Subgroups — C₈₉×#36545 #36414393

Order 22784.

2304 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#557×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2851	C₂	1	2	yes	maximal
5	C₈₉×#2584	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2582	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2581	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2473	C₂	1	4	yes	maximal
10	C₈₉×#2462	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2446	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2434	C₂	1	2	yes	maximal
13	C₈₉×#2365	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2360	C₂	1	2	yes	maximal
15	C₈₉×#2355	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂²⋊Q₈×C₈₉	C₂	1	2	yes	maximal
18	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	#557×C₈₉	—	2	8	no	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×#125×C₈₉	C₂²	1	2	yes	—
24	C₂×#125×C₈₉	C₂²	1	4	yes	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
39	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
41	#400×C₈₉	C₂²	1	4	yes	—
42	#398×C₈₉	C₂²	1	4	yes	—
43	#398×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	4	yes	—
45	#395×C₈₉	C₂²	1	4	yes	—
46	#395×C₈₉	C₂²	1	4	yes	—
47	#391×C₈₉	C₂²	1	1	yes	characteristic
48	#391×C₈₉	C₂²	1	2	yes	—
49	#391×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	2	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#391×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	1	yes	characteristic
54	#389×C₈₉	C₂²	1	2	yes	—
55	#389×C₈₉	C₂²	1	2	yes	—
56	#389×C₈₉	C₂²	1	2	yes	—
57	#389×C₈₉	C₂²	1	2	yes	—
58	#389×C₈₉	C₂²	1	2	yes	—
59	#389×C₈₉	C₂²	1	4	yes	—
60	#389×C₈₉	C₂²	1	4	yes	—
61	#389×C₈₉	C₂²	1	2	yes	—
62	#387×C₈₉	C₂²	1	4	yes	—
63	#387×C₈₉	C₂²	1	2	yes	—
64	#387×C₈₉	C₂²	1	4	yes	—
65	#387×C₈₉	C₂²	1	4	yes	—
66	#387×C₈₉	C₂²	1	4	yes	—
67	#387×C₈₉	C₂²	1	4	yes	—
68	#387×C₈₉	C₂²	1	4	yes	—
69	#385×C₈₉	C₂²	1	4	yes	—
70	#385×C₈₉	C₂²	1	2	yes	—
71	#385×C₈₉	C₂²	1	4	yes	—
72	#385×C₈₉	C₂²	1	4	yes	—
73	#384×C₈₉	C₂²	1	1	yes	characteristic
74	#382×C₈₉	C₂²	1	2	yes	—
75	#380×C₈₉	C₂²	1	1	yes	characteristic
76	#380×C₈₉	C₂²	1	2	yes	—
77	#380×C₈₉	C₂²	1	2	yes	—
78	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
79	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
80	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
81	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
82	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
85	C₂²×Q₈×C₈₉	—	2	4	no	—
86	C₂²×Q₈×C₈₉	—	2	4	no	—
87	C₂²×Q₈×C₈₉	—	2	4	no	—
88	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₉	—	2	8	no	—
99	C₄⋊Q₈×C₈₉	—	2	8	no	—
100	C₄⋊Q₈×C₈₉	—	2	4	no	—
101	#125×C₈₉	—	2	16	no	—
102	#125×C₈₉	—	2	8	no	—
103	C₂²⋊Q₈×C₈₉	—	2	8	no	—
104	C₂²⋊Q₈×C₈₉	Q₈	1	8	yes	complemented
105	C₄×Q₈×C₈₉	—	2	4	no	—
106	C₄×Q₈×C₈₉	—	2	4	no	—
107	C₄×Q₈×C₈₉	—	2	8	no	—
108	C₄×Q₈×C₈₉	—	2	8	no	—
109	C₄×Q₈×C₈₉	—	2	8	no	—
110	C₄×Q₈×C₈₉	—	2	4	no	—
111	C₄×Q₈×C₈₉	—	2	8	no	—
112	C₄×Q₈×C₈₉	—	2	4	no	—
113	C₄×Q₈×C₈₉	D₄	1	8	yes	—
114	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
115	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₈₉	—	2	8	no	—
145	C₂×C₄²×C₈₉	—	2	4	no	—
146	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
147	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
151	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
155	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
156	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
157	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
158	#95×C₈₉	C₂³	1	2	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	#95×C₈₉	C₂³	1	2	yes	—
