Subgroups — #25065130

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583449	C₂	1	1	yes	maximal, characteristic
2	#19143228	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133318	C₂	1	4	yes	maximal, complemented
4	#19133313	C₂	1	2	yes	maximal, complemented
5	#19133308	C₂	1	2	yes	maximal, complemented
6	#19133245	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621898	—	2	1	no	—
9	#14583449	—	2	1	no	—
10	#14583449	—	2	1	no	—
11	#14583449	—	2	1	no	—
12	#14583449	—	2	1	no	—
13	#14583449	C₄	1	2	yes	—
14	#14583449	C₄	1	2	yes	—
15	#14583449	C₂²	1	2	yes	—
16	#14583449	C₂²	1	2	yes	—
17	C₂×#13063325	C₂²	1	1	yes	characteristic
18	C₂×#13063322	C₂²	1	1	yes	characteristic
19	C₂×#13063313	—	2	1	no	—
20	C₂×#13063299	—	2	1	no	—
21	C₂×#13063299	C₄	1	2	yes	—
22	C₂×C₄×D₁₇₂	—	2	1	no	—
23	C₂×C₄×D₁₇₂	C₄	1	2	yes	—
24	#14582956	—	2	1	no	—
25	#14582956	C₂²	1	2	yes	—
26	#14582952	—	2	1	no	—
27	#14582952	C₂²	1	2	yes	complemented
28	#14582923	C₂²	1	2	yes	complemented
29	#14582863	—	2	1	no	—
30	C₄×#10621877	—	2	1	no	—
31	#14582646	C₂²	1	8	yes	complemented
32	#14582642	C₂²	1	8	yes	complemented
33	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
34	C₄₃×#432	—	2	1	no	—
35	C₄₃×#432	—	2	1	no	—
36	C₄₃×#432	C₂²	1	2	yes	—
37	C₄₃×#432	C₂²	1	2	yes	complemented
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
39	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
40	C₂×#97×C₄₃	—	2	1	no	—
41	C₂×#10621898	—	2	2	no	—
42	C₂×#10621898	—	2	2	no	—
43	C₂×#10621898	—	2	2	no	—
44	C₂×#10621898	—	2	2	no	—
45	C₂×#10621898	—	4	8	no	—
46	C₂²×Dic₈₆	—	2	1	no	—
47	C₂²×D₁₇₂	—	2	1	no	—
48	C₂²×D₁₇₂	—	2	1	no	—
49	C₂²×D₁₇₂	C₂×C₄	1	2	yes	—
50	C₂²×C₂²⋊D₄₃	—	2	2	no	—
51	C₂²×C₄×D₄₃	—	2	2	no	—
52	C₂×#10621877	—	2	2	no	—
53	#13063325	—	2	1	no	—
54	#13063325	—	2	1	no	—
55	#13063325	C₂×C₄	1	2	yes	—
56	#13063325	C₂³	1	2	yes	—
57	#13063322	—	2	1	no	—
58	#13063322	—	2	1	no	—
59	#13063322	C₂×C₄	1	2	yes	—
60	#13063322	C₂³	1	2	yes	—
61	#13063313	—	2	2	no	—
62	#13063313	—	2	2	no	—
63	#13063313	—	2	2	no	—
64	#13063313	—	2	2	no	—
65	#13063299	—	2	2	no	—
66	#13063299	—	2	2	no	—
67	#13063299	—	2	2	no	—
68	#13063299	—	2	2	no	—
69	#13063299	—	2	2	no	—
70	#13063299	—	2	2	no	—
71	#13063299	C₂×C₄	1	4	yes	—
72	#13063299	C₂×C₄	1	4	yes	—
73	C₄×D₁₇₂	—	2	2	no	—
74	C₄×D₁₇₂	—	2	2	no	—
75	C₄×D₁₇₂	—	2	2	no	—
76	C₄×D₁₇₂	—	2	2	no	—
77	C₄×D₁₇₂	—	2	2	no	—
78	C₄×D₁₇₂	—	2	2	no	—
79	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
80	C₄×D₁₇₂	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊Dic₄₃	—	2	1	no	—
82	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
83	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
84	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
85	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
86	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
89	#13063236	—	2	2	no	—
90	C₄×C₄₃⋊C₈	—	2	2	no	—
91	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
93	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	—	2	2	no	—
