Subgroups — #25115534

Order 11008.

822 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583023	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	#19137507	C₂	1	1	yes	maximal, characteristic
4	#19135359	C₂	1	1	yes	maximal, characteristic
5	#19135357	C₂	1	2	yes	maximal
6	#19135355	C₂	1	2	yes	maximal
7	#19134722	C₂	1	1	yes	maximal, characteristic
8	#19134721	C₂	1	2	yes	maximal
9	#106×Dic₄₃	C₂	1	2	yes	maximal
10	C₄×#13063256	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1948	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₈₆	—	2	1	no	—
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	C₂×#13063290	—	2	1	no	—
15	#14583023	C₄	1	8	yes	complemented
16	C₂×#13063257	C₂²	1	2	yes	—
17	C₂×#13063256	C₂²	1	1	yes	characteristic
18	C₂×#13063256	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
22	#14582797	—	2	1	no	—
23	#14582796	—	2	2	no	—
24	#14582795	—	2	1	no	—
25	#14582794	—	2	2	no	—
26	#14582769	C₂²	1	1	yes	characteristic
27	#14582768	C₂²	1	2	yes	—
28	#14582768	C₂²	1	2	yes	—
29	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
32	#14582662	C₂²	1	2	yes	—
33	#14582661	C₂²	1	1	yes	characteristic
34	#14582661	C₂²	1	2	yes	—
35	#14582661	C₂²	1	2	yes	—
36	#14582661	C₂²	1	1	yes	characteristic
37	C₂×#106×C₄₃	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
39	C₄₃×#384	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#340	C₂²	1	2	yes	—
42	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
43	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
45	C₄×Dic₈₆	—	4	4	no	—
46	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
47	C₄×Dic₈₆	Q₈	1	4	yes	—
48	#13063290	—	4	4	no	—
49	C₂×C₄⋊Dic₄₃	—	2	1	no	—
50	C₂×C₄⋊Dic₄₃	—	2	1	no	—
51	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
55	C₂×Dic₄₃⋊C₄	—	2	2	no	—
56	C₂×Dic₄₃⋊C₄	—	2	2	no	—
57	C₂×Dic₄₃⋊C₄	—	2	2	no	—
58	C₂×Dic₄₃⋊C₄	—	2	2	no	—
59	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₃	—	2	1	no	—
61	C₂×C₄×Dic₄₃	—	2	2	no	—
62	C₂×C₄×Dic₄₃	—	2	2	no	—
63	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
64	#13063257	—	2	4	no	—
65	#13063256	—	2	2	no	—
66	#13063256	—	2	2	no	—
67	Dic₄₃⋊C₈	C₂×C₄	1	8	yes	—
68	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
69	C₈×Dic₄₃	C₂×C₄	1	8	yes	—
70	C₄₃⋊#95	—	2	1	no	—
71	C₄₃⋊#95	—	2	2	no	—
72	C₄₃⋊#95	—	2	2	no	—
73	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₃	—	2	1	no	—
80	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
81	#106×C₄₃	—	2	4	no	—
82	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
83	#95×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	2	2	no	—
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₃	—	2	1	no	—
91	C₂²×Dic₄₃	—	2	1	no	—
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
94	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
95	C₂×Dic₈₆	C₄⋊C₄	1	4	yes	—
96	C₂×Dic₈₆	SD₁₆	1	4	yes	—
97	C₂×Dic₈₆	SD₁₆	1	4	yes	—
98	C₂×C₈×C₄₃	—	2	2	no	—
99	C₂×C₈×C₄₃	—	2	2	no	—
