Subgroups — #25106410

Order 11008.

1158 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137002	C₂	1	1	yes	maximal, characteristic, complemented
2	#19136993	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135581	C₂	1	2	yes	maximal, complemented
4	#19135432	C₂	1	2	yes	maximal
5	#19135054	C₂	1	4	yes	maximal, complemented
6	#19134583	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₃×#529	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063284	C₂²	1	2	yes	—
9	C₂×#13063240	C₂²	1	8	yes	—
10	#14582769	—	2	1	no	—
11	#14582767	—	2	1	no	—
12	#14582765	—	2	1	no	—
13	#14582765	—	2	1	no	—
14	#14582762	C₂²	1	2	yes	—
15	#14582759	C₂²	1	2	yes	—
16	#14582759	C₂²	1	2	yes	—
17	#14582759	C₂²	1	2	yes	—
18	C₄×C₄⋊Dic₄₃	—	2	1	no	—
19	C₄×C₄⋊Dic₄₃	—	2	1	no	—
20	C₄×C₄⋊Dic₄₃	—	2	1	no	—
21	C₄×C₂²⋊Dic₄₃	C₂²	1	2	yes	—
22	#14582745	—	2	1	no	—
23	#14582666	C₂²	1	8	yes	—
24	C₄₃×#529	—	2	1	no	—
25	C₄₃×#529	—	2	1	no	—
26	C₄₃×#529	—	2	1	no	—
27	C₄₃×#529	—	2	1	no	—
28	C₄₃×#529	—	2	1	no	—
29	C₄₃×#529	—	2	1	no	—
30	C₄₃×#529	—	2	1	no	—
31	C₄₃×#529	—	2	1	no	—
32	C₂×#126×C₄₃	C₄	1	2	yes	complemented
33	C₂×#125×C₄₃	C₄	1	1	yes	characteristic, complemented
34	C₂×#124×C₄₃	C₄	1	1	yes	characteristic, complemented
35	C₂×#123×C₄₃	C₂²	1	2	yes	—
36	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₄₃	C₄	1	1	yes	characteristic, complemented
40	C₂×C₄×D₄×C₄₃	C₂²	1	2	yes	—
41	C₂×#117×C₄₃	C₄	1	2	yes	complemented
42	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
43	#13063284	—	4	4	no	—
44	C₂×C₄⋊Dic₄₃	—	2	2	no	—
45	C₂×C₄⋊Dic₄₃	—	2	2	no	—
46	C₂×C₄⋊Dic₄₃	—	2	2	no	—
47	C₂×C₄⋊Dic₄₃	—	2	2	no	—
48	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
49	C₂×C₂²⋊Dic₄₃	C₂³	1	4	yes	—
50	C₂×C₄×Dic₄₃	—	2	2	no	—
51	C₂×C₄×Dic₄₃	—	2	2	no	—
52	#13063240	—	4	8	no	—
53	C₄₃⋊#95	—	2	2	no	—
54	C₄₃⋊#95	—	2	2	no	—
55	C₄₃⋊#95	—	2	2	no	—
56	C₄₃⋊#95	—	2	2	no	—
57	C₄₃⋊#95	—	2	2	no	—
58	C₄₃⋊#95	—	2	2	no	—
59	C₂²×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
66	#126×C₄₃	—	2	2	no	—
67	#126×C₄₃	—	2	2	no	—
68	#126×C₄₃	—	2	2	no	—
69	#126×C₄₃	—	2	2	no	—
70	#125×C₄₃	—	2	1	no	—
71	#125×C₄₃	—	2	1	no	—
72	#125×C₄₃	—	2	1	no	—
73	#125×C₄₃	—	2	1	no	—
74	#124×C₄₃	—	2	1	no	—
75	#124×C₄₃	—	2	1	no	—
76	#124×C₄₃	—	2	1	no	—
77	#124×C₄₃	—	2	1	no	—
78	#123×C₄₃	—	2	2	no	—
79	#123×C₄₃	—	2	2	no	—
80	#123×C₄₃	—	2	2	no	—
81	#123×C₄₃	—	2	2	no	—
82	C₂²⋊Q₈×C₄₃	—	2	1	no	—
83	C₂²⋊Q₈×C₄₃	—	2	1	no	—
84	C₂²⋊Q₈×C₄₃	—	2	1	no	—
85	C₂²⋊Q₈×C₄₃	—	2	1	no	—
86	#121×C₄₃	—	2	1	no	—
87	#121×C₄₃	—	2	1	no	—
88	#121×C₄₃	—	2	1	no	—
89	#121×C₄₃	—	2	1	no	—
90	C₄×Q₈×C₄₃	—	2	1	no	—
91	C₄×Q₈×C₄₃	—	2	1	no	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×D₄×C₄₃	—	2	2	no	—
95	C₄×D₄×C₄₃	—	2	2	no	—
96	C₄×D₄×C₄₃	—	2	2	no	—
97	C₄×D₄×C₄₃	—	2	2	no	—
98	C₄×D₄×C₄₃	—	2	1	no	—
99	C₄×D₄×C₄₃	—	2	1	no	—
100	C₄×D₄×C₄₃	—	2	1	no	—
