Subgroups — C₂²×#459×C₈₉ #36438251

Order 22784.

3910 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₂²×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₄×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#459×C₈₉	C₂	1	24	yes	maximal, direct product factor
5	C₂²×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#102×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂³×D₄×C₈₉	—	2	1	no	—
8	C₂³×D₄×C₈₉	—	2	1	no	—
9	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₈₉	—	2	1	no	—
12	C₂²×D₈×C₈₉	—	2	16	no	—
13	C₂²×D₈×C₈₉	C₂²	1	24	yes	complemented
14	C₂³×C₈×C₈₉	C₂²	1	2	yes	—
15	C₂×#127×C₈₉	—	2	6	no	—
16	C₂×#127×C₈₉	C₂²	1	12	yes	complemented
17	C₂×C₄×D₄×C₈₉	—	2	6	no	—
18	C₂×C₄×D₄×C₈₉	C₂²	1	12	yes	complemented
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
21	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
22	#459×C₈₉	C₂²	1	64	yes	direct product factor
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	12	yes	complemented
24	C₂×#102×C₈₉	C₂²	1	24	yes	complemented
25	C₂⁵×C₈₉	—	2	1	no	—
26	C₂⁵×C₈₉	—	2	2	no	—
27	C₂²×D₄×C₈₉	—	2	3	no	—
28	C₂²×D₄×C₈₉	—	2	8	no	—
29	C₂²×D₄×C₈₉	—	2	6	no	—
30	C₂²×D₄×C₈₉	—	2	12	no	—
31	C₂²×D₄×C₈₉	—	2	12	no	—
32	C₂²×D₄×C₈₉	—	2	4	no	—
33	C₂²×D₄×C₈₉	—	2	8	no	—
34	C₂²×D₄×C₈₉	—	4	8	no	—
35	C₂²×D₄×C₈₉	—	4	8	no	—
36	C₂²×D₄×C₈₉	D₄	1	8	yes	complemented
37	C₂²×D₄×C₈₉	C₂³	1	12	yes	—
38	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
39	C₂³×C₄×C₈₉	—	2	1	no	—
40	C₂³×C₄×C₈₉	—	2	12	no	—
41	C₂³×C₄×C₈₉	—	4	8	no	—
42	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂×D₈×C₈₉	—	2	96	no	—
46	C₂×D₈×C₈₉	C₂³	1	32	yes	complemented
47	C₂²×C₈×C₈₉	—	2	8	no	—
48	C₂²×C₈×C₈₉	C₂³	1	12	yes	—
49	#127×C₈₉	—	2	24	no	—
50	#127×C₈₉	C₂³	1	16	yes	complemented
51	C₄×D₄×C₈₉	—	2	24	no	—
52	C₄×D₄×C₈₉	C₂³	1	16	yes	complemented
53	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
55	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
56	C₂×C₄²×C₈₉	D₄	1	6	yes	—
57	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
58	C₄⋊C₈×C₈₉	C₂³	1	16	yes	complemented
59	#102×C₈₉	C₂³	1	32	yes	complemented
60	C₂⁴×C₈₉	—	2	8	no	—
61	C₂⁴×C₈₉	—	2	6	no	—
62	C₂⁴×C₈₉	—	2	12	no	—
63	C₂⁴×C₈₉	—	4	4	no	—
64	C₂⁴×C₈₉	—	4	4	no	—
65	C₂⁴×C₈₉	—	4	8	no	—
66	C₂⁴×C₈₉	—	4	8	no	—
67	C₂⁴×C₈₉	—	4	8	no	—
68	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₈₉	—	2	24	no	—
70	C₂×D₄×C₈₉	—	2	6	no	—
71	C₂×D₄×C₈₉	—	2	24	no	—
72	C₂×D₄×C₈₉	—	2	12	no	—
73	C₂×D₄×C₈₉	—	2	16	no	—
74	C₂×D₄×C₈₉	—	2	16	no	—
75	C₂×D₄×C₈₉	—	2	12	no	—
76	C₂×D₄×C₈₉	—	2	24	no	—
77	C₂×D₄×C₈₉	—	4	48	no	—
78	C₂×D₄×C₈₉	—	4	24	no	—
79	C₂×D₄×C₈₉	—	4	48	no	—
80	C₂×D₄×C₈₉	C₂×D₄	1	24	yes	complemented
