Subgroups — C₈₉×#62886 #36440734

Order 22784.

6918 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3551	C₂	1	4	yes	maximal, complemented
2	C₈₉×#3550	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3547	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3545	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3544	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3541	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3540	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3538	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3533	C₂	1	8	yes	maximal, complemented
10	C₈₉×#3495	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3493	C₂	1	2	yes	maximal, complemented
12	C₈₉×#3489	C₂	1	4	yes	maximal, complemented
13	C₈₉×#3486	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3449	C₂	1	2	yes	maximal, complemented
15	C₂×#536×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
17	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₈₉	C₂²	1	2	yes	complemented
19	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	#563×C₈₉	C₂²	1	8	yes	complemented
21	#563×C₈₉	C₂²	1	4	yes	complemented
22	#563×C₈₉	C₂²	1	8	yes	complemented
23	#563×C₈₉	C₂²	1	8	yes	complemented
24	#562×C₈₉	C₂²	1	16	yes	complemented
25	#562×C₈₉	C₂²	1	8	yes	complemented
26	H(3,𝔽₄)×C₈₉	C₂²	1	4	yes	complemented
27	#560×C₈₉	C₂²	1	8	yes	complemented
28	#559×C₈₉	C₂²	1	8	yes	complemented
29	Q₈²×C₈₉	C₂²	1	4	yes	complemented
30	#556×C₈₉	C₂²	1	8	yes	complemented
31	#556×C₈₉	C₂²	1	8	yes	complemented
32	#555×C₈₉	C₂²	1	8	yes	complemented
33	#555×C₈₉	C₂²	1	4	yes	complemented
34	#555×C₈₉	C₂²	1	8	yes	complemented
35	#554×C₈₉	C₂²	1	8	yes	complemented
36	#554×C₈₉	C₂²	1	8	yes	complemented
37	#553×C₈₉	C₂²	1	8	yes	complemented
38	#553×C₈₉	C₂²	1	16	yes	complemented
39	#552×C₈₉	C₂²	1	8	yes	complemented
40	#552×C₈₉	C₂²	1	16	yes	complemented
41	#552×C₈₉	C₂²	1	8	yes	complemented
42	#552×C₈₉	C₂²	1	8	yes	complemented
43	#551×C₈₉	C₂²	1	16	yes	complemented
44	#551×C₈₉	C₂²	1	8	yes	complemented
45	#551×C₈₉	C₂²	1	8	yes	complemented
46	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
47	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
48	D₄×Q₈×C₈₉	C₂²	1	8	yes	complemented
49	#548×C₈₉	C₂²	1	8	yes	complemented
50	#548×C₈₉	C₂²	1	8	yes	complemented
51	#548×C₈₉	C₂²	1	8	yes	complemented
52	#547×C₈₉	C₂²	1	16	yes	complemented
53	#547×C₈₉	C₂²	1	8	yes	complemented
54	#546×C₈₉	C₂²	1	16	yes	complemented
55	#546×C₈₉	C₂²	1	8	yes	complemented
56	#544×C₈₉	C₂²	1	2	yes	complemented
57	#544×C₈₉	C₂²	1	16	yes	complemented
58	#542×C₈₉	C₂²	1	8	yes	complemented
59	#542×C₈₉	C₂²	1	16	yes	complemented
60	#542×C₈₉	C₂²	1	16	yes	complemented
61	#542×C₈₉	C₂²	1	16	yes	complemented
62	#541×C₈₉	C₂²	1	8	yes	complemented
63	#540×C₈₉	C₂²	1	16	yes	complemented
64	#539×C₈₉	C₂²	1	16	yes	complemented
65	#538×C₈₉	C₂²	1	8	yes	complemented
66	#538×C₈₉	C₂²	1	16	yes	complemented
67	#538×C₈₉	C₂²	1	16	yes	complemented
68	#537×C₈₉	C₂²	1	4	yes	—
69	#537×C₈₉	C₂²	1	2	yes	—
70	#537×C₈₉	C₂²	1	4	yes	complemented
71	#537×C₈₉	C₂²	1	8	yes	complemented
72	#536×C₈₉	C₂²	1	4	yes	—
73	#536×C₈₉	C₂²	1	2	yes	—
74	#536×C₈₉	C₂²	1	4	yes	complemented
75	#536×C₈₉	C₂²	1	4	yes	complemented
76	#536×C₈₉	C₂²	1	4	yes	complemented
77	#536×C₈₉	C₂²	1	4	yes	complemented
78	#536×C₈₉	C₂²	1	2	yes	complemented
79	#536×C₈₉	C₂²	1	4	yes	complemented
80	#536×C₈₉	C₂²	1	8	yes	complemented
81	#536×C₈₉	C₂²	1	8	yes	complemented
82	#535×C₈₉	C₂²	1	4	yes	—
83	#535×C₈₉	C₂²	1	2	yes	—
84	#535×C₈₉	C₂²	1	2	yes	complemented
85	#534×C₈₉	C₂²	1	4	yes	—
86	#534×C₈₉	C₂²	1	4	yes	complemented
87	#533×C₈₉	C₂²	1	8	yes	complemented
88	#532×C₈₉	C₂²	1	4	yes	—
89	#532×C₈₉	C₂²	1	4	yes	complemented
90	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
91	#529×C₈₉	C₂²	1	8	yes	complemented
92	#529×C₈₉	C₂²	1	8	yes	complemented
93	C₂×#124×C₈₉	C₂²	1	2	yes	—
94	#525×C₈₉	C₂²	1	4	yes	—
95	#525×C₈₉	C₂²	1	4	yes	—
96	#525×C₈₉	C₂²	1	4	yes	complemented
97	#525×C₈₉	C₂²	1	4	yes	complemented
98	#525×C₈₉	C₂²	1	8	yes	complemented
99	#525×C₈₉	C₂²	1	8	yes	complemented
100	C₂×#123×C₈₉	C₂²	1	4	yes	complemented
101	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
102	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
103	#520×C₈₉	C₂²	1	4	yes	complemented
104	#519×C₈₉	C₂²	1	2	yes	complemented
105	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic, complemented
106	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
107	2₋¹⁺⁴×C₈₉	—	4	8	no	—
108	C₂×#41×C₈₉	—	4	4	no	—
109	C₂×#41×C₈₉	—	4	8	no	—
110	C₂×#41×C₈₉	C₂³	1	4	yes	—
111	C₂×#41×C₈₉	C₂³	1	2	yes	—
112	C₂×#41×C₈₉	C₂³	1	2	yes	—
113	C₂×#41×C₈₉	C₂³	1	8	yes	—
114	C₂×#41×C₈₉	C₂³	1	8	yes	—
115	C₂×#41×C₈₉	C₂³	1	2	yes	—
116	C₂×#41×C₈₉	C₂³	1	4	yes	—
117	C₂×#41×C₈₉	C₂³	1	2	yes	—
118	C₂×#41×C₈₉	C₂³	1	4	yes	—
119	C₂×#41×C₈₉	C₂³	1	4	yes	—
120	C₂²×Q₈×C₈₉	—	4	4	no	—
121	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
122	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
123	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
