Subgroups — C₈₉×#35533 #36413381

Order 22784.

3398 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2548	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2545	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2544	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2541	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2424	C₂	1	8	yes	maximal, complemented
10	C₈₉×#2416	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2414	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	#535×C₈₉	—	2	8	no	—
19	#535×C₈₉	—	2	8	no	—
20	#532×C₈₉	—	2	8	no	—
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×#127×C₈₉	C₂²	1	2	yes	—
23	C₂×#127×C₈₉	C₂²	1	2	yes	—
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#124×C₈₉	C₂²	1	2	yes	—
26	C₂×#124×C₈₉	C₂²	1	2	yes	—
27	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#121×C₈₉	C₂²	1	2	yes	—
30	C₂×#121×C₈₉	C₂²	1	4	yes	—
31	C₂×#121×C₈₉	C₂²	1	2	yes	—
32	C₂×#121×C₈₉	C₂²	1	4	yes	—
33	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
34	C₂×#120×C₈₉	C₂²	1	4	yes	—
35	C₂×#120×C₈₉	C₂²	1	4	yes	—
36	#520×C₈₉	—	2	8	no	—
37	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
38	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
39	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
41	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
44	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
46	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
47	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
48	#396×C₈₉	C₂²	1	8	yes	complemented
49	#394×C₈₉	C₂²	1	8	yes	complemented
50	#394×C₈₉	C₂²	1	8	yes	complemented
51	#392×C₈₉	C₂²	1	8	yes	complemented
52	#391×C₈₉	C₂²	1	2	yes	complemented
53	#390×C₈₉	C₂²	1	4	yes	—
54	#390×C₈₉	C₂²	1	2	yes	—
55	#390×C₈₉	C₂²	1	2	yes	—
56	#390×C₈₉	C₂²	1	2	yes	complemented
57	#390×C₈₉	C₂²	1	8	yes	complemented
58	#389×C₈₉	C₂²	1	2	yes	complemented
59	#389×C₈₉	C₂²	1	2	yes	complemented
60	#388×C₈₉	C₂²	1	8	yes	complemented
61	#386×C₈₉	C₂²	1	4	yes	—
62	#386×C₈₉	C₂²	1	8	yes	complemented
63	#385×C₈₉	C₂²	1	4	yes	—
64	#380×C₈₉	C₂²	1	4	yes	complemented
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
67	C₂⁵×C₈₉	C₂³	1	2	yes	—
68	C₂×#41×C₈₉	—	2	4	no	—
69	C₂×#41×C₈₉	—	2	4	no	—
70	C₂×#41×C₈₉	—	2	4	no	—
71	C₂×#41×C₈₉	—	2	4	no	—
72	C₂×#41×C₈₉	—	2	4	no	—
73	C₂×#41×C₈₉	D₄	1	8	yes	complemented
74	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	—	2	4	no	—
77	C₂²×D₄×C₈₉	—	2	4	no	—
78	C₂²×D₄×C₈₉	—	2	4	no	—
79	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
81	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
88	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
94	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₈₉	—	2	4	no	—
96	#127×C₈₉	—	2	8	no	—
97	#127×C₈₉	—	2	4	no	—
98	#127×C₈₉	—	2	8	no	—
99	#124×C₈₉	—	2	8	no	—
100	#124×C₈₉	—	2	4	no	—
101	#124×C₈₉	—	2	4	no	—
102	#124×C₈₉	—	2	8	no	—
103	#121×C₈₉	—	2	16	no	—
104	#121×C₈₉	—	2	16	no	—
105	#121×C₈₉	—	2	8	no	—
106	#121×C₈₉	—	2	8	no	—
107	#121×C₈₉	—	4	16	no	—
108	#120×C₈₉	—	2	16	no	—
109	#120×C₈₉	—	2	16	no	—
110	C₄×Q₈×C₈₉	—	2	8	no	—
111	C₄×D₄×C₈₉	—	2	16	no	—
112	C₄×D₄×C₈₉	—	2	16	no	—
113	C₄×D₄×C₈₉	—	2	8	no	—
114	#117×C₈₉	—	2	4	no	—
115	#117×C₈₉	—	2	8	no	—
116	#117×C₈₉	D₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
140	C₂×C₄²×C₈₉	—	2	4	no	—
141	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
144	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
145	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
147	#95×C₈₉	C₂³	1	4	yes	—
