Subgroups — C₈₉×#33650 #36411498

Order 22784.

588 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3058	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2234	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2234	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2233	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2232	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2159	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2158	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#357×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2113	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
14	#535×C₈₉	—	2	1	no	—
15	#520×C₈₉	—	2	1	no	—
16	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	#469×C₈₉	—	2	2	no	—
19	#466×C₈₉	C₂²	1	2	yes	—
20	#466×C₈₉	C₂²	1	2	yes	—
21	#428×C₈₉	—	2	2	no	—
22	#428×C₈₉	—	2	1	no	—
23	#427×C₈₉	C₂²	1	1	yes	characteristic
24	#427×C₈₉	C₂²	1	1	yes	characteristic
25	#427×C₈₉	C₂²	1	2	yes	complemented
26	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
28	#418×C₈₉	—	2	1	no	—
29	#367×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	#367×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	#367×C₈₉	C₂²	1	2	yes	complemented
32	#366×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#366×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	#366×C₈₉	C₂²	1	2	yes	complemented
35	#357×C₈₉	C₂²	1	2	yes	—
36	#357×C₈₉	C₂²	1	2	yes	—
37	#357×C₈₉	C₂²	1	2	yes	—
38	#357×C₈₉	C₂²	1	2	yes	—
39	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	complemented
40	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	complemented
41	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
42	C₂²×D₄×C₈₉	—	2	1	no	—
43	C₂×D₈×C₈₉	—	2	1	no	—
44	C₂×D₈×C₈₉	—	2	2	no	—
45	C₂×D₈×C₈₉	—	2	2	no	—
46	C₂×D₈×C₈₉	C₂³	1	2	yes	—
47	#131×C₈₉	—	2	2	no	—
48	#131×C₈₉	—	2	2	no	—
49	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
50	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
51	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	#127×C₈₉	—	4	1	no	—
54	#124×C₈₉	—	4	1	no	—
55	#121×C₈₉	—	2	2	no	—
56	#121×C₈₉	—	2	2	no	—
57	#120×C₈₉	—	4	2	no	—
58	C₄×Q₈×C₈₉	—	4	1	no	—
59	C₄×D₄×C₈₉	—	4	2	no	—
60	C₄×D₄×C₈₉	—	4	1	no	—
61	#117×C₈₉	—	2	1	no	—
62	#117×C₈₉	—	2	1	no	—
63	#117×C₈₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
66	M₃₂×C₈₉	—	2	2	no	—
67	C₂×C₁₆×C₈₉	—	2	2	no	—
68	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
71	#107×C₈₉	—	2	1	no	—
72	#107×C₈₉	—	2	2	no	—
73	#107×C₈₉	C₂³	1	2	yes	—
74	#107×C₈₉	C₂³	1	1	yes	characteristic
75	#107×C₈₉	C₂³	1	1	yes	characteristic
76	#107×C₈₉	C₂³	1	1	yes	characteristic
77	#107×C₈₉	C₂³	1	1	yes	characteristic
78	#106×C₈₉	—	2	1	no	—
79	#106×C₈₉	—	2	1	no	—
80	#106×C₈₉	—	2	2	no	—
81	#102×C₈₉	—	2	2	no	—
82	#102×C₈₉	—	2	2	no	—
83	C₂⁴×C₈₉	—	4	1	no	—
84	#41×C₈₉	—	2	2	no	—
85	#41×C₈₉	—	2	2	no	—
86	C₂×Q₈×C₈₉	D₈	1	1	yes	characteristic
87	C₂×D₄×C₈₉	—	2	2	no	—
88	C₂×D₄×C₈₉	—	4	2	no	—
89	C₂×D₄×C₈₉	—	4	2	no	—
90	C₂×D₄×C₈₉	—	4	2	no	—
91	C₂×D₄×C₈₉	—	4	1	no	—
92	C₂×D₄×C₈₉	—	4	2	no	—
93	C₂×D₄×C₈₉	D₈	1	2	yes	—
