Subgroups — C₈₉×#23612 #36401460

Order 22784.

1214 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#418×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2067	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2065	C₂	1	4	yes	maximal, complemented
9	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
17	#427×C₈₉	—	2	4	no	—
18	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
19	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
20	#424×C₈₉	—	2	4	no	—
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
23	#418×C₈₉	—	2	4	no	—
24	C₂×#102×C₈₉	—	2	4	no	—
25	C₂×#102×C₈₉	C₂²	1	2	yes	—
26	C₂×#102×C₈₉	C₂²	1	4	yes	—
27	C₂×#102×C₈₉	C₂²	1	2	yes	—
28	#390×C₈₉	—	2	1	no	—
29	#390×C₈₉	—	2	1	no	—
30	#390×C₈₉	C₂²	1	4	yes	—
31	#389×C₈₉	C₂²	1	4	yes	complemented
32	#385×C₈₉	—	2	2	no	—
33	#384×C₈₉	—	2	1	no	—
34	#382×C₈₉	—	2	1	no	—
35	#379×C₈₉	—	2	2	no	—
36	#340×C₈₉	C₂²	1	4	yes	complemented
37	C₂⁵×C₈₉	—	2	1	no	—
38	C₂²×D₄×C₈₉	—	2	2	no	—
39	C₂²×D₄×C₈₉	—	2	2	no	—
40	C₂²×D₄×C₈₉	—	2	1	no	—
41	C₂²×D₄×C₈₉	—	2	2	no	—
42	C₂²×D₄×C₈₉	—	2	2	no	—
43	C₂²×D₄×C₈₉	—	2	2	no	—
44	C₂²×D₄×C₈₉	Q₈	1	4	yes	—
45	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₈₉	—	2	1	no	—
47	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₈₉	—	2	2	no	—
49	C₂×M₁₆×C₈₉	—	2	2	no	—
50	C₂×M₁₆×C₈₉	—	2	2	no	—
51	C₂²×C₈×C₈₉	—	2	2	no	—
52	C₂²×C₈×C₈₉	—	2	2	no	—
53	C₂²×C₈×C₈₉	D₄	1	4	yes	—
54	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
57	#117×C₈₉	—	2	2	no	—
58	#117×C₈₉	—	2	2	no	—
59	#117×C₈₉	—	2	2	no	—
60	#117×C₈₉	—	2	2	no	—
61	#117×C₈₉	—	2	2	no	—
62	#117×C₈₉	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
77	C₂×C₄²×C₈₉	—	2	1	no	—
78	C₂×C₄²×C₈₉	—	2	1	no	—
79	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
80	#107×C₈₉	—	2	4	no	—
81	#106×C₈₉	—	2	4	no	—
82	C₄⋊C₈×C₈₉	—	2	4	no	—
83	C₄⋊C₈×C₈₉	—	2	4	no	—
84	#102×C₈₉	—	2	4	no	—
85	#102×C₈₉	—	2	4	no	—
86	#102×C₈₉	—	2	8	no	—
87	#95×C₈₉	—	2	4	no	—
88	C₂⁴×C₈₉	—	2	2	no	—
89	C₂⁴×C₈₉	—	2	4	no	—
90	C₂⁴×C₈₉	—	4	2	no	—
91	C₂⁴×C₈₉	—	4	2	no	—
92	C₂⁴×C₈₉	—	8	2	no	—
93	C₂⁴×C₈₉	—	8	2	no	—
94	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂×D₄×C₈₉	—	2	8	no	—
96	C₂×D₄×C₈₉	—	2	8	no	—
97	C₂×D₄×C₈₉	—	2	4	no	—
98	C₂×D₄×C₈₉	—	2	2	no	—
99	C₂×D₄×C₈₉	—	2	2	no	—
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	4	4	no	—
104	C₂×D₄×C₈₉	—	4	2	no	—
105	C₂×D₄×C₈₉	—	4	2	no	—
106	C₂×D₄×C₈₉	—	4	4	no	—
107	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₈₉	—	2	2	no	—
109	C₂²×C₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	4	2	no	—
112	C₂²×C₄×C₈₉	—	8	2	no	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₈₉	#41	1	2	yes	—
120	C₂²×C₄×C₈₉	#41	1	2	yes	—
121	C₂²×C₄×C₈₉	#41	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₈₉	—	4	4	no	—
124	C₂×C₈×C₈₉	—	2	8	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
133	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
134	C₄⋊C₄×C₈₉	—	2	2	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	2	no	—
137	C₄⋊C₄×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	2	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	4	2	no	—
142	C₄⋊C₄×C₈₉	—	8	4	no	—
143	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
144	C₂²⋊C₄×C₈₉	—	2	4	no	—
145	C₂²⋊C₄×C₈₉	—	2	4	no	—
146	C₂²⋊C₄×C₈₉	—	4	2	no	—
147	C₂²⋊C₄×C₈₉	—	8	4	no	—
148	C₂²⋊C₄×C₈₉	—	8	4	no	—
149	C₄²×C₈₉	—	2	4	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	4	2	no	—
153	C₂³×C₈₉	—	2	2	no	—
154	C₂³×C₈₉	—	2	2	no	—
155	C₂³×C₈₉	—	2	4	no	—
156	C₂³×C₈₉	—	4	2	no	—
157	C₂³×C₈₉	—	4	2	no	—
158	C₂³×C₈₉	—	4	4	no	—
159	C₂³×C₈₉	—	4	4	no	—
160	C₂³×C₈₉	—	4	8	no	—
161	C₂³×C₈₉	—	8	8	no	—
162	C₂³×C₈₉	—	8	8	no	—
163	C₂³×C₈₉	—	8	4	no	—
164	C₂³×C₈₉	—	8	4	no	—
165	C₂³×C₈₉	#121	1	2	yes	—
166	C₂³×C₈₉	#121	1	2	yes	—
167	C₂³×C₈₉	C₂²⋊Q₈	1	2	yes	—
168	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	D₄×C₈₉	—	2	4	no	—
170	D₄×C₈₉	—	2	4	no	—
