Subgroups — C₈₉×#33646 #36411494

Order 22784.

628 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂²×#107×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2236	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2235	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	2	yes	maximal, complemented
8	C₈₉×#2139	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2112	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	#525×C₈₉	—	2	1	no	—
13	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
14	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
15	#467×C₈₉	C₂²	1	1	yes	characteristic
16	#467×C₈₉	C₂²	1	1	yes	characteristic
17	#466×C₈₉	C₂²	1	1	yes	characteristic
18	#466×C₈₉	C₂²	1	1	yes	characteristic
19	#465×C₈₉	—	2	1	no	—
20	#465×C₈₉	—	2	1	no	—
21	#427×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#107×C₈₉	—	2	1	no	—
23	C₂×#107×C₈₉	—	2	1	no	—
24	C₂×#107×C₈₉	—	2	1	no	—
25	C₂×#107×C₈₉	C₂²	1	2	yes	—
26	C₂×#107×C₈₉	C₂²	1	2	yes	—
27	C₂×#107×C₈₉	C₂²	1	2	yes	—
28	#416×C₈₉	—	2	1	no	—
29	#367×C₈₉	C₂²	1	4	yes	complemented
30	#366×C₈₉	C₂²	1	4	yes	complemented
31	#358×C₈₉	C₂²	1	4	yes	complemented
32	#357×C₈₉	C₂²	1	4	yes	complemented
33	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
34	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
35	C₂×#41×C₈₉	—	2	1	no	—
36	C₂³×C₄×C₈₉	—	4	1	no	—
37	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
38	#135×C₈₉	—	2	4	no	—
39	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
40	C₂×SD₁₆×C₈₉	—	2	1	no	—
41	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₈₉	—	2	4	no	—
43	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
49	#123×C₈₉	—	4	1	no	—
50	C₂²⋊Q₈×C₈₉	—	2	1	no	—
51	C₂²⋊Q₈×C₈₉	—	2	1	no	—
52	#121×C₈₉	—	2	1	no	—
53	#121×C₈₉	—	2	1	no	—
54	#120×C₈₉	—	4	1	no	—
55	C₄×D₄×C₈₉	—	4	1	no	—
56	C₄×D₄×C₈₉	—	4	1	no	—
57	#117×C₈₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	4	1	no	—
64	M₃₂×C₈₉	—	2	4	no	—
65	C₂×C₁₆×C₈₉	C₂³	1	4	yes	—
66	#107×C₈₉	—	2	2	no	—
67	#107×C₈₉	—	2	2	no	—
68	#107×C₈₉	—	2	2	no	—
69	#107×C₈₉	C₂³	1	4	yes	—
70	#107×C₈₉	C₂³	1	1	yes	characteristic
71	#107×C₈₉	C₂³	1	1	yes	characteristic
72	#106×C₈₉	—	2	1	no	—
73	#103×C₈₉	—	2	1	no	—
74	#103×C₈₉	—	2	1	no	—
75	#102×C₈₉	—	2	1	no	—
76	#102×C₈₉	—	2	1	no	—
77	C₂⁴×C₈₉	D₈	1	1	yes	characteristic
78	#41×C₈₉	—	4	2	no	—
79	#41×C₈₉	—	4	2	no	—
80	C₂×Q₈×C₈₉	—	2	1	no	—
81	C₂×D₄×C₈₉	—	2	1	no	—
82	C₂×D₄×C₈₉	—	4	1	no	—
83	C₂×D₄×C₈₉	—	4	1	no	—
84	C₂×D₄×C₈₉	—	4	1	no	—
85	C₂²×C₄×C₈₉	—	2	2	no	—
86	C₂²×C₄×C₈₉	—	2	2	no	—
87	C₂²×C₄×C₈₉	—	4	2	no	—
88	C₂²×C₄×C₈₉	—	4	2	no	—
89	C₂²×C₄×C₈₉	—	4	2	no	—
90	C₂²×C₄×C₈₉	—	4	1	no	—
91	C₂²×C₄×C₈₉	—	8	4	no	—
92	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
93	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
98	Q₁₆×C₈₉	—	2	2	no	—
99	SD₁₆×C₈₉	—	4	2	no	—
100	D₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	2	2	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	—	2	2	no	—
106	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₈₉	#41	1	4	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	4	no	—
114	C₄⋊C₄×C₈₉	—	4	2	no	—
115	C₄⋊C₄×C₈₉	—	4	2	no	—
116	C₄⋊C₄×C₈₉	—	4	2	no	—
117	C₄⋊C₄×C₈₉	—	4	1	no	—
118	C₄⋊C₄×C₈₉	—	4	1	no	—
119	C₂²⋊C₄×C₈₉	—	4	1	no	—
120	C₂²⋊C₄×C₈₉	—	4	1	no	—
121	C₂²⋊C₄×C₈₉	—	4	1	no	—
122	C₂²⋊C₄×C₈₉	—	4	1	no	—
123	C₂²⋊C₄×C₈₉	—	4	1	no	—
124	C₄²×C₈₉	—	4	1	no	—
125	C₁₆×C₈₉	—	2	4	no	—
126	C₂³×C₈₉	—	2	2	no	—
127	C₂³×C₈₉	—	2	2	no	—
128	C₂³×C₈₉	—	2	2	no	—
129	C₂³×C₈₉	—	4	1	no	—
130	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
131	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
