Subgroups — C₈₉×#60424 #36438272

Order 22784.

2674 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic
3	C₂×#519×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3044	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3043	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3037	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2896	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₈₉	C₂²	1	2	yes	—
10	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#137×C₈₉	—	2	16	no	—
12	C₂×#137×C₈₉	C₂²	1	8	yes	—
13	C₂×#137×C₈₉	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₈₉	C₂²	1	4	yes	complemented
15	C₂²×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
16	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
17	#537×C₈₉	—	2	2	no	—
18	#536×C₈₉	C₂²	1	4	yes	—
19	#535×C₈₉	C₂²	1	4	yes	—
20	#534×C₈₉	—	2	2	no	—
21	#532×C₈₉	C₂²	1	4	yes	—
22	#525×C₈₉	—	2	4	no	—
23	#519×C₈₉	—	2	4	no	—
24	#519×C₈₉	C₂²	1	8	yes	complemented
25	C₂×C₄×Q₈×C₈₉	—	2	2	no	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
27	C₂×#117×C₈₉	—	2	2	no	—
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	#464×C₈₉	C₂²	1	32	yes	complemented
31	#462×C₈₉	C₂²	1	16	yes	complemented
32	#460×C₈₉	C₂²	1	16	yes	complemented
33	#424×C₈₉	C₂²	1	8	yes	complemented
34	#423×C₈₉	C₂²	1	4	yes	complemented
35	#419×C₈₉	C₂²	1	4	yes	complemented
36	#418×C₈₉	C₂²	1	4	yes	complemented
37	#417×C₈₉	C₂²	1	8	yes	complemented
38	#416×C₈₉	C₂²	1	8	yes	—
39	C₂×#41×C₈₉	—	2	2	no	—
40	C₂×#41×C₈₉	—	2	2	no	—
41	C₂×#41×C₈₉	—	2	8	no	—
42	C₂×#41×C₈₉	—	2	8	no	—
43	C₂×#41×C₈₉	C₂³	1	4	yes	—
44	C₂×#41×C₈₉	C₂³	1	4	yes	—
45	C₂²×Q₈×C₈₉	—	2	1	no	—
46	C₂²×Q₈×C₈₉	—	2	2	no	—
47	C₂²×Q₈×C₈₉	—	2	4	no	—
48	C₂²×Q₈×C₈₉	D₄	1	8	yes	complemented
49	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
50	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
52	C₂²×D₄×C₈₉	—	2	2	no	—
53	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₈₉	—	2	1	no	—
55	C₂³×C₄×C₈₉	—	2	2	no	—
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	#137×C₈₉	—	2	32	no	—
58	#137×C₈₉	—	2	32	no	—
59	C₂×Q₁₆×C₈₉	—	2	16	no	—
60	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
61	C₂×SD₁₆×C₈₉	—	2	16	no	—
62	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
63	C₂×M₁₆×C₈₉	—	2	8	no	—
64	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
65	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
66	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
67	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
68	#127×C₈₉	C₂³	1	4	yes	—
69	#124×C₈₉	C₂³	1	8	yes	—
70	#123×C₈₉	—	2	8	no	—
71	C₂²⋊Q₈×C₈₉	—	2	8	no	—
72	#121×C₈₉	—	2	8	no	—
73	#121×C₈₉	—	2	8	no	—
74	#120×C₈₉	—	2	8	no	—
75	C₄×Q₈×C₈₉	—	2	16	no	—
76	C₄×Q₈×C₈₉	—	2	8	no	—
77	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
78	C₄×D₄×C₈₉	—	2	8	no	—
79	#117×C₈₉	—	2	2	no	—
80	#117×C₈₉	—	2	16	no	—
81	#117×C₈₉	D₄	1	4	yes	—
82	#117×C₈₉	C₂³	1	4	yes	—
83	#117×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
89	C₂×C₄²×C₈₉	—	2	4	no	—
90	C₂×C₄²×C₈₉	—	2	1	no	—
91	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
92	C₄⋊C₈×C₈₉	C₂³	1	16	yes	—
93	#103×C₈₉	C₂³	1	16	yes	—
94	#102×C₈₉	C₂³	1	16	yes	—
95	C₂⁴×C₈₉	—	2	2	no	—
96	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
97	#41×C₈₉	—	2	8	no	—
98	#41×C₈₉	—	2	8	no	—
99	#41×C₈₉	—	2	8	no	—
100	#41×C₈₉	—	2	8	no	—
101	#41×C₈₉	—	4	8	no	—
102	#41×C₈₉	—	4	8	no	—
103	C₂×Q₈×C₈₉	—	2	16	no	—
104	C₂×Q₈×C₈₉	—	2	8	no	—
105	C₂×Q₈×C₈₉	—	2	4	no	—
106	C₂×Q₈×C₈₉	—	2	2	no	—
107	C₂×Q₈×C₈₉	—	2	2	no	—
108	C₂×Q₈×C₈₉	—	2	8	no	—
109	C₂×Q₈×C₈₉	—	2	4	no	—
