Subgroups — C₈₉×#19238 #36397086

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3151	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1688	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1686	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1668	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×#1540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#331×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
13	C₂×AGL(1,ℤ/8)×C₈₉	—	2	1	no	—
14	#533×C₈₉	C₂²	1	1	yes	characteristic
15	#532×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
17	#496×C₈₉	—	2	2	no	—
18	#493×C₈₉	C₂²	1	2	yes	—
19	#492×C₈₉	—	2	1	no	—
20	#492×C₈₉	C₂²	1	2	yes	—
21	#486×C₈₉	—	2	1	no	—
22	#476×C₈₉	—	2	1	no	—
23	#475×C₈₉	C₂²	1	2	yes	complemented
24	#465×C₈₉	—	2	2	no	—
25	#461×C₈₉	—	2	1	no	—
26	#460×C₈₉	C₂²	1	2	yes	—
27	#460×C₈₉	C₂²	1	2	yes	—
28	#460×C₈₉	C₂²	1	2	yes	complemented
29	#450×C₈₉	—	2	2	no	—
30	#446×C₈₉	—	2	2	no	—
31	#446×C₈₉	C₂²	1	2	yes	complemented
32	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
33	#431×C₈₉	C₂²	1	1	yes	characteristic
34	#424×C₈₉	—	2	1	no	—
35	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	#405×C₈₉	—	2	1	no	—
38	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	#335×C₈₉	C₂²	1	2	yes	complemented
40	#334×C₈₉	C₂²	1	2	yes	complemented
41	#332×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#332×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#331×C₈₉	C₂²	1	2	yes	—
44	#331×C₈₉	C₂²	1	2	yes	—
45	#331×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#331×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×#41×C₈₉	—	2	1	no	—
48	C₂²×D₄×C₈₉	—	2	1	no	—
49	C₂²×D₄×C₈₉	—	2	1	no	—
50	C₂²×D₄×C₈₉	—	2	1	no	—
51	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
52	AGL(1,ℤ/8)×C₈₉	—	4	4	no	—
53	C₂×SD₁₆×C₈₉	—	2	2	no	—
54	C₂×SD₁₆×C₈₉	—	2	2	no	—
55	C₂×SD₁₆×C₈₉	—	2	2	no	—
56	C₂×SD₁₆×C₈₉	—	2	2	no	—
57	C₂×SD₁₆×C₈₉	—	2	2	no	—
58	C₂×D₈×C₈₉	—	2	2	no	—
59	C₂×D₈×C₈₉	—	2	2	no	—
60	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
61	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₈₉	—	2	1	no	—
63	C₂²×C₈×C₈₉	—	2	1	no	—
64	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
67	#127×C₈₉	—	2	1	no	—
68	#127×C₈₉	—	2	1	no	—
69	#127×C₈₉	—	2	1	no	—
70	#127×C₈₉	C₂³	1	2	yes	—
71	#127×C₈₉	C₂³	1	1	yes	characteristic
72	#125×C₈₉	—	2	1	no	—
73	#124×C₈₉	—	2	1	no	—
74	C₂²⋊Q₈×C₈₉	—	2	1	no	—
75	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
76	#121×C₈₉	—	2	1	no	—
77	#121×C₈₉	—	2	1	no	—
78	C₄×Q₈×C₈₉	—	2	1	no	—
79	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
80	C₄×D₄×C₈₉	—	2	1	no	—
81	C₄×D₄×C₈₉	—	2	1	no	—
82	#117×C₈₉	—	2	1	no	—
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	#106×C₈₉	—	2	2	no	—
85	C₄⋊C₈×C₈₉	—	2	2	no	—
86	C₄⋊C₈×C₈₉	—	2	2	no	—
87	C₄⋊C₈×C₈₉	—	2	1	no	—
88	C₄⋊C₈×C₈₉	—	2	1	no	—
89	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	#103×C₈₉	—	2	2	no	—
95	#102×C₈₉	—	2	2	no	—
96	#102×C₈₉	—	2	2	no	—
97	#102×C₈₉	—	2	2	no	—
98	C₂²⋊C₈×C₈₉	—	2	1	no	—
99	#97×C₈₉	—	2	2	no	—