81	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
82	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
83	C₂²×C₄×C₈₉	—	2	4	no	—
84	C₂²×C₄×C₈₉	—	2	6	no	—
85	C₂²×C₄×C₈₉	—	2	16	no	—
86	C₂²×C₄×C₈₉	—	4	4	no	—
87	C₂²×C₄×C₈₉	—	4	48	no	—
88	C₂²×C₄×C₈₉	D₈	1	8	yes	complemented
89	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
90	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
91	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
92	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
93	C₂²×C₄×C₈₉	#41	1	4	yes	—
94	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
95	D₈×C₈₉	—	2	64	no	—
96	C₂×C₈×C₈₉	—	2	24	no	—
97	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
98	C₄⋊C₄×C₈₉	—	2	6	no	—
99	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
100	C₂²⋊C₄×C₈₉	—	2	16	no	—
101	C₄²×C₈₉	C₂×D₄	1	12	yes	—
102	C₄²×C₈₉	C₂⁴	1	4	yes	—
103	C₂³×C₈₉	—	2	24	no	—
104	C₂³×C₈₉	—	2	4	no	—
105	C₂³×C₈₉	—	2	8	no	—
106	C₂³×C₈₉	—	4	12	no	—
107	C₂³×C₈₉	—	4	12	no	—
108	C₂³×C₈₉	—	4	32	no	—
109	C₂³×C₈₉	—	4	24	no	—
110	C₂³×C₈₉	—	4	24	no	—
111	C₂³×C₈₉	—	4	24	no	—
112	C₂³×C₈₉	—	8	32	no	—
113	C₂³×C₈₉	#121	1	4	yes	—
114	C₂³×C₈₉	C₂×D₈	1	4	yes	—
115	C₂³×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
116	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
117	D₄×C₈₉	—	2	24	no	—
118	D₄×C₈₉	—	2	8	no	—
119	D₄×C₈₉	—	2	4	no	—
120	D₄×C₈₉	—	2	8	no	—
121	D₄×C₈₉	—	4	32	no	—
122	D₄×C₈₉	—	4	24	no	—
123	D₄×C₈₉	—	4	32	no	—
124	D₄×C₈₉	C₂²×D₄	1	8	yes	complemented
125	C₂×C₄×C₈₉	—	2	12	no	—
126	C₂×C₄×C₈₉	—	2	4	no	—
127	C₂×C₄×C₈₉	—	4	12	no	—
128	C₂×C₄×C₈₉	—	4	32	no	—
129	C₂×C₄×C₈₉	#121	1	12	yes	—
130	C₂×C₄×C₈₉	C₂×D₈	1	24	yes	complemented
131	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
132	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
133	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
134	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
135	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
136	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
137	C₈×C₈₉	—	2	8	no	—
138	C₂²×C₈₉	—	2	8	no	—
139	C₂²×C₈₉	—	4	48	no	—
140	C₂²×C₈₉	—	4	4	no	—
141	C₂²×C₈₉	—	4	4	no	—
142	C₂²×C₈₉	—	4	8	no	—
143	C₂²×C₈₉	—	4	8	no	—
144	C₂²×C₈₉	—	4	8	no	—
145	C₂²×C₈₉	—	8	48	no	—
146	C₂²×C₈₉	#459	1	16	yes	direct product factor
147	C₂²×C₈₉	C₂×#121	1	6	yes	—
148	C₂²×C₈₉	C₂²×D₈	1	6	yes	—
149	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
150	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
151	C₄×C₈₉	—	2	4	no	—
152	C₄×C₈₉	—	4	4	no	—
153	C₄×C₈₉	C₂×#121	1	6	yes	—
154	C₄×C₈₉	C₂²×D₈	1	8	yes	complemented
155	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
