Subgroups — C₈₉×#62811 #36440659

Order 22784.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3489	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3488	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3487	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3486	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3485	C₂	1	6	yes	maximal, complemented
8	C₈₉×#3484	C₂	1	6	yes	maximal, complemented
9	D₄×#41×C₈₉	C₂	1	16	yes	maximal, complemented
10	C₈₉×#3449	C₂	1	6	yes	maximal, complemented
11	C₂×#525×C₈₉	C₂	1	6	yes	maximal, complemented
12	C₈₉×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	#585×C₈₉	—	2	16	no	—
14	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	complemented
15	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	4	yes	complemented
16	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	6	yes	complemented
17	C₂×H(5,𝔽₂)×C₈₉	C₂²	1	4	yes	complemented
18	C₂²×#41×C₈₉	—	2	16	no	—
19	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₈₉	C₂²	1	3	yes	complemented
21	C₂²×#41×C₈₉	C₂²	1	8	yes	complemented
22	C₂²×#41×C₈₉	C₂²	1	3	yes	complemented
23	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂²×#41×C₈₉	C₂²	1	8	yes	complemented
25	C₂²×#41×C₈₉	C₂²	1	6	yes	complemented
26	C₂²×#41×C₈₉	C₂²	1	8	yes	complemented
27	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂³×D₄×C₈₉	C₂²	1	3	yes	complemented
29	C₂⁴×C₄×C₈₉	C₂²	1	3	yes	complemented
30	#550×C₈₉	C₂²	1	16	yes	complemented
31	D₄×Q₈×C₈₉	C₂²	1	16	yes	complemented
32	#548×C₈₉	C₂²	1	16	yes	complemented
33	#548×C₈₉	C₂²	1	16	yes	complemented
34	#547×C₈₉	C₂²	1	48	yes	complemented
35	#546×C₈₉	C₂²	1	48	yes	complemented
36	#546×C₈₉	C₂²	1	48	yes	complemented
37	D₄²×C₈₉	C₂²	1	48	yes	complemented
38	#537×C₈₉	C₂²	1	24	yes	complemented
39	#536×C₈₉	C₂²	1	12	yes	complemented
40	#536×C₈₉	C₂²	1	12	yes	complemented
41	#535×C₈₉	C₂²	1	12	yes	complemented
42	#535×C₈₉	C₂²	1	12	yes	complemented
43	#534×C₈₉	C₂²	1	24	yes	complemented
44	#532×C₈₉	C₂²	1	24	yes	complemented
45	#525×C₈₉	C₂²	1	4	yes	complemented
46	#525×C₈₉	C₂²	1	12	yes	complemented
47	#525×C₈₉	C₂²	1	12	yes	complemented
48	#525×C₈₉	C₂²	1	12	yes	complemented
49	#525×C₈₉	C₂²	1	24	yes	complemented
50	#525×C₈₉	C₂²	1	24	yes	complemented
51	#525×C₈₉	C₂²	1	24	yes	complemented
52	C₂×#123×C₈₉	C₂²	1	12	yes	complemented
53	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	12	yes	complemented
54	C₂×#121×C₈₉	C₂²	1	12	yes	complemented
55	C₂×#120×C₈₉	C₂²	1	12	yes	complemented
56	#520×C₈₉	C₂²	1	8	yes	complemented
57	#519×C₈₉	C₂²	1	2	yes	complemented
58	#518×C₈₉	C₂²	1	6	yes	complemented
59	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
60	C₂×C₄×D₄×C₈₉	C₂²	1	24	yes	complemented
61	C₂×#117×C₈₉	C₂²	1	6	yes	complemented
62	C₂⁵×C₈₉	C₂³	1	3	yes	—
63	2₋¹⁺⁴×C₈₉	—	2	32	no	—
64	2₋¹⁺⁴×C₈₉	—	2	16	no	—
65	H(5,𝔽₂)×C₈₉	—	2	32	no	—
66	H(5,𝔽₂)×C₈₉	—	2	48	no	—
67	C₂×#41×C₈₉	—	2	64	no	—
68	C₂×#41×C₈₉	—	2	64	no	—
69	C₂×#41×C₈₉	—	2	64	no	—
70	C₂×#41×C₈₉	—	2	8	no	—
71	C₂×#41×C₈₉	—	2	24	no	—
72	C₂×#41×C₈₉	—	2	24	no	—
73	C₂×#41×C₈₉	—	2	48	no	—
74	C₂×#41×C₈₉	D₄	1	16	yes	complemented
75	C₂×#41×C₈₉	C₂³	1	4	yes	—
76	C₂×#41×C₈₉	C₂³	1	12	yes	—
77	C₂×#41×C₈₉	C₂³	1	12	yes	—
78	C₂×#41×C₈₉	C₂³	1	12	yes	—
79	C₂×#41×C₈₉	C₂³	1	24	yes	—
80	C₂×#41×C₈₉	C₂³	1	8	yes	—
81	C₂×#41×C₈₉	C₂³	1	4	yes	—
82	C₂×#41×C₈₉	C₂³	1	4	yes	—
83	C₂×#41×C₈₉	C₂³	1	12	yes	complemented
84	C₂×#41×C₈₉	C₂³	1	12	yes	complemented
85	C₂×#41×C₈₉	C₂³	1	24	yes	complemented
86	C₂×#41×C₈₉	C₂³	1	8	yes	complemented
87	C₂²×Q₈×C₈₉	—	2	8	no	—
88	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
89	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
90	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₂²×Q₈×C₈₉	C₂³	1	6	yes	complemented
92	C₂²×Q₈×C₈₉	C₂³	1	8	yes	complemented
93	C₂²×D₄×C₈₉	—	2	24	no	—
