Subgroups — C₈₉×#62636 #36440484

Order 22784.

2078 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3584	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#576×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3416	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3415	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3414	C₂	1	6	yes	maximal, complemented
6	C₂×#509×C₈₉	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3407	C₂	1	1	yes	maximal, characteristic, complemented
8	#585×C₈₉	—	2	1	no	—
9	C₂×H(5,𝔽₂)×C₈₉	—	2	1	no	—
10	#578×C₈₉	C₂²	1	4	yes	complemented
11	#577×C₈₉	—	2	4	no	—
12	#576×C₈₉	—	2	4	no	—
13	#576×C₈₉	C₂²	1	8	yes	complemented
14	#576×C₈₉	C₂²	1	4	yes	complemented
15	#575×C₈₉	—	2	3	no	—
16	C₂×AGL(1,ℤ/8)×C₈₉	—	2	3	no	—
17	C₂×#135×C₈₉	C₂²	1	3	yes	complemented
18	C₂×#135×C₈₉	C₂²	1	6	yes	complemented
19	C₂²×D₈×C₈₉	C₂²	1	3	yes	complemented
20	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
21	#510×C₈₉	C₂²	1	4	yes	complemented
22	#510×C₈₉	C₂²	1	12	yes	complemented
23	#509×C₈₉	C₂²	1	12	yes	complemented
24	#509×C₈₉	C₂²	1	24	yes	complemented
25	#509×C₈₉	C₂²	1	12	yes	complemented
26	#508×C₈₉	C₂²	1	24	yes	complemented
27	C₂×SD₃₂×C₈₉	C₂²	1	12	yes	complemented
28	C₂×D₁₆×C₈₉	C₂²	1	12	yes	complemented
29	#504×C₈₉	C₂²	1	8	yes	complemented
30	C₂×M₃₂×C₈₉	C₂²	1	6	yes	complemented
31	2₋¹⁺⁴×C₈₉	—	2	4	no	—
32	2₋¹⁺⁴×C₈₉	—	4	1	no	—
33	H(5,𝔽₂)×C₈₉	—	2	8	no	—
34	H(5,𝔽₂)×C₈₉	—	2	4	no	—
35	H(5,𝔽₂)×C₈₉	—	4	4	no	—
36	H(5,𝔽₂)×C₈₉	—	4	3	no	—
37	C₂×#41×C₈₉	—	2	3	no	—
38	C₂×#41×C₈₉	—	2	6	no	—
39	C₂×#41×C₈₉	—	4	4	no	—
40	C₂×#41×C₈₉	—	4	1	no	—
41	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₈₉	—	2	3	no	—
43	C₂²×D₄×C₈₉	—	4	3	no	—
44	#137×C₈₉	—	2	12	no	—
45	AGL(1,ℤ/8)×C₈₉	—	2	24	no	—
46	AGL(1,ℤ/8)×C₈₉	—	2	12	no	—
47	#135×C₈₉	—	2	6	no	—
48	#135×C₈₉	—	2	6	no	—
49	#135×C₈₉	—	2	6	no	—
50	#135×C₈₉	C₂³	1	12	yes	—
51	#135×C₈₉	C₂³	1	4	yes	—
52	#135×C₈₉	C₂³	1	12	yes	complemented
53	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×Q₁₆×C₈₉	C₂³	1	6	yes	complemented
55	C₂×SD₁₆×C₈₉	—	2	3	no	—
56	C₂×SD₁₆×C₈₉	—	2	6	no	—
57	C₂×D₈×C₈₉	—	2	3	no	—
