Subgroups — C₈₉×#35237 #36413085

Order 22784.

3294 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2847	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2631	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2563	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2541	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2535	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2504	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2433	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2404	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2328	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2283	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
15	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
16	#532×C₈₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#127×C₈₉	C₂²	1	4	yes	—
19	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×#124×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#121×C₈₉	C₂²	1	2	yes	—
22	C₂×#121×C₈₉	C₂²	1	2	yes	—
23	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
24	C₂×#120×C₈₉	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₈₉	—	2	8	no	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
34	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
35	#397×C₈₉	C₂²	1	8	yes	complemented
36	#393×C₈₉	C₂²	1	8	yes	complemented
37	#392×C₈₉	C₂²	1	8	yes	—
38	#392×C₈₉	C₂²	1	8	yes	complemented
39	#390×C₈₉	C₂²	1	4	yes	—
40	#390×C₈₉	C₂²	1	4	yes	complemented
41	#386×C₈₉	C₂²	1	8	yes	—
42	#386×C₈₉	C₂²	1	16	yes	complemented
43	#386×C₈₉	C₂²	1	16	yes	complemented
44	#383×C₈₉	C₂²	1	2	yes	complemented
45	#382×C₈₉	C₂²	1	4	yes	complemented
46	#382×C₈₉	C₂²	1	2	yes	complemented
47	#381×C₈₉	C₂²	1	2	yes	—
48	#380×C₈₉	C₂²	1	2	yes	—
49	#380×C₈₉	C₂²	1	8	yes	complemented
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
52	#376×C₈₉	C₂²	1	2	yes	complemented
53	C₂⁵×C₈₉	C₂³	1	2	yes	—
54	C₂×#41×C₈₉	—	2	8	no	—
55	C₂×#41×C₈₉	—	4	8	no	—
56	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
57	C₂²×D₄×C₈₉	—	2	8	no	—
58	C₂²×D₄×C₈₉	—	2	4	no	—
59	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₈₉	C₂³	1	16	yes	—
65	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
66	C₂³×C₄×C₈₉	—	2	8	no	—
67	C₂³×C₄×C₈₉	—	4	8	no	—
68	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
69	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
75	C₄⋊Q₈×C₈₉	—	2	4	no	—
76	#127×C₈₉	—	2	16	no	—
77	#127×C₈₉	—	2	4	no	—
78	#124×C₈₉	—	2	8	no	—
79	#121×C₈₉	—	2	8	no	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	—	4	16	no	—
82	#120×C₈₉	—	4	16	no	—
83	C₄×D₄×C₈₉	—	2	8	no	—
84	C₄×D₄×C₈₉	—	2	8	no	—
85	C₄×D₄×C₈₉	—	2	8	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	C₄×D₄×C₈₉	—	2	8	no	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
103	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
104	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	#95×C₈₉	C₂³	1	4	yes	—
110	#95×C₈₉	C₂³	1	4	yes	—
111	#95×C₈₉	C₂³	1	4	yes	—
112	#95×C₈₉	C₂³	1	4	yes	—
113	#95×C₈₉	C₂³	1	16	yes	—
114	C₂⁴×C₈₉	—	2	4	no	—
115	C₂⁴×C₈₉	—	2	8	no	—
116	C₂⁴×C₈₉	—	2	8	no	—
117	C₂⁴×C₈₉	—	4	4	no	—
118	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
119	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
120	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
121	#41×C₈₉	—	4	32	no	—
122	C₂×Q₈×C₈₉	—	2	4	no	—
123	C₂×Q₈×C₈₉	—	4	4	no	—
124	C₂×D₄×C₈₉	—	2	32	no	—
125	C₂×D₄×C₈₉	—	2	8	no	—
126	C₂×D₄×C₈₉	—	2	8	no	—
127	C₂×D₄×C₈₉	—	2	16	no	—
128	C₂×D₄×C₈₉	—	2	32	no	—
129	C₂×D₄×C₈₉	—	2	4	no	—
130	C₂×D₄×C₈₉	—	2	4	no	—
131	C₂×D₄×C₈₉	—	2	4	no	—
132	C₂×D₄×C₈₉	—	2	4	no	—
133	C₂×D₄×C₈₉	—	2	4	no	—
134	C₂×D₄×C₈₉	—	2	4	no	—
135	C₂×D₄×C₈₉	—	2	8	no	—
136	C₂×D₄×C₈₉	—	2	8	no	—
