Subgroups — #36524215

Order 22784.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029219	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19151676	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019166	C₂	1	2	yes	maximal, complemented
4	#26019155	C₂	1	2	yes	maximal, complemented
5	#26019143	C₂	1	2	yes	maximal, complemented
6	#26019137	C₂	1	2	yes	maximal, complemented
7	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018643	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018639	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×AGL(1,ℤ/8)×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#13083558	—	2	1	no	—
13	#19151729	C₂²	1	1	yes	characteristic, complemented
14	#19151729	C₂²	1	1	yes	characteristic, complemented
15	#19151676	—	2	1	no	—
16	#19151676	—	2	1	no	—
17	#19151676	C₂²	1	2	yes	—
18	#19151676	C₂²	1	2	yes	—
19	#19151676	C₂²	1	1	yes	characteristic, complemented
20	#19151676	C₂²	1	1	yes	characteristic, complemented
21	#19151670	—	2	1	no	—
22	#19151670	—	2	1	no	—
23	#19151651	—	2	1	no	—
24	#19151651	C₂²	1	1	yes	characteristic
25	#19151651	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#10623494	—	2	1	no	—
28	C₄×#13083558	—	2	1	no	—
29	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
30	#19151351	C₂²	1	2	yes	complemented
31	#19151349	C₂²	1	2	yes	complemented
32	Q₈⋊#10623494	C₂²	1	2	yes	complemented
33	D₄⋊#10623494	C₂²	1	2	yes	—
34	D₄⋊#10623494	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	complemented
36	#19151319	C₂²	1	2	yes	complemented
37	C₈×#10623494	C₂²	1	2	yes	complemented
38	C₂×AGL(1,ℤ/8)×C₈₉	C₄	1	1	yes	characteristic
39	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	#442×C₈₉	C₄	1	2	yes	—
42	#440×C₈₉	C₄	1	2	yes	—
43	C₄×SD₁₆×C₈₉	C₂²	1	2	yes	—
44	C₄×D₈×C₈₉	C₂²	1	2	yes	—
45	#428×C₈₉	C₄	1	1	yes	characteristic
46	#418×C₈₉	C₄	1	1	yes	characteristic
47	#417×C₈₉	C₄	1	1	yes	characteristic
48	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083558	—	2	2	no	—
52	C₂×#13083558	—	2	2	no	—
53	C₂×#13083558	—	4	4	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂²×#10623494	D₄	1	1	yes	characteristic
56	C₂²×#10623494	D₄	1	1	yes	characteristic
57	C₄⋊#10623494	—	2	1	no	—
58	C₄⋊#10623494	—	2	1	no	—
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	—	2	1	no	—
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₄⋊#10623494	C₂³	1	1	yes	characteristic
63	C₄⋊#10623494	C₂³	1	1	yes	characteristic
64	C₂²⋊#10623494	—	2	1	no	—
65	C₂²⋊#10623494	—	2	1	no	—
66	C₂²⋊#10623494	—	2	2	no	—
67	C₂²⋊#10623494	—	2	2	no	—
68	C₂²⋊#10623494	—	2	1	no	—
69	C₂²⋊#10623494	—	2	1	no	—
70	#15667923	—	2	1	no	—
71	#15667923	—	2	1	no	—
72	C₄×#10623494	—	2	1	no	—
73	C₄×#10623494	D₄	1	1	yes	characteristic
74	C₄×#10623494	D₄	1	1	yes	characteristic
75	C₄×#10623494	C₂³	1	2	yes	—
76	C₄×#10623494	C₂³	1	1	yes	characteristic
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
79	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	—	2	1	no	—
81	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
82	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	—
83	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	—	2	1	no	—
91	C₄×D₄×C₈₉	—	2	1	no	—
92	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄×D₄×C₈₉	C₂³	1	2	yes	—
95	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
