Subgroups — C₈₉×#61290 #36439138

Order 22784.

1774 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3512	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3355	C₂	1	4	yes	maximal, complemented
3	C₈₉×#3352	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3337	C₂	1	8	yes	maximal, complemented
5	C₂×#499×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3098	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3080	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3060	C₂	1	2	yes	maximal, complemented
9	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2912	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₈₉	C₂²	1	2	yes	—
14	#553×C₈₉	—	2	8	no	—
15	#553×C₈₉	C₂²	1	8	yes	—
16	#552×C₈₉	C₂²	1	8	yes	—
17	#541×C₈₉	—	2	2	no	—
18	#540×C₈₉	—	2	2	no	—
19	#537×C₈₉	C₂²	1	4	yes	—
20	#532×C₈₉	C₂²	1	1	yes	characteristic
21	#529×C₈₉	—	2	4	no	—
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	#520×C₈₉	C₂²	1	4	yes	—
24	C₄×#41×C₈₉	C₂²	1	2	yes	—
25	#499×C₈₉	C₂²	1	4	yes	—
26	#499×C₈₉	C₂²	1	4	yes	—
27	#485×C₈₉	C₂²	1	8	yes	—
28	#484×C₈₉	C₂²	1	8	yes	—
29	#482×C₈₉	C₂²	1	8	yes	—
30	#480×C₈₉	C₂²	1	8	yes	—
31	#479×C₈₉	C₂²	1	8	yes	—
32	#478×C₈₉	C₂²	1	8	yes	—
33	#470×C₈₉	C₂²	1	4	yes	—
34	#469×C₈₉	C₂²	1	4	yes	—
35	#465×C₈₉	C₂²	1	8	yes	—
36	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
37	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
38	C₄×D₈×C₈₉	C₂²	1	2	yes	—
39	#436×C₈₉	C₂²	1	4	yes	—
40	C₈×D₄×C₈₉	C₂²	1	4	yes	—
41	#428×C₈₉	C₂²	1	4	yes	—
42	#428×C₈₉	C₂²	1	8	yes	—
43	#427×C₈₉	C₂²	1	4	yes	—
44	#427×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#107×C₈₉	C₂²	1	2	yes	—
46	C₂×#106×C₈₉	C₂²	1	4	yes	—
47	C₂×#106×C₈₉	C₂²	1	2	yes	—
48	#423×C₈₉	C₂²	1	1	yes	characteristic
49	#417×C₈₉	C₂²	1	4	yes	—
50	#416×C₈₉	C₂²	1	2	yes	—
51	#408×C₈₉	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#41×C₈₉	C₂³	1	2	yes	—
54	C₂×#41×C₈₉	C₂³	1	2	yes	—
55	#135×C₈₉	—	2	4	no	—
56	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
57	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
58	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
59	#131×C₈₉	—	2	8	no	—
60	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
64	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
66	#127×C₈₉	D₄	1	1	yes	characteristic
67	#126×C₈₉	—	2	8	no	—
68	#126×C₈₉	—	2	8	no	—
69	#125×C₈₉	—	2	8	no	—
70	#125×C₈₉	—	2	2	no	—
71	#125×C₈₉	—	2	2	no	—
72	#125×C₈₉	C₂³	1	8	yes	—
73	#124×C₈₉	D₄	1	2	yes	—
74	#123×C₈₉	—	2	8	no	—
75	#123×C₈₉	—	2	8	no	—
76	C₂²⋊Q₈×C₈₉	—	2	4	no	—
77	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
78	#121×C₈₉	—	2	4	no	—
79	#121×C₈₉	—	2	8	no	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	D₄	1	4	yes	—
82	#121×C₈₉	C₂³	1	8	yes	—
83	C₄×Q₈×C₈₉	—	2	4	no	—
84	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
85	C₄×D₄×C₈₉	—	2	4	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	C₄×D₄×C₈₉	—	2	4	no	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₄×D₄×C₈₉	C₂³	1	4	yes	—
90	C₄×D₄×C₈₉	C₂³	1	4	yes	—
91	#117×C₈₉	—	2	8	no	—
92	#117×C₈₉	—	2	2	no	—
93	#117×C₈₉	C₂³	1	2	yes	—
94	#117×C₈₉	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
98	C₂×C₄²×C₈₉	—	2	2	no	—
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	#107×C₈₉	C₂³	1	4	yes	—
101	#107×C₈₉	C₂³	1	4	yes	—
102	#107×C₈₉	C₂³	1	2	yes	—
103	#107×C₈₉	C₂³	1	8	yes	—
