Subgroups — C₂²×#482×C₈₉ #36438350

Order 22784.

2702 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#482×C₈₉	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#107×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#106×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₂²⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₈₉	—	2	1	no	—
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#121×C₈₉	—	2	6	no	—
15	C₂×#121×C₈₉	C₂²	1	12	yes	—
16	C₂×#117×C₈₉	—	2	6	no	—
17	C₂×#117×C₈₉	C₂²	1	12	yes	complemented
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
22	C₂²×C₂²⋊C₄×C₈₉	—	2	1	no	—
23	C₂²×C₄²×C₈₉	—	2	1	no	—
24	#482×C₈₉	C₂²	1	64	yes	direct product factor
25	C₂×#107×C₈₉	C₂²	1	12	yes	complemented
26	C₂×#106×C₈₉	C₂²	1	12	yes	complemented
27	C₂×#102×C₈₉	C₂²	1	12	yes	complemented
28	C₂×#102×C₈₉	C₂²	1	12	yes	complemented
29	C₂×C₂²⋊C₈×C₈₉	C₂²	1	12	yes	complemented
30	C₂⁵×C₈₉	—	2	1	no	—
31	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
32	C₂²×D₄×C₈₉	—	2	12	no	—
33	C₂²×D₄×C₈₉	—	2	3	no	—
34	C₂²×D₄×C₈₉	—	2	4	no	—
35	C₂²×D₄×C₈₉	—	2	4	no	—
36	C₂²×D₄×C₈₉	—	4	8	no	—
37	C₂²×D₄×C₈₉	C₂³	1	6	yes	—
38	C₂³×C₄×C₈₉	—	2	4	no	—
39	C₂³×C₄×C₈₉	—	2	4	no	—
40	C₂³×C₄×C₈₉	—	2	1	no	—
41	C₂³×C₄×C₈₉	—	2	1	no	—
42	C₂³×C₄×C₈₉	—	2	1	no	—
43	C₂³×C₄×C₈₉	D₄	1	6	yes	—
44	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₈₉	—	2	4	no	—
48	C₂²×C₈×C₈₉	—	2	4	no	—
49	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
50	C₂²×C₈×C₈₉	C₂³	1	6	yes	—
51	#121×C₈₉	—	2	24	no	—
52	#121×C₈₉	C₂³	1	16	yes	—
53	#117×C₈₉	—	2	24	no	—
54	#117×C₈₉	C₂³	1	16	yes	complemented
55	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
61	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	12	no	—
63	C₂×C₄²×C₈₉	—	2	12	no	—
64	#107×C₈₉	C₂³	1	16	yes	complemented
65	#106×C₈₉	C₂³	1	16	yes	complemented
66	#102×C₈₉	C₂³	1	16	yes	complemented
67	#102×C₈₉	C₂³	1	16	yes	complemented
68	C₂²⋊C₈×C₈₉	C₂³	1	16	yes	complemented
69	C₂⁴×C₈₉	—	2	4	no	—
70	C₂⁴×C₈₉	—	2	4	no	—
71	C₂⁴×C₈₉	—	2	4	no	—
72	C₂⁴×C₈₉	—	2	6	no	—
73	C₂⁴×C₈₉	—	4	4	no	—
74	C₂⁴×C₈₉	—	4	4	no	—
75	C₂⁴×C₈₉	—	4	4	no	—
76	C₂⁴×C₈₉	C₂×D₄	1	6	yes	—
77	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₈₉	—	2	16	no	—
79	C₂×D₄×C₈₉	—	2	6	no	—
80	C₂×D₄×C₈₉	—	2	12	no	—
81	C₂×D₄×C₈₉	—	2	12	no	—
82	C₂×D₄×C₈₉	—	4	48	no	—
83	C₂×D₄×C₈₉	—	4	12	no	—
84	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
85	C₂²×C₄×C₈₉	—	2	4	no	—
86	C₂²×C₄×C₈₉	—	2	24	no	—
87	C₂²×C₄×C₈₉	—	2	12	no	—
88	C₂²×C₄×C₈₉	—	2	12	no	—
89	C₂²×C₄×C₈₉	—	2	6	no	—
90	C₂²×C₄×C₈₉	—	2	6	no	—
91	C₂²×C₄×C₈₉	—	2	6	no	—
92	C₂²×C₄×C₈₉	—	4	4	no	—
93	C₂²×C₄×C₈₉	—	4	4	no	—
94	C₂²×C₄×C₈₉	—	4	4	no	—
95	C₂²×C₄×C₈₉	C₂×D₄	1	6	yes	—
96	C₂²×C₄×C₈₉	C₂×D₄	1	12	yes	—
97	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
98	C₂²×C₄×C₈₉	#41	1	4	yes	—
99	C₂²×C₄×C₈₉	#41	1	4	yes	—
100	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
101	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
102	C₂×C₈×C₈₉	—	2	12	no	—
103	C₂×C₈×C₈₉	—	2	12	no	—
104	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
105	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
106	C₄⋊C₄×C₈₉	—	2	6	no	—
107	C₄⋊C₄×C₈₉	—	2	6	no	—
108	C₄⋊C₄×C₈₉	—	2	6	no	—
109	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
110	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
