Subgroups — C₈₉×#33530 #36411378

Order 22784.

1132 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3414	C₂	1	2	yes	maximal, complemented
3	C₈₉×#3054	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2191	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2190	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2145	C₂	1	2	yes	maximal, complemented
7	C₂×#349×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₈₉	—	2	1	no	—
9	#575×C₈₉	—	2	4	no	—
10	#575×C₈₉	—	2	2	no	—
11	#575×C₈₉	C₂²	1	4	yes	—
12	C₂×#137×C₈₉	—	2	2	no	—
13	C₂×AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
14	C₂×#135×C₈₉	—	2	1	no	—
15	C₂×#135×C₈₉	C₂²	1	2	yes	—
16	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	#525×C₈₉	—	2	1	no	—
19	#510×C₈₉	—	2	2	no	—
20	#510×C₈₉	C₂²	1	4	yes	complemented
21	#509×C₈₉	—	2	2	no	—
22	#509×C₈₉	C₂²	1	4	yes	complemented
23	#508×C₈₉	—	2	4	no	—
24	C₂×M₃₂×C₈₉	C₂²	1	2	yes	complemented
25	#470×C₈₉	C₂²	1	2	yes	complemented
26	#469×C₈₉	C₂²	1	2	yes	complemented
27	#468×C₈₉	—	2	2	no	—
28	#427×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	#416×C₈₉	—	2	1	no	—
30	#360×C₈₉	C₂²	1	8	yes	complemented
31	#349×C₈₉	C₂²	1	4	yes	complemented
32	C₂×#41×C₈₉	—	2	2	no	—
33	C₂×#41×C₈₉	—	2	4	no	—
34	C₂×#41×C₈₉	—	2	4	no	—
35	C₂×#41×C₈₉	—	2	2	no	—
36	C₂×#41×C₈₉	—	2	1	no	—
37	C₂×#41×C₈₉	—	4	1	no	—
38	C₂×#41×C₈₉	—	4	2	no	—
39	C₂×#41×C₈₉	—	4	2	no	—
40	C₂×#41×C₈₉	—	4	1	no	—
41	C₂²×Q₈×C₈₉	—	2	1	no	—
42	C₂²×D₄×C₈₉	—	2	1	no	—
43	C₂²×D₄×C₈₉	—	4	1	no	—
44	C₂³×C₄×C₈₉	—	4	1	no	—
45	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
46	#137×C₈₉	—	2	8	no	—
47	#137×C₈₉	—	2	8	no	—
48	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
49	AGL(1,ℤ/8)×C₈₉	—	2	8	no	—
50	#135×C₈₉	—	2	4	no	—
51	#135×C₈₉	—	2	4	no	—
52	#135×C₈₉	—	2	2	no	—
53	#135×C₈₉	—	2	2	no	—
54	#135×C₈₉	—	2	2	no	—
55	#135×C₈₉	—	2	2	no	—
56	#135×C₈₉	D₄	1	4	yes	complemented
57	#135×C₈₉	C₂³	1	4	yes	—
58	C₂×Q₁₆×C₈₉	—	2	1	no	—
59	C₂×Q₁₆×C₈₉	D₄	1	2	yes	complemented
60	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic, complemented
61	C₂×SD₁₆×C₈₉	—	2	2	no	—
62	C₂×SD₁₆×C₈₉	—	2	2	no	—
63	C₂×SD₁₆×C₈₉	—	2	1	no	—
64	C₂×D₈×C₈₉	—	2	1	no	—
65	C₂×D₈×C₈₉	D₄	1	2	yes	complemented
66	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic, complemented
67	C₂×M₁₆×C₈₉	—	2	2	no	—
68	C₂×M₁₆×C₈₉	—	2	2	no	—
69	C₂×M₁₆×C₈₉	D₄	1	2	yes	—
70	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	#123×C₈₉	—	4	1	no	—
74	C₂²⋊Q₈×C₈₉	—	2	2	no	—
75	#121×C₈₉	—	2	2	no	—
76	#120×C₈₉	—	4	1	no	—
77	C₄×D₄×C₈₉	—	4	2	no	—
78	#117×C₈₉	—	2	1	no	—
79	Q₃₂×C₈₉	—	2	4	no	—
80	SD₃₂×C₈₉	—	2	4	no	—
81	SD₃₂×C₈₉	—	2	4	no	—
82	D₁₆×C₈₉	—	2	4	no	—
83	M₃₂×C₈₉	—	2	2	no	—
84	M₃₂×C₈₉	C₂³	1	4	yes	complemented
85	C₂×C₁₆×C₈₉	—	2	2	no	—
86	#107×C₈₉	—	2	1	no	—
87	#106×C₈₉	C₂³	1	2	yes	complemented
88	#103×C₈₉	—	2	2	no	—
