Subgroups — #25103512

Order 11008.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583175	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063358	C₂	1	2	yes	maximal
3	C₂×#14583007	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143020	C₂	1	1	yes	maximal, characteristic
5	#19135508	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135376	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135251	C₂	1	2	yes	maximal, complemented
8	#19135109	C₂	1	2	yes	maximal
9	#19134651	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063243	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	C₂²	1	2	yes	—
13	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic
14	C₂×#13063331	C₂²	1	1	yes	characteristic
15	C₂×#13063331	C₂²	1	1	yes	characteristic
16	C₄×#10621898	C₂²	1	1	yes	characteristic
17	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
18	#14583175	C₄	1	8	yes	complemented
19	#14583007	—	2	2	no	—
20	#14583007	—	2	1	no	—
21	#14583007	—	2	1	no	—
22	#14583007	—	2	1	no	—
23	#14583007	—	2	1	no	—
24	#14583001	—	2	2	no	—
25	C₄×Dic₁₇₂	—	2	2	no	—
26	C₄×#10621873	—	2	2	no	—
27	#14582941	C₂²	1	2	yes	—
28	C₂×#13063257	C₂²	1	1	yes	characteristic
29	#14582909	C₂²	1	2	yes	—
30	#14582901	C₂²	1	2	yes	—
31	C₂×#13063250	C₂²	1	2	yes	—
32	C₂×#13063243	C₂²	1	2	yes	—
33	C₂×#13063243	C₂²	1	2	yes	—
34	#14582856	—	2	1	no	—
35	#14582856	—	2	1	no	—
36	#14582854	C₂²	1	1	yes	characteristic
37	#14582854	C₂²	1	1	yes	characteristic
38	C₄×#10621877	C₂²	1	1	yes	characteristic
39	#14582851	—	2	1	no	—
40	#97×D₄₃	—	2	1	no	—
41	#14582667	C₂²	1	2	yes	—
42	#14582667	C₂²	1	2	yes	—
43	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	2	yes	—
46	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#341	C₂²	1	2	yes	—
48	C₂×#10621898	C₂³	1	1	yes	characteristic
49	C₂²×Dic₈₆	C₂³	1	2	yes	—
50	#13063358	—	2	4	no	—
51	#13063358	C₂×C₄	1	8	yes	—
52	C₂×Dic₁₇₂	—	2	2	no	—
53	C₂×Dic₁₇₂	—	2	1	no	—
54	C₂×Dic₁₇₂	—	2	1	no	—
55	C₂×Dic₁₇₂	—	2	2	no	—
56	C₂×Dic₁₇₂	C₂×C₄	1	4	yes	complemented
57	C₂×#10621873	—	2	2	no	—
58	#13063331	—	2	2	no	—
59	#13063331	—	2	2	no	—
60	#13063331	—	2	2	no	—
61	#13063331	C₂×C₄	1	4	yes	—
62	C₂×#10621877	C₂³	1	1	yes	characteristic
63	C₂×#10621877	C₂³	1	1	yes	characteristic
64	C₂×#10621872	—	2	1	no	—
65	C₂×#10621872	—	2	1	no	—
66	C₂×C₈×D₄₃	—	2	1	no	—
67	C₂×C₈×D₄₃	—	2	1	no	—
68	C₄×Dic₈₆	—	2	2	no	—
69	C₄×Dic₈₆	—	2	2	no	—
70	C₄×Dic₈₆	—	2	2	no	—
71	C₄×Dic₈₆	—	2	2	no	—
72	C₄×Dic₈₆	D₄	1	2	yes	—
73	C₄×D₁₇₂	D₄	1	2	yes	—
74	C₄×C₂²⋊D₄₃	—	2	2	no	—
75	#13063284	C₂³	1	1	yes	characteristic
76	#13063282	—	2	1	no	—
77	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
78	C₂×Dic₄₃⋊C₄	—	2	2	no	—
79	C₂×C₄×Dic₄₃	—	2	2	no	—
80	C₄²×D₄₃	—	2	1	no	—
81	#13063259	—	2	2	no	—