96	#117×C₈₉	—	2	1	no	—
97	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	#107×C₈₉	C₂×C₄	1	2	yes	—
103	#106×C₈₉	C₂×C₄	1	2	yes	—
104	#103×C₈₉	C₂×C₄	1	2	yes	—
105	#102×C₈₉	C₂×C₄	1	2	yes	—
106	#102×C₈₉	C₂×C₄	1	2	yes	—
107	#102×C₈₉	C₂×C₄	1	2	yes	—
108	#97×C₈₉	C₂×C₄	1	2	yes	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	#13083558	—	4	2	no	—
111	#13083558	—	4	4	no	—
112	#13083558	—	4	2	no	—
113	#13083558	—	4	4	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₂×#10623494	—	4	1	no	—
120	C₂×#10623494	—	4	2	no	—
121	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂⁴×C₈₉	—	2	1	no	—
126	#41×C₈₉	—	2	2	no	—
127	#41×C₈₉	—	2	2	no	—
128	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×D₄×C₈₉	—	2	1	no	—
130	C₂×D₄×C₈₉	—	2	1	no	—
131	C₂×D₄×C₈₉	—	2	2	no	—
132	C₂×D₄×C₈₉	—	2	2	no	—
133	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₈₉	—	2	1	no	—
136	C₂²×C₄×C₈₉	—	2	1	no	—
137	C₂²×C₄×C₈₉	—	2	1	no	—
138	C₂²×C₄×C₈₉	—	2	2	no	—
139	C₂²×C₄×C₈₉	—	2	1	no	—
140	C₂²×C₄×C₈₉	—	2	2	no	—
141	C₂²×C₄×C₈₉	—	4	2	no	—
142	C₂²×C₄×C₈₉	—	4	2	no	—
143	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
146	SD₁₆×C₈₉	—	2	4	no	—
147	D₈×C₈₉	—	2	4	no	—
148	M₁₆×C₈₉	—	2	2	no	—
149	M₁₆×C₈₉	M₁₆	1	4	yes	complemented
150	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₂²⋊C₄×C₈₉	—	2	2	no	—
160	C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₄²×C₈₉	—	2	1	no	—
164	C₄²×C₈₉	—	2	1	no	—
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	#41	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	—	2	1	no	—
171	C₂³×C₈₉	—	2	2	no	—
172	C₂³×C₈₉	—	4	2	no	—
173	C₂³×C₈₉	—	4	2	no	—
174	C₂³×C₈₉	—	4	2	no	—
175	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
176	Q₈×C₈₉	—	2	1	no	—
177	Q₈×C₈₉	—	2	1	no	—
178	D₄×C₈₉	—	2	1	no	—
179	D₄×C₈₉	—	2	2	no	—
180	D₄×C₈₉	—	2	2	no	—
181	D₄×C₈₉	—	2	1	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	4	2	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	4	1	no	—
191	C₂×C₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	—	4	4	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	4	2	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
203	C₂×C₄×C₈₉	#131	1	2	yes	—
204	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
207	C₈×C₈₉	—	2	2	no	—
208	C₈×C₈₉	C₂×M₁₆	1	4	yes	complemented
209	#10623494	—	2	1	no	—
210	#10623494	—	2	1	no	—
211	#10623494	—	2	1	no	—
212	#10623494	—	4	2	no	—
213	#10623494	—	4	2	no	—
214	#10623494	—	4	1	no	—
215	#10623494	—	4	1	no	—
216	#10623494	AGL(1,ℤ/8)	1	2	yes	complemented
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	4	1	no	—
220	C₂²×C₈₉	—	4	2	no	—
221	C₂²×C₈₉	—	4	2	no	—
222	C₂²×C₈₉	—	4	1	no	—
223	C₂²×C₈₉	—	4	1	no	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	8	4	no	—
226	C₂²×C₈₉	#436	1	2	yes	—
227	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	4	1	no	—
232	C₄×C₈₉	—	4	1	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	4	1	no	—
235	C₄×C₈₉	#436	1	2	yes	—
236	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
237	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
238	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₈₉	#575	1	1	yes	characteristic
240	#17891	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	2	no	—
242	C₂×C₈₉	—	8	1	no	—
243	C₂×C₈₉	—	8	2	no	—
