Subgroups — #25966237

Order 11008.

1770 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148000	C₂	1	2	yes	maximal
2	#19145135	C₂	1	4	yes	maximal, complemented
3	#19145131	C₂	1	4	yes	maximal, complemented
4	#19145127	C₂	1	4	yes	maximal, complemented
5	#19145123	C₂	1	4	yes	maximal, complemented
6	#19145118	C₂	1	4	yes	maximal, complemented
7	#19145107	C₂	1	4	yes	maximal, complemented
8	#19143184	C₂	1	2	yes	maximal
9	C₂×#14582937	C₂	1	1	yes	maximal, characteristic
10	C₂×#14582854	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10621877	C₂²	1	1	yes	characteristic
13	#14583530	C₂²	1	8	yes	—
14	#14583527	—	2	4	no	—
15	#14583527	C₂²	1	8	yes	—
16	#14583525	—	2	4	no	—
17	#14583456	—	2	4	no	—
18	#14583452	—	2	4	no	—
19	#14583452	C₂²	1	8	yes	—
20	C₂×#13063284	C₂²	1	2	yes	—
21	C₂×#13063284	C₂²	1	1	yes	characteristic
22	#14583307	C₂²	1	16	yes	complemented
23	#14583306	C₂²	1	16	yes	complemented
24	#14583303	C₂²	1	8	yes	complemented
25	#14583300	C₂²	1	8	yes	complemented
26	#14583299	C₂²	1	8	yes	complemented
27	#14583296	C₂²	1	8	yes	complemented
28	#14582942	C₂²	1	8	yes	—
29	#14582939	C₂²	1	8	yes	—
30	#14582937	C₂²	1	2	yes	—
31	#14582937	C₂²	1	2	yes	—
32	#14582937	C₂²	1	2	yes	—
33	#14582937	C₂²	1	2	yes	—
34	#14582935	C₂²	1	8	yes	—
35	C₂×#13063259	C₂²	1	2	yes	—
36	C₂×#13063257	C₂²	1	2	yes	—
37	#14582854	C₂²	1	2	yes	—
38	#14582854	C₂²	1	2	yes	—
39	#14582854	C₂²	1	2	yes	—
40	#14582854	C₂²	1	2	yes	—
41	C₂×#13063235	C₂²	1	2	yes	—
42	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
43	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#117×C₄₃	C₂²	1	2	yes	—
45	C₄₃×#427	C₂²	1	2	yes	—
46	C₄₃×#427	C₂²	1	2	yes	—
47	C₄₃×#427	C₂²	1	2	yes	—
48	C₄₃×#427	C₂²	1	2	yes	—
49	C₂×#107×C₄₃	C₂²	1	2	yes	—
50	C₂×#106×C₄₃	C₂²	1	2	yes	—
51	C₂×#10621877	Q₈	1	8	yes	complemented
52	C₂×#10621877	C₂³	1	2	yes	—
53	C₂×#10621877	C₂³	1	2	yes	—
54	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
55	#13063325	—	2	8	no	—
56	#13063324	—	2	8	no	—
57	#13063324	C₂³	1	16	yes	—
58	#13063317	—	2	8	no	—
59	#13063316	—	2	8	no	—
60	#13063316	C₂³	1	16	yes	—
61	#13063304	—	2	16	no	—
62	#13063302	—	2	16	no	—
63	#13063302	—	2	16	no	—
64	C₄×Dic₈₆	—	2	16	no	—
65	#13063284	—	2	2	no	—
66	#13063284	—	2	2	no	—
67	#13063284	D₄	1	2	yes	—
68	#13063284	D₄	1	2	yes	—
69	#13063284	C₂³	1	4	yes	—
70	#13063284	C₂³	1	4	yes	—
71	#13063284	C₂³	1	2	yes	—
72	#13063284	C₂³	1	2	yes	—
73	C₂×C₄⋊Dic₄₃	D₄	1	2	yes	—
74	C₂×C₄⋊Dic₄₃	C₂³	1	4	yes	—
75	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
76	C₂×C₂²⋊Dic₄₃	D₄	1	2	yes	—
77	C₂×C₄×Dic₄₃	—	2	2	no	—
78	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
79	#13063259	C₂³	1	4	yes	—
80	#13063259	C₂³	1	4	yes	—
81	#13063258	C₂³	1	16	yes	—
82	#13063257	C₂³	1	4	yes	—
83	#13063257	C₂³	1	4	yes	—
84	#13063256	C₂³	1	16	yes	—
85	#13063235	C₂³	1	4	yes	—
86	#13063235	C₂³	1	4	yes	—
87	C₈×Dic₄₃	C₂³	1	4	yes	—
88	C₈×Dic₄₃	C₂³	1	4	yes	—
89	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₃	Q₈	1	8	yes	complemented
91	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
97	#117×C₄₃	—	2	2	no	—
98	#117×C₄₃	—	2	2	no	—
99	#117×C₄₃	C₂³	1	4	yes	—
100	#117×C₄₃	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
103	C₂×C₄²×C₄₃	—	2	2	no	—
104	#107×C₄₃	C₂³	1	4	yes	—
105	#107×C₄₃	C₂³	1	4	yes	—
106	#106×C₄₃	C₂³	1	4	yes	—
107	#106×C₄₃	C₂³	1	4	yes	—
