Subgroups — C₈₉×#62838 #36440686

Order 22784.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3565	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3555	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3547	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3541	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3518	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3516	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3515	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3512	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3511	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3511	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3509	C₂	1	4	yes	maximal, complemented
12	C₈₉×#3504	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3503	C₂	1	2	yes	maximal, complemented
14	C₈₉×#3493	C₂	1	4	yes	maximal, complemented
15	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
16	C₈₉×#3444	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	#563×C₈₉	C₂²	1	16	yes	—
19	#562×C₈₉	C₂²	1	16	yes	—
20	Q₈²×C₈₉	C₂²	1	4	yes	complemented
21	#557×C₈₉	C₂²	1	4	yes	complemented
22	#557×C₈₉	C₂²	1	8	yes	complemented
23	#557×C₈₉	C₂²	1	8	yes	complemented
24	#556×C₈₉	C₂²	1	8	yes	—
25	#556×C₈₉	C₂²	1	8	yes	—
26	#556×C₈₉	C₂²	1	8	yes	—
27	#556×C₈₉	C₂²	1	8	yes	complemented
28	#556×C₈₉	C₂²	1	4	yes	complemented
29	#556×C₈₉	C₂²	1	16	yes	complemented
30	#555×C₈₉	C₂²	1	8	yes	—
31	#555×C₈₉	C₂²	1	8	yes	—
32	#555×C₈₉	C₂²	1	4	yes	complemented
33	#554×C₈₉	C₂²	1	8	yes	—
34	#554×C₈₉	C₂²	1	16	yes	—
35	#554×C₈₉	C₂²	1	4	yes	complemented
36	#554×C₈₉	C₂²	1	8	yes	complemented
37	#554×C₈₉	C₂²	1	4	yes	complemented
38	#553×C₈₉	C₂²	1	8	yes	—
39	#553×C₈₉	C₂²	1	8	yes	—
40	#553×C₈₉	C₂²	1	8	yes	—
41	#553×C₈₉	C₂²	1	16	yes	—
42	#553×C₈₉	C₂²	1	8	yes	complemented
43	#552×C₈₉	C₂²	1	8	yes	—
44	#552×C₈₉	C₂²	1	8	yes	—
45	#552×C₈₉	C₂²	1	8	yes	—
46	#552×C₈₉	C₂²	1	8	yes	complemented
47	#552×C₈₉	C₂²	1	8	yes	complemented
48	#552×C₈₉	C₂²	1	16	yes	complemented
49	D₄×Q₈×C₈₉	C₂²	1	8	yes	—
50	D₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
51	#548×C₈₉	C₂²	1	8	yes	—
52	#548×C₈₉	C₂²	1	8	yes	—
53	#548×C₈₉	C₂²	1	8	yes	complemented
54	#547×C₈₉	C₂²	1	8	yes	—
55	#547×C₈₉	C₂²	1	4	yes	complemented
56	#544×C₈₉	C₂²	1	4	yes	—
57	#544×C₈₉	C₂²	1	8	yes	complemented
58	#544×C₈₉	C₂²	1	8	yes	complemented
59	#542×C₈₉	C₂²	1	8	yes	—
60	#542×C₈₉	C₂²	1	16	yes	—
61	#542×C₈₉	C₂²	1	8	yes	complemented
62	#542×C₈₉	C₂²	1	8	yes	complemented
63	#542×C₈₉	C₂²	1	16	yes	complemented
64	#541×C₈₉	C₂²	1	8	yes	—
65	#541×C₈₉	C₂²	1	8	yes	complemented
66	#541×C₈₉	C₂²	1	4	yes	complemented
67	#541×C₈₉	C₂²	1	16	yes	complemented
68	#540×C₈₉	C₂²	1	4	yes	complemented
69	#539×C₈₉	C₂²	1	16	yes	—
70	#538×C₈₉	C₂²	1	16	yes	—
71	#537×C₈₉	C₂²	1	4	yes	—
72	#537×C₈₉	C₂²	1	8	yes	—
73	#536×C₈₉	C₂²	1	8	yes	—
74	#533×C₈₉	C₂²	1	4	yes	—
75	#533×C₈₉	C₂²	1	4	yes	—
76	#533×C₈₉	C₂²	1	4	yes	—
77	#533×C₈₉	C₂²	1	4	yes	—
78	#533×C₈₉	C₂²	1	1	yes	characteristic
79	#533×C₈₉	C₂²	1	1	yes	characteristic
80	#533×C₈₉	C₂²	1	2	yes	—
81	#533×C₈₉	C₂²	1	2	yes	—
82	#533×C₈₉	C₂²	1	4	yes	complemented
83	#533×C₈₉	C₂²	1	4	yes	complemented
84	#533×C₈₉	C₂²	1	4	yes	complemented
85	#532×C₈₉	C₂²	1	1	yes	characteristic
86	#532×C₈₉	C₂²	1	2	yes	—
87	#532×C₈₉	C₂²	1	1	yes	characteristic
88	#532×C₈₉	C₂²	1	2	yes	—
89	#532×C₈₉	C₂²	1	4	yes	complemented
90	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
91	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
92	#529×C₈₉	C₂²	1	2	yes	—
93	#529×C₈₉	C₂²	1	4	yes	—
94	#529×C₈₉	C₂²	1	4	yes	—
95	#529×C₈₉	C₂²	1	2	yes	—
96	#529×C₈₉	C₂²	1	4	yes	—
97	#529×C₈₉	C₂²	1	4	yes	—
98	#529×C₈₉	C₂²	1	4	yes	—
99	#529×C₈₉	C₂²	1	16	yes	—
100	#529×C₈₉	C₂²	1	8	yes	complemented
101	C₂×#125×C₈₉	C₂²	1	2	yes	—
102	C₂×#125×C₈₉	C₂²	1	4	yes	complemented
103	#525×C₈₉	C₂²	1	2	yes	—
104	#525×C₈₉	C₂²	1	2	yes	—
105	#525×C₈₉	C₂²	1	4	yes	—
106	#525×C₈₉	C₂²	1	4	yes	—
107	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
108	#520×C₈₉	C₂²	1	4	yes	—
109	#520×C₈₉	C₂²	1	4	yes	—
110	#520×C₈₉	C₂²	1	8	yes	complemented
111	#519×C₈₉	C₂²	1	8	yes	complemented
112	C₄×#41×C₈₉	C₂²	1	2	yes	—
113	C₄×#41×C₈₉	C₂²	1	2	yes	—
114	C₄×#41×C₈₉	C₂²	1	4	yes	—
115	C₄×#41×C₈₉	C₂²	1	4	yes	—
116	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
117	C₂×#117×C₈₉	C₂²	1	2	yes	—
118	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
119	C₂×#41×C₈₉	C₂³	1	2	yes	—
120	C₂×#41×C₈₉	C₂³	1	2	yes	—
121	C₂×#41×C₈₉	C₂³	1	4	yes	—
122	C₂×#41×C₈₉	C₂³	1	4	yes	—
123	C₂×#41×C₈₉	C₂³	1	8	yes	—
124	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
125	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
126	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
128	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
129	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
130	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
131	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
134	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
135	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
