Subgroups — #25079308

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145174	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144052	C₂	1	2	yes	maximal, complemented
3	#19143561	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134164	C₂	1	2	yes	maximal, complemented
5	#19134157	C₂	1	2	yes	maximal, complemented
6	#19134114	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134109	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134080	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134075	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133245	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	—	2	2	no	—
13	#14583449	C₂²	1	2	yes	—
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	#14583304	C₂²	1	1	yes	characteristic
16	#14583276	C₂²	1	1	yes	characteristic
17	#14583246	C₂²	1	2	yes	—
18	#14583135	—	2	1	no	—
19	#14583135	—	2	1	no	—
20	#14583122	—	2	2	no	—
21	#14583115	—	2	2	no	—
22	#14583110	C₂²	1	2	yes	—
23	#14583105	C₂²	1	2	yes	—
24	#14583100	C₂²	1	2	yes	—
25	#14583095	C₂²	1	2	yes	—
26	#14583029	C₂²	1	1	yes	characteristic
27	#14583029	C₂²	1	1	yes	characteristic
28	C₄×D₃₄₄	—	2	1	no	—
29	C₄×D₃₄₄	—	2	1	no	—
30	#14582978	C₂²	1	1	yes	characteristic
31	#14582978	C₂²	1	1	yes	characteristic
32	#14582970	—	2	1	no	—
33	#14582970	—	2	1	no	—
34	#14582952	C₂²	1	1	yes	characteristic
35	#14582950	—	2	1	no	—
36	#14582896	—	2	2	no	—
37	C₄×#10621872	—	2	1	no	—
38	#14582646	C₂²	1	2	yes	—
39	#14582646	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	#14582642	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄₃×#334	C₂²	1	1	yes	characteristic
45	C₄₃×#334	C₂²	1	1	yes	characteristic
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	2	no	—
48	C₂×#10621898	D₄	1	1	yes	characteristic
49	#13063347	—	4	8	no	—
50	C₂×Dic₁₇₂	—	2	2	no	—
51	C₂×#10621873	—	2	2	no	—
52	C₂×#10621873	—	2	2	no	—
53	C₂×D₃₄₄	—	2	2	no	—
54	C₂×D₃₄₄	—	2	1	no	—
55	C₂×D₃₄₄	—	2	1	no	—
56	C₂×#10621872	—	2	1	no	—
57	C₂×#10621872	—	2	1	no	—
58	#13063325	C₂³	1	2	yes	—
59	#13063322	C₂³	1	2	yes	—
60	#13063313	—	2	2	no	—
61	#13063299	—	2	2	no	—
62	#13063299	—	2	2	no	—
63	C₄×Dic₈₆	D₄	1	1	yes	characteristic
64	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
65	C₄×D₁₇₂	—	2	2	no	—
66	C₄×D₁₇₂	—	2	2	no	—
67	C₄×D₁₇₂	D₄	1	1	yes	characteristic
68	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
69	C₄×C₂²⋊D₄₃	—	2	1	no	—
70	C₄×C₂²⋊D₄₃	—	2	1	no	—
71	#13063284	D₄	1	1	yes	characteristic
72	#13063282	—	2	1	no	—
73	C₄²×D₄₃	—	2	1	no	—
74	#13063259	—	2	1	no	—
75	#13063259	—	2	1	no	—
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₄₃⋊C₈	—	2	1	no	—
79	Dic₄₃⋊C₈	—	2	1	no	—
80	#13063250	—	2	2	no	—
81	#13063250	—	2	2	no	—
82	#13063247	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	#13063247	—	2	2	no	—
86	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
87	(C₂×D₄₃)⋊C₈	—	2	1	no	—
88	(C₂×D₄₃)⋊C₈	—	2	1	no	—
89	#13063235	—	2	1	no	—
90	#13063235	—	2	1	no	—
91	C₄×C₄₃⋊C₈	—	2	1	no	—
92	C₂²×C₈×C₄₃	—	2	2	no	—
93	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	—	2	2	no	—
97	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
