Subgroups — C₈₉×#62588 #36440436

Order 22784.

2046 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3518	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3362	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3358	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3325	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3324	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3235	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3217	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3171	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3138	C₂	1	3	yes	maximal, complemented
11	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×H(5,𝔽₂)×C₈₉	—	2	1	no	—
13	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
14	#556×C₈₉	—	2	3	no	—
15	#556×C₈₉	C₂²	1	3	yes	complemented
16	#555×C₈₉	C₂²	1	3	yes	complemented
17	#550×C₈₉	—	2	1	no	—
18	#550×C₈₉	C₂²	1	2	yes	—
19	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#548×C₈₉	—	2	1	no	—
21	D₄²×C₈₉	—	2	3	no	—
22	D₄²×C₈₉	C₂²	1	6	yes	—
23	#542×C₈₉	—	2	3	no	—
24	#535×C₈₉	—	2	3	no	—
25	#533×C₈₉	C₂²	1	3	yes	complemented
26	#532×C₈₉	C₂²	1	3	yes	—
27	C₂×#127×C₈₉	C₂²	1	3	yes	—
28	#529×C₈₉	C₂²	1	3	yes	complemented
29	#519×C₈₉	—	2	1	no	—
30	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
31	#501×C₈₉	C₂²	1	3	yes	complemented
32	#496×C₈₉	C₂²	1	3	yes	complemented
33	#490×C₈₉	C₂²	1	3	yes	complemented
34	#490×C₈₉	C₂²	1	6	yes	complemented
35	#489×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	#486×C₈₉	C₂²	1	6	yes	complemented
37	#486×C₈₉	C₂²	1	6	yes	complemented
38	#482×C₈₉	C₂²	1	12	yes	complemented
39	#476×C₈₉	C₂²	1	6	yes	complemented
40	#474×C₈₉	C₂²	1	6	yes	complemented
41	#469×C₈₉	C₂²	1	6	yes	complemented
42	#468×C₈₉	C₂²	1	6	yes	complemented
43	#460×C₈₉	C₂²	1	6	yes	complemented
44	#459×C₈₉	C₂²	1	6	yes	complemented
45	#450×C₈₉	C₂²	1	6	yes	complemented
46	#447×C₈₉	C₂²	1	6	yes	complemented
47	C₈×Q₈×C₈₉	C₂²	1	2	yes	complemented
48	C₄×SD₁₆×C₈₉	C₂²	1	6	yes	complemented
49	C₄×D₈×C₈₉	C₂²	1	6	yes	complemented
50	#436×C₈₉	C₂²	1	6	yes	complemented
51	#432×C₈₉	C₂²	1	3	yes	complemented
52	#418×C₈₉	C₂²	1	12	yes	complemented
53	C₄×M₁₆×C₈₉	C₂²	1	3	yes	complemented
54	H(5,𝔽₂)×C₈₉	—	4	8	no	—
55	C₂×#41×C₈₉	—	2	2	no	—
56	C₂×#41×C₈₉	—	2	3	no	—
57	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₈₉	—	2	1	no	—
59	C₂²×D₄×C₈₉	—	2	6	no	—
60	C₂²×D₄×C₈₉	—	2	3	no	—
61	C₂²×D₄×C₈₉	—	2	3	no	—
62	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
63	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
64	C₂×D₈×C₈₉	C₂³	1	6	yes	—
65	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
66	C₄⋊Q₈×C₈₉	—	2	3	no	—
67	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