136	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
139	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
140	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
141	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
142	#127×C₈₉	C₂³	1	1	yes	characteristic
143	#127×C₈₉	C₂³	1	1	yes	characteristic
144	#126×C₈₉	C₂³	1	8	yes	—
145	#126×C₈₉	C₂³	1	4	yes	—
146	#126×C₈₉	C₂³	1	4	yes	—
147	#126×C₈₉	C₂³	1	16	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	4	yes	—
155	#125×C₈₉	C₂³	1	4	yes	—
156	#125×C₈₉	C₂³	1	8	yes	—
157	#125×C₈₉	C₂³	1	1	yes	characteristic
158	#125×C₈₉	C₂³	1	16	yes	—
159	#125×C₈₉	C₂³	1	8	yes	—
160	#125×C₈₉	C₂³	1	1	yes	characteristic
161	#125×C₈₉	C₂³	1	4	yes	—
162	#125×C₈₉	C₂³	1	2	yes	—
163	#125×C₈₉	C₂³	1	4	yes	—
164	#125×C₈₉	C₂³	1	16	yes	—
165	#125×C₈₉	C₂³	1	8	yes	—
166	#125×C₈₉	C₂³	1	8	yes	—
167	#125×C₈₉	C₂³	1	16	yes	—
168	#125×C₈₉	C₂³	1	16	yes	—
169	#125×C₈₉	C₂³	1	16	yes	—
170	#124×C₈₉	C₂³	1	2	yes	—
171	#124×C₈₉	C₂³	1	2	yes	—
172	#124×C₈₉	C₂³	1	4	yes	—
173	#124×C₈₉	C₂³	1	4	yes	—
174	#124×C₈₉	C₂³	1	16	yes	—
175	#124×C₈₉	C₂³	1	8	yes	—
176	#124×C₈₉	C₂³	1	16	yes	—
177	#124×C₈₉	C₂³	1	16	yes	—
178	#124×C₈₉	C₂³	1	16	yes	—
179	#123×C₈₉	C₂³	1	4	yes	—
180	#123×C₈₉	C₂³	1	4	yes	—
181	#123×C₈₉	C₂³	1	4	yes	—
182	#123×C₈₉	C₂³	1	4	yes	—
183	#123×C₈₉	C₂³	1	8	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	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
190	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
191	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
192	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
193	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
194	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
195	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
197	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
198	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
199	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
200	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
201	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
202	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
203	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
204	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
205	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
206	C₂²⋊Q₈×C₈₉	C₂³	1	16	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	4	yes	—
215	#121×C₈₉	C₂³	1	2	yes	—
216	#121×C₈₉	C₂³	1	4	yes	—
217	#121×C₈₉	C₂³	1	2	yes	—
218	#121×C₈₉	C₂³	1	4	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	16	yes	—
224	#121×C₈₉	C₂³	1	16	yes	—
225	#121×C₈₉	C₂³	1	16	yes	—
226	#120×C₈₉	C₂³	1	4	yes	—
227	#120×C₈₉	C₂³	1	4	yes	—
228	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
229	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
230	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
231	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
232	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
233	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
234	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
235	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
236	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
237	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
238	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
239	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
240	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
241	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
242	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
243	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
244	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
245	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
246	C₄×D₄×C₈₉	C₂³	1	4	yes	—
247	C₄×D₄×C₈₉	C₂³	1	8	yes	—
248	C₄×D₄×C₈₉	C₂³	1	4	yes	—
249	C₄×D₄×C₈₉	C₂³	1	4	yes	—
250	C₄×D₄×C₈₉	C₂³	1	4	yes	—
251	C₄×D₄×C₈₉	C₂³	1	4	yes	—
252	C₄×D₄×C₈₉	C₂³	1	4	yes	—
253	C₄×D₄×C₈₉	C₂³	1	8	yes	—
254	C₄×D₄×C₈₉	C₂³	1	8	yes	—
255	C₄×D₄×C₈₉	C₂³	1	4	yes	—
256	C₄×D₄×C₈₉	C₂³	1	2	yes	—
257	C₄×D₄×C₈₉	C₂³	1	4	yes	—
258	C₄×D₄×C₈₉	C₂³	1	4	yes	—
259	C₄×D₄×C₈₉	C₂³	1	2	yes	—
260	C₄×D₄×C₈₉	C₂³	1	4	yes	—
261	C₄×D₄×C₈₉	C₂³	1	4	yes	—
262	C₄×D₄×C₈₉	C₂³	1	16	yes	—
263	C₄×D₄×C₈₉	C₂³	1	16	yes	—
264	C₄×D₄×C₈₉	C₂³	1	8	yes	—
265	C₄×D₄×C₈₉	C₂³	1	8	yes	—
266	C₄×D₄×C₈₉	C₂³	1	16	yes	—
267	C₄×D₄×C₈₉	C₂³	1	16	yes	—
268	C₄×D₄×C₈₉	C₂³	1	8	yes	—
269	#117×C₈₉	C₂³	1	8	yes	—
270	#117×C₈₉	C₂³	1	8	yes	—
271	#117×C₈₉	C₂³	1	4	yes	—
272	#117×C₈₉	C₂³	1	2	yes	—
273	#117×C₈₉	C₂³	1	2	yes	—
274	#117×C₈₉	C₂³	1	4	yes	—
275	#117×C₈₉	C₂³	1	4	yes	—
276	#117×C₈₉	C₂³	1	4	yes	—
277	#117×C₈₉	C₂³	1	4	yes	—
278	#117×C₈₉	C₂³	1	4	yes	—
279	#117×C₈₉	C₂³	1	8	yes	—
280	#117×C₈₉	C₂³	1	16	yes	—
281	#117×C₈₉	C₂³	1	16	yes	—
282	#117×C₈₉	C₂³	1	8	yes	—
283	#117×C₈₉	C₂³	1	8	yes	—
284	#117×C₈₉	C₂³	1	8	yes	—
285	#117×C₈₉	C₂³	1	16	yes	—
286	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
287	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
288	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
