Subgroups — C₈₉×#35180 #36413028

Order 22784.

2474 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2850	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2639	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2592	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2568	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2563	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2562	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2548	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2547	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2311	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	2	yes	—
14	#533×C₈₉	—	2	8	no	—
15	#532×C₈₉	—	2	8	no	—
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#125×C₈₉	C₂²	1	2	yes	—
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#124×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×#121×C₈₉	C₂²	1	2	yes	—
26	C₂×#121×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	#400×C₈₉	C₂²	1	8	yes	—
36	#397×C₈₉	C₂²	1	8	yes	—
37	#394×C₈₉	C₂²	1	8	yes	—
38	#393×C₈₉	C₂²	1	8	yes	—
39	#391×C₈₉	C₂²	1	8	yes	—
40	#391×C₈₉	C₂²	1	4	yes	—
41	#390×C₈₉	C₂²	1	4	yes	—
42	#390×C₈₉	C₂²	1	8	yes	—
43	#388×C₈₉	C₂²	1	16	yes	—
44	#386×C₈₉	C₂²	1	16	yes	—
45	#382×C₈₉	C₂²	1	4	yes	—
46	#380×C₈₉	C₂²	1	8	yes	—
47	#380×C₈₉	C₂²	1	8	yes	—
48	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₂×#95×C₈₉	C₂²	1	2	yes	—
53	C₂×#41×C₈₉	—	2	8	no	—
54	C₂×#41×C₈₉	—	2	16	no	—
55	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₈₉	—	2	4	no	—
68	C₄⋊Q₈×C₈₉	—	2	4	no	—
69	C₄⋊Q₈×C₈₉	—	2	4	no	—
70	#127×C₈₉	—	2	4	no	—
71	#125×C₈₉	—	2	8	no	—
72	#124×C₈₉	—	2	8	no	—
73	#124×C₈₉	—	4	8	no	—
74	C₂²⋊Q₈×C₈₉	—	2	8	no	—
75	C₂²⋊Q₈×C₈₉	—	2	8	no	—
76	#121×C₈₉	—	2	8	no	—
77	#121×C₈₉	—	2	8	no	—
78	C₄×Q₈×C₈₉	—	2	8	no	—
79	C₄×Q₈×C₈₉	—	2	8	no	—
80	C₄×D₄×C₈₉	—	2	8	no	—
81	C₄×D₄×C₈₉	—	2	8	no	—
82	#117×C₈₉	—	2	8	no	—
83	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
99	C₂×C₄²×C₈₉	—	4	4	no	—
100	C₂×C₄²×C₈₉	D₄	1	8	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	#95×C₈₉	C₂³	1	4	yes	—
109	#95×C₈₉	C₂³	1	4	yes	—
110	#95×C₈₉	C₂³	1	16	yes	—
111	#95×C₈₉	C₂³	1	16	yes	—
112	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
113	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
114	#41×C₈₉	—	4	32	no	—
115	C₂×Q₈×C₈₉	—	2	4	no	—
116	C₂×Q₈×C₈₉	—	2	4	no	—
117	C₂×Q₈×C₈₉	—	2	4	no	—
118	C₂×Q₈×C₈₉	—	2	8	no	—
119	C₂×Q₈×C₈₉	—	2	4	no	—
120	C₂×Q₈×C₈₉	—	2	4	no	—
121	C₂×Q₈×C₈₉	—	4	4	no	—
122	C₂×D₄×C₈₉	—	2	8	no	—
123	C₂×D₄×C₈₉	—	2	16	no	—
124	C₂×D₄×C₈₉	—	2	4	no	—
125	C₂×D₄×C₈₉	—	2	4	no	—
126	C₂×D₄×C₈₉	—	2	4	no	—
127	C₂×D₄×C₈₉	—	2	8	no	—
128	C₂×D₄×C₈₉	—	2	4	no	—
129	C₂×D₄×C₈₉	—	2	4	no	—
130	C₂×D₄×C₈₉	—	4	4	no	—
131	C₂²×C₄×C₈₉	—	2	2	no	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	C₂²×C₄×C₈₉	—	2	8	no	—
134	C₂²×C₄×C₈₉	—	2	8	no	—
135	C₂²×C₄×C₈₉	—	2	16	no	—
136	C₂²×C₄×C₈₉	—	4	4	no	—
137	C₂²×C₄×C₈₉	—	4	2	no	—
138	C₂²×C₄×C₈₉	—	4	4	no	—
139	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₈₉	#41	1	8	yes	—
143	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	—	2	4	no	—
155	C₄⋊C₄×C₈₉	—	2	4	no	—
156	C₄⋊C₄×C₈₉	—	2	4	no	—
157	C₄⋊C₄×C₈₉	—	2	8	no	—
158	C₄⋊C₄×C₈₉	—	2	8	no	—
159	C₄⋊C₄×C₈₉	—	2	4	no	—
160	C₄⋊C₄×C₈₉	—	2	4	no	—
161	C₄⋊C₄×C₈₉	—	2	8	no	—
162	C₄⋊C₄×C₈₉	—	2	8	no	—
163	C₂²⋊C₄×C₈₉	—	2	8	no	—
164	C₂²⋊C₄×C₈₉	—	2	8	no	—