100	C₂×C₈×C₄₃	C₂²×C₄	1	4	yes	—
101	C₄⋊C₄×C₄₃	—	2	1	no	—
102	C₄⋊C₄×C₄₃	—	2	2	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	—	2	1	no	—
106	C₄⋊C₄×C₄₃	—	4	2	no	—
107	C₄⋊C₄×C₄₃	—	8	1	no	—
108	C₄⋊C₄×C₄₃	#41	1	2	yes	—
109	C₄²×C₄₃	—	4	2	no	—
110	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₄₃	C₂×Q₈	1	2	yes	—
112	C₄⋊Dic₄₃	—	2	1	no	—
113	C₄⋊Dic₄₃	—	2	1	no	—
114	C₄⋊Dic₄₃	—	2	2	no	—
115	C₄⋊Dic₄₃	—	2	1	no	—
116	C₄⋊Dic₄₃	—	2	2	no	—
117	C₄⋊Dic₄₃	—	4	2	no	—
118	C₄⋊Dic₄₃	—	8	1	no	—
119	C₄⋊Dic₄₃	C₄⋊C₄	1	4	yes	—
120	C₄⋊Dic₄₃	#41	1	2	yes	—
121	Dic₄₃⋊C₄	—	4	4	no	—
122	Dic₄₃⋊C₄	—	4	4	no	—
123	Dic₄₃⋊C₄	—	8	2	no	—
124	Dic₄₃⋊C₄	—	8	2	no	—
125	Dic₄₃⋊C₄	C₄⋊C₄	1	8	yes	—
126	C₄×Dic₄₃	—	4	2	no	—
127	C₄×Dic₄₃	—	4	4	no	—
128	C₄×Dic₄₃	—	4	4	no	—
129	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
130	C₄×Dic₄₃	C₂×Q₈	1	4	yes	—
131	C₂×C₄₃⋊C₈	—	2	1	no	—
132	C₂×C₄₃⋊C₈	—	2	1	no	—
133	C₂×C₄₃⋊C₈	—	2	1	no	—
134	C₂×C₄₃⋊C₈	—	2	1	no	—
135	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	2	no	—
141	C₂×C₄×C₄₃	—	4	1	no	—
142	C₂×C₄×C₄₃	—	4	1	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	2	no	—
146	C₂×C₄×C₄₃	—	4	1	no	—
147	C₂×C₄×C₄₃	—	4	1	no	—
148	C₂×C₄×C₄₃	—	4	2	no	—
149	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
152	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
153	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
158	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×Dic₄₃	—	2	2	no	—
160	C₂×Dic₄₃	—	2	2	no	—
161	C₂×Dic₄₃	—	2	2	no	—
162	C₂×Dic₄₃	—	4	1	no	—
163	C₂×Dic₄₃	—	4	1	no	—
164	C₂×Dic₄₃	—	4	1	no	—
165	C₂×Dic₄₃	—	4	2	no	—
166	C₂×Dic₄₃	—	4	1	no	—
167	C₂×Dic₄₃	—	4	2	no	—
168	C₂×Dic₄₃	—	4	1	no	—
169	C₂×Dic₄₃	—	4	2	no	—
170	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
171	C₂×Dic₄₃	C₂×C₄⋊C₄	1	4	yes	—
172	C₂×Dic₄₃	C₂×SD₁₆	1	4	yes	—
173	C₂×Dic₄₃	C₂×SD₁₆	1	4	yes	—
174	Dic₈₆	#106	1	16	yes	complemented
175	C₈×C₄₃	—	2	4	no	—
176	C₄₃⋊C₈	—	2	2	no	—
177	C₄₃⋊C₈	—	2	2	no	—
178	#22738	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
180	C₂²×C₄₃	#548	1	1	yes	characteristic
181	C₂²×C₄₃	#548	1	1	yes	characteristic
182	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
183	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
184	C₂²×C₄₃	#576	1	1	yes	characteristic
185	C₂²×C₄₃	#578	1	1	yes	characteristic
186	C₄×C₄₃	—	2	2	no	—
187	C₄×C₄₃	—	4	2	no	—
188	C₄×C₄₃	—	8	1	no	—
189	C₄×C₄₃	—	8	2	no	—
190	C₄×C₄₃	C₂×#106	1	4	yes	—
191	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
192	C₄×C₄₃	#519	1	1	yes	characteristic
193	C₄×C₄₃	#557	1	1	yes	characteristic
194	C₄×C₄₃	#557	1	1	yes	characteristic
195	Dic₄₃	—	2	4	no	—
196	Dic₄₃	—	4	2	no	—
197	Dic₄₃	—	8	2	no	—
198	Dic₄₃	—	8	1	no	—
199	Dic₄₃	C₂×#106	1	8	yes	—
200	C₂×C₈×Q₈	—	43	1	no	—
201	Q₈×C₄⋊C₄	—	43	1	no	—
202	Q₈×C₄⋊C₄	—	43	1	no	—
203	#1948	—	43	2	no	—
204	#1948	—	43	1	no	—
205	#1948	—	43	2	no	—
206	#1948	D₄₃	1	1	yes	characteristic
207	#1834	—	43	1	no	—
