Subgroups — #25148178

Order 11008.

778 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	C₂×#14583302	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583186	C₂	1	1	yes	maximal, characteristic
3	#19139764	C₂	1	1	yes	maximal, characteristic
4	#19136076	C₂	1	2	yes	maximal, complemented
5	#19135980	C₂	1	2	yes	maximal
6	#19135543	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135363	C₂	1	2	yes	maximal, complemented
8	#19135314	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135215	C₂	1	2	yes	maximal
10	C₄×#13063245	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2369	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063325	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
14	#14583302	—	2	4	no	—
15	#14583186	—	2	4	no	—
16	C₂×#13063258	C₂²	1	2	yes	—
17	C₂×#13063258	C₂²	1	2	yes	—
18	C₂×#13063256	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
21	C₂×#13063245	C₂²	1	2	yes	—
22	C₂×#13063245	C₂²	1	1	yes	characteristic
23	C₂×#13063245	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	#14582812	—	2	2	no	—
26	#14582801	C₂²	1	2	yes	—
27	#14582765	C₂²	1	2	yes	—
28	#14582756	—	2	1	no	—
29	#14582756	—	2	1	no	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582661	C₂²	1	1	yes	characteristic
33	#14582661	C₂²	1	1	yes	characteristic
34	#14582654	C₂²	1	2	yes	—
35	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
36	C₄₃×#391	—	2	2	no	—
37	C₄₃×#389	—	2	1	no	—
38	C₄₃×#389	C₂²	1	2	yes	—
39	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²×Dic₈₆	—	2	1	no	—
44	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₄₃	—	2	1	no	—
46	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	#13063325	—	2	2	no	—
50	#13063325	—	2	2	no	—
51	C₄×D₁₇₂	—	2	2	no	—
52	C₄×D₁₇₂	—	2	2	no	—
53	C₂×C₄⋊Dic₄₃	—	2	1	no	—
54	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
56	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
57	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
59	#13063258	—	2	4	no	—
60	#13063258	—	2	4	no	—
61	#13063256	—	2	4	no	—
62	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
64	#13063245	—	2	4	no	—
65	#13063245	—	2	2	no	—
66	#13063245	Q₈	1	4	yes	complemented
67	C₄×C₄₃⋊C₈	—	2	2	no	—
68	C₄₃⋊#95	—	2	2	no	—
69	C₄₃⋊#95	—	2	2	no	—
70	C₂²×Q₈×C₄₃	—	2	1	no	—
71	C₄⋊Q₈×C₄₃	—	2	2	no	—
72	C₄⋊Q₈×C₄₃	D₄	1	4	yes	—
73	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	—	2	2	no	—
82	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
84	#95×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	1	no	—
87	#95×C₄₃	D₄	1	2	yes	—
88	C₂³×D₄₃	—	2	1	no	—
89	C₂×Q₈×C₄₃	—	2	4	no	—
90	C₂×Q₈×C₄₃	—	8	1	no	—
91	C₂×Q₈×C₄₃	—	8	1	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	1	no	—
95	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₃	—	2	1	no	—
101	C₂²×Dic₄₃	—	2	2	no	—
102	C₂×D₁₇₂	—	2	1	no	—
103	C₂×D₁₇₂	—	2	1	no	—
104	C₂×D₁₇₂	—	2	1	no	—
105	C₂×D₁₇₂	—	2	1	no	—
106	C₂×D₁₇₂	—	2	1	no	—
107	C₂×D₁₇₂	C₂×Q₈	1	2	yes	—
108	C₂×C₄×D₄₃	—	4	2	no	—
109	C₂×C₄×D₄₃	—	4	2	no	—
110	C₂×C₄×D₄₃	—	4	2	no	—
