Subgroups — C₂×C₈₉×#3532 #36440566

Order 22784.

9542 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3532	C₂	1	32	yes	maximal, direct product factor
2	C₂×H(3,𝔽₄)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#560×C₈₉	C₂	1	3	yes	maximal, complemented
4	C₂×#551×C₈₉	C₂	1	3	yes	maximal, complemented
5	C₂×#546×C₈₉	C₂	1	6	yes	maximal, complemented
6	C₂×D₄²×C₈₉	C₂	1	3	yes	maximal, complemented
7	C₂×#538×C₈₉	C₂	1	6	yes	maximal, complemented
8	C₂×#535×C₈₉	C₂	1	3	yes	maximal, complemented
9	C₂×#534×C₈₉	C₂	1	3	yes	maximal, complemented
10	C₂²×#120×C₈₉	C₂	1	3	yes	maximal, complemented
11	C₂⁶×C₈₉	C₂²	1	1	yes	characteristic, complemented
12	C₂²×#41×C₈₉	C₂²	1	3	yes	complemented
13	C₂³×D₄×C₈₉	C₂²	1	3	yes	complemented
14	C₂³×D₄×C₈₉	C₂²	1	6	yes	complemented
15	C₂³×D₄×C₈₉	C₂²	1	3	yes	complemented
16	H(3,𝔽₄)×C₈₉	C₂²	1	16	yes	complemented
17	#560×C₈₉	C₂²	1	48	yes	complemented
18	#551×C₈₉	C₂²	1	48	yes	complemented
19	#546×C₈₉	C₂²	1	96	yes	complemented
20	D₄²×C₈₉	C₂²	1	48	yes	complemented
21	#538×C₈₉	C₂²	1	96	yes	complemented
22	#535×C₈₉	C₂²	1	48	yes	complemented
23	#534×C₈₉	C₂²	1	48	yes	complemented
24	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×#127×C₈₉	C₂²	1	3	yes	complemented
26	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
27	C₂×#126×C₈₉	C₂²	1	6	yes	complemented
28	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
29	C₂×#124×C₈₉	C₂²	1	3	yes	complemented
30	C₂×#124×C₈₉	C₂²	1	6	yes	complemented
31	C₂×#123×C₈₉	C₂²	1	3	yes	complemented
32	C₂×#123×C₈₉	C₂²	1	3	yes	complemented
33	C₂×#123×C₈₉	C₂²	1	6	yes	complemented
34	C₂×#123×C₈₉	C₂²	1	6	yes	complemented
35	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	complemented
36	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
37	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
38	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
39	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
40	C₂×#121×C₈₉	C₂²	1	6	yes	complemented
41	C₂×#120×C₈₉	C₂²	1	3	yes	—
42	C₂×#120×C₈₉	C₂²	1	6	yes	complemented
43	C₂×#120×C₈₉	C₂²	1	6	yes	complemented
44	C₂×#120×C₈₉	C₂²	1	3	yes	complemented
45	C₂×#120×C₈₉	C₂²	1	3	yes	complemented
46	C₂×#120×C₈₉	C₂²	1	3	yes	complemented
47	C₂×#120×C₈₉	C₂²	1	6	yes	complemented
48	C₂×#120×C₈₉	C₂²	1	48	yes	complemented
49	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	C₂×#120×C₈₉	C₂²	1	3	yes	complemented
51	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	complemented
52	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	complemented
53	C₂×#117×C₈₉	C₂²	1	3	yes	complemented
54	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	complemented
55	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	complemented
56	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	complemented
57	C₂⁵×C₈₉	—	4	12	no	—
58	C₂⁵×C₈₉	C₂³	1	3	yes	—
59	C₂⁵×C₈₉	C₂³	1	3	yes	—
60	C₂⁵×C₈₉	C₂³	1	3	yes	—
61	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
62	C₂⁵×C₈₉	C₂³	1	8	yes	complemented
63	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic, complemented
64	C₂×#41×C₈₉	—	4	12	no	—
65	C₂×#41×C₈₉	C₂³	1	24	yes	complemented
66	C₂²×Q₈×C₈₉	C₂³	1	3	yes	complemented
67	C₂²×D₄×C₈₉	—	4	12	no	—
68	C₂²×D₄×C₈₉	—	4	24	no	—
69	C₂²×D₄×C₈₉	—	4	12	no	—
70	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
71	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
72	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
74	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
76	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
77	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
78	C₂²×D₄×C₈₉	C₂³	1	24	yes	complemented
79	C₂²×D₄×C₈₉	C₂³	1	48	yes	complemented
80	C₂²×D₄×C₈₉	C₂³	1	3	yes	complemented
81	C₂²×D₄×C₈₉	C₂³	1	6	yes	complemented
82	C₂²×D₄×C₈₉	C₂³	1	24	yes	complemented
83	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
84	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
85	C₂³×C₄×C₈₉	C₂³	1	6	yes	complemented
86	C₂³×C₄×C₈₉	C₂³	1	3	yes	complemented
