Subgroups — #25002485

Order 11008.

782 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13063260	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582935	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13063236	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582659	C₂	1	1	yes	maximal, characteristic
5	#19134293	C₂	1	1	yes	maximal, characteristic
6	#19134292	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₃×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10621877	C₂²	1	1	yes	characteristic
9	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13063284	C₂²	1	1	yes	characteristic
12	C₂×#13063260	—	2	2	no	—
13	C₂×#13063260	—	2	2	no	—
14	C₂×#13063260	C₄	1	4	yes	complemented
15	#14582935	—	2	2	no	—
16	#14582935	—	2	2	no	—
17	C₂×#13063258	C₄	1	2	yes	complemented
18	C₂×#13063256	C₄	1	2	yes	complemented
19	C₂×#13063236	—	2	2	no	—
20	C₂×#13063236	—	2	2	no	—
21	C₂×#13063236	C₄	1	4	yes	complemented
22	#14582659	—	2	2	no	—
23	#14582654	—	2	2	no	—
24	#14582653	—	2	2	no	—
25	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
28	C₄₃×#339	—	2	2	no	—
29	C₂×#10621877	—	2	1	no	—
30	C₂×#10621877	—	2	1	no	—
31	C₂×#10621877	—	2	1	no	—
32	C₂×#10621877	—	2	1	no	—
33	C₂×#10621877	—	2	1	no	—
34	C₂×#10621877	C₂×C₄	1	2	yes	—
35	C₂²×C₄₃⋊C₈	—	2	1	no	—
36	C₂²×C₄₃⋊C₈	—	2	1	no	—
37	C₂²×C₄₃⋊C₈	—	2	1	no	—
38	C₂²×C₄₃⋊C₈	—	2	1	no	—
39	C₂²×C₄₃⋊C₈	—	2	1	no	—
40	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
45	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
46	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
47	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
48	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
49	C₂²×C₄₃⋊C₈	Q₈	1	2	yes	—
50	C₂²×C₄₃⋊C₈	Q₈	1	2	yes	—
51	#13063284	—	2	1	no	—
52	#13063284	—	2	1	no	—
53	#13063284	—	2	1	no	—
54	#13063284	—	2	1	no	—
55	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
57	C₂×C₄×Dic₄₃	—	2	1	no	—
58	#13063260	—	2	8	no	—
59	#13063258	—	2	4	no	—
60	#13063256	—	2	4	no	—
61	#13063236	—	2	8	no	—
62	C₂³×C₄×C₄₃	—	2	1	no	—
63	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×M₁₆×C₄₃	—	2	1	no	—
65	C₂×M₁₆×C₄₃	—	2	1	no	—
66	C₂×M₁₆×C₄₃	—	2	1	no	—
67	C₂×M₁₆×C₄₃	—	2	1	no	—
68	C₂×M₁₆×C₄₃	—	2	1	no	—
69	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₄₃	—	2	1	no	—
71	#117×C₄₃	—	2	1	no	—
72	#117×C₄₃	—	2	1	no	—
73	#117×C₄₃	—	2	1	no	—
74	#117×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
77	C₂×C₄²×C₄₃	—	2	1	no	—
78	C₂×C₄²×C₄₃	—	2	1	no	—
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	—	2	1	no	—
81	C₂×C₄²×C₄₃	C₂×C₄	1	2	yes	—
82	C₂×C₄²×C₄₃	D₄	1	2	yes	—
83	C₂×C₄²×C₄₃	Q₈	1	2	yes	—
84	C₂⁴×C₄₃	#41	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	—	2	2	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	—	2	2	no	—
88	C₂²×C₄×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	4	4	no	—
90	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
100	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂²×Dic₄₃	—	2	2	no	—
105	M₁₆×C₄₃	—	2	2	no	—
106	M₁₆×C₄₃	—	2	2	no	—
107	M₁₆×C₄₃	—	4	1	no	—
108	M₁₆×C₄₃	—	4	1	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	4	1	no	—
111	C₂×C₈×C₄₃	—	4	1	no	—
112	C₄⋊C₄×C₄₃	—	2	2	no	—
113	C₄⋊C₄×C₄₃	—	2	2	no	—
114	C₂²⋊C₄×C₄₃	—	4	1	no	—
