—
100	C₂²×D₁₇₂	C₂³	1	2	yes	—
101	C₂²×D₁₇₂	C₂³	1	2	yes	—
102	C₂²×D₁₇₂	C₂³	1	8	yes	complemented
103	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
105	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
106	C₂²×C₂²⋊D₄₃	C₂³	1	4	yes	—
107	C₂³×Dic₄₃	C₂³	1	2	yes	—
108	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
109	C₂²×C₄×D₄₃	C₂³	1	4	yes	—
110	#13063325	C₂³	1	16	yes	complemented
111	#13063323	C₂³	1	16	yes	complemented
112	#13063321	C₂³	1	16	yes	—
113	#13063320	C₂³	1	32	yes	complemented
114	#13063318	C₂³	1	32	yes	complemented
115	#13063318	C₂³	1	32	yes	complemented
116	#13063314	C₂³	1	16	yes	complemented
117	#13063313	C₂³	1	16	yes	complemented
118	#13063312	C₂³	1	16	yes	—
119	#13063312	C₂³	1	32	yes	—
120	#13063311	C₂³	1	32	yes	complemented
121	#13063311	C₂³	1	32	yes	complemented
122	#13063311	C₂³	1	32	yes	complemented
123	#13063311	C₂³	1	32	yes	complemented
124	#13063310	C₂³	1	32	yes	complemented
125	#13063308	C₂³	1	32	yes	complemented
126	#13063307	C₂³	1	32	yes	complemented
127	#13063306	C₂³	1	16	yes	complemented
128	#13063306	C₂³	1	16	yes	complemented
129	#13063304	C₂³	1	16	yes	complemented
130	#13063304	C₂³	1	16	yes	complemented
131	#13063304	C₂³	1	16	yes	complemented
132	#13063303	C₂³	1	32	yes	complemented
133	#13063303	C₂³	1	32	yes	complemented
134	#13063299	C₂³	1	16	yes	—
135	#13063299	C₂³	1	16	yes	—
136	#13063299	C₂³	1	16	yes	complemented
137	#13063298	C₂³	1	32	yes	—
138	#13063297	C₂³	1	32	yes	complemented
139	#13063296	C₂³	1	32	yes	complemented
140	#13063294	C₂³	1	32	yes	complemented
141	#13063293	C₂³	1	16	yes	—
142	#13063293	C₂³	1	32	yes	—
143	#13063293	C₂³	1	16	yes	complemented
144	C₄×Dic₈₆	C₂³	1	16	yes	complemented
145	#13063290	C₂³	1	32	yes	complemented
146	C₄×D₁₇₂	C₂³	1	16	yes	complemented
147	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
148	C₄×C₂²⋊D₄₃	C₂³	1	32	yes	complemented
149	(C₂²⋊D₄₃)⋊C₄	C₂³	1	32	yes	complemented
150	#13063284	C₂³	1	8	yes	complemented
151	#13063284	C₂³	1	16	yes	complemented
152	#13063284	C₂³	1	8	yes	complemented
153	#13063283	C₂³	1	32	yes	complemented
154	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
155	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
156	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
157	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
158	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
159	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
160	C₂×Dic₄₃⋊C₄	C₂³	1	4	yes	—
161	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
162	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
164	C₂×C₂²⋊Dic₄₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
166	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
167	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
168	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
169	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
170	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
171	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
172	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	4	yes	—
173	C₂²⋊C₄×D₄₃	C₂³	1	32	yes	complemented
174	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
175	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
176	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
177	C₂×C₄×Dic₄₃	C₂³	1	4	yes	—
178	C₂⁵×C₄₃	C₂³	1	1	yes	characteristic
179	C₂×#41×C₄₃	—	4	4	no	—
180	C₂×#41×C₄₃	C₂³	1	8	yes	—
181	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
