Subgroups — #25147007

Order 11008.

732 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	#19144989	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583185	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144069	C₂	1	1	yes	maximal, characteristic
4	#19143338	C₂	1	1	yes	maximal, characteristic
5	#19136042	C₂	1	2	yes	maximal, complemented
6	#19135896	C₂	1	2	yes	maximal, complemented
7	#19135583	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135109	C₂	1	2	yes	maximal, complemented
9	#19134651	C₂	1	2	yes	maximal, complemented
10	C₄×#13063243	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	C₂²	1	2	yes	—
13	C₂×#13063331	C₂²	1	2	yes	—
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
17	#14583259	—	2	2	no	—
18	#14583250	—	2	1	no	—
19	#14583246	—	2	1	no	—
20	#14583185	—	2	1	no	—
21	#14583185	—	2	2	no	—
22	#14583185	—	2	1	no	—
23	#14583122	—	2	2	no	—
24	#14583110	—	2	1	no	—
25	#14583100	—	2	1	no	—
26	#14582976	—	2	1	no	—
27	#14582969	—	2	2	no	—
28	#14582964	—	2	1	no	—
29	C₂×#13063257	C₂²	1	2	yes	—
30	#14582901	C₂²	1	2	yes	—
31	#14582901	C₂²	1	2	yes	—
32	#14582901	C₂²	1	2	yes	—
33	C₂×#13063250	C₂²	1	2	yes	—
34	C₂×#13063243	C₂²	1	1	yes	characteristic
35	C₂×#13063243	C₂²	1	1	yes	characteristic
36	#14582865	C₂²	1	2	yes	—
37	C₄×#10621877	C₂²	1	1	yes	characteristic
38	#14582667	C₂²	1	1	yes	characteristic
39	#14582667	C₂²	1	2	yes	—
40	#14582667	C₂²	1	2	yes	—
41	#14582667	C₂²	1	1	yes	characteristic
42	C₂×#108×C₄₃	C₂²	1	2	yes	—
43	C₄₃×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₄₃×#341	C₂²	1	2	yes	—
47	C₂×#10621898	C₂³	1	2	yes	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
50	#13063358	—	2	4	no	—
51	#13063358	—	4	2	no	—
52	C₂×Dic₁₇₂	—	2	2	no	—
53	C₂×#10621873	—	2	2	no	—
54	#13063331	—	2	4	no	—
55	#13063331	—	4	2	no	—
56	C₂×#10621877	C₂³	1	1	yes	characteristic
57	C₂×#10621877	C₂³	1	1	yes	characteristic
58	C₂×#10621872	—	2	2	no	—
59	C₂×C₈×D₄₃	—	2	2	no	—
60	#13063325	—	2	1	no	—
61	#13063325	—	2	1	no	—
62	#13063325	—	2	1	no	—
63	#13063325	—	2	1	no	—
64	#13063325	D₄	1	1	yes	characteristic
65	#13063322	D₄	1	1	yes	characteristic
66	#13063313	D₄	1	2	yes	—
67	#13063299	—	2	1	no	—
68	#13063299	—	2	1	no	—
69	C₄×Dic₈₆	—	2	1	no	—
70	C₄×Dic₈₆	—	2	1	no	—
71	C₄×Dic₈₆	—	2	1	no	—
72	C₄×Dic₈₆	—	2	1	no	—
73	C₄×D₁₇₂	—	2	1	no	—
74	C₄×D₁₇₂	—	2	1	no	—
75	C₂×C₄⋊Dic₄₃	—	2	1	no	—
76	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
78	C₂×Dic₄₃⋊C₄	—	2	1	no	—
79	C₂×C₄×Dic₄₃	—	2	1	no	—
80	#13063257	—	2	2	no	—
81	#13063257	—	2	2	no	—
82	#13063250	—	2	2	no	—
83	#13063250	—	2	2	no	—
84	#13063250	—	2	2	no	—
85	#13063250	—	2	2	no	—
86	#13063250	—	2	2	no	—
87	#13063247	—	2	2	no	—
88	#13063247	—	2	2	no	—
89	#13063247	—	2	2	no	—
