Subgroups — C₈₉×#25434 #36403282

Order 22784.

1012 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#472×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3058	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3041	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2045	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2002	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1945	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1887	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
17	#535×C₈₉	C₂²	1	2	yes	—
18	C₂×#127×C₈₉	C₂²	1	2	yes	—
19	#518×C₈₉	C₂²	1	2	yes	—
20	#493×C₈₉	—	2	4	no	—
21	#472×C₈₉	—	2	4	no	—
22	#469×C₈₉	—	2	2	no	—
23	#466×C₈₉	—	2	2	no	—
24	#463×C₈₉	—	2	4	no	—
25	#459×C₈₉	—	2	4	no	—
26	#442×C₈₉	—	2	2	no	—
27	C₄×D₈×C₈₉	—	2	2	no	—
28	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
29	#427×C₈₉	C₂²	1	1	yes	characteristic
30	#424×C₈₉	C₂²	1	2	yes	—
31	C₂×#104×C₈₉	C₂²	1	1	yes	characteristic
32	#418×C₈₉	C₂²	1	2	yes	—
33	#418×C₈₉	C₂²	1	2	yes	—
34	#418×C₈₉	C₂²	1	2	yes	—
35	#416×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#100×C₈₉	C₂²	1	2	yes	—
37	C₂×#100×C₈₉	C₂²	1	2	yes	—
38	#405×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	#341×C₈₉	C₂²	1	1	yes	characteristic
41	#339×C₈₉	C₂²	1	1	yes	characteristic
42	#339×C₈₉	C₂²	1	2	yes	—
43	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₈₉	—	4	2	no	—
45	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
47	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
48	AGL(1,ℤ/8)×C₈₉	—	4	2	no	—
49	C₂×SD₁₆×C₈₉	—	2	2	no	—
50	C₂×D₈×C₈₉	—	2	2	no	—
51	C₂×D₈×C₈₉	—	2	4	no	—
52	C₂×D₈×C₈₉	—	2	1	no	—
53	C₂×D₈×C₈₉	—	2	1	no	—
54	C₂×D₈×C₈₉	—	2	4	no	—
55	C₂×D₈×C₈₉	—	2	1	no	—
56	C₂×D₈×C₈₉	—	2	1	no	—
57	C₂×D₈×C₈₉	—	2	2	no	—
58	C₂×D₈×C₈₉	—	2	2	no	—
59	C₂×D₈×C₈₉	—	2	2	no	—
60	C₂×D₈×C₈₉	—	4	2	no	—
61	C₂×D₈×C₈₉	D₄	1	4	yes	complemented
62	#131×C₈₉	—	2	2	no	—
63	#131×C₈₉	—	2	2	no	—
64	C₂×M₁₆×C₈₉	—	2	1	no	—
65	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₈₉	—	2	1	no	—
69	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	#127×C₈₉	—	2	2	no	—
72	#127×C₈₉	—	2	4	no	—
73	#127×C₈₉	—	2	4	no	—
74	#124×C₈₉	—	2	2	no	—
75	#121×C₈₉	—	2	4	no	—
76	#120×C₈₉	—	4	2	no	—
77	C₄×D₄×C₈₉	—	2	4	no	—
78	C₄×D₄×C₈₉	—	2	4	no	—
79	#117×C₈₉	C₂³	1	1	yes	characteristic
80	#117×C₈₉	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₈₉	—	4	2	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	#108×C₈₉	—	2	2	no	—
84	#107×C₈₉	D₄	1	2	yes	complemented
85	#106×C₈₉	D₄	1	2	yes	complemented
86	C₄⋊C₈×C₈₉	—	2	4	no	—
87	#104×C₈₉	—	2	2	no	—
88	#103×C₈₉	D₄	1	2	yes	complemented
89	#102×C₈₉	—	2	4	no	—
90	#102×C₈₉	—	2	4	no	—
91	#102×C₈₉	—	2	4	no	—
92	#102×C₈₉	D₄	1	2	yes	complemented
93	#100×C₈₉	—	2	4	no	—
94	#100×C₈₉	—	4	2	no	—
95	#97×C₈₉	—	2	1	no	—
96	C₄×C₈×C₈₉	—	2	2	no	—
97	C₄×C₈×C₈₉	—	2	1	no	—
98	C₂⁴×C₈₉	—	2	2	no	—
99	C₂⁴×C₈₉	—	2	2	no	—
100	#41×C₈₉	—	2	1	no	—
101	#41×C₈₉	—	2	1	no	—
102	#41×C₈₉	—	2	1	no	—
103	#41×C₈₉	—	2	1	no	—
104	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₈₉	—	2	1	no	—
106	C₂×D₄×C₈₉	—	2	2	no	—
107	C₂×D₄×C₈₉	—	2	2	no	—
108	C₂×D₄×C₈₉	—	2	2	no	—
109	C₂×D₄×C₈₉	—	2	2	no	—
110	C₂×D₄×C₈₉	—	2	2	no	—
111	C₂×D₄×C₈₉	—	2	2	no	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	2	no	—
