Subgroups — #25148477

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583181	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19139965	C₂	1	1	yes	maximal, characteristic
4	#19136096	C₂	1	2	yes	maximal
5	#19135973	C₂	1	2	yes	maximal
6	#19135557	C₂	1	1	yes	maximal, characteristic
7	#19135358	C₂	1	1	yes	maximal, characteristic
8	#19135320	C₂	1	2	yes	maximal
9	#19135270	C₂	1	2	yes	maximal
10	C₄×#13063248	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#2546	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	#14583181	—	2	4	no	—
14	Q₈×C₄₃⋊C₈	—	2	4	no	—
15	C₂×#13063256	C₂²	1	2	yes	—
16	C₂×#13063256	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×#13063248	C₂²	1	2	yes	—
20	C₂×#13063248	C₂²	1	1	yes	characteristic
21	C₂×#13063248	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	#14582832	—	2	2	no	—
25	#14582806	—	2	1	no	—
26	#14582805	C₂²	1	2	yes	—
27	#14582797	C₂²	1	2	yes	—
28	#14582795	—	2	1	no	—
29	#14582769	C₂²	1	1	yes	characteristic
30	#14582661	C₂²	1	2	yes	—
31	#14582661	C₂²	1	2	yes	—
32	#14582661	C₂²	1	2	yes	—
33	#14582661	C₂²	1	1	yes	characteristic
34	#14582661	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Q₈×C₄₃	—	2	1	no	—
36	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₄₃×#398	—	2	2	no	—
39	C₄₃×#391	—	2	1	no	—
40	C₄₃×#389	C₂²	1	2	yes	—
41	C₄₃×#389	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
47	C₄×Dic₈₆	—	2	2	no	—
48	C₄×Dic₈₆	—	2	2	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×Dic₄₃⋊C₄	—	2	1	no	—
54	C₂×Dic₄₃⋊C₄	—	2	2	no	—
55	C₂×C₄×Dic₄₃	—	2	1	no	—
56	#13063256	—	2	4	no	—
57	#13063256	—	2	4	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	4	no	—
59	C₄⋊(C₄₃⋊C₈)	D₄	1	4	yes	—
60	#13063248	—	2	2	no	—
61	#13063248	—	2	4	no	—
62	#13063248	Q₈	1	4	yes	complemented
63	C₄×C₄₃⋊C₈	—	2	2	no	—
64	C₄×C₄₃⋊C₈	—	2	4	no	—
65	C₄₃⋊#95	—	2	2	no	—
66	C₄₃⋊#95	—	2	2	no	—
67	C₄₃⋊#95	—	2	2	no	—
68	C₂²×Q₈×C₄₃	—	2	1	no	—
69	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₃	—	2	2	no	—
71	C₄⋊Q₈×C₄₃	—	2	2	no	—
72	C₄⋊Q₈×C₄₃	—	4	4	no	—
73	C₄×Q₈×C₄₃	—	2	2	no	—
74	C₄×Q₈×C₄₃	—	2	2	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
78	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₃	—	2	1	no	—
84	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
86	#95×C₄₃	—	2	1	no	—
87	#95×C₄₃	—	2	2	no	—
88	#95×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	2	no	—
91	C₂×Q₈×C₄₃	—	4	2	no	—
92	C₂×Q₈×C₄₃	—	4	2	no	—
93	C₂×Q₈×C₄₃	—	4	2	no	—
94	C₂×Q₈×C₄₃	SD₁₆	1	4	yes	—
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	2	yes	—
99	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
103	C₂²×Dic₄₃	—	2	1	no	—
104	C₂²×Dic₄₃	—	2	2	no	—
105	C₂²×Dic₄₃	—	2	1	no	—
106	C₂×Dic₈₆	—	2	1	no	—
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	—	2	1	no	—
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	1	no	—
115	C₄⋊C₄×C₄₃	—	2	1	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	4	2	no	—
119	C₄⋊C₄×C₄₃	—	4	4	no	—
120	C₄⋊C₄×C₄₃	—	4	4	no	—
121	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
122	C₄⋊C₄×C₄₃	#41	1	2	yes	—
123	C₄²×C₄₃	—	2	2	no	—
124	C₄²×C₄₃	—	2	2	no	—
125	C₄²×C₄₃	—	4	2	no	—
126	C₄²×C₄₃	C₂×D₄	1	2	yes	—
127	C₄²×C₄₃	#41	1	2	yes	—
128	C₄⋊Dic₄₃	—	2	1	no	—
129	C₄⋊Dic₄₃	—	2	2	no	—
130	C₄⋊Dic₄₃	—	2	1	no	—
131	C₄⋊Dic₄₃	—	2	2	no	—
132	C₄⋊Dic₄₃	—	4	2	no	—
133	C₄⋊Dic₄₃	—	8	1	no	—
134	Dic₄₃⋊C₄	—	4	2	no	—
135	Dic₄₃⋊C₄	—	8	2	no	—
136	C₄×Dic₄₃	—	4	2	no	—
137	C₂×C₄₃⋊C₈	—	2	1	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	2	1	no	—
143	C₂×C₄₃⋊C₈	—	2	1	no	—
144	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
145	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
146	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₃	—	2	8	no	—
148	Q₈×C₄₃	—	8	4	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	1	no	—