98	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
99	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₃	—	2	1	no	—
107	C₂×C₂²⋊D₄₃	—	4	2	no	—
108	#10621898	—	2	4	no	—
109	#10621898	—	4	4	no	—
110	#10621898	—	4	4	no	—
111	C₂×D₁₇₂	—	2	2	no	—
112	C₂×D₁₇₂	—	2	2	no	—
113	C₂×D₁₇₂	—	2	2	no	—
114	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	2	1	no	—
117	C₂×C₄×D₄₃	—	2	1	no	—
118	C₂×C₄×D₄₃	—	4	2	no	—
119	C₂×Dic₈₆	—	2	2	no	—
120	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	4	1	no	—
125	C₂×C₈×C₄₃	—	4	4	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	#41	1	1	yes	characteristic
133	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₂²⋊Dic₄₃	—	2	1	no	—
135	(C₂×D₄₃)⋊C₄	—	2	1	no	—
136	(C₂×D₄₃)⋊C₄	—	2	1	no	—
137	(C₂×D₄₃)⋊C₄	—	4	2	no	—
138	(C₂×D₄₃)⋊C₄	—	4	2	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	2	no	—
141	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
142	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
143	Dic₄₃⋊C₄	—	2	1	no	—
144	Dic₄₃⋊C₄	—	2	1	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	Dic₁₇₂	—	4	4	no	—
151	D₃₄₄	—	4	2	no	—
152	D₃₄₄	—	4	4	no	—
153	D₃₄₄	—	4	2	no	—
154	#10621873	—	4	4	no	—
155	#10621873	—	4	4	no	—
156	#10621872	—	4	2	no	—
157	#10621872	—	4	2	no	—
158	C₂³×C₄₃	#121	1	1	yes	characteristic
159	C₂²×D₄₃	—	2	1	no	—
160	C₂²×D₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	4	1	no	—
164	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
167	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₄₃	—	4	2	no	—
172	C₂²⋊D₄₃	—	8	4	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	—	2	1	no	—
175	C₂×Dic₄₃	—	2	1	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	D₁₇₂	—	2	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	4	2	no	—
182	D₁₇₂	—	8	2	no	—
183	C₄×D₄₃	—	4	2	no	—
184	C₄×D₄₃	—	4	1	no	—
185	C₄×D₄₃	—	4	1	no	—
186	C₄×D₄₃	—	4	2	no	—
187	C₄×D₄₃	—	8	4	no	—
188	Dic₈₆	—	2	2	no	—
189	Dic₈₆	—	4	2	no	—
190	Dic₈₆	—	4	2	no	—
191	C₈×C₄₃	—	2	1	no	—
192	C₈×C₄₃	—	2	1	no	—
193	C₈×C₄₃	—	2	1	no	—
194	C₈×C₄₃	—	4	2	no	—
195	C₈×C₄₃	—	4	2	no	—
196	C₈×C₄₃	#135	1	2	yes	complemented
197	C₄₃⋊C₈	—	4	1	no	—
198	C₄₃⋊C₈	—	4	1	no	—
199	#19157	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	#469	1	2	yes	—
203	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₂×D₄₃	—	4	1	no	—
205	C₂×D₄₃	—	4	1	no	—
206	C₂×D₄₃	—	4	1	no	—
207	C₂×D₄₃	—	8	2	no	—
208	C₂×D₄₃	—	8	2	no	—
209	C₂×D₄₃	—	8	2	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	#469	1	2	yes	—
214	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
215	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
216	C₄×C₄₃	#575	1	1	yes	characteristic
217	Dic₄₃	—	4	1	no	—
218	Dic₄₃	—	4	1	no	—
219	Dic₄₃	—	4	1	no	—
220	Dic₄₃	—	8	2	no	—
221	#3169	—	43	1	no	—
222	#3035	—	43	2	no	—
223	#2965	—	43	1	no	—
224	#1702	—	43	2	no	—
225	#1701	—	43	2	no	—
226	#1694	—	43	1	no	—
227	#1693	—	43	1	no	—
228	#1688	—	43	1	no	—
229	#1687	—	43	1	no	—
230	C₂×#334	D₄₃	1	1	yes	characteristic, complemented
231	#1540	—	43	2	no	—
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	#3035	1	1	yes	characteristic