90	#13063243	—	2	2	no	—
91	#13063243	—	2	2	no	—
92	(C₂×D₄₃)⋊C₈	—	2	2	no	—
93	(C₂×D₄₃)⋊C₈	—	2	2	no	—
94	#13063236	—	2	1	no	—
95	C₄×C₄₃⋊C₈	—	2	1	no	—
96	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
97	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
98	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
99	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	#108×C₄₃	—	4	2	no	—
102	C₄⋊C₈×C₄₃	—	2	1	no	—
103	C₄⋊C₈×C₄₃	—	2	1	no	—
104	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
106	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
107	#97×C₄₃	—	2	1	no	—
108	C₄×C₈×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	2	2	no	—
113	C₂²×Dic₄₃	—	2	1	no	—
114	C₂²×Dic₄₃	—	2	1	no	—
115	C₂²×Dic₄₃	—	2	2	no	—
116	#10621898	—	2	2	no	—
117	#10621898	—	2	2	no	—
118	#10621898	—	2	2	no	—
119	#10621898	—	2	2	no	—
120	C₂×D₁₇₂	—	2	1	no	—
121	C₂×D₁₇₂	—	2	1	no	—
122	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
123	C₂×C₄×D₄₃	—	2	2	no	—
124	C₂×Dic₈₆	—	2	1	no	—
125	C₂×Dic₈₆	—	2	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	C₂×Dic₈₆	—	2	1	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	C₂×Dic₈₆	—	4	1	no	—
130	C₂×Dic₈₆	—	4	1	no	—
131	C₂×Dic₈₆	—	8	2	no	—
132	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
133	C₂×Dic₈₆	#41	1	2	yes	—
134	M₁₆×C₄₃	—	2	1	no	—
135	M₁₆×C₄₃	—	2	1	no	—
136	M₁₆×C₄₃	—	2	2	no	—
137	M₁₆×C₄₃	—	2	1	no	—
138	M₁₆×C₄₃	—	2	2	no	—
139	M₁₆×C₄₃	—	2	1	no	—
140	C₂×C₈×C₄₃	—	2	2	no	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₂×C₈×C₄₃	—	2	1	no	—
143	C₂×C₈×C₄₃	—	2	1	no	—
144	C₂×C₈×C₄₃	—	2	2	no	—
145	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
147	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	(C₂×D₄₃)⋊C₄	—	2	2	no	—
152	(C₂×D₄₃)⋊C₄	—	2	2	no	—
153	C₄⋊Dic₄₃	—	2	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₄⋊Dic₄₃	—	2	2	no	—
157	C₄⋊Dic₄₃	—	2	2	no	—
158	C₄⋊Dic₄₃	—	2	1	no	—
159	C₄⋊Dic₄₃	—	4	1	no	—
160	C₄⋊Dic₄₃	—	4	1	no	—
161	Dic₄₃⋊C₄	—	4	1	no	—
162	Dic₄₃⋊C₄	—	4	1	no	—
163	C₄×Dic₄₃	—	4	1	no	—
164	C₄×Dic₄₃	—	4	1	no	—
165	#10621877	—	2	1	no	—
166	#10621877	—	2	1	no	—
167	#10621877	—	2	1	no	—
168	#10621877	#41	1	2	yes	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	Dic₁₇₂	—	4	4	no	—
172	#10621873	—	4	4	no	—
173	#10621872	—	4	4	no	—
174	C₈×D₄₃	—	4	4	no	—
175	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
176	C₂²×D₄₃	—	2	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂²⋊D₄₃	—	4	2	no	—
190	C₂²⋊D₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	C₂×Dic₄₃	—	4	1	no	—
195	C₂×Dic₄₃	—	4	1	no	—
196	C₂×Dic₄₃	—	4	2	no	—
197	C₂×Dic₄₃	—	8	2	no	—
198	C₂×Dic₄₃	—	8	1	no	—
199	D₁₇₂	—	2	2	no	—
200	D₁₇₂	—	2	2	no	—
201	D₁₇₂	—	4	2	no	—
