Subgroups — C₈₉×#60859 #36438707

Order 22784.

1654 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3244	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3243	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3242	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3241	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3162	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3160	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3135	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3091	C₂	1	4	yes	maximal, complemented
12	C₈₉×#3076	C₂	1	4	yes	maximal, complemented
13	C₂×#433×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#544×C₈₉	—	2	2	no	—
15	#544×C₈₉	C₂²	1	4	yes	—
16	#544×C₈₉	C₂²	1	4	yes	—
17	#543×C₈₉	—	2	2	no	—
18	#542×C₈₉	C₂²	1	4	yes	—
19	#541×C₈₉	C₂²	1	2	yes	—
20	#540×C₈₉	C₂²	1	2	yes	—
21	#539×C₈₉	—	2	2	no	—
22	#538×C₈₉	—	2	2	no	—
23	#533×C₈₉	—	2	4	no	—
24	#533×C₈₉	C₂²	1	2	yes	—
25	#533×C₈₉	C₂²	1	1	yes	characteristic
26	#533×C₈₉	C₂²	1	1	yes	characteristic
27	#533×C₈₉	C₂²	1	1	yes	characteristic
28	#532×C₈₉	C₂²	1	1	yes	characteristic
29	#529×C₈₉	—	2	4	no	—
30	#525×C₈₉	C₂²	1	2	yes	—
31	C₄×#41×C₈₉	C₂²	1	2	yes	—
32	C₂×#117×C₈₉	C₂²	1	2	yes	—
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	#501×C₈₉	C₂²	1	4	yes	complemented
35	#501×C₈₉	C₂²	1	4	yes	complemented
36	#500×C₈₉	C₂²	1	2	yes	complemented
37	#499×C₈₉	C₂²	1	4	yes	complemented
38	#498×C₈₉	C₂²	1	2	yes	complemented
39	#491×C₈₉	C₂²	1	2	yes	complemented
40	#490×C₈₉	C₂²	1	2	yes	complemented
41	#489×C₈₉	C₂²	1	4	yes	complemented
42	#488×C₈₉	C₂²	1	2	yes	complemented
43	#488×C₈₉	C₂²	1	2	yes	complemented
44	#487×C₈₉	C₂²	1	2	yes	complemented
45	#486×C₈₉	C₂²	1	2	yes	complemented
46	#485×C₈₉	C₂²	1	4	yes	—
47	#485×C₈₉	C₂²	1	4	yes	—
48	#484×C₈₉	C₂²	1	4	yes	—
49	#483×C₈₉	C₂²	1	4	yes	—
50	#482×C₈₉	C₂²	1	4	yes	—
51	#482×C₈₉	C₂²	1	4	yes	—
52	#481×C₈₉	C₂²	1	4	yes	—
53	#480×C₈₉	C₂²	1	4	yes	—
54	#479×C₈₉	C₂²	1	4	yes	complemented
55	#479×C₈₉	C₂²	1	4	yes	complemented
56	#478×C₈₉	C₂²	1	4	yes	complemented
57	#478×C₈₉	C₂²	1	4	yes	complemented
58	#477×C₈₉	C₂²	1	4	yes	complemented
59	#476×C₈₉	C₂²	1	4	yes	complemented
60	#475×C₈₉	C₂²	1	4	yes	complemented
61	#474×C₈₉	C₂²	1	4	yes	complemented
62	#433×C₈₉	C₂²	1	4	yes	—
63	#433×C₈₉	C₂²	1	2	yes	—
64	#433×C₈₉	C₂²	1	2	yes	—
65	#427×C₈₉	C₂²	1	4	yes	—
66	#427×C₈₉	C₂²	1	4	yes	—
67	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
68	#416×C₈₉	C₂²	1	4	yes	—
69	#416×C₈₉	C₂²	1	4	yes	—
70	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
71	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
72	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
73	C₂×#41×C₈₉	C₂³	1	2	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
76	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
77	C₄⋊Q₈×C₈₉	—	2	4	no	—
78	C₄⋊Q₈×C₈₉	—	2	4	no	—
79	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
81	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
84	#127×C₈₉	C₂³	1	1	yes	characteristic
85	#126×C₈₉	—	2	4	no	—
86	#126×C₈₉	—	2	4	no	—
87	#125×C₈₉	—	2	4	no	—
88	#125×C₈₉	—	2	4	no	—
89	#125×C₈₉	—	2	4	no	—
90	#125×C₈₉	C₂³	1	4	yes	—
91	#125×C₈₉	C₂³	1	2	yes	—
92	#125×C₈₉	C₂³	1	2	yes	—
93	#125×C₈₉	C₂³	1	2	yes	—
