Subgroups — C₈₉×#62151 #36439999

Order 22784.

1986 conjugacy classes of subgroups.

The subgroup lattice has 648 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	D₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#3362	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3354	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3353	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3325	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3324	C₂	1	3	yes	maximal, complemented
11	C₈₉×#3251	C₂	1	3	yes	maximal, complemented
12	C₈₉×#3228	C₂	1	3	yes	maximal, complemented
13	C₈₉×#3105	C₂	1	3	yes	maximal, complemented
14	C₈₉×#3077	C₂	1	3	yes	maximal, complemented
15	C₈₉×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₈₉	—	2	1	no	—
17	Q₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	#556×C₈₉	—	2	3	no	—
19	#556×C₈₉	C₂²	1	3	yes	complemented
20	#555×C₈₉	C₂²	1	3	yes	complemented
21	#550×C₈₉	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	D₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#548×C₈₉	—	2	1	no	—
25	#548×C₈₉	—	2	1	no	—
26	#547×C₈₉	C₂²	1	3	yes	—
27	#546×C₈₉	—	2	3	no	—
28	D₄²×C₈₉	C₂²	1	3	yes	—
29	#542×C₈₉	—	2	3	no	—
30	#533×C₈₉	C₂²	1	3	yes	complemented
31	#532×C₈₉	C₂²	1	3	yes	—
32	#529×C₈₉	C₂²	1	3	yes	complemented
33	#525×C₈₉	—	2	3	no	—
34	#519×C₈₉	—	2	1	no	—
35	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
37	#500×C₈₉	C₂²	1	3	yes	complemented
38	#498×C₈₉	C₂²	1	3	yes	complemented
39	#486×C₈₉	C₂²	1	3	yes	complemented
40	#486×C₈₉	C₂²	1	3	yes	complemented
41	#484×C₈₉	C₂²	1	3	yes	complemented
42	#482×C₈₉	C₂²	1	6	yes	complemented
43	#482×C₈₉	C₂²	1	6	yes	complemented
44	#481×C₈₉	C₂²	1	3	yes	complemented
45	#478×C₈₉	C₂²	1	3	yes	—
46	#478×C₈₉	C₂²	1	6	yes	complemented
47	#478×C₈₉	C₂²	1	3	yes	complemented
48	#476×C₈₉	C₂²	1	3	yes	—
49	#476×C₈₉	C₂²	1	3	yes	complemented
50	#475×C₈₉	C₂²	1	3	yes	complemented
51	#474×C₈₉	C₂²	1	3	yes	—
52	#474×C₈₉	C₂²	1	3	yes	complemented
53	#474×C₈₉	C₂²	1	3	yes	complemented
54	#469×C₈₉	C₂²	1	6	yes	complemented
55	#468×C₈₉	C₂²	1	6	yes	complemented
56	#463×C₈₉	C₂²	1	1	yes	characteristic
57	#463×C₈₉	C₂²	1	3	yes	complemented
58	#460×C₈₉	C₂²	1	3	yes	complemented
59	#459×C₈₉	C₂²	1	3	yes	complemented
60	#450×C₈₉	C₂²	1	3	yes	—
61	#447×C₈₉	C₂²	1	3	yes	—
62	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₄×SD₁₆×C₈₉	C₂²	1	3	yes	—
65	C₄×SD₁₆×C₈₉	C₂²	1	3	yes	complemented
66	C₄×D₈×C₈₉	C₂²	1	3	yes	—
67	C₄×D₈×C₈₉	C₂²	1	3	yes	complemented
68	#436×C₈₉	C₂²	1	3	yes	complemented
69	#436×C₈₉	C₂²	1	3	yes	complemented
70	#431×C₈₉	C₂²	1	3	yes	complemented
71	#428×C₈₉	C₂²	1	6	yes	complemented
72	#423×C₈₉	C₂²	1	3	yes	complemented
73	#418×C₈₉	C₂²	1	6	yes	—
74	C₂×#41×C₈₉	—	2	1	no	—
75	C₂×#41×C₈₉	—	2	3	no	—
76	C₂×#41×C₈₉	—	2	3	no	—
77	C₂×#41×C₈₉	—	4	8	no	—
78	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	—	2	1	no	—
80	C₂²×Q₈×C₈₉	—	2	1	no	—
81	C₂²×D₄×C₈₉	—	2	3	no	—
82	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
83	C₂³×C₄×C₈₉	—	2	3	no	—
