Subgroups — C₈₉×#19909 #36397757

Order 22784.

638 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3391	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3333	C₂	1	2	yes	maximal, complemented
4	C₈₉×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1697	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1631	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1622	C₂	1	2	yes	maximal, complemented
10	C₈₉×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#554×C₈₉	C₂²	1	2	yes	—
13	#550×C₈₉	C₂²	1	2	yes	—
14	#500×C₈₉	C₂²	1	1	yes	characteristic
15	#499×C₈₉	—	2	1	no	—
16	#493×C₈₉	—	2	1	no	—
17	#493×C₈₉	C₂²	1	1	yes	characteristic
18	#492×C₈₉	C₂²	1	2	yes	—
19	#486×C₈₉	C₂²	1	2	yes	—
20	#480×C₈₉	—	2	2	no	—
21	#478×C₈₉	—	2	2	no	—
22	#477×C₈₉	C₂²	1	2	yes	—
23	#476×C₈₉	C₂²	1	2	yes	—
24	#468×C₈₉	—	2	2	no	—
25	#460×C₈₉	C₂²	1	2	yes	—
26	#459×C₈₉	—	2	2	no	—
27	#459×C₈₉	C₂²	1	2	yes	—
28	#452×C₈₉	—	2	2	no	—
29	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₈₉	—	2	1	no	—
33	C₄×D₈×C₈₉	—	2	1	no	—
34	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
35	#436×C₈₉	C₂²	1	2	yes	—
36	#417×C₈₉	—	2	2	no	—
37	#335×C₈₉	C₂²	1	1	yes	characteristic
38	#335×C₈₉	C₂²	1	1	yes	characteristic
39	#333×C₈₉	C₂²	1	2	yes	—
40	#331×C₈₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#41×C₈₉	—	2	2	no	—
46	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
47	C₂×SD₁₆×C₈₉	—	2	2	no	—
48	C₂×SD₁₆×C₈₉	—	4	2	no	—
49	C₂×D₈×C₈₉	—	2	2	no	—
50	C₂×D₈×C₈₉	—	2	1	no	—
51	C₂×D₈×C₈₉	—	2	1	no	—
52	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₈₉	—	2	2	no	—
54	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
55	#127×C₈₉	—	2	2	no	—
56	#127×C₈₉	C₂³	1	2	yes	—
57	#125×C₈₉	—	2	2	no	—
58	C₂²⋊Q₈×C₈₉	—	2	2	no	—
59	C₂²⋊Q₈×C₈₉	—	4	2	no	—
60	#121×C₈₉	—	2	2	no	—
61	#121×C₈₉	—	4	2	no	—
62	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₈₉	—	2	2	no	—
65	C₄×D₄×C₈₉	—	2	2	no	—
66	C₄×D₄×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
68	#107×C₈₉	—	2	1	no	—
69	#107×C₈₉	—	2	1	no	—
70	#107×C₈₉	—	2	2	no	—
71	#107×C₈₉	D₄	1	1	yes	characteristic
72	#107×C₈₉	D₄	1	1	yes	characteristic
73	#106×C₈₉	—	2	2	no	—
74	C₄⋊C₈×C₈₉	—	2	1	no	—
75	C₄⋊C₈×C₈₉	—	2	1	no	—
76	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
77	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
79	#103×C₈₉	—	2	2	no	—
80	#103×C₈₉	D₄	1	1	yes	characteristic
81	#103×C₈₉	D₄	1	1	yes	characteristic
82	#102×C₈₉	—	2	2	no	—
83	#102×C₈₉	—	2	2	no	—
84	#102×C₈₉	—	2	2	no	—
85	#102×C₈₉	—	2	2	no	—
86	#102×C₈₉	—	2	2	no	—
87	#102×C₈₉	D₄	1	2	yes	—
88	C₂²⋊C₈×C₈₉	—	2	2	no	—
89	C₄×C₈×C₈₉	—	2	1	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	#41×C₈₉	—	4	4	no	—
95	#41×C₈₉	—	8	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₈₉	—	2	2	no	—
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	4	2	no	—
103	C₂×D₄×C₈₉	—	4	2	no	—
104	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₈₉	—	2	2	no	—
106	C₂²×C₄×C₈₉	—	4	2	no	—
107	C₂²×C₄×C₈₉	—	4	2	no	—
108	Q₁₆×C₈₉	—	2	2	no	—
109	SD₁₆×C₈₉	—	8	4	no	—
110	SD₁₆×C₈₉	—	8	2	no	—
111	D₈×C₈₉	—	2	2	no	—
112	D₈×C₈₉	—	4	2	no	—
113	D₈×C₈₉	—	8	1	no	—
114	D₈×C₈₉	—	8	2	no	—
115	M₁₆×C₈₉	—	8	2	no	—
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	2	no	—
120	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₄⋊C₄×C₈₉	—	2	1	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	4	2	no	—
129	C₄⋊C₄×C₈₉	—	4	2	no	—
130	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₈₉	—	2	2	no	—
134	C₂²⋊C₄×C₈₉	—	4	2	no	—
135	C₂²⋊C₄×C₈₉	—	4	2	no	—
136	C₄²×C₈₉	—	2	1	no	—
137	C₄²×C₈₉	—	2	1	no	—
