Subgroups — C₈₉×#60046 #36437894

Order 22784.

1898 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2805	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2724	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2683	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2599	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2586	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2573	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2477	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2470	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2406	C₂	1	2	yes	maximal
10	C₈₉×#2374	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2360	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2296	C₂	1	2	yes	maximal, complemented
14	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#123×C₈₉	C₂²	1	2	yes	—
16	C₂×#123×C₈₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×#117×C₈₉	C₂²	1	2	yes	—
20	C₂×#117×C₈₉	C₂²	1	2	yes	—
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
23	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
24	#400×C₈₉	C₂²	1	4	yes	—
25	#400×C₈₉	C₂²	1	4	yes	—
26	#398×C₈₉	C₂²	1	2	yes	—
27	#397×C₈₉	C₂²	1	4	yes	—
28	#397×C₈₉	C₂²	1	2	yes	—
29	#396×C₈₉	C₂²	1	4	yes	—
30	#395×C₈₉	C₂²	1	2	yes	—
31	#395×C₈₉	C₂²	1	4	yes	—
32	#394×C₈₉	C₂²	1	4	yes	—
33	#393×C₈₉	C₂²	1	2	yes	—
34	#391×C₈₉	C₂²	1	1	yes	characteristic
35	#391×C₈₉	C₂²	1	1	yes	characteristic
36	#391×C₈₉	C₂²	1	4	yes	—
37	#390×C₈₉	C₂²	1	1	yes	characteristic
38	#390×C₈₉	C₂²	1	1	yes	characteristic
39	#389×C₈₉	C₂²	1	2	yes	—
40	#389×C₈₉	C₂²	1	2	yes	—
41	#389×C₈₉	C₂²	1	2	yes	—
42	#389×C₈₉	C₂²	1	2	yes	—
43	#389×C₈₉	C₂²	1	4	yes	—
44	#389×C₈₉	C₂²	1	4	yes	—
45	#388×C₈₉	C₂²	1	4	yes	—
46	#388×C₈₉	C₂²	1	4	yes	—
47	#388×C₈₉	C₂²	1	4	yes	—
48	#387×C₈₉	C₂²	1	4	yes	—
49	#387×C₈₉	C₂²	1	4	yes	—
50	#387×C₈₉	C₂²	1	4	yes	—
51	#387×C₈₉	C₂²	1	4	yes	—
52	#387×C₈₉	C₂²	1	4	yes	—
53	#386×C₈₉	C₂²	1	4	yes	—
54	#386×C₈₉	C₂²	1	2	yes	—
55	#386×C₈₉	C₂²	1	2	yes	—
56	#385×C₈₉	C₂²	1	4	yes	—
57	#385×C₈₉	C₂²	1	4	yes	—
58	#385×C₈₉	C₂²	1	4	yes	—
59	#385×C₈₉	C₂²	1	4	yes	—
60	#383×C₈₉	C₂²	1	2	yes	—
61	#381×C₈₉	C₂²	1	2	yes	—
62	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
64	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
65	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
66	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
67	C₂×#41×C₈₉	—	2	4	no	—
68	C₂×#41×C₈₉	—	4	2	no	—
69	C₂×#41×C₈₉	—	4	2	no	—
70	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
71	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
78	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
79	#123×C₈₉	—	2	8	no	—
80	#123×C₈₉	—	4	4	no	—
81	C₂²⋊Q₈×C₈₉	—	2	16	no	—
82	C₄×Q₈×C₈₉	—	4	4	no	—
83	#117×C₈₉	—	2	8	no	—
84	#117×C₈₉	—	4	2	no	—
85	#117×C₈₉	—	4	4	no	—
86	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
109	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₈₉	—	4	2	no	—
111	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
113	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