104	#106×C₈₉	C₂³	1	2	yes	—
105	#106×C₈₉	C₂³	1	4	yes	—
106	#106×C₈₉	C₂³	1	4	yes	—
107	#106×C₈₉	C₂³	1	8	yes	—
108	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
109	#103×C₈₉	C₂³	1	4	yes	—
110	#103×C₈₉	C₂³	1	8	yes	—
111	#102×C₈₉	C₂³	1	4	yes	—
112	#102×C₈₉	C₂³	1	8	yes	—
113	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
114	C₄×C₈×C₈₉	C₂³	1	2	yes	—
115	C₄×C₈×C₈₉	C₂³	1	2	yes	—
116	#41×C₈₉	—	2	4	no	—
117	#41×C₈₉	—	2	4	no	—
118	#41×C₈₉	—	2	4	no	—
119	#41×C₈₉	—	2	4	no	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
122	C₂×D₄×C₈₉	—	2	2	no	—
123	C₂×D₄×C₈₉	—	2	8	no	—
124	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₈₉	—	2	4	no	—
129	C₂²×C₄×C₈₉	—	2	8	no	—
130	C₂²×C₄×C₈₉	—	2	2	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₈₉	—	2	2	no	—
136	SD₁₆×C₈₉	—	2	4	no	—
137	D₈×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	2	4	no	—
139	M₁₆×C₈₉	—	2	8	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	8	no	—
142	C₂×C₈×C₈₉	#41	1	4	yes	—
143	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
144	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
145	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	8	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	8	no	—
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	2	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₂²⋊C₄×C₈₉	—	2	4	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
162	C₄²×C₈₉	—	2	4	no	—
163	C₄²×C₈₉	—	2	2	no	—
164	C₄²×C₈₉	—	2	8	no	—
165	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂⁴	1	2	yes	—
168	C₂³×C₈₉	—	2	2	no	—
169	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
170	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₈₉	—	2	4	no	—
172	Q₈×C₈₉	—	2	2	no	—
173	Q₈×C₈₉	—	2	2	no	—
174	D₄×C₈₉	—	2	8	no	—
175	D₄×C₈₉	—	2	4	no	—
176	D₄×C₈₉	—	2	2	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	4	4	no	—
179	D₄×C₈₉	—	4	4	no	—
180	D₄×C₈₉	—	8	8	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	4	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	8	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	4	no	—
188	C₂×C₄×C₈₉	—	8	4	no	—
189	C₂×C₄×C₈₉	—	8	8	no	—
190	C₂×C₄×C₈₉	—	8	4	no	—
191	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
196	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
197	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
198	C₈×C₈₉	—	2	4	no	—
199	C₈×C₈₉	—	2	2	no	—
200	C₈×C₈₉	C₂×#41	1	2	yes	—
201	C₈×C₈₉	C₂×#41	1	2	yes	—
202	C₂²×C₈₉	—	2	2	no	—
203	C₂²×C₈₉	—	2	8	no	—
204	C₂²×C₈₉	—	2	4	no	—
205	C₂²×C₈₉	—	4	4	no	—
206	C₂²×C₈₉	—	4	2	no	—
207	C₂²×C₈₉	#547	1	2	yes	—
208	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	—	2	4	no	—
212	C₄×C₈₉	—	4	4	no	—
213	C₄×C₈₉	—	4	8	no	—
214	C₄×C₈₉	—	4	2	no	—
215	C₄×C₈₉	#547	1	2	yes	—
216	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
217	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
218	#61290	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₈₉	—	2	2	no	—
220	C₂×C₈₉	—	4	4	no	—
221	C₂×C₈₉	—	8	2	no	—
222	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
223	C₂×C₈₉	#3584	1	2	yes	—
224	#3512	C₂×C₈₉	1	2	yes	complemented
225	#3355	C₂×C₈₉	1	4	yes	complemented
226	#3352	C₂×C₈₉	1	4	yes	complemented
227	#3337	C₂×C₈₉	1	8	yes	complemented
228	C₂×#499	C₂×C₈₉	1	1	yes	characteristic, complemented
229	#3098	C₂×C₈₉	1	4	yes	complemented