182	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
183	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
184	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
185	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
186	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
187	C₂³×C₄×C₄₃	—	4	4	no	—
188	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
189	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
191	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
193	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₄₃	C₂³	1	8	yes	complemented
195	#123×C₄₃	C₂³	1	8	yes	—
196	#123×C₄₃	C₂³	1	8	yes	complemented
197	C₂²⋊Q₈×C₄₃	C₂³	1	16	yes	complemented
198	#121×C₄₃	C₂³	1	16	yes	—
199	#120×C₄₃	C₂³	1	8	yes	—
200	#120×C₄₃	C₂³	1	8	yes	complemented
201	C₄×D₄×C₄₃	C₂³	1	16	yes	—
202	C₄×D₄×C₄₃	C₂³	1	16	yes	complemented
203	#117×C₄₃	C₂³	1	8	yes	complemented
204	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
214	C₂⁴×C₄₃	—	4	2	no	—
215	C₂⁴×C₄₃	—	4	4	no	—
216	C₂⁴×C₄₃	C₂⁴	1	2	yes	—
217	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
218	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
219	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₄₃	C₂⁴	1	4	yes	—
221	C₂³×D₄₃	—	4	4	no	—
222	C₂³×D₄₃	—	4	8	no	—
223	C₂³×D₄₃	C₂⁴	1	4	yes	—
224	C₂³×D₄₃	C₂⁴	1	8	yes	—
225	#41×C₄₃	—	4	16	no	—
226	C₂×Q₈×C₄₃	—	4	2	no	—
227	C₂×Q₈×C₄₃	C₂⁴	1	4	yes	—
228	C₂×D₄×C₄₃	—	4	4	no	—
229	C₂×D₄×C₄₃	—	4	4	no	—
230	C₂×D₄×C₄₃	—	4	2	no	—
231	C₂×D₄×C₄₃	—	4	2	no	—
232	C₂×D₄×C₄₃	—	4	2	no	—
233	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
234	C₂×D₄×C₄₃	C₂⁴	1	8	yes	—
235	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
236	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
237	C₂×D₄×C₄₃	C₂⁴	1	4	yes	—
238	C₂²×C₄×C₄₃	—	2	4	no	—
239	C₂²×C₄×C₄₃	—	2	8	no	—
240	C₂²×C₄×C₄₃	—	2	4	no	—
241	C₂²×C₄×C₄₃	—	2	4	no	—
242	C₂²×C₄×C₄₃	—	4	4	no	—
243	C₂²×C₄×C₄₃	—	4	2	no	—
244	C₂²×C₄×C₄₃	—	4	16	no	—
245	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
252	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
253	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
254	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
255	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	—
256	C₂²×C₄×C₄₃	C₂⁴	1	4	yes	—
257	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₂²⋊D₄₃	—	4	8	no	—
259	C₂×C₂²⋊D₄₃	—	4	8	no	—
260	C₂×C₂²⋊D₄₃	—	4	8	no	—
261	C₂×C₂²⋊D₄₃	—	4	8	no	—
262	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
263	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
264	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
265	C₂×C₂²⋊D₄₃	C₂⁴	1	16	yes	—
266	C₂²×Dic₄₃	—	4	4	no	—
267	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
268	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
269	C₂²×Dic₄₃	C₂⁴	1	4	yes	—
270	C₂²×Dic₄₃	C₂⁴	1	8	yes	—
271	#10621898	—	4	32	no	—
272	C₂×D₁₇₂	—	2	8	no	—
273	C₂×D₁₇₂	—	4	4	no	—
274	C₂×D₁₇₂	—	4	16	no	—
275	C₂×D₁₇₂	C₂⁴	1	8	yes	—
276	C₂×D₁₇₂	C₂⁴	1	8	yes	—
277	C₂×C₄×D₄₃	—	4	8	no	—
278	C₂×C₄×D₄₃	—	4	8	no	—
279	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
280	C₂×C₄×D₄₃	C₂⁴	1	16	yes	—
281	C₂×Dic₈₆	—	2	8	no	—
282	C₂×Dic₈₆	—	4	16	no	—
283	C₂×Dic₈₆	—	4	4	no	—
284	C₂×Dic₈₆	—	4	8	no	—
285	C₂×Dic₈₆	C₂⁴	1	8	yes	—
286	C₂×Dic₈₆	C₂⁴	1	16	yes	—
287	C₂×Dic₈₆	C₂⁴	1	8	yes	—
288	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
289	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
290	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