137	C₂×D₄×C₈₉	—	4	4	no	—
138	C₂×D₄×C₈₉	—	4	16	no	—
139	C₂×D₄×C₈₉	—	4	16	no	—
140	C₂×D₄×C₈₉	#41	1	8	yes	complemented
141	C₂²×C₄×C₈₉	—	2	4	no	—
142	C₂²×C₄×C₈₉	—	2	4	no	—
143	C₂²×C₄×C₈₉	—	2	4	no	—
144	C₂²×C₄×C₈₉	—	2	4	no	—
145	C₂²×C₄×C₈₉	—	2	8	no	—
146	C₂²×C₄×C₈₉	—	2	8	no	—
147	C₂²×C₄×C₈₉	—	2	8	no	—
148	C₂²×C₄×C₈₉	—	2	16	no	—
149	C₂²×C₄×C₈₉	—	4	8	no	—
150	C₂²×C₄×C₈₉	—	4	4	no	—
151	C₂²×C₄×C₈₉	—	4	8	no	—
152	C₂²×C₄×C₈₉	—	4	32	no	—
153	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
159	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₈₉	—	2	4	no	—
166	C₄⋊C₄×C₈₉	—	2	4	no	—
167	C₄⋊C₄×C₈₉	—	2	4	no	—
168	C₄⋊C₄×C₈₉	—	2	4	no	—
169	C₄⋊C₄×C₈₉	—	2	8	no	—
170	C₂²⋊C₄×C₈₉	—	2	8	no	—
171	C₂²⋊C₄×C₈₉	—	2	8	no	—
172	C₂²⋊C₄×C₈₉	—	2	8	no	—
173	C₂²⋊C₄×C₈₉	—	2	8	no	—
174	C₂²⋊C₄×C₈₉	—	2	8	no	—
175	C₂²⋊C₄×C₈₉	—	4	16	no	—
176	C₂²⋊C₄×C₈₉	—	4	16	no	—
177	C₄²×C₈₉	—	2	8	no	—
178	C₄²×C₈₉	C₂×D₄	1	4	yes	—
179	C₄²×C₈₉	C₂×D₄	1	4	yes	—
180	C₄²×C₈₉	C₂×D₄	1	4	yes	—
181	C₄²×C₈₉	C₂×D₄	1	4	yes	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	—	2	2	no	—
184	C₂³×C₈₉	—	2	16	no	—
185	C₂³×C₈₉	—	2	4	no	—
186	C₂³×C₈₉	—	2	4	no	—
187	C₂³×C₈₉	—	2	8	no	—
188	C₂³×C₈₉	—	2	8	no	—
189	C₂³×C₈₉	—	2	4	no	—
190	C₂³×C₈₉	—	2	8	no	—
191	C₂³×C₈₉	—	2	8	no	—
192	C₂³×C₈₉	—	2	8	no	—
193	C₂³×C₈₉	—	4	32	no	—
194	C₂³×C₈₉	—	4	8	no	—
195	C₂³×C₈₉	—	4	8	no	—
196	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₈₉	C₂×#41	1	8	yes	—
198	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
199	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
200	Q₈×C₈₉	—	4	8	no	—
201	D₄×C₈₉	—	2	16	no	—
202	D₄×C₈₉	—	2	16	no	—
203	D₄×C₈₉	—	4	8	no	—
204	D₄×C₈₉	—	4	16	no	—
205	D₄×C₈₉	—	4	8	no	—
206	D₄×C₈₉	—	4	8	no	—
207	D₄×C₈₉	—	8	32	no	—
208	C₂×C₄×C₈₉	—	2	8	no	—
209	C₂×C₄×C₈₉	—	2	2	no	—
210	C₂×C₄×C₈₉	—	2	2	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	8	no	—
214	C₂×C₄×C₈₉	—	2	8	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	4	no	—
217	C₂×C₄×C₈₉	—	2	8	no	—
218	C₂×C₄×C₈₉	—	2	8	no	—
219	C₂×C₄×C₈₉	—	2	8	no	—
220	C₂×C₄×C₈₉	—	2	8	no	—
221	C₂×C₄×C₈₉	—	2	8	no	—
222	C₂×C₄×C₈₉	—	4	16	no	—
223	C₂×C₄×C₈₉	—	4	16	no	—
224	C₂×C₄×C₈₉	—	4	8	no	—
225	C₂×C₄×C₈₉	—	4	16	no	—
226	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
233	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	2	2	no	—
236	C₂²×C₈₉	—	2	8	no	—
237	C₂²×C₈₉	—	2	8	no	—
238	C₂²×C₈₉	—	2	16	no	—
239	C₂²×C₈₉	—	4	32	no	—
240	C₂²×C₈₉	—	4	4	no	—
241	C₂²×C₈₉	—	4	4	no	—
242	C₂²×C₈₉	—	4	8	no	—
243	C₂²×C₈₉	—	4	4	no	—
244	C₂²×C₈₉	—	4	4	no	—
245	C₂²×C₈₉	—	4	4	no	—
246	C₂²×C₈₉	—	4	16	no	—
247	C₂²×C₈₉	#535	1	4	yes	—
248	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
249	C₂²×C₈₉	C₂²×#41	1	2	yes	—
250	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
251	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
252	C₄×C₈₉	—	2	2	no	—
253	C₄×C₈₉	—	2	2	no	—
254	C₄×C₈₉	—	2	2	no	—
255	C₄×C₈₉	—	2	2	no	—
256	C₄×C₈₉	—	4	4	no	—
257	C₄×C₈₉	—	4	4	no	—
258	C₄×C₈₉	—	4	8	no	—
259	C₄×C₈₉	#525	1	4	yes	—
260	C₄×C₈₉	#535	1	4	yes	—
261	#35237	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂×C₈₉	—	2	4	no	—
263	C₂×C₈₉	—	4	8	no	—
264	C₂×C₈₉	—	8	4	no	—
265	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
266	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
267	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
268	C₂×C₈₉	#3519	1	4	yes	—
269	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
270	C₂²×C₄×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
271	#2847	C₂×C₈₉	1	4	yes	complemented
272	#2631	C₂×C₈₉	1	4	yes	complemented
273	#2563	C₂×C₈₉	1	2	yes	complemented
274	#2541	C₂×C₈₉	1	2	yes	complemented
275	#2535	C₂×C₈₉	1	4	yes	complemented
