Subgroups — C₈₉×#35515 #36413363

Order 22784.

2634 conjugacy classes of subgroups.

The subgroup lattice has 538 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×#518×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2580	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2538	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2454	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2452	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2437	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	#533×C₈₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
16	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
19	#518×C₈₉	—	2	8	no	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
21	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#399×C₈₉	C₂²	1	8	yes	complemented
32	#396×C₈₉	C₂²	1	8	yes	complemented
33	#396×C₈₉	C₂²	1	8	yes	complemented
34	#393×C₈₉	C₂²	1	8	yes	complemented
35	#390×C₈₉	C₂²	1	2	yes	—
36	#390×C₈₉	C₂²	1	4	yes	—
37	#390×C₈₉	C₂²	1	2	yes	—
38	#390×C₈₉	C₂²	1	4	yes	—
39	#390×C₈₉	C₂²	1	2	yes	—
40	#390×C₈₉	C₂²	1	2	yes	—
41	#389×C₈₉	C₂²	1	2	yes	complemented
42	#389×C₈₉	C₂²	1	2	yes	complemented
43	#389×C₈₉	C₂²	1	4	yes	complemented
44	#389×C₈₉	C₂²	1	4	yes	complemented
45	#389×C₈₉	C₂²	1	4	yes	complemented
46	#385×C₈₉	C₂²	1	4	yes	—
47	#385×C₈₉	C₂²	1	4	yes	—
48	#385×C₈₉	C₂²	1	8	yes	complemented
49	#385×C₈₉	C₂²	1	8	yes	complemented
50	#384×C₈₉	C₂²	1	2	yes	complemented
51	#382×C₈₉	C₂²	1	2	yes	complemented
52	#380×C₈₉	C₂²	1	4	yes	—
53	#380×C₈₉	C₂²	1	8	yes	complemented
54	#379×C₈₉	C₂²	1	4	yes	—
55	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
56	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
57	C₂⁵×C₈₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₈₉	—	2	4	no	—
60	C₂²×D₄×C₈₉	—	2	4	no	—
61	C₂²×D₄×C₈₉	Q₈	1	8	yes	complemented
62	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₈₉	—	2	8	no	—
69	#125×C₈₉	—	2	8	no	—
70	C₂²⋊Q₈×C₈₉	—	2	16	no	—
71	C₂²⋊Q₈×C₈₉	—	4	16	no	—
72	C₄×Q₈×C₈₉	—	2	16	no	—
73	C₄×D₄×C₈₉	—	2	16	no	—
74	C₄×D₄×C₈₉	—	2	16	no	—
75	#117×C₈₉	—	2	4	no	—
76	#117×C₈₉	—	2	4	no	—
77	#117×C₈₉	—	2	4	no	—
78	#117×C₈₉	D₄	1	8	yes	—
79	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	8	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
95	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
105	C₂×C₄²×C₈₉	—	2	4	no	—
106	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
113	#95×C₈₉	C₂³	1	4	yes	—
114	#95×C₈₉	C₂³	1	4	yes	—
115	#95×C₈₉	C₂³	1	8	yes	—
116	#95×C₈₉	C₂³	1	8	yes	—
117	C₂⁴×C₈₉	—	2	4	no	—
118	C₂⁴×C₈₉	—	2	4	no	—
119	C₂⁴×C₈₉	—	4	4	no	—
120	C₂⁴×C₈₉	—	4	4	no	—
121	C₂⁴×C₈₉	C₂×Q₈	1	8	yes	—
122	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
123	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₂×Q₈×C₈₉	—	2	8	no	—
125	C₂×Q₈×C₈₉	—	2	8	no	—
126	C₂×Q₈×C₈₉	—	4	4	no	—
127	C₂×D₄×C₈₉	—	2	32	no	—
128	C₂×D₄×C₈₉	—	2	4	no	—
129	C₂×D₄×C₈₉	—	2	4	no	—
130	C₂×D₄×C₈₉	—	2	4	no	—
131	C₂×D₄×C₈₉	—	2	4	no	—
132	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
133	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
134	C₂²×C₄×C₈₉	—	2	4	no	—
135	C₂²×C₄×C₈₉	—	2	4	no	—
136	C₂²×C₄×C₈₉	—	2	4	no	—
137	C₂²×C₄×C₈₉	—	2	16	no	—
138	C₂²×C₄×C₈₉	—	4	2	no	—
139	C₂²×C₄×C₈₉	—	4	4	no	—
140	C₂²×C₄×C₈₉	—	4	8	no	—
141	C₂²×C₄×C₈₉	—	4	8	no	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
