Subgroups — C₈₉×#61807 #36439655

Order 22784.

1788 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3354	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3346	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3334	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3330	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3309	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3303	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3235	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3231	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3198	C₂	1	4	yes	maximal, complemented
12	C₈₉×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#3098	C₂	1	4	yes	maximal, complemented
15	C₈₉×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	#562×C₈₉	—	2	2	no	—
17	#559×C₈₉	—	2	2	no	—
18	#556×C₈₉	—	2	1	no	—
19	#555×C₈₉	C₂²	1	2	yes	—
20	#554×C₈₉	—	2	1	no	—
21	#554×C₈₉	C₂²	1	2	yes	complemented
22	#553×C₈₉	C₂²	1	4	yes	—
23	#550×C₈₉	—	2	1	no	—
24	#550×C₈₉	—	2	1	no	—
25	#550×C₈₉	C₂²	1	2	yes	complemented
26	#547×C₈₉	C₂²	1	2	yes	—
27	#547×C₈₉	C₂²	1	2	yes	complemented
28	#547×C₈₉	C₂²	1	2	yes	complemented
29	#540×C₈₉	—	2	2	no	—
30	#538×C₈₉	—	2	2	no	—
31	#537×C₈₉	—	2	2	no	—
32	#537×C₈₉	C₂²	1	4	yes	—
33	#535×C₈₉	C₂²	1	2	yes	—
34	#533×C₈₉	C₂²	1	1	yes	characteristic
35	#533×C₈₉	C₂²	1	1	yes	characteristic
36	#532×C₈₉	C₂²	1	1	yes	characteristic
37	#532×C₈₉	C₂²	1	1	yes	characteristic
38	#525×C₈₉	—	2	2	no	—
39	#520×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
41	#501×C₈₉	C₂²	1	2	yes	complemented
42	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#490×C₈₉	C₂²	1	2	yes	complemented
45	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	#485×C₈₉	C₂²	1	4	yes	—
48	#485×C₈₉	C₂²	1	4	yes	complemented
49	#484×C₈₉	C₂²	1	2	yes	—
50	#484×C₈₉	C₂²	1	4	yes	complemented
51	#482×C₈₉	C₂²	1	4	yes	—
52	#482×C₈₉	C₂²	1	4	yes	complemented
53	#481×C₈₉	C₂²	1	4	yes	—
54	#480×C₈₉	C₂²	1	4	yes	—
55	#480×C₈₉	C₂²	1	2	yes	—
56	#480×C₈₉	C₂²	1	4	yes	complemented
57	#479×C₈₉	C₂²	1	4	yes	complemented
58	#476×C₈₉	C₂²	1	2	yes	complemented
59	#474×C₈₉	C₂²	1	2	yes	—
60	#474×C₈₉	C₂²	1	2	yes	—
61	#474×C₈₉	C₂²	1	2	yes	complemented
62	#469×C₈₉	C₂²	1	4	yes	—
63	#468×C₈₉	C₂²	1	4	yes	—
64	#466×C₈₉	C₂²	1	4	yes	—
65	#465×C₈₉	C₂²	1	4	yes	—
66	#461×C₈₉	C₂²	1	2	yes	—
67	#459×C₈₉	C₂²	1	2	yes	—
68	#450×C₈₉	C₂²	1	2	yes	—
69	#449×C₈₉	C₂²	1	4	yes	—
70	#449×C₈₉	C₂²	1	4	yes	—
71	#447×C₈₉	C₂²	1	2	yes	—
72	#440×C₈₉	C₂²	1	4	yes	—
73	C₄×D₈×C₈₉	C₂²	1	2	yes	—
74	C₄×D₈×C₈₉	C₂²	1	2	yes	—
75	#436×C₈₉	C₂²	1	2	yes	complemented
76	#435×C₈₉	C₂²	1	4	yes	complemented
77	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
78	#432×C₈₉	C₂²	1	1	yes	characteristic
79	#431×C₈₉	C₂²	1	1	yes	characteristic
80	#428×C₈₉	C₂²	1	4	yes	complemented
81	C₂×#107×C₈₉	C₂²	1	4	yes	complemented
82	#417×C₈₉	C₂²	1	4	yes	complemented
83	#416×C₈₉	C₂²	1	4	yes	complemented
84	#408×C₈₉	C₂²	1	4	yes	—
85	C₂×#41×C₈₉	—	2	2	no	—
86	C₂×#41×C₈₉	—	2	2	no	—
87	C₂×#41×C₈₉	—	2	1	no	—
88	C₂×#41×C₈₉	C₂³	1	4	yes	—
89	C₂×#41×C₈₉	C₂³	1	2	yes	—
90	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	—	2	1	no	—