94	C₂²×D₄×C₈₉	C₂³	1	12	yes	—
95	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
96	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
97	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
98	C₂²×D₄×C₈₉	C₂³	1	24	yes	—
99	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
100	C₂²×D₄×C₈₉	C₂³	1	6	yes	complemented
101	C₂²×D₄×C₈₉	C₂³	1	24	yes	complemented
102	C₂³×C₄×C₈₉	—	2	24	no	—
103	C₂³×C₄×C₈₉	C₂³	1	12	yes	—
104	C₂³×C₄×C₈₉	C₂³	1	12	yes	—
105	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
106	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
108	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
109	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
110	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
111	C₂³×C₄×C₈₉	C₂³	1	12	yes	complemented
112	C₄⋊Q₈×C₈₉	C₂³	1	24	yes	complemented
113	#127×C₈₉	C₂³	1	24	yes	complemented
114	#124×C₈₉	C₂³	1	24	yes	complemented
115	#124×C₈₉	C₂³	1	24	yes	complemented
116	#123×C₈₉	C₂³	1	8	yes	—
117	#123×C₈₉	C₂³	1	24	yes	—
118	#123×C₈₉	C₂³	1	48	yes	complemented
119	#123×C₈₉	C₂³	1	48	yes	complemented
120	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
121	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	—
122	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	complemented
123	C₂²⋊Q₈×C₈₉	C₂³	1	24	yes	complemented
124	C₂²⋊Q₈×C₈₉	C₂³	1	48	yes	complemented
125	#121×C₈₉	C₂³	1	8	yes	—
126	#121×C₈₉	C₂³	1	24	yes	—
127	#121×C₈₉	C₂³	1	24	yes	complemented
128	#121×C₈₉	C₂³	1	24	yes	complemented
129	#121×C₈₉	C₂³	1	48	yes	complemented
130	#121×C₈₉	C₂³	1	96	yes	complemented
131	#120×C₈₉	C₂³	1	8	yes	—
132	#120×C₈₉	C₂³	1	24	yes	—
133	#120×C₈₉	C₂³	1	48	yes	—
134	#120×C₈₉	C₂³	1	48	yes	complemented
135	C₄×Q₈×C₈₉	C₂³	1	16	yes	complemented
136	C₄×D₄×C₈₉	C₂³	1	16	yes	—
137	C₄×D₄×C₈₉	C₂³	1	48	yes	—
138	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
139	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
140	C₄×D₄×C₈₉	C₂³	1	48	yes	complemented
141	#117×C₈₉	C₂³	1	4	yes	—
142	#117×C₈₉	C₂³	1	12	yes	—
143	#117×C₈₉	C₂³	1	12	yes	complemented
144	#117×C₈₉	C₂³	1	12	yes	complemented
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	12	yes	complemented
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	24	yes	complemented
147	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
148	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	—
149	C₂×C₂²⋊C₄×C₈₉	C₂³	1	24	yes	complemented
150	C₂×C₄²×C₈₉	C₂³	1	12	yes	complemented
151	C₂⁴×C₈₉	—	2	12	no	—
152	C₂⁴×C₈₉	—	4	12	no	—
153	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
155	C₂⁴×C₈₉	C₂⁴	1	12	yes	—
156	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
157	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
158	#41×C₈₉	—	2	32	no	—
159	#41×C₈₉	—	2	32	no	—
160	#41×C₈₉	—	2	96	no	—
161	#41×C₈₉	—	2	96	no	—
162	#41×C₈₉	—	2	16	no	—
163	#41×C₈₉	—	2	48	no	—
164	#41×C₈₉	—	2	48	no	—
165	#41×C₈₉	—	2	48	no	—
166	#41×C₈₉	—	2	48	no	—
167	#41×C₈₉	—	2	48	no	—
168	#41×C₈₉	C₂×D₄	1	32	yes	complemented
169	#41×C₈₉	C₂×D₄	1	32	yes	complemented
170	C₂×Q₈×C₈₉	—	2	32	no	—
171	C₂×Q₈×C₈₉	—	2	32	no	—
172	C₂×Q₈×C₈₉	—	2	12	no	—
173	C₂×Q₈×C₈₉	—	2	24	no	—
174	C₂×Q₈×C₈₉	C₂×D₄	1	8	yes	complemented
175	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
176	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
177	C₂×Q₈×C₈₉	C₂⁴	1	12	yes	—
178	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
179	C₂×D₄×C₈₉	—	2	24	no	—
180	C₂×D₄×C₈₉	—	2	48	no	—
181	C₂×D₄×C₈₉	—	2	96	no	—
182	C₂×D₄×C₈₉	—	2	96	no	—
183	C₂×D₄×C₈₉	—	2	12	no	—
184	C₂×D₄×C₈₉	—	2	24	no	—
185	C₂×D₄×C₈₉	—	4	48	no	—
186	C₂×D₄×C₈₉	C₂×D₄	1	24	yes	complemented
187	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
188	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
189	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