94	C₂×D₄×C₈₉	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	—	4	2	no	—
96	C₂²×C₄×C₈₉	—	4	1	no	—
97	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
99	D₈×C₈₉	—	2	2	no	—
100	D₈×C₈₉	—	2	2	no	—
101	D₈×C₈₉	—	4	2	no	—
102	M₁₆×C₈₉	—	2	2	no	—
103	M₁₆×C₈₉	—	2	4	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	#41	1	2	yes	—
109	C₂×C₈×C₈₉	#41	1	2	yes	—
110	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
111	C₄⋊C₄×C₈₉	—	2	1	no	—
112	C₄⋊C₄×C₈₉	—	2	1	no	—
113	C₄⋊C₄×C₈₉	—	2	1	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₄⋊C₄×C₈₉	—	4	2	no	—
117	C₄⋊C₄×C₈₉	—	4	1	no	—
118	C₂²⋊C₄×C₈₉	—	4	2	no	—
119	C₂²⋊C₄×C₈₉	—	4	1	no	—
120	C₂²⋊C₄×C₈₉	—	4	1	no	—
121	C₂²⋊C₄×C₈₉	—	4	2	no	—
122	C₂²⋊C₄×C₈₉	—	4	2	no	—
123	C₄²×C₈₉	—	4	2	no	—
124	C₄²×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	—	4	1	no	—
126	C₁₆×C₈₉	—	2	1	no	—
127	C₁₆×C₈₉	—	2	1	no	—
128	C₁₆×C₈₉	—	2	2	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	8	2	no	—
131	C₂³×C₈₉	—	16	1	no	—
132	C₂³×C₈₉	—	16	1	no	—
133	C₂³×C₈₉	C₂×D₈	1	2	yes	—
134	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
135	Q₈×C₈₉	—	2	2	no	—
136	D₄×C₈₉	—	2	4	no	—
137	D₄×C₈₉	—	2	2	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	—	8	2	no	—
141	D₄×C₈₉	—	16	2	no	—
142	D₄×C₈₉	—	16	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	16	1	no	—
151	C₂×C₄×C₈₉	—	16	2	no	—
152	C₂×C₄×C₈₉	#123	1	2	yes	—
153	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₈₉	#137	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₈₉	—	2	2	no	—
158	C₈×C₈₉	#123	1	2	yes	—
159	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
160	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
161	C₂²×C₈₉	—	2	1	no	—
162	C₂²×C₈₉	—	2	1	no	—
163	C₂²×C₈₉	—	2	2	no	—
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	2	2	no	—
166	C₂²×C₈₉	—	8	2	no	—
167	C₂²×C₈₉	—	8	2	no	—
168	C₂²×C₈₉	—	8	2	no	—
169	C₂²×C₈₉	—	16	4	no	—
170	C₂²×C₈₉	#480	1	2	yes	—
171	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
172	C₄×C₈₉	—	2	2	no	—
173	C₄×C₈₉	—	8	2	no	—
174	C₄×C₈₉	—	8	1	no	—
175	C₄×C₈₉	—	8	1	no	—
176	C₄×C₈₉	—	8	1	no	—
177	C₄×C₈₉	—	8	1	no	—
178	C₄×C₈₉	#480	1	2	yes	—
179	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
180	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
181	#33650	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂×C₈₉	—	2	2	no	—
183	C₂×C₈₉	—	4	2	no	—
184	C₂×C₈₉	—	16	2	no	—
185	C₂×C₈₉	C₂×#480	1	1	yes	characteristic
186	C₂×C₈₉	#3415	1	1	yes	characteristic
187	C₂×C₈₉	#3416	1	1	yes	characteristic
188	#3058	C₂×C₈₉	1	1	yes	characteristic
189	#2913	C₂×C₈₉	1	1	yes	characteristic, complemented
190	#2234	C₂×C₈₉	1	2	yes	complemented
191	#2234	C₂×C₈₉	1	2	yes	complemented
192	#2233	C₂×C₈₉	1	2	yes	complemented
193	#2232	C₂×C₈₉	1	2	yes	complemented
194	#2159	C₂×C₈₉	1	1	yes	characteristic, complemented
195	#2158	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#2140	C₂×C₈₉	1	1	yes	characteristic, complemented
197	C₂×#357	C₂×C₈₉	1	1	yes	characteristic, complemented
198	#2113	C₂×C₈₉	1	1	yes	characteristic, complemented
