Subgroups — #25118434

Order 11008.

794 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583191	C₂	1	1	yes	maximal, characteristic
2	#19137685	C₂	1	1	yes	maximal, characteristic
3	#19137507	C₂	1	1	yes	maximal, characteristic
4	#19135351	C₂	1	1	yes	maximal, characteristic
5	#19135327	C₂	1	2	yes	maximal
6	#19135185	C₂	1	2	yes	maximal
7	#19134850	C₂	1	2	yes	maximal
8	C₈×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
9	C₄×#13063250	C₂	1	1	yes	maximal, characteristic
10	#19134414	C₂	1	2	yes	maximal
11	C₄₃×#1990	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
13	C₂×#13063290	C₂²	1	2	yes	—
14	#14583191	C₄	1	8	yes	complemented
15	C₂×#13063258	C₂²	1	2	yes	—
16	C₂×#13063258	C₂²	1	2	yes	—
17	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×#13063250	C₂²	1	1	yes	characteristic
19	C₂×#13063250	C₂²	1	1	yes	characteristic
20	C₂×#13063248	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
22	#14582806	—	2	2	no	—
23	#14582798	—	2	1	no	—
24	#14582798	C₂²	1	2	yes	—
25	#14582795	C₂²	1	2	yes	—
26	#14582794	—	2	2	no	—
27	#14582768	—	2	1	no	—
28	C₄⋊C₄×Dic₄₃	—	2	1	no	—
29	C₄⋊C₄×Dic₄₃	—	2	1	no	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
33	#14582662	C₂²	1	1	yes	characteristic
34	#14582662	C₂²	1	1	yes	characteristic
35	#14582661	C₂²	1	2	yes	—
36	#14582653	C₂²	1	2	yes	—
37	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄₃×#340	C₂²	1	2	yes	—
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
44	C₄×Dic₈₆	—	2	2	no	—
45	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
46	#13063290	—	2	4	no	—
47	#13063290	—	4	2	no	—
48	C₂×C₄⋊Dic₄₃	—	2	2	no	—
49	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂×Dic₄₃⋊C₄	—	2	1	no	—
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×Dic₄₃⋊C₄	—	2	2	no	—
57	C₂×C₄×Dic₄₃	—	2	1	no	—
58	C₂×C₄×Dic₄₃	—	2	1	no	—
59	C₂×C₄×Dic₄₃	—	2	2	no	—
60	C₂×C₄×Dic₄₃	—	2	2	no	—
61	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
62	#13063258	—	4	2	no	—
63	#13063258	C₂×C₄	1	8	yes	—
64	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
65	#13063250	—	2	2	no	—
66	#13063250	Q₈	1	4	yes	complemented
67	#13063248	C₂×C₄	1	8	yes	—
68	C₈×Dic₄₃	—	4	2	no	—
69	C₄₃⋊#95	—	2	1	no	—
70	C₄₃⋊#95	—	2	2	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₄₃⋊#95	D₄	1	2	yes	—
74	C₂²×Q₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₄₃	—	2	2	no	—
78	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×Q₈×C₄₃	—	8	1	no	—
88	C₂×Q₈×C₄₃	—	8	1	no	—
89	C₂²×C₄×C₄₃	—	2	2	no	—
90	C₂²×C₄×C₄₃	—	2	2	no	—
91	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
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	1	no	—
97	C₂²×Dic₄₃	—	2	1	no	—
98	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
99	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
100	C₂×Dic₈₆	—	2	1	no	—
101	C₂×Dic₈₆	—	2	1	no	—
102	C₂×Dic₈₆	—	2	1	no	—
103	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
104	C₂×Dic₈₆	C₂×Q₈	1	2	yes	—
105	C₂×Dic₈₆	#41	1	2	yes	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	1	no	—