82	#13063257	—	2	1	no	—
83	#13063257	—	2	1	no	—
84	#13063257	—	2	2	no	—
85	#13063250	—	2	2	no	—
86	#13063250	—	2	2	no	—
87	#13063250	—	2	2	no	—
88	#13063250	—	2	2	no	—
89	#13063250	—	2	2	no	—
90	#13063247	—	2	2	no	—
91	#13063243	—	2	4	no	—
92	#13063243	C₂×C₄	1	8	yes	complemented
93	#13063236	—	2	1	no	—
94	#13063235	—	2	1	no	—
95	#13063235	—	2	1	no	—
96	C₄×C₄₃⋊C₈	—	2	1	no	—
97	C₈×Dic₄₃	—	2	1	no	—
98	C₈×Dic₄₃	—	2	1	no	—
99	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#108×C₄₃	—	2	2	no	—
105	#108×C₄₃	C₂×C₄	1	4	yes	complemented
106	#97×C₄₃	—	2	2	no	—
107	#97×C₄₃	D₄	1	1	yes	characteristic
108	#97×C₄₃	D₄	1	1	yes	characteristic
109	#97×C₄₃	D₄	1	1	yes	characteristic
110	#97×C₄₃	D₄	1	1	yes	characteristic
111	C₄×C₈×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	#41	1	2	yes	—
113	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₃	—	2	1	no	—
115	C₂²×Dic₄₃	—	2	2	no	—
116	C₂²×Dic₄₃	—	2	2	no	—
117	#10621898	—	2	1	no	—
118	#10621898	—	2	1	no	—
119	#10621898	C₂²×C₄	1	2	yes	—
120	#10621898	#41	1	2	yes	—
121	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₄₃	—	2	1	no	—
123	C₂×C₄×D₄₃	—	2	2	no	—
124	C₂×Dic₈₆	—	2	2	no	—
125	C₂×Dic₈₆	—	2	2	no	—
126	C₂×Dic₈₆	—	2	2	no	—
127	C₂×Dic₈₆	—	2	2	no	—
128	C₂×Dic₈₆	—	2	2	no	—
129	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
130	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
131	M₁₆×C₄₃	—	2	2	no	—
132	M₁₆×C₄₃	—	2	2	no	—
133	M₁₆×C₄₃	—	2	2	no	—
134	M₁₆×C₄₃	C₂²×C₄	1	4	yes	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₂×C₈×C₄₃	—	2	1	no	—
138	C₂×C₈×C₄₃	—	2	2	no	—
139	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₄₃	#41	1	2	yes	—
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂×D₄	1	2	yes	—
148	C₂²⋊Dic₄₃	—	2	1	no	—
149	(C₂×D₄₃)⋊C₄	—	2	2	no	—
150	C₄⋊Dic₄₃	—	2	2	no	—
151	C₄⋊Dic₄₃	—	2	2	no	—
152	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
153	Dic₄₃⋊C₄	—	2	2	no	—
154	Dic₄₃⋊C₄	—	4	2	no	—
155	Dic₄₃⋊C₄	—	4	2	no	—
156	C₄×Dic₄₃	—	2	2	no	—
157	C₄×Dic₄₃	—	2	1	no	—
158	C₄×Dic₄₃	—	4	2	no	—
159	C₄×Dic₄₃	—	4	2	no	—
160	#10621877	—	2	1	no	—
161	#10621877	—	2	1	no	—
162	#10621877	C₂²×C₄	1	2	yes	—
163	#10621877	#41	1	2	yes	—
164	C₂×C₄₃⋊C₈	—	2	1	no	—
165	C₂×C₄₃⋊C₈	—	2	1	no	—
166	Dic₁₇₂	—	2	8	no	—
167	Dic₁₇₂	—	2	4	no	—
168	Dic₁₇₂	—	2	4	no	—
169	#10621873	—	2	8	no	—
170	#10621872	—	2	4	no	—
171	#10621872	—	2	4	no	—
172	C₈×D₄₃	—	2	4	no	—
173	C₈×D₄₃	—	2	4	no	—
174	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²×D₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	#121	1	2	yes	—
178	C₂×C₄×C₄₃	#121	1	2	yes	—
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂²⋊D₄₃	—	2	2	no	—
186	C₂²⋊D₄₃	—	2	2	no	—
187	C₂×Dic₄₃	—	2	1	no	—
188	C₂×Dic₄₃	—	2	4	no	—