87	#127×C₈₉	C₂³	1	8	yes	complemented
88	#127×C₈₉	C₂³	1	24	yes	complemented
89	#126×C₈₉	C₂³	1	16	yes	complemented
90	#126×C₈₉	C₂³	1	48	yes	complemented
91	#124×C₈₉	C₂³	1	24	yes	complemented
92	#124×C₈₉	C₂³	1	24	yes	complemented
93	#124×C₈₉	C₂³	1	48	yes	complemented
94	#123×C₈₉	C₂³	1	24	yes	complemented
95	#123×C₈₉	C₂³	1	24	yes	complemented
96	#123×C₈₉	C₂³	1	48	yes	complemented
97	#123×C₈₉	C₂³	1	48	yes	complemented
98	C₂²⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
99	#121×C₈₉	C₂³	1	48	yes	complemented
100	#121×C₈₉	C₂³	1	48	yes	complemented
101	#121×C₈₉	C₂³	1	48	yes	complemented
102	#121×C₈₉	C₂³	1	48	yes	complemented
103	#121×C₈₉	C₂³	1	48	yes	complemented
104	#120×C₈₉	C₂³	1	24	yes	—
105	#120×C₈₉	C₂³	1	48	yes	complemented
106	#120×C₈₉	C₂³	1	48	yes	complemented
107	#120×C₈₉	C₂³	1	24	yes	complemented
108	#120×C₈₉	C₂³	1	24	yes	complemented
109	#120×C₈₉	C₂³	1	24	yes	complemented
110	#120×C₈₉	C₂³	1	48	yes	complemented
111	#120×C₈₉	C₂³	1	8	yes	complemented
112	#120×C₈₉	C₂³	1	24	yes	complemented
113	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
114	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
115	#117×C₈₉	C₂³	1	24	yes	complemented
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	complemented
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	complemented
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	48	yes	complemented
128	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	complemented
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	complemented
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	complemented
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	complemented
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	complemented
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic, complemented
134	C₂×C₄²×C₈₉	C₂³	1	3	yes	complemented
135	C₂×C₄²×C₈₉	C₂³	1	2	yes	complemented
136	C₂⁴×C₈₉	—	2	24	no	—
137	C₂⁴×C₈₉	—	2	12	no	—
138	C₂⁴×C₈₉	—	2	12	no	—
139	C₂⁴×C₈₉	—	4	6	no	—
140	C₂⁴×C₈₉	—	4	12	no	—
141	C₂⁴×C₈₉	—	4	6	no	—
142	C₂⁴×C₈₉	—	4	48	no	—
143	C₂⁴×C₈₉	—	4	12	no	—
144	C₂⁴×C₈₉	—	4	6	no	—
145	C₂⁴×C₈₉	—	4	64	no	—
146	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
147	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
148	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
149	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
150	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
151	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
152	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
153	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
154	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
155	C₂⁴×C₈₉	C₂⁴	1	4	yes	complemented
156	#41×C₈₉	—	4	48	no	—
157	C₂×Q₈×C₈₉	—	4	6	no	—
158	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	complemented
159	C₂×D₄×C₈₉	—	2	24	no	—
160	C₂×D₄×C₈₉	—	2	24	no	—
161	C₂×D₄×C₈₉	—	4	6	no	—
162	C₂×D₄×C₈₉	—	4	6	no	—
163	C₂×D₄×C₈₉	—	4	6	no	—
164	C₂×D₄×C₈₉	—	4	6	no	—
165	C₂×D₄×C₈₉	—	4	12	no	—
166	C₂×D₄×C₈₉	—	4	12	no	—
167	C₂×D₄×C₈₉	—	4	48	no	—
168	C₂×D₄×C₈₉	—	4	12	no	—
169	C₂×D₄×C₈₉	—	4	6	no	—
170	C₂×D₄×C₈₉	—	4	96	no	—
171	C₂×D₄×C₈₉	—	4	48	no	—
172	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
173	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
174	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
175	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
176	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
177	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
178	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
179	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
180	C₂×D₄×C₈₉	C₂⁴	1	12	yes	complemented
181	C₂×D₄×C₈₉	C₂⁴	1	24	yes	complemented
182	C₂²×C₄×C₈₉	—	2	12	no	—
183	C₂²×C₄×C₈₉	—	4	12	no	—
184	C₂²×C₄×C₈₉	—	4	6	no	—
185	C₂²×C₄×C₈₉	—	4	12	no	—
186	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
187	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
188	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