58	C₂×D₈×C₈₉	—	2	6	no	—
59	C₂×D₈×C₈₉	C₂³	1	12	yes	—
60	C₂×D₈×C₈₉	C₂³	1	3	yes	—
61	C₂×D₈×C₈₉	C₂³	1	6	yes	complemented
62	#131×C₈₉	D₄	1	4	yes	—
63	#131×C₈₉	C₂³	1	4	yes	—
64	C₂×M₁₆×C₈₉	D₄	1	3	yes	—
65	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
66	Q₃₂×C₈₉	C₂³	1	8	yes	complemented
67	SD₃₂×C₈₉	C₂³	1	24	yes	complemented
68	SD₃₂×C₈₉	C₂³	1	8	yes	complemented
69	D₁₆×C₈₉	C₂³	1	24	yes	complemented
70	M₃₂×C₈₉	C₂³	1	4	yes	—
71	M₃₂×C₈₉	C₂³	1	12	yes	complemented
72	C₂×C₁₆×C₈₉	C₂³	1	12	yes	complemented
73	C₂⁴×C₈₉	—	4	3	no	—
74	#41×C₈₉	—	2	4	no	—
75	#41×C₈₉	—	2	12	no	—
76	#41×C₈₉	—	2	12	no	—
77	#41×C₈₉	—	4	8	no	—
78	#41×C₈₉	—	4	4	no	—
79	#41×C₈₉	—	4	12	no	—
80	#41×C₈₉	—	4	6	no	—
81	#41×C₈₉	—	4	6	no	—
82	#41×C₈₉	—	4	6	no	—
83	#41×C₈₉	D₈	1	4	yes	—
84	#41×C₈₉	C₂×D₄	1	4	yes	—
85	C₂×Q₈×C₈₉	—	2	1	no	—
86	C₂×Q₈×C₈₉	—	2	6	no	—
87	C₂×Q₈×C₈₉	—	4	4	no	—
88	C₂×Q₈×C₈₉	D₈	1	1	yes	characteristic
89	C₂×D₄×C₈₉	—	2	3	no	—
90	C₂×D₄×C₈₉	—	2	12	no	—
91	C₂×D₄×C₈₉	—	2	6	no	—
92	C₂×D₄×C₈₉	—	4	3	no	—
93	C₂×D₄×C₈₉	—	4	6	no	—
94	C₂×D₄×C₈₉	—	4	24	no	—
95	C₂×D₄×C₈₉	—	4	12	no	—
96	C₂×D₄×C₈₉	—	4	3	no	—
97	C₂×D₄×C₈₉	—	4	6	no	—
98	C₂×D₄×C₈₉	D₈	1	3	yes	—
99	C₂²×C₄×C₈₉	—	4	3	no	—
100	C₂²×C₄×C₈₉	—	4	6	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
102	Q₁₆×C₈₉	—	2	1	no	—
103	Q₁₆×C₈₉	—	2	6	no	—
104	Q₁₆×C₈₉	C₂⁴	1	4	yes	—
105	Q₁₆×C₈₉	C₂⁴	1	2	yes	—
106	SD₁₆×C₈₉	—	2	4	no	—
107	SD₁₆×C₈₉	—	2	12	no	—
108	SD₁₆×C₈₉	—	2	12	no	—
109	D₈×C₈₉	—	2	3	no	—
110	D₈×C₈₉	—	2	12	no	—
111	D₈×C₈₉	—	2	6	no	—
112	D₈×C₈₉	C₂⁴	1	4	yes	—
113	D₈×C₈₉	C₂⁴	1	6	yes	—
114	M₁₆×C₈₉	C₂×D₄	1	12	yes	—
115	C₂×C₈×C₈₉	C₂×D₄	1	3	yes	—
116	C₂×C₈×C₈₉	C₂×D₄	1	6	yes	—
117	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
118	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
119	C₁₆×C₈₉	C₂⁴	1	8	yes	—
120	C₂³×C₈₉	—	4	3	no	—
121	C₂³×C₈₉	—	4	6	no	—
122	C₂³×C₈₉	—	4	12	no	—
123	C₂³×C₈₉	—	16	6	no	—
124	C₂³×C₈₉	C₂×D₈	1	3	yes	—
125	Q₈×C₈₉	—	2	2	no	—
126	Q₈×C₈₉	—	2	4	no	—
127	Q₈×C₈₉	—	4	6	no	—
128	Q₈×C₈₉	—	4	1	no	—
129	Q₈×C₈₉	C₂×D₈	1	4	yes	—
130	D₄×C₈₉	—	2	6	no	—
131	D₄×C₈₉	—	2	4	no	—
132	D₄×C₈₉	—	4	12	no	—
133	D₄×C₈₉	—	4	4	no	—
134	D₄×C₈₉	—	4	12	no	—
