Subgroups — C₈₉×#60673 #36438521

Order 22784.

2050 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3444	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3170	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3169	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3168	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3167	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3160	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3131	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3050	C₂	1	4	yes	maximal, complemented
10	C₄×#135×C₈₉	C₂	1	4	yes	maximal, complemented
11	C₂²×C₄×C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₈₉	C₂²	1	4	yes	—
13	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
14	#533×C₈₉	C₂²	1	4	yes	—
15	#533×C₈₉	C₂²	1	2	yes	—
16	#532×C₈₉	C₂²	1	2	yes	—
17	#532×C₈₉	C₂²	1	4	yes	—
18	#529×C₈₉	—	2	4	no	—
19	#529×C₈₉	—	2	4	no	—
20	#529×C₈₉	C₂²	1	8	yes	—
21	#525×C₈₉	—	2	4	no	—
22	#525×C₈₉	C₂²	1	4	yes	—
23	C₄×#41×C₈₉	—	2	4	no	—
24	C₄×#41×C₈₉	C₂²	1	4	yes	—
25	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
26	#500×C₈₉	C₂²	1	2	yes	complemented
27	#499×C₈₉	C₂²	1	4	yes	complemented
28	#498×C₈₉	C₂²	1	2	yes	complemented
29	#495×C₈₉	C₂²	1	4	yes	complemented
30	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#493×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	#492×C₈₉	C₂²	1	2	yes	complemented
33	#488×C₈₉	C₂²	1	8	yes	complemented
34	#487×C₈₉	C₂²	1	4	yes	complemented
35	#486×C₈₉	C₂²	1	4	yes	complemented
36	#467×C₈₉	C₂²	1	8	yes	—
37	#466×C₈₉	C₂²	1	8	yes	—
38	#465×C₈₉	C₂²	1	16	yes	—
39	C₄×Q₁₆×C₈₉	C₂²	1	8	yes	complemented
40	C₄×SD₁₆×C₈₉	C₂²	1	16	yes	complemented
41	C₄×D₈×C₈₉	C₂²	1	8	yes	complemented
42	#427×C₈₉	C₂²	1	4	yes	—
43	#416×C₈₉	C₂²	1	8	yes	—
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
47	C₂×C₄×C₈×C₈₉	C₂²	1	4	yes	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
49	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
50	C₂×#41×C₈₉	—	2	4	no	—
51	C₂×#41×C₈₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₈₉	D₄	1	2	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	#135×C₈₉	—	2	16	no	—
55	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
56	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
57	C₂×D₈×C₈₉	C₂³	1	4	yes	—
58	C₂²×C₈×C₈₉	—	2	8	no	—
59	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
61	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
64	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
65	#127×C₈₉	C₂³	1	2	yes	—
66	#126×C₈₉	—	2	8	no	—
67	#125×C₈₉	—	2	4	no	—
68	#125×C₈₉	C₂³	1	4	yes	—
69	#124×C₈₉	—	2	4	no	—
70	#124×C₈₉	C₂³	1	4	yes	—
71	#123×C₈₉	—	2	8	no	—
72	#123×C₈₉	—	2	4	no	—
73	C₂²⋊Q₈×C₈₉	—	2	4	no	—
74	C₂²⋊Q₈×C₈₉	—	2	4	no	—
75	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
76	#121×C₈₉	—	2	4	no	—
77	#121×C₈₉	—	2	4	no	—
78	#121×C₈₉	C₂³	1	8	yes	—
79	#120×C₈₉	—	2	4	no	—
80	C₄×Q₈×C₈₉	—	2	4	no	—
81	C₄×Q₈×C₈₉	—	2	4	no	—
