Subgroups — C₂²×#464×C₈₉ #36438256

Order 22784.

2918 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#124×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#464×C₈₉	C₂	1	24	yes	maximal, direct product factor
6	C₂²×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×Q₁₆×C₈₉	—	2	8	no	—
13	C₂²×Q₁₆×C₈₉	C₂²	1	12	yes	complemented
14	C₂²×SD₁₆×C₈₉	—	2	8	no	—
15	C₂²×SD₁₆×C₈₉	C₂²	1	12	yes	—
16	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#124×C₈₉	—	2	6	no	—
19	C₂×#124×C₈₉	C₂²	1	12	yes	—
20	C₂×C₄×Q₈×C₈₉	—	2	6	no	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	12	yes	complemented
22	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
25	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
26	C₂²×C₄²×C₈₉	—	2	1	no	—
27	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
28	#464×C₈₉	C₂²	1	64	yes	direct product factor
29	C₂×C₄⋊C₈×C₈₉	C₂²	1	12	yes	complemented
30	C₂×#103×C₈₉	C₂²	1	12	yes	complemented
31	C₂×#102×C₈₉	C₂²	1	12	yes	—
32	C₂⁵×C₈₉	—	2	1	no	—
33	C₂²×Q₈×C₈₉	—	2	3	no	—
34	C₂²×Q₈×C₈₉	—	2	3	no	—
35	C₂²×Q₈×C₈₉	—	2	4	no	—
36	C₂²×Q₈×C₈₉	—	2	4	no	—
37	C₂²×Q₈×C₈₉	—	2	4	no	—
38	C₂²×Q₈×C₈₉	D₄	1	8	yes	—
39	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
40	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
41	C₂²×D₄×C₈₉	—	2	4	no	—
42	C₂²×D₄×C₈₉	—	2	3	no	—
43	C₂²×D₄×C₈₉	—	2	4	no	—
44	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
45	C₂³×C₄×C₈₉	—	2	1	no	—
46	C₂³×C₄×C₈₉	—	2	1	no	—
47	C₂³×C₄×C₈₉	—	2	1	no	—
48	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂×Q₁₆×C₈₉	—	2	48	no	—
52	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	complemented
53	C₂×SD₁₆×C₈₉	—	2	48	no	—
54	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
55	C₂²×C₈×C₈₉	—	2	4	no	—
56	C₂²×C₈×C₈₉	—	2	4	no	—
57	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
58	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
59	#124×C₈₉	—	2	24	no	—
60	#124×C₈₉	C₂³	1	16	yes	—
61	C₄×Q₈×C₈₉	—	2	24	no	—
62	C₄×Q₈×C₈₉	C₂³	1	16	yes	complemented
63	C₂×C₄⋊C₄×C₈₉	—	2	12	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
68	C₂×C₄²×C₈₉	—	2	12	no	—
69	C₂×C₄²×C₈₉	D₄	1	6	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
71	C₄⋊C₈×C₈₉	C₂³	1	16	yes	complemented
72	#103×C₈₉	C₂³	1	16	yes	complemented
73	#102×C₈₉	C₂³	1	16	yes	—
74	C₂⁴×C₈₉	—	2	6	no	—
75	C₂⁴×C₈₉	—	4	4	no	—
76	C₂⁴×C₈₉	—	4	4	no	—
77	C₂⁴×C₈₉	—	4	4	no	—
78	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
79	C₂×Q₈×C₈₉	—	2	24	no	—
80	C₂×Q₈×C₈₉	—	2	6	no	—
81	C₂×Q₈×C₈₉	—	2	6	no	—
82	C₂×Q₈×C₈₉	—	2	12	no	—
83	C₂×Q₈×C₈₉	—	2	12	no	—
84	C₂×Q₈×C₈₉	—	2	12	no	—
85	C₂×Q₈×C₈₉	—	4	12	no	—
86	C₂×Q₈×C₈₉	C₂×D₄	1	24	yes	—
87	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
88	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
89	C₂×D₄×C₈₉	—	2	12	no	—
90	C₂×D₄×C₈₉	—	2	6	no	—
91	C₂×D₄×C₈₉	—	2	12	no	—
92	C₂×D₄×C₈₉	—	4	12	no	—
93	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
94	C₂²×C₄×C₈₉	—	2	8	no	—
95	C₂²×C₄×C₈₉	—	2	4	no	—
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	—	2	6	no	—
98	C₂²×C₄×C₈₉	—	2	6	no	—
99	C₂²×C₄×C₈₉	—	2	6	no	—
100	C₂²×C₄×C₈₉	—	4	4	no	—
101	C₂²×C₄×C₈₉	—	4	4	no	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
104	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₈₉	#41	1	4	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