135	D₄×C₈₉	—	4	3	no	—
136	D₄×C₈₉	—	4	12	no	—
137	D₄×C₈₉	—	4	6	no	—
138	D₄×C₈₉	C₂×D₈	1	12	yes	—
139	C₂×C₄×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	4	6	no	—
141	C₂×C₄×C₈₉	—	4	4	no	—
142	C₂×C₄×C₈₉	—	4	12	no	—
143	C₂×C₄×C₈₉	—	4	12	no	—
144	C₂×C₄×C₈₉	C₂×D₈	1	3	yes	—
145	C₂×C₄×C₈₉	C₂×D₈	1	6	yes	—
146	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
148	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
149	C₈×C₈₉	C₂²×D₄	1	6	yes	—
150	C₈×C₈₉	C₂⁵	1	1	yes	characteristic
151	C₂²×C₈₉	—	4	3	no	—
152	C₂²×C₈₉	—	4	4	no	—
153	C₂²×C₈₉	—	4	6	no	—
154	C₂²×C₈₉	—	8	6	no	—
155	C₂²×C₈₉	—	16	6	no	—
156	C₂²×C₈₉	—	16	12	no	—
157	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
158	C₂²×C₈₉	C₂²×D₈	1	6	yes	—
159	C₄×C₈₉	—	4	2	no	—
160	C₄×C₈₉	—	4	4	no	—
161	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
162	C₄×C₈₉	C₂²×D₈	1	6	yes	—
163	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
164	#62636	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₈₉	—	2	1	no	—
166	C₂×C₈₉	—	2	6	no	—
167	C₂×C₈₉	—	8	6	no	—
168	C₂×C₈₉	—	8	4	no	—
169	C₂×C₈₉	C₂³×D₈	1	1	yes	characteristic
170	#3584	C₂×C₈₉	1	1	yes	characteristic, complemented
171	C₂×#576	C₂×C₈₉	1	1	yes	characteristic, complemented
172	#3416	C₂×C₈₉	1	8	yes	complemented
173	#3415	C₂×C₈₉	1	8	yes	complemented
174	#3414	C₂×C₈₉	1	6	yes	complemented
175	C₂×#509	C₂×C₈₉	1	6	yes	complemented
176	#3407	C₂×C₈₉	1	1	yes	characteristic, complemented
177	C₈₉	#62636	1	1	yes	characteristic, direct product factor, Sylow
178	#585	—	2	1	no	—
179	C₂×H(5,𝔽₂)	—	2	1	no	—
180	#578	C₂²×C₈₉	1	4	yes	complemented
181	#577	—	2	4	no	—
182	#576	—	2	4	no	—
183	#576	C₂²×C₈₉	1	8	yes	complemented
184	#576	C₂²×C₈₉	1	4	yes	complemented
185	#575	—	2	3	no	—
186	C₂×AGL(1,ℤ/8)	—	2	3	no	—
187	C₂×#135	C₂²×C₈₉	1	3	yes	complemented
188	C₂×#135	C₂²×C₈₉	1	6	yes	complemented
189	C₂²×D₈	C₂²×C₈₉	1	3	yes	complemented
190	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
191	#510	C₂²×C₈₉	1	4	yes	complemented
192	#510	C₂²×C₈₉	1	12	yes	complemented
193	#509	C₂²×C₈₉	1	12	yes	complemented
194	#509	C₂²×C₈₉	1	24	yes	complemented
195	#509	C₂²×C₈₉	1	12	yes	complemented