152	C₂×C₄×C₄₃	—	2	1	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	2	no	—
155	C₂×C₄×C₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	#121	1	2	yes	—
166	C₂×C₄×C₄₃	#121	1	2	yes	—
167	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
168	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₄₃	#135	1	2	yes	—
170	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
175	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
176	C₂×Dic₄₃	—	2	2	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	—	4	1	no	—
180	C₂×Dic₄₃	—	4	2	no	—
181	C₂×Dic₄₃	—	4	2	no	—
182	C₂×Dic₄₃	—	4	1	no	—
183	C₂×Dic₄₃	—	4	2	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	Dic₈₆	—	2	2	no	—
186	Dic₈₆	—	2	2	no	—
187	Dic₈₆	—	4	1	no	—
188	Dic₈₆	—	4	1	no	—
189	C₄₃⋊C₈	—	2	4	no	—
190	C₄₃⋊C₈	—	2	2	no	—
191	C₄₃⋊C₈	—	4	1	no	—
192	#25472	—	43	1	no	maximal, Sylow
193	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
194	C₂²×C₄₃	#548	1	1	yes	characteristic
195	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
196	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
197	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
198	C₂²×C₄₃	#577	1	1	yes	characteristic
199	C₂²×C₄₃	#578	1	1	yes	characteristic
200	C₄×C₄₃	—	2	4	no	—
201	C₄×C₄₃	—	2	2	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	4	2	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	8	2	no	—
206	C₄×C₄₃	#465	1	4	yes	—
207	C₄×C₄₃	#533	1	1	yes	characteristic
208	C₄×C₄₃	#541	1	1	yes	characteristic
209	C₄×C₄₃	#547	1	1	yes	characteristic
210	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
211	Dic₄₃	—	4	2	no	—
212	Dic₄₃	—	8	2	no	—
213	Dic₄₃	—	8	1	no	—
214	C₂×#475	—	43	1	no	—
215	C₂×C₈×Q₈	—	43	1	no	—
216	#2582	—	43	1	no	—
217	#2546	D₄₃	1	1	yes	characteristic
218	#2088	—	43	2	no	—
219	#2066	—	43	2	no	—
220	#1990	—	43	1	no	—
221	#1948	—	43	1	no	—
222	#1941	—	43	2	no	—
223	#1933	—	43	2	no	—
224	C₄×#103	—	43	1	no	—
225	C₂×C₄₃	#2429	1	1	yes	characteristic
226	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
227	C₂×C₄₃	#3063	1	1	yes	characteristic
228	C₂×C₄₃	#3359	1	1	yes	characteristic
229	C₂×C₄₃	#3365	1	1	yes	characteristic
230	C₂×C₄₃	Q₈×SD₁₆	1	1	yes	characteristic
231	C₂×C₄₃	#3383	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	—	2	1	no	—
233	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
234	C₂×C₄×Q₈	—	43	1	no	—
235	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
236	#475	—	86	4	no	—
237	C₈×Q₈	—	86	4	no	—
238	C₂×#106	—	43	2	no	—
239	C₂×#106	—	43	2	no	—
240	C₂×C₄⋊C₈	—	43	1	no	—
241	C₂×C₄⋊C₈	—	43	2	no	—
242	C₂×#103	—	43	1	no	—
243	C₂×#103	—	43	2	no	—
244	C₂×#103	—	43	1	no	—
245	C₂×C₄×C₈	—	43	2	no	—
246	C₂×C₄×C₈	—	43	1	no	—
247	#398	—	2	2	no	—
248	#398	—	86	2	no	—
249	#391	—	2	1	no	—
250	#391	—	43	2	no	—
251	#391	—	86	1	no	—
252	#389	—	43	2	no	—
253	#389	—	86	1	no	—
254	#389	C₂×D₄₃	1	2	yes	—
255	#389	C₂×D₄₃	1	2	yes	—
256	#384	—	43	1	no	—
257	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
258	#340	—	43	2	no	—
259	#340	—	43	1	no	—
260	#340	—	43	2	no	—
261	#340	—	43	2	no	—
262	#340	—	43	1	no	—
263	C₄₃	#25472	1	1	yes	characteristic, complemented, Sylow
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	43	1	no	—
266	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
267	C₂²×C₈	—	43	1	no	—
268	C₂²×C₈	—	43	2	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	4	4	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	86	2	no	—
276	C₄×Q₈	—	86	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	43	1	no	—
281	C₂×C₄⋊C₄	—	43	2	no	—
282	C₂×C₄⋊C₄	—	86	2	no	—
283	C₂×C₄⋊C₄	—	86	1	no	—
284	C₂×C₄⋊C₄	—	86	1	no	—
285	C₂×C₄⋊C₄	—	86	1	no	—
286	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	2	yes	—
288	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
289	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	—	86	1	no	—