110	C₂×C₈×C₄₃	—	2	1	no	—
111	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
112	C₄⋊C₄×C₄₃	—	2	4	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₄⋊C₄×C₄₃	—	2	2	no	—
115	C₄⋊C₄×C₄₃	—	2	2	no	—
116	C₄⋊C₄×C₄₃	—	4	2	no	—
117	C₄⋊C₄×C₄₃	—	8	1	no	—
118	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
119	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₃	#41	1	2	yes	—
121	C₄⋊Dic₄₃	—	2	2	no	—
122	C₄⋊Dic₄₃	—	2	1	no	—
123	C₄⋊Dic₄₃	—	2	1	no	—
124	C₄⋊Dic₄₃	—	2	1	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	—	8	2	no	—
127	C₄⋊Dic₄₃	Q₁₆	1	4	yes	—
128	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
129	C₄⋊Dic₄₃	C₂×Q₈	1	2	yes	—
130	Dic₄₃⋊C₄	—	2	4	no	—
131	Dic₄₃⋊C₄	—	4	4	no	—
132	Dic₄₃⋊C₄	—	8	2	no	—
133	C₄×Dic₄₃	—	2	4	no	—
134	C₄×Dic₄₃	—	2	2	no	—
135	C₄×Dic₄₃	—	2	2	no	—
136	C₄×Dic₄₃	—	4	4	no	—
137	C₄×Dic₄₃	—	4	2	no	—
138	C₄×Dic₄₃	—	8	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	2	no	—
141	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
142	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₄₃	—	8	4	no	—
144	C₂×C₄×C₄₃	—	2	1	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	4	no	—
147	C₂×C₄×C₄₃	—	4	2	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	2	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
155	C₂×C₄×C₄₃	#135	1	2	yes	—
156	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×Dic₄₃	—	2	2	no	—
163	C₂×Dic₄₃	—	2	2	no	—
164	C₂×Dic₄₃	—	2	2	no	—
165	C₂×Dic₄₃	—	2	2	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	2	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	2	no	—
170	C₂×Dic₄₃	—	2	2	no	—
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	1	no	—
176	C₂×Dic₄₃	—	4	1	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	4	1	no	—
179	C₂×Dic₄₃	C₂×Q₁₆	1	4	yes	—
180	Dic₈₆	—	2	2	no	—
181	Dic₈₆	—	2	2	no	—
182	Dic₈₆	—	2	2	no	—
183	Dic₈₆	C₄×Q₈	1	4	yes	—
184	C₈×C₄₃	—	2	2	no	—
185	C₈×C₄₃	—	4	1	no	—
186	C₄₃⋊C₈	—	2	4	no	—
187	#22965	—	43	1	no	maximal, Sylow
188	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂²×C₄₃	#546	1	1	yes	characteristic
190	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
191	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
192	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
193	C₂²×C₄₃	#576	1	1	yes	characteristic
194	C₂²×C₄₃	#577	1	1	yes	characteristic
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	4	4	no	—
197	C₄×C₄₃	—	8	2	no	—
198	C₄×C₄₃	C₄×Q₁₆	1	4	yes	—
199	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
200	C₄×C₄₃	#520	1	1	yes	characteristic
201	C₄×C₄₃	#552	1	1	yes	characteristic
202	C₄×C₄₃	#554	1	1	yes	characteristic
203	Dic₄₃	—	2	4	no	—
204	Dic₄₃	—	2	4	no	—
205	Dic₄₃	—	4	2	no	—
206	Dic₄₃	—	4	2	no	—
207	Dic₄₃	—	4	2	no	—
208	Dic₄₃	—	8	1	no	—
209	C₂×#477	—	43	1	no	—
210	#2369	—	43	1	no	—
211	Q₈×C₄⋊C₄	—	43	1	no	—
212	#1990	D₄₃	1	1	yes	characteristic
213	#1947	—	43	1	no	—
214	#1942	—	43	2	no	—
215	#1921	—	43	2	no	—
216	#1863	—	43	2	no	—
217	C₈×C₄⋊C₄	—	43	1	no	—
218	C₄×#103	—	43	1	no	—