89	#102×C₈₉	—	2	2	no	—
90	C₂⁴×C₈₉	—	4	1	no	—
91	C₂⁴×C₈₉	D₈	1	1	yes	characteristic
92	#41×C₈₉	—	2	8	no	—
93	#41×C₈₉	—	2	4	no	—
94	#41×C₈₉	—	2	4	no	—
95	#41×C₈₉	—	4	4	no	—
96	#41×C₈₉	—	4	4	no	—
97	#41×C₈₉	—	4	4	no	—
98	#41×C₈₉	—	4	4	no	—
99	#41×C₈₉	—	4	4	no	—
100	#41×C₈₉	—	4	2	no	—
101	#41×C₈₉	—	4	2	no	—
102	#41×C₈₉	—	4	1	no	—
103	#41×C₈₉	—	4	1	no	—
104	#41×C₈₉	—	4	1	no	—
105	#41×C₈₉	—	4	1	no	—
106	C₂×Q₈×C₈₉	—	2	4	no	—
107	C₂×Q₈×C₈₉	—	2	2	no	—
108	C₂×Q₈×C₈₉	—	2	1	no	—
109	C₂×Q₈×C₈₉	—	4	1	no	—
110	C₂×Q₈×C₈₉	—	4	2	no	—
111	C₂×D₄×C₈₉	—	2	4	no	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	1	no	—
114	C₂×D₄×C₈₉	—	4	1	no	—
115	C₂×D₄×C₈₉	—	4	2	no	—
116	C₂×D₄×C₈₉	—	4	4	no	—
117	C₂×D₄×C₈₉	—	4	2	no	—
118	C₂×D₄×C₈₉	—	4	4	no	—
119	C₂×D₄×C₈₉	—	4	2	no	—
120	C₂×D₄×C₈₉	—	4	2	no	—
121	C₂×D₄×C₈₉	—	4	1	no	—
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	—	2	1	no	—
126	C₂²×C₄×C₈₉	—	4	2	no	—
127	C₂²×C₄×C₈₉	—	4	4	no	—
128	C₂²×C₄×C₈₉	—	4	4	no	—
129	C₂²×C₄×C₈₉	—	4	1	no	—
130	C₂²×C₄×C₈₉	—	4	2	no	—
131	C₂²×C₄×C₈₉	—	4	1	no	—
132	C₂²×C₄×C₈₉	D₈	1	2	yes	—
133	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	Q₁₆×C₈₉	—	2	4	no	—
137	Q₁₆×C₈₉	—	2	2	no	—
138	Q₁₆×C₈₉	—	2	2	no	—
139	Q₁₆×C₈₉	C₂×D₄	1	4	yes	—
140	SD₁₆×C₈₉	—	2	8	no	—
141	SD₁₆×C₈₉	—	2	4	no	—
142	SD₁₆×C₈₉	—	2	4	no	—
143	SD₁₆×C₈₉	—	4	2	no	—
144	D₈×C₈₉	—	2	4	no	—
145	D₈×C₈₉	—	2	2	no	—
146	D₈×C₈₉	—	2	2	no	—
147	D₈×C₈₉	C₂×D₄	1	4	yes	—
148	M₁₆×C₈₉	—	2	4	no	—
149	M₁₆×C₈₉	—	2	4	no	—
150	C₂×C₈×C₈₉	—	2	1	no	—
151	C₂×C₈×C₈₉	—	2	1	no	—
152	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
157	C₄⋊C₄×C₈₉	—	2	2	no	—
158	C₄⋊C₄×C₈₉	—	4	2	no	—
159	C₂²⋊C₄×C₈₉	—	4	1	no	—
160	C₂²⋊C₄×C₈₉	—	4	2	no	—
161	C₂²⋊C₄×C₈₉	—	4	2	no	—
162	C₄²×C₈₉	—	4	1	no	—
163	C₁₆×C₈₉	—	2	4	no	—
164	C₂³×C₈₉	—	2	1	no	—
165	C₂³×C₈₉	—	2	1	no	—
166	C₂³×C₈₉	—	4	4	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	—	4	1	no	—
169	C₂³×C₈₉	—	8	1	no	—
170	C₂³×C₈₉	—	8	4	no	—
171	C₂³×C₈₉	C₂×D₈	1	2	yes	—
172	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
173	Q₈×C₈₉	—	2	4	no	—
174	Q₈×C₈₉	—	4	4	no	—
175	Q₈×C₈₉	—	4	2	no	—
176	Q₈×C₈₉	—	4	1	no	—
177	Q₈×C₈₉	—	4	1	no	—
178	D₄×C₈₉	—	2	4	no	—
179	D₄×C₈₉	—	4	4	no	—
180	D₄×C₈₉	—	4	8	no	—
181	D₄×C₈₉	—	4	4	no	—
182	D₄×C₈₉	—	4	4	no	—
183	D₄×C₈₉	—	4	1	no	—
184	D₄×C₈₉	—	4	1	no	—
185	D₄×C₈₉	—	4	2	no	—
186	D₄×C₈₉	—	8	4	no	—
187	D₄×C₈₉	—	8	1	no	—
188	D₄×C₈₉	—	8	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	4	8	no	—
196	C₂×C₄×C₈₉	—	4	4	no	—
197	C₂×C₄×C₈₉	—	4	2	no	—
198	C₂×C₄×C₈₉	—	4	4	no	—
199	C₂×C₄×C₈₉	—	4	4	no	—
200	C₂×C₄×C₈₉	—	4	2	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	8	1	no	—
203	C₂×C₄×C₈₉	—	8	1	no	—
204	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
207	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₈×C₈₉	—	2	2	no	—
212	C₈×C₈₉	#120	1	2	yes	—