165	C₂²⋊C₄×C₈₉	—	2	8	no	—
166	C₂²⋊C₄×C₈₉	—	4	16	no	—
167	C₂²⋊C₄×C₈₉	—	4	16	no	—
168	C₄²×C₈₉	—	2	8	no	—
169	C₄²×C₈₉	—	2	8	no	—
170	C₄²×C₈₉	—	4	4	no	—
171	C₄²×C₈₉	C₂×D₄	1	4	yes	—
172	C₄²×C₈₉	C₂×D₄	1	4	yes	—
173	C₄²×C₈₉	C₂×D₄	1	4	yes	—
174	C₄²×C₈₉	C₂×D₄	1	4	yes	—
175	C₂³×C₈₉	—	2	1	no	—
176	C₂³×C₈₉	—	2	1	no	—
177	C₂³×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	2	4	no	—
179	C₂³×C₈₉	—	2	8	no	—
180	C₂³×C₈₉	—	2	4	no	—
181	C₂³×C₈₉	—	2	4	no	—
182	C₂³×C₈₉	—	2	8	no	—
183	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
184	C₂³×C₈₉	C₂×#41	1	4	yes	—
185	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
186	Q₈×C₈₉	—	4	8	no	—
187	Q₈×C₈₉	—	4	8	no	—
188	Q₈×C₈₉	—	4	8	no	—
189	D₄×C₈₉	—	4	8	no	—
190	D₄×C₈₉	—	4	16	no	—
191	D₄×C₈₉	—	4	8	no	—
192	D₄×C₈₉	—	4	8	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	1	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	8	no	—
198	C₂×C₄×C₈₉	—	2	4	no	—
199	C₂×C₄×C₈₉	—	2	4	no	—
200	C₂×C₄×C₈₉	—	2	4	no	—
201	C₂×C₄×C₈₉	—	2	8	no	—
202	C₂×C₄×C₈₉	—	2	8	no	—
203	C₂×C₄×C₈₉	—	2	8	no	—
204	C₂×C₄×C₈₉	—	2	4	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	8	no	—
207	C₂×C₄×C₈₉	—	2	8	no	—
208	C₂×C₄×C₈₉	—	4	4	no	—
209	C₂×C₄×C₈₉	—	4	16	no	—
210	C₂×C₄×C₈₉	—	4	16	no	—
211	C₂×C₄×C₈₉	#124	1	16	yes	complemented
212	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
219	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
220	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
221	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
222	C₂²×C₈₉	—	2	2	no	—
223	C₂²×C₈₉	—	2	2	no	—
224	C₂²×C₈₉	—	2	4	no	—
225	C₂²×C₈₉	—	2	4	no	—
226	C₂²×C₈₉	—	4	4	no	—
227	C₂²×C₈₉	—	4	4	no	—
228	C₂²×C₈₉	—	4	4	no	—
229	C₂²×C₈₉	—	4	8	no	—
230	C₂²×C₈₉	—	4	8	no	—
231	C₂²×C₈₉	C₂×#124	1	4	yes	—
232	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
233	C₂²×C₈₉	C₂²×#41	1	2	yes	—
234	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
235	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
236	C₂²×C₈₉	#585	1	2	yes	—
237	C₄×C₈₉	—	2	2	no	—
238	C₄×C₈₉	—	2	2	no	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	4	4	no	—
241	C₄×C₈₉	—	4	4	no	—
242	C₄×C₈₉	—	4	4	no	—
243	C₄×C₈₉	—	4	8	no	—
244	C₄×C₈₉	C₂×#124	1	4	yes	—
245	C₄×C₈₉	C₂×#124	1	4	yes	—
246	C₄×C₈₉	#537	1	4	yes	—
247	#35180	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₈₉	—	2	4	no	—
249	C₂×C₈₉	—	8	4	no	—
250	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
251	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
252	C₂×C₈₉	#3449	1	1	yes	characteristic
253	C₂×C₈₉	#3506	1	2	yes	—
254	C₂×C₈₉	#3507	1	2	yes	—
255	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
256	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
257	#2850	C₂×C₈₉	1	4	yes	complemented
258	#2639	C₂×C₈₉	1	4	yes	complemented
259	#2592	C₂×C₈₉	1	4	yes	complemented
260	#2568	C₂×C₈₉	1	2	yes	complemented
261	#2563	C₂×C₈₉	1	2	yes	complemented
262	#2562	C₂×C₈₉	1	4	yes	complemented
263	#2548	C₂×C₈₉	1	2	yes	complemented
264	#2547	C₂×C₈₉	1	2	yes	complemented
265	#2311	C₂×C₈₉	1	4	yes	complemented
266	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
267	C₈₉	#35180	1	1	yes	characteristic, direct product factor, Sylow
268	C₂²×#41	C₂²×C₈₉	1	2	yes	—
269	#533	—	2	8	no	—
270	#532	—	2	8	no	—
271	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