208	#1834	—	43	2	no	—
209	C₄×#106	—	43	2	no	—
210	C₄×#106	—	43	1	no	—
211	C₂×C₄₃	#2351	1	1	yes	characteristic
212	C₂×C₄₃	C₂²×#106	1	1	yes	characteristic
213	C₂×C₄₃	#2913	1	1	yes	characteristic
214	C₂×C₄₃	#3359	1	1	yes	characteristic
215	C₂×C₄₃	#3359	1	1	yes	characteristic
216	C₂×C₄₃	#3362	1	1	yes	characteristic
217	C₂×C₄₃	#3362	1	1	yes	characteristic
218	C₂×C₄×Q₈	—	43	1	no	—
219	C₂×C₄×Q₈	—	86	1	no	—
220	C₂×C₄×Q₈	—	86	1	no	—
221	C₈×Q₈	—	43	8	no	—
222	C₂×#106	—	43	2	no	—
223	C₂×#106	—	43	1	no	—
224	C₂×#106	—	43	1	no	—
225	C₂×#106	C₂×D₄₃	1	2	yes	—
226	C₂×C₄⋊C₈	—	43	2	no	—
227	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×C₄×C₈	—	43	2	no	—
229	C₂×C₄×C₈	—	43	1	no	—
230	#389	—	86	2	no	—
231	#389	—	86	1	no	—
232	#389	—	86	2	no	—
233	#389	—	86	1	no	—
234	#384	—	43	2	no	—
235	#384	—	43	2	no	—
236	#384	—	43	1	no	—
237	#384	C₂×D₄₃	1	1	yes	characteristic
238	C₄×C₄⋊C₄	—	43	2	no	—
239	C₄×C₄⋊C₄	—	43	2	no	—
240	C₄×C₄⋊C₄	—	43	1	no	—
241	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
242	#340	—	43	2	no	—
243	#340	—	43	2	no	—
244	#340	—	43	1	no	—
245	#340	—	43	2	no	—
246	#340	—	43	1	no	—
247	#340	C₂×D₄₃	1	2	yes	—
248	C₄₃	#22738	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	—	43	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
253	C₄×Q₈	—	43	4	no	—
254	C₄×Q₈	—	43	4	no	—
255	C₄×Q₈	—	172	4	no	—
256	C₄×Q₈	—	172	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	43	2	no	—
260	C₂×C₄⋊C₄	—	43	1	no	—
261	C₂×C₄⋊C₄	—	43	1	no	—
262	C₂×C₄⋊C₄	—	43	2	no	—
263	C₂×C₄⋊C₄	—	43	1	no	—
264	C₂×C₄⋊C₄	—	86	2	no	—
265	C₂×C₄⋊C₄	—	86	2	no	—
266	C₂×C₄⋊C₄	—	86	1	no	—
267	C₂×C₄⋊C₄	—	86	2	no	—
268	C₂×C₄⋊C₄	—	86	2	no	—
269	C₂×C₄⋊C₄	—	86	1	no	—
270	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
271	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	43	2	no	—
275	C₂×C₄²	—	86	2	no	—
276	C₂×C₄²	—	86	2	no	—
277	C₂×C₄²	—	86	1	no	—
278	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
279	#106	—	2	4	no	—
280	#106	—	86	2	no	—
281	#106	—	86	4	no	—
282	#106	—	86	2	no	—
283	C₄⋊C₈	—	43	8	no	—
284	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
285	C₄×C₈	—	43	8	no	—
286	C₄×C₈	—	43	4	no	—
287	#95	—	2	1	no	—
288	#95	—	86	2	no	—
289	#95	—	86	2	no	—
290	#95	—	86	1	no	—
291	C₂×Q₈	—	43	4	no	—
292	C₂×Q₈	—	43	4	no	—
293	C₂×Q₈	—	43	4	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	43	2	no	—
298	C₂²×C₄	—	43	2	no	—
299	C₂²×C₄	—	86	1	no	—
300	C₂²×C₄	—	86	1	no	—
301	C₂²×C₄	—	86	2	no	—
302	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
303	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	43	2	no	—
308	C₂×C₈	—	43	2	no	—
309	C₂×C₈	—	86	1	no	—
310	C₂×C₈	—	86	1	no	—
311	C₂×C₈	—	86	1	no	—
312	C₂×C₈	—	86	1	no	—
313	C₂×C₈	C₂×C₄×D₄₃	1	4	yes	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	8	1	no	—
321	C₄⋊C₄	—	43	8	no	—
322	C₄⋊C₄	—	43	4	no	—
323	C₄⋊C₄	—	43	2	no	—
324	C₄⋊C₄	—	86	1	no	—
325	C₄⋊C₄	—	86	2	no	—
326	C₄⋊C₄	—	86	1	no	—
