Subgroups — C₈₉×#60519 #36438367

Order 22784.

2106 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3428	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3097	C₂	1	16	yes	maximal, complemented
4	C₈₉×#3095	C₂	1	8	yes	maximal, complemented
5	C₈₉×#2911	C₂	1	2	yes	maximal, complemented
6	C₂×#419×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2879	C₂	1	1	yes	maximal, characteristic
8	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
11	#536×C₈₉	—	2	4	no	—
12	#536×C₈₉	C₂²	1	8	yes	—
13	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
14	C₂×#124×C₈₉	—	2	1	no	—
15	C₂×#123×C₈₉	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
17	#520×C₈₉	C₂²	1	8	yes	—
18	#519×C₈₉	—	2	1	no	—
19	#518×C₈₉	—	2	2	no	—
20	#518×C₈₉	—	2	1	no	—
21	C₄×#41×C₈₉	—	2	4	no	—
22	C₂×#117×C₈₉	C₂²	1	4	yes	—
23	C₂×#117×C₈₉	C₂²	1	2	yes	—
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	#485×C₈₉	C₂²	1	32	yes	complemented
26	#484×C₈₉	C₂²	1	16	yes	complemented
27	#483×C₈₉	C₂²	1	16	yes	complemented
28	#428×C₈₉	C₂²	1	8	yes	—
29	#428×C₈₉	C₂²	1	8	yes	complemented
30	#427×C₈₉	C₂²	1	8	yes	complemented
31	#419×C₈₉	C₂²	1	8	yes	—
32	#419×C₈₉	C₂²	1	8	yes	complemented
33	C₂×#103×C₈₉	C₂²	1	8	yes	complemented
34	#408×C₈₉	C₂²	1	8	yes	—
35	#407×C₈₉	C₂²	1	4	yes	—
36	C₂×#41×C₈₉	—	2	8	no	—
37	C₂×#41×C₈₉	D₄	1	4	yes	—
38	C₂×#41×C₈₉	C₂³	1	4	yes	—
39	C₂²×Q₈×C₈₉	—	2	1	no	—
40	C₂²×Q₈×C₈₉	—	2	2	no	—
41	C₂²×Q₈×C₈₉	—	2	8	no	—
42	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
44	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
45	C₂²×D₄×C₈₉	D₄	1	2	yes	—
46	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₈₉	—	2	1	no	—
48	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₈₉	—	2	8	no	—
51	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
52	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
53	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
54	C₄⋊Q₈×C₈₉	—	2	8	no	—
55	#124×C₈₉	—	2	8	no	—
56	#123×C₈₉	—	2	16	no	—
57	C₂²⋊Q₈×C₈₉	—	2	8	no	—
58	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
59	C₄×Q₈×C₈₉	—	2	8	no	—
60	C₄×D₄×C₈₉	—	2	16	no	—
61	C₄×D₄×C₈₉	—	2	8	no	—
62	#117×C₈₉	—	2	4	no	—
63	#117×C₈₉	—	2	2	no	—
64	#117×C₈₉	—	2	4	no	—
65	#117×C₈₉	—	2	2	no	—
66	#117×C₈₉	—	2	2	no	—
67	#117×C₈₉	C₂³	1	4	yes	—
68	#117×C₈₉	C₂³	1	4	yes	—
69	#117×C₈₉	C₂³	1	4	yes	—
70	#117×C₈₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
79	C₂×C₄²×C₈₉	—	2	4	no	—
80	C₂×C₄²×C₈₉	—	2	2	no	—
81	C₂×C₄²×C₈₉	—	2	1	no	—
82	#107×C₈₉	C₂³	1	16	yes	—
83	#106×C₈₉	C₂³	1	16	yes	—
84	#103×C₈₉	C₂³	1	32	yes	—
85	C₂²⋊C₈×C₈₉	C₂³	1	16	yes	—
86	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
87	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
88	#41×C₈₉	—	2	16	no	—
89	#41×C₈₉	—	2	8	no	—
90	#41×C₈₉	—	2	8	no	—
91	C₂×Q₈×C₈₉	—	2	4	no	—
92	C₂×Q₈×C₈₉	—	2	2	no	—
93	C₂×Q₈×C₈₉	—	2	4	no	—
94	C₂×Q₈×C₈₉	—	2	8	no	—
95	C₂×Q₈×C₈₉	—	2	8	no	—
96	C₂×Q₈×C₈₉	—	2	8	no	—