111	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
112	C₂²⋊C₄×C₈₉	—	2	16	no	—
113	C₂²⋊C₄×C₈₉	—	2	16	no	—
114	C₄²×C₈₉	—	2	16	no	—
115	C₂³×C₈₉	—	2	12	no	—
116	C₂³×C₈₉	—	2	12	no	—
117	C₂³×C₈₉	—	2	12	no	—
118	C₂³×C₈₉	—	2	4	no	—
119	C₂³×C₈₉	—	4	16	no	—
120	C₂³×C₈₉	—	4	12	no	—
121	C₂³×C₈₉	—	4	12	no	—
122	C₂³×C₈₉	—	4	12	no	—
123	C₂³×C₈₉	—	8	16	no	—
124	C₂³×C₈₉	#123	1	4	yes	—
125	C₂³×C₈₉	#135	1	4	yes	—
126	C₂³×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
127	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
128	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
129	D₄×C₈₉	—	2	4	no	—
130	D₄×C₈₉	—	2	4	no	—
131	D₄×C₈₉	—	4	32	no	—
132	D₄×C₈₉	—	4	12	no	—
133	C₂×C₄×C₈₉	—	2	12	no	—
134	C₂×C₄×C₈₉	—	2	24	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	4	no	—
138	C₂×C₄×C₈₉	—	2	4	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	4	12	no	—
141	C₂×C₄×C₈₉	—	4	12	no	—
142	C₂×C₄×C₈₉	—	4	12	no	—
143	C₂×C₄×C₈₉	#123	1	12	yes	—
144	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
146	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
147	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
148	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
149	C₈×C₈₉	—	2	4	no	—
150	C₈×C₈₉	—	2	4	no	—
151	C₂²×C₈₉	—	2	4	no	—
152	C₂²×C₈₉	—	2	4	no	—
153	C₂²×C₈₉	—	2	4	no	—
154	C₂²×C₈₉	—	4	24	no	—
155	C₂²×C₈₉	—	4	4	no	—
156	C₂²×C₈₉	—	4	4	no	—
157	C₂²×C₈₉	—	4	4	no	—
158	C₂²×C₈₉	—	8	24	no	—
159	C₂²×C₈₉	#482	1	16	yes	direct product factor
160	C₂²×C₈₉	C₂×#123	1	6	yes	—
161	C₂²×C₈₉	C₂×#135	1	6	yes	—
162	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
163	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
164	C₄×C₈₉	—	2	4	no	—
165	C₄×C₈₉	—	4	4	no	—
166	C₄×C₈₉	—	4	4	no	—
167	C₄×C₈₉	—	4	4	no	—
168	C₄×C₈₉	C₂×#123	1	6	yes	—
169	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
170	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
171	C₂²×#482	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₈₉	—	4	4	no	—
173	C₂×C₈₉	—	8	4	no	—
174	C₂×C₈₉	C₂×#482	1	12	yes	direct product factor
175	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
176	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
177	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic
179	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
180	C₂×#482	C₂×C₈₉	1	24	yes	direct product factor
181	C₂²×#107	C₂×C₈₉	1	1	yes	characteristic, complemented
182	C₂²×#106	C₂×C₈₉	1	1	yes	characteristic, complemented
183	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
184	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
185	C₂²×C₂²⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
186	C₈₉	C₂²×#482	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×D₄	—	2	1	no	—
188	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
189	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
190	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
191	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
192	C₂×#121	—	2	6	no	—
193	C₂×#121	C₂²×C₈₉	1	12	yes	—
194	C₂×#117	—	2	6	no	—
195	C₂×#117	C₂²×C₈₉	1	12	yes	complemented
196	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
197	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
198	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
199	C₂²×C₂²⋊C₄	—	2	1	no	—
200	C₂²×C₂²⋊C₄	—	2	1	no	—
201	C₂²×C₄²	—	2	1	no	—