115	C₂²⋊C₄×C₄₃	—	4	1	no	—
116	C₄²×C₄₃	—	2	2	no	—
117	C₄²×C₄₃	—	2	2	no	—
118	C₄²×C₄₃	—	2	2	no	—
119	C₄²×C₄₃	—	4	1	no	—
120	C₄²×C₄₃	—	4	1	no	—
121	C₄²×C₄₃	C₄⋊C₄	1	4	yes	—
122	C₂²⋊Dic₄₃	—	4	1	no	—
123	C₂²⋊Dic₄₃	—	4	1	no	—
124	C₄⋊Dic₄₃	—	2	2	no	—
125	C₄⋊Dic₄₃	—	2	2	no	—
126	C₄×Dic₄₃	—	4	1	no	—
127	C₄×Dic₄₃	—	4	1	no	—
128	#10621877	—	2	2	no	—
129	#10621877	—	2	2	no	—
130	#10621877	—	4	1	no	—
131	#10621877	—	4	1	no	—
132	C₂×C₄₃⋊C₈	—	2	2	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	2	no	—
137	C₂×C₄₃⋊C₈	—	2	2	no	—
138	C₂×C₄₃⋊C₈	—	2	2	no	—
139	C₂×C₄₃⋊C₈	—	4	1	no	—
140	C₂×C₄₃⋊C₈	—	4	1	no	—
141	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
142	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
143	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
144	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
145	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	2	yes	—
146	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	4	yes	—
147	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
148	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
149	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
150	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
151	C₂×C₄₃⋊C₈	C₄⋊C₄	1	4	yes	—
152	C₂³×C₄₃	—	2	4	no	—
153	C₂³×C₄₃	#117	1	1	yes	characteristic
154	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂³×C₄₃	C₄×Q₈	1	1	yes	characteristic
156	C₂³×C₄₃	#121	1	1	yes	characteristic
157	C₂³×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂³×C₄₃	#124	1	1	yes	characteristic
159	C₂³×C₄₃	#125	1	1	yes	characteristic
160	C₂×C₄×C₄₃	—	2	4	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	4	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
176	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₄×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#125	1	1	yes	characteristic
190	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₄⋊Q₈	1	1	yes	characteristic
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	—	4	4	no	—
196	C₈×C₄₃	—	4	2	no	—
197	C₄₃⋊C₈	—	2	4	no	—
198	C₄₃⋊C₈	—	4	2	no	—
199	C₄₃⋊C₈	#95	1	4	yes	—
200	C₄₃⋊C₈	#95	1	4	yes	—
201	#10860	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	2	no	—
204	C₂²×C₄₃	—	2	2	no	—
205	C₂²×C₄₃	—	2	2	no	—
206	C₂²×C₄₃	—	2	2	no	—
207	C₂²×C₄₃	—	2	2	no	—
208	C₂²×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
209	C₂²×C₄₃	#380	1	1	yes	characteristic
210	C₂²×C₄₃	#382	1	1	yes	characteristic
211	C₂²×C₄₃	#389	1	1	yes	characteristic
212	C₂²×C₄₃	#389	1	1	yes	characteristic
213	C₂²×C₄₃	#390	1	1	yes	characteristic
214	C₂²×C₄₃	#391	1	1	yes	characteristic
215	C₂²×C₄₃	#444	1	4	yes	—
216	C₄×C₄₃	—	4	4	no	—
217	C₄×C₄₃	—	8	2	no	—
218	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
219	C₄×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
220	C₄×C₄₃	#380	1	1	yes	characteristic
221	C₄×C₄₃	#384	1	1	yes	characteristic
222	C₄×C₄₃	#389	1	1	yes	characteristic
223	C₄×C₄₃	#389	1	1	yes	characteristic
224	C₄×C₄₃	#390	1	1	yes	characteristic
225	C₄×C₄₃	#391	1	1	yes	characteristic
226	Dic₄₃	—	8	2	no	—
227	C₂²×#108	—	43	1	no	—
228	C₂×#427	—	43	1	no	—
229	C₂²×#97	—	43	1	no	—
230	C₂×#339	—	43	1	no	—
231	C₂×#339	D₄₃	1	1	yes	characteristic
232	#1729	—	43	1	no	—
233	#1729	—	43	1	no	—
234	C₂×C₄₃	—	2	1	no	—