126	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
127	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
128	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
129	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
131	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
132	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
133	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
135	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
137	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
138	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
142	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
143	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
144	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
145	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
146	#127×C₈₉	C₂³	1	4	yes	—
147	#127×C₈₉	C₂³	1	4	yes	—
148	#126×C₈₉	C₂³	1	16	yes	—
149	#126×C₈₉	C₂³	1	16	yes	—
150	#126×C₈₉	C₂³	1	16	yes	—
151	#126×C₈₉	C₂³	1	16	yes	—
152	#126×C₈₉	C₂³	1	16	yes	—
153	#126×C₈₉	C₂³	1	16	yes	—
154	#125×C₈₉	C₂³	1	8	yes	—
155	#125×C₈₉	C₂³	1	8	yes	—
156	#125×C₈₉	C₂³	1	16	yes	—
157	#125×C₈₉	C₂³	1	16	yes	—
158	#125×C₈₉	C₂³	1	16	yes	—
159	#124×C₈₉	C₂³	1	4	yes	—
160	#124×C₈₉	C₂³	1	8	yes	—
161	#124×C₈₉	C₂³	1	4	yes	—
162	#124×C₈₉	C₂³	1	8	yes	—
163	#124×C₈₉	C₂³	1	8	yes	—
164	#124×C₈₉	C₂³	1	4	yes	—
165	#124×C₈₉	C₂³	1	4	yes	—
166	#124×C₈₉	C₂³	1	4	yes	—
167	#124×C₈₉	C₂³	1	4	yes	—
168	#124×C₈₉	C₂³	1	8	yes	—
169	#124×C₈₉	C₂³	1	16	yes	—
170	#124×C₈₉	C₂³	1	8	yes	—
171	#124×C₈₉	C₂³	1	16	yes	—
172	#124×C₈₉	C₂³	1	16	yes	—
173	#123×C₈₉	C₂³	1	8	yes	—
174	#123×C₈₉	C₂³	1	8	yes	—
175	#123×C₈₉	C₂³	1	8	yes	—
176	#123×C₈₉	C₂³	1	8	yes	—
177	#123×C₈₉	C₂³	1	4	yes	—
178	#123×C₈₉	C₂³	1	8	yes	—
179	#123×C₈₉	C₂³	1	4	yes	—
180	#123×C₈₉	C₂³	1	8	yes	—
181	#123×C₈₉	C₂³	1	4	yes	—
182	#123×C₈₉	C₂³	1	4	yes	—
183	#123×C₈₉	C₂³	1	16	yes	—
184	#123×C₈₉	C₂³	1	16	yes	—
185	#123×C₈₉	C₂³	1	16	yes	—
186	#123×C₈₉	C₂³	1	16	yes	—
187	#123×C₈₉	C₂³	1	16	yes	—
188	#123×C₈₉	C₂³	1	16	yes	—
189	#123×C₈₉	C₂³	1	16	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
207	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
208	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
209	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
210	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
211	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
212	#121×C₈₉	C₂³	1	4	yes	—
213	#121×C₈₉	C₂³	1	4	yes	—
214	#121×C₈₉	C₂³	1	8	yes	—
215	#121×C₈₉	C₂³	1	4	yes	—
216	#121×C₈₉	C₂³	1	8	yes	—
217	#121×C₈₉	C₂³	1	4	yes	—
218	#121×C₈₉	C₂³	1	8	yes	—
219	#121×C₈₉	C₂³	1	16	yes	—
220	#121×C₈₉	C₂³	1	8	yes	—
221	#121×C₈₉	C₂³	1	8	yes	—
222	#121×C₈₉	C₂³	1	8	yes	—
223	#121×C₈₉	C₂³	1	8	yes	—
224	#121×C₈₉	C₂³	1	8	yes	—
225	#121×C₈₉	C₂³	1	16	yes	—
226	#121×C₈₉	C₂³	1	16	yes	—
227	#121×C₈₉	C₂³	1	16	yes	—
228	#121×C₈₉	C₂³	1	16	yes	—
229	#120×C₈₉	C₂³	1	8	yes	—
230	#120×C₈₉	C₂³	1	4	yes	—
231	#120×C₈₉	C₂³	1	4	yes	—
232	#120×C₈₉	C₂³	1	8	yes	—
233	#120×C₈₉	C₂³	1	4	yes	—
234	#120×C₈₉	C₂³	1	4	yes	—
235	#120×C₈₉	C₂³	1	16	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
237	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
241	C₄×D₄×C₈₉	C₂³	1	16	yes	—
242	C₄×D₄×C₈₉	C₂³	1	8	yes	—
243	C₄×D₄×C₈₉	C₂³	1	8	yes	—
244	C₄×D₄×C₈₉	C₂³	1	8	yes	—
245	C₄×D₄×C₈₉	C₂³	1	8	yes	—
246	C₄×D₄×C₈₉	C₂³	1	8	yes	—
247	C₄×D₄×C₈₉	C₂³	1	16	yes	—
248	C₄×D₄×C₈₉	C₂³	1	16	yes	—
249	C₄×D₄×C₈₉	C₂³	1	16	yes	—
250	C₄×D₄×C₈₉	C₂³	1	16	yes	—
251	C₄×D₄×C₈₉	C₂³	1	8	yes	—
252	C₄×D₄×C₈₉	C₂³	1	16	yes	—
253	#117×C₈₉	C₂³	1	4	yes	—
254	#117×C₈₉	C₂³	1	4	yes	—
255	#117×C₈₉	C₂³	1	4	yes	—
256	#117×C₈₉	C₂³	1	2	yes	—
257	#117×C₈₉	C₂³	1	2	yes	—
258	#117×C₈₉	C₂³	1	4	yes	—
259	#117×C₈₉	C₂³	1	4	yes	—
260	#117×C₈₉	C₂³	1	8	yes	—
261	#117×C₈₉	C₂³	1	8	yes	—
262	#117×C₈₉	C₂³	1	16	yes	—
263	#117×C₈₉	C₂³	1	16	yes	—
264	#117×C₈₉	C₂³	1	16	yes	—
265	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
267	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
268	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
269	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
270	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
272	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
273	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
274	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
275	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
276	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
277	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
278	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
279	#41×C₈₉	—	2	16	no	—
280	#41×C₈₉	—	4	4	no	—
281	#41×C₈₉	—	4	4	no	—
282	#41×C₈₉	—	4	4	no	—
283	#41×C₈₉	—	4	4	no	—
284	#41×C₈₉	—	4	8	no	—
285	#41×C₈₉	—	4	8	no	—
286	#41×C₈₉	—	4	16	no	—
287	#41×C₈₉	—	4	8	no	—
288	#41×C₈₉	—	4	16	no	—
289	C₂×Q₈×C₈₉	—	2	8	no	—
290	C₂×Q₈×C₈₉	—	4	4	no	—
291	C₂×Q₈×C₈₉	—	4	2	no	—
292	C₂×Q₈×C₈₉	—	4	8	no	—
293	C₂×Q₈×C₈₉	—	4	8	no	—
294	C₂×Q₈×C₈₉	—	4	4	no	—
