Subgroups — C₈₉×#62851 #36440699

Order 22784.

7066 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3524	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3522	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3517	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3516	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3506	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3502	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3497	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3492	C₂	1	6	yes	maximal, complemented
9	C₈₉×#3487	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3460	C₂	1	6	yes	maximal, complemented
11	C₈₉×#3455	C₂	1	6	yes	maximal, complemented
12	C₄×2₋¹⁺⁴×C₈₉	C₂	1	2	yes	maximal, complemented
13	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	#559×C₈₉	C₂²	1	24	yes	complemented
17	Q₈²×C₈₉	C₂²	1	4	yes	complemented
18	#557×C₈₉	C₂²	1	8	yes	complemented
19	#557×C₈₉	C₂²	1	4	yes	complemented
20	#556×C₈₉	C₂²	1	12	yes	complemented
21	#555×C₈₉	C₂²	1	12	yes	complemented
22	#554×C₈₉	C₂²	1	24	yes	complemented
23	#553×C₈₉	C₂²	1	24	yes	complemented
24	#553×C₈₉	C₂²	1	24	yes	complemented
25	#552×C₈₉	C₂²	1	24	yes	complemented
26	#550×C₈₉	C₂²	1	8	yes	—
27	#550×C₈₉	C₂²	1	8	yes	—
28	#550×C₈₉	C₂²	1	4	yes	complemented
29	#550×C₈₉	C₂²	1	12	yes	complemented
30	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
31	#548×C₈₉	C₂²	1	8	yes	—
32	#548×C₈₉	C₂²	1	8	yes	—
33	#548×C₈₉	C₂²	1	8	yes	complemented
34	#547×C₈₉	C₂²	1	24	yes	complemented
35	#547×C₈₉	C₂²	1	12	yes	complemented
36	#544×C₈₉	C₂²	1	6	yes	—
37	#542×C₈₉	C₂²	1	12	yes	complemented
38	#542×C₈₉	C₂²	1	12	yes	complemented
39	#542×C₈₉	C₂²	1	24	yes	complemented
40	#541×C₈₉	C₂²	1	12	yes	complemented
41	#540×C₈₉	C₂²	1	12	yes	complemented
42	#540×C₈₉	C₂²	1	24	yes	complemented
43	#539×C₈₉	C₂²	1	4	yes	—
44	#539×C₈₉	C₂²	1	12	yes	—
45	#538×C₈₉	C₂²	1	12	yes	—
46	#538×C₈₉	C₂²	1	12	yes	—
47	#537×C₈₉	C₂²	1	6	yes	—
48	#535×C₈₉	C₂²	1	12	yes	—
49	#533×C₈₉	C₂²	1	6	yes	—
50	#532×C₈₉	C₂²	1	6	yes	—
51	#532×C₈₉	C₂²	1	24	yes	complemented
52	#529×C₈₉	C₂²	1	24	yes	complemented
53	#529×C₈₉	C₂²	1	24	yes	complemented
54	#529×C₈₉	C₂²	1	24	yes	complemented
55	#525×C₈₉	C₂²	1	12	yes	—
56	#525×C₈₉	C₂²	1	24	yes	—
57	#520×C₈₉	C₂²	1	8	yes	—
58	#520×C₈₉	C₂²	1	8	yes	—
59	#520×C₈₉	C₂²	1	12	yes	—
60	#520×C₈₉	C₂²	1	8	yes	complemented
61	#519×C₈₉	C₂²	1	2	yes	—
62	#519×C₈₉	C₂²	1	8	yes	complemented
63	C₄×#41×C₈₉	C₂²	1	12	yes	—
64	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
65	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×C₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
68	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
69	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
70	C₂×#117×C₈₉	C₂²	1	3	yes	—
71	C₂²×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
72	2₋¹⁺⁴×C₈₉	—	2	16	no	—
73	C₂×#41×C₈₉	—	2	8	no	—
74	C₂×#41×C₈₉	C₂³	1	12	yes	—
75	C₂×#41×C₈₉	C₂³	1	8	yes	—
76	C₂×#41×C₈₉	C₂³	1	8	yes	—
77	C₂×#41×C₈₉	C₂³	1	24	yes	—
78	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
82	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
83	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
84	C₄⋊Q₈×C₈₉	C₂³	1	24	yes	—
85	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
86	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
87	#127×C₈₉	C₂³	1	6	yes	—
88	#127×C₈₉	C₂³	1	24	yes	—
89	#126×C₈₉	C₂³	1	24	yes	—
90	#126×C₈₉	C₂³	1	8	yes	—
91	#126×C₈₉	C₂³	1	24	yes	—
92	#126×C₈₉	C₂³	1	24	yes	—
93	#125×C₈₉	C₂³	1	8	yes	—
94	#125×C₈₉	C₂³	1	24	yes	—
95	#125×C₈₉	C₂³	1	24	yes	—
96	#125×C₈₉	C₂³	1	12	yes	—
97	#124×C₈₉	C₂³	1	24	yes	—
98	#124×C₈₉	C₂³	1	24	yes	—
99	#124×C₈₉	C₂³	1	24	yes	—
100	#124×C₈₉	C₂³	1	12	yes	—
101	#123×C₈₉	C₂³	1	8	yes	—
102	#123×C₈₉	C₂³	1	48	yes	—