161	#95×C₈₉	C₂³	1	4	yes	—
162	#95×C₈₉	C₂³	1	2	yes	—
163	#95×C₈₉	C₂³	1	4	yes	—
164	#95×C₈₉	C₂³	1	4	yes	—
165	#95×C₈₉	C₂³	1	2	yes	—
166	#95×C₈₉	C₂³	1	4	yes	—
167	#95×C₈₉	C₂³	1	2	yes	—
168	#95×C₈₉	C₂³	1	4	yes	—
169	#95×C₈₉	C₂³	1	4	yes	—
170	#95×C₈₉	C₂³	1	4	yes	—
171	#95×C₈₉	C₂³	1	4	yes	—
172	#95×C₈₉	C₂³	1	4	yes	—
173	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₈₉	—	2	32	no	—
175	C₂×Q₈×C₈₉	—	2	2	no	—
176	C₂×Q₈×C₈₉	—	2	4	no	—
177	C₂×Q₈×C₈₉	—	2	2	no	—
178	C₂×Q₈×C₈₉	—	2	4	no	—
179	C₂×Q₈×C₈₉	—	2	4	no	—
180	C₂×Q₈×C₈₉	—	2	4	no	—
181	C₂×Q₈×C₈₉	—	2	2	no	—
182	C₂×Q₈×C₈₉	—	2	2	no	—
183	C₂×Q₈×C₈₉	—	2	2	no	—
184	C₂×Q₈×C₈₉	—	2	4	no	—
185	C₂×Q₈×C₈₉	—	2	4	no	—
186	C₂×Q₈×C₈₉	—	2	2	no	—
187	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
188	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	complemented
189	C₂×Q₈×C₈₉	#41	1	4	yes	—
190	C₂²×C₄×C₈₉	—	2	4	no	—
191	C₂²×C₄×C₈₉	—	2	2	no	—
192	C₂²×C₄×C₈₉	—	2	4	no	—
193	C₂²×C₄×C₈₉	—	2	2	no	—
194	C₂²×C₄×C₈₉	—	2	4	no	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	2	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	4	no	—
200	C₂²×C₄×C₈₉	—	2	2	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	1	no	—
203	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
204	C₂²×C₄×C₈₉	#41	1	4	yes	—
205	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
209	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
214	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	4	no	—
224	C₄⋊C₄×C₈₉	—	2	4	no	—
225	C₄⋊C₄×C₈₉	—	2	2	no	—
226	C₄⋊C₄×C₈₉	—	2	4	no	—
227	C₄⋊C₄×C₈₉	—	2	2	no	—
228	C₄⋊C₄×C₈₉	—	2	8	no	—
229	C₄⋊C₄×C₈₉	—	2	8	no	—
230	C₄⋊C₄×C₈₉	—	2	4	no	—
231	C₄⋊C₄×C₈₉	—	2	8	no	—
232	C₄⋊C₄×C₈₉	—	2	4	no	—
233	C₄⋊C₄×C₈₉	—	2	4	no	—
234	C₄⋊C₄×C₈₉	—	2	8	no	—
235	C₄⋊C₄×C₈₉	—	2	8	no	—
236	C₄⋊C₄×C₈₉	—	2	8	no	—
237	C₄⋊C₄×C₈₉	—	2	2	no	—
238	C₄⋊C₄×C₈₉	—	2	4	no	—
239	C₄⋊C₄×C₈₉	—	4	2	no	—
240	C₄⋊C₄×C₈₉	—	4	2	no	—
241	C₄⋊C₄×C₈₉	—	4	4	no	—
242	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
243	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
244	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	complemented
245	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	complemented
246	C₂²⋊C₄×C₈₉	—	2	8	no	—
247	C₂²⋊C₄×C₈₉	—	2	4	no	—
248	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
249	C₄²×C₈₉	—	2	4	no	—
250	C₄²×C₈₉	—	2	2	no	—
251	C₄²×C₈₉	—	2	4	no	—
252	C₄²×C₈₉	—	2	2	no	—
253	C₄²×C₈₉	—	2	4	no	—
254	C₄²×C₈₉	—	2	2	no	—
255	C₄²×C₈₉	—	2	8	no	—
256	C₄²×C₈₉	—	2	4	no	—
257	C₄²×C₈₉	—	2	4	no	—
258	C₄²×C₈₉	—	4	4	no	—
259	C₄²×C₈₉	C₂×D₄	1	8	yes	—
260	C₄²×C₈₉	C₂×D₄	1	4	yes	—
261	C₂³×C₈₉	—	2	1	no	—
262	C₂³×C₈₉	—	2	1	no	—
263	C₂³×C₈₉	—	2	1	no	—
264	C₂³×C₈₉	—	2	1	no	—
265	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
266	C₂³×C₈₉	C₂×#41	1	2	yes	—
267	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
268	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
269	Q₈×C₈₉	—	2	16	no	—
270	Q₈×C₈₉	—	2	8	no	—
271	Q₈×C₈₉	—	2	8	no	—
272	Q₈×C₈₉	—	2	8	no	—
273	Q₈×C₈₉	—	4	8	no	—
274	C₂×C₄×C₈₉	—	2	16	no	—
275	C₂×C₄×C₈₉	—	2	1	no	—
276	C₂×C₄×C₈₉	—	2	2	no	—
277	C₂×C₄×C₈₉	—	2	2	no	—
278	C₂×C₄×C₈₉	—	2	1	no	—
279	C₂×C₄×C₈₉	—	2	2	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	2	no	—
282	C₂×C₄×C₈₉	—	2	2	no	—
283	C₂×C₄×C₈₉	—	2	1	no	—
284	C₂×C₄×C₈₉	—	2	1	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	2	1	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	2	no	—
290	C₂×C₄×C₈₉	—	2	1	no	—
291	C₂×C₄×C₈₉	—	2	8	no	—
292	C₂×C₄×C₈₉	—	2	8	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	1	no	—