213	C₈×C₈₉	C₂²×D₄	1	2	yes	—
214	C₂²×C₈₉	—	2	2	no	—
215	C₂²×C₈₉	—	4	1	no	—
216	C₂²×C₈₉	—	4	2	no	—
217	C₂²×C₈₉	—	4	2	no	—
218	C₂²×C₈₉	—	4	4	no	—
219	C₂²×C₈₉	—	8	1	no	—
220	C₂²×C₈₉	—	8	4	no	—
221	C₂²×C₈₉	—	8	2	no	—
222	C₂²×C₈₉	—	8	8	no	—
223	C₂²×C₈₉	—	8	1	no	—
224	C₂²×C₈₉	#447	1	1	yes	characteristic
225	C₂²×C₈₉	#447	1	1	yes	characteristic
226	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
227	C₄×C₈₉	—	2	2	no	—
228	C₄×C₈₉	—	4	4	no	—
229	C₄×C₈₉	—	8	2	no	—
230	C₄×C₈₉	—	8	1	no	—
231	C₄×C₈₉	#447	1	1	yes	characteristic
232	C₄×C₈₉	#447	1	1	yes	characteristic
233	C₄×C₈₉	C₂×#120	1	1	yes	characteristic
234	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	#33530	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂×C₈₉	—	2	1	no	—
237	C₂×C₈₉	—	2	1	no	—
238	C₂×C₈₉	—	2	1	no	—
239	C₂×C₈₉	—	4	2	no	—
240	C₂×C₈₉	—	8	4	no	—
241	C₂×C₈₉	—	16	1	no	—
242	C₂×C₈₉	C₂×#447	1	1	yes	characteristic
243	C₂×#575	C₂×C₈₉	1	1	yes	characteristic, complemented
244	#3414	C₂×C₈₉	1	2	yes	complemented
245	#3054	C₂×C₈₉	1	1	yes	characteristic, complemented
246	#2191	C₂×C₈₉	1	4	yes	complemented
247	#2190	C₂×C₈₉	1	4	yes	complemented
248	#2145	C₂×C₈₉	1	2	yes	complemented
249	C₂×#349	C₂×C₈₉	1	1	yes	characteristic, complemented
250	C₈₉	#33530	1	1	yes	characteristic, direct product factor, Sylow
251	C₂²×#41	—	2	1	no	—
252	#575	—	2	4	no	—
253	#575	—	2	2	no	—
254	#575	C₂²×C₈₉	1	4	yes	—
255	C₂×#137	—	2	2	no	—
256	C₂×AGL(1,ℤ/8)	—	2	2	no	—
257	C₂×#135	—	2	1	no	—
258	C₂×#135	C₂²×C₈₉	1	2	yes	—
259	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic, complemented
260	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
261	#525	—	2	1	no	—
262	#510	—	2	2	no	—
263	#510	C₂²×C₈₉	1	4	yes	complemented
264	#509	—	2	2	no	—
265	#509	C₂²×C₈₉	1	4	yes	complemented
266	#508	—	2	4	no	—
267	C₂×M₃₂	C₂²×C₈₉	1	2	yes	complemented
268	#470	C₂²×C₈₉	1	2	yes	complemented
269	#469	C₂²×C₈₉	1	2	yes	complemented
270	#468	—	2	2	no	—
271	#427	C₂²×C₈₉	1	1	yes	characteristic, complemented
272	#416	—	2	1	no	—
273	#360	C₂²×C₈₉	1	8	yes	complemented
274	#349	C₂²×C₈₉	1	4	yes	complemented
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	4	no	—
277	C₂×#41	—	2	2	no	—
278	C₂×#41	—	2	4	no	—
279	C₂×#41	—	2	1	no	—
280	C₂×#41	—	4	1	no	—
281	C₂×#41	—	4	2	no	—
282	C₂×#41	—	4	2	no	—
283	C₂×#41	—	4	1	no	—
284	C₂²×Q₈	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	4	1	no	—
287	C₂³×C₄	—	4	1	no	—
288	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
289	#137	—	2	8	no	—
290	#137	—	2	8	no	—
291	AGL(1,ℤ/8)	—	2	8	no	—
292	AGL(1,ℤ/8)	—	2	8	no	—
293	#135	—	2	4	no	—
294	#135	—	2	4	no	—
295	#135	—	2	2	no	—
296	#135	—	2	2	no	—
297	#135	—	2	2	no	—
298	#135	—	2	2	no	—
299	#135	D₄×C₈₉	1	4	yes	complemented
300	#135	C₂³×C₈₉	1	4	yes	—
301	C₂×Q₁₆	—	2	1	no	—
302	C₂×Q₁₆	D₄×C₈₉	1	2	yes	complemented
