Subgroups — C₈₉×#19199 #36397047

Order 22784.

650 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3227	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3226	C₂	1	1	yes	maximal, characteristic
3	C₂×#487×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2931	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1703	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1683	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1548	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₈₉	—	2	1	no	—
11	#532×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	#500×C₈₉	—	2	1	no	—
15	#498×C₈₉	—	2	1	no	—
16	#487×C₈₉	—	2	1	no	—
17	#487×C₈₉	—	2	1	no	—
18	#487×C₈₉	C₂²	1	2	yes	—
19	#487×C₈₉	C₂²	1	2	yes	—
20	#486×C₈₉	—	2	1	no	—
21	#486×C₈₉	—	2	1	no	—
22	#481×C₈₉	—	2	2	no	—
23	#480×C₈₉	—	2	2	no	—
24	#476×C₈₉	C₂²	1	4	yes	—
25	#474×C₈₉	C₂²	1	4	yes	—
26	#436×C₈₉	—	2	1	no	—
27	#436×C₈₉	C₂²	1	2	yes	—
28	C₈×D₄×C₈₉	—	2	1	no	—
29	C₈×D₄×C₈₉	C₂²	1	2	yes	—
30	#431×C₈₉	C₂²	1	1	yes	characteristic
31	#431×C₈₉	C₂²	1	1	yes	characteristic
32	#423×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#103×C₈₉	—	2	1	no	—
34	C₂×#103×C₈₉	—	2	1	no	—
35	#408×C₈₉	—	2	1	no	—
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	#335×C₈₉	C₂²	1	2	yes	—
38	#334×C₈₉	C₂²	1	2	yes	—
39	#333×C₈₉	C₂²	1	4	yes	—
40	#332×C₈₉	C₂²	1	4	yes	—
41	C₂×#41×C₈₉	—	2	1	no	—
42	C₂²×Q₈×C₈₉	—	2	1	no	—
43	C₂²×Q₈×C₈₉	—	2	1	no	—
44	#131×C₈₉	—	4	4	no	—
45	C₂×M₁₆×C₈₉	—	2	1	no	—
46	C₂×M₁₆×C₈₉	—	2	2	no	—
47	C₂²×C₈×C₈₉	—	2	2	no	—
48	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₈₉	—	2	1	no	—
51	C₄⋊Q₈×C₈₉	—	2	1	no	—
52	C₄⋊Q₈×C₈₉	—	2	1	no	—
53	C₄⋊Q₈×C₈₉	—	2	1	no	—
54	C₄⋊Q₈×C₈₉	—	2	1	no	—
55	C₄⋊Q₈×C₈₉	—	2	1	no	—
56	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
59	#127×C₈₉	D₄	1	1	yes	characteristic
60	#124×C₈₉	—	2	1	no	—
61	#121×C₈₉	—	2	1	no	—
62	#121×C₈₉	D₄	1	2	yes	—
63	C₄×D₄×C₈₉	—	2	1	no	—
64	C₄×D₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#107×C₈₉	—	2	4	no	—
71	#106×C₈₉	—	2	4	no	—
72	C₄⋊C₈×C₈₉	—	2	1	no	—
73	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
74	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
75	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
76	#103×C₈₉	—	2	2	no	—
77	#103×C₈₉	—	2	2	no	—
78	#103×C₈₉	—	2	2	no	—
79	#103×C₈₉	—	2	2	no	—
80	#102×C₈₉	—	2	4	no	—
81	#102×C₈₉	—	2	4	no	—
82	C₂²⋊C₈×C₈₉	—	2	1	no	—
83	C₂²⋊C₈×C₈₉	—	2	1	no	—
84	C₂²⋊C₈×C₈₉	—	2	2	no	—
85	C₂²⋊C₈×C₈₉	—	2	2	no	—
86	C₄×C₈×C₈₉	—	2	1	no	—
87	C₄×C₈×C₈₉	—	2	1	no	—
88	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
89	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
90	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	#41×C₈₉	—	4	2	no	—
93	#41×C₈₉	—	4	2	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	4	1	no	—
98	C₂×Q₈×C₈₉	—	4	1	no	—
99	C₂×Q₈×C₈₉	—	4	2	no	—
100	C₂×Q₈×C₈₉	—	4	2	no	—
101	C₂×Q₈×C₈₉	—	8	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	—	2	1	no	—
104	C₂×D₄×C₈₉	—	2	1	no	—
105	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₈₉	—	2	2	no	—
107	C₂²×C₄×C₈₉	—	4	1	no	—
108	C₂²×C₄×C₈₉	—	4	1	no	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
112	M₁₆×C₈₉	—	4	4	no	—
113	M₁₆×C₈₉	—	4	2	no	—
114	C₂×C₈×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	—	2	2	no	—