295	C₂×Q₈×C₈₉	—	4	16	no	—
296	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
297	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
298	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
299	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
300	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
301	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
302	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
304	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
305	C₂×Q₈×C₈₉	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₈₉	—	4	4	no	—
307	C₂×D₄×C₈₉	—	4	2	no	—
308	C₂×D₄×C₈₉	—	4	4	no	—
309	C₂×D₄×C₈₉	—	4	8	no	—
310	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
311	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
312	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
313	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
314	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
315	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
316	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
317	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
322	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
323	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
324	C₂×D₄×C₈₉	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
327	C₂²×C₄×C₈₉	—	2	4	no	—
328	C₂²×C₄×C₈₉	—	2	8	no	—
329	C₂²×C₄×C₈₉	—	4	8	no	—
330	C₂²×C₄×C₈₉	—	4	4	no	—
331	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
332	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
356	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
357	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
358	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
359	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
366	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
367	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
368	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
369	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
370	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
371	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
372	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
373	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
374	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
375	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
376	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
384	C₄²×C₈₉	C₂⁴	1	4	yes	—
385	C₄²×C₈₉	C₂⁴	1	4	yes	—
386	C₄²×C₈₉	C₂⁴	1	8	yes	—
387	C₄²×C₈₉	C₂⁴	1	4	yes	—
388	C₄²×C₈₉	C₂⁴	1	4	yes	—
389	C₄²×C₈₉	C₂⁴	1	8	yes	—
390	C₄²×C₈₉	C₂⁴	1	16	yes	—
391	C₄²×C₈₉	C₂⁴	1	8	yes	—
392	C₂³×C₈₉	—	2	2	no	—
393	C₂³×C₈₉	—	2	4	no	—
394	C₂³×C₈₉	—	4	2	no	—
395	C₂³×C₈₉	—	4	4	no	—
396	C₂³×C₈₉	—	4	4	no	—
397	C₂³×C₈₉	—	4	8	no	—
398	C₂³×C₈₉	C₂⁵	1	2	yes	—
399	C₂³×C₈₉	C₂⁵	1	2	yes	—
400	C₂³×C₈₉	C₂⁵	1	2	yes	—
401	C₂³×C₈₉	C₂⁵	1	8	yes	—
402	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
403	Q₈×C₈₉	—	2	16	no	—
404	Q₈×C₈₉	—	2	8	no	—
405	Q₈×C₈₉	—	4	4	no	—
406	Q₈×C₈₉	—	4	4	no	—
407	Q₈×C₈₉	—	4	8	no	—
408	Q₈×C₈₉	—	4	1	no	—
409	Q₈×C₈₉	—	4	2	no	—
410	Q₈×C₈₉	—	4	1	no	—
411	Q₈×C₈₉	—	4	4	no	—
412	Q₈×C₈₉	—	4	8	no	—
413	D₄×C₈₉	—	2	16	no	—
414	D₄×C₈₉	—	2	8	no	—
415	D₄×C₈₉	—	4	2	no	—
416	D₄×C₈₉	—	4	2	no	—
417	D₄×C₈₉	—	4	2	no	—
418	D₄×C₈₉	—	4	2	no	—
419	D₄×C₈₉	—	4	4	no	—
420	D₄×C₈₉	—	4	1	no	—
421	D₄×C₈₉	—	4	2	no	—
422	D₄×C₈₉	—	4	1	no	—
423	D₄×C₈₉	—	4	8	no	—
424	D₄×C₈₉	—	4	8	no	—
425	D₄×C₈₉	—	4	8	no	—
426	D₄×C₈₉	—	4	8	no	—
427	D₄×C₈₉	—	4	8	no	—
428	D₄×C₈₉	—	4	8	no	—
429	D₄×C₈₉	—	4	8	no	—
430	C₂×C₄×C₈₉	—	2	2	no	—
431	C₂×C₄×C₈₉	—	2	4	no	—
432	C₂×C₄×C₈₉	—	2	8	no	—
433	C₂×C₄×C₈₉	—	2	4	no	—
434	C₂×C₄×C₈₉	—	2	4	no	—
435	C₂×C₄×C₈₉	—	2	4	no	—
436	C₂×C₄×C₈₉	—	2	4	no	—
437	C₂×C₄×C₈₉	—	2	4	no	—
438	C₂×C₄×C₈₉	—	2	4	no	—
439	C₂×C₄×C₈₉	—	2	16	no	—
440	C₂×C₄×C₈₉	—	4	4	no	—
441	C₂×C₄×C₈₉	—	4	8	no	—
442	C₂×C₄×C₈₉	—	4	8	no	—
443	C₂×C₄×C₈₉	—	4	16	no	—
444	C₂×C₄×C₈₉	—	4	8	no	—
445	C₂×C₄×C₈₉	—	4	4	no	—
446	C₂×C₄×C₈₉	—	4	16	no	—
447	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
448	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
449	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
450	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
451	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
452	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
453	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
454	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
455	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
456	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
457	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
458	C₂²×C₈₉	—	2	2	no	—
459	C₂²×C₈₉	—	2	2	no	—
460	C₂²×C₈₉	—	2	2	no	—
461	C₂²×C₈₉	—	2	2	no	—
462	C₂²×C₈₉	—	2	8	no	—
463	C₂²×C₈₉	—	2	4	no	—
464	C₂²×C₈₉	—	2	8	no	—
465	C₂²×C₈₉	—	2	4	no	—
466	C₂²×C₈₉	—	2	8	no	—
467	C₂²×C₈₉	—	2	4	no	—
468	C₂²×C₈₉	—	4	4	no	—
469	C₂²×C₈₉	—	8	4	no	—
470	C₂²×C₈₉	—	8	8	no	—
471	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
