Subgroups — C₈₉×#35272 #36413120

Order 22784.

3950 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×#535×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₂²×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2856	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2619	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2548	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2541	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2408	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2309	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
12	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₈₉	C₂²	1	4	yes	—
14	#535×C₈₉	—	2	16	no	—
15	C₂×#127×C₈₉	—	2	8	no	—
16	C₂×#127×C₈₉	C₂²	1	2	yes	—
17	C₂×#127×C₈₉	C₂²	1	2	yes	—
18	C₂×#127×C₈₉	C₂²	1	4	yes	—
19	C₂×#127×C₈₉	C₂²	1	4	yes	complemented
20	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
21	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
22	C₂×#121×C₈₉	C₂²	1	16	yes	complemented
23	C₂×#120×C₈₉	C₂²	1	8	yes	—
24	C₄×#41×C₈₉	—	2	8	no	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	2	yes	—
30	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
31	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₈₉	C₂²	1	2	yes	complemented
33	#394×C₈₉	C₂²	1	16	yes	complemented
34	#392×C₈₉	C₂²	1	16	yes	complemented
35	#390×C₈₉	C₂²	1	8	yes	complemented
36	#390×C₈₉	C₂²	1	8	yes	complemented
37	#390×C₈₉	C₂²	1	16	yes	complemented
38	#384×C₈₉	C₂²	1	2	yes	complemented
39	#382×C₈₉	C₂²	1	2	yes	complemented
40	#380×C₈₉	C₂²	1	4	yes	—
41	#379×C₈₉	C₂²	1	8	yes	—
42	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
43	C₂⁵×C₈₉	C₂³	1	4	yes	—
44	C₂×#41×C₈₉	—	2	4	no	—
45	C₂×#41×C₈₉	—	2	4	no	—
46	C₂×#41×C₈₉	D₄	1	8	yes	complemented
47	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₈₉	—	2	16	no	—
49	C₂²×D₄×C₈₉	—	2	8	no	—
50	C₂²×D₄×C₈₉	—	2	8	no	—
51	C₂²×D₄×C₈₉	—	2	8	no	—
52	C₂²×D₄×C₈₉	—	4	16	no	—
53	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
54	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
55	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
56	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	#127×C₈₉	—	2	16	no	—
65	#127×C₈₉	—	2	8	no	—
66	#127×C₈₉	—	2	8	no	—
67	#127×C₈₉	—	2	16	no	—
68	#124×C₈₉	—	2	16	no	—
69	#121×C₈₉	—	2	32	no	—
70	#121×C₈₉	—	4	32	no	—
71	#120×C₈₉	—	2	32	no	—
72	C₄×Q₈×C₈₉	—	2	8	no	—
73	C₄×D₄×C₈₉	—	2	16	no	—
74	C₄×D₄×C₈₉	—	2	8	no	—
75	#117×C₈₉	—	2	4	no	—
76	#117×C₈₉	—	2	8	no	—
77	#117×C₈₉	—	2	8	no	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
82	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	—
87	C₂×C₄²×C₈₉	—	2	8	no	—
88	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
89	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	#95×C₈₉	C₂³	1	8	yes	—
96	C₂⁴×C₈₉	—	2	8	no	—
97	C₂⁴×C₈₉	—	2	8	no	—
98	C₂⁴×C₈₉	—	2	8	no	—
99	C₂⁴×C₈₉	—	4	16	no	—
100	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
101	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
102	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
103	#41×C₈₉	—	2	32	no	—
104	C₂×Q₈×C₈₉	—	2	2	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	complemented
107	C₂×D₄×C₈₉	—	2	4	no	—
108	C₂×D₄×C₈₉	—	2	4	no	—
109	C₂×D₄×C₈₉	—	2	32	no	—
110	C₂×D₄×C₈₉	—	2	2	no	—
111	C₂×D₄×C₈₉	—	2	8	no	—
112	C₂×D₄×C₈₉	—	2	8	no	—
