Subgroups — #103×Dic₈₆ #25113202

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×Dic₈₆	C₂	1	1	yes	maximal, characteristic
4	#19135556	C₂	1	1	yes	maximal, characteristic
5	#19135554	C₂	1	2	yes	maximal
6	#19135543	C₂	1	1	yes	maximal, characteristic
7	#19135541	C₂	1	2	yes	maximal
8	#19134600	C₂	1	1	yes	maximal, characteristic
9	#19134598	C₂	1	2	yes	maximal
10	#103×Dic₄₃	C₂	1	2	yes	maximal
11	C₄×#103×C₄₃	C₂	1	1	yes	maximal, characteristic
12	Q₈×Dic₈₆	—	2	4	no	—
13	Q₈×Dic₈₆	C₄	1	8	yes	complemented
14	C₂×#13063325	—	2	1	no	—
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	C₂×#13063324	—	2	2	no	—
17	C₂×#13063324	C₂²	1	2	yes	—
18	C₂×Q₈×Dic₄₃	C₂²	1	2	yes	—
19	C₂×C₄×Dic₈₆	—	2	1	no	—
20	C₂×C₄×Dic₈₆	—	2	1	no	—
21	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
22	C₈×Dic₈₆	—	2	4	no	—
23	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₃⋊C₈	C₂²	1	2	yes	—
25	C₂×#13063249	C₂²	1	2	yes	—
26	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
27	#14582797	—	2	1	no	—
28	#14582796	—	2	2	no	—
29	#14582769	C₂²	1	1	yes	characteristic
30	#14582768	C₂²	1	2	yes	—
31	C₄⋊C₄×Dic₄₃	C₂²	1	2	yes	—
32	#14582662	C₂²	1	2	yes	—
33	#14582662	C₂²	1	2	yes	—
34	#14582661	C₂²	1	2	yes	—
35	#14582661	C₂²	1	2	yes	—
36	#14582661	C₂²	1	2	yes	—
37	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
38	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
39	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#340	C₂²	1	1	yes	characteristic
43	C₄₃×#340	C₂²	1	1	yes	characteristic
44	C₂²×Dic₈₆	—	2	1	no	—
45	C₂²×Dic₈₆	—	2	2	no	—
46	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
47	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
48	#13063325	—	2	2	no	—
49	#13063325	—	2	8	no	—
50	#13063325	C₂×C₄	1	4	yes	—
51	#13063324	—	2	16	no	—
52	#13063324	—	2	4	no	—
53	#13063324	C₂×C₄	1	8	yes	—
54	Q₈×Dic₄₃	—	2	4	no	—
55	Q₈×Dic₄₃	C₂×C₄	1	8	yes	—
56	C₄×Dic₈₆	—	2	8	no	—
57	C₄×Dic₈₆	—	4	4	no	—
58	C₄×Dic₈₆	C₂×C₄	1	4	yes	—
59	C₄×Dic₈₆	D₄	1	4	yes	—
60	C₂×C₄⋊Dic₄₃	—	2	1	no	—
61	C₂×C₄⋊Dic₄₃	—	2	2	no	—
62	C₂×C₄⋊Dic₄₃	—	2	1	no	—
63	C₂×C₄⋊Dic₄₃	—	2	1	no	—
64	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
67	C₂×Dic₄₃⋊C₄	—	2	2	no	—
68	C₂×Dic₄₃⋊C₄	—	2	2	no	—
69	C₂×Dic₄₃⋊C₄	—	2	2	no	—
70	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
71	C₂×C₄×Dic₄₃	—	2	2	no	—
72	C₂×C₄×Dic₄₃	—	2	2	no	—
73	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
74	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
75	Dic₄₃⋊C₈	—	2	4	no	—
76	#13063249	—	2	4	no	—
77	C₈×Dic₄₃	—	2	4	no	—
78	C₄₃⋊#95	—	2	2	no	—
79	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
82	C₄×Q₈×C₄₃	—	2	2	no	—
83	C₄×Q₈×C₄₃	C₂×C₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	—	2	1	no	—
90	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
91	#103×C₄₃	—	2	2	no	—
92	#103×C₄₃	Q₈	1	4	yes	complemented
93	C₄×C₈×C₄₃	—	2	2	no	—
94	#95×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	1	no	—
98	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₄₃	C₂×Q₈	1	2	yes	—
100	C₂×Q₈×C₄₃	#41	1	2	yes	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	1	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₃	—	2	2	no	—
109	C₂²×Dic₄₃	—	2	2	no	—
