Subgroups — C₈₉×#35528 #36413376

Order 22784.

3962 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2544	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2541	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2428	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2410	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×D₄×C₈₉	C₂²	1	4	yes	—
16	#535×C₈₉	—	2	8	no	—
17	#535×C₈₉	—	2	8	no	—
18	C₂×#127×C₈₉	—	2	8	no	—
19	C₂×#127×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	4	yes	—
21	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
22	C₂×#127×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
25	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
26	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
27	C₂×#121×C₈₉	C₂²	1	16	yes	complemented
28	C₂×#120×C₈₉	C₂²	1	4	yes	—
29	C₂×#120×C₈₉	C₂²	1	4	yes	—
30	#518×C₈₉	—	2	8	no	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
32	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
37	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
38	#394×C₈₉	C₂²	1	16	yes	complemented
39	#392×C₈₉	C₂²	1	16	yes	complemented
40	#391×C₈₉	C₂²	1	2	yes	complemented
41	#390×C₈₉	C₂²	1	2	yes	complemented
42	#390×C₈₉	C₂²	1	4	yes	complemented
43	#390×C₈₉	C₂²	1	4	yes	complemented
44	#389×C₈₉	C₂²	1	4	yes	complemented
45	#386×C₈₉	C₂²	1	4	yes	—
46	#386×C₈₉	C₂²	1	16	yes	complemented
47	#385×C₈₉	C₂²	1	4	yes	—
48	#379×C₈₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
50	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
51	C₂⁵×C₈₉	C₂³	1	2	yes	—
52	C₂⁵×C₈₉	C₂³	1	2	yes	—
53	C₂×#41×C₈₉	—	2	4	no	—
54	C₂×#41×C₈₉	—	2	4	no	—
55	C₂×#41×C₈₉	—	2	4	no	—
56	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
57	C₂²×D₄×C₈₉	—	2	16	no	—
58	C₂²×D₄×C₈₉	—	2	4	no	—
59	C₂²×D₄×C₈₉	—	2	4	no	—
60	C₂²×D₄×C₈₉	—	2	4	no	—
61	C₂²×D₄×C₈₉	—	2	4	no	—
62	C₂²×D₄×C₈₉	—	2	4	no	—
63	C₂²×D₄×C₈₉	—	4	16	no	—
64	C₂²×D₄×C₈₉	D₄	1	8	yes	complemented
65	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
66	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
67	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
68	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
70	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	#127×C₈₉	—	2	16	no	—
79	#127×C₈₉	—	2	16	no	—
80	#127×C₈₉	—	2	8	no	—
81	#127×C₈₉	—	2	8	no	—
82	#124×C₈₉	—	2	8	no	—
83	#124×C₈₉	—	2	8	no	—
84	#121×C₈₉	—	2	16	no	—
85	#121×C₈₉	—	2	16	no	—
86	#121×C₈₉	—	4	32	no	—
87	#120×C₈₉	—	2	16	no	—
88	#120×C₈₉	—	2	16	no	—
89	C₄×D₄×C₈₉	—	2	16	no	—
90	C₄×D₄×C₈₉	—	2	16	no	—
91	#117×C₈₉	—	2	4	no	—
92	#117×C₈₉	—	2	4	no	—
93	#117×C₈₉	D₄	1	8	yes	complemented
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
105	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
106	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₈₉	—	2	4	no	—
108	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
113	#95×C₈₉	C₂³	1	8	yes	—
114	#95×C₈₉	C₂³	1	8	yes	—
115	C₂⁴×C₈₉	—	2	4	no	—
116	C₂⁴×C₈₉	—	2	4	no	—
117	C₂⁴×C₈₉	—	2	4	no	—
118	C₂⁴×C₈₉	—	2	4	no	—
119	C₂⁴×C₈₉	—	2	4	no	—
120	C₂⁴×C₈₉	—	4	8	no	—
121	C₂⁴×C₈₉	—	4	8	no	—
122	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