202	D₁₇₂	—	8	1	no	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	Dic₈₆	—	2	2	no	—
206	Dic₈₆	—	2	2	no	—
207	Dic₈₆	—	2	2	no	—
208	Dic₈₆	—	2	2	no	—
209	Dic₈₆	—	4	1	no	—
210	Dic₈₆	—	4	1	no	—
211	Dic₈₆	—	8	2	no	—
212	Dic₈₆	—	8	2	no	—
213	C₈×C₄₃	—	2	2	no	—
214	C₈×C₄₃	—	2	2	no	—
215	C₈×C₄₃	—	4	2	no	—
216	C₈×C₄₃	—	4	1	no	—
217	C₈×C₄₃	—	4	1	no	—
218	C₄₃⋊C₈	—	2	2	no	—
219	C₄₃⋊C₈	—	4	1	no	—
220	#25361	—	43	1	no	maximal, Sylow
221	C₂²×C₄₃	—	2	1	no	—
222	C₂²×C₄₃	—	2	1	no	—
223	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₃	#529	1	1	yes	characteristic
225	C₂²×C₄₃	#542	1	1	yes	characteristic
226	C₂×D₄₃	—	4	2	no	—
227	C₂×D₄₃	—	4	2	no	—
228	C₂×D₄₃	—	4	2	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	—	2	1	no	—
232	C₄×C₄₃	#471	1	2	yes	—
233	C₄×C₄₃	#546	1	1	yes	characteristic
234	C₄×C₄₃	#546	1	1	yes	characteristic
235	C₄×C₄₃	#547	1	1	yes	characteristic
236	C₄×C₄₃	#548	1	1	yes	characteristic
237	Dic₄₃	—	4	2	no	—
238	Dic₄₃	—	4	2	no	—
239	Dic₄₃	—	8	2	no	—
240	Dic₄₃	—	8	1	no	—
241	#3141	—	43	1	no	—
242	C₂×#475	—	43	1	no	—
243	#3037	—	43	1	no	—
244	#2935	—	43	1	no	—
245	#2079	—	43	2	no	—
246	#2052	—	43	2	no	—
247	#1997	—	43	1	no	—
248	#1950	D₄₃	1	1	yes	characteristic, complemented
249	#1908	—	43	2	no	—
250	#1815	—	43	2	no	—
251	C₄×#101	—	43	1	no	—
252	C₂×C₄₃	—	2	1	no	—
253	C₂×C₄₃	—	2	1	no	—
254	C₂×C₄₃	#2427	1	1	yes	characteristic
255	C₂×C₄₃	C₂×#471	1	1	yes	characteristic
256	C₂×C₄₃	#3069	1	1	yes	characteristic
257	D₄₃	—	8	2	no	—
258	C₂×#137	—	43	2	no	—
259	C₂×#131	—	43	2	no	—
260	#532	—	43	1	no	—
261	C₂×C₄⋊Q₈	—	43	1	no	—
262	C₂×C₄×Q₈	—	43	1	no	—
263	#489	—	86	2	no	—
264	#487	—	86	1	no	—
265	#486	—	86	1	no	—
266	#475	—	86	1	no	—
267	#475	—	86	2	no	—
268	#475	—	86	1	no	—
269	#464	—	86	2	no	—
270	#462	—	86	1	no	—
271	#460	—	86	1	no	—
272	#436	—	86	1	no	—
273	#435	—	86	2	no	—
274	C₈×D₄	—	86	1	no	—
275	C₂×#108	C₂×D₄₃	1	2	yes	—
276	C₂×#106	—	43	2	no	—
277	#423	C₂×D₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
279	#417	—	43	2	no	—
280	#417	—	43	2	no	—
281	#417	—	43	2	no	—
282	C₂×#103	—	43	2	no	—
283	C₂×#101	—	43	1	no	—
284	C₂×#101	—	43	1	no	—
285	#408	—	43	2	no	—
286	C₄×M₁₆	—	43	1	no	—
287	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
288	#343	—	43	2	no	—
289	#343	—	43	1	no	—
290	#343	—	43	2	no	—
291	#343	—	43	1	no	—
292	#341	C₂×D₄₃	1	2	yes	—
293	C₄₃	#25361	1	1	yes	characteristic, complemented, Sylow
294	C₂×#41	—	43	2	no	—
295	C₂²×Q₈	—	43	1	no	—
296	C₂²×Q₈	—	86	1	no	—
297	#137	—	86	4	no	—
298	#137	—	172	2	no	—
299	C₂×Q₁₆	—	86	2	no	—
300	C₂×SD₁₆	—	86	2	no	—
301	#131	—	86	4	no	—
302	#131	—	172	2	no	—
303	C₂×M₁₆	—	43	1	no	—
304	C₂×M₁₆	—	43	1	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
308	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
