Subgroups — #24998948

Order 11008.

628 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583195	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14583190	C₂	1	1	yes	maximal, characteristic
3	#19139518	C₂	1	1	yes	maximal, characteristic
4	#19135396	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582629	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582626	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13063325	C₂²	1	1	yes	characteristic
9	C₂×#13063305	—	2	1	no	—
10	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
12	#14583195	—	2	2	no	—
13	#14583195	—	2	2	no	—
14	#14583190	—	2	2	no	—
15	#14583190	—	2	2	no	—
16	C₂×#13063259	—	2	1	no	—
17	C₂×#13063257	—	2	1	no	—
18	C₂×#13063250	—	2	1	no	—
19	C₂×#13063248	—	2	2	no	—
20	C₂×#13063247	—	2	1	no	—
21	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582821	—	2	2	no	—
23	#14582800	—	2	1	no	—
24	#14582798	—	2	1	no	—
25	#14582756	—	2	1	no	—
26	#14582629	—	2	2	no	—
27	#14582626	—	2	2	no	—
28	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#384	C₂²	1	1	yes	characteristic
31	C₂²×Dic₈₆	—	2	1	no	—
32	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
33	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₃	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	#13063325	—	2	1	no	—
37	#13063325	—	2	1	no	—
38	#13063325	—	2	1	no	—
39	#13063325	D₄	1	2	yes	—
40	#13063305	—	4	2	no	—
41	#13063305	—	4	2	no	—
42	C₄×Dic₈₆	—	2	1	no	—
43	C₄×Dic₈₆	—	2	1	no	—
44	C₄×Dic₈₆	—	2	1	no	—
45	C₄×Dic₈₆	—	2	1	no	—
46	C₄×D₁₇₂	—	2	1	no	—
47	C₄×D₁₇₂	—	2	1	no	—
48	C₄×D₁₇₂	—	2	1	no	—
49	C₄×D₁₇₂	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	—	2	1	no	—
52	C₂×C₄⋊Dic₄₃	—	2	2	no	—
53	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
55	C₂×Dic₄₃⋊C₄	—	2	1	no	—
56	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
57	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
58	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
59	C₂×C₄×Dic₄₃	—	2	1	no	—
60	#13063259	—	2	4	no	—
61	#13063257	—	2	4	no	—
62	#13063250	—	2	4	no	—
63	#13063248	—	4	4	no	—
64	#13063247	—	2	4	no	—
65	C₄×C₄₃⋊C₈	—	2	1	no	—
66	C₄×C₄₃⋊C₈	—	2	1	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₂²×C₈×C₄₃	—	2	1	no	—
69	C₂²×C₈×C₄₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	—	2	1	no	—
75	C₄⋊C₈×C₄₃	—	2	1	no	—
76	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
77	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
78	C₂³×D₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×Dic₄₃	—	2	1	no	—
84	C₂²×Dic₄₃	—	2	1	no	—
