Subgroups — #25154698

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19137550	C₂	1	1	yes	maximal, characteristic
2	#19135973	C₂	1	2	yes	maximal
3	#19135733	C₂	1	2	yes	maximal
4	#19135548	C₂	1	2	yes	maximal
5	#19135358	C₂	1	1	yes	maximal, characteristic
6	#19135314	C₂	1	1	yes	maximal, characteristic
7	#19135170	C₂	1	2	yes	maximal
8	#19134722	C₂	1	1	yes	maximal, characteristic
9	#19134597	C₂	1	1	yes	maximal, characteristic
10	C₄×#13063248	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2551	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₂×#13063256	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
16	C₂×#13063248	C₂²	1	1	yes	characteristic
17	C₂×#13063248	C₂²	1	1	yes	characteristic
18	C₂×#13063248	C₂²	1	2	yes	—
19	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
20	#14582805	C₂²	1	2	yes	—
21	#14582786	—	2	2	no	—
22	#14582769	C₂²	1	1	yes	characteristic
23	#14582764	—	2	1	no	—
24	C₄⋊C₄×Dic₄₃	—	2	1	no	—
25	C₄×C₄⋊Dic₄₃	C₂²	1	2	yes	—
26	#14582661	C₂²	1	2	yes	—
27	#14582661	C₂²	1	2	yes	—
28	#14582661	C₂²	1	1	yes	characteristic
29	#14582661	C₂²	1	2	yes	—
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	1	yes	characteristic
32	#14582654	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
34	C₂×C₄⋊Q₈×C₄₃	C₂²	1	2	yes	—
35	C₄₃×#395	—	2	2	no	—
36	C₄₃×#389	—	2	1	no	—
37	C₄₃×#389	C₂²	1	2	yes	—
38	C₄₃×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
42	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
45	C₄×Dic₈₆	—	2	2	no	—
46	C₄×Dic₈₆	Q₈	1	4	yes	complemented
47	C₂×C₄⋊Dic₄₃	—	2	1	no	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
51	C₂×Dic₄₃⋊C₄	—	2	1	no	—
52	C₂×C₄×Dic₄₃	—	2	1	no	—
53	C₂×C₄×Dic₄₃	—	2	2	no	—
54	#13063256	—	2	4	no	—
55	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
56	C₄⋊(C₄₃⋊C₈)	—	4	2	no	—
57	#13063248	—	2	2	no	—
58	#13063248	—	2	2	no	—
59	#13063248	—	4	2	no	—
60	C₄×C₄₃⋊C₈	—	2	2	no	—
61	C₄₃⋊#95	—	2	2	no	—
62	C₄₃⋊#95	—	2	2	no	—
63	C₄₃⋊#95	—	2	2	no	—
64	C₂²×Q₈×C₄₃	—	2	2	no	—
65	C₄⋊Q₈×C₄₃	—	2	4	no	—
66	C₄⋊Q₈×C₄₃	—	4	2	no	—
67	C₄⋊Q₈×C₄₃	—	4	4	no	—
68	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₃	—	2	1	no	—
78	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
80	#95×C₄₃	—	2	1	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	D₄	1	2	yes	—
83	C₂×Q₈×C₄₃	—	4	4	no	—
84	C₂×Q₈×C₄₃	—	4	4	no	—
85	C₂×Q₈×C₄₃	—	8	2	no	—
86	C₂²×C₄×C₄₃	—	2	1	no	—
87	C₂²×C₄×C₄₃	—	2	1	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₃	—	2	1	no	—
95	C₂²×Dic₄₃	—	2	1	no	—
96	C₂²×Dic₄₃	—	2	2	no	—
97	C₂×Dic₈₆	—	2	1	no	—
98	C₂×Dic₈₆	—	2	1	no	—
99	C₂×Dic₈₆	—	2	1	no	—
100	C₂×Dic₈₆	—	2	1	no	—
101	C₂×Dic₈₆	—	2	1	no	—
102	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
103	C₄⋊C₄×C₄₃	—	2	2	no	—