94	#124×C₈₉	—	2	4	no	—
95	#124×C₈₉	C₂³	1	2	yes	—
96	#123×C₈₉	—	2	2	no	—
97	#123×C₈₉	—	2	4	no	—
98	#123×C₈₉	—	2	4	no	—
99	C₂²⋊Q₈×C₈₉	—	2	2	no	—
100	C₂²⋊Q₈×C₈₉	—	2	4	no	—
101	C₂²⋊Q₈×C₈₉	—	2	2	no	—
102	C₂²⋊Q₈×C₈₉	—	2	2	no	—
103	C₂²⋊Q₈×C₈₉	—	2	4	no	—
104	C₂²⋊Q₈×C₈₉	—	2	4	no	—
105	C₂²⋊Q₈×C₈₉	—	2	4	no	—
106	C₂²⋊Q₈×C₈₉	—	2	4	no	—
107	C₂²⋊Q₈×C₈₉	—	2	4	no	—
108	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
109	#121×C₈₉	—	2	2	no	—
110	#121×C₈₉	—	2	4	no	—
111	#121×C₈₉	C₂³	1	4	yes	—
112	#120×C₈₉	—	2	2	no	—
113	C₄×Q₈×C₈₉	—	2	2	no	—
114	C₄×Q₈×C₈₉	—	2	4	no	—
115	C₄×Q₈×C₈₉	—	2	2	no	—
116	C₄×Q₈×C₈₉	—	2	2	no	—
117	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
118	C₄×D₄×C₈₉	—	2	4	no	—
119	C₄×D₄×C₈₉	—	2	4	no	—
120	C₄×D₄×C₈₉	—	2	2	no	—
121	C₄×D₄×C₈₉	C₂³	1	4	yes	—
122	#117×C₈₉	—	2	2	no	—
123	#117×C₈₉	—	2	2	no	—
124	#117×C₈₉	—	2	2	no	—
125	#117×C₈₉	D₄	1	4	yes	—
126	#117×C₈₉	C₂³	1	2	yes	—
127	#117×C₈₉	C₂³	1	2	yes	—
128	#117×C₈₉	C₂³	1	2	yes	—
129	#117×C₈₉	C₂³	1	4	yes	—
130	#117×C₈₉	C₂³	1	2	yes	—
131	#117×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
133	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
136	C₂×C₄²×C₈₉	—	2	2	no	—
137	C₂×C₄²×C₈₉	—	2	2	no	—
138	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
139	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
140	#107×C₈₉	C₂³	1	4	yes	—
141	#107×C₈₉	C₂³	1	4	yes	—
142	#107×C₈₉	C₂³	1	4	yes	—
143	#107×C₈₉	C₂³	1	4	yes	—
144	#106×C₈₉	C₂³	1	4	yes	—
145	#106×C₈₉	C₂³	1	4	yes	—
146	#106×C₈₉	C₂³	1	4	yes	—
147	#106×C₈₉	C₂³	1	4	yes	—
148	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
149	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
150	#103×C₈₉	C₂³	1	4	yes	—
151	#103×C₈₉	C₂³	1	4	yes	—
152	#103×C₈₉	C₂³	1	4	yes	—
153	#103×C₈₉	C₂³	1	4	yes	—
154	#102×C₈₉	C₂³	1	4	yes	—
155	#102×C₈₉	C₂³	1	4	yes	—
156	#102×C₈₉	C₂³	1	4	yes	—
157	#102×C₈₉	C₂³	1	4	yes	—
158	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
159	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
160	#97×C₈₉	C₂³	1	2	yes	—
161	#97×C₈₉	C₂³	1	2	yes	—
162	C₄×C₈×C₈₉	C₂³	1	2	yes	—
163	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
164	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
165	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
166	#41×C₈₉	—	2	8	no	—
167	C₂×Q₈×C₈₉	—	2	2	no	—
168	C₂×Q₈×C₈₉	—	2	4	no	—
169	C₂×Q₈×C₈₉	—	2	2	no	—
170	C₂×Q₈×C₈₉	—	2	2	no	—
171	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
172	C₂×D₄×C₈₉	—	2	2	no	—
173	C₂×D₄×C₈₉	—	2	4	no	—
174	C₂×D₄×C₈₉	—	2	2	no	—
175	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₈₉	—	2	4	no	—
177	C₂²×C₄×C₈₉	—	2	4	no	—
178	C₂²×C₄×C₈₉	—	2	2	no	—
179	C₂²×C₄×C₈₉	—	2	4	no	—
180	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
186	C₂×C₈×C₈₉	—	2	4	no	—
187	C₂×C₈×C₈₉	—	2	4	no	—
188	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
189	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
190	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	2	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	—	2	4	no	—
197	C₄⋊C₄×C₈₉	—	2	2	no	—
198	C₄⋊C₄×C₈₉	—	2	2	no	—
199	C₄⋊C₄×C₈₉	—	2	4	no	—
200	C₄⋊C₄×C₈₉	—	2	4	no	—
201	C₄⋊C₄×C₈₉	—	2	4	no	—
202	C₄⋊C₄×C₈₉	—	2	4	no	—
203	C₄⋊C₄×C₈₉	—	2	2	no	—