103	#123×C₈₉	C₂³	1	24	yes	—
104	#123×C₈₉	C₂³	1	8	yes	—
105	#123×C₈₉	C₂³	1	24	yes	—
106	#123×C₈₉	C₂³	1	24	yes	—
107	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
108	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
109	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
110	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
111	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
112	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
113	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
114	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
115	#121×C₈₉	C₂³	1	12	yes	—
116	#121×C₈₉	C₂³	1	24	yes	—
117	#121×C₈₉	C₂³	1	12	yes	—
118	#121×C₈₉	C₂³	1	12	yes	—
119	#121×C₈₉	C₂³	1	24	yes	—
120	#121×C₈₉	C₂³	1	24	yes	—
121	#121×C₈₉	C₂³	1	24	yes	—
122	#121×C₈₉	C₂³	1	4	yes	—
123	#121×C₈₉	C₂³	1	24	yes	—
124	#121×C₈₉	C₂³	1	24	yes	—
125	#120×C₈₉	C₂³	1	24	yes	—
126	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
127	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
128	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
129	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
130	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
131	C₄×Q₈×C₈₉	C₂³	1	24	yes	—
132	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
133	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
134	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
135	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
136	C₄×D₄×C₈₉	C₂³	1	24	yes	—
137	C₄×D₄×C₈₉	C₂³	1	12	yes	—
138	C₄×D₄×C₈₉	C₂³	1	12	yes	—
139	C₄×D₄×C₈₉	C₂³	1	8	yes	—
140	C₄×D₄×C₈₉	C₂³	1	12	yes	—
141	C₄×D₄×C₈₉	C₂³	1	24	yes	—
142	C₄×D₄×C₈₉	C₂³	1	12	yes	—
143	C₄×D₄×C₈₉	C₂³	1	24	yes	—
144	C₄×D₄×C₈₉	C₂³	1	24	yes	—
145	C₄×D₄×C₈₉	C₂³	1	24	yes	—
146	C₄×D₄×C₈₉	C₂³	1	48	yes	—
147	C₄×D₄×C₈₉	C₂³	1	12	yes	—
148	C₄×D₄×C₈₉	C₂³	1	12	yes	—
149	#117×C₈₉	C₂³	1	12	yes	—
150	#117×C₈₉	C₂³	1	12	yes	—
151	#117×C₈₉	C₂³	1	12	yes	—
152	#117×C₈₉	C₂³	1	24	yes	—
153	#117×C₈₉	C₂³	1	24	yes	—
154	#117×C₈₉	C₂³	1	24	yes	—
155	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
156	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
157	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
158	C₂×C₄⋊C₄×C₈₉	C₂³	1	24	yes	—
159	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₈₉	C₂³	1	24	yes	—
161	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
162	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
163	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
164	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
165	C₂×C₄²×C₈₉	C₂³	1	24	yes	—
166	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
167	#41×C₈₉	—	2	32	no	—
168	#41×C₈₉	—	2	32	no	—
169	#41×C₈₉	—	2	48	no	—
170	#41×C₈₉	—	8	24	no	—
171	C₂×Q₈×C₈₉	—	2	32	no	—
172	C₂×Q₈×C₈₉	#41	1	8	yes	complemented
173	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
174	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
175	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
176	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
177	C₂×D₄×C₈₉	—	2	12	no	—
178	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
179	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
180	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
181	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
182	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
183	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
184	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
185	C₂²×C₄×C₈₉	—	2	12	no	—
186	C₂²×C₄×C₈₉	—	8	6	no	—
187	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
188	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
193	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
194	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
