Subgroups — C₈₉×#19171 #36397019

Order 22784.

682 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3152	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3103	C₂	1	1	yes	maximal, characteristic
3	C₂×#475×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1690	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1670	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1666	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1547	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₈₉	—	2	1	no	—
13	C₂×#137×C₈₉	—	2	1	no	—
14	#532×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	#497×C₈₉	—	2	2	no	—
18	#494×C₈₉	C₂²	1	2	yes	—
19	#492×C₈₉	C₂²	1	2	yes	—
20	#481×C₈₉	—	2	1	no	—
21	#475×C₈₉	—	2	1	no	—
22	#475×C₈₉	—	2	1	no	—
23	#475×C₈₉	C₂²	1	2	yes	—
24	#475×C₈₉	C₂²	1	2	yes	—
25	#475×C₈₉	C₂²	1	1	yes	characteristic
26	#475×C₈₉	C₂²	1	1	yes	characteristic
27	#460×C₈₉	C₂²	1	1	yes	characteristic
28	#460×C₈₉	C₂²	1	1	yes	characteristic
29	#448×C₈₉	—	2	1	no	—
30	#446×C₈₉	—	2	2	no	—
31	#446×C₈₉	C₂²	1	2	yes	—
32	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₄×SD₁₆×C₈₉	—	2	1	no	—
34	C₄×SD₁₆×C₈₉	—	2	1	no	—
35	#431×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#106×C₈₉	—	2	1	no	—
37	#423×C₈₉	—	2	1	no	—
38	#423×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#103×C₈₉	—	2	1	no	—
41	C₄×M₁₆×C₈₉	—	2	1	no	—
42	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
43	#335×C₈₉	C₂²	1	2	yes	—
44	#334×C₈₉	C₂²	1	2	yes	—
45	#332×C₈₉	C₂²	1	2	yes	—
46	#332×C₈₉	C₂²	1	2	yes	—
47	#332×C₈₉	C₂²	1	2	yes	—
48	#331×C₈₉	C₂²	1	2	yes	—
49	C₂×#41×C₈₉	—	2	1	no	—
50	C₂²×Q₈×C₈₉	—	2	1	no	—
51	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
52	#137×C₈₉	—	4	4	no	—
53	#137×C₈₉	—	4	4	no	—
54	C₂×Q₁₆×C₈₉	—	2	2	no	—
55	C₂×Q₁₆×C₈₉	—	2	2	no	—
56	C₂×SD₁₆×C₈₉	—	2	1	no	—
57	C₂×SD₁₆×C₈₉	—	2	1	no	—
58	C₂×SD₁₆×C₈₉	—	2	2	no	—
59	C₂×SD₁₆×C₈₉	—	2	2	no	—
60	C₂×M₁₆×C₈₉	—	2	1	no	—
61	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
62	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	—	2	1	no	—
64	C₄⋊Q₈×C₈₉	—	2	1	no	—
65	C₄⋊Q₈×C₈₉	—	2	1	no	—
66	C₄⋊Q₈×C₈₉	—	2	1	no	—
67	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
69	#127×C₈₉	C₂³	1	1	yes	characteristic
70	#124×C₈₉	—	2	1	no	—
71	#121×C₈₉	—	2	1	no	—
72	#121×C₈₉	—	2	1	no	—
73	C₄×Q₈×C₈₉	—	2	1	no	—
74	C₄×Q₈×C₈₉	—	2	1	no	—
75	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
76	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
77	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₈₉	—	2	1	no	—
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
84	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	—	2	1	no	—
86	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
87	#106×C₈₉	—	2	2	no	—
88	#106×C₈₉	—	2	2	no	—
89	#106×C₈₉	—	2	1	no	—
90	#106×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	—	2	2	no	—
92	C₄⋊C₈×C₈₉	—	2	2	no	—
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₄⋊C₈×C₈₉	—	2	1	no	—
95	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	#103×C₈₉	—	2	2	no	—
100	#103×C₈₉	—	2	2	no	—
101	#103×C₈₉	—	2	1	no	—
102	#103×C₈₉	—	2	1	no	—
103	#102×C₈₉	—	2	1	no	—
104	#102×C₈₉	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	2	no	—
107	#97×C₈₉	D₄	1	2	yes	—
108	C₄×C₈×C₈₉	—	2	2	no	—
109	C₄×C₈×C₈₉	—	2	1	no	—
110	C₄×C₈×C₈₉	C₂³	1	2	yes	—
111	#41×C₈₉	—	4	2	no	—
112	#41×C₈₉	—	4	2	no	—
113	C₂×Q₈×C₈₉	—	2	1	no	—