100	#97×C₈₉	D₄	1	2	yes	—
101	C₄×C₈×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	C₂³	1	2	yes	—
104	C₂⁴×C₈₉	—	4	1	no	—
105	#41×C₈₉	—	4	2	no	—
106	#41×C₈₉	—	4	2	no	—
107	C₂×Q₈×C₈₉	—	2	1	no	—
108	C₂×Q₈×C₈₉	—	2	1	no	—
109	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₈₉	—	2	1	no	—
111	C₂×D₄×C₈₉	—	2	2	no	—
112	C₂×D₄×C₈₉	—	2	1	no	—
113	C₂×D₄×C₈₉	—	2	2	no	—
114	C₂×D₄×C₈₉	—	2	1	no	—
115	C₂×D₄×C₈₉	—	2	2	no	—
116	C₂×D₄×C₈₉	—	4	1	no	—
117	C₂×D₄×C₈₉	—	4	1	no	—
118	C₂×D₄×C₈₉	—	4	1	no	—
119	C₂×D₄×C₈₉	—	4	1	no	—
120	C₂×D₄×C₈₉	—	4	2	no	—
121	C₂×D₄×C₈₉	—	4	2	no	—
122	C₂×D₄×C₈₉	—	8	1	no	—
123	C₂×D₄×C₈₉	—	8	1	no	—
124	C₂×D₄×C₈₉	—	8	2	no	—
125	C₂²×C₄×C₈₉	—	4	1	no	—
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
129	SD₁₆×C₈₉	—	4	4	no	—
130	SD₁₆×C₈₉	—	4	4	no	—
131	SD₁₆×C₈₉	—	8	2	no	—
132	SD₁₆×C₈₉	—	8	2	no	—
133	SD₁₆×C₈₉	—	8	2	no	—
134	D₈×C₈₉	—	4	4	no	—
135	D₈×C₈₉	—	4	4	no	—
136	M₁₆×C₈₉	—	2	2	no	—
137	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	—	8	1	no	—
145	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₈₉	—	2	2	no	—
156	C₂²⋊C₄×C₈₉	—	4	1	no	—
157	C₂²⋊C₄×C₈₉	—	4	1	no	—
158	C₄²×C₈₉	—	2	2	no	—
159	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	#41	1	1	yes	characteristic
162	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂³×C₈₉	—	4	1	no	—
164	C₂³×C₈₉	—	4	2	no	—
165	C₂³×C₈₉	—	8	2	no	—
166	C₂³×C₈₉	—	8	2	no	—
167	C₂³×C₈₉	—	8	2	no	—
168	C₂³×C₈₉	#121	1	1	yes	characteristic
169	Q₈×C₈₉	—	2	2	no	—
170	Q₈×C₈₉	—	2	2	no	—
171	Q₈×C₈₉	—	4	1	no	—
172	Q₈×C₈₉	—	4	1	no	—
173	Q₈×C₈₉	—	8	1	no	—
174	D₄×C₈₉	—	4	1	no	—
175	D₄×C₈₉	—	4	2	no	—
176	D₄×C₈₉	—	4	1	no	—
177	D₄×C₈₉	—	4	2	no	—
178	D₄×C₈₉	—	4	1	no	—
179	D₄×C₈₉	—	4	2	no	—
180	D₄×C₈₉	—	4	2	no	—
181	D₄×C₈₉	—	4	1	no	—
182	D₄×C₈₉	—	8	1	no	—
183	D₄×C₈₉	—	8	2	no	—
184	D₄×C₈₉	—	8	2	no	—
185	D₄×C₈₉	—	8	2	no	—
186	D₄×C₈₉	—	8	2	no	—
187	D₄×C₈₉	—	8	2	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	8	2	no	—
195	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
199	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₈×C₈₉	—	2	2	no	—
204	C₈×C₈₉	—	4	1	no	—
205	C₈×C₈₉	—	4	1	no	—
206	C₈×C₈₉	—	4	2	no	—
207	C₈×C₈₉	—	4	1	no	—
208	C₈×C₈₉	—	4	1	no	—
209	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	—	8	1	no	—
213	C₂²×C₈₉	—	8	2	no	—
214	C₂²×C₈₉	—	8	2	no	—
215	C₂²×C₈₉	—	8	1	no	—
216	C₂²×C₈₉	—	8	2	no	—
217	C₂²×C₈₉	—	8	1	no	—
218	C₂²×C₈₉	—	16	4	no	—
219	C₂²×C₈₉	#460	1	2	yes	—
220	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	—	4	2	no	—
226	C₄×C₈₉	—	8	1	no	—
227	C₄×C₈₉	#460	1	2	yes	—
228	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
229	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₄×C₈₉	#576	1	1	yes	characteristic
231	C₄×C₈₉	#577	1	1	yes	characteristic
232	#19238	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂×C₈₉	—	2	2	no	—
234	C₂×C₈₉	—	16	1	no	—
235	C₂×C₈₉	—	16	2	no	—
236	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
237	C₂×C₈₉	#3062	1	1	yes	characteristic
238	C₂×C₈₉	#3068	1	1	yes	characteristic
239	#3246	C₂×C₈₉	1	1	yes	characteristic, complemented