82	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
83	C₄×D₄×C₈₉	—	2	8	no	—
84	C₄×D₄×C₈₉	—	2	8	no	—
85	C₄×D₄×C₈₉	—	2	8	no	—
86	C₄×D₄×C₈₉	—	2	4	no	—
87	C₄×D₄×C₈₉	—	2	4	no	—
88	C₄×D₄×C₈₉	C₂³	1	8	yes	—
89	#117×C₈₉	—	2	4	no	—
90	#117×C₈₉	—	2	8	no	—
91	#117×C₈₉	—	2	4	no	—
92	#117×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₈₉	—	2	4	no	—
94	C₂×C₄²×C₈₉	D₄	1	2	yes	—
95	C₂×C₄²×C₈₉	D₄	1	2	yes	—
96	C₂×C₄²×C₈₉	D₄	1	2	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	#107×C₈₉	C₂³	1	8	yes	—
102	#106×C₈₉	C₂³	1	8	yes	—
103	#103×C₈₉	C₂³	1	16	yes	—
104	#102×C₈₉	C₂³	1	16	yes	—
105	C₄×C₈×C₈₉	C₂³	1	4	yes	—
106	C₄×C₈×C₈₉	C₂³	1	4	yes	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₄×C₈×C₈₉	C₂³	1	2	yes	—
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₈₉	C₂³	1	2	yes	—
112	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
113	#41×C₈₉	—	2	16	no	—
114	#41×C₈₉	—	4	16	no	—
115	C₂×Q₈×C₈₉	—	2	4	no	—
116	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
117	C₂×D₄×C₈₉	—	2	4	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	4	no	—
120	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₈₉	—	2	8	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	8	no	—
125	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₈₉	—	2	8	no	—
136	SD₁₆×C₈₉	—	2	16	no	—
137	D₈×C₈₉	—	2	8	no	—
138	C₂×C₈×C₈₉	—	2	4	no	—
139	C₂×C₈×C₈₉	—	2	8	no	—
140	C₂×C₈×C₈₉	—	2	8	no	—
141	C₂×C₈×C₈₉	#41	1	8	yes	complemented
142	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
143	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
144	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	4	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	8	no	—
149	C₄⋊C₄×C₈₉	—	2	8	no	—
150	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
151	C₂²⋊C₄×C₈₉	—	2	8	no	—
152	C₂²⋊C₄×C₈₉	—	2	4	no	—
153	C₂²⋊C₄×C₈₉	—	2	8	no	—
154	C₂²⋊C₄×C₈₉	—	2	8	no	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₄²×C₈₉	—	2	8	no	—
157	C₄²×C₈₉	—	2	4	no	—
158	C₄²×C₈₉	C₂×D₄	1	2	yes	—
159	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₈₉	C₂×D₄	1	2	yes	—
161	C₄²×C₈₉	C₂×D₄	1	2	yes	—
162	C₄²×C₈₉	C₂×D₄	1	2	yes	—
163	C₄²×C₈₉	C₂×D₄	1	2	yes	—
164	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₈₉	C₂⁴	1	2	yes	—
166	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₂³×C₈₉	—	2	2	no	—
169	C₂³×C₈₉	—	2	4	no	—
170	C₂³×C₈₉	—	2	4	no	—
171	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	Q₈×C₈₉	—	2	8	no	—
174	Q₈×C₈₉	—	4	8	no	—
175	D₄×C₈₉	—	2	8	no	—
176	D₄×C₈₉	—	4	8	no	—
177	D₄×C₈₉	—	4	16	no	—
178	D₄×C₈₉	—	4	8	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	4	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	8	no	—
189	C₂×C₄×C₈₉	—	4	8	no	—
190	C₂×C₄×C₈₉	—	4	16	no	—
191	C₂×C₄×C₈₉	#135	1	8	yes	complemented
192	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
199	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
200	C₈×C₈₉	—	2	4	no	—
201	C₈×C₈₉	C₂×#41	1	4	yes	—
