Subgroups — #25065525

Order 11008.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148481	C₂	1	1	yes	maximal, characteristic
2	#19143720	C₂	1	1	yes	maximal, characteristic
3	#19133332	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133323	C₂	1	2	yes	maximal, complemented
5	#19133303	C₂	1	2	yes	maximal, complemented
6	#19133286	C₂	1	2	yes	maximal, complemented
7	#19133277	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133275	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133259	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133250	C₂	1	2	yes	maximal, complemented
11	C₄₃×#2991	C₂	1	1	yes	maximal, characteristic
12	#14583627	—	2	1	no	—
13	#14583627	—	2	1	no	—
14	#14583619	—	2	1	no	—
15	#14583619	—	2	1	no	—
16	#14583589	—	2	2	no	—
17	#14583589	—	2	2	no	—
18	#14583511	C₄	1	4	yes	—
19	#14583470	C₄	1	2	yes	—
20	#14583456	C₂²	1	2	yes	—
21	#14583456	C₂²	1	2	yes	—
22	#14583456	C₂²	1	1	yes	characteristic
23	C₂×#13063325	C₂²	1	1	yes	characteristic
24	#14583376	C₄	1	2	yes	—
25	#14583030	—	2	1	no	—
26	#14582971	—	2	2	no	—
27	D₄×C₄₃⋊C₈	—	2	1	no	—
28	#14582956	C₂²	1	2	yes	—
29	#14582952	C₂²	1	1	yes	characteristic
30	#14582923	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
32	#14582647	C₂²	1	2	yes	—
33	#14582647	C₂²	1	2	yes	—
34	#14582647	C₂²	1	2	yes	—
35	#14582647	C₂²	1	2	yes	—
36	#14582646	C₂²	1	1	yes	characteristic
37	#14582646	C₂²	1	2	yes	—
38	#14582646	C₂²	1	1	yes	characteristic
39	#14582644	C₂²	1	1	yes	characteristic
40	#14582644	C₂²	1	1	yes	characteristic
41	#14582644	C₂²	1	2	yes	—
42	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
43	C₈×Q₈×C₄₃	—	2	1	no	—
44	C₄₃×#436	—	2	2	no	—
45	C₄₃×#436	—	2	1	no	—
46	C₄₃×#431	C₂²	1	2	yes	—
47	C₄₃×#431	C₂²	1	1	yes	characteristic
48	C₄₃×#423	C₂²	1	1	yes	characteristic
49	C₄₃×#423	C₂²	1	2	yes	—
50	C₂²×Dic₈₆	C₂×C₄	1	2	yes	—
51	C₂×#10621877	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	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	#13063325	C₂³	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063323	—	2	2	no	—
60	#13063318	—	2	4	no	—
61	#13063318	—	2	4	no	—
62	#13063317	—	2	2	no	—
63	#13063317	—	2	2	no	—
64	#13063317	C₂×C₄	1	2	yes	—
65	#13063315	—	2	4	no	—
66	#13063315	—	2	4	no	—
67	#13063312	—	2	2	no	—
68	#13063306	—	2	4	no	—
69	#13063304	—	2	1	no	—
70	#13063304	—	2	1	no	—
71	#13063304	—	2	2	no	—
72	#13063304	—	2	2	no	—
73	#13063304	C₂×C₄	1	4	yes	—
74	#13063304	C₂×C₄	1	4	yes	—
75	C₄×Dic₈₆	—	2	2	no	—
76	C₄×Dic₈₆	—	2	2	no	—
77	C₄×Dic₈₆	—	2	1	no	—
78	C₄×Dic₈₆	—	2	1	no	—
79	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
80	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
81	#13063290	—	2	2	no	—
82	#13063290	—	2	2	no	—
83	#13063284	—	2	2	no	—
84	#13063284	—	2	2	no	—
85	#13063284	C₂×C₄	1	2	yes	—
86	#13063281	—	2	4	no	—
87	C₂×C₄⋊Dic₄₃	—	2	1	no	—
88	C₂×C₄⋊Dic₄₃	—	2	1	no	—
89	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
90	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