114	C₂×Q₈×C₈₉	—	2	2	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	—	2	2	no	—
117	C₂×Q₈×C₈₉	—	4	1	no	—
118	C₂×Q₈×C₈₉	—	4	1	no	—
119	C₂×Q₈×C₈₉	—	4	2	no	—
120	C₂×Q₈×C₈₉	—	4	2	no	—
121	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×D₄×C₈₉	—	2	1	no	—
124	C₂×D₄×C₈₉	—	2	1	no	—
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	—	4	1	no	—
127	C₂²×C₄×C₈₉	—	2	1	no	—
128	C₂²×C₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	4	1	no	—
130	C₂²×C₄×C₈₉	—	4	1	no	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	Q₁₆×C₈₉	—	4	4	no	—
135	Q₁₆×C₈₉	—	4	4	no	—
136	SD₁₆×C₈₉	—	4	4	no	—
137	SD₁₆×C₈₉	—	4	2	no	—
138	SD₁₆×C₈₉	—	4	2	no	—
139	SD₁₆×C₈₉	—	4	4	no	—
140	M₁₆×C₈₉	—	2	2	no	—
141	M₁₆×C₈₉	—	4	2	no	—
142	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	4	2	no	—
148	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
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	—	2	2	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	2	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	4	1	no	—
160	C₄⋊C₄×C₈₉	—	4	1	no	—
161	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₈₉	—	4	1	no	—
164	C₂²⋊C₄×C₈₉	—	4	1	no	—
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	—	2	1	no	—
167	C₄²×C₈₉	—	2	1	no	—
168	C₄²×C₈₉	—	2	1	no	—
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₈₉	#41	1	1	yes	characteristic
172	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂³×C₈₉	—	4	1	no	—
174	C₂³×C₈₉	#121	1	1	yes	characteristic
175	Q₈×C₈₉	—	2	1	no	—
176	Q₈×C₈₉	—	2	1	no	—
177	Q₈×C₈₉	—	2	1	no	—
178	Q₈×C₈₉	—	4	2	no	—
179	Q₈×C₈₉	—	4	2	no	—
180	Q₈×C₈₉	—	4	1	no	—
181	Q₈×C₈₉	—	4	2	no	—
182	Q₈×C₈₉	—	4	1	no	—
183	Q₈×C₈₉	—	8	2	no	—
184	Q₈×C₈₉	#137	1	2	yes	complemented
185	D₄×C₈₉	—	4	1	no	—
186	D₄×C₈₉	—	4	1	no	—
187	D₄×C₈₉	—	4	1	no	—
188	D₄×C₈₉	—	4	1	no	—
189	D₄×C₈₉	—	8	1	no	—
190	D₄×C₈₉	—	8	2	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	2	1	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	2	no	—
199	C₂×C₄×C₈₉	—	4	1	no	—
200	C₂×C₄×C₈₉	—	4	2	no	—
201	C₂×C₄×C₈₉	—	8	1	no	—
202	C₂×C₄×C₈₉	—	8	2	no	—
203	C₂×C₄×C₈₉	—	8	2	no	—
204	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
205	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
206	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
208	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
212	C₈×C₈₉	—	2	2	no	—
213	C₈×C₈₉	—	4	2	no	—
214	C₈×C₈₉	—	4	1	no	—
215	C₈×C₈₉	—	4	2	no	—
216	C₈×C₈₉	—	4	1	no	—
217	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	8	1	no	—
221	C₂²×C₈₉	—	8	1	no	—
222	C₂²×C₈₉	—	8	1	no	—
223	C₂²×C₈₉	#460	1	2	yes	—
224	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	2	2	no	—
227	C₄×C₈₉	—	2	1	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	4	1	no	—
230	C₄×C₈₉	—	4	1	no	—
231	C₄×C₈₉	—	4	1	no	—
232	C₄×C₈₉	—	8	1	no	—
233	C₄×C₈₉	—	8	2	no	—
234	C₄×C₈₉	#460	1	2	yes	—
235	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
236	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
238	C₄×C₈₉	#575	1	1	yes	characteristic
239	#19171	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
240	C₂×C₈₉	—	2	2	no	—
241	C₂×C₈₉	—	16	1	no	—
242	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
243	C₂×C₈₉	#3056	1	1	yes	characteristic
244	C₂×C₈₉	#3069	1	1	yes	characteristic
245	#3152	C₂×C₈₉	1	1	yes	characteristic
246	#3103	C₂×C₈₉	1	1	yes	characteristic
247	C₂×#475	C₂×C₈₉	1	1	yes	characteristic, complemented