289	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
290	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
291	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
292	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
293	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
294	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
295	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
297	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
299	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
300	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
301	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
302	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
303	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
304	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
305	#41×C₈₉	—	2	8	no	—
306	#41×C₈₉	—	2	8	no	—
307	#41×C₈₉	—	4	8	no	—
308	#41×C₈₉	—	4	8	no	—
309	#41×C₈₉	—	4	16	no	—
310	C₂×Q₈×C₈₉	—	4	8	no	—
311	C₂×Q₈×C₈₉	—	4	16	no	—
312	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
313	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
314	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
315	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
316	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
317	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
318	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
319	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
320	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
321	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
322	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
323	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
324	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
325	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
326	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
327	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
328	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
329	C₂²×C₄×C₈₉	—	2	4	no	—
330	C₂²×C₄×C₈₉	—	4	4	no	—
331	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
338	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
339	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
340	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
341	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
342	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
345	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
346	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
347	C₂²×C₄×C₈₉	C₂⁴	1	16	yes	—
348	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
350	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
351	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
352	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
353	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
354	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
355	C₄⋊C₄×C₈₉	C₂⁴	1	4	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	16	yes	—
360	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
361	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
362	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
363	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
366	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
367	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
368	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
369	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
370	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
371	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
372	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
373	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
375	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
376	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
377	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
378	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
379	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
380	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
381	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
382	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
383	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
384	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
385	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
386	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
387	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
389	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
391	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
392	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
393	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
394	C₂²⋊C₄×C₈₉	C₂⁴	1	4	yes	—
395	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
396	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
397	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
398	C₄²×C₈₉	C₂⁴	1	2	yes	—
399	C₄²×C₈₉	C₂⁴	1	2	yes	—
400	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