113	C₂×D₄×C₈₉	—	2	16	no	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	8	no	—
116	C₂×D₄×C₈₉	—	2	16	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	8	no	—
120	C₂×D₄×C₈₉	—	2	32	no	—
121	C₂×D₄×C₈₉	—	4	16	no	—
122	C₂×D₄×C₈₉	—	4	64	no	—
123	C₂×D₄×C₈₉	—	4	32	no	—
124	C₂×D₄×C₈₉	—	4	32	no	—
125	C₂×D₄×C₈₉	C₂×D₄	1	8	yes	—
126	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	complemented
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	2	4	no	—
129	C₂²×C₄×C₈₉	—	2	8	no	—
130	C₂²×C₄×C₈₉	—	2	8	no	—
131	C₂²×C₄×C₈₉	—	2	16	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	complemented
136	C₂²×C₄×C₈₉	#41	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
144	C₄⋊C₄×C₈₉	—	2	8	no	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	8	no	—
147	C₄⋊C₄×C₈₉	—	2	16	no	—
148	C₂²⋊C₄×C₈₉	—	2	4	no	—
149	C₂²⋊C₄×C₈₉	—	2	8	no	—
150	C₂²⋊C₄×C₈₉	—	2	8	no	—
151	C₂²⋊C₄×C₈₉	—	2	32	no	—
152	C₂²⋊C₄×C₈₉	—	4	32	no	—
153	C₄²×C₈₉	—	2	4	no	—
154	C₄²×C₈₉	—	2	8	no	—
155	C₄²×C₈₉	—	2	8	no	—
156	C₄²×C₈₉	C₂×D₄	1	4	yes	—
157	C₄²×C₈₉	C₂×D₄	1	4	yes	—
158	C₄²×C₈₉	C₂×D₄	1	8	yes	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	2	2	no	—
161	C₂³×C₈₉	—	2	2	no	—
162	C₂³×C₈₉	—	2	8	no	—
163	C₂³×C₈₉	—	2	8	no	—
164	C₂³×C₈₉	—	2	8	no	—
165	C₂³×C₈₉	—	2	8	no	—
166	C₂³×C₈₉	—	2	32	no	—
167	C₂³×C₈₉	—	4	32	no	—
168	C₂³×C₈₉	—	4	16	no	—
169	C₂³×C₈₉	—	8	16	no	—
170	C₂³×C₈₉	—	8	16	no	—
171	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
174	C₂³×C₈₉	C₂×#41	1	2	yes	—
175	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
176	Q₈×C₈₉	—	2	8	no	—
177	D₄×C₈₉	—	2	16	no	—
178	D₄×C₈₉	—	2	8	no	—
179	D₄×C₈₉	—	4	32	no	—
180	D₄×C₈₉	—	4	16	no	—
181	D₄×C₈₉	—	4	16	no	—
182	D₄×C₈₉	—	4	32	no	—
183	D₄×C₈₉	—	8	32	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	16	no	—
188	C₂×C₄×C₈₉	—	2	16	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	2	8	no	—
191	C₂×C₄×C₈₉	—	2	8	no	—
192	C₂×C₄×C₈₉	—	2	16	no	—
193	C₂×C₄×C₈₉	—	4	16	no	—
194	C₂×C₄×C₈₉	#121	1	16	yes	complemented
195	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
202	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
203	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₈₉	H(5,𝔽₂)	1	8	yes	—
205	C₂²×C₈₉	—	2	4	no	—
206	C₂²×C₈₉	—	2	4	no	—
207	C₂²×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	4	no	—
209	C₂²×C₈₉	—	2	8	no	—
210	C₂²×C₈₉	—	4	4	no	—
211	C₂²×C₈₉	—	4	4	no	—
212	C₂²×C₈₉	—	4	8	no	—
213	C₂²×C₈₉	—	4	16	no	—
214	C₂²×C₈₉	—	4	16	no	—
215	C₂²×C₈₉	—	4	16	no	—
216	C₂²×C₈₉	—	8	32	no	—
217	C₂²×C₈₉	C₂×#121	1	4	yes	—
218	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
219	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
220	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
221	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
222	C₄×C₈₉	—	2	4	no	—
223	C₄×C₈₉	—	2	4	no	—
224	C₄×C₈₉	—	4	4	no	—
225	C₄×C₈₉	—	4	8	no	—
226	C₄×C₈₉	C₂×#121	1	4	yes	—
227	C₄×C₈₉	C₂×#121	1	4	yes	—
228	C₄×C₈₉	#535	1	8	yes	complemented
229	#35272	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
230	C₂×C₈₉	—	2	4	no	—
231	C₂×C₈₉	—	4	4	no	—
232	C₂×C₈₉	—	8	8	no	—
233	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
234	C₂×C₈₉	C₂×#535	1	2	yes	—
235	C₂×C₈₉	#3498	1	2	yes	—
236	C₂×C₈₉	#3508	1	2	yes	—
237	C₂×#535	C₂×C₈₉	1	2	yes	complemented