171	D₄×C₈₉	—	4	2	no	—
172	D₄×C₈₉	—	4	2	no	—
173	D₄×C₈₉	—	4	8	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	4	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	—	4	2	no	—
184	C₂×C₄×C₈₉	—	4	4	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	8	4	no	—
187	C₂×C₄×C₈₉	#121	1	4	yes	—
188	C₂×C₄×C₈₉	#121	1	2	yes	—
189	C₂×C₄×C₈₉	#121	1	2	yes	—
190	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
191	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
192	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
193	C₂×C₄×C₈₉	#126	1	4	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₈×C₈₉	—	2	2	no	—
201	C₈×C₈₉	—	2	2	no	—
202	C₈×C₈₉	—	4	2	no	—
203	C₂²×C₈₉	—	2	4	no	—
204	C₂²×C₈₉	—	2	4	no	—
205	C₂²×C₈₉	—	2	2	no	—
206	C₂²×C₈₉	—	2	2	no	—
207	C₂²×C₈₉	—	4	8	no	—
208	C₂²×C₈₉	—	4	4	no	—
209	C₂²×C₈₉	—	8	16	no	—
210	C₂²×C₈₉	—	8	4	no	—
211	C₂²×C₈₉	—	8	2	no	—
212	C₂²×C₈₉	—	8	2	no	—
213	C₂²×C₈₉	#396	1	4	yes	—
214	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
215	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
216	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
217	C₂²×C₈₉	#576	1	2	yes	—
218	C₂²×C₈₉	#577	1	2	yes	—
219	C₄×C₈₉	—	4	4	no	—
220	C₄×C₈₉	—	4	2	no	—
221	C₄×C₈₉	—	4	2	no	—
222	C₄×C₈₉	—	8	2	no	—
223	C₄×C₈₉	—	8	2	no	—
224	C₄×C₈₉	#396	1	4	yes	—
225	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
226	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₄×C₈₉	C₂×#126	1	1	yes	characteristic
229	#23612	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₈₉	—	2	4	no	—
231	C₂×C₈₉	—	8	4	no	—
232	C₂×C₈₉	C₂×#396	1	1	yes	characteristic
233	C₂×C₈₉	#3045	1	2	yes	—
234	C₂×C₈₉	#3057	1	1	yes	characteristic
235	C₂×C₈₉	#3058	1	1	yes	characteristic
236	C₂×C₈₉	#3081	1	2	yes	—
237	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
238	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
239	C₂×#418	C₂×C₈₉	1	1	yes	characteristic
240	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic
241	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
242	#2309	C₂×C₈₉	1	1	yes	characteristic
243	#2067	C₂×C₈₉	1	4	yes	complemented
244	#2065	C₂×C₈₉	1	4	yes	complemented
245	#1736	C₂×C₈₉	1	1	yes	characteristic, complemented
246	C₈₉	#23612	1	1	yes	characteristic, direct product factor, Sylow
247	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
254	#427	—	2	4	no	—
255	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
256	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
257	#424	—	2	4	no	—
258	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
259	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
260	#418	—	2	4	no	—
261	C₂×#102	—	2	4	no	—
262	C₂×#102	C₂²×C₈₉	1	2	yes	—
263	C₂×#102	C₂²×C₈₉	1	4	yes	—
264	C₂×#102	C₂²×C₈₉	1	2	yes	—
265	#390	—	2	1	no	—
266	#390	—	2	1	no	—
267	#390	C₂²×C₈₉	1	4	yes	—
268	#389	C₂²×C₈₉	1	4	yes	complemented
269	#385	—	2	2	no	—
270	#384	—	2	1	no	—
271	#382	—	2	1	no	—
272	#379	—	2	2	no	—
273	#340	C₂²×C₈₉	1	4	yes	complemented
274	C₂⁵	—	2	1	no	—
275	C₂²×D₄	—	2	2	no	—
276	C₂²×D₄	—	2	2	no	—
277	C₂²×D₄	—	2	1	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	Q₈×C₈₉	1	4	yes	—
282	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
283	C₂³×C₄	—	2	1	no	—
284	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂²×C₈	—	2	2	no	—
289	C₂²×C₈	—	2	2	no	—
290	C₂²×C₈	D₄×C₈₉	1	4	yes	—
291	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
292	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	2	no	—
299	#117	D₄×C₈₉	1	4	yes	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	4	no	—
304	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
305	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
306	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
317	#107	—	2	4	no	—
318	#106	—	2	4	no	—
319	C₄⋊C₈	—	2	4	no	—
320	C₄⋊C₈	—	2	4	no	—
321	#102	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	—	2	8	no	—