114	C₂×D₄×C₈₉	—	2	2	no	—
115	C₂×D₄×C₈₉	—	2	2	no	—
116	C₂×D₄×C₈₉	—	2	2	no	—
117	C₂×D₄×C₈₉	—	4	8	no	—
118	C₂×D₄×C₈₉	—	4	4	no	—
119	C₂×D₄×C₈₉	—	8	8	no	—
120	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
121	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	—	2	1	no	—
123	C₂²×C₄×C₈₉	—	2	1	no	—
124	C₂²×C₄×C₈₉	—	4	4	no	—
125	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
126	SD₁₆×C₈₉	—	4	4	no	—
127	D₈×C₈₉	—	2	4	no	—
128	D₈×C₈₉	—	2	4	no	—
129	D₈×C₈₉	—	4	8	no	—
130	D₈×C₈₉	—	4	4	no	—
131	D₈×C₈₉	—	4	2	no	—
132	D₈×C₈₉	—	4	2	no	—
133	M₁₆×C₈₉	—	2	1	no	—
134	M₁₆×C₈₉	—	2	2	no	—
135	M₁₆×C₈₉	—	2	1	no	—
136	M₁₆×C₈₉	—	2	1	no	—
137	M₁₆×C₈₉	—	2	1	no	—
138	M₁₆×C₈₉	—	2	2	no	—
139	M₁₆×C₈₉	—	4	2	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	2	no	—
145	C₂×C₈×C₈₉	—	4	2	no	—
146	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	#41	1	2	yes	—
151	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
153	C₂²⋊C₄×C₈₉	—	2	1	no	—
154	C₂²⋊C₄×C₈₉	—	2	2	no	—
155	C₂²⋊C₄×C₈₉	—	4	4	no	—
156	C₂²⋊C₄×C₈₉	—	4	4	no	—
157	C₄²×C₈₉	—	2	1	no	—
158	C₄²×C₈₉	—	2	1	no	—
159	C₄²×C₈₉	—	2	2	no	—
160	C₄²×C₈₉	#41	1	2	yes	—
161	C₂³×C₈₉	—	2	1	no	—
162	C₂³×C₈₉	—	2	4	no	—
163	C₂³×C₈₉	—	4	2	no	—
164	C₂³×C₈₉	—	4	2	no	—
165	C₂³×C₈₉	—	4	2	no	—
166	C₂³×C₈₉	—	4	2	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	—	8	4	no	—
169	C₂³×C₈₉	—	8	4	no	—
170	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
171	Q₈×C₈₉	—	2	1	no	—
172	Q₈×C₈₉	—	2	1	no	—
173	D₄×C₈₉	—	2	4	no	—
174	D₄×C₈₉	—	2	1	no	—
175	D₄×C₈₉	—	2	1	no	—
176	D₄×C₈₉	—	2	4	no	—
177	D₄×C₈₉	—	4	1	no	—
178	D₄×C₈₉	—	4	1	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	—	4	2	no	—
184	D₄×C₈₉	—	4	2	no	—
185	D₄×C₈₉	—	8	16	no	—
186	D₄×C₈₉	—	16	4	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	4	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	16	4	no	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
201	C₈×C₈₉	—	2	2	no	—
202	C₈×C₈₉	—	4	1	no	—
203	C₈×C₈₉	—	4	2	no	—
204	C₈×C₈₉	—	4	1	no	—
205	C₈×C₈₉	#121	1	2	yes	—
206	C₈×C₈₉	#121	1	2	yes	—
207	C₂²×C₈₉	—	2	2	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	4	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	—	8	4	no	—
212	C₂²×C₈₉	—	8	4	no	—
213	C₂²×C₈₉	—	8	4	no	—
214	C₂²×C₈₉	—	8	2	no	—
215	C₂²×C₈₉	—	8	4	no	—
216	C₂²×C₈₉	—	16	2	no	—
217	C₂²×C₈₉	—	16	2	no	—
218	C₂²×C₈₉	#540	1	1	yes	characteristic
219	C₂²×C₈₉	D₄²	1	1	yes	characteristic
220	C₂²×C₈₉	#546	1	1	yes	characteristic
221	C₄×C₈₉	—	2	4	no	—
222	C₄×C₈₉	—	4	1	no	—
223	C₄×C₈₉	—	4	2	no	—
224	C₄×C₈₉	—	4	4	no	—
225	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
226	C₄×C₈₉	#532	1	1	yes	characteristic
227	C₄×C₈₉	D₄²	1	1	yes	characteristic
228	C₄×C₈₉	#550	1	1	yes	characteristic
229	#25434	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₈₉	—	2	1	no	—
231	C₂×C₈₉	—	2	1	no	—
232	C₂×C₈₉	—	8	1	no	—
233	C₂×C₈₉	—	8	4	no	—
234	C₂×C₈₉	—	16	2	no	—
235	C₂×C₈₉	#2428	1	1	yes	characteristic
236	C₂×C₈₉	#3292	1	2	yes	—
237	C₂×#493	C₂×C₈₉	1	1	yes	characteristic, complemented
238	C₂×#472	C₂×C₈₉	1	1	yes	characteristic, complemented
239	#3058	C₂×C₈₉	1	1	yes	characteristic, complemented
240	#3041	C₂×C₈₉	1	2	yes	complemented
241	#2948	C₂×C₈₉	1	1	yes	characteristic, complemented