195	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
196	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
198	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
199	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
200	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
201	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
202	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
203	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
204	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
205	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
206	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
207	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
208	C₄⋊C₄×C₈₉	C₂⁴	1	12	yes	—
209	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
210	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
211	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
212	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
213	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
214	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
215	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
216	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
217	C₂²⋊C₄×C₈₉	C₂⁴	1	6	yes	—
218	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
219	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
220	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
221	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
222	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
223	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
224	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
225	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
226	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
227	C₄²×C₈₉	C₂⁴	1	12	yes	—
228	C₄²×C₈₉	C₂⁴	1	8	yes	—
229	C₄²×C₈₉	C₂⁴	1	24	yes	—
230	C₄²×C₈₉	C₂⁴	1	6	yes	—
231	C₄²×C₈₉	C₂⁴	1	6	yes	—
232	C₄²×C₈₉	C₂⁴	1	24	yes	—
233	C₂³×C₈₉	—	2	6	no	—
234	C₂³×C₈₉	—	4	3	no	—
235	C₂³×C₈₉	—	4	3	no	—
236	C₂³×C₈₉	C₂⁵	1	6	yes	—
237	C₂³×C₈₉	C₂⁵	1	8	yes	—
238	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
239	Q₈×C₈₉	—	2	24	no	—
240	Q₈×C₈₉	—	4	4	no	—
241	Q₈×C₈₉	—	4	12	no	—
242	Q₈×C₈₉	C₂×#41	1	16	yes	—
243	D₄×C₈₉	—	2	16	no	—
244	D₄×C₈₉	—	2	24	no	—
245	D₄×C₈₉	—	2	24	no	—
246	D₄×C₈₉	—	4	4	no	—
247	D₄×C₈₉	—	4	24	no	—
248	D₄×C₈₉	—	4	12	no	—
249	D₄×C₈₉	—	4	24	no	—
250	C₂×C₄×C₈₉	—	2	2	no	—
251	C₂×C₄×C₈₉	—	2	24	no	—
252	C₂×C₄×C₈₉	—	2	48	no	—
253	C₂×C₄×C₈₉	—	4	3	no	—
254	C₂×C₄×C₈₉	—	4	3	no	—
255	C₂×C₄×C₈₉	—	4	24	no	—
256	C₂×C₄×C₈₉	—	4	1	no	—
257	C₂×C₄×C₈₉	—	4	8	no	—
258	C₂×C₄×C₈₉	—	4	1	no	—
259	C₂×C₄×C₈₉	—	4	24	no	—
260	C₂×C₄×C₈₉	C₂×#41	1	12	yes	—
261	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
262	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
263	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
264	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
265	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
266	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
267	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
268	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
269	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
270	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
271	C₂²×C₈₉	—	2	1	no	—
272	C₂²×C₈₉	—	2	1	no	—
273	C₂²×C₈₉	—	2	8	no	—
274	C₂²×C₈₉	—	2	6	no	—
275	C₂²×C₈₉	—	2	6	no	—
276	C₂²×C₈₉	—	2	8	no	—
277	C₂²×C₈₉	—	2	8	no	—
278	C₂²×C₈₉	—	2	6	no	—
279	C₂²×C₈₉	—	4	12	no	—
280	C₂²×C₈₉	C₂²×#41	1	2	yes	—
281	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
282	C₄×C₈₉	—	2	2	no	—
283	C₄×C₈₉	—	2	8	no	—
284	C₄×C₈₉	—	2	6	no	—
285	C₄×C₈₉	—	2	6	no	—
286	C₄×C₈₉	—	2	8	no	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	1	no	—
