Subgroups — #25148707

Order 11008.

664 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145141	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144394	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583180	C₂	1	1	yes	maximal, characteristic
4	#19143538	C₂	1	1	yes	maximal, characteristic, complemented
5	#19136102	C₂	1	2	yes	maximal, complemented
6	#19135950	C₂	1	2	yes	maximal
7	#19135583	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135381	C₂	1	2	yes	maximal, complemented
9	#19135258	C₂	1	2	yes	maximal
10	C₄×#13063241	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583456	C₂²	1	1	yes	characteristic
13	C₂×#13063325	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583308	—	2	2	no	—
16	#14583304	—	2	1	no	—
17	#14583297	—	2	1	no	—
18	#14583200	—	2	2	no	—
19	#14583190	—	2	1	no	—
20	#14583180	—	2	1	no	—
21	#14583180	—	2	1	no	—
22	#14583180	—	2	1	no	—
23	#14583180	—	2	2	no	—
24	#14583028	—	2	2	no	—
25	#14583026	—	2	1	no	—
26	#14583023	—	2	1	no	—
27	#14582941	C₂²	1	2	yes	—
28	#14582941	C₂²	1	2	yes	—
29	#14582941	C₂²	1	2	yes	—
30	C₂×#13063259	C₂²	1	2	yes	—
31	#14582925	C₂²	1	2	yes	—
32	#14582905	C₂²	1	2	yes	—
33	C₂×#13063247	C₂²	1	2	yes	—
34	C₂×#13063241	C₂²	1	1	yes	characteristic
35	C₂×#13063241	C₂²	1	1	yes	characteristic
36	#14582854	C₂²	1	2	yes	—
37	C₄×#10621877	C₂²	1	1	yes	characteristic
38	#14582667	C₂²	1	2	yes	—
39	#14582667	C₂²	1	2	yes	—
40	#14582667	C₂²	1	1	yes	characteristic
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	C₂²×Dic₈₆	—	2	1	no	—
48	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
49	C₂²×C₄×D₄₃	—	2	1	no	—
50	C₂×#10621877	C₂³	1	1	yes	characteristic
51	C₂×#10621877	C₂³	1	1	yes	characteristic
52	#13063325	—	2	1	no	—
53	#13063325	—	2	1	no	—
54	#13063325	—	2	1	no	—
55	#13063325	—	2	1	no	—
56	#13063325	D₄	1	1	yes	characteristic
57	#13063325	D₄	1	1	yes	characteristic
58	#13063317	D₄	1	2	yes	—
59	#13063304	—	2	1	no	—
60	#13063304	—	2	1	no	—
61	C₄×Dic₈₆	—	2	1	no	—
62	C₄×Dic₈₆	—	2	1	no	—
63	C₄×D₁₇₂	—	2	1	no	—
64	C₄×D₁₇₂	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	#13063284	C₂³	1	2	yes	—
68	C₂×C₄⋊Dic₄₃	—	2	1	no	—
69	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
71	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
72	#13063259	—	2	2	no	—
73	#13063259	—	2	2	no	—
74	#13063259	—	2	2	no	—
75	#13063259	—	2	2	no	—
76	#13063259	—	2	2	no	—
77	#13063257	—	2	2	no	—
78	#13063257	—	2	2	no	—
79	#13063257	—	2	2	no	—
80	Dic₄₃⋊C₈	—	2	2	no	—
81	Dic₄₃⋊C₈	—	2	2	no	—
82	#13063247	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063247	—	2	2	no	—
85	#13063247	—	2	2	no	—
86	#13063241	—	2	2	no	—
87	#13063241	Q₈	1	4	yes	complemented
88	#13063236	—	2	1	no	—
89	#13063235	—	2	2	no	—
90	C₄×C₄₃⋊C₈	—	2	1	no	—
91	C₈×Dic₄₃	—	2	2	no	—
92	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
93	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
94	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	#108×C₄₃	—	2	4	no	—
98	C₄⋊C₈×C₄₃	—	2	1	no	—
99	C₄⋊C₈×C₄₃	—	2	1	no	—
100	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
101	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