84	C₂×SD₁₆×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×SD₁₆×C₈₉	C₂³	1	3	yes	—
86	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂×D₈×C₈₉	C₂³	1	3	yes	—
88	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
89	C₄⋊Q₈×C₈₉	—	2	3	no	—
90	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
91	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
92	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
93	#127×C₈₉	C₂³	1	3	yes	—
94	#126×C₈₉	—	2	6	no	—
95	#126×C₈₉	—	2	3	no	—
96	#125×C₈₉	C₂³	1	3	yes	—
97	#124×C₈₉	—	2	3	no	—
98	#124×C₈₉	—	2	6	no	—
99	#124×C₈₉	—	2	3	no	—
100	#124×C₈₉	C₂³	1	1	yes	characteristic
101	#123×C₈₉	—	2	3	no	—
102	#123×C₈₉	—	2	6	no	—
103	C₂²⋊Q₈×C₈₉	—	2	3	no	—
104	C₂²⋊Q₈×C₈₉	—	2	3	no	—
105	C₂²⋊Q₈×C₈₉	—	2	3	no	—
106	C₂²⋊Q₈×C₈₉	—	2	3	no	—
107	C₂²⋊Q₈×C₈₉	—	2	3	no	—
108	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
109	#121×C₈₉	—	2	3	no	—
110	#121×C₈₉	—	2	3	no	—
111	#121×C₈₉	—	2	3	no	—
112	#121×C₈₉	—	2	3	no	—
113	#121×C₈₉	C₂³	1	3	yes	—
114	#121×C₈₉	C₂³	1	6	yes	—
115	#120×C₈₉	—	2	6	no	—
116	C₄×Q₈×C₈₉	—	2	1	no	—
117	C₄×Q₈×C₈₉	—	2	3	no	—
118	C₄×Q₈×C₈₉	—	2	3	no	—
119	C₄×Q₈×C₈₉	—	2	3	no	—
120	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
121	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
122	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄×D₄×C₈₉	—	2	3	no	—
124	C₄×D₄×C₈₉	—	2	3	no	—
125	C₄×D₄×C₈₉	—	2	3	no	—
126	C₄×D₄×C₈₉	—	2	3	no	—
127	C₄×D₄×C₈₉	D₄	1	3	yes	—
128	C₄×D₄×C₈₉	C₂³	1	3	yes	—
129	C₄×D₄×C₈₉	C₂³	1	3	yes	—
130	C₄×D₄×C₈₉	C₂³	1	3	yes	—
131	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₈₉	C₂³	1	3	yes	—
133	C₄×D₄×C₈₉	C₂³	1	3	yes	—
134	#117×C₈₉	—	2	3	no	—
135	#117×C₈₉	—	2	3	no	—
136	#117×C₈₉	D₄	1	3	yes	—
137	#117×C₈₉	C₂³	1	6	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
139	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
140	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
141	#107×C₈₉	C₂³	1	3	yes	—
142	#107×C₈₉	C₂³	1	6	yes	—
143	#107×C₈₉	C₂³	1	3	yes	—
144	#106×C₈₉	C₂³	1	3	yes	—
145	#106×C₈₉	C₂³	1	6	yes	—
146	#106×C₈₉	C₂³	1	3	yes	—
147	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
148	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
149	C₄⋊C₈×C₈₉	C₂³	1	3	yes	—
150	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
151	#103×C₈₉	C₂³	1	3	yes	—
152	#103×C₈₉	C₂³	1	1	yes	characteristic
153	#102×C₈₉	C₂³	1	3	yes	—
154	#102×C₈₉	C₂³	1	3	yes	—
155	#102×C₈₉	C₂³	1	6	yes	—
156	#102×C₈₉	C₂³	1	6	yes	—
157	#102×C₈₉	C₂³	1	3	yes	—
158	#102×C₈₉	C₂³	1	1	yes	characteristic
159	#102×C₈₉	C₂³	1	3	yes	—
160	#102×C₈₉	C₂³	1	3	yes	—
161	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
162	C₂²⋊C₈×C₈₉	C₂³	1	3	yes	—
163	C₄×C₈×C₈₉	C₂³	1	3	yes	—
164	C₄×C₈×C₈₉	C₂³	1	3	yes	—
165	C₂⁴×C₈₉	—	2	3	no	—
166	#41×C₈₉	—	2	4	no	—
167	#41×C₈₉	—	4	12	no	—
168	#41×C₈₉	—	4	12	no	—
169	#41×C₈₉	—	4	4	no	—
170	C₂×Q₈×C₈₉	—	2	3	no	—
171	C₂×Q₈×C₈₉	—	2	3	no	—
172	C₂×Q₈×C₈₉	—	2	3	no	—
173	C₂×Q₈×C₈₉	—	4	4	no	—
174	C₂×Q₈×C₈₉	—	4	4	no	—