204	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
205	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
206	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
207	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
208	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
209	C₂²⋊C₄×C₈₉	—	2	4	no	—
210	C₂²⋊C₄×C₈₉	—	2	2	no	—
211	C₂²⋊C₄×C₈₉	—	2	2	no	—
212	C₂²⋊C₄×C₈₉	—	2	2	no	—
213	C₂²⋊C₄×C₈₉	—	2	4	no	—
214	C₂²⋊C₄×C₈₉	—	2	4	no	—
215	C₂²⋊C₄×C₈₉	—	2	4	no	—
216	C₂²⋊C₄×C₈₉	—	2	4	no	—
217	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
218	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
219	C₄²×C₈₉	—	2	4	no	—
220	C₄²×C₈₉	—	2	4	no	—
221	C₄²×C₈₉	—	2	2	no	—
222	C₄²×C₈₉	—	2	2	no	—
223	C₄²×C₈₉	—	2	2	no	—
224	C₄²×C₈₉	C₂×D₄	1	2	yes	—
225	C₄²×C₈₉	C₂×D₄	1	2	yes	—
226	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
228	C₄²×C₈₉	C₂⁴	1	2	yes	—
229	C₂³×C₈₉	—	2	2	no	—
230	C₂³×C₈₉	—	2	2	no	—
231	C₂³×C₈₉	—	4	2	no	—
232	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
233	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
234	Q₈×C₈₉	—	2	4	no	—
235	Q₈×C₈₉	—	8	4	no	—
236	Q₈×C₈₉	—	8	2	no	—
237	Q₈×C₈₉	—	8	2	no	—
238	Q₈×C₈₉	—	8	2	no	—
239	D₄×C₈₉	—	2	4	no	—
240	D₄×C₈₉	—	4	4	no	—
241	D₄×C₈₉	—	8	2	no	—
242	D₄×C₈₉	—	8	4	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	4	no	—
245	C₂×C₄×C₈₉	—	2	4	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	4	no	—
248	C₂×C₄×C₈₉	—	2	4	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	4	2	no	—
251	C₂×C₄×C₈₉	—	4	2	no	—
252	C₂×C₄×C₈₉	—	4	4	no	—
253	C₂×C₄×C₈₉	—	8	4	no	—
254	C₂×C₄×C₈₉	—	8	4	no	—
255	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
257	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
258	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
259	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
261	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
262	C₈×C₈₉	—	2	2	no	—
263	C₈×C₈₉	—	2	2	no	—
264	C₈×C₈₉	—	2	4	no	—
265	C₂²×C₈₉	—	2	2	no	—
266	C₂²×C₈₉	—	2	4	no	—
267	C₂²×C₈₉	—	2	2	no	—
268	C₂²×C₈₉	—	4	4	no	—
269	C₂²×C₈₉	—	4	2	no	—
270	C₂²×C₈₉	—	8	2	no	—
271	C₂²×C₈₉	#536	1	2	yes	—
272	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
273	C₄×C₈₉	—	2	4	no	—
274	C₄×C₈₉	—	2	2	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	4	4	no	—
278	C₄×C₈₉	—	4	4	no	—
279	C₄×C₈₉	—	4	4	no	—
280	C₄×C₈₉	—	4	2	no	—
281	C₄×C₈₉	#536	1	2	yes	—
282	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
283	#60859	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
284	C₂×C₈₉	—	2	2	no	—
285	C₂×C₈₉	—	4	2	no	—
286	C₂×C₈₉	—	8	2	no	—
287	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
288	C₂×C₈₉	#3584	1	2	yes	—
289	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
290	#3455	C₂×C₈₉	1	1	yes	characteristic
291	#3244	C₂×C₈₉	1	4	yes	complemented
292	#3243	C₂×C₈₉	1	4	yes	complemented
293	#3242	C₂×C₈₉	1	4	yes	complemented
294	#3241	C₂×C₈₉	1	4	yes	complemented
295	#3162	C₂×C₈₉	1	1	yes	characteristic, complemented
296	#3160	C₂×C₈₉	1	1	yes	characteristic, complemented
297	#3135	C₂×C₈₉	1	1	yes	characteristic, complemented
298	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
299	#3091	C₂×C₈₉	1	4	yes	complemented
300	#3076	C₂×C₈₉	1	4	yes	complemented