132	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₈₉	—	4	1	no	—
134	Q₈×C₈₉	—	4	1	no	—
135	D₄×C₈₉	—	4	1	no	—
136	D₄×C₈₉	—	4	1	no	—
137	D₄×C₈₉	—	8	2	no	—
138	D₄×C₈₉	—	8	2	no	—
139	D₄×C₈₉	—	8	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	4	no	—
151	C₂×C₄×C₈₉	—	8	4	no	—
152	C₂×C₄×C₈₉	—	8	4	no	—
153	C₂×C₄×C₈₉	—	8	4	no	—
154	C₂×C₄×C₈₉	—	8	2	no	—
155	C₂×C₄×C₈₉	#123	1	2	yes	—
156	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	#137	1	2	yes	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₈×C₈₉	—	2	1	no	—
162	C₈×C₈₉	—	2	1	no	—
163	C₈×C₈₉	#123	1	2	yes	—
164	C₈×C₈₉	C₂×#41	1	2	yes	—
165	C₂²×C₈₉	—	2	8	no	—
166	C₂²×C₈₉	—	2	1	no	—
167	C₂²×C₈₉	—	2	1	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	—	8	1	no	—
173	C₂²×C₈₉	—	8	1	no	—
174	C₂²×C₈₉	—	8	1	no	—
175	C₂²×C₈₉	#480	1	2	yes	—
176	C₂²×C₈₉	#509	1	2	yes	—
177	C₂²×C₈₉	#510	1	2	yes	—
178	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	8	1	no	—
182	C₄×C₈₉	—	8	4	no	—
183	C₄×C₈₉	—	8	1	no	—
184	C₄×C₈₉	—	8	1	no	—
185	C₄×C₈₉	#480	1	2	yes	—
186	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
187	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
188	#33646	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₈₉	—	2	2	no	—
190	C₂×C₈₉	—	2	2	no	—
191	C₂×C₈₉	—	2	2	no	—
192	C₂×C₈₉	—	16	1	no	—
193	C₂×C₈₉	C₂×#480	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
195	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
196	#3050	C₂×C₈₉	1	1	yes	characteristic
197	C₂²×#107	C₂×C₈₉	1	1	yes	characteristic, complemented
198	#2236	C₂×C₈₉	1	2	yes	complemented
199	#2235	C₂×C₈₉	1	2	yes	complemented
200	#2233	C₂×C₈₉	1	2	yes	complemented
201	#2232	C₂×C₈₉	1	2	yes	complemented
202	#2159	C₂×C₈₉	1	2	yes	complemented
203	#2139	C₂×C₈₉	1	2	yes	complemented
204	#2112	C₂×C₈₉	1	1	yes	characteristic, complemented
205	C₈₉	#33646	1	1	yes	characteristic, direct product factor, Sylow
206	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
208	#525	—	2	1	no	—
209	C₂²×C₄⋊C₄	—	2	1	no	—
210	C₂×M₃₂	C₂²×C₈₉	1	2	yes	—
211	#467	C₂²×C₈₉	1	1	yes	characteristic
212	#467	C₂²×C₈₉	1	1	yes	characteristic
213	#466	C₂²×C₈₉	1	1	yes	characteristic
214	#466	C₂²×C₈₉	1	1	yes	characteristic
215	#465	—	2	1	no	—
216	#465	—	2	1	no	—
217	#427	C₂²×C₈₉	1	1	yes	characteristic
218	C₂×#107	—	2	1	no	—
219	C₂×#107	—	2	1	no	—
220	C₂×#107	—	2	1	no	—
221	C₂×#107	C₂²×C₈₉	1	2	yes	—
222	C₂×#107	C₂²×C₈₉	1	2	yes	—
223	C₂×#107	C₂²×C₈₉	1	2	yes	—
224	#416	—	2	1	no	—
225	#367	C₂²×C₈₉	1	4	yes	complemented
226	#366	C₂²×C₈₉	1	4	yes	complemented
227	#358	C₂²×C₈₉	1	4	yes	complemented
228	#357	C₂²×C₈₉	1	4	yes	complemented
229	C₂²⋊C₁₆	C₂²×C₈₉	1	2	yes	—
230	C₂²⋊C₁₆	C₂²×C₈₉	1	2	yes	—
231	C₂×#41	—	2	1	no	—
232	C₂³×C₄	—	4	1	no	—
233	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
234	#135	—	2	4	no	—
235	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	1	no	—
237	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
238	C₂²×C₈	—	2	4	no	—
239	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
240	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
241	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
245	#123	—	4	1	no	—
246	C₂²⋊Q₈	—	2	1	no	—
247	C₂²⋊Q₈	—	2	1	no	—
248	#121	—	2	1	no	—
249	#121	—	2	1	no	—
250	#120	—	4	1	no	—
251	C₄×D₄	—	4	1	no	—
252	C₄×D₄	—	4	1	no	—
253	#117	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	4	1	no	—
258	C₂×C₄⋊C₄	—	4	1	no	—
259	C₂×C₄⋊C₄	—	4	1	no	—
260	M₃₂	—	2	4	no	—
261	C₂×C₁₆	C₂³×C₈₉	1	4	yes	—
262	#107	—	2	2	no	—
263	#107	—	2	2	no	—
264	#107	—	2	2	no	—
265	#107	C₂³×C₈₉	1	4	yes	—