293	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	#106	—	86	4	no	—
296	#106	—	86	4	no	—
297	C₄⋊C₈	—	43	4	no	—
298	C₄⋊C₈	—	86	4	no	—
299	#103	—	43	4	no	—
300	#103	—	86	4	no	—
301	#103	—	86	2	no	—
302	C₄×C₈	—	86	4	no	—
303	C₄×C₈	—	86	2	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	86	2	no	—
308	#95	—	86	2	no	—
309	#95	—	86	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	2	no	—
315	C₂×Q₈	—	43	2	no	—
316	C₂×Q₈	—	86	1	no	—
317	C₂×Q₈	—	86	1	no	—
318	C₂×Q₈	—	86	1	no	—
319	C₂×Q₈	—	86	1	no	—
320	C₂×Q₈	—	86	1	no	—
321	C₂×Q₈	#10621883	1	4	yes	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	—	86	2	no	—
327	C₂²×C₄	—	86	1	no	—
328	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
329	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
331	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
333	C₂×C₈	—	43	4	no	—
334	C₂×C₈	—	43	2	no	—
335	C₂×C₈	—	86	1	no	—
336	C₂×C₈	—	86	2	no	—
337	C₂×C₈	—	86	2	no	—
338	C₂×C₈	—	86	1	no	—
339	C₂×C₈	—	86	1	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	—	86	1	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	86	1	no	—
352	C₄⋊C₄	—	86	1	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₄⋊C₄	—	86	2	no	—
355	C₄⋊C₄	—	344	2	no	—
356	C₄⋊C₄	—	344	1	no	—
357	C₄⋊C₄	—	172	2	no	—
358	C₄⋊C₄	—	172	2	no	—
359	C₄⋊C₄	Q₈×D₄₃	1	2	yes	—
360	C₄⋊C₄	#10621902	1	2	yes	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	2	no	—
364	C₄²	—	172	2	no	—
365	C₄²	D₄×D₄₃	1	2	yes	—
366	C₄²	#10621900	1	2	yes	—
367	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
368	Q₈	—	2	8	no	—
369	Q₈	—	8	4	no	—
370	Q₈	—	86	2	no	—
371	Q₈	—	86	2	no	—
372	Q₈	—	172	1	no	—
373	Q₈	—	172	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	86	2	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	—	172	1	no	—
393	C₂×C₄	—	172	2	no	—
394	C₂×C₄	—	172	2	no	—
395	C₂×C₄	—	172	1	no	—
396	C₂×C₄	—	172	1	no	—
397	C₂×C₄	—	172	1	no	—
398	C₂×C₄	—	172	1	no	—
399	C₂×C₄	#13063297	1	2	yes	—
400	C₂×C₄	#13063297	1	2	yes	—
401	C₂×C₄	C₂×#10621883	1	4	yes	—
402	C₂×C₄	C₂×#10621883	1	2	yes	—
403	C₂×C₄	#13063345	1	2	yes	—
404	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
407	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
408	C₂×C₄	#13063373	1	1	yes	characteristic
409	C₂×C₄	#13063373	1	1	yes	characteristic
410	C₈	—	86	4	no	—
411	C₈	—	86	2	no	—
412	C₈	—	172	1	no	—
413	C₂²	C₂×#13063297	1	1	yes	characteristic
414	C₂²	#14583560	1	1	yes	characteristic
415	C₂²	Q₈×C₂²⋊D₄₃	1	1	yes	characteristic
416	C₂²	C₂²×#10621883	1	1	yes	characteristic
417	C₂²	C₂×#13063345	1	1	yes	characteristic
418	C₂²	#14583707	1	1	yes	characteristic
419	C₂²	#14583714	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	2	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	2	no	—
426	C₄	—	344	2	no	—
427	C₄	—	344	1	no	—
428	C₄	—	172	2	no	—
429	C₄	#14583126	1	4	yes	—
430	C₄	#14583454	1	1	yes	characteristic
431	C₄	#14583510	1	1	yes	characteristic
432	C₄	#14583552	1	1	yes	characteristic
433	C₄	#14583564	1	1	yes	characteristic
434	C₂	#19138197	1	1	yes	characteristic
435	C₂	C₂×#14583126	1	1	yes	characteristic
436	C₂	#19144282	1	1	yes	characteristic
437	C₂	#19147237	1	1	yes	characteristic
438	C₂	#19147291	1	1	yes	characteristic
439	C₂	Q₈×#10621883	1	1	yes	characteristic
440	C₂	#19147482	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×#2546	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
hypercenter	#2546	D₄₃
hypocenter	C₄₃	#25472
LCS	G ▷ C₂²×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ #2546

Complements

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

N	H ≅ G/N	type
62. #13063248	Q₈	semidirect
263. C₄₃	#25472	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583181	2
C₂×Q₈×C₄₃⋊C₈	2
#19139965	2
#19136096	2
#19135973	2
#19135557	2
#19135358	2
#19135320	2
#19135270	2
C₄×#13063248	2
C₄₃×#2546	2
#25472	43