276	#2504	C₂×C₈₉	1	2	yes	complemented
277	#2433	C₂×C₈₉	1	2	yes	complemented
278	#2404	C₂×C₈₉	1	4	yes	complemented
279	#2328	C₂×C₈₉	1	4	yes	complemented
280	#2283	C₂×C₈₉	1	1	yes	characteristic, complemented
281	C₈₉	#35237	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×#41	C₂²×C₈₉	1	2	yes	—
283	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
284	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
285	#532	—	2	8	no	—
286	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
287	C₂×#127	C₂²×C₈₉	1	4	yes	—
288	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
289	C₂×#124	C₂²×C₈₉	1	2	yes	complemented
290	C₂×#121	C₂²×C₈₉	1	2	yes	—
291	C₂×#121	C₂²×C₈₉	1	2	yes	—
292	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
293	C₂×#120	C₂²×C₈₉	1	8	yes	—
294	C₂×C₄×D₄	—	2	8	no	—
295	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
296	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
297	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
298	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
299	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
300	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
301	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
302	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
303	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
304	#397	C₂²×C₈₉	1	8	yes	complemented
305	#393	C₂²×C₈₉	1	8	yes	complemented
306	#392	C₂²×C₈₉	1	8	yes	—
307	#392	C₂²×C₈₉	1	8	yes	complemented
308	#390	C₂²×C₈₉	1	4	yes	—
309	#390	C₂²×C₈₉	1	4	yes	complemented
310	#386	C₂²×C₈₉	1	8	yes	—
311	#386	C₂²×C₈₉	1	16	yes	complemented
312	#386	C₂²×C₈₉	1	16	yes	complemented
313	#383	C₂²×C₈₉	1	2	yes	complemented
314	#382	C₂²×C₈₉	1	4	yes	complemented
315	#382	C₂²×C₈₉	1	2	yes	complemented
316	#381	C₂²×C₈₉	1	2	yes	—
317	#380	C₂²×C₈₉	1	2	yes	—
318	#380	C₂²×C₈₉	1	8	yes	complemented
319	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
320	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
321	#376	C₂²×C₈₉	1	2	yes	complemented
322	C₂⁵	C₂³×C₈₉	1	2	yes	—
323	C₂×#41	—	2	8	no	—
324	C₂×#41	—	4	8	no	—
325	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
326	C₂²×D₄	—	2	8	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
329	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
330	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
331	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
332	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
333	C₂²×D₄	C₂³×C₈₉	1	16	yes	—
334	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
335	C₂³×C₄	—	2	8	no	—
336	C₂³×C₄	—	4	8	no	—
337	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
338	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
339	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
342	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
343	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
344	C₄⋊Q₈	—	2	4	no	—
345	#127	—	2	16	no	—
346	#127	—	2	4	no	—
347	#124	—	2	8	no	—
348	#121	—	2	8	no	—
349	#121	—	2	8	no	—
350	#121	—	4	16	no	—
351	#120	—	4	16	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	8	no	—
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	8	no	—
358	C₂×C₄⋊C₄	—	2	4	no	—
359	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
360	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
363	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
364	C₂×C₂²⋊C₄	—	2	8	no	—
365	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
369	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
371	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
372	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
373	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