189	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
190	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
191	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
192	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	complemented
193	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	complemented
194	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	complemented
195	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	complemented
196	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	complemented
197	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
198	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
199	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
200	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
201	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
202	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
203	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	—
204	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	complemented
205	C₂²⋊C₄×C₈₉	C₂⁴	1	12	yes	complemented
206	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	complemented
207	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	complemented
208	C₄²×C₈₉	C₂⁴	1	4	yes	complemented
209	C₄²×C₈₉	C₂⁴	1	12	yes	complemented
210	C₄²×C₈₉	C₂⁴	1	8	yes	complemented
211	C₂³×C₈₉	—	2	12	no	—
212	C₂³×C₈₉	—	2	12	no	—
213	C₂³×C₈₉	—	2	6	no	—
214	C₂³×C₈₉	—	2	12	no	—
215	C₂³×C₈₉	—	2	6	no	—
216	C₂³×C₈₉	—	2	48	no	—
217	C₂³×C₈₉	—	2	24	no	—
218	C₂³×C₈₉	—	2	6	no	—
219	C₂³×C₈₉	—	2	12	no	—
220	C₂³×C₈₉	—	2	6	no	—
221	C₂³×C₈₉	—	2	24	no	—
222	C₂³×C₈₉	—	4	12	no	—
223	C₂³×C₈₉	—	4	24	no	—
224	C₂³×C₈₉	—	4	12	no	—
225	C₂³×C₈₉	—	4	24	no	—
226	C₂³×C₈₉	—	4	12	no	—
227	C₂³×C₈₉	—	4	48	no	—
228	C₂³×C₈₉	—	4	48	no	—
229	C₂³×C₈₉	—	4	128	no	—
230	C₂³×C₈₉	—	4	16	no	—
231	C₂³×C₈₉	—	8	24	no	—
232	C₂³×C₈₉	—	8	8	no	—
233	C₂³×C₈₉	H(5,𝔽₂)	1	12	yes	—
234	C₂³×C₈₉	C₂⁵	1	6	yes	—
235	C₂³×C₈₉	C₂⁵	1	2	yes	—
236	C₂³×C₈₉	C₂⁵	1	6	yes	—
237	C₂³×C₈₉	C₂⁵	1	6	yes	—
238	C₂³×C₈₉	C₂⁵	1	6	yes	—
239	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₈₉	—	4	12	no	—
241	D₄×C₈₉	—	2	48	no	—
242	D₄×C₈₉	—	2	48	no	—
243	D₄×C₈₉	—	4	12	no	—
244	D₄×C₈₉	—	4	12	no	—
245	D₄×C₈₉	—	4	12	no	—
246	D₄×C₈₉	—	4	12	no	—
247	D₄×C₈₉	—	4	24	no	—
248	D₄×C₈₉	—	4	24	no	—
249	D₄×C₈₉	—	4	24	no	—
250	D₄×C₈₉	—	4	12	no	—
251	C₂×C₄×C₈₉	—	2	6	no	—
252	C₂×C₄×C₈₉	—	2	6	no	—
253	C₂×C₄×C₈₉	—	2	24	no	—
254	C₂×C₄×C₈₉	—	2	12	no	—
255	C₂×C₄×C₈₉	—	2	12	no	—
256	C₂×C₄×C₈₉	—	4	24	no	—
257	C₂×C₄×C₈₉	—	4	12	no	—
258	C₂×C₄×C₈₉	—	4	24	no	—
259	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
260	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
261	C₂×C₄×C₈₉	C₂⁵	1	12	yes	—
262	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
263	C₂²×C₈₉	—	2	12	no	—
264	C₂²×C₈₉	—	2	24	no	—
265	C₂²×C₈₉	—	2	12	no	—
266	C₂²×C₈₉	—	2	6	no	—
267	C₂²×C₈₉	—	2	12	no	—
268	C₂²×C₈₉	—	2	6	no	—
269	C₂²×C₈₉	—	2	6	no	—
270	C₂²×C₈₉	—	2	12	no	—
271	C₂²×C₈₉	—	2	6	no	—
272	C₂²×C₈₉	—	4	48	no	—
273	C₂²×C₈₉	—	4	48	no	—
274	C₂²×C₈₉	—	4	16	no	—
275	C₂²×C₈₉	—	4	12	no	—
276	C₂²×C₈₉	—	4	4	no	—
277	C₂²×C₈₉	—	4	12	no	—
278	C₂²×C₈₉	—	4	12	no	—
279	C₂²×C₈₉	—	8	24	no	—
280	C₂²×C₈₉	—	8	8	no	—
281	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	12	yes	—
282	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	6	yes	—
283	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
284	C₄×C₈₉	—	2	6	no	—
285	C₄×C₈₉	—	2	6	no	—
286	C₄×C₈₉	—	2	12	no	—
287	C₄×C₈₉	—	2	12	no	—
288	C₂×#3532	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
289	C₂×C₈₉	—	2	12	no	—
290	C₂×C₈₉	—	4	6	no	—
291	C₂×C₈₉	—	4	2	no	—
292	C₂×C₈₉	—	4	6	no	—
293	C₂×C₈₉	—	4	6	no	—
294	C₂×C₈₉	#3532	1	4	yes	direct product factor
295	C₂×C₈₉	C₂²×H(5,𝔽₂)	1	3	yes	—
296	#3532	C₂×C₈₉	1	32	yes	direct product factor
297	C₂×H(3,𝔽₄)	C₂×C₈₉	1	1	yes	characteristic, complemented
298	C₂×#560	C₂×C₈₉	1	3	yes	complemented
299	C₂×#551	C₂×C₈₉	1	3	yes	complemented
300	C₂×#546	C₂×C₈₉	1	6	yes	complemented