301	C₂×#433	C₂×C₈₉	1	1	yes	characteristic, complemented
302	C₈₉	#60859	1	1	yes	characteristic, direct product factor, Sylow
303	#544	—	2	2	no	—
304	#544	C₂²×C₈₉	1	4	yes	—
305	#544	C₂²×C₈₉	1	4	yes	—
306	#543	—	2	2	no	—
307	#542	C₂²×C₈₉	1	4	yes	—
308	#541	C₂²×C₈₉	1	2	yes	—
309	#540	C₂²×C₈₉	1	2	yes	—
310	#539	—	2	2	no	—
311	#538	—	2	2	no	—
312	#533	—	2	4	no	—
313	#533	C₂²×C₈₉	1	2	yes	—
314	#533	C₂²×C₈₉	1	1	yes	characteristic
315	#533	C₂²×C₈₉	1	1	yes	characteristic
316	#533	C₂²×C₈₉	1	1	yes	characteristic
317	#532	C₂²×C₈₉	1	1	yes	characteristic
318	#529	—	2	4	no	—
319	#525	C₂²×C₈₉	1	2	yes	—
320	C₄×#41	C₂²×C₈₉	1	2	yes	—
321	C₂×#117	C₂²×C₈₉	1	2	yes	—
322	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
323	#501	C₂²×C₈₉	1	4	yes	complemented
324	#501	C₂²×C₈₉	1	4	yes	complemented
325	#500	C₂²×C₈₉	1	2	yes	complemented
326	#499	C₂²×C₈₉	1	4	yes	complemented
327	#498	C₂²×C₈₉	1	2	yes	complemented
328	#491	C₂²×C₈₉	1	2	yes	complemented
329	#490	C₂²×C₈₉	1	2	yes	complemented
330	#489	C₂²×C₈₉	1	4	yes	complemented
331	#488	C₂²×C₈₉	1	2	yes	complemented
332	#488	C₂²×C₈₉	1	2	yes	complemented
333	#487	C₂²×C₈₉	1	2	yes	complemented
334	#486	C₂²×C₈₉	1	2	yes	complemented
335	#485	C₂²×C₈₉	1	4	yes	—
336	#485	C₂²×C₈₉	1	4	yes	—
337	#484	C₂²×C₈₉	1	4	yes	—
338	#483	C₂²×C₈₉	1	4	yes	—
339	#482	C₂²×C₈₉	1	4	yes	—
340	#482	C₂²×C₈₉	1	4	yes	—
341	#481	C₂²×C₈₉	1	4	yes	—
342	#480	C₂²×C₈₉	1	4	yes	—
343	#479	C₂²×C₈₉	1	4	yes	complemented
344	#479	C₂²×C₈₉	1	4	yes	complemented
345	#478	C₂²×C₈₉	1	4	yes	complemented
346	#478	C₂²×C₈₉	1	4	yes	complemented
347	#477	C₂²×C₈₉	1	4	yes	complemented
348	#476	C₂²×C₈₉	1	4	yes	complemented
349	#475	C₂²×C₈₉	1	4	yes	complemented
350	#474	C₂²×C₈₉	1	4	yes	complemented
351	#433	C₂²×C₈₉	1	4	yes	—
352	#433	C₂²×C₈₉	1	2	yes	—
353	#433	C₂²×C₈₉	1	2	yes	—
354	#427	C₂²×C₈₉	1	4	yes	—
355	#427	C₂²×C₈₉	1	4	yes	—
356	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
357	#416	C₂²×C₈₉	1	4	yes	—
358	#416	C₂²×C₈₉	1	4	yes	—
359	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
360	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
361	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
362	C₂×#41	C₂³×C₈₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
364	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
365	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
366	C₄⋊Q₈	—	2	4	no	—
367	C₄⋊Q₈	—	2	4	no	—
368	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
371	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
372	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
373	#127	C₂³×C₈₉	1	1	yes	characteristic
374	#126	—	2	4	no	—
375	#126	—	2	4	no	—
376	#125	—	2	4	no	—
377	#125	—	2	4	no	—
378	#125	—	2	4	no	—
379	#125	C₂³×C₈₉	1	2	yes	—
380	#125	C₂³×C₈₉	1	4	yes	—
381	#125	C₂³×C₈₉	1	2	yes	—
382	#125	C₂³×C₈₉	1	2	yes	—
383	#124	—	2	4	no	—
384	#124	C₂³×C₈₉	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	2	4	no	—
387	#123	—	2	4	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	C₂²⋊Q₈	—	2	2	no	—
391	C₂²⋊Q₈	—	2	2	no	—
392	C₂²⋊Q₈	—	2	4	no	—
393	C₂²⋊Q₈	—	2	4	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	4	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
398	#121	—	2	2	no	—
399	#121	—	2	4	no	—
400	#121	C₂³×C₈₉	1	4	yes	—
