Subgroups — C₈₉×#35396 #36413244

Order 22784.

2714 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#539×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2591	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2583	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2558	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2554	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2461	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2445	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2435	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2433	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2411	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2411	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2321	C₂	1	2	yes	maximal, complemented
14	C₄×#120×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
18	#539×C₈₉	—	2	8	no	—
19	C₂×#127×C₈₉	C₂²	1	2	yes	—
20	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#123×C₈₉	—	2	8	no	—
24	C₂×#123×C₈₉	C₂²	1	4	yes	—
25	C₂×#123×C₈₉	C₂²	1	4	yes	—
26	C₂×#123×C₈₉	C₂²	1	2	yes	—
27	C₂×#123×C₈₉	C₂²	1	2	yes	complemented
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
30	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#120×C₈₉	C₂²	1	2	yes	—
32	C₂×#120×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	#400×C₈₉	C₂²	1	2	yes	complemented
42	#398×C₈₉	C₂²	1	2	yes	complemented
43	#396×C₈₉	C₂²	1	4	yes	complemented
44	#396×C₈₉	C₂²	1	4	yes	complemented
45	#395×C₈₉	C₂²	1	2	yes	complemented
46	#394×C₈₉	C₂²	1	4	yes	—
47	#394×C₈₉	C₂²	1	4	yes	complemented
48	#394×C₈₉	C₂²	1	2	yes	complemented
49	#394×C₈₉	C₂²	1	4	yes	complemented
50	#392×C₈₉	C₂²	1	4	yes	—
51	#390×C₈₉	C₂²	1	2	yes	—
52	#390×C₈₉	C₂²	1	2	yes	—
53	#390×C₈₉	C₂²	1	4	yes	complemented
54	#390×C₈₉	C₂²	1	4	yes	complemented
55	#390×C₈₉	C₂²	1	4	yes	complemented
56	#389×C₈₉	C₂²	1	4	yes	complemented
57	#388×C₈₉	C₂²	1	4	yes	complemented
58	#388×C₈₉	C₂²	1	4	yes	complemented
59	#388×C₈₉	C₂²	1	4	yes	complemented
60	#388×C₈₉	C₂²	1	4	yes	complemented
61	#388×C₈₉	C₂²	1	4	yes	complemented
62	#386×C₈₉	C₂²	1	2	yes	—
63	#386×C₈₉	C₂²	1	2	yes	—
64	#386×C₈₉	C₂²	1	4	yes	complemented
65	#386×C₈₉	C₂²	1	4	yes	complemented
66	#385×C₈₉	C₂²	1	2	yes	—
67	#385×C₈₉	C₂²	1	2	yes	—
68	#385×C₈₉	C₂²	1	4	yes	complemented
69	#379×C₈₉	C₂²	1	2	yes	—
70	#379×C₈₉	C₂²	1	2	yes	—
71	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
72	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
73	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×D₄×C₈₉	—	2	4	no	—
81	C₂²×D₄×C₈₉	—	4	4	no	—
82	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
85	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
86	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
87	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	—	2	4	no	—
89	C₂³×C₄×C₈₉	—	4	4	no	—
90	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
95	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
97	#127×C₈₉	—	4	4	no	—
98	#126×C₈₉	—	2	8	no	—
99	#125×C₈₉	—	2	8	no	—
100	#124×C₈₉	—	4	4	no	—
101	#123×C₈₉	—	2	8	no	—
102	#123×C₈₉	—	2	16	no	—
103	#123×C₈₉	—	2	16	no	—
104	#123×C₈₉	—	2	8	no	—
105	C₂²⋊Q₈×C₈₉	—	2	4	no	—
106	C₂²⋊Q₈×C₈₉	—	2	8	no	—
107	#121×C₈₉	—	2	4	no	—
108	#120×C₈₉	—	2	8	no	—
109	#120×C₈₉	—	2	8	no	—
110	C₄×D₄×C₈₉	—	2	8	no	—