289	C₄×C₈₉	—	2	8	no	—
290	C₄×C₈₉	—	2	1	no	—
291	C₄×C₈₉	C₂²×#41	1	12	yes	—
292	#62851	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
293	C₂×C₈₉	—	2	2	no	—
294	C₂×C₈₉	—	4	8	no	—
295	C₂×C₈₉	—	4	6	no	—
296	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
297	C₂×C₈₉	H(7,𝔽₂)	1	1	yes	characteristic
298	C₂×C₈₉	2₋¹⁺⁶	1	1	yes	characteristic
299	#3524	C₂×C₈₉	1	8	yes	complemented
300	#3522	C₂×C₈₉	1	8	yes	complemented
301	#3517	C₂×C₈₉	1	8	yes	complemented
302	#3516	C₂×C₈₉	1	8	yes	complemented
303	#3506	C₂×C₈₉	1	6	yes	complemented
304	#3502	C₂×C₈₉	1	1	yes	characteristic, complemented
305	#3497	C₂×C₈₉	1	1	yes	characteristic, complemented
306	#3492	C₂×C₈₉	1	6	yes	complemented
307	#3487	C₂×C₈₉	1	2	yes	complemented
308	#3460	C₂×C₈₉	1	6	yes	complemented
309	#3455	C₂×C₈₉	1	6	yes	complemented
310	C₄×2₋¹⁺⁴	C₂×C₈₉	1	2	yes	complemented
311	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
312	C₈₉	#62851	1	1	yes	characteristic, direct product factor, Sylow
313	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
314	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
315	#559	C₂²×C₈₉	1	24	yes	complemented
316	Q₈²	C₂²×C₈₉	1	4	yes	complemented
317	#557	C₂²×C₈₉	1	8	yes	complemented
318	#557	C₂²×C₈₉	1	4	yes	complemented
319	#556	C₂²×C₈₉	1	12	yes	complemented
320	#555	C₂²×C₈₉	1	12	yes	complemented
321	#554	C₂²×C₈₉	1	24	yes	complemented
322	#553	C₂²×C₈₉	1	24	yes	complemented
323	#553	C₂²×C₈₉	1	24	yes	complemented
324	#552	C₂²×C₈₉	1	24	yes	complemented
325	#550	C₂²×C₈₉	1	8	yes	—
326	#550	C₂²×C₈₉	1	8	yes	—
327	#550	C₂²×C₈₉	1	4	yes	complemented
328	#550	C₂²×C₈₉	1	12	yes	complemented
329	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
330	#548	C₂²×C₈₉	1	8	yes	—
331	#548	C₂²×C₈₉	1	8	yes	—
332	#548	C₂²×C₈₉	1	8	yes	complemented
333	#547	C₂²×C₈₉	1	24	yes	complemented
334	#547	C₂²×C₈₉	1	12	yes	complemented
335	#544	C₂²×C₈₉	1	6	yes	—
336	#542	C₂²×C₈₉	1	12	yes	complemented
337	#542	C₂²×C₈₉	1	12	yes	complemented
338	#542	C₂²×C₈₉	1	24	yes	complemented
339	#541	C₂²×C₈₉	1	12	yes	complemented
340	#540	C₂²×C₈₉	1	12	yes	complemented
341	#540	C₂²×C₈₉	1	24	yes	complemented
342	#539	C₂²×C₈₉	1	4	yes	—
343	#539	C₂²×C₈₉	1	12	yes	—
344	#538	C₂²×C₈₉	1	12	yes	—
345	#538	C₂²×C₈₉	1	12	yes	—
346	#537	C₂²×C₈₉	1	6	yes	—
347	#535	C₂²×C₈₉	1	12	yes	—
348	#533	C₂²×C₈₉	1	6	yes	—
349	#532	C₂²×C₈₉	1	6	yes	—
350	#532	C₂²×C₈₉	1	24	yes	complemented
351	#529	C₂²×C₈₉	1	24	yes	complemented
352	#529	C₂²×C₈₉	1	24	yes	complemented
353	#529	C₂²×C₈₉	1	24	yes	complemented
354	#525	C₂²×C₈₉	1	12	yes	—
355	#525	C₂²×C₈₉	1	24	yes	—
356	#520	C₂²×C₈₉	1	8	yes	—
357	#520	C₂²×C₈₉	1	8	yes	—
358	#520	C₂²×C₈₉	1	12	yes	—
359	#520	C₂²×C₈₉	1	8	yes	complemented
360	#519	C₂²×C₈₉	1	2	yes	—
361	#519	C₂²×C₈₉	1	8	yes	complemented
362	C₄×#41	C₂²×C₈₉	1	12	yes	—
363	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
364	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
365	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
366	C₂×C₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
367	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
368	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
369	C₂×#117	C₂²×C₈₉	1	3	yes	—
370	C₂²×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
371	2₋¹⁺⁴	—	2	16	no	—
372	C₂×#41	—	2	8	no	—
373	C₂×#41	C₂³×C₈₉	1	12	yes	—
374	C₂×#41	C₂³×C₈₉	1	8	yes	—
375	C₂×#41	C₂³×C₈₉	1	8	yes	—
376	C₂×#41	C₂³×C₈₉	1	24	yes	—
377	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
378	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
379	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
380	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
381	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
382	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
