Subgroups — C₈₉×#25590 #36403438

Order 22784.

1188 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2004	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1994	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1965	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1885	C₂	1	4	yes	maximal, complemented
9	C₄×#104×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#137×C₈₉	C₂²	1	2	yes	—
11	#559×C₈₉	—	2	2	no	—
12	#550×C₈₉	—	2	2	no	—
13	#546×C₈₉	—	2	4	no	—
14	#540×C₈₉	—	2	2	no	—
15	#535×C₈₉	C₂²	1	2	yes	—
16	#533×C₈₉	C₂²	1	1	yes	characteristic
17	#532×C₈₉	—	2	2	no	—
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#124×C₈₉	C₂²	1	4	yes	—
21	#518×C₈₉	C₂²	1	2	yes	—
22	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
23	#491×C₈₉	—	2	2	no	—
24	#487×C₈₉	—	2	2	no	—
25	#462×C₈₉	—	2	2	no	—
26	#461×C₈₉	—	2	2	no	—
27	#423×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#104×C₈₉	C₂²	1	2	yes	—
29	#419×C₈₉	C₂²	1	4	yes	—
30	#419×C₈₉	C₂²	1	2	yes	—
31	C₂×#100×C₈₉	C₂²	1	4	yes	—
32	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
33	#390×C₈₉	—	2	4	no	—
34	C₄³×C₈₉	C₂²	1	1	yes	characteristic
35	#339×C₈₉	C₂²	1	2	yes	—
36	#339×C₈₉	C₂²	1	4	yes	—
37	C₂×#41×C₈₉	—	2	4	no	—
38	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
39	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
40	C₂²×D₄×C₈₉	D₄	1	4	yes	—
41	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
42	#137×C₈₉	—	4	4	no	—
43	C₂×Q₁₆×C₈₉	—	2	2	no	—
44	C₂×SD₁₆×C₈₉	—	2	2	no	—
45	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
46	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
47	C₄⋊Q₈×C₈₉	—	2	2	no	—
48	C₄⋊Q₈×C₈₉	—	2	1	no	—
49	C₄⋊Q₈×C₈₉	—	2	1	no	—
50	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
51	#127×C₈₉	—	2	2	no	—
52	#127×C₈₉	—	2	1	no	—
53	#127×C₈₉	—	2	1	no	—
54	#127×C₈₉	—	2	2	no	—
55	#125×C₈₉	D₄	1	2	yes	—
56	#124×C₈₉	—	2	4	no	—
57	#124×C₈₉	—	2	2	no	—
58	#124×C₈₉	—	2	8	no	—
59	#124×C₈₉	—	4	4	no	—
60	#123×C₈₉	—	2	8	no	—
61	C₂²⋊Q₈×C₈₉	—	2	2	no	—
62	#121×C₈₉	—	2	4	no	—
63	#121×C₈₉	—	2	8	no	—
64	#121×C₈₉	—	2	4	no	—
65	#120×C₈₉	—	2	4	no	—
66	C₄×Q₈×C₈₉	—	2	2	no	—
67	C₄×Q₈×C₈₉	D₄	1	2	yes	—
68	C₄×D₄×C₈₉	—	2	4	no	—
69	C₄×D₄×C₈₉	—	2	2	no	—
70	C₄×D₄×C₈₉	—	2	4	no	—
71	C₄×D₄×C₈₉	—	2	4	no	—
72	C₄×D₄×C₈₉	D₄	1	2	yes	—
73	#117×C₈₉	—	2	1	no	—
74	#117×C₈₉	C₂³	1	1	yes	characteristic
75	#117×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
79	C₂×C₄²×C₈₉	—	2	1	no	—
80	C₂×C₄²×C₈₉	—	2	2	no	—
81	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₈₉	—	2	2	no	—
84	#104×C₈₉	—	2	4	no	—
85	#103×C₈₉	—	2	4	no	—
86	#103×C₈₉	—	2	8	no	—
87	#100×C₈₉	—	4	4	no	—
88	#97×C₈₉	—	2	1	no	—
89	C₄×C₈×C₈₉	—	2	1	no	—
90	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
91	#41×C₈₉	—	2	2	no	—
92	#41×C₈₉	—	2	2	no	—
93	#41×C₈₉	—	8	8	no	—
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	4	no	—
98	C₂×Q₈×C₈₉	—	2	4	no	—
99	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂×D₄×C₈₉	—	2	1	no	—
101	C₂×D₄×C₈₉	—	2	8	no	—
102	C₂×D₄×C₈₉	—	2	4	no	—
103	C₂×D₄×C₈₉	—	2	4	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	4	no	—
107	C₂×D₄×C₈₉	—	2	4	no	—
108	C₂×D₄×C₈₉	—	4	8	no	—
109	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	8	no	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₈₉	—	4	4	no	—
118	SD₁₆×C₈₉	—	4	4	no	—
119	M₁₆×C₈₉	—	2	2	no	—
120	M₁₆×C₈₉	—	2	2	no	—
121	M₁₆×C₈₉	—	2	4	no	—
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	4	2	no	—
128	C₄⋊C₄×C₈₉	—	4	2	no	—
129	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²⋊C₄×C₈₉	—	2	8	no	—
132	C₂²⋊C₄×C₈₉	—	2	8	no	—
133	C₂²⋊C₄×C₈₉	—	2	1	no	—
134	C₂²⋊C₄×C₈₉	—	2	2	no	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₂²⋊C₄×C₈₉	—	4	16	no	—