92	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
93	C₂×D₈×C₈₉	C₂³	1	2	yes	—
94	C₂×D₈×C₈₉	C₂³	1	2	yes	—
95	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
96	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
97	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
98	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	#127×C₈₉	—	2	2	no	—
104	#127×C₈₉	—	2	2	no	—
105	#127×C₈₉	D₄	1	1	yes	characteristic
106	#127×C₈₉	C₂³	1	1	yes	characteristic
107	#126×C₈₉	—	2	4	no	—
108	#125×C₈₉	—	2	2	no	—
109	#125×C₈₉	—	2	1	no	—
110	#125×C₈₉	C₂³	1	2	yes	—
111	#124×C₈₉	—	2	2	no	—
112	#124×C₈₉	—	2	4	no	—
113	#124×C₈₉	—	2	1	no	—
114	#124×C₈₉	D₄	1	2	yes	—
115	#123×C₈₉	—	2	4	no	—
116	#123×C₈₉	—	2	4	no	—
117	#123×C₈₉	—	2	4	no	—
118	#123×C₈₉	—	2	4	no	—
119	C₂²⋊Q₈×C₈₉	—	2	4	no	—
120	C₂²⋊Q₈×C₈₉	—	2	1	no	—
121	C₂²⋊Q₈×C₈₉	—	2	1	no	—
122	C₂²⋊Q₈×C₈₉	—	2	1	no	—
123	C₂²⋊Q₈×C₈₉	—	2	2	no	—
124	C₂²⋊Q₈×C₈₉	—	2	2	no	—
125	C₂²⋊Q₈×C₈₉	—	2	4	no	—
126	C₂²⋊Q₈×C₈₉	C₂³	1	2	yes	—
127	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
128	#121×C₈₉	—	2	2	no	—
129	#121×C₈₉	—	2	4	no	—
130	#121×C₈₉	—	2	4	no	—
131	#121×C₈₉	—	2	2	no	—
132	#121×C₈₉	—	2	4	no	—
133	#121×C₈₉	—	2	4	no	—
134	#121×C₈₉	—	2	1	no	—
135	#121×C₈₉	—	2	4	no	—
136	#121×C₈₉	D₄	1	2	yes	—
137	#121×C₈₉	D₄	1	2	yes	—
138	#121×C₈₉	C₂³	1	2	yes	—
139	#121×C₈₉	C₂³	1	4	yes	—
140	#121×C₈₉	C₂³	1	4	yes	—
141	#121×C₈₉	C₂³	1	4	yes	—
142	#120×C₈₉	—	2	4	no	—
143	C₄×Q₈×C₈₉	—	2	2	no	—
144	C₄×Q₈×C₈₉	—	2	1	no	—
145	C₄×Q₈×C₈₉	—	2	1	no	—
146	C₄×Q₈×C₈₉	—	2	1	no	—
147	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
148	C₄×D₄×C₈₉	—	2	4	no	—
149	C₄×D₄×C₈₉	—	2	2	no	—
150	C₄×D₄×C₈₉	—	2	2	no	—
151	C₄×D₄×C₈₉	—	2	2	no	—
152	C₄×D₄×C₈₉	—	2	4	no	—
153	C₄×D₄×C₈₉	—	2	1	no	—
154	C₄×D₄×C₈₉	—	2	1	no	—
155	C₄×D₄×C₈₉	—	2	1	no	—
156	C₄×D₄×C₈₉	C₂³	1	2	yes	—
157	C₄×D₄×C₈₉	C₂³	1	2	yes	—
158	C₄×D₄×C₈₉	C₂³	1	2	yes	—
159	C₄×D₄×C₈₉	C₂³	1	2	yes	—
160	C₄×D₄×C₈₉	C₂³	1	2	yes	—
161	#117×C₈₉	—	2	1	no	—
162	#117×C₈₉	—	2	2	no	—
163	#117×C₈₉	C₂³	1	4	yes	—
164	#117×C₈₉	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
166	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
167	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
168	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	#107×C₈₉	C₂³	1	2	yes	—
172	#107×C₈₉	C₂³	1	4	yes	—
173	#107×C₈₉	C₂³	1	4	yes	—
174	#107×C₈₉	C₂³	1	4	yes	—
175	#107×C₈₉	C₂³	1	2	yes	—
176	#106×C₈₉	C₂³	1	4	yes	—
177	#106×C₈₉	C₂³	1	4	yes	—
178	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
179	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
180	#103×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	4	yes	—
182	#103×C₈₉	C₂³	1	4	yes	—
183	#102×C₈₉	C₂³	1	2	yes	—
184	#102×C₈₉	C₂³	1	4	yes	—
185	#102×C₈₉	C₂³	1	2	yes	—
186	#102×C₈₉	C₂³	1	4	yes	—
187	#102×C₈₉	C₂³	1	2	yes	—
188	#102×C₈₉	C₂³	1	2	yes	—
189	#102×C₈₉	C₂³	1	4	yes	—
190	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
191	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
192	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
193	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