190	C₂×D₄×C₈₉	C₂⁴	1	24	yes	—
191	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
192	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
193	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
194	C₂×D₄×C₈₉	C₂⁴	1	48	yes	—
195	C₂×D₄×C₈₉	C₂⁴	1	12	yes	—
196	C₂²×C₄×C₈₉	—	2	12	no	—
197	C₂²×C₄×C₈₉	—	2	4	no	—
198	C₂²×C₄×C₈₉	—	2	12	no	—
199	C₂²×C₄×C₈₉	—	2	12	no	—
200	C₂²×C₄×C₈₉	—	2	12	no	—
201	C₂²×C₄×C₈₉	—	2	48	no	—
202	C₂²×C₄×C₈₉	—	2	48	no	—
203	C₂²×C₄×C₈₉	—	2	48	no	—
204	C₂²×C₄×C₈₉	C₂×D₄	1	24	yes	complemented
205	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
206	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
207	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
208	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
209	C₂²×C₄×C₈₉	C₂⁴	1	12	yes	—
210	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
211	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
212	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
214	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
216	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
217	C₂²×C₄×C₈₉	C₂⁴	1	24	yes	—
218	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
219	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
220	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
221	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
222	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
223	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
224	C₄⋊C₄×C₈₉	C₂⁴	1	24	yes	—
225	C₄⋊C₄×C₈₉	C₂⁴	1	48	yes	—
226	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
227	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
228	C₂²⋊C₄×C₈₉	C₂⁴	1	24	yes	—
229	C₂²⋊C₄×C₈₉	C₂⁴	1	48	yes	—
230	C₂²⋊C₄×C₈₉	C₂⁴	1	16	yes	—
231	C₂²⋊C₄×C₈₉	C₂⁴	1	48	yes	—
232	C₄²×C₈₉	C₂⁴	1	24	yes	—
233	C₄²×C₈₉	C₂⁴	1	8	yes	—
234	C₂³×C₈₉	—	2	2	no	—
235	C₂³×C₈₉	—	2	4	no	—
236	C₂³×C₈₉	—	2	24	no	—
237	C₂³×C₈₉	—	2	6	no	—
238	C₂³×C₈₉	—	2	24	no	—
239	C₂³×C₈₉	—	2	24	no	—
240	C₂³×C₈₉	—	4	6	no	—
241	C₂³×C₈₉	—	4	12	no	—
242	C₂³×C₈₉	—	4	6	no	—
243	C₂³×C₈₉	—	4	24	no	—
244	C₂³×C₈₉	—	4	48	no	—
245	C₂³×C₈₉	C₂²×D₄	1	12	yes	—
246	C₂³×C₈₉	C₂⁵	1	8	yes	—
247	C₂³×C₈₉	C₂⁵	1	6	yes	—
248	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
249	C₂³×C₈₉	C₂⁵	1	6	yes	—
250	C₂³×C₈₉	C₂⁵	1	2	yes	—
251	Q₈×C₈₉	—	2	8	no	—
252	Q₈×C₈₉	—	2	24	no	—
253	Q₈×C₈₉	—	2	24	no	—
254	Q₈×C₈₉	C₂²×D₄	1	16	yes	—
255	D₄×C₈₉	—	2	16	no	—
256	D₄×C₈₉	—	2	48	no	—
257	D₄×C₈₉	—	2	48	no	—
258	D₄×C₈₉	—	2	32	no	—
259	D₄×C₈₉	—	2	8	no	—
260	D₄×C₈₉	—	2	24	no	—
261	D₄×C₈₉	—	2	24	no	—
262	D₄×C₈₉	—	4	48	no	—
263	D₄×C₈₉	C₂²×D₄	1	48	yes	—
264	C₂×C₄×C₈₉	—	2	2	no	—
265	C₂×C₄×C₈₉	—	2	6	no	—
266	C₂×C₄×C₈₉	—	2	24	no	—
267	C₂×C₄×C₈₉	—	2	24	no	—
268	C₂×C₄×C₈₉	—	2	4	no	—
269	C₂×C₄×C₈₉	—	2	4	no	—
270	C₂×C₄×C₈₉	—	2	24	no	—
271	C₂×C₄×C₈₉	—	2	24	no	—
272	C₂×C₄×C₈₉	—	2	12	no	—
273	C₂×C₄×C₈₉	—	2	16	no	—
274	C₂×C₄×C₈₉	—	2	12	no	—
275	C₂×C₄×C₈₉	—	2	48	no	—
276	C₂×C₄×C₈₉	—	4	24	no	—
277	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
278	C₂×C₄×C₈₉	C₂²×D₄	1	24	yes	—
279	C₂×C₄×C₈₉	C₂²×D₄	1	12	yes	—
280	C₂×C₄×C₈₉	C₂²×D₄	1	24	yes	—
281	C₂×C₄×C₈₉	C₂⁵	1	16	yes	—
282	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
283	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
284	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
285	C₂×C₄×C₈₉	C₂⁵	1	6	yes	—
286	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
287	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
288	C₂²×C₈₉	—	2	8	no	—
289	C₂²×C₈₉	—	2	2	no	—
290	C₂²×C₈₉	—	2	12	no	—
291	C₂²×C₈₉	—	2	2	no	—
292	C₂²×C₈₉	—	2	2	no	—
293	C₂²×C₈₉	—	2	6	no	—
294	C₂²×C₈₉	—	2	8	no	—
295	C₂²×C₈₉	—	2	16	no	—
296	C₂²×C₈₉	—	2	12	no	—
297	C₂²×C₈₉	—	4	12	no	—
298	C₂²×C₈₉	—	4	48	no	—
299	C₂²×C₈₉	—	4	12	no	—
300	C₂²×C₈₉	—	8	24	no	—