144	C₂²×C₄×C₈₉	#41	1	4	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	8	no	—
160	C₄⋊C₄×C₈₉	—	2	4	no	—
161	C₄⋊C₄×C₈₉	—	2	4	no	—
162	C₄⋊C₄×C₈₉	—	2	2	no	—
163	C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₄⋊C₄×C₈₉	—	2	8	no	—
165	C₄⋊C₄×C₈₉	—	4	4	no	—
166	C₄⋊C₄×C₈₉	—	4	8	no	—
167	C₄⋊C₄×C₈₉	—	4	8	no	—
168	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
169	C₂²⋊C₄×C₈₉	—	2	4	no	—
170	C₂²⋊C₄×C₈₉	—	2	4	no	—
171	C₂²⋊C₄×C₈₉	—	2	4	no	—
172	C₂²⋊C₄×C₈₉	—	2	16	no	—
173	C₂²⋊C₄×C₈₉	—	2	16	no	—
174	C₂²⋊C₄×C₈₉	—	4	8	no	—
175	C₂²⋊C₄×C₈₉	—	4	8	no	—
176	C₂²⋊C₄×C₈₉	—	4	8	no	—
177	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
178	C₄²×C₈₉	—	2	4	no	—
179	C₄²×C₈₉	—	2	2	no	—
180	C₄²×C₈₉	—	2	2	no	—
181	C₄²×C₈₉	—	2	4	no	—
182	C₄²×C₈₉	—	2	4	no	—
183	C₄²×C₈₉	—	2	4	no	—
184	C₄²×C₈₉	C₂×D₄	1	8	yes	—
185	C₂³×C₈₉	—	2	2	no	—
186	C₂³×C₈₉	—	2	2	no	—
187	C₂³×C₈₉	—	2	4	no	—
188	C₂³×C₈₉	—	2	4	no	—
189	C₂³×C₈₉	—	2	8	no	—
190	C₂³×C₈₉	—	2	8	no	—
191	C₂³×C₈₉	—	2	16	no	—
192	C₂³×C₈₉	—	4	16	no	—
193	C₂³×C₈₉	—	8	8	no	—
194	C₂³×C₈₉	—	8	4	no	—
195	C₂³×C₈₉	—	8	4	no	—
196	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₈₉	C₂²×Q₈	1	8	yes	—
198	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
199	C₂³×C₈₉	C₂×#41	1	2	yes	—
200	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
201	Q₈×C₈₉	—	4	16	no	—
202	D₄×C₈₉	—	2	16	no	—
203	D₄×C₈₉	—	2	16	no	—
204	C₂×C₄×C₈₉	—	2	2	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	2	4	no	—
210	C₂×C₄×C₈₉	—	2	4	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	4	no	—
214	C₂×C₄×C₈₉	—	2	8	no	—
215	C₂×C₄×C₈₉	—	2	2	no	—
216	C₂×C₄×C₈₉	—	2	4	no	—
217	C₂×C₄×C₈₉	—	2	4	no	—
218	C₂×C₄×C₈₉	—	2	4	no	—
219	C₂×C₄×C₈₉	—	2	4	no	—
220	C₂×C₄×C₈₉	—	2	4	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	2	4	no	—
223	C₂×C₄×C₈₉	—	4	8	no	—
224	C₂×C₄×C₈₉	—	8	16	no	—
225	C₂×C₄×C₈₉	—	8	4	no	—
226	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	complemented
227	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
228	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
231	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
232	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
233	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
234	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
235	C₂²×C₈₉	—	2	4	no	—
236	C₂²×C₈₉	—	2	4	no	—
237	C₂²×C₈₉	—	2	2	no	—
238	C₂²×C₈₉	—	2	2	no	—
239	C₂²×C₈₉	—	2	8	no	—
240	C₂²×C₈₉	—	2	16	no	—
241	C₂²×C₈₉	—	4	8	no	—
242	C₂²×C₈₉	—	4	4	no	—
243	C₂²×C₈₉	—	4	4	no	—
244	C₂²×C₈₉	—	8	16	no	—
245	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
246	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
247	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
248	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
249	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
250	C₂²×C₈₉	#585	1	2	yes	—
251	C₄×C₈₉	—	2	4	no	—
252	C₄×C₈₉	—	2	8	no	—
253	C₄×C₈₉	—	4	2	no	—
254	C₄×C₈₉	—	4	4	no	—
255	C₄×C₈₉	—	4	4	no	—
256	C₄×C₈₉	—	4	2	no	—
257	C₄×C₈₉	—	4	4	no	—
258	C₄×C₈₉	—	4	2	no	—
259	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
260	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
261	#35515	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂×C₈₉	—	2	4	no	—
263	C₂×C₈₉	—	4	8	no	—
264	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₈₉	#3488	1	2	yes	—
266	C₂×C₈₉	#3501	1	2	yes	—
267	C₂×C₈₉	#3508	1	1	yes	characteristic
268	C₂×C₈₉	#3510	1	1	yes	characteristic