401	#120	—	2	2	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	4	no	—
404	C₄×Q₈	—	2	2	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	C₂³×C₈₉	1	4	yes	—
411	#117	—	2	2	no	—
412	#117	—	2	2	no	—
413	#117	—	2	2	no	—
414	#117	D₄×C₈₉	1	4	yes	—
415	#117	C₂³×C₈₉	1	2	yes	—
416	#117	C₂³×C₈₉	1	2	yes	—
417	#117	C₂³×C₈₉	1	4	yes	—
418	#117	C₂³×C₈₉	1	2	yes	—
419	#117	C₂³×C₈₉	1	2	yes	—
420	#117	C₂³×C₈₉	1	2	yes	—
421	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
423	C₂×C₂²⋊C₄	—	2	2	no	—
424	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
425	C₂×C₄²	—	2	2	no	—
426	C₂×C₄²	—	2	2	no	—
427	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
428	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
429	#107	C₂³×C₈₉	1	4	yes	—
430	#107	C₂³×C₈₉	1	4	yes	—
431	#107	C₂³×C₈₉	1	4	yes	—
432	#107	C₂³×C₈₉	1	4	yes	—
433	#106	C₂³×C₈₉	1	4	yes	—
434	#106	C₂³×C₈₉	1	4	yes	—
435	#106	C₂³×C₈₉	1	4	yes	—
436	#106	C₂³×C₈₉	1	4	yes	—
437	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
438	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
439	#103	C₂³×C₈₉	1	4	yes	—
440	#103	C₂³×C₈₉	1	4	yes	—
441	#103	C₂³×C₈₉	1	4	yes	—
442	#103	C₂³×C₈₉	1	4	yes	—
443	#102	C₂³×C₈₉	1	4	yes	—
444	#102	C₂³×C₈₉	1	4	yes	—
445	#102	C₂³×C₈₉	1	4	yes	—
446	#102	C₂³×C₈₉	1	4	yes	—
447	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
448	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
449	#97	C₂³×C₈₉	1	2	yes	—
450	#97	C₂³×C₈₉	1	2	yes	—
451	C₄×C₈	C₂³×C₈₉	1	2	yes	—
452	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
454	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
455	#41	—	2	8	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
474	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	—	2	4	no	—
477	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
478	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
479	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	4	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	4	no	—
484	C₄⋊C₄	—	2	4	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	4	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
494	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
495	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
496	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
497	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	4	no	—
506	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
507	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	4	no	—
512	C₄²	—	2	4	no	—
513	C₄²	C₂×D₄×C₈₉	1	2	yes	—
514	C₄²	C₂×D₄×C₈₉	1	2	yes	—
515	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
516	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
517	C₄²	C₂⁴×C₈₉	1	2	yes	—
518	C₂³	—	2	2	no	—
519	C₂³	—	2	2	no	—
520	C₂³	—	4	2	no	—
521	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
522	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
523	Q₈	—	2	4	no	—
524	Q₈	—	8	4	no	—
525	Q₈	—	8	2	no	—
526	Q₈	—	8	2	no	—
527	Q₈	—	8	2	no	—
528	D₄	—	2	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	8	2	no	—
531	D₄	—	8	4	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	8	4	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
545	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
