Subgroups — #25064172

Order 11008.

882 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143684	C₂	1	1	yes	maximal, characteristic, complemented
2	#19137246	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133172	C₂	1	2	yes	maximal
4	#19133159	C₂	1	2	yes	maximal, complemented
5	#19133146	C₂	1	2	yes	maximal, complemented
6	#19133133	C₂	1	2	yes	maximal
7	#19133120	C₂	1	1	yes	maximal, characteristic
8	#19133107	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133094	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133081	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#3523	C₂	1	1	yes	maximal, characteristic
12	#14583030	—	2	1	no	—
13	#14583030	—	2	2	no	—
14	Q₈×C₄₃⋊C₈	—	2	1	no	—
15	#14582956	C₂²	1	1	yes	characteristic
16	#14582956	C₂²	1	2	yes	—
17	#14582952	C₂²	1	1	yes	characteristic
18	#14582952	C₂²	1	2	yes	—
19	#14582806	—	2	1	no	—
20	#14582798	—	2	1	no	—
21	#14582785	—	2	2	no	—
22	#14582767	C₂²	1	2	yes	—
23	#14582765	C₂²	1	2	yes	—
24	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
25	#14582745	C₂²	1	1	yes	characteristic
26	#14582636	C₂²	1	1	yes	characteristic
27	#14582636	C₂²	1	1	yes	characteristic
28	#14582636	C₂²	1	2	yes	—
29	#14582636	C₂²	1	2	yes	—
30	#14582636	C₂²	1	2	yes	—
31	#14582636	C₂²	1	2	yes	—
32	#14582636	C₂²	1	2	yes	—
33	#14582633	C₂²	1	1	yes	characteristic
34	#14582633	C₂²	1	1	yes	characteristic
35	#14582633	C₂²	1	2	yes	—
36	C₄₃×#557	C₄	1	1	yes	characteristic, complemented
37	C₄₃×#557	C₄	1	1	yes	characteristic, complemented
38	C₄₃×#557	C₄	1	2	yes	complemented
39	C₄₃×#556	C₄	1	1	yes	characteristic, complemented
40	C₄₃×#556	C₄	1	2	yes	complemented
41	C₄₃×#552	—	2	2	no	—
42	C₄₃×#552	—	2	1	no	—
43	D₄×Q₈×C₄₃	—	2	1	no	—
44	D₄×Q₈×C₄₃	C₄	1	1	yes	characteristic, complemented
45	C₄₃×#541	—	2	1	no	—
46	C₄₃×#541	—	2	2	no	—
47	C₄₃×#533	C₂²	1	1	yes	characteristic
48	C₄₃×#533	C₂²	1	2	yes	—
49	C₄₃×#529	C₂²	1	1	yes	characteristic
50	C₄₃×#529	C₂²	1	2	yes	—
51	C₄₃×#519	—	2	1	no	—
52	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₂×C₄⋊Dic₄₃	—	2	2	no	—
55	C₂×C₄×Dic₄₃	—	2	1	no	—
56	C₂×C₄×Dic₄₃	—	2	1	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
59	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
61	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
62	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
63	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
64	#13063236	—	2	2	no	—
65	#13063236	—	2	1	no	—
66	C₄×C₄₃⋊C₈	—	2	1	no	—
67	C₄×C₄₃⋊C₈	—	2	2	no	—
68	C₄₃⋊#95	—	2	1	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	C₂³	1	1	yes	characteristic
73	C₄₃⋊#95	C₂³	1	1	yes	characteristic
74	C₄₃⋊#95	C₂³	1	2	yes	—
75	C₂²×Q₈×C₄₃	—	2	1	no	—
76	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₃	—	2	1	no	—
78	C₄⋊Q₈×C₄₃	—	2	2	no	—
79	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
81	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
83	#126×C₄₃	—	2	2	no	—
84	#126×C₄₃	—	2	2	no	—
85	#126×C₄₃	—	2	2	no	—
86	#126×C₄₃	—	2	2	no	—
87	#126×C₄₃	—	2	1	no	—
88	#125×C₄₃	—	2	2	no	—
89	#125×C₄₃	—	2	2	no	—
90	#125×C₄₃	—	2	2	no	—
91	#125×C₄₃	—	2	2	no	—
92	#125×C₄₃	—	2	1	no	—
93	#125×C₄₃	—	2	2	no	—
94	#125×C₄₃	—	2	1	no	—
95	#125×C₄₃	C₂×C₄	1	1	yes	characteristic
96	#125×C₄₃	C₂×C₄	1	2	yes	—
97	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
98	#124×C₄₃	C₂×C₄	1	2	yes	—
99	#123×C₄₃	—	2	1	no	—
100	#123×C₄₃	—	2	2	no	—
101	C₂²⋊Q₈×C₄₃	—	2	1	no	—
102	C₂²⋊Q₈×C₄₃	—	2	2	no	—
103	C₂²⋊Q₈×C₄₃	—	2	1	no	—
104	C₂²⋊Q₈×C₄₃	—	2	2	no	—