111	C₄×D₄×C₈₉	—	4	8	no	—
112	#117×C₈₉	—	2	8	no	—
113	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
114	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	1	yes	characteristic
123	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
127	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
150	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
151	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
152	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
153	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	4	yes	—
155	#95×C₈₉	C₂³	1	2	yes	—
156	#95×C₈₉	C₂³	1	2	yes	—
157	#95×C₈₉	C₂³	1	4	yes	—
158	#95×C₈₉	C₂³	1	4	yes	—
159	#95×C₈₉	C₂³	1	4	yes	—
160	#95×C₈₉	C₂³	1	4	yes	—
161	C₂⁴×C₈₉	—	2	2	no	—
162	C₂⁴×C₈₉	—	2	4	no	—
163	C₂⁴×C₈₉	—	2	2	no	—
164	C₂⁴×C₈₉	—	2	4	no	—
165	C₂⁴×C₈₉	—	2	4	no	—
166	C₂⁴×C₈₉	—	4	2	no	—
167	C₂⁴×C₈₉	—	4	2	no	—
168	C₂⁴×C₈₉	—	4	2	no	—
169	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
170	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
171	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
172	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂×Q₈×C₈₉	—	2	2	no	—
174	C₂×Q₈×C₈₉	—	4	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	8	no	—
179	C₂×D₄×C₈₉	—	2	4	no	—
180	C₂×D₄×C₈₉	—	2	4	no	—
181	C₂×D₄×C₈₉	—	2	4	no	—
182	C₂×D₄×C₈₉	—	2	4	no	—
183	C₂×D₄×C₈₉	—	2	2	no	—
184	C₂×D₄×C₈₉	—	2	8	no	—
185	C₂×D₄×C₈₉	—	2	8	no	—
186	C₂×D₄×C₈₉	—	4	2	no	—
187	C₂×D₄×C₈₉	—	4	2	no	—
188	C₂×D₄×C₈₉	—	4	4	no	—
189	C₂×D₄×C₈₉	—	4	4	no	—
190	C₂×D₄×C₈₉	—	4	2	no	—
191	C₂×D₄×C₈₉	—	4	4	no	—
192	C₂×D₄×C₈₉	—	4	16	no	—
193	C₂²×C₄×C₈₉	—	2	4	no	—
194	C₂²×C₄×C₈₉	—	2	2	no	—
195	C₂²×C₄×C₈₉	—	2	2	no	—
196	C₂²×C₄×C₈₉	—	2	8	no	—
197	C₂²×C₄×C₈₉	—	2	8	no	—
198	C₂²×C₄×C₈₉	—	2	4	no	—
199	C₂²×C₄×C₈₉	—	4	2	no	—
200	C₂²×C₄×C₈₉	—	4	4	no	—
201	C₂²×C₄×C₈₉	—	4	2	no	—
202	C₂²×C₄×C₈₉	—	4	2	no	—
203	C₂²×C₄×C₈₉	—	4	2	no	—
204	C₂²×C₄×C₈₉	—	4	4	no	—
205	C₂²×C₄×C₈₉	—	4	16	no	—
206	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
207	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
208	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
220	C₄⋊C₄×C₈₉	—	2	4	no	—
221	C₄⋊C₄×C₈₉	—	2	4	no	—
222	C₄⋊C₄×C₈₉	—	2	4	no	—
223	C₄⋊C₄×C₈₉	—	2	2	no	—
224	C₄⋊C₄×C₈₉	—	2	4	no	—
225	C₄⋊C₄×C₈₉	—	2	4	no	—
226	C₄⋊C₄×C₈₉	—	2	2	no	—
227	C₄⋊C₄×C₈₉	—	2	4	no	—
228	C₄⋊C₄×C₈₉	—	2	8	no	—
229	C₄⋊C₄×C₈₉	—	4	4	no	—
230	C₄⋊C₄×C₈₉	—	4	4	no	—
231	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
232	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
233	C₂²⋊C₄×C₈₉	—	2	4	no	—
234	C₂²⋊C₄×C₈₉	—	2	4	no	—
235	C₂²⋊C₄×C₈₉	—	2	8	no	—
236	C₂²⋊C₄×C₈₉	—	2	8	no	—
237	C₂²⋊C₄×C₈₉	—	2	8	no	—
238	C₂²⋊C₄×C₈₉	—	2	8	no	—
239	C₂²⋊C₄×C₈₉	—	2	4	no	—
240	C₂²⋊C₄×C₈₉	—	2	4	no	—
241	C₂²⋊C₄×C₈₉	—	2	4	no	—
242	C₂²⋊C₄×C₈₉	—	2	4	no	—
243	C₂²⋊C₄×C₈₉	—	2	8	no	—
244	C₂²⋊C₄×C₈₉	—	2	8	no	—
245	C₂²⋊C₄×C₈₉	—	4	4	no	—
246	C₂²⋊C₄×C₈₉	—	4	4	no	—
247	C₂²⋊C₄×C₈₉	—	4	4	no	—
248	C₂²⋊C₄×C₈₉	—	4	4	no	—
249	C₂²⋊C₄×C₈₉	—	4	4	no	—
250	C₂²⋊C₄×C₈₉	#41	1	8	yes	—
251	C₄²×C₈₉	—	2	4	no	—
252	C₄²×C₈₉	—	2	8	no	—
253	C₄²×C₈₉	—	4	4	no	—
254	C₄²×C₈₉	—	4	2	no	—
255	C₄²×C₈₉	—	4	2	no	—
256	C₂³×C₈₉	—	2	2	no	—
257	C₂³×C₈₉	—	2	2	no	—
258	C₂³×C₈₉	—	2	8	no	—
259	C₂³×C₈₉	—	2	2	no	—
260	C₂³×C₈₉	—	2	4	no	—
261	C₂³×C₈₉	—	2	2	no	—
262	C₂³×C₈₉	—	2	4	no	—
263	C₂³×C₈₉	—	2	2	no	—