301	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
302	C₂²×C₈₉	C₂³×D₄	1	12	yes	—
303	C₂²×C₈₉	#585	1	4	yes	complemented
304	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
305	C₄×C₈₉	—	2	2	no	—
306	C₄×C₈₉	—	2	6	no	—
307	C₄×C₈₉	—	2	8	no	—
308	C₄×C₈₉	—	2	16	no	—
309	C₄×C₈₉	C₂³×D₄	1	2	yes	—
310	C₄×C₈₉	C₂³×D₄	1	2	yes	—
311	C₄×C₈₉	C₂³×D₄	1	12	yes	—
312	#62811	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×C₈₉	—	2	2	no	—
314	C₂×C₈₉	—	2	4	no	—
315	C₂×C₈₉	—	2	12	no	—
316	C₂×C₈₉	—	4	6	no	—
317	C₂×C₈₉	—	4	8	no	—
318	C₂×C₈₉	C₂⁴×D₄	1	1	yes	characteristic
319	C₂×C₈₉	C₂×#585	1	2	yes	—
320	C₂×#585	C₂×C₈₉	1	1	yes	characteristic, complemented
321	C₂³×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
322	#3489	C₂×C₈₉	1	8	yes	complemented
323	#3488	C₂×C₈₉	1	8	yes	complemented
324	#3487	C₂×C₈₉	1	2	yes	complemented
325	#3486	C₂×C₈₉	1	2	yes	complemented
326	#3485	C₂×C₈₉	1	6	yes	complemented
327	#3484	C₂×C₈₉	1	6	yes	complemented
328	D₄×#41	C₂×C₈₉	1	16	yes	complemented
329	#3449	C₂×C₈₉	1	6	yes	complemented
330	C₂×#525	C₂×C₈₉	1	6	yes	complemented
331	#3428	C₂×C₈₉	1	1	yes	characteristic, complemented
332	C₈₉	#62811	1	1	yes	characteristic, direct product factor, Sylow
333	#585	—	2	16	no	—
334	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	complemented
335	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	4	yes	complemented
336	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	6	yes	complemented
337	C₂×H(5,𝔽₂)	C₂²×C₈₉	1	4	yes	complemented
338	C₂²×#41	—	2	16	no	—
339	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
340	C₂²×#41	C₂²×C₈₉	1	3	yes	complemented
341	C₂²×#41	C₂²×C₈₉	1	8	yes	complemented
342	C₂²×#41	C₂²×C₈₉	1	3	yes	complemented
343	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic, complemented
344	C₂²×#41	C₂²×C₈₉	1	8	yes	complemented
345	C₂²×#41	C₂²×C₈₉	1	6	yes	complemented
346	C₂²×#41	C₂²×C₈₉	1	8	yes	complemented
347	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
348	C₂³×D₄	C₂²×C₈₉	1	3	yes	complemented
349	C₂⁴×C₄	C₂²×C₈₉	1	3	yes	complemented
350	#550	C₂²×C₈₉	1	16	yes	complemented
351	D₄×Q₈	C₂²×C₈₉	1	16	yes	complemented
352	#548	C₂²×C₈₉	1	16	yes	complemented
353	#548	C₂²×C₈₉	1	16	yes	complemented
354	#547	C₂²×C₈₉	1	48	yes	complemented
355	#546	C₂²×C₈₉	1	48	yes	complemented
356	#546	C₂²×C₈₉	1	48	yes	complemented
357	D₄²	C₂²×C₈₉	1	48	yes	complemented
358	#537	C₂²×C₈₉	1	24	yes	complemented
359	#536	C₂²×C₈₉	1	12	yes	complemented
360	#536	C₂²×C₈₉	1	12	yes	complemented
361	#535	C₂²×C₈₉	1	12	yes	complemented
362	#535	C₂²×C₈₉	1	12	yes	complemented
363	#534	C₂²×C₈₉	1	24	yes	complemented
364	#532	C₂²×C₈₉	1	24	yes	complemented
365	#525	C₂²×C₈₉	1	4	yes	complemented
366	#525	C₂²×C₈₉	1	12	yes	complemented
367	#525	C₂²×C₈₉	1	12	yes	complemented
368	#525	C₂²×C₈₉	1	12	yes	complemented
369	#525	C₂²×C₈₉	1	24	yes	complemented
370	#525	C₂²×C₈₉	1	24	yes	complemented
371	#525	C₂²×C₈₉	1	24	yes	complemented
372	C₂×#123	C₂²×C₈₉	1	12	yes	complemented
373	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	12	yes	complemented
374	C₂×#121	C₂²×C₈₉	1	12	yes	complemented
375	C₂×#120	C₂²×C₈₉	1	12	yes	complemented
376	#520	C₂²×C₈₉	1	8	yes	complemented
377	#519	C₂²×C₈₉	1	2	yes	complemented
378	#518	C₂²×C₈₉	1	6	yes	complemented
379	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
380	C₂×C₄×D₄	C₂²×C₈₉	1	24	yes	complemented
381	C₂×#117	C₂²×C₈₉	1	6	yes	complemented
382	C₂⁵	C₂³×C₈₉	1	3	yes	—
383	2₋¹⁺⁴	—	2	32	no	—
384	2₋¹⁺⁴	—	2	16	no	—
385	H(5,𝔽₂)	—	2	32	no	—
386	H(5,𝔽₂)	—	2	48	no	—
387	C₂×#41	—	2	64	no	—
388	C₂×#41	—	2	64	no	—
389	C₂×#41	—	2	64	no	—
390	C₂×#41	—	2	8	no	—
391	C₂×#41	—	2	24	no	—
392	C₂×#41	—	2	24	no	—
393	C₂×#41	—	2	48	no	—
394	C₂×#41	D₄×C₈₉	1	16	yes	complemented
395	C₂×#41	C₂³×C₈₉	1	4	yes	—
396	C₂×#41	C₂³×C₈₉	1	12	yes	—