303	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic, complemented
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×SD₁₆	—	2	1	no	—
307	C₂×D₈	—	2	1	no	—
308	C₂×D₈	D₄×C₈₉	1	2	yes	complemented
309	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic, complemented
310	C₂×M₁₆	—	2	2	no	—
311	C₂×M₁₆	—	2	2	no	—
312	C₂×M₁₆	D₄×C₈₉	1	2	yes	—
313	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
314	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
316	#123	—	4	1	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	#121	—	2	2	no	—
319	#120	—	4	1	no	—
320	C₄×D₄	—	4	2	no	—
321	#117	—	2	1	no	—
322	Q₃₂	—	2	4	no	—
323	SD₃₂	—	2	4	no	—
324	SD₃₂	—	2	4	no	—
325	D₁₆	—	2	4	no	—
326	M₃₂	—	2	2	no	—
327	M₃₂	C₂³×C₈₉	1	4	yes	complemented
328	C₂×C₁₆	—	2	2	no	—
329	#107	—	2	1	no	—
330	#106	C₂³×C₈₉	1	2	yes	complemented
331	#103	—	2	2	no	—
332	#102	—	2	2	no	—
333	C₂⁴	—	4	1	no	—
334	C₂⁴	D₈×C₈₉	1	1	yes	characteristic
335	#41	—	2	8	no	—
336	#41	—	2	4	no	—
337	#41	—	2	4	no	—
338	#41	—	4	4	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	#41	—	4	4	no	—
342	#41	—	4	4	no	—
343	#41	—	4	2	no	—
344	#41	—	4	2	no	—
345	#41	—	4	1	no	—
346	#41	—	4	1	no	—
347	#41	—	4	1	no	—
348	#41	—	4	1	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×Q₈	—	4	2	no	—
354	C₂×D₄	—	2	4	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	4	4	no	—
362	C₂×D₄	—	4	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	D₈×C₈₉	1	2	yes	—
376	C₂²×C₄	D₈×C₈₉	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
379	Q₁₆	—	2	4	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	—	2	2	no	—
382	Q₁₆	C₂×D₄×C₈₉	1	4	yes	—
383	SD₁₆	—	2	8	no	—
384	SD₁₆	—	2	4	no	—
385	SD₁₆	—	2	4	no	—
386	SD₁₆	—	4	2	no	—
387	D₈	—	2	4	no	—
388	D₈	—	2	2	no	—
389	D₈	—	2	2	no	—
390	D₈	C₂×D₄×C₈₉	1	4	yes	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	2	4	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
397	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
399	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₂²⋊C₄	—	4	1	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₂²⋊C₄	—	4	2	no	—
405	C₄²	—	4	1	no	—
406	C₁₆	—	2	4	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	4	no	—
414	C₂³	C₂×D₈×C₈₉	1	2	yes	—
415	C₂³	C₂×D₈×C₈₉	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	4	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	1	no	—
420	Q₈	—	4	1	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	8	no	—
424	D₄	—	4	4	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	2	no	—
427	D₄	—	4	1	no	—
428	D₄	—	4	1	no	—
429	D₄	—	8	4	no	—
430	D₄	—	8	1	no	—
431	D₄	—	8	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	8	1	no	—
446	C₂×C₄	—	8	1	no	—
447	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
448	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