291	C₂²⋊C₄×C₄₃	C₂⁴	1	4	yes	—
292	C₂²⋊C₄×C₄₃	C₂⁴	1	4	yes	—
293	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
294	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
295	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
296	C₂²⋊C₄×C₄₃	C₂⁴	1	8	yes	—
297	C₄²×C₄₃	C₂⁴	1	8	yes	—
298	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
299	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
300	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
301	C₂²⋊Dic₄₃	C₂⁴	1	8	yes	—
302	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
303	C₂²⋊Dic₄₃	C₂⁴	1	16	yes	—
304	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
305	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
306	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
307	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
308	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
309	(C₂×D₄₃)⋊C₄	C₂⁴	1	16	yes	—
310	C₄⋊Dic₄₃	C₂⁴	1	16	yes	—
311	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
312	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
313	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
314	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
315	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
316	Dic₄₃⋊C₄	C₂⁴	1	16	yes	—
317	C₄×Dic₄₃	C₂⁴	1	8	yes	—
318	C₄×Dic₄₃	C₂⁴	1	16	yes	—
319	C₄×Dic₄₃	C₂⁴	1	8	yes	—
320	C₄×Dic₄₃	C₂⁴	1	16	yes	—
321	C₂³×C₄₃	—	2	2	no	—
322	C₂³×C₄₃	—	2	4	no	—
323	C₂³×C₄₃	—	2	2	no	—
324	C₂³×C₄₃	—	2	2	no	—
325	C₂³×C₄₃	—	2	4	no	—
326	C₂³×C₄₃	—	2	4	no	—
327	C₂³×C₄₃	—	2	4	no	—
328	C₂³×C₄₃	—	2	4	no	—
329	C₂³×C₄₃	—	2	4	no	—
330	C₂³×C₄₃	—	4	4	no	—
331	C₂³×C₄₃	—	4	8	no	—
332	C₂³×C₄₃	—	4	16	no	—
333	C₂³×C₄₃	C₂⁵	1	2	yes	—
334	C₂³×C₄₃	C₂⁵	1	4	yes	—
335	C₂³×C₄₃	C₂⁵	1	2	yes	—
336	C₂³×C₄₃	C₂⁵	1	2	yes	—
337	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
338	C₂²×D₄₃	—	2	8	no	—
339	C₂²×D₄₃	—	2	8	no	—
340	C₂²×D₄₃	—	2	8	no	—
341	C₂²×D₄₃	—	4	8	no	—
342	C₂²×D₄₃	—	4	16	no	—
343	C₂²×D₄₃	—	8	16	no	—
344	C₂²×D₄₃	C₂⁵	1	8	yes	—
345	Q₈×C₄₃	—	4	4	no	—
346	D₄×C₄₃	—	4	8	no	—
347	D₄×C₄₃	—	4	8	no	—
348	D₄×C₄₃	—	4	4	no	—
349	D₄×C₄₃	—	4	4	no	—
350	D₄×C₄₃	—	4	4	no	—
351	C₂×C₄×C₄₃	—	2	2	no	—
352	C₂×C₄×C₄₃	—	2	4	no	—
353	C₂×C₄×C₄₃	—	2	2	no	—
354	C₂×C₄×C₄₃	—	2	2	no	—
355	C₂×C₄×C₄₃	—	2	4	no	—
356	C₂×C₄×C₄₃	—	2	4	no	—
357	C₂×C₄×C₄₃	—	2	8	no	—
358	C₂×C₄×C₄₃	—	2	8	no	—
359	C₂×C₄×C₄₃	—	2	16	no	—
360	C₂×C₄×C₄₃	—	2	8	no	—
361	C₂×C₄×C₄₃	—	4	4	no	—
362	C₂×C₄×C₄₃	—	4	8	no	—
363	C₂×C₄×C₄₃	H(5,𝔽₂)	1	4	yes	—
364	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
365	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
366	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
367	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
368	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₄₃	C₂⁵	1	4	yes	—
370	C₂×C₄×C₄₃	C₂⁵	1	2	yes	—
371	C₂²⋊D₄₃	—	4	16	no	—
372	C₂²⋊D₄₃	—	4	16	no	—
373	C₂²⋊D₄₃	—	4	16	no	—
374	C₂²⋊D₄₃	—	4	16	no	—
375	C₂×Dic₄₃	—	2	8	no	—
376	C₂×Dic₄₃	—	2	8	no	—
377	C₂×Dic₄₃	—	2	8	no	—
378	C₂×Dic₄₃	—	4	8	no	—
379	C₂×Dic₄₃	C₂⁵	1	8	yes	—
380	C₂×Dic₄₃	C₂⁵	1	8	yes	—
381	C₂×Dic₄₃	C₂⁵	1	8	yes	—
382	D₁₇₂	—	2	16	no	—
383	D₁₇₂	—	4	8	no	—
384	C₄×D₄₃	—	4	16	no	—
385	C₄×D₄₃	—	4	16	no	—
386	Dic₈₆	—	2	16	no	—
387	Dic₈₆	—	4	8	no	—
388	Dic₈₆	—	4	16	no	—
389	C₂×#3540	—	43	1	no	maximal, Sylow
390	C₂²×C₄₃	—	2	2	no	—
391	C₂²×C₄₃	—	2	4	no	—
392	C₂²×C₄₃	—	2	2	no	—
393	C₂²×C₄₃	—	2	2	no	—
394	C₂²×C₄₃	—	2	4	no	—
395	C₂²×C₄₃	—	2	4	no	—
396	C₂²×C₄₃	—	2	4	no	—
397	C₂²×C₄₃	—	2	4	no	—
398	C₂²×C₄₃	—	2	4	no	—
399	C₂²×C₄₃	—	4	16	no	—