238	C₂²×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
239	C₂×C₄×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
240	#2856	C₂×C₈₉	1	4	yes	complemented
241	#2619	C₂×C₈₉	1	4	yes	complemented
242	#2548	C₂×C₈₉	1	4	yes	complemented
243	#2541	C₂×C₈₉	1	4	yes	complemented
244	#2408	C₂×C₈₉	1	8	yes	complemented
245	#2309	C₂×C₈₉	1	2	yes	complemented
246	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
247	C₈₉	#35272	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
249	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
250	C₂³×D₄	C₂²×C₈₉	1	4	yes	—
251	#535	—	2	16	no	—
252	C₂×#127	—	2	8	no	—
253	C₂×#127	C₂²×C₈₉	1	2	yes	—
254	C₂×#127	C₂²×C₈₉	1	2	yes	—
255	C₂×#127	C₂²×C₈₉	1	4	yes	—
256	C₂×#127	C₂²×C₈₉	1	4	yes	complemented
257	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
258	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
259	C₂×#121	C₂²×C₈₉	1	16	yes	complemented
260	C₂×#120	C₂²×C₈₉	1	8	yes	—
261	C₄×#41	—	2	8	no	—
262	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
263	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
264	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
265	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#117	C₂²×C₈₉	1	2	yes	—
267	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
268	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
269	C₂²×C₄²	C₂²×C₈₉	1	2	yes	complemented
270	#394	C₂²×C₈₉	1	16	yes	complemented
271	#392	C₂²×C₈₉	1	16	yes	complemented
272	#390	C₂²×C₈₉	1	8	yes	complemented
273	#390	C₂²×C₈₉	1	8	yes	complemented
274	#390	C₂²×C₈₉	1	16	yes	complemented
275	#384	C₂²×C₈₉	1	2	yes	complemented
276	#382	C₂²×C₈₉	1	2	yes	complemented
277	#380	C₂²×C₈₉	1	4	yes	—
278	#379	C₂²×C₈₉	1	8	yes	—
279	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
280	C₂⁵	C₂³×C₈₉	1	4	yes	—
281	C₂×#41	—	2	4	no	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	D₄×C₈₉	1	8	yes	complemented
284	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
285	C₂²×D₄	—	2	16	no	—
286	C₂²×D₄	—	2	8	no	—
287	C₂²×D₄	—	2	8	no	—
288	C₂²×D₄	—	2	8	no	—
289	C₂²×D₄	—	4	16	no	—
290	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
291	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
292	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
293	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
294	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
295	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
296	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
297	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
298	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
299	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
300	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
301	#127	—	2	16	no	—
302	#127	—	2	8	no	—
303	#127	—	2	8	no	—
304	#127	—	2	16	no	—
305	#124	—	2	16	no	—
306	#121	—	2	32	no	—
307	#121	—	4	32	no	—
308	#120	—	2	32	no	—
309	C₄×Q₈	—	2	8	no	—
310	C₄×D₄	—	2	16	no	—
311	C₄×D₄	—	2	8	no	—
312	#117	—	2	4	no	—
313	#117	—	2	8	no	—
314	#117	—	2	8	no	—
315	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
317	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
318	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
321	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
322	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
