Subgroups — #25082101

Order 11008.

608 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145746	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144404	C₂	1	1	yes	maximal, characteristic
3	#19144385	C₂	1	1	yes	maximal, characteristic
4	#19143704	C₂	1	1	yes	maximal, characteristic
5	#19134056	C₂	1	2	yes	maximal, complemented
6	#19134049	C₂	1	2	yes	maximal, complemented
7	#19133998	C₂	1	2	yes	maximal, complemented
8	#19133993	C₂	1	2	yes	maximal, complemented
9	#19133369	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#333	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583302	C₂²	1	2	yes	—
15	#14583251	C₂²	1	2	yes	—
16	#14583234	—	2	2	no	—
17	#14583207	—	2	1	no	—
18	#14583200	—	2	1	no	—
19	#14583195	C₂²	1	1	yes	characteristic
20	#14583191	—	2	1	no	—
21	#14583191	—	2	1	no	—
22	#14583191	C₂²	1	2	yes	—
23	#14583190	C₂²	1	1	yes	characteristic
24	#14583186	C₂²	1	2	yes	—
25	#14583185	C₂²	1	1	yes	characteristic
26	#14583181	—	2	1	no	—
27	#14583180	C₂²	1	1	yes	characteristic
28	#14583176	—	2	1	no	—
29	#14583023	C₂²	1	2	yes	—
30	#14582964	C₂²	1	2	yes	—
31	C₈×C₂²⋊D₄₃	—	2	2	no	—
32	#14582952	C₂²	1	1	yes	characteristic
33	#14582951	—	2	1	no	—
34	#14582939	—	2	1	no	—
35	#14582937	—	2	1	no	—
36	#14582923	C₂²	1	1	yes	characteristic
37	C₄⋊C₈×D₄₃	—	2	1	no	—
38	#14582898	—	2	1	no	—
39	#14582896	—	2	1	no	—
40	#14582651	C₂²	1	2	yes	—
41	#14582651	C₂²	1	2	yes	—
42	#14582647	C₂²	1	2	yes	—
43	#14582646	C₂²	1	2	yes	—
44	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#333	C₂²	1	2	yes	—
48	C₄₃×#333	C₂²	1	2	yes	—
49	C₂×#10621898	D₄	1	1	yes	characteristic
50	C₂×#10621877	—	2	1	no	—
51	C₂×C₈×D₄₃	—	2	2	no	—
52	#13063325	C₂³	1	1	yes	characteristic
53	#13063325	C₂³	1	1	yes	characteristic
54	#13063317	—	2	1	no	—
55	#13063304	—	2	1	no	—
56	#13063304	—	2	1	no	—
57	C₄×Dic₈₆	—	2	1	no	—
58	C₄×Dic₈₆	—	2	1	no	—
59	C₄×Dic₈₆	D₄	1	1	yes	characteristic
60	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
61	C₄×D₁₇₂	D₄	1	1	yes	characteristic
62	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
63	C₄×C₂²⋊D₄₃	—	2	1	no	—
64	C₄×C₂²⋊D₄₃	—	2	1	no	—
65	#13063284	—	2	1	no	—
66	#13063284	D₄	1	1	yes	characteristic
67	#13063282	—	2	1	no	—
68	C₄²×D₄₃	—	2	1	no	—
69	#13063259	—	2	1	no	—
70	#13063259	—	2	1	no	—
71	#13063258	—	2	2	no	—
72	#13063258	—	2	2	no	—
73	#13063258	—	2	2	no	—
74	#13063257	—	2	1	no	—
75	#13063257	—	2	1	no	—
76	#13063256	—	2	2	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
80	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
81	Dic₄₃⋊C₈	—	2	2	no	—
82	#13063250	—	2	1	no	—
83	#13063250	—	2	1	no	—
84	#13063248	—	2	2	no	—
85	#13063248	—	2	2	no	—
86	#13063248	—	2	2	no	—
87	#13063247	—	2	1	no	—
88	#13063247	—	2	1	no	—
89	#13063245	—	2	2	no	—
90	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
91	(C₂×D₄₃)⋊C₈	—	2	2	no	—
92	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
93	C₈×Dic₄₃	—	2	2	no	—
94	C₂²×Q₈×C₄₃	—	2	1	no	—
95	C₂²×C₈×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	—	2	1	no	—
97	C₄⋊Q₈×C₄₃	—	2	1	no	—
98	C₄⋊Q₈×C₄₃	—	2	1	no	—
99	C₄⋊Q₈×C₄₃	—	2	1	no	—