123	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
124	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
125	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
126	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
127	#41×C₈₉	—	4	16	no	—
128	C₂×Q₈×C₈₉	—	2	2	no	—
129	C₂×Q₈×C₈₉	—	2	2	no	—
130	C₂×Q₈×C₈₉	—	2	2	no	—
131	C₂×D₄×C₈₉	—	2	4	no	—
132	C₂×D₄×C₈₉	—	2	4	no	—
133	C₂×D₄×C₈₉	—	2	32	no	—
134	C₂×D₄×C₈₉	—	2	4	no	—
135	C₂×D₄×C₈₉	—	2	16	no	—
136	C₂×D₄×C₈₉	—	2	32	no	—
137	C₂×D₄×C₈₉	—	2	4	no	—
138	C₂×D₄×C₈₉	—	2	4	no	—
139	C₂×D₄×C₈₉	—	2	4	no	—
140	C₂×D₄×C₈₉	—	2	4	no	—
141	C₂×D₄×C₈₉	—	2	4	no	—
142	C₂×D₄×C₈₉	—	2	4	no	—
143	C₂×D₄×C₈₉	—	2	2	no	—
144	C₂×D₄×C₈₉	—	2	2	no	—
145	C₂×D₄×C₈₉	—	2	16	no	—
146	C₂×D₄×C₈₉	—	2	4	no	—
147	C₂×D₄×C₈₉	—	2	4	no	—
148	C₂×D₄×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	2	no	—
151	C₂×D₄×C₈₉	—	2	32	no	—
152	C₂×D₄×C₈₉	—	4	16	no	—
153	C₂×D₄×C₈₉	—	4	64	no	—
154	C₂×D₄×C₈₉	—	4	16	no	—
155	C₂×D₄×C₈₉	—	4	16	no	—
156	C₂×D₄×C₈₉	—	4	16	no	—
157	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
158	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	2	8	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	2	4	no	—
164	C₂²×C₄×C₈₉	—	2	16	no	—
165	C₂²×C₄×C₈₉	—	4	16	no	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
168	C₂²×C₄×C₈₉	#41	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	4	no	—
178	C₄⋊C₄×C₈₉	—	2	16	no	—
179	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	complemented
180	C₂²⋊C₄×C₈₉	—	2	4	no	—
181	C₂²⋊C₄×C₈₉	—	2	4	no	—
182	C₂²⋊C₄×C₈₉	—	2	16	no	—
183	C₂²⋊C₄×C₈₉	—	2	16	no	—
184	C₂²⋊C₄×C₈₉	—	2	16	no	—
185	C₂²⋊C₄×C₈₉	—	2	16	no	—
186	C₂²⋊C₄×C₈₉	—	4	16	no	—
187	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
188	C₄²×C₈₉	—	2	4	no	—
189	C₄²×C₈₉	—	2	4	no	—
190	C₄²×C₈₉	—	2	4	no	—
191	C₄²×C₈₉	—	2	4	no	—
192	C₄²×C₈₉	C₂×D₄	1	8	yes	complemented
193	C₂³×C₈₉	—	2	4	no	—
194	C₂³×C₈₉	—	2	4	no	—
195	C₂³×C₈₉	—	2	4	no	—
196	C₂³×C₈₉	—	2	16	no	—
197	C₂³×C₈₉	—	2	16	no	—
198	C₂³×C₈₉	—	2	4	no	—
199	C₂³×C₈₉	—	2	2	no	—
200	C₂³×C₈₉	—	2	2	no	—
201	C₂³×C₈₉	—	2	4	no	—
202	C₂³×C₈₉	—	2	2	no	—
203	C₂³×C₈₉	—	2	4	no	—
204	C₂³×C₈₉	—	2	8	no	—
205	C₂³×C₈₉	—	2	16	no	—
206	C₂³×C₈₉	—	4	16	no	—
207	C₂³×C₈₉	—	4	16	no	—
208	C₂³×C₈₉	—	4	8	no	—
209	C₂³×C₈₉	—	8	8	no	—
210	C₂³×C₈₉	—	8	8	no	—
211	C₂³×C₈₉	—	8	8	no	—
212	C₂³×C₈₉	—	8	8	no	—
213	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
214	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
216	C₂³×C₈₉	C₂×#41	1	2	yes	—
217	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
218	Q₈×C₈₉	—	4	4	no	—
219	D₄×C₈₉	—	2	16	no	—
220	D₄×C₈₉	—	2	16	no	—
221	D₄×C₈₉	—	4	64	no	—
222	D₄×C₈₉	—	4	8	no	—
223	D₄×C₈₉	—	4	8	no	—
224	D₄×C₈₉	—	4	8	no	—
225	D₄×C₈₉	—	4	4	no	—
226	D₄×C₈₉	—	8	16	no	—
227	D₄×C₈₉	—	8	16	no	—
228	C₂×C₄×C₈₉	—	2	16	no	—
229	C₂×C₄×C₈₉	—	2	4	no	—
230	C₂×C₄×C₈₉	—	2	8	no	—
231	C₂×C₄×C₈₉	—	2	4	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	4	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	8	no	—
238	C₂×C₄×C₈₉	—	2	8	no	—
239	C₂×C₄×C₈₉	—	4	8	no	—
240	C₂×C₄×C₈₉	—	8	16	no	—
241	C₂×C₄×C₈₉	#121	1	16	yes	complemented
242	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