111	C₂×Dic₈₆	—	4	2	no	—
112	C₂×Dic₈₆	—	8	1	no	—
113	C₂×Dic₈₆	—	8	1	no	—
114	C₄⋊C₄×C₄₃	—	2	4	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	—	8	2	no	—
122	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
123	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	2	2	no	—
126	C₄²×C₄₃	—	4	2	no	—
127	C₄²×C₄₃	—	8	2	no	—
128	C₄²×C₄₃	C₂×D₄	1	2	yes	—
129	C₄²×C₄₃	#41	1	2	yes	—
130	(C₂×D₄₃)⋊C₄	—	4	2	no	—
131	(C₂×D₄₃)⋊C₄	—	8	2	no	—
132	(C₂×D₄₃)⋊C₄	—	8	2	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	1	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	4	2	no	—
138	C₂×C₄₃⋊C₈	—	2	1	no	—
139	C₂×C₄₃⋊C₈	—	2	1	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	2	no	—
143	C₂×C₄₃⋊C₈	—	2	2	no	—
144	C₂×C₄₃⋊C₈	—	2	2	no	—
145	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
146	C₂×C₄₃⋊C₈	#41	1	2	yes	—
147	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
148	C₂²×D₄₃	—	2	2	no	—
149	C₂²×D₄₃	—	4	1	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂²×D₄₃	—	4	1	no	—
153	C₂²×D₄₃	—	4	1	no	—
154	C₂²×D₄₃	—	4	1	no	—
155	Q₈×C₄₃	—	8	4	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	4	1	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	#121	1	2	yes	—
174	C₂×C₄×C₄₃	#121	1	2	yes	—
175	C₂×C₄×C₄₃	#135	1	2	yes	—
176	C₂×C₄×C₄₃	#137	1	2	yes	—
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	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₂×Dic₄₃	—	4	2	no	—
188	C₂×Dic₄₃	—	4	2	no	—
189	D₁₇₂	—	2	2	no	—
190	D₁₇₂	—	2	2	no	—
191	D₁₇₂	—	4	1	no	—
192	D₁₇₂	—	4	1	no	—
193	C₄×D₄₃	—	8	4	no	—
194	Dic₈₆	—	8	4	no	—
195	C₄₃⋊C₈	—	2	2	no	—
196	C₄₃⋊C₈	—	2	2	no	—
197	C₄₃⋊C₈	—	4	2	no	—
198	#25450	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
200	C₂²×C₄₃	#547	1	1	yes	characteristic
201	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
202	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
204	C₂²×C₄₃	#576	1	1	yes	characteristic
205	C₂²×C₄₃	#576	1	1	yes	characteristic
206	C₂×D₄₃	—	4	2	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₂×D₄₃	—	4	2	no	—
209	C₂×D₄₃	—	8	1	no	—
210	C₂×D₄₃	—	8	1	no	—
211	C₂×D₄₃	—	8	1	no	—
212	C₂×D₄₃	—	8	1	no	—
213	C₄×C₄₃	—	2	2	no	—
214	C₄×C₄₃	—	4	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	—	4	4	no	—
218	C₄×C₄₃	—	8	1	no	—
219	C₄×C₄₃	#464	1	4	yes	—
220	C₄×C₄₃	#533	1	1	yes	characteristic
221	C₄×C₄₃	#541	1	1	yes	characteristic
222	C₄×C₄₃	#548	1	1	yes	characteristic
223	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
224	Dic₄₃	—	8	1	no	—
225	Dic₄₃	—	8	2	no	—
226	C₂×#500	—	43	1	no	—
227	C₂×#476	—	43	1	no	—
228	#2563	—	43	1	no	—
229	#2369	D₄₃	1	1	yes	characteristic, complemented
230	#2085	—	43	2	no	—
231	#2067	—	43	2	no	—
232	#1987	—	43	1	no	—
233	#1949	—	43	2	no	—
234	#1939	—	43	1	no	—
235	#1925	—	43	2	no	—
236	C₄×#102	—	43	1	no	—
237	C₂×C₄₃	#2429	1	1	yes	characteristic
238	C₂×C₄₃	C₂×#464	1	1	yes	characteristic
239	C₂×C₄₃	#3041	1	1	yes	characteristic
240	C₂×C₄₃	#3341	1	1	yes	characteristic
241	C₂×C₄₃	#3357	1	1	yes	characteristic
242	C₂×C₄₃	#3380	1	1	yes	characteristic