546	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
547	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
548	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
549	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
550	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
551	C₈	—	2	2	no	—
552	C₈	—	2	2	no	—
553	C₈	—	2	4	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	#536×C₈₉	1	2	yes	—
561	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	2	2	no	—
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	4	4	no	—
567	C₄	—	4	4	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	2	no	—
570	C₄	#536×C₈₉	1	2	yes	—
571	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
572	C₂	—	2	2	no	—
573	C₂	—	4	2	no	—
574	C₂	—	8	2	no	—
575	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
576	C₂	C₈₉×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂²×C₈₉	C₂³×D₄
prime radical	C₈₉×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3458	C₂	semidirect
3. C₈₉×#3244	C₂	semidirect
4. C₈₉×#3243	C₂	semidirect
5. C₈₉×#3242	C₂	semidirect
6. C₈₉×#3241	C₂	semidirect
7. C₈₉×#3162	C₂	semidirect
8. C₈₉×#3160	C₂	semidirect
9. C₈₉×#3135	C₂	semidirect
10. C₈₉×#3131	C₂	semidirect
11. C₈₉×#3091	C₂	semidirect
12. C₈₉×#3076	C₂	semidirect
13. C₂×#433×C₈₉	C₂	semidirect
34. #501×C₈₉	C₂²	semidirect
35. #501×C₈₉	C₂²	semidirect
36. #500×C₈₉	C₂²	semidirect
37. #499×C₈₉	C₂²	semidirect
38. #498×C₈₉	C₂²	semidirect
39. #491×C₈₉	C₂²	semidirect
40. #490×C₈₉	C₂²	semidirect
41. #489×C₈₉	C₂²	semidirect
42. #488×C₈₉	C₂²	semidirect
43. #488×C₈₉	C₂²	semidirect
44. #487×C₈₉	C₂²	semidirect
45. #486×C₈₉	C₂²	semidirect
54. #479×C₈₉	C₂²	semidirect
55. #479×C₈₉	C₂²	semidirect
56. #478×C₈₉	C₂²	semidirect
57. #478×C₈₉	C₂²	semidirect
58. #477×C₈₉	C₂²	semidirect
59. #476×C₈₉	C₂²	semidirect
60. #475×C₈₉	C₂²	semidirect
61. #474×C₈₉	C₂²	semidirect
283. #60859	C₈₉	direct (N × H)
289. #3458	C₂×C₈₉	semidirect
291. #3244	C₂×C₈₉	semidirect
292. #3243	C₂×C₈₉	semidirect
293. #3242	C₂×C₈₉	semidirect
294. #3241	C₂×C₈₉	semidirect
295. #3162	C₂×C₈₉	semidirect
296. #3160	C₂×C₈₉	semidirect
297. #3135	C₂×C₈₉	semidirect
298. #3131	C₂×C₈₉	semidirect
299. #3091	C₂×C₈₉	semidirect
300. #3076	C₂×C₈₉	semidirect
301. C₂×#433	C₂×C₈₉	semidirect
302. C₈₉	#60859	direct (N × H)
323. #501	C₂²×C₈₉	semidirect
324. #501	C₂²×C₈₉	semidirect
325. #500	C₂²×C₈₉	semidirect
326. #499	C₂²×C₈₉	semidirect
327. #498	C₂²×C₈₉	semidirect
328. #491	C₂²×C₈₉	semidirect
329. #490	C₂²×C₈₉	semidirect
330. #489	C₂²×C₈₉	semidirect
331. #488	C₂²×C₈₉	semidirect
332. #488	C₂²×C₈₉	semidirect
333. #487	C₂²×C₈₉	semidirect
334. #486	C₂²×C₈₉	semidirect
343. #479	C₂²×C₈₉	semidirect
344. #479	C₂²×C₈₉	semidirect
345. #478	C₂²×C₈₉	semidirect
346. #478	C₂²×C₈₉	semidirect
347. #477	C₂²×C₈₉	semidirect
348. #476	C₂²×C₈₉	semidirect
349. #475	C₂²×C₈₉	semidirect
350. #474	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3458	2
C₈₉×#3455	2
C₈₉×#3244	2
C₈₉×#3243	2
C₈₉×#3242	2
C₈₉×#3241	2
C₈₉×#3162	2
C₈₉×#3160	2
C₈₉×#3135	2
C₈₉×#3131	2
C₈₉×#3091	2
C₈₉×#3076	2
C₂×#433×C₈₉	2
#60859	89

Subgroups — C89×#60859 #36438707

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60859 #36438707