110	C₂×Q₈×C₈₉	—	2	4	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×Q₈×C₈₉	C₂×D₄	1	16	yes	—
113	C₂×Q₈×C₈₉	C₂×D₄	1	8	yes	—
114	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
116	C₂×D₄×C₈₉	—	2	4	no	—
117	C₂×D₄×C₈₉	—	2	4	no	—
118	C₂×D₄×C₈₉	—	2	4	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	8	no	—
121	C₂×D₄×C₈₉	—	2	4	no	—
122	C₂×D₄×C₈₉	—	4	8	no	—
123	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₈₉	—	2	8	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	4	no	—
127	C₂²×C₄×C₈₉	—	2	2	no	—
128	C₂²×C₄×C₈₉	—	2	2	no	—
129	C₂²×C₄×C₈₉	—	2	4	no	—
130	C₂²×C₄×C₈₉	—	2	4	no	—
131	C₂²×C₄×C₈₉	—	4	8	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₈₉	#41	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
139	Q₁₆×C₈₉	—	2	32	no	—
140	SD₁₆×C₈₉	—	2	32	no	—
141	M₁₆×C₈₉	—	2	8	no	—
142	M₁₆×C₈₉	—	2	8	no	—
143	C₂×C₈×C₈₉	—	2	8	no	—
144	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
145	C₄⋊C₄×C₈₉	—	2	16	no	—
146	C₄⋊C₄×C₈₉	—	2	2	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
149	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
150	C₂²⋊C₄×C₈₉	—	2	4	no	—
151	C₂²⋊C₄×C₈₉	—	2	16	no	—
152	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
153	C₄²×C₈₉	—	2	16	no	—
154	C₄²×C₈₉	—	2	4	no	—
155	C₄²×C₈₉	C₂×D₄	1	4	yes	—
156	C₄²×C₈₉	C₂⁴	1	4	yes	—
157	C₂³×C₈₉	—	2	4	no	—
158	C₂³×C₈₉	—	4	2	no	—
159	C₂³×C₈₉	—	4	4	no	—
160	C₂³×C₈₉	—	8	4	no	—
161	C₂³×C₈₉	#121	1	4	yes	—
162	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
163	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	8	no	—
165	Q₈×C₈₉	—	2	16	no	—
166	Q₈×C₈₉	—	2	4	no	—
167	Q₈×C₈₉	—	2	4	no	—
168	Q₈×C₈₉	—	2	4	no	—
169	Q₈×C₈₉	—	4	4	no	—
170	Q₈×C₈₉	C₂²×D₄	1	8	yes	—
171	D₄×C₈₉	—	2	4	no	—
172	D₄×C₈₉	—	2	4	no	—
173	D₄×C₈₉	—	4	8	no	—
174	D₄×C₈₉	—	4	8	no	—
175	D₄×C₈₉	—	4	4	no	—
176	D₄×C₈₉	—	8	8	no	—
177	C₂×C₄×C₈₉	—	2	16	no	—
178	C₂×C₄×C₈₉	—	2	8	no	—
179	C₂×C₄×C₈₉	—	2	4	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	4	4	no	—
183	C₂×C₄×C₈₉	—	4	4	no	—
184	C₂×C₄×C₈₉	—	4	4	no	—
185	C₂×C₄×C₈₉	—	4	8	no	—
186	C₂×C₄×C₈₉	—	4	8	no	—
187	C₂×C₄×C₈₉	#121	1	8	yes	—
188	C₂×C₄×C₈₉	#121	1	4	yes	—
189	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
190	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
195	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
197	C₈×C₈₉	—	2	8	no	—
198	C₂²×C₈₉	—	2	2	no	—
199	C₂²×C₈₉	—	2	4	no	—
200	C₂²×C₈₉	—	4	4	no	—
201	C₂²×C₈₉	—	4	8	no	—
202	C₂²×C₈₉	—	4	4	no	—
203	C₂²×C₈₉	—	8	8	no	—
204	C₂²×C₈₉	C₂×#121	1	4	yes	—
205	C₂²×C₈₉	C₂×#121	1	2	yes	—
206	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
207	C₄×C₈₉	—	2	8	no	—
208	C₄×C₈₉	—	2	8	no	—
209	C₄×C₈₉	—	4	4	no	—
210	C₄×C₈₉	—	4	4	no	—
211	C₄×C₈₉	C₂×#121	1	2	yes	—
212	C₄×C₈₉	C₂×#121	1	4	yes	—
213	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
214	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
215	#60424	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
216	C₂×C₈₉	—	2	4	no	—
217	C₂×C₈₉	—	2	2	no	—
218	C₂×C₈₉	—	8	4	no	—
219	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
220	C₂×C₈₉	#3586	1	2	yes	—
221	C₂²×#137	C₂×C₈₉	1	2	yes	complemented
222	#3449	C₂×C₈₉	1	1	yes	characteristic
223	C₂×#519	C₂×C₈₉	1	1	yes	characteristic, complemented
224	#3044	C₂×C₈₉	1	8	yes	complemented
225	#3043	C₂×C₈₉	1	8	yes	complemented
226	#3037	C₂×C₈₉	1	8	yes	complemented
227	#2905	C₂×C₈₉	1	1	yes	characteristic, complemented
228	#2896	C₂×C₈₉	1	2	yes	complemented
229	C₈₉	#60424	1	1	yes	characteristic, direct product factor, Sylow
230	C₂²×#41	C₂²×C₈₉	1	2	yes	—
231	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×#137	—	2	16	no	—