194	#97×C₈₉	C₂³	1	2	yes	—
195	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
197	C₂⁴×C₈₉	—	2	1	no	—
198	#41×C₈₉	—	4	4	no	—
199	#41×C₈₉	—	4	4	no	—
200	#41×C₈₉	—	4	4	no	—
201	#41×C₈₉	—	8	2	no	—
202	#41×C₈₉	—	8	4	no	—
203	#41×C₈₉	—	8	4	no	—
204	C₂×Q₈×C₈₉	—	2	1	no	—
205	C₂×Q₈×C₈₉	—	2	1	no	—
206	C₂×Q₈×C₈₉	—	2	1	no	—
207	C₂×Q₈×C₈₉	—	2	1	no	—
208	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
210	C₂×D₄×C₈₉	—	2	4	no	—
211	C₂×D₄×C₈₉	—	2	4	no	—
212	C₂×D₄×C₈₉	—	2	2	no	—
213	C₂×D₄×C₈₉	—	2	4	no	—
214	C₂×D₄×C₈₉	—	2	4	no	—
215	C₂×D₄×C₈₉	—	2	1	no	—
216	C₂×D₄×C₈₉	—	2	1	no	—
217	C₂×D₄×C₈₉	—	2	1	no	—
218	C₂×D₄×C₈₉	—	4	2	no	—
219	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
220	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
221	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
223	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
224	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₈₉	—	2	1	no	—
226	C₂²×C₄×C₈₉	—	2	4	no	—
227	C₂²×C₄×C₈₉	—	2	4	no	—
228	C₂²×C₄×C₈₉	—	2	2	no	—
229	C₂²×C₄×C₈₉	—	2	2	no	—
230	C₂²×C₄×C₈₉	—	2	4	no	—
231	C₂²×C₄×C₈₉	—	2	2	no	—
232	C₂²×C₄×C₈₉	—	8	2	no	—
233	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
235	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
236	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
237	SD₁₆×C₈₉	—	4	4	no	—
238	D₈×C₈₉	—	4	2	no	—
239	D₈×C₈₉	—	4	2	no	—
240	M₁₆×C₈₉	—	4	4	no	—
241	C₂×C₈×C₈₉	—	4	4	no	—
242	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
243	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
244	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
245	C₄⋊C₄×C₈₉	—	2	1	no	—
246	C₄⋊C₄×C₈₉	—	2	4	no	—
247	C₄⋊C₄×C₈₉	—	2	1	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	1	no	—
251	C₄⋊C₄×C₈₉	—	2	1	no	—
252	C₄⋊C₄×C₈₉	—	2	1	no	—
253	C₄⋊C₄×C₈₉	—	2	1	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	—	2	2	no	—
256	C₄⋊C₄×C₈₉	—	2	2	no	—
257	C₄⋊C₄×C₈₉	—	2	1	no	—
258	C₄⋊C₄×C₈₉	—	2	2	no	—
259	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
260	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
264	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
265	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
266	C₂²⋊C₄×C₈₉	—	2	2	no	—
267	C₂²⋊C₄×C₈₉	—	2	2	no	—
268	C₂²⋊C₄×C₈₉	—	2	4	no	—
269	C₂²⋊C₄×C₈₉	—	2	4	no	—
270	C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂²⋊C₄×C₈₉	—	2	2	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	—	2	4	no	—
274	C₂²⋊C₄×C₈₉	—	2	4	no	—
275	C₂²⋊C₄×C₈₉	—	2	2	no	—
276	C₂²⋊C₄×C₈₉	—	2	2	no	—
277	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
278	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
279	C₄²×C₈₉	—	2	4	no	—
280	C₄²×C₈₉	—	2	2	no	—
281	C₄²×C₈₉	—	2	2	no	—
282	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
284	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
285	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	4	2	no	—
289	C₂³×C₈₉	—	8	1	no	—
290	C₂³×C₈₉	—	8	1	no	—
291	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
292	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
293	Q₈×C₈₉	—	2	4	no	—
294	Q₈×C₈₉	—	4	2	no	—
295	Q₈×C₈₉	—	4	2	no	—