295	C₂×C₄×C₈₉	—	2	2	no	—
296	C₂×C₄×C₈₉	—	2	4	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	4	no	—
299	C₂×C₄×C₈₉	—	2	4	no	—
300	C₂×C₄×C₈₉	—	2	4	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	4	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	1	no	—
307	C₂×C₄×C₈₉	—	2	4	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	4	8	no	—
312	C₂×C₄×C₈₉	—	4	4	no	—
313	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
314	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
317	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
318	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
319	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
320	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
321	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
322	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
323	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
324	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
325	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
326	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
327	C₂²×C₈₉	—	2	2	no	—
328	C₂²×C₈₉	—	2	2	no	—
329	C₂²×C₈₉	—	2	2	no	—
330	C₂²×C₈₉	—	2	2	no	—
331	C₂²×C₈₉	—	2	2	no	—
332	C₂²×C₈₉	—	2	2	no	—
333	C₂²×C₈₉	#557	1	4	yes	complemented
334	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
335	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
336	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
337	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
338	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
340	C₂²×C₈₉	#585	1	1	yes	characteristic
341	C₄×C₈₉	—	2	4	no	—
342	C₄×C₈₉	—	2	4	no	—
343	C₄×C₈₉	—	2	2	no	—
344	C₄×C₈₉	—	2	2	no	—
345	C₄×C₈₉	—	2	4	no	—
346	C₄×C₈₉	—	2	4	no	—
347	C₄×C₈₉	—	2	4	no	—
348	C₄×C₈₉	—	2	2	no	—
349	C₄×C₈₉	—	4	4	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	2	no	—
352	C₄×C₈₉	—	4	1	no	—
353	C₄×C₈₉	—	4	4	no	—
354	C₄×C₈₉	—	4	2	no	—
355	C₄×C₈₉	#525	1	4	yes	—
356	C₄×C₈₉	D₄×Q₈	1	4	yes	—
357	#36545	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
358	C₂×C₈₉	—	2	4	no	—
359	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
360	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
361	C₂×C₈₉	C₂×#557	1	1	yes	characteristic
362	C₂×C₈₉	Q₈×#41	1	1	yes	characteristic
363	C₂×C₈₉	#3489	1	1	yes	characteristic
364	C₂×C₈₉	#3507	1	1	yes	characteristic
365	C₂×C₈₉	#3523	1	1	yes	characteristic
366	C₂×#557	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
368	#2857	C₂×C₈₉	1	1	yes	characteristic
369	#2851	C₂×C₈₉	1	2	yes	—
370	#2584	C₂×C₈₉	1	2	yes	complemented
371	#2582	C₂×C₈₉	1	1	yes	characteristic, complemented
372	#2581	C₂×C₈₉	1	2	yes	complemented
373	#2546	C₂×C₈₉	1	1	yes	characteristic, complemented
374	#2473	C₂×C₈₉	1	4	yes	—
375	#2462	C₂×C₈₉	1	4	yes	complemented
376	#2446	C₂×C₈₉	1	2	yes	complemented
377	#2434	C₂×C₈₉	1	2	yes	—
378	#2365	C₂×C₈₉	1	2	yes	complemented
379	#2360	C₂×C₈₉	1	2	yes	—
380	#2355	C₂×C₈₉	1	1	yes	characteristic, complemented
381	C₄×C₂²⋊Q₈	C₂×C₈₉	1	2	yes	—
382	C₄×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
383	C₈₉	#36545	1	1	yes	characteristic, direct product factor, Sylow
384	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
385	#557	—	2	8	no	—
386	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
387	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
388	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
389	C₂×#125	C₂²×C₈₉	1	2	yes	—
390	C₂×#125	C₂²×C₈₉	1	4	yes	—
391	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
392	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