91	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
92	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
93	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
94	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
95	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
96	#13063236	—	2	2	no	—
97	C₄×C₄₃⋊C₈	—	2	1	no	—
98	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₂×M₁₆×C₄₃	—	2	1	no	—
100	C₂×M₁₆×C₄₃	—	2	2	no	—
101	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
102	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
103	C₄×D₄×C₄₃	D₄	1	2	yes	—
104	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
105	C₄×D₄×C₄₃	D₄	1	2	yes	—
106	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
107	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
108	#117×C₄₃	C₂×C₄	1	2	yes	—
109	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
110	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₄₃	—	2	2	no	—
112	C₄⋊C₈×C₄₃	—	2	1	no	—
113	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
115	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₂²⋊C₈×C₄₃	—	2	1	no	—
117	C₂²⋊C₈×C₄₃	—	2	2	no	—
118	C₄×C₈×C₄₃	—	2	2	no	—
119	C₄×C₈×C₄₃	—	2	1	no	—
120	#41×C₄₃	—	4	2	no	—
121	C₂×Q₈×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×D₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₂×D₄×C₄₃	C₂²⋊C₄	1	2	yes	—
124	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
130	C₂²×Dic₄₃	—	2	2	no	—
131	C₂×Dic₈₆	—	2	2	no	—
132	C₂×Dic₈₆	—	2	1	no	—
133	C₂×Dic₈₆	—	2	1	no	—
134	C₂×Dic₈₆	—	4	4	no	—
135	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
136	M₁₆×C₄₃	—	8	1	no	—
137	M₁₆×C₄₃	—	8	2	no	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	2	no	—
140	C₂×C₈×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
142	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
143	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
144	C₄⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
145	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
146	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
147	C₂²⋊C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
148	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
149	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂×D₄	1	2	yes	—
152	C₄²×C₄₃	C₂×D₄	1	2	yes	—
153	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
155	C₂²⋊Dic₄₃	—	2	2	no	—
156	C₂²⋊Dic₄₃	—	2	4	no	—
157	C₂²⋊Dic₄₃	—	2	4	no	—
158	C₄⋊Dic₄₃	—	2	2	no	—
159	C₄⋊Dic₄₃	—	2	2	no	—
160	C₄⋊Dic₄₃	—	2	2	no	—
161	C₄⋊Dic₄₃	—	2	2	no	—
162	C₄⋊Dic₄₃	—	2	1	no	—
163	C₄⋊Dic₄₃	—	2	1	no	—
164	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
165	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
166	Dic₄₃⋊C₄	—	2	4	no	—
167	Dic₄₃⋊C₄	—	2	4	no	—
168	Dic₄₃⋊C₄	—	2	2	no	—
169	Dic₄₃⋊C₄	—	2	2	no	—
170	Dic₄₃⋊C₄	—	2	4	no	—
171	Dic₄₃⋊C₄	—	2	4	no	—
172	C₄×Dic₄₃	—	2	4	no	—
173	C₄×Dic₄₃	—	2	4	no	—
174	C₄×Dic₄₃	—	2	2	no	—
175	#10621877	—	8	1	no	—
176	C₂×C₄₃⋊C₈	—	2	1	no	—