175	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂×D₄×C₈₉	—	2	6	no	—
178	C₂×D₄×C₈₉	—	2	6	no	—
179	C₂×D₄×C₈₉	—	2	3	no	—
180	C₂×D₄×C₈₉	—	2	3	no	—
181	C₂×D₄×C₈₉	—	2	3	no	—
182	C₂×D₄×C₈₉	—	2	3	no	—
183	C₂×D₄×C₈₉	—	4	3	no	—
184	C₂×D₄×C₈₉	—	4	12	no	—
185	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
186	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
187	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	—	2	3	no	—
190	C₂²×C₄×C₈₉	—	2	3	no	—
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	C₂²×C₄×C₈₉	—	2	3	no	—
193	C₂²×C₄×C₈₉	—	2	3	no	—
194	C₂²×C₄×C₈₉	—	2	3	no	—
195	C₂²×C₄×C₈₉	—	4	12	no	—
196	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
197	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
198	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
199	SD₁₆×C₈₉	—	2	2	no	—
200	SD₁₆×C₈₉	—	4	3	no	—
201	D₈×C₈₉	—	2	2	no	—
202	D₈×C₈₉	—	4	3	no	—
203	M₁₆×C₈₉	—	4	6	no	—
204	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
206	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
207	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
208	C₄⋊C₄×C₈₉	—	2	3	no	—
209	C₄⋊C₄×C₈₉	—	2	3	no	—
210	C₄⋊C₄×C₈₉	—	2	3	no	—
211	C₄⋊C₄×C₈₉	—	2	3	no	—
212	C₄⋊C₄×C₈₉	—	2	3	no	—
213	C₄⋊C₄×C₈₉	—	2	3	no	—
214	C₄⋊C₄×C₈₉	—	2	3	no	—
215	C₄⋊C₄×C₈₉	—	2	3	no	—
216	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
217	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
218	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
219	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
220	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₄⋊C₄×C₈₉	C₂⁴	1	3	yes	—
222	C₂²⋊C₄×C₈₉	—	2	6	no	—
223	C₂²⋊C₄×C₈₉	—	2	3	no	—
224	C₂²⋊C₄×C₈₉	—	2	1	no	—
225	C₂²⋊C₄×C₈₉	—	2	3	no	—
226	C₂²⋊C₄×C₈₉	—	2	3	no	—
227	C₂²⋊C₄×C₈₉	—	2	3	no	—
228	C₂²⋊C₄×C₈₉	—	2	3	no	—
229	C₂²⋊C₄×C₈₉	—	2	1	no	—
230	C₂²⋊C₄×C₈₉	—	2	1	no	—
231	C₂²⋊C₄×C₈₉	—	2	6	no	—
232	C₂²⋊C₄×C₈₉	—	2	3	no	—
233	C₂²⋊C₄×C₈₉	C₂×D₄	1	6	yes	—
234	C₄²×C₈₉	—	2	6	no	—
235	C₄²×C₈₉	—	2	3	no	—
236	C₄²×C₈₉	C₂×D₄	1	3	yes	—
237	C₄²×C₈₉	C₂×D₄	1	3	yes	—
238	C₄²×C₈₉	C₂⁴	1	3	yes	—
239	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂³×C₈₉	—	2	1	no	—
241	C₂³×C₈₉	—	2	1	no	—
242	C₂³×C₈₉	—	2	3	no	—
243	C₂³×C₈₉	—	4	6	no	—
244	C₂³×C₈₉	—	4	6	no	—
245	C₂³×C₈₉	—	8	3	no	—
246	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
247	Q₈×C₈₉	—	2	1	no	—
248	Q₈×C₈₉	—	2	1	no	—
249	Q₈×C₈₉	—	4	6	no	—
250	Q₈×C₈₉	—	4	6	no	—
251	Q₈×C₈₉	—	8	3	no	—
252	Q₈×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
253	D₄×C₈₉	—	2	6	no	—
254	D₄×C₈₉	—	2	1	no	—
255	D₄×C₈₉	—	2	3	no	—
256	D₄×C₈₉	—	2	1	no	—
257	D₄×C₈₉	—	2	1	no	—
258	D₄×C₈₉	—	2	3	no	—
259	D₄×C₈₉	—	4	6	no	—
260	D₄×C₈₉	—	4	12	no	—
261	D₄×C₈₉	—	4	6	no	—
262	D₄×C₈₉	—	8	3	no	—
263	D₄×C₈₉	—	8	3	no	—
264	D₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
265	C₂×C₄×C₈₉	—	2	6	no	—
266	C₂×C₄×C₈₉	—	2	3	no	—
267	C₂×C₄×C₈₉	—	2	3	no	—
268	C₂×C₄×C₈₉	—	2	1	no	—
269	C₂×C₄×C₈₉	—	2	3	no	—
270	C₂×C₄×C₈₉	—	2	3	no	—
271	C₂×C₄×C₈₉	—	2	1	no	—
272	C₂×C₄×C₈₉	—	2	3	no	—