202	C₈×C₈₉	C₂×#41	1	4	yes	—
203	C₂²×C₈₉	—	2	8	no	—
204	C₂²×C₈₉	—	2	2	no	—
205	C₂²×C₈₉	—	2	2	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	4	4	no	—
208	C₂²×C₈₉	—	4	8	no	—
209	C₂²×C₈₉	#532	1	2	yes	—
210	C₂²×C₈₉	C₂×#135	1	4	yes	—
211	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
212	C₄×C₈₉	—	2	2	no	—
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	4	4	no	—
216	C₄×C₈₉	—	4	8	no	—
217	C₄×C₈₉	#532	1	2	yes	—
218	C₄×C₈₉	C₂×#135	1	4	yes	—
219	C₄×C₈₉	C₂×#135	1	4	yes	—
220	C₄×C₈₉	C₂²×#41	1	2	yes	—
221	#60673	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂×C₈₉	—	2	2	no	—
223	C₂×C₈₉	—	2	4	no	—
224	C₂×C₈₉	—	8	4	no	—
225	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
226	C₂×C₈₉	C₂²×#135	1	2	yes	—
227	#3444	C₂×C₈₉	1	2	yes	complemented
228	#3170	C₂×C₈₉	1	2	yes	complemented
229	#3169	C₂×C₈₉	1	2	yes	complemented
230	#3168	C₂×C₈₉	1	8	yes	complemented
231	#3167	C₂×C₈₉	1	4	yes	complemented
232	#3160	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#3147	C₂×C₈₉	1	1	yes	characteristic, complemented
234	#3131	C₂×C₈₉	1	2	yes	complemented
235	#3050	C₂×C₈₉	1	4	yes	complemented
236	C₄×#135	C₂×C₈₉	1	4	yes	complemented
237	C₂²×C₄×C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
238	C₈₉	#60673	1	1	yes	characteristic, direct product factor, Sylow
239	C₂×#135	C₂²×C₈₉	1	4	yes	—
240	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
241	#533	C₂²×C₈₉	1	4	yes	—
242	#533	C₂²×C₈₉	1	2	yes	—
243	#532	C₂²×C₈₉	1	2	yes	—
244	#532	C₂²×C₈₉	1	4	yes	—
245	#529	—	2	4	no	—
246	#529	—	2	4	no	—
247	#529	C₂²×C₈₉	1	8	yes	—
248	#525	—	2	4	no	—
249	#525	C₂²×C₈₉	1	4	yes	—
250	C₄×#41	—	2	4	no	—
251	C₄×#41	C₂²×C₈₉	1	4	yes	—
252	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
253	#500	C₂²×C₈₉	1	2	yes	complemented
254	#499	C₂²×C₈₉	1	4	yes	complemented
255	#498	C₂²×C₈₉	1	2	yes	complemented
256	#495	C₂²×C₈₉	1	4	yes	complemented
257	#494	C₂²×C₈₉	1	1	yes	characteristic, complemented
258	#493	C₂²×C₈₉	1	1	yes	characteristic, complemented
259	#492	C₂²×C₈₉	1	2	yes	complemented
260	#488	C₂²×C₈₉	1	8	yes	complemented
261	#487	C₂²×C₈₉	1	4	yes	complemented
262	#486	C₂²×C₈₉	1	4	yes	complemented
263	#467	C₂²×C₈₉	1	8	yes	—
264	#466	C₂²×C₈₉	1	8	yes	—
265	#465	C₂²×C₈₉	1	16	yes	—
266	C₄×Q₁₆	C₂²×C₈₉	1	8	yes	complemented
267	C₄×SD₁₆	C₂²×C₈₉	1	16	yes	complemented
268	C₄×D₈	C₂²×C₈₉	1	8	yes	complemented
269	#427	C₂²×C₈₉	1	4	yes	—
270	#416	C₂²×C₈₉	1	8	yes	—
271	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
272	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
273	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
274	C₂×C₄×C₈	C₂²×C₈₉	1	4	yes	—
275	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
277	C₂×#41	—	2	4	no	—
278	C₂×#41	C₂³×C₈₉	1	4	yes	—
279	C₂³×C₄	D₄×C₈₉	1	2	yes	—
280	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
281	#135	—	2	16	no	—
282	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
283	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