85	C₂²×Dic₄₃	—	2	1	no	—
86	C₂²×Dic₄₃	—	4	1	no	—
87	C₂×D₁₇₂	—	2	1	no	—
88	C₂×D₁₇₂	—	2	1	no	—
89	C₂×D₁₇₂	—	2	1	no	—
90	C₂×D₁₇₂	—	2	1	no	—
91	C₂×D₁₇₂	—	2	1	no	—
92	C₂×D₁₇₂	Q₁₆	1	2	yes	—
93	C₂×C₄×D₄₃	—	4	1	no	—
94	C₂×C₄×D₄₃	—	4	1	no	—
95	C₂×C₄×D₄₃	—	4	1	no	—
96	C₂×C₄×D₄₃	—	4	1	no	—
97	C₂×C₄×D₄₃	—	4	1	no	—
98	C₂×C₄×D₄₃	—	4	1	no	—
99	C₂×Dic₈₆	—	2	1	no	—
100	C₂×Dic₈₆	—	2	1	no	—
101	C₂×Dic₈₆	—	2	1	no	—
102	C₂×Dic₈₆	—	2	1	no	—
103	C₂×Dic₈₆	—	2	1	no	—
104	C₂×Dic₈₆	—	2	2	no	—
105	C₂×Dic₈₆	—	4	2	no	—
106	C₂×Dic₈₆	—	4	2	no	—
107	C₂×Dic₈₆	—	4	1	no	—
108	C₂×Dic₈₆	SD₁₆	1	2	yes	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	4	1	no	—
112	C₂×C₈×C₄₃	—	4	1	no	—
113	C₂×C₈×C₄₃	—	4	1	no	—
114	C₂×C₈×C₄₃	—	4	1	no	—
115	C₄⋊C₄×C₄₃	—	4	2	no	—
116	C₄⋊C₄×C₄₃	—	4	1	no	—
117	C₄⋊C₄×C₄₃	—	4	1	no	—
118	C₄⋊C₄×C₄₃	—	4	1	no	—
119	C₄⋊C₄×C₄₃	—	4	1	no	—
120	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₃	#41	1	1	yes	characteristic
124	(C₂×D₄₃)⋊C₄	—	4	4	no	—
125	(C₂×D₄₃)⋊C₄	—	4	1	no	—
126	(C₂×D₄₃)⋊C₄	—	4	1	no	—
127	(C₂×D₄₃)⋊C₄	—	8	2	no	—
128	C₄⋊Dic₄₃	—	2	2	no	—
129	C₄⋊Dic₄₃	—	2	2	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	—	2	1	no	—
132	C₄⋊Dic₄₃	—	2	1	no	—
133	C₄⋊Dic₄₃	—	2	1	no	—
134	C₄⋊Dic₄₃	—	4	4	no	—
135	C₄⋊Dic₄₃	—	4	1	no	—
136	C₄⋊Dic₄₃	—	4	1	no	—
137	Dic₄₃⋊C₄	—	4	1	no	—
138	Dic₄₃⋊C₄	—	4	1	no	—
139	C₄×Dic₄₃	—	4	1	no	—
140	C₄×Dic₄₃	—	4	1	no	—
141	C₂×C₄₃⋊C₈	—	2	2	no	—
142	C₂×C₄₃⋊C₈	—	4	1	no	—
143	C₂×C₄₃⋊C₈	—	4	1	no	—
144	C₂³×C₄₃	#120	1	1	yes	characteristic
145	C₂²×D₄₃	—	2	2	no	—
146	C₂²×D₄₃	—	4	1	no	—
147	C₂²×D₄₃	—	4	1	no	—
148	C₂²×D₄₃	—	4	1	no	—
149	C₂²×D₄₃	—	4	1	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	C₂²×D₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
159	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×Q₁₆	1	1	yes	characteristic
165	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
167	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
171	C₂×Dic₄₃	—	2	2	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	1	no	—
174	C₂×Dic₄₃	—	4	1	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	1	no	—
181	C₂×Dic₄₃	—	8	1	no	—
182	C₂×Dic₄₃	—	8	1	no	—
183	D₁₇₂	—	2	2	no	—
184	D₁₇₂	—	2	2	no	—
185	D₁₇₂	—	4	1	no	—
186	D₁₇₂	—	4	1	no	—
187	C₄×D₄₃	—	8	1	no	—
188	C₄×D₄₃	—	8	1	no	—
189	C₄×D₄₃	—	8	1	no	—
190	C₄×D₄₃	—	8	1	no	—
191	Dic₈₆	—	2	2	no	—
192	Dic₈₆	—	2	2	no	—
193	Dic₈₆	—	4	1	no	—
194	Dic₈₆	—	4	1	no	—
195	Dic₈₆	—	4	4	no	—
196	Dic₈₆	—	8	2	no	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	#10236	—	43	1	no	maximal, Sylow