177	C₂×C₄₃⋊C₈	—	2	1	no	—
178	C₂×C₄₃⋊C₈	—	2	2	no	—
179	C₂×C₄₃⋊C₈	—	8	2	no	—
180	C₂³×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	Q₈×C₄₃	—	2	2	no	—
183	D₄×C₄₃	—	2	2	no	—
184	D₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	4	2	no	—
195	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
198	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×Dic₄₃	—	2	2	no	—
205	C₂×Dic₄₃	—	2	2	no	—
206	C₂×Dic₄₃	—	2	4	no	—
207	C₂×Dic₄₃	—	4	4	no	—
208	Dic₈₆	—	4	1	no	—
209	Dic₈₆	—	4	1	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	4	1	no	—
212	Dic₈₆	—	4	4	no	—
213	Dic₈₆	—	4	4	no	—
214	C₈×C₄₃	—	4	2	no	—
215	C₈×C₄₃	—	4	1	no	—
216	C₈×C₄₃	—	4	1	no	—
217	C₄₃⋊C₈	—	4	1	no	—
218	C₄₃⋊C₈	—	4	2	no	—
219	C₄₃⋊C₈	—	4	1	no	—
220	#17778	—	43	1	no	maximal, Sylow
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	2	2	no	—
223	C₂²×C₄₃	—	2	2	no	—
224	C₂²×C₄₃	—	2	1	no	—
225	C₂²×C₄₃	—	2	2	no	—
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	2	no	—
230	C₄×C₄₃	—	2	2	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	—	2	2	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	#413	1	2	yes	—
235	C₄×C₄₃	#577	1	1	yes	characteristic
236	C₄×C₄₃	#577	1	1	yes	characteristic
237	C₄×C₄₃	#578	1	1	yes	characteristic
238	C₄×C₄₃	#578	1	1	yes	characteristic
239	Dic₄₃	—	4	4	no	—
240	Dic₄₃	—	4	2	no	—
241	Dic₄₃	—	4	2	no	—
242	#3509	—	43	1	no	—
243	#2991	D₄₃	1	1	yes	characteristic
244	#2990	—	43	1	no	—
245	#1561	—	43	1	no	—
246	#1559	—	43	2	no	—
247	#1554	—	43	2	no	—
248	#1550	—	43	2	no	—
249	#1548	—	43	1	no	—
250	#1548	—	43	1	no	—
251	#1544	—	43	1	no	—
252	#1542	—	43	2	no	—
253	C₂×C₄₃	—	4	1	no	—
254	C₂×C₄₃	—	4	2	no	—
255	C₂×C₄₃	C₂×#413	1	1	yes	characteristic
256	C₂×C₄₃	#2898	1	1	yes	characteristic
257	C₂×C₄₃	#2898	1	1	yes	characteristic
258	#557	—	86	1	no	—
259	#557	—	86	1	no	—
260	#556	—	86	1	no	—
261	#556	—	86	1	no	—
262	#552	—	86	2	no	—
263	#552	—	86	2	no	—
264	#541	—	43	4	no	—
265	#536	—	43	2	no	—
266	#533	—	43	1	no	—
267	#533	—	43	2	no	—
268	#533	—	43	2	no	—
269	C₂×C₄⋊Q₈	—	43	1	no	—
270	#519	—	43	2	no	—
271	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
272	#446	—	86	1	no	—
273	C₈×Q₈	—	2	1	no	—
274	#436	—	2	2	no	—
275	#436	—	2	1	no	—
276	#435	—	86	2	no	—
277	C₈×D₄	—	86	1	no	—
278	#432	—	43	2	no	—
279	#431	—	43	1	no	—
280	#431	C₂×D₄₃	1	2	yes	—
281	#431	C₂×D₄₃	1	1	yes	characteristic
282	#423	—	43	1	no	—
283	#423	C₂×D₄₃	1	1	yes	characteristic
284	#423	C₂×D₄₃	1	2	yes	—
285	C₂×C₄⋊C₈	—	43	2	no	—
286	#333	—	43	2	no	—
287	#333	—	43	2	no	—
288	#333	—	43	2	no	—
289	#333	—	43	2	no	—
290	#332	—	43	1	no	—
291	#332	—	43	2	no	—
292	#332	—	43	1	no	—
293	#332	—	43	1	no	—
294	#332	—	43	1	no	—
295	#332	—	43	2	no	—
296	C₄₃	#17778	1	1	yes	characteristic, complemented, Sylow
297	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
298	C₂²×Q₈	—	43	2	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	86	1	no	—
302	C₂²×C₈	—	86	2	no	—
303	C₄⋊Q₈	—	43	2	no	—
304	C₄⋊Q₈	—	43	1	no	—
305	C₄⋊Q₈	—	43	1	no	—