95	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₄⋊C₈×C₄₃	—	2	2	no	—
108	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
109	C₂²⋊C₈×C₄₃	—	2	2	no	—
110	C₂²⋊C₈×C₄₃	—	2	2	no	—
111	#97×C₄₃	—	2	2	no	—
112	#97×C₄₃	—	2	2	no	—
113	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₂³×D₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	4	no	—
116	C₂²×C₄×C₄₃	—	4	2	no	—
117	C₂²×C₄×C₄₃	—	4	2	no	—
118	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₃	—	2	4	no	—
137	C₂×C₂²⋊D₄₃	—	2	4	no	—
138	C₂×C₂²⋊D₄₃	—	4	8	no	—
139	C₂²×Dic₄₃	—	2	2	no	—
140	#10621898	—	4	8	no	—
141	#10621898	—	4	8	no	—
142	#10621898	—	4	8	no	—
143	#10621898	—	4	8	no	—
144	C₂×D₁₇₂	—	2	2	no	—
145	C₂×D₁₇₂	—	2	2	no	—
146	C₂×D₁₇₂	—	2	2	no	—
147	C₂×D₁₇₂	—	2	2	no	—
148	C₂×D₁₇₂	—	2	2	no	—
149	C₂×D₁₇₂	—	4	4	no	—
150	C₂×D₁₇₂	—	4	4	no	—
151	C₂×D₁₇₂	—	4	4	no	—
152	C₂×D₁₇₂	C₂²×C₄	1	4	yes	—
153	C₂×C₄×D₄₃	—	2	4	no	—
154	C₂×C₄×D₄₃	—	2	4	no	—
155	C₂×C₄×D₄₃	—	4	8	no	—
156	C₂×Dic₈₆	—	2	2	no	—
157	C₂×Dic₈₆	—	2	2	no	—
158	C₂×Dic₈₆	—	4	4	no	—
159	C₂×C₈×C₄₃	—	2	4	no	—
160	C₂×C₈×C₄₃	—	4	4	no	—
161	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
164	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
165	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
166	C₄²×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
167	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	(C₂×D₄₃)⋊C₄	—	2	4	no	—
178	(C₂×D₄₃)⋊C₄	—	2	4	no	—
179	(C₂×D₄₃)⋊C₄	—	2	4	no	—
180	(C₂×D₄₃)⋊C₄	—	2	4	no	—
181	C₄⋊Dic₄₃	—	2	2	no	—
182	C₄⋊Dic₄₃	—	2	2	no	—
183	C₄⋊Dic₄₃	—	2	2	no	—
184	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
185	#10621877	—	4	4	no	—
186	C₂×C₄₃⋊C₈	—	2	4	no	—
187	C₂³×C₄₃	—	2	2	no	—
188	C₂³×C₄₃	—	2	2	no	—
189	C₂³×C₄₃	—	4	1	no	—
190	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
191	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
193	C₂²×D₄₃	—	2	4	no	—
194	C₂²×D₄₃	—	4	4	no	—
195	C₂²×D₄₃	—	4	4	no	—
196	C₂²×D₄₃	—	4	4	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	2	no	—
200	C₂×C₄×C₄₃	—	2	2	no	—
201	C₂×C₄×C₄₃	—	2	2	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	2	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	2	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	1	no	—
210	C₂×C₄×C₄₃	—	4	1	no	—
211	C₂×C₄×C₄₃	—	4	1	no	—
212	C₂×C₄×C₄₃	—	4	1	no	—
213	C₂×C₄×C₄₃	—	4	1	no	—
214	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
224	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
225	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₂²⋊D₄₃	—	4	8	no	—
228	C₂²⋊D₄₃	—	4	8	no	—
229	C₂×Dic₄₃	—	2	4	no	—
230	C₂×Dic₄₃	—	4	4	no	—
231	D₁₇₂	—	4	4	no	—
232	D₁₇₂	—	4	4	no	—
233	D₁₇₂	—	4	4	no	—
234	D₁₇₂	—	4	4	no	—
235	D₁₇₂	—	4	4	no	—
236	D₁₇₂	—	4	4	no	—
237	C₄×D₄₃	—	4	8	no	—
238	C₄×D₄₃	—	4	8	no	—
239	Dic₈₆	—	4	4	no	—
240	Dic₈₆	—	4	4	no	—
241	C₈×C₄₃	—	4	4	no	—
242	C₄₃⋊C₈	—	4	4	no	—
243	#17731	—	43	1	no	maximal, Sylow
244	C₂²×C₄₃	—	2	1	no	—
245	C₂²×C₄₃	—	2	1	no	—
246	C₂²×C₄₃	—	2	1	no	—
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	2	1	no	—