219	C₄×#103	—	43	2	no	—
220	C₂×C₄₃	#2360	1	1	yes	characteristic
221	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₄₃	#2946	1	1	yes	characteristic
223	C₂×C₄₃	#3299	1	1	yes	characteristic
224	C₂×C₄₃	#3305	1	1	yes	characteristic
225	C₂×C₄₃	#3381	1	1	yes	characteristic
226	C₂×C₄₃	Q₈×Q₁₆	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×C₄×Q₈	—	43	2	no	—
229	C₂×C₄×Q₈	—	43	1	no	—
230	#477	—	43	8	no	—
231	C₂×#107	—	43	2	no	—
232	C₂×#107	—	43	2	no	—
233	C₂×C₄⋊C₈	—	43	1	no	—
234	C₂×#103	—	43	1	no	—
235	C₂×#103	—	43	2	no	—
236	C₂×#103	—	43	1	no	—
237	C₂×C₄×C₈	—	43	2	no	—
238	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
239	#391	—	86	2	no	—
240	#389	—	43	2	no	—
241	#389	—	43	2	no	—
242	#389	—	86	2	no	—
243	#389	—	86	1	no	—
244	#384	—	86	1	no	—
245	#384	C₂×D₄₃	1	1	yes	characteristic
246	C₄×C₄⋊C₄	—	43	1	no	—
247	C₄×C₄⋊C₄	—	43	2	no	—
248	C₄×C₄⋊C₄	—	43	1	no	—
249	C₄×C₄⋊C₄	—	86	1	no	—
250	C₄×C₄⋊C₄	—	86	1	no	—
251	#340	—	43	1	no	—
252	#340	—	43	1	no	—
253	#340	—	43	2	no	—
254	#340	C₂×D₄₃	1	2	yes	—
255	#340	C₂×D₄₃	1	2	yes	—
256	#336	—	43	2	no	—
257	C₄₃	#22965	1	1	yes	characteristic, complemented, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	43	1	no	—
260	C₂²×C₈	—	43	2	no	—
261	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
262	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₄×D₄₃	1	4	yes	—
265	C₄×Q₈	—	43	4	no	—
266	C₄×Q₈	—	86	2	no	—
267	C₄×Q₈	—	86	4	no	—
268	C₄×Q₈	—	172	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	43	1	no	—
273	C₂×C₄⋊C₄	—	43	1	no	—
274	C₂×C₄⋊C₄	—	43	1	no	—
275	C₂×C₄⋊C₄	—	43	1	no	—
276	C₂×C₄⋊C₄	—	43	1	no	—
277	C₂×C₄⋊C₄	—	86	1	no	—
278	C₂×C₄⋊C₄	—	86	2	no	—
279	C₂×C₄⋊C₄	—	86	2	no	—
280	C₂×C₄⋊C₄	—	86	2	no	—
281	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
282	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
283	C₂×C₄²	—	43	2	no	—
284	C₂×C₄²	—	86	1	no	—
285	C₂×C₄²	—	86	2	no	—
286	C₂×C₄²	—	86	2	no	—
287	C₂×C₄²	—	86	1	no	—
288	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
289	#107	—	43	8	no	—
290	#107	—	172	2	no	—
291	C₄⋊C₈	—	43	4	no	—
292	#103	—	43	4	no	—
293	#103	—	43	8	no	—
294	#103	—	86	2	no	—
295	C₄×C₈	—	2	2	no	—
296	C₄×C₈	—	172	2	no	—
297	#95	—	43	2	no	—
298	#95	—	86	2	no	—
299	#95	—	86	2	no	—
300	#95	—	86	2	no	—
301	#95	—	86	1	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	8	1	no	—
304	C₂×Q₈	—	8	1	no	—
305	C₂×Q₈	—	43	2	no	—
306	C₂×Q₈	—	43	2	no	—
307	C₂×Q₈	—	43	2	no	—
308	C₂×Q₈	—	86	1	no	—
309	C₂×Q₈	—	86	1	no	—
310	C₂×Q₈	—	86	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	43	2	no	—
314	C₂²×C₄	—	43	2	no	—
315	C₂²×C₄	—	86	1	no	—
316	C₂²×C₄	—	86	1	no	—
317	C₂²×C₄	—	86	1	no	—
318	C₂²×C₄	—	86	1	no	—
319	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	43	4	no	—
328	C₂×C₈	—	86	2	no	—
329	C₂×C₈	—	86	2	no	—
330	C₂×C₈	Q₈×D₄₃	1	2	yes	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	8	1	no	—
337	C₄⋊C₄	—	43	4	no	—
338	C₄⋊C₄	—	43	2	no	—
339	C₄⋊C₄	—	43	2	no	—
340	C₄⋊C₄	—	86	4	no	—
341	C₄⋊C₄	—	86	2	no	—