230	#3080	C₂×C₈₉	1	2	yes	complemented
231	#3060	C₂×C₈₉	1	2	yes	complemented
232	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#2931	C₂×C₈₉	1	1	yes	characteristic, complemented
234	#2912	C₂×C₈₉	1	2	yes	complemented
235	C₈₉	#61290	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
237	C₂×#131	C₂²×C₈₉	1	2	yes	—
238	#553	—	2	8	no	—
239	#553	C₂²×C₈₉	1	8	yes	—
240	#552	C₂²×C₈₉	1	8	yes	—
241	#541	—	2	2	no	—
242	#540	—	2	2	no	—
243	#537	C₂²×C₈₉	1	4	yes	—
244	#532	C₂²×C₈₉	1	1	yes	characteristic
245	#529	—	2	4	no	—
246	C₂×#125	C₂²×C₈₉	1	2	yes	—
247	#520	C₂²×C₈₉	1	4	yes	—
248	C₄×#41	C₂²×C₈₉	1	2	yes	—
249	#499	C₂²×C₈₉	1	4	yes	—
250	#499	C₂²×C₈₉	1	4	yes	—
251	#485	C₂²×C₈₉	1	8	yes	—
252	#484	C₂²×C₈₉	1	8	yes	—
253	#482	C₂²×C₈₉	1	8	yes	—
254	#480	C₂²×C₈₉	1	8	yes	—
255	#479	C₂²×C₈₉	1	8	yes	—
256	#478	C₂²×C₈₉	1	8	yes	—
257	#470	C₂²×C₈₉	1	4	yes	—
258	#469	C₂²×C₈₉	1	4	yes	—
259	#465	C₂²×C₈₉	1	8	yes	—
260	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
261	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
262	C₄×D₈	C₂²×C₈₉	1	2	yes	—
263	#436	C₂²×C₈₉	1	4	yes	—
264	C₈×D₄	C₂²×C₈₉	1	4	yes	—
265	#428	C₂²×C₈₉	1	4	yes	—
266	#428	C₂²×C₈₉	1	8	yes	—
267	#427	C₂²×C₈₉	1	4	yes	—
268	#427	C₂²×C₈₉	1	1	yes	characteristic
269	C₂×#107	C₂²×C₈₉	1	2	yes	—
270	C₂×#106	C₂²×C₈₉	1	4	yes	—
271	C₂×#106	C₂²×C₈₉	1	2	yes	—
272	#423	C₂²×C₈₉	1	1	yes	characteristic
273	#417	C₂²×C₈₉	1	4	yes	—
274	#416	C₂²×C₈₉	1	2	yes	—
275	#408	C₂²×C₈₉	1	2	yes	—
276	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
277	C₂×#41	C₂³×C₈₉	1	2	yes	—
278	C₂×#41	C₂³×C₈₉	1	2	yes	—
279	#135	—	2	4	no	—
280	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
281	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
282	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
283	#131	—	2	8	no	—
284	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
285	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
286	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
287	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
289	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
290	#127	D₄×C₈₉	1	1	yes	characteristic
291	#126	—	2	8	no	—
292	#126	—	2	8	no	—
293	#125	—	2	8	no	—
294	#125	—	2	2	no	—
295	#125	—	2	2	no	—
296	#125	C₂³×C₈₉	1	8	yes	—
297	#124	D₄×C₈₉	1	2	yes	—
298	#123	—	2	8	no	—
299	#123	—	2	8	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
302	#121	—	2	4	no	—
303	#121	—	2	8	no	—
304	#121	—	2	8	no	—
305	#121	D₄×C₈₉	1	4	yes	—
306	#121	C₂³×C₈₉	1	8	yes	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	—	2	8	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	8	no	—
313	C₄×D₄	C₂³×C₈₉	1	4	yes	—
314	C₄×D₄	C₂³×C₈₉	1	4	yes	—
315	#117	—	2	8	no	—
316	#117	—	2	2	no	—
317	#117	C₂³×C₈₉	1	2	yes	—
318	#117	C₂³×C₈₉	1	8	yes	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
321	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
324	#107	C₂³×C₈₉	1	4	yes	—
325	#107	C₂³×C₈₉	1	4	yes	—
326	#107	C₂³×C₈₉	1	2	yes	—
327	#107	C₂³×C₈₉	1	8	yes	—
328	#106	C₂³×C₈₉	1	2	yes	—
329	#106	C₂³×C₈₉	1	4	yes	—
330	#106	C₂³×C₈₉	1	4	yes	—
331	#106	C₂³×C₈₉	1	8	yes	—
332	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
333	#103	C₂³×C₈₉	1	4	yes	—
334	#103	C₂³×C₈₉	1	8	yes	—
335	#102	C₂³×C₈₉	1	4	yes	—
336	#102	C₂³×C₈₉	1	8	yes	—
337	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