68	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
69	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	#127×C₈₉	—	2	3	no	—
71	#127×C₈₉	—	2	3	no	—
72	#127×C₈₉	C₂³	1	6	yes	—
73	#127×C₈₉	C₂³	1	3	yes	—
74	#126×C₈₉	—	2	6	no	—
75	#126×C₈₉	—	2	3	no	—
76	#125×C₈₉	C₂³	1	3	yes	—
77	#124×C₈₉	—	2	3	no	—
78	#124×C₈₉	—	2	6	no	—
79	#124×C₈₉	—	2	3	no	—
80	#124×C₈₉	C₂³	1	1	yes	characteristic
81	#123×C₈₉	—	2	3	no	—
82	C₂²⋊Q₈×C₈₉	—	2	3	no	—
83	C₂²⋊Q₈×C₈₉	—	2	3	no	—
84	C₂²⋊Q₈×C₈₉	—	2	3	no	—
85	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
86	#121×C₈₉	—	2	3	no	—
87	#121×C₈₉	—	2	3	no	—
88	#121×C₈₉	—	2	6	no	—
89	#121×C₈₉	—	2	6	no	—
90	#121×C₈₉	C₂³	1	3	yes	—
91	#121×C₈₉	C₂³	1	6	yes	—
92	#120×C₈₉	—	2	12	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	C₄×Q₈×C₈₉	—	2	3	no	—
95	C₄×Q₈×C₈₉	—	2	3	no	—
96	C₄×Q₈×C₈₉	—	2	3	no	—
97	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
98	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
99	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄×D₄×C₈₉	—	2	3	no	—
101	C₄×D₄×C₈₉	—	2	3	no	—
102	C₄×D₄×C₈₉	D₄	1	3	yes	—
103	C₄×D₄×C₈₉	C₂³	1	3	yes	—
104	C₄×D₄×C₈₉	C₂³	1	6	yes	—
105	C₄×D₄×C₈₉	C₂³	1	3	yes	—
106	#117×C₈₉	—	2	3	no	—
107	#117×C₈₉	—	2	3	no	—
108	#117×C₈₉	D₄	1	3	yes	—
109	#117×C₈₉	C₂³	1	6	yes	—
110	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
111	#107×C₈₉	C₂³	1	6	yes	—
112	#106×C₈₉	C₂³	1	6	yes	—
113	C₄⋊C₈×C₈₉	C₂³	1	6	yes	—
114	#103×C₈₉	C₂³	1	2	yes	—
115	#102×C₈₉	C₂³	1	6	yes	—
116	#102×C₈₉	C₂³	1	6	yes	—
117	#102×C₈₉	C₂³	1	12	yes	—
118	#102×C₈₉	C₂³	1	12	yes	—
119	#102×C₈₉	C₂³	1	2	yes	—
120	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
121	#97×C₈₉	C₂³	1	1	yes	characteristic
122	#97×C₈₉	C₂³	1	3	yes	—
123	C₄×C₈×C₈₉	C₂³	1	6	yes	—
124	C₂⁴×C₈₉	—	2	6	no	—
125	#41×C₈₉	—	2	4	no	—
126	#41×C₈₉	—	4	12	no	—
127	#41×C₈₉	—	4	8	no	—
128	C₂×Q₈×C₈₉	—	2	3	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	3	no	—
131	C₂×Q₈×C₈₉	—	4	4	no	—
132	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₂×D₄×C₈₉	—	2	6	no	—
135	C₂×D₄×C₈₉	—	2	3	no	—
136	C₂×D₄×C₈₉	—	2	3	no	—
137	C₂×D₄×C₈₉	—	2	6	no	—
138	C₂×D₄×C₈₉	—	2	3	no	—
139	C₂×D₄×C₈₉	—	2	6	no	—
140	C₂×D₄×C₈₉	—	2	6	no	—
141	C₂×D₄×C₈₉	—	4	12	no	—
142	C₂×D₄×C₈₉	—	4	12	no	—
143	C₂×D₄×C₈₉	—	4	24	no	—
144	C₂×D₄×C₈₉	—	8	6	no	—
145	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
146	C₂×D₄×C₈₉	C₂⁴	1	6	yes	—
147	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	—	2	3	no	—
149	C₂²×C₄×C₈₉	—	2	6	no	—
150	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
152	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
153	SD₁₆×C₈₉	—	4	6	no	—
154	D₈×C₈₉	—	4	6	no	—
155	M₁₆×C₈₉	—	4	6	no	—