240	#3208	C₂×C₈₉	1	1	yes	characteristic, complemented
241	#3151	C₂×C₈₉	1	1	yes	characteristic
242	#2962	C₂×C₈₉	1	1	yes	characteristic, complemented
243	#1688	C₂×C₈₉	1	2	yes	complemented
244	#1686	C₂×C₈₉	1	2	yes	complemented
245	#1668	C₂×C₈₉	1	2	yes	complemented
246	#1666	C₂×C₈₉	1	2	yes	complemented
247	#1565	C₂×C₈₉	1	1	yes	characteristic, complemented
248	#1540	C₂×C₈₉	1	1	yes	characteristic, complemented
249	C₂×#331	C₂×C₈₉	1	1	yes	characteristic, complemented
250	C₈₉	#19238	1	1	yes	characteristic, direct product factor, Sylow
251	C₂×AGL(1,ℤ/8)	—	2	1	no	—
252	C₂×AGL(1,ℤ/8)	—	2	1	no	—
253	#533	C₂²×C₈₉	1	1	yes	characteristic
254	#532	C₂²×C₈₉	1	1	yes	characteristic
255	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
256	#496	—	2	2	no	—
257	#493	C₂²×C₈₉	1	2	yes	—
258	#492	—	2	1	no	—
259	#492	C₂²×C₈₉	1	2	yes	—
260	#486	—	2	1	no	—
261	#476	—	2	1	no	—
262	#475	C₂²×C₈₉	1	2	yes	complemented
263	#465	—	2	2	no	—
264	#461	—	2	1	no	—
265	#460	C₂²×C₈₉	1	2	yes	—
266	#460	C₂²×C₈₉	1	2	yes	—
267	#460	C₂²×C₈₉	1	2	yes	complemented
268	#450	—	2	2	no	—
269	#446	—	2	2	no	—
270	#446	C₂²×C₈₉	1	2	yes	complemented
271	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
272	#431	C₂²×C₈₉	1	1	yes	characteristic
273	#424	—	2	1	no	—
274	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
275	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
276	#405	—	2	1	no	—
277	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
278	#335	C₂²×C₈₉	1	2	yes	complemented
279	#334	C₂²×C₈₉	1	2	yes	complemented
280	#332	C₂²×C₈₉	1	1	yes	characteristic, complemented
281	#332	C₂²×C₈₉	1	1	yes	characteristic, complemented
282	#331	C₂²×C₈₉	1	2	yes	—
283	#331	C₂²×C₈₉	1	2	yes	—
284	#331	C₂²×C₈₉	1	1	yes	characteristic, complemented
285	#331	C₂²×C₈₉	1	1	yes	characteristic, complemented
286	C₂×#41	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	AGL(1,ℤ/8)	—	4	4	no	—
291	AGL(1,ℤ/8)	—	4	4	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
300	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
304	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
305	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	C₂³×C₈₉	1	2	yes	—
310	#127	C₂³×C₈₉	1	1	yes	characteristic
311	#125	—	2	1	no	—
312	#124	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	—	2	1	no	—
322	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
323	#106	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
331	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
333	#103	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	#97	—	2	2	no	—
339	#97	D₄×C₈₉	1	2	yes	—
340	C₄×C₈	—	2	2	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	C₂³×C₈₉	1	2	yes	—
343	C₂⁴	—	4	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	8	1	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
367	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
368	SD₁₆	—	4	4	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	8	2	no	—
371	SD₁₆	—	8	2	no	—
372	SD₁₆	—	8	2	no	—
373	D₈	—	4	4	no	—