138	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂³×C₈₉	—	2	2	no	—
140	C₂³×C₈₉	—	4	2	no	—
141	Q₈×C₈₉	—	2	1	no	—
142	Q₈×C₈₉	—	2	1	no	—
143	Q₈×C₈₉	—	2	1	no	—
144	Q₈×C₈₉	—	8	2	no	—
145	Q₈×C₈₉	#135	1	2	yes	—
146	D₄×C₈₉	—	2	2	no	—
147	D₄×C₈₉	—	2	2	no	—
148	D₄×C₈₉	—	4	2	no	—
149	D₄×C₈₉	—	4	2	no	—
150	D₄×C₈₉	—	4	2	no	—
151	D₄×C₈₉	—	4	2	no	—
152	D₄×C₈₉	—	8	4	no	—
153	D₄×C₈₉	—	8	2	no	—
154	D₄×C₈₉	—	16	2	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	8	4	no	—
164	C₂×C₄×C₈₉	—	16	2	no	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
168	C₈×C₈₉	—	2	2	no	—
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	—	4	2	no	—
173	C₈×C₈₉	—	4	1	no	—
174	C₈×C₈₉	—	4	1	no	—
175	C₈×C₈₉	#137	1	2	yes	—
176	C₂²×C₈₉	—	4	2	no	—
177	C₂²×C₈₉	—	4	2	no	—
178	C₂²×C₈₉	—	4	2	no	—
179	C₂²×C₈₉	—	8	2	no	—
180	C₂²×C₈₉	—	8	2	no	—
181	C₂²×C₈₉	—	8	2	no	—
182	C₂²×C₈₉	D₄²	1	1	yes	characteristic
183	C₄×C₈₉	—	2	2	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	4	2	no	—
186	C₄×C₈₉	—	4	1	no	—
187	C₄×C₈₉	—	4	1	no	—
188	C₄×C₈₉	—	4	1	no	—
189	C₄×C₈₉	—	8	2	no	—
190	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
191	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
192	C₄×C₈₉	#576	1	1	yes	characteristic
193	C₄×C₈₉	#577	1	1	yes	characteristic
194	#19909	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₈₉	—	8	2	no	—
196	C₂×C₈₉	—	16	2	no	—
197	C₂×C₈₉	#3278	1	1	yes	characteristic
198	C₂×C₈₉	#3280	1	1	yes	characteristic
199	C₂×C₈₉	#3292	1	1	yes	characteristic
200	#3391	C₂×C₈₉	1	1	yes	characteristic
201	#3380	C₂×C₈₉	1	1	yes	characteristic, complemented
202	#3333	C₂×C₈₉	1	2	yes	complemented
203	#1706	C₂×C₈₉	1	1	yes	characteristic, complemented
204	#1697	C₂×C₈₉	1	2	yes	complemented
205	#1676	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#1668	C₂×C₈₉	1	1	yes	characteristic, complemented
207	#1631	C₂×C₈₉	1	2	yes	complemented
208	#1622	C₂×C₈₉	1	2	yes	complemented
209	#1589	C₂×C₈₉	1	1	yes	characteristic, complemented
210	C₈×Q₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
211	C₈₉	#19909	1	1	yes	characteristic, direct product factor, Sylow
212	#554	C₂²×C₈₉	1	2	yes	—
213	#550	C₂²×C₈₉	1	2	yes	—
214	#500	C₂²×C₈₉	1	1	yes	characteristic
215	#499	—	2	1	no	—
216	#493	—	2	1	no	—
217	#493	C₂²×C₈₉	1	1	yes	characteristic
218	#492	C₂²×C₈₉	1	2	yes	—
219	#486	C₂²×C₈₉	1	2	yes	—
220	#480	—	2	2	no	—
221	#478	—	2	2	no	—
222	#477	C₂²×C₈₉	1	2	yes	—
223	#476	C₂²×C₈₉	1	2	yes	—
224	#468	—	2	2	no	—
225	#460	C₂²×C₈₉	1	2	yes	—
226	#459	—	2	2	no	—
227	#459	C₂²×C₈₉	1	2	yes	—
228	#452	—	2	2	no	—
229	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
230	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic
231	C₄×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
232	C₄×D₈	—	2	1	no	—
233	C₄×D₈	—	2	1	no	—
234	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
235	#436	C₂²×C₈₉	1	2	yes	—
236	#417	—	2	2	no	—
237	#335	C₂²×C₈₉	1	1	yes	characteristic
238	#335	C₂²×C₈₉	1	1	yes	characteristic
239	#333	C₂²×C₈₉	1	2	yes	—
240	#331	C₂²×C₈₉	1	2	yes	—
241	Q₈⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
242	Q₈⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
243	D₄⋊C₈	C₂²×C₈₉	1	2	yes	—
244	C₈²	C₂²×C₈₉	1	1	yes	characteristic
245	C₂×#41	—	2	2	no	—
246	C₂×Q₁₆	D₄×C₈₉	1	1	yes	characteristic
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×SD₁₆	—	4	2	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	D₄×C₈₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
255	#127	—	2	2	no	—
256	#127	C₂³×C₈₉	1	2	yes	—
257	#125	—	2	2	no	—
258	C₂²⋊Q₈	—	2	2	no	—