342	C₄⋊C₄	—	86	1	no	—
343	C₄⋊C₄	—	86	1	no	—
344	C₄⋊C₄	—	86	1	no	—
345	C₄⋊C₄	—	86	1	no	—
346	C₄⋊C₄	—	344	2	no	—
347	C₄⋊C₄	—	344	2	no	—
348	C₄⋊C₄	—	172	4	no	—
349	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
350	C₄²	—	86	4	no	—
351	C₄²	—	86	2	no	—
352	C₄²	—	86	2	no	—
353	C₄²	—	344	2	no	—
354	C₄²	—	172	4	no	—
355	C₄²	—	172	2	no	—
356	C₄²	C₂×C₄×D₄₃	1	2	yes	—
357	C₄²	#10621900	1	2	yes	—
358	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
359	Q₈	—	8	4	no	—
360	Q₈	—	43	4	no	—
361	Q₈	—	86	2	no	—
362	Q₈	—	86	2	no	—
363	Q₈	—	86	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	43	4	no	—
373	C₂×C₄	—	86	2	no	—
374	C₂×C₄	—	86	2	no	—
375	C₂×C₄	—	86	2	no	—
376	C₂×C₄	—	86	2	no	—
377	C₂×C₄	—	86	2	no	—
378	C₂×C₄	—	86	2	no	—
379	C₂×C₄	—	86	2	no	—
380	C₂×C₄	—	86	2	no	—
381	C₂×C₄	—	86	2	no	—
382	C₂×C₄	—	86	2	no	—
383	C₂×C₄	—	172	1	no	—
384	C₂×C₄	—	172	1	no	—
385	C₂×C₄	—	172	1	no	—
386	C₂×C₄	—	172	1	no	—
387	C₂×C₄	—	172	1	no	—
388	C₂×C₄	—	172	1	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
391	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
392	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
393	C₂×C₄	#13063346	1	2	yes	—
394	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
395	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
396	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
398	C₂×C₄	#13063371	1	1	yes	characteristic
399	C₂×C₄	#13063373	1	1	yes	characteristic
400	C₈	—	2	2	no	—
401	C₈	—	4	1	no	—
402	C₈	—	86	4	no	—
403	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
404	C₂²	#14583542	1	1	yes	characteristic
405	C₂²	#14583564	1	1	yes	characteristic
406	C₂²	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
407	C₂²	C₂×#13063346	1	1	yes	characteristic
408	C₂²	#14583700	1	1	yes	characteristic
409	C₂²	#14583705	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	86	4	no	—
414	C₄	—	86	4	no	—
415	C₄	—	344	1	no	—
416	C₄	—	172	2	no	—
417	C₄	—	172	2	no	—
418	C₄	—	172	2	no	—
419	C₄	#14582991	1	4	yes	—
420	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
421	C₄	#14583381	1	1	yes	characteristic
422	C₄	#14583583	1	1	yes	characteristic
423	C₄	#14583607	1	1	yes	characteristic
424	C₂	#19137605	1	1	yes	characteristic
425	C₂	C₂×#14582991	1	1	yes	characteristic
426	C₂	#19143421	1	1	yes	characteristic
427	C₂	#19146470	1	1	yes	characteristic
428	C₂	#19146544	1	1	yes	characteristic
429	C₂	#19147475	1	1	yes	characteristic
430	C₂	#19147478	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1990	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1990	D₄₃
hypocenter	C₄₃	#22965
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1990

Complements

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

N	H ≅ G/N	type
14. #14583191	C₄	semidirect
66. #13063250	Q₈	semidirect
257. C₄₃	#22965	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583191	2
#19137685	2
#19137507	2
#19135351	2
#19135327	2
#19135185	2
#19134850	2
C₈×C₄⋊Dic₄₃	2
C₄×#13063250	2
#19134414	2
C₄₃×#1990	2
#22965	43