101	C₄×D₄×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	2	no	—
103	#117×C₄₃	—	2	2	no	—
104	#117×C₄₃	—	2	2	no	—
105	#117×C₄₃	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
112	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
113	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
114	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
115	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
117	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
118	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
123	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
127	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
128	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
129	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
130	C₂⁴×C₄₃	C₂²×C₄	1	2	yes	—
131	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂×Q₈×C₄₃	—	2	1	no	—
133	C₂×Q₈×C₄₃	—	2	1	no	—
134	C₂×Q₈×C₄₃	—	4	2	no	—
135	C₂×D₄×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	1	no	—
137	C₂×D₄×C₄₃	—	2	2	no	—
138	C₂×D₄×C₄₃	—	2	2	no	—
139	C₂×D₄×C₄₃	—	2	4	no	—
140	C₂×D₄×C₄₃	—	2	4	no	—
141	C₂×D₄×C₄₃	—	4	2	no	—
142	C₂²×C₄×C₄₃	—	2	2	no	—
143	C₂²×C₄×C₄₃	—	2	2	no	—
144	C₂²×C₄×C₄₃	—	2	2	no	—
145	C₂²×C₄×C₄₃	—	2	2	no	—
146	C₂²×C₄×C₄₃	—	4	2	no	—
147	C₂²×C₄×C₄₃	—	4	2	no	—
148	C₂²×C₄×C₄₃	—	4	4	no	—
149	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×Dic₄₃	—	2	4	no	—
171	C₂²×Dic₄₃	—	2	4	no	—
172	C₄⋊C₄×C₄₃	—	2	2	no	—
173	C₄⋊C₄×C₄₃	—	2	2	no	—
174	C₄⋊C₄×C₄₃	—	2	2	no	—
175	C₄⋊C₄×C₄₃	—	2	2	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	1	no	—
178	C₄⋊C₄×C₄₃	—	2	2	no	—
179	C₄⋊C₄×C₄₃	—	2	2	no	—
180	C₄⋊C₄×C₄₃	—	2	1	no	—
181	C₄⋊C₄×C₄₃	—	2	1	no	—
182	C₄⋊C₄×C₄₃	—	2	2	no	—
183	C₄⋊C₄×C₄₃	—	2	2	no	—
184	C₂²⋊C₄×C₄₃	—	2	2	no	—
185	C₂²⋊C₄×C₄₃	—	2	2	no	—
186	C₂²⋊C₄×C₄₃	—	2	2	no	—
187	C₂²⋊C₄×C₄₃	—	2	2	no	—
188	C₂²⋊C₄×C₄₃	—	2	2	no	—
189	C₂²⋊C₄×C₄₃	—	2	2	no	—
190	C₂²⋊C₄×C₄₃	—	2	2	no	—
191	C₂²⋊C₄×C₄₃	—	2	2	no	—
192	C₂²⋊C₄×C₄₃	—	2	2	no	—
193	C₂²⋊C₄×C₄₃	—	2	2	no	—
194	C₄²×C₄₃	—	2	2	no	—
195	C₄²×C₄₃	—	2	2	no	—
196	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
205	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
206	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
207	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
212	C₂²⋊Dic₄₃	—	2	4	no	—
213	C₂²⋊Dic₄₃	—	2	8	no	—
214	C₂²⋊Dic₄₃	—	2	4	no	—
215	C₄⋊Dic₄₃	—	4	4	no	—
216	C₄⋊Dic₄₃	—	4	4	no	—
217	C₄⋊Dic₄₃	—	4	4	no	—
218	C₄⋊Dic₄₃	—	4	4	no	—
219	C₄×Dic₄₃	—	4	4	no	—
220	C₄×Dic₄₃	—	4	4	no	—
221	C₂³×C₄₃	—	2	2	no	—
222	C₂³×C₄₃	—	2	4	no	—
223	C₂³×C₄₃	—	4	1	no	—
224	C₂³×C₄₃	—	4	1	no	—
225	C₂³×C₄₃	—	4	2	no	—
226	C₂³×C₄₃	—	4	2	no	—
227	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
228	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
229	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
230	C₂³×C₄₃	H(5,𝔽₂)	1	2	yes	—