273	C₂×C₄×C₈₉	—	4	3	no	—
274	C₂×C₄×C₈₉	—	4	2	no	—
275	C₂×C₄×C₈₉	—	4	6	no	—
276	C₂×C₄×C₈₉	—	4	6	no	—
277	C₂×C₄×C₈₉	—	4	6	no	—
278	C₂×C₄×C₈₉	—	4	6	no	—
279	C₂×C₄×C₈₉	—	4	6	no	—
280	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
281	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
284	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
285	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
286	C₈×C₈₉	—	2	1	no	—
287	C₈×C₈₉	—	2	1	no	—
288	C₈×C₈₉	—	2	3	no	—
289	C₈×C₈₉	—	2	3	no	—
290	C₂²×C₈₉	—	2	3	no	—
291	C₂²×C₈₉	—	2	3	no	—
292	C₂²×C₈₉	—	2	2	no	—
293	C₂²×C₈₉	—	2	3	no	—
294	C₂²×C₈₉	—	4	1	no	—
295	C₂²×C₈₉	—	4	1	no	—
296	C₂²×C₈₉	—	4	1	no	—
297	C₂²×C₈₉	—	4	3	no	—
298	C₂²×C₈₉	—	4	3	no	—
299	C₂²×C₈₉	—	4	1	no	—
300	C₂²×C₈₉	—	4	1	no	—
301	C₂²×C₈₉	—	4	3	no	—
302	C₂²×C₈₉	—	8	12	no	—
303	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
304	C₄×C₈₉	—	2	1	no	—
305	C₄×C₈₉	—	2	3	no	—
306	C₄×C₈₉	—	2	3	no	—
307	C₄×C₈₉	—	2	1	no	—
308	C₄×C₈₉	—	4	3	no	—
309	C₄×C₈₉	—	4	1	no	—
310	C₄×C₈₉	—	4	1	no	—
311	C₄×C₈₉	—	4	3	no	—
312	C₄×C₈₉	—	4	3	no	—
313	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
314	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₄×C₈₉	#585	1	1	yes	characteristic
316	#62151	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
317	C₂×C₈₉	—	4	3	no	—
318	C₂×C₈₉	—	4	2	no	—
319	C₂×C₈₉	—	8	1	no	—
320	C₂×C₈₉	—	8	3	no	—
321	C₂×C₈₉	#3489	1	1	yes	characteristic
322	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
323	C₂×C₈₉	#3584	1	1	yes	characteristic
324	#3518	C₂×C₈₉	1	1	yes	characteristic, complemented
325	D₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
326	Q₈×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
327	Q₈×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
328	#3362	C₂×C₈₉	1	1	yes	characteristic, complemented
329	#3358	C₂×C₈₉	1	1	yes	characteristic, complemented
330	#3354	C₂×C₈₉	1	3	yes	complemented
331	#3353	C₂×C₈₉	1	3	yes	complemented
332	#3325	C₂×C₈₉	1	3	yes	complemented
333	#3324	C₂×C₈₉	1	3	yes	complemented
334	#3251	C₂×C₈₉	1	3	yes	complemented
335	#3228	C₂×C₈₉	1	3	yes	complemented
336	#3105	C₂×C₈₉	1	3	yes	complemented
337	#3077	C₂×C₈₉	1	3	yes	complemented
338	#2991	C₂×C₈₉	1	1	yes	characteristic, complemented
339	C₈₉	#62151	1	1	yes	characteristic, direct product factor, Sylow
340	C₂²×#41	—	2	1	no	—
341	Q₈²	C₂²×C₈₉	1	1	yes	characteristic, complemented
342	#556	—	2	3	no	—
343	#556	C₂²×C₈₉	1	3	yes	complemented
344	#555	C₂²×C₈₉	1	3	yes	complemented
345	#550	C₂²×C₈₉	1	1	yes	characteristic
346	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
347	D₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
348	#548	—	2	1	no	—
349	#548	—	2	1	no	—
350	#547	C₂²×C₈₉	1	3	yes	—
351	#546	—	2	3	no	—
352	D₄²	C₂²×C₈₉	1	3	yes	—
353	#542	—	2	3	no	—
354	#533	C₂²×C₈₉	1	3	yes	complemented
355	#532	C₂²×C₈₉	1	3	yes	—
356	#529	C₂²×C₈₉	1	3	yes	complemented
357	#525	—	2	3	no	—
358	#519	—	2	1	no	—
359	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