243	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
244	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
248	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
249	C₂×C₄×C₈₉	H(5,𝔽₂)	1	8	yes	—
250	C₂²×C₈₉	—	2	4	no	—
251	C₂²×C₈₉	—	2	4	no	—
252	C₂²×C₈₉	—	2	4	no	—
253	C₂²×C₈₉	—	2	8	no	—
254	C₂²×C₈₉	—	2	16	no	—
255	C₂²×C₈₉	—	4	8	no	—
256	C₂²×C₈₉	—	4	8	no	—
257	C₂²×C₈₉	—	4	2	no	—
258	C₂²×C₈₉	—	4	4	no	—
259	C₂²×C₈₉	—	4	8	no	—
260	C₂²×C₈₉	—	4	4	no	—
261	C₂²×C₈₉	—	4	4	no	—
262	C₂²×C₈₉	—	4	8	no	—
263	C₂²×C₈₉	—	4	4	no	—
264	C₂²×C₈₉	—	4	8	no	—
265	C₂²×C₈₉	—	8	16	no	—
266	C₂²×C₈₉	—	8	16	no	—
267	C₂²×C₈₉	C₂×#121	1	4	yes	—
268	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
269	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
270	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
271	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
272	C₄×C₈₉	—	2	8	no	—
273	C₄×C₈₉	—	2	8	no	—
274	C₄×C₈₉	—	4	2	no	—
275	C₄×C₈₉	—	4	4	no	—
276	C₄×C₈₉	—	4	4	no	—
277	C₄×C₈₉	C₂×#121	1	4	yes	—
278	C₄×C₈₉	C₂×#121	1	4	yes	—
279	#35528	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₈₉	—	2	4	no	—
281	C₂×C₈₉	—	4	8	no	—
282	C₂×C₈₉	—	8	2	no	—
283	C₂×C₈₉	—	8	4	no	—
284	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
285	C₂×C₈₉	#3484	1	2	yes	—
286	C₂×C₈₉	#3498	1	2	yes	—
287	C₂×C₈₉	#3508	1	2	yes	—
288	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
289	C₂×#535	C₂×C₈₉	1	1	yes	characteristic, complemented
290	C₂²×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
291	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
292	#2544	C₂×C₈₉	1	4	yes	complemented
293	#2541	C₂×C₈₉	1	4	yes	complemented
294	#2428	C₂×C₈₉	1	8	yes	complemented
295	#2410	C₂×C₈₉	1	8	yes	complemented
296	#2309	C₂×C₈₉	1	1	yes	characteristic, complemented
297	#2297	C₂×C₈₉	1	1	yes	characteristic, complemented
298	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
299	C₈₉	#35528	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
301	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
302	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
303	C₂³×D₄	C₂²×C₈₉	1	4	yes	—
304	#535	—	2	8	no	—
305	#535	—	2	8	no	—
306	C₂×#127	—	2	8	no	—
307	C₂×#127	C₂²×C₈₉	1	4	yes	—
308	C₂×#127	C₂²×C₈₉	1	4	yes	—
309	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
310	C₂×#127	C₂²×C₈₉	1	2	yes	complemented
311	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
312	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
313	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
314	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
315	C₂×#121	C₂²×C₈₉	1	16	yes	complemented
316	C₂×#120	C₂²×C₈₉	1	4	yes	—
317	C₂×#120	C₂²×C₈₉	1	4	yes	—
318	#518	—	2	8	no	—
319	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
320	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
321	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
322	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
325	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
326	#394	C₂²×C₈₉	1	16	yes	complemented
327	#392	C₂²×C₈₉	1	16	yes	complemented
328	#391	C₂²×C₈₉	1	2	yes	complemented
329	#390	C₂²×C₈₉	1	4	yes	complemented
330	#390	C₂²×C₈₉	1	4	yes	complemented