397	C₂×#41	C₂³×C₈₉	1	12	yes	—
398	C₂×#41	C₂³×C₈₉	1	12	yes	—
399	C₂×#41	C₂³×C₈₉	1	24	yes	—
400	C₂×#41	C₂³×C₈₉	1	8	yes	—
401	C₂×#41	C₂³×C₈₉	1	4	yes	—
402	C₂×#41	C₂³×C₈₉	1	4	yes	—
403	C₂×#41	C₂³×C₈₉	1	12	yes	complemented
404	C₂×#41	C₂³×C₈₉	1	12	yes	complemented
405	C₂×#41	C₂³×C₈₉	1	24	yes	complemented
406	C₂×#41	C₂³×C₈₉	1	8	yes	complemented
407	C₂²×Q₈	—	2	8	no	—
408	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
409	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
410	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
411	C₂²×Q₈	C₂³×C₈₉	1	6	yes	complemented
412	C₂²×Q₈	C₂³×C₈₉	1	8	yes	complemented
413	C₂²×D₄	—	2	24	no	—
414	C₂²×D₄	C₂³×C₈₉	1	12	yes	—
415	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
416	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
417	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
418	C₂²×D₄	C₂³×C₈₉	1	24	yes	—
419	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
420	C₂²×D₄	C₂³×C₈₉	1	6	yes	complemented
421	C₂²×D₄	C₂³×C₈₉	1	24	yes	complemented
422	C₂³×C₄	—	2	24	no	—
423	C₂³×C₄	C₂³×C₈₉	1	12	yes	—
424	C₂³×C₄	C₂³×C₈₉	1	12	yes	—
425	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
426	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
427	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
428	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
429	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
430	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
431	C₂³×C₄	C₂³×C₈₉	1	12	yes	complemented
432	C₄⋊Q₈	C₂³×C₈₉	1	24	yes	complemented
433	#127	C₂³×C₈₉	1	24	yes	complemented
434	#124	C₂³×C₈₉	1	24	yes	complemented
435	#124	C₂³×C₈₉	1	24	yes	complemented
436	#123	C₂³×C₈₉	1	8	yes	—
437	#123	C₂³×C₈₉	1	24	yes	—
438	#123	C₂³×C₈₉	1	48	yes	complemented
439	#123	C₂³×C₈₉	1	48	yes	complemented
440	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
441	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	—
442	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	complemented
443	C₂²⋊Q₈	C₂³×C₈₉	1	24	yes	complemented
444	C₂²⋊Q₈	C₂³×C₈₉	1	48	yes	complemented
445	#121	C₂³×C₈₉	1	8	yes	—
446	#121	C₂³×C₈₉	1	24	yes	—
447	#121	C₂³×C₈₉	1	24	yes	complemented
448	#121	C₂³×C₈₉	1	24	yes	complemented
449	#121	C₂³×C₈₉	1	48	yes	complemented
450	#121	C₂³×C₈₉	1	96	yes	complemented
451	#120	C₂³×C₈₉	1	8	yes	—
452	#120	C₂³×C₈₉	1	24	yes	—
453	#120	C₂³×C₈₉	1	48	yes	—
454	#120	C₂³×C₈₉	1	48	yes	complemented
455	C₄×Q₈	C₂³×C₈₉	1	16	yes	complemented
456	C₄×D₄	C₂³×C₈₉	1	16	yes	—
457	C₄×D₄	C₂³×C₈₉	1	48	yes	—
458	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
459	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
460	C₄×D₄	C₂³×C₈₉	1	48	yes	complemented
461	#117	C₂³×C₈₉	1	4	yes	—
462	#117	C₂³×C₈₉	1	12	yes	—
463	#117	C₂³×C₈₉	1	12	yes	complemented
464	#117	C₂³×C₈₉	1	12	yes	complemented
465	C₂×C₄⋊C₄	C₂³×C₈₉	1	12	yes	complemented
466	C₂×C₄⋊C₄	C₂³×C₈₉	1	24	yes	complemented
467	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₈₉	1	24	yes	complemented
470	C₂×C₄²	C₂³×C₈₉	1	12	yes	complemented
471	C₂⁴	—	2	12	no	—
472	C₂⁴	—	4	12	no	—
473	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
474	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
475	C₂⁴	C₂⁴×C₈₉	1	12	yes	—
476	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
477	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
478	#41	—	2	32	no	—
479	#41	—	2	32	no	—
480	#41	—	2	96	no	—
481	#41	—	2	96	no	—
482	#41	—	2	16	no	—
483	#41	—	2	48	no	—
484	#41	—	2	48	no	—
485	#41	—	2	48	no	—
486	#41	—	2	48	no	—
487	#41	—	2	48	no	—
488	#41	C₂×D₄×C₈₉	1	32	yes	complemented
489	#41	C₂×D₄×C₈₉	1	32	yes	complemented
490	C₂×Q₈	—	2	32	no	—
491	C₂×Q₈	—	2	32	no	—
492	C₂×Q₈	—	2	12	no	—
493	C₂×Q₈	—	2	24	no	—
494	C₂×Q₈	C₂×D₄×C₈₉	1	8	yes	complemented
495	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