148	#95×C₈₉	C₂³	1	4	yes	—
149	#95×C₈₉	C₂³	1	8	yes	—
150	C₂⁴×C₈₉	—	2	4	no	—
151	C₂⁴×C₈₉	—	2	4	no	—
152	C₂⁴×C₈₉	—	2	4	no	—
153	C₂⁴×C₈₉	—	4	4	no	—
154	C₂⁴×C₈₉	—	4	4	no	—
155	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
156	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
157	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
158	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
159	#41×C₈₉	—	2	32	no	—
160	#41×C₈₉	—	4	16	no	—
161	C₂×Q₈×C₈₉	—	2	2	no	—
162	C₂×Q₈×C₈₉	—	2	2	no	—
163	C₂×Q₈×C₈₉	—	2	2	no	—
164	C₂×Q₈×C₈₉	—	2	2	no	—
165	C₂×Q₈×C₈₉	—	2	2	no	—
166	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
167	C₂×D₄×C₈₉	—	2	4	no	—
168	C₂×D₄×C₈₉	—	2	4	no	—
169	C₂×D₄×C₈₉	—	2	8	no	—
170	C₂×D₄×C₈₉	—	2	4	no	—
171	C₂×D₄×C₈₉	—	2	4	no	—
172	C₂×D₄×C₈₉	—	2	4	no	—
173	C₂×D₄×C₈₉	—	2	16	no	—
174	C₂×D₄×C₈₉	—	2	2	no	—
175	C₂×D₄×C₈₉	—	2	4	no	—
176	C₂×D₄×C₈₉	—	2	4	no	—
177	C₂×D₄×C₈₉	—	2	4	no	—
178	C₂×D₄×C₈₉	—	2	4	no	—
179	C₂×D₄×C₈₉	—	2	2	no	—
180	C₂×D₄×C₈₉	—	2	2	no	—
181	C₂×D₄×C₈₉	—	2	8	no	—
182	C₂×D₄×C₈₉	—	2	8	no	—
183	C₂×D₄×C₈₉	—	2	2	no	—
184	C₂×D₄×C₈₉	—	2	4	no	—
185	C₂×D₄×C₈₉	—	2	4	no	—
186	C₂×D₄×C₈₉	—	2	2	no	—
187	C₂×D₄×C₈₉	—	2	8	no	—
188	C₂×D₄×C₈₉	—	4	4	no	—
189	C₂×D₄×C₈₉	—	4	8	no	—
190	C₂×D₄×C₈₉	—	4	8	no	—
191	C₂×D₄×C₈₉	—	4	8	no	—
192	C₂×D₄×C₈₉	—	4	8	no	—
193	C₂×D₄×C₈₉	—	4	16	no	—
194	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
195	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
196	C₂²×C₄×C₈₉	—	2	4	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	2	4	no	—
200	C₂²×C₄×C₈₉	—	2	4	no	—
201	C₂²×C₄×C₈₉	—	2	4	no	—
202	C₂²×C₄×C₈₉	—	2	4	no	—
203	C₂²×C₄×C₈₉	—	2	4	no	—
204	C₂²×C₄×C₈₉	—	2	8	no	—
205	C₂²×C₄×C₈₉	—	4	2	no	—
206	C₂²×C₄×C₈₉	—	4	4	no	—
207	C₂²×C₄×C₈₉	—	4	8	no	—
208	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
209	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
210	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
211	C₂²×C₄×C₈₉	#41	1	4	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	8	no	—
224	C₄⋊C₄×C₈₉	—	2	4	no	—
225	C₄⋊C₄×C₈₉	—	2	4	no	—
226	C₄⋊C₄×C₈₉	—	2	8	no	—
227	C₄⋊C₄×C₈₉	—	2	8	no	—
228	C₄⋊C₄×C₈₉	—	4	4	no	—
229	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
230	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
231	C₂²⋊C₄×C₈₉	—	2	4	no	—
232	C₂²⋊C₄×C₈₉	—	2	8	no	—
233	C₂²⋊C₄×C₈₉	—	2	8	no	—
234	C₂²⋊C₄×C₈₉	—	2	8	no	—
235	C₂²⋊C₄×C₈₉	—	2	16	no	—
236	C₂²⋊C₄×C₈₉	—	2	8	no	—
237	C₂²⋊C₄×C₈₉	—	2	8	no	—
238	C₂²⋊C₄×C₈₉	—	2	16	no	—
239	C₂²⋊C₄×C₈₉	—	4	8	no	—
240	C₂²⋊C₄×C₈₉	—	4	8	no	—
241	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
242	C₄²×C₈₉	—	2	4	no	—
243	C₄²×C₈₉	—	2	2	no	—
244	C₄²×C₈₉	—	2	2	no	—
245	C₄²×C₈₉	—	2	8	no	—
246	C₄²×C₈₉	—	2	4	no	—
247	C₄²×C₈₉	C₂×D₄	1	8	yes	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	2	2	no	—
250	C₂³×C₈₉	—	2	2	no	—
251	C₂³×C₈₉	—	2	2	no	—
252	C₂³×C₈₉	—	2	4	no	—
253	C₂³×C₈₉	—	2	4	no	—
254	C₂³×C₈₉	—	2	2	no	—
255	C₂³×C₈₉	—	2	4	no	—
256	C₂³×C₈₉	—	2	4	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	2	no	—
259	C₂³×C₈₉	—	2	4	no	—
260	C₂³×C₈₉	—	2	8	no	—
261	C₂³×C₈₉	—	2	4	no	—
262	C₂³×C₈₉	—	2	4	no	—
263	C₂³×C₈₉	—	2	8	no	—
264	C₂³×C₈₉	—	4	16	no	—
265	C₂³×C₈₉	—	4	8	no	—
266	C₂³×C₈₉	—	8	8	no	—
267	C₂³×C₈₉	—	8	4	no	—
268	C₂³×C₈₉	—	8	4	no	—
269	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
270	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
271	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
272	C₂³×C₈₉	C₂×#41	1	2	yes	—