202	#482	C₂²×C₈₉	1	64	yes	direct product factor
203	C₂×#107	C₂²×C₈₉	1	12	yes	complemented
204	C₂×#106	C₂²×C₈₉	1	12	yes	complemented
205	C₂×#102	C₂²×C₈₉	1	12	yes	complemented
206	C₂×#102	C₂²×C₈₉	1	12	yes	complemented
207	C₂×C₂²⋊C₈	C₂²×C₈₉	1	12	yes	complemented
208	C₂⁵	—	2	1	no	—
209	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
210	C₂²×D₄	—	2	12	no	—
211	C₂²×D₄	—	2	3	no	—
212	C₂²×D₄	—	2	4	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	4	8	no	—
215	C₂²×D₄	C₂³×C₈₉	1	6	yes	—
216	C₂³×C₄	—	2	4	no	—
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	—	2	1	no	—
219	C₂³×C₄	—	2	1	no	—
220	C₂³×C₄	—	2	1	no	—
221	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
222	C₂³×C₄	D₄×C₈₉	1	6	yes	—
223	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
224	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
225	C₂²×C₈	—	2	4	no	—
226	C₂²×C₈	—	2	4	no	—
227	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
228	C₂²×C₈	C₂³×C₈₉	1	6	yes	—
229	#121	—	2	24	no	—
230	#121	C₂³×C₈₉	1	16	yes	—
231	#117	—	2	24	no	—
232	#117	C₂³×C₈₉	1	16	yes	complemented
233	C₂×C₄⋊C₄	—	2	3	no	—
234	C₂×C₄⋊C₄	—	2	3	no	—
235	C₂×C₄⋊C₄	—	2	3	no	—
236	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
237	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
238	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
239	C₂×C₂²⋊C₄	—	2	12	no	—
240	C₂×C₂²⋊C₄	—	2	12	no	—
241	C₂×C₄²	—	2	12	no	—
242	#107	C₂³×C₈₉	1	16	yes	complemented
243	#106	C₂³×C₈₉	1	16	yes	complemented
244	#102	C₂³×C₈₉	1	16	yes	complemented
245	#102	C₂³×C₈₉	1	16	yes	complemented
246	C₂²⋊C₈	C₂³×C₈₉	1	16	yes	complemented
247	C₂⁴	—	2	4	no	—
248	C₂⁴	—	2	4	no	—
249	C₂⁴	—	2	4	no	—
250	C₂⁴	—	2	6	no	—
251	C₂⁴	—	4	4	no	—
252	C₂⁴	—	4	4	no	—
253	C₂⁴	—	4	4	no	—
254	C₂⁴	C₂×D₄×C₈₉	1	6	yes	—
255	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
256	C₂×D₄	—	2	16	no	—
257	C₂×D₄	—	2	6	no	—
258	C₂×D₄	—	2	12	no	—
259	C₂×D₄	—	2	12	no	—
260	C₂×D₄	—	4	48	no	—
261	C₂×D₄	—	4	12	no	—
262	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	24	no	—
265	C₂²×C₄	—	2	12	no	—
266	C₂²×C₄	—	2	12	no	—
267	C₂²×C₄	—	2	6	no	—
268	C₂²×C₄	—	2	6	no	—
269	C₂²×C₄	—	2	6	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	C₂×D₄×C₈₉	1	6	yes	—
274	C₂²×C₄	C₂×D₄×C₈₉	1	12	yes	—
275	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
276	C₂²×C₄	#41×C₈₉	1	4	yes	—
277	C₂²×C₄	#41×C₈₉	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
279	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
280	C₂×C₈	—	2	12	no	—
281	C₂×C₈	—	2	12	no	—
282	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
283	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
284	C₄⋊C₄	—	2	6	no	—
285	C₄⋊C₄	—	2	6	no	—
286	C₄⋊C₄	—	2	6	no	—
287	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
288	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
289	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
290	C₂²⋊C₄	—	2	16	no	—
291	C₂²⋊C₄	—	2	16	no	—
292	C₄²	—	2	16	no	—
293	C₂³	—	2	12	no	—
294	C₂³	—	2	12	no	—
295	C₂³	—	2	12	no	—
296	C₂³	—	2	4	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	4	12	no	—
299	C₂³	—	4	12	no	—
300	C₂³	—	4	12	no	—
301	C₂³	—	8	16	no	—
302	C₂³	#123×C₈₉	1	4	yes	—
303	C₂³	#135×C₈₉	1	4	yes	—
304	C₂³	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
305	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