264	C₂³×C₈₉	—	2	2	no	—
265	C₂³×C₈₉	—	2	4	no	—
266	C₂³×C₈₉	—	2	2	no	—
267	C₂³×C₈₉	—	2	2	no	—
268	C₂³×C₈₉	—	2	2	no	—
269	C₂³×C₈₉	—	2	4	no	—
270	C₂³×C₈₉	—	2	2	no	—
271	C₂³×C₈₉	—	2	4	no	—
272	C₂³×C₈₉	—	2	4	no	—
273	C₂³×C₈₉	—	4	16	no	—
274	C₂³×C₈₉	—	4	4	no	—
275	C₂³×C₈₉	—	4	4	no	—
276	C₂³×C₈₉	—	4	4	no	—
277	C₂³×C₈₉	—	4	4	no	—
278	C₂³×C₈₉	—	4	4	no	—
279	C₂³×C₈₉	—	8	8	no	—
280	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
281	C₂³×C₈₉	C₂×#41	1	4	yes	—
282	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
283	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
284	Q₈×C₈₉	—	8	2	no	—
285	D₄×C₈₉	—	4	16	no	—
286	D₄×C₈₉	—	4	8	no	—
287	D₄×C₈₉	—	4	8	no	—
288	D₄×C₈₉	—	4	8	no	—
289	D₄×C₈₉	—	8	2	no	—
290	D₄×C₈₉	—	8	8	no	—
291	C₂×C₄×C₈₉	—	2	8	no	—
292	C₂×C₄×C₈₉	—	2	2	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	4	no	—
299	C₂×C₄×C₈₉	—	2	2	no	—
300	C₂×C₄×C₈₉	—	2	2	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	4	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	4	no	—
308	C₂×C₄×C₈₉	—	2	4	no	—
309	C₂×C₄×C₈₉	—	2	4	no	—
310	C₂×C₄×C₈₉	—	2	4	no	—
311	C₂×C₄×C₈₉	—	2	4	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	4	4	no	—
315	C₂×C₄×C₈₉	—	4	4	no	—
316	C₂×C₄×C₈₉	—	4	16	no	—
317	C₂×C₄×C₈₉	—	4	4	no	—
318	C₂×C₄×C₈₉	—	4	4	no	—
319	C₂×C₄×C₈₉	—	8	4	no	—
320	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
321	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
322	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
325	C₂²×C₈₉	—	2	2	no	—
326	C₂²×C₈₉	—	2	2	no	—
327	C₂²×C₈₉	—	2	8	no	—
328	C₂²×C₈₉	—	2	4	no	—
329	C₂²×C₈₉	—	2	8	no	—
330	C₂²×C₈₉	—	4	16	no	—
331	C₂²×C₈₉	—	4	2	no	—
332	C₂²×C₈₉	—	4	2	no	—
333	C₂²×C₈₉	—	4	4	no	—
334	C₂²×C₈₉	—	4	2	no	—
335	C₂²×C₈₉	—	4	2	no	—
336	C₂²×C₈₉	—	4	2	no	—
337	C₂²×C₈₉	—	4	2	no	—
338	C₂²×C₈₉	—	4	2	no	—
339	C₂²×C₈₉	—	4	2	no	—
340	C₂²×C₈₉	—	4	4	no	—
341	C₂²×C₈₉	—	4	4	no	—
342	C₂²×C₈₉	—	4	4	no	—
343	C₂²×C₈₉	—	4	4	no	—
344	C₂²×C₈₉	—	8	8	no	—
345	C₂²×C₈₉	#532	1	4	yes	—
346	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
347	C₂²×C₈₉	C₂²×#41	1	2	yes	—
348	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
349	C₂²×C₈₉	#585	1	2	yes	—
350	C₄×C₈₉	—	2	4	no	—
351	C₄×C₈₉	—	2	4	no	—
352	C₄×C₈₉	—	2	2	no	—
353	C₄×C₈₉	—	2	2	no	—
354	C₄×C₈₉	—	2	8	no	—
355	C₄×C₈₉	—	4	2	no	—
356	C₄×C₈₉	—	4	2	no	—
357	C₄×C₈₉	—	4	2	no	—
358	C₄×C₈₉	—	4	2	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	4	no	—
361	#35396	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂×C₈₉	—	2	4	no	—
363	C₂×C₈₉	—	4	4	no	—
364	C₂×C₈₉	—	8	2	no	—
365	C₂×C₈₉	—	8	2	no	—
366	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
367	C₂×C₈₉	#3484	1	1	yes	characteristic
368	C₂×C₈₉	#3487	1	1	yes	characteristic
369	C₂×C₈₉	#3513	1	4	yes	—
370	C₂×#539	C₂×C₈₉	1	1	yes	characteristic, complemented
371	C₂²×#123	C₂×C₈₉	1	1	yes	characteristic, complemented
372	#2591	C₂×C₈₉	1	1	yes	characteristic, complemented
373	#2583	C₂×C₈₉	1	1	yes	characteristic, complemented
374	#2558	C₂×C₈₉	1	4	yes	complemented
375	#2554	C₂×C₈₉	1	4	yes	complemented
376	#2461	C₂×C₈₉	1	4	yes	complemented
377	#2445	C₂×C₈₉	1	4	yes	complemented
378	#2435	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#2433	C₂×C₈₉	1	1	yes	characteristic
380	#2411	C₂×C₈₉	1	2	yes	complemented
381	#2411	C₂×C₈₉	1	2	yes	complemented