108	Q₁₆×C₈₉	—	2	32	no	—
109	SD₁₆×C₈₉	—	2	32	no	—
110	C₂×C₈×C₈₉	—	2	12	no	—
111	C₂×C₈×C₈₉	—	2	12	no	—
112	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
113	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
114	C₄⋊C₄×C₈₉	—	2	16	no	—
115	C₄⋊C₄×C₈₉	—	2	6	no	—
116	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
117	C₂²⋊C₄×C₈₉	—	2	16	no	—
118	C₂²⋊C₄×C₈₉	—	2	16	no	—
119	C₄²×C₈₉	—	2	16	no	—
120	C₄²×C₈₉	C₂×D₄	1	12	yes	—
121	C₄²×C₈₉	C₂⁴	1	4	yes	—
122	C₂³×C₈₉	—	2	4	no	—
123	C₂³×C₈₉	—	4	12	no	—
124	C₂³×C₈₉	—	4	12	no	—
125	C₂³×C₈₉	—	4	12	no	—
126	C₂³×C₈₉	—	8	16	no	—
127	C₂³×C₈₉	#121	1	4	yes	—
128	C₂³×C₈₉	#135	1	4	yes	—
129	C₂³×C₈₉	#137	1	4	yes	—
130	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
131	Q₈×C₈₉	—	2	24	no	—
132	Q₈×C₈₉	—	2	4	no	—
133	Q₈×C₈₉	—	2	4	no	—
134	Q₈×C₈₉	—	2	4	no	—
135	Q₈×C₈₉	—	4	12	no	—
136	Q₈×C₈₉	C₂²×D₄	1	8	yes	—
137	D₄×C₈₉	—	2	4	no	—
138	D₄×C₈₉	—	2	4	no	—
139	D₄×C₈₉	—	4	12	no	—
140	C₂×C₄×C₈₉	—	2	24	no	—
141	C₂×C₄×C₈₉	—	2	12	no	—
142	C₂×C₄×C₈₉	—	2	12	no	—
143	C₂×C₄×C₈₉	—	2	4	no	—
144	C₂×C₄×C₈₉	—	2	4	no	—
145	C₂×C₄×C₈₉	—	2	4	no	—
146	C₂×C₄×C₈₉	—	4	12	no	—
147	C₂×C₄×C₈₉	—	4	12	no	—
148	C₂×C₄×C₈₉	#121	1	12	yes	—
149	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
150	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
153	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
154	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
155	C₈×C₈₉	—	2	4	no	—
156	C₈×C₈₉	—	2	4	no	—
157	C₂²×C₈₉	—	4	4	no	—
158	C₂²×C₈₉	—	4	4	no	—
159	C₂²×C₈₉	—	4	4	no	—
160	C₂²×C₈₉	—	8	24	no	—
161	C₂²×C₈₉	#464	1	16	yes	direct product factor
162	C₂²×C₈₉	C₂×#121	1	6	yes	—
163	C₂²×C₈₉	C₂×#135	1	6	yes	—
164	C₂²×C₈₉	C₂×#137	1	6	yes	—
165	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
166	C₄×C₈₉	—	2	8	no	—
167	C₄×C₈₉	—	2	4	no	—
168	C₄×C₈₉	—	2	4	no	—
169	C₄×C₈₉	—	4	4	no	—
170	C₄×C₈₉	—	4	4	no	—
171	C₄×C₈₉	C₂×#121	1	6	yes	—
172	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
174	C₂²×#464	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₈₉	—	8	4	no	—
176	C₂×C₈₉	C₂×#464	1	12	yes	direct product factor
177	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
178	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
179	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
180	C₂³×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
181	C₂³×SD₁₆	C₂×C₈₉	1	1	yes	characteristic
182	C₂²×#124	C₂×C₈₉	1	1	yes	characteristic
183	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
184	C₂×#464	C₂×C₈₉	1	24	yes	direct product factor
185	C₂²×C₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
186	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic, complemented
187	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic
188	C₈₉	C₂²×#464	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
190	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
191	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
192	C₂²×Q₁₆	—	2	8	no	—
193	C₂²×Q₁₆	C₂²×C₈₉	1	12	yes	complemented
194	C₂²×SD₁₆	—	2	8	no	—
195	C₂²×SD₁₆	C₂²×C₈₉	1	12	yes	—
196	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
197	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
198	C₂×#124	—	2	6	no	—
199	C₂×#124	C₂²×C₈₉	1	12	yes	—
200	C₂×C₄×Q₈	—	2	6	no	—