400	C₂²×C₄₃	—	4	4	no	—
401	C₂²×C₄₃	—	4	4	no	—
402	C₂²×C₄₃	—	4	8	no	—
403	C₂²×C₄₃	—	4	4	no	—
404	C₂²×C₄₃	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂²×C₄₃	#585	1	4	yes	—
406	C₂²×C₄₃	C₂⁶	1	1	yes	characteristic
407	C₂×D₄₃	—	2	8	no	—
408	C₂×D₄₃	—	2	8	no	—
409	C₂×D₄₃	—	2	8	no	—
410	C₂×D₄₃	—	4	16	no	—
411	C₂×D₄₃	—	8	16	no	—
412	C₄×C₄₃	—	2	2	no	—
413	C₄×C₄₃	—	2	4	no	—
414	C₄×C₄₃	—	2	2	no	—
415	C₄×C₄₃	—	2	2	no	—
416	C₄×C₄₃	—	2	4	no	—
417	C₄×C₄₃	—	2	4	no	—
418	C₄×C₄₃	C₂×H(5,𝔽₂)	1	4	yes	—
419	Dic₄₃	—	2	8	no	—
420	Dic₄₃	—	2	8	no	—
421	Dic₄₃	—	2	8	no	—
422	#3540	—	43	32	no	—
423	C₂×H(3,𝔽₄)	—	43	2	no	—
424	C₂×#560	—	43	2	no	—
425	C₂×#559	—	43	2	no	—
426	C₂×#556	—	43	2	no	—
427	C₂×#555	—	43	2	no	—
428	C₂×#551	—	43	2	no	—
429	C₂×#548	—	43	2	no	—
430	C₂×#546	—	43	2	no	—
431	C₂×#542	—	43	4	no	—
432	C₂×#542	—	43	2	no	—
433	C₂×#538	—	43	4	no	—
434	C₂×#536	—	43	1	no	—
435	C₂×#535	—	43	1	no	—
436	C₂×#525	—	43	2	no	—
437	C₂×#525	D₄₃	1	1	yes	characteristic, complemented
438	C₂×C₄₃	—	4	2	no	—
439	C₂×C₄₃	—	4	2	no	—
440	C₂×C₄₃	—	4	4	no	—
441	C₂×C₄₃	—	4	2	no	—
442	C₂×C₄₃	#3540	1	4	yes	complemented
443	C₂×C₄₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂×C₄₃	C₂×#585	1	2	yes	—
445	D₄₃	—	4	8	no	—
446	C₂²×#41	—	43	2	no	—
447	C₂²×#41	C₂×D₄₃	1	1	yes	characteristic
448	C₂³×Q₈	—	43	1	no	—
449	C₂³×D₄	—	43	1	no	—
450	C₂⁴×C₄	C₂×D₄₃	1	1	yes	characteristic, complemented
451	H(3,𝔽₄)	—	43	32	no	—
452	#560	—	43	32	no	—
453	#559	—	43	32	no	—
454	#556	—	43	32	no	—
455	#555	—	43	32	no	—
456	#551	—	43	32	no	—
457	#548	—	43	32	no	—
458	#546	—	43	32	no	—
459	#542	—	43	64	no	—
460	#542	—	43	32	no	—
461	#538	—	43	64	no	—
462	#536	—	43	16	no	—
463	#535	—	43	16	no	—
464	C₂×C₄⋊Q₈	—	43	2	no	—
465	C₂×C₄⋊Q₈	—	43	2	no	—
466	C₂×#127	—	43	2	no	—
467	C₂×#126	—	43	4	no	—
468	C₂×#126	—	43	4	no	—
469	C₂×#126	—	43	4	no	—
470	C₂×#124	—	43	2	no	—
471	C₂×#124	—	43	2	no	—
472	C₂×#124	—	43	4	no	—
473	C₂×#124	—	43	4	no	—
474	C₂×#124	—	43	4	no	—
475	C₂×#124	—	43	4	no	—
476	C₂×#124	—	43	4	no	—
477	C₂×#124	—	43	2	no	—
478	#525	—	43	32	no	—
479	#525	C₂×D₄₃	1	16	yes	complemented
480	C₂×#123	—	43	2	no	—
481	C₂×#123	—	43	2	no	—
482	C₂×#123	—	43	4	no	—
483	C₂×#123	—	43	4	no	—
484	C₂×#123	—	43	4	no	—
485	C₂×#123	C₂×D₄₃	1	1	yes	characteristic
486	C₂×#123	C₂×D₄₃	1	1	yes	characteristic, complemented
487	C₂×C₂²⋊Q₈	—	43	2	no	—
488	C₂×C₂²⋊Q₈	—	43	2	no	—
489	C₂×C₂²⋊Q₈	—	43	2	no	—
490	C₂×C₂²⋊Q₈	—	43	4	no	—
491	C₂×C₂²⋊Q₈	—	43	4	no	—
492	C₂×C₂²⋊Q₈	C₂×D₄₃	1	2	yes	complemented
493	C₂×#121	—	43	4	no	—
494	C₂×#121	—	43	4	no	—
495	C₂×#121	—	43	2	no	—
496	C₂×#121	—	43	2	no	—
497	C₂×#121	—	43	2	no	—
498	C₂×#121	—	43	4	no	—
499	C₂×#121	C₂×D₄₃	1	2	yes	—
500	C₂×#120	—	43	4	no	—
501	C₂×#120	—	43	2	no	—
502	C₂×#120	—	43	4	no	—
503	C₂×#120	—	43	2	no	—
504	C₂×#120	C₂×D₄₃	1	1	yes	characteristic
505	C₂×#120	C₂×D₄₃	1	1	yes	characteristic, complemented
506	C₂×C₄×Q₈	—	43	4	no	—
507	C₂×C₄×Q₈	—	43	2	no	—
508	C₂×C₄×D₄	—	43	4	no	—
509	C₂×C₄×D₄	—	43	4	no	—
510	C₂×C₄×D₄	—	43	4	no	—
511	C₂×C₄×D₄	—	43	2	no	—
512	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
513	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	complemented
514	C₂×#117	—	43	2	no	—
515	C₂×#117	—	43	1	no	—
516	C₂×#117	—	43	1	no	—
517	C₂×#117	—	43	4	no	—
518	C₂×#117	C₂×D₄₃	1	1	yes	characteristic, complemented
519	C₂²×C₂²⋊C₄	—	43	4	no	—
520	C₄₃	C₂×#3540	1	1	yes	characteristic, complemented, Sylow
521	C₂⁵	—	43	2	no	—
522	C₂⁵	C₂²×D₄₃	1	1	yes	characteristic
523	C₂×#41	—	4	4	no	—