382	#2321	C₂×C₈₉	1	2	yes	complemented
383	C₄×#120	C₂×C₈₉	1	2	yes	complemented
384	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
385	C₈₉	#35396	1	1	yes	characteristic, direct product factor, Sylow
386	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
387	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
388	#539	—	2	8	no	—
389	C₂×#127	C₂²×C₈₉	1	2	yes	—
390	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
391	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
392	C₂×#124	C₂²×C₈₉	1	2	yes	—
393	C₂×#123	—	2	8	no	—
394	C₂×#123	C₂²×C₈₉	1	4	yes	—
395	C₂×#123	C₂²×C₈₉	1	4	yes	—
396	C₂×#123	C₂²×C₈₉	1	2	yes	—
397	C₂×#123	C₂²×C₈₉	1	2	yes	complemented
398	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
399	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
400	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
401	C₂×#120	C₂²×C₈₉	1	2	yes	—
402	C₂×#120	C₂²×C₈₉	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
405	C₂×#117	C₂²×C₈₉	1	2	yes	—
406	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
407	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
411	#400	C₂²×C₈₉	1	2	yes	complemented
412	#398	C₂²×C₈₉	1	2	yes	complemented
413	#396	C₂²×C₈₉	1	4	yes	complemented
414	#396	C₂²×C₈₉	1	4	yes	complemented
415	#395	C₂²×C₈₉	1	2	yes	complemented
416	#394	C₂²×C₈₉	1	4	yes	—
417	#394	C₂²×C₈₉	1	2	yes	complemented
418	#394	C₂²×C₈₉	1	4	yes	complemented
419	#394	C₂²×C₈₉	1	4	yes	complemented
420	#392	C₂²×C₈₉	1	4	yes	—
421	#390	C₂²×C₈₉	1	2	yes	—
422	#390	C₂²×C₈₉	1	2	yes	—
423	#390	C₂²×C₈₉	1	4	yes	complemented
424	#390	C₂²×C₈₉	1	4	yes	complemented
425	#390	C₂²×C₈₉	1	4	yes	complemented
426	#389	C₂²×C₈₉	1	4	yes	complemented
427	#388	C₂²×C₈₉	1	4	yes	complemented
428	#388	C₂²×C₈₉	1	4	yes	complemented
429	#388	C₂²×C₈₉	1	4	yes	complemented
430	#388	C₂²×C₈₉	1	4	yes	complemented
431	#388	C₂²×C₈₉	1	4	yes	complemented
432	#386	C₂²×C₈₉	1	2	yes	—
433	#386	C₂²×C₈₉	1	2	yes	—
434	#386	C₂²×C₈₉	1	4	yes	complemented
435	#386	C₂²×C₈₉	1	4	yes	complemented
436	#385	C₂²×C₈₉	1	2	yes	—
437	#385	C₂²×C₈₉	1	2	yes	—
438	#385	C₂²×C₈₉	1	4	yes	complemented
439	#379	C₂²×C₈₉	1	2	yes	—
440	#379	C₂²×C₈₉	1	2	yes	—
441	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
442	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
443	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
444	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
447	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
448	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
449	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
450	C₂²×D₄	—	2	4	no	—
451	C₂²×D₄	—	4	4	no	—
452	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
453	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
454	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
455	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
456	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
457	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
458	C₂³×C₄	—	2	4	no	—
459	C₂³×C₄	—	4	4	no	—
460	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
461	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
462	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
463	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
465	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