301	C₂×D₄²	C₂×C₈₉	1	3	yes	complemented
302	C₂×#538	C₂×C₈₉	1	6	yes	complemented
303	C₂×#535	C₂×C₈₉	1	3	yes	complemented
304	C₂×#534	C₂×C₈₉	1	3	yes	complemented
305	C₂²×#120	C₂×C₈₉	1	3	yes	complemented
306	C₈₉	C₂×#3532	1	1	yes	characteristic, direct product factor, Sylow
307	C₂⁶	C₂²×C₈₉	1	1	yes	characteristic, complemented
308	C₂²×#41	C₂²×C₈₉	1	3	yes	complemented
309	C₂³×D₄	C₂²×C₈₉	1	3	yes	complemented
310	C₂³×D₄	C₂²×C₈₉	1	6	yes	complemented
311	C₂³×D₄	C₂²×C₈₉	1	3	yes	complemented
312	H(3,𝔽₄)	C₂²×C₈₉	1	16	yes	complemented
313	#560	C₂²×C₈₉	1	48	yes	complemented
314	#551	C₂²×C₈₉	1	48	yes	complemented
315	#546	C₂²×C₈₉	1	96	yes	complemented
316	D₄²	C₂²×C₈₉	1	48	yes	complemented
317	#538	C₂²×C₈₉	1	96	yes	complemented
318	#535	C₂²×C₈₉	1	48	yes	complemented
319	#534	C₂²×C₈₉	1	48	yes	complemented
320	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
321	C₂×#127	C₂²×C₈₉	1	3	yes	complemented
322	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
323	C₂×#126	C₂²×C₈₉	1	6	yes	complemented
324	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
325	C₂×#124	C₂²×C₈₉	1	3	yes	complemented
326	C₂×#124	C₂²×C₈₉	1	6	yes	complemented
327	C₂×#123	C₂²×C₈₉	1	3	yes	complemented
328	C₂×#123	C₂²×C₈₉	1	3	yes	complemented
329	C₂×#123	C₂²×C₈₉	1	6	yes	complemented
330	C₂×#123	C₂²×C₈₉	1	6	yes	complemented
331	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	complemented
332	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
333	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
334	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
335	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
336	C₂×#121	C₂²×C₈₉	1	6	yes	complemented
337	C₂×#120	C₂²×C₈₉	1	3	yes	—
338	C₂×#120	C₂²×C₈₉	1	6	yes	complemented
339	C₂×#120	C₂²×C₈₉	1	6	yes	complemented
340	C₂×#120	C₂²×C₈₉	1	3	yes	complemented
341	C₂×#120	C₂²×C₈₉	1	3	yes	complemented
342	C₂×#120	C₂²×C₈₉	1	3	yes	complemented
343	C₂×#120	C₂²×C₈₉	1	6	yes	complemented
344	C₂×#120	C₂²×C₈₉	1	48	yes	complemented
345	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic, complemented
346	C₂×#120	C₂²×C₈₉	1	3	yes	complemented
347	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	complemented
348	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	complemented
349	C₂×#117	C₂²×C₈₉	1	3	yes	complemented
350	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	complemented
351	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	complemented
352	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	complemented
353	C₂⁵	—	4	12	no	—
354	C₂⁵	C₂³×C₈₉	1	3	yes	—
355	C₂⁵	C₂³×C₈₉	1	3	yes	—
356	C₂⁵	C₂³×C₈₉	1	3	yes	—
357	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
358	C₂⁵	C₂³×C₈₉	1	8	yes	complemented
359	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic, complemented
360	C₂×#41	—	4	12	no	—
361	C₂×#41	C₂³×C₈₉	1	24	yes	complemented
362	C₂²×Q₈	C₂³×C₈₉	1	3	yes	complemented
363	C₂²×D₄	—	4	12	no	—
364	C₂²×D₄	—	4	24	no	—
365	C₂²×D₄	—	4	12	no	—
366	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
367	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
368	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
369	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
370	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
371	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
372	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
373	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
374	C₂²×D₄	C₂³×C₈₉	1	24	yes	complemented
375	C₂²×D₄	C₂³×C₈₉	1	48	yes	complemented
376	C₂²×D₄	C₂³×C₈₉	1	3	yes	complemented
377	C₂²×D₄	C₂³×C₈₉	1	6	yes	complemented
378	C₂²×D₄	C₂³×C₈₉	1	24	yes	complemented
379	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
380	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
381	C₂³×C₄	C₂³×C₈₉	1	6	yes	complemented
382	C₂³×C₄	C₂³×C₈₉	1	3	yes	complemented
383	#127	C₂³×C₈₉	1	8	yes	complemented
384	#127	C₂³×C₈₉	1	24	yes	complemented
385	#126	C₂³×C₈₉	1	16	yes	complemented