360	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
361	#500	C₂²×C₈₉	1	3	yes	complemented
362	#498	C₂²×C₈₉	1	3	yes	complemented
363	#486	C₂²×C₈₉	1	3	yes	complemented
364	#486	C₂²×C₈₉	1	3	yes	complemented
365	#484	C₂²×C₈₉	1	3	yes	complemented
366	#482	C₂²×C₈₉	1	6	yes	complemented
367	#482	C₂²×C₈₉	1	6	yes	complemented
368	#481	C₂²×C₈₉	1	3	yes	complemented
369	#478	C₂²×C₈₉	1	3	yes	—
370	#478	C₂²×C₈₉	1	6	yes	complemented
371	#478	C₂²×C₈₉	1	3	yes	complemented
372	#476	C₂²×C₈₉	1	3	yes	—
373	#476	C₂²×C₈₉	1	3	yes	complemented
374	#475	C₂²×C₈₉	1	3	yes	complemented
375	#474	C₂²×C₈₉	1	3	yes	—
376	#474	C₂²×C₈₉	1	3	yes	complemented
377	#474	C₂²×C₈₉	1	3	yes	complemented
378	#469	C₂²×C₈₉	1	6	yes	complemented
379	#468	C₂²×C₈₉	1	6	yes	complemented
380	#463	C₂²×C₈₉	1	1	yes	characteristic
381	#463	C₂²×C₈₉	1	3	yes	complemented
382	#460	C₂²×C₈₉	1	3	yes	complemented
383	#459	C₂²×C₈₉	1	3	yes	complemented
384	#450	C₂²×C₈₉	1	3	yes	—
385	#447	C₂²×C₈₉	1	3	yes	—
386	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
387	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
388	C₄×SD₁₆	C₂²×C₈₉	1	3	yes	—
389	C₄×SD₁₆	C₂²×C₈₉	1	3	yes	complemented
390	C₄×D₈	C₂²×C₈₉	1	3	yes	—
391	C₄×D₈	C₂²×C₈₉	1	3	yes	complemented
392	#436	C₂²×C₈₉	1	3	yes	complemented
393	#436	C₂²×C₈₉	1	3	yes	complemented
394	#431	C₂²×C₈₉	1	3	yes	complemented
395	#428	C₂²×C₈₉	1	6	yes	complemented
396	#423	C₂²×C₈₉	1	3	yes	complemented
397	#418	C₂²×C₈₉	1	6	yes	—
398	C₂×#41	—	2	1	no	—
399	C₂×#41	—	2	3	no	—
400	C₂×#41	—	2	3	no	—
401	C₂×#41	—	4	8	no	—
402	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×D₄	—	2	3	no	—
406	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
407	C₂³×C₄	—	2	3	no	—
408	C₂×SD₁₆	C₂³×C₈₉	1	1	yes	characteristic
409	C₂×SD₁₆	C₂³×C₈₉	1	3	yes	—
410	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
411	C₂×D₈	C₂³×C₈₉	1	3	yes	—
412	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
413	C₄⋊Q₈	—	2	3	no	—
414	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
415	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
416	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
417	#127	C₂³×C₈₉	1	3	yes	—
418	#126	—	2	6	no	—
419	#126	—	2	3	no	—
420	#125	C₂³×C₈₉	1	3	yes	—
421	#124	—	2	3	no	—
422	#124	—	2	6	no	—
423	#124	—	2	3	no	—
424	#124	C₂³×C₈₉	1	1	yes	characteristic
425	#123	—	2	3	no	—
426	#123	—	2	6	no	—
427	C₂²⋊Q₈	—	2	3	no	—
428	C₂²⋊Q₈	—	2	3	no	—
429	C₂²⋊Q₈	—	2	3	no	—
430	C₂²⋊Q₈	—	2	3	no	—
431	C₂²⋊Q₈	—	2	3	no	—
432	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
433	#121	—	2	3	no	—
434	#121	—	2	3	no	—
435	#121	—	2	3	no	—
436	#121	—	2	3	no	—
437	#121	C₂³×C₈₉	1	3	yes	—
438	#121	C₂³×C₈₉	1	6	yes	—
439	#120	—	2	6	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	3	no	—
442	C₄×Q₈	—	2	3	no	—
443	C₄×Q₈	—	2	3	no	—
444	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
445	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
446	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
447	C₄×D₄	—	2	3	no	—
448	C₄×D₄	—	2	3	no	—