466	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
467	#127	—	4	4	no	—
468	#126	—	2	8	no	—
469	#125	—	2	8	no	—
470	#124	—	4	4	no	—
471	#123	—	2	8	no	—
472	#123	—	2	16	no	—
473	#123	—	2	16	no	—
474	#123	—	2	8	no	—
475	C₂²⋊Q₈	—	2	4	no	—
476	C₂²⋊Q₈	—	2	8	no	—
477	#121	—	2	4	no	—
478	#120	—	2	8	no	—
479	#120	—	2	8	no	—
480	C₄×D₄	—	2	8	no	—
481	C₄×D₄	—	4	8	no	—
482	#117	—	2	8	no	—
483	C₂×C₄⋊C₄	—	2	4	no	—
484	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
485	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
486	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
487	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
489	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
490	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
491	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
492	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
493	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
494	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
495	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
496	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
497	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
498	C₂×C₂²⋊C₄	—	2	4	no	—
499	C₂×C₂²⋊C₄	—	2	4	no	—
500	C₂×C₂²⋊C₄	—	2	4	no	—
501	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
502	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
520	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
522	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
523	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
524	#95	C₂³×C₈₉	1	4	yes	—
525	#95	C₂³×C₈₉	1	2	yes	—
526	#95	C₂³×C₈₉	1	2	yes	—
527	#95	C₂³×C₈₉	1	4	yes	—
528	#95	C₂³×C₈₉	1	4	yes	—
529	#95	C₂³×C₈₉	1	4	yes	—
530	#95	C₂³×C₈₉	1	4	yes	—
531	C₂⁴	—	2	2	no	—
532	C₂⁴	—	2	4	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	—	2	4	no	—
535	C₂⁴	—	2	4	no	—
536	C₂⁴	—	4	2	no	—
537	C₂⁴	—	4	2	no	—
538	C₂⁴	—	4	2	no	—
539	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
540	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
541	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
542	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
543	C₂×Q₈	—	2	2	no	—
544	C₂×Q₈	—	4	2	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	4	no	—
548	C₂×D₄	—	2	8	no	—
549	C₂×D₄	—	2	4	no	—
550	C₂×D₄	—	2	4	no	—
551	C₂×D₄	—	2	4	no	—
552	C₂×D₄	—	2	4	no	—
553	C₂×D₄	—	2	2	no	—
554	C₂×D₄	—	2	8	no	—
555	C₂×D₄	—	2	8	no	—
556	C₂×D₄	—	4	2	no	—
557	C₂×D₄	—	4	2	no	—
558	C₂×D₄	—	4	4	no	—
559	C₂×D₄	—	4	4	no	—
560	C₂×D₄	—	4	2	no	—
561	C₂×D₄	—	4	4	no	—
562	C₂×D₄	—	4	16	no	—
563	C₂²×C₄	—	2	4	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	8	no	—
567	C₂²×C₄	—	2	8	no	—
568	C₂²×C₄	—	2	4	no	—
569	C₂²×C₄	—	4	2	no	—
570	C₂²×C₄	—	4	4	no	—
571	C₂²×C₄	—	4	2	no	—
572	C₂²×C₄	—	4	2	no	—
573	C₂²×C₄	—	4	2	no	—
574	C₂²×C₄	—	4	4	no	—
575	C₂²×C₄	—	4	16	no	—
576	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
577	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
578	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
579	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₈₉	1	2	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	2	yes	—
586	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
587	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