386	#126	C₂³×C₈₉	1	48	yes	complemented
387	#124	C₂³×C₈₉	1	24	yes	complemented
388	#124	C₂³×C₈₉	1	24	yes	complemented
389	#124	C₂³×C₈₉	1	48	yes	complemented
390	#123	C₂³×C₈₉	1	24	yes	complemented
391	#123	C₂³×C₈₉	1	24	yes	complemented
392	#123	C₂³×C₈₉	1	48	yes	complemented
393	#123	C₂³×C₈₉	1	48	yes	complemented
394	C₂²⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
395	#121	C₂³×C₈₉	1	48	yes	complemented
396	#121	C₂³×C₈₉	1	48	yes	complemented
397	#121	C₂³×C₈₉	1	48	yes	complemented
398	#121	C₂³×C₈₉	1	48	yes	complemented
399	#121	C₂³×C₈₉	1	48	yes	complemented
400	#120	C₂³×C₈₉	1	24	yes	—
401	#120	C₂³×C₈₉	1	48	yes	complemented
402	#120	C₂³×C₈₉	1	48	yes	complemented
403	#120	C₂³×C₈₉	1	24	yes	complemented
404	#120	C₂³×C₈₉	1	24	yes	complemented
405	#120	C₂³×C₈₉	1	24	yes	complemented
406	#120	C₂³×C₈₉	1	48	yes	complemented
407	#120	C₂³×C₈₉	1	8	yes	complemented
408	#120	C₂³×C₈₉	1	24	yes	complemented
409	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
410	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
411	#117	C₂³×C₈₉	1	24	yes	complemented
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	complemented
415	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	complemented
423	C₂×C₂²⋊C₄	C₂³×C₈₉	1	48	yes	complemented
424	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	complemented
425	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	complemented
426	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	complemented
427	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	complemented
428	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	complemented
429	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic, complemented
430	C₂×C₄²	C₂³×C₈₉	1	3	yes	complemented
431	C₂×C₄²	C₂³×C₈₉	1	2	yes	complemented
432	C₂⁴	—	2	24	no	—
433	C₂⁴	—	2	12	no	—
434	C₂⁴	—	2	12	no	—
435	C₂⁴	—	4	6	no	—
436	C₂⁴	—	4	12	no	—
437	C₂⁴	—	4	6	no	—
438	C₂⁴	—	4	48	no	—
439	C₂⁴	—	4	12	no	—
440	C₂⁴	—	4	6	no	—
441	C₂⁴	—	4	64	no	—
442	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
443	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
444	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
445	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
446	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
447	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
448	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
449	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
450	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
451	C₂⁴	C₂⁴×C₈₉	1	4	yes	complemented
452	#41	—	4	48	no	—
453	C₂×Q₈	—	4	6	no	—
454	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	complemented
455	C₂×D₄	—	2	24	no	—
456	C₂×D₄	—	2	24	no	—
457	C₂×D₄	—	4	6	no	—
458	C₂×D₄	—	4	6	no	—
459	C₂×D₄	—	4	6	no	—
460	C₂×D₄	—	4	6	no	—
461	C₂×D₄	—	4	12	no	—
462	C₂×D₄	—	4	12	no	—
463	C₂×D₄	—	4	48	no	—
464	C₂×D₄	—	4	12	no	—
465	C₂×D₄	—	4	6	no	—
466	C₂×D₄	—	4	96	no	—
467	C₂×D₄	—	4	48	no	—
468	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
469	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
470	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
471	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
472	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
473	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
474	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
475	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
476	C₂×D₄	C₂⁴×C₈₉	1	12	yes	complemented
477	C₂×D₄	C₂⁴×C₈₉	1	24	yes	complemented
478	C₂²×C₄	—	2	12	no	—
479	C₂²×C₄	—	4	12	no	—
480	C₂²×C₄	—	4	6	no	—
481	C₂²×C₄	—	4	12	no	—
482	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
484	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
485	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
486	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
487	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
488	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	complemented