108	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	—	2	4	no	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
114	C₂²×C₄×C₄₃	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₄₃	—	2	4	no	—
119	C₂²×Dic₄₃	C₂×D₄	1	4	yes	—
120	C₂×Dic₈₆	—	2	16	no	—
121	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
122	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
123	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
124	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
125	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
126	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
127	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₄₃	—	2	4	no	—
132	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
133	C₂²⋊C₄×C₄₃	—	2	4	no	—
134	C₂²⋊C₄×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	4	no	—
136	C₄²×C₄₃	—	2	4	no	—
137	C₂²⋊Dic₄₃	—	2	4	no	—
138	C₂²⋊Dic₄₃	—	2	4	no	—
139	C₂²⋊Dic₄₃	C₂×D₄	1	4	yes	—
140	C₂²⋊Dic₄₃	C₂×D₄	1	4	yes	—
141	C₄⋊Dic₄₃	—	2	4	no	—
142	C₄⋊Dic₄₃	—	2	16	no	—
143	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
144	C₄⋊Dic₄₃	C₂×D₄	1	4	yes	—
145	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
146	Dic₄₃⋊C₄	—	2	16	no	—
147	Dic₄₃⋊C₄	—	2	16	no	—
148	C₄×Dic₄₃	—	2	4	no	—
149	C₄×Dic₄₃	—	2	4	no	—
150	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
151	C₄×Dic₄₃	C₂⁴	1	4	yes	—
152	#10621877	C₂×Q₈	1	8	yes	—
153	#10621877	C₂×Q₈	1	8	yes	—
154	C₂×C₄₃⋊C₈	C₂×Q₈	1	8	yes	—
155	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
156	C₂³×C₄₃	—	4	2	no	—
157	C₂³×C₄₃	C₄⋊Q₈	1	4	yes	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
160	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	—	2	8	no	—
162	C₂×C₄×C₄₃	—	8	4	no	—
163	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
164	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
165	C₂×C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
170	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
171	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
172	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
173	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
174	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
175	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
176	C₂×Dic₄₃	—	2	8	no	—
177	C₂×Dic₄₃	—	4	4	no	—
178	C₂×Dic₄₃	—	8	4	no	—
179	C₂×Dic₄₃	C₂²×D₄	1	8	yes	—
180	Dic₈₆	—	8	16	no	—
181	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
182	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
183	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
184	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
185	C₄₃⋊C₈	C₂²×Q₈	1	8	yes	—
186	#60660	—	43	1	no	maximal, Sylow
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	4	4	no	—
191	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
192	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
193	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
194	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
195	C₄×C₄₃	—	4	8	no	—
196	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
197	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
198	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
199	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
200	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
201	Dic₄₃	—	2	8	no	—
202	Dic₄₃	—	4	8	no	—