383	C₄⋊Q₈	C₂³×C₈₉	1	24	yes	—
384	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
385	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
386	#127	C₂³×C₈₉	1	6	yes	—
387	#127	C₂³×C₈₉	1	24	yes	—
388	#126	C₂³×C₈₉	1	24	yes	—
389	#126	C₂³×C₈₉	1	8	yes	—
390	#126	C₂³×C₈₉	1	24	yes	—
391	#126	C₂³×C₈₉	1	24	yes	—
392	#125	C₂³×C₈₉	1	8	yes	—
393	#125	C₂³×C₈₉	1	24	yes	—
394	#125	C₂³×C₈₉	1	24	yes	—
395	#125	C₂³×C₈₉	1	12	yes	—
396	#124	C₂³×C₈₉	1	24	yes	—
397	#124	C₂³×C₈₉	1	24	yes	—
398	#124	C₂³×C₈₉	1	24	yes	—
399	#124	C₂³×C₈₉	1	12	yes	—
400	#123	C₂³×C₈₉	1	8	yes	—
401	#123	C₂³×C₈₉	1	48	yes	—
402	#123	C₂³×C₈₉	1	24	yes	—
403	#123	C₂³×C₈₉	1	8	yes	—
404	#123	C₂³×C₈₉	1	24	yes	—
405	#123	C₂³×C₈₉	1	24	yes	—
406	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
407	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
408	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
409	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
410	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
411	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
412	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
413	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
414	#121	C₂³×C₈₉	1	12	yes	—
415	#121	C₂³×C₈₉	1	24	yes	—
416	#121	C₂³×C₈₉	1	12	yes	—
417	#121	C₂³×C₈₉	1	12	yes	—
418	#121	C₂³×C₈₉	1	24	yes	—
419	#121	C₂³×C₈₉	1	24	yes	—
420	#121	C₂³×C₈₉	1	24	yes	—
421	#121	C₂³×C₈₉	1	4	yes	—
422	#121	C₂³×C₈₉	1	24	yes	—
423	#121	C₂³×C₈₉	1	24	yes	—
424	#120	C₂³×C₈₉	1	24	yes	—
425	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
426	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
427	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
428	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
429	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
430	C₄×Q₈	C₂³×C₈₉	1	24	yes	—
431	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
432	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
433	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
434	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
435	C₄×D₄	C₂³×C₈₉	1	24	yes	—
436	C₄×D₄	C₂³×C₈₉	1	12	yes	—
437	C₄×D₄	C₂³×C₈₉	1	12	yes	—
438	C₄×D₄	C₂³×C₈₉	1	8	yes	—
439	C₄×D₄	C₂³×C₈₉	1	12	yes	—
440	C₄×D₄	C₂³×C₈₉	1	24	yes	—
441	C₄×D₄	C₂³×C₈₉	1	12	yes	—
442	C₄×D₄	C₂³×C₈₉	1	24	yes	—
443	C₄×D₄	C₂³×C₈₉	1	24	yes	—
444	C₄×D₄	C₂³×C₈₉	1	24	yes	—
445	C₄×D₄	C₂³×C₈₉	1	48	yes	—
446	C₄×D₄	C₂³×C₈₉	1	12	yes	—
447	C₄×D₄	C₂³×C₈₉	1	12	yes	—
448	#117	C₂³×C₈₉	1	12	yes	—
449	#117	C₂³×C₈₉	1	12	yes	—
450	#117	C₂³×C₈₉	1	12	yes	—
451	#117	C₂³×C₈₉	1	24	yes	—
452	#117	C₂³×C₈₉	1	24	yes	—
453	#117	C₂³×C₈₉	1	24	yes	—
454	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
455	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
456	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
457	C₂×C₄⋊C₄	C₂³×C₈₉	1	24	yes	—
458	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₈₉	1	24	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
462	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
463	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
464	C₂×C₄²	C₂³×C₈₉	1	24	yes	—
465	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
466	#41	—	2	32	no	—
467	#41	—	2	32	no	—
468	#41	—	2	48	no	—
469	#41	—	8	24	no	—
470	C₂×Q₈	—	2	32	no	—
471	C₂×Q₈	#41×C₈₉	1	8	yes	complemented
472	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
473	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
474	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
475	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
476	C₂×D₄	—	2	12	no	—
477	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
478	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
479	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