273	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
274	Q₈×C₈₉	—	2	8	no	—
275	Q₈×C₈₉	—	4	4	no	—
276	D₄×C₈₉	—	2	16	no	—
277	D₄×C₈₉	—	2	8	no	—
278	D₄×C₈₉	—	4	16	no	—
279	D₄×C₈₉	—	4	8	no	—
280	D₄×C₈₉	—	4	8	no	—
281	D₄×C₈₉	—	4	8	no	—
282	D₄×C₈₉	—	4	4	no	—
283	D₄×C₈₉	—	8	8	no	—
284	D₄×C₈₉	—	8	8	no	—
285	D₄×C₈₉	—	8	16	no	—
286	C₂×C₄×C₈₉	—	2	2	no	—
287	C₂×C₄×C₈₉	—	2	2	no	—
288	C₂×C₄×C₈₉	—	2	2	no	—
289	C₂×C₄×C₈₉	—	2	4	no	—
290	C₂×C₄×C₈₉	—	2	4	no	—
291	C₂×C₄×C₈₉	—	2	2	no	—
292	C₂×C₄×C₈₉	—	2	16	no	—
293	C₂×C₄×C₈₉	—	2	2	no	—
294	C₂×C₄×C₈₉	—	2	4	no	—
295	C₂×C₄×C₈₉	—	2	4	no	—
296	C₂×C₄×C₈₉	—	2	2	no	—
297	C₂×C₄×C₈₉	—	2	2	no	—
298	C₂×C₄×C₈₉	—	2	2	no	—
299	C₂×C₄×C₈₉	—	2	8	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	4	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	4	no	—
304	C₂×C₄×C₈₉	—	4	8	no	—
305	C₂×C₄×C₈₉	—	4	8	no	—
306	C₂×C₄×C₈₉	—	8	8	no	—
307	C₂×C₄×C₈₉	—	8	4	no	—
308	C₂×C₄×C₈₉	#121	1	16	yes	complemented
309	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
310	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
311	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
312	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
313	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
314	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
315	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
316	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
317	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
318	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
319	C₂²×C₈₉	—	2	4	no	—
320	C₂²×C₈₉	—	2	2	no	—
321	C₂²×C₈₉	—	2	2	no	—
322	C₂²×C₈₉	—	2	4	no	—
323	C₂²×C₈₉	—	2	4	no	—
324	C₂²×C₈₉	—	2	8	no	—
325	C₂²×C₈₉	—	4	2	no	—
326	C₂²×C₈₉	—	4	2	no	—
327	C₂²×C₈₉	—	4	4	no	—
328	C₂²×C₈₉	—	4	2	no	—
329	C₂²×C₈₉	—	4	4	no	—
330	C₂²×C₈₉	—	4	4	no	—
331	C₂²×C₈₉	—	4	8	no	—
332	C₂²×C₈₉	—	4	2	no	—
333	C₂²×C₈₉	—	4	4	no	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	4	no	—
336	C₂²×C₈₉	—	4	4	no	—
337	C₂²×C₈₉	—	4	8	no	—
338	C₂²×C₈₉	—	8	16	no	—
339	C₂²×C₈₉	C₂×#121	1	4	yes	—
340	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
341	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
342	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
343	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
344	C₂²×C₈₉	#585	1	2	yes	—
345	C₄×C₈₉	—	2	4	no	—
346	C₄×C₈₉	—	2	4	no	—
347	C₄×C₈₉	—	2	4	no	—
348	C₄×C₈₉	—	2	4	no	—
349	C₄×C₈₉	—	4	2	no	—
350	C₄×C₈₉	—	4	2	no	—
351	C₄×C₈₉	—	4	4	no	—
352	C₄×C₈₉	—	4	4	no	—
353	C₄×C₈₉	C₂×#121	1	4	yes	—
354	C₄×C₈₉	C₂×#121	1	4	yes	—
355	#35533	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
356	C₂×C₈₉	—	2	4	no	—
357	C₂×C₈₉	—	4	4	no	—
358	C₂×C₈₉	—	8	2	no	—
359	C₂×C₈₉	—	8	4	no	—
360	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
361	C₂×C₈₉	#3488	1	2	yes	—
362	C₂×C₈₉	#3498	1	1	yes	characteristic
363	C₂×C₈₉	#3500	1	1	yes	characteristic
364	C₂×C₈₉	#3506	1	2	yes	—
365	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
366	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
367	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
368	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
369	#2548	C₂×C₈₉	1	2	yes	complemented
370	#2545	C₂×C₈₉	1	2	yes	complemented
371	#2544	C₂×C₈₉	1	2	yes	complemented
372	#2541	C₂×C₈₉	1	2	yes	complemented
373	#2424	C₂×C₈₉	1	8	yes	complemented
374	#2416	C₂×C₈₉	1	4	yes	complemented
375	#2414	C₂×C₈₉	1	4	yes	complemented
376	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
377	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
