Subgroups — C₈₉×#19362 #36397210

Order 22784.

648 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3238	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3217	C₂	1	1	yes	maximal, characteristic
3	C₂×#486×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2966	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1698	C₂	1	2	yes	maximal, complemented
6	C₈₉×#1697	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1678	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1677	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
14	#529×C₈₉	C₂²	1	1	yes	characteristic
15	#501×C₈₉	—	2	1	no	—
16	#496×C₈₉	—	2	1	no	—
17	#490×C₈₉	—	2	1	no	—
18	#489×C₈₉	—	2	1	no	—
19	#486×C₈₉	—	2	1	no	—
20	#486×C₈₉	—	2	1	no	—
21	#486×C₈₉	C₂²	1	2	yes	—
22	#486×C₈₉	C₂²	1	2	yes	—
23	#483×C₈₉	—	2	1	no	—
24	#480×C₈₉	—	2	1	no	—
25	#477×C₈₉	C₂²	1	2	yes	complemented
26	#476×C₈₉	C₂²	1	2	yes	complemented
27	#460×C₈₉	C₂²	1	2	yes	—
28	#459×C₈₉	C₂²	1	2	yes	—
29	#450×C₈₉	—	2	1	no	—
30	#447×C₈₉	—	2	1	no	—
31	#446×C₈₉	C₂²	1	1	yes	characteristic, complemented
32	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	#436×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	#435×C₈₉	—	2	1	no	—
35	C₈×D₄×C₈₉	—	2	1	no	—
36	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
37	#433×C₈₉	—	2	1	no	—
38	#432×C₈₉	C₂²	1	1	yes	characteristic
39	#432×C₈₉	C₂²	1	1	yes	characteristic
40	#432×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₈₉	—	2	1	no	—
42	C₂×#102×C₈₉	—	2	1	no	—
43	#405×C₈₉	—	2	1	no	—
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	2	yes	complemented
46	#334×C₈₉	C₂²	1	2	yes	complemented
47	#333×C₈₉	C₂²	1	2	yes	complemented
48	#333×C₈₉	C₂²	1	2	yes	complemented
49	#331×C₈₉	C₂²	1	2	yes	—
50	#331×C₈₉	C₂²	1	2	yes	—
51	C₂²×Q₈×C₈₉	—	2	1	no	—
52	C₂²×D₄×C₈₉	—	2	1	no	—
53	C₂²×D₄×C₈₉	—	2	1	no	—
54	C₂²×D₄×C₈₉	—	2	1	no	—
55	C₂×SD₁₆×C₈₉	—	2	2	no	—
56	C₂×D₈×C₈₉	—	2	2	no	—
57	C₂×M₁₆×C₈₉	—	2	1	no	—
58	C₂²×C₈×C₈₉	—	2	1	no	—
59	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₈₉	—	2	1	no	—
62	C₄⋊Q₈×C₈₉	—	2	1	no	—
63	C₄⋊Q₈×C₈₉	—	2	1	no	—
64	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
65	#127×C₈₉	—	2	1	no	—
66	#127×C₈₉	—	2	1	no	—
67	#127×C₈₉	—	2	1	no	—
68	#127×C₈₉	C₂³	1	2	yes	—
69	#126×C₈₉	—	2	1	no	—
70	#125×C₈₉	D₄	1	1	yes	characteristic
71	#124×C₈₉	D₄	1	1	yes	characteristic
72	#123×C₈₉	—	2	1	no	—
73	C₂²⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
74	#121×C₈₉	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₄×D₄×C₈₉	—	2	1	no	—
77	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
78	#117×C₈₉	—	2	1	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	#107×C₈₉	—	2	2	no	—
83	#106×C₈₉	—	2	2	no	—
84	C₄⋊C₈×C₈₉	—	2	1	no	—
85	C₄⋊C₈×C₈₉	—	2	1	no	—
86	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	#103×C₈₉	—	2	2	no	—
91	#102×C₈₉	—	2	2	no	—
92	#102×C₈₉	—	2	2	no	—
93	#102×C₈₉	—	2	2	no	—
94	#102×C₈₉	—	2	2	no	—
95	#102×C₈₉	—	2	2	no	—
96	#102×C₈₉	—	2	2	no	—
97	#102×C₈₉	—	2	2	no	—
98	C₂²⋊C₈×C₈₉	—	2	1	no	—
99	C₂²⋊C₈×C₈₉	—	2	1	no	—
100	C₂²⋊C₈×C₈₉	—	2	1	no	—
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₂²⋊C₈×C₈₉	—	2	1	no	—
103	#97×C₈₉	—	2	1	no	—
104	#97×C₈₉	—	2	1	no	—
105	#97×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