104	C₄⋊C₄×C₄₃	—	2	1	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	2	2	no	—
107	C₄⋊C₄×C₄₃	—	2	2	no	—
108	C₄⋊C₄×C₄₃	—	4	4	no	—
109	C₄⋊C₄×C₄₃	—	4	4	no	—
110	C₄⋊C₄×C₄₃	—	4	2	no	—
111	C₄⋊C₄×C₄₃	—	8	1	no	—
112	C₄⋊C₄×C₄₃	SD₁₆	1	4	yes	—
113	C₄⋊C₄×C₄₃	#41	1	2	yes	—
114	C₄⋊C₄×C₄₃	#41	1	2	yes	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	—	4	2	no	—
118	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
119	C₄²×C₄₃	#41	1	2	yes	—
120	C₄⋊Dic₄₃	—	2	1	no	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	2	no	—
123	C₄⋊Dic₄₃	—	4	2	no	—
124	C₄⋊Dic₄₃	—	8	1	no	—
125	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
126	Dic₄₃⋊C₄	—	2	4	no	—
127	C₄×Dic₄₃	—	2	4	no	—
128	C₄×Dic₄₃	—	8	2	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	2	1	no	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	2	no	—
134	C₂×C₄₃⋊C₈	—	2	2	no	—
135	C₂×C₄₃⋊C₈	—	2	2	no	—
136	C₂×C₄₃⋊C₈	—	2	1	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₄₃	—	8	8	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	2	2	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	4	1	no	—
150	C₂×C₄×C₄₃	—	4	1	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₃	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
159	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
160	C₂×C₄×C₄₃	#137	1	2	yes	—
161	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
166	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	1	no	—
172	C₂×Dic₄₃	—	4	1	no	—
173	C₂×Dic₄₃	—	4	2	no	—
174	C₂×Dic₄₃	—	4	2	no	—
175	C₂×Dic₄₃	—	4	2	no	—
176	Dic₈₆	—	2	2	no	—
177	Dic₈₆	—	2	2	no	—
178	Dic₈₆	—	4	1	no	—
179	Dic₈₆	—	4	1	no	—
180	C₄₃⋊C₈	—	4	1	no	—
181	C₄₃⋊C₈	—	4	2	no	—
182	C₄₃⋊C₈	—	4	1	no	—
183	#26022	—	43	1	no	maximal, Sylow
184	C₂²×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
185	C₂²×C₄₃	#546	1	1	yes	characteristic
186	C₂²×C₄₃	#548	1	1	yes	characteristic
187	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
188	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
189	C₂²×C₄₃	#576	1	1	yes	characteristic
190	C₂²×C₄₃	#578	1	1	yes	characteristic
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	4	no	—
193	C₄×C₄₃	—	4	2	no	—
194	C₄×C₄₃	—	4	2	no	—
195	C₄×C₄₃	—	4	2	no	—
196	C₄×C₄₃	—	8	2	no	—
197	C₄×C₄₃	#475	1	4	yes	—
198	C₄×C₄₃	#533	1	1	yes	characteristic
199	C₄×C₄₃	#544	1	1	yes	characteristic
200	C₄×C₄₃	#555	1	1	yes	characteristic
201	C₄×C₄₃	#556	1	1	yes	characteristic
202	Dic₄₃	—	4	2	no	—
203	Dic₄₃	—	4	2	no	—
204	Dic₄₃	—	8	2	no	—
205	#2551	D₄₃	1	1	yes	characteristic
206	#2355	—	43	1	no	—
207	#2066	—	43	2	no	—
208	#2024	—	43	2	no	—
209	#1988	—	43	2	no	—
210	#1948	—	43	1	no	—
211	#1939	—	43	1	no	—
212	#1919	—	43	2	no	—
213	#1834	—	43	1	no	—
214	#1803	—	43	1	no	—
215	C₄×#103	—	43	1	no	—
216	C₂×C₄₃	#2439	1	1	yes	characteristic