449	C₄×D₄	—	2	3	no	—
450	C₄×D₄	—	2	3	no	—
451	C₄×D₄	D₄×C₈₉	1	3	yes	—
452	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
453	C₄×D₄	C₂³×C₈₉	1	3	yes	—
454	C₄×D₄	C₂³×C₈₉	1	3	yes	—
455	C₄×D₄	C₂³×C₈₉	1	3	yes	—
456	C₄×D₄	C₂³×C₈₉	1	3	yes	—
457	C₄×D₄	C₂³×C₈₉	1	3	yes	—
458	#117	—	2	3	no	—
459	#117	—	2	3	no	—
460	#117	D₄×C₈₉	1	3	yes	—
461	#117	C₂³×C₈₉	1	6	yes	—
462	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
463	C₂×C₂²⋊C₄	—	2	3	no	—
464	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
465	#107	C₂³×C₈₉	1	3	yes	—
466	#107	C₂³×C₈₉	1	6	yes	—
467	#107	C₂³×C₈₉	1	3	yes	—
468	#106	C₂³×C₈₉	1	3	yes	—
469	#106	C₂³×C₈₉	1	6	yes	—
470	#106	C₂³×C₈₉	1	3	yes	—
471	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
472	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
473	C₄⋊C₈	C₂³×C₈₉	1	3	yes	—
474	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
475	#103	C₂³×C₈₉	1	3	yes	—
476	#103	C₂³×C₈₉	1	1	yes	characteristic
477	#102	C₂³×C₈₉	1	3	yes	—
478	#102	C₂³×C₈₉	1	3	yes	—
479	#102	C₂³×C₈₉	1	6	yes	—
480	#102	C₂³×C₈₉	1	6	yes	—
481	#102	C₂³×C₈₉	1	3	yes	—
482	#102	C₂³×C₈₉	1	1	yes	characteristic
483	#102	C₂³×C₈₉	1	3	yes	—
484	#102	C₂³×C₈₉	1	3	yes	—
485	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
486	C₂²⋊C₈	C₂³×C₈₉	1	3	yes	—
487	C₄×C₈	C₂³×C₈₉	1	3	yes	—
488	C₄×C₈	C₂³×C₈₉	1	3	yes	—
489	C₂⁴	—	2	3	no	—
490	#41	—	2	4	no	—
491	#41	—	4	12	no	—
492	#41	—	4	12	no	—
493	#41	—	4	4	no	—
494	C₂×Q₈	—	2	3	no	—
495	C₂×Q₈	—	2	3	no	—
496	C₂×Q₈	—	2	3	no	—
497	C₂×Q₈	—	4	4	no	—
498	C₂×Q₈	—	4	4	no	—
499	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
500	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
501	C₂×D₄	—	2	6	no	—
502	C₂×D₄	—	2	6	no	—
503	C₂×D₄	—	2	3	no	—
504	C₂×D₄	—	2	3	no	—
505	C₂×D₄	—	2	3	no	—
506	C₂×D₄	—	2	3	no	—
507	C₂×D₄	—	4	3	no	—
508	C₂×D₄	—	4	12	no	—
509	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
510	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
511	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
512	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
513	C₂²×C₄	—	2	3	no	—
514	C₂²×C₄	—	2	3	no	—
515	C₂²×C₄	—	2	1	no	—
516	C₂²×C₄	—	2	3	no	—
517	C₂²×C₄	—	2	3	no	—
518	C₂²×C₄	—	2	3	no	—
519	C₂²×C₄	—	4	12	no	—
520	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
521	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
522	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
523	SD₁₆	—	2	2	no	—
524	SD₁₆	—	4	3	no	—
525	D₈	—	2	2	no	—
526	D₈	—	4	3	no	—
527	M₁₆	—	4	6	no	—
528	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
529	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
530	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
531	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
532	C₄⋊C₄	—	2	3	no	—
533	C₄⋊C₄	—	2	3	no	—
534	C₄⋊C₄	—	2	3	no	—
535	C₄⋊C₄	—	2	3	no	—
536	C₄⋊C₄	—	2	3	no	—
537	C₄⋊C₄	—	2	3	no	—
538	C₄⋊C₄	—	2	3	no	—
539	C₄⋊C₄	—	2	3	no	—
540	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