118	#95×C₈₉	C₂³	1	4	yes	—
119	#95×C₈₉	C₂³	1	4	yes	—
120	#95×C₈₉	C₂³	1	4	yes	—
121	#95×C₈₉	C₂³	1	4	yes	—
122	#95×C₈₉	C₂³	1	4	yes	—
123	#95×C₈₉	C₂³	1	4	yes	—
124	#95×C₈₉	C₂³	1	4	yes	—
125	#95×C₈₉	C₂³	1	4	yes	—
126	#95×C₈₉	C₂³	1	4	yes	—
127	#95×C₈₉	C₂³	1	2	yes	—
128	#95×C₈₉	C₂³	1	2	yes	—
129	#95×C₈₉	C₂³	1	4	yes	—
130	#95×C₈₉	C₂³	1	4	yes	—
131	#95×C₈₉	C₂³	1	4	yes	—
132	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
133	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
134	#41×C₈₉	—	4	16	no	—
135	C₂×Q₈×C₈₉	—	2	8	no	—
136	C₂×Q₈×C₈₉	—	2	2	no	—
137	C₂×Q₈×C₈₉	—	4	2	no	—
138	C₂×Q₈×C₈₉	—	4	1	no	—
139	C₂×Q₈×C₈₉	—	4	1	no	—
140	C₂×D₄×C₈₉	—	2	4	no	—
141	C₂×D₄×C₈₉	—	2	4	no	—
142	C₂×D₄×C₈₉	—	4	1	no	—
143	C₂×D₄×C₈₉	—	4	1	no	—
144	C₂×D₄×C₈₉	—	4	2	no	—
145	C₂×D₄×C₈₉	#41	1	4	yes	—
146	C₂²×C₄×C₈₉	—	2	4	no	—
147	C₂²×C₄×C₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	4	no	—
149	C₂²×C₄×C₈₉	—	2	2	no	—
150	C₂²×C₄×C₈₉	—	2	2	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	4	no	—
153	C₂²×C₄×C₈₉	—	2	4	no	—
154	C₂²×C₄×C₈₉	—	2	8	no	—
155	C₂²×C₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	4	2	no	—
157	C₂²×C₄×C₈₉	—	4	2	no	—
158	C₂²×C₄×C₈₉	—	4	2	no	—
159	C₂²×C₄×C₈₉	—	4	2	no	—
160	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	8	no	—
173	C₄⋊C₄×C₈₉	—	2	8	no	—
174	C₄⋊C₄×C₈₉	—	2	8	no	—
175	C₄⋊C₄×C₈₉	—	2	8	no	—
176	C₄⋊C₄×C₈₉	—	2	8	no	—
177	C₄⋊C₄×C₈₉	—	4	4	no	—
178	C₄⋊C₄×C₈₉	—	4	2	no	—
179	C₄⋊C₄×C₈₉	—	4	2	no	—
180	C₄⋊C₄×C₈₉	—	4	1	no	—
181	C₄⋊C₄×C₈₉	—	4	1	no	—
182	C₄⋊C₄×C₈₉	—	4	2	no	—
183	C₄⋊C₄×C₈₉	—	4	4	no	—
184	C₄⋊C₄×C₈₉	#41	1	8	yes	complemented
185	C₂²⋊C₄×C₈₉	—	2	4	no	—
186	C₂²⋊C₄×C₈₉	—	2	8	no	—
187	C₂²⋊C₄×C₈₉	—	2	8	no	—
188	C₂²⋊C₄×C₈₉	—	2	8	no	—
189	C₂²⋊C₄×C₈₉	—	2	8	no	—
190	C₂²⋊C₄×C₈₉	—	2	8	no	—
191	C₂²⋊C₄×C₈₉	—	2	8	no	—
192	C₂²⋊C₄×C₈₉	—	4	2	no	—
193	C₂²⋊C₄×C₈₉	—	4	2	no	—
194	C₄²×C₈₉	—	2	8	no	—
195	C₄²×C₈₉	—	2	4	no	—
196	C₄²×C₈₉	—	4	1	no	—
197	C₄²×C₈₉	—	4	2	no	—
198	C₄²×C₈₉	—	4	1	no	—
199	C₄²×C₈₉	—	4	4	no	—
200	C₄²×C₈₉	—	4	4	no	—
201	C₂³×C₈₉	—	2	4	no	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	1	no	—
204	C₂³×C₈₉	—	2	1	no	—
205	C₂³×C₈₉	—	2	2	no	—
206	C₂³×C₈₉	—	2	2	no	—
207	C₂³×C₈₉	—	2	4	no	—
208	C₂³×C₈₉	—	2	2	no	—
209	C₂³×C₈₉	C₂×#41	1	4	yes	—
210	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
211	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
212	Q₈×C₈₉	—	4	8	no	—
213	Q₈×C₈₉	—	4	4	no	—
214	D₄×C₈₉	—	4	4	no	—
215	D₄×C₈₉	—	4	8	no	—
216	C₂×C₄×C₈₉	—	2	16	no	—
217	C₂×C₄×C₈₉	—	2	8	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	4	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	2	no	—
222	C₂×C₄×C₈₉	—	2	2	no	—
223	C₂×C₄×C₈₉	—	2	1	no	—
224	C₂×C₄×C₈₉	—	2	1	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	4	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	4	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	2	4	no	—
238	C₂×C₄×C₈₉	—	2	4	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	4	no	—
242	C₂×C₄×C₈₉	—	2	4	no	—
243	C₂×C₄×C₈₉	—	2	4	no	—
244	C₂×C₄×C₈₉	—	4	8	no	—