199	C₈₉	#33650	1	1	yes	characteristic, direct product factor, Sylow
200	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
201	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
202	#535	—	2	1	no	—
203	#520	—	2	1	no	—
204	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
205	C₂²×C₁₆	C₂²×C₈₉	1	1	yes	characteristic
206	#469	—	2	2	no	—
207	#466	C₂²×C₈₉	1	2	yes	—
208	#466	C₂²×C₈₉	1	2	yes	—
209	#428	—	2	2	no	—
210	#428	—	2	1	no	—
211	#427	C₂²×C₈₉	1	1	yes	characteristic
212	#427	C₂²×C₈₉	1	1	yes	characteristic
213	#427	C₂²×C₈₉	1	2	yes	complemented
214	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
215	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
216	#418	—	2	1	no	—
217	#367	C₂²×C₈₉	1	1	yes	characteristic, complemented
218	#367	C₂²×C₈₉	1	1	yes	characteristic, complemented
219	#367	C₂²×C₈₉	1	2	yes	complemented
220	#366	C₂²×C₈₉	1	1	yes	characteristic, complemented
221	#366	C₂²×C₈₉	1	1	yes	characteristic, complemented
222	#366	C₂²×C₈₉	1	2	yes	complemented
223	#357	C₂²×C₈₉	1	2	yes	—
224	#357	C₂²×C₈₉	1	2	yes	—
225	#357	C₂²×C₈₉	1	2	yes	—
226	#357	C₂²×C₈₉	1	2	yes	—
227	C₂²⋊C₁₆	C₂²×C₈₉	1	2	yes	complemented
228	C₂²⋊C₁₆	C₂²×C₈₉	1	2	yes	complemented
229	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
230	C₂²×D₄	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	2	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	C₂³×C₈₉	1	2	yes	—
235	#131	—	2	2	no	—
236	#131	—	2	2	no	—
237	C₂×M₁₆	D₄×C₈₉	1	1	yes	characteristic
238	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
239	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
240	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
241	#127	—	4	1	no	—
242	#124	—	4	1	no	—
243	#121	—	2	2	no	—
244	#121	—	2	2	no	—
245	#120	—	4	2	no	—
246	C₄×Q₈	—	4	1	no	—
247	C₄×D₄	—	4	2	no	—
248	C₄×D₄	—	4	1	no	—
249	#117	—	2	1	no	—
250	#117	—	2	2	no	—
251	#117	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	M₃₂	—	2	2	no	—
255	C₂×C₁₆	—	2	2	no	—
256	C₂×C₁₆	C₂³×C₈₉	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₈₉	1	2	yes	—
258	C₂×C₁₆	C₂³×C₈₉	1	1	yes	characteristic
259	#107	—	2	1	no	—
260	#107	—	2	2	no	—
261	#107	C₂³×C₈₉	1	2	yes	—
262	#107	C₂³×C₈₉	1	1	yes	characteristic
263	#107	C₂³×C₈₉	1	1	yes	characteristic
264	#107	C₂³×C₈₉	1	1	yes	characteristic
265	#107	C₂³×C₈₉	1	1	yes	characteristic
266	#106	—	2	1	no	—
267	#106	—	2	1	no	—
268	#106	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	C₂⁴	—	4	1	no	—
272	#41	—	2	2	no	—
273	#41	—	2	2	no	—
274	C₂×Q₈	D₈×C₈₉	1	1	yes	characteristic
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	D₈×C₈₉	1	2	yes	—
282	C₂×D₄	D₈×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
286	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
287	D₈	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	4	2	no	—
290	M₁₆	—	2	2	no	—
291	M₁₆	—	2	4	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
295	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
296	C₂×C₈	#41×C₈₉	1	2	yes	—
297	C₂×C₈	#41×C₈₉	1	2	yes	—
298	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	4	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₁₆	—	2	1	no	—