378	C₂×#390	C₂×C₈₉	1	1	yes	characteristic, complemented
379	C₈₉	#35533	1	1	yes	characteristic, direct product factor, Sylow
380	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
381	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
382	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
383	#535	—	2	8	no	—
384	#535	—	2	8	no	—
385	#532	—	2	8	no	—
386	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
387	C₂×#127	C₂²×C₈₉	1	2	yes	—
388	C₂×#127	C₂²×C₈₉	1	2	yes	—
389	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
390	C₂×#124	C₂²×C₈₉	1	2	yes	—
391	C₂×#124	C₂²×C₈₉	1	2	yes	—
392	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
393	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
394	C₂×#121	C₂²×C₈₉	1	2	yes	—
395	C₂×#121	C₂²×C₈₉	1	4	yes	—
396	C₂×#121	C₂²×C₈₉	1	2	yes	—
397	C₂×#121	C₂²×C₈₉	1	4	yes	—
398	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
399	C₂×#120	C₂²×C₈₉	1	4	yes	—
400	C₂×#120	C₂²×C₈₉	1	4	yes	—
401	#520	—	2	8	no	—
402	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
403	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
404	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
405	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
406	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
407	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
408	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
409	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
411	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
412	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
413	#396	C₂²×C₈₉	1	8	yes	complemented
414	#394	C₂²×C₈₉	1	8	yes	complemented
415	#394	C₂²×C₈₉	1	8	yes	complemented
416	#392	C₂²×C₈₉	1	8	yes	complemented
417	#391	C₂²×C₈₉	1	2	yes	complemented
418	#390	C₂²×C₈₉	1	4	yes	—
419	#390	C₂²×C₈₉	1	2	yes	—
420	#390	C₂²×C₈₉	1	2	yes	—
421	#390	C₂²×C₈₉	1	2	yes	complemented
422	#390	C₂²×C₈₉	1	8	yes	complemented
423	#389	C₂²×C₈₉	1	2	yes	complemented
424	#389	C₂²×C₈₉	1	2	yes	complemented
425	#388	C₂²×C₈₉	1	8	yes	complemented
426	#386	C₂²×C₈₉	1	4	yes	—
427	#386	C₂²×C₈₉	1	8	yes	complemented
428	#385	C₂²×C₈₉	1	4	yes	—
429	#380	C₂²×C₈₉	1	4	yes	complemented
430	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
431	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
432	C₂⁵	C₂³×C₈₉	1	2	yes	—
433	C₂×#41	—	2	4	no	—
434	C₂×#41	—	2	4	no	—
435	C₂×#41	—	2	4	no	—
436	C₂×#41	—	2	4	no	—
437	C₂×#41	—	2	4	no	—
438	C₂×#41	D₄×C₈₉	1	8	yes	complemented
439	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
440	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
441	C₂²×D₄	—	2	4	no	—
442	C₂²×D₄	—	2	4	no	—
443	C₂²×D₄	—	2	4	no	—
444	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
445	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
446	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
447	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
449	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
450	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
451	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
452	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
453	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
454	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
455	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
456	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
457	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
458	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