245	C₂×C₄×C₈₉	—	4	8	no	—
246	C₂×C₄×C₈₉	—	8	4	no	—
247	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
248	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
249	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
250	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
251	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
252	C₂²×C₈₉	—	2	8	no	—
253	C₂²×C₈₉	—	2	2	no	—
254	C₂²×C₈₉	—	2	4	no	—
255	C₂²×C₈₉	—	2	4	no	—
256	C₂²×C₈₉	—	4	2	no	—
257	C₂²×C₈₉	—	4	1	no	—
258	C₂²×C₈₉	—	4	2	no	—
259	C₂²×C₈₉	—	4	4	no	—
260	C₂²×C₈₉	—	4	1	no	—
261	C₂²×C₈₉	—	4	2	no	—
262	C₂²×C₈₉	C₂²×#41	1	2	yes	—
263	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
264	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
266	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
267	C₄×C₈₉	—	2	8	no	—
268	C₄×C₈₉	—	2	2	no	—
269	C₄×C₈₉	—	2	2	no	—
270	C₄×C₈₉	—	2	4	no	—
271	C₄×C₈₉	—	2	4	no	—
272	C₄×C₈₉	—	4	2	no	—
273	C₄×C₈₉	—	4	4	no	—
274	C₄×C₈₉	—	4	2	no	—
275	C₄×C₈₉	—	4	4	no	—
276	C₄×C₈₉	—	4	4	no	—
277	C₄×C₈₉	—	4	2	no	—
278	#60046	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
279	C₂×C₈₉	—	4	4	no	—
280	C₂×C₈₉	—	4	2	no	—
281	C₂×C₈₉	#3481	1	1	yes	characteristic
282	C₂×C₈₉	#3482	1	2	yes	—
283	C₂×C₈₉	#3490	1	1	yes	characteristic
284	C₂×C₈₉	#3492	1	2	yes	—
285	C₂×C₈₉	#3550	1	1	yes	characteristic
286	#2805	C₂×C₈₉	1	2	yes	complemented
287	#2724	C₂×C₈₉	1	1	yes	characteristic, complemented
288	#2683	C₂×C₈₉	1	1	yes	characteristic, complemented
289	#2599	C₂×C₈₉	1	2	yes	complemented
290	#2586	C₂×C₈₉	1	2	yes	complemented
291	#2573	C₂×C₈₉	1	4	yes	complemented
292	#2477	C₂×C₈₉	1	4	yes	complemented
293	#2470	C₂×C₈₉	1	4	yes	complemented
294	#2406	C₂×C₈₉	1	2	yes	—
295	#2374	C₂×C₈₉	1	2	yes	complemented
296	#2360	C₂×C₈₉	1	4	yes	complemented
297	#2297	C₂×C₈₉	1	1	yes	characteristic
298	#2296	C₂×C₈₉	1	2	yes	complemented
299	C₈₉	#60046	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
301	C₂×#123	C₂²×C₈₉	1	2	yes	—
302	C₂×#123	C₂²×C₈₉	1	2	yes	—
303	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
304	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
305	C₂×#117	C₂²×C₈₉	1	2	yes	—
306	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
307	C₂×#117	C₂²×C₈₉	1	2	yes	—
308	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
309	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
310	#400	C₂²×C₈₉	1	4	yes	—
311	#400	C₂²×C₈₉	1	4	yes	—
312	#398	C₂²×C₈₉	1	2	yes	—
313	#397	C₂²×C₈₉	1	4	yes	—
314	#397	C₂²×C₈₉	1	2	yes	—
315	#396	C₂²×C₈₉	1	4	yes	—
316	#395	C₂²×C₈₉	1	2	yes	—
317	#395	C₂²×C₈₉	1	4	yes	—
318	#394	C₂²×C₈₉	1	4	yes	—
319	#393	C₂²×C₈₉	1	2	yes	—
320	#391	C₂²×C₈₉	1	1	yes	characteristic
321	#391	C₂²×C₈₉	1	4	yes	—
322	#391	C₂²×C₈₉	1	1	yes	characteristic
323	#390	C₂²×C₈₉	1	1	yes	characteristic
324	#390	C₂²×C₈₉	1	1	yes	characteristic
325	#389	C₂²×C₈₉	1	2	yes	—
326	#389	C₂²×C₈₉	1	4	yes	—
327	#389	C₂²×C₈₉	1	2	yes	—
328	#389	C₂²×C₈₉	1	4	yes	—
329	#389	C₂²×C₈₉	1	2	yes	—
330	#389	C₂²×C₈₉	1	2	yes	—
331	#388	C₂²×C₈₉	1	4	yes	—
332	#388	C₂²×C₈₉	1	4	yes	—