524	C₂×#41	—	43	16	no	—
525	C₂×#41	—	172	8	no	—
526	C₂×#41	C₂²×D₄₃	1	8	yes	—
527	C₂²×Q₈	—	43	2	no	—
528	C₂²×Q₈	—	43	4	no	—
529	C₂²×Q₈	—	43	2	no	—
530	C₂²×Q₈	—	43	8	no	—
531	C₂²×Q₈	—	172	4	no	—
532	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
533	C₂²×D₄	—	43	4	no	—
534	C₂²×D₄	—	43	4	no	—
535	C₂²×D₄	—	43	4	no	—
536	C₂²×D₄	—	43	4	no	—
537	C₂²×D₄	—	43	2	no	—
538	C₂²×D₄	—	43	2	no	—
539	C₂²×D₄	—	43	8	no	—
540	C₂²×D₄	—	172	4	no	—
541	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
542	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
543	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
544	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
545	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
546	C₂³×C₄	—	4	4	no	—
547	C₂³×C₄	—	43	2	no	—
548	C₂³×C₄	—	43	4	no	—
549	C₂³×C₄	—	43	4	no	—
550	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
551	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
552	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
553	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
554	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
555	C₂³×C₄	C₂²×D₄₃	1	2	yes	—
556	C₂³×C₄	C₂²×D₄₃	1	8	yes	complemented
557	C₄⋊Q₈	—	43	16	no	—
558	C₄⋊Q₈	—	43	16	no	—
559	#127	—	43	16	no	—
560	#126	—	43	32	no	—
561	#126	—	43	32	no	—
562	#126	—	43	32	no	—
563	#124	—	43	16	no	—
564	#124	—	43	16	no	—
565	#124	—	43	32	no	—
566	#124	—	43	32	no	—
567	#124	—	43	32	no	—
568	#124	—	43	32	no	—
569	#124	—	43	32	no	—
570	#124	—	43	16	no	—
571	#123	—	43	16	no	—
572	#123	—	43	16	no	—
573	#123	—	43	32	no	—
574	#123	—	43	32	no	—
575	#123	—	43	32	no	—
576	#123	C₂²×D₄₃	1	8	yes	—
577	#123	C₂²×D₄₃	1	8	yes	complemented
578	C₂²⋊Q₈	—	43	16	no	—
579	C₂²⋊Q₈	—	43	16	no	—
580	C₂²⋊Q₈	—	43	16	no	—
581	C₂²⋊Q₈	—	43	32	no	—
582	C₂²⋊Q₈	—	43	32	no	—
583	C₂²⋊Q₈	C₂²×D₄₃	1	16	yes	complemented
584	#121	—	43	32	no	—
585	#121	—	43	32	no	—
586	#121	—	43	16	no	—
587	#121	—	43	16	no	—
588	#121	—	43	16	no	—
589	#121	—	43	32	no	—
590	#121	C₂²×D₄₃	1	16	yes	—
591	#120	—	43	32	no	—
592	#120	—	43	16	no	—
593	#120	—	43	16	no	—
594	#120	—	43	32	no	—
595	#120	C₂²×D₄₃	1	8	yes	—
596	#120	C₂²×D₄₃	1	8	yes	complemented
597	C₄×Q₈	—	43	32	no	—
598	C₄×Q₈	—	43	16	no	—
599	C₄×D₄	—	43	32	no	—
600	C₄×D₄	—	43	32	no	—
601	C₄×D₄	—	43	32	no	—
602	C₄×D₄	—	43	16	no	—
603	C₄×D₄	C₂²×D₄₃	1	16	yes	—
604	C₄×D₄	C₂²×D₄₃	1	16	yes	complemented
605	#117	—	43	16	no	—
606	#117	—	43	8	no	—
607	#117	—	43	8	no	—
608	#117	—	43	32	no	—
609	#117	C₂²×D₄₃	1	8	yes	complemented
610	C₂×C₄⋊C₄	—	43	2	no	—
611	C₂×C₄⋊C₄	—	43	2	no	—
612	C₂×C₄⋊C₄	—	43	4	no	—
613	C₂×C₄⋊C₄	—	43	4	no	—
614	C₂×C₄⋊C₄	—	43	4	no	—
615	C₂×C₄⋊C₄	—	43	4	no	—
616	C₂×C₄⋊C₄	—	43	4	no	—
617	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
620	C₂×C₂²⋊C₄	—	43	4	no	—
621	C₂×C₂²⋊C₄	—	43	2	no	—
622	C₂×C₂²⋊C₄	—	43	4	no	—
623	C₂×C₂²⋊C₄	—	43	2	no	—
624	C₂×C₂²⋊C₄	—	43	4	no	—
625	C₂×C₂²⋊C₄	—	43	4	no	—
626	C₂×C₂²⋊C₄	—	43	4	no	—
627	C₂×C₂²⋊C₄	—	43	4	no	—
628	C₂×C₂²⋊C₄	—	43	4	no	—
629	C₂×C₂²⋊C₄	—	43	4	no	—
630	C₂×C₂²⋊C₄	—	43	4	no	—
631	C₂×C₂²⋊C₄	—	43	4	no	—
632	C₂×C₂²⋊C₄	—	43	32	no	—
633	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
635	C₂×C₂²⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
636	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
639	C₂×C₄²	—	43	2	no	—
640	C₂×C₄²	—	43	4	no	—
641	C₂×C₄²	—	43	2	no	—
642	C₂×C₄²	—	43	4	no	—
643	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
644	C₂⁴	—	4	2	no	—
645	C₂⁴	—	4	4	no	—
646	C₂⁴	—	43	4	no	—