472	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
473	C₄×C₈₉	—	2	2	no	—
474	C₄×C₈₉	—	2	2	no	—
475	C₄×C₈₉	—	2	1	no	—
476	C₄×C₈₉	—	2	1	no	—
477	C₄×C₈₉	—	2	8	no	—
478	C₄×C₈₉	—	2	8	no	—
479	C₄×C₈₉	—	2	8	no	—
480	C₄×C₈₉	—	2	8	no	—
481	C₄×C₈₉	—	2	8	no	—
482	C₄×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
483	#62886	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
484	C₂×C₈₉	—	2	2	no	—
485	C₂×C₈₉	—	4	2	no	—
486	C₂×C₈₉	—	4	2	no	—
487	C₂×C₈₉	—	4	8	no	—
488	C₂×C₈₉	—	4	2	no	—
489	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
491	#3551	C₂×C₈₉	1	4	yes	complemented
492	#3550	C₂×C₈₉	1	4	yes	complemented
493	#3547	C₂×C₈₉	1	8	yes	complemented
494	#3545	C₂×C₈₉	1	4	yes	complemented
495	#3544	C₂×C₈₉	1	4	yes	complemented
496	#3541	C₂×C₈₉	1	8	yes	complemented
497	#3540	C₂×C₈₉	1	4	yes	complemented
498	#3538	C₂×C₈₉	1	4	yes	complemented
499	#3533	C₂×C₈₉	1	8	yes	complemented
500	#3495	C₂×C₈₉	1	4	yes	complemented
501	#3493	C₂×C₈₉	1	2	yes	complemented
502	#3489	C₂×C₈₉	1	4	yes	complemented
503	#3486	C₂×C₈₉	1	2	yes	complemented
504	#3449	C₂×C₈₉	1	2	yes	complemented
505	C₂×#536	C₂×C₈₉	1	1	yes	characteristic, complemented
506	C₈₉	#62886	1	1	yes	characteristic, direct product factor, Sylow
507	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
508	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
509	C₂²×#41	C₂²×C₈₉	1	2	yes	complemented
510	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
511	#563	C₂²×C₈₉	1	8	yes	complemented
512	#563	C₂²×C₈₉	1	4	yes	complemented
513	#563	C₂²×C₈₉	1	8	yes	complemented
514	#563	C₂²×C₈₉	1	8	yes	complemented
515	#562	C₂²×C₈₉	1	16	yes	complemented
516	#562	C₂²×C₈₉	1	8	yes	complemented
517	H(3,𝔽₄)	C₂²×C₈₉	1	4	yes	complemented
518	#560	C₂²×C₈₉	1	8	yes	complemented
519	#559	C₂²×C₈₉	1	8	yes	complemented
520	Q₈²	C₂²×C₈₉	1	4	yes	complemented
521	#556	C₂²×C₈₉	1	8	yes	complemented
522	#556	C₂²×C₈₉	1	8	yes	complemented
523	#555	C₂²×C₈₉	1	8	yes	complemented
524	#555	C₂²×C₈₉	1	4	yes	complemented
525	#555	C₂²×C₈₉	1	8	yes	complemented
526	#554	C₂²×C₈₉	1	8	yes	complemented
527	#554	C₂²×C₈₉	1	8	yes	complemented
528	#553	C₂²×C₈₉	1	8	yes	complemented
529	#553	C₂²×C₈₉	1	16	yes	complemented
530	#552	C₂²×C₈₉	1	8	yes	complemented
531	#552	C₂²×C₈₉	1	16	yes	complemented
532	#552	C₂²×C₈₉	1	8	yes	complemented
533	#552	C₂²×C₈₉	1	8	yes	complemented
534	#551	C₂²×C₈₉	1	16	yes	complemented
535	#551	C₂²×C₈₉	1	8	yes	complemented
536	#551	C₂²×C₈₉	1	8	yes	complemented
537	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
538	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
539	D₄×Q₈	C₂²×C₈₉	1	8	yes	complemented
540	#548	C₂²×C₈₉	1	8	yes	complemented
541	#548	C₂²×C₈₉	1	8	yes	complemented
542	#548	C₂²×C₈₉	1	8	yes	complemented
543	#547	C₂²×C₈₉	1	16	yes	complemented
544	#547	C₂²×C₈₉	1	8	yes	complemented
545	#546	C₂²×C₈₉	1	16	yes	complemented
546	#546	C₂²×C₈₉	1	8	yes	complemented
547	#544	C₂²×C₈₉	1	2	yes	complemented
548	#544	C₂²×C₈₉	1	16	yes	complemented
549	#542	C₂²×C₈₉	1	8	yes	complemented
550	#542	C₂²×C₈₉	1	16	yes	complemented
551	#542	C₂²×C₈₉	1	16	yes	complemented
552	#542	C₂²×C₈₉	1	16	yes	complemented
553	#541	C₂²×C₈₉	1	8	yes	complemented
554	#540	C₂²×C₈₉	1	16	yes	complemented
555	#539	C₂²×C₈₉	1	16	yes	complemented
556	#538	C₂²×C₈₉	1	8	yes	complemented
557	#538	C₂²×C₈₉	1	16	yes	complemented
558	#538	C₂²×C₈₉	1	16	yes	complemented
559	#537	C₂²×C₈₉	1	4	yes	—
560	#537	C₂²×C₈₉	1	2	yes	—
561	#537	C₂²×C₈₉	1	4	yes	complemented
562	#537	C₂²×C₈₉	1	8	yes	complemented
563	#536	C₂²×C₈₉	1	4	yes	—
564	#536	C₂²×C₈₉	1	2	yes	—
565	#536	C₂²×C₈₉	1	4	yes	complemented
566	#536	C₂²×C₈₉	1	4	yes	complemented
567	#536	C₂²×C₈₉	1	4	yes	complemented
568	#536	C₂²×C₈₉	1	4	yes	complemented
569	#536	C₂²×C₈₉	1	2	yes	complemented
570	#536	C₂²×C₈₉	1	4	yes	complemented
571	#536	C₂²×C₈₉	1	8	yes	complemented
572	#536	C₂²×C₈₉	1	8	yes	complemented
573	#535	C₂²×C₈₉	1	4	yes	—
574	#535	C₂²×C₈₉	1	2	yes	—
575	#535	C₂²×C₈₉	1	2	yes	complemented
576	#534	C₂²×C₈₉	1	4	yes	—
577	#534	C₂²×C₈₉	1	4	yes	complemented
578	#533	C₂²×C₈₉	1	8	yes	complemented
579	#532	C₂²×C₈₉	1	4	yes	—
580	#532	C₂²×C₈₉	1	4	yes	complemented
581	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
582	#529	C₂²×C₈₉	1	8	yes	complemented
583	#529	C₂²×C₈₉	1	8	yes	complemented
584	C₂×#124	C₂²×C₈₉	1	2	yes	—
585	#525	C₂²×C₈₉	1	4	yes	—
586	#525	C₂²×C₈₉	1	4	yes	—
587	#525	C₂²×C₈₉	1	4	yes	complemented
588	#525	C₂²×C₈₉	1	4	yes	complemented
589	#525	C₂²×C₈₉	1	8	yes	complemented
590	#525	C₂²×C₈₉	1	8	yes	complemented
591	C₂×#123	C₂²×C₈₉	1	4	yes	complemented
592	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
593	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
594	#520	C₂²×C₈₉	1	4	yes	complemented
595	#519	C₂²×C₈₉	1	2	yes	complemented
596	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic, complemented
597	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
598	2₋¹⁺⁴	—	4	8	no	—
599	C₂×#41	—	4	4	no	—
600	C₂×#41	—	4	8	no	—
601	C₂×#41	C₂³×C₈₉	1	4	yes	—