309	C₂²×C₈	—	86	2	no	—
310	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
311	C₄⋊Q₈	—	43	1	no	—
312	C₄⋊Q₈	—	86	1	no	—
313	C₄⋊Q₈	—	86	1	no	—
314	C₄⋊Q₈	—	86	1	no	—
315	C₄⋊Q₈	—	86	1	no	—
316	#127	—	43	1	no	—
317	#124	—	43	2	no	—
318	#121	—	86	1	no	—
319	#121	—	86	1	no	—
320	C₄×Q₈	—	86	1	no	—
321	C₄×Q₈	—	86	1	no	—
322	C₄×Q₈	—	86	1	no	—
323	C₄×Q₈	—	86	1	no	—
324	C₄×D₄	—	86	1	no	—
325	C₄×D₄	—	86	1	no	—
326	C₂×C₄⋊C₄	—	43	1	no	—
327	C₂×C₄⋊C₄	—	43	2	no	—
328	C₂×C₄⋊C₄	—	86	1	no	—
329	C₂×C₄⋊C₄	—	86	1	no	—
330	C₂×C₄²	—	86	1	no	—
331	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
332	#108	—	4	2	no	—
333	#106	—	86	2	no	—
334	#106	—	86	2	no	—
335	C₄⋊C₈	—	2	1	no	—
336	C₄⋊C₈	—	2	1	no	—
337	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
338	C₄⋊C₈	D₁₇₂	1	2	yes	—
339	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
340	#103	—	86	2	no	—
341	#103	—	86	2	no	—
342	#103	—	86	2	no	—
343	#103	—	86	2	no	—
344	#103	—	86	2	no	—
345	#102	—	86	2	no	—
346	#102	—	86	2	no	—
347	#102	—	86	2	no	—
348	#101	—	86	2	no	—
349	#101	—	86	2	no	—
350	C₂²⋊C₈	—	86	2	no	—
351	C₂²⋊C₈	—	86	2	no	—
352	#97	—	2	1	no	—
353	#97	—	86	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	86	1	no	—
356	#41	—	86	2	no	—
357	#41	—	86	2	no	—
358	#41	—	86	2	no	—
359	#41	—	86	2	no	—
360	C₂×Q₈	—	43	2	no	—
361	C₂×Q₈	—	43	2	no	—
362	C₂×Q₈	—	86	1	no	—
363	C₂×Q₈	—	86	1	no	—
364	C₂×Q₈	—	86	1	no	—
365	C₂×Q₈	—	86	1	no	—
366	C₂×Q₈	—	86	1	no	—
367	C₂×Q₈	—	344	2	no	—
368	C₂×Q₈	—	172	1	no	—
369	C₂×Q₈	—	172	1	no	—
370	C₂×D₄	—	43	2	no	—
371	C₂×D₄	—	86	2	no	—
372	C₂×D₄	—	86	1	no	—
373	C₂×D₄	—	86	1	no	—
374	C₂²×C₄	—	86	1	no	—
375	C₂²×C₄	—	86	2	no	—
376	C₂²×C₄	—	86	1	no	—
377	C₂²×C₄	—	86	2	no	—
378	C₂²×C₄	#10621902	1	1	yes	characteristic
379	C₂²×C₄	#10621902	1	1	yes	characteristic
380	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
381	Q₁₆	—	172	4	no	—
382	SD₁₆	—	172	4	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	1	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	1	no	—
389	M₁₆	—	43	2	no	—
390	M₁₆	—	86	1	no	—
391	M₁₆	—	86	1	no	—
392	M₁₆	—	86	1	no	—
393	M₁₆	—	172	4	no	—
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	86	1	no	—
400	C₂×C₈	—	86	1	no	—
401	C₂×C₈	—	172	4	no	—
402	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
403	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
404	C₄⋊C₄	—	86	1	no	—
405	C₄⋊C₄	—	86	1	no	—
406	C₄⋊C₄	—	86	1	no	—
407	C₄⋊C₄	—	86	2	no	—
408	C₄⋊C₄	—	86	2	no	—
409	C₄⋊C₄	—	86	1	no	—
410	C₄⋊C₄	—	172	1	no	—
411	C₄⋊C₄	—	172	1	no	—
412	C₄⋊C₄	—	172	1	no	—
413	C₄⋊C₄	—	172	1	no	—
414	C₂²⋊C₄	—	86	2	no	—
415	C₂²⋊C₄	—	86	2	no	—
416	C₄²	—	172	1	no	—
417	C₄²	—	172	1	no	—
418	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