306	C₄⋊Q₈	—	43	2	no	—
307	C₄⋊Q₈	—	86	2	no	—
308	C₄⋊Q₈	—	86	1	no	—
309	C₄⋊Q₈	—	86	1	no	—
310	#126	—	86	4	no	—
311	#126	—	86	4	no	—
312	#125	—	43	2	no	—
313	#125	—	86	4	no	—
314	#125	—	86	4	no	—
315	#125	—	86	2	no	—
316	#125	—	86	2	no	—
317	#124	—	86	2	no	—
318	#123	—	86	4	no	—
319	C₂²⋊Q₈	—	43	4	no	—
320	C₂²⋊Q₈	—	43	4	no	—
321	C₂²⋊Q₈	—	86	1	no	—
322	C₂²⋊Q₈	—	86	2	no	—
323	C₂²⋊Q₈	—	86	1	no	—
324	C₂²⋊Q₈	—	86	2	no	—
325	C₄×Q₈	—	43	4	no	—
326	C₄×Q₈	—	43	4	no	—
327	C₄×Q₈	—	86	2	no	—
328	C₄×Q₈	—	86	2	no	—
329	C₄×Q₈	—	86	2	no	—
330	C₄×Q₈	—	86	1	no	—
331	C₄×Q₈	—	86	2	no	—
332	C₄×Q₈	—	86	1	no	—
333	C₄×Q₈	D₁₇₂	1	1	yes	characteristic
334	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
335	C₄×D₄	D₁₇₂	1	2	yes	—
336	C₄×D₄	D₁₇₂	1	1	yes	characteristic
337	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
338	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
339	#117	—	43	2	no	—
340	#117	—	86	2	no	—
341	#117	—	86	2	no	—
342	#117	—	86	4	no	—
343	#117	C₄×D₄₃	1	1	yes	characteristic
344	#117	C₄×D₄₃	1	2	yes	—
345	C₂×C₄⋊C₄	—	86	1	no	—
346	C₂×C₄⋊C₄	—	86	1	no	—
347	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
349	C₄⋊C₈	—	2	2	no	—
350	C₄⋊C₈	—	2	1	no	—
351	C₄⋊C₈	—	43	1	no	—
352	C₄⋊C₈	—	43	2	no	—
353	C₄⋊C₈	—	43	1	no	—
354	C₄⋊C₈	—	86	2	no	—
355	C₄⋊C₈	—	86	1	no	—
356	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
357	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	2	2	no	—
361	C₂²⋊C₈	—	86	1	no	—
362	C₂²⋊C₈	—	86	2	no	—
363	#97	—	86	2	no	—
364	C₄×C₈	—	2	2	no	—
365	C₄×C₈	—	2	1	no	—
366	C₄×C₈	—	86	1	no	—
367	#41	—	4	2	no	—
368	C₂×Q₈	—	43	4	no	—
369	C₂×Q₈	—	86	2	no	—
370	C₂×Q₈	—	86	1	no	—
371	C₂×Q₈	—	86	1	no	—
372	C₂×Q₈	—	172	4	no	—
373	C₂×Q₈	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
374	C₂×D₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
375	C₂×D₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
376	C₂²×C₄	—	86	2	no	—
377	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
379	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
380	C₂²×C₄	C₂×D₁₇₂	1	2	yes	—
381	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
383	M₁₆	—	8	1	no	—
384	M₁₆	—	8	2	no	—
385	M₁₆	—	344	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	86	1	no	—
390	C₂×C₈	—	86	1	no	—
391	C₂×C₈	—	86	2	no	—
392	C₂×C₈	—	344	2	no	—
393	C₄⋊C₄	—	43	2	no	—
394	C₄⋊C₄	—	43	2	no	—
395	C₄⋊C₄	—	86	2	no	—
396	C₄⋊C₄	—	86	2	no	—
397	C₄⋊C₄	—	86	4	no	—
398	C₄⋊C₄	—	86	4	no	—
399	C₄⋊C₄	—	86	4	no	—
400	C₄⋊C₄	—	86	4	no	—
401	C₄⋊C₄	—	86	2	no	—
402	C₄⋊C₄	—	86	2	no	—
403	C₄⋊C₄	—	86	2	no	—
404	C₄⋊C₄	—	86	1	no	—
405	C₄⋊C₄	—	86	2	no	—
406	C₄⋊C₄	—	86	1	no	—
407	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
408	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
409	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
410	C₄⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
411	C₂²⋊C₄	—	86	2	no	—
412	C₂²⋊C₄	—	86	4	no	—
413	C₂²⋊C₄	—	86	4	no	—
414	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