459	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
460	C₄⋊Q₈	—	2	4	no	—
461	#127	—	2	8	no	—
462	#127	—	2	4	no	—
463	#127	—	2	8	no	—
464	#124	—	2	8	no	—
465	#124	—	2	4	no	—
466	#124	—	2	4	no	—
467	#124	—	2	8	no	—
468	#121	—	2	16	no	—
469	#121	—	2	16	no	—
470	#121	—	2	8	no	—
471	#121	—	2	8	no	—
472	#121	—	4	16	no	—
473	#120	—	2	16	no	—
474	#120	—	2	16	no	—
475	C₄×Q₈	—	2	8	no	—
476	C₄×D₄	—	2	16	no	—
477	C₄×D₄	—	2	16	no	—
478	C₄×D₄	—	2	8	no	—
479	#117	—	2	4	no	—
480	#117	—	2	8	no	—
481	#117	D₄×C₈₉	1	8	yes	complemented
482	C₂×C₄⋊C₄	—	2	4	no	—
483	C₂×C₄⋊C₄	—	2	8	no	—
484	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
493	C₂×C₂²⋊C₄	—	4	8	no	—
494	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
495	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
496	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
497	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
498	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
499	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
500	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₄²	—	2	4	no	—
506	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
507	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
508	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
509	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
510	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
511	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
512	#95	C₂³×C₈₉	1	4	yes	—
513	#95	C₂³×C₈₉	1	4	yes	—
514	#95	C₂³×C₈₉	1	8	yes	—
515	C₂⁴	—	2	4	no	—
516	C₂⁴	—	2	4	no	—
517	C₂⁴	—	2	4	no	—
518	C₂⁴	—	4	4	no	—
519	C₂⁴	—	4	4	no	—
520	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
521	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
522	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
523	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
524	#41	—	2	32	no	—
525	#41	—	4	16	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
532	C₂×D₄	—	2	4	no	—
533	C₂×D₄	—	2	4	no	—
534	C₂×D₄	—	2	8	no	—
535	C₂×D₄	—	2	4	no	—
536	C₂×D₄	—	2	4	no	—
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	16	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	4	no	—
543	C₂×D₄	—	2	4	no	—
544	C₂×D₄	—	2	2	no	—
545	C₂×D₄	—	2	2	no	—
546	C₂×D₄	—	2	8	no	—
547	C₂×D₄	—	2	8	no	—
548	C₂×D₄	—	2	2	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	8	no	—
553	C₂×D₄	—	4	4	no	—
554	C₂×D₄	—	4	8	no	—
555	C₂×D₄	—	4	8	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	—	4	8	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
560	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
561	C₂²×C₄	—	2	4	no	—
562	C₂²×C₄	—	2	4	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	4	no	—
565	C₂²×C₄	—	2	4	no	—
566	C₂²×C₄	—	2	4	no	—
567	C₂²×C₄	—	2	4	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	2	8	no	—
570	C₂²×C₄	—	4	2	no	—
571	C₂²×C₄	—	4	4	no	—
572	C₂²×C₄	—	4	8	no	—
573	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
574	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
575	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
576	C₂²×C₄	#41×C₈₉	1	4	yes	—
577	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
578	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
581	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
582	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
584	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
585	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