588	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
590	C₄⋊C₄	—	2	4	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	4	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	4	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	8	no	—
599	C₄⋊C₄	—	4	4	no	—
600	C₄⋊C₄	—	4	4	no	—
601	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
602	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
603	C₂²⋊C₄	—	2	4	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	8	no	—
606	C₂²⋊C₄	—	2	8	no	—
607	C₂²⋊C₄	—	2	8	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	4	no	—
611	C₂²⋊C₄	—	2	4	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	8	no	—
614	C₂²⋊C₄	—	2	8	no	—
615	C₂²⋊C₄	—	4	4	no	—
616	C₂²⋊C₄	—	4	4	no	—
617	C₂²⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	4	4	no	—
619	C₂²⋊C₄	—	4	4	no	—
620	C₂²⋊C₄	#41×C₈₉	1	8	yes	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	8	no	—
623	C₄²	—	4	4	no	—
624	C₄²	—	4	2	no	—
625	C₄²	—	4	2	no	—
626	C₂³	—	2	2	no	—
627	C₂³	—	2	2	no	—
628	C₂³	—	2	8	no	—
629	C₂³	—	2	2	no	—
630	C₂³	—	2	4	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	4	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	4	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	2	no	—
638	C₂³	—	2	2	no	—
639	C₂³	—	2	4	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	4	no	—
642	C₂³	—	2	4	no	—
643	C₂³	—	4	16	no	—
644	C₂³	—	4	4	no	—
645	C₂³	—	4	4	no	—
646	C₂³	—	4	4	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	8	8	no	—
650	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
651	C₂³	C₂×#41×C₈₉	1	4	yes	—
652	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
653	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
654	Q₈	—	8	2	no	—
655	D₄	—	4	16	no	—
656	D₄	—	4	8	no	—
657	D₄	—	4	8	no	—
658	D₄	—	4	8	no	—
659	D₄	—	8	2	no	—
660	D₄	—	8	8	no	—
661	C₂×C₄	—	2	8	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	4	no	—
665	C₂×C₄	—	2	4	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	4	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	4	4	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	16	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	8	4	no	—
690	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
691	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
692	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
694	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	2	no	—
697	C₂²	—	2	8	no	—
698	C₂²	—	2	4	no	—
699	C₂²	—	2	8	no	—
700	C₂²	—	4	16	no	—
701	C₂²	—	4	2	no	—
702	C₂²	—	4	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	—	4	4	no	—
711	C₂²	—	4	4	no	—
712	C₂²	—	4	4	no	—
713	C₂²	—	4	4	no	—
714	C₂²	—	8	8	no	—
715	C₂²	#532×C₈₉	1	4	yes	—
716	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
717	C₂²	C₂²×#41×C₈₉	1	2	yes	—
718	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
719	C₂²	#585×C₈₉	1	2	yes	—
720	C₄	—	2	4	no	—
721	C₄	—	2	4	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	8	no	—
725	C₄	—	4	2	no	—
726	C₄	—	4	2	no	—
727	C₄	—	4	2	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	2	no	—
730	C₄	—	4	4	no	—
731	C₂	—	2	4	no	—
732	C₂	—	4	4	no	—
733	C₂	—	8	2	no	—
734	C₂	—	8	2	no	—
735	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
736	C₂	C₈₉×#3484	1	1	yes	characteristic