105	C₂²⋊Q₈×C₄₃	—	2	2	no	—
106	C₂²⋊Q₈×C₄₃	—	2	1	no	—
107	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
109	#121×C₄₃	C₂³	1	1	yes	characteristic
110	C₄×Q₈×C₄₃	—	2	1	no	—
111	C₄×Q₈×C₄₃	—	2	2	no	—
112	C₄×Q₈×C₄₃	—	2	1	no	—
113	C₄×Q₈×C₄₃	—	2	1	no	—
114	C₄×Q₈×C₄₃	—	2	2	no	—
115	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
116	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
117	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
118	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
119	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
120	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
121	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
122	C₄×Q₈×C₄₃	C₂×C₄	1	2	yes	—
123	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
124	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
125	C₄×Q₈×C₄₃	D₄	1	2	yes	—
126	C₄×D₄×C₄₃	—	2	1	no	—
127	C₄×D₄×C₄₃	—	2	2	no	—
128	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
129	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
130	#117×C₄₃	—	2	1	no	—
131	#117×C₄₃	—	2	2	no	—
132	#117×C₄₃	—	2	2	no	—
133	#117×C₄₃	—	2	1	no	—
134	#117×C₄₃	—	2	1	no	—
135	#117×C₄₃	—	2	2	no	—
136	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
137	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
138	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
140	C₂×Q₈×C₄₃	—	2	2	no	—
141	C₂×Q₈×C₄₃	—	2	1	no	—
142	C₂×Q₈×C₄₃	—	4	2	no	—
143	C₂×Q₈×C₄₃	—	4	4	no	—
144	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
145	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×Q₈×C₄₃	C₂²⋊C₄	1	2	yes	—
147	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
149	C₂×D₄×C₄₃	—	2	1	no	—
150	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₃	—	2	2	no	—
152	C₂²×C₄×C₄₃	—	2	1	no	—
153	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
158	C₂²×Dic₄₃	—	2	1	no	—
159	C₂²×Dic₄₃	—	2	1	no	—
160	C₂²×Dic₄₃	—	2	2	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	2	no	—
165	C₄⋊C₄×C₄₃	—	2	2	no	—
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	2	no	—
168	C₄⋊C₄×C₄₃	—	2	1	no	—
169	C₄⋊C₄×C₄₃	—	2	1	no	—
170	C₄⋊C₄×C₄₃	—	2	2	no	—
171	C₄⋊C₄×C₄₃	—	2	2	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	1	no	—
176	C₄⋊C₄×C₄₃	—	2	1	no	—
177	C₄⋊C₄×C₄₃	—	2	2	no	—
178	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
179	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
180	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
181	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
182	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
183	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
184	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
185	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
187	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
188	C₂²⋊C₄×C₄₃	—	2	1	no	—
189	C₂²⋊C₄×C₄₃	—	2	2	no	—
190	C₂²⋊C₄×C₄₃	—	2	1	no	—
191	C₂²⋊C₄×C₄₃	—	2	2	no	—
192	C₂²⋊C₄×C₄₃	—	2	2	no	—
193	C₂²⋊C₄×C₄₃	—	2	1	no	—
194	C₂²⋊C₄×C₄₃	—	2	1	no	—
195	C₂²⋊C₄×C₄₃	—	2	2	no	—
196	C₂²⋊C₄×C₄₃	—	2	1	no	—
197	C₄²×C₄₃	—	2	2	no	—
198	C₄²×C₄₃	—	2	2	no	—
199	C₄²×C₄₃	—	2	2	no	—
200	C₄²×C₄₃	—	2	2	no	—
201	C₄²×C₄₃	—	2	1	no	—
202	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
203	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
206	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₃	C₂×D₄	1	2	yes	—
208	C₄²×C₄₃	C₂×D₄	1	2	yes	—
209	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
210	C₄⋊Dic₄₃	—	4	2	no	—