203	#3458	—	43	2	no	—
204	#3164	—	43	4	no	—
205	#3164	—	43	4	no	—
206	#3163	—	43	4	no	—
207	#3163	—	43	4	no	—
208	#3162	—	43	4	no	—
209	#3160	—	43	4	no	—
210	#2911	—	43	2	no	—
211	C₂×#427	—	43	1	no	—
212	C₂×#427	D₄₃	1	1	yes	characteristic
213	C₂×#405	—	43	1	no	—
214	C₂×C₄₃	—	2	2	no	—
215	C₂×C₄₃	—	2	2	no	—
216	C₂×C₄₃	—	2	2	no	—
217	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
218	C₂×C₄₃	#3584	1	2	yes	—
219	C₂²×M₁₆	—	43	1	no	—
220	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
221	#544	—	43	8	no	—
222	#544	—	43	8	no	—
223	#544	—	86	4	no	—
224	#543	—	86	4	no	—
225	#533	—	43	8	no	—
226	#533	—	86	4	no	—
227	#533	—	86	4	no	—
228	C₂×#117	—	43	1	no	—
229	C₂×#117	—	43	2	no	—
230	C₂×#117	C₂×D₄₃	1	2	yes	—
231	#501	—	43	16	no	—
232	#501	—	43	16	no	—
233	#500	—	43	8	no	—
234	#499	—	43	8	no	—
235	#499	—	43	8	no	—
236	#498	—	43	8	no	—
237	#428	—	43	8	no	—
238	#428	—	43	8	no	—
239	#427	—	43	2	no	—
240	#427	—	43	2	no	—
241	#427	—	43	2	no	—
242	#427	—	43	2	no	—
243	#427	—	43	8	no	—
244	#427	C₂×D₄₃	1	2	yes	—
245	#427	C₂×D₄₃	1	2	yes	—
246	#427	C₂×D₄₃	1	2	yes	—
247	#427	C₂×D₄₃	1	2	yes	—
248	C₂×#107	—	43	2	no	—
249	C₂×#107	C₂×D₄₃	1	2	yes	—
250	C₂×#106	—	43	2	no	—
251	C₂×#106	C₂×D₄₃	1	2	yes	—
252	#405	—	43	2	no	—
253	#405	—	43	2	no	—
254	#405	—	43	2	no	—
255	#405	—	43	2	no	—
256	C₂×#97	—	43	2	no	—
257	C₂×C₄×C₈	—	43	2	no	—
258	C₄₃	#60660	1	1	yes	characteristic, complemented, Sylow
259	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
260	C₂×M₁₆	—	43	8	no	—
261	C₂×M₁₆	—	43	2	no	—
262	C₂×M₁₆	—	43	2	no	—
263	C₂²×C₈	—	43	2	no	—
264	C₂²×C₈	Dic₈₆	1	8	yes	complemented
265	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	43	16	no	—
272	C₄⋊Q₈	—	86	8	no	—
273	C₄⋊Q₈	—	86	8	no	—
274	#125	—	43	16	no	—
275	#125	—	86	8	no	—
276	#125	—	86	8	no	—
277	C₂²⋊Q₈	—	86	16	no	—
278	C₂²⋊Q₈	—	86	16	no	—
279	C₂²⋊Q₈	—	86	16	no	—
280	C₄×Q₈	—	86	16	no	—
281	#117	—	2	2	no	—
282	#117	—	2	2	no	—
283	#117	—	43	2	no	—
284	#117	—	43	2	no	—
285	#117	—	43	2	no	—
286	#117	—	43	2	no	—
287	#117	—	43	4	no	—
288	#117	—	43	4	no	—
289	#117	—	86	2	no	—
290	#117	—	86	2	no	—
291	#117	C₂²×D₄₃	1	4	yes	—
292	#117	C₂²×D₄₃	1	4	yes	—
293	C₂×C₄⋊C₄	—	43	2	no	—
294	C₂×C₄⋊C₄	—	43	4	no	—
295	C₂×C₄⋊C₄	C₂²×D₄₃	1	4	yes	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	43	2	no	—
298	C₂×C₂²⋊C₄	—	86	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	—	43	2	no	—
301	C₂×C₄²	—	86	2	no	—
302	#107	—	43	4	no	—
303	#107	—	43	4	no	—
304	#107	—	43	16	no	—
305	#107	C₂²×D₄₃	1	4	yes	—
306	#107	C₂²×D₄₃	1	4	yes	—
307	#106	—	43	4	no	—
308	#106	—	43	4	no	—
309	#106	—	43	16	no	—
310	#106	C₂²×D₄₃	1	4	yes	—
311	#106	C₂²×D₄₃	1	4	yes	—
312	#97	—	43	4	no	—
313	#97	—	43	4	no	—
314	C₄×C₈	—	43	4	no	—
315	C₄×C₈	—	43	4	no	—
316	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
317	C₂×Q₈	—	86	16	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	43	4	no	—
320	C₂²×C₄	—	86	4	no	—
321	C₂²×C₄	C₂×Dic₈₆	1	4	yes	—
322	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
325	C₂²×C₄	Q₈×D₄₃	1	4	yes	—
326	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
328	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
329	M₁₆	—	43	8	no	—
330	M₁₆	—	43	8	no	—
331	C₂×C₈	—	43	8	no	—
332	C₂×C₈	—	43	4	no	—
333	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
334	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