331	#390	C₂²×C₈₉	1	2	yes	complemented
332	#389	C₂²×C₈₉	1	4	yes	complemented
333	#386	C₂²×C₈₉	1	4	yes	—
334	#386	C₂²×C₈₉	1	16	yes	complemented
335	#385	C₂²×C₈₉	1	4	yes	—
336	#379	C₂²×C₈₉	1	4	yes	—
337	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
338	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
339	C₂⁵	C₂³×C₈₉	1	2	yes	—
340	C₂⁵	C₂³×C₈₉	1	2	yes	—
341	C₂×#41	—	2	4	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	2	4	no	—
344	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
345	C₂²×D₄	—	2	16	no	—
346	C₂²×D₄	—	2	4	no	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	4	no	—
349	C₂²×D₄	—	2	4	no	—
350	C₂²×D₄	—	2	4	no	—
351	C₂²×D₄	—	4	16	no	—
352	C₂²×D₄	D₄×C₈₉	1	8	yes	complemented
353	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
354	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
355	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
356	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
358	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
359	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
360	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
361	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
362	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
363	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
364	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
365	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
366	#127	—	2	16	no	—
367	#127	—	2	16	no	—
368	#127	—	2	8	no	—
369	#127	—	2	8	no	—
370	#124	—	2	8	no	—
371	#124	—	2	8	no	—
372	#121	—	2	16	no	—
373	#121	—	2	16	no	—
374	#121	—	4	32	no	—
375	#120	—	2	16	no	—
376	#120	—	2	16	no	—
377	C₄×D₄	—	2	16	no	—
378	C₄×D₄	—	2	16	no	—
379	#117	—	2	4	no	—
380	#117	—	2	4	no	—
381	#117	D₄×C₈₉	1	8	yes	complemented
382	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	16	no	—
387	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
388	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
389	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
390	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
391	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
395	C₂×C₄²	—	2	4	no	—
396	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
397	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
398	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
399	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
400	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
401	#95	C₂³×C₈₉	1	8	yes	—
402	#95	C₂³×C₈₉	1	8	yes	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	2	4	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	4	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	4	8	no	—
409	C₂⁴	—	4	8	no	—
410	C₂⁴	C₂×D₄×C₈₉	1	8	yes	—
411	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
412	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
413	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
414	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
415	#41	—	4	16	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	32	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	16	no	—