489	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	complemented
490	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	complemented
491	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	complemented
492	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	complemented
493	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
494	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
495	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
496	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
497	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
498	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
499	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	—
500	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	complemented
501	C₂²⋊C₄	C₂⁴×C₈₉	1	12	yes	complemented
502	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	complemented
503	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	complemented
504	C₄²	C₂⁴×C₈₉	1	4	yes	complemented
505	C₄²	C₂⁴×C₈₉	1	12	yes	complemented
506	C₄²	C₂⁴×C₈₉	1	8	yes	complemented
507	C₂³	—	2	12	no	—
508	C₂³	—	2	12	no	—
509	C₂³	—	2	6	no	—
510	C₂³	—	2	12	no	—
511	C₂³	—	2	6	no	—
512	C₂³	—	2	48	no	—
513	C₂³	—	2	24	no	—
514	C₂³	—	2	6	no	—
515	C₂³	—	2	12	no	—
516	C₂³	—	2	6	no	—
517	C₂³	—	2	24	no	—
518	C₂³	—	4	12	no	—
519	C₂³	—	4	24	no	—
520	C₂³	—	4	12	no	—
521	C₂³	—	4	24	no	—
522	C₂³	—	4	12	no	—
523	C₂³	—	4	48	no	—
524	C₂³	—	4	48	no	—
525	C₂³	—	4	128	no	—
526	C₂³	—	4	16	no	—
527	C₂³	—	8	24	no	—
528	C₂³	—	8	8	no	—
529	C₂³	H(5,𝔽₂)×C₈₉	1	12	yes	—
530	C₂³	C₂⁵×C₈₉	1	6	yes	—
531	C₂³	C₂⁵×C₈₉	1	2	yes	—
532	C₂³	C₂⁵×C₈₉	1	6	yes	—
533	C₂³	C₂⁵×C₈₉	1	6	yes	—
534	C₂³	C₂⁵×C₈₉	1	6	yes	—
535	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
536	Q₈	—	4	12	no	—
537	D₄	—	2	48	no	—
538	D₄	—	2	48	no	—
539	D₄	—	4	12	no	—
540	D₄	—	4	12	no	—
541	D₄	—	4	12	no	—
542	D₄	—	4	12	no	—
543	D₄	—	4	24	no	—
544	D₄	—	4	24	no	—
545	D₄	—	4	24	no	—
546	D₄	—	4	12	no	—
547	C₂×C₄	—	2	6	no	—
548	C₂×C₄	—	2	6	no	—
549	C₂×C₄	—	2	24	no	—
550	C₂×C₄	—	2	12	no	—
551	C₂×C₄	—	2	12	no	—
552	C₂×C₄	—	4	24	no	—
553	C₂×C₄	—	4	12	no	—
554	C₂×C₄	—	4	24	no	—
555	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
556	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
557	C₂×C₄	C₂⁵×C₈₉	1	12	yes	—
558	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
559	C₂²	—	2	12	no	—
560	C₂²	—	2	24	no	—
561	C₂²	—	2	12	no	—
562	C₂²	—	2	6	no	—
563	C₂²	—	2	12	no	—
564	C₂²	—	2	6	no	—
565	C₂²	—	2	6	no	—
566	C₂²	—	2	12	no	—
567	C₂²	—	2	6	no	—
568	C₂²	—	4	48	no	—
569	C₂²	—	4	48	no	—
570	C₂²	—	4	16	no	—
571	C₂²	—	4	12	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	12	no	—
574	C₂²	—	4	12	no	—
575	C₂²	—	8	24	no	—
576	C₂²	—	8	8	no	—
577	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	12	yes	—
578	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	6	yes	—
579	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
580	C₄	—	2	6	no	—
581	C₄	—	2	6	no	—
582	C₄	—	2	12	no	—
583	C₄	—	2	12	no	—
584	C₂	—	2	12	no	—
585	C₂	—	4	6	no	—
586	C₂	—	4	2	no	—
587	C₂	—	4	6	no	—
588	C₂	—	4	6	no	—
589	C₂	C₈₉×#3532	1	4	yes	direct product factor
590	C₂	C₂²×H(5,𝔽₂)×C₈₉	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3532	C₂	direct (N × H)
2. C₂×H(3,𝔽₄)×C₈₉	C₂	semidirect
3. C₂×#560×C₈₉	C₂	semidirect
4. C₂×#551×C₈₉	C₂	semidirect
5. C₂×#546×C₈₉	C₂	semidirect
6. C₂×D₄²×C₈₉	C₂	semidirect
7. C₂×#538×C₈₉	C₂	semidirect
8. C₂×#535×C₈₉	C₂	semidirect
9. C₂×#534×C₈₉	C₂	semidirect
10. C₂²×#120×C₈₉	C₂	semidirect
11. C₂⁶×C₈₉	C₂²	semidirect
12. C₂²×#41×C₈₉	C₂²	semidirect
13. C₂³×D₄×C₈₉	C₂²	semidirect
14. C₂³×D₄×C₈₉	C₂²	semidirect
15. C₂³×D₄×C₈₉	C₂²	semidirect
16. H(3,𝔽₄)×C₈₉	C₂²	semidirect
17. #560×C₈₉	C₂²	semidirect
18. #551×C₈₉	C₂²	semidirect
19. #546×C₈₉	C₂²	semidirect
20. D₄²×C₈₉	C₂²	semidirect
21. #538×C₈₉	C₂²	semidirect
22. #535×C₈₉	C₂²	semidirect
23. #534×C₈₉	C₂²	semidirect
24. C₂×#127×C₈₉	C₂²	semidirect
25. C₂×#127×C₈₉	C₂²	semidirect
26. C₂×#126×C₈₉	C₂²	semidirect
27. C₂×#126×C₈₉	C₂²	semidirect