102	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
103	#97×C₄₃	—	2	1	no	—
104	C₄×C₈×C₄₃	—	2	1	no	—
105	C₂³×D₄₃	—	2	1	no	—
106	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
109	C₂²×Dic₄₃	—	2	1	no	—
110	C₂²×Dic₄₃	—	2	2	no	—
111	C₂×D₁₇₂	—	2	1	no	—
112	C₂×D₁₇₂	—	2	1	no	—
113	C₂×D₁₇₂	—	2	1	no	—
114	C₂×D₁₇₂	—	2	1	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	C₂×Q₈	1	2	yes	—
117	C₂×C₄×D₄₃	—	4	1	no	—
118	C₂×C₄×D₄₃	—	4	1	no	—
119	C₂×C₄×D₄₃	—	8	2	no	—
120	C₂×Dic₈₆	—	2	1	no	—
121	C₂×Dic₈₆	—	2	1	no	—
122	C₂×Dic₈₆	—	4	1	no	—
123	C₂×Dic₈₆	—	4	1	no	—
124	C₂×Dic₈₆	—	8	2	no	—
125	M₁₆×C₄₃	—	2	1	no	—
126	M₁₆×C₄₃	—	2	1	no	—
127	M₁₆×C₄₃	—	2	2	no	—
128	M₁₆×C₄₃	—	2	2	no	—
129	M₁₆×C₄₃	C₂×Q₈	1	2	yes	—
130	M₁₆×C₄₃	#41	1	2	yes	—
131	C₂×C₈×C₄₃	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊Dic₄₃	—	2	2	no	—
143	(C₂×D₄₃)⋊C₄	—	4	1	no	—
144	(C₂×D₄₃)⋊C₄	—	4	1	no	—
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	2	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	2	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	4	1	no	—
152	C₄⋊Dic₄₃	—	4	1	no	—
153	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
154	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
155	Dic₄₃⋊C₄	—	2	2	no	—
156	Dic₄₃⋊C₄	—	2	2	no	—
157	C₄×Dic₄₃	—	2	2	no	—
158	#10621877	—	2	1	no	—
159	#10621877	—	2	1	no	—
160	#10621877	—	2	1	no	—
161	#10621877	C₂×Q₈	1	2	yes	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	1	no	—
164	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂²×D₄₃	—	2	2	no	—
166	C₂²×D₄₃	—	4	1	no	—
167	C₂²×D₄₃	—	4	1	no	—
168	C₂²×D₄₃	—	8	1	no	—
169	C₂²×D₄₃	—	8	1	no	—
170	C₂×C₄×C₄₃	—	2	2	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	8	2	no	—
187	C₂×Dic₄₃	—	8	1	no	—
188	D₁₇₂	—	2	2	no	—
189	D₁₇₂	—	2	2	no	—
190	D₁₇₂	—	4	1	no	—
191	D₁₇₂	—	4	1	no	—
192	C₄×D₄₃	—	8	2	no	—
193	C₄×D₄₃	—	8	2	no	—
194	Dic₈₆	—	4	2	no	—
195	Dic₈₆	—	8	1	no	—
196	Dic₈₆	—	8	2	no	—
197	Dic₈₆	—	8	2	no	—
198	C₈×C₄₃	—	2	2	no	—
199	C₈×C₄₃	—	2	2	no	—
200	C₈×C₄₃	—	2	2	no	—
201	C₈×C₄₃	—	2	2	no	—
202	C₈×C₄₃	—	4	2	no	—
203	C₄₃⋊C₈	—	2	2	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	#25489	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
209	C₂²×C₄₃	#533	1	1	yes	characteristic
210	C₂²×C₄₃	#541	1	1	yes	characteristic
211	C₂×D₄₃	—	4	2	no	—
212	C₂×D₄₃	—	8	2	no	—
213	C₂×D₄₃	—	8	1	no	—
214	C₂×D₄₃	—	8	1	no	—
215	C₂×D₄₃	—	8	2	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	#472	1	2	yes	—
220	C₄×C₄₃	#547	1	1	yes	characteristic
221	C₄×C₄₃	#548	1	1	yes	characteristic
222	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
223	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
224	Dic₄₃	—	4	2	no	—
225	Dic₄₃	—	4	2	no	—
226	Dic₄₃	—	8	2	no	—
227	Dic₄₃	—	8	1	no	—
228	#3165	—	43	1	no	—
229	#3077	—	43	1	no	—
230	C₂×#474	—	43	1	no	—
231	#2962	—	43	1	no	—
232	#2089	—	43	2	no	—
233	#2063	—	43	2	no	—
234	#1997	—	43	1	no	—
235	#1952	—	43	2	no	—
236	#1950	D₄₃	1	1	yes	characteristic, complemented
237	#1931	—	43	2	no	—
238	C₄×#100	—	43	1	no	—
239	C₂×C₄₃	—	2	1	no	—
240	C₂×C₄₃	—	2	1	no	—
241	C₂×C₄₃	#2429	1	1	yes	characteristic
242	C₂×C₄₃	C₂×#472	1	1	yes	characteristic
243	C₂×C₄₃	#3069	1	1	yes	characteristic