189	C₂×Dic₄₃	—	2	2	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	8	2	no	—
194	D₁₇₂	—	2	1	no	—
195	D₁₇₂	C₄×D₄	1	2	yes	—
196	C₄×D₄₃	—	2	2	no	—
197	C₄×D₄₃	—	2	2	no	—
198	C₄×D₄₃	—	8	2	no	—
199	Dic₈₆	—	2	1	no	—
200	Dic₈₆	—	2	4	no	—
201	Dic₈₆	—	2	4	no	—
202	Dic₈₆	—	4	2	no	—
203	Dic₈₆	—	4	2	no	—
204	Dic₈₆	C₄×D₄	1	2	yes	—
205	C₈×C₄₃	—	2	4	no	—
206	C₈×C₄₃	—	2	1	no	—
207	C₈×C₄₃	—	2	1	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	C₄×D₄	1	2	yes	—
210	C₈×C₄₃	C₄×D₄	1	2	yes	—
211	C₄₃⋊C₈	—	2	2	no	—
212	C₄₃⋊C₈	—	2	2	no	—
213	#21556	—	43	1	no	maximal, Sylow
214	C₂²×C₄₃	—	2	2	no	—
215	C₂²×C₄₃	C₄×#41	1	1	yes	characteristic
216	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
217	C₂²×C₄₃	#529	1	1	yes	characteristic
218	C₂×D₄₃	—	2	2	no	—
219	C₂×D₄₃	—	4	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	2	2	no	—
222	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
223	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
224	C₄×C₄₃	#525	1	1	yes	characteristic
225	C₄×C₄₃	#532	1	1	yes	characteristic
226	Dic₄₃	—	2	2	no	—
227	Dic₄₃	—	4	4	no	—
228	Dic₄₃	—	4	2	no	—
229	Dic₄₃	—	8	2	no	—
230	C₂×#473	—	43	1	no	—
231	C₄×#137	—	43	2	no	—
232	C₂×#441	—	43	1	no	—
233	#2875	—	43	1	no	—
234	#1979	—	43	1	no	—
235	#1951	—	43	1	no	—
236	#1930	—	43	2	no	—
237	#1908	—	43	2	no	—
238	#1815	—	43	1	no	—
239	#1778	D₄₃	1	1	yes	characteristic, complemented
240	C₄×#101	—	43	2	no	—
241	C₂×C₄₃	—	2	1	no	—
242	C₂×C₄₃	—	2	1	no	—
243	C₂×C₄₃	C₄×#121	1	1	yes	characteristic
244	C₂×C₄₃	#3069	1	2	yes	—
245	D₄₃	—	4	2	no	—
246	C₂×#137	—	43	2	no	—
247	C₂²×Q₁₆	—	43	1	no	—
248	C₂×#131	—	43	1	no	—
249	C₂×#131	—	43	1	no	—
250	C₄×#41	—	43	1	no	—
251	C₂×C₄×Q₈	—	43	2	no	—
252	#473	—	43	8	no	—
253	#441	—	86	2	no	—
254	#441	—	86	1	no	—
255	#441	—	86	1	no	—
256	#441	—	86	1	no	—
257	#441	—	86	1	no	—
258	#440	—	86	2	no	—
259	C₄×Q₁₆	—	86	2	no	—
260	C₄×SD₁₆	—	86	2	no	—
261	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
262	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
263	#428	—	43	2	no	—
264	C₂×#106	—	43	1	no	—
265	#419	—	43	2	no	—
266	#417	—	43	2	no	—
267	C₂×#103	—	43	2	no	—
268	C₂×#101	—	43	2	no	—
269	C₂×#101	—	43	2	no	—
270	#405	—	43	1	no	—
271	#405	—	43	1	no	—
272	#405	—	86	1	no	—
273	#405	—	86	1	no	—
274	C₄×M₁₆	—	43	1	no	—
275	C₄×M₁₆	—	86	1	no	—
276	C₄×M₁₆	C₂×D₄₃	1	2	yes	—
277	C₂×#97	—	86	1	no	—
278	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
279	#343	—	43	2	no	—
280	#343	—	43	2	no	—
281	#341	C₂×D₄₃	1	2	yes	—
282	C₄₃	#21556	1	1	yes	characteristic, complemented, Sylow
283	C₂×#41	—	43	1	no	—
284	C₂²×Q₈	—	43	2	no	—
285	#137	—	43	8	no	—
286	#137	—	86	4	no	—
287	C₂×Q₁₆	—	43	4	no	—
288	C₂×Q₁₆	—	86	2	no	—
289	C₂×Q₁₆	—	86	1	no	—
290	C₂×Q₁₆	—	86	1	no	—
291	C₂×Q₁₆	—	86	2	no	—