156	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
157	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
158	C₄⋊C₄×C₈₉	—	2	3	no	—
159	C₄⋊C₄×C₈₉	—	2	3	no	—
160	C₄⋊C₄×C₈₉	—	2	3	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	2	3	no	—
163	C₄⋊C₄×C₈₉	—	2	3	no	—
164	C₄⋊C₄×C₈₉	—	2	3	no	—
165	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
166	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
168	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
169	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂²⋊C₄×C₈₉	—	2	6	no	—
171	C₂²⋊C₄×C₈₉	—	2	3	no	—
172	C₂²⋊C₄×C₈₉	—	2	3	no	—
173	C₂²⋊C₄×C₈₉	—	2	1	no	—
174	C₂²⋊C₄×C₈₉	—	2	1	no	—
175	C₂²⋊C₄×C₈₉	—	2	6	no	—
176	C₂²⋊C₄×C₈₉	—	2	6	no	—
177	C₂²⋊C₄×C₈₉	—	2	3	no	—
178	C₂²⋊C₄×C₈₉	C₂×D₄	1	6	yes	—
179	C₄²×C₈₉	—	2	6	no	—
180	C₄²×C₈₉	—	2	3	no	—
181	C₄²×C₈₉	C₂×D₄	1	3	yes	—
182	C₄²×C₈₉	C₂×D₄	1	3	yes	—
183	C₄²×C₈₉	C₂⁴	1	3	yes	—
184	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
185	C₂³×C₈₉	—	2	1	no	—
186	C₂³×C₈₉	—	2	6	no	—
187	C₂³×C₈₉	—	4	12	no	—
188	C₂³×C₈₉	—	8	6	no	—
189	C₂³×C₈₉	—	8	6	no	—
190	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
191	Q₈×C₈₉	—	2	2	no	—
192	Q₈×C₈₉	—	4	2	no	—
193	Q₈×C₈₉	—	4	6	no	—
194	Q₈×C₈₉	—	8	3	no	—
195	Q₈×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
196	D₄×C₈₉	—	2	6	no	—
197	D₄×C₈₉	—	2	2	no	—
198	D₄×C₈₉	—	2	6	no	—
199	D₄×C₈₉	—	2	6	no	—
200	D₄×C₈₉	—	4	6	no	—
201	D₄×C₈₉	—	4	6	no	—
202	D₄×C₈₉	—	4	12	no	—
203	D₄×C₈₉	—	4	12	no	—
204	D₄×C₈₉	—	8	6	no	—
205	D₄×C₈₉	—	8	6	no	—
206	D₄×C₈₉	—	8	3	no	—
207	C₂×C₄×C₈₉	—	2	6	no	—
208	C₂×C₄×C₈₉	—	2	6	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	3	no	—
211	C₂×C₄×C₈₉	—	2	3	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	4	3	no	—
214	C₂×C₄×C₈₉	—	4	12	no	—
215	C₂×C₄×C₈₉	—	4	6	no	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
220	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
221	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
222	C₈×C₈₉	—	2	2	no	—
223	C₈×C₈₉	—	2	6	no	—
224	C₂²×C₈₉	—	2	3	no	—
225	C₂²×C₈₉	—	2	3	no	—
226	C₂²×C₈₉	—	2	3	no	—
227	C₂²×C₈₉	—	4	6	no	—
228	C₂²×C₈₉	—	4	1	no	—
229	C₂²×C₈₉	—	4	6	no	—
230	C₂²×C₈₉	—	4	1	no	—
231	C₂²×C₈₉	—	4	1	no	—
232	C₂²×C₈₉	—	4	6	no	—
233	C₂²×C₈₉	—	16	12	no	—
234	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
235	C₄×C₈₉	—	2	1	no	—
236	C₄×C₈₉	—	2	3	no	—
237	C₄×C₈₉	—	2	3	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	—	4	3	no	—
240	C₄×C₈₉	—	4	1	no	—
241	C₄×C₈₉	—	4	2	no	—
242	C₄×C₈₉	—	4	3	no	—
243	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
244	C₄×C₈₉	#585	1	2	yes	—
245	#62588	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂×C₈₉	—	4	3	no	—
247	C₂×C₈₉	—	8	1	no	—
248	C₂×C₈₉	—	8	6	no	—