211	C₄⋊Dic₄₃	—	8	2	no	—
212	C₄×Dic₄₃	—	4	2	no	—
213	C₄×Dic₄₃	—	8	1	no	—
214	C₂×C₄₃⋊C₈	—	2	1	no	—
215	C₂×C₄₃⋊C₈	—	2	1	no	—
216	C₂×C₄₃⋊C₈	—	2	2	no	—
217	C₂³×C₄₃	—	2	1	no	—
218	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₄₃	—	2	2	no	—
220	Q₈×C₄₃	—	2	2	no	—
221	Q₈×C₄₃	—	4	2	no	—
222	Q₈×C₄₃	—	4	1	no	—
223	Q₈×C₄₃	—	4	2	no	—
224	Q₈×C₄₃	—	4	4	no	—
225	Q₈×C₄₃	—	4	2	no	—
226	D₄×C₄₃	—	4	1	no	—
227	D₄×C₄₃	—	4	1	no	—
228	D₄×C₄₃	—	4	1	no	—
229	C₂×C₄×C₄₃	—	2	1	no	—
230	C₂×C₄×C₄₃	—	2	2	no	—
231	C₂×C₄×C₄₃	—	2	1	no	—
232	C₂×C₄×C₄₃	—	2	2	no	—
233	C₂×C₄×C₄₃	—	2	2	no	—
234	C₂×C₄×C₄₃	—	2	2	no	—
235	C₂×C₄×C₄₃	—	2	1	no	—
236	C₂×C₄×C₄₃	—	2	1	no	—
237	C₂×C₄×C₄₃	—	2	2	no	—
238	C₂×C₄×C₄₃	—	2	1	no	—
239	C₂×C₄×C₄₃	—	4	2	no	—
240	C₂×C₄×C₄₃	—	4	1	no	—
241	C₂×C₄×C₄₃	—	4	4	no	—
242	C₂×C₄×C₄₃	—	4	2	no	—
243	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
245	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
246	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
247	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
250	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
252	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
253	C₂×Dic₄₃	—	4	1	no	—
254	C₂×Dic₄₃	—	4	1	no	—
255	C₂×Dic₄₃	—	4	2	no	—
256	C₂×Dic₄₃	—	4	1	no	—
257	C₂×Dic₄₃	—	4	1	no	—
258	C₂×Dic₄₃	—	4	2	no	—
259	C₂×Dic₄₃	—	4	2	no	—
260	C₂×Dic₄₃	—	4	1	no	—
261	C₂×Dic₄₃	—	4	1	no	—
262	C₄₃⋊C₈	—	4	1	no	—
263	C₄₃⋊C₈	—	4	1	no	—
264	C₄₃⋊C₈	—	4	2	no	—
265	#17601	—	43	1	no	maximal, Sylow
266	C₂²×C₄₃	—	2	1	no	—
267	C₂²×C₄₃	—	2	1	no	—
268	C₂²×C₄₃	—	4	1	no	—
269	C₂²×C₄₃	—	4	1	no	—
270	C₂²×C₄₃	—	4	1	no	—
271	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂²×C₄₃	#577	1	1	yes	characteristic
273	C₂²×C₄₃	#578	1	1	yes	characteristic
274	C₄×C₄₃	—	2	1	no	—
275	C₄×C₄₃	—	2	1	no	—
276	C₄×C₄₃	—	2	1	no	—
277	C₄×C₄₃	—	2	1	no	—
278	C₄×C₄₃	—	2	2	no	—
279	C₄×C₄₃	—	2	2	no	—
280	C₄×C₄₃	—	2	1	no	—
281	C₄×C₄₃	—	2	2	no	—
282	C₄×C₄₃	—	2	2	no	—
283	C₄×C₄₃	—	4	2	no	—
284	C₄×C₄₃	—	4	1	no	—
285	C₄×C₄₃	—	4	1	no	—
286	C₄×C₄₃	—	4	2	no	—
287	C₄×C₄₃	—	4	1	no	—
288	C₄×C₄₃	#421	1	2	yes	—
289	Dic₄₃	—	8	1	no	—
290	Dic₄₃	—	8	2	no	—
291	Dic₄₃	—	8	1	no	—
292	#3523	D₄₃	1	1	yes	characteristic
293	#2984	—	43	1	no	—
294	#2320	—	43	1	no	—
295	#1521	—	43	2	no	—
296	#1518	—	43	2	no	—
297	#1515	—	43	2	no	—
298	#1512	—	43	2	no	—
299	#1509	—	43	1	no	—
300	#1506	—	43	1	no	—
301	#1503	—	43	1	no	—
302	#1500	—	43	1	no	—
303	C₂×C₄₃	—	2	1	no	—
304	C₂×C₄₃	—	2	1	no	—
305	C₂×C₄₃	—	8	1	no	—
306	C₂×C₄₃	#2884	1	1	yes	characteristic
307	C₂×C₄₃	#2898	1	1	yes	characteristic
308	C₂×C₄₃	C₂×#421	1	1	yes	characteristic
309	#557	Dic₄₃	1	1	yes	characteristic, complemented
310	#557	Dic₄₃	1	1	yes	characteristic, complemented
311	#557	Dic₄₃	1	2	yes	complemented
312	#556	Dic₄₃	1	1	yes	characteristic, complemented
313	#556	Dic₄₃	1	2	yes	complemented
314	#552	—	2	2	no	—
315	#552	—	2	1	no	—
316	D₄×Q₈	—	2	1	no	—
317	D₄×Q₈	Dic₄₃	1	1	yes	characteristic, complemented
318	#541	—	2	1	no	—
319	#541	—	2	2	no	—
320	#533	C₂×D₄₃	1	1	yes	characteristic
321	#533	C₂×D₄₃	1	2	yes	—
322	#529	C₂×D₄₃	1	1	yes	characteristic
323	#529	C₂×D₄₃	1	2	yes	—
324	#519	—	2	1	no	—
325	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
326	#446	—	86	1	no	—
327	#446	—	86	2	no	—
328	C₈×Q₈	—	86	1	no	—
329	#432	—	43	1	no	—
330	#432	—	43	2	no	—
331	#431	—	43	1	no	—
332	#431	—	43	2	no	—
333	#391	—	86	1	no	—
334	#389	—	86	1	no	—
335	#387	—	86	2	no	—
336	#383	—	43	2	no	—
337	#382	—	43	2	no	—
338	C₄×C₄⋊C₄	—	43	1	no	—