248	Q₈×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#1690	C₂×C₈₉	1	2	yes	complemented
250	#1686	C₂×C₈₉	1	2	yes	complemented
251	#1670	C₂×C₈₉	1	2	yes	complemented
252	#1666	C₂×C₈₉	1	2	yes	complemented
253	#1565	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#1547	C₂×C₈₉	1	1	yes	characteristic
255	#1546	C₂×C₈₉	1	1	yes	characteristic, complemented
256	C₈₉	#19171	1	1	yes	characteristic, direct product factor, Sylow
257	C₂×#137	—	2	1	no	—
258	C₂×#137	—	2	1	no	—
259	#532	C₂²×C₈₉	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
261	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
262	#497	—	2	2	no	—
263	#494	C₂²×C₈₉	1	2	yes	—
264	#492	C₂²×C₈₉	1	2	yes	—
265	#481	—	2	1	no	—
266	#475	—	2	1	no	—
267	#475	—	2	1	no	—
268	#475	C₂²×C₈₉	1	2	yes	—
269	#475	C₂²×C₈₉	1	2	yes	—
270	#475	C₂²×C₈₉	1	1	yes	characteristic
271	#475	C₂²×C₈₉	1	1	yes	characteristic
272	#460	C₂²×C₈₉	1	1	yes	characteristic
273	#460	C₂²×C₈₉	1	1	yes	characteristic
274	#448	—	2	1	no	—
275	#446	—	2	2	no	—
276	#446	C₂²×C₈₉	1	2	yes	—
277	C₈×Q₈	C₂²×C₈₉	1	2	yes	—
278	C₄×SD₁₆	—	2	1	no	—
279	C₄×SD₁₆	—	2	1	no	—
280	#431	C₂²×C₈₉	1	1	yes	characteristic
281	C₂×#106	—	2	1	no	—
282	#423	—	2	1	no	—
283	#423	C₂²×C₈₉	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
285	C₂×#103	—	2	1	no	—
286	C₄×M₁₆	—	2	1	no	—
287	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
288	#335	C₂²×C₈₉	1	2	yes	—
289	#334	C₂²×C₈₉	1	2	yes	—
290	#332	C₂²×C₈₉	1	2	yes	—
291	#332	C₂²×C₈₉	1	2	yes	—
292	#332	C₂²×C₈₉	1	2	yes	—
293	#331	C₂²×C₈₉	1	2	yes	—
294	C₂×#41	—	2	1	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
297	#137	—	4	4	no	—
298	#137	—	4	4	no	—
299	C₂×Q₁₆	—	2	2	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×SD₁₆	—	2	1	no	—
302	C₂×SD₁₆	—	2	1	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
307	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
308	C₂²×C₈	—	2	1	no	—
309	C₄⋊Q₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	1	no	—
311	C₄⋊Q₈	—	2	1	no	—
312	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
313	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
314	#127	C₂³×C₈₉	1	1	yes	characteristic
315	#124	—	2	1	no	—
316	#121	—	2	1	no	—
317	#121	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
321	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
322	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
323	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
332	#106	—	2	2	no	—
333	#106	—	2	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	C₄⋊C₈	—	2	2	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
341	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
342	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
343	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
344	#103	—	2	2	no	—
345	#103	—	2	2	no	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#102	—	2	1	no	—
349	#102	—	2	1	no	—
350	C₂²⋊C₈	—	2	1	no	—
351	#97	—	2	2	no	—
352	#97	D₄×C₈₉	1	2	yes	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	C₂³×C₈₉	1	2	yes	—
356	#41	—	4	2	no	—
357	#41	—	4	2	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	4	1	no	—
363	C₂×Q₈	—	4	1	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	—	4	2	no	—
366	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
367	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	4	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	4	1	no	—