234	C₂×C₄₃	C₂×#469	1	1	yes	characteristic
235	C₂×C₄₃	#3067	1	1	yes	characteristic
236	D₄₃	—	8	1	no	—
237	D₄₃	—	16	2	no	—
238	C₂×#135	—	86	2	no	—
239	#532	—	43	2	no	—
240	C₄×#41	—	43	1	no	—
241	#500	—	43	1	no	—
242	#493	—	43	1	no	—
243	#486	—	43	2	no	—
244	#466	—	86	1	no	—
245	#466	—	86	1	no	—
246	#464	—	86	2	no	—
247	#463	—	86	2	no	—
248	#462	—	43	2	no	—
249	#461	—	43	2	no	—
250	#460	—	43	2	no	—
251	#459	—	43	2	no	—
252	#446	—	43	1	no	—
253	#446	—	43	1	no	—
254	C₄×D₈	—	86	1	no	—
255	C₄×D₈	—	86	1	no	—
256	#436	—	43	1	no	—
257	#436	—	43	1	no	—
258	#435	—	86	1	no	—
259	#435	—	86	1	no	—
260	#431	—	43	1	no	—
261	#431	—	86	1	no	—
262	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	—
263	#416	—	86	2	no	—
264	C₄×M₁₆	—	86	1	no	—
265	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
266	#334	C₂×D₄₃	1	1	yes	characteristic
267	#334	C₂×D₄₃	1	1	yes	characteristic
268	#334	C₂×D₄₃	1	2	yes	—
269	#332	—	43	2	no	—
270	#332	—	43	2	no	—
271	#331	—	43	2	no	—
272	#331	—	43	2	no	—
273	C₄₃	#19157	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	43	1	no	—
275	C₂×#41	—	86	2	no	—
276	#135	—	172	8	no	—
277	C₂×Q₁₆	—	86	2	no	—
278	C₂×SD₁₆	—	86	2	no	—
279	C₂×SD₁₆	—	86	2	no	—
280	C₂×D₈	—	86	2	no	—
281	C₂×D₈	—	86	1	no	—
282	C₂×D₈	—	86	1	no	—
283	C₂×M₁₆	—	86	1	no	—
284	C₂×M₁₆	—	86	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
287	C₂²×C₈	D₁₇₂	1	1	yes	characteristic
288	C₄⋊Q₈	—	43	2	no	—
289	#127	—	43	2	no	—
290	#124	—	86	2	no	—
291	#121	—	86	2	no	—
292	#121	—	86	2	no	—
293	C₄×Q₈	—	43	1	no	—
294	C₄×Q₈	—	43	1	no	—
295	C₄×D₄	—	43	1	no	—
296	C₄×D₄	—	43	1	no	—
297	C₄×D₄	—	86	1	no	—
298	C₄×D₄	—	86	1	no	—
299	C₄×D₄	—	86	2	no	—
300	C₄×D₄	—	86	2	no	—
301	#117	—	43	1	no	—
302	#117	—	86	1	no	—
303	C₂×C₄²	—	86	1	no	—
304	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
305	#107	—	86	1	no	—
306	#107	—	86	1	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	43	1	no	—
309	C₄⋊C₈	—	43	1	no	—
310	C₄⋊C₈	—	86	1	no	—
311	C₄⋊C₈	—	86	1	no	—
312	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
313	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
314	#103	—	86	2	no	—
315	#103	—	86	2	no	—
316	#102	—	86	2	no	—
317	#102	—	86	2	no	—
318	#102	—	86	2	no	—
319	#102	—	86	2	no	—
320	C₂²⋊C₈	—	86	1	no	—
321	C₂²⋊C₈	—	86	1	no	—
322	C₂²⋊C₈	—	86	1	no	—
323	#97	—	86	1	no	—
324	#97	—	86	1	no	—
325	C₄×C₈	—	86	1	no	—
326	C₄×C₈	D₁₇₂	1	1	yes	characteristic
327	C₄×C₈	D₁₇₂	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
330	#41	—	86	4	no	—
331	#41	—	172	4	no	—
332	#41	—	172	4	no	—
333	C₂×Q₈	—	43	1	no	—
334	C₂×Q₈	—	86	2	no	—
335	C₂×D₄	—	43	1	no	—
336	C₂×D₄	—	86	1	no	—
337	C₂×D₄	—	86	2	no	—
338	C₂×D₄	—	86	2	no	—
339	C₂×D₄	—	86	2	no	—
340	C₂×D₄	—	172	2	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	172	2	no	—
345	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
347	C₂²×C₄	#10621902	1	1	yes	characteristic
348	Q₁₆	—	172	4	no	—
349	SD₁₆	—	172	4	no	—
350	SD₁₆	—	172	4	no	—
351	D₈	—	172	2	no	—
352	D₈	—	172	4	no	—
353	D₈	—	172	2	no	—
354	M₁₆	—	172	2	no	—
355	M₁₆	—	172	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	—	86	1	no	—