284	C₂×D₈	C₂³×C₈₉	1	4	yes	—
285	C₂²×C₈	—	2	8	no	—
286	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
287	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
288	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
289	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
290	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
291	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
292	#127	C₂³×C₈₉	1	2	yes	—
293	#126	—	2	8	no	—
294	#125	—	2	4	no	—
295	#125	C₂³×C₈₉	1	4	yes	—
296	#124	—	2	4	no	—
297	#124	C₂³×C₈₉	1	4	yes	—
298	#123	—	2	8	no	—
299	#123	—	2	4	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
303	#121	—	2	4	no	—
304	#121	—	2	4	no	—
305	#121	C₂³×C₈₉	1	8	yes	—
306	#120	—	2	4	no	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
310	C₄×D₄	—	2	8	no	—
311	C₄×D₄	—	2	8	no	—
312	C₄×D₄	—	2	8	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	C₂³×C₈₉	1	8	yes	—
316	#117	—	2	4	no	—
317	#117	—	2	8	no	—
318	#117	—	2	4	no	—
319	#117	C₂³×C₈₉	1	4	yes	—
320	C₂×C₄²	—	2	4	no	—
321	C₂×C₄²	D₄×C₈₉	1	2	yes	—
322	C₂×C₄²	D₄×C₈₉	1	2	yes	—
323	C₂×C₄²	D₄×C₈₉	1	2	yes	—
324	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
325	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
326	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
328	#107	C₂³×C₈₉	1	8	yes	—
329	#106	C₂³×C₈₉	1	8	yes	—
330	#103	C₂³×C₈₉	1	16	yes	—
331	#102	C₂³×C₈₉	1	16	yes	—
332	C₄×C₈	C₂³×C₈₉	1	4	yes	—
333	C₄×C₈	C₂³×C₈₉	1	4	yes	—
334	C₄×C₈	C₂³×C₈₉	1	2	yes	—
335	C₄×C₈	C₂³×C₈₉	1	2	yes	—
336	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
337	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
338	C₄×C₈	C₂³×C₈₉	1	2	yes	—
339	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
340	#41	—	2	16	no	—
341	#41	—	4	16	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	8	no	—
352	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
357	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
358	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
361	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
362	Q₁₆	—	2	8	no	—
363	SD₁₆	—	2	16	no	—
364	D₈	—	2	8	no	—
365	C₂×C₈	—	2	4	no	—
366	C₂×C₈	—	2	8	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	#41×C₈₉	1	8	yes	complemented
369	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
370	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
371	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	—	2	4	no	—
385	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
386	C₄²	C₂×D₄×C₈₉	1	2	yes	—
387	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
388	C₄²	C₂×D₄×C₈₉	1	2	yes	—
389	C₄²	C₂×D₄×C₈₉	1	2	yes	—
390	C₄²	C₂×D₄×C₈₉	1	2	yes	—
391	C₄²	C₂×D₄×C₈₉	1	2	yes	—
392	C₄²	C₂⁴×C₈₉	1	2	yes	—
393	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
394	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
399	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
400	Q₈	—	2	8	no	—