335	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
336	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
337	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
338	C₂×C₈	C₂×Dic₈₆	1	4	yes	—
339	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
340	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
341	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	43	4	no	—
345	C₄⋊C₄	—	43	4	no	—
346	C₄⋊C₄	—	43	8	no	—
347	C₄⋊C₄	—	86	16	no	—
348	C₄⋊C₄	—	86	16	no	—
349	C₄⋊C₄	—	86	16	no	—
350	C₄⋊C₄	—	86	4	no	—
351	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	43	4	no	—
355	C₂²⋊C₄	—	43	4	no	—
356	C₂²⋊C₄	—	86	4	no	—
357	C₂²⋊C₄	—	86	4	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	43	4	no	—
361	C₄²	—	43	4	no	—
362	C₄²	—	86	4	no	—
363	C₄²	—	86	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	#13063324	1	4	yes	—
366	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
367	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
368	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
369	Q₈	—	344	16	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	8	4	no	—
372	C₂×C₄	—	43	8	no	—
373	C₂×C₄	—	86	8	no	—
374	C₂×C₄	—	344	4	no	—
375	C₂×C₄	—	172	4	no	—
376	C₂×C₄	#13063324	1	4	yes	—
377	C₂×C₄	#13063324	1	4	yes	—
378	C₂×C₄	#13063324	1	4	yes	—
379	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
380	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
383	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
384	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
385	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
386	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
387	C₂×C₄	C₂²×Dic₈₆	1	2	yes	—
388	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
389	C₈	—	43	8	no	—
390	C₈	C₂²×Dic₈₆	1	2	yes	—
391	C₈	C₂²×Dic₈₆	1	2	yes	—
392	C₈	C₂²×Dic₈₆	1	2	yes	—
393	C₈	C₂²×Dic₈₆	1	2	yes	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	4	no	—
398	C₂²	C₂×#13063324	1	2	yes	—
399	C₂²	C₂×#13063324	1	2	yes	—
400	C₂²	C₂×#13063324	1	2	yes	—
401	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
402	C₄	—	4	8	no	—
403	C₄	—	86	8	no	—
404	C₄	—	172	8	no	—
405	C₄	C₂×#13063324	1	2	yes	—
406	C₄	C₂×#13063324	1	2	yes	—
407	C₄	C₂×#13063324	1	2	yes	—
408	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
409	C₄	C₂³×Dic₈₆	1	1	yes	characteristic
410	C₂	—	2	2	no	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	C₂²×#13063324	1	1	yes	characteristic
414	C₂	#19149364	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#427	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂⁴×C₄₃	C₂×D₄
hypercenter	C₂×#427	D₄₃
hypocenter	C₄₃	#60660
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
2. #19145135	C₂	semidirect
3. #19145131	C₂	semidirect
4. #19145127	C₂	semidirect
5. #19145123	C₂	semidirect
6. #19145118	C₂	semidirect
7. #19145107	C₂	semidirect
22. #14583307	C₂²	semidirect
23. #14583306	C₂²	semidirect
24. #14583303	C₂²	semidirect
25. #14583300	C₂²	semidirect
26. #14583299	C₂²	semidirect
27. #14583296	C₂²	semidirect
51. C₂×#10621877	Q₈	semidirect
90. C₂²×C₈×C₄₃	Q₈	semidirect
258. C₄₃	#60660	semidirect
264. C₂²×C₈	Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
#19148000	2
#19145135	2
#19145131	2
#19145127	2
#19145123	2
#19145118	2
#19145107	2
#19143184	2
C₂×#14582937	2
C₂×#14582854	2
C₂×C₄₃×#427	2
#60660	43