338	C₄×C₈	C₂³×C₈₉	1	2	yes	—
339	C₄×C₈	C₂³×C₈₉	1	2	yes	—
340	#41	—	2	4	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
345	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	8	no	—
348	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
349	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
350	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
351	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
359	Q₁₆	—	2	2	no	—
360	SD₁₆	—	2	4	no	—
361	D₈	—	2	2	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	8	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	8	no	—
366	C₂×C₈	#41×C₈₉	1	4	yes	—
367	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
368	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
369	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
370	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
378	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
379	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	2	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
386	C₄²	—	2	4	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	8	no	—
389	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
390	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
391	C₄²	C₂⁴×C₈₉	1	2	yes	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
394	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	2	no	—
397	Q₈	—	2	2	no	—
398	D₄	—	2	8	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	8	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	8	4	no	—
413	C₂×C₄	—	8	8	no	—
414	C₂×C₄	—	8	4	no	—
415	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
420	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
421	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	2	2	no	—
424	C₈	C₂×#41×C₈₉	1	2	yes	—
425	C₈	C₂×#41×C₈₉	1	2	yes	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	#547×C₈₉	1	2	yes	—
432	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	8	no	—
438	C₄	—	4	2	no	—
439	C₄	#547×C₈₉	1	2	yes	—
440	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
441	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
442	C₂	—	2	2	no	—
443	C₂	—	4	4	no	—
444	C₂	—	8	2	no	—
445	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
446	C₂	C₈₉×#3584	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #532×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3512	C₂	semidirect
2. C₈₉×#3355	C₂	semidirect
3. C₈₉×#3352	C₂	semidirect
4. C₈₉×#3337	C₂	semidirect
5. C₂×#499×C₈₉	C₂	semidirect
6. C₈₉×#3098	C₂	semidirect
7. C₈₉×#3080	C₂	semidirect
8. C₈₉×#3060	C₂	semidirect
9. C₄×#135×C₈₉	C₂	semidirect
10. C₈₉×#2931	C₂	semidirect
11. C₈₉×#2912	C₂	semidirect
218. #61290	C₈₉	direct (N × H)
224. #3512	C₂×C₈₉	semidirect
225. #3355	C₂×C₈₉	semidirect
226. #3352	C₂×C₈₉	semidirect
227. #3337	C₂×C₈₉	semidirect
228. C₂×#499	C₂×C₈₉	semidirect
229. #3098	C₂×C₈₉	semidirect
230. #3080	C₂×C₈₉	semidirect
231. #3060	C₂×C₈₉	semidirect
232. C₄×#135	C₂×C₈₉	semidirect
233. #2931	C₂×C₈₉	semidirect
234. #2912	C₂×C₈₉	semidirect
235. C₈₉	#61290	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×#3512	2
C₈₉×#3355	2
C₈₉×#3352	2
C₈₉×#3337	2
C₂×#499×C₈₉	2
C₈₉×#3098	2
C₈₉×#3080	2
C₈₉×#3060	2
C₄×#135×C₈₉	2
C₈₉×#2931	2
C₈₉×#2912	2
#61290	89

Subgroups — C89×#61290 #36439138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61290 #36439138