249	C₂²×C₄₃	—	2	1	no	—
250	C₂²×C₄₃	—	2	1	no	—
251	C₂²×C₄₃	—	4	4	no	—
252	C₂²×C₄₃	#413	1	2	yes	—
253	C₂²×C₄₃	#418	1	2	yes	—
254	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×D₄₃	—	4	4	no	—
256	C₂×D₄₃	—	4	4	no	—
257	C₂×D₄₃	—	4	4	no	—
258	C₂×D₄₃	—	8	8	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	2	1	no	—
261	C₄×C₄₃	—	2	1	no	—
262	C₄×C₄₃	—	2	1	no	—
263	C₄×C₄₃	—	2	1	no	—
264	C₄×C₄₃	—	2	1	no	—
265	C₄×C₄₃	—	2	1	no	—
266	C₄×C₄₃	—	2	1	no	—
267	C₄×C₄₃	—	2	1	no	—
268	C₄×C₄₃	#418	1	2	yes	—
269	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
270	C₄×C₄₃	#575	1	2	yes	—
271	Dic₄₃	—	4	4	no	—
272	C₂×#532	—	43	1	no	—
273	#2920	—	43	1	no	—
274	C₂×#432	D₄₃	1	1	yes	characteristic, complemented
275	#1557	—	43	4	no	—
276	#1556	—	43	2	no	—
277	#1555	—	43	2	no	—
278	#1540	—	43	4	no	—
279	C₂×C₄₃	—	2	2	no	—
280	C₂×C₄₃	—	2	2	no	—
281	C₂×C₄₃	—	4	1	no	—
282	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
283	C₂×C₄₃	C₂×#418	1	1	yes	characteristic
284	C₂×C₄₃	#2896	1	1	yes	characteristic
285	D₄₃	—	8	4	no	—
286	C₂²×#41	—	86	1	no	—
287	#532	—	43	2	no	—
288	#532	—	43	2	no	—
289	#532	—	43	2	no	—
290	#532	—	43	2	no	—
291	#532	—	86	1	no	—
292	#532	—	86	1	no	—
293	#532	—	86	1	no	—
294	#532	—	86	1	no	—
295	C₂×C₄⋊Q₈	—	43	1	no	—
296	C₂×#127	—	43	1	no	—
297	C₂×#124	—	86	1	no	—
298	C₂×#121	—	43	2	no	—
299	C₂×#121	—	86	1	no	—
300	C₂×C₄×D₄	—	43	2	no	—
301	C₂×C₄×D₄	—	86	1	no	—
302	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
303	#432	—	2	1	no	—
304	#432	—	2	1	no	—
305	#432	—	43	2	no	—
306	#432	—	86	1	no	—
307	#432	C₂×D₄₃	1	2	yes	—
308	#432	C₂×D₄₃	1	2	yes	complemented
309	#431	—	43	2	no	—
310	#431	—	86	1	no	—
311	#423	—	43	2	no	—
312	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	complemented
313	#407	—	86	1	no	—
314	C₂×C₂²⋊C₈	—	2	1	no	—
315	C₄×M₁₆	—	86	1	no	—
316	C₂×#97	—	2	1	no	—
317	#332	—	43	8	no	—
318	#331	—	43	8	no	—
319	C₄₃	#17731	1	1	yes	characteristic, complemented, Sylow
320	C₂×#41	—	86	2	no	—
321	C₂×#41	—	86	2	no	—
322	C₂×#41	—	86	2	no	—
323	C₂×#41	—	86	2	no	—
324	C₂×#41	—	172	8	no	—
325	C₂²×Q₈	—	86	1	no	—
326	C₂²×D₄	—	43	2	no	—
327	C₂²×D₄	—	86	2	no	—
328	C₂²×D₄	—	86	1	no	—
329	C₂²×D₄	—	86	1	no	—
330	C₂³×C₄	—	86	2	no	—
331	C₂³×C₄	C₄×D₄₃	1	1	yes	characteristic
332	C₂³×C₄	D₁₇₂	1	1	yes	characteristic
333	C₂³×C₄	C₂²⋊D₄₃	1	1	yes	characteristic
334	C₂×M₁₆	—	86	2	no	—
335	C₂²×C₈	—	2	2	no	—
336	C₄⋊Q₈	—	43	2	no	—
337	C₄⋊Q₈	—	43	2	no	—
338	C₄⋊Q₈	—	86	1	no	—
339	C₄⋊Q₈	—	86	1	no	—
340	#127	—	43	2	no	—
341	#127	—	43	2	no	—
342	#127	—	86	1	no	—
343	#127	—	86	1	no	—
344	#124	—	86	2	no	—
345	#124	—	86	2	no	—
346	#124	—	86	2	no	—
347	#124	—	86	2	no	—
348	#121	—	43	4	no	—
349	#121	—	43	4	no	—
350	#121	—	86	2	no	—
351	#121	—	86	2	no	—
352	#121	—	86	2	no	—
353	#121	—	86	2	no	—
354	#121	—	86	2	no	—
355	#121	—	86	2	no	—
356	C₄×D₄	—	43	4	no	—
357	C₄×D₄	—	43	4	no	—
358	C₄×D₄	—	86	2	no	—
359	C₄×D₄	—	86	2	no	—
360	C₄×D₄	—	86	2	no	—
361	C₄×D₄	—	86	2	no	—
362	C₄×D₄	—	86	2	no	—
363	C₄×D₄	—	86	2	no	—