196	#508	C₂²×C₈₉	1	24	yes	complemented
197	C₂×SD₃₂	C₂²×C₈₉	1	12	yes	complemented
198	C₂×D₁₆	C₂²×C₈₉	1	12	yes	complemented
199	#504	C₂²×C₈₉	1	8	yes	complemented
200	C₂×M₃₂	C₂²×C₈₉	1	6	yes	complemented
201	2₋¹⁺⁴	—	2	4	no	—
202	2₋¹⁺⁴	—	4	1	no	—
203	H(5,𝔽₂)	—	2	8	no	—
204	H(5,𝔽₂)	—	2	4	no	—
205	H(5,𝔽₂)	—	4	4	no	—
206	H(5,𝔽₂)	—	4	3	no	—
207	C₂×#41	—	2	3	no	—
208	C₂×#41	—	2	6	no	—
209	C₂×#41	—	4	4	no	—
210	C₂×#41	—	4	1	no	—
211	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
212	C₂²×D₄	—	2	3	no	—
213	C₂²×D₄	—	4	3	no	—
214	#137	—	2	12	no	—
215	AGL(1,ℤ/8)	—	2	24	no	—
216	AGL(1,ℤ/8)	—	2	12	no	—
217	#135	—	2	6	no	—
218	#135	—	2	6	no	—
219	#135	—	2	6	no	—
220	#135	C₂³×C₈₉	1	4	yes	—
221	#135	C₂³×C₈₉	1	12	yes	—
222	#135	C₂³×C₈₉	1	12	yes	complemented
223	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
224	C₂×Q₁₆	C₂³×C₈₉	1	6	yes	complemented
225	C₂×SD₁₆	—	2	3	no	—
226	C₂×SD₁₆	—	2	6	no	—
227	C₂×D₈	—	2	3	no	—
228	C₂×D₈	—	2	6	no	—
229	C₂×D₈	C₂³×C₈₉	1	3	yes	—
230	C₂×D₈	C₂³×C₈₉	1	12	yes	—
231	C₂×D₈	C₂³×C₈₉	1	6	yes	complemented
232	#131	D₄×C₈₉	1	4	yes	—
233	#131	C₂³×C₈₉	1	4	yes	—
234	C₂×M₁₆	D₄×C₈₉	1	3	yes	—
235	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
236	Q₃₂	C₂³×C₈₉	1	8	yes	complemented
237	SD₃₂	C₂³×C₈₉	1	24	yes	complemented
238	SD₃₂	C₂³×C₈₉	1	8	yes	complemented
239	D₁₆	C₂³×C₈₉	1	24	yes	complemented
240	M₃₂	C₂³×C₈₉	1	4	yes	—
241	M₃₂	C₂³×C₈₉	1	12	yes	complemented
242	C₂×C₁₆	C₂³×C₈₉	1	12	yes	complemented
243	C₂⁴	—	4	3	no	—
244	#41	—	2	4	no	—
245	#41	—	2	12	no	—
246	#41	—	2	12	no	—
247	#41	—	4	8	no	—
248	#41	—	4	4	no	—
249	#41	—	4	12	no	—
250	#41	—	4	6	no	—
251	#41	—	4	6	no	—
252	#41	—	4	6	no	—
253	#41	D₈×C₈₉	1	4	yes	—
254	#41	C₂×D₄×C₈₉	1	4	yes	—
255	C₂×Q₈	—	2	1	no	—
256	C₂×Q₈	—	2	6	no	—
257	C₂×Q₈	—	4	4	no	—
258	C₂×Q₈	D₈×C₈₉	1	1	yes	characteristic
259	C₂×D₄	—	2	3	no	—
260	C₂×D₄	—	2	12	no	—
261	C₂×D₄	—	2	6	no	—
262	C₂×D₄	—	4	3	no	—
263	C₂×D₄	—	4	6	no	—
264	C₂×D₄	—	4	24	no	—
265	C₂×D₄	—	4	12	no	—
266	C₂×D₄	—	4	3	no	—
267	C₂×D₄	—	4	6	no	—
268	C₂×D₄	D₈×C₈₉	1	3	yes	—
269	C₂²×C₄	—	4	3	no	—
270	C₂²×C₄	—	4	6	no	—
271	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