480	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
481	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
482	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
483	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
484	C₂²×C₄	—	2	12	no	—
485	C₂²×C₄	—	8	6	no	—
486	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
487	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
489	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
492	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
493	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
494	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
495	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
496	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
497	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
498	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
499	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
500	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
501	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
502	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
503	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
504	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
505	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
506	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
507	C₄⋊C₄	C₂⁴×C₈₉	1	12	yes	—
508	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
509	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
510	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
511	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
512	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
513	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
514	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
515	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
516	C₂²⋊C₄	C₂⁴×C₈₉	1	6	yes	—
517	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
518	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
519	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
520	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
521	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
522	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
523	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
524	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
525	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
526	C₄²	C₂⁴×C₈₉	1	12	yes	—
527	C₄²	C₂⁴×C₈₉	1	8	yes	—
528	C₄²	C₂⁴×C₈₉	1	24	yes	—
529	C₄²	C₂⁴×C₈₉	1	6	yes	—
530	C₄²	C₂⁴×C₈₉	1	6	yes	—
531	C₄²	C₂⁴×C₈₉	1	24	yes	—
532	C₂³	—	2	6	no	—
533	C₂³	—	4	3	no	—
534	C₂³	—	4	3	no	—
535	C₂³	C₂⁵×C₈₉	1	6	yes	—
536	C₂³	C₂⁵×C₈₉	1	8	yes	—
537	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
538	Q₈	—	2	24	no	—
539	Q₈	—	4	4	no	—
540	Q₈	—	4	12	no	—
541	Q₈	C₂×#41×C₈₉	1	16	yes	—
542	D₄	—	2	16	no	—
543	D₄	—	2	24	no	—
544	D₄	—	2	24	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	24	no	—
547	D₄	—	4	12	no	—
548	D₄	—	4	24	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	24	no	—
551	C₂×C₄	—	2	48	no	—
552	C₂×C₄	—	4	3	no	—
553	C₂×C₄	—	4	3	no	—
554	C₂×C₄	—	4	24	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	8	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	24	no	—
559	C₂×C₄	C₂×#41×C₈₉	1	12	yes	—
560	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
561	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
562	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
563	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
564	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
565	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
566	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
567	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