327	C₄⋊C₄	—	86	1	no	—
328	C₄⋊C₄	—	86	2	no	—
329	C₄⋊C₄	—	344	1	no	—
330	C₄⋊C₄	—	344	2	no	—
331	C₄⋊C₄	—	344	2	no	—
332	C₄⋊C₄	—	172	4	no	—
333	C₄⋊C₄	—	172	4	no	—
334	C₄⋊C₄	—	172	2	no	—
335	C₄⋊C₄	#10621900	1	2	yes	—
336	C₄²	—	4	2	no	—
337	C₄²	—	43	4	no	—
338	C₄²	—	43	4	no	—
339	C₄²	—	172	4	no	—
340	C₄²	—	172	4	no	—
341	C₄²	—	172	2	no	—
342	C₄²	C₂×C₄×D₄₃	1	2	yes	—
343	C₄²	Q₈×D₄₃	1	2	yes	—
344	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
345	Q₈	—	43	16	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	43	4	no	—
358	C₂×C₄	—	43	4	no	—
359	C₂×C₄	—	43	4	no	—
360	C₂×C₄	—	43	4	no	—
361	C₂×C₄	—	86	2	no	—
362	C₂×C₄	—	86	2	no	—
363	C₂×C₄	—	86	2	no	—
364	C₂×C₄	—	172	1	no	—
365	C₂×C₄	—	172	2	no	—
366	C₂×C₄	—	172	2	no	—
367	C₂×C₄	—	172	1	no	—
368	C₂×C₄	—	172	2	no	—
369	C₂×C₄	—	172	1	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	1	no	—
372	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
373	C₂×C₄	C₄⋊C₄×D₄₃	1	2	yes	—
374	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
375	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
376	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
377	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
378	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
379	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
380	C₂×C₄	#13063372	1	1	yes	characteristic
381	C₂×C₄	#13063373	1	1	yes	characteristic
382	C₈	—	2	4	no	—
383	C₈	—	86	2	no	—
384	C₈	—	86	2	no	—
385	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
386	C₂²	#14583555	1	1	yes	characteristic
387	C₂²	#14583559	1	1	yes	characteristic
388	C₂²	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
389	C₂²	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
390	C₂²	#14583703	1	1	yes	characteristic
391	C₂²	#14583715	1	1	yes	characteristic
392	C₄	—	2	2	no	—
393	C₄	—	4	2	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	43	8	no	—
397	C₄	—	86	4	no	—
398	C₄	—	344	2	no	—
399	C₄	—	344	1	no	—
400	C₄	—	172	2	no	—
401	C₄	#106×D₄₃	1	4	yes	—
402	C₄	C₄×#10621900	1	1	yes	characteristic
403	C₄	#14583375	1	1	yes	characteristic
404	C₄	#14583624	1	1	yes	characteristic
405	C₄	#14583626	1	1	yes	characteristic
406	C₂	#19137514	1	1	yes	characteristic
407	C₂	C₂×#106×D₄₃	1	1	yes	characteristic
408	C₂	#19143194	1	1	yes	characteristic
409	C₂	#19147232	1	1	yes	characteristic
410	C₂	#19147236	1	1	yes	characteristic
411	C₂	#19147261	1	1	yes	characteristic
412	C₂	#19147265	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×#1948	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1948	D₄₃
hypocenter	C₄₃	#22738
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
15. #14583023	C₄	semidirect
174. Dic₈₆	#106	semidirect
248. C₄₃	#22738	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583023	2
C₄⋊C₄×Dic₈₆	2
#19137507	2
#19135359	2
#19135357	2
#19135355	2
#19134722	2
#19134721	2
#106×Dic₄₃	2
C₄×#13063256	2
C₄₃×#1948	2
#22738	43