137	C₄²×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	—	2	1	no	—
139	C₄²×C₈₉	—	2	2	no	—
140	C₄²×C₈₉	—	2	2	no	—
141	C₄²×C₈₉	—	4	4	no	—
142	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₈₉	C₂×D₄	1	2	yes	—
145	C₄²×C₈₉	#41	1	4	yes	complemented
146	C₂³×C₈₉	—	2	4	no	—
147	C₂³×C₈₉	—	2	1	no	—
148	C₂³×C₈₉	—	2	8	no	—
149	C₂³×C₈₉	—	4	8	no	—
150	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₈₉	—	2	1	no	—
152	Q₈×C₈₉	—	2	1	no	—
153	Q₈×C₈₉	—	4	4	no	—
154	Q₈×C₈₉	—	4	2	no	—
155	Q₈×C₈₉	—	4	2	no	—
156	Q₈×C₈₉	—	4	4	no	—
157	D₄×C₈₉	—	2	1	no	—
158	D₄×C₈₉	—	2	1	no	—
159	D₄×C₈₉	—	4	2	no	—
160	D₄×C₈₉	—	4	2	no	—
161	D₄×C₈₉	—	4	2	no	—
162	D₄×C₈₉	—	4	4	no	—
163	D₄×C₈₉	—	4	8	no	—
164	D₄×C₈₉	—	8	4	no	—
165	D₄×C₈₉	—	8	8	no	—
166	C₂×C₄×C₈₉	—	2	4	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	2	4	no	—
170	C₂×C₄×C₈₉	—	2	4	no	—
171	C₂×C₄×C₈₉	—	4	4	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	4	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	4	no	—
176	C₂×C₄×C₈₉	—	8	8	no	—
177	C₂×C₄×C₈₉	#120	1	2	yes	—
178	C₂×C₄×C₈₉	#120	1	2	yes	—
179	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
182	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
183	C₈×C₈₉	—	4	2	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₂²×C₈₉	—	2	2	no	—
186	C₂²×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	—	4	2	no	—
189	C₂²×C₈₉	—	4	8	no	—
190	C₂²×C₈₉	—	8	8	no	—
191	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
192	C₂²×C₈₉	#546	1	2	yes	—
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	4	4	no	—
195	C₄×C₈₉	—	4	1	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	—	4	4	no	—
198	C₄×C₈₉	—	8	2	no	—
199	C₄×C₈₉	#455	1	4	yes	—
200	C₄×C₈₉	#532	1	1	yes	characteristic
201	C₄×C₈₉	#535	1	1	yes	characteristic
202	C₄×C₈₉	#550	1	2	yes	—
203	#25590	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₂×C₈₉	—	2	2	no	—
205	C₂×C₈₉	—	8	1	no	—
206	C₂×C₈₉	—	8	4	no	—
207	C₂×C₈₉	#2431	1	1	yes	characteristic
208	C₂×C₈₉	C₂×#455	1	2	yes	—
209	#3508	C₂×C₈₉	1	1	yes	characteristic
210	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
211	#3039	C₂×C₈₉	1	1	yes	characteristic, complemented
212	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
213	#2004	C₂×C₈₉	1	4	yes	complemented
214	#1994	C₂×C₈₉	1	1	yes	characteristic, complemented
215	#1965	C₂×C₈₉	1	1	yes	characteristic, complemented
216	#1885	C₂×C₈₉	1	4	yes	complemented
217	C₄×#104	C₂×C₈₉	1	1	yes	characteristic, complemented
218	C₈₉	#25590	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×#137	C₂²×C₈₉	1	2	yes	—
220	#559	—	2	2	no	—
221	#550	—	2	2	no	—
222	#546	—	2	4	no	—
223	#540	—	2	2	no	—
224	#535	C₂²×C₈₉	1	2	yes	—
225	#533	C₂²×C₈₉	1	1	yes	characteristic
226	#532	—	2	2	no	—
227	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
229	C₂×#124	C₂²×C₈₉	1	4	yes	—
230	#518	C₂²×C₈₉	1	2	yes	—
231	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
232	#491	—	2	2	no	—
233	#487	—	2	2	no	—
234	#462	—	2	2	no	—
235	#461	—	2	2	no	—
236	#423	C₂²×C₈₉	1	1	yes	characteristic
237	C₂×#104	C₂²×C₈₉	1	2	yes	—
238	#419	C₂²×C₈₉	1	4	yes	—
239	#419	C₂²×C₈₉	1	2	yes	—
240	C₂×#100	C₂²×C₈₉	1	4	yes	—
241	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
242	#390	—	2	4	no	—
243	C₄³	C₂²×C₈₉	1	1	yes	characteristic
244	#339	C₂²×C₈₉	1	2	yes	—
245	#339	C₂²×C₈₉	1	4	yes	—
246	C₂×#41	—	2	4	no	—
247	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
248	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
249	C₂²×D₄	D₄×C₈₉	1	4	yes	—
250	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
251	#137	—	4	4	no	—
252	C₂×Q₁₆	—	2	2	no	—
253	C₂×SD₁₆	—	2	2	no	—