401	Q₈	—	4	8	no	—
402	D₄	—	2	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	4	16	no	—
405	D₄	—	4	8	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	4	8	no	—
417	C₂×C₄	—	4	16	no	—
418	C₂×C₄	#135×C₈₉	1	8	yes	complemented
419	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
425	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
426	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	C₂×#41×C₈₉	1	4	yes	—
429	C₈	C₂×#41×C₈₉	1	4	yes	—
430	C₂²	—	2	8	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	8	no	—
435	C₂²	—	4	4	no	—
436	C₂²	#532×C₈₉	1	2	yes	—
437	C₂²	C₂×#135×C₈₉	1	4	yes	—
438	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	8	no	—
443	C₄	—	4	4	no	—
444	C₄	#532×C₈₉	1	2	yes	—
445	C₄	C₂×#135×C₈₉	1	4	yes	—
446	C₄	C₂×#135×C₈₉	1	4	yes	—
447	C₄	C₂²×#41×C₈₉	1	2	yes	—
448	C₂	—	2	2	no	—
449	C₂	—	2	4	no	—
450	C₂	—	8	4	no	—
451	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
452	C₂	C₂²×#135×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₄²×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3444	C₂	semidirect
2. C₈₉×#3170	C₂	semidirect
3. C₈₉×#3169	C₂	semidirect
4. C₈₉×#3168	C₂	semidirect
5. C₈₉×#3167	C₂	semidirect
6. C₈₉×#3160	C₂	semidirect
7. C₈₉×#3147	C₂	semidirect
8. C₈₉×#3131	C₂	semidirect
9. C₈₉×#3050	C₂	semidirect
10. C₄×#135×C₈₉	C₂	semidirect
11. C₂²×C₄×C₈×C₈₉	C₂	semidirect
26. #500×C₈₉	C₂²	semidirect
27. #499×C₈₉	C₂²	semidirect
28. #498×C₈₉	C₂²	semidirect
29. #495×C₈₉	C₂²	semidirect
30. #494×C₈₉	C₂²	semidirect
31. #493×C₈₉	C₂²	semidirect
32. #492×C₈₉	C₂²	semidirect
33. #488×C₈₉	C₂²	semidirect
34. #487×C₈₉	C₂²	semidirect
35. #486×C₈₉	C₂²	semidirect
39. C₄×Q₁₆×C₈₉	C₂²	semidirect
40. C₄×SD₁₆×C₈₉	C₂²	semidirect
41. C₄×D₈×C₈₉	C₂²	semidirect
141. C₂×C₈×C₈₉	#41	semidirect
191. C₂×C₄×C₈₉	#135	semidirect
221. #60673	C₈₉	direct (N × H)
227. #3444	C₂×C₈₉	semidirect
228. #3170	C₂×C₈₉	semidirect
229. #3169	C₂×C₈₉	semidirect
230. #3168	C₂×C₈₉	semidirect
231. #3167	C₂×C₈₉	semidirect
232. #3160	C₂×C₈₉	semidirect
233. #3147	C₂×C₈₉	semidirect
234. #3131	C₂×C₈₉	semidirect
235. #3050	C₂×C₈₉	semidirect
236. C₄×#135	C₂×C₈₉	semidirect
237. C₂²×C₄×C₈	C₂×C₈₉	semidirect
238. C₈₉	#60673	direct (N × H)
253. #500	C₂²×C₈₉	semidirect
254. #499	C₂²×C₈₉	semidirect
255. #498	C₂²×C₈₉	semidirect
256. #495	C₂²×C₈₉	semidirect
257. #494	C₂²×C₈₉	semidirect
258. #493	C₂²×C₈₉	semidirect
259. #492	C₂²×C₈₉	semidirect
260. #488	C₂²×C₈₉	semidirect
261. #487	C₂²×C₈₉	semidirect
262. #486	C₂²×C₈₉	semidirect
266. C₄×Q₁₆	C₂²×C₈₉	semidirect
267. C₄×SD₁₆	C₂²×C₈₉	semidirect
268. C₄×D₈	C₂²×C₈₉	semidirect
368. C₂×C₈	#41×C₈₉	semidirect
418. C₂×C₄	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3444	2
C₈₉×#3170	2
C₈₉×#3169	2
C₈₉×#3168	2
C₈₉×#3167	2
C₈₉×#3160	2
C₈₉×#3147	2
C₈₉×#3131	2
C₈₉×#3050	2
C₄×#135×C₈₉	2
C₂²×C₄×C₈×C₈₉	2
#60673	89

Subgroups — C89×#60673 #36438521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60673 #36438521