242	#2045	C₂×C₈₉	1	2	yes	complemented
243	#2002	C₂×C₈₉	1	2	yes	complemented
244	#1978	C₂×C₈₉	1	1	yes	characteristic, complemented
245	#1945	C₂×C₈₉	1	1	yes	characteristic, complemented
246	#1887	C₂×C₈₉	1	2	yes	complemented
247	#1764	C₂×C₈₉	1	1	yes	characteristic, complemented
248	C₈₉	#25434	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	2	yes	—
250	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
251	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
252	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
254	#535	C₂²×C₈₉	1	2	yes	—
255	C₂×#127	C₂²×C₈₉	1	2	yes	—
256	#518	C₂²×C₈₉	1	2	yes	—
257	#493	—	2	4	no	—
258	#472	—	2	4	no	—
259	#469	—	2	2	no	—
260	#466	—	2	2	no	—
261	#463	—	2	4	no	—
262	#459	—	2	4	no	—
263	#442	—	2	2	no	—
264	C₄×D₈	—	2	2	no	—
265	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
266	#427	C₂²×C₈₉	1	1	yes	characteristic
267	#424	C₂²×C₈₉	1	2	yes	—
268	C₂×#104	C₂²×C₈₉	1	1	yes	characteristic
269	#418	C₂²×C₈₉	1	2	yes	—
270	#418	C₂²×C₈₉	1	2	yes	—
271	#418	C₂²×C₈₉	1	2	yes	—
272	#416	C₂²×C₈₉	1	1	yes	characteristic
273	C₂×#100	C₂²×C₈₉	1	2	yes	—
274	C₂×#100	C₂²×C₈₉	1	2	yes	—
275	#405	C₂²×C₈₉	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
277	#341	C₂²×C₈₉	1	1	yes	characteristic
278	#339	C₂²×C₈₉	1	1	yes	characteristic
279	#339	C₂²×C₈₉	1	2	yes	—
280	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
281	C₂²×D₄	—	4	2	no	—
282	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
283	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
284	AGL(1,ℤ/8)	—	2	4	no	—
285	AGL(1,ℤ/8)	—	4	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	4	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×D₈	—	2	1	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	4	no	—
292	C₂×D₈	—	2	1	no	—
293	C₂×D₈	—	2	1	no	—
294	C₂×D₈	—	2	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂×D₈	—	2	2	no	—
297	C₂×D₈	—	4	2	no	—
298	C₂×D₈	D₄×C₈₉	1	4	yes	complemented
299	#131	—	2	2	no	—
300	#131	—	2	2	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
303	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
304	C₂×M₁₆	C₂³×C₈₉	1	1	yes	characteristic
305	C₂²×C₈	—	2	1	no	—
306	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
308	#127	—	2	4	no	—
309	#127	—	2	2	no	—
310	#127	—	2	4	no	—
311	#124	—	2	2	no	—
312	#121	—	2	4	no	—
313	#120	—	4	2	no	—
314	C₄×D₄	—	2	4	no	—
315	C₄×D₄	—	2	4	no	—
316	#117	C₂³×C₈₉	1	1	yes	characteristic
317	#117	C₂³×C₈₉	1	2	yes	—
318	C₂×C₂²⋊C₄	—	4	2	no	—
319	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
320	#108	—	2	2	no	—
321	#107	D₄×C₈₉	1	2	yes	complemented
322	#106	D₄×C₈₉	1	2	yes	complemented
323	C₄⋊C₈	—	2	4	no	—
324	#104	—	2	2	no	—
325	#103	D₄×C₈₉	1	2	yes	complemented
326	#102	—	2	4	no	—
327	#102	—	2	4	no	—
328	#102	—	2	4	no	—
329	#102	D₄×C₈₉	1	2	yes	complemented
330	#100	—	2	4	no	—
331	#100	—	4	2	no	—
332	#97	—	2	1	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	2	1	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	2	no	—
337	#41	—	2	1	no	—
338	#41	—	2	1	no	—
339	#41	—	2	1	no	—
340	#41	—	2	1	no	—
341	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	4	8	no	—
355	C₂×D₄	—	4	4	no	—
356	C₂×D₄	—	8	8	no	—