233	C₂×#137	C₂²×C₈₉	1	8	yes	—
234	C₂×#137	C₂²×C₈₉	1	8	yes	complemented
235	C₂²×Q₁₆	C₂²×C₈₉	1	4	yes	complemented
236	C₂²×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
237	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
238	#537	—	2	2	no	—
239	#536	C₂²×C₈₉	1	4	yes	—
240	#535	C₂²×C₈₉	1	4	yes	—
241	#534	—	2	2	no	—
242	#532	C₂²×C₈₉	1	4	yes	—
243	#525	—	2	4	no	—
244	#519	—	2	4	no	—
245	#519	C₂²×C₈₉	1	8	yes	complemented
246	C₂×C₄×Q₈	—	2	2	no	—
247	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
248	C₂×#117	—	2	2	no	—
249	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
251	#464	C₂²×C₈₉	1	32	yes	complemented
252	#462	C₂²×C₈₉	1	16	yes	complemented
253	#460	C₂²×C₈₉	1	16	yes	complemented
254	#424	C₂²×C₈₉	1	8	yes	complemented
255	#423	C₂²×C₈₉	1	4	yes	complemented
256	#419	C₂²×C₈₉	1	4	yes	complemented
257	#418	C₂²×C₈₉	1	4	yes	complemented
258	#417	C₂²×C₈₉	1	8	yes	complemented
259	#416	C₂²×C₈₉	1	8	yes	—
260	C₂×#41	—	2	2	no	—
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	8	no	—
263	C₂×#41	—	2	8	no	—
264	C₂×#41	C₂³×C₈₉	1	4	yes	—
265	C₂×#41	C₂³×C₈₉	1	4	yes	—
266	C₂²×Q₈	—	2	1	no	—
267	C₂²×Q₈	—	2	2	no	—
268	C₂²×Q₈	—	2	4	no	—
269	C₂²×Q₈	D₄×C₈₉	1	8	yes	complemented
270	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
271	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
272	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
273	C₂²×D₄	—	2	2	no	—
274	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
275	C₂³×C₄	—	2	1	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
278	#137	—	2	32	no	—
279	#137	—	2	32	no	—
280	C₂×Q₁₆	—	2	16	no	—
281	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
282	C₂×SD₁₆	—	2	16	no	—
283	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
284	C₂×M₁₆	—	2	8	no	—
285	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
286	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
287	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
288	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
289	#127	C₂³×C₈₉	1	4	yes	—
290	#124	C₂³×C₈₉	1	8	yes	—
291	#123	—	2	8	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	#121	—	2	8	no	—
294	#121	—	2	8	no	—
295	#120	—	2	8	no	—
296	C₄×Q₈	—	2	16	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
299	C₄×D₄	—	2	8	no	—
300	#117	—	2	2	no	—
301	#117	—	2	16	no	—
302	#117	D₄×C₈₉	1	4	yes	—
303	#117	C₂³×C₈₉	1	4	yes	—
304	#117	C₂³×C₈₉	1	4	yes	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
310	C₂×C₄²	—	2	4	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
313	C₄⋊C₈	C₂³×C₈₉	1	16	yes	—
314	#103	C₂³×C₈₉	1	16	yes	—
315	#102	C₂³×C₈₉	1	16	yes	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
318	#41	—	2	8	no	—
319	#41	—	2	8	no	—
320	#41	—	2	8	no	—
321	#41	—	2	8	no	—
322	#41	—	4	8	no	—
323	#41	—	4	8	no	—
324	C₂×Q₈	—	2	16	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	C₂×D₄×C₈₉	1	16	yes	—
334	C₂×Q₈	C₂×D₄×C₈₉	1	8	yes	—
335	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
336	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	4	8	no	—
344	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	4	8	no	—
353	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
354	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
357	C₂²×C₄	#41×C₈₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
360	Q₁₆	—	2	32	no	—
361	SD₁₆	—	2	32	no	—
362	M₁₆	—	2	8	no	—
363	M₁₆	—	2	8	no	—
364	C₂×C₈	—	2	8	no	—
365	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
366	C₄⋊C₄	—	2	16	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	8	no	—