97	C₂×Q₈×C₈₉	—	4	4	no	—
98	C₂×Q₈×C₈₉	—	4	8	no	—
99	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
100	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
101	C₂×D₄×C₈₉	—	2	8	no	—
102	C₂×D₄×C₈₉	—	2	4	no	—
103	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
104	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
105	C₂²×C₄×C₈₉	—	2	8	no	—
106	C₂²×C₄×C₈₉	—	2	2	no	—
107	C₂²×C₄×C₈₉	—	2	2	no	—
108	C₂²×C₄×C₈₉	—	2	4	no	—
109	C₂²×C₄×C₈₉	—	2	8	no	—
110	C₂²×C₄×C₈₉	—	2	4	no	—
111	C₂²×C₄×C₈₉	—	4	4	no	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₈₉	#41	1	8	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
120	M₁₆×C₈₉	—	2	8	no	—
121	M₁₆×C₈₉	—	2	8	no	—
122	C₂×C₈×C₈₉	—	2	8	no	—
123	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
124	C₄⋊C₄×C₈₉	—	2	16	no	—
125	C₄⋊C₄×C₈₉	—	2	8	no	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
129	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
130	C₂²⋊C₄×C₈₉	—	2	4	no	—
131	C₂²⋊C₄×C₈₉	—	2	8	no	—
132	C₂²⋊C₄×C₈₉	—	2	4	no	—
133	C₂²⋊C₄×C₈₉	—	2	4	no	—
134	C₂²⋊C₄×C₈₉	—	2	16	no	—
135	C₄²×C₈₉	—	2	4	no	—
136	C₄²×C₈₉	—	2	8	no	—
137	C₄²×C₈₉	—	2	4	no	—
138	C₄²×C₈₉	—	2	4	no	—
139	C₂³×C₈₉	—	2	4	no	—
140	C₂³×C₈₉	—	4	2	no	—
141	C₂³×C₈₉	—	4	4	no	—
142	C₂³×C₈₉	#123	1	4	yes	—
143	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
144	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
146	Q₈×C₈₉	—	2	8	no	—
147	Q₈×C₈₉	—	2	8	no	—
148	Q₈×C₈₉	—	4	4	no	—
149	Q₈×C₈₉	—	4	8	no	—
150	D₄×C₈₉	—	2	16	no	—
151	D₄×C₈₉	—	2	8	no	—
152	C₂×C₄×C₈₉	—	2	4	no	—
153	C₂×C₄×C₈₉	—	2	8	no	—
154	C₂×C₄×C₈₉	—	2	8	no	—
155	C₂×C₄×C₈₉	—	2	8	no	—
156	C₂×C₄×C₈₉	—	2	4	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	4	4	no	—
159	C₂×C₄×C₈₉	—	4	4	no	—
160	C₂×C₄×C₈₉	—	4	8	no	—
161	C₂×C₄×C₈₉	—	8	4	no	—
162	C₂×C₄×C₈₉	—	8	8	no	—
163	C₂×C₄×C₈₉	#123	1	4	yes	—
164	C₂×C₄×C₈₉	#123	1	8	yes	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
169	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
170	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
171	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
172	C₈×C₈₉	—	2	8	no	—
173	C₂²×C₈₉	—	2	2	no	—
174	C₂²×C₈₉	—	2	4	no	—
175	C₂²×C₈₉	—	2	8	no	—
176	C₂²×C₈₉	—	2	4	no	—
177	C₂²×C₈₉	—	4	4	no	—
178	C₂²×C₈₉	—	8	4	no	—
179	C₂²×C₈₉	C₂×#123	1	2	yes	—
180	C₂²×C₈₉	C₂×#123	1	4	yes	—
181	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
182	C₄×C₈₉	—	2	4	no	—
183	C₄×C₈₉	—	4	4	no	—
184	C₄×C₈₉	—	4	8	no	—
185	C₄×C₈₉	—	4	4	no	—
186	C₄×C₈₉	C₂×#123	1	2	yes	—
187	C₄×C₈₉	C₂×#123	1	4	yes	—
188	C₄×C₈₉	C₂²×#41	1	2	yes	—
189	#60519	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₈₉	—	2	2	no	—
191	C₂×C₈₉	—	2	4	no	—
192	C₂×C₈₉	—	4	4	no	—
193	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
194	C₂×C₈₉	#3586	1	2	yes	—
195	C₂×#536	C₂×C₈₉	1	1	yes	characteristic
196	#3428	C₂×C₈₉	1	1	yes	characteristic
197	#3097	C₂×C₈₉	1	16	yes	complemented