323	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	—
324	C₂×C₄²	—	2	8	no	—
325	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
326	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
327	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
328	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
329	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
330	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
331	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
332	#95	C₂³×C₈₉	1	8	yes	—
333	C₂⁴	—	2	8	no	—
334	C₂⁴	—	2	8	no	—
335	C₂⁴	—	2	8	no	—
336	C₂⁴	—	4	16	no	—
337	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
338	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
339	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
340	#41	—	2	32	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	complemented
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	2	32	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	8	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	—	2	16	no	—
351	C₂×D₄	—	2	8	no	—
352	C₂×D₄	—	2	8	no	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	32	no	—
358	C₂×D₄	—	4	16	no	—
359	C₂×D₄	—	4	64	no	—
360	C₂×D₄	—	4	32	no	—
361	C₂×D₄	—	4	32	no	—
362	C₂×D₄	C₂×D₄×C₈₉	1	8	yes	—
363	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	complemented
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	16	no	—
369	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
370	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	complemented
373	C₂²×C₄	#41×C₈₉	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
375	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
378	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	16	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	32	no	—
389	C₂²⋊C₄	—	4	32	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	C₂×D₄×C₈₉	1	4	yes	—
394	C₄²	C₂×D₄×C₈₉	1	4	yes	—
395	C₄²	C₂×D₄×C₈₉	1	8	yes	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	8	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	8	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	32	no	—
404	C₂³	—	4	32	no	—
405	C₂³	—	4	16	no	—
406	C₂³	—	8	16	no	—
407	C₂³	—	8	16	no	—
408	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
409	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
410	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
411	C₂³	C₂×#41×C₈₉	1	2	yes	—
412	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
413	Q₈	—	2	8	no	—
414	D₄	—	2	16	no	—
415	D₄	—	2	8	no	—
416	D₄	—	4	32	no	—
417	D₄	—	4	16	no	—
418	D₄	—	4	16	no	—
419	D₄	—	4	32	no	—
420	D₄	—	8	32	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	16	no	—
425	C₂×C₄	—	2	16	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	16	no	—
430	C₂×C₄	—	4	16	no	—
431	C₂×C₄	#121×C₈₉	1	16	yes	complemented
432	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
433	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
434	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
435	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
437	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
438	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
439	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
440	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