100	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	—	2	1	no	—
105	C₄⋊C₈×C₄₃	—	2	1	no	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
108	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	4	1	no	—
111	C₂×Q₈×C₄₃	—	8	2	no	—
112	C₂²×C₄×C₄₃	—	4	1	no	—
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₃	—	2	1	no	—
117	#10621898	—	2	2	no	—
118	#10621898	Q₁₆	1	4	yes	—
119	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₄₃	—	2	1	no	—
121	C₂×C₄×D₄₃	—	2	1	no	—
122	C₂×C₄×D₄₃	—	2	1	no	—
123	C₂×Dic₈₆	—	2	1	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	1	no	—
128	C₂×C₈×C₄₃	—	2	1	no	—
129	C₂×C₈×C₄₃	—	4	2	no	—
130	C₂×C₈×C₄₃	—	8	1	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₃	#41	1	1	yes	characteristic
138	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₄₃	—	2	1	no	—
140	C₂²⋊Dic₄₃	—	4	1	no	—
141	(C₂×D₄₃)⋊C₄	—	2	1	no	—
142	(C₂×D₄₃)⋊C₄	—	2	1	no	—
143	C₄⋊Dic₄₃	—	2	1	no	—
144	C₄⋊Dic₄₃	—	2	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
148	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
149	Dic₄₃⋊C₄	—	2	1	no	—
150	Dic₄₃⋊C₄	—	2	1	no	—
151	Dic₄₃⋊C₄	—	4	1	no	—
152	Dic₄₃⋊C₄	—	4	1	no	—
153	C₄×Dic₄₃	—	2	1	no	—
154	C₄×Dic₄₃	—	2	1	no	—
155	C₄×Dic₄₃	—	2	1	no	—
156	C₄×Dic₄₃	—	4	1	no	—
157	#10621877	—	4	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
160	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
161	C₈×D₄₃	—	8	2	no	—
162	C₂³×C₄₃	#121	1	1	yes	characteristic
163	C₂²×D₄₃	—	2	1	no	—
164	Q₈×C₄₃	—	8	2	no	—
165	Q₈×C₄₃	—	8	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	4	1	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	8	2	no	—
171	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₄₃	—	2	4	no	—
180	C₂×Dic₄₃	—	2	1	no	—
181	C₂×Dic₄₃	—	2	1	no	—
182	C₂×Dic₄₃	—	2	1	no	—
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	D₁₇₂	—	2	1	no	—
186	D₁₇₂	C₂×Q₁₆	1	2	yes	—
187	C₄×D₄₃	—	2	4	no	—
188	C₄×D₄₃	—	4	1	no	—
189	C₄×D₄₃	—	4	1	no	—
190	C₄×D₄₃	—	8	1	no	—
191	Dic₈₆	—	2	1	no	—
192	Dic₈₆	—	4	1	no	—
193	Dic₈₆	—	4	1	no	—
194	Dic₈₆	—	8	1	no	—
195	Dic₈₆	C₂×Q₁₆	1	2	yes	—
196	C₈×C₄₃	—	4	1	no	—
197	C₈×C₄₃	—	4	1	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	2	no	—
202	#19417	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	#467	1	2	yes	—
206	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	4	1	no	—
209	C₂×D₄₃	—	4	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	#467	1	2	yes	—
215	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
216	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
217	C₄×C₄₃	#577	1	1	yes	characteristic
218	C₄×C₄₃	#578	1	1	yes	characteristic
219	Dic₄₃	—	2	2	no	—
220	Dic₄₃	—	4	1	no	—
221	Dic₄₃	—	4	1	no	—
222	Dic₄₃	—	8	1	no	—
223	Dic₄₃	—	8	1	no	—
224	#3230	—	43	1	no	—
225	#3079	—	43	1	no	—
226	#3076	—	43	1	no	—
227	#2988	—	43	1	no	—
228	#1684	—	43	2	no	—
229	#1683	—	43	2	no	—
230	#1676	—	43	2	no	—
231	#1675	—	43	2	no	—
232	#1571	—	43	1	no	—
233	#1550	—	43	1	no	—
234	C₂×#333	D₄₃	1	1	yes	characteristic, complemented
235	C₂×C₄₃	—	2	2	no	—
236	C₂×C₄₃	#3046	1	1	yes	characteristic