339	#376	—	43	1	no	—
340	#328	—	43	1	no	—
341	#328	—	43	1	no	—
342	#328	—	43	2	no	—
343	#328	—	43	2	no	—
344	#328	—	43	2	no	—
345	#328	—	43	2	no	—
346	#328	—	43	2	no	—
347	#327	—	43	1	no	—
348	#327	—	43	1	no	—
349	#327	—	43	2	no	—
350	C₄₃	#17601	1	1	yes	characteristic, complemented, Sylow
351	C₂²×Q₈	—	2	1	no	—
352	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	2	no	—
355	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
356	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
357	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
358	C₄⋊Q₈	C₂×Dic₄₃	1	2	yes	—
359	#126	—	2	2	no	—
360	#126	—	2	2	no	—
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	1	no	—
364	#125	—	2	2	no	—
365	#125	—	2	2	no	—
366	#125	—	2	2	no	—
367	#125	—	2	2	no	—
368	#125	—	2	1	no	—
369	#125	—	2	2	no	—
370	#125	—	2	1	no	—
371	#125	C₂×Dic₄₃	1	1	yes	characteristic
372	#125	C₂×Dic₄₃	1	2	yes	—
373	#124	C₂×Dic₄₃	1	1	yes	characteristic
374	#124	C₂×Dic₄₃	1	2	yes	—
375	#123	—	2	1	no	—
376	#123	—	2	2	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	—	2	2	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	—	2	1	no	—
383	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
385	#121	C₂²×D₄₃	1	1	yes	characteristic
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	2	no	—
391	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
392	C₄×Q₈	C₂×Dic₄₃	1	2	yes	—
393	C₄×Q₈	C₂×Dic₄₃	1	2	yes	—
394	C₄×Q₈	C₂×Dic₄₃	1	2	yes	—
395	C₄×Q₈	C₂×Dic₄₃	1	2	yes	—
396	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
397	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
398	C₄×Q₈	C₂×Dic₄₃	1	2	yes	—
399	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
400	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
405	C₄×D₄	C₂×Dic₄₃	1	2	yes	—
406	#117	—	2	1	no	—
407	#117	—	2	2	no	—
408	#117	—	2	2	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	—	2	2	no	—
412	C₂×C₄⋊C₄	—	86	2	no	—
413	C₂×C₄⋊C₄	—	86	1	no	—
414	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
415	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
416	C₂×C₄²	—	86	1	no	—
417	C₂×C₄²	—	86	1	no	—
418	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
419	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
420	C₄⋊C₈	—	86	2	no	—
421	C₄⋊C₈	—	86	1	no	—
422	C₄⋊C₈	—	86	1	no	—
423	C₄⋊C₈	—	86	2	no	—
424	C₂²⋊C₈	—	43	1	no	—
425	C₂²⋊C₈	—	43	1	no	—
426	C₂²⋊C₈	—	43	2	no	—
427	#97	—	86	2	no	—
428	#97	—	86	1	no	—
429	C₄×C₈	—	86	1	no	—
430	C₄×C₈	—	86	2	no	—
431	#95	—	43	1	no	—
432	#95	—	43	1	no	—
433	#95	—	43	2	no	—
434	#95	—	86	1	no	—
435	#95	—	86	2	no	—
436	#95	—	86	2	no	—
437	#95	—	86	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	4	4	no	—
442	C₂×Q₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
443	C₂×Q₈	C₂²⋊Dic₄₃	1	1	yes	characteristic
444	C₂×Q₈	C₂²⋊Dic₄₃	1	2	yes	—
445	C₂×Q₈	C₂²×Dic₄₃	1	1	yes	characteristic
446	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	86	1	no	—
452	C₂²×C₄	—	86	1	no	—
453	C₂²×C₄	—	86	2	no	—
454	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
456	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
458	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
459	C₂×C₈	—	86	1	no	—
460	C₂×C₈	—	86	1	no	—
461	C₂×C₈	—	86	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	344	2	no	—
480	C₄⋊C₄	—	172	2	no	—
481	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
482	C₄⋊C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
484	C₄⋊C₄	C₂²⋊Dic₄₃	1	1	yes	characteristic