259	C₂²⋊Q₈	—	4	2	no	—
260	#121	—	2	2	no	—
261	#121	—	4	2	no	—
262	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
263	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	C₂³×C₈₉	1	2	yes	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	#107	—	2	1	no	—
269	#107	—	2	1	no	—
270	#107	—	2	2	no	—
271	#107	D₄×C₈₉	1	1	yes	characteristic
272	#107	D₄×C₈₉	1	1	yes	characteristic
273	#106	—	2	2	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
277	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
279	#103	—	2	2	no	—
280	#103	D₄×C₈₉	1	1	yes	characteristic
281	#103	D₄×C₈₉	1	1	yes	characteristic
282	#102	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	D₄×C₈₉	1	2	yes	—
288	C₂²⋊C₈	—	2	2	no	—
289	C₄×C₈	—	2	1	no	—
290	C₄×C₈	—	2	1	no	—
291	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
294	#41	—	4	4	no	—
295	#41	—	8	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
298	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	Q₁₆	—	2	2	no	—
309	SD₁₆	—	8	4	no	—
310	SD₁₆	—	8	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	4	2	no	—
313	D₈	—	8	1	no	—
314	D₈	—	8	2	no	—
315	M₁₆	—	8	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
321	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
322	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
323	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
331	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
332	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₂²⋊C₄	—	4	2	no	—
336	C₄²	—	2	1	no	—
337	C₄²	—	2	1	no	—
338	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	—	4	2	no	—
341	Q₈	—	2	1	no	—
342	Q₈	—	2	1	no	—
343	Q₈	—	2	1	no	—
344	Q₈	—	8	2	no	—
345	Q₈	#135×C₈₉	1	2	yes	—
346	D₄	—	2	2	no	—
347	D₄	—	2	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	8	4	no	—
353	D₄	—	8	2	no	—
354	D₄	—	16	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	16	2	no	—
365	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
367	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
368	C₈	—	2	2	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	#137×C₈₉	1	2	yes	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	D₄²×C₈₉	1	1	yes	characteristic
383	C₄	—	2	2	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
391	C₄	C₂×#137×C₈₉	1	1	yes	characteristic
392	C₄	#576×C₈₉	1	1	yes	characteristic
393	C₄	#577×C₈₉	1	1	yes	characteristic
394	C₂	—	8	2	no	—
395	C₂	—	16	2	no	—
396	C₂	C₈₉×#3278	1	1	yes	characteristic
397	C₂	C₈₉×#3280	1	1	yes	characteristic
398	C₂	C₈₉×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3391	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
2. C₈₉×#3380	C₂	semidirect
3. C₈₉×#3333	C₂	semidirect
4. C₈₉×#1706	C₂	semidirect
5. C₈₉×#1697	C₂	semidirect
6. C₈₉×#1676	C₂	semidirect
7. C₈₉×#1668	C₂	semidirect
8. C₈₉×#1631	C₂	semidirect
9. C₈₉×#1622	C₂	semidirect
10. C₈₉×#1589	C₂	semidirect
11. C₈×Q₁₆×C₈₉	C₂	semidirect
194. #19909	C₈₉	direct (N × H)
201. #3380	C₂×C₈₉	semidirect
202. #3333	C₂×C₈₉	semidirect
203. #1706	C₂×C₈₉	semidirect
204. #1697	C₂×C₈₉	semidirect
205. #1676	C₂×C₈₉	semidirect
206. #1668	C₂×C₈₉	semidirect
207. #1631	C₂×C₈₉	semidirect
208. #1622	C₂×C₈₉	semidirect
209. #1589	C₂×C₈₉	semidirect
210. C₈×Q₁₆	C₂×C₈₉	semidirect
211. C₈₉	#19909	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3391	2
C₈₉×#3380	2
C₈₉×#3333	2
C₈₉×#1706	2
C₈₉×#1697	2
C₈₉×#1676	2
C₈₉×#1668	2
C₈₉×#1631	2
C₈₉×#1622	2
C₈₉×#1589	2
C₈×Q₁₆×C₈₉	2
#19909	89

Subgroups — C89×#19909 #36397757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19909 #36397757