274	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
275	C₂×#125	C₂²×C₈₉	1	2	yes	—
276	C₂×#124	C₂²×C₈₉	1	2	yes	—
277	C₂×#124	C₂²×C₈₉	1	4	yes	—
278	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
279	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
280	C₂×#121	C₂²×C₈₉	1	2	yes	—
281	C₂×#121	C₂²×C₈₉	1	2	yes	—
282	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
283	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
284	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
285	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
286	C₂×#117	C₂²×C₈₉	1	2	yes	—
287	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
288	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
289	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
290	#400	C₂²×C₈₉	1	8	yes	—
291	#397	C₂²×C₈₉	1	8	yes	—
292	#394	C₂²×C₈₉	1	8	yes	—
293	#393	C₂²×C₈₉	1	8	yes	—
294	#391	C₂²×C₈₉	1	8	yes	—
295	#391	C₂²×C₈₉	1	4	yes	—
296	#390	C₂²×C₈₉	1	4	yes	—
297	#390	C₂²×C₈₉	1	8	yes	—
298	#388	C₂²×C₈₉	1	16	yes	—
299	#386	C₂²×C₈₉	1	16	yes	—
300	#382	C₂²×C₈₉	1	4	yes	—
301	#380	C₂²×C₈₉	1	8	yes	—
302	#380	C₂²×C₈₉	1	8	yes	—
303	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
304	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
305	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
306	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
307	C₂×#95	C₂²×C₈₉	1	2	yes	—
308	C₂×#41	—	2	8	no	—
309	C₂×#41	—	2	16	no	—
310	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
311	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
312	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
313	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
314	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
315	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
316	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
318	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
320	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
322	C₄⋊Q₈	—	2	4	no	—
323	C₄⋊Q₈	—	2	4	no	—
324	C₄⋊Q₈	—	2	4	no	—
325	#127	—	2	4	no	—
326	#125	—	2	8	no	—
327	#124	—	2	8	no	—
328	#124	—	4	8	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	8	no	—
331	#121	—	2	8	no	—
332	#121	—	2	8	no	—
333	C₄×Q₈	—	2	8	no	—
334	C₄×Q₈	—	2	8	no	—
335	C₄×D₄	—	2	8	no	—
336	C₄×D₄	—	2	8	no	—
337	#117	—	2	8	no	—
338	C₂×C₄⋊C₄	—	2	8	no	—
339	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
354	C₂×C₄²	—	4	4	no	—
355	C₂×C₄²	D₄×C₈₉	1	8	yes	—
356	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
357	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
358	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
359	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
363	#95	C₂³×C₈₉	1	4	yes	—
364	#95	C₂³×C₈₉	1	4	yes	—
365	#95	C₂³×C₈₉	1	16	yes	—
366	#95	C₂³×C₈₉	1	16	yes	—
367	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
368	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
369	#41	—	4	32	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	4	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	8	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	2	4	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	2	16	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	4	no	—
394	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
397	C₂²×C₄	#41×C₈₉	1	8	yes	—