237	C₂×C₄₃	C₂×#467	1	1	yes	characteristic
238	C₂×C₄₃	#3068	1	1	yes	characteristic
239	D₄₃	—	4	2	no	—
240	#533	—	43	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
242	C₄×#41	—	43	1	no	—
243	#500	—	43	2	no	—
244	#487	—	43	2	no	—
245	#484	—	86	2	no	—
246	#479	—	86	1	no	—
247	#478	—	86	1	no	—
248	#477	—	43	2	no	—
249	#477	—	43	1	no	—
250	#477	—	86	1	no	—
251	#477	—	86	1	no	—
252	#476	—	43	2	no	—
253	#476	—	43	1	no	—
254	#475	—	43	1	no	—
255	#475	—	86	1	no	—
256	#474	—	43	1	no	—
257	#474	—	86	1	no	—
258	C₈×Q₈	—	43	2	no	—
259	C₈×D₄	—	43	2	no	—
260	C₈×D₄	—	86	2	no	—
261	#431	—	43	1	no	—
262	#431	—	86	1	no	—
263	#428	—	86	1	no	—
264	#427	—	86	1	no	—
265	#423	—	43	1	no	—
266	C₂×C₄⋊C₈	—	86	1	no	—
267	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
269	#417	—	86	1	no	—
270	#416	—	86	1	no	—
271	#335	—	43	2	no	—
272	#335	—	43	2	no	—
273	#333	—	43	2	no	—
274	#333	C₂×D₄₃	1	2	yes	—
275	#333	C₂×D₄₃	1	2	yes	—
276	#332	—	43	2	no	—
277	C₄₃	#19417	1	1	yes	characteristic, complemented, Sylow
278	C₂×#41	—	43	1	no	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂×M₁₆	—	86	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	86	2	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	1	no	—
287	C₄⋊Q₈	—	43	1	no	—
288	C₄⋊Q₈	—	43	1	no	—
289	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
290	#125	—	86	1	no	—
291	C₂²⋊Q₈	—	86	1	no	—
292	C₂²⋊Q₈	—	86	1	no	—
293	C₄×Q₈	—	43	1	no	—
294	C₄×Q₈	—	43	1	no	—
295	C₄×Q₈	—	86	1	no	—
296	C₄×Q₈	—	86	1	no	—
297	C₄×D₄	—	43	1	no	—
298	C₄×D₄	—	43	1	no	—
299	C₄×D₄	—	86	1	no	—
300	C₄×D₄	—	86	1	no	—
301	#117	—	43	1	no	—
302	#117	—	86	1	no	—
303	#117	—	86	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄²	—	86	1	no	—
307	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
308	#107	—	86	2	no	—
309	#107	—	86	2	no	—
310	#107	—	86	2	no	—
311	#107	—	86	1	no	—
312	#107	—	86	1	no	—
313	#106	—	86	2	no	—
314	#106	—	86	1	no	—
315	#106	—	86	1	no	—
316	C₄⋊C₈	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	43	1	no	—
319	C₄⋊C₈	—	43	1	no	—
320	C₄⋊C₈	—	43	2	no	—
321	C₄⋊C₈	—	86	2	no	—
322	C₄⋊C₈	—	86	1	no	—
323	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
324	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
325	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
326	#103	—	86	2	no	—
327	#103	—	86	2	no	—
328	#103	—	86	2	no	—
329	#103	—	86	1	no	—
330	#103	—	86	1	no	—
331	#102	—	86	2	no	—
332	#102	—	86	1	no	—
333	#102	—	86	1	no	—
334	C₂²⋊C₈	—	43	2	no	—
335	C₂²⋊C₈	—	86	2	no	—
336	C₄×C₈	—	43	2	no	—
337	C₄×C₈	—	86	2	no	—
338	#41	—	43	4	no	—
339	#41	—	86	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	8	2	no	—
343	C₂×Q₈	—	43	1	no	—
344	C₂×Q₈	—	86	1	no	—
345	C₂×Q₈	—	86	1	no	—
346	C₂×D₄	—	43	1	no	—
347	C₂×D₄	—	86	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	86	1	no	—
350	C₂²×C₄	—	86	1	no	—
351	C₂²×C₄	—	86	1	no	—
352	C₂²×C₄	#10621898	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
355	M₁₆	—	172	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	4	2	no	—
360	C₂×C₈	—	8	1	no	—
361	C₂×C₈	—	43	2	no	—