156	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
157	C₂²×#459	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂×C₈₉	—	4	8	no	—
159	C₂×C₈₉	—	8	8	no	—
160	C₂×C₈₉	C₂×#459	1	12	yes	direct product factor
161	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
162	C₂×C₈₉	C₂³×D₈	1	1	yes	characteristic
163	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂³×D₈	C₂×C₈₉	1	2	yes	complemented
165	C₂²×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
166	C₂²×C₄×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
167	C₂×#459	C₂×C₈₉	1	24	yes	direct product factor
168	C₂²×C₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
169	C₂²×#102	C₂×C₈₉	1	2	yes	complemented
170	C₈₉	C₂²×#459	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³×D₄	—	2	1	no	—
172	C₂³×D₄	—	2	1	no	—
173	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
174	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
175	C₂⁴×C₄	—	2	1	no	—
176	C₂²×D₈	—	2	16	no	—
177	C₂²×D₈	C₂²×C₈₉	1	24	yes	complemented
178	C₂³×C₈	C₂²×C₈₉	1	2	yes	—
179	C₂×#127	—	2	6	no	—
180	C₂×#127	C₂²×C₈₉	1	12	yes	complemented
181	C₂×C₄×D₄	—	2	6	no	—
182	C₂×C₄×D₄	C₂²×C₈₉	1	12	yes	complemented
183	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
184	C₂²×C₂²⋊C₄	—	2	1	no	—
185	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
186	#459	C₂²×C₈₉	1	64	yes	direct product factor
187	C₂×C₄⋊C₈	C₂²×C₈₉	1	12	yes	complemented
188	C₂×#102	C₂²×C₈₉	1	24	yes	complemented
189	C₂⁵	—	2	1	no	—
190	C₂⁵	—	2	2	no	—
191	C₂²×D₄	—	2	3	no	—
192	C₂²×D₄	—	2	8	no	—
193	C₂²×D₄	—	2	6	no	—
194	C₂²×D₄	—	2	12	no	—
195	C₂²×D₄	—	2	12	no	—
196	C₂²×D₄	—	2	4	no	—
197	C₂²×D₄	—	2	8	no	—
198	C₂²×D₄	—	4	8	no	—
199	C₂²×D₄	—	4	8	no	—
200	C₂²×D₄	D₄×C₈₉	1	8	yes	complemented
201	C₂²×D₄	C₂³×C₈₉	1	12	yes	—
202	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
203	C₂³×C₄	—	2	1	no	—
204	C₂³×C₄	—	2	12	no	—
205	C₂³×C₄	—	4	8	no	—
206	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
207	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
208	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
209	C₂×D₈	—	2	96	no	—
210	C₂×D₈	C₂³×C₈₉	1	32	yes	complemented
211	C₂²×C₈	—	2	8	no	—
212	C₂²×C₈	C₂³×C₈₉	1	12	yes	—
213	#127	—	2	24	no	—
214	#127	C₂³×C₈₉	1	16	yes	complemented
215	C₄×D₄	—	2	24	no	—
216	C₄×D₄	C₂³×C₈₉	1	16	yes	complemented
217	C₂×C₄⋊C₄	—	2	3	no	—
218	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
219	C₂×C₂²⋊C₄	—	2	12	no	—
220	C₂×C₄²	D₄×C₈₉	1	6	yes	—
221	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
222	C₄⋊C₈	C₂³×C₈₉	1	16	yes	complemented
223	#102	C₂³×C₈₉	1	32	yes	complemented
224	C₂⁴	—	2	8	no	—