269	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
270	C₂×#518	C₂×C₈₉	1	1	yes	characteristic
271	#2580	C₂×C₈₉	1	4	yes	complemented
272	#2538	C₂×C₈₉	1	4	yes	complemented
273	#2454	C₂×C₈₉	1	4	yes	complemented
274	#2452	C₂×C₈₉	1	4	yes	complemented
275	#2437	C₂×C₈₉	1	8	yes	complemented
276	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
277	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
278	#2309	C₂×C₈₉	1	1	yes	characteristic
279	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
280	C₂×#390	C₂×C₈₉	1	1	yes	characteristic
281	C₈₉	#35515	1	1	yes	characteristic, direct product factor, Sylow
282	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
283	#533	—	2	8	no	—
284	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
285	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
286	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
288	#518	—	2	8	no	—
289	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
290	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
291	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
292	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
293	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
294	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
295	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
297	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
298	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
299	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
300	#399	C₂²×C₈₉	1	8	yes	complemented
301	#396	C₂²×C₈₉	1	8	yes	complemented
302	#396	C₂²×C₈₉	1	8	yes	complemented
303	#393	C₂²×C₈₉	1	8	yes	complemented
304	#390	C₂²×C₈₉	1	2	yes	—
305	#390	C₂²×C₈₉	1	4	yes	—
306	#390	C₂²×C₈₉	1	2	yes	—
307	#390	C₂²×C₈₉	1	4	yes	—
308	#390	C₂²×C₈₉	1	2	yes	—
309	#390	C₂²×C₈₉	1	2	yes	—
310	#389	C₂²×C₈₉	1	4	yes	complemented
311	#389	C₂²×C₈₉	1	4	yes	complemented
312	#389	C₂²×C₈₉	1	4	yes	complemented
313	#389	C₂²×C₈₉	1	2	yes	complemented
314	#389	C₂²×C₈₉	1	2	yes	complemented
315	#385	C₂²×C₈₉	1	4	yes	—
316	#385	C₂²×C₈₉	1	4	yes	—
317	#385	C₂²×C₈₉	1	8	yes	complemented
318	#385	C₂²×C₈₉	1	8	yes	complemented
319	#384	C₂²×C₈₉	1	2	yes	complemented
320	#382	C₂²×C₈₉	1	2	yes	complemented
321	#380	C₂²×C₈₉	1	4	yes	—
322	#380	C₂²×C₈₉	1	8	yes	complemented
323	#379	C₂²×C₈₉	1	4	yes	—
324	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
325	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
326	C₂⁵	C₂³×C₈₉	1	2	yes	—
327	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	—	2	4	no	—
330	C₂²×D₄	Q₈×C₈₉	1	8	yes	complemented
331	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
332	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
333	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
334	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
335	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
336	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
337	C₄⋊Q₈	—	2	8	no	—
338	#125	—	2	8	no	—
339	C₂²⋊Q₈	—	2	16	no	—
340	C₂²⋊Q₈	—	4	16	no	—
341	C₄×Q₈	—	2	16	no	—
342	C₄×D₄	—	2	16	no	—
343	C₄×D₄	—	2	16	no	—
344	#117	—	2	4	no	—
345	#117	—	2	4	no	—
346	#117	—	2	4	no	—
347	#117	D₄×C₈₉	1	8	yes	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
356	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
357	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
358	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