737	C₂	C₈₉×#3487	1	1	yes	characteristic
738	C₂	C₈₉×#3513	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2433	C₂
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×#539×C₈₉	C₂	semidirect
2. C₂²×#123×C₈₉	C₂	semidirect
3. C₈₉×#2591	C₂	semidirect
4. C₈₉×#2583	C₂	semidirect
5. C₈₉×#2558	C₂	semidirect
6. C₈₉×#2554	C₂	semidirect
7. C₈₉×#2461	C₂	semidirect
8. C₈₉×#2445	C₂	semidirect
9. C₈₉×#2435	C₂	semidirect
11. C₈₉×#2411	C₂	semidirect
12. C₈₉×#2411	C₂	semidirect
13. C₈₉×#2321	C₂	semidirect
14. C₄×#120×C₈₉	C₂	semidirect
15. C₈₉×#2274	C₂	semidirect
20. C₂×#126×C₈₉	C₂²	semidirect
21. C₂×#125×C₈₉	C₂²	semidirect
27. C₂×#123×C₈₉	C₂²	semidirect
29. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
34. C₂×C₄×D₄×C₈₉	C₂²	semidirect
41. #400×C₈₉	C₂²	semidirect
42. #398×C₈₉	C₂²	semidirect
43. #396×C₈₉	C₂²	semidirect
44. #396×C₈₉	C₂²	semidirect
45. #395×C₈₉	C₂²	semidirect
47. #394×C₈₉	C₂²	semidirect
48. #394×C₈₉	C₂²	semidirect
49. #394×C₈₉	C₂²	semidirect
53. #390×C₈₉	C₂²	semidirect
54. #390×C₈₉	C₂²	semidirect
55. #390×C₈₉	C₂²	semidirect
56. #389×C₈₉	C₂²	semidirect
57. #388×C₈₉	C₂²	semidirect
58. #388×C₈₉	C₂²	semidirect
59. #388×C₈₉	C₂²	semidirect
60. #388×C₈₉	C₂²	semidirect
61. #388×C₈₉	C₂²	semidirect
64. #386×C₈₉	C₂²	semidirect
65. #386×C₈₉	C₂²	semidirect
68. #385×C₈₉	C₂²	semidirect
71. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
72. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
114. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
361. #35396	C₈₉	direct (N × H)
370. C₂×#539	C₂×C₈₉	semidirect
371. C₂²×#123	C₂×C₈₉	semidirect
372. #2591	C₂×C₈₉	semidirect
373. #2583	C₂×C₈₉	semidirect
374. #2558	C₂×C₈₉	semidirect
375. #2554	C₂×C₈₉	semidirect
376. #2461	C₂×C₈₉	semidirect
377. #2445	C₂×C₈₉	semidirect
378. #2435	C₂×C₈₉	semidirect
380. #2411	C₂×C₈₉	semidirect
381. #2411	C₂×C₈₉	semidirect
382. #2321	C₂×C₈₉	semidirect
383. C₄×#120	C₂×C₈₉	semidirect
384. #2274	C₂×C₈₉	semidirect
385. C₈₉	#35396	direct (N × H)
390. C₂×#126	C₂²×C₈₉	semidirect
391. C₂×#125	C₂²×C₈₉	semidirect
397. C₂×#123	C₂²×C₈₉	semidirect
399. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
404. C₂×C₄×D₄	C₂²×C₈₉	semidirect
411. #400	C₂²×C₈₉	semidirect
412. #398	C₂²×C₈₉	semidirect
413. #396	C₂²×C₈₉	semidirect
414. #396	C₂²×C₈₉	semidirect
415. #395	C₂²×C₈₉	semidirect
417. #394	C₂²×C₈₉	semidirect
418. #394	C₂²×C₈₉	semidirect
419. #394	C₂²×C₈₉	semidirect
423. #390	C₂²×C₈₉	semidirect
424. #390	C₂²×C₈₉	semidirect
425. #390	C₂²×C₈₉	semidirect
426. #389	C₂²×C₈₉	semidirect
427. #388	C₂²×C₈₉	semidirect
428. #388	C₂²×C₈₉	semidirect
429. #388	C₂²×C₈₉	semidirect
430. #388	C₂²×C₈₉	semidirect
431. #388	C₂²×C₈₉	semidirect
434. #386	C₂²×C₈₉	semidirect
435. #386	C₂²×C₈₉	semidirect
438. #385	C₂²×C₈₉	semidirect
441. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
442. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
446. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
484. C₂×C₄⋊C₄	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#539×C₈₉	2
C₂²×#123×C₈₉	2
C₈₉×#2591	2
C₈₉×#2583	2
C₈₉×#2558	2
C₈₉×#2554	2
C₈₉×#2461	2
C₈₉×#2445	2
C₈₉×#2435	2
C₈₉×#2433	2
C₈₉×#2411	2
C₈₉×#2321	2
C₄×#120×C₈₉	2
C₈₉×#2274	2
#35396	89

Subgroups — C89×#35396 #36413244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35396 #36413244