296	Q₈×C₈₉	—	4	2	no	—
297	Q₈×C₈₉	—	8	1	no	—
298	Q₈×C₈₉	—	8	1	no	—
299	D₄×C₈₉	—	2	4	no	—
300	D₄×C₈₉	—	2	2	no	—
301	D₄×C₈₉	—	2	2	no	—
302	D₄×C₈₉	—	2	2	no	—
303	D₄×C₈₉	—	2	2	no	—
304	D₄×C₈₉	—	4	2	no	—
305	D₄×C₈₉	—	4	4	no	—
306	D₄×C₈₉	—	4	2	no	—
307	D₄×C₈₉	—	4	2	no	—
308	D₄×C₈₉	—	4	2	no	—
309	D₄×C₈₉	—	8	1	no	—
310	D₄×C₈₉	—	8	4	no	—
311	D₄×C₈₉	—	8	4	no	—
312	D₄×C₈₉	—	8	2	no	—
313	D₄×C₈₉	—	8	4	no	—
314	D₄×C₈₉	—	8	4	no	—
315	C₂×C₄×C₈₉	—	2	2	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	2	4	no	—
318	C₂×C₄×C₈₉	—	2	2	no	—
319	C₂×C₄×C₈₉	—	2	2	no	—
320	C₂×C₄×C₈₉	—	2	2	no	—
321	C₂×C₄×C₈₉	—	2	2	no	—
322	C₂×C₄×C₈₉	—	2	2	no	—
323	C₂×C₄×C₈₉	—	2	2	no	—
324	C₂×C₄×C₈₉	—	2	2	no	—
325	C₂×C₄×C₈₉	—	4	1	no	—
326	C₂×C₄×C₈₉	—	4	4	no	—
327	C₂×C₄×C₈₉	—	4	4	no	—
328	C₂×C₄×C₈₉	—	8	2	no	—
329	C₂×C₄×C₈₉	—	8	4	no	—
330	C₂×C₄×C₈₉	—	8	1	no	—
331	C₂×C₄×C₈₉	—	8	4	no	—
332	C₂×C₄×C₈₉	—	8	4	no	—
333	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
336	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
338	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
339	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
340	C₈×C₈₉	—	2	2	no	—
341	C₈×C₈₉	—	2	4	no	—
342	C₈×C₈₉	—	2	2	no	—
343	C₂²×C₈₉	—	2	1	no	—
344	C₂²×C₈₉	—	2	4	no	—
345	C₂²×C₈₉	—	2	1	no	—
346	C₂²×C₈₉	—	2	4	no	—
347	C₂²×C₈₉	—	2	1	no	—
348	C₂²×C₈₉	—	2	4	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	4	2	no	—
352	C₂²×C₈₉	—	4	2	no	—
353	C₂²×C₈₉	—	4	2	no	—
354	C₂²×C₈₉	—	4	2	no	—
355	C₂²×C₈₉	—	8	4	no	—
356	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
357	C₄×C₈₉	—	2	1	no	—
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	2	4	no	—
360	C₄×C₈₉	—	2	1	no	—
361	C₄×C₈₉	—	2	1	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	—	4	2	no	—
365	C₄×C₈₉	—	4	2	no	—
366	C₄×C₈₉	—	4	2	no	—
367	C₄×C₈₉	—	4	2	no	—
368	C₄×C₈₉	#576	1	2	yes	—
369	C₄×C₈₉	#585	1	2	yes	—
370	#61807	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₈₉	—	4	4	no	—
372	C₂×C₈₉	—	4	1	no	—
373	C₂×C₈₉	—	8	2	no	—
374	C₂×C₈₉	—	8	2	no	—
375	C₂×C₈₉	#3485	1	1	yes	characteristic
376	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
377	C₂×C₈₉	#3586	1	1	yes	characteristic
378	#3548	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#3506	C₂×C₈₉	1	1	yes	characteristic, complemented
380	#3354	C₂×C₈₉	1	2	yes	complemented
381	#3346	C₂×C₈₉	1	4	yes	complemented
382	#3334	C₂×C₈₉	1	2	yes	complemented
383	#3330	C₂×C₈₉	1	2	yes	complemented
384	#3309	C₂×C₈₉	1	4	yes	complemented
385	#3303	C₂×C₈₉	1	2	yes	complemented
386	#3235	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#3231	C₂×C₈₉	1	1	yes	characteristic, complemented
388	#3198	C₂×C₈₉	1	4	yes	complemented
389	#3110	C₂×C₈₉	1	1	yes	characteristic, complemented
390	#3100	C₂×C₈₉	1	1	yes	characteristic, complemented
391	#3098	C₂×C₈₉	1	4	yes	complemented
392	#2981	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₈₉	#61807	1	1	yes	characteristic, direct product factor, Sylow
394	#562	—	2	2	no	—
395	#559	—	2	2	no	—
396	#556	—	2	1	no	—
397	#555	C₂²×C₈₉	1	2	yes	—
398	#554	—	2	1	no	—
399	#554	C₂²×C₈₉	1	2	yes	complemented
400	#553	C₂²×C₈₉	1	4	yes	—