217	C₂×C₄₃	C₂×#475	1	1	yes	characteristic
218	C₂×C₄₃	#3083	1	1	yes	characteristic
219	C₂×C₄₃	#3295	1	1	yes	characteristic
220	C₂×C₄₃	#3328	1	1	yes	characteristic
221	C₂×C₄₃	#3359	1	1	yes	characteristic
222	C₂×C₄₃	#3375	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	—	2	1	no	—
224	C₂×C₄⋊Q₈	C₂×D₄₃	1	2	yes	—
225	C₂×C₄×Q₈	—	43	1	no	—
226	C₂×#106	—	43	2	no	—
227	C₂×C₄⋊C₈	—	43	1	no	—
228	C₂×C₄⋊C₈	—	43	2	no	—
229	C₂×#103	—	43	1	no	—
230	C₂×#103	—	43	1	no	—
231	C₂×#103	—	43	2	no	—
232	C₂×C₄×C₈	—	43	1	no	—
233	#395	—	2	2	no	—
234	#391	—	43	2	no	—
235	#389	—	2	1	no	—
236	#389	C₂×D₄₃	1	2	yes	—
237	#387	—	86	2	no	—
238	#384	—	43	1	no	—
239	#384	C₂×D₄₃	1	1	yes	characteristic
240	#382	—	86	1	no	—
241	C₄×C₄⋊C₄	—	43	2	no	—
242	C₄×C₄⋊C₄	—	86	1	no	—
243	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
244	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
245	#340	—	43	2	no	—
246	#340	—	43	2	no	—
247	#340	—	43	2	no	—
248	#340	—	43	1	no	—
249	#340	—	43	2	no	—
250	#340	—	43	1	no	—
251	#336	—	43	2	no	—
252	C₄₃	#26022	1	1	yes	characteristic, complemented, Sylow
253	C₂²×Q₈	—	2	2	no	—
254	C₂²×Q₈	—	43	1	no	—
255	C₂²×C₈	—	43	1	no	—
256	C₂²×C₈	—	43	2	no	—
257	C₂²×C₈	—	43	1	no	—
258	C₄⋊Q₈	—	2	4	no	—
259	C₄⋊Q₈	—	4	2	no	—
260	C₄⋊Q₈	—	4	4	no	—
261	C₄×Q₈	—	43	4	no	—
262	C₄×Q₈	—	86	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	43	1	no	—
268	C₂×C₄⋊C₄	—	43	2	no	—
269	C₂×C₄⋊C₄	—	86	1	no	—
270	C₂×C₄⋊C₄	—	86	1	no	—
271	C₂×C₄⋊C₄	—	86	1	no	—
272	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
275	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	86	1	no	—
279	C₂×C₄²	—	86	2	no	—
280	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
281	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
282	#106	—	86	4	no	—
283	C₄⋊C₈	—	86	2	no	—
284	C₄⋊C₈	—	172	2	no	—
285	#103	—	86	2	no	—
286	#103	—	86	2	no	—
287	#103	—	172	2	no	—
288	C₄×C₈	—	86	2	no	—
289	#95	—	2	1	no	—
290	#95	—	2	2	no	—
291	#95	—	86	2	no	—
292	#95	—	86	2	no	—
293	#95	—	86	2	no	—
294	#95	C₂²⋊D₄₃	1	2	yes	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	8	2	no	—
298	C₂×Q₈	—	43	2	no	—
299	C₂×Q₈	—	86	1	no	—
300	C₂×Q₈	—	86	1	no	—
301	C₂×Q₈	—	86	1	no	—
302	C₂×Q₈	—	86	1	no	—
303	C₂×Q₈	—	86	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	86	1	no	—
308	C₂²×C₄	—	86	1	no	—
309	C₂²×C₄	—	86	2	no	—
310	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
311	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
315	C₂×C₈	—	86	1	no	—
316	C₂×C₈	—	86	1	no	—
317	C₂×C₈	—	86	1	no	—
318	C₂×C₈	—	86	1	no	—
319	C₂×C₈	—	86	2	no	—
320	C₂×C₈	—	86	2	no	—
321	C₂×C₈	—	86	2	no	—
322	C₂×C₈	—	86	1	no	—
323	C₂×C₈	—	86	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	8	1	no	—
333	C₄⋊C₄	—	43	2	no	—
334	C₄⋊C₄	—	86	4	no	—
