Subgroups — C₈₉×#26090 #36403938

Order 22784.

750 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2354	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2094	C₂	1	2	yes	maximal
4	C₈₉×#2065	C₂	1	2	yes	maximal
5	C₈₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1948	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1920	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1844	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1802	C₂	1	1	yes	maximal, characteristic
11	C₄×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₈₉	—	2	1	no	—
13	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#117×C₈₉	—	2	1	no	—
15	C₂×#106×C₈₉	C₂²	1	2	yes	—
16	C₂×#106×C₈₉	C₂²	1	2	yes	—
17	C₂×#106×C₈₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
20	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
24	#398×C₈₉	—	2	2	no	—
25	#390×C₈₉	C₂²	1	2	yes	—
26	#389×C₈₉	—	2	1	no	—
27	#389×C₈₉	C₂²	1	2	yes	—
28	#388×C₈₉	—	2	2	no	—
29	#384×C₈₉	C₂²	1	1	yes	characteristic
30	#384×C₈₉	C₂²	1	2	yes	—
31	#384×C₈₉	C₂²	1	1	yes	characteristic
32	#380×C₈₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	#340×C₈₉	C₂²	1	2	yes	—
37	#340×C₈₉	C₂²	1	2	yes	—
38	#340×C₈₉	C₂²	1	1	yes	characteristic
39	#340×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	2	yes	—
41	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₈₉	—	2	1	no	—
43	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
46	#125×C₈₉	—	4	4	no	—
47	C₄×D₄×C₈₉	—	2	2	no	—
48	C₄×D₄×C₈₉	Q₈	1	4	yes	—
49	#117×C₈₉	—	4	4	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
67	C₂×C₄²×C₈₉	—	2	2	no	—
68	C₂×C₄²×C₈₉	—	2	1	no	—
69	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
71	#106×C₈₉	—	2	4	no	—
72	#106×C₈₉	—	4	2	no	—
73	#106×C₈₉	—	4	2	no	—
74	C₄⋊C₈×C₈₉	—	2	4	no	—
75	C₄⋊C₈×C₈₉	—	2	2	no	—
76	#102×C₈₉	—	2	2	no	—
77	#102×C₈₉	—	2	2	no	—
78	#102×C₈₉	—	4	2	no	—
79	C₄×C₈×C₈₉	—	2	2	no	—
80	#95×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	1	no	—
82	#95×C₈₉	—	2	2	no	—
83	#95×C₈₉	D₄	1	2	yes	—
84	C₂⁴×C₈₉	—	2	1	no	—
85	C₂×D₄×C₈₉	—	2	1	no	—
86	C₂×D₄×C₈₉	—	2	1	no	—
87	C₂×D₄×C₈₉	—	2	1	no	—
88	C₂×D₄×C₈₉	—	2	1	no	—
89	C₂×D₄×C₈₉	—	2	1	no	—
90	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₈₉	—	2	1	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	2	1	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	2	1	no	—
96	C₂²×C₄×C₈₉	—	2	2	no	—
97	C₂²×C₄×C₈₉	—	4	2	no	—
98	C₂²×C₄×C₈₉	—	4	2	no	—
99	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
104	C₂×C₈×C₈₉	—	2	1	no	—
105	C₂×C₈×C₈₉	—	2	1	no	—
106	C₂×C₈×C₈₉	—	2	1	no	—
107	C₂×C₈×C₈₉	—	2	1	no	—
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	2	no	—
111	C₂×C₈×C₈₉	#41	1	2	yes	—
112	C₂×C₈×C₈₉	#41	1	2	yes	—
113	C₄⋊C₄×C₈₉	—	2	2	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	—	2	1	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	—	2	2	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	—	2	1	no	—
121	C₄⋊C₄×C₈₉	—	2	2	no	—
122	C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₄⋊C₄×C₈₉	—	4	4	no	—
124	C₄⋊C₄×C₈₉	—	4	4	no	—
125	C₄⋊C₄×C₈₉	—	4	2	no	—
126	C₄⋊C₄×C₈₉	—	4	2	no	—
127	C₄⋊C₄×C₈₉	—	8	1	no	—
128	C₄⋊C₄×C₈₉	—	8	2	no	—
129	C₄⋊C₄×C₈₉	—	8	1	no	—
130	C₄⋊C₄×C₈₉	SD₁₆	1	4	yes	—
131	C₄⋊C₄×C₈₉	C₂×Q₈	1	2	yes	—
132	C₂²⋊C₄×C₈₉	—	2	4	no	—
133	C₂²⋊C₄×C₈₉	—	4	4	no	—
134	C₂²⋊C₄×C₈₉	—	8	2	no	—
135	C₄²×C₈₉	—	2	2	no	—