374	D₈	—	4	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	SD₁₆×C₈₉	1	4	yes	complemented
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	—	8	1	no	—
384	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
385	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
400	C₄²	#41×C₈₉	1	1	yes	characteristic
401	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	#121×C₈₉	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	1	no	—
412	Q₈	—	8	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	1	no	—
421	D₄	—	8	1	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
435	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
436	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
437	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
438	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	C₂×SD₁₆×C₈₉	1	4	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	2	no	—
457	C₂²	—	16	4	no	—
458	C₂²	#460×C₈₉	1	2	yes	—
459	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	#460×C₈₉	1	2	yes	—
467	C₄	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
468	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
469	C₄	#576×C₈₉	1	1	yes	characteristic
470	C₄	#577×C₈₉	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	16	1	no	—
473	C₂	—	16	2	no	—
474	C₂	C₂×#460×C₈₉	1	1	yes	characteristic
475	C₂	C₈₉×#3062	1	1	yes	characteristic
476	C₂	C₈₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3151	C₂
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
1. C₈₉×#3246	C₂	semidirect
2. C₈₉×#3208	C₂	semidirect
4. C₈₉×#2962	C₂	semidirect
5. C₈₉×#1688	C₂	semidirect
6. C₈₉×#1686	C₂	semidirect
7. C₈₉×#1668	C₂	semidirect
8. C₈₉×#1666	C₂	semidirect
9. C₈₉×#1565	C₂	semidirect
10. C₈₉×#1540	C₂	semidirect
11. C₂×#331×C₈₉	C₂	semidirect
23. #475×C₈₉	C₂²	semidirect
28. #460×C₈₉	C₂²	semidirect
31. #446×C₈₉	C₂²	semidirect
32. C₈×Q₈×C₈₉	C₂²	semidirect
39. #335×C₈₉	C₂²	semidirect
40. #334×C₈₉	C₂²	semidirect
41. #332×C₈₉	C₂²	semidirect
42. #332×C₈₉	C₂²	semidirect
45. #331×C₈₉	C₂²	semidirect
46. #331×C₈₉	C₂²	semidirect
137. M₁₆×C₈₉	SD₁₆	semidirect
232. #19238	C₈₉	direct (N × H)
239. #3246	C₂×C₈₉	semidirect
240. #3208	C₂×C₈₉	semidirect
242. #2962	C₂×C₈₉	semidirect
243. #1688	C₂×C₈₉	semidirect
244. #1686	C₂×C₈₉	semidirect
245. #1668	C₂×C₈₉	semidirect
246. #1666	C₂×C₈₉	semidirect
247. #1565	C₂×C₈₉	semidirect
248. #1540	C₂×C₈₉	semidirect
249. C₂×#331	C₂×C₈₉	semidirect
250. C₈₉	#19238	direct (N × H)
262. #475	C₂²×C₈₉	semidirect
267. #460	C₂²×C₈₉	semidirect
270. #446	C₂²×C₈₉	semidirect
271. C₈×Q₈	C₂²×C₈₉	semidirect
278. #335	C₂²×C₈₉	semidirect
279. #334	C₂²×C₈₉	semidirect
280. #332	C₂²×C₈₉	semidirect
281. #332	C₂²×C₈₉	semidirect
284. #331	C₂²×C₈₉	semidirect
285. #331	C₂²×C₈₉	semidirect
376. M₁₆	SD₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3246	2
C₈₉×#3208	2
C₈₉×#3151	2
C₈₉×#2962	2
C₈₉×#1688	2
C₈₉×#1686	2
C₈₉×#1668	2
C₈₉×#1666	2
C₈₉×#1565	2
C₈₉×#1540	2
C₂×#331×C₈₉	2
#19238	89

Subgroups — C89×#19238 #36397086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19238 #36397086