315	C₁₆	—	2	1	no	—
316	C₁₆	—	2	2	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	8	2	no	—
319	C₂³	—	16	1	no	—
320	C₂³	—	16	1	no	—
321	C₂³	C₂×D₈×C₈₉	1	2	yes	—
322	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	D₄	—	2	4	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	8	2	no	—
329	D₄	—	16	2	no	—
330	D₄	—	16	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	16	1	no	—
339	C₂×C₄	—	16	2	no	—
340	C₂×C₄	#123×C₈₉	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
342	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
343	C₂×C₄	#137×C₈₉	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	#123×C₈₉	1	2	yes	—
347	C₈	C₂×#41×C₈₉	1	1	yes	characteristic
348	C₈	C₂×#41×C₈₉	1	1	yes	characteristic
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	2	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	16	4	no	—
358	C₂²	#480×C₈₉	1	2	yes	—
359	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	8	2	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	1	no	—
364	C₄	—	8	1	no	—
365	C₄	—	8	1	no	—
366	C₄	#480×C₈₉	1	2	yes	—
367	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
368	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
369	C₂	—	2	2	no	—
370	C₂	—	4	2	no	—
371	C₂	—	16	2	no	—
372	C₂	C₂×#480×C₈₉	1	1	yes	characteristic
373	C₂	C₈₉×#3415	1	1	yes	characteristic
374	C₂	C₈₉×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
prime radical	C₈₉×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#41×C₈₉ ◁ C₂×#131×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#2913	C₂	semidirect
3. C₈₉×#2234	C₂	semidirect
4. C₈₉×#2234	C₂	semidirect
5. C₈₉×#2233	C₂	semidirect
6. C₈₉×#2232	C₂	semidirect
7. C₈₉×#2159	C₂	semidirect
8. C₈₉×#2158	C₂	semidirect
9. C₈₉×#2140	C₂	semidirect
10. C₂×#357×C₈₉	C₂	semidirect
11. C₈₉×#2113	C₂	semidirect
25. #427×C₈₉	C₂²	semidirect
27. C₂×#107×C₈₉	C₂²	semidirect
29. #367×C₈₉	C₂²	semidirect
30. #367×C₈₉	C₂²	semidirect
31. #367×C₈₉	C₂²	semidirect
32. #366×C₈₉	C₂²	semidirect
33. #366×C₈₉	C₂²	semidirect
34. #366×C₈₉	C₂²	semidirect
39. C₂²⋊C₁₆×C₈₉	C₂²	semidirect
40. C₂²⋊C₁₆×C₈₉	C₂²	semidirect
181. #33650	C₈₉	direct (N × H)
189. #2913	C₂×C₈₉	semidirect
190. #2234	C₂×C₈₉	semidirect
191. #2234	C₂×C₈₉	semidirect
192. #2233	C₂×C₈₉	semidirect
193. #2232	C₂×C₈₉	semidirect
194. #2159	C₂×C₈₉	semidirect
195. #2158	C₂×C₈₉	semidirect
196. #2140	C₂×C₈₉	semidirect
197. C₂×#357	C₂×C₈₉	semidirect
198. #2113	C₂×C₈₉	semidirect
199. C₈₉	#33650	direct (N × H)
213. #427	C₂²×C₈₉	semidirect
215. C₂×#107	C₂²×C₈₉	semidirect
217. #367	C₂²×C₈₉	semidirect
218. #367	C₂²×C₈₉	semidirect
219. #367	C₂²×C₈₉	semidirect
220. #366	C₂²×C₈₉	semidirect
221. #366	C₂²×C₈₉	semidirect
222. #366	C₂²×C₈₉	semidirect
227. C₂²⋊C₁₆	C₂²×C₈₉	semidirect
228. C₂²⋊C₁₆	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3058	2
C₈₉×#2913	2
C₈₉×#2234	2
C₈₉×#2233	2
C₈₉×#2232	2
C₈₉×#2159	2
C₈₉×#2158	2
C₈₉×#2140	2
C₂×#357×C₈₉	2
C₈₉×#2113	2
#33650	89

Subgroups — C89×#33650 #36411498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#33650 #36411498