401	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
402	C₄²×C₈₉	C₂⁴	1	2	yes	—
403	C₄²×C₈₉	C₂⁴	1	2	yes	—
404	C₄²×C₈₉	C₂⁴	1	2	yes	—
405	C₄²×C₈₉	C₂⁴	1	2	yes	—
406	C₄²×C₈₉	C₂⁴	1	8	yes	—
407	C₄²×C₈₉	C₂⁴	1	16	yes	—
408	C₄²×C₈₉	C₂⁴	1	4	yes	—
409	C₄²×C₈₉	C₂⁴	1	4	yes	—
410	C₄²×C₈₉	C₂⁴	1	4	yes	—
411	C₄²×C₈₉	C₂⁴	1	4	yes	—
412	C₄²×C₈₉	C₂⁴	1	16	yes	—
413	C₄²×C₈₉	C₂⁴	1	16	yes	—
414	C₂³×C₈₉	—	2	2	no	—
415	C₂³×C₈₉	—	4	2	no	—
416	C₂³×C₈₉	C₂⁵	1	2	yes	—
417	C₂³×C₈₉	C₂⁵	1	4	yes	—
418	C₂³×C₈₉	C₂⁵	1	4	yes	—
419	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
420	Q₈×C₈₉	—	2	4	no	—
421	Q₈×C₈₉	—	2	4	no	—
422	Q₈×C₈₉	—	2	16	no	—
423	Q₈×C₈₉	—	2	8	no	—
424	Q₈×C₈₉	—	4	8	no	—
425	Q₈×C₈₉	—	4	16	no	—
426	Q₈×C₈₉	—	4	4	no	—
427	D₄×C₈₉	—	2	8	no	—
428	D₄×C₈₉	—	2	8	no	—
429	D₄×C₈₉	—	2	4	no	—
430	D₄×C₈₉	—	2	4	no	—
431	D₄×C₈₉	—	2	8	no	—
432	D₄×C₈₉	—	4	4	no	—
433	D₄×C₈₉	—	4	4	no	—
434	D₄×C₈₉	—	4	4	no	—
435	D₄×C₈₉	—	4	8	no	—
436	D₄×C₈₉	—	4	16	no	—
437	C₂×C₄×C₈₉	—	2	2	no	—
438	C₂×C₄×C₈₉	—	2	4	no	—
439	C₂×C₄×C₈₉	—	2	4	no	—
440	C₂×C₄×C₈₉	—	2	8	no	—
441	C₂×C₄×C₈₉	—	2	8	no	—
442	C₂×C₄×C₈₉	—	2	4	no	—
443	C₂×C₄×C₈₉	—	2	4	no	—
444	C₂×C₄×C₈₉	—	2	4	no	—
445	C₂×C₄×C₈₉	—	2	8	no	—
446	C₂×C₄×C₈₉	—	2	8	no	—
447	C₂×C₄×C₈₉	—	4	2	no	—
448	C₂×C₄×C₈₉	—	4	2	no	—
449	C₂×C₄×C₈₉	—	4	2	no	—
450	C₂×C₄×C₈₉	—	4	8	no	—
451	C₂×C₄×C₈₉	—	4	16	no	—
452	C₂×C₄×C₈₉	—	4	8	no	—
453	C₂×C₄×C₈₉	—	4	16	no	—
454	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
455	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
456	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
457	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
458	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
459	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
460	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
461	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
462	C₂×C₄×C₈₉	C₂⁵	1	16	yes	—
463	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
464	C₂×C₄×C₈₉	C₂⁵	1	4	yes	—
465	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
466	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
467	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
468	C₂²×C₈₉	—	2	2	no	—
469	C₂²×C₈₉	—	2	2	no	—
470	C₂²×C₈₉	—	2	4	no	—
471	C₂²×C₈₉	—	2	4	no	—
472	C₂²×C₈₉	—	2	4	no	—
473	C₂²×C₈₉	—	2	2	no	—
474	C₂²×C₈₉	—	2	2	no	—
475	C₂²×C₈₉	—	2	4	no	—
476	C₂²×C₈₉	—	2	8	no	—
477	C₂²×C₈₉	—	4	4	no	—
478	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
479	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
480	C₄×C₈₉	—	2	2	no	—
481	C₄×C₈₉	—	2	4	no	—
482	C₄×C₈₉	—	2	4	no	—
483	C₄×C₈₉	—	2	2	no	—
484	C₄×C₈₉	—	2	4	no	—
485	C₄×C₈₉	—	2	2	no	—
486	C₄×C₈₉	—	2	2	no	—
487	C₄×C₈₉	—	2	4	no	—
488	C₄×C₈₉	—	2	16	no	—
489	C₄×C₈₉	—	2	8	no	—
490	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
491	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
492	C₄×C₈₉	#585	1	4	yes	—
493	#62838	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₂×C₈₉	—	2	2	no	—
495	C₂×C₈₉	—	4	4	no	—
496	C₂×C₈₉	—	4	4	no	—
497	C₂×C₈₉	—	4	2	no	—
498	C₂×C₈₉	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
499	C₂×C₈₉	C₂×#585	1	2	yes	—
500	#3565	C₂×C₈₉	1	8	yes	complemented
501	#3555	C₂×C₈₉	1	4	yes	complemented
502	#3547	C₂×C₈₉	1	4	yes	complemented
503	#3541	C₂×C₈₉	1	8	yes	complemented
504	#3518	C₂×C₈₉	1	4	yes	complemented
505	#3516	C₂×C₈₉	1	8	yes	complemented
506	#3515	C₂×C₈₉	1	4	yes	complemented
507	#3512	C₂×C₈₉	1	2	yes	complemented
508	#3511	C₂×C₈₉	1	2	yes	complemented
509	#3511	C₂×C₈₉	1	4	yes	complemented
510	#3509	C₂×C₈₉	1	4	yes	complemented
511	#3504	C₂×C₈₉	1	2	yes	complemented
512	#3503	C₂×C₈₉	1	2	yes	complemented
513	#3493	C₂×C₈₉	1	4	yes	complemented
514	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
515	#3444	C₂×C₈₉	1	1	yes	characteristic, complemented
516	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
517	C₈₉	#62838	1	1	yes	characteristic, direct product factor, Sylow
518	#563	C₂²×C₈₉	1	16	yes	—
519	#562	C₂²×C₈₉	1	16	yes	—
520	Q₈²	C₂²×C₈₉	1	4	yes	complemented
521	#557	C₂²×C₈₉	1	4	yes	complemented
522	#557	C₂²×C₈₉	1	8	yes	complemented
523	#557	C₂²×C₈₉	1	8	yes	complemented
524	#556	C₂²×C₈₉	1	8	yes	—
525	#556	C₂²×C₈₉	1	8	yes	—
526	#556	C₂²×C₈₉	1	8	yes	—
527	#556	C₂²×C₈₉	1	8	yes	complemented
528	#556	C₂²×C₈₉	1	4	yes	complemented
529	#556	C₂²×C₈₉	1	16	yes	complemented
530	#555	C₂²×C₈₉	1	8	yes	—
531	#555	C₂²×C₈₉	1	8	yes	—
532	#555	C₂²×C₈₉	1	4	yes	complemented
533	#554	C₂²×C₈₉	1	8	yes	—
534	#554	C₂²×C₈₉	1	16	yes	—
535	#554	C₂²×C₈₉	1	4	yes	complemented
536	#554	C₂²×C₈₉	1	8	yes	complemented
537	#554	C₂²×C₈₉	1	4	yes	complemented
538	#553	C₂²×C₈₉	1	8	yes	—
539	#553	C₂²×C₈₉	1	8	yes	—
540	#553	C₂²×C₈₉	1	8	yes	—
541	#553	C₂²×C₈₉	1	16	yes	—
542	#553	C₂²×C₈₉	1	8	yes	complemented
543	#552	C₂²×C₈₉	1	8	yes	—
544	#552	C₂²×C₈₉	1	8	yes	—
545	#552	C₂²×C₈₉	1	8	yes	—
546	#552	C₂²×C₈₉	1	8	yes	complemented
547	#552	C₂²×C₈₉	1	8	yes	complemented
548	#552	C₂²×C₈₉	1	16	yes	complemented
549	D₄×Q₈	C₂²×C₈₉	1	8	yes	—
550	D₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
551	#548	C₂²×C₈₉	1	8	yes	—