110	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
111	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
112	C₂×Dic₈₆	—	2	4	no	—
113	C₂×Dic₈₆	—	2	8	no	—
114	C₂×Dic₈₆	—	8	2	no	—
115	C₂×Dic₈₆	—	8	2	no	—
116	C₂×Dic₈₆	—	8	1	no	—
117	C₂×Dic₈₆	—	8	1	no	—
118	C₂×Dic₈₆	C₂²⋊C₄	1	4	yes	—
119	C₂×Dic₈₆	SD₁₆	1	4	yes	—
120	C₂×Dic₈₆	Q₁₆	1	4	yes	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	1	no	—
126	C₂×C₈×C₄₃	C₂×Q₈	1	2	yes	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₃	C₂×Q₈	1	2	yes	—
134	C₄²×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	4	2	no	—
136	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	C₄⋊Dic₄₃	—	2	4	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	8	no	—
141	C₄⋊Dic₄₃	—	2	2	no	—
142	C₄⋊Dic₄₃	—	2	2	no	—
143	C₄⋊Dic₄₃	—	4	2	no	—
144	C₄⋊Dic₄₃	—	8	1	no	—
145	C₄⋊Dic₄₃	C₂²⋊C₄	1	4	yes	—
146	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
147	Dic₄₃⋊C₄	—	2	8	no	—
148	Dic₄₃⋊C₄	—	4	4	no	—
149	Dic₄₃⋊C₄	—	8	2	no	—
150	Dic₄₃⋊C₄	C₂²⋊C₄	1	8	yes	—
151	C₄×Dic₄₃	—	2	8	no	—
152	C₄×Dic₄₃	—	4	4	no	—
153	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
154	C₄×Dic₄₃	C₂×D₄	1	4	yes	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₃	—	2	2	no	—
160	Q₈×C₄₃	—	2	2	no	—
161	Q₈×C₄₃	—	2	2	no	—
162	Q₈×C₄₃	C₄×Q₈	1	4	yes	complemented
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	2	2	no	—
169	C₂×C₄×C₄₃	—	2	2	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
181	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
187	C₂×Dic₄₃	—	2	2	no	—
188	C₂×Dic₄₃	—	2	2	no	—
189	C₂×Dic₄₃	—	2	4	no	—
190	C₂×Dic₄₃	—	4	2	no	—
191	C₂×Dic₄₃	—	4	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	C₂×Dic₄₃	—	4	2	no	—
195	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	4	yes	—
196	C₂×Dic₄₃	C₂×C₂²⋊C₄	1	4	yes	—
197	C₂×Dic₄₃	C₂×SD₁₆	1	4	yes	—
198	C₂×Dic₄₃	C₂×Q₁₆	1	4	yes	—
199	Dic₈₆	—	8	8	no	—
200	Dic₈₆	—	8	4	no	—
201	Dic₈₆	#103	1	16	yes	direct product factor
202	C₈×C₄₃	—	2	2	no	—
203	C₈×C₄₃	—	4	1	no	—
204	C₄₃⋊C₈	—	4	2	no	—
205	Q₈×#103	—	43	1	no	maximal, Sylow
206	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
207	C₂²×C₄₃	#548	1	1	yes	characteristic
208	C₂²×C₄₃	D₄×Q₈	1	1	yes	characteristic
209	C₂²×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
210	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
211	C₂²×C₄₃	#576	1	1	yes	characteristic
212	C₂²×C₄₃	#577	1	1	yes	characteristic
213	C₄×C₄₃	—	2	4	no	—
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	4	2	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	—	8	1	no	—
218	C₄×C₄₃	C₂×#103	1	4	yes	—
219	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
220	C₄×C₄₃	#519	1	1	yes	characteristic
221	C₄×C₄₃	#548	1	1	yes	characteristic
222	C₄×C₄₃	D₄×Q₈	1	1	yes	characteristic
223	Dic₄₃	—	2	4	no	—
224	Dic₄₃	—	4	4	no	—
225	Dic₄₃	—	8	2	no	—
226	Dic₄₃	C₂×#103	1	8	yes	—
227	C₂×Q₈²	—	43	1	no	—
228	C₂×C₈×Q₈	—	43	1	no	—
229	Q₈×C₄⋊C₄	—	43	1	no	—
230	#1990	—	43	1	no	—
231	#1990	—	43	2	no	—
232	#1987	—	43	1	no	—
233	#1987	—	43	2	no	—
234	#1803	—	43	2	no	—
235	#1803	—	43	1	no	—
236	C₄×#103	—	43	2	no	—
237	C₄×#103	D₄₃	1	1	yes	characteristic
238	C₂×C₄₃	Q₈×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄₃	C₂²×#103	1	1	yes	characteristic