602	C₂×#41	C₂³×C₈₉	1	2	yes	—
603	C₂×#41	C₂³×C₈₉	1	2	yes	—
604	C₂×#41	C₂³×C₈₉	1	8	yes	—
605	C₂×#41	C₂³×C₈₉	1	8	yes	—
606	C₂×#41	C₂³×C₈₉	1	2	yes	—
607	C₂×#41	C₂³×C₈₉	1	4	yes	—
608	C₂×#41	C₂³×C₈₉	1	2	yes	—
609	C₂×#41	C₂³×C₈₉	1	4	yes	—
610	C₂×#41	C₂³×C₈₉	1	4	yes	—
611	C₂²×Q₈	—	4	4	no	—
612	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
613	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
614	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
615	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
616	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
617	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
618	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
619	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
620	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
621	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
622	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
623	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
624	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
625	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
626	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
627	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
628	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
629	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
630	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
631	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
632	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
633	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
634	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
635	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
636	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
637	#127	C₂³×C₈₉	1	4	yes	—
638	#127	C₂³×C₈₉	1	4	yes	—
639	#126	C₂³×C₈₉	1	16	yes	—
640	#126	C₂³×C₈₉	1	16	yes	—
641	#126	C₂³×C₈₉	1	16	yes	—
642	#126	C₂³×C₈₉	1	16	yes	—
643	#126	C₂³×C₈₉	1	16	yes	—
644	#126	C₂³×C₈₉	1	16	yes	—
645	#125	C₂³×C₈₉	1	8	yes	—
646	#125	C₂³×C₈₉	1	8	yes	—
647	#125	C₂³×C₈₉	1	16	yes	—
648	#125	C₂³×C₈₉	1	16	yes	—
649	#125	C₂³×C₈₉	1	16	yes	—
650	#124	C₂³×C₈₉	1	4	yes	—
651	#124	C₂³×C₈₉	1	8	yes	—
652	#124	C₂³×C₈₉	1	4	yes	—
653	#124	C₂³×C₈₉	1	8	yes	—
654	#124	C₂³×C₈₉	1	8	yes	—
655	#124	C₂³×C₈₉	1	4	yes	—
656	#124	C₂³×C₈₉	1	4	yes	—
657	#124	C₂³×C₈₉	1	4	yes	—
658	#124	C₂³×C₈₉	1	4	yes	—
659	#124	C₂³×C₈₉	1	8	yes	—
660	#124	C₂³×C₈₉	1	16	yes	—
661	#124	C₂³×C₈₉	1	8	yes	—
662	#124	C₂³×C₈₉	1	16	yes	—
663	#124	C₂³×C₈₉	1	16	yes	—
664	#123	C₂³×C₈₉	1	8	yes	—
665	#123	C₂³×C₈₉	1	8	yes	—
666	#123	C₂³×C₈₉	1	8	yes	—
667	#123	C₂³×C₈₉	1	8	yes	—
668	#123	C₂³×C₈₉	1	4	yes	—
669	#123	C₂³×C₈₉	1	8	yes	—
670	#123	C₂³×C₈₉	1	4	yes	—
671	#123	C₂³×C₈₉	1	8	yes	—
672	#123	C₂³×C₈₉	1	4	yes	—
673	#123	C₂³×C₈₉	1	4	yes	—
674	#123	C₂³×C₈₉	1	16	yes	—
675	#123	C₂³×C₈₉	1	16	yes	—
676	#123	C₂³×C₈₉	1	16	yes	—
677	#123	C₂³×C₈₉	1	16	yes	—
678	#123	C₂³×C₈₉	1	16	yes	—
679	#123	C₂³×C₈₉	1	16	yes	—
680	#123	C₂³×C₈₉	1	16	yes	—
681	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
682	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
683	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
684	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
685	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
686	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
687	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
688	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
689	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
690	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
691	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
697	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
698	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
699	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
700	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
701	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
702	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
703	#121	C₂³×C₈₉	1	4	yes	—
704	#121	C₂³×C₈₉	1	4	yes	—
705	#121	C₂³×C₈₉	1	8	yes	—
706	#121	C₂³×C₈₉	1	4	yes	—
707	#121	C₂³×C₈₉	1	8	yes	—
708	#121	C₂³×C₈₉	1	4	yes	—
709	#121	C₂³×C₈₉	1	8	yes	—
710	#121	C₂³×C₈₉	1	16	yes	—
711	#121	C₂³×C₈₉	1	8	yes	—
712	#121	C₂³×C₈₉	1	8	yes	—
713	#121	C₂³×C₈₉	1	8	yes	—
714	#121	C₂³×C₈₉	1	8	yes	—
715	#121	C₂³×C₈₉	1	8	yes	—
716	#121	C₂³×C₈₉	1	16	yes	—
717	#121	C₂³×C₈₉	1	16	yes	—
718	#121	C₂³×C₈₉	1	16	yes	—
719	#121	C₂³×C₈₉	1	16	yes	—
720	#120	C₂³×C₈₉	1	8	yes	—
721	#120	C₂³×C₈₉	1	4	yes	—
722	#120	C₂³×C₈₉	1	4	yes	—
723	#120	C₂³×C₈₉	1	8	yes	—
724	#120	C₂³×C₈₉	1	4	yes	—
725	#120	C₂³×C₈₉	1	4	yes	—
726	#120	C₂³×C₈₉	1	16	yes	—
727	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
728	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
729	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
730	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
731	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
732	C₄×D₄	C₂³×C₈₉	1	16	yes	—