306	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
307	D₄	—	2	4	no	—
308	D₄	—	2	4	no	—
309	D₄	—	4	32	no	—
310	D₄	—	4	12	no	—
311	C₂×C₄	—	2	12	no	—
312	C₂×C₄	—	2	24	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	4	12	no	—
319	C₂×C₄	—	4	12	no	—
320	C₂×C₄	—	4	12	no	—
321	C₂×C₄	#123×C₈₉	1	12	yes	—
322	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
323	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
324	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
325	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
326	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
327	C₈	—	2	4	no	—
328	C₈	—	2	4	no	—
329	C₂²	—	2	4	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	24	no	—
333	C₂²	—	4	4	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	8	24	no	—
337	C₂²	#482×C₈₉	1	16	yes	direct product factor
338	C₂²	C₂×#123×C₈₉	1	6	yes	—
339	C₂²	C₂×#135×C₈₉	1	6	yes	—
340	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	6	yes	—
341	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
342	C₄	—	2	4	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	4	4	no	—
346	C₄	C₂×#123×C₈₉	1	6	yes	—
347	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
348	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
349	C₂	—	4	4	no	—
350	C₂	—	8	4	no	—
351	C₂	C₂×#482×C₈₉	1	12	yes	direct product factor
352	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
353	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
354	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
prime radical	C₂²×#121×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₂×#482×C₈₉	C₂	direct (N × H)
4. C₂²×#107×C₈₉	C₂	semidirect
5. C₂²×#106×C₈₉	C₂	semidirect
6. C₂²×#102×C₈₉	C₂	semidirect
7. C₂²×#102×C₈₉	C₂	semidirect
8. C₂²×C₂²⋊C₈×C₈₉	C₂	semidirect
17. C₂×#117×C₈₉	C₂²	semidirect
24. #482×C₈₉	C₂²	direct (N × H)
25. C₂×#107×C₈₉	C₂²	semidirect
26. C₂×#106×C₈₉	C₂²	semidirect
27. C₂×#102×C₈₉	C₂²	semidirect
28. C₂×#102×C₈₉	C₂²	semidirect
29. C₂×C₂²⋊C₈×C₈₉	C₂²	semidirect
54. #117×C₈₉	C₂³	semidirect
64. #107×C₈₉	C₂³	semidirect
65. #106×C₈₉	C₂³	semidirect
66. #102×C₈₉	C₂³	semidirect
67. #102×C₈₉	C₂³	semidirect
68. C₂²⋊C₈×C₈₉	C₂³	semidirect
159. C₂²×C₈₉	#482	direct (N × H)
171. C₂²×#482	C₈₉	direct (N × H)
174. C₂×C₈₉	C₂×#482	direct (N × H)
179. C₂²×#117	C₂×C₈₉	semidirect
180. C₂×#482	C₂×C₈₉	direct (N × H)
181. C₂²×#107	C₂×C₈₉	semidirect
182. C₂²×#106	C₂×C₈₉	semidirect
183. C₂²×#102	C₂×C₈₉	semidirect
184. C₂²×#102	C₂×C₈₉	semidirect
185. C₂²×C₂²⋊C₈	C₂×C₈₉	semidirect
186. C₈₉	C₂²×#482	direct (N × H)
195. C₂×#117	C₂²×C₈₉	semidirect
202. #482	C₂²×C₈₉	direct (N × H)
203. C₂×#107	C₂²×C₈₉	semidirect
204. C₂×#106	C₂²×C₈₉	semidirect
205. C₂×#102	C₂²×C₈₉	semidirect
206. C₂×#102	C₂²×C₈₉	semidirect
207. C₂×C₂²⋊C₈	C₂²×C₈₉	semidirect
232. #117	C₂³×C₈₉	semidirect
242. #107	C₂³×C₈₉	semidirect
243. #106	C₂³×C₈₉	semidirect
244. #102	C₂³×C₈₉	semidirect
245. #102	C₂³×C₈₉	semidirect
246. C₂²⋊C₈	C₂³×C₈₉	semidirect
337. C₂²	#482×C₈₉	direct (N × H)
351. C₂	C₂×#482×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
C₂²×#121×C₈₉	2
C₂²×#117×C₈₉	2
C₂×#482×C₈₉	2
C₂²×#107×C₈₉	2
C₂²×#106×C₈₉	2
C₂²×#102×C₈₉	2
C₂²×C₂²⋊C₈×C₈₉	2
C₂²×#482	89

Subgroups — C22×#482×C89 #36438350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#482×C₈₉ #36438350