586	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₄⋊C₄	—	2	4	no	—
588	C₄⋊C₄	—	2	8	no	—
589	C₄⋊C₄	—	2	4	no	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	8	no	—
592	C₄⋊C₄	—	2	8	no	—
593	C₄⋊C₄	—	4	4	no	—
594	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
595	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
596	C₂²⋊C₄	—	2	4	no	—
597	C₂²⋊C₄	—	2	8	no	—
598	C₂²⋊C₄	—	2	8	no	—
599	C₂²⋊C₄	—	2	8	no	—
600	C₂²⋊C₄	—	2	16	no	—
601	C₂²⋊C₄	—	2	8	no	—
602	C₂²⋊C₄	—	2	8	no	—
603	C₂²⋊C₄	—	2	16	no	—
604	C₂²⋊C₄	—	4	8	no	—
605	C₂²⋊C₄	—	4	8	no	—
606	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
607	C₄²	—	2	4	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	8	no	—
611	C₄²	—	2	4	no	—
612	C₄²	C₂×D₄×C₈₉	1	8	yes	—
613	C₂³	—	2	2	no	—
614	C₂³	—	2	2	no	—
615	C₂³	—	2	2	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	4	no	—
618	C₂³	—	2	4	no	—
619	C₂³	—	2	2	no	—
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	2	8	no	—
626	C₂³	—	2	4	no	—
627	C₂³	—	2	4	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	4	16	no	—
630	C₂³	—	4	8	no	—
631	C₂³	—	8	8	no	—
632	C₂³	—	8	4	no	—
633	C₂³	—	8	4	no	—
634	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
635	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
636	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
637	C₂³	C₂×#41×C₈₉	1	2	yes	—
638	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
639	Q₈	—	2	8	no	—
640	Q₈	—	4	4	no	—
641	D₄	—	2	16	no	—
642	D₄	—	2	8	no	—
643	D₄	—	4	16	no	—
644	D₄	—	4	8	no	—
645	D₄	—	4	8	no	—
646	D₄	—	4	8	no	—
647	D₄	—	4	4	no	—
648	D₄	—	8	8	no	—
649	D₄	—	8	8	no	—
650	D₄	—	8	16	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	4	no	—
655	C₂×C₄	—	2	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	16	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	4	no	—
660	C₂×C₄	—	2	4	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	8	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	4	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	4	8	no	—
670	C₂×C₄	—	4	8	no	—
671	C₂×C₄	—	8	8	no	—
672	C₂×C₄	—	8	4	no	—
673	C₂×C₄	#121×C₈₉	1	16	yes	complemented
674	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
675	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
677	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
678	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
679	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
680	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
681	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
682	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
683	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
684	C₂²	—	2	4	no	—
685	C₂²	—	2	2	no	—
686	C₂²	—	2	2	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	8	no	—
690	C₂²	—	4	2	no	—
691	C₂²	—	4	2	no	—
692	C₂²	—	4	4	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	4	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	8	no	—
697	C₂²	—	4	2	no	—
698	C₂²	—	4	4	no	—
699	C₂²	—	4	2	no	—
700	C₂²	—	4	4	no	—
701	C₂²	—	4	8	no	—
702	C₂²	—	4	4	no	—
703	C₂²	—	8	16	no	—
704	C₂²	C₂×#121×C₈₉	1	4	yes	—
705	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
706	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
707	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
708	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
709	C₂²	#585×C₈₉	1	2	yes	—
710	C₄	—	2	4	no	—
711	C₄	—	2	4	no	—
712	C₄	—	2	4	no	—
713	C₄	—	2	4	no	—
714	C₄	—	4	2	no	—
715	C₄	—	4	2	no	—
716	C₄	—	4	4	no	—
717	C₄	—	4	4	no	—