449	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
450	C₂×C₄	C₂×D₈×C₈₉	1	1	yes	characteristic
451	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
452	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	#120×C₈₉	1	2	yes	—
456	C₈	C₂²×D₄×C₈₉	1	2	yes	—
457	C₂²	—	2	2	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	4	no	—
462	C₂²	—	8	1	no	—
463	C₂²	—	8	4	no	—
464	C₂²	—	8	2	no	—
465	C₂²	—	8	8	no	—
466	C₂²	—	8	1	no	—
467	C₂²	#447×C₈₉	1	1	yes	characteristic
468	C₂²	#447×C₈₉	1	1	yes	characteristic
469	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	4	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	#447×C₈₉	1	1	yes	characteristic
475	C₄	#447×C₈₉	1	1	yes	characteristic
476	C₄	C₂×#120×C₈₉	1	1	yes	characteristic
477	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
478	C₂	—	2	1	no	—
479	C₂	—	2	1	no	—
480	C₂	—	2	1	no	—
481	C₂	—	4	2	no	—
482	C₂	—	8	4	no	—
483	C₂	—	16	1	no	—
484	C₂	C₂×#447×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈₉	#447
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
socle	C₂×C₈₉	C₂×#447
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ C₂²×M₁₆×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₈₉	C₂	semidirect
2. C₈₉×#3414	C₂	semidirect
3. C₈₉×#3054	C₂	semidirect
4. C₈₉×#2191	C₂	semidirect
5. C₈₉×#2190	C₂	semidirect
6. C₈₉×#2145	C₂	semidirect
7. C₂×#349×C₈₉	C₂	semidirect
16. C₂×#135×C₈₉	C₂²	semidirect
20. #510×C₈₉	C₂²	semidirect
22. #509×C₈₉	C₂²	semidirect
24. C₂×M₃₂×C₈₉	C₂²	semidirect
25. #470×C₈₉	C₂²	semidirect
26. #469×C₈₉	C₂²	semidirect
28. #427×C₈₉	C₂²	semidirect
30. #360×C₈₉	C₂²	semidirect
31. #349×C₈₉	C₂²	semidirect
56. #135×C₈₉	D₄	semidirect
59. C₂×Q₁₆×C₈₉	D₄	semidirect
60. C₂×Q₁₆×C₈₉	C₂³	semidirect
65. C₂×D₈×C₈₉	D₄	semidirect
66. C₂×D₈×C₈₉	C₂³	semidirect
84. M₃₂×C₈₉	C₂³	semidirect
87. #106×C₈₉	C₂³	semidirect
235. #33530	C₈₉	direct (N × H)
243. C₂×#575	C₂×C₈₉	semidirect
244. #3414	C₂×C₈₉	semidirect
245. #3054	C₂×C₈₉	semidirect
246. #2191	C₂×C₈₉	semidirect
247. #2190	C₂×C₈₉	semidirect
248. #2145	C₂×C₈₉	semidirect
249. C₂×#349	C₂×C₈₉	semidirect
250. C₈₉	#33530	direct (N × H)
259. C₂×#135	C₂²×C₈₉	semidirect
263. #510	C₂²×C₈₉	semidirect
265. #509	C₂²×C₈₉	semidirect
267. C₂×M₃₂	C₂²×C₈₉	semidirect
268. #470	C₂²×C₈₉	semidirect
269. #469	C₂²×C₈₉	semidirect
271. #427	C₂²×C₈₉	semidirect
273. #360	C₂²×C₈₉	semidirect
274. #349	C₂²×C₈₉	semidirect
299. #135	D₄×C₈₉	semidirect
302. C₂×Q₁₆	D₄×C₈₉	semidirect
303. C₂×Q₁₆	C₂³×C₈₉	semidirect
308. C₂×D₈	D₄×C₈₉	semidirect
309. C₂×D₈	C₂³×C₈₉	semidirect
327. M₃₂	C₂³×C₈₉	semidirect
330. #106	C₂³×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₈₉	2
C₈₉×#3414	2
C₈₉×#3054	2
C₈₉×#2191	2
C₈₉×#2190	2
C₈₉×#2145	2
C₂×#349×C₈₉	2
#33530	89

Subgroups — C89×#33530 #36411378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#33530 #36411378