231	C₂³×C₄₃	2₋¹⁺⁴	1	2	yes	—
232	Q₈×C₄₃	—	4	2	no	—
233	Q₈×C₄₃	—	4	2	no	—
234	D₄×C₄₃	—	4	2	no	—
235	D₄×C₄₃	—	4	2	no	—
236	D₄×C₄₃	—	4	2	no	—
237	D₄×C₄₃	—	4	4	no	—
238	D₄×C₄₃	—	4	2	no	—
239	C₂×C₄×C₄₃	—	2	2	no	—
240	C₂×C₄×C₄₃	—	2	2	no	—
241	C₂×C₄×C₄₃	—	2	1	no	—
242	C₂×C₄×C₄₃	—	2	1	no	—
243	C₂×C₄×C₄₃	—	2	1	no	—
244	C₂×C₄×C₄₃	—	2	1	no	—
245	C₂×C₄×C₄₃	—	2	2	no	—
246	C₂×C₄×C₄₃	—	2	2	no	—
247	C₂×C₄×C₄₃	—	2	2	no	—
248	C₂×C₄×C₄₃	—	2	2	no	—
249	C₂×C₄×C₄₃	—	2	2	no	—
250	C₂×C₄×C₄₃	—	2	2	no	—
251	C₂×C₄×C₄₃	—	2	2	no	—
252	C₂×C₄×C₄₃	—	2	2	no	—
253	C₂×C₄×C₄₃	—	2	2	no	—
254	C₂×C₄×C₄₃	—	2	2	no	—
255	C₂×C₄×C₄₃	—	2	2	no	—
256	C₂×C₄×C₄₃	—	2	4	no	—
257	C₂×C₄×C₄₃	—	4	1	no	—
258	C₂×C₄×C₄₃	—	4	1	no	—
259	C₂×C₄×C₄₃	—	4	1	no	—
260	C₂×C₄×C₄₃	—	4	1	no	—
261	C₂×C₄×C₄₃	—	4	1	no	—
262	C₂×C₄×C₄₃	—	4	1	no	—
263	C₂×C₄×C₄₃	—	4	4	no	—
264	C₂×C₄×C₄₃	—	4	4	no	—
265	C₂×C₄×C₄₃	—	4	2	no	—
266	C₂×C₄×C₄₃	—	4	2	no	—
267	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂×Dic₄₃	—	4	4	no	—
280	C₂×Dic₄₃	—	4	4	no	—
281	C₂×Dic₄₃	—	4	4	no	—
282	C₂×Dic₄₃	—	4	4	no	—
283	C₂×Dic₄₃	—	4	4	no	—
284	C₂×Dic₄₃	—	4	4	no	—
285	#21875	—	43	1	no	maximal, Sylow
286	C₂²×C₄₃	—	2	1	no	—
287	C₂²×C₄₃	—	2	1	no	—
288	C₂²×C₄₃	—	2	1	no	—
289	C₂²×C₄₃	—	2	1	no	—
290	C₂²×C₄₃	—	2	1	no	—
291	C₂²×C₄₃	—	2	1	no	—
292	C₂²×C₄₃	—	4	2	no	—
293	C₂²×C₄₃	—	4	2	no	—
294	C₂²×C₄₃	—	4	2	no	—
295	C₂²×C₄₃	—	4	2	no	—
296	C₂²×C₄₃	—	4	2	no	—
297	C₂²×C₄₃	—	8	4	no	—
298	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
299	C₂²×C₄₃	#520	1	2	yes	—
300	C₂²×C₄₃	#535	1	1	yes	characteristic
301	C₂²×C₄₃	#536	1	1	yes	characteristic
302	C₂²×C₄₃	#537	1	2	yes	—
303	C₄×C₄₃	—	2	1	no	—
304	C₄×C₄₃	—	2	1	no	—
305	C₄×C₄₃	—	2	1	no	—
306	C₄×C₄₃	—	2	1	no	—
307	C₄×C₄₃	—	2	1	no	—
308	C₄×C₄₃	—	2	1	no	—
309	C₄×C₄₃	—	2	1	no	—
310	C₄×C₄₃	—	2	1	no	—
311	C₄×C₄₃	—	2	1	no	—
312	C₄×C₄₃	—	2	1	no	—
313	C₄×C₄₃	—	4	2	no	—
314	C₄×C₄₃	—	4	2	no	—
315	C₄×C₄₃	—	4	2	no	—
316	C₄×C₄₃	#410	1	2	yes	—
317	C₄×C₄₃	#410	1	2	yes	—
318	Dic₄₃	—	8	4	no	—
319	Dic₄₃	—	8	4	no	—
320	C₂×#529	D₄₃	1	1	yes	characteristic
321	#2285	—	43	1	no	—
322	#2283	—	43	1	no	—
323	#1996	—	43	2	no	—
324	#1964	—	43	2	no	—
325	#1899	—	43	4	no	—
326	#1799	—	43	4	no	—
327	C₂×C₄₃	—	2	1	no	—
328	C₂×C₄₃	—	2	2	no	—
329	C₂×C₄₃	—	2	2	no	—
330	C₂×C₄₃	—	2	1	no	—
331	C₂×C₄₃	—	8	2	no	—
332	C₂×C₄₃	#2311	1	1	yes	characteristic
333	C₂×C₄₃	C₂×#410	1	1	yes	characteristic
334	C₂×C₄₃	C₂×#410	1	1	yes	characteristic
335	#529	—	2	1	no	—
336	#529	—	2	1	no	—
337	#529	—	2	1	no	—
338	#529	—	2	1	no	—
339	#529	—	2	1	no	—
340	#529	—	2	1	no	—
341	#529	—	2	1	no	—
342	#529	—	2	1	no	—
343	C₂×#126	Dic₄₃	1	2	yes	complemented
344	C₂×#125	Dic₄₃	1	1	yes	characteristic, complemented
345	C₂×#124	Dic₄₃	1	1	yes	characteristic, complemented
346	C₂×#123	C₂×D₄₃	1	2	yes	—
347	C₂×C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
348	C₂×#121	C₂×D₄₃	1	1	yes	characteristic