718	C₄	C₂×#121×C₈₉	1	4	yes	—
719	C₄	C₂×#121×C₈₉	1	4	yes	—
720	C₂	—	2	4	no	—
721	C₂	—	4	4	no	—
722	C₂	—	8	2	no	—
723	C₂	—	8	4	no	—
724	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
725	C₂	C₈₉×#3488	1	2	yes	—
726	C₂	C₈₉×#3498	1	1	yes	characteristic
727	C₂	C₈₉×#3500	1	1	yes	characteristic
728	C₂	C₈₉×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₈₉	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₂×#532×C₈₉	C₂	semidirect
4. C₂×#520×C₈₉	C₂	semidirect
5. C₈₉×#2548	C₂	semidirect
6. C₈₉×#2545	C₂	semidirect
7. C₈₉×#2544	C₂	semidirect
8. C₈₉×#2541	C₂	semidirect
9. C₈₉×#2424	C₂	semidirect
10. C₈₉×#2416	C₂	semidirect
11. C₈₉×#2414	C₂	semidirect
12. C₈₉×#2311	C₂	semidirect
13. C₈₉×#2296	C₂	semidirect
14. C₂×#390×C₈₉	C₂	semidirect
21. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
24. C₂×#127×C₈₉	C₂²	semidirect
27. C₂×#124×C₈₉	C₂²	semidirect
28. C₂×#124×C₈₉	C₂²	semidirect
33. C₂×#121×C₈₉	C₂²	semidirect
37. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
39. C₂×C₄×D₄×C₈₉	C₂²	semidirect
40. C₂×C₄×D₄×C₈₉	C₂²	semidirect
43. C₂×#117×C₈₉	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
48. #396×C₈₉	C₂²	semidirect
49. #394×C₈₉	C₂²	semidirect
50. #394×C₈₉	C₂²	semidirect
51. #392×C₈₉	C₂²	semidirect
52. #391×C₈₉	C₂²	semidirect
56. #390×C₈₉	C₂²	semidirect
57. #390×C₈₉	C₂²	semidirect
58. #389×C₈₉	C₂²	semidirect
59. #389×C₈₉	C₂²	semidirect
60. #388×C₈₉	C₂²	semidirect
62. #386×C₈₉	C₂²	semidirect
64. #380×C₈₉	C₂²	semidirect
65. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
66. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
73. C₂×#41×C₈₉	D₄	semidirect
116. #117×C₈₉	D₄	semidirect
308. C₂×C₄×C₈₉	#121	semidirect
355. #35533	C₈₉	direct (N × H)
365. C₂×#535	C₂×C₈₉	semidirect
366. C₂×#535	C₂×C₈₉	semidirect
367. C₂×#532	C₂×C₈₉	semidirect
368. C₂×#520	C₂×C₈₉	semidirect
369. #2548	C₂×C₈₉	semidirect
370. #2545	C₂×C₈₉	semidirect
371. #2544	C₂×C₈₉	semidirect
372. #2541	C₂×C₈₉	semidirect
373. #2424	C₂×C₈₉	semidirect
374. #2416	C₂×C₈₉	semidirect
375. #2414	C₂×C₈₉	semidirect
376. #2311	C₂×C₈₉	semidirect
377. #2296	C₂×C₈₉	semidirect
378. C₂×#390	C₂×C₈₉	semidirect
379. C₈₉	#35533	direct (N × H)
386. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
389. C₂×#127	C₂²×C₈₉	semidirect
392. C₂×#124	C₂²×C₈₉	semidirect
393. C₂×#124	C₂²×C₈₉	semidirect
398. C₂×#121	C₂²×C₈₉	semidirect
402. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
404. C₂×C₄×D₄	C₂²×C₈₉	semidirect
405. C₂×C₄×D₄	C₂²×C₈₉	semidirect
408. C₂×#117	C₂²×C₈₉	semidirect
410. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
413. #396	C₂²×C₈₉	semidirect
414. #394	C₂²×C₈₉	semidirect
415. #394	C₂²×C₈₉	semidirect
416. #392	C₂²×C₈₉	semidirect
417. #391	C₂²×C₈₉	semidirect
421. #390	C₂²×C₈₉	semidirect
422. #390	C₂²×C₈₉	semidirect
423. #389	C₂²×C₈₉	semidirect
424. #389	C₂²×C₈₉	semidirect
425. #388	C₂²×C₈₉	semidirect
427. #386	C₂²×C₈₉	semidirect
429. #380	C₂²×C₈₉	semidirect
430. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
431. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
438. C₂×#41	D₄×C₈₉	semidirect
481. #117	D₄×C₈₉	semidirect
673. C₂×C₄	#121×C₈₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#535×C₈₉	2
C₂×#532×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2548	2
C₈₉×#2545	2
C₈₉×#2544	2
C₈₉×#2541	2
C₈₉×#2424	2
C₈₉×#2416	2
C₈₉×#2414	2
C₈₉×#2311	2
C₈₉×#2296	2
C₂×#390×C₈₉	2
#35533	89

Subgroups — C89×#35533 #36413381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35533 #36413381