110	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	C₂⁴×C₈₉	—	4	1	no	—
113	C₂×Q₈×C₈₉	—	2	2	no	—
114	C₂×Q₈×C₈₉	—	4	1	no	—
115	C₂×Q₈×C₈₉	—	8	2	no	—
116	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂×D₄×C₈₉	—	2	2	no	—
121	C₂×D₄×C₈₉	—	4	2	no	—
122	C₂×D₄×C₈₉	—	4	2	no	—
123	C₂×D₄×C₈₉	—	4	1	no	—
124	C₂×D₄×C₈₉	—	4	1	no	—
125	C₂×D₄×C₈₉	—	4	1	no	—
126	C₂×D₄×C₈₉	—	8	2	no	—
127	C₂×D₄×C₈₉	—	8	2	no	—
128	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	—	2	1	no	—
130	C₂²×C₄×C₈₉	—	4	1	no	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	SD₁₆×C₈₉	—	8	2	no	—
135	D₈×C₈₉	—	8	2	no	—
136	M₁₆×C₈₉	—	4	2	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	4	1	no	—
142	C₂×C₈×C₈₉	—	4	1	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	—	4	1	no	—
155	C₄⋊C₄×C₈₉	—	4	1	no	—
156	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂²⋊C₄×C₈₉	—	2	1	no	—
159	C₂²⋊C₄×C₈₉	—	2	1	no	—
160	C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₂²⋊C₄×C₈₉	—	2	1	no	—
162	C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₄²×C₈₉	—	2	1	no	—
164	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₈₉	#41	1	1	yes	characteristic
167	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₂³×C₈₉	—	2	1	no	—
169	C₂³×C₈₉	—	4	2	no	—
170	C₂³×C₈₉	—	8	2	no	—
171	C₂³×C₈₉	—	8	2	no	—
172	C₂³×C₈₉	—	8	2	no	—
173	C₂³×C₈₉	#121	1	1	yes	characteristic
174	Q₈×C₈₉	—	2	2	no	—
175	Q₈×C₈₉	—	8	2	no	—
176	Q₈×C₈₉	—	8	2	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	4	2	no	—
179	D₄×C₈₉	—	4	2	no	—
180	D₄×C₈₉	—	4	2	no	—
181	D₄×C₈₉	—	4	2	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	8	2	no	—
184	D₄×C₈₉	—	8	2	no	—
185	D₄×C₈₉	—	8	2	no	—
186	D₄×C₈₉	—	8	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	2	no	—
197	C₂×C₄×C₈₉	—	8	2	no	—
198	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
200	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	—	2	1	no	—
208	C₈×C₈₉	—	4	1	no	—
209	C₈×C₈₉	—	4	1	no	—
210	C₈×C₈₉	—	4	2	no	—
211	C₈×C₈₉	—	4	2	no	—
212	C₂²×C₈₉	—	2	1	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	4	1	no	—
215	C₂²×C₈₉	—	4	1	no	—
216	C₂²×C₈₉	—	4	1	no	—
217	C₂²×C₈₉	—	8	2	no	—
218	C₂²×C₈₉	—	8	2	no	—
219	C₂²×C₈₉	—	8	2	no	—
220	C₂²×C₈₉	—	16	4	no	—
221	C₂²×C₈₉	#472	1	2	yes	—
222	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	2	1	no	—
227	C₄×C₈₉	—	4	1	no	—
228	C₄×C₈₉	—	4	1	no	—
229	C₄×C₈₉	—	4	1	no	—
230	C₄×C₈₉	—	8	2	no	—
231	C₄×C₈₉	#575	1	1	yes	characteristic
232	C₄×C₈₉	#575	1	1	yes	characteristic
233	C₄×C₈₉	#577	1	2	yes	—
234	#19362	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₈₉	—	2	2	no	—
236	C₂×C₈₉	—	8	1	no	—
237	C₂×C₈₉	—	16	2	no	—
238	C₂×C₈₉	#3040	1	1	yes	characteristic
239	C₂×C₈₉	#3057	1	1	yes	characteristic
240	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
241	#3238	C₂×C₈₉	1	1	yes	characteristic, complemented
242	#3217	C₂×C₈₉	1	1	yes	characteristic
243	C₂×#486	C₂×C₈₉	1	1	yes	characteristic, complemented
244	#2966	C₂×C₈₉	1	1	yes	characteristic, complemented
245	#1698	C₂×C₈₉	1	2	yes	complemented
246	#1697	C₂×C₈₉	1	2	yes	complemented
247	#1678	C₂×C₈₉	1	2	yes	complemented
248	#1677	C₂×C₈₉	1	2	yes	complemented
249	#1568	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#1558	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#1555	C₂×C₈₉	1	1	yes	characteristic, complemented
