Subgroups — C₈₉×#19905 #36397753

Order 22784.

604 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3341	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3329	C₂	1	2	yes	maximal, complemented
4	C₈₉×#1710	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1703	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1646	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1637	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#555×C₈₉	C₂²	1	2	yes	—
13	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
14	#500×C₈₉	—	2	1	no	—
15	#500×C₈₉	C₂²	1	1	yes	characteristic
16	#500×C₈₉	C₂²	1	1	yes	characteristic
17	#487×C₈₉	C₂²	1	2	yes	—
18	#487×C₈₉	C₂²	1	2	yes	—
19	#485×C₈₉	—	2	2	no	—
20	#482×C₈₉	—	2	2	no	—
21	#477×C₈₉	C₂²	1	2	yes	—
22	#476×C₈₉	C₂²	1	2	yes	—
23	#474×C₈₉	—	2	2	no	—
24	#474×C₈₉	C₂²	1	2	yes	—
25	#468×C₈₉	—	2	2	no	—
26	#466×C₈₉	—	2	1	no	—
27	#461×C₈₉	C₂²	1	2	yes	—
28	#448×C₈₉	—	2	2	no	—
29	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
31	C₄×D₈×C₈₉	—	2	1	no	—
32	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
33	#436×C₈₉	C₂²	1	2	yes	—
34	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
35	#427×C₈₉	—	2	1	no	—
36	#419×C₈₉	—	2	2	no	—
37	#335×C₈₉	C₂²	1	1	yes	characteristic
38	#334×C₈₉	C₂²	1	1	yes	characteristic
39	#333×C₈₉	C₂²	1	2	yes	—
40	#332×C₈₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₈₉	—	2	2	no	—
46	C₂×SD₁₆×C₈₉	—	2	2	no	—
47	C₂×SD₁₆×C₈₉	D₄	1	1	yes	characteristic
48	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
49	C₂×M₁₆×C₈₉	—	2	2	no	—
50	C₂²×C₈×C₈₉	—	2	1	no	—
51	C₄⋊Q₈×C₈₉	—	2	2	no	—
52	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
54	#124×C₈₉	—	4	2	no	—
55	C₂²⋊Q₈×C₈₉	—	2	2	no	—
56	C₂²⋊Q₈×C₈₉	—	4	2	no	—
57	#121×C₈₉	—	2	2	no	—
58	#121×C₈₉	—	2	2	no	—
59	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₄×D₄×C₈₉	—	2	2	no	—
61	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₈₉	C₂³	1	2	yes	—
63	#117×C₈₉	—	2	2	no	—
64	#117×C₈₉	—	2	2	no	—
65	#107×C₈₉	—	2	1	no	—
66	#107×C₈₉	—	2	1	no	—
67	#107×C₈₉	—	2	1	no	—
68	#107×C₈₉	—	2	1	no	—
69	#107×C₈₉	—	2	2	no	—
70	#107×C₈₉	—	2	2	no	—
71	#107×C₈₉	D₄	1	1	yes	characteristic
72	#106×C₈₉	—	2	2	no	—
73	#106×C₈₉	D₄	1	1	yes	characteristic
74	C₄⋊C₈×C₈₉	—	2	1	no	—
75	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
77	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
78	#103×C₈₉	—	2	2	no	—
79	#103×C₈₉	—	2	2	no	—
80	#103×C₈₉	—	2	2	no	—
81	#103×C₈₉	—	2	2	no	—
82	#103×C₈₉	—	4	2	no	—
83	#103×C₈₉	D₄	1	1	yes	characteristic
84	#102×C₈₉	—	2	2	no	—
85	#102×C₈₉	—	2	2	no	—
86	#102×C₈₉	D₄	1	2	yes	—
87	#102×C₈₉	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₈₉	—	2	1	no	—
89	C₂²⋊C₈×C₈₉	—	2	2	no	—
90	C₄×C₈×C₈₉	—	2	1	no	—
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	4	2	no	—
97	C₂×Q₈×C₈₉	—	4	4	no	—
98	C₂×Q₈×C₈₉	—	8	2	no	—
99	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₈₉	—	4	2	no	—
101	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	—	2	1	no	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	—	4	2	no	—
106	SD₁₆×C₈₉	—	2	2	no	—
107	SD₁₆×C₈₉	—	8	2	no	—
108	D₈×C₈₉	—	2	2	no	—
109	M₁₆×C₈₉	—	8	2	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	2	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	—	4	2	no	—
115	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
119	C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₄⋊C₄×C₈₉	—	2	2	no	—
122	C₄⋊C₄×C₈₉	—	2	2	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	4	2	no	—
125	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²⋊C₄×C₈₉	—	2	2	no	—
129	C₂²⋊C₄×C₈₉	—	2	1	no	—
130	C₂²⋊C₄×C₈₉	—	4	2	no	—
131	C₂²⋊C₄×C₈₉	—	4	2	no	—