496	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
497	C₂×Q₈	C₂⁴×C₈₉	1	12	yes	—
498	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
499	C₂×D₄	—	2	24	no	—
500	C₂×D₄	—	2	48	no	—
501	C₂×D₄	—	2	96	no	—
502	C₂×D₄	—	2	96	no	—
503	C₂×D₄	—	2	12	no	—
504	C₂×D₄	—	2	24	no	—
505	C₂×D₄	—	4	48	no	—
506	C₂×D₄	C₂×D₄×C₈₉	1	24	yes	complemented
507	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
508	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
509	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
510	C₂×D₄	C₂⁴×C₈₉	1	24	yes	—
511	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
512	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
513	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
514	C₂×D₄	C₂⁴×C₈₉	1	48	yes	—
515	C₂×D₄	C₂⁴×C₈₉	1	12	yes	—
516	C₂²×C₄	—	2	12	no	—
517	C₂²×C₄	—	2	4	no	—
518	C₂²×C₄	—	2	12	no	—
519	C₂²×C₄	—	2	12	no	—
520	C₂²×C₄	—	2	12	no	—
521	C₂²×C₄	—	2	48	no	—
522	C₂²×C₄	—	2	48	no	—
523	C₂²×C₄	—	2	48	no	—
524	C₂²×C₄	C₂×D₄×C₈₉	1	24	yes	complemented
525	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
526	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
527	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
529	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
530	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
531	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
532	C₂²×C₄	C₂⁴×C₈₉	1	12	yes	—
533	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
535	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
536	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
537	C₂²×C₄	C₂⁴×C₈₉	1	24	yes	—
538	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
539	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
540	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
541	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
542	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
543	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
544	C₄⋊C₄	C₂⁴×C₈₉	1	24	yes	—
545	C₄⋊C₄	C₂⁴×C₈₉	1	48	yes	—
546	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
547	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
548	C₂²⋊C₄	C₂⁴×C₈₉	1	24	yes	—
549	C₂²⋊C₄	C₂⁴×C₈₉	1	48	yes	—
550	C₂²⋊C₄	C₂⁴×C₈₉	1	16	yes	—
551	C₂²⋊C₄	C₂⁴×C₈₉	1	48	yes	—
552	C₄²	C₂⁴×C₈₉	1	8	yes	—
553	C₄²	C₂⁴×C₈₉	1	24	yes	—
554	C₂³	—	2	2	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	24	no	—
557	C₂³	—	2	6	no	—
558	C₂³	—	2	24	no	—
559	C₂³	—	2	24	no	—
560	C₂³	—	4	6	no	—
561	C₂³	—	4	12	no	—
562	C₂³	—	4	6	no	—
563	C₂³	—	4	24	no	—
564	C₂³	—	4	48	no	—
565	C₂³	C₂²×D₄×C₈₉	1	12	yes	—
566	C₂³	C₂⁵×C₈₉	1	8	yes	—
567	C₂³	C₂⁵×C₈₉	1	6	yes	—
568	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
569	C₂³	C₂⁵×C₈₉	1	6	yes	—
570	C₂³	C₂⁵×C₈₉	1	2	yes	—
571	Q₈	—	2	8	no	—
572	Q₈	—	2	24	no	—
573	Q₈	—	2	24	no	—
574	Q₈	C₂²×D₄×C₈₉	1	16	yes	—
575	D₄	—	2	16	no	—
576	D₄	—	2	48	no	—
577	D₄	—	2	48	no	—
578	D₄	—	2	32	no	—
579	D₄	—	2	8	no	—
580	D₄	—	2	24	no	—
581	D₄	—	2	24	no	—
582	D₄	—	4	48	no	—
583	D₄	C₂²×D₄×C₈₉	1	48	yes	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	6	no	—
586	C₂×C₄	—	2	24	no	—
587	C₂×C₄	—	2	24	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	24	no	—
591	C₂×C₄	—	2	24	no	—
592	C₂×C₄	—	2	12	no	—
593	C₂×C₄	—	2	16	no	—
594	C₂×C₄	—	2	12	no	—
595	C₂×C₄	—	2	48	no	—
596	C₂×C₄	—	4	24	no	—
597	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₈₉	1	24	yes	—
599	C₂×C₄	C₂²×D₄×C₈₉	1	12	yes	—
600	C₂×C₄	C₂²×D₄×C₈₉	1	24	yes	—
601	C₂×C₄	C₂⁵×C₈₉	1	16	yes	—
602	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
603	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
604	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
605	C₂×C₄	C₂⁵×C₈₉	1	6	yes	—
606	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