249	C₂×C₈₉	#3500	1	1	yes	characteristic
250	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
251	C₂×C₈₉	#3585	1	1	yes	characteristic
252	#3518	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#3498	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#3362	C₂×C₈₉	1	2	yes	complemented
255	#3358	C₂×C₈₉	1	2	yes	complemented
256	#3325	C₂×C₈₉	1	6	yes	complemented
257	#3324	C₂×C₈₉	1	6	yes	complemented
258	#3235	C₂×C₈₉	1	3	yes	complemented
259	#3217	C₂×C₈₉	1	3	yes	complemented
260	#3171	C₂×C₈₉	1	3	yes	complemented
261	#3138	C₂×C₈₉	1	3	yes	complemented
262	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
263	C₈₉	#62588	1	1	yes	characteristic, direct product factor, Sylow
264	C₂×H(5,𝔽₂)	—	2	1	no	—
265	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
266	#556	—	2	3	no	—
267	#556	C₂²×C₈₉	1	3	yes	complemented
268	#555	C₂²×C₈₉	1	3	yes	complemented
269	#550	—	2	1	no	—
270	#550	C₂²×C₈₉	1	2	yes	—
271	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
272	#548	—	2	1	no	—
273	D₄²	—	2	3	no	—
274	D₄²	C₂²×C₈₉	1	6	yes	—
275	#542	—	2	3	no	—
276	#535	—	2	3	no	—
277	#533	C₂²×C₈₉	1	3	yes	complemented
278	#532	C₂²×C₈₉	1	3	yes	—
279	C₂×#127	C₂²×C₈₉	1	3	yes	—
280	#529	C₂²×C₈₉	1	3	yes	complemented
281	#519	—	2	1	no	—
282	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
283	#501	C₂²×C₈₉	1	3	yes	complemented
284	#496	C₂²×C₈₉	1	3	yes	complemented
285	#490	C₂²×C₈₉	1	3	yes	complemented
286	#490	C₂²×C₈₉	1	6	yes	complemented
287	#489	C₂²×C₈₉	1	1	yes	characteristic, complemented
288	#486	C₂²×C₈₉	1	6	yes	complemented
289	#486	C₂²×C₈₉	1	6	yes	complemented
290	#482	C₂²×C₈₉	1	12	yes	complemented
291	#476	C₂²×C₈₉	1	6	yes	complemented
292	#474	C₂²×C₈₉	1	6	yes	complemented
293	#469	C₂²×C₈₉	1	6	yes	complemented
294	#468	C₂²×C₈₉	1	6	yes	complemented
295	#460	C₂²×C₈₉	1	6	yes	complemented
296	#459	C₂²×C₈₉	1	6	yes	complemented
297	#450	C₂²×C₈₉	1	6	yes	complemented
298	#447	C₂²×C₈₉	1	6	yes	complemented
299	C₈×Q₈	C₂²×C₈₉	1	2	yes	complemented
300	C₄×SD₁₆	C₂²×C₈₉	1	6	yes	complemented
301	C₄×D₈	C₂²×C₈₉	1	6	yes	complemented
302	#436	C₂²×C₈₉	1	6	yes	complemented
303	#432	C₂²×C₈₉	1	3	yes	complemented
304	#418	C₂²×C₈₉	1	12	yes	complemented
305	C₄×M₁₆	C₂²×C₈₉	1	3	yes	complemented
306	H(5,𝔽₂)	—	4	8	no	—
307	C₂×#41	—	2	2	no	—
308	C₂×#41	—	2	3	no	—
309	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
310	C₂²×Q₈	—	2	1	no	—
311	C₂²×D₄	—	2	6	no	—
312	C₂²×D₄	—	2	3	no	—
313	C₂²×D₄	—	2	3	no	—
314	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
315	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
316	C₂×D₈	C₂³×C₈₉	1	6	yes	—
317	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
318	C₄⋊Q₈	—	2	3	no	—