541	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
542	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
543	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
544	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
545	C₄⋊C₄	C₂⁴×C₈₉	1	3	yes	—
546	C₂²⋊C₄	—	2	6	no	—
547	C₂²⋊C₄	—	2	3	no	—
548	C₂²⋊C₄	—	2	1	no	—
549	C₂²⋊C₄	—	2	3	no	—
550	C₂²⋊C₄	—	2	3	no	—
551	C₂²⋊C₄	—	2	3	no	—
552	C₂²⋊C₄	—	2	3	no	—
553	C₂²⋊C₄	—	2	1	no	—
554	C₂²⋊C₄	—	2	1	no	—
555	C₂²⋊C₄	—	2	6	no	—
556	C₂²⋊C₄	—	2	3	no	—
557	C₂²⋊C₄	C₂×D₄×C₈₉	1	6	yes	—
558	C₄²	—	2	6	no	—
559	C₄²	—	2	3	no	—
560	C₄²	C₂×D₄×C₈₉	1	3	yes	—
561	C₄²	C₂×D₄×C₈₉	1	3	yes	—
562	C₄²	C₂⁴×C₈₉	1	3	yes	—
563	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	3	no	—
567	C₂³	—	4	6	no	—
568	C₂³	—	4	6	no	—
569	C₂³	—	8	3	no	—
570	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
571	Q₈	—	2	1	no	—
572	Q₈	—	2	1	no	—
573	Q₈	—	4	6	no	—
574	Q₈	—	4	6	no	—
575	Q₈	—	8	3	no	—
576	Q₈	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
577	D₄	—	2	6	no	—
578	D₄	—	2	1	no	—
579	D₄	—	2	3	no	—
580	D₄	—	2	1	no	—
581	D₄	—	2	1	no	—
582	D₄	—	2	3	no	—
583	D₄	—	4	6	no	—
584	D₄	—	4	12	no	—
585	D₄	—	4	6	no	—
586	D₄	—	8	3	no	—
587	D₄	—	8	3	no	—
588	D₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
589	C₂×C₄	—	2	6	no	—
590	C₂×C₄	—	2	3	no	—
591	C₂×C₄	—	2	3	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	3	no	—
594	C₂×C₄	—	2	3	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	3	no	—
597	C₂×C₄	—	4	3	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	6	no	—
600	C₂×C₄	—	4	6	no	—
601	C₂×C₄	—	4	6	no	—
602	C₂×C₄	—	4	6	no	—
603	C₂×C₄	—	4	6	no	—
604	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
605	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
608	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
609	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	2	3	no	—
613	C₈	—	2	3	no	—
614	C₂²	—	2	3	no	—
615	C₂²	—	2	3	no	—
616	C₂²	—	2	3	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	3	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	3	no	—
624	C₂²	—	4	3	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	8	12	no	—
627	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
628	C₄	—	2	1	no	—
629	C₄	—	2	1	no	—
630	C₄	—	2	3	no	—
631	C₄	—	2	3	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	3	no	—
634	C₄	—	4	3	no	—
635	C₄	—	4	3	no	—
636	C₄	—	4	1	no	—
637	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	6	yes	—
638	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
639	C₄	#585×C₈₉	1	1	yes	characteristic
640	C₂	—	4	3	no	—
641	C₂	—	4	2	no	—
642	C₂	—	8	1	no	—
643	C₂	—	8	3	no	—
644	C₂	C₈₉×#3489	1	1	yes	characteristic
645	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
646	C₂	C₈₉×#3584	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. D₄×#41×C₈₉	C₂	semidirect
3. Q₈×SD₁₆×C₈₉	C₂	semidirect
4. Q₈×D₈×C₈₉	C₂	semidirect
5. C₈₉×#3362	C₂	semidirect
6. C₈₉×#3358	C₂	semidirect
7. C₈₉×#3354	C₂	semidirect
8. C₈₉×#3353	C₂	semidirect
9. C₈₉×#3325	C₂	semidirect