201	C₂²×C₄₃	#392	1	1	yes	characteristic
202	C₂²×C₄₃	#450	1	1	yes	characteristic
203	C₂²×C₄₃	#451	1	1	yes	characteristic
204	C₂²×C₄₃	#452	1	1	yes	characteristic
205	C₂²×C₄₃	#452	1	1	yes	characteristic
206	C₂²×C₄₃	#453	1	1	yes	characteristic
207	C₂²×C₄₃	#454	1	1	yes	characteristic
208	C₂×D₄₃	—	4	2	no	—
209	C₂×D₄₃	—	4	2	no	—
210	C₂×D₄₃	—	4	2	no	—
211	C₂×D₄₃	—	8	1	no	—
212	C₂×D₄₃	—	8	1	no	—
213	C₂×D₄₃	—	8	1	no	—
214	C₂×D₄₃	—	8	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	8	2	no	—
218	C₄×C₄₃	#448	1	1	yes	characteristic
219	C₄×C₄₃	#449	1	1	yes	characteristic
220	C₄×C₄₃	#451	1	1	yes	characteristic
221	C₄×C₄₃	#452	1	1	yes	characteristic
222	C₄×C₄₃	#465	1	1	yes	characteristic
223	C₄×C₄₃	#467	1	1	yes	characteristic
224	C₄×C₄₃	#468	1	1	yes	characteristic
225	C₄×C₄₃	#470	1	1	yes	characteristic
226	Dic₄₃	—	4	2	no	—
227	Dic₄₃	—	8	1	no	—
228	Dic₄₃	—	8	2	no	—
229	Dic₄₃	—	8	1	no	—
230	C₂×#477	—	43	1	no	—
231	C₂×#476	—	43	1	no	—
232	#2538	—	43	1	no	—
233	#1956	—	43	1	no	—
234	C₂×Q₈⋊C₈	—	43	1	no	—
235	C₂×D₄⋊C₈	—	43	1	no	—
236	#1296	D₄₃	1	1	yes	characteristic, complemented
237	C₂×C₄₃	#1631	1	1	yes	characteristic
238	C₂×C₄₃	#1632	1	1	yes	characteristic
239	C₂×C₄₃	#1637	1	1	yes	characteristic
240	C₂×C₄₃	#1638	1	1	yes	characteristic
241	C₂×C₄₃	#2000	1	1	yes	characteristic
242	C₂×C₄₃	#2001	1	1	yes	characteristic
243	C₂×C₄₃	#2006	1	1	yes	characteristic
244	D₄₃	—	8	2	no	—
245	C₂×C₄⋊Q₈	—	43	1	no	—
246	C₂×C₂²⋊Q₈	—	86	1	no	—
247	C₂×C₄×Q₈	—	43	1	no	—
248	C₂×C₄×D₄	—	43	1	no	—
249	#477	—	86	2	no	—
250	#477	—	86	2	no	—
251	#476	—	86	2	no	—
252	#476	—	86	2	no	—
253	C₂×#107	—	86	1	no	—
254	C₂×#106	—	86	1	no	—
255	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
256	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
257	C₂×#103	—	86	1	no	—
258	C₂×#103	—	86	2	no	—
259	C₂×#102	—	86	1	no	—
260	C₂×C₄×C₈	—	43	1	no	—
261	#396	—	86	2	no	—
262	#390	—	86	1	no	—
263	#389	—	86	1	no	—
264	#384	C₂×D₄₃	1	1	yes	characteristic
265	#380	—	86	1	no	—
266	Q₈⋊C₈	—	86	2	no	—
267	D₄⋊C₈	—	86	2	no	—
268	C₄₃	#10236	1	1	yes	characteristic, complemented, Sylow
269	C₂²×Q₈	—	43	1	no	—
270	C₂²×Q₈	—	86	1	no	—
271	C₂²×D₄	—	43	1	no	—
272	C₂³×C₄	—	86	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	86	1	no	—
276	C₄⋊Q₈	—	43	2	no	—
277	C₄⋊Q₈	—	86	1	no	—
278	C₄⋊Q₈	—	86	1	no	—
279	C₄⋊Q₈	—	86	1	no	—
280	C₂²⋊Q₈	—	172	2	no	—
281	C₂²⋊Q₈	—	172	2	no	—
282	C₄×Q₈	—	86	1	no	—
283	C₄×Q₈	—	86	1	no	—
284	C₄×Q₈	—	86	1	no	—
285	C₄×Q₈	—	86	1	no	—
286	C₄×D₄	—	86	1	no	—
287	C₄×D₄	—	86	1	no	—
288	C₄×D₄	—	86	1	no	—