244	D₄₃	—	8	2	no	—
245	#533	—	43	1	no	—
246	C₂×C₄⋊Q₈	—	43	1	no	—
247	C₂×C₄×D₄	—	43	1	no	—
248	#501	—	86	2	no	—
249	#500	—	86	1	no	—
250	#498	—	86	1	no	—
251	#478	—	86	2	no	—
252	#476	—	86	1	no	—
253	#474	—	86	1	no	—
254	#474	—	86	1	no	—
255	#474	—	86	2	no	—
256	#474	—	86	1	no	—
257	#446	—	86	1	no	—
258	#446	—	86	2	no	—
259	C₈×Q₈	—	86	1	no	—
260	C₂×#108	C₂×D₄₃	1	2	yes	—
261	#428	—	43	2	no	—
262	#428	—	43	2	no	—
263	#428	—	43	2	no	—
264	C₂×#107	—	43	2	no	—
265	#424	—	43	2	no	—
266	#423	C₂×D₄₃	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
268	#418	—	43	2	no	—
269	C₂×#102	—	43	2	no	—
270	C₂×#100	—	43	1	no	—
271	C₂×#100	—	43	1	no	—
272	#405	—	43	2	no	—
273	C₄×M₁₆	—	43	1	no	—
274	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
275	#343	—	43	2	no	—
276	#343	—	43	1	no	—
277	#343	—	43	2	no	—
278	#343	—	43	1	no	—
279	#341	C₂×D₄₃	1	2	yes	—
280	C₄₃	#25489	1	1	yes	characteristic, complemented, Sylow
281	C₂²×Q₈	—	86	1	no	—
282	C₂²×D₄	—	43	1	no	—
283	C₂³×C₄	—	86	1	no	—
284	C₂×M₁₆	—	43	1	no	—
285	C₂×M₁₆	—	43	1	no	—
286	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
287	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
288	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
289	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
290	C₄⋊Q₈	—	43	1	no	—
291	C₄⋊Q₈	—	43	1	no	—
292	C₄⋊Q₈	—	86	1	no	—
293	C₄⋊Q₈	—	86	1	no	—
294	C₄⋊Q₈	—	86	1	no	—
295	C₄⋊Q₈	—	86	1	no	—
296	#125	—	43	2	no	—
297	C₂²⋊Q₈	—	86	1	no	—
298	C₂²⋊Q₈	—	86	1	no	—
299	C₄×Q₈	—	86	1	no	—
300	C₄×Q₈	—	86	1	no	—
301	C₄×D₄	—	86	1	no	—
302	C₄×D₄	—	86	1	no	—
303	C₄×D₄	—	86	1	no	—
304	C₄×D₄	—	86	1	no	—
305	#117	—	43	2	no	—
306	C₂×C₄⋊C₄	—	43	1	no	—
307	C₂×C₄⋊C₄	—	43	2	no	—
308	C₂×C₄⋊C₄	—	86	1	no	—
309	C₂×C₂²⋊C₄	—	86	1	no	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	#108	—	2	4	no	—
312	#107	—	86	2	no	—
313	#107	—	86	2	no	—
314	#107	—	86	2	no	—
315	#107	—	86	2	no	—
316	#107	—	86	2	no	—
317	#106	—	86	2	no	—
318	#106	—	86	2	no	—
319	#106	—	86	2	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	86	2	no	—
323	C₄⋊C₈	—	86	2	no	—
324	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
325	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
326	C₄⋊C₈	D₁₇₂	1	2	yes	—
327	#102	—	86	2	no	—
328	#102	—	86	2	no	—
329	#102	—	86	2	no	—
330	#102	—	86	2	no	—
331	#100	—	43	4	no	—
332	#100	—	86	2	no	—
333	#97	—	2	1	no	—
334	#97	—	86	2	no	—
335	#97	—	86	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	86	2	no	—
338	C₄×C₈	—	86	1	no	—
339	C₂⁴	—	86	1	no	—
340	C₂×Q₈	—	86	1	no	—
341	C₂×Q₈	—	86	1	no	—
342	C₂×Q₈	—	344	2	no	—
343	C₂×Q₈	—	172	1	no	—
344	C₂×Q₈	—	172	1	no	—
345	C₂×D₄	—	43	2	no	—
346	C₂×D₄	—	86	1	no	—
347	C₂×D₄	—	86	1	no	—
348	C₂×D₄	—	86	1	no	—
349	C₂×D₄	—	86	1	no	—
350	C₂×D₄	—	86	1	no	—
351	C₂²×C₄	—	86	1	no	—
352	C₂²×C₄	—	86	2	no	—
353	C₂²×C₄	—	344	2	no	—
354	C₂²×C₄	—	172	1	no	—
355	C₂²×C₄	—	172	1	no	—
356	C₂²×C₄	#10621902	1	1	yes	characteristic
357	C₂²×C₄	#10621902	1	1	yes	characteristic
358	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
359	M₁₆	—	2	1	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	2	2	no	—
363	M₁₆	—	43	2	no	—
364	M₁₆	—	86	1	no	—