10. C₈₉×#3324	C₂	semidirect
11. C₈₉×#3251	C₂	semidirect
12. C₈₉×#3228	C₂	semidirect
13. C₈₉×#3105	C₂	semidirect
14. C₈₉×#3077	C₂	semidirect
15. C₈₉×#2991	C₂	semidirect
17. Q₈²×C₈₉	C₂²	semidirect
19. #556×C₈₉	C₂²	semidirect
20. #555×C₈₉	C₂²	semidirect
23. D₄×Q₈×C₈₉	C₂²	semidirect
30. #533×C₈₉	C₂²	semidirect
32. #529×C₈₉	C₂²	semidirect
37. #500×C₈₉	C₂²	semidirect
38. #498×C₈₉	C₂²	semidirect
39. #486×C₈₉	C₂²	semidirect
40. #486×C₈₉	C₂²	semidirect
41. #484×C₈₉	C₂²	semidirect
42. #482×C₈₉	C₂²	semidirect
43. #482×C₈₉	C₂²	semidirect
44. #481×C₈₉	C₂²	semidirect
46. #478×C₈₉	C₂²	semidirect
47. #478×C₈₉	C₂²	semidirect
49. #476×C₈₉	C₂²	semidirect
50. #475×C₈₉	C₂²	semidirect
52. #474×C₈₉	C₂²	semidirect
53. #474×C₈₉	C₂²	semidirect
54. #469×C₈₉	C₂²	semidirect
55. #468×C₈₉	C₂²	semidirect
57. #463×C₈₉	C₂²	semidirect
58. #460×C₈₉	C₂²	semidirect
59. #459×C₈₉	C₂²	semidirect
62. C₈×Q₈×C₈₉	C₂²	semidirect
63. C₈×Q₈×C₈₉	C₂²	semidirect
65. C₄×SD₁₆×C₈₉	C₂²	semidirect
67. C₄×D₈×C₈₉	C₂²	semidirect
68. #436×C₈₉	C₂²	semidirect
69. #436×C₈₉	C₂²	semidirect
70. #431×C₈₉	C₂²	semidirect
71. #428×C₈₉	C₂²	semidirect
72. #423×C₈₉	C₂²	semidirect
316. #62151	C₈₉	direct (N × H)
324. #3518	C₂×C₈₉	semidirect
325. D₄×#41	C₂×C₈₉	semidirect
326. Q₈×SD₁₆	C₂×C₈₉	semidirect
327. Q₈×D₈	C₂×C₈₉	semidirect
328. #3362	C₂×C₈₉	semidirect
329. #3358	C₂×C₈₉	semidirect
330. #3354	C₂×C₈₉	semidirect
331. #3353	C₂×C₈₉	semidirect
332. #3325	C₂×C₈₉	semidirect
333. #3324	C₂×C₈₉	semidirect
334. #3251	C₂×C₈₉	semidirect
335. #3228	C₂×C₈₉	semidirect
336. #3105	C₂×C₈₉	semidirect
337. #3077	C₂×C₈₉	semidirect
338. #2991	C₂×C₈₉	semidirect
339. C₈₉	#62151	direct (N × H)
341. Q₈²	C₂²×C₈₉	semidirect
343. #556	C₂²×C₈₉	semidirect
344. #555	C₂²×C₈₉	semidirect
347. D₄×Q₈	C₂²×C₈₉	semidirect
354. #533	C₂²×C₈₉	semidirect
356. #529	C₂²×C₈₉	semidirect
361. #500	C₂²×C₈₉	semidirect
362. #498	C₂²×C₈₉	semidirect
363. #486	C₂²×C₈₉	semidirect
364. #486	C₂²×C₈₉	semidirect
365. #484	C₂²×C₈₉	semidirect
366. #482	C₂²×C₈₉	semidirect
367. #482	C₂²×C₈₉	semidirect
368. #481	C₂²×C₈₉	semidirect
370. #478	C₂²×C₈₉	semidirect
371. #478	C₂²×C₈₉	semidirect
373. #476	C₂²×C₈₉	semidirect
374. #475	C₂²×C₈₉	semidirect
376. #474	C₂²×C₈₉	semidirect
377. #474	C₂²×C₈₉	semidirect
378. #469	C₂²×C₈₉	semidirect
379. #468	C₂²×C₈₉	semidirect
381. #463	C₂²×C₈₉	semidirect
382. #460	C₂²×C₈₉	semidirect
383. #459	C₂²×C₈₉	semidirect
386. C₈×Q₈	C₂²×C₈₉	semidirect
387. C₈×Q₈	C₂²×C₈₉	semidirect
389. C₄×SD₁₆	C₂²×C₈₉	semidirect
391. C₄×D₈	C₂²×C₈₉	semidirect
392. #436	C₂²×C₈₉	semidirect
393. #436	C₂²×C₈₉	semidirect
394. #431	C₂²×C₈₉	semidirect
395. #428	C₂²×C₈₉	semidirect
396. #423	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
D₄×#41×C₈₉	2
Q₈×SD₁₆×C₈₉	2
Q₈×D₈×C₈₉	2
C₈₉×#3362	2
C₈₉×#3358	2
C₈₉×#3354	2
C₈₉×#3353	2
C₈₉×#3325	2
C₈₉×#3324	2
C₈₉×#3251	2
C₈₉×#3228	2
C₈₉×#3105	2
C₈₉×#3077	2
C₈₉×#2991	2
#62151	89

Subgroups — C89×#62151 #36439999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62151 #36439999