647	C₂⁴	—	43	8	no	—
648	C₂⁴	—	172	4	no	—
649	C₂⁴	—	172	8	no	—
650	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
651	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
652	C₂⁴	C₂³×D₄₃	1	2	yes	—
653	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
654	C₂⁴	C₂³×D₄₃	1	4	yes	—
655	#41	—	4	16	no	—
656	#41	—	172	32	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	43	8	no	—
659	C₂×Q₈	—	43	16	no	—
660	C₂×Q₈	—	43	8	no	—
661	C₂×Q₈	—	86	8	no	—
662	C₂×Q₈	—	172	4	no	—
663	C₂×Q₈	—	172	8	no	—
664	C₂×Q₈	—	172	16	no	—
665	C₂×Q₈	C₂³×D₄₃	1	4	yes	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	2	no	—
668	C₂×D₄	—	4	2	no	—
669	C₂×D₄	—	4	4	no	—
670	C₂×D₄	—	4	4	no	—
671	C₂×D₄	—	43	16	no	—
672	C₂×D₄	—	43	16	no	—
673	C₂×D₄	—	43	16	no	—
674	C₂×D₄	—	43	16	no	—
675	C₂×D₄	—	43	8	no	—
676	C₂×D₄	—	43	8	no	—
677	C₂×D₄	—	86	8	no	—
678	C₂×D₄	—	172	16	no	—
679	C₂×D₄	—	172	4	no	—
680	C₂×D₄	—	172	8	no	—
681	C₂×D₄	—	172	8	no	—
682	C₂×D₄	—	172	8	no	—
683	C₂×D₄	—	172	8	no	—
684	C₂×D₄	C₂³×D₄₃	1	8	yes	—
685	C₂×D₄	C₂³×D₄₃	1	8	yes	—
686	C₂×D₄	C₂³×D₄₃	1	4	yes	—
687	C₂×D₄	C₂³×D₄₃	1	4	yes	—
688	C₂×D₄	C₂³×D₄₃	1	4	yes	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	2	8	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	—	2	4	no	—
693	C₂²×C₄	—	4	16	no	—
694	C₂²×C₄	—	4	2	no	—
695	C₂²×C₄	—	4	4	no	—
696	C₂²×C₄	—	43	4	no	—
697	C₂²×C₄	—	43	4	no	—
698	C₂²×C₄	—	43	4	no	—
699	C₂²×C₄	—	43	8	no	—
700	C₂²×C₄	—	43	16	no	—
701	C₂²×C₄	—	43	16	no	—
702	C₂²×C₄	—	172	8	no	—
703	C₂²×C₄	—	172	8	no	—
704	C₂²×C₄	—	172	4	no	—
705	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
706	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
707	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
708	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
709	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
710	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
711	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
712	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
713	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
714	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
715	C₂²×C₄	C₂³×D₄₃	1	4	yes	—
716	C₂²×C₄	C₂³×D₄₃	1	8	yes	—
717	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
718	C₄⋊C₄	—	43	8	no	—
719	C₄⋊C₄	—	43	8	no	—
720	C₄⋊C₄	—	43	16	no	—
721	C₄⋊C₄	—	43	16	no	—
722	C₄⋊C₄	—	43	16	no	—
723	C₄⋊C₄	—	43	16	no	—
724	C₄⋊C₄	—	43	16	no	—
725	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
726	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
727	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
728	C₂²⋊C₄	—	43	16	no	—
729	C₂²⋊C₄	—	43	8	no	—
730	C₂²⋊C₄	—	43	16	no	—
731	C₂²⋊C₄	—	43	8	no	—
732	C₂²⋊C₄	—	43	16	no	—
733	C₂²⋊C₄	—	43	16	no	—
734	C₂²⋊C₄	—	43	16	no	—
735	C₂²⋊C₄	—	43	16	no	—
736	C₂²⋊C₄	—	43	16	no	—
737	C₂²⋊C₄	—	43	16	no	—
738	C₂²⋊C₄	—	43	16	no	—
739	C₂²⋊C₄	—	43	16	no	—
740	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
741	C₂²⋊C₄	C₂³×D₄₃	1	4	yes	—
742	C₂²⋊C₄	C₂³×D₄₃	1	4	yes	—
743	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
744	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
745	C₂²⋊C₄	C₂³×D₄₃	1	8	yes	—
746	C₄²	—	43	8	no	—
747	C₄²	—	43	16	no	—
748	C₄²	—	43	8	no	—
749	C₄²	—	43	16	no	—
750	C₄²	C₂³×D₄₃	1	8	yes	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	4	no	—
756	C₂³	—	2	4	no	—
757	C₂³	—	2	4	no	—
758	C₂³	—	2	4	no	—
759	C₂³	—	2	4	no	—
760	C₂³	—	4	4	no	—
761	C₂³	—	4	8	no	—
762	C₂³	—	4	16	no	—
763	C₂³	—	43	8	no	—
764	C₂³	—	86	8	no	—