349	C₂×C₄×Q₈	Dic₄₃	1	1	yes	characteristic, complemented
350	C₂×C₄×D₄	Dic₄₃	1	1	yes	characteristic, complemented
351	C₂×C₄×D₄	C₂×D₄₃	1	2	yes	—
352	C₂×#117	—	43	2	no	—
353	C₂×#117	Dic₄₃	1	2	yes	complemented
354	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
355	C₂×#99	—	43	8	no	—
356	#384	—	86	1	no	—
357	#383	—	86	1	no	—
358	#382	—	86	1	no	—
359	#382	—	86	1	no	—
360	#381	—	43	2	no	—
361	#380	—	43	2	no	—
362	#380	—	43	2	no	—
363	#380	—	43	2	no	—
364	C₄×C₄⋊C₄	—	86	1	no	—
365	C₄×C₄⋊C₄	—	86	1	no	—
366	C₄×C₄⋊C₄	—	86	1	no	—
367	C₄×C₂²⋊C₄	—	43	2	no	—
368	#376	—	86	1	no	—
369	#342	—	43	8	no	—
370	C₄₃	#21875	1	1	yes	characteristic, complemented, Sylow
371	C₂²×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
372	C₂²×D₄	C₂×Dic₄₃	1	1	yes	characteristic
373	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
374	C₂³×C₄	C₂×Dic₄₃	1	2	yes	—
375	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
376	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
377	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
378	#126	—	2	2	no	—
379	#126	—	2	2	no	—
380	#126	—	2	2	no	—
381	#126	—	2	2	no	—
382	#125	—	2	1	no	—
383	#125	—	2	1	no	—
384	#125	—	2	1	no	—
385	#125	—	2	1	no	—
386	#124	—	2	1	no	—
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#124	—	2	1	no	—
390	#123	—	2	2	no	—
391	#123	—	2	2	no	—
392	#123	—	2	2	no	—
393	#123	—	2	2	no	—
394	C₂²⋊Q₈	—	2	1	no	—
395	C₂²⋊Q₈	—	2	1	no	—
396	C₂²⋊Q₈	—	2	1	no	—
397	C₂²⋊Q₈	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	—	2	1	no	—
400	#121	—	2	1	no	—
401	#121	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	—	2	1	no	—
404	C₄×Q₈	—	2	1	no	—
405	C₄×Q₈	—	2	1	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	#117	—	2	2	no	—
415	#117	—	2	2	no	—
416	#117	—	2	2	no	—
417	#117	—	2	2	no	—
418	#117	—	172	4	no	—
419	C₂×C₄⋊C₄	—	86	2	no	—
420	C₂×C₄⋊C₄	—	86	2	no	—
421	C₂×C₄⋊C₄	—	86	2	no	—
422	C₂×C₄⋊C₄	—	86	2	no	—
423	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
424	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
427	C₂×C₄⋊C₄	C₂×Dic₄₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂×Dic₄₃	1	2	yes	—
429	C₂×C₂²⋊C₄	—	43	4	no	—
430	C₂×C₂²⋊C₄	—	43	4	no	—
431	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
432	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂×Dic₄₃	1	2	yes	—
435	C₂×C₂²⋊C₄	C₂²×D₄₃	1	2	yes	—
436	C₂×C₄²	—	86	2	no	—
437	C₂×C₄²	—	86	2	no	—
438	C₂×C₄²	C₂×Dic₄₃	1	2	yes	—
439	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
440	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
441	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
442	C₂×C₄²	C₂×Dic₄₃	1	1	yes	characteristic
443	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
444	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
446	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