441	C₂×C₄	H(5,𝔽₂)×C₈₉	1	8	yes	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	8	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	16	no	—
451	C₂²	—	4	16	no	—
452	C₂²	—	4	16	no	—
453	C₂²	—	8	32	no	—
454	C₂²	C₂×#121×C₈₉	1	4	yes	—
455	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
456	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
457	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
458	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
459	C₄	—	2	4	no	—
460	C₄	—	2	4	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	8	no	—
463	C₄	C₂×#121×C₈₉	1	4	yes	—
464	C₄	C₂×#121×C₈₉	1	4	yes	—
465	C₄	#535×C₈₉	1	8	yes	complemented
466	C₂	—	2	4	no	—
467	C₂	—	4	4	no	—
468	C₂	—	8	8	no	—
469	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
470	C₂	C₂×#535×C₈₉	1	2	yes	—
471	C₂	C₈₉×#3498	1	2	yes	—
472	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. C₂²×#127×C₈₉	C₂	semidirect
3. C₂×C₄×#41×C₈₉	C₂	semidirect
4. C₈₉×#2856	C₂	semidirect
5. C₈₉×#2619	C₂	semidirect
6. C₈₉×#2548	C₂	semidirect
7. C₈₉×#2541	C₂	semidirect
8. C₈₉×#2408	C₂	semidirect
9. C₈₉×#2309	C₂	semidirect
10. C₈₉×#2285	C₂	semidirect
19. C₂×#127×C₈₉	C₂²	semidirect
20. C₂×#124×C₈₉	C₂²	semidirect
21. C₂×#121×C₈₉	C₂²	semidirect
22. C₂×#121×C₈₉	C₂²	semidirect
25. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
27. C₂×C₄×D₄×C₈₉	C₂²	semidirect
30. C₂×#117×C₈₉	C₂²	semidirect
32. C₂²×C₄²×C₈₉	C₂²	semidirect
33. #394×C₈₉	C₂²	semidirect
34. #392×C₈₉	C₂²	semidirect
35. #390×C₈₉	C₂²	semidirect
36. #390×C₈₉	C₂²	semidirect
37. #390×C₈₉	C₂²	semidirect
38. #384×C₈₉	C₂²	semidirect
39. #382×C₈₉	C₂²	semidirect
42. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
46. C₂×#41×C₈₉	D₄	semidirect
88. C₂×C₄²×C₈₉	D₄	semidirect
106. C₂×Q₈×C₈₉	C₂×D₄	semidirect
126. C₂×D₄×C₈₉	C₂×D₄	semidirect
135. C₂²×C₄×C₈₉	C₂×D₄	semidirect
194. C₂×C₄×C₈₉	#121	semidirect
228. C₄×C₈₉	#535	semidirect
229. #35272	C₈₉	direct (N × H)
237. C₂×#535	C₂×C₈₉	semidirect
238. C₂²×#127	C₂×C₈₉	semidirect
239. C₂×C₄×#41	C₂×C₈₉	semidirect
240. #2856	C₂×C₈₉	semidirect
241. #2619	C₂×C₈₉	semidirect
242. #2548	C₂×C₈₉	semidirect
243. #2541	C₂×C₈₉	semidirect
244. #2408	C₂×C₈₉	semidirect
245. #2309	C₂×C₈₉	semidirect
246. #2285	C₂×C₈₉	semidirect
247. C₈₉	#35272	direct (N × H)
256. C₂×#127	C₂²×C₈₉	semidirect
257. C₂×#124	C₂²×C₈₉	semidirect
258. C₂×#121	C₂²×C₈₉	semidirect
259. C₂×#121	C₂²×C₈₉	semidirect
262. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
264. C₂×C₄×D₄	C₂²×C₈₉	semidirect
267. C₂×#117	C₂²×C₈₉	semidirect
269. C₂²×C₄²	C₂²×C₈₉	semidirect
270. #394	C₂²×C₈₉	semidirect
271. #392	C₂²×C₈₉	semidirect
272. #390	C₂²×C₈₉	semidirect
273. #390	C₂²×C₈₉	semidirect
274. #390	C₂²×C₈₉	semidirect
275. #384	C₂²×C₈₉	semidirect
276. #382	C₂²×C₈₉	semidirect
279. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
283. C₂×#41	D₄×C₈₉	semidirect
325. C₂×C₄²	D₄×C₈₉	semidirect
343. C₂×Q₈	C₂×D₄×C₈₉	semidirect
363. C₂×D₄	C₂×D₄×C₈₉	semidirect
372. C₂²×C₄	C₂×D₄×C₈₉	semidirect
431. C₂×C₄	#121×C₈₉	semidirect
465. C₄	#535×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×C₄×#41×C₈₉	2
C₈₉×#2856	2
C₈₉×#2619	2
C₈₉×#2548	2
C₈₉×#2541	2
C₈₉×#2408	2
C₈₉×#2309	2
C₈₉×#2285	2
#35272	89

Subgroups — C89×#35272 #36413120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35272 #36413120