393	C₂×C₄×Q₈	—	2	8	no	—
394	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
395	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
396	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
397	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
398	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
399	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
400	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
401	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
402	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
403	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
404	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
405	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
406	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
407	#400	C₂²×C₈₉	1	4	yes	—
408	#398	C₂²×C₈₉	1	4	yes	—
409	#398	C₂²×C₈₉	1	4	yes	—
410	#398	C₂²×C₈₉	1	4	yes	—
411	#395	C₂²×C₈₉	1	4	yes	—
412	#395	C₂²×C₈₉	1	4	yes	—
413	#391	C₂²×C₈₉	1	1	yes	characteristic
414	#391	C₂²×C₈₉	1	2	yes	—
415	#391	C₂²×C₈₉	1	2	yes	—
416	#391	C₂²×C₈₉	1	2	yes	—
417	#391	C₂²×C₈₉	1	2	yes	—
418	#391	C₂²×C₈₉	1	2	yes	—
419	#389	C₂²×C₈₉	1	2	yes	—
420	#389	C₂²×C₈₉	1	2	yes	—
421	#389	C₂²×C₈₉	1	2	yes	—
422	#389	C₂²×C₈₉	1	2	yes	—
423	#389	C₂²×C₈₉	1	1	yes	characteristic
424	#389	C₂²×C₈₉	1	4	yes	—
425	#389	C₂²×C₈₉	1	4	yes	—
426	#389	C₂²×C₈₉	1	2	yes	—
427	#389	C₂²×C₈₉	1	2	yes	—
428	#387	C₂²×C₈₉	1	4	yes	—
429	#387	C₂²×C₈₉	1	4	yes	—
430	#387	C₂²×C₈₉	1	4	yes	—
431	#387	C₂²×C₈₉	1	4	yes	—
432	#387	C₂²×C₈₉	1	4	yes	—
433	#387	C₂²×C₈₉	1	4	yes	—
434	#387	C₂²×C₈₉	1	2	yes	—
435	#385	C₂²×C₈₉	1	4	yes	—
436	#385	C₂²×C₈₉	1	4	yes	—
437	#385	C₂²×C₈₉	1	4	yes	—
438	#385	C₂²×C₈₉	1	2	yes	—
439	#384	C₂²×C₈₉	1	1	yes	characteristic
440	#382	C₂²×C₈₉	1	2	yes	—
441	#380	C₂²×C₈₉	1	1	yes	characteristic
442	#380	C₂²×C₈₉	1	2	yes	—
443	#380	C₂²×C₈₉	1	2	yes	—
444	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
448	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
451	C₂²×Q₈	—	2	4	no	—
452	C₂²×Q₈	—	2	4	no	—
453	C₂²×Q₈	—	2	4	no	—
454	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
455	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
456	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
457	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
458	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
459	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
460	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
461	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₄⋊Q₈	—	2	8	no	—
465	C₄⋊Q₈	—	2	8	no	—
466	C₄⋊Q₈	—	2	4	no	—
467	#125	—	2	16	no	—
468	#125	—	2	8	no	—
469	C₂²⋊Q₈	—	2	8	no	—
470	C₂²⋊Q₈	Q₈×C₈₉	1	8	yes	complemented
471	C₄×Q₈	—	2	4	no	—
472	C₄×Q₈	—	2	4	no	—
473	C₄×Q₈	—	2	8	no	—
474	C₄×Q₈	—	2	8	no	—
475	C₄×Q₈	—	2	8	no	—
476	C₄×Q₈	—	2	4	no	—
477	C₄×Q₈	—	2	8	no	—
478	C₄×Q₈	—	2	4	no	—
479	C₄×Q₈	D₄×C₈₉	1	8	yes	—
480	C₂×C₄⋊C₄	—	2	4	no	—
481	C₂×C₄⋊C₄	—	2	8	no	—
482	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
483	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
498	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
499	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
502	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
510	C₂×C₄²	—	2	8	no	—
511	C₂×C₄²	—	2	4	no	—
512	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
513	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
514	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
515	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
516	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