333	#388	C₂²×C₈₉	1	4	yes	—
334	#387	C₂²×C₈₉	1	4	yes	—
335	#387	C₂²×C₈₉	1	4	yes	—
336	#387	C₂²×C₈₉	1	4	yes	—
337	#387	C₂²×C₈₉	1	4	yes	—
338	#387	C₂²×C₈₉	1	4	yes	—
339	#386	C₂²×C₈₉	1	2	yes	—
340	#386	C₂²×C₈₉	1	2	yes	—
341	#386	C₂²×C₈₉	1	4	yes	—
342	#385	C₂²×C₈₉	1	4	yes	—
343	#385	C₂²×C₈₉	1	4	yes	—
344	#385	C₂²×C₈₉	1	4	yes	—
345	#385	C₂²×C₈₉	1	4	yes	—
346	#383	C₂²×C₈₉	1	2	yes	—
347	#381	C₂²×C₈₉	1	2	yes	—
348	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
349	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
352	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
353	C₂×#41	—	2	4	no	—
354	C₂×#41	—	4	2	no	—
355	C₂×#41	—	4	2	no	—
356	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
357	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
360	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
361	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
364	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
365	#123	—	2	8	no	—
366	#123	—	4	4	no	—
367	C₂²⋊Q₈	—	2	16	no	—
368	C₄×Q₈	—	4	4	no	—
369	#117	—	2	8	no	—
370	#117	—	4	2	no	—
371	#117	—	4	4	no	—
372	C₂×C₄⋊C₄	—	4	4	no	—
373	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
374	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
379	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
381	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
386	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
387	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
396	C₂×C₄²	—	4	2	no	—
397	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
399	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
400	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
401	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
402	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
403	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
404	#95	C₂³×C₈₉	1	4	yes	—
405	#95	C₂³×C₈₉	1	4	yes	—
406	#95	C₂³×C₈₉	1	4	yes	—
407	#95	C₂³×C₈₉	1	4	yes	—
408	#95	C₂³×C₈₉	1	4	yes	—
409	#95	C₂³×C₈₉	1	4	yes	—
410	#95	C₂³×C₈₉	1	4	yes	—
411	#95	C₂³×C₈₉	1	4	yes	—
412	#95	C₂³×C₈₉	1	4	yes	—
413	#95	C₂³×C₈₉	1	2	yes	—
414	#95	C₂³×C₈₉	1	2	yes	—
415	#95	C₂³×C₈₉	1	4	yes	—
416	#95	C₂³×C₈₉	1	4	yes	—
417	#95	C₂³×C₈₉	1	4	yes	—
418	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
419	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
420	#41	—	4	16	no	—
421	C₂×Q₈	—	2	8	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	—	4	1	no	—
425	C₂×Q₈	—	4	1	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	2	no	—
431	C₂×D₄	#41×C₈₉	1	4	yes	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
447	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
449	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
453	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	8	no	—
459	C₄⋊C₄	—	2	8	no	—
460	C₄⋊C₄	—	2	8	no	—
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	4	4	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	4	4	no	—
470	C₄⋊C₄	#41×C₈₉	1	8	yes	complemented
471	C₂²⋊C₄	—	2	4	no	—