552	#548	C₂²×C₈₉	1	8	yes	—
553	#548	C₂²×C₈₉	1	8	yes	complemented
554	#547	C₂²×C₈₉	1	8	yes	—
555	#547	C₂²×C₈₉	1	4	yes	complemented
556	#544	C₂²×C₈₉	1	4	yes	—
557	#544	C₂²×C₈₉	1	8	yes	complemented
558	#544	C₂²×C₈₉	1	8	yes	complemented
559	#542	C₂²×C₈₉	1	8	yes	—
560	#542	C₂²×C₈₉	1	16	yes	—
561	#542	C₂²×C₈₉	1	8	yes	complemented
562	#542	C₂²×C₈₉	1	8	yes	complemented
563	#542	C₂²×C₈₉	1	16	yes	complemented
564	#541	C₂²×C₈₉	1	8	yes	—
565	#541	C₂²×C₈₉	1	8	yes	complemented
566	#541	C₂²×C₈₉	1	4	yes	complemented
567	#541	C₂²×C₈₉	1	16	yes	complemented
568	#540	C₂²×C₈₉	1	4	yes	complemented
569	#539	C₂²×C₈₉	1	16	yes	—
570	#538	C₂²×C₈₉	1	16	yes	—
571	#537	C₂²×C₈₉	1	4	yes	—
572	#537	C₂²×C₈₉	1	8	yes	—
573	#536	C₂²×C₈₉	1	8	yes	—
574	#533	C₂²×C₈₉	1	4	yes	—
575	#533	C₂²×C₈₉	1	4	yes	—
576	#533	C₂²×C₈₉	1	4	yes	—
577	#533	C₂²×C₈₉	1	4	yes	—
578	#533	C₂²×C₈₉	1	1	yes	characteristic
579	#533	C₂²×C₈₉	1	1	yes	characteristic
580	#533	C₂²×C₈₉	1	2	yes	—
581	#533	C₂²×C₈₉	1	2	yes	—
582	#533	C₂²×C₈₉	1	4	yes	complemented
583	#533	C₂²×C₈₉	1	4	yes	complemented
584	#533	C₂²×C₈₉	1	4	yes	complemented
585	#532	C₂²×C₈₉	1	1	yes	characteristic
586	#532	C₂²×C₈₉	1	2	yes	—
587	#532	C₂²×C₈₉	1	1	yes	characteristic
588	#532	C₂²×C₈₉	1	2	yes	—
589	#532	C₂²×C₈₉	1	4	yes	complemented
590	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
591	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
592	#529	C₂²×C₈₉	1	2	yes	—
593	#529	C₂²×C₈₉	1	4	yes	—
594	#529	C₂²×C₈₉	1	4	yes	—
595	#529	C₂²×C₈₉	1	2	yes	—
596	#529	C₂²×C₈₉	1	4	yes	—
597	#529	C₂²×C₈₉	1	4	yes	—
598	#529	C₂²×C₈₉	1	4	yes	—
599	#529	C₂²×C₈₉	1	16	yes	—
600	#529	C₂²×C₈₉	1	8	yes	complemented
601	C₂×#125	C₂²×C₈₉	1	2	yes	—
602	C₂×#125	C₂²×C₈₉	1	4	yes	complemented
603	#525	C₂²×C₈₉	1	2	yes	—
604	#525	C₂²×C₈₉	1	2	yes	—
605	#525	C₂²×C₈₉	1	4	yes	—
606	#525	C₂²×C₈₉	1	4	yes	—
607	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
608	#520	C₂²×C₈₉	1	4	yes	—
609	#520	C₂²×C₈₉	1	4	yes	—
610	#520	C₂²×C₈₉	1	8	yes	complemented
611	#519	C₂²×C₈₉	1	8	yes	complemented
612	C₄×#41	C₂²×C₈₉	1	2	yes	—
613	C₄×#41	C₂²×C₈₉	1	2	yes	—
614	C₄×#41	C₂²×C₈₉	1	4	yes	—
615	C₄×#41	C₂²×C₈₉	1	4	yes	—
616	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
617	C₂×#117	C₂²×C₈₉	1	2	yes	—
618	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
619	C₂×#41	C₂³×C₈₉	1	2	yes	—
620	C₂×#41	C₂³×C₈₉	1	2	yes	—
621	C₂×#41	C₂³×C₈₉	1	4	yes	—
622	C₂×#41	C₂³×C₈₉	1	4	yes	—
623	C₂×#41	C₂³×C₈₉	1	8	yes	—
624	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
625	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
626	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
627	C₂³×C₄	C₂³×C₈₉	1	2	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	2	yes	—
633	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
634	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
635	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
636	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
639	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
640	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
641	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
642	#127	C₂³×C₈₉	1	1	yes	characteristic
643	#127	C₂³×C₈₉	1	1	yes	characteristic
644	#126	C₂³×C₈₉	1	8	yes	—
645	#126	C₂³×C₈₉	1	4	yes	—
646	#126	C₂³×C₈₉	1	4	yes	—
647	#126	C₂³×C₈₉	1	16	yes	—
648	#126	C₂³×C₈₉	1	16	yes	—
649	#126	C₂³×C₈₉	1	16	yes	—
650	#126	C₂³×C₈₉	1	16	yes	—
651	#126	C₂³×C₈₉	1	16	yes	—
652	#126	C₂³×C₈₉	1	16	yes	—
653	#126	C₂³×C₈₉	1	16	yes	—
654	#125	C₂³×C₈₉	1	4	yes	—
655	#125	C₂³×C₈₉	1	4	yes	—
656	#125	C₂³×C₈₉	1	8	yes	—
657	#125	C₂³×C₈₉	1	1	yes	characteristic
658	#125	C₂³×C₈₉	1	16	yes	—
659	#125	C₂³×C₈₉	1	8	yes	—
660	#125	C₂³×C₈₉	1	1	yes	characteristic
661	#125	C₂³×C₈₉	1	4	yes	—
662	#125	C₂³×C₈₉	1	2	yes	—
663	#125	C₂³×C₈₉	1	4	yes	—
664	#125	C₂³×C₈₉	1	16	yes	—
665	#125	C₂³×C₈₉	1	8	yes	—
666	#125	C₂³×C₈₉	1	8	yes	—
667	#125	C₂³×C₈₉	1	16	yes	—
668	#125	C₂³×C₈₉	1	16	yes	—
669	#125	C₂³×C₈₉	1	16	yes	—
670	#124	C₂³×C₈₉	1	2	yes	—
671	#124	C₂³×C₈₉	1	2	yes	—
672	#124	C₂³×C₈₉	1	4	yes	—
673	#124	C₂³×C₈₉	1	4	yes	—
674	#124	C₂³×C₈₉	1	16	yes	—
675	#124	C₂³×C₈₉	1	8	yes	—
676	#124	C₂³×C₈₉	1	16	yes	—
677	#124	C₂³×C₈₉	1	16	yes	—
678	#124	C₂³×C₈₉	1	16	yes	—
679	#123	C₂³×C₈₉	1	4	yes	—
680	#123	C₂³×C₈₉	1	4	yes	—
681	#123	C₂³×C₈₉	1	4	yes	—
682	#123	C₂³×C₈₉	1	4	yes	—
683	#123	C₂³×C₈₉	1	8	yes	—
684	#123	C₂³×C₈₉	1	16	yes	—
685	#123	C₂³×C₈₉	1	16	yes	—
686	#123	C₂³×C₈₉	1	16	yes	—
687	#123	C₂³×C₈₉	1	16	yes	—
688	#123	C₂³×C₈₉	1	16	yes	—
689	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
690	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
692	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
694	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
695	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
696	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
698	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
700	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
701	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