319	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
321	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
322	#127	—	2	3	no	—
323	#127	—	2	3	no	—
324	#127	C₂³×C₈₉	1	3	yes	—
325	#127	C₂³×C₈₉	1	6	yes	—
326	#126	—	2	6	no	—
327	#126	—	2	3	no	—
328	#125	C₂³×C₈₉	1	3	yes	—
329	#124	—	2	3	no	—
330	#124	—	2	6	no	—
331	#124	—	2	3	no	—
332	#124	C₂³×C₈₉	1	1	yes	characteristic
333	#123	—	2	3	no	—
334	C₂²⋊Q₈	—	2	3	no	—
335	C₂²⋊Q₈	—	2	3	no	—
336	C₂²⋊Q₈	—	2	3	no	—
337	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
338	#121	—	2	3	no	—
339	#121	—	2	3	no	—
340	#121	—	2	6	no	—
341	#121	—	2	6	no	—
342	#121	C₂³×C₈₉	1	3	yes	—
343	#121	C₂³×C₈₉	1	6	yes	—
344	#120	—	2	12	no	—
345	C₄×Q₈	—	2	1	no	—
346	C₄×Q₈	—	2	3	no	—
347	C₄×Q₈	—	2	3	no	—
348	C₄×Q₈	—	2	3	no	—
349	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
350	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
351	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
352	C₄×D₄	—	2	3	no	—
353	C₄×D₄	—	2	3	no	—
354	C₄×D₄	D₄×C₈₉	1	3	yes	—
355	C₄×D₄	C₂³×C₈₉	1	3	yes	—
356	C₄×D₄	C₂³×C₈₉	1	6	yes	—
357	C₄×D₄	C₂³×C₈₉	1	3	yes	—
358	#117	—	2	3	no	—
359	#117	—	2	3	no	—
360	#117	D₄×C₈₉	1	3	yes	—
361	#117	C₂³×C₈₉	1	6	yes	—
362	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
363	#107	C₂³×C₈₉	1	6	yes	—
364	#106	C₂³×C₈₉	1	6	yes	—
365	C₄⋊C₈	C₂³×C₈₉	1	6	yes	—
366	#103	C₂³×C₈₉	1	2	yes	—
367	#102	C₂³×C₈₉	1	6	yes	—
368	#102	C₂³×C₈₉	1	6	yes	—
369	#102	C₂³×C₈₉	1	12	yes	—
370	#102	C₂³×C₈₉	1	12	yes	—
371	#102	C₂³×C₈₉	1	2	yes	—
372	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
373	#97	C₂³×C₈₉	1	1	yes	characteristic
374	#97	C₂³×C₈₉	1	3	yes	—
375	C₄×C₈	C₂³×C₈₉	1	6	yes	—
376	C₂⁴	—	2	6	no	—
377	#41	—	2	4	no	—
378	#41	—	4	12	no	—
379	#41	—	4	8	no	—
380	C₂×Q₈	—	2	3	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	3	no	—
383	C₂×Q₈	—	4	4	no	—
384	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
385	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
386	C₂×D₄	—	2	6	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	2	3	no	—
389	C₂×D₄	—	2	6	no	—
390	C₂×D₄	—	2	3	no	—
391	C₂×D₄	—	2	6	no	—
392	C₂×D₄	—	2	6	no	—
393	C₂×D₄	—	4	12	no	—
394	C₂×D₄	—	4	12	no	—
395	C₂×D₄	—	4	24	no	—
396	C₂×D₄	—	8	6	no	—
397	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
398	C₂×D₄	C₂⁴×C₈₉	1	6	yes	—
399	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
400	C₂²×C₄	—	2	3	no	—
401	C₂²×C₄	—	2	6	no	—
402	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
403	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
404	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
405	SD₁₆	—	4	6	no	—
406	D₈	—	4	6	no	—
407	M₁₆	—	4	6	no	—
408	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