401	#550	—	2	1	no	—
402	#550	—	2	1	no	—
403	#550	C₂²×C₈₉	1	2	yes	complemented
404	#547	C₂²×C₈₉	1	2	yes	—
405	#547	C₂²×C₈₉	1	2	yes	complemented
406	#547	C₂²×C₈₉	1	2	yes	complemented
407	#540	—	2	2	no	—
408	#538	—	2	2	no	—
409	#537	—	2	2	no	—
410	#537	C₂²×C₈₉	1	4	yes	—
411	#535	C₂²×C₈₉	1	2	yes	—
412	#533	C₂²×C₈₉	1	1	yes	characteristic
413	#533	C₂²×C₈₉	1	1	yes	characteristic
414	#532	C₂²×C₈₉	1	1	yes	characteristic
415	#532	C₂²×C₈₉	1	1	yes	characteristic
416	#525	—	2	2	no	—
417	#520	C₂²×C₈₉	1	2	yes	—
418	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
419	#501	C₂²×C₈₉	1	2	yes	complemented
420	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
421	#498	C₂²×C₈₉	1	1	yes	characteristic, complemented
422	#490	C₂²×C₈₉	1	2	yes	complemented
423	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
424	#487	C₂²×C₈₉	1	1	yes	characteristic, complemented
425	#485	C₂²×C₈₉	1	4	yes	—
426	#485	C₂²×C₈₉	1	4	yes	complemented
427	#484	C₂²×C₈₉	1	2	yes	—
428	#484	C₂²×C₈₉	1	4	yes	complemented
429	#482	C₂²×C₈₉	1	4	yes	—
430	#482	C₂²×C₈₉	1	4	yes	complemented
431	#481	C₂²×C₈₉	1	4	yes	—
432	#480	C₂²×C₈₉	1	4	yes	—
433	#480	C₂²×C₈₉	1	2	yes	—
434	#480	C₂²×C₈₉	1	4	yes	complemented
435	#479	C₂²×C₈₉	1	4	yes	complemented
436	#476	C₂²×C₈₉	1	2	yes	complemented
437	#474	C₂²×C₈₉	1	2	yes	—
438	#474	C₂²×C₈₉	1	2	yes	—
439	#474	C₂²×C₈₉	1	2	yes	complemented
440	#469	C₂²×C₈₉	1	4	yes	—
441	#468	C₂²×C₈₉	1	4	yes	—
442	#466	C₂²×C₈₉	1	4	yes	—
443	#465	C₂²×C₈₉	1	4	yes	—
444	#461	C₂²×C₈₉	1	2	yes	—
445	#459	C₂²×C₈₉	1	2	yes	—
446	#450	C₂²×C₈₉	1	2	yes	—
447	#449	C₂²×C₈₉	1	4	yes	—
448	#449	C₂²×C₈₉	1	4	yes	—
449	#447	C₂²×C₈₉	1	2	yes	—
450	#440	C₂²×C₈₉	1	4	yes	—
451	C₄×D₈	C₂²×C₈₉	1	2	yes	—
452	C₄×D₈	C₂²×C₈₉	1	2	yes	—
453	#436	C₂²×C₈₉	1	2	yes	complemented
454	#435	C₂²×C₈₉	1	4	yes	complemented
455	C₈×D₄	C₂²×C₈₉	1	2	yes	complemented
456	#432	C₂²×C₈₉	1	1	yes	characteristic
457	#431	C₂²×C₈₉	1	1	yes	characteristic
458	#428	C₂²×C₈₉	1	4	yes	complemented
459	C₂×#107	C₂²×C₈₉	1	4	yes	complemented
460	#417	C₂²×C₈₉	1	4	yes	complemented
461	#416	C₂²×C₈₉	1	4	yes	complemented
462	#408	C₂²×C₈₉	1	4	yes	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	2	no	—
465	C₂×#41	—	2	1	no	—
466	C₂×#41	C₂³×C₈₉	1	4	yes	—
467	C₂×#41	C₂³×C₈₉	1	2	yes	—
468	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂³×C₄	—	2	1	no	—
470	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
471	C₂×D₈	C₂³×C₈₉	1	2	yes	—
472	C₂×D₈	C₂³×C₈₉	1	2	yes	—
473	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
474	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
475	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
476	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
478	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
479	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
480	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
481	#127	—	2	2	no	—
482	#127	—	2	2	no	—
483	#127	D₄×C₈₉	1	1	yes	characteristic
484	#127	C₂³×C₈₉	1	1	yes	characteristic
485	#126	—	2	4	no	—
486	#125	—	2	2	no	—
487	#125	—	2	1	no	—
488	#125	C₂³×C₈₉	1	2	yes	—
489	#124	—	2	2	no	—
490	#124	—	2	4	no	—