243	C₂×C₄₃	#3385	1	1	yes	characteristic
244	D₄₃	—	8	2	no	—
245	C₂×C₄⋊Q₈	—	43	1	no	—
246	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
247	C₂×C₄×D₄	—	43	1	no	—
248	#500	—	86	4	no	—
249	#476	—	86	4	no	—
250	C₂×#107	—	43	2	no	—
251	C₂×#107	—	43	2	no	—
252	C₂×#106	—	43	2	no	—
253	C₂×C₄⋊C₈	—	43	2	no	—
254	C₂×C₄⋊C₈	—	43	1	no	—
255	C₂×#102	—	43	1	no	—
256	C₂×#102	—	43	1	no	—
257	C₂×#102	—	43	2	no	—
258	C₂×C₄×C₈	—	43	1	no	—
259	#393	—	86	2	no	—
260	#391	—	2	2	no	—
261	#390	—	43	2	no	—
262	#389	—	2	1	no	—
263	#389	C₂×D₄₃	1	2	yes	—
264	#382	—	43	2	no	—
265	#380	—	86	1	no	—
266	#380	—	86	1	no	—
267	C₄×C₄⋊C₄	—	2	1	no	—
268	C₄×C₄⋊C₄	C₂×D₄₃	1	2	yes	—
269	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
270	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
271	#340	—	43	2	no	—
272	#340	—	43	1	no	—
273	#340	—	43	2	no	—
274	#340	—	43	1	no	—
275	#336	—	43	2	no	—
276	C₄₃	#25450	1	1	yes	characteristic, complemented, Sylow
277	C₂²×Q₈	—	2	1	no	—
278	C₂²×Q₈	—	86	1	no	—
279	C₂²×D₄	—	43	1	no	—
280	C₂³×C₄	—	86	1	no	—
281	C₂²×C₈	—	43	1	no	—
282	C₂²×C₈	—	43	1	no	—
283	C₂²×C₈	—	43	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₄⋊Q₈	—	86	2	no	—
286	C₄⋊Q₈	—	86	2	no	—
287	C₄⋊Q₈	D₁₇₂	1	4	yes	—
288	C₄×D₄	—	86	2	no	—
289	C₄×D₄	—	86	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	43	1	no	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	86	1	no	—
295	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₄	—	86	2	no	—
301	C₂×C₂²⋊C₄	—	86	2	no	—
302	C₂×C₂²⋊C₄	—	86	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
306	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
307	#107	—	86	4	no	—
308	#107	—	86	4	no	—
309	#106	—	86	4	no	—
310	C₄⋊C₈	—	86	4	no	—
311	C₄⋊C₈	—	86	2	no	—
312	#102	—	43	4	no	—
313	#102	—	86	2	no	—
314	#102	—	86	4	no	—
315	C₄×C₈	—	86	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	86	2	no	—
320	#95	—	86	2	no	—
321	#95	C₂²⋊D₄₃	1	2	yes	—
322	C₂⁴	—	86	1	no	—
323	C₂×Q₈	—	2	4	no	—
324	C₂×Q₈	—	8	1	no	—
325	C₂×Q₈	—	8	1	no	—
326	C₂×Q₈	—	344	1	no	—
327	C₂×Q₈	—	344	1	no	—
328	C₂×Q₈	—	172	2	no	—
329	C₂×D₄	—	43	2	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂×D₄	—	86	1	no	—
333	C₂×D₄	—	86	1	no	—
334	C₂×D₄	—	86	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	86	1	no	—
339	C₂²×C₄	—	86	2	no	—
340	C₂²×C₄	—	172	2	no	—
341	C₂²×C₄	—	172	2	no	—
342	C₂²×C₄	—	172	2	no	—
343	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
344	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
345	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
347	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
348	C₂×C₈	—	43	2	no	—
349	C₂×C₈	—	43	2	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	—	86	1	no	—
352	C₂×C₈	—	86	1	no	—
353	C₂×C₈	—	86	1	no	—
354	C₂×C₈	—	86	2	no	—
355	C₂×C₈	—	86	2	no	—
356	C₂×C₈	—	86	2	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	8	2	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₄⋊C₄	—	86	2	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	2	no	—