733	C₄×D₄	C₂³×C₈₉	1	8	yes	—
734	C₄×D₄	C₂³×C₈₉	1	8	yes	—
735	C₄×D₄	C₂³×C₈₉	1	8	yes	—
736	C₄×D₄	C₂³×C₈₉	1	8	yes	—
737	C₄×D₄	C₂³×C₈₉	1	8	yes	—
738	C₄×D₄	C₂³×C₈₉	1	16	yes	—
739	C₄×D₄	C₂³×C₈₉	1	16	yes	—
740	C₄×D₄	C₂³×C₈₉	1	16	yes	—
741	C₄×D₄	C₂³×C₈₉	1	16	yes	—
742	C₄×D₄	C₂³×C₈₉	1	8	yes	—
743	C₄×D₄	C₂³×C₈₉	1	16	yes	—
744	#117	C₂³×C₈₉	1	4	yes	—
745	#117	C₂³×C₈₉	1	4	yes	—
746	#117	C₂³×C₈₉	1	4	yes	—
747	#117	C₂³×C₈₉	1	2	yes	—
748	#117	C₂³×C₈₉	1	2	yes	—
749	#117	C₂³×C₈₉	1	4	yes	—
750	#117	C₂³×C₈₉	1	4	yes	—
751	#117	C₂³×C₈₉	1	8	yes	—
752	#117	C₂³×C₈₉	1	8	yes	—
753	#117	C₂³×C₈₉	1	16	yes	—
754	#117	C₂³×C₈₉	1	16	yes	—
755	#117	C₂³×C₈₉	1	16	yes	—
756	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
757	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
758	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
759	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
760	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
765	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
766	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
767	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
768	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
769	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
770	#41	—	2	16	no	—
771	#41	—	4	4	no	—
772	#41	—	4	4	no	—
773	#41	—	4	4	no	—
774	#41	—	4	4	no	—
775	#41	—	4	8	no	—
776	#41	—	4	8	no	—
777	#41	—	4	16	no	—
778	#41	—	4	8	no	—
779	#41	—	4	16	no	—
780	C₂×Q₈	—	2	8	no	—
781	C₂×Q₈	—	4	4	no	—
782	C₂×Q₈	—	4	2	no	—
783	C₂×Q₈	—	4	8	no	—
784	C₂×Q₈	—	4	8	no	—
785	C₂×Q₈	—	4	4	no	—
786	C₂×Q₈	—	4	16	no	—
787	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
788	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
789	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
790	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
791	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
792	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
793	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
794	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
795	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
796	C₂×Q₈	C₂⁴×C₈₉	1	1	yes	characteristic
797	C₂×D₄	—	4	4	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	—	4	4	no	—
800	C₂×D₄	—	4	8	no	—
801	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
802	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
803	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
804	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
805	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
806	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
807	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
808	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
809	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
810	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
811	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
812	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
813	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
814	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
815	C₂×D₄	C₂⁴×C₈₉	1	1	yes	characteristic
816	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
817	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	2	8	no	—
820	C₂²×C₄	—	4	8	no	—
821	C₂²×C₄	—	4	4	no	—
822	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
823	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
824	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
825	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
826	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
827	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
828	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
829	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
830	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
833	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
834	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
835	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
836	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
837	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
838	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
839	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
840	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
841	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
842	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
843	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
844	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
845	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
846	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
847	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
848	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
849	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
850	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
851	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