292	C₂×SD₁₆	—	86	2	no	—
293	#131	—	43	4	no	—
294	#131	—	86	2	no	—
295	#131	—	86	2	no	—
296	#131	—	86	2	no	—
297	C₂×M₁₆	—	43	1	no	—
298	C₂×M₁₆	—	43	1	no	—
299	C₂×M₁₆	—	86	1	no	—
300	C₂×M₁₆	—	86	1	no	—
301	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
302	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
303	C₂²×C₈	—	86	1	no	—
304	C₂²×C₈	—	86	1	no	—
305	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
307	C₄×Q₈	—	43	2	no	—
308	C₄×Q₈	—	86	2	no	—
309	C₄×Q₈	—	86	2	no	—
310	C₄×Q₈	—	86	2	no	—
311	C₄×Q₈	—	86	2	no	—
312	C₄×D₄	—	43	2	no	—
313	C₄×D₄	—	86	2	no	—
314	#117	—	43	1	no	—
315	#117	—	86	1	no	—
316	C₂×C₄⋊C₄	—	43	2	no	—
317	C₂×C₄⋊C₄	—	86	2	no	—
318	C₂×C₄²	—	86	1	no	—
319	C₂×C₄²	—	86	2	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#108	—	2	2	no	—
322	#108	C₄×D₄₃	1	4	yes	complemented
323	#107	—	86	2	no	—
324	#106	—	86	2	no	—
325	#106	—	86	1	no	—
326	#106	—	86	1	no	—
327	#103	—	86	2	no	—
328	#103	—	86	2	no	—
329	#103	—	86	2	no	—
330	#103	—	86	2	no	—
331	#103	—	86	2	no	—
332	#102	—	86	2	no	—
333	#101	—	43	8	no	—
334	#101	—	86	4	no	—
335	#97	—	2	2	no	—
336	#97	—	86	1	no	—
337	#97	—	86	1	no	—
338	#97	—	86	1	no	—
339	#97	D₁₇₂	1	1	yes	characteristic
340	#97	D₁₇₂	1	1	yes	characteristic
341	#97	D₁₇₂	1	1	yes	characteristic
342	#97	D₁₇₂	1	1	yes	characteristic
343	C₄×C₈	—	2	2	no	—
344	C₄×C₈	—	86	1	no	—
345	C₄×C₈	—	86	1	no	—
346	C₄×C₈	—	86	1	no	—
347	#41	—	43	2	no	—
348	#41	—	43	2	no	—
349	#41	—	86	1	no	—
350	#41	—	86	1	no	—
351	C₂×Q₈	—	43	4	no	—
352	C₂×Q₈	—	43	1	no	—
353	C₂×Q₈	—	86	2	no	—
354	C₂×Q₈	—	86	2	no	—
355	C₂×Q₈	—	86	2	no	—
356	C₂×Q₈	—	86	2	no	—
357	C₂×Q₈	—	86	2	no	—
358	C₂×D₄	—	43	1	no	—
359	C₂×D₄	—	86	1	no	—
360	C₂²×C₄	—	86	1	no	—
361	C₂²×C₄	—	86	2	no	—
362	C₂²×C₄	—	86	2	no	—
363	C₂²×C₄	—	86	2	no	—
364	C₂²×C₄	#10621902	1	2	yes	—
365	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
366	Q₁₆	—	86	8	no	—
367	Q₁₆	—	86	4	no	—
368	Q₁₆	—	86	4	no	—
369	SD₁₆	—	86	8	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	43	2	no	—
374	M₁₆	—	43	2	no	—
375	M₁₆	—	86	4	no	—
376	M₁₆	—	86	1	no	—
377	M₁₆	—	86	1	no	—
378	M₁₆	—	86	4	no	—
379	M₁₆	C₂×C₄×D₄₃	1	4	yes	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	86	4	no	—
385	C₂×C₈	—	86	1	no	—
386	C₂×C₈	—	86	1	no	—
387	C₂×C₈	—	86	4	no	—
388	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
389	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
390	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
391	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
392	C₂×C₈	C₂×D₁₇₂	1	1	yes	characteristic
393	C₂×C₈	#10621898	1	2	yes	—
394	C₄⋊C₄	—	43	2	no	—
395	C₄⋊C₄	—	86	2	no	—
396	C₄⋊C₄	—	86	2	no	—
397	C₄⋊C₄	—	86	2	no	—
398	C₄⋊C₄	—	172	2	no	—
399	C₄⋊C₄	—	172	2	no	—
400	C₂²⋊C₄	—	86	1	no	—