235	C₂×C₄₃	—	2	1	no	—
236	C₂×C₄₃	—	2	1	no	—
237	C₂×C₄₃	—	2	1	no	—
238	C₂×C₄₃	C₄⋊#95	1	1	yes	characteristic
239	C₂×C₄₃	#1773	1	2	yes	—
240	C₂×C₄₃	#1946	1	2	yes	—
241	C₂×C₄₃	#1975	1	2	yes	—
242	C₂²×M₁₆	—	43	1	no	—
243	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
244	C₂³×C₈	—	43	1	no	—
245	C₂³×C₈	—	43	1	no	—
246	C₂×#117	—	43	1	no	—
247	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
248	C₂²×C₄²	C₂×D₄₃	1	1	yes	characteristic
249	C₂×#108	—	43	4	no	—
250	C₂×#108	—	86	2	no	—
251	C₂×#108	—	86	2	no	—
252	#427	—	86	2	no	—
253	#427	—	86	2	no	—
254	C₂×#107	—	43	2	no	—
255	C₂×#106	—	43	2	no	—
256	C₂×#97	—	43	4	no	—
257	C₂×#97	—	86	2	no	—
258	C₂×#97	—	86	2	no	—
259	#339	—	2	2	no	—
260	#339	—	86	2	no	—
261	#336	—	86	2	no	—
262	#336	—	86	2	no	—
263	C₄₃	#10860	1	1	yes	characteristic, complemented, Sylow
264	C₂³×C₄	—	2	1	no	—
265	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	43	2	no	—
272	C₂×M₁₆	—	86	1	no	—
273	C₂×M₁₆	—	86	1	no	—
274	C₂×M₁₆	—	86	1	no	—
275	C₂×M₁₆	—	86	1	no	—
276	C₂×M₁₆	—	86	1	no	—
277	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	43	2	no	—
280	C₂²×C₈	—	43	1	no	—
281	C₂²×C₈	—	43	1	no	—
282	C₂²×C₈	—	43	2	no	—
283	C₂²×C₈	—	43	2	no	—
284	C₂²×C₈	—	43	2	no	—
285	C₂²×C₈	—	43	2	no	—
286	C₂²×C₈	—	43	2	no	—
287	C₂²×C₈	—	43	2	no	—
288	C₂²×C₈	—	43	2	no	—
289	C₂²×C₈	—	43	2	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₂²×C₈	—	86	1	no	—
292	C₂²×C₈	—	86	1	no	—
293	C₂²×C₈	—	86	1	no	—
294	C₂²×C₈	—	86	1	no	—
295	#117	—	2	1	no	—
296	#117	—	2	1	no	—
297	#117	—	2	1	no	—
298	#117	—	2	1	no	—
299	#117	—	86	1	no	—
300	#117	—	86	1	no	—
301	#117	—	86	1	no	—
302	#117	—	86	1	no	—
303	C₂×C₄⋊C₄	—	43	2	no	—
304	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	86	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	—	86	1	no	—
312	C₂×C₄²	Dic₈₆	1	2	yes	—
313	C₂×C₄²	C₄×D₄₃	1	2	yes	—
314	C₂×C₄²	C₂²⋊D₄₃	1	2	yes	—
315	#108	—	86	8	no	—
316	#107	—	86	4	no	—
317	#106	—	86	4	no	—
318	#97	—	86	8	no	—
319	C₂⁴	#10621900	1	1	yes	characteristic
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	4	4	no	—
325	C₂²×C₄	—	86	2	no	—
326	C₂²×C₄	C₂×Dic₈₆	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
330	C₂²×C₄	#10621898	1	1	yes	characteristic
331	C₂²×C₄	#10621898	1	1	yes	characteristic
332	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	#10621900	1	1	yes	characteristic
337	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
338	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	86	2	no	—
345	M₁₆	—	86	2	no	—
346	M₁₆	—	172	1	no	—
347	M₁₆	—	172	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	1	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	43	2	no	—
352	C₂×C₈	—	43	2	no	—
353	C₂×C₈	—	43	4	no	—
354	C₂×C₈	—	43	2	no	—
355	C₂×C₈	—	43	2	no	—
356	C₂×C₈	—	43	4	no	—
357	C₂×C₈	—	43	2	no	—
358	C₂×C₈	—	43	2	no	—
359	C₂×C₈	—	43	4	no	—
360	C₂×C₈	—	43	4	no	—
361	C₂×C₈	—	43	4	no	—
362	C₂×C₈	—	86	2	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	86	2	no	—
365	C₂×C₈	—	86	2	no	—
366	C₂×C₈	—	86	2	no	—
367	C₂×C₈	—	86	2	no	—
368	C₂×C₈	—	86	2	no	—
369	C₂×C₈	—	172	1	no	—
370	C₂×C₈	—	172	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	86	2	no	—
374	C₄⋊C₄	—	86	2	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	172	1	no	—