703	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
704	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
705	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
706	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
707	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
708	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
709	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
710	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
711	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
712	#121	C₂³×C₈₉	1	4	yes	—
713	#121	C₂³×C₈₉	1	4	yes	—
714	#121	C₂³×C₈₉	1	4	yes	—
715	#121	C₂³×C₈₉	1	2	yes	—
716	#121	C₂³×C₈₉	1	4	yes	—
717	#121	C₂³×C₈₉	1	2	yes	—
718	#121	C₂³×C₈₉	1	4	yes	—
719	#121	C₂³×C₈₉	1	16	yes	—
720	#121	C₂³×C₈₉	1	8	yes	—
721	#121	C₂³×C₈₉	1	8	yes	—
722	#121	C₂³×C₈₉	1	8	yes	—
723	#121	C₂³×C₈₉	1	16	yes	—
724	#121	C₂³×C₈₉	1	16	yes	—
725	#121	C₂³×C₈₉	1	16	yes	—
726	#120	C₂³×C₈₉	1	4	yes	—
727	#120	C₂³×C₈₉	1	4	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	8	yes	—
732	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
733	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
734	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
735	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
736	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
737	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
738	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
739	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
740	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
741	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
742	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
743	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
744	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
745	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
746	C₄×D₄	C₂³×C₈₉	1	4	yes	—
747	C₄×D₄	C₂³×C₈₉	1	8	yes	—
748	C₄×D₄	C₂³×C₈₉	1	4	yes	—
749	C₄×D₄	C₂³×C₈₉	1	4	yes	—
750	C₄×D₄	C₂³×C₈₉	1	4	yes	—
751	C₄×D₄	C₂³×C₈₉	1	4	yes	—
752	C₄×D₄	C₂³×C₈₉	1	4	yes	—
753	C₄×D₄	C₂³×C₈₉	1	8	yes	—
754	C₄×D₄	C₂³×C₈₉	1	8	yes	—
755	C₄×D₄	C₂³×C₈₉	1	4	yes	—
756	C₄×D₄	C₂³×C₈₉	1	2	yes	—
757	C₄×D₄	C₂³×C₈₉	1	4	yes	—
758	C₄×D₄	C₂³×C₈₉	1	4	yes	—
759	C₄×D₄	C₂³×C₈₉	1	2	yes	—
760	C₄×D₄	C₂³×C₈₉	1	4	yes	—
761	C₄×D₄	C₂³×C₈₉	1	4	yes	—
762	C₄×D₄	C₂³×C₈₉	1	16	yes	—
763	C₄×D₄	C₂³×C₈₉	1	16	yes	—
764	C₄×D₄	C₂³×C₈₉	1	8	yes	—
765	C₄×D₄	C₂³×C₈₉	1	8	yes	—
766	C₄×D₄	C₂³×C₈₉	1	16	yes	—
767	C₄×D₄	C₂³×C₈₉	1	16	yes	—
768	C₄×D₄	C₂³×C₈₉	1	8	yes	—
769	#117	C₂³×C₈₉	1	8	yes	—
770	#117	C₂³×C₈₉	1	8	yes	—
771	#117	C₂³×C₈₉	1	4	yes	—
772	#117	C₂³×C₈₉	1	2	yes	—
773	#117	C₂³×C₈₉	1	2	yes	—
774	#117	C₂³×C₈₉	1	4	yes	—
775	#117	C₂³×C₈₉	1	4	yes	—
776	#117	C₂³×C₈₉	1	4	yes	—
777	#117	C₂³×C₈₉	1	4	yes	—
778	#117	C₂³×C₈₉	1	4	yes	—
779	#117	C₂³×C₈₉	1	8	yes	—
780	#117	C₂³×C₈₉	1	16	yes	—
781	#117	C₂³×C₈₉	1	16	yes	—
782	#117	C₂³×C₈₉	1	8	yes	—
783	#117	C₂³×C₈₉	1	8	yes	—
784	#117	C₂³×C₈₉	1	8	yes	—
785	#117	C₂³×C₈₉	1	16	yes	—
786	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
787	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
788	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
789	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
790	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
791	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
792	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
794	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
795	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
796	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
797	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
798	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
799	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
800	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
801	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
802	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
803	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
804	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
805	#41	—	2	8	no	—
806	#41	—	2	8	no	—
807	#41	—	4	8	no	—
808	#41	—	4	8	no	—
809	#41	—	4	16	no	—
810	C₂×Q₈	—	4	8	no	—
811	C₂×Q₈	—	4	16	no	—
812	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
813	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
814	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
815	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
816	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
817	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
818	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
819	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
820	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
821	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
822	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
823	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
824	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
825	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