244	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
245	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₂×C₈₉	#2955	1	1	yes	characteristic
247	#2965	—	89	1	no	—
248	C₄×AGL(1,ℤ/8)	D₈₉	1	1	yes	characteristic
249	C₂×#436	—	89	1	no	—
250	#1594	—	89	2	no	—
251	#1592	—	89	2	no	—
252	#1590	—	89	2	no	—
253	#1589	—	89	2	no	—
254	#1565	—	89	1	no	—
255	#1478	—	89	1	no	—
256	#1477	—	89	1	no	—
257	C₈×M₁₆	—	89	1	no	—
258	C₈₉	#17891	1	1	yes	characteristic, complemented, Sylow
259	C₂×AGL(1,ℤ/8)	Dic₈₉	1	1	yes	characteristic
260	C₂²×M₁₆	—	178	1	no	—
261	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
262	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
263	#446	—	89	1	no	—
264	#446	—	89	1	no	—
265	#442	Dic₈₉	1	2	yes	—
266	#440	Dic₈₉	1	2	yes	—
267	C₄×SD₁₆	C₂×D₈₉	1	2	yes	—
268	C₄×D₈	C₂×D₈₉	1	2	yes	—
269	#436	—	89	1	no	—
270	#436	—	89	2	no	—
271	#436	—	89	2	no	—
272	#436	—	89	1	no	—
273	#436	—	178	1	no	—
274	#436	—	178	1	no	—
275	#435	—	178	1	no	—
276	#435	—	178	1	no	—
277	#431	—	89	1	no	—
278	#431	—	89	1	no	—
279	#431	—	178	1	no	—
280	#428	Dic₈₉	1	1	yes	characteristic
281	C₂×C₄⋊C₈	—	89	1	no	—
282	#418	Dic₈₉	1	1	yes	characteristic
283	#417	Dic₈₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	—	178	1	no	—
285	C₄×M₁₆	—	178	1	no	—
286	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
287	C₂×C₄×C₈	—	89	1	no	—
288	#335	—	89	2	no	—
289	#334	—	89	2	no	—
290	Q₈⋊C₈	—	89	2	no	—
291	D₄⋊C₈	—	89	2	no	—
292	D₄⋊C₈	—	89	2	no	—
293	D₄⋊C₈	—	89	2	no	—
294	#322	—	89	2	no	—
295	C₈²	—	89	2	no	—
296	C₂×#41	C₂×Dic₈₉	1	1	yes	characteristic
297	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
298	C₂³×C₄	—	2	1	no	—
299	AGL(1,ℤ/8)	—	2	4	no	—
300	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	—
301	C₂×D₈	C₂×Dic₈₉	1	2	yes	—
302	C₂×M₁₆	—	356	4	no	—
303	C₂×M₁₆	—	178	2	no	—
304	C₂×M₁₆	—	178	2	no	—
305	C₂×M₁₆	—	178	1	no	—
306	C₂×M₁₆	—	178	1	no	—
307	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
308	C₂×M₁₆	C₂×Dic₈₉	1	1	yes	characteristic
309	C₂²×C₈	—	89	1	no	—
310	C₂²×C₈	—	89	1	no	—
311	C₂²×C₈	—	178	1	no	—
312	C₄×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
319	C₄×D₄	C₂×Dic₈₉	1	1	yes	characteristic
320	C₄×D₄	C₂²×D₈₉	1	2	yes	—
321	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₂×Dic₈₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	#107	C₂×Dic₈₉	1	2	yes	—
329	#106	C₂×Dic₈₉	1	2	yes	—
330	C₄⋊C₈	—	89	1	no	—
331	C₄⋊C₈	—	89	1	no	—
332	C₄⋊C₈	—	89	2	no	—
333	C₄⋊C₈	—	178	1	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	—	178	1	no	—
337	#103	C₂×Dic₈₉	1	2	yes	—
338	#102	C₂×Dic₈₉	1	2	yes	—
339	#102	C₂×Dic₈₉	1	2	yes	—
340	#102	C₂×Dic₈₉	1	2	yes	—
341	C₂²⋊C₈	—	178	2	no	—
342	C₂²⋊C₈	—	178	2	no	—
343	C₂²⋊C₈	—	178	1	no	—
344	C₂²⋊C₈	—	178	1	no	—
345	C₂²⋊C₈	—	178	1	no	—
346	C₂²⋊C₈	—	178	1	no	—
347	#97	—	178	1	no	—
348	#97	—	178	1	no	—
349	#97	C₂×Dic₈₉	1	2	yes	—
350	C₄×C₈	—	89	1	no	—
351	C₄×C₈	—	89	1	no	—
352	C₄×C₈	—	89	1	no	—
353	C₄×C₈	—	89	1	no	—
354	C₄×C₈	—	89	2	no	—
355	C₄×C₈	—	178	1	no	—
356	C₄×C₈	C₂²×D₈₉	1	2	yes	—
357	C₂⁴	—	2	1	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
366	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
377	C₂²×C₄	#13083573	1	1	yes	characteristic
378	SD₁₆	—	2	4	no	—
379	D₈	—	2	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	356	4	no	—
382	M₁₆	—	356	2	no	—
