Subgroups — #25146496

Order 11008.

790 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583251	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583110	C₂	1	1	yes	maximal, characteristic
3	#19139811	C₂	1	1	yes	maximal, characteristic
4	#19137653	C₂	1	1	yes	maximal, characteristic
5	#19136017	C₂	1	2	yes	maximal
6	#19135919	C₂	1	2	yes	maximal
7	#19135311	C₂	1	1	yes	maximal, characteristic
8	#19134937	C₂	1	2	yes	maximal
9	#19134609	C₂	1	2	yes	maximal
10	C₄×#13063248	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1988	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₁₇₂	C₂²	1	2	yes	—
13	C₂×#13063325	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
15	C₂×#13063290	C₂²	1	2	yes	—
16	#14583251	—	2	4	no	—
17	#14583110	—	2	4	no	—
18	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
19	C₂×#13063250	C₂²	1	2	yes	—
20	C₂×#13063248	C₂²	1	2	yes	—
21	C₂×#13063248	C₂²	1	2	yes	—
22	C₂×#13063248	C₂²	1	1	yes	characteristic
23	C₂×#13063248	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
25	#14582837	—	2	2	no	—
26	#14582806	—	2	1	no	—
27	#14582806	—	2	1	no	—
28	#14582804	C₂²	1	2	yes	—
29	#14582804	C₂²	1	2	yes	—
30	#14582797	—	2	1	no	—
31	#14582784	—	2	2	no	—
32	#14582764	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₃	—	2	1	no	—
34	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
35	#14582661	C₂²	1	1	yes	characteristic
36	#14582661	C₂²	1	1	yes	characteristic
37	#14582653	C₂²	1	2	yes	—
38	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₄₃×#340	C₂²	1	2	yes	—
43	C₂²×Dic₈₆	C₂³	1	2	yes	—
44	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
45	C₂×Dic₁₇₂	—	2	4	no	—
46	C₂×Dic₁₇₂	—	2	4	no	—
47	C₂×Dic₁₇₂	—	4	2	no	—
48	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
50	#13063325	—	2	2	no	—
51	#13063325	D₄	1	4	yes	—
52	C₄×Dic₈₆	—	2	2	no	—
53	C₄×Dic₈₆	—	2	2	no	—
54	#13063290	—	2	4	no	—
55	#13063290	—	4	2	no	—
56	C₂×C₄⋊Dic₄₃	—	2	1	no	—
57	C₂×C₄⋊Dic₄₃	—	2	1	no	—
58	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
60	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
61	C₂×Dic₄₃⋊C₄	—	2	1	no	—
62	C₂×Dic₄₃⋊C₄	—	2	2	no	—
63	C₂×C₄×Dic₄₃	—	2	1	no	—
64	C₂×C₄×Dic₄₃	—	2	2	no	—
65	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
66	Dic₄₃⋊C₈	—	4	2	no	—
67	#13063250	—	2	4	no	—
68	#13063248	—	2	4	no	—
69	#13063248	—	2	4	no	—
70	#13063248	—	2	2	no	—
71	#13063248	—	2	2	no	—
72	C₄×C₄₃⋊C₈	—	2	2	no	—
73	C₄₃⋊#95	—	2	2	no	—
74	C₄₃⋊#95	—	2	2	no	—
75	C₄₃⋊#95	—	2	2	no	—
76	C₄₃⋊#95	—	2	2	no	—
77	C₄₃⋊#95	—	2	2	no	—
78	C₄₃⋊#95	—	2	2	no	—
79	C₄₃⋊#95	D₄	1	2	yes	—
80	C₂²×Q₈×C₄₃	—	2	1	no	—
81	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₄₃	—	2	2	no	—
83	C₄⋊Q₈×C₄₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	—	2	2	no	—
91	#95×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	—	4	2	no	—
93	C₂×Q₈×C₄₃	—	4	2	no	—
94	C₂×Q₈×C₄₃	—	4	2	no	—
95	C₂²×C₄×C₄₃	—	2	1	no	—
96	C₂²×C₄×C₄₃	—	2	1	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
101	C₂²×Dic₄₃	—	2	1	no	—
102	C₂²×Dic₄₃	—	2	2	no	—