472	C₂²⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	4	2	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₄²	—	2	8	no	—
481	C₄²	—	2	4	no	—
482	C₄²	—	4	1	no	—
483	C₄²	—	4	2	no	—
484	C₄²	—	4	1	no	—
485	C₄²	—	4	4	no	—
486	C₄²	—	4	4	no	—
487	C₂³	—	2	4	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	2	no	—
495	C₂³	C₂×#41×C₈₉	1	4	yes	—
496	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
497	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
498	Q₈	—	4	8	no	—
499	Q₈	—	4	4	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	8	no	—
502	C₂×C₄	—	2	16	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	4	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	4	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	8	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	8	4	no	—
533	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
534	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
535	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
536	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
537	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
538	C₂²	—	2	8	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	1	no	—
547	C₂²	—	4	2	no	—
548	C₂²	C₂²×#41×C₈₉	1	2	yes	—
549	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
550	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
551	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
552	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
553	C₄	—	2	8	no	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	4	no	—
558	C₄	—	4	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	4	no	—
562	C₄	—	4	4	no	—
563	C₄	—	4	2	no	—
564	C₂	—	4	4	no	—
565	C₂	—	4	2	no	—
566	C₂	C₈₉×#3481	1	1	yes	characteristic
567	C₂	C₈₉×#3482	1	2	yes	—
568	C₂	C₈₉×#3490	1	1	yes	characteristic
569	C₂	C₈₉×#3492	1	2	yes	—
570	C₂	C₈₉×#3550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#41×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. C₈₉×#2805	C₂	semidirect
2. C₈₉×#2724	C₂	semidirect
3. C₈₉×#2683	C₂	semidirect
4. C₈₉×#2599	C₂	semidirect
5. C₈₉×#2586	C₂	semidirect
6. C₈₉×#2573	C₂	semidirect
7. C₈₉×#2477	C₂	semidirect
8. C₈₉×#2470	C₂	semidirect
10. C₈₉×#2374	C₂	semidirect
11. C₈₉×#2360	C₂	semidirect
13. C₈₉×#2296	C₂	semidirect
184. C₄⋊C₄×C₈₉	#41	semidirect
278. #60046	C₈₉	direct (N × H)
286. #2805	C₂×C₈₉	semidirect
287. #2724	C₂×C₈₉	semidirect
288. #2683	C₂×C₈₉	semidirect
289. #2599	C₂×C₈₉	semidirect
290. #2586	C₂×C₈₉	semidirect
291. #2573	C₂×C₈₉	semidirect
292. #2477	C₂×C₈₉	semidirect
293. #2470	C₂×C₈₉	semidirect
295. #2374	C₂×C₈₉	semidirect
296. #2360	C₂×C₈₉	semidirect
298. #2296	C₂×C₈₉	semidirect
299. C₈₉	#60046	direct (N × H)
470. C₄⋊C₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2805	2
C₈₉×#2724	2
C₈₉×#2683	2
C₈₉×#2599	2
C₈₉×#2586	2
C₈₉×#2573	2
C₈₉×#2477	2
C₈₉×#2470	2
C₈₉×#2406	2
C₈₉×#2374	2
C₈₉×#2360	2
C₈₉×#2297	2
C₈₉×#2296	2
#60046	89

Subgroups — C89×#60046 #36437894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60046 #36437894