401	C₂²⋊C₄	—	86	2	no	—
402	C₄²	—	86	2	no	—
403	C₄²	—	86	1	no	—
404	C₄²	—	172	2	no	—
405	C₄²	—	172	2	no	—
406	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
407	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
408	C₄²	D₄×D₄₃	1	2	yes	—
409	C₂³	—	86	1	no	—
410	C₂³	C₂×#10621902	1	1	yes	characteristic
411	Q₈	—	43	2	no	—
412	Q₈	—	86	1	no	—
413	Q₈	—	86	4	no	—
414	Q₈	—	86	4	no	—
415	Q₈	—	172	2	no	—
416	Q₈	—	172	2	no	—
417	D₄	—	43	2	no	—
418	D₄	—	86	2	no	—
419	D₄	—	86	2	no	—
420	D₄	—	86	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	86	1	no	—
423	C₂×C₄	—	86	2	no	—
424	C₂×C₄	—	86	2	no	—
425	C₂×C₄	—	86	4	no	—
426	C₂×C₄	—	86	2	no	—
427	C₂×C₄	—	344	2	no	—
428	C₂×C₄	—	344	2	no	—
429	C₂×C₄	—	172	2	no	—
430	C₂×C₄	—	172	2	no	—
431	C₂×C₄	—	172	2	no	—
432	C₂×C₄	#13063300	1	2	yes	—
433	C₂×C₄	#13063300	1	2	yes	—
434	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
437	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
438	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
439	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
440	C₈	—	2	4	no	—
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	4	2	no	—
444	C₈	—	86	2	no	—
445	C₈	—	86	2	no	—
446	C₈	C₄×D₁₇₂	1	2	yes	—
447	C₈	C₄×D₁₇₂	1	2	yes	—
448	C₂²	—	2	2	no	—
449	C₂²	—	86	2	no	—
450	C₂²	—	172	2	no	—
451	C₂²	C₄×#10621902	1	1	yes	characteristic
452	C₂²	C₂×#13063300	1	1	yes	characteristic
453	C₂²	#14583436	1	1	yes	characteristic
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	86	2	no	—
457	C₄	—	344	2	no	—
458	C₄	—	172	4	no	—
459	C₄	—	172	2	no	—
460	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
461	C₄	C₂×C₄×D₁₇₂	1	1	yes	characteristic
462	C₄	#14583411	1	1	yes	characteristic
463	C₄	#14583446	1	1	yes	characteristic
464	C₂	—	2	1	no	—
465	C₂	—	2	1	no	—
466	C₂	—	172	2	no	—
467	C₂	C₄×#13063300	1	1	yes	characteristic
468	C₂	#19144333	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1778	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1778	D₄₃
hypocenter	C₄₃	#21556
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1778

Complements

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

N	H ≅ G/N	type
3. C₂×#14583007	C₂	semidirect
5. #19135508	C₂	semidirect
6. #19135376	C₂	semidirect
7. #19135251	C₂	semidirect
10. C₄×#13063243	C₂	semidirect
11. C₄₃×#1778	C₂	semidirect
18. #14583175	C₄	semidirect
56. C₂×Dic₁₇₂	C₂×C₄	semidirect
92. #13063243	C₂×C₄	semidirect
105. #108×C₄₃	C₂×C₄	semidirect
239. #1778	D₄₃	semidirect
282. C₄₃	#21556	semidirect
322. #108	C₄×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583175	2
C₄×#13063358	2
C₂×#14583007	2
#19143020	2
#19135508	2
#19135376	2
#19135251	2
#19135109	2
#19134651	2
C₄×#13063243	2
C₄₃×#1778	2
#21556	43