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
105	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	2	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	2	no	—
111	C₂×Dic₈₆	—	2	2	no	—
112	C₂×Dic₈₆	—	2	1	no	—
113	C₂×Dic₈₆	—	2	2	no	—
114	C₂×Dic₈₆	—	2	2	no	—
115	C₂×Dic₈₆	—	2	1	no	—
116	C₂×Dic₈₆	C₂×D₄	1	4	yes	—
117	C₂×Dic₈₆	#41	1	2	yes	—
118	C₂×C₈×C₄₃	—	2	2	no	—
119	C₂×C₈×C₄₃	—	2	2	no	—
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₄⋊C₄×C₄₃	#41	1	2	yes	—
128	C₄²×C₄₃	—	4	2	no	—
129	C₄²×C₄₃	C₂×D₄	1	2	yes	—
130	C₄²×C₄₃	#41	1	2	yes	—
131	C₄⋊Dic₄₃	—	2	4	no	—
132	C₄⋊Dic₄₃	—	2	4	no	—
133	C₄⋊Dic₄₃	—	2	2	no	—
134	C₄⋊Dic₄₃	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	1	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	Dic₄₃⋊C₄	—	4	4	no	—
138	Dic₄₃⋊C₄	—	4	2	no	—
139	C₄×Dic₄₃	—	2	2	no	—
140	C₄×Dic₄₃	—	2	2	no	—
141	C₄×Dic₄₃	—	4	4	no	—
142	C₄×Dic₄₃	—	4	2	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	—	2	1	no	—
145	C₂×C₄₃⋊C₈	—	2	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	Dic₁₇₂	—	4	8	no	—
150	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₃	—	8	4	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	1	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	4	1	no	—
156	C₂×C₄×C₄₃	—	4	1	no	—
157	C₂×C₄×C₄₃	—	4	2	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	#121	1	2	yes	—
164	C₂×C₄×C₄₃	#121	1	2	yes	—
165	C₂×C₄×C₄₃	#135	1	2	yes	—
166	C₂×C₄×C₄₃	#137	1	2	yes	—
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₃	—	2	4	no	—
174	C₂×Dic₄₃	—	2	2	no	—
175	C₂×Dic₄₃	—	2	2	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	2	2	no	—
178	C₂×Dic₄₃	—	2	2	no	—
179	C₂×Dic₄₃	—	2	2	no	—
180	C₂×Dic₄₃	—	2	2	no	—
181	C₂×Dic₄₃	—	4	1	no	—
182	C₂×Dic₄₃	—	4	2	no	—
183	C₂×Dic₄₃	—	4	1	no	—
184	C₂×Dic₄₃	—	4	2	no	—
185	C₂×Dic₄₃	—	4	1	no	—
186	C₂×Dic₄₃	—	4	1	no	—
187	C₂×Dic₄₃	—	4	1	no	—
188	Dic₈₆	—	2	2	no	—
189	Dic₈₆	—	2	2	no	—
190	Dic₈₆	—	2	4	no	—
191	Dic₈₆	—	2	4	no	—
192	Dic₈₆	—	4	2	no	—
193	Dic₈₆	—	4	1	no	—
194	Dic₈₆	—	4	2	no	—
195	Dic₈₆	—	4	1	no	—
196	C₈×C₄₃	—	4	2	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	C₄₃⋊C₈	—	4	1	no	—
199	#25323	—	43	1	no	maximal, Sylow
200	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
201	C₂²×C₄₃	#546	1	1	yes	characteristic
202	C₂²×C₄₃	#548	1	1	yes	characteristic
203	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
205	C₂²×C₄₃	#578	1	1	yes	characteristic
206	C₂²×C₄₃	#578	1	1	yes	characteristic
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	4	2	no	—
209	C₄×C₄₃	—	8	1	no	—
210	C₄×C₄₃	—	8	2	no	—
211	C₄×C₄₃	#464	1	4	yes	—
212	C₄×C₄₃	#529	1	1	yes	characteristic
213	C₄×C₄₃	#542	1	1	yes	characteristic
214	C₄×C₄₃	#546	1	1	yes	characteristic
215	C₄×C₄₃	#547	1	1	yes	characteristic
216	Dic₄₃	—	4	2	no	—
217	Dic₄₃	—	4	2	no	—
218	Dic₄₃	—	4	4	no	—
219	Dic₄₃	—	4	2	no	—
220	Dic₄₃	—	8	1	no	—
221	C₂×#487	—	43	1	no	—
222	C₂×#462	—	43	1	no	—
223	#2568	—	43	1	no	—
224	#2365	—	43	1	no	—
225	#2074	—	43	2	no	—
226	#2056	—	43	2	no	—
227	#1988	D₄₃	1	1	yes	characteristic