198	#3095	C₂×C₈₉	1	8	yes	complemented
199	#2911	C₂×C₈₉	1	2	yes	complemented
200	C₂×#419	C₂×C₈₉	1	2	yes	complemented
201	#2879	C₂×C₈₉	1	1	yes	characteristic
202	C₈₉	#60519	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
204	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
206	#536	—	2	4	no	—
207	#536	C₂²×C₈₉	1	8	yes	—
208	C₂×C₄⋊Q₈	—	2	1	no	—
209	C₂×#124	—	2	1	no	—
210	C₂×#123	—	2	2	no	—
211	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
212	#520	C₂²×C₈₉	1	8	yes	—
213	#519	—	2	1	no	—
214	#518	—	2	2	no	—
215	#518	—	2	1	no	—
216	C₄×#41	—	2	4	no	—
217	C₂×#117	C₂²×C₈₉	1	4	yes	—
218	C₂×#117	C₂²×C₈₉	1	2	yes	—
219	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
220	#485	C₂²×C₈₉	1	32	yes	complemented
221	#484	C₂²×C₈₉	1	16	yes	complemented
222	#483	C₂²×C₈₉	1	16	yes	complemented
223	#428	C₂²×C₈₉	1	8	yes	—
224	#428	C₂²×C₈₉	1	8	yes	complemented
225	#427	C₂²×C₈₉	1	8	yes	complemented
226	#419	C₂²×C₈₉	1	8	yes	—
227	#419	C₂²×C₈₉	1	8	yes	complemented
228	C₂×#103	C₂²×C₈₉	1	8	yes	complemented
229	#408	C₂²×C₈₉	1	8	yes	—
230	#407	C₂²×C₈₉	1	4	yes	—
231	C₂×#41	—	2	8	no	—
232	C₂×#41	D₄×C₈₉	1	4	yes	—
233	C₂×#41	C₂³×C₈₉	1	4	yes	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	8	no	—
237	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
239	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
240	C₂²×D₄	D₄×C₈₉	1	2	yes	—
241	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	8	no	—
246	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
247	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
248	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
249	C₄⋊Q₈	—	2	8	no	—
250	#124	—	2	8	no	—
251	#123	—	2	16	no	—
252	C₂²⋊Q₈	—	2	8	no	—
253	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
254	C₄×Q₈	—	2	8	no	—
255	C₄×D₄	—	2	16	no	—
256	C₄×D₄	—	2	8	no	—
257	#117	—	2	4	no	—
258	#117	—	2	2	no	—
259	#117	—	2	4	no	—
260	#117	—	2	2	no	—
261	#117	—	2	2	no	—
262	#117	C₂³×C₈₉	1	4	yes	—
263	#117	C₂³×C₈₉	1	4	yes	—
264	#117	C₂³×C₈₉	1	8	yes	—
265	#117	C₂³×C₈₉	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	—	2	2	no	—
276	C₂×C₄²	—	2	1	no	—
277	#107	C₂³×C₈₉	1	16	yes	—
278	#106	C₂³×C₈₉	1	16	yes	—
279	#103	C₂³×C₈₉	1	32	yes	—
280	C₂²⋊C₈	C₂³×C₈₉	1	16	yes	—
281	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
282	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
283	#41	—	2	16	no	—
284	#41	—	2	8	no	—
285	#41	—	2	8	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	8	no	—
290	C₂×Q₈	—	2	8	no	—
291	C₂×Q₈	—	2	8	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	4	8	no	—
294	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
295	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
299	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
308	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
311	C₂²×C₄	#41×C₈₉	1	8	yes	—
312	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