201	C₂×C₄×Q₈	C₂²×C₈₉	1	12	yes	complemented
202	C₂²×C₄⋊C₄	—	2	1	no	—
203	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
204	C₂²×C₂²⋊C₄	—	2	1	no	—
205	C₂²×C₂²⋊C₄	—	2	1	no	—
206	C₂²×C₄²	—	2	1	no	—
207	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
208	#464	C₂²×C₈₉	1	64	yes	direct product factor
209	C₂×C₄⋊C₈	C₂²×C₈₉	1	12	yes	complemented
210	C₂×#103	C₂²×C₈₉	1	12	yes	complemented
211	C₂×#102	C₂²×C₈₉	1	12	yes	—
212	C₂⁵	—	2	1	no	—
213	C₂²×Q₈	—	2	3	no	—
214	C₂²×Q₈	—	2	3	no	—
215	C₂²×Q₈	—	2	4	no	—
216	C₂²×Q₈	—	2	4	no	—
217	C₂²×Q₈	—	2	4	no	—
218	C₂²×Q₈	D₄×C₈₉	1	8	yes	—
219	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
220	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
221	C₂²×D₄	—	2	4	no	—
222	C₂²×D₄	—	2	3	no	—
223	C₂²×D₄	—	2	4	no	—
224	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	—	2	1	no	—
227	C₂³×C₄	—	2	1	no	—
228	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
229	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
230	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
231	C₂×Q₁₆	—	2	48	no	—
232	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	complemented
233	C₂×SD₁₆	—	2	48	no	—
234	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
235	C₂²×C₈	—	2	4	no	—
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
238	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
239	#124	—	2	24	no	—
240	#124	C₂³×C₈₉	1	16	yes	—
241	C₄×Q₈	—	2	24	no	—
242	C₄×Q₈	C₂³×C₈₉	1	16	yes	complemented
243	C₂×C₄⋊C₄	—	2	12	no	—
244	C₂×C₄⋊C₄	—	2	3	no	—
245	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
246	C₂×C₂²⋊C₄	—	2	12	no	—
247	C₂×C₂²⋊C₄	—	2	12	no	—
248	C₂×C₄²	—	2	12	no	—
249	C₂×C₄²	D₄×C₈₉	1	6	yes	—
250	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
251	C₄⋊C₈	C₂³×C₈₉	1	16	yes	complemented
252	#103	C₂³×C₈₉	1	16	yes	complemented
253	#102	C₂³×C₈₉	1	16	yes	—
254	C₂⁴	—	2	6	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	—	4	4	no	—
258	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
259	C₂×Q₈	—	2	24	no	—
260	C₂×Q₈	—	2	6	no	—
261	C₂×Q₈	—	2	6	no	—
262	C₂×Q₈	—	2	12	no	—
263	C₂×Q₈	—	2	12	no	—
264	C₂×Q₈	—	2	12	no	—
265	C₂×Q₈	—	4	12	no	—
266	C₂×Q₈	C₂×D₄×C₈₉	1	24	yes	—
267	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
268	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
269	C₂×D₄	—	2	12	no	—
270	C₂×D₄	—	2	6	no	—
271	C₂×D₄	—	2	12	no	—
272	C₂×D₄	—	4	12	no	—
273	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	4	no	—
277	C₂²×C₄	—	2	6	no	—
278	C₂²×C₄	—	2	6	no	—
279	C₂²×C₄	—	2	6	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	4	no	—
282	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
283	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
284	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
285	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
286	C₂²×C₄	#41×C₈₉	1	4	yes	—
287	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
288	Q₁₆	—	2	32	no	—
289	SD₁₆	—	2	32	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	2	12	no	—
292	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
293	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
294	C₄⋊C₄	—	2	16	no	—
295	C₄⋊C₄	—	2	6	no	—
296	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
297	C₂²⋊C₄	—	2	16	no	—
298	C₂²⋊C₄	—	2	16	no	—