228	#1939	—	43	1	no	—
229	#1878	—	43	2	no	—
230	#1805	—	43	2	no	—
231	C₄×#103	—	43	1	no	—
232	C₂×C₄₃	#2427	1	1	yes	characteristic
233	C₂×C₄₃	C₂×#464	1	1	yes	characteristic
234	C₂×C₄₃	#3044	1	1	yes	characteristic
235	C₂×C₄₃	#3302	1	1	yes	characteristic
236	C₂×C₄₃	#3328	1	1	yes	characteristic
237	C₂×C₄₃	#3364	1	1	yes	characteristic
238	C₂×C₄₃	#3374	1	1	yes	characteristic
239	C₂²×Q₁₆	—	43	2	no	—
240	C₂×C₄⋊Q₈	—	43	1	no	—
241	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
242	C₂×C₄×Q₈	—	43	2	no	—
243	C₂×C₄×Q₈	—	43	1	no	—
244	#487	—	86	4	no	—
245	#462	—	86	4	no	—
246	C₂×C₄⋊C₈	—	43	2	no	—
247	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
248	C₂×#103	—	43	2	no	—
249	C₂×#103	—	43	1	no	—
250	C₂×#103	—	43	2	no	—
251	C₂×#103	—	43	2	no	—
252	C₂×#103	—	43	1	no	—
253	C₂×C₄×C₈	—	43	1	no	—
254	#400	—	86	2	no	—
255	#391	—	43	2	no	—
256	#391	—	43	2	no	—
257	#391	—	86	1	no	—
258	#391	—	86	1	no	—
259	#389	—	86	1	no	—
260	#387	—	86	2	no	—
261	#382	—	43	2	no	—
262	C₄×C₄⋊C₄	—	43	1	no	—
263	C₄×C₄⋊C₄	—	86	1	no	—
264	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
265	#340	—	43	1	no	—
266	#340	—	43	1	no	—
267	#340	C₂×D₄₃	1	2	yes	—
268	#340	C₂×D₄₃	1	2	yes	—
269	#336	—	43	2	no	—
270	C₄₃	#25323	1	1	yes	characteristic, complemented, Sylow
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	43	2	no	—
273	C₂²×Q₈	—	43	1	no	—
274	C₂×Q₁₆	—	86	4	no	—
275	C₂×Q₁₆	—	86	4	no	—
276	C₂×Q₁₆	—	172	2	no	—
277	C₂²×C₈	—	43	1	no	—
278	C₂²×C₈	—	43	1	no	—
279	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄⋊Q₈	—	43	4	no	—
283	C₄⋊Q₈	—	86	2	no	—
284	C₄×Q₈	—	86	4	no	—
285	C₄×Q₈	—	86	2	no	—
286	C₄×Q₈	—	86	2	no	—
287	C₄×Q₈	—	172	2	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	43	1	no	—
290	C₂×C₄⋊C₄	—	43	1	no	—
291	C₂×C₄⋊C₄	—	43	1	no	—
292	C₂×C₄⋊C₄	—	86	1	no	—
293	C₂×C₄⋊C₄	—	86	1	no	—
294	C₂×C₄⋊C₄	—	86	2	no	—
295	C₂×C₄⋊C₄	—	86	1	no	—
296	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	43	2	no	—
301	C₂×C₄²	—	86	2	no	—
302	C₂×C₄²	—	86	1	no	—
303	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	—	172	2	no	—
306	#103	—	86	2	no	—
307	#103	—	86	4	no	—
308	#103	—	86	4	no	—
309	#103	—	86	4	no	—
310	#103	—	86	2	no	—
311	C₄×C₈	—	86	2	no	—
312	#95	—	2	1	no	—
313	#95	—	43	2	no	—
314	#95	—	86	2	no	—
315	#95	—	86	2	no	—
316	#95	—	86	2	no	—
317	#95	—	86	2	no	—
318	#95	—	86	2	no	—
319	#95	—	86	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	—	4	2	no	—
323	C₂×Q₈	—	43	4	no	—
324	C₂×Q₈	—	43	2	no	—
325	C₂×Q₈	—	86	2	no	—
326	C₂×Q₈	—	86	1	no	—
327	C₂×Q₈	—	86	1	no	—
328	C₂×Q₈	—	86	2	no	—
329	C₂×Q₈	—	86	1	no	—
330	C₂×Q₈	—	86	1	no	—
331	C₂×Q₈	—	86	2	no	—
332	C₂×Q₈	—	86	2	no	—
333	C₂×Q₈	—	86	1	no	—
334	C₂×Q₈	—	86	2	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	43	2	no	—
339	C₂²×C₄	—	43	2	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	2	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
344	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
346	Q₁₆	—	172	8	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	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	1	no	—