491	#124	—	2	1	no	—
492	#124	D₄×C₈₉	1	2	yes	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	#123	—	2	4	no	—
497	C₂²⋊Q₈	—	2	4	no	—
498	C₂²⋊Q₈	—	2	1	no	—
499	C₂²⋊Q₈	—	2	1	no	—
500	C₂²⋊Q₈	—	2	1	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	4	no	—
504	C₂²⋊Q₈	C₂³×C₈₉	1	2	yes	—
505	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
506	#121	—	2	2	no	—
507	#121	—	2	4	no	—
508	#121	—	2	4	no	—
509	#121	—	2	2	no	—
510	#121	—	2	4	no	—
511	#121	—	2	4	no	—
512	#121	—	2	1	no	—
513	#121	—	2	4	no	—
514	#121	D₄×C₈₉	1	2	yes	—
515	#121	D₄×C₈₉	1	2	yes	—
516	#121	C₂³×C₈₉	1	2	yes	—
517	#121	C₂³×C₈₉	1	4	yes	—
518	#121	C₂³×C₈₉	1	4	yes	—
519	#121	C₂³×C₈₉	1	4	yes	—
520	#120	—	2	4	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	1	no	—
523	C₄×Q₈	—	2	1	no	—
524	C₄×Q₈	—	2	1	no	—
525	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
526	C₄×D₄	—	2	4	no	—
527	C₄×D₄	—	2	2	no	—
528	C₄×D₄	—	2	2	no	—
529	C₄×D₄	—	2	2	no	—
530	C₄×D₄	—	2	4	no	—
531	C₄×D₄	—	2	1	no	—
532	C₄×D₄	—	2	1	no	—
533	C₄×D₄	—	2	1	no	—
534	C₄×D₄	C₂³×C₈₉	1	2	yes	—
535	C₄×D₄	C₂³×C₈₉	1	2	yes	—
536	C₄×D₄	C₂³×C₈₉	1	2	yes	—
537	C₄×D₄	C₂³×C₈₉	1	2	yes	—
538	C₄×D₄	C₂³×C₈₉	1	2	yes	—
539	#117	—	2	1	no	—
540	#117	—	2	2	no	—
541	#117	C₂³×C₈₉	1	2	yes	—
542	#117	C₂³×C₈₉	1	4	yes	—
543	C₂×C₄⋊C₄	—	2	2	no	—
544	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
546	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
549	#107	C₂³×C₈₉	1	2	yes	—
550	#107	C₂³×C₈₉	1	4	yes	—
551	#107	C₂³×C₈₉	1	4	yes	—
552	#107	C₂³×C₈₉	1	4	yes	—
553	#107	C₂³×C₈₉	1	2	yes	—
554	#106	C₂³×C₈₉	1	4	yes	—
555	#106	C₂³×C₈₉	1	4	yes	—
556	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
557	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
558	#103	C₂³×C₈₉	1	4	yes	—
559	#103	C₂³×C₈₉	1	4	yes	—
560	#103	C₂³×C₈₉	1	4	yes	—
561	#102	C₂³×C₈₉	1	2	yes	—
562	#102	C₂³×C₈₉	1	4	yes	—
563	#102	C₂³×C₈₉	1	2	yes	—
564	#102	C₂³×C₈₉	1	4	yes	—
565	#102	C₂³×C₈₉	1	2	yes	—
566	#102	C₂³×C₈₉	1	2	yes	—
567	#102	C₂³×C₈₉	1	4	yes	—
568	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
569	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
570	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
571	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
572	#97	C₂³×C₈₉	1	2	yes	—
573	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
574	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
575	C₂⁴	—	2	1	no	—
576	#41	—	4	4	no	—
577	#41	—	4	4	no	—
578	#41	—	4	4	no	—
579	#41	—	8	2	no	—
580	#41	—	8	4	no	—
581	#41	—	8	4	no	—
582	C₂×Q₈	—	2	1	no	—
583	C₂×Q₈	—	2	1	no	—
584	C₂×Q₈	—	2	1	no	—
585	C₂×Q₈	—	2	1	no	—
586	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
587	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
588	C₂×D₄	—	2	4	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	2	no	—
591	C₂×D₄	—	2	4	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	1	no	—
594	C₂×D₄	—	2	1	no	—
595	C₂×D₄	—	2	1	no	—
596	C₂×D₄	—	4	2	no	—
597	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
598	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
599	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