517	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
518	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
522	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
524	#95	C₂³×C₈₉	1	2	yes	—
525	#95	C₂³×C₈₉	1	4	yes	—
526	#95	C₂³×C₈₉	1	2	yes	—
527	#95	C₂³×C₈₉	1	4	yes	—
528	#95	C₂³×C₈₉	1	2	yes	—
529	#95	C₂³×C₈₉	1	4	yes	—
530	#95	C₂³×C₈₉	1	4	yes	—
531	#95	C₂³×C₈₉	1	2	yes	—
532	#95	C₂³×C₈₉	1	4	yes	—
533	#95	C₂³×C₈₉	1	2	yes	—
534	#95	C₂³×C₈₉	1	4	yes	—
535	#95	C₂³×C₈₉	1	4	yes	—
536	#95	C₂³×C₈₉	1	4	yes	—
537	#95	C₂³×C₈₉	1	4	yes	—
538	#95	C₂³×C₈₉	1	4	yes	—
539	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
540	C₂×Q₈	—	2	32	no	—
541	C₂×Q₈	—	2	2	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	2	4	no	—
545	C₂×Q₈	—	2	4	no	—
546	C₂×Q₈	—	2	4	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	2	no	—
550	C₂×Q₈	—	2	4	no	—
551	C₂×Q₈	—	2	4	no	—
552	C₂×Q₈	—	2	2	no	—
553	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
554	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	complemented
555	C₂×Q₈	#41×C₈₉	1	4	yes	—
556	C₂²×C₄	—	2	4	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	4	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	4	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	4	2	no	—
568	C₂²×C₄	—	4	1	no	—
569	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
570	C₂²×C₄	#41×C₈₉	1	4	yes	—
571	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
572	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
573	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
574	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
575	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
576	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
578	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
580	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
585	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	4	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	8	no	—
595	C₄⋊C₄	—	2	8	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	8	no	—
598	C₄⋊C₄	—	2	4	no	—
599	C₄⋊C₄	—	2	4	no	—
600	C₄⋊C₄	—	2	8	no	—
601	C₄⋊C₄	—	2	8	no	—
602	C₄⋊C₄	—	2	8	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	4	2	no	—
606	C₄⋊C₄	—	4	2	no	—
607	C₄⋊C₄	—	4	4	no	—
608	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
609	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
610	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	complemented
611	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	complemented
612	C₂²⋊C₄	—	2	8	no	—
613	C₂²⋊C₄	—	2	4	no	—
614	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
615	C₄²	—	2	4	no	—
616	C₄²	—	2	2	no	—
617	C₄²	—	2	4	no	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	4	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	8	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	4	4	no	—
625	C₄²	C₂×D₄×C₈₉	1	8	yes	—
626	C₄²	C₂×D₄×C₈₉	1	4	yes	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
632	C₂³	C₂×#41×C₈₉	1	2	yes	—
633	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
634	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
635	Q₈	—	2	16	no	—
636	Q₈	—	2	8	no	—
637	Q₈	—	2	8	no	—
638	Q₈	—	2	8	no	—
639	Q₈	—	4	8	no	—
640	C₂×C₄	—	2	16	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	2	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	2	no	—
646	C₂×C₄	—	2	2	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	2	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	8	no	—