313	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
315	M₁₆	—	2	8	no	—
316	M₁₆	—	2	8	no	—
317	C₂×C₈	—	2	8	no	—
318	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
319	C₄⋊C₄	—	2	16	no	—
320	C₄⋊C₄	—	2	8	no	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
324	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	2	16	no	—
330	C₄²	—	2	4	no	—
331	C₄²	—	2	8	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	4	no	—
337	C₂³	#123×C₈₉	1	4	yes	—
338	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
339	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
340	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
341	Q₈	—	2	8	no	—
342	Q₈	—	2	8	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	4	8	no	—
345	D₄	—	2	16	no	—
346	D₄	—	2	8	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	8	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	8	4	no	—
357	C₂×C₄	—	8	8	no	—
358	C₂×C₄	#123×C₈₉	1	4	yes	—
359	C₂×C₄	#123×C₈₉	1	8	yes	—
360	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
361	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
362	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
363	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
364	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
365	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
366	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
367	C₈	—	2	8	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	2	8	no	—
371	C₂²	—	2	4	no	—
372	C₂²	—	4	4	no	—
373	C₂²	—	8	4	no	—
374	C₂²	C₂×#123×C₈₉	1	2	yes	—
375	C₂²	C₂×#123×C₈₉	1	4	yes	—
376	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
377	C₄	—	2	4	no	—
378	C₄	—	4	4	no	—
379	C₄	—	4	8	no	—
380	C₄	—	4	4	no	—
381	C₄	C₂×#123×C₈₉	1	2	yes	—
382	C₄	C₂×#123×C₈₉	1	4	yes	—
383	C₄	C₂²×#41×C₈₉	1	2	yes	—
384	C₂	—	2	2	no	—
385	C₂	—	2	4	no	—
386	C₂	—	4	4	no	—
387	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
388	C₂	C₈₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₉×#3097	C₂	semidirect
4. C₈₉×#3095	C₂	semidirect
5. C₈₉×#2911	C₂	semidirect
6. C₂×#419×C₈₉	C₂	semidirect
25. #485×C₈₉	C₂²	semidirect
26. #484×C₈₉	C₂²	semidirect
27. #483×C₈₉	C₂²	semidirect
29. #428×C₈₉	C₂²	semidirect
30. #427×C₈₉	C₂²	semidirect
32. #419×C₈₉	C₂²	semidirect
33. C₂×#103×C₈₉	C₂²	semidirect
189. #60519	C₈₉	direct (N × H)
197. #3097	C₂×C₈₉	semidirect
198. #3095	C₂×C₈₉	semidirect
199. #2911	C₂×C₈₉	semidirect
200. C₂×#419	C₂×C₈₉	semidirect
202. C₈₉	#60519	direct (N × H)
220. #485	C₂²×C₈₉	semidirect
221. #484	C₂²×C₈₉	semidirect
222. #483	C₂²×C₈₉	semidirect
224. #428	C₂²×C₈₉	semidirect
225. #427	C₂²×C₈₉	semidirect
227. #419	C₂²×C₈₉	semidirect
228. C₂×#103	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₈₉	2
C₈₉×#3428	2
C₈₉×#3097	2
C₈₉×#3095	2
C₈₉×#2911	2
C₂×#419×C₈₉	2
C₈₉×#2879	2
#60519	89

Subgroups — C89×#60519 #36438367

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60519 #36438367