299	C₄²	—	2	16	no	—
300	C₄²	C₂×D₄×C₈₉	1	12	yes	—
301	C₄²	C₂⁴×C₈₉	1	4	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	12	no	—
304	C₂³	—	4	12	no	—
305	C₂³	—	4	12	no	—
306	C₂³	—	8	16	no	—
307	C₂³	#121×C₈₉	1	4	yes	—
308	C₂³	#135×C₈₉	1	4	yes	—
309	C₂³	#137×C₈₉	1	4	yes	—
310	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
311	Q₈	—	2	24	no	—
312	Q₈	—	2	4	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	2	4	no	—
315	Q₈	—	4	12	no	—
316	Q₈	C₂²×D₄×C₈₉	1	8	yes	—
317	D₄	—	2	4	no	—
318	D₄	—	2	4	no	—
319	D₄	—	4	12	no	—
320	C₂×C₄	—	2	24	no	—
321	C₂×C₄	—	2	12	no	—
322	C₂×C₄	—	2	12	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	12	no	—
327	C₂×C₄	—	4	12	no	—
328	C₂×C₄	#121×C₈₉	1	12	yes	—
329	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
331	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
332	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
333	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
334	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
335	C₈	—	2	4	no	—
336	C₈	—	2	4	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	4	no	—
340	C₂²	—	8	24	no	—
341	C₂²	#464×C₈₉	1	16	yes	direct product factor
342	C₂²	C₂×#121×C₈₉	1	6	yes	—
343	C₂²	C₂×#135×C₈₉	1	6	yes	—
344	C₂²	C₂×#137×C₈₉	1	6	yes	—
345	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
346	C₄	—	2	4	no	—
347	C₄	—	2	4	no	—
348	C₄	—	2	8	no	—
349	C₄	—	4	4	no	—
350	C₄	—	4	4	no	—
351	C₄	C₂×#121×C₈₉	1	6	yes	—
352	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
353	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
354	C₂	—	8	4	no	—
355	C₂	C₂×#464×C₈₉	1	12	yes	direct product factor
356	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
357	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
358	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₈₉	C₂	semidirect
4. C₂²×C₄×Q₈×C₈₉	C₂	semidirect
5. C₂×#464×C₈₉	C₂	direct (N × H)
6. C₂²×C₄⋊C₈×C₈₉	C₂	semidirect
7. C₂²×#103×C₈₉	C₂	semidirect
13. C₂²×Q₁₆×C₈₉	C₂²	semidirect
21. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
28. #464×C₈₉	C₂²	direct (N × H)
29. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
30. C₂×#103×C₈₉	C₂²	semidirect
52. C₂×Q₁₆×C₈₉	C₂³	semidirect
62. C₄×Q₈×C₈₉	C₂³	semidirect
71. C₄⋊C₈×C₈₉	C₂³	semidirect
72. #103×C₈₉	C₂³	semidirect
161. C₂²×C₈₉	#464	direct (N × H)
174. C₂²×#464	C₈₉	direct (N × H)
176. C₂×C₈₉	C₂×#464	direct (N × H)
180. C₂³×Q₁₆	C₂×C₈₉	semidirect
183. C₂²×C₄×Q₈	C₂×C₈₉	semidirect
184. C₂×#464	C₂×C₈₉	direct (N × H)
185. C₂²×C₄⋊C₈	C₂×C₈₉	semidirect
186. C₂²×#103	C₂×C₈₉	semidirect
188. C₈₉	C₂²×#464	direct (N × H)
193. C₂²×Q₁₆	C₂²×C₈₉	semidirect
201. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
208. #464	C₂²×C₈₉	direct (N × H)
209. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
210. C₂×#103	C₂²×C₈₉	semidirect
232. C₂×Q₁₆	C₂³×C₈₉	semidirect
242. C₄×Q₈	C₂³×C₈₉	semidirect
251. C₄⋊C₈	C₂³×C₈₉	semidirect
252. #103	C₂³×C₈₉	semidirect
341. C₂²	#464×C₈₉	direct (N × H)
355. C₂	C₂×#464×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₈₉	2
C₂³×SD₁₆×C₈₉	2
C₂²×#124×C₈₉	2
C₂²×C₄×Q₈×C₈₉	2
C₂×#464×C₈₉	2
C₂²×C₄⋊C₈×C₈₉	2
C₂²×#103×C₈₉	2
C₂²×#102×C₈₉	2
C₂²×#464	89

Subgroups — C22×#464×C89 #36438256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#464×C₈₉ #36438256