409	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
410	C₄⋊C₄	—	2	3	no	—
411	C₄⋊C₄	—	2	3	no	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	3	no	—
415	C₄⋊C₄	—	2	3	no	—
416	C₄⋊C₄	—	2	3	no	—
417	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
418	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
419	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
420	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
421	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
422	C₂²⋊C₄	—	2	6	no	—
423	C₂²⋊C₄	—	2	3	no	—
424	C₂²⋊C₄	—	2	3	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	6	no	—
428	C₂²⋊C₄	—	2	6	no	—
429	C₂²⋊C₄	—	2	3	no	—
430	C₂²⋊C₄	C₂×D₄×C₈₉	1	6	yes	—
431	C₄²	—	2	6	no	—
432	C₄²	—	2	3	no	—
433	C₄²	C₂×D₄×C₈₉	1	3	yes	—
434	C₄²	C₂×D₄×C₈₉	1	3	yes	—
435	C₄²	C₂⁴×C₈₉	1	3	yes	—
436	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
437	C₂³	—	2	1	no	—
438	C₂³	—	2	6	no	—
439	C₂³	—	4	12	no	—
440	C₂³	—	8	6	no	—
441	C₂³	—	8	6	no	—
442	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
443	Q₈	—	2	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	6	no	—
446	Q₈	—	8	3	no	—
447	Q₈	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
448	D₄	—	2	6	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	6	no	—
451	D₄	—	2	6	no	—
452	D₄	—	4	6	no	—
453	D₄	—	4	6	no	—
454	D₄	—	4	12	no	—
455	D₄	—	4	12	no	—
456	D₄	—	8	6	no	—
457	D₄	—	8	6	no	—
458	D₄	—	8	3	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	6	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	3	no	—
463	C₂×C₄	—	2	3	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	4	3	no	—
466	C₂×C₄	—	4	12	no	—
467	C₂×C₄	—	4	6	no	—
468	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
469	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
471	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
472	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
473	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	6	no	—
476	C₂²	—	2	3	no	—
477	C₂²	—	2	3	no	—
478	C₂²	—	2	3	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	6	no	—
481	C₂²	—	4	6	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	6	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	16	12	no	—
486	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	3	no	—
490	C₄	—	2	3	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	3	no	—
493	C₄	—	4	3	no	—
494	C₄	—	4	1	no	—
495	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	6	yes	—
496	C₄	#585×C₈₉	1	2	yes	—
497	C₂	—	4	3	no	—
498	C₂	—	8	1	no	—
499	C₂	—	8	6	no	—
500	C₂	C₈₉×#3500	1	1	yes	characteristic
501	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
502	C₂	C₈₉×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3518	C₂	semidirect