240	C₂×C₄₃	#2897	1	1	yes	characteristic
241	C₂×C₄₃	#3362	1	1	yes	characteristic
242	C₂×C₄₃	#3363	1	1	yes	characteristic
243	C₂×C₄₃	Q₈×SD₁₆	1	1	yes	characteristic
244	C₂×C₄₃	Q₈×Q₁₆	1	1	yes	characteristic
245	Q₈²	—	43	8	no	—
246	Q₈²	—	86	4	no	—
247	C₂×C₄⋊Q₈	—	43	2	no	—
248	C₂×C₄⋊Q₈	—	43	1	no	—
249	C₂×C₄⋊Q₈	—	86	1	no	—
250	C₂×C₄⋊Q₈	—	86	2	no	—
251	C₂×C₄×Q₈	—	43	1	no	—
252	C₂×C₄×Q₈	—	43	2	no	—
253	C₂×C₄×Q₈	—	86	1	no	—
254	C₂×C₄×Q₈	—	86	1	no	—
255	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
256	C₈×Q₈	—	86	4	no	—
257	C₂×C₄⋊C₈	—	43	2	no	—
258	C₂×C₄⋊C₈	—	43	1	no	—
259	C₂×#103	—	43	2	no	—
260	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
261	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
262	C₂×C₄×C₈	—	43	2	no	—
263	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
264	#389	—	86	2	no	—
265	#389	—	86	1	no	—
266	#384	—	43	2	no	—
267	#384	—	43	1	no	—
268	C₄×C₄⋊C₄	—	43	2	no	—
269	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
270	#340	—	43	2	no	—
271	#340	—	43	2	no	—
272	#340	—	43	2	no	—
273	#340	—	43	2	no	—
274	#340	—	43	2	no	—
275	#340	C₂×D₄₃	1	1	yes	characteristic
276	#340	C₂×D₄₃	1	1	yes	characteristic
277	C₄₃	Q₈×#103	1	1	yes	characteristic, complemented, Sylow
278	C₂²×Q₈	—	43	1	no	—
279	C₂²×Q₈	—	86	2	no	—
280	C₂²×Q₈	—	86	1	no	—
281	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
282	C₂²×C₈	—	43	2	no	—
283	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
284	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
285	C₄⋊Q₈	—	43	8	no	—
286	C₄⋊Q₈	—	43	4	no	—
287	C₄⋊Q₈	—	86	8	no	—
288	C₄⋊Q₈	—	86	4	no	—
289	C₄⋊Q₈	—	86	16	no	—
290	C₄⋊Q₈	—	86	2	no	—
291	C₄×Q₈	—	2	2	no	—
292	C₄×Q₈	—	43	4	no	—
293	C₄×Q₈	—	43	4	no	—
294	C₄×Q₈	—	43	8	no	—
295	C₄×Q₈	—	86	8	no	—
296	C₄×Q₈	—	86	4	no	—
297	C₄×Q₈	—	172	4	no	—
298	C₄×Q₈	C₄×D₄₃	1	4	yes	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	43	2	no	—
301	C₂×C₄⋊C₄	—	43	1	no	—
302	C₂×C₄⋊C₄	—	43	2	no	—
303	C₂×C₄⋊C₄	—	43	2	no	—
304	C₂×C₄⋊C₄	—	86	2	no	—
305	C₂×C₄⋊C₄	—	86	2	no	—
306	C₂×C₄⋊C₄	—	86	1	no	—
307	C₂×C₄⋊C₄	—	86	2	no	—
308	C₂×C₄⋊C₄	—	86	1	no	—
309	C₂×C₄⋊C₄	—	86	2	no	—
310	C₂×C₄⋊C₄	—	86	1	no	—
311	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	—	43	2	no	—
317	C₂×C₄²	—	86	2	no	—
318	C₂×C₄²	—	86	2	no	—
319	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
320	C₄⋊C₈	—	86	4	no	—
321	C₄⋊C₈	—	86	2	no	—
322	#103	—	2	2	no	—
323	#103	—	86	4	no	—
324	#103	Dic₈₆	1	4	yes	direct product factor
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	86	4	no	—
327	#95	—	2	1	no	—
328	#95	—	86	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	43	4	no	—
333	C₂×Q₈	—	43	4	no	—
334	C₂×Q₈	—	43	4	no	—
335	C₂×Q₈	—	86	8	no	—
336	C₂×Q₈	—	86	4	no	—
337	C₂×Q₈	—	344	1	no	—
338	C₂×Q₈	—	344	1	no	—
339	C₂×Q₈	—	344	2	no	—
340	C₂×Q₈	—	344	2	no	—
341	C₂×Q₈	C₂×Dic₈₆	1	2	yes	—
342	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
343	C₂×Q₈	#10621898	1	2	yes	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	43	2	no	—
349	C₂²×C₄	—	43	2	no	—
350	C₂²×C₄	—	86	2	no	—
351	C₂²×C₄	—	86	2	no	—
352	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
353	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	—	86	2	no	—