447	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
448	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
449	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
450	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
451	#99	—	172	8	no	—
452	#95	—	86	2	no	—
453	#95	—	86	2	no	—
454	#95	—	86	2	no	—
455	#95	—	86	2	no	—
456	#95	—	86	2	no	—
457	#95	—	86	2	no	—
458	C₂⁴	C₂²×Dic₄₃	1	2	yes	—
459	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	1	no	—
469	C₂×D₄	—	4	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	86	4	no	—
478	C₂²×C₄	—	86	4	no	—
479	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
480	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
481	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
482	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
483	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
484	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
485	C₂²×C₄	C₂²×Dic₄₃	1	2	yes	—
486	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
492	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
493	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
494	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
495	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	2	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	172	4	no	—
513	C₄⋊C₄	—	172	4	no	—
514	C₄⋊C₄	—	172	4	no	—
515	C₄⋊C₄	—	172	4	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	2	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	2	2	no	—
525	C₂²⋊C₄	—	2	2	no	—
526	C₂²⋊C₄	—	86	4	no	—
527	C₂²⋊C₄	—	86	8	no	—
528	C₂²⋊C₄	—	86	4	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	2	no	—
531	C₄²	—	172	4	no	—
532	C₄²	—	172	4	no	—
533	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
534	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
535	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
536	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
537	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
538	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
539	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
540	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
541	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
542	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
543	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
544	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
545	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
546	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
547	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
548	C₄²	C₂²⋊Dic₄₃	1	1	yes	characteristic
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	2	no	—
554	C₂³	—	4	2	no	—
555	C₂³	C₂³×Dic₄₃	1	1	yes	characteristic
556	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
557	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