132	C₂²⋊C₄×C₈₉	—	4	2	no	—
133	C₄²×C₈₉	—	2	1	no	—
134	C₄²×C₈₉	—	4	2	no	—
135	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
136	C₂³×C₈₉	—	2	2	no	—
137	C₂³×C₈₉	—	2	1	no	—
138	Q₈×C₈₉	—	2	1	no	—
139	Q₈×C₈₉	—	4	2	no	—
140	Q₈×C₈₉	—	4	2	no	—
141	Q₈×C₈₉	—	8	4	no	—
142	Q₈×C₈₉	—	8	2	no	—
143	Q₈×C₈₉	#135	1	2	yes	—
144	D₄×C₈₉	—	2	1	no	—
145	D₄×C₈₉	—	2	2	no	—
146	D₄×C₈₉	—	2	1	no	—
147	D₄×C₈₉	—	2	2	no	—
148	D₄×C₈₉	—	16	2	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	—	4	1	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	8	4	no	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	—	2	1	no	—
165	C₈×C₈₉	—	2	1	no	—
166	C₈×C₈₉	—	4	1	no	—
167	C₈×C₈₉	—	4	1	no	—
168	C₈×C₈₉	—	4	2	no	—
169	C₈×C₈₉	—	4	1	no	—
170	C₈×C₈₉	#137	1	2	yes	—
171	C₂²×C₈₉	—	4	1	no	—
172	C₂²×C₈₉	—	4	2	no	—
173	C₂²×C₈₉	—	4	2	no	—
174	C₂²×C₈₉	—	4	1	no	—
175	C₂²×C₈₉	—	4	1	no	—
176	C₂²×C₈₉	—	4	2	no	—
177	C₂²×C₈₉	D₄²	1	1	yes	characteristic
178	C₄×C₈₉	—	2	2	no	—
179	C₄×C₈₉	—	2	1	no	—
180	C₄×C₈₉	—	4	1	no	—
181	C₄×C₈₉	—	4	2	no	—
182	C₄×C₈₉	—	4	1	no	—
183	C₄×C₈₉	—	8	2	no	—
184	C₄×C₈₉	—	8	2	no	—
185	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
186	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
187	C₄×C₈₉	#576	1	1	yes	characteristic
188	C₄×C₈₉	#578	1	1	yes	characteristic
189	#19905	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₈₉	—	8	1	no	—
191	C₂×C₈₉	—	8	2	no	—
192	C₂×C₈₉	#3276	1	1	yes	characteristic
193	C₂×C₈₉	#3280	1	1	yes	characteristic
194	C₂×C₈₉	#3290	1	1	yes	characteristic
195	Q₈×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
196	#3341	C₂×C₈₉	1	1	yes	characteristic
197	#3329	C₂×C₈₉	1	2	yes	complemented
198	#1710	C₂×C₈₉	1	1	yes	characteristic, complemented
199	#1703	C₂×C₈₉	1	2	yes	complemented
200	#1676	C₂×C₈₉	1	1	yes	characteristic, complemented
201	#1673	C₂×C₈₉	1	1	yes	characteristic, complemented
202	#1646	C₂×C₈₉	1	2	yes	complemented
203	#1637	C₂×C₈₉	1	2	yes	complemented
204	#1589	C₂×C₈₉	1	1	yes	characteristic, complemented
205	C₈×SD₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
206	C₈₉	#19905	1	1	yes	characteristic, direct product factor, Sylow
207	#555	C₂²×C₈₉	1	2	yes	—
208	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
209	#500	—	2	1	no	—
210	#500	C₂²×C₈₉	1	1	yes	characteristic
211	#500	C₂²×C₈₉	1	1	yes	characteristic
212	#487	C₂²×C₈₉	1	2	yes	—
213	#487	C₂²×C₈₉	1	2	yes	—
214	#485	—	2	2	no	—
215	#482	—	2	2	no	—
216	#477	C₂²×C₈₉	1	2	yes	—
217	#476	C₂²×C₈₉	1	2	yes	—
218	#474	—	2	2	no	—
219	#474	C₂²×C₈₉	1	2	yes	—
220	#468	—	2	2	no	—
221	#466	—	2	1	no	—
222	#461	C₂²×C₈₉	1	2	yes	—
223	#448	—	2	2	no	—
224	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
225	C₄×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
226	C₄×D₈	—	2	1	no	—
227	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
228	#436	C₂²×C₈₉	1	2	yes	—
229	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic
230	#427	—	2	1	no	—
231	#419	—	2	2	no	—
232	#335	C₂²×C₈₉	1	1	yes	characteristic
233	#334	C₂²×C₈₉	1	1	yes	characteristic
234	#333	C₂²×C₈₉	1	2	yes	—
235	#332	C₂²×C₈₉	1	2	yes	—
236	Q₈⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
237	D₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
238	D₄⋊C₈	C₂²×C₈₉	1	2	yes	—
239	C₈²	C₂²×C₈₉	1	1	yes	characteristic
240	C₂²×Q₈	—	2	2	no	—
241	C₂×SD₁₆	—	2	2	no	—
242	C₂×SD₁₆	D₄×C₈₉	1	1	yes	characteristic
243	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
244	C₂×M₁₆	—	2	2	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₄⋊Q₈	—	2	2	no	—
247	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
248	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