415	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
416	C₂²⋊C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
417	C₄²	—	86	2	no	—
418	C₄²	—	86	4	no	—
419	C₄²	—	86	4	no	—
420	C₄²	C₂×C₄×D₄₃	1	2	yes	—
421	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
422	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
423	C₄²	C₂×D₁₇₂	1	2	yes	—
424	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
425	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
426	C₄²	C₂³×D₄₃	1	1	yes	characteristic
427	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
428	C₂³	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
429	Q₈	—	2	2	no	—
430	Q₈	—	172	4	no	—
431	Q₈	—	172	4	no	—
432	Q₈	—	172	1	no	—
433	Q₈	—	172	1	no	—
434	Q₈	—	172	1	no	—
435	Q₈	—	172	1	no	—
436	D₄	—	2	2	no	—
437	D₄	—	4	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	86	2	no	—
449	C₂×C₄	—	86	2	no	—
450	C₂×C₄	—	86	4	no	—
451	C₂×C₄	—	172	4	no	—
452	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
453	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
454	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
455	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
456	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	2	yes	—
457	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
458	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
461	C₈	—	4	2	no	—
462	C₈	—	4	1	no	—
463	C₈	—	4	1	no	—
464	C₈	—	172	1	no	—
465	C₈	—	172	2	no	—
466	C₈	—	172	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	2	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	1	no	—
473	C₂²	C₂²×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	1	no	—
480	C₄	—	172	4	no	—
481	C₄	—	172	2	no	—
482	C₄	—	172	2	no	—
483	C₄	#14582881	1	2	yes	—
484	C₄	#14583710	1	1	yes	characteristic
485	C₄	#14583711	1	1	yes	characteristic
486	C₄	#14583714	1	1	yes	characteristic
487	C₄	#14583716	1	1	yes	characteristic
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	C₂×#14582881	1	1	yes	characteristic
491	C₂	#19143125	1	1	yes	characteristic
492	C₂	#19143129	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×(C₂×D₄₃)⋊C₄
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#2991	C₂
socle	C₂²×C₄₃	C₂²×C₂²⋊C₄
prime radical	C₂×#41×C₄₃	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#2991	D₄₃
hypocenter	C₄₃	#17778
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #2991

Complements

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

N	H ≅ G/N	type
3. #19133332	C₂	semidirect
4. #19133323	C₂	semidirect
5. #19133303	C₂	semidirect
6. #19133286	C₂	semidirect
7. #19133277	C₂	semidirect
8. #19133275	C₂	semidirect
9. #19133259	C₂	semidirect
10. #19133250	C₂	semidirect
296. C₄₃	#17778	semidirect

Maximal subgroups

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

subgroup	index
#19148481	2
#19143720	2
#19133332	2
#19133323	2
#19133303	2
#19133286	2
#19133277	2
#19133275	2
#19133259	2
#19133250	2
C₄₃×#2991	2
#17778	43