136	C₄²×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	—	4	4	no	—
138	C₄²×C₈₉	—	4	2	no	—
139	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
140	C₄²×C₈₉	#41	1	2	yes	—
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	—	4	1	no	—
143	C₂³×C₈₉	—	4	1	no	—
144	C₂³×C₈₉	—	4	1	no	—
145	C₂³×C₈₉	—	4	1	no	—
146	C₂³×C₈₉	—	4	1	no	—
147	C₂³×C₈₉	—	4	1	no	—
148	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
149	D₄×C₈₉	—	2	2	no	—
150	D₄×C₈₉	—	2	2	no	—
151	D₄×C₈₉	—	4	1	no	—
152	D₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	4	1	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	8	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₈₉	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
181	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₈₉	—	2	2	no	—
188	C₈×C₈₉	—	2	2	no	—
189	C₈×C₈₉	—	4	2	no	—
190	C₂²×C₈₉	—	4	2	no	—
191	C₂²×C₈₉	—	4	2	no	—
192	C₂²×C₈₉	—	4	2	no	—
193	C₂²×C₈₉	—	8	1	no	—
194	C₂²×C₈₉	—	8	1	no	—
195	C₂²×C₈₉	—	8	1	no	—
196	C₂²×C₈₉	—	8	1	no	—
197	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
198	C₂²×C₈₉	#547	1	1	yes	characteristic
199	C₂²×C₈₉	#550	1	1	yes	characteristic
200	C₂²×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
201	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₂²×C₈₉	#577	1	1	yes	characteristic
203	C₂²×C₈₉	#577	1	1	yes	characteristic
204	C₄×C₈₉	—	2	4	no	—
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	4	2	no	—
207	C₄×C₈₉	—	4	2	no	—
208	C₄×C₈₉	—	8	1	no	—
209	C₄×C₈₉	—	8	2	no	—
210	C₄×C₈₉	—	8	1	no	—
211	C₄×C₈₉	—	8	2	no	—
212	C₄×C₈₉	#476	1	4	yes	—
213	C₄×C₈₉	#533	1	1	yes	characteristic
214	C₄×C₈₉	#544	1	1	yes	characteristic
215	C₄×C₈₉	#552	1	1	yes	characteristic
216	C₄×C₈₉	#553	1	1	yes	characteristic
217	#26090	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂×C₈₉	—	8	2	no	—
219	C₂×C₈₉	#2441	1	1	yes	characteristic
220	C₂×C₈₉	C₂×#476	1	1	yes	characteristic
221	C₂×C₈₉	#3084	1	1	yes	characteristic
222	C₂×C₈₉	#3335	1	1	yes	characteristic
223	C₂×C₈₉	#3354	1	1	yes	characteristic
224	C₂×C₈₉	#3392	1	1	yes	characteristic
225	C₂×C₈₉	#3397	1	1	yes	characteristic
226	#2552	C₂×C₈₉	1	1	yes	characteristic, complemented
227	#2354	C₂×C₈₉	1	1	yes	characteristic
228	#2094	C₂×C₈₉	1	2	yes	—
229	#2065	C₂×C₈₉	1	2	yes	—
230	#1948	C₂×C₈₉	1	2	yes	complemented
231	#1948	C₂×C₈₉	1	1	yes	characteristic, complemented
232	#1939	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#1920	C₂×C₈₉	1	2	yes	complemented
234	#1844	C₂×C₈₉	1	1	yes	characteristic, complemented
235	#1802	C₂×C₈₉	1	1	yes	characteristic
236	C₄×#102	C₂×C₈₉	1	1	yes	characteristic
237	C₈₉	#26090	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#125	—	2	1	no	—
239	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	C₂×#106	C₂²×C₈₉	1	2	yes	—
242	C₂×#106	C₂²×C₈₉	1	2	yes	—
243	C₂×#106	C₂²×C₈₉	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
246	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
247	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
248	C₂×#102	C₂²×C₈₉	1	2	yes	—
249	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
250	#398	—	2	2	no	—
251	#390	C₂²×C₈₉	1	2	yes	—
252	#389	—	2	1	no	—
253	#389	C₂²×C₈₉	1	2	yes	—
254	#388	—	2	2	no	—
255	#384	C₂²×C₈₉	1	1	yes	characteristic
256	#384	C₂²×C₈₉	1	2	yes	—
257	#384	C₂²×C₈₉	1	1	yes	characteristic
258	#380	—	2	1	no	—
259	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
262	#340	C₂²×C₈₉	1	2	yes	—