252	C₈₉	#19362	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
254	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
255	#529	C₂²×C₈₉	1	1	yes	characteristic
256	#501	—	2	1	no	—
257	#496	—	2	1	no	—
258	#490	—	2	1	no	—
259	#489	—	2	1	no	—
260	#486	—	2	1	no	—
261	#486	—	2	1	no	—
262	#486	C₂²×C₈₉	1	2	yes	—
263	#486	C₂²×C₈₉	1	2	yes	—
264	#483	—	2	1	no	—
265	#480	—	2	1	no	—
266	#477	C₂²×C₈₉	1	2	yes	complemented
267	#476	C₂²×C₈₉	1	2	yes	complemented
268	#460	C₂²×C₈₉	1	2	yes	—
269	#459	C₂²×C₈₉	1	2	yes	—
270	#450	—	2	1	no	—
271	#447	—	2	1	no	—
272	#446	C₂²×C₈₉	1	1	yes	characteristic, complemented
273	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
274	#436	C₂²×C₈₉	1	1	yes	characteristic, complemented
275	#435	—	2	1	no	—
276	C₈×D₄	—	2	1	no	—
277	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
278	#433	—	2	1	no	—
279	#432	C₂²×C₈₉	1	1	yes	characteristic
280	#432	C₂²×C₈₉	1	1	yes	characteristic
281	#432	C₂²×C₈₉	1	1	yes	characteristic
282	C₂×#102	—	2	1	no	—
283	C₂×#102	—	2	1	no	—
284	#405	—	2	1	no	—
285	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
286	#335	C₂²×C₈₉	1	2	yes	complemented
287	#334	C₂²×C₈₉	1	2	yes	complemented
288	#333	C₂²×C₈₉	1	2	yes	complemented
289	#333	C₂²×C₈₉	1	2	yes	complemented
290	#331	C₂²×C₈₉	1	2	yes	—
291	#331	C₂²×C₈₉	1	2	yes	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	1	no	—
295	C₂²×D₄	—	2	1	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂²×C₈	—	2	1	no	—
300	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
301	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
302	C₄⋊Q₈	—	2	1	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	C₂³×C₈₉	1	2	yes	—
310	#126	—	2	1	no	—
311	#125	D₄×C₈₉	1	1	yes	characteristic
312	#124	D₄×C₈₉	1	1	yes	characteristic
313	#123	—	2	1	no	—
314	C₂²⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
315	#121	D₄×C₈₉	1	1	yes	characteristic
316	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
319	#117	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
323	#107	—	2	2	no	—
324	#106	—	2	2	no	—
325	C₄⋊C₈	—	2	1	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
328	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
330	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
331	#103	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	2	2	no	—
338	#102	—	2	2	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	2	1	no	—
343	C₂²⋊C₈	—	2	1	no	—
344	#97	—	2	1	no	—
345	#97	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
350	C₄×C₈	D₄×C₈₉	1	1	yes	characteristic
351	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
352	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
353	C₂⁴	—	4	1	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	4	1	no	—
356	C₂×Q₈	—	8	2	no	—
357	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	2	no	—
360	C₂×D₄	—	2	2	no	—
361	C₂×D₄	—	2	2	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	—	4	1	no	—
366	C₂×D₄	—	4	1	no	—
367	C₂×D₄	—	8	2	no	—
368	C₂×D₄	—	8	2	no	—
369	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
374	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
375	SD₁₆	—	8	2	no	—
376	D₈	—	8	2	no	—
377	M₁₆	—	4	2	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	1	no	—