116	C₂×C₈×C₈₉	—	2	2	no	—
117	C₂×C₈×C₈₉	—	2	2	no	—
118	C₂×C₈×C₈₉	—	2	2	no	—
119	C₂×C₈×C₈₉	—	4	4	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	2	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	4	1	no	—
130	C₄⋊C₄×C₈₉	—	4	1	no	—
131	C₄⋊C₄×C₈₉	—	4	1	no	—
132	C₄⋊C₄×C₈₉	—	4	1	no	—
133	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₈₉	#41	1	1	yes	characteristic
139	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂³×C₈₉	—	2	2	no	—
141	C₂³×C₈₉	#121	1	1	yes	characteristic
142	Q₈×C₈₉	—	4	2	no	—
143	Q₈×C₈₉	—	4	2	no	—
144	Q₈×C₈₉	—	4	2	no	—
145	Q₈×C₈₉	—	8	2	no	—
146	Q₈×C₈₉	—	8	2	no	—
147	Q₈×C₈₉	—	8	2	no	—
148	D₄×C₈₉	—	2	4	no	—
149	D₄×C₈₉	—	4	4	no	—
150	D₄×C₈₉	—	4	2	no	—
151	D₄×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	8	2	no	—
160	C₂×C₄×C₈₉	—	8	2	no	—
161	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#135	1	2	yes	—
165	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	—	2	1	no	—
173	C₈×C₈₉	—	4	2	no	—
174	C₈×C₈₉	—	4	2	no	—
175	C₈×C₈₉	—	4	2	no	—
176	C₂²×C₈₉	—	2	1	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	4	2	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	#463	1	2	yes	—
182	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	—	4	2	no	—
186	C₄×C₈₉	—	8	2	no	—
187	C₄×C₈₉	—	8	2	no	—
188	C₄×C₈₉	#463	1	2	yes	—
189	C₄×C₈₉	#471	1	2	yes	—
190	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
191	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₄×C₈₉	#578	1	2	yes	—
193	#19199	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂×C₈₉	—	2	2	no	—
195	C₂×C₈₉	—	8	2	no	—
196	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
197	C₂×C₈₉	#3059	1	1	yes	characteristic
198	C₂×C₈₉	C₂×#471	1	1	yes	characteristic
199	#3227	C₂×C₈₉	1	1	yes	characteristic
200	#3226	C₂×C₈₉	1	1	yes	characteristic
201	C₂×#487	C₂×C₈₉	1	1	yes	characteristic, complemented
202	#2931	C₂×C₈₉	1	1	yes	characteristic
203	#1703	C₂×C₈₉	1	4	yes	complemented
204	#1683	C₂×C₈₉	1	4	yes	complemented
205	#1564	C₂×C₈₉	1	1	yes	characteristic, complemented
206	#1548	C₂×C₈₉	1	1	yes	characteristic, complemented
207	#1546	C₂×C₈₉	1	1	yes	characteristic, complemented
208	C₈₉	#19199	1	1	yes	characteristic, direct product factor, Sylow
209	C₂×#131	—	2	1	no	—
210	#532	C₂²×C₈₉	1	1	yes	characteristic
211	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
212	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
213	#500	—	2	1	no	—
214	#498	—	2	1	no	—
215	#487	—	2	1	no	—
216	#487	—	2	1	no	—
217	#487	C₂²×C₈₉	1	2	yes	—
218	#487	C₂²×C₈₉	1	2	yes	—
219	#486	—	2	1	no	—
220	#486	—	2	1	no	—
221	#481	—	2	2	no	—
222	#480	—	2	2	no	—
223	#476	C₂²×C₈₉	1	4	yes	—
224	#474	C₂²×C₈₉	1	4	yes	—
225	#436	—	2	1	no	—
226	#436	C₂²×C₈₉	1	2	yes	—
227	C₈×D₄	—	2	1	no	—
228	C₈×D₄	C₂²×C₈₉	1	2	yes	—
229	#431	C₂²×C₈₉	1	1	yes	characteristic
230	#431	C₂²×C₈₉	1	1	yes	characteristic
231	#423	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×#103	—	2	1	no	—
233	C₂×#103	—	2	1	no	—
234	#408	—	2	1	no	—
235	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
236	#335	C₂²×C₈₉	1	2	yes	—
237	#334	C₂²×C₈₉	1	2	yes	—
238	#333	C₂²×C₈₉	1	4	yes	—
239	#332	C₂²×C₈₉	1	4	yes	—
240	C₂×#41	—	2	1	no	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	—	2	1	no	—