765	C₂³	—	86	8	no	—
766	C₂³	—	86	8	no	—
767	C₂³	—	344	16	no	—
768	C₂³	—	172	8	no	—
769	C₂³	—	172	16	no	—
770	C₂³	C₂⁴×D₄₃	1	2	yes	—
771	C₂³	C₂⁴×D₄₃	1	2	yes	—
772	C₂³	C₂⁴×D₄₃	1	4	yes	—
773	C₂³	C₂⁴×D₄₃	1	2	yes	—
774	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
775	Q₈	—	4	4	no	—
776	Q₈	—	86	16	no	—
777	Q₈	—	172	8	no	—
778	Q₈	—	172	16	no	—
779	D₄	—	4	4	no	—
780	D₄	—	4	4	no	—
781	D₄	—	4	4	no	—
782	D₄	—	4	8	no	—
783	D₄	—	4	8	no	—
784	D₄	—	86	16	no	—
785	D₄	—	172	8	no	—
786	D₄	—	172	16	no	—
787	D₄	—	172	16	no	—
788	D₄	—	172	16	no	—
789	D₄	—	172	16	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	16	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	4	8	no	—
802	C₂×C₄	—	43	8	no	—
803	C₂×C₄	—	43	8	no	—
804	C₂×C₄	—	43	8	no	—
805	C₂×C₄	—	86	8	no	—
806	C₂×C₄	—	86	8	no	—
807	C₂×C₄	—	86	8	no	—
808	C₂×C₄	—	172	16	no	—
809	C₂×C₄	—	172	16	no	—
810	C₂×C₄	—	172	8	no	—
811	C₂×C₄	#13063370	1	4	yes	—
812	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
813	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
814	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
815	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
816	C₂×C₄	C₂⁴×D₄₃	1	4	yes	—
817	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
818	C₂×C₄	C₂⁴×D₄₃	1	2	yes	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	4	16	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	8	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	86	8	no	—
834	C₂²	—	86	8	no	—
835	C₂²	—	86	8	no	—
836	C₂²	—	344	16	no	—
837	C₂²	—	172	16	no	—
838	C₂²	C₂×#13063370	1	2	yes	—
839	C₂²	#14583735	1	4	yes	—
840	C₂²	C₂⁵×D₄₃	1	1	yes	characteristic
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	2	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	86	8	no	—
848	C₄	—	86	8	no	—
849	C₄	—	86	8	no	—
850	C₄	C₂×#13063370	1	4	yes	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	172	8	no	—
856	C₂	#19148870	1	4	yes	direct product factor
857	C₂	C₂²×#13063370	1	1	yes	characteristic
858	C₂	C₂×#14583735	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₄₃
commutator, cosocle	C₂²×C₄₃	C₂⁶
Frattini	C₂²	C₂⁵×D₄₃
Fitting	C₂×C₄₃×#525	C₂
socle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#525	D₄₃
hypocenter	C₄₃	C₂×#3540
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #19148870	C₂	direct (N × H)
2. C₂×#14583642	C₂	semidirect
3. C₂×#14583638	C₂	semidirect
4. C₂×#14583633	C₂	semidirect
5. C₂×#14583619	C₂	semidirect
6. C₂×#14583614	C₂	semidirect
7. C₂×#14583577	C₂	semidirect
8. C₂×#14583558	C₂	semidirect
9. C₂×#14583545	C₂	semidirect
10. C₂×#14583520	C₂	semidirect
11. C₂×#14583519	C₂	semidirect
12. C₂×#14583481	C₂	semidirect
13. C₂×#14583470	C₂	semidirect
14. C₂×#14583463	C₂	semidirect
15. C₂×#14583410	C₂	semidirect
16. C₂×C₄₃×#525	C₂	semidirect
18. C₂³×Dic₈₆	C₂²	semidirect
19. C₂³×D₁₇₂	C₂²	semidirect
20. #14583642	C₂²	semidirect
21. #14583638	C₂²	semidirect
22. #14583633	C₂²	semidirect
23. #14583619	C₂²	semidirect
24. #14583614	C₂²	semidirect
25. #14583577	C₂²	semidirect
26. #14583558	C₂²	semidirect
27. #14583545	C₂²	semidirect
28. #14583520	C₂²	semidirect
29. #14583519	C₂²	semidirect
30. #14583481	C₂²	semidirect
31. #14583470	C₂²	semidirect
32. #14583463	C₂²	semidirect
33. C₂×#13063325	C₂²	semidirect
34. C₂×#13063323	C₂²	semidirect
36. C₂×#13063320	C₂²	semidirect
37. C₂×#13063318	C₂²	semidirect
38. C₂×#13063318	C₂²	semidirect
39. C₂×#13063314	C₂²	semidirect
40. C₂×#13063313	C₂²	semidirect
43. C₂×#13063311	C₂²	semidirect