357	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
358	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
363	SD₁₆	—	4	4	no	—
364	D₈	—	2	4	no	—
365	D₈	—	2	4	no	—
366	D₈	—	4	8	no	—
367	D₈	—	4	4	no	—
368	D₈	—	4	2	no	—
369	D₈	—	4	2	no	—
370	M₁₆	—	2	1	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	1	no	—
374	M₁₆	—	2	1	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
384	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
386	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
387	C₂×C₈	#41×C₈₉	1	2	yes	—
388	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
389	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	2	no	—
397	C₄²	#41×C₈₉	1	2	yes	—
398	C₂³	—	2	1	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	4	2	no	—
405	C₂³	—	8	4	no	—
406	C₂³	—	8	4	no	—
407	C₂³	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
408	Q₈	—	2	1	no	—
409	Q₈	—	2	1	no	—
410	D₄	—	2	4	no	—
411	D₄	—	2	1	no	—
412	D₄	—	2	1	no	—
413	D₄	—	2	4	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	16	no	—
423	D₄	—	16	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	16	4	no	—
432	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	#121×C₈₉	1	2	yes	—
443	C₈	#121×C₈₉	1	2	yes	—
444	C₂²	—	2	2	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	8	4	no	—
449	C₂²	—	8	4	no	—
450	C₂²	—	8	4	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	4	no	—
453	C₂²	—	16	2	no	—
454	C₂²	—	16	2	no	—
455	C₂²	#540×C₈₉	1	1	yes	characteristic
456	C₂²	D₄²×C₈₉	1	1	yes	characteristic
457	C₂²	#546×C₈₉	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	2	no	—
461	C₄	—	4	4	no	—
462	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
463	C₄	#532×C₈₉	1	1	yes	characteristic
464	C₄	D₄²×C₈₉	1	1	yes	characteristic
465	C₄	#550×C₈₉	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	8	1	no	—
469	C₂	—	8	4	no	—
470	C₂	—	16	2	no	—
471	C₂	C₈₉×#2428	1	1	yes	characteristic
472	C₂	C₈₉×#3292	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#493×C₈₉	C₂	semidirect
2. C₂×#472×C₈₉	C₂	semidirect
3. C₈₉×#3058	C₂	semidirect
4. C₈₉×#3041	C₂	semidirect
5. C₈₉×#2948	C₂	semidirect
6. C₈₉×#2045	C₂	semidirect
7. C₈₉×#2002	C₂	semidirect
8. C₈₉×#1978	C₂	semidirect
9. C₈₉×#1945	C₂	semidirect
10. C₈₉×#1887	C₂	semidirect
11. C₈₉×#1764	C₂	semidirect
61. C₂×D₈×C₈₉	D₄	semidirect
84. #107×C₈₉	D₄	semidirect
85. #106×C₈₉	D₄	semidirect
88. #103×C₈₉	D₄	semidirect
92. #102×C₈₉	D₄	semidirect
229. #25434	C₈₉	direct (N × H)
237. C₂×#493	C₂×C₈₉	semidirect
238. C₂×#472	C₂×C₈₉	semidirect
239. #3058	C₂×C₈₉	semidirect
240. #3041	C₂×C₈₉	semidirect
241. #2948	C₂×C₈₉	semidirect
242. #2045	C₂×C₈₉	semidirect
243. #2002	C₂×C₈₉	semidirect
244. #1978	C₂×C₈₉	semidirect
245. #1945	C₂×C₈₉	semidirect
246. #1887	C₂×C₈₉	semidirect
247. #1764	C₂×C₈₉	semidirect
248. C₈₉	#25434	direct (N × H)
298. C₂×D₈	D₄×C₈₉	semidirect
321. #107	D₄×C₈₉	semidirect
322. #106	D₄×C₈₉	semidirect
325. #103	D₄×C₈₉	semidirect
329. #102	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#493×C₈₉	2
C₂×#472×C₈₉	2
C₈₉×#3058	2
C₈₉×#3041	2
C₈₉×#2948	2
C₈₉×#2045	2
C₈₉×#2002	2
C₈₉×#1978	2
C₈₉×#1945	2
C₈₉×#1887	2
C₈₉×#1764	2
#25434	89

Subgroups — C89×#25434 #36403282

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25434 #36403282