355	C₂×C₈	—	86	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	2	no	—
362	C₄⋊C₄	—	86	4	no	—
363	C₄⋊C₄	—	86	4	no	—
364	C₄⋊C₄	—	86	2	no	—
365	C₄⋊C₄	—	86	2	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	172	4	no	—
369	C₄⋊C₄	—	172	2	no	—
370	C₄⋊C₄	#10621902	1	2	yes	—
371	C₄²	—	4	2	no	—
372	C₄²	—	86	2	no	—
373	C₄²	—	86	2	no	—
374	C₄²	—	172	4	no	—
375	C₄²	—	172	2	no	—
376	C₄²	#10621898	1	2	yes	—
377	C₄²	D₄×D₄₃	1	2	yes	—
378	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
379	Q₈	—	8	4	no	—
380	Q₈	—	86	4	no	—
381	Q₈	—	86	2	no	—
382	Q₈	—	86	2	no	—
383	Q₈	—	86	4	no	—
384	Q₈	—	172	1	no	—
385	Q₈	—	172	2	no	—
386	Q₈	—	172	2	no	—
387	Q₈	—	172	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	86	2	no	—
400	C₂×C₄	—	86	4	no	—
401	C₂×C₄	—	86	2	no	—
402	C₂×C₄	—	86	2	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	86	2	no	—
405	C₂×C₄	—	86	2	no	—
406	C₂×C₄	—	86	2	no	—
407	C₂×C₄	—	172	1	no	—
408	C₂×C₄	—	172	1	no	—
409	C₂×C₄	—	172	1	no	—
410	C₂×C₄	—	172	2	no	—
411	C₂×C₄	—	172	1	no	—
412	C₂×C₄	—	172	2	no	—
413	C₂×C₄	—	172	1	no	—
414	C₂×C₄	#13063298	1	2	yes	—
415	C₂×C₄	#13063298	1	2	yes	—
416	C₂×C₄	#13063344	1	2	yes	—
417	C₂×C₄	#13063354	1	2	yes	—
418	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
419	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
421	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
422	C₂×C₄	#13063371	1	1	yes	characteristic
423	C₂×C₄	#13063373	1	1	yes	characteristic
424	C₈	—	4	2	no	—
425	C₈	—	172	1	no	—
426	C₈	—	172	1	no	—
427	C₂²	C₂×#13063298	1	1	yes	characteristic
428	C₂²	#14583540	1	1	yes	characteristic
429	C₂²	#14583559	1	1	yes	characteristic
430	C₂²	C₂×#13063344	1	1	yes	characteristic
431	C₂²	C₂×#13063354	1	1	yes	characteristic
432	C₂²	#14583715	1	1	yes	characteristic
433	C₂²	#14583715	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	344	1	no	—
439	C₄	—	172	2	no	—
440	C₄	—	172	2	no	—
441	C₄	—	172	2	no	—
442	C₄	—	172	4	no	—
443	C₄	#14583120	1	4	yes	—
444	C₄	#14583436	1	1	yes	characteristic
445	C₄	#14583521	1	1	yes	characteristic
446	C₄	#14583542	1	1	yes	characteristic
447	C₄	#14583552	1	1	yes	characteristic
448	C₂	#19138173	1	1	yes	characteristic
449	C₂	C₂×#14583120	1	1	yes	characteristic
450	C₂	#19144124	1	1	yes	characteristic
451	C₂	#19146509	1	1	yes	characteristic
452	C₂	#19146875	1	1	yes	characteristic
453	C₂	#19147279	1	1	yes	characteristic
454	C₂	#19147397	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator, cosocle	C₂²×C₄×C₄₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1988	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#1988	D₄₃
hypocenter	C₄₃	#25323
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1988

Complements

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

N	H ≅ G/N	type
270. C₄₃	#25323	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583251	2
C₂×#14583110	2
#19139811	2
#19137653	2
#19136017	2
#19135919	2
#19135311	2
#19134937	2
#19134609	2
C₄×#13063248	2
C₄₃×#1988	2
#25323	43