568	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
569	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	6	no	—
574	C₂²	—	2	6	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	2	6	no	—
578	C₂²	—	4	12	no	—
579	C₂²	C₂²×#41×C₈₉	1	2	yes	—
580	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
581	C₄	—	2	2	no	—
582	C₄	—	2	8	no	—
583	C₄	—	2	6	no	—
584	C₄	—	2	6	no	—
585	C₄	—	2	8	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	8	no	—
589	C₄	—	2	1	no	—
590	C₄	C₂²×#41×C₈₉	1	12	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	4	8	no	—
593	C₂	—	4	6	no	—
594	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
595	C₂	C₈₉×H(7,𝔽₂)	1	1	yes	characteristic
596	C₂	C₈₉×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3524	C₂	semidirect
2. C₈₉×#3522	C₂	semidirect
3. C₈₉×#3517	C₂	semidirect
4. C₈₉×#3516	C₂	semidirect
5. C₈₉×#3506	C₂	semidirect
6. C₈₉×#3502	C₂	semidirect
7. C₈₉×#3497	C₂	semidirect
8. C₈₉×#3492	C₂	semidirect
9. C₈₉×#3487	C₂	semidirect
10. C₈₉×#3460	C₂	semidirect
11. C₈₉×#3455	C₂	semidirect
12. C₄×2₋¹⁺⁴×C₈₉	C₂	semidirect
13. C₂×#520×C₈₉	C₂	semidirect
16. #559×C₈₉	C₂²	semidirect
17. Q₈²×C₈₉	C₂²	semidirect
18. #557×C₈₉	C₂²	semidirect
19. #557×C₈₉	C₂²	semidirect
20. #556×C₈₉	C₂²	semidirect
21. #555×C₈₉	C₂²	semidirect
22. #554×C₈₉	C₂²	semidirect
23. #553×C₈₉	C₂²	semidirect
24. #553×C₈₉	C₂²	semidirect
25. #552×C₈₉	C₂²	semidirect
28. #550×C₈₉	C₂²	semidirect
29. #550×C₈₉	C₂²	semidirect
30. D₄×Q₈×C₈₉	C₂²	semidirect
33. #548×C₈₉	C₂²	semidirect
34. #547×C₈₉	C₂²	semidirect
35. #547×C₈₉	C₂²	semidirect
37. #542×C₈₉	C₂²	semidirect
38. #542×C₈₉	C₂²	semidirect
39. #542×C₈₉	C₂²	semidirect
40. #541×C₈₉	C₂²	semidirect
41. #540×C₈₉	C₂²	semidirect
42. #540×C₈₉	C₂²	semidirect
51. #532×C₈₉	C₂²	semidirect
52. #529×C₈₉	C₂²	semidirect
53. #529×C₈₉	C₂²	semidirect
54. #529×C₈₉	C₂²	semidirect
60. #520×C₈₉	C₂²	semidirect
62. #519×C₈₉	C₂²	semidirect
64. C₄×#41×C₈₉	C₂²	semidirect
67. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
172. C₂×Q₈×C₈₉	#41	semidirect
292. #62851	C₈₉	direct (N × H)
299. #3524	C₂×C₈₉	semidirect
300. #3522	C₂×C₈₉	semidirect
301. #3517	C₂×C₈₉	semidirect
302. #3516	C₂×C₈₉	semidirect
303. #3506	C₂×C₈₉	semidirect
304. #3502	C₂×C₈₉	semidirect
305. #3497	C₂×C₈₉	semidirect
306. #3492	C₂×C₈₉	semidirect
307. #3487	C₂×C₈₉	semidirect
308. #3460	C₂×C₈₉	semidirect
309. #3455	C₂×C₈₉	semidirect
310. C₄×2₋¹⁺⁴	C₂×C₈₉	semidirect
311. C₂×#520	C₂×C₈₉	semidirect
312. C₈₉	#62851	direct (N × H)
315. #559	C₂²×C₈₉	semidirect
316. Q₈²	C₂²×C₈₉	semidirect
317. #557	C₂²×C₈₉	semidirect
318. #557	C₂²×C₈₉	semidirect
319. #556	C₂²×C₈₉	semidirect
320. #555	C₂²×C₈₉	semidirect
321. #554	C₂²×C₈₉	semidirect
322. #553	C₂²×C₈₉	semidirect
323. #553	C₂²×C₈₉	semidirect
324. #552	C₂²×C₈₉	semidirect
327. #550	C₂²×C₈₉	semidirect
328. #550	C₂²×C₈₉	semidirect
329. D₄×Q₈	C₂²×C₈₉	semidirect
332. #548	C₂²×C₈₉	semidirect
333. #547	C₂²×C₈₉	semidirect
334. #547	C₂²×C₈₉	semidirect
336. #542	C₂²×C₈₉	semidirect
337. #542	C₂²×C₈₉	semidirect
338. #542	C₂²×C₈₉	semidirect
339. #541	C₂²×C₈₉	semidirect
340. #540	C₂²×C₈₉	semidirect
341. #540	C₂²×C₈₉	semidirect
350. #532	C₂²×C₈₉	semidirect
351. #529	C₂²×C₈₉	semidirect
352. #529	C₂²×C₈₉	semidirect
353. #529	C₂²×C₈₉	semidirect
359. #520	C₂²×C₈₉	semidirect
361. #519	C₂²×C₈₉	semidirect
363. C₄×#41	C₂²×C₈₉	semidirect
366. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
471. C₂×Q₈	#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×#3524	2
C₈₉×#3522	2
C₈₉×#3517	2
C₈₉×#3516	2
C₈₉×#3506	2
C₈₉×#3502	2
C₈₉×#3497	2
C₈₉×#3492	2
C₈₉×#3487	2
C₈₉×#3460	2
C₈₉×#3455	2
C₄×2₋¹⁺⁴×C₈₉	2
C₂×#520×C₈₉	2
#62851	89

Subgroups — C89×#62851 #36440699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62851 #36440699