558	C₂³	#13063371	1	2	yes	—
559	C₂³	#13063372	1	2	yes	—
560	Q₈	—	4	2	no	—
561	Q₈	—	4	2	no	—
562	D₄	—	4	2	no	—
563	D₄	—	4	2	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	4	no	—
592	C₂×C₄	—	4	4	no	—
593	C₂×C₄	—	4	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	172	4	no	—
596	C₂×C₄	—	172	4	no	—
597	C₂×C₄	—	172	4	no	—
598	C₂×C₄	—	172	4	no	—
599	C₂×C₄	—	172	4	no	—
600	C₂×C₄	—	172	4	no	—
601	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
602	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
603	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
604	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
605	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
606	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
607	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
608	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
609	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
610	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
611	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
612	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	2	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	8	4	no	—
625	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
626	C₂²	#14583382	1	2	yes	—
627	C₂²	#14583463	1	1	yes	characteristic
628	C₂²	#14583470	1	1	yes	characteristic
629	C₂²	#14583477	1	2	yes	—
630	C₄	—	2	1	no	—
631	C₄	—	2	1	no	—
632	C₄	—	2	1	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	4	2	no	—
643	C₄	—	344	4	no	—
644	C₄	—	344	4	no	—
645	C₄	#14582873	1	2	yes	—
646	C₄	#14582873	1	2	yes	—
647	C₂	—	2	1	no	—
648	C₂	—	2	2	no	—
649	C₂	—	2	2	no	—
650	C₂	—	2	1	no	—
651	C₂	—	8	2	no	—
652	C₂	#19137187	1	1	yes	characteristic
653	C₂	C₂×#14582873	1	1	yes	characteristic
654	C₂	C₂×#14582873	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₃
commutator	C₂³×C₄₃	C₂³×C₄
Frattini	C₂⁴	C₂³×D₄₃
Fitting	C₂×C₄₃×#529	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₄₃	C₂²
cosocle	C₂⁴×C₄₃	C₂⁴
hypercenter	C₂×#529	D₄₃
hypocenter	C₄₃	#21875
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #19137002	C₂	semidirect
2. #19136993	C₂	semidirect
3. #19135581	C₂	semidirect
5. #19135054	C₂	semidirect
6. #19134583	C₂	semidirect
32. C₂×#126×C₄₃	C₄	semidirect
33. C₂×#125×C₄₃	C₄	semidirect
34. C₂×#124×C₄₃	C₄	semidirect
38. C₂×C₄×Q₈×C₄₃	C₄	semidirect
39. C₂×C₄×D₄×C₄₃	C₄	semidirect
41. C₂×#117×C₄₃	C₄	semidirect
343. C₂×#126	Dic₄₃	semidirect
344. C₂×#125	Dic₄₃	semidirect
345. C₂×#124	Dic₄₃	semidirect
349. C₂×C₄×Q₈	Dic₄₃	semidirect
350. C₂×C₄×D₄	Dic₄₃	semidirect
353. C₂×#117	Dic₄₃	semidirect
370. C₄₃	#21875	semidirect

Maximal subgroups

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

subgroup	index
#19137002	2
#19136993	2
#19135581	2
#19135432	2
#19135054	2
#19134583	2
C₂×C₄₃×#529	2
#21875	43