826	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
827	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
828	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
829	C₂²×C₄	—	2	4	no	—
830	C₂²×C₄	—	4	4	no	—
831	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
832	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
838	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
839	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
840	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
841	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
844	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
845	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
847	C₂²×C₄	C₂⁴×C₈₉	1	16	yes	—
848	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
849	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
850	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
851	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
852	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
853	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
854	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
855	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
856	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
857	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
858	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
859	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
860	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
861	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
862	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
863	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
864	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
865	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
866	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
867	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
869	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
870	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
871	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
872	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
873	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
874	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
875	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
876	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
877	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
878	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
879	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
880	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
881	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
882	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
883	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
884	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
885	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
886	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
887	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
888	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
889	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
891	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
892	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
893	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
894	C₂²⋊C₄	C₂⁴×C₈₉	1	4	yes	—
895	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
896	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
897	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
898	C₄²	C₂⁴×C₈₉	1	2	yes	—
899	C₄²	C₂⁴×C₈₉	1	2	yes	—
900	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
901	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
902	C₄²	C₂⁴×C₈₉	1	2	yes	—
903	C₄²	C₂⁴×C₈₉	1	2	yes	—
904	C₄²	C₂⁴×C₈₉	1	2	yes	—
905	C₄²	C₂⁴×C₈₉	1	2	yes	—
906	C₄²	C₂⁴×C₈₉	1	8	yes	—
907	C₄²	C₂⁴×C₈₉	1	16	yes	—
908	C₄²	C₂⁴×C₈₉	1	4	yes	—
909	C₄²	C₂⁴×C₈₉	1	4	yes	—
910	C₄²	C₂⁴×C₈₉	1	4	yes	—
911	C₄²	C₂⁴×C₈₉	1	4	yes	—
912	C₄²	C₂⁴×C₈₉	1	16	yes	—
913	C₄²	C₂⁴×C₈₉	1	16	yes	—
914	C₂³	—	2	2	no	—
915	C₂³	—	4	2	no	—
916	C₂³	C₂⁵×C₈₉	1	2	yes	—
917	C₂³	C₂⁵×C₈₉	1	4	yes	—
918	C₂³	C₂⁵×C₈₉	1	4	yes	—
919	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
920	Q₈	—	2	4	no	—
921	Q₈	—	2	4	no	—
922	Q₈	—	2	16	no	—
923	Q₈	—	2	8	no	—
924	Q₈	—	4	8	no	—
925	Q₈	—	4	16	no	—
926	Q₈	—	4	4	no	—
927	D₄	—	2	8	no	—
928	D₄	—	2	8	no	—
929	D₄	—	2	4	no	—
930	D₄	—	2	4	no	—
931	D₄	—	2	8	no	—
932	D₄	—	4	4	no	—
933	D₄	—	4	4	no	—
934	D₄	—	4	4	no	—
935	D₄	—	4	8	no	—
936	D₄	—	4	16	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	4	no	—
939	C₂×C₄	—	2	4	no	—
940	C₂×C₄	—	2	8	no	—
941	C₂×C₄	—	2	8	no	—
942	C₂×C₄	—	2	4	no	—
943	C₂×C₄	—	2	4	no	—
944	C₂×C₄	—	2	4	no	—
945	C₂×C₄	—	2	8	no	—
946	C₂×C₄	—	2	8	no	—
947	C₂×C₄	—	4	2	no	—
948	C₂×C₄	—	4	2	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	4	8	no	—
951	C₂×C₄	—	4	16	no	—
952	C₂×C₄	—	4	8	no	—
953	C₂×C₄	—	4	16	no	—
954	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
955	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
956	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