359	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
360	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
361	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
362	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	16	no	—
364	C₂×C₂²⋊C₄	—	4	8	no	—
365	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
372	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
373	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
374	C₂×C₄²	—	2	4	no	—
375	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
376	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
377	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
378	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
379	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
380	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
382	#95	C₂³×C₈₉	1	4	yes	—
383	#95	C₂³×C₈₉	1	4	yes	—
384	#95	C₂³×C₈₉	1	8	yes	—
385	#95	C₂³×C₈₉	1	8	yes	—
386	C₂⁴	—	2	4	no	—
387	C₂⁴	—	2	4	no	—
388	C₂⁴	—	4	4	no	—
389	C₂⁴	—	4	4	no	—
390	C₂⁴	C₂×Q₈×C₈₉	1	8	yes	—
391	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
392	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	8	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×D₄	—	2	32	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
402	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	16	no	—
407	C₂²×C₄	—	4	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	8	no	—
411	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
412	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
413	C₂²×C₄	#41×C₈₉	1	4	yes	—
414	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
416	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
423	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	8	no	—
427	C₄⋊C₄	—	2	8	no	—
428	C₄⋊C₄	—	2	8	no	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	4	8	no	—
435	C₄⋊C₄	—	4	8	no	—
436	C₄⋊C₄	—	4	4	no	—
437	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	16	no	—
442	C₂²⋊C₄	—	2	16	no	—
443	C₂²⋊C₄	—	4	8	no	—
444	C₂²⋊C₄	—	4	8	no	—
445	C₂²⋊C₄	—	4	8	no	—
446	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	—	2	4	no	—
451	C₄²	—	2	4	no	—
452	C₄²	—	2	4	no	—
453	C₄²	C₂×D₄×C₈₉	1	8	yes	—
454	C₂³	—	2	2	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	4	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	2	8	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	16	no	—
461	C₂³	—	4	16	no	—
462	C₂³	—	8	8	no	—
463	C₂³	—	8	4	no	—
464	C₂³	—	8	4	no	—
465	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
466	C₂³	C₂²×Q₈×C₈₉	1	8	yes	—
467	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
468	C₂³	C₂×#41×C₈₉	1	2	yes	—
469	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
470	Q₈	—	4	16	no	—
471	D₄	—	2	16	no	—
472	D₄	—	2	16	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	8	16	no	—
494	C₂×C₄	—	8	4	no	—
495	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	complemented
496	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
497	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
499	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
500	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
501	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
502	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
503	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
504	C₂²	—	2	4	no	—