424	C₂×D₄	—	2	32	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	4	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	4	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	16	no	—
434	C₂×D₄	—	2	4	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	32	no	—
440	C₂×D₄	—	4	16	no	—
441	C₂×D₄	—	4	64	no	—
442	C₂×D₄	—	4	16	no	—
443	C₂×D₄	—	4	16	no	—
444	C₂×D₄	—	4	16	no	—
445	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
446	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	4	no	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	—	4	16	no	—
454	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
455	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
456	C₂²×C₄	#41×C₈₉	1	4	yes	—
457	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
458	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
463	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	16	no	—
467	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	complemented
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	16	no	—
471	C₂²⋊C₄	—	2	16	no	—
472	C₂²⋊C₄	—	2	16	no	—
473	C₂²⋊C₄	—	2	16	no	—
474	C₂²⋊C₄	—	4	16	no	—
475	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
476	C₄²	—	2	4	no	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	4	no	—
480	C₄²	C₂×D₄×C₈₉	1	8	yes	complemented
481	C₂³	—	2	4	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	2	16	no	—
485	C₂³	—	2	16	no	—
486	C₂³	—	2	4	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	4	no	—
492	C₂³	—	2	8	no	—
493	C₂³	—	2	16	no	—
494	C₂³	—	4	16	no	—
495	C₂³	—	4	16	no	—
496	C₂³	—	4	8	no	—
497	C₂³	—	8	8	no	—
498	C₂³	—	8	8	no	—
499	C₂³	—	8	8	no	—
500	C₂³	—	8	8	no	—
501	C₂³	C₂²×D₄×C₈₉	1	8	yes	—
502	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
503	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
504	C₂³	C₂×#41×C₈₉	1	2	yes	—
505	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
506	Q₈	—	4	4	no	—
507	D₄	—	2	16	no	—
508	D₄	—	2	16	no	—
509	D₄	—	4	64	no	—
510	D₄	—	4	8	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	8	no	—
513	D₄	—	4	4	no	—
514	D₄	—	8	16	no	—
515	D₄	—	8	16	no	—
516	C₂×C₄	—	2	16	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	2	8	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	8	no	—
527	C₂×C₄	—	4	8	no	—
528	C₂×C₄	—	8	16	no	—
529	C₂×C₄	#121×C₈₉	1	16	yes	complemented
530	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
531	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
532	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
533	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
535	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
536	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
537	C₂×C₄	H(5,𝔽₂)×C₈₉	1	8	yes	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	2	8	no	—
542	C₂²	—	2	16	no	—
543	C₂²	—	4	8	no	—
544	C₂²	—	4	8	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	8	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	8	no	—
551	C₂²	—	4	8	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	8	16	no	—
554	C₂²	—	8	16	no	—
555	C₂²	C₂×#121×C₈₉	1	4	yes	—
556	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
557	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