362	C₂×C₈	—	43	2	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	344	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	43	1	no	—
370	C₄⋊C₄	—	43	1	no	—
371	C₄⋊C₄	—	86	1	no	—
372	C₄⋊C₄	—	86	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	—	86	1	no	—
377	C₄⋊C₄	—	172	1	no	—
378	C₄⋊C₄	—	172	1	no	—
379	C₂²⋊C₄	—	86	1	no	—
380	C₂²⋊C₄	—	86	1	no	—
381	C₂²⋊C₄	—	86	1	no	—
382	C₂²⋊C₄	—	172	1	no	—
383	C₄²	—	86	1	no	—
384	C₄²	—	86	1	no	—
385	C₄²	—	86	1	no	—
386	C₄²	—	172	1	no	—
387	C₄²	#10621898	1	1	yes	characteristic
388	C₄²	D₄×D₄₃	1	1	yes	characteristic
389	C₄²	D₄×D₄₃	1	1	yes	characteristic
390	C₄²	C₂³×D₄₃	1	1	yes	characteristic
391	C₂³	—	86	1	no	—
392	C₂³	#13063298	1	1	yes	characteristic
393	Q₈	—	8	2	no	—
394	Q₈	—	8	2	no	—
395	Q₈	—	43	2	no	—
396	Q₈	—	86	1	no	—
397	Q₈	—	344	1	no	—
398	Q₈	—	172	1	no	—
399	Q₈	—	172	1	no	—
400	D₄	—	43	2	no	—
401	D₄	—	86	4	no	—
402	D₄	—	86	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	86	1	no	—
409	C₂×C₄	—	86	4	no	—
410	C₂×C₄	—	86	1	no	—
411	C₂×C₄	—	86	1	no	—
412	C₂×C₄	—	344	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	1	no	—
417	C₂×C₄	#13063298	1	1	yes	characteristic
418	C₂×C₄	#13063298	1	1	yes	characteristic
419	C₂×C₄	#13063298	1	1	yes	characteristic
420	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
421	C₂×C₄	#13063346	1	2	yes	—
422	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
423	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
424	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
425	C₈	—	4	1	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₈	—	86	2	no	—
429	C₈	—	86	2	no	—
430	C₈	—	172	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	86	2	no	—
434	C₂²	—	172	1	no	—
435	C₂²	—	172	1	no	—
436	C₂²	#14583139	1	2	yes	—
437	C₂²	C₂×#13063298	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	86	2	no	—
443	C₄	—	344	1	no	—
444	C₄	—	344	1	no	—
445	C₄	—	172	1	no	—
446	C₄	—	172	1	no	—
447	C₄	#14583139	1	2	yes	—
448	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
449	C₄	C₂×#13063346	1	1	yes	characteristic
450	C₄	#14583705	1	1	yes	characteristic
451	C₄	#14583712	1	1	yes	characteristic
452	C₂	—	2	2	no	—
453	C₂	—	172	2	no	—
454	C₂	#19144150	1	1	yes	characteristic
455	C₂	C₂×#14583139	1	1	yes	characteristic
456	C₂	#19144322	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063298
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₂×C₄₃×#333	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#10621898	D₄
hypercenter	C₂×#333	D₄₃
hypocenter	C₄₃	#19417
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
1. #19145746	C₂	semidirect
5. #19134056	C₂	semidirect
6. #19134049	C₂	semidirect
7. #19133998	C₂	semidirect
8. #19133993	C₂	semidirect
9. #19133369	C₂	semidirect
10. #19133283	C₂	semidirect
11. C₂×C₄₃×#333	C₂	semidirect
234. C₂×#333	D₄₃	semidirect
277. C₄₃	#19417	semidirect

Maximal subgroups

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

subgroup	index
#19145746	2
#19144404	2
#19144385	2
#19143704	2
#19134056	2
#19134049	2
#19133998	2
#19133993	2
#19133369	2
#19133283	2
C₂×C₄₃×#333	2
#19417	43