505	C₂²	—	2	4	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	8	no	—
509	C₂²	—	2	16	no	—
510	C₂²	—	4	8	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	8	16	no	—
514	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
515	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
516	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
517	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
518	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
519	C₂²	#585×C₈₉	1	2	yes	—
520	C₄	—	2	4	no	—
521	C₄	—	2	8	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
529	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
530	C₂	—	2	4	no	—
531	C₂	—	4	8	no	—
532	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
533	C₂	C₈₉×#3488	1	2	yes	—
534	C₂	C₈₉×#3501	1	2	yes	—
535	C₂	C₈₉×#3508	1	1	yes	characteristic
536	C₂	C₈₉×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
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×#2580	C₂	semidirect
4. C₈₉×#2538	C₂	semidirect
5. C₈₉×#2454	C₂	semidirect
6. C₈₉×#2452	C₂	semidirect
7. C₈₉×#2437	C₂	semidirect
8. C₈₉×#2317	C₂	semidirect
9. C₈₉×#2316	C₂	semidirect
11. C₈₉×#2296	C₂	semidirect
15. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
16. C₂×#125×C₈₉	C₂²	semidirect
18. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
20. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
31. #399×C₈₉	C₂²	semidirect
32. #396×C₈₉	C₂²	semidirect
33. #396×C₈₉	C₂²	semidirect
34. #393×C₈₉	C₂²	semidirect
41. #389×C₈₉	C₂²	semidirect
42. #389×C₈₉	C₂²	semidirect
43. #389×C₈₉	C₂²	semidirect
44. #389×C₈₉	C₂²	semidirect
45. #389×C₈₉	C₂²	semidirect
48. #385×C₈₉	C₂²	semidirect
49. #385×C₈₉	C₂²	semidirect
50. #384×C₈₉	C₂²	semidirect
51. #382×C₈₉	C₂²	semidirect
53. #380×C₈₉	C₂²	semidirect
55. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
56. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
61. C₂²×D₄×C₈₉	Q₈	semidirect
226. C₂×C₄×C₈₉	C₂²⋊Q₈	semidirect
261. #35515	C₈₉	direct (N × H)
269. C₂×#533	C₂×C₈₉	semidirect
271. #2580	C₂×C₈₉	semidirect
272. #2538	C₂×C₈₉	semidirect
273. #2454	C₂×C₈₉	semidirect
274. #2452	C₂×C₈₉	semidirect
275. #2437	C₂×C₈₉	semidirect
276. #2317	C₂×C₈₉	semidirect
277. #2316	C₂×C₈₉	semidirect
279. #2296	C₂×C₈₉	semidirect
281. C₈₉	#35515	direct (N × H)
284. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
285. C₂×#125	C₂²×C₈₉	semidirect
287. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
289. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
300. #399	C₂²×C₈₉	semidirect
301. #396	C₂²×C₈₉	semidirect
302. #396	C₂²×C₈₉	semidirect
303. #393	C₂²×C₈₉	semidirect
310. #389	C₂²×C₈₉	semidirect
311. #389	C₂²×C₈₉	semidirect
312. #389	C₂²×C₈₉	semidirect
313. #389	C₂²×C₈₉	semidirect
314. #389	C₂²×C₈₉	semidirect
317. #385	C₂²×C₈₉	semidirect
318. #385	C₂²×C₈₉	semidirect
319. #384	C₂²×C₈₉	semidirect
320. #382	C₂²×C₈₉	semidirect
322. #380	C₂²×C₈₉	semidirect
324. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
325. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
330. C₂²×D₄	Q₈×C₈₉	semidirect
495. C₂×C₄	C₂²⋊Q₈×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×#518×C₈₉	2
C₈₉×#2580	2
C₈₉×#2538	2
C₈₉×#2454	2
C₈₉×#2452	2
C₈₉×#2437	2
C₈₉×#2317	2
C₈₉×#2316	2
C₈₉×#2309	2
C₈₉×#2296	2
C₂×#390×C₈₉	2
#35515	89

Subgroups — C89×#35515 #36413363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35515 #36413363