957	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
958	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
959	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
960	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
961	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
962	C₂×C₄	C₂⁵×C₈₉	1	16	yes	—
963	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
964	C₂×C₄	C₂⁵×C₈₉	1	4	yes	—
965	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
966	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
967	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
968	C₂²	—	2	2	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	4	no	—
971	C₂²	—	2	4	no	—
972	C₂²	—	2	4	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	2	no	—
975	C₂²	—	2	4	no	—
976	C₂²	—	2	8	no	—
977	C₂²	—	4	4	no	—
978	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
979	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
980	C₄	—	2	2	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	2	2	no	—
984	C₄	—	2	4	no	—
985	C₄	—	2	2	no	—
986	C₄	—	2	2	no	—
987	C₄	—	2	4	no	—
988	C₄	—	2	16	no	—
989	C₄	—	2	8	no	—
990	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
991	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
992	C₄	#585×C₈₉	1	4	yes	—
993	C₂	—	2	2	no	—
994	C₂	—	4	4	no	—
995	C₂	—	4	4	no	—
996	C₂	—	4	2	no	—
997	C₂	C₂²×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
998	C₂	C₂×#585×C₈₉	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×#3565	C₂	semidirect
2. C₈₉×#3555	C₂	semidirect
3. C₈₉×#3547	C₂	semidirect
4. C₈₉×#3541	C₂	semidirect
5. C₈₉×#3518	C₂	semidirect
6. C₈₉×#3516	C₂	semidirect
7. C₈₉×#3515	C₂	semidirect
8. C₈₉×#3512	C₂	semidirect
9. C₈₉×#3511	C₂	semidirect
10. C₈₉×#3511	C₂	semidirect
11. C₈₉×#3509	C₂	semidirect
12. C₈₉×#3504	C₂	semidirect
13. C₈₉×#3503	C₂	semidirect
14. C₈₉×#3493	C₂	semidirect
15. C₈₉×#3444	C₂	semidirect
16. C₈₉×#3444	C₂	semidirect
17. C₂×#533×C₈₉	C₂	semidirect
20. Q₈²×C₈₉	C₂²	semidirect
21. #557×C₈₉	C₂²	semidirect
22. #557×C₈₉	C₂²	semidirect
23. #557×C₈₉	C₂²	semidirect
27. #556×C₈₉	C₂²	semidirect
28. #556×C₈₉	C₂²	semidirect
29. #556×C₈₉	C₂²	semidirect
32. #555×C₈₉	C₂²	semidirect
35. #554×C₈₉	C₂²	semidirect
36. #554×C₈₉	C₂²	semidirect
37. #554×C₈₉	C₂²	semidirect
42. #553×C₈₉	C₂²	semidirect
46. #552×C₈₉	C₂²	semidirect
47. #552×C₈₉	C₂²	semidirect
48. #552×C₈₉	C₂²	semidirect
50. D₄×Q₈×C₈₉	C₂²	semidirect
53. #548×C₈₉	C₂²	semidirect
55. #547×C₈₉	C₂²	semidirect
57. #544×C₈₉	C₂²	semidirect
58. #544×C₈₉	C₂²	semidirect
61. #542×C₈₉	C₂²	semidirect
62. #542×C₈₉	C₂²	semidirect
63. #542×C₈₉	C₂²	semidirect
65. #541×C₈₉	C₂²	semidirect
66. #541×C₈₉	C₂²	semidirect
67. #541×C₈₉	C₂²	semidirect
68. #540×C₈₉	C₂²	semidirect
82. #533×C₈₉	C₂²	semidirect
83. #533×C₈₉	C₂²	semidirect
84. #533×C₈₉	C₂²	semidirect
89. #532×C₈₉	C₂²	semidirect
91. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
100. #529×C₈₉	C₂²	semidirect
102. C₂×#125×C₈₉	C₂²	semidirect
110. #520×C₈₉	C₂²	semidirect
111. #519×C₈₉	C₂²	semidirect
493. #62838	C₈₉	direct (N × H)
500. #3565	C₂×C₈₉	semidirect
501. #3555	C₂×C₈₉	semidirect
502. #3547	C₂×C₈₉	semidirect
503. #3541	C₂×C₈₉	semidirect
504. #3518	C₂×C₈₉	semidirect
505. #3516	C₂×C₈₉	semidirect
506. #3515	C₂×C₈₉	semidirect
507. #3512	C₂×C₈₉	semidirect
508. #3511	C₂×C₈₉	semidirect
509. #3511	C₂×C₈₉	semidirect
510. #3509	C₂×C₈₉	semidirect
511. #3504	C₂×C₈₉	semidirect
512. #3503	C₂×C₈₉	semidirect
513. #3493	C₂×C₈₉	semidirect
514. #3444	C₂×C₈₉	semidirect
515. #3444	C₂×C₈₉	semidirect
516. C₂×#533	C₂×C₈₉	semidirect
517. C₈₉	#62838	direct (N × H)
520. Q₈²	C₂²×C₈₉	semidirect
521. #557	C₂²×C₈₉	semidirect
522. #557	C₂²×C₈₉	semidirect
523. #557	C₂²×C₈₉	semidirect
527. #556	C₂²×C₈₉	semidirect
528. #556	C₂²×C₈₉	semidirect
529. #556	C₂²×C₈₉	semidirect
532. #555	C₂²×C₈₉	semidirect
535. #554	C₂²×C₈₉	semidirect
536. #554	C₂²×C₈₉	semidirect
537. #554	C₂²×C₈₉	semidirect
542. #553	C₂²×C₈₉	semidirect
546. #552	C₂²×C₈₉	semidirect
547. #552	C₂²×C₈₉	semidirect
548. #552	C₂²×C₈₉	semidirect
550. D₄×Q₈	C₂²×C₈₉	semidirect
553. #548	C₂²×C₈₉	semidirect
555. #547	C₂²×C₈₉	semidirect
557. #544	C₂²×C₈₉	semidirect
558. #544	C₂²×C₈₉	semidirect
561. #542	C₂²×C₈₉	semidirect
562. #542	C₂²×C₈₉	semidirect
563. #542	C₂²×C₈₉	semidirect
565. #541	C₂²×C₈₉	semidirect
566. #541	C₂²×C₈₉	semidirect
567. #541	C₂²×C₈₉	semidirect
568. #540	C₂²×C₈₉	semidirect
582. #533	C₂²×C₈₉	semidirect
583. #533	C₂²×C₈₉	semidirect
584. #533	C₂²×C₈₉	semidirect
589. #532	C₂²×C₈₉	semidirect
591. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
600. #529	C₂²×C₈₉	semidirect
602. C₂×#125	C₂²×C₈₉	semidirect
610. #520	C₂²×C₈₉	semidirect
611. #519	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×#3565	2
C₈₉×#3555	2
C₈₉×#3547	2
C₈₉×#3541	2
C₈₉×#3518	2
C₈₉×#3516	2
C₈₉×#3515	2
C₈₉×#3512	2
C₈₉×#3511	2
C₈₉×#3509	2
C₈₉×#3504	2
C₈₉×#3503	2
C₈₉×#3493	2
C₈₉×#3444	2
C₂×#533×C₈₉	2
#62838	89

Subgroups — C89×#62838 #36440686

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62838 #36440686