607	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
608	C₂²	—	2	8	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	12	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	16	no	—
616	C₂²	—	2	12	no	—
617	C₂²	—	4	12	no	—
618	C₂²	—	4	48	no	—
619	C₂²	—	4	12	no	—
620	C₂²	—	8	24	no	—
621	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
622	C₂²	C₂³×D₄×C₈₉	1	12	yes	—
623	C₂²	#585×C₈₉	1	4	yes	complemented
624	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
625	C₄	—	2	2	no	—
626	C₄	—	2	6	no	—
627	C₄	—	2	8	no	—
628	C₄	—	2	16	no	—
629	C₄	C₂³×D₄×C₈₉	1	2	yes	—
630	C₄	C₂³×D₄×C₈₉	1	2	yes	—
631	C₄	C₂³×D₄×C₈₉	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	4	no	—
634	C₂	—	2	12	no	—
635	C₂	—	4	6	no	—
636	C₂	—	4	8	no	—
637	C₂	C₂⁴×D₄×C₈₉	1	1	yes	characteristic
638	C₂	C₂×#585×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
socle	C₂²×C₈₉	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₈₉	C₂	semidirect
2. C₂³×#41×C₈₉	C₂	semidirect
3. C₈₉×#3489	C₂	semidirect
4. C₈₉×#3488	C₂	semidirect
5. C₈₉×#3487	C₂	semidirect
6. C₈₉×#3486	C₂	semidirect
7. C₈₉×#3485	C₂	semidirect
8. C₈₉×#3484	C₂	semidirect
9. D₄×#41×C₈₉	C₂	semidirect
10. C₈₉×#3449	C₂	semidirect
11. C₂×#525×C₈₉	C₂	semidirect
12. C₈₉×#3428	C₂	semidirect
14. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
15. C₂×2₋¹⁺⁴×C₈₉	C₂²	semidirect
16. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
17. C₂×H(5,𝔽₂)×C₈₉	C₂²	semidirect
20. C₂²×#41×C₈₉	C₂²	semidirect
21. C₂²×#41×C₈₉	C₂²	semidirect
22. C₂²×#41×C₈₉	C₂²	semidirect
23. C₂²×#41×C₈₉	C₂²	semidirect
24. C₂²×#41×C₈₉	C₂²	semidirect
25. C₂²×#41×C₈₉	C₂²	semidirect
26. C₂²×#41×C₈₉	C₂²	semidirect
27. C₂³×Q₈×C₈₉	C₂²	semidirect
28. C₂³×D₄×C₈₉	C₂²	semidirect
29. C₂⁴×C₄×C₈₉	C₂²	semidirect
30. #550×C₈₉	C₂²	semidirect
31. D₄×Q₈×C₈₉	C₂²	semidirect
32. #548×C₈₉	C₂²	semidirect
33. #548×C₈₉	C₂²	semidirect
34. #547×C₈₉	C₂²	semidirect
35. #546×C₈₉	C₂²	semidirect
36. #546×C₈₉	C₂²	semidirect
37. D₄²×C₈₉	C₂²	semidirect
38. #537×C₈₉	C₂²	semidirect
39. #536×C₈₉	C₂²	semidirect
40. #536×C₈₉	C₂²	semidirect
41. #535×C₈₉	C₂²	semidirect
42. #535×C₈₉	C₂²	semidirect
43. #534×C₈₉	C₂²	semidirect
44. #532×C₈₉	C₂²	semidirect
45. #525×C₈₉	C₂²	semidirect
46. #525×C₈₉	C₂²	semidirect
47. #525×C₈₉	C₂²	semidirect
48. #525×C₈₉	C₂²	semidirect
49. #525×C₈₉	C₂²	semidirect
50. #525×C₈₉	C₂²	semidirect
51. #525×C₈₉	C₂²	semidirect
52. C₂×#123×C₈₉	C₂²	semidirect
53. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
54. C₂×#121×C₈₉	C₂²	semidirect
55. C₂×#120×C₈₉	C₂²	semidirect
56. #520×C₈₉	C₂²	semidirect
57. #519×C₈₉	C₂²	semidirect
58. #518×C₈₉	C₂²	semidirect
59. C₄×#41×C₈₉	C₂²	semidirect
60. C₂×C₄×D₄×C₈₉	C₂²	semidirect
61. C₂×#117×C₈₉	C₂²	semidirect
74. C₂×#41×C₈₉	D₄	semidirect
83. C₂×#41×C₈₉	C₂³	semidirect
84. C₂×#41×C₈₉	C₂³	semidirect
85. C₂×#41×C₈₉	C₂³	semidirect
86. C₂×#41×C₈₉	C₂³	semidirect
91. C₂²×Q₈×C₈₉	C₂³	semidirect
92. C₂²×Q₈×C₈₉	C₂³	semidirect
100. C₂²×D₄×C₈₉	C₂³	semidirect
101. C₂²×D₄×C₈₉	C₂³	semidirect
111. C₂³×C₄×C₈₉	C₂³	semidirect
112. C₄⋊Q₈×C₈₉	C₂³	semidirect
113. #127×C₈₉	C₂³	semidirect
114. #124×C₈₉	C₂³	semidirect
115. #124×C₈₉	C₂³	semidirect
118. #123×C₈₉	C₂³	semidirect
119. #123×C₈₉	C₂³	semidirect
122. C₂²⋊Q₈×C₈₉	C₂³	semidirect
123. C₂²⋊Q₈×C₈₉	C₂³	semidirect
124. C₂²⋊Q₈×C₈₉	C₂³	semidirect
127. #121×C₈₉	C₂³	semidirect
128. #121×C₈₉	C₂³	semidirect
129. #121×C₈₉	C₂³	semidirect
130. #121×C₈₉	C₂³	semidirect
134. #120×C₈₉	C₂³	semidirect
135. C₄×Q₈×C₈₉	C₂³	semidirect
138. C₄×D₄×C₈₉	C₂³	semidirect
139. C₄×D₄×C₈₉	C₂³	semidirect
140. C₄×D₄×C₈₉	C₂³	semidirect
143. #117×C₈₉	C₂³	semidirect
144. #117×C₈₉	C₂³	semidirect
145. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
146. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
149. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