383	C₂×C₈	—	4	1	no	—
384	C₂×C₈	—	4	2	no	—
385	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
387	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
388	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	—	4	1	no	—
397	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
398	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
399	C₂²⋊C₄	—	2	1	no	—
400	C₂²⋊C₄	—	2	1	no	—
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	2	1	no	—
403	C₂²⋊C₄	—	2	1	no	—
404	C₄²	—	2	1	no	—
405	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
407	C₄²	#41×C₈₉	1	1	yes	characteristic
408	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	8	2	no	—
412	C₂³	—	8	2	no	—
413	C₂³	—	8	2	no	—
414	C₂³	#121×C₈₉	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	8	2	no	—
417	Q₈	—	8	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	D₄	—	8	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	8	2	no	—
439	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
440	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
441	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
442	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	8	2	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	16	4	no	—
462	C₂²	#472×C₈₉	1	2	yes	—
463	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	8	2	no	—
472	C₄	#575×C₈₉	1	1	yes	characteristic
473	C₄	#575×C₈₉	1	1	yes	characteristic
474	C₄	#577×C₈₉	1	2	yes	—
475	C₂	—	2	2	no	—
476	C₂	—	8	1	no	—
477	C₂	—	16	2	no	—
478	C₂	C₈₉×#3040	1	1	yes	characteristic
479	C₂	C₈₉×#3057	1	1	yes	characteristic
480	C₂	C₂×#472×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3217	C₂
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
1. C₈₉×#3238	C₂	semidirect
3. C₂×#486×C₈₉	C₂	semidirect
4. C₈₉×#2966	C₂	semidirect
5. C₈₉×#1698	C₂	semidirect
6. C₈₉×#1697	C₂	semidirect
7. C₈₉×#1678	C₂	semidirect
8. C₈₉×#1677	C₂	semidirect
9. C₈₉×#1568	C₂	semidirect
10. C₈₉×#1558	C₂	semidirect
11. C₈₉×#1555	C₂	semidirect
25. #477×C₈₉	C₂²	semidirect
26. #476×C₈₉	C₂²	semidirect
31. #446×C₈₉	C₂²	semidirect
32. C₈×Q₈×C₈₉	C₂²	semidirect
33. #436×C₈₉	C₂²	semidirect
36. C₈×D₄×C₈₉	C₂²	semidirect
45. #335×C₈₉	C₂²	semidirect
46. #334×C₈₉	C₂²	semidirect
47. #333×C₈₉	C₂²	semidirect
48. #333×C₈₉	C₂²	semidirect
234. #19362	C₈₉	direct (N × H)
241. #3238	C₂×C₈₉	semidirect
243. C₂×#486	C₂×C₈₉	semidirect
244. #2966	C₂×C₈₉	semidirect
245. #1698	C₂×C₈₉	semidirect
246. #1697	C₂×C₈₉	semidirect
247. #1678	C₂×C₈₉	semidirect
248. #1677	C₂×C₈₉	semidirect
249. #1568	C₂×C₈₉	semidirect
250. #1558	C₂×C₈₉	semidirect
251. #1555	C₂×C₈₉	semidirect
252. C₈₉	#19362	direct (N × H)
266. #477	C₂²×C₈₉	semidirect
267. #476	C₂²×C₈₉	semidirect
272. #446	C₂²×C₈₉	semidirect
273. C₈×Q₈	C₂²×C₈₉	semidirect
274. #436	C₂²×C₈₉	semidirect
277. C₈×D₄	C₂²×C₈₉	semidirect
286. #335	C₂²×C₈₉	semidirect
287. #334	C₂²×C₈₉	semidirect
288. #333	C₂²×C₈₉	semidirect
289. #333	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3238	2
C₈₉×#3217	2
C₂×#486×C₈₉	2
C₈₉×#2966	2
C₈₉×#1698	2
C₈₉×#1697	2
C₈₉×#1678	2
C₈₉×#1677	2
C₈₉×#1568	2
C₈₉×#1558	2
C₈₉×#1555	2
#19362	89

Subgroups — C89×#19362 #36397210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#19362 #36397210