419	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
420	C₄²	D₄×D₄₃	1	1	yes	characteristic
421	C₄²	D₄×D₄₃	1	1	yes	characteristic
422	C₂³	—	86	2	no	—
423	C₂³	C₂×#10621902	1	1	yes	characteristic
424	Q₈	—	86	2	no	—
425	Q₈	—	86	2	no	—
426	Q₈	—	86	2	no	—
427	Q₈	—	86	2	no	—
428	Q₈	—	344	2	no	—
429	Q₈	—	344	2	no	—
430	Q₈	—	172	1	no	—
431	Q₈	—	172	1	no	—
432	D₄	—	86	2	no	—
433	D₄	—	86	2	no	—
434	D₄	—	344	1	no	—
435	D₄	—	172	2	no	—
436	D₄	—	172	2	no	—
437	D₄	—	172	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	86	2	no	—
441	C₂×C₄	—	86	2	no	—
442	C₂×C₄	—	344	2	no	—
443	C₂×C₄	—	344	1	no	—
444	C₂×C₄	—	172	1	no	—
445	C₂×C₄	—	172	2	no	—
446	C₂×C₄	—	172	1	no	—
447	C₂×C₄	—	172	1	no	—
448	C₂×C₄	—	172	2	no	—
449	C₂×C₄	—	172	2	no	—
450	C₂×C₄	#13063300	1	1	yes	characteristic
451	C₂×C₄	#13063300	1	1	yes	characteristic
452	C₂×C₄	#13063300	1	1	yes	characteristic
453	C₂×C₄	#13063300	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
456	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
457	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
458	C₂×C₄	#13063370	1	1	yes	characteristic
459	C₂×C₄	#13063373	1	1	yes	characteristic
460	C₈	—	2	2	no	—
461	C₈	—	2	2	no	—
462	C₈	—	4	2	no	—
463	C₈	—	4	1	no	—
464	C₈	—	4	1	no	—
465	C₈	—	86	2	no	—
466	C₈	—	172	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	172	2	no	—
470	C₂²	—	172	2	no	—
471	C₂²	—	172	2	no	—
472	C₂²	C₂×#13063300	1	1	yes	characteristic
473	C₂²	#14583434	1	1	yes	characteristic
474	C₂²	#14583523	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	344	2	no	—
479	C₄	—	344	1	no	—
480	C₄	—	172	2	no	—
481	C₄	—	172	2	no	—
482	C₄	#14583163	1	2	yes	—
483	C₄	#14583544	1	1	yes	characteristic
484	C₄	#14583546	1	1	yes	characteristic
485	C₄	#14583551	1	1	yes	characteristic
486	C₄	#14583561	1	1	yes	characteristic
487	C₂	—	2	1	no	—
488	C₂	—	2	1	no	—
489	C₂	—	344	2	no	—
490	C₂	#19138170	1	1	yes	characteristic
491	C₂	C₂×#14583163	1	1	yes	characteristic
492	C₂	#19144333	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1950	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1950	D₄₃
hypocenter	C₄₃	#25361
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
2. C₂×#14583185	C₂	semidirect
5. #19136042	C₂	semidirect
6. #19135896	C₂	semidirect
7. #19135583	C₂	semidirect
8. #19135109	C₂	semidirect
9. #19134651	C₂	semidirect
10. C₄×#13063243	C₂	semidirect
11. C₄₃×#1950	C₂	semidirect
248. #1950	D₄₃	semidirect
293. C₄₃	#25361	semidirect

Maximal subgroups

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

subgroup	index
#19144989	2
C₂×#14583185	2
#19144069	2
#19143338	2
#19136042	2
#19135896	2
#19135583	2
#19135109	2
#19134651	2
C₄×#13063243	2
C₄₃×#1950	2
#25361	43