254	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
255	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	D₄×C₈₉	1	2	yes	—
260	#127	—	2	2	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	2	no	—
264	#125	D₄×C₈₉	1	2	yes	—
265	#124	—	2	4	no	—
266	#124	—	2	2	no	—
267	#124	—	2	8	no	—
268	#124	—	4	4	no	—
269	#123	—	2	8	no	—
270	C₂²⋊Q₈	—	2	2	no	—
271	#121	—	2	4	no	—
272	#121	—	2	8	no	—
273	#121	—	2	4	no	—
274	#120	—	2	4	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	D₄×C₈₉	1	2	yes	—
277	C₄×D₄	—	2	4	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	—	2	4	no	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	D₄×C₈₉	1	2	yes	—
282	#117	—	2	1	no	—
283	#117	C₂³×C₈₉	1	1	yes	characteristic
284	#117	C₂³×C₈₉	1	2	yes	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	2	8	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	2	no	—
293	#104	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	8	no	—
296	#100	—	4	4	no	—
297	#97	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	#41	—	8	8	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	4	8	no	—
318	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
326	Q₁₆	—	4	4	no	—
327	SD₁₆	—	4	4	no	—
328	M₁₆	—	2	2	no	—
329	M₁₆	—	2	2	no	—
330	M₁₆	—	2	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
339	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	1	no	—
343	C₂²⋊C₄	—	2	2	no	—
344	C₂²⋊C₄	—	2	2	no	—
345	C₂²⋊C₄	—	4	16	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	4	no	—
351	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
352	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
353	C₄²	C₂×D₄×C₈₉	1	2	yes	—
354	C₄²	#41×C₈₉	1	4	yes	complemented
355	C₂³	—	2	4	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	4	8	no	—
359	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
360	Q₈	—	2	1	no	—
361	Q₈	—	2	1	no	—
362	Q₈	—	4	4	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	4	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	4	no	—
373	D₄	—	8	4	no	—
374	D₄	—	8	8	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	8	8	no	—
386	C₂×C₄	#120×C₈₉	1	2	yes	—
387	C₂×C₄	#120×C₈₉	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
391	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	8	no	—
399	C₂²	—	8	8	no	—
400	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
401	C₂²	#546×C₈₉	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	4	no	—
407	C₄	—	8	2	no	—
408	C₄	#455×C₈₉	1	4	yes	—
409	C₄	#532×C₈₉	1	1	yes	characteristic
410	C₄	#535×C₈₉	1	1	yes	characteristic
411	C₄	#550×C₈₉	1	2	yes	—
412	C₂	—	2	2	no	—
413	C₂	—	8	1	no	—
414	C₂	—	8	4	no	—
415	C₂	C₈₉×#2431	1	1	yes	characteristic
416	C₂	C₂×#455×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₈₉×#3508	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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
2. C₈₉×#3139	C₂	semidirect
3. C₈₉×#3039	C₂	semidirect
4. C₈₉×#2858	C₂	semidirect
5. C₈₉×#2004	C₂	semidirect
6. C₈₉×#1994	C₂	semidirect
7. C₈₉×#1965	C₂	semidirect
8. C₈₉×#1885	C₂	semidirect
9. C₄×#104×C₈₉	C₂	semidirect
145. C₄²×C₈₉	#41	semidirect
203. #25590	C₈₉	direct (N × H)
210. #3139	C₂×C₈₉	semidirect
211. #3039	C₂×C₈₉	semidirect
212. #2858	C₂×C₈₉	semidirect
213. #2004	C₂×C₈₉	semidirect
214. #1994	C₂×C₈₉	semidirect
215. #1965	C₂×C₈₉	semidirect
216. #1885	C₂×C₈₉	semidirect
217. C₄×#104	C₂×C₈₉	semidirect
218. C₈₉	#25590	direct (N × H)
354. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3139	2
C₈₉×#3039	2
C₈₉×#2858	2
C₈₉×#2004	2
C₈₉×#1994	2
C₈₉×#1965	2
C₈₉×#1885	2
C₄×#104×C₈₉	2
#25590	89

Subgroups — C89×#25590 #36403438

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25590 #36403438