289	C₄×D₄	—	86	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	43	1	no	—
293	C₂×C₄⋊C₄	—	43	1	no	—
294	C₂×C₄⋊C₄	—	86	1	no	—
295	C₂×C₄⋊C₄	—	86	1	no	—
296	C₂×C₄⋊C₄	—	86	2	no	—
297	C₂×C₄⋊C₄	—	86	1	no	—
298	C₂×C₄⋊C₄	D₁₇₂	1	2	yes	—
299	C₂×C₂²⋊C₄	—	86	2	no	—
300	C₂×C₂²⋊C₄	—	86	2	no	—
301	C₂×C₂²⋊C₄	—	86	1	no	—
302	C₂×C₄²	—	86	1	no	—
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	#107	—	86	4	no	—
305	#106	—	86	4	no	—
306	C₄⋊C₈	—	2	1	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	D₁₇₂	1	2	yes	—
309	C₄⋊C₈	D₁₇₂	1	2	yes	—
310	#103	—	86	4	no	—
311	#103	—	172	4	no	—
312	#102	—	86	4	no	—
313	C₄×C₈	—	86	1	no	—
314	C₄×C₈	—	86	1	no	—
315	#95	—	86	2	no	—
316	C₂⁴	—	86	1	no	—
317	C₂×Q₈	—	43	2	no	—
318	C₂×Q₈	—	86	1	no	—
319	C₂×Q₈	—	86	1	no	—
320	C₂×Q₈	—	86	1	no	—
321	C₂×Q₈	—	86	2	no	—
322	C₂×Q₈	—	86	1	no	—
323	C₂×Q₈	—	86	1	no	—
324	C₂×Q₈	—	172	2	no	—
325	C₂×Q₈	—	172	2	no	—
326	C₂×Q₈	—	172	1	no	—
327	C₂×D₄	—	43	2	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂×D₄	—	86	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	86	1	no	—
335	C₂²×C₄	—	86	1	no	—
336	C₂²×C₄	—	86	1	no	—
337	C₂²×C₄	—	172	1	no	—
338	C₂²×C₄	—	172	1	no	—
339	C₂²×C₄	—	172	1	no	—
340	C₂²×C₄	—	172	1	no	—
341	C₂²×C₄	—	172	1	no	—
342	C₂²×C₄	—	172	1	no	—
343	C₂²×C₄	—	172	1	no	—
344	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	—	86	2	no	—
354	C₂×C₈	—	172	1	no	—
355	C₂×C₈	—	172	1	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	86	2	no	—
362	C₄⋊C₄	—	86	2	no	—
363	C₄⋊C₄	—	86	1	no	—
364	C₄⋊C₄	—	86	1	no	—
365	C₄⋊C₄	—	86	1	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	172	4	no	—
368	C₄⋊C₄	—	172	1	no	—
369	C₄⋊C₄	—	172	1	no	—
370	C₄⋊C₄	—	172	1	no	—
371	C₄⋊C₄	—	172	1	no	—
372	C₂²⋊C₄	—	344	2	no	—
373	C₂²⋊C₄	—	172	4	no	—
374	C₂²⋊C₄	—	172	1	no	—
375	C₂²⋊C₄	—	172	1	no	—
376	C₄²	—	172	1	no	—
377	C₄²	—	172	1	no	—
378	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
379	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
380	C₄²	D₄×D₄₃	1	1	yes	characteristic
381	C₄²	#10621902	1	1	yes	characteristic
382	C₂³	—	86	2	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	—	172	1	no	—
389	C₂³	#13063295	1	1	yes	characteristic
390	Q₈	—	86	2	no	—
391	Q₈	—	86	2	no	—
392	Q₈	—	344	2	no	—
393	Q₈	—	172	4	no	—
394	Q₈	—	172	1	no	—
395	Q₈	—	172	1	no	—
396	D₄	—	86	2	no	—
397	D₄	—	86	2	no	—
398	D₄	—	172	1	no	—
399	D₄	—	172	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	344	1	no	—
407	C₂×C₄	—	344	1	no	—
408	C₂×C₄	—	344	1	no	—
409	C₂×C₄	—	344	1	no	—
410	C₂×C₄	—	344	1	no	—
411	C₂×C₄	—	344	1	no	—