365	M₁₆	—	86	1	no	—
366	M₁₆	—	86	1	no	—
367	M₁₆	#10621900	1	2	yes	—
368	M₁₆	Q₈×D₄₃	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	86	1	no	—
376	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
377	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
378	C₄⋊C₄	—	43	2	no	—
379	C₄⋊C₄	—	43	2	no	—
380	C₄⋊C₄	—	86	2	no	—
381	C₄⋊C₄	—	86	2	no	—
382	C₄⋊C₄	—	86	1	no	—
383	C₄⋊C₄	—	86	1	no	—
384	C₄⋊C₄	—	86	1	no	—
385	C₄⋊C₄	—	86	2	no	—
386	C₄⋊C₄	—	86	2	no	—
387	C₄⋊C₄	—	86	1	no	—
388	C₄⋊C₄	—	172	1	no	—
389	C₄⋊C₄	—	172	1	no	—
390	C₂²⋊C₄	—	86	2	no	—
391	C₂²⋊C₄	—	172	1	no	—
392	C₂²⋊C₄	—	172	1	no	—
393	C₄²	—	86	2	no	—
394	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
395	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
396	C₄²	D₄×D₄₃	1	1	yes	characteristic
397	C₄²	D₄×D₄₃	1	1	yes	characteristic
398	C₂³	—	86	2	no	—
399	C₂³	—	344	1	no	—
400	C₂³	—	344	1	no	—
401	C₂³	—	172	1	no	—
402	C₂³	—	172	1	no	—
403	C₂³	C₂×#10621902	1	1	yes	characteristic
404	Q₈	—	344	2	no	—
405	Q₈	—	344	1	no	—
406	Q₈	—	344	2	no	—
407	Q₈	—	172	2	no	—
408	D₄	—	86	2	no	—
409	D₄	—	86	2	no	—
410	D₄	—	172	1	no	—
411	D₄	—	172	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	86	2	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	344	2	no	—
417	C₂×C₄	—	344	2	no	—
418	C₂×C₄	—	344	1	no	—
419	C₂×C₄	—	344	2	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	#13063300	1	1	yes	characteristic
423	C₂×C₄	#13063300	1	1	yes	characteristic
424	C₂×C₄	#13063300	1	1	yes	characteristic
425	C₂×C₄	#13063300	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
428	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
430	C₂×C₄	#13063372	1	1	yes	characteristic
431	C₂×C₄	#13063372	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	86	2	no	—
438	C₈	—	172	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	344	2	no	—
442	C₂²	—	344	2	no	—
443	C₂²	—	344	1	no	—
444	C₂²	—	344	1	no	—
445	C₂²	—	172	2	no	—
446	C₂²	C₂×#13063300	1	1	yes	characteristic
447	C₂²	#14583454	1	1	yes	characteristic
448	C₂²	#14583512	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	344	1	no	—
453	C₄	—	344	2	no	—
454	C₄	—	172	2	no	—
455	C₄	—	172	2	no	—
456	C₄	#14583170	1	2	yes	—
457	C₄	#14583553	1	1	yes	characteristic
458	C₄	#14583555	1	1	yes	characteristic
459	C₄	#14583562	1	1	yes	characteristic
460	C₄	Q₈×D₁₇₂	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	344	2	no	—
464	C₂	#19138192	1	1	yes	characteristic
465	C₂	C₂×#14583170	1	1	yes	characteristic
466	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	C₂²×D₁₇₂	C₂³
hypercenter	#1950	D₄₃
hypocenter	C₄₃	#25489
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
1. #19145141	C₂	semidirect
4. #19143538	C₂	semidirect
5. #19136102	C₂	semidirect
7. #19135583	C₂	semidirect
8. #19135381	C₂	semidirect
11. C₄₃×#1950	C₂	semidirect
87. #13063241	Q₈	semidirect
236. #1950	D₄₃	semidirect
280. C₄₃	#25489	semidirect

Maximal subgroups

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

subgroup	index
#19145141	2
#19144394	2
C₂×#14583180	2
#19143538	2
#19136102	2
#19135950	2
#19135583	2
#19135381	2
#19135258	2
C₄×#13063241	2
C₄₃×#1950	2
#25489	43