362	C₂×C₈	—	86	1	no	—
363	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
364	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
365	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
366	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
367	C₄⋊C₄	—	43	1	no	—
368	C₄⋊C₄	—	43	1	no	—
369	C₄⋊C₄	—	86	1	no	—
370	C₄⋊C₄	—	86	1	no	—
371	C₄⋊C₄	—	86	2	no	—
372	C₄⋊C₄	—	86	2	no	—
373	C₂²⋊C₄	—	86	1	no	—
374	C₂²⋊C₄	—	86	1	no	—
375	C₂²⋊C₄	—	86	1	no	—
376	C₂²⋊C₄	—	172	2	no	—
377	C₂²⋊C₄	—	172	2	no	—
378	C₄²	—	86	1	no	—
379	C₄²	—	86	1	no	—
380	C₄²	—	86	1	no	—
381	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
382	C₄²	D₄×D₄₃	1	1	yes	characteristic
383	C₄²	#10621902	1	1	yes	characteristic
384	C₄²	C₂³×D₄₃	1	1	yes	characteristic
385	C₂³	—	86	1	no	—
386	C₂³	—	172	2	no	—
387	C₂³	#13063300	1	1	yes	characteristic
388	Q₈	—	86	2	no	—
389	Q₈	—	172	2	no	—
390	Q₈	—	172	2	no	—
391	D₄	—	86	2	no	—
392	D₄	—	344	2	no	—
393	D₄	—	344	4	no	—
394	D₄	—	172	2	no	—
395	D₄	—	172	2	no	—
396	D₄	—	172	2	no	—
397	D₄	—	172	2	no	—
398	D₄	—	172	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	1	no	—
404	C₂×C₄	—	86	1	no	—
405	C₂×C₄	—	344	4	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	2	no	—
409	C₂×C₄	—	172	1	no	—
410	C₂×C₄	—	172	1	no	—
411	C₂×C₄	#13063300	1	1	yes	characteristic
412	C₂×C₄	#13063300	1	1	yes	characteristic
413	C₂×C₄	#13063300	1	1	yes	characteristic
414	C₂×C₄	#13063352	1	4	yes	—
415	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
417	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₈	—	172	1	no	—
424	C₈	—	172	1	no	—
425	C₈	#13063347	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	344	2	no	—
429	C₂²	—	344	2	no	—
430	C₂²	—	344	2	no	—
431	C₂²	—	172	1	no	—
432	C₂²	—	172	1	no	—
433	C₂²	—	172	1	no	—
434	C₂²	#14583153	1	2	yes	—
435	C₂²	C₂×#13063300	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	344	2	no	—
440	C₄	—	172	1	no	—
441	C₄	—	172	1	no	—
442	C₄	—	172	1	no	—
443	C₄	#14583153	1	2	yes	—
444	C₄	C₂×#13063347	1	1	yes	characteristic
445	C₄	C₂×#13063352	1	2	yes	—
446	C₄	#14583699	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	344	1	no	—
449	C₂	—	688	2	no	—
450	C₂	#19144052	1	1	yes	characteristic
451	C₂	C₂×#14583153	1	1	yes	characteristic
452	C₂	#19144316	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#334	C₂
socle	C₂²×C₄₃	C₂×#121
hypercenter	C₂×#334	D₄₃
hypocenter	C₄₃	#19157
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
1. #19145174	C₂	semidirect
2. #19144052	C₂	semidirect
3. #19143561	C₂	semidirect
4. #19134164	C₂	semidirect
5. #19134157	C₂	semidirect
6. #19134114	C₂	semidirect
7. #19134109	C₂	semidirect
8. #19134080	C₂	semidirect
9. #19134075	C₂	semidirect
10. #19133245	C₂	semidirect
11. C₂×C₄₃×#334	C₂	semidirect
196. C₈×C₄₃	#135	semidirect
230. C₂×#334	D₄₃	semidirect
273. C₄₃	#19157	semidirect
425. C₈	#13063347	semidirect

Maximal subgroups

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

subgroup	index
#19145174	2
#19144052	2
#19143561	2
#19134164	2
#19134157	2
#19134114	2
#19134109	2
#19134080	2
#19134075	2
#19133245	2
C₂×C₄₃×#334	2
#19157	43