364	C₂×C₄⋊C₄	—	43	2	no	—
365	C₂×C₄⋊C₄	—	86	1	no	—
366	C₂×C₂²⋊C₄	—	86	2	no	—
367	C₂×C₂²⋊C₄	—	86	2	no	—
368	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
369	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
370	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
371	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
372	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
373	C₂×C₄²	D₁₇₂	1	1	yes	characteristic
374	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
375	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
380	C₄⋊C₈	—	2	2	no	—
381	C₄⋊C₈	—	43	4	no	—
382	C₄⋊C₈	—	86	2	no	—
383	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
384	C₂²⋊C₈	—	2	2	no	—
385	C₂²⋊C₈	—	2	2	no	—
386	C₂²⋊C₈	—	86	2	no	—
387	C₂²⋊C₈	—	86	2	no	—
388	#97	—	2	2	no	—
389	#97	—	2	2	no	—
390	#97	—	86	2	no	—
391	C₄×C₈	—	86	2	no	—
392	C₂⁴	—	86	2	no	—
393	C₂⁴	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
394	#41	—	172	8	no	—
395	#41	—	172	8	no	—
396	#41	—	172	8	no	—
397	#41	—	172	8	no	—
398	C₂×Q₈	—	86	2	no	—
399	C₂×Q₈	—	86	2	no	—
400	C₂×Q₈	—	172	4	no	—
401	C₂×D₄	—	43	4	no	—
402	C₂×D₄	—	86	4	no	—
403	C₂×D₄	—	86	4	no	—
404	C₂×D₄	—	86	2	no	—
405	C₂×D₄	—	86	2	no	—
406	C₂×D₄	—	86	2	no	—
407	C₂×D₄	—	86	2	no	—
408	C₂×D₄	—	86	2	no	—
409	C₂×D₄	—	172	4	no	—
410	C₂×D₄	—	172	4	no	—
411	C₂×D₄	—	172	4	no	—
412	C₂×D₄	—	172	8	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	4	2	no	—
415	C₂²×C₄	—	4	2	no	—
416	C₂²×C₄	—	86	2	no	—
417	C₂²×C₄	—	86	4	no	—
418	C₂²×C₄	—	86	4	no	—
419	C₂²×C₄	—	172	8	no	—
420	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
422	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
423	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
424	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
425	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
426	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
427	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
428	C₂²×C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
430	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
438	M₁₆	—	172	4	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	4	4	no	—
441	C₂×C₈	—	86	4	no	—
442	C₄⋊C₄	—	43	4	no	—
443	C₄⋊C₄	—	86	2	no	—
444	C₄⋊C₄	—	86	2	no	—
445	C₄⋊C₄	—	86	2	no	—
446	C₂²⋊C₄	—	86	4	no	—
447	C₂²⋊C₄	—	86	4	no	—
448	C₂²⋊C₄	—	86	4	no	—
449	C₂²⋊C₄	—	86	4	no	—
450	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
451	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
452	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
453	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
454	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
455	C₄²	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
456	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
457	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
458	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
459	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