852	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
853	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
854	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
855	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
856	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
857	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
858	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
859	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
860	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
861	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
862	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
864	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
865	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
866	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
867	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
868	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
869	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
870	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
871	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
872	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
874	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
875	C₄²	C₂⁴×C₈₉	1	4	yes	—
876	C₄²	C₂⁴×C₈₉	1	4	yes	—
877	C₄²	C₂⁴×C₈₉	1	8	yes	—
878	C₄²	C₂⁴×C₈₉	1	4	yes	—
879	C₄²	C₂⁴×C₈₉	1	4	yes	—
880	C₄²	C₂⁴×C₈₉	1	8	yes	—
881	C₄²	C₂⁴×C₈₉	1	16	yes	—
882	C₄²	C₂⁴×C₈₉	1	8	yes	—
883	C₂³	—	2	2	no	—
884	C₂³	—	2	4	no	—
885	C₂³	—	4	2	no	—
886	C₂³	—	4	4	no	—
887	C₂³	—	4	4	no	—
888	C₂³	—	4	8	no	—
889	C₂³	C₂⁵×C₈₉	1	2	yes	—
890	C₂³	C₂⁵×C₈₉	1	2	yes	—
891	C₂³	C₂⁵×C₈₉	1	2	yes	—
892	C₂³	C₂⁵×C₈₉	1	8	yes	—
893	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
894	Q₈	—	2	16	no	—
895	Q₈	—	2	8	no	—
896	Q₈	—	4	4	no	—
897	Q₈	—	4	4	no	—
898	Q₈	—	4	8	no	—
899	Q₈	—	4	1	no	—
900	Q₈	—	4	2	no	—
901	Q₈	—	4	1	no	—
902	Q₈	—	4	4	no	—
903	Q₈	—	4	8	no	—
904	D₄	—	2	16	no	—
905	D₄	—	2	8	no	—
906	D₄	—	4	2	no	—
907	D₄	—	4	2	no	—
908	D₄	—	4	2	no	—
909	D₄	—	4	2	no	—
910	D₄	—	4	4	no	—
911	D₄	—	4	1	no	—
912	D₄	—	4	2	no	—
913	D₄	—	4	1	no	—
914	D₄	—	4	8	no	—
915	D₄	—	4	8	no	—
916	D₄	—	4	8	no	—
917	D₄	—	4	8	no	—
918	D₄	—	4	8	no	—
919	D₄	—	4	8	no	—
920	D₄	—	4	8	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	4	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	4	no	—
928	C₂×C₄	—	2	4	no	—
929	C₂×C₄	—	2	4	no	—
930	C₂×C₄	—	2	16	no	—
931	C₂×C₄	—	4	4	no	—
932	C₂×C₄	—	4	8	no	—
933	C₂×C₄	—	4	8	no	—
934	C₂×C₄	—	4	16	no	—
935	C₂×C₄	—	4	8	no	—
936	C₂×C₄	—	4	4	no	—
937	C₂×C₄	—	4	16	no	—
938	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
939	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
940	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
941	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
942	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
943	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
944	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
945	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
946	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
947	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
948	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	8	no	—
954	C₂²	—	2	4	no	—
955	C₂²	—	2	8	no	—
956	C₂²	—	2	4	no	—
957	C₂²	—	2	8	no	—
958	C₂²	—	2	4	no	—
959	C₂²	—	4	4	no	—
960	C₂²	—	8	4	no	—
961	C₂²	—	8	8	no	—
962	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
963	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
964	C₄	—	2	2	no	—
965	C₄	—	2	2	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	8	no	—
969	C₄	—	2	8	no	—
970	C₄	—	2	8	no	—
971	C₄	—	2	8	no	—
972	C₄	—	2	8	no	—
973	C₄	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
974	C₂	—	2	2	no	—
975	C₂	—	4	2	no	—
976	C₂	—	4	2	no	—
977	C₂	—	4	8	no	—
978	C₂	—	4	2	no	—
979	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
980	C₂	C₈₉×2₋¹⁺⁶	1	2	yes	—

	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×#3551	C₂	semidirect
2. C₈₉×#3550	C₂	semidirect
3. C₈₉×#3547	C₂	semidirect
4. C₈₉×#3545	C₂	semidirect
5. C₈₉×#3544	C₂	semidirect
6. C₈₉×#3541	C₂	semidirect
7. C₈₉×#3540	C₂	semidirect
8. C₈₉×#3538	C₂	semidirect
9. C₈₉×#3533	C₂	semidirect
10. C₈₉×#3495	C₂	semidirect
11. C₈₉×#3493	C₂	semidirect
12. C₈₉×#3489	C₂	semidirect
13. C₈₉×#3486	C₂	semidirect
14. C₈₉×#3449	C₂	semidirect
15. C₂×#536×C₈₉	C₂	semidirect
18. C₂²×#41×C₈₉	C₂²	semidirect
19. C₂³×Q₈×C₈₉	C₂²	semidirect
20. #563×C₈₉	C₂²	semidirect
21. #563×C₈₉	C₂²	semidirect
22. #563×C₈₉	C₂²	semidirect
23. #563×C₈₉	C₂²	semidirect
24. #562×C₈₉	C₂²	semidirect
25. #562×C₈₉	C₂²	semidirect
26. H(3,𝔽₄)×C₈₉	C₂²	semidirect
27. #560×C₈₉	C₂²	semidirect
28. #559×C₈₉	C₂²	semidirect
29. Q₈²×C₈₉	C₂²	semidirect
30. #556×C₈₉	C₂²	semidirect
31. #556×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
33. #555×C₈₉	C₂²	semidirect
34. #555×C₈₉	C₂²	semidirect
35. #554×C₈₉	C₂²	semidirect
36. #554×C₈₉	C₂²	semidirect
37. #553×C₈₉	C₂²	semidirect
38. #553×C₈₉	C₂²	semidirect