658	C₂×C₄	—	2	8	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	4	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	4	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	4	8	no	—
678	C₂×C₄	—	4	4	no	—
679	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
680	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
681	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
682	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
683	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
684	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
685	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
686	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
687	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
688	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
689	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
690	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
691	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
692	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
693	C₂²	—	2	2	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	2	no	—
698	C₂²	—	2	2	no	—
699	C₂²	#557×C₈₉	1	4	yes	complemented
700	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
701	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
702	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
703	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
704	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
705	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
706	C₂²	#585×C₈₉	1	1	yes	characteristic
707	C₄	—	2	4	no	—
708	C₄	—	2	4	no	—
709	C₄	—	2	2	no	—
710	C₄	—	2	2	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	4	no	—
713	C₄	—	2	4	no	—
714	C₄	—	2	2	no	—
715	C₄	—	4	4	no	—
716	C₄	—	4	2	no	—
717	C₄	—	4	1	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	4	no	—
720	C₄	—	4	2	no	—
721	C₄	#525×C₈₉	1	4	yes	—
722	C₄	D₄×Q₈×C₈₉	1	4	yes	—
723	C₂	—	2	4	no	—
724	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
725	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
726	C₂	C₂×#557×C₈₉	1	1	yes	characteristic
727	C₂	Q₈×#41×C₈₉	1	1	yes	characteristic
728	C₂	C₈₉×#3489	1	1	yes	characteristic
729	C₂	C₈₉×#3507	1	1	yes	characteristic
730	C₂	C₈₉×#3523	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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×#557×C₈₉	C₂	semidirect
5. C₈₉×#2584	C₂	semidirect
6. C₈₉×#2582	C₂	semidirect
7. C₈₉×#2581	C₂	semidirect
8. C₈₉×#2546	C₂	semidirect
10. C₈₉×#2462	C₂	semidirect
11. C₈₉×#2446	C₂	semidirect
13. C₈₉×#2365	C₂	semidirect
15. C₈₉×#2355	C₂	semidirect
104. C₂²⋊Q₈×C₈₉	Q₈	semidirect
188. C₂×Q₈×C₈₉	C₂×Q₈	semidirect
244. C₄⋊C₄×C₈₉	C₂×Q₈	semidirect
245. C₄⋊C₄×C₈₉	C₂×Q₈	semidirect
333. C₂²×C₈₉	#557	semidirect
357. #36545	C₈₉	direct (N × H)
366. C₂×#557	C₂×C₈₉	semidirect
370. #2584	C₂×C₈₉	semidirect
371. #2582	C₂×C₈₉	semidirect
372. #2581	C₂×C₈₉	semidirect
373. #2546	C₂×C₈₉	semidirect
375. #2462	C₂×C₈₉	semidirect
376. #2446	C₂×C₈₉	semidirect
378. #2365	C₂×C₈₉	semidirect
380. #2355	C₂×C₈₉	semidirect
383. C₈₉	#36545	direct (N × H)
470. C₂²⋊Q₈	Q₈×C₈₉	semidirect
554. C₂×Q₈	C₂×Q₈×C₈₉	semidirect
610. C₄⋊C₄	C₂×Q₈×C₈₉	semidirect
611. C₄⋊C₄	C₂×Q₈×C₈₉	semidirect
699. C₂²	#557×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#557×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2857	2
C₈₉×#2851	2
C₈₉×#2584	2
C₈₉×#2582	2
C₈₉×#2581	2
C₈₉×#2546	2
C₈₉×#2473	2
C₈₉×#2462	2
C₈₉×#2446	2
C₈₉×#2434	2
C₈₉×#2365	2
C₈₉×#2360	2
C₈₉×#2355	2
C₄×C₂²⋊Q₈×C₈₉	2
#36545	89

Subgroups — C89×#36545 #36414393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36545 #36414393