324	#95	—	2	4	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	4	2	no	—
328	C₂⁴	—	4	2	no	—
329	C₂⁴	—	8	2	no	—
330	C₂⁴	—	8	2	no	—
331	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	2	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	—	4	4	no	—
344	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	8	2	no	—
350	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
355	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
356	C₂²×C₄	#41×C₈₉	1	2	yes	—
357	C₂²×C₄	#41×C₈₉	1	2	yes	—
358	C₂²×C₄	#41×C₈₉	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
360	M₁₆	—	4	4	no	—
361	C₂×C₈	—	2	8	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	8	4	no	—
380	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	2	no	—
384	C₂²⋊C₄	—	8	4	no	—
385	C₂²⋊C₄	—	8	4	no	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	4	2	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	4	8	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	4	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	8	8	no	—
399	C₂³	—	8	8	no	—
400	C₂³	—	8	4	no	—
401	C₂³	—	8	4	no	—
402	C₂³	#121×C₈₉	1	2	yes	—
403	C₂³	#121×C₈₉	1	2	yes	—
404	C₂³	C₂²⋊Q₈×C₈₉	1	2	yes	—
405	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	8	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	#121×C₈₉	1	2	yes	—
425	C₂×C₄	#121×C₈₉	1	2	yes	—
426	C₂×C₄	#121×C₈₉	1	4	yes	—
427	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
428	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
429	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
430	C₂×C₄	#126×C₈₉	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
437	C₈	—	2	2	no	—
438	C₈	—	2	2	no	—
439	C₈	—	4	2	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	4	8	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	8	16	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	#396×C₈₉	1	4	yes	—
451	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
452	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
453	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
454	C₂²	#576×C₈₉	1	2	yes	—
455	C₂²	#577×C₈₉	1	2	yes	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	2	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	2	no	—
461	C₄	#396×C₈₉	1	4	yes	—
462	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
463	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
464	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
465	C₄	C₂×#126×C₈₉	1	1	yes	characteristic
466	C₂	—	2	4	no	—
467	C₂	—	8	4	no	—
468	C₂	C₂×#396×C₈₉	1	1	yes	characteristic
469	C₂	C₈₉×#3045	1	2	yes	—
470	C₂	C₈₉×#3057	1	1	yes	characteristic
471	C₂	C₈₉×#3058	1	1	yes	characteristic
472	C₂	C₈₉×#3081	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#427×C₈₉	C₂	semidirect
2. C₂×#424×C₈₉	C₂	semidirect
5. C₈₉×#2317	C₂	semidirect
7. C₈₉×#2067	C₂	semidirect
8. C₈₉×#2065	C₂	semidirect
9. C₈₉×#1736	C₂	semidirect
18. C₂×#107×C₈₉	C₂²	semidirect
19. C₂×#106×C₈₉	C₂²	semidirect
21. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
22. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
31. #389×C₈₉	C₂²	semidirect
36. #340×C₈₉	C₂²	semidirect
229. #23612	C₈₉	direct (N × H)
237. C₂×#427	C₂×C₈₉	semidirect
238. C₂×#424	C₂×C₈₉	semidirect
241. #2317	C₂×C₈₉	semidirect
243. #2067	C₂×C₈₉	semidirect
244. #2065	C₂×C₈₉	semidirect
245. #1736	C₂×C₈₉	semidirect
246. C₈₉	#23612	direct (N × H)
255. C₂×#107	C₂²×C₈₉	semidirect
256. C₂×#106	C₂²×C₈₉	semidirect
258. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
259. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
268. #389	C₂²×C₈₉	semidirect
273. #340	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×#427×C₈₉	2
C₂×#424×C₈₉	2
C₂×#418×C₈₉	2
C₂²×#102×C₈₉	2
C₈₉×#2317	2
C₈₉×#2309	2
C₈₉×#2067	2
C₈₉×#2065	2
C₈₉×#1736	2
#23612	89

Subgroups — C89×#23612 #36401460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23612 #36401460