150. C₂×C₄²×C₈₉	C₂³	semidirect
168. #41×C₈₉	C₂×D₄	semidirect
169. #41×C₈₉	C₂×D₄	semidirect
174. C₂×Q₈×C₈₉	C₂×D₄	semidirect
186. C₂×D₄×C₈₉	C₂×D₄	semidirect
204. C₂²×C₄×C₈₉	C₂×D₄	semidirect
303. C₂²×C₈₉	#585	semidirect
312. #62811	C₈₉	direct (N × H)
320. C₂×#585	C₂×C₈₉	semidirect
321. C₂³×#41	C₂×C₈₉	semidirect
322. #3489	C₂×C₈₉	semidirect
323. #3488	C₂×C₈₉	semidirect
324. #3487	C₂×C₈₉	semidirect
325. #3486	C₂×C₈₉	semidirect
326. #3485	C₂×C₈₉	semidirect
327. #3484	C₂×C₈₉	semidirect
328. D₄×#41	C₂×C₈₉	semidirect
329. #3449	C₂×C₈₉	semidirect
330. C₂×#525	C₂×C₈₉	semidirect
331. #3428	C₂×C₈₉	semidirect
332. C₈₉	#62811	direct (N × H)
334. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
335. C₂×2₋¹⁺⁴	C₂²×C₈₉	semidirect
336. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
337. C₂×H(5,𝔽₂)	C₂²×C₈₉	semidirect
340. C₂²×#41	C₂²×C₈₉	semidirect
341. C₂²×#41	C₂²×C₈₉	semidirect
342. C₂²×#41	C₂²×C₈₉	semidirect
343. C₂²×#41	C₂²×C₈₉	semidirect
344. C₂²×#41	C₂²×C₈₉	semidirect
345. C₂²×#41	C₂²×C₈₉	semidirect
346. C₂²×#41	C₂²×C₈₉	semidirect
347. C₂³×Q₈	C₂²×C₈₉	semidirect
348. C₂³×D₄	C₂²×C₈₉	semidirect
349. C₂⁴×C₄	C₂²×C₈₉	semidirect
350. #550	C₂²×C₈₉	semidirect
351. D₄×Q₈	C₂²×C₈₉	semidirect
352. #548	C₂²×C₈₉	semidirect
353. #548	C₂²×C₈₉	semidirect
354. #547	C₂²×C₈₉	semidirect
355. #546	C₂²×C₈₉	semidirect
356. #546	C₂²×C₈₉	semidirect
357. D₄²	C₂²×C₈₉	semidirect
358. #537	C₂²×C₈₉	semidirect
359. #536	C₂²×C₈₉	semidirect
360. #536	C₂²×C₈₉	semidirect
361. #535	C₂²×C₈₉	semidirect
362. #535	C₂²×C₈₉	semidirect
363. #534	C₂²×C₈₉	semidirect
364. #532	C₂²×C₈₉	semidirect
365. #525	C₂²×C₈₉	semidirect
366. #525	C₂²×C₈₉	semidirect
367. #525	C₂²×C₈₉	semidirect
368. #525	C₂²×C₈₉	semidirect
369. #525	C₂²×C₈₉	semidirect
370. #525	C₂²×C₈₉	semidirect
371. #525	C₂²×C₈₉	semidirect
372. C₂×#123	C₂²×C₈₉	semidirect
373. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
374. C₂×#121	C₂²×C₈₉	semidirect
375. C₂×#120	C₂²×C₈₉	semidirect
376. #520	C₂²×C₈₉	semidirect
377. #519	C₂²×C₈₉	semidirect
378. #518	C₂²×C₈₉	semidirect
379. C₄×#41	C₂²×C₈₉	semidirect
380. C₂×C₄×D₄	C₂²×C₈₉	semidirect
381. C₂×#117	C₂²×C₈₉	semidirect
394. C₂×#41	D₄×C₈₉	semidirect
403. C₂×#41	C₂³×C₈₉	semidirect
404. C₂×#41	C₂³×C₈₉	semidirect
405. C₂×#41	C₂³×C₈₉	semidirect
406. C₂×#41	C₂³×C₈₉	semidirect
411. C₂²×Q₈	C₂³×C₈₉	semidirect
412. C₂²×Q₈	C₂³×C₈₉	semidirect
420. C₂²×D₄	C₂³×C₈₉	semidirect
421. C₂²×D₄	C₂³×C₈₉	semidirect
431. C₂³×C₄	C₂³×C₈₉	semidirect
432. C₄⋊Q₈	C₂³×C₈₉	semidirect
433. #127	C₂³×C₈₉	semidirect
434. #124	C₂³×C₈₉	semidirect
435. #124	C₂³×C₈₉	semidirect
438. #123	C₂³×C₈₉	semidirect
439. #123	C₂³×C₈₉	semidirect
442. C₂²⋊Q₈	C₂³×C₈₉	semidirect
443. C₂²⋊Q₈	C₂³×C₈₉	semidirect
444. C₂²⋊Q₈	C₂³×C₈₉	semidirect
447. #121	C₂³×C₈₉	semidirect
448. #121	C₂³×C₈₉	semidirect
449. #121	C₂³×C₈₉	semidirect
450. #121	C₂³×C₈₉	semidirect
454. #120	C₂³×C₈₉	semidirect
455. C₄×Q₈	C₂³×C₈₉	semidirect
458. C₄×D₄	C₂³×C₈₉	semidirect
459. C₄×D₄	C₂³×C₈₉	semidirect
460. C₄×D₄	C₂³×C₈₉	semidirect
463. #117	C₂³×C₈₉	semidirect
464. #117	C₂³×C₈₉	semidirect
465. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
466. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
469. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
470. C₂×C₄²	C₂³×C₈₉	semidirect
488. #41	C₂×D₄×C₈₉	semidirect
489. #41	C₂×D₄×C₈₉	semidirect
494. C₂×Q₈	C₂×D₄×C₈₉	semidirect
506. C₂×D₄	C₂×D₄×C₈₉	semidirect
524. C₂²×C₄	C₂×D₄×C₈₉	semidirect
623. C₂²	#585×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₈₉	2
C₂³×#41×C₈₉	2
C₈₉×#3489	2
C₈₉×#3488	2
C₈₉×#3487	2
C₈₉×#3486	2
C₈₉×#3485	2
C₈₉×#3484	2
D₄×#41×C₈₉	2
C₈₉×#3449	2
C₂×#525×C₈₉	2
C₈₉×#3428	2
#62811	89

Subgroups — C89×#62811 #36440659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62811 #36440659