225	C₂⁴	—	2	6	no	—
226	C₂⁴	—	2	12	no	—
227	C₂⁴	—	4	4	no	—
228	C₂⁴	—	4	4	no	—
229	C₂⁴	—	4	8	no	—
230	C₂⁴	—	4	8	no	—
231	C₂⁴	—	4	8	no	—
232	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
233	C₂×D₄	—	2	24	no	—
234	C₂×D₄	—	2	6	no	—
235	C₂×D₄	—	2	24	no	—
236	C₂×D₄	—	2	12	no	—
237	C₂×D₄	—	2	16	no	—
238	C₂×D₄	—	2	16	no	—
239	C₂×D₄	—	2	12	no	—
240	C₂×D₄	—	2	24	no	—
241	C₂×D₄	—	4	48	no	—
242	C₂×D₄	—	4	24	no	—
243	C₂×D₄	—	4	48	no	—
244	C₂×D₄	C₂×D₄×C₈₉	1	24	yes	complemented
245	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
246	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	6	no	—
249	C₂²×C₄	—	2	16	no	—
250	C₂²×C₄	—	4	4	no	—
251	C₂²×C₄	—	4	48	no	—
252	C₂²×C₄	D₈×C₈₉	1	8	yes	complemented
253	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
254	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
255	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
256	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
257	C₂²×C₄	#41×C₈₉	1	4	yes	—
258	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
259	D₈	—	2	64	no	—
260	C₂×C₈	—	2	24	no	—
261	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
262	C₄⋊C₄	—	2	6	no	—
263	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
264	C₂²⋊C₄	—	2	16	no	—
265	C₄²	C₂×D₄×C₈₉	1	12	yes	—
266	C₄²	C₂⁴×C₈₉	1	4	yes	—
267	C₂³	—	2	24	no	—
268	C₂³	—	2	4	no	—
269	C₂³	—	2	8	no	—
270	C₂³	—	4	32	no	—
271	C₂³	—	4	12	no	—
272	C₂³	—	4	12	no	—
273	C₂³	—	4	24	no	—
274	C₂³	—	4	24	no	—
275	C₂³	—	4	24	no	—
276	C₂³	—	8	32	no	—
277	C₂³	#121×C₈₉	1	4	yes	—
278	C₂³	C₂×D₈×C₈₉	1	4	yes	—
279	C₂³	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
280	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
281	D₄	—	2	24	no	—
282	D₄	—	2	8	no	—
283	D₄	—	2	4	no	—
284	D₄	—	2	8	no	—
285	D₄	—	4	32	no	—
286	D₄	—	4	24	no	—
287	D₄	—	4	32	no	—
288	D₄	C₂²×D₄×C₈₉	1	8	yes	complemented
289	C₂×C₄	—	2	12	no	—
290	C₂×C₄	—	2	4	no	—
291	C₂×C₄	—	4	12	no	—
292	C₂×C₄	—	4	32	no	—
293	C₂×C₄	#121×C₈₉	1	12	yes	—
294	C₂×C₄	C₂×D₈×C₈₉	1	24	yes	complemented
295	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
296	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
297	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
298	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
299	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
300	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
301	C₈	—	2	8	no	—
302	C₂²	—	2	8	no	—
303	C₂²	—	4	4	no	—
304	C₂²	—	4	4	no	—
305	C₂²	—	4	48	no	—
306	C₂²	—	4	8	no	—
307	C₂²	—	4	8	no	—
308	C₂²	—	4	8	no	—
309	C₂²	—	8	48	no	—
310	C₂²	#459×C₈₉	1	16	yes	direct product factor
311	C₂²	C₂×#121×C₈₉	1	6	yes	—