249	#124	—	4	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	C₂²⋊Q₈	—	4	2	no	—
252	#121	—	2	2	no	—
253	#121	—	2	2	no	—
254	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	C₂³×C₈₉	1	2	yes	—
257	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	—	2	1	no	—
263	#107	—	2	1	no	—
264	#107	—	2	2	no	—
265	#107	—	2	2	no	—
266	#107	D₄×C₈₉	1	1	yes	characteristic
267	#106	—	2	2	no	—
268	#106	D₄×C₈₉	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
271	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	—	4	2	no	—
278	#103	D₄×C₈₉	1	1	yes	characteristic
279	#102	—	2	2	no	—
280	#102	—	2	2	no	—
281	#102	D₄×C₈₉	1	2	yes	—
282	#102	D₄×C₈₉	1	1	yes	characteristic
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
287	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×Q₈	—	4	4	no	—
293	C₂×Q₈	—	8	2	no	—
294	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
297	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	8	2	no	—
303	D₈	—	2	2	no	—
304	M₁₆	—	8	2	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	4	2	no	—
310	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
311	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
312	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
313	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
321	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
322	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
323	C₂²⋊C₄	—	2	2	no	—
324	C₂²⋊C₄	—	2	1	no	—
325	C₂²⋊C₄	—	4	2	no	—
326	C₂²⋊C₄	—	4	2	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	4	2	no	—
330	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
331	C₂³	—	2	2	no	—
332	C₂³	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	4	2	no	—
336	Q₈	—	8	4	no	—
337	Q₈	—	8	2	no	—
338	Q₈	#135×C₈₉	1	2	yes	—
339	D₄	—	2	1	no	—
340	D₄	—	2	2	no	—
341	D₄	—	2	1	no	—
342	D₄	—	2	2	no	—
343	D₄	—	16	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	4	no	—
355	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
356	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
357	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	4	1	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	#137×C₈₉	1	2	yes	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	D₄²×C₈₉	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
381	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
382	C₄	#576×C₈₉	1	1	yes	characteristic
383	C₄	#578×C₈₉	1	1	yes	characteristic
384	C₂	—	8	1	no	—
385	C₂	—	8	2	no	—
386	C₂	C₈₉×#3276	1	1	yes	characteristic
387	C₂	C₈₉×#3280	1	1	yes	characteristic
388	C₂	C₈₉×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. Q₈×D₈×C₈₉	C₂	semidirect
3. C₈₉×#3329	C₂	semidirect
4. C₈₉×#1710	C₂	semidirect
5. C₈₉×#1703	C₂	semidirect
6. C₈₉×#1676	C₂	semidirect
7. C₈₉×#1673	C₂	semidirect
8. C₈₉×#1646	C₂	semidirect
9. C₈₉×#1637	C₂	semidirect
10. C₈₉×#1589	C₂	semidirect
11. C₈×SD₁₆×C₈₉	C₂	semidirect
189. #19905	C₈₉	direct (N × H)
195. Q₈×D₈	C₂×C₈₉	semidirect
197. #3329	C₂×C₈₉	semidirect
198. #1710	C₂×C₈₉	semidirect
199. #1703	C₂×C₈₉	semidirect
200. #1676	C₂×C₈₉	semidirect
201. #1673	C₂×C₈₉	semidirect
202. #1646	C₂×C₈₉	semidirect
203. #1637	C₂×C₈₉	semidirect
204. #1589	C₂×C₈₉	semidirect
205. C₈×SD₁₆	C₂×C₈₉	semidirect
206. C₈₉	#19905	direct (N × H)

Maximal subgroups

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

subgroup	index
Q₈×D₈×C₈₉	2
C₈₉×#3341	2
C₈₉×#3329	2
C₈₉×#1710	2
C₈₉×#1703	2
C₈₉×#1676	2
C₈₉×#1673	2
C₈₉×#1646	2
C₈₉×#1637	2
C₈₉×#1589	2
C₈×SD₁₆×C₈₉	2
#19905	89

Subgroups — C89×#19905 #36397753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19905 #36397753