44. C₂×#13063311	C₂²	semidirect
45. C₂×#13063311	C₂²	semidirect
46. C₂×#13063311	C₂²	semidirect
47. #14583410	C₂²	semidirect
48. C₂×#13063310	C₂²	semidirect
49. C₂×#13063308	C₂²	semidirect
50. C₂×#13063307	C₂²	semidirect
51. C₂×#13063306	C₂²	semidirect
52. C₂×#13063306	C₂²	semidirect
53. C₂×#13063304	C₂²	semidirect
54. C₂×#13063304	C₂²	semidirect
55. C₂×#13063304	C₂²	semidirect
56. C₂×#13063303	C₂²	semidirect
57. C₂×#13063303	C₂²	semidirect
60. C₂×#13063299	C₂²	semidirect
62. C₂×#13063297	C₂²	semidirect
63. C₂×#13063296	C₂²	semidirect
64. C₂×#13063294	C₂²	semidirect
67. C₂×#13063293	C₂²	semidirect
68. C₂×C₄×Dic₈₆	C₂²	semidirect
69. C₂×#13063290	C₂²	semidirect
70. 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
74. C₂×#13063284	C₂²	semidirect
75. C₂×#13063284	C₂²	semidirect
76. C₂×#13063284	C₂²	semidirect
77. C₂×#13063283	C₂²	semidirect
78. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
80. C₂⁴×C₄×C₄₃	C₂²	semidirect
81. C₄₃×#525	C₂²	semidirect
83. C₂×#123×C₄₃	C₂²	semidirect
84. C₂×C₂²⋊Q₈×C₄₃	C₂²	semidirect
87. C₂×#120×C₄₃	C₂²	semidirect
89. C₂×C₄×D₄×C₄₃	C₂²	semidirect
90. C₂×#117×C₄₃	C₂²	semidirect
98. C₂²×Dic₈₆	C₂³	semidirect
102. C₂²×D₁₇₂	C₂³	semidirect
110. #13063325	C₂³	semidirect
111. #13063323	C₂³	semidirect
113. #13063320	C₂³	semidirect
114. #13063318	C₂³	semidirect
115. #13063318	C₂³	semidirect
116. #13063314	C₂³	semidirect
117. #13063313	C₂³	semidirect
120. #13063311	C₂³	semidirect
121. #13063311	C₂³	semidirect
122. #13063311	C₂³	semidirect
123. #13063311	C₂³	semidirect
124. #13063310	C₂³	semidirect
125. #13063308	C₂³	semidirect
126. #13063307	C₂³	semidirect
127. #13063306	C₂³	semidirect
128. #13063306	C₂³	semidirect
129. #13063304	C₂³	semidirect
130. #13063304	C₂³	semidirect
131. #13063304	C₂³	semidirect
132. #13063303	C₂³	semidirect
133. #13063303	C₂³	semidirect
136. #13063299	C₂³	semidirect
138. #13063297	C₂³	semidirect
139. #13063296	C₂³	semidirect
140. #13063294	C₂³	semidirect
143. #13063293	C₂³	semidirect
144. C₄×Dic₈₆	C₂³	semidirect
145. #13063290	C₂³	semidirect
146. C₄×D₁₇₂	C₂³	semidirect
147. C₄×C₂²⋊D₄₃	C₂³	semidirect
148. C₄×C₂²⋊D₄₃	C₂³	semidirect
149. (C₂²⋊D₄₃)⋊C₄	C₂³	semidirect
150. #13063284	C₂³	semidirect
151. #13063284	C₂³	semidirect
152. #13063284	C₂³	semidirect
153. #13063283	C₂³	semidirect
173. C₂²⋊C₄×D₄₃	C₂³	semidirect
194. C₂³×C₄×C₄₃	C₂³	semidirect
196. #123×C₄₃	C₂³	semidirect
197. C₂²⋊Q₈×C₄₃	C₂³	semidirect
200. #120×C₄₃	C₂³	semidirect
202. C₄×D₄×C₄₃	C₂³	semidirect
203. #117×C₄₃	C₂³	semidirect
437. C₂×#525	D₄₃	semidirect
442. C₂×C₄₃	#3540	semidirect
450. C₂⁴×C₄	C₂×D₄₃	semidirect
479. #525	C₂×D₄₃	semidirect
486. C₂×#123	C₂×D₄₃	semidirect
492. C₂×C₂²⋊Q₈	C₂×D₄₃	semidirect
505. C₂×#120	C₂×D₄₃	semidirect
513. C₂×C₄×D₄	C₂×D₄₃	semidirect
518. C₂×#117	C₂×D₄₃	semidirect
520. C₄₃	C₂×#3540	semidirect
556. C₂³×C₄	C₂²×D₄₃	semidirect
577. #123	C₂²×D₄₃	semidirect
583. C₂²⋊Q₈	C₂²×D₄₃	semidirect
596. #120	C₂²×D₄₃	semidirect
604. C₄×D₄	C₂²×D₄₃	semidirect
609. #117	C₂²×D₄₃	semidirect
856. C₂	#19148870	direct (N × H)

Maximal subgroups

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

subgroup	index
#19148870	2
C₂×#14583642	2
C₂×#14583638	2
C₂×#14583633	2
C₂×#14583619	2
C₂×#14583614	2
C₂×#14583577	2
C₂×#14583558	2
C₂×#14583545	2
C₂×#14583520	2
C₂×#14583519	2
C₂×#14583481	2
C₂×#14583470	2
C₂×#14583463	2
C₂×#14583410	2
C₂×C₄₃×#525	2
C₂×#3540	43

Subgroups — C2×#19148870 #26003888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19148870 #26003888