369	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
370	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	16	no	—
373	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
374	C₄²	—	2	16	no	—
375	C₄²	—	2	4	no	—
376	C₄²	C₂×D₄×C₈₉	1	4	yes	—
377	C₄²	C₂⁴×C₈₉	1	4	yes	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	8	4	no	—
382	C₂³	#121×C₈₉	1	4	yes	—
383	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
384	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	2	16	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	2	4	no	—
389	Q₈	—	2	4	no	—
390	Q₈	—	4	4	no	—
391	Q₈	C₂²×D₄×C₈₉	1	8	yes	—
392	D₄	—	2	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	4	8	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	4	no	—
397	D₄	—	8	8	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	8	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	8	no	—
407	C₂×C₄	—	4	8	no	—
408	C₂×C₄	#121×C₈₉	1	8	yes	—
409	C₂×C₄	#121×C₈₉	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
411	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
414	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
415	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
416	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
417	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
418	C₈	—	2	8	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	8	8	no	—
425	C₂²	C₂×#121×C₈₉	1	4	yes	—
426	C₂²	C₂×#121×C₈₉	1	2	yes	—
427	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
428	C₄	—	2	8	no	—
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	4	no	—
432	C₄	C₂×#121×C₈₉	1	2	yes	—
433	C₄	C₂×#121×C₈₉	1	4	yes	—
434	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
435	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
436	C₂	—	2	4	no	—
437	C₂	—	2	2	no	—
438	C₂	—	8	4	no	—
439	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
440	C₂	C₈₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#137×C₈₉	C₂	semidirect
3. C₂×#519×C₈₉	C₂	semidirect
4. C₈₉×#3044	C₂	semidirect
5. C₈₉×#3043	C₂	semidirect
6. C₈₉×#3037	C₂	semidirect
7. C₈₉×#2905	C₂	semidirect
8. C₈₉×#2896	C₂	semidirect
13. C₂×#137×C₈₉	C₂²	semidirect
14. C₂²×Q₁₆×C₈₉	C₂²	semidirect
15. C₂²×SD₁₆×C₈₉	C₂²	semidirect
24. #519×C₈₉	C₂²	semidirect
26. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
30. #464×C₈₉	C₂²	semidirect
31. #462×C₈₉	C₂²	semidirect
32. #460×C₈₉	C₂²	semidirect
33. #424×C₈₉	C₂²	semidirect
34. #423×C₈₉	C₂²	semidirect
35. #419×C₈₉	C₂²	semidirect
36. #418×C₈₉	C₂²	semidirect
37. #417×C₈₉	C₂²	semidirect
48. C₂²×Q₈×C₈₉	D₄	semidirect
215. #60424	C₈₉	direct (N × H)
221. C₂²×#137	C₂×C₈₉	semidirect
223. C₂×#519	C₂×C₈₉	semidirect
224. #3044	C₂×C₈₉	semidirect
225. #3043	C₂×C₈₉	semidirect
226. #3037	C₂×C₈₉	semidirect
227. #2905	C₂×C₈₉	semidirect
228. #2896	C₂×C₈₉	semidirect
229. C₈₉	#60424	direct (N × H)
234. C₂×#137	C₂²×C₈₉	semidirect
235. C₂²×Q₁₆	C₂²×C₈₉	semidirect
236. C₂²×SD₁₆	C₂²×C₈₉	semidirect
245. #519	C₂²×C₈₉	semidirect
247. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
251. #464	C₂²×C₈₉	semidirect
252. #462	C₂²×C₈₉	semidirect
253. #460	C₂²×C₈₉	semidirect
254. #424	C₂²×C₈₉	semidirect
255. #423	C₂²×C₈₉	semidirect
256. #419	C₂²×C₈₉	semidirect
257. #418	C₂²×C₈₉	semidirect
258. #417	C₂²×C₈₉	semidirect
269. C₂²×Q₈	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₈₉	2
C₈₉×#3449	2
C₂×#519×C₈₉	2
C₈₉×#3044	2
C₈₉×#3043	2
C₈₉×#3037	2
C₈₉×#2905	2
C₈₉×#2896	2
#60424	89

Subgroups — C89×#60424 #36438272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60424 #36438272