558	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
559	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
560	C₄	—	2	8	no	—
561	C₄	—	2	8	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	4	no	—
564	C₄	—	4	4	no	—
565	C₄	C₂×#121×C₈₉	1	4	yes	—
566	C₄	C₂×#121×C₈₉	1	4	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	4	8	no	—
569	C₂	—	8	2	no	—
570	C₂	—	8	4	no	—
571	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
572	C₂	C₈₉×#3484	1	2	yes	—
573	C₂	C₈₉×#3498	1	2	yes	—
574	C₂	C₈₉×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#535×C₈₉	C₂	semidirect
2. C₂×#535×C₈₉	C₂	semidirect
3. C₂²×#127×C₈₉	C₂	semidirect
4. C₂×#518×C₈₉	C₂	semidirect
5. C₈₉×#2544	C₂	semidirect
6. C₈₉×#2541	C₂	semidirect
7. C₈₉×#2428	C₂	semidirect
8. C₈₉×#2410	C₂	semidirect
9. C₈₉×#2309	C₂	semidirect
10. C₈₉×#2297	C₂	semidirect
11. C₈₉×#2296	C₂	semidirect
21. C₂×#127×C₈₉	C₂²	semidirect
22. C₂×#127×C₈₉	C₂²	semidirect
23. C₂×#124×C₈₉	C₂²	semidirect
24. C₂×#124×C₈₉	C₂²	semidirect
25. C₂×#121×C₈₉	C₂²	semidirect
26. C₂×#121×C₈₉	C₂²	semidirect
27. C₂×#121×C₈₉	C₂²	semidirect
31. C₂×C₄×D₄×C₈₉	C₂²	semidirect
32. C₂×C₄×D₄×C₈₉	C₂²	semidirect
38. #394×C₈₉	C₂²	semidirect
39. #392×C₈₉	C₂²	semidirect
40. #391×C₈₉	C₂²	semidirect
41. #390×C₈₉	C₂²	semidirect
42. #390×C₈₉	C₂²	semidirect
43. #390×C₈₉	C₂²	semidirect
44. #389×C₈₉	C₂²	semidirect
46. #386×C₈₉	C₂²	semidirect
49. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
50. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
64. C₂²×D₄×C₈₉	D₄	semidirect
93. #117×C₈₉	D₄	semidirect
179. C₄⋊C₄×C₈₉	C₂×D₄	semidirect
192. C₄²×C₈₉	C₂×D₄	semidirect
241. C₂×C₄×C₈₉	#121	semidirect
279. #35528	C₈₉	direct (N × H)
288. C₂×#535	C₂×C₈₉	semidirect
289. C₂×#535	C₂×C₈₉	semidirect
290. C₂²×#127	C₂×C₈₉	semidirect
291. C₂×#518	C₂×C₈₉	semidirect
292. #2544	C₂×C₈₉	semidirect
293. #2541	C₂×C₈₉	semidirect
294. #2428	C₂×C₈₉	semidirect
295. #2410	C₂×C₈₉	semidirect
296. #2309	C₂×C₈₉	semidirect
297. #2297	C₂×C₈₉	semidirect
298. #2296	C₂×C₈₉	semidirect
299. C₈₉	#35528	direct (N × H)
309. C₂×#127	C₂²×C₈₉	semidirect
310. C₂×#127	C₂²×C₈₉	semidirect
311. C₂×#124	C₂²×C₈₉	semidirect
312. C₂×#124	C₂²×C₈₉	semidirect
313. C₂×#121	C₂²×C₈₉	semidirect
314. C₂×#121	C₂²×C₈₉	semidirect
315. C₂×#121	C₂²×C₈₉	semidirect
319. C₂×C₄×D₄	C₂²×C₈₉	semidirect
320. C₂×C₄×D₄	C₂²×C₈₉	semidirect
326. #394	C₂²×C₈₉	semidirect
327. #392	C₂²×C₈₉	semidirect
328. #391	C₂²×C₈₉	semidirect
329. #390	C₂²×C₈₉	semidirect
330. #390	C₂²×C₈₉	semidirect
331. #390	C₂²×C₈₉	semidirect
332. #389	C₂²×C₈₉	semidirect
334. #386	C₂²×C₈₉	semidirect
337. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
338. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
352. C₂²×D₄	D₄×C₈₉	semidirect
381. #117	D₄×C₈₉	semidirect
467. C₄⋊C₄	C₂×D₄×C₈₉	semidirect
480. C₄²	C₂×D₄×C₈₉	semidirect
529. C₂×C₄	#121×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#535×C₈₉	2
C₂²×#127×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2544	2
C₈₉×#2541	2
C₈₉×#2428	2
C₈₉×#2410	2
C₈₉×#2309	2
C₈₉×#2297	2
C₈₉×#2296	2
#35528	89

Subgroups — C89×#35528 #36413376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35528 #36413376