28. C₂×#124×C₈₉	C₂²	semidirect
29. C₂×#124×C₈₉	C₂²	semidirect
30. C₂×#124×C₈₉	C₂²	semidirect
31. C₂×#123×C₈₉	C₂²	semidirect
32. C₂×#123×C₈₉	C₂²	semidirect
33. C₂×#123×C₈₉	C₂²	semidirect
34. C₂×#123×C₈₉	C₂²	semidirect
35. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
36. C₂×#121×C₈₉	C₂²	semidirect
37. C₂×#121×C₈₉	C₂²	semidirect
38. C₂×#121×C₈₉	C₂²	semidirect
39. C₂×#121×C₈₉	C₂²	semidirect
40. C₂×#121×C₈₉	C₂²	semidirect
42. C₂×#120×C₈₉	C₂²	semidirect
43. C₂×#120×C₈₉	C₂²	semidirect
44. C₂×#120×C₈₉	C₂²	semidirect
45. C₂×#120×C₈₉	C₂²	semidirect
46. C₂×#120×C₈₉	C₂²	semidirect
47. C₂×#120×C₈₉	C₂²	semidirect
48. C₂×#120×C₈₉	C₂²	semidirect
49. C₂×#120×C₈₉	C₂²	semidirect
50. C₂×#120×C₈₉	C₂²	semidirect
51. C₂×C₄×D₄×C₈₉	C₂²	semidirect
52. C₂×C₄×D₄×C₈₉	C₂²	semidirect
53. C₂×#117×C₈₉	C₂²	semidirect
54. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
55. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
56. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
62. C₂⁵×C₈₉	C₂³	semidirect
63. C₂⁵×C₈₉	C₂³	semidirect
65. C₂×#41×C₈₉	C₂³	semidirect
66. C₂²×Q₈×C₈₉	C₂³	semidirect
78. C₂²×D₄×C₈₉	C₂³	semidirect
79. C₂²×D₄×C₈₉	C₂³	semidirect
80. C₂²×D₄×C₈₉	C₂³	semidirect
81. C₂²×D₄×C₈₉	C₂³	semidirect
82. C₂²×D₄×C₈₉	C₂³	semidirect
85. C₂³×C₄×C₈₉	C₂³	semidirect
86. C₂³×C₄×C₈₉	C₂³	semidirect
87. #127×C₈₉	C₂³	semidirect
88. #127×C₈₉	C₂³	semidirect
89. #126×C₈₉	C₂³	semidirect
90. #126×C₈₉	C₂³	semidirect
91. #124×C₈₉	C₂³	semidirect
92. #124×C₈₉	C₂³	semidirect
93. #124×C₈₉	C₂³	semidirect
94. #123×C₈₉	C₂³	semidirect
95. #123×C₈₉	C₂³	semidirect
96. #123×C₈₉	C₂³	semidirect
97. #123×C₈₉	C₂³	semidirect
98. C₂²⋊Q₈×C₈₉	C₂³	semidirect
99. #121×C₈₉	C₂³	semidirect
100. #121×C₈₉	C₂³	semidirect
101. #121×C₈₉	C₂³	semidirect
102. #121×C₈₉	C₂³	semidirect
103. #121×C₈₉	C₂³	semidirect
105. #120×C₈₉	C₂³	semidirect
106. #120×C₈₉	C₂³	semidirect
107. #120×C₈₉	C₂³	semidirect
108. #120×C₈₉	C₂³	semidirect
109. #120×C₈₉	C₂³	semidirect
110. #120×C₈₉	C₂³	semidirect
111. #120×C₈₉	C₂³	semidirect
112. #120×C₈₉	C₂³	semidirect
113. C₄×D₄×C₈₉	C₂³	semidirect
114. C₄×D₄×C₈₉	C₂³	semidirect
115. #117×C₈₉	C₂³	semidirect
116. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
117. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
118. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
126. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
127. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
128. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
129. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
130. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
131. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
132. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
133. C₂×C₄²×C₈₉	C₂³	semidirect
134. C₂×C₄²×C₈₉	C₂³	semidirect
135. C₂×C₄²×C₈₉	C₂³	semidirect
155. C₂⁴×C₈₉	C₂⁴	semidirect
158. C₂×Q₈×C₈₉	C₂⁴	semidirect
180. C₂×D₄×C₈₉	C₂⁴	semidirect
181. C₂×D₄×C₈₉	C₂⁴	semidirect
192. C₂²×C₄×C₈₉	C₂⁴	semidirect
193. C₂²×C₄×C₈₉	C₂⁴	semidirect
194. C₄⋊C₄×C₈₉	C₂⁴	semidirect
195. C₄⋊C₄×C₈₉	C₂⁴	semidirect
196. C₄⋊C₄×C₈₉	C₂⁴	semidirect
204. C₂²⋊C₄×C₈₉	C₂⁴	semidirect
205. C₂²⋊C₄×C₈₉	C₂⁴	semidirect
206. C₂²⋊C₄×C₈₉	C₂⁴	semidirect
207. C₂²⋊C₄×C₈₉	C₂⁴	semidirect
208. C₄²×C₈₉	C₂⁴	semidirect
209. C₄²×C₈₉	C₂⁴	semidirect
210. C₄²×C₈₉	C₂⁴	semidirect
288. C₂×#3532	C₈₉	direct (N × H)
294. C₂×C₈₉	#3532	direct (N × H)
296. #3532	C₂×C₈₉	direct (N × H)
297. C₂×H(3,𝔽₄)	C₂×C₈₉	semidirect
298. C₂×#560	C₂×C₈₉	semidirect
299. C₂×#551	C₂×C₈₉	semidirect
300. C₂×#546	C₂×C₈₉	semidirect
301. C₂×D₄²	C₂×C₈₉	semidirect
302. C₂×#538	C₂×C₈₉	semidirect
303. C₂×#535	C₂×C₈₉	semidirect
304. C₂×#534	C₂×C₈₉	semidirect
305. C₂²×#120	C₂×C₈₉	semidirect
306. C₈₉	C₂×#3532	direct (N × H)
307. C₂⁶	C₂²×C₈₉	semidirect
308. C₂²×#41	C₂²×C₈₉	semidirect
309. C₂³×D₄	C₂²×C₈₉	semidirect
310. C₂³×D₄	C₂²×C₈₉	semidirect
311. C₂³×D₄	C₂²×C₈₉	semidirect
312. H(3,𝔽₄)	C₂²×C₈₉	semidirect
313. #560	C₂²×C₈₉	semidirect
314. #551	C₂²×C₈₉	semidirect