39. #552×C₈₉	C₂²	semidirect
40. #552×C₈₉	C₂²	semidirect
41. #552×C₈₉	C₂²	semidirect
42. #552×C₈₉	C₂²	semidirect
43. #551×C₈₉	C₂²	semidirect
44. #551×C₈₉	C₂²	semidirect
45. #551×C₈₉	C₂²	semidirect
46. D₄×Q₈×C₈₉	C₂²	semidirect
47. D₄×Q₈×C₈₉	C₂²	semidirect
48. D₄×Q₈×C₈₉	C₂²	semidirect
49. #548×C₈₉	C₂²	semidirect
50. #548×C₈₉	C₂²	semidirect
51. #548×C₈₉	C₂²	semidirect
52. #547×C₈₉	C₂²	semidirect
53. #547×C₈₉	C₂²	semidirect
54. #546×C₈₉	C₂²	semidirect
55. #546×C₈₉	C₂²	semidirect
56. #544×C₈₉	C₂²	semidirect
57. #544×C₈₉	C₂²	semidirect
58. #542×C₈₉	C₂²	semidirect
59. #542×C₈₉	C₂²	semidirect
60. #542×C₈₉	C₂²	semidirect
61. #542×C₈₉	C₂²	semidirect
62. #541×C₈₉	C₂²	semidirect
63. #540×C₈₉	C₂²	semidirect
64. #539×C₈₉	C₂²	semidirect
65. #538×C₈₉	C₂²	semidirect
66. #538×C₈₉	C₂²	semidirect
67. #538×C₈₉	C₂²	semidirect
70. #537×C₈₉	C₂²	semidirect
71. #537×C₈₉	C₂²	semidirect
74. #536×C₈₉	C₂²	semidirect
75. #536×C₈₉	C₂²	semidirect
76. #536×C₈₉	C₂²	semidirect
77. #536×C₈₉	C₂²	semidirect
78. #536×C₈₉	C₂²	semidirect
79. #536×C₈₉	C₂²	semidirect
80. #536×C₈₉	C₂²	semidirect
81. #536×C₈₉	C₂²	semidirect
84. #535×C₈₉	C₂²	semidirect
86. #534×C₈₉	C₂²	semidirect
87. #533×C₈₉	C₂²	semidirect
89. #532×C₈₉	C₂²	semidirect
90. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
91. #529×C₈₉	C₂²	semidirect
92. #529×C₈₉	C₂²	semidirect
96. #525×C₈₉	C₂²	semidirect
97. #525×C₈₉	C₂²	semidirect
98. #525×C₈₉	C₂²	semidirect
99. #525×C₈₉	C₂²	semidirect
100. C₂×#123×C₈₉	C₂²	semidirect
101. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
102. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
103. #520×C₈₉	C₂²	semidirect
104. #519×C₈₉	C₂²	semidirect
105. C₂×#117×C₈₉	C₂²	semidirect
106. C₂×#117×C₈₉	C₂²	semidirect
483. #62886	C₈₉	direct (N × H)
491. #3551	C₂×C₈₉	semidirect
492. #3550	C₂×C₈₉	semidirect
493. #3547	C₂×C₈₉	semidirect
494. #3545	C₂×C₈₉	semidirect
495. #3544	C₂×C₈₉	semidirect
496. #3541	C₂×C₈₉	semidirect
497. #3540	C₂×C₈₉	semidirect
498. #3538	C₂×C₈₉	semidirect
499. #3533	C₂×C₈₉	semidirect
500. #3495	C₂×C₈₉	semidirect
501. #3493	C₂×C₈₉	semidirect
502. #3489	C₂×C₈₉	semidirect
503. #3486	C₂×C₈₉	semidirect
504. #3449	C₂×C₈₉	semidirect
505. C₂×#536	C₂×C₈₉	semidirect
506. C₈₉	#62886	direct (N × H)
509. C₂²×#41	C₂²×C₈₉	semidirect
510. C₂³×Q₈	C₂²×C₈₉	semidirect
511. #563	C₂²×C₈₉	semidirect
512. #563	C₂²×C₈₉	semidirect
513. #563	C₂²×C₈₉	semidirect
514. #563	C₂²×C₈₉	semidirect
515. #562	C₂²×C₈₉	semidirect
516. #562	C₂²×C₈₉	semidirect
517. H(3,𝔽₄)	C₂²×C₈₉	semidirect
518. #560	C₂²×C₈₉	semidirect
519. #559	C₂²×C₈₉	semidirect
520. Q₈²	C₂²×C₈₉	semidirect
521. #556	C₂²×C₈₉	semidirect
522. #556	C₂²×C₈₉	semidirect
523. #555	C₂²×C₈₉	semidirect
524. #555	C₂²×C₈₉	semidirect
525. #555	C₂²×C₈₉	semidirect
526. #554	C₂²×C₈₉	semidirect
527. #554	C₂²×C₈₉	semidirect
528. #553	C₂²×C₈₉	semidirect
529. #553	C₂²×C₈₉	semidirect
530. #552	C₂²×C₈₉	semidirect
531. #552	C₂²×C₈₉	semidirect
532. #552	C₂²×C₈₉	semidirect
533. #552	C₂²×C₈₉	semidirect
534. #551	C₂²×C₈₉	semidirect
535. #551	C₂²×C₈₉	semidirect
536. #551	C₂²×C₈₉	semidirect
537. D₄×Q₈	C₂²×C₈₉	semidirect
538. D₄×Q₈	C₂²×C₈₉	semidirect
539. D₄×Q₈	C₂²×C₈₉	semidirect
540. #548	C₂²×C₈₉	semidirect
541. #548	C₂²×C₈₉	semidirect
542. #548	C₂²×C₈₉	semidirect
543. #547	C₂²×C₈₉	semidirect
544. #547	C₂²×C₈₉	semidirect
545. #546	C₂²×C₈₉	semidirect
546. #546	C₂²×C₈₉	semidirect
547. #544	C₂²×C₈₉	semidirect
548. #544	C₂²×C₈₉	semidirect
549. #542	C₂²×C₈₉	semidirect
550. #542	C₂²×C₈₉	semidirect
551. #542	C₂²×C₈₉	semidirect
552. #542	C₂²×C₈₉	semidirect
553. #541	C₂²×C₈₉	semidirect
554. #540	C₂²×C₈₉	semidirect
555. #539	C₂²×C₈₉	semidirect
556. #538	C₂²×C₈₉	semidirect
557. #538	C₂²×C₈₉	semidirect
558. #538	C₂²×C₈₉	semidirect
561. #537	C₂²×C₈₉	semidirect
562. #537	C₂²×C₈₉	semidirect
565. #536	C₂²×C₈₉	semidirect
566. #536	C₂²×C₈₉	semidirect
567. #536	C₂²×C₈₉	semidirect
568. #536	C₂²×C₈₉	semidirect
569. #536	C₂²×C₈₉	semidirect
570. #536	C₂²×C₈₉	semidirect
571. #536	C₂²×C₈₉	semidirect
572. #536	C₂²×C₈₉	semidirect
575. #535	C₂²×C₈₉	semidirect
577. #534	C₂²×C₈₉	semidirect
578. #533	C₂²×C₈₉	semidirect
580. #532	C₂²×C₈₉	semidirect
581. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
582. #529	C₂²×C₈₉	semidirect
583. #529	C₂²×C₈₉	semidirect
587. #525	C₂²×C₈₉	semidirect
588. #525	C₂²×C₈₉	semidirect
589. #525	C₂²×C₈₉	semidirect
590. #525	C₂²×C₈₉	semidirect
591. C₂×#123	C₂²×C₈₉	semidirect
592. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
593. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
594. #520	C₂²×C₈₉	semidirect
595. #519	C₂²×C₈₉	semidirect
596. C₂×#117	C₂²×C₈₉	semidirect
597. C₂×#117	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×#3551	2
C₈₉×#3550	2
C₈₉×#3547	2
C₈₉×#3545	2
C₈₉×#3544	2
C₈₉×#3541	2
C₈₉×#3540	2
C₈₉×#3538	2
C₈₉×#3533	2
C₈₉×#3495	2
C₈₉×#3493	2
C₈₉×#3489	2
C₈₉×#3486	2
C₈₉×#3449	2
C₂×#536×C₈₉	2
#62886	89

Subgroups — C89×#62886 #36440734

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62886 #36440734