485	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
486	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
487	C₄⋊C₄	C₂²⋊Dic₄₃	1	2	yes	—
488	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
490	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	1	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	344	1	no	—
506	C₄²	—	172	2	no	—
507	C₄²	C₂²×Dic₄₃	1	2	yes	—
508	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
509	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
510	C₄²	C₂²×Dic₄₃	1	2	yes	—
511	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
512	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
513	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
514	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
515	C₂³	—	2	1	no	—
516	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	2	no	—
520	Q₈	—	4	1	no	—
521	Q₈	—	4	2	no	—
522	Q₈	—	4	4	no	—
523	Q₈	—	4	2	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	4	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	4	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	172	1	no	—
542	C₂×C₄	—	172	1	no	—
543	C₂×C₄	—	172	2	no	—
544	C₂×C₄	—	172	1	no	—
545	C₂×C₄	—	172	1	no	—
546	C₂×C₄	—	172	2	no	—
547	C₂×C₄	—	172	2	no	—
548	C₂×C₄	—	172	1	no	—
549	C₂×C₄	—	172	1	no	—
550	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
551	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
552	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
553	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
554	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
555	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
556	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	2	yes	—
557	C₂×C₄	C₂×C₂²⋊Dic₄₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
559	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
560	C₈	—	172	1	no	—
561	C₈	—	172	1	no	—
562	C₈	—	172	2	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	C₂²×C₂²⋊Dic₄₃	1	1	yes	characteristic
569	C₂²	#14583707	1	1	yes	characteristic
570	C₂²	#14583714	1	1	yes	characteristic
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	344	1	no	—
586	C₄	—	344	2	no	—
587	C₄	—	344	1	no	—
588	C₄	#14582916	1	2	yes	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	8	1	no	—
592	C₂	#19143059	1	1	yes	characteristic
593	C₂	#19143128	1	1	yes	characteristic
594	C₂	C₂×#14582916	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#3523	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	#121×C₄₃	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#3523	D₄₃
hypocenter	C₄₃	#17601
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ #3523

Complements

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

N	H ≅ G/N	type
1. #19143684	C₂	semidirect
2. #19137246	C₂	semidirect
4. #19133159	C₂	semidirect
5. #19133146	C₂	semidirect
8. #19133107	C₂	semidirect
9. #19133094	C₂	semidirect
36. C₄₃×#557	C₄	semidirect
37. C₄₃×#557	C₄	semidirect
38. C₄₃×#557	C₄	semidirect
39. C₄₃×#556	C₄	semidirect
40. C₄₃×#556	C₄	semidirect
44. D₄×Q₈×C₄₃	C₄	semidirect
309. #557	Dic₄₃	semidirect
310. #557	Dic₄₃	semidirect
311. #557	Dic₄₃	semidirect
312. #556	Dic₄₃	semidirect
313. #556	Dic₄₃	semidirect
317. D₄×Q₈	Dic₄₃	semidirect
350. C₄₃	#17601	semidirect

Maximal subgroups

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

subgroup	index
#19143684	2
#19137246	2
#19133172	2
#19133159	2
#19133146	2
#19133133	2
#19133120	2
#19133107	2
#19133094	2
#19133081	2
C₄₃×#3523	2
#17601	43