383	M₁₆	—	356	4	no	—
384	M₁₆	—	356	2	no	—
385	M₁₆	#13083558	1	4	yes	complemented
386	C₂×C₈	—	89	1	no	—
387	C₂×C₈	—	89	1	no	—
388	C₂×C₈	—	89	1	no	—
389	C₂×C₈	—	89	1	no	—
390	C₂×C₈	—	356	2	no	—
391	C₂×C₈	—	356	1	no	—
392	C₂×C₈	—	178	2	no	—
393	C₂×C₈	—	178	1	no	—
394	C₂×C₈	—	178	1	no	—
395	C₂×C₈	—	178	2	no	—
396	C₂×C₈	—	178	2	no	—
397	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
398	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
403	C₄⋊C₄	C₂²×Dic₈₉	1	1	yes	characteristic
404	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	2	2	no	—
409	C₂²⋊C₄	—	2	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
414	C₄²	D₄×D₈₉	1	1	yes	characteristic
415	C₄²	#13083573	1	1	yes	characteristic
416	C₄²	C₂³×D₈₉	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	4	2	no	—
420	C₂³	—	4	2	no	—
421	C₂³	—	4	2	no	—
422	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	2	1	no	—
429	D₄	—	4	2	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
447	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
448	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
449	C₂×C₄	C₂×#13083558	1	2	yes	—
450	C₂×C₄	#15668019	1	2	yes	—
451	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	89	2	no	—
456	C₈	—	356	2	no	—
457	C₈	—	356	1	no	—
458	C₈	—	356	2	no	—
459	C₈	—	356	1	no	—
460	C₈	—	178	1	no	—
461	C₈	—	178	1	no	—
462	C₈	—	178	1	no	—
463	C₈	C₂×#13083558	1	4	yes	complemented
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	1	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	8	4	no	—
473	C₂²	#19151676	1	2	yes	—
474	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	1	no	—
482	C₄	#19151676	1	2	yes	—
483	C₄	C₂²×#13083558	1	1	yes	characteristic
484	C₄	C₂×#15668019	1	1	yes	characteristic
485	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
486	C₄	#19152394	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	8	2	no	—
490	C₂	C₂×#19151676	1	1	yes	characteristic
491	C₂	AGL(1,ℤ/8)×Dic₈₉	1	1	yes	characteristic
492	C₂	#26029155	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₄×AGL(1,ℤ/8)×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×AGL(1,ℤ/8)×C₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₄×AGL(1,ℤ/8)	D₈₉
hypocenter	C₈₉	#17891
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #26029219	C₂	semidirect
2. C₂×#19151676	C₂	semidirect
3. #26019166	C₂	semidirect
4. #26019155	C₂	semidirect
5. #26019143	C₂	semidirect
6. #26019137	C₂	semidirect
7. #26019004	C₂	semidirect
8. #26018643	C₂	semidirect
9. #26018639	C₂	semidirect
10. M₁₆×#10623494	C₂	semidirect
13. #19151729	C₂²	semidirect
14. #19151729	C₂²	semidirect
19. #19151676	C₂²	semidirect
20. #19151676	C₂²	semidirect
30. #19151351	C₂²	semidirect
31. #19151349	C₂²	semidirect
32. Q₈⋊#10623494	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151319	C₂²	semidirect
37. C₈×#10623494	C₂²	semidirect
149. M₁₆×C₈₉	M₁₆	semidirect
208. C₈×C₈₉	C₂×M₁₆	semidirect
216. #10623494	AGL(1,ℤ/8)	semidirect
258. C₈₉	#17891	semidirect
385. M₁₆	#13083558	semidirect
463. C₈	C₂×#13083558	semidirect

Maximal subgroups

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

subgroup	index
#26029219	2
C₂×#19151676	2
#26019166	2
#26019155	2
#26019143	2
#26019137	2
#26019004	2
#26018643	2
#26018639	2
M₁₆×#10623494	2
C₄×AGL(1,ℤ/8)×C₈₉	2
#17891	89