600	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
601	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
602	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
603	C₂²×C₄	—	2	1	no	—
604	C₂²×C₄	—	2	4	no	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	2	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	2	no	—
610	C₂²×C₄	—	8	2	no	—
611	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
612	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
613	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
614	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
615	SD₁₆	—	4	4	no	—
616	D₈	—	4	2	no	—
617	D₈	—	4	2	no	—
618	M₁₆	—	4	4	no	—
619	C₂×C₈	—	4	4	no	—
620	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
621	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
622	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
638	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
639	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
640	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
641	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
642	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
643	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	4	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	2	no	—
649	C₂²⋊C₄	—	2	2	no	—
650	C₂²⋊C₄	—	2	4	no	—
651	C₂²⋊C₄	—	2	4	no	—
652	C₂²⋊C₄	—	2	4	no	—
653	C₂²⋊C₄	—	2	2	no	—
654	C₂²⋊C₄	—	2	2	no	—
655	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
656	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
657	C₄²	—	2	4	no	—
658	C₄²	—	2	2	no	—
659	C₄²	—	2	2	no	—
660	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
661	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
662	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
663	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
664	C₂³	—	2	2	no	—
665	C₂³	—	2	2	no	—
666	C₂³	—	4	2	no	—
667	C₂³	—	8	1	no	—
668	C₂³	—	8	1	no	—
669	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
670	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
671	Q₈	—	2	4	no	—
672	Q₈	—	4	2	no	—
673	Q₈	—	4	2	no	—
674	Q₈	—	4	2	no	—
675	Q₈	—	8	1	no	—
676	Q₈	—	8	1	no	—
677	D₄	—	2	4	no	—
678	D₄	—	2	2	no	—
679	D₄	—	2	2	no	—
680	D₄	—	2	2	no	—
681	D₄	—	2	2	no	—
682	D₄	—	4	2	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	2	no	—
685	D₄	—	4	2	no	—
686	D₄	—	4	2	no	—
687	D₄	—	8	1	no	—
688	D₄	—	8	4	no	—
689	D₄	—	8	4	no	—
690	D₄	—	8	2	no	—
691	D₄	—	8	4	no	—
692	D₄	—	8	4	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	4	no	—
705	C₂×C₄	—	4	4	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	—	8	4	no	—
708	C₂×C₄	—	8	1	no	—
709	C₂×C₄	—	8	4	no	—
710	C₂×C₄	—	8	4	no	—
711	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
714	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
716	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
717	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
718	C₈	—	2	2	no	—
719	C₈	—	2	4	no	—
720	C₈	—	2	2	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	8	4	no	—
734	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	4	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	2	no	—