263	#340	C₂²×C₈₉	1	2	yes	—
264	#340	C₂²×C₈₉	1	1	yes	characteristic
265	#340	C₂²×C₈₉	1	1	yes	characteristic
266	#336	C₂²×C₈₉	1	2	yes	—
267	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
270	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
272	#125	—	4	4	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	Q₈×C₈₉	1	4	yes	—
275	#117	—	4	4	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	2	no	—
293	C₂×C₄²	—	2	2	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
297	#106	—	2	4	no	—
298	#106	—	4	2	no	—
299	#106	—	4	2	no	—
300	C₄⋊C₈	—	2	4	no	—
301	C₄⋊C₈	—	2	2	no	—
302	#102	—	2	2	no	—
303	#102	—	2	2	no	—
304	#102	—	4	2	no	—
305	C₄×C₈	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	1	no	—
308	#95	—	2	2	no	—
309	#95	D₄×C₈₉	1	2	yes	—
310	C₂⁴	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂×Q₈×C₈₉	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
328	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	#41×C₈₉	1	2	yes	—
338	C₂×C₈	#41×C₈₉	1	2	yes	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	4	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	8	1	no	—
354	C₄⋊C₄	—	8	2	no	—
355	C₄⋊C₄	—	8	1	no	—
356	C₄⋊C₄	SD₁₆×C₈₉	1	4	yes	—
357	C₄⋊C₄	C₂×Q₈×C₈₉	1	2	yes	—
358	C₂²⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
366	C₄²	#41×C₈₉	1	2	yes	—
367	C₂³	—	2	2	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	4	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
403	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
404	C₂×C₄	C₂×SD₁₆×C₈₉	1	4	yes	—
405	C₂×C₄	C₂×SD₁₆×C₈₉	1	2	yes	—
406	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
407	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
408	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
411	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
412	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
424	C₂²	#547×C₈₉	1	1	yes	characteristic
425	C₂²	#550×C₈₉	1	1	yes	characteristic
426	C₂²	C₂²×SD₁₆×C₈₉	1	1	yes	characteristic
427	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
428	C₂²	#577×C₈₉	1	1	yes	characteristic
429	C₂²	#577×C₈₉	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	2	no	—
438	C₄	#476×C₈₉	1	4	yes	—
439	C₄	#533×C₈₉	1	1	yes	characteristic
440	C₄	#544×C₈₉	1	1	yes	characteristic
441	C₄	#552×C₈₉	1	1	yes	characteristic
442	C₄	#553×C₈₉	1	1	yes	characteristic
443	C₂	—	8	2	no	—
444	C₂	C₈₉×#2441	1	1	yes	characteristic
445	C₂	C₂×#476×C₈₉	1	1	yes	characteristic
446	C₂	C₈₉×#3084	1	1	yes	characteristic
447	C₂	C₈₉×#3335	1	1	yes	characteristic
448	C₂	C₈₉×#3354	1	1	yes	characteristic
449	C₂	C₈₉×#3392	1	1	yes	characteristic
450	C₂	C₈₉×#3397	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2552	C₂	semidirect
5. C₈₉×#1948	C₂	semidirect
6. C₈₉×#1948	C₂	semidirect
7. C₈₉×#1939	C₂	semidirect
8. C₈₉×#1920	C₂	semidirect
9. C₈₉×#1844	C₂	semidirect
217. #26090	C₈₉	direct (N × H)
226. #2552	C₂×C₈₉	semidirect
230. #1948	C₂×C₈₉	semidirect
231. #1948	C₂×C₈₉	semidirect
232. #1939	C₂×C₈₉	semidirect
233. #1920	C₂×C₈₉	semidirect
234. #1844	C₂×C₈₉	semidirect
237. C₈₉	#26090	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2552	2
C₈₉×#2354	2
C₈₉×#2094	2
C₈₉×#2065	2
C₈₉×#1948	2
C₈₉×#1939	2
C₈₉×#1920	2
C₈₉×#1844	2
C₈₉×#1802	2
C₄×#102×C₈₉	2
#26090	89

Subgroups — C89×#26090 #36403938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26090 #36403938