243	#131	—	4	4	no	—
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
248	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
256	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
257	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
258	#127	D₄×C₈₉	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	D₄×C₈₉	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	C₂³×C₈₉	1	2	yes	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
269	#107	—	2	4	no	—
270	#106	—	2	4	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
273	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
274	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
275	#103	—	2	2	no	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
288	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
291	#41	—	4	2	no	—
292	#41	—	4	2	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	8	2	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
310	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
311	M₁₆	—	4	4	no	—
312	M₁₆	—	4	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	4	4	no	—
319	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
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	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
336	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
337	C₄²	#41×C₈₉	1	1	yes	characteristic
338	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
339	C₂³	—	2	2	no	—
340	C₂³	#121×C₈₉	1	1	yes	characteristic
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	8	2	no	—
345	Q₈	—	8	2	no	—
346	Q₈	—	8	2	no	—
347	D₄	—	2	4	no	—
348	D₄	—	4	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
361	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
362	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
363	C₂×C₄	#135×C₈₉	1	2	yes	—
364	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
367	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	4	2	no	—
374	C₈	—	4	2	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	#463×C₈₉	1	2	yes	—
381	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	#463×C₈₉	1	2	yes	—
388	C₄	#471×C₈₉	1	2	yes	—
389	C₄	C₂×#135×C₈₉	1	1	yes	characteristic
390	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
391	C₄	#578×C₈₉	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	8	2	no	—
394	C₂	C₂×#463×C₈₉	1	1	yes	characteristic
395	C₂	C₈₉×#3059	1	1	yes	characteristic
396	C₂	C₂×#471×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	#532×C₈₉	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#487×C₈₉	C₂	semidirect
5. C₈₉×#1703	C₂	semidirect
6. C₈₉×#1683	C₂	semidirect
7. C₈₉×#1564	C₂	semidirect
8. C₈₉×#1548	C₂	semidirect
9. C₈₉×#1546	C₂	semidirect
193. #19199	C₈₉	direct (N × H)
201. C₂×#487	C₂×C₈₉	semidirect
203. #1703	C₂×C₈₉	semidirect
204. #1683	C₂×C₈₉	semidirect
205. #1564	C₂×C₈₉	semidirect
206. #1548	C₂×C₈₉	semidirect
207. #1546	C₂×C₈₉	semidirect
208. C₈₉	#19199	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×#3227	2
C₈₉×#3226	2
C₂×#487×C₈₉	2
C₈₉×#2931	2
C₈₉×#1703	2
C₈₉×#1683	2
C₈₉×#1564	2
C₈₉×#1548	2
C₈₉×#1546	2
#19199	89

Subgroups — C89×#19199 #36397047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19199 #36397047