266	#107	C₂³×C₈₉	1	1	yes	characteristic
267	#107	C₂³×C₈₉	1	1	yes	characteristic
268	#106	—	2	1	no	—
269	#103	—	2	1	no	—
270	#103	—	2	1	no	—
271	#102	—	2	1	no	—
272	#102	—	2	1	no	—
273	C₂⁴	D₈×C₈₉	1	1	yes	characteristic
274	#41	—	4	2	no	—
275	#41	—	4	2	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×D₄	—	2	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	8	4	no	—
288	C₂²×C₄	D₈×C₈₉	1	1	yes	characteristic
289	C₂²×C₄	D₈×C₈₉	1	1	yes	characteristic
290	C₂²×C₄	D₈×C₈₉	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
294	Q₁₆	—	2	2	no	—
295	SD₁₆	—	4	2	no	—
296	D₈	—	2	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
303	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
305	C₂×C₈	#41×C₈₉	1	4	yes	—
306	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
307	C₄⋊C₄	—	2	1	no	—
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	2	4	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₂²⋊C₄	—	4	1	no	—
318	C₂²⋊C₄	—	4	1	no	—
319	C₂²⋊C₄	—	4	1	no	—
320	C₄²	—	4	1	no	—
321	C₁₆	—	2	4	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	1	no	—
326	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
327	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
328	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
329	Q₈	—	4	1	no	—
330	Q₈	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	1	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	2	no	—
335	D₄	—	8	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	—	8	4	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	#123×C₈₉	1	2	yes	—
352	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
353	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
354	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
355	C₂×C₄	#137×C₈₉	1	2	yes	—
356	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	#123×C₈₉	1	2	yes	—
360	C₈	C₂×#41×C₈₉	1	2	yes	—
361	C₂²	—	2	8	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	#480×C₈₉	1	2	yes	—
372	C₂²	#509×C₈₉	1	2	yes	—
373	C₂²	#510×C₈₉	1	2	yes	—
374	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	4	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	#480×C₈₉	1	2	yes	—
382	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
383	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	16	1	no	—
388	C₂	C₂×#480×C₈₉	1	1	yes	characteristic
389	C₂	C₂×#509×C₈₉	1	1	yes	characteristic
390	C₂	C₂×#510×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
prime radical	C₈₉×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂³×C₄×C₈₉ ◁ C₂³×C₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#107×C₈₉	C₂	semidirect
3. C₈₉×#2236	C₂	semidirect
4. C₈₉×#2235	C₂	semidirect
5. C₈₉×#2233	C₂	semidirect
6. C₈₉×#2232	C₂	semidirect
7. C₈₉×#2159	C₂	semidirect
8. C₈₉×#2139	C₂	semidirect
9. C₈₉×#2112	C₂	semidirect
29. #367×C₈₉	C₂²	semidirect
30. #366×C₈₉	C₂²	semidirect
31. #358×C₈₉	C₂²	semidirect
32. #357×C₈₉	C₂²	semidirect
188. #33646	C₈₉	direct (N × H)
197. C₂²×#107	C₂×C₈₉	semidirect
198. #2236	C₂×C₈₉	semidirect
199. #2235	C₂×C₈₉	semidirect
200. #2233	C₂×C₈₉	semidirect
201. #2232	C₂×C₈₉	semidirect
202. #2159	C₂×C₈₉	semidirect
203. #2139	C₂×C₈₉	semidirect
204. #2112	C₂×C₈₉	semidirect
205. C₈₉	#33646	direct (N × H)
225. #367	C₂²×C₈₉	semidirect
226. #366	C₂²×C₈₉	semidirect
227. #358	C₂²×C₈₉	semidirect
228. #357	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×#3050	2
C₂²×#107×C₈₉	2
C₈₉×#2236	2
C₈₉×#2235	2
C₈₉×#2233	2
C₈₉×#2232	2
C₈₉×#2159	2
C₈₉×#2139	2
C₈₉×#2112	2
#33646	89

Subgroups — C89×#33646 #36411494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#33646 #36411494