398	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
400	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
404	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	8	no	—
413	C₄⋊C₄	—	2	8	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	4	16	no	—
422	C₂²⋊C₄	—	4	16	no	—
423	C₄²	—	2	8	no	—
424	C₄²	—	2	8	no	—
425	C₄²	—	4	4	no	—
426	C₄²	C₂×D₄×C₈₉	1	4	yes	—
427	C₄²	C₂×D₄×C₈₉	1	4	yes	—
428	C₄²	C₂×D₄×C₈₉	1	4	yes	—
429	C₄²	C₂×D₄×C₈₉	1	4	yes	—
430	C₂³	—	2	1	no	—
431	C₂³	—	2	1	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	8	no	—
438	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
439	C₂³	C₂×#41×C₈₉	1	4	yes	—
440	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
441	Q₈	—	4	8	no	—
442	Q₈	—	4	8	no	—
443	Q₈	—	4	8	no	—
444	D₄	—	4	8	no	—
445	D₄	—	4	16	no	—
446	D₄	—	4	8	no	—
447	D₄	—	4	8	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	8	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	4	4	no	—
464	C₂×C₄	—	4	16	no	—
465	C₂×C₄	—	4	16	no	—
466	C₂×C₄	#124×C₈₉	1	16	yes	complemented
467	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
469	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
473	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
474	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
475	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
476	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	2	4	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	4	no	—
483	C₂²	—	4	4	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	8	no	—
486	C₂²	C₂×#124×C₈₉	1	4	yes	—
487	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
488	C₂²	C₂²×#41×C₈₉	1	2	yes	—
489	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
490	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
491	C₂²	#585×C₈₉	1	2	yes	—
492	C₄	—	2	2	no	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	—	4	8	no	—
499	C₄	C₂×#124×C₈₉	1	4	yes	—
500	C₄	C₂×#124×C₈₉	1	4	yes	—
501	C₄	#537×C₈₉	1	4	yes	—
502	C₂	—	2	4	no	—
503	C₂	—	8	4	no	—
504	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
505	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
506	C₂	C₈₉×#3449	1	1	yes	characteristic
507	C₂	C₈₉×#3506	1	2	yes	—
508	C₂	C₈₉×#3507	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#2850	C₂	semidirect
4. C₈₉×#2639	C₂	semidirect
5. C₈₉×#2592	C₂	semidirect
6. C₈₉×#2568	C₂	semidirect
7. C₈₉×#2563	C₂	semidirect
8. C₈₉×#2562	C₂	semidirect
9. C₈₉×#2548	C₂	semidirect
10. C₈₉×#2547	C₂	semidirect
11. C₈₉×#2311	C₂	semidirect
12. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
211. C₂×C₄×C₈₉	#124	semidirect
247. #35180	C₈₉	direct (N × H)
255. C₂×#533	C₂×C₈₉	semidirect
257. #2850	C₂×C₈₉	semidirect
258. #2639	C₂×C₈₉	semidirect
259. #2592	C₂×C₈₉	semidirect
260. #2568	C₂×C₈₉	semidirect
261. #2563	C₂×C₈₉	semidirect
262. #2562	C₂×C₈₉	semidirect
263. #2548	C₂×C₈₉	semidirect
264. #2547	C₂×C₈₉	semidirect
265. #2311	C₂×C₈₉	semidirect
266. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
267. C₈₉	#35180	direct (N × H)
466. C₂×C₄	#124×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#2850	2
C₈₉×#2639	2
C₈₉×#2592	2
C₈₉×#2568	2
C₈₉×#2563	2
C₈₉×#2562	2
C₈₉×#2548	2
C₈₉×#2547	2
C₈₉×#2311	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#35180	89

Subgroups — C89×#35180 #36413028

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35180 #36413028