312	C₂²	C₂²×D₈×C₈₉	1	6	yes	—
313	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	6	yes	—
314	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
315	C₄	—	2	4	no	—
316	C₄	—	4	4	no	—
317	C₄	C₂×#121×C₈₉	1	6	yes	—
318	C₄	C₂²×D₈×C₈₉	1	8	yes	complemented
319	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
320	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
321	C₂	—	4	8	no	—
322	C₂	—	8	8	no	—
323	C₂	C₂×#459×C₈₉	1	12	yes	direct product factor
324	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
325	C₂	C₂³×D₈×C₈₉	1	1	yes	characteristic
326	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
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×D₈×C₈₉	C₂	semidirect
2. C₂²×#127×C₈₉	C₂	semidirect
3. C₂²×C₄×D₄×C₈₉	C₂	semidirect
4. C₂×#459×C₈₉	C₂	direct (N × H)
5. C₂²×C₄⋊C₈×C₈₉	C₂	semidirect
6. C₂²×#102×C₈₉	C₂	semidirect
13. C₂²×D₈×C₈₉	C₂²	semidirect
16. C₂×#127×C₈₉	C₂²	semidirect
18. C₂×C₄×D₄×C₈₉	C₂²	semidirect
22. #459×C₈₉	C₂²	direct (N × H)
23. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
24. C₂×#102×C₈₉	C₂²	semidirect
36. C₂²×D₄×C₈₉	D₄	semidirect
46. C₂×D₈×C₈₉	C₂³	semidirect
50. #127×C₈₉	C₂³	semidirect
52. C₄×D₄×C₈₉	C₂³	semidirect
58. C₄⋊C₈×C₈₉	C₂³	semidirect
59. #102×C₈₉	C₂³	semidirect
80. C₂×D₄×C₈₉	C₂×D₄	semidirect
88. C₂²×C₄×C₈₉	D₈	semidirect
124. D₄×C₈₉	C₂²×D₄	semidirect
130. C₂×C₄×C₈₉	C₂×D₈	semidirect
146. C₂²×C₈₉	#459	direct (N × H)
154. C₄×C₈₉	C₂²×D₈	semidirect
157. C₂²×#459	C₈₉	direct (N × H)
160. C₂×C₈₉	C₂×#459	direct (N × H)
164. C₂³×D₈	C₂×C₈₉	semidirect
165. C₂²×#127	C₂×C₈₉	semidirect
166. C₂²×C₄×D₄	C₂×C₈₉	semidirect
167. C₂×#459	C₂×C₈₉	direct (N × H)
168. C₂²×C₄⋊C₈	C₂×C₈₉	semidirect
169. C₂²×#102	C₂×C₈₉	semidirect
170. C₈₉	C₂²×#459	direct (N × H)
177. C₂²×D₈	C₂²×C₈₉	semidirect
180. C₂×#127	C₂²×C₈₉	semidirect
182. C₂×C₄×D₄	C₂²×C₈₉	semidirect
186. #459	C₂²×C₈₉	direct (N × H)
187. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
188. C₂×#102	C₂²×C₈₉	semidirect
200. C₂²×D₄	D₄×C₈₉	semidirect
210. C₂×D₈	C₂³×C₈₉	semidirect
214. #127	C₂³×C₈₉	semidirect
216. C₄×D₄	C₂³×C₈₉	semidirect
222. C₄⋊C₈	C₂³×C₈₉	semidirect
223. #102	C₂³×C₈₉	semidirect
244. C₂×D₄	C₂×D₄×C₈₉	semidirect
252. C₂²×C₄	D₈×C₈₉	semidirect
288. D₄	C₂²×D₄×C₈₉	semidirect
294. C₂×C₄	C₂×D₈×C₈₉	semidirect
310. C₂²	#459×C₈₉	direct (N × H)
318. C₄	C₂²×D₈×C₈₉	semidirect
323. C₂	C₂×#459×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×D₈×C₈₉	2
C₂²×#127×C₈₉	2
C₂²×C₄×D₄×C₈₉	2
C₂×#459×C₈₉	2
C₂²×C₄⋊C₈×C₈₉	2
C₂²×#102×C₈₉	2
C₂²×#459	89

Subgroups — C22×#459×C89 #36438251

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#459×C₈₉ #36438251