315. #546	C₂²×C₈₉	semidirect
316. D₄²	C₂²×C₈₉	semidirect
317. #538	C₂²×C₈₉	semidirect
318. #535	C₂²×C₈₉	semidirect
319. #534	C₂²×C₈₉	semidirect
320. C₂×#127	C₂²×C₈₉	semidirect
321. C₂×#127	C₂²×C₈₉	semidirect
322. C₂×#126	C₂²×C₈₉	semidirect
323. C₂×#126	C₂²×C₈₉	semidirect
324. C₂×#124	C₂²×C₈₉	semidirect
325. C₂×#124	C₂²×C₈₉	semidirect
326. C₂×#124	C₂²×C₈₉	semidirect
327. C₂×#123	C₂²×C₈₉	semidirect
328. C₂×#123	C₂²×C₈₉	semidirect
329. C₂×#123	C₂²×C₈₉	semidirect
330. C₂×#123	C₂²×C₈₉	semidirect
331. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
332. C₂×#121	C₂²×C₈₉	semidirect
333. C₂×#121	C₂²×C₈₉	semidirect
334. C₂×#121	C₂²×C₈₉	semidirect
335. C₂×#121	C₂²×C₈₉	semidirect
336. C₂×#121	C₂²×C₈₉	semidirect
338. C₂×#120	C₂²×C₈₉	semidirect
339. C₂×#120	C₂²×C₈₉	semidirect
340. C₂×#120	C₂²×C₈₉	semidirect
341. C₂×#120	C₂²×C₈₉	semidirect
342. C₂×#120	C₂²×C₈₉	semidirect
343. C₂×#120	C₂²×C₈₉	semidirect
344. C₂×#120	C₂²×C₈₉	semidirect
345. C₂×#120	C₂²×C₈₉	semidirect
346. C₂×#120	C₂²×C₈₉	semidirect
347. C₂×C₄×D₄	C₂²×C₈₉	semidirect
348. C₂×C₄×D₄	C₂²×C₈₉	semidirect
349. C₂×#117	C₂²×C₈₉	semidirect
350. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
351. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
352. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
358. C₂⁵	C₂³×C₈₉	semidirect
359. C₂⁵	C₂³×C₈₉	semidirect
361. C₂×#41	C₂³×C₈₉	semidirect
362. C₂²×Q₈	C₂³×C₈₉	semidirect
374. C₂²×D₄	C₂³×C₈₉	semidirect
375. C₂²×D₄	C₂³×C₈₉	semidirect
376. C₂²×D₄	C₂³×C₈₉	semidirect
377. C₂²×D₄	C₂³×C₈₉	semidirect
378. C₂²×D₄	C₂³×C₈₉	semidirect
381. C₂³×C₄	C₂³×C₈₉	semidirect
382. C₂³×C₄	C₂³×C₈₉	semidirect
383. #127	C₂³×C₈₉	semidirect
384. #127	C₂³×C₈₉	semidirect
385. #126	C₂³×C₈₉	semidirect
386. #126	C₂³×C₈₉	semidirect
387. #124	C₂³×C₈₉	semidirect
388. #124	C₂³×C₈₉	semidirect
389. #124	C₂³×C₈₉	semidirect
390. #123	C₂³×C₈₉	semidirect
391. #123	C₂³×C₈₉	semidirect
392. #123	C₂³×C₈₉	semidirect
393. #123	C₂³×C₈₉	semidirect
394. C₂²⋊Q₈	C₂³×C₈₉	semidirect
395. #121	C₂³×C₈₉	semidirect
396. #121	C₂³×C₈₉	semidirect
397. #121	C₂³×C₈₉	semidirect
398. #121	C₂³×C₈₉	semidirect
399. #121	C₂³×C₈₉	semidirect
401. #120	C₂³×C₈₉	semidirect
402. #120	C₂³×C₈₉	semidirect
403. #120	C₂³×C₈₉	semidirect
404. #120	C₂³×C₈₉	semidirect
405. #120	C₂³×C₈₉	semidirect
406. #120	C₂³×C₈₉	semidirect
407. #120	C₂³×C₈₉	semidirect
408. #120	C₂³×C₈₉	semidirect
409. C₄×D₄	C₂³×C₈₉	semidirect
410. C₄×D₄	C₂³×C₈₉	semidirect
411. #117	C₂³×C₈₉	semidirect
412. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
413. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
414. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
422. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
423. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
424. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
425. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
426. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
427. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
428. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
429. C₂×C₄²	C₂³×C₈₉	semidirect
430. C₂×C₄²	C₂³×C₈₉	semidirect
431. C₂×C₄²	C₂³×C₈₉	semidirect
451. C₂⁴	C₂⁴×C₈₉	semidirect
454. C₂×Q₈	C₂⁴×C₈₉	semidirect
476. C₂×D₄	C₂⁴×C₈₉	semidirect
477. C₂×D₄	C₂⁴×C₈₉	semidirect
488. C₂²×C₄	C₂⁴×C₈₉	semidirect
489. C₂²×C₄	C₂⁴×C₈₉	semidirect
490. C₄⋊C₄	C₂⁴×C₈₉	semidirect
491. C₄⋊C₄	C₂⁴×C₈₉	semidirect
492. C₄⋊C₄	C₂⁴×C₈₉	semidirect
500. C₂²⋊C₄	C₂⁴×C₈₉	semidirect
501. C₂²⋊C₄	C₂⁴×C₈₉	semidirect
502. C₂²⋊C₄	C₂⁴×C₈₉	semidirect
503. C₂²⋊C₄	C₂⁴×C₈₉	semidirect
504. C₄²	C₂⁴×C₈₉	semidirect
505. C₄²	C₂⁴×C₈₉	semidirect
506. C₄²	C₂⁴×C₈₉	semidirect
589. C₂	C₈₉×#3532	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3532	2
C₂×H(3,𝔽₄)×C₈₉	2
C₂×#560×C₈₉	2
C₂×#551×C₈₉	2
C₂×#546×C₈₉	2
C₂×D₄²×C₈₉	2
C₂×#538×C₈₉	2
C₂×#535×C₈₉	2
C₂×#534×C₈₉	2
C₂²×#120×C₈₉	2
C₂×#3532	89

Subgroups — C2×C89×#3532 #36440566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3532 #36440566