363	C₂×C₈	C₂×Dic₈₆	1	2	yes	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	43	8	no	—
370	C₄⋊C₄	—	43	4	no	—
371	C₄⋊C₄	—	43	4	no	—
372	C₄⋊C₄	—	86	8	no	—
373	C₄⋊C₄	—	86	8	no	—
374	C₄⋊C₄	—	86	4	no	—
375	C₄⋊C₄	—	86	2	no	—
376	C₄⋊C₄	—	86	2	no	—
377	C₄⋊C₄	—	86	2	no	—
378	C₄⋊C₄	—	344	1	no	—
379	C₄⋊C₄	—	344	2	no	—
380	C₄⋊C₄	—	172	4	no	—
381	C₄⋊C₄	—	172	2	no	—
382	C₄⋊C₄	C₂×Dic₈₆	1	2	yes	—
383	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
384	C₄²	—	2	4	no	—
385	C₄²	—	4	2	no	—
386	C₄²	—	43	4	no	—
387	C₄²	—	43	4	no	—
388	C₄²	—	86	8	no	—
389	C₄²	—	172	4	no	—
390	C₄²	C₂×C₄×D₄₃	1	2	yes	—
391	C₄²	D₄×D₄₃	1	2	yes	—
392	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
393	Q₈	—	2	2	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	43	16	no	—
397	Q₈	—	344	4	no	—
398	Q₈	—	344	8	no	—
399	Q₈	C₄×Dic₈₆	1	4	yes	complemented
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	43	4	no	—
415	C₂×C₄	—	43	4	no	—
416	C₂×C₄	—	43	4	no	—
417	C₂×C₄	—	43	4	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	4	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	—	172	2	no	—
424	C₂×C₄	—	172	2	no	—
425	C₂×C₄	—	172	2	no	—
426	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
427	C₂×C₄	C₂²⋊C₄×D₄₃	1	2	yes	—
428	C₂×C₄	SD₁₆×D₄₃	1	2	yes	—
429	C₂×C₄	Q₁₆×D₄₃	1	2	yes	—
430	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×Dic₈₆	1	1	yes	characteristic
433	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
434	C₂×C₄	#13063372	1	1	yes	characteristic
435	C₂×C₄	#13063372	1	1	yes	characteristic
436	C₈	—	2	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	172	2	no	—
439	C₂²	C₂×C₂²⋊C₄×D₄₃	1	1	yes	characteristic
440	C₂²	#14583558	1	1	yes	characteristic
441	C₂²	D₄×Dic₈₆	1	1	yes	characteristic
442	C₂²	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
443	C₂²	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
444	C₂²	#14583701	1	1	yes	characteristic
445	C₂²	#14583706	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	43	8	no	—
452	C₄	—	86	4	no	—
453	C₄	—	344	2	no	—
454	C₄	—	172	4	no	—
455	C₄	#103×D₄₃	1	4	yes	—
456	C₄	C₂×C₄×Dic₈₆	1	1	yes	characteristic
457	C₄	#14583376	1	1	yes	characteristic
458	C₄	#14583558	1	1	yes	characteristic
459	C₄	D₄×Dic₈₆	1	1	yes	characteristic
460	C₂	C₂²⋊C₄×Dic₈₆	1	1	yes	characteristic
461	C₂	C₂×#103×D₄₃	1	1	yes	characteristic
462	C₂	#19143117	1	1	yes	characteristic
463	C₂	#19147264	1	1	yes	characteristic
464	C₂	#19147271	1	1	yes	characteristic
465	C₂	SD₁₆×Dic₈₆	1	1	yes	characteristic
466	C₂	Q₁₆×Dic₈₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#103×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#103	D₄₃
hypocenter	C₄₃	Q₈×#103
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
13. Q₈×Dic₈₆	C₄	semidirect
92. #103×C₄₃	Q₈	semidirect
162. Q₈×C₄₃	C₄×Q₈	semidirect
201. Dic₈₆	#103	direct (N × H)
277. C₄₃	Q₈×#103	semidirect
324. #103	Dic₈₆	direct (N × H)
399. Q₈	C₄×Dic₈₆	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×Dic₈₆	2
C₂×C₈×Dic₈₆	2
C₄⋊C₄×Dic₈₆	2
#19135556	2
#19135554	2
#19135543	2
#19135541	2
#19134600	2
#19134598	2
#103×Dic₄₃	2
C₄×#103×C₄₃	2
Q₈×#103	43

Subgroups — #103×Dic86 #25113202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #103×Dic₈₆ #25113202