272	Q₁₆	—	2	1	no	—
273	Q₁₆	—	2	6	no	—
274	Q₁₆	C₂⁴×C₈₉	1	4	yes	—
275	Q₁₆	C₂⁴×C₈₉	1	2	yes	—
276	SD₁₆	—	2	4	no	—
277	SD₁₆	—	2	12	no	—
278	SD₁₆	—	2	12	no	—
279	D₈	—	2	3	no	—
280	D₈	—	2	12	no	—
281	D₈	—	2	6	no	—
282	D₈	C₂⁴×C₈₉	1	4	yes	—
283	D₈	C₂⁴×C₈₉	1	6	yes	—
284	M₁₆	C₂×D₄×C₈₉	1	12	yes	—
285	C₂×C₈	C₂×D₄×C₈₉	1	3	yes	—
286	C₂×C₈	C₂×D₄×C₈₉	1	6	yes	—
287	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
288	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
289	C₁₆	C₂⁴×C₈₉	1	8	yes	—
290	C₂³	—	4	3	no	—
291	C₂³	—	4	6	no	—
292	C₂³	—	4	12	no	—
293	C₂³	—	16	6	no	—
294	C₂³	C₂×D₈×C₈₉	1	3	yes	—
295	Q₈	—	2	2	no	—
296	Q₈	—	2	4	no	—
297	Q₈	—	4	6	no	—
298	Q₈	—	4	1	no	—
299	Q₈	C₂×D₈×C₈₉	1	4	yes	—
300	D₄	—	2	6	no	—
301	D₄	—	2	4	no	—
302	D₄	—	4	12	no	—
303	D₄	—	4	4	no	—
304	D₄	—	4	12	no	—
305	D₄	—	4	3	no	—
306	D₄	—	4	12	no	—
307	D₄	—	4	6	no	—
308	D₄	C₂×D₈×C₈₉	1	12	yes	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	6	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	12	no	—
313	C₂×C₄	—	4	12	no	—
314	C₂×C₄	C₂×D₈×C₈₉	1	3	yes	—
315	C₂×C₄	C₂×D₈×C₈₉	1	6	yes	—
316	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
317	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
318	C₈	C₂²×D₄×C₈₉	1	1	yes	characteristic
319	C₈	C₂²×D₄×C₈₉	1	6	yes	—
320	C₈	C₂⁵×C₈₉	1	1	yes	characteristic
321	C₂²	—	4	3	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	6	no	—
324	C₂²	—	8	6	no	—
325	C₂²	—	16	12	no	—
326	C₂²	—	16	6	no	—
327	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
328	C₂²	C₂²×D₈×C₈₉	1	6	yes	—
329	C₄	—	4	2	no	—
330	C₄	—	4	4	no	—
331	C₄	C₂²×D₈×C₈₉	1	1	yes	characteristic
332	C₄	C₂²×D₈×C₈₉	1	6	yes	—
333	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
334	C₂	—	2	1	no	—
335	C₂	—	2	6	no	—
336	C₂	—	8	6	no	—
337	C₂	—	8	4	no	—
338	C₂	C₂³×D₈×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₈₉	C₂³×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₈₉
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈₉ ◁ C₂×#41×C₈₉ ◁ C₂×#131×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3584	C₂	semidirect
2. C₂×#576×C₈₉	C₂	semidirect