335	C₄⋊C₄	—	86	1	no	—
336	C₄⋊C₄	—	86	2	no	—
337	C₄⋊C₄	—	86	2	no	—
338	C₄⋊C₄	—	344	1	no	—
339	C₄⋊C₄	—	172	2	no	—
340	C₄⋊C₄	#10621883	1	4	yes	—
341	C₄⋊C₄	#10621900	1	2	yes	—
342	C₄⋊C₄	#10621902	1	2	yes	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	4	2	no	—
346	C₄²	—	86	4	no	—
347	C₄²	—	344	2	no	—
348	C₄²	Q₈×D₄₃	1	2	yes	—
349	C₄²	#10621902	1	2	yes	—
350	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
351	Q₈	—	8	8	no	—
352	Q₈	—	86	2	no	—
353	Q₈	—	86	2	no	—
354	Q₈	—	172	1	no	—
355	Q₈	—	172	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	86	2	no	—
373	C₂×C₄	—	86	2	no	—
374	C₂×C₄	—	172	2	no	—
375	C₂×C₄	—	172	2	no	—
376	C₂×C₄	—	172	2	no	—
377	C₂×C₄	—	172	1	no	—
378	C₂×C₄	—	172	1	no	—
379	C₂×C₄	—	172	1	no	—
380	C₂×C₄	—	172	1	no	—
381	C₂×C₄	#13063301	1	2	yes	—
382	C₂×C₄	#13063301	1	2	yes	—
383	C₂×C₄	C₂×#10621883	1	4	yes	—
384	C₂×C₄	C₂×#10621883	1	2	yes	—
385	C₂×C₄	#13063356	1	2	yes	—
386	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
388	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
389	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
390	C₂×C₄	#13063370	1	1	yes	characteristic
391	C₂×C₄	#13063373	1	1	yes	characteristic
392	C₈	—	172	1	no	—
393	C₈	—	172	2	no	—
394	C₈	—	172	1	no	—
395	C₂²	C₂×#13063301	1	1	yes	characteristic
396	C₂²	#14583543	1	1	yes	characteristic
397	C₂²	#14583560	1	1	yes	characteristic
398	C₂²	C₂²×#10621883	1	1	yes	characteristic
399	C₂²	C₂×#13063356	1	1	yes	characteristic
400	C₂²	#14583702	1	1	yes	characteristic
401	C₂²	#14583714	1	1	yes	characteristic
402	C₄	—	2	4	no	—
403	C₄	—	2	2	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	8	2	no	—
408	C₄	—	344	2	no	—
409	C₄	—	172	2	no	—
410	C₄	—	172	2	no	—
411	C₄	#14583181	1	4	yes	—
412	C₄	#14583454	1	1	yes	characteristic
413	C₄	#14583526	1	1	yes	characteristic
414	C₄	#14583615	1	1	yes	characteristic
415	C₄	#14583623	1	1	yes	characteristic
416	C₂	#19138282	1	1	yes	characteristic
417	C₂	C₂×#14583181	1	1	yes	characteristic
418	C₂	#19144442	1	1	yes	characteristic
419	C₂	#19146419	1	1	yes	characteristic
420	C₂	#19146878	1	1	yes	characteristic
421	C₂	#19147237	1	1	yes	characteristic
422	C₂	#19147409	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×#2551	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2551	D₄₃
hypocenter	C₄₃	#26022
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2551

Complements

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

N	H ≅ G/N	type
46. C₄×Dic₈₆	Q₈	semidirect
252. C₄₃	#26022	semidirect

Maximal subgroups

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

subgroup	index
#19137550	2
#19135973	2
#19135733	2
#19135548	2
#19135358	2
#19135314	2
#19135170	2
#19134722	2
#19134597	2
C₄×#13063248	2
C₄₃×#2551	2
#26022	43