369	C₄⋊C₄	—	172	2	no	—
370	C₄⋊C₄	C₂×D₁₇₂	1	4	yes	—
371	C₄⋊C₄	Q₈×D₄₃	1	2	yes	—
372	C₂²⋊C₄	—	344	2	no	—
373	C₂²⋊C₄	—	344	2	no	—
374	C₂²⋊C₄	—	172	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	8	2	no	—
379	C₄²	C₂×D₁₇₂	1	2	yes	—
380	C₄²	#10621898	1	2	yes	—
381	C₂³	—	86	2	no	—
382	C₂³	—	172	1	no	—
383	C₂³	—	172	1	no	—
384	C₂³	—	172	1	no	—
385	C₂³	—	172	1	no	—
386	C₂³	—	172	1	no	—
387	C₂³	—	172	1	no	—
388	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
389	Q₈	—	8	4	no	—
390	Q₈	—	344	4	no	—
391	D₄	—	86	2	no	—
392	D₄	—	86	2	no	—
393	D₄	—	172	1	no	—
394	D₄	—	172	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	344	4	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	2	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	1	no	—
417	C₂×C₄	—	172	2	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	#13063299	1	2	yes	—
420	C₂×C₄	#13063299	1	2	yes	—
421	C₂×C₄	#13063345	1	2	yes	—
422	C₂×C₄	#13063356	1	2	yes	—
423	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
424	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
425	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
427	C₂×C₄	#13063372	1	1	yes	characteristic
428	C₂×C₄	#13063373	1	1	yes	characteristic
429	C₈	—	86	2	no	—
430	C₈	—	86	2	no	—
431	C₈	—	172	2	no	—
432	C₂²	—	344	1	no	—
433	C₂²	—	344	1	no	—
434	C₂²	—	344	1	no	—
435	C₂²	—	344	1	no	—
436	C₂²	—	172	2	no	—
437	C₂²	—	172	2	no	—
438	C₂²	—	172	2	no	—
439	C₂²	C₂×#13063299	1	1	yes	characteristic
440	C₂²	#14583548	1	1	yes	characteristic
441	C₂²	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
442	C₂²	C₂×#13063345	1	1	yes	characteristic
443	C₂²	C₂×#13063356	1	1	yes	characteristic
444	C₂²	#14583702	1	1	yes	characteristic
445	C₂²	#14583702	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	344	1	no	—
453	C₄	—	344	2	no	—
454	C₄	#14583121	1	4	yes	—
455	C₄	#14583453	1	1	yes	characteristic
456	C₄	#14583507	1	1	yes	characteristic
457	C₄	#14583561	1	1	yes	characteristic
458	C₄	Q₈×D₁₇₂	1	1	yes	characteristic
459	C₂	—	344	2	no	—
460	C₂	#19138188	1	1	yes	characteristic
461	C₂	C₂×#14583121	1	1	yes	characteristic
462	C₂	#19144098	1	1	yes	characteristic
463	C₂	#19147013	1	1	yes	characteristic
464	C₂	#19147221	1	1	yes	characteristic
465	C₂	#19147458	1	1	yes	characteristic
466	C₂	#19147501	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#2369	C₂
socle	C₂³×C₄₃	C₂²×D₄
prime radical	C₂²×D₁₇₂	C₂³
hypercenter	#2369	D₄₃
hypocenter	C₄₃	#25450
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2369

Complements

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

N	H ≅ G/N	type
1. C₂×#14583302	C₂	semidirect
4. #19136076	C₂	semidirect
6. #19135543	C₂	semidirect
7. #19135363	C₂	semidirect
8. #19135314	C₂	semidirect
11. C₄₃×#2369	C₂	semidirect
66. #13063245	Q₈	semidirect
229. #2369	D₄₃	semidirect
276. C₄₃	#25450	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583302	2
C₂×#14583186	2
#19139764	2
#19136076	2
#19135980	2
#19135543	2
#19135363	2
#19135314	2
#19135215	2
C₄×#13063245	2
C₄₃×#2369	2
#25450	43