3. C₈₉×#3416	C₂	semidirect
4. C₈₉×#3415	C₂	semidirect
5. C₈₉×#3414	C₂	semidirect
6. C₂×#509×C₈₉	C₂	semidirect
7. C₈₉×#3407	C₂	semidirect
10. #578×C₈₉	C₂²	semidirect
13. #576×C₈₉	C₂²	semidirect
14. #576×C₈₉	C₂²	semidirect
17. C₂×#135×C₈₉	C₂²	semidirect
18. C₂×#135×C₈₉	C₂²	semidirect
19. C₂²×D₈×C₈₉	C₂²	semidirect
21. #510×C₈₉	C₂²	semidirect
22. #510×C₈₉	C₂²	semidirect
23. #509×C₈₉	C₂²	semidirect
24. #509×C₈₉	C₂²	semidirect
25. #509×C₈₉	C₂²	semidirect
26. #508×C₈₉	C₂²	semidirect
27. C₂×SD₃₂×C₈₉	C₂²	semidirect
28. C₂×D₁₆×C₈₉	C₂²	semidirect
29. #504×C₈₉	C₂²	semidirect
30. C₂×M₃₂×C₈₉	C₂²	semidirect
52. #135×C₈₉	C₂³	semidirect
54. C₂×Q₁₆×C₈₉	C₂³	semidirect
61. C₂×D₈×C₈₉	C₂³	semidirect
66. Q₃₂×C₈₉	C₂³	semidirect
67. SD₃₂×C₈₉	C₂³	semidirect
68. SD₃₂×C₈₉	C₂³	semidirect
69. D₁₆×C₈₉	C₂³	semidirect
71. M₃₂×C₈₉	C₂³	semidirect
72. C₂×C₁₆×C₈₉	C₂³	semidirect
164. #62636	C₈₉	direct (N × H)
170. #3584	C₂×C₈₉	semidirect
171. C₂×#576	C₂×C₈₉	semidirect
172. #3416	C₂×C₈₉	semidirect
173. #3415	C₂×C₈₉	semidirect
174. #3414	C₂×C₈₉	semidirect
175. C₂×#509	C₂×C₈₉	semidirect
176. #3407	C₂×C₈₉	semidirect
177. C₈₉	#62636	direct (N × H)
180. #578	C₂²×C₈₉	semidirect
183. #576	C₂²×C₈₉	semidirect
184. #576	C₂²×C₈₉	semidirect
187. C₂×#135	C₂²×C₈₉	semidirect
188. C₂×#135	C₂²×C₈₉	semidirect
189. C₂²×D₈	C₂²×C₈₉	semidirect
191. #510	C₂²×C₈₉	semidirect
192. #510	C₂²×C₈₉	semidirect
193. #509	C₂²×C₈₉	semidirect
194. #509	C₂²×C₈₉	semidirect
195. #509	C₂²×C₈₉	semidirect
196. #508	C₂²×C₈₉	semidirect
197. C₂×SD₃₂	C₂²×C₈₉	semidirect
198. C₂×D₁₆	C₂²×C₈₉	semidirect
199. #504	C₂²×C₈₉	semidirect
200. C₂×M₃₂	C₂²×C₈₉	semidirect
222. #135	C₂³×C₈₉	semidirect
224. C₂×Q₁₆	C₂³×C₈₉	semidirect
231. C₂×D₈	C₂³×C₈₉	semidirect
236. Q₃₂	C₂³×C₈₉	semidirect
237. SD₃₂	C₂³×C₈₉	semidirect
238. SD₃₂	C₂³×C₈₉	semidirect
239. D₁₆	C₂³×C₈₉	semidirect
241. M₃₂	C₂³×C₈₉	semidirect
242. C₂×C₁₆	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3584	2
C₂×#576×C₈₉	2
C₈₉×#3416	2
C₈₉×#3415	2
C₈₉×#3414	2
C₂×#509×C₈₉	2
C₈₉×#3407	2
#62636	89

Subgroups — C89×#62636 #36440484

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62636 #36440484