741	C₄	—	4	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	#576×C₈₉	1	2	yes	—
747	C₄	#585×C₈₉	1	2	yes	—
748	C₂	—	4	4	no	—
749	C₂	—	4	1	no	—
750	C₂	—	8	2	no	—
751	C₂	—	8	2	no	—
752	C₂	C₈₉×#3485	1	1	yes	characteristic
753	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
754	C₂	C₈₉×#3586	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 ◁ #532×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3548	C₂	semidirect
2. C₈₉×#3506	C₂	semidirect
3. C₈₉×#3354	C₂	semidirect
4. C₈₉×#3346	C₂	semidirect
5. C₈₉×#3334	C₂	semidirect
6. C₈₉×#3330	C₂	semidirect
7. C₈₉×#3309	C₂	semidirect
8. C₈₉×#3303	C₂	semidirect
9. C₈₉×#3235	C₂	semidirect
10. C₈₉×#3231	C₂	semidirect
11. C₈₉×#3198	C₂	semidirect
12. C₈₉×#3110	C₂	semidirect
13. C₈₉×#3100	C₂	semidirect
14. C₈₉×#3098	C₂	semidirect
15. C₈₉×#2981	C₂	semidirect
21. #554×C₈₉	C₂²	semidirect
25. #550×C₈₉	C₂²	semidirect
27. #547×C₈₉	C₂²	semidirect
28. #547×C₈₉	C₂²	semidirect
41. #501×C₈₉	C₂²	semidirect
42. #500×C₈₉	C₂²	semidirect
43. #498×C₈₉	C₂²	semidirect
44. #490×C₈₉	C₂²	semidirect
45. #487×C₈₉	C₂²	semidirect
46. #487×C₈₉	C₂²	semidirect
48. #485×C₈₉	C₂²	semidirect
50. #484×C₈₉	C₂²	semidirect
52. #482×C₈₉	C₂²	semidirect
56. #480×C₈₉	C₂²	semidirect
57. #479×C₈₉	C₂²	semidirect
58. #476×C₈₉	C₂²	semidirect
61. #474×C₈₉	C₂²	semidirect
75. #436×C₈₉	C₂²	semidirect
76. #435×C₈₉	C₂²	semidirect
77. C₈×D₄×C₈₉	C₂²	semidirect
80. #428×C₈₉	C₂²	semidirect
81. C₂×#107×C₈₉	C₂²	semidirect
82. #417×C₈₉	C₂²	semidirect
83. #416×C₈₉	C₂²	semidirect
370. #61807	C₈₉	direct (N × H)
378. #3548	C₂×C₈₉	semidirect
379. #3506	C₂×C₈₉	semidirect
380. #3354	C₂×C₈₉	semidirect
381. #3346	C₂×C₈₉	semidirect
382. #3334	C₂×C₈₉	semidirect
383. #3330	C₂×C₈₉	semidirect
384. #3309	C₂×C₈₉	semidirect
385. #3303	C₂×C₈₉	semidirect
386. #3235	C₂×C₈₉	semidirect
387. #3231	C₂×C₈₉	semidirect
388. #3198	C₂×C₈₉	semidirect
389. #3110	C₂×C₈₉	semidirect
390. #3100	C₂×C₈₉	semidirect
391. #3098	C₂×C₈₉	semidirect
392. #2981	C₂×C₈₉	semidirect
393. C₈₉	#61807	direct (N × H)
399. #554	C₂²×C₈₉	semidirect
403. #550	C₂²×C₈₉	semidirect
405. #547	C₂²×C₈₉	semidirect
406. #547	C₂²×C₈₉	semidirect
419. #501	C₂²×C₈₉	semidirect
420. #500	C₂²×C₈₉	semidirect
421. #498	C₂²×C₈₉	semidirect
422. #490	C₂²×C₈₉	semidirect
423. #487	C₂²×C₈₉	semidirect
424. #487	C₂²×C₈₉	semidirect
426. #485	C₂²×C₈₉	semidirect
428. #484	C₂²×C₈₉	semidirect
430. #482	C₂²×C₈₉	semidirect
434. #480	C₂²×C₈₉	semidirect
435. #479	C₂²×C₈₉	semidirect
436. #476	C₂²×C₈₉	semidirect
439. #474	C₂²×C₈₉	semidirect
453. #436	C₂²×C₈₉	semidirect
454. #435	C₂²×C₈₉	semidirect
455. C₈×D₄	C₂²×C₈₉	semidirect
458. #428	C₂²×C₈₉	semidirect
459. C₂×#107	C₂²×C₈₉	semidirect
460. #417	C₂²×C₈₉	semidirect
461. #416	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×#3548	2
C₈₉×#3506	2
C₈₉×#3354	2
C₈₉×#3346	2
C₈₉×#3334	2
C₈₉×#3330	2
C₈₉×#3309	2
C₈₉×#3303	2
C₈₉×#3235	2
C₈₉×#3231	2
C₈₉×#3198	2
C₈₉×#3110	2
C₈₉×#3100	2
C₈₉×#3098	2
C₈₉×#2981	2
#61807	89

Subgroups — C89×#61807 #36439655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61807 #36439655