412	C₂×C₄	—	172	1	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	—	172	1	no	—
415	C₂×C₄	—	172	1	no	—
416	C₂×C₄	—	172	2	no	—
417	C₂×C₄	—	172	1	no	—
418	C₂×C₄	—	172	1	no	—
419	C₂×C₄	—	172	1	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	#13063295	1	1	yes	characteristic
422	C₂×C₄	#13063295	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	#13063322	1	1	yes	characteristic
427	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
428	C₂×C₄	Q₁₆×D₄₃	1	1	yes	characteristic
429	C₂×C₄	#13063344	1	1	yes	characteristic
430	C₂×C₄	#13063346	1	1	yes	characteristic
431	C₂×C₄	#13063349	1	1	yes	characteristic
432	C₂×C₄	#13063354	1	1	yes	characteristic
433	C₂×C₄	#13063354	1	1	yes	characteristic
434	C₂×C₄	#13063357	1	1	yes	characteristic
435	C₈	—	4	2	no	—
436	C₈	—	4	2	no	—
437	C₈	—	172	2	no	—
438	C₂²	—	344	1	no	—
439	C₂²	—	344	1	no	—
440	C₂²	—	344	1	no	—
441	C₂²	—	344	1	no	—
442	C₂²	—	172	2	no	—
443	C₂²	—	172	2	no	—
444	C₂²	—	172	2	no	—
445	C₂²	#14582809	1	1	yes	characteristic
446	C₂²	#14583051	1	1	yes	characteristic
447	C₂²	#14583056	1	1	yes	characteristic
448	C₂²	#14583062	1	1	yes	characteristic
449	C₂²	#14583064	1	1	yes	characteristic
450	C₂²	#14583069	1	1	yes	characteristic
451	C₂²	#14583074	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	344	1	no	—
456	C₄	—	344	2	no	—
457	C₄	—	344	1	no	—
458	C₄	—	172	2	no	—
459	C₄	#14583039	1	1	yes	characteristic
460	C₄	#14583045	1	1	yes	characteristic
461	C₄	#14583056	1	1	yes	characteristic
462	C₄	#14583062	1	1	yes	characteristic
463	C₄	#14583129	1	1	yes	characteristic
464	C₄	#14583141	1	1	yes	characteristic
465	C₄	#14583146	1	1	yes	characteristic
466	C₄	#14583158	1	1	yes	characteristic
467	C₂	—	344	2	no	—
468	C₂	#19133723	1	1	yes	characteristic
469	C₂	#19133730	1	1	yes	characteristic
470	C₂	#19133761	1	1	yes	characteristic
471	C₂	#19133768	1	1	yes	characteristic
472	C₂	#19135601	1	1	yes	characteristic
473	C₂	#19135606	1	1	yes	characteristic
474	C₂	#19135639	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063295
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1296	C₂
socle	C₂³×C₄₃	#120
prime radical	C₂²×D₁₇₂	D₄
hypercenter	#1296	D₄₃
hypocenter	C₄₃	#10236
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
1. C₂×#14583195	C₂	semidirect
4. #19135396	C₂	semidirect
5. C₂×#14582629	C₂	semidirect
7. C₄₃×#1296	C₂	semidirect
236. #1296	D₄₃	semidirect
268. C₄₃	#10236	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583195	2
C₂×#14583190	2
#19139518	2
#19135396	2
C₂×#14582629	2
C₂×#14582626	2
C₄₃×#1296	2
#10236	43