378	C₂²⋊C₄	—	172	1	no	—
379	C₄²	—	2	2	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	—	172	1	no	—
385	C₄²	—	172	1	no	—
386	C₄²	Dic₄₃⋊C₄	1	4	yes	—
387	C₂³	—	2	4	no	—
388	C₂³	#13063281	1	1	yes	characteristic
389	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
390	C₂³	#13063290	1	1	yes	characteristic
391	C₂³	#13063297	1	1	yes	characteristic
392	C₂³	#13063302	1	1	yes	characteristic
393	C₂³	#13063311	1	1	yes	characteristic
394	C₂³	#13063315	1	1	yes	characteristic
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	172	2	no	—
402	C₂×C₄	—	172	4	no	—
403	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
406	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
408	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
409	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
411	C₂×C₄	C₂×Dic₄₃⋊C₄	1	1	yes	characteristic
412	C₂×C₄	#13063282	1	1	yes	characteristic
413	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
415	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
416	C₂×C₄	#13063290	1	1	yes	characteristic
417	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
418	C₂×C₄	C₄×Dic₈₆	1	1	yes	characteristic
419	C₂×C₄	#13063297	1	1	yes	characteristic
420	C₂×C₄	#13063298	1	1	yes	characteristic
421	C₂×C₄	#13063298	1	1	yes	characteristic
422	C₂×C₄	#13063302	1	1	yes	characteristic
423	C₂×C₄	#13063303	1	1	yes	characteristic
424	C₂×C₄	#13063303	1	1	yes	characteristic
425	C₂×C₄	#13063311	1	1	yes	characteristic
426	C₂×C₄	#13063315	1	1	yes	characteristic
427	C₂×C₄	#13063321	1	1	yes	characteristic
428	C₂×C₄	#13063323	1	1	yes	characteristic
429	C₂×C₄	#13063324	1	1	yes	characteristic
430	C₂×C₄	#13063324	1	1	yes	characteristic
431	C₈	—	4	2	no	—
432	C₈	—	43	4	no	—
433	C₈	—	43	4	no	—
434	C₈	—	86	4	no	—
435	C₈	—	172	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	#14582750	1	1	yes	characteristic
443	C₂²	#14582757	1	1	yes	characteristic
444	C₂²	#14582763	1	1	yes	characteristic
445	C₂²	#14582794	1	1	yes	characteristic
446	C₂²	#14582796	1	1	yes	characteristic
447	C₂²	#14582799	1	1	yes	characteristic
448	C₂²	#14582803	1	1	yes	characteristic
449	C₂²	#14583018	1	4	yes	—
450	C₄	—	4	4	no	—
451	C₄	—	8	2	no	—
452	C₄	—	344	2	no	—
453	C₄	#95×D₄₃	1	1	yes	characteristic
454	C₄	C₄×Dic₄₃⋊C₄	1	1	yes	characteristic
455	C₄	#14582758	1	1	yes	characteristic
456	C₄	#14582768	1	1	yes	characteristic
457	C₄	#14582794	1	1	yes	characteristic
458	C₄	#14582796	1	1	yes	characteristic
459	C₄	#14582799	1	1	yes	characteristic
460	C₄	#14582803	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	—	2	1	no	—
465	C₂	Dic₄₃⋊#95	1	1	yes	characteristic
466	C₂	#19134478	1	2	yes	—
467	C₂	#19135347	1	2	yes	—
468	C₂	#19135485	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₃
Fitting	C₂×C₄₃×#339	C₂
socle	C₂³×C₄₃	C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂³×C₄×C₄₃	C₂³
hypercenter	C₂×#339	D₄₃
hypocenter	C₄₃	#10860
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
14. C₂×#13063260	C₄	semidirect
17. C₂×#13063258	C₄	semidirect
18. C₂×#13063256	C₄	semidirect
21. C₂×#13063236	C₄	semidirect
263. C₄₃	#10860	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13063260	2
C₂×#14582935	2
C₂²×#13063236	2
C₂×#14582659	2
#19134293	2
#19134292	2
C₂×C₄₃×#339	2
#10860	43