460	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
461	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
462	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
463	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
464	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
465	C₄²	C₂³×D₄₃	1	1	yes	characteristic
466	C₂³	—	2	2	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	86	4	no	—
470	C₂³	—	172	4	no	—
471	C₂³	—	172	4	no	—
472	C₂³	—	172	4	no	—
473	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
474	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
475	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
476	Q₈	—	172	4	no	—
477	Q₈	—	172	4	no	—
478	D₄	—	172	4	no	—
479	D₄	—	172	4	no	—
480	D₄	—	172	4	no	—
481	D₄	—	172	4	no	—
482	D₄	—	172	8	no	—
483	D₄	—	172	8	no	—
484	D₄	—	172	4	no	—
485	D₄	—	172	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	86	4	no	—
504	C₂×C₄	—	172	8	no	—
505	C₂×C₄	—	172	4	no	—
506	C₂×C₄	—	172	8	no	—
507	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
509	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
511	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
512	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
513	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
514	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
515	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
516	C₂×C₄	#13063350	1	4	yes	—
517	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
520	C₈	—	4	4	no	—
521	C₈	—	172	4	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	344	8	no	—
531	C₂²	—	172	4	no	—
532	C₂²	—	172	4	no	—
533	C₂²	—	172	4	no	—
534	C₂²	#14582881	1	2	yes	—
535	C₂²	#14582903	1	2	yes	—
536	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	172	4	no	—
547	C₄	#14582903	1	2	yes	—
548	C₄	C₂×#13063350	1	2	yes	—
549	C₄	#14583699	1	2	yes	—
550	C₂	—	2	2	no	—
551	C₂	—	2	2	no	—
552	C₂	—	4	1	no	—
553	C₂	—	344	4	no	—
554	C₂	C₂×#14582881	1	1	yes	characteristic
555	C₂	C₂×#14582903	1	1	yes	characteristic
556	C₂	#19143115	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#432	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#14583449	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₂×#432	D₄₃
hypocenter	C₄₃	#17731
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#432

Complements

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

N	H ≅ G/N	type
2. #19143228	C₂	semidirect
3. #19133318	C₂	semidirect
4. #19133313	C₂	semidirect
5. #19133308	C₂	semidirect
6. #19133245	C₂	semidirect
7. C₂×C₄₃×#432	C₂	semidirect
27. #14582952	C₂²	semidirect
28. #14582923	C₂²	semidirect
31. #14582646	C₂²	semidirect
32. #14582642	C₂²	semidirect
37. C₄₃×#432	C₂²	semidirect
38. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
274. C₂×#432	D₄₃	semidirect
308. #432	C₂×D₄₃	semidirect
312. C₂×C₄⋊C₈	C₂×D₄₃	semidirect
319. C₄₃	#17731	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583449	2
#19143228	2
#19133318	2
#19133313	2
#19133308	2
#19133245	2
C₂×C₄₃×#432	2
#17731	43