2. C₈₉×#3498	C₂	semidirect
3. C₈₉×#3362	C₂	semidirect
4. C₈₉×#3358	C₂	semidirect
5. C₈₉×#3325	C₂	semidirect
6. C₈₉×#3324	C₂	semidirect
7. C₈₉×#3235	C₂	semidirect
8. C₈₉×#3217	C₂	semidirect
9. C₈₉×#3171	C₂	semidirect
10. C₈₉×#3138	C₂	semidirect
11. C₈₉×#2971	C₂	semidirect
13. Q₈²×C₈₉	C₂²	semidirect
15. #556×C₈₉	C₂²	semidirect
16. #555×C₈₉	C₂²	semidirect
19. D₄×Q₈×C₈₉	C₂²	semidirect
25. #533×C₈₉	C₂²	semidirect
28. #529×C₈₉	C₂²	semidirect
31. #501×C₈₉	C₂²	semidirect
32. #496×C₈₉	C₂²	semidirect
33. #490×C₈₉	C₂²	semidirect
34. #490×C₈₉	C₂²	semidirect
35. #489×C₈₉	C₂²	semidirect
36. #486×C₈₉	C₂²	semidirect
37. #486×C₈₉	C₂²	semidirect
38. #482×C₈₉	C₂²	semidirect
39. #476×C₈₉	C₂²	semidirect
40. #474×C₈₉	C₂²	semidirect
41. #469×C₈₉	C₂²	semidirect
42. #468×C₈₉	C₂²	semidirect
43. #460×C₈₉	C₂²	semidirect
44. #459×C₈₉	C₂²	semidirect
45. #450×C₈₉	C₂²	semidirect
46. #447×C₈₉	C₂²	semidirect
47. C₈×Q₈×C₈₉	C₂²	semidirect
48. C₄×SD₁₆×C₈₉	C₂²	semidirect
49. C₄×D₈×C₈₉	C₂²	semidirect
50. #436×C₈₉	C₂²	semidirect
51. #432×C₈₉	C₂²	semidirect
52. #418×C₈₉	C₂²	semidirect
53. C₄×M₁₆×C₈₉	C₂²	semidirect
245. #62588	C₈₉	direct (N × H)
252. #3518	C₂×C₈₉	semidirect
253. #3498	C₂×C₈₉	semidirect
254. #3362	C₂×C₈₉	semidirect
255. #3358	C₂×C₈₉	semidirect
256. #3325	C₂×C₈₉	semidirect
257. #3324	C₂×C₈₉	semidirect
258. #3235	C₂×C₈₉	semidirect
259. #3217	C₂×C₈₉	semidirect
260. #3171	C₂×C₈₉	semidirect
261. #3138	C₂×C₈₉	semidirect
262. #2971	C₂×C₈₉	semidirect
263. C₈₉	#62588	direct (N × H)
265. Q₈²	C₂²×C₈₉	semidirect
267. #556	C₂²×C₈₉	semidirect
268. #555	C₂²×C₈₉	semidirect
271. D₄×Q₈	C₂²×C₈₉	semidirect
277. #533	C₂²×C₈₉	semidirect
280. #529	C₂²×C₈₉	semidirect
283. #501	C₂²×C₈₉	semidirect
284. #496	C₂²×C₈₉	semidirect
285. #490	C₂²×C₈₉	semidirect
286. #490	C₂²×C₈₉	semidirect
287. #489	C₂²×C₈₉	semidirect
288. #486	C₂²×C₈₉	semidirect
289. #486	C₂²×C₈₉	semidirect
290. #482	C₂²×C₈₉	semidirect
291. #476	C₂²×C₈₉	semidirect
292. #474	C₂²×C₈₉	semidirect
293. #469	C₂²×C₈₉	semidirect
294. #468	C₂²×C₈₉	semidirect
295. #460	C₂²×C₈₉	semidirect
296. #459	C₂²×C₈₉	semidirect
297. #450	C₂²×C₈₉	semidirect
298. #447	C₂²×C₈₉	semidirect
299. C₈×Q₈	C₂²×C₈₉	semidirect
300. C₄×SD₁₆	C₂²×C₈₉	semidirect
301. C₄×D₈	C₂²×C₈₉	semidirect
302. #436	C₂²×C₈₉	semidirect
303. #432	C₂²×C₈₉	semidirect
304. #418	C₂²×C₈₉	semidirect
305. C₄×M₁₆	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×#3518	2
C₈₉×#3498	2
C₈₉×#3362	2
C₈₉×#3358	2
C₈₉×#3325	2
C₈₉×#3324	2
C₈₉×#3235	2
C₈₉×#3217	2
C₈₉×#3171	2
C₈₉×#3138	2
C₈₉×#2971	2
#62588	89

Subgroups — C89×#62588 #36440436

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62588 #36440436