376	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
378	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
379	Q₁₆	—	4	4	no	—
380	Q₁₆	—	4	4	no	—
381	SD₁₆	—	4	4	no	—
382	SD₁₆	—	4	2	no	—
383	SD₁₆	—	4	2	no	—
384	SD₁₆	—	4	4	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	4	2	no	—
387	M₁₆	SD₁₆×C₈₉	1	4	yes	complemented
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
394	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
407	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
408	C₂²⋊C₄	—	4	1	no	—
409	C₂²⋊C₄	—	4	1	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
415	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
416	C₄²	#41×C₈₉	1	1	yes	characteristic
417	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
418	C₂³	—	4	1	no	—
419	C₂³	#121×C₈₉	1	1	yes	characteristic
420	Q₈	—	2	1	no	—
421	Q₈	—	2	1	no	—
422	Q₈	—	2	1	no	—
423	Q₈	—	4	2	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	1	no	—
426	Q₈	—	4	2	no	—
427	Q₈	—	4	1	no	—
428	Q₈	—	8	2	no	—
429	Q₈	#137×C₈₉	1	2	yes	complemented
430	D₄	—	4	1	no	—
431	D₄	—	4	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	8	1	no	—
435	D₄	—	8	2	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	8	2	no	—
449	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
450	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
451	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
453	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
454	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₈	—	4	2	no	—
461	C₈	—	4	1	no	—
462	C₈	C₂×SD₁₆×C₈₉	1	4	yes	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	8	1	no	—
466	C₂²	—	8	1	no	—
467	C₂²	—	8	1	no	—
468	C₂²	#460×C₈₉	1	2	yes	—
469	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
470	C₄	—	2	1	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	1	no	—
473	C₄	—	2	2	no	—
474	C₄	—	4	1	no	—
475	C₄	—	4	1	no	—
476	C₄	—	4	1	no	—
477	C₄	—	8	1	no	—
478	C₄	—	8	2	no	—
479	C₄	#460×C₈₉	1	2	yes	—
480	C₄	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
481	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
482	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
483	C₄	#575×C₈₉	1	1	yes	characteristic
484	C₂	—	2	2	no	—
485	C₂	—	16	1	no	—
486	C₂	C₂×#460×C₈₉	1	1	yes	characteristic
487	C₂	C₈₉×#3056	1	1	yes	characteristic
488	C₂	C₈₉×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	#532×C₈₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#475×C₈₉	C₂	semidirect
4. Q₈×M₁₆×C₈₉	C₂	semidirect
5. C₈₉×#1690	C₂	semidirect
6. C₈₉×#1686	C₂	semidirect
7. C₈₉×#1670	C₂	semidirect
8. C₈₉×#1666	C₂	semidirect
9. C₈₉×#1565	C₂	semidirect
11. C₈₉×#1546	C₂	semidirect
142. M₁₆×C₈₉	SD₁₆	semidirect
184. Q₈×C₈₉	#137	semidirect
239. #19171	C₈₉	direct (N × H)
247. C₂×#475	C₂×C₈₉	semidirect
248. Q₈×M₁₆	C₂×C₈₉	semidirect
249. #1690	C₂×C₈₉	semidirect
250. #1686	C₂×C₈₉	semidirect
251. #1670	C₂×C₈₉	semidirect
252. #1666	C₂×C₈₉	semidirect
253. #1565	C₂×C₈₉	semidirect
255. #1546	C₂×C₈₉	semidirect
256. C₈₉	#19171	direct (N × H)
387. M₁₆	SD₁₆×C₈₉	semidirect
429. Q₈	#137×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3152	2
C₈₉×#3103	2
C₂×#475×C₈₉	2
Q₈×M₁₆×C₈₉	2
C₈₉×#1690	2
C₈₉×#1686	2
C₈₉×#1670	2
C₈₉×#1666	2
C₈₉×#1565	2
C₈₉×#1547	2
C₈₉×#1546	2
#19171	89

Subgroups — C89×#19171 #36397019

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19171 #36397019