374	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
378	#95	C₂³×C₈₉	1	4	yes	—
379	#95	C₂³×C₈₉	1	4	yes	—
380	#95	C₂³×C₈₉	1	4	yes	—
381	#95	C₂³×C₈₉	1	4	yes	—
382	#95	C₂³×C₈₉	1	16	yes	—
383	C₂⁴	—	2	4	no	—
384	C₂⁴	—	2	8	no	—
385	C₂⁴	—	2	8	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
388	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
389	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
390	#41	—	4	32	no	—
391	C₂×Q₈	—	2	4	no	—
392	C₂×Q₈	—	4	4	no	—
393	C₂×D₄	—	2	32	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	16	no	—
397	C₂×D₄	—	2	32	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	8	no	—
405	C₂×D₄	—	2	8	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	16	no	—
408	C₂×D₄	—	4	16	no	—
409	C₂×D₄	#41×C₈₉	1	8	yes	complemented
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	8	no	—
415	C₂²×C₄	—	2	8	no	—
416	C₂²×C₄	—	2	8	no	—
417	C₂²×C₄	—	2	16	no	—
418	C₂²×C₄	—	4	8	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	—	4	32	no	—
422	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
424	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
425	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
426	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
427	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
428	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	—	2	8	no	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	4	16	no	—
445	C₂²⋊C₄	—	4	16	no	—
446	C₄²	—	2	8	no	—
447	C₄²	C₂×D₄×C₈₉	1	4	yes	—
448	C₄²	C₂×D₄×C₈₉	1	4	yes	—
449	C₄²	C₂×D₄×C₈₉	1	4	yes	—
450	C₄²	C₂×D₄×C₈₉	1	4	yes	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	2	4	no	—
456	C₂³	—	2	8	no	—
457	C₂³	—	2	8	no	—
458	C₂³	—	2	4	no	—
459	C₂³	—	2	8	no	—
460	C₂³	—	2	8	no	—
461	C₂³	—	2	8	no	—
462	C₂³	—	4	32	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	8	no	—
465	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
466	C₂³	C₂×#41×C₈₉	1	8	yes	—
467	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
468	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
469	Q₈	—	4	8	no	—
470	D₄	—	2	16	no	—
471	D₄	—	2	16	no	—
472	D₄	—	4	8	no	—
473	D₄	—	4	16	no	—
474	D₄	—	4	8	no	—
475	D₄	—	4	8	no	—
476	D₄	—	8	32	no	—
477	C₂×C₄	—	2	8	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	8	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	4	16	no	—
492	C₂×C₄	—	4	16	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	16	no	—
495	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
501	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
502	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
503	C₂²	—	2	2	no	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	8	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	16	no	—
508	C₂²	—	4	32	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	16	no	—
516	C₂²	#535×C₈₉	1	4	yes	—
517	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
518	C₂²	C₂²×#41×C₈₉	1	2	yes	—
519	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
520	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	4	4	no	—
526	C₄	—	4	4	no	—
527	C₄	—	4	8	no	—
528	C₄	#525×C₈₉	1	4	yes	—
529	C₄	#535×C₈₉	1	4	yes	—
530	C₂	—	2	4	no	—
531	C₂	—	4	8	no	—
532	C₂	—	8	4	no	—
533	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
534	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
535	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
536	C₂	C₈₉×#3519	1	4	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×#532×C₈₉	C₂	semidirect
2. C₂²×C₄×D₄×C₈₉	C₂	semidirect
3. C₈₉×#2847	C₂	semidirect
4. C₈₉×#2631	C₂	semidirect
5. C₈₉×#2563	C₂	semidirect
6. C₈₉×#2541	C₂	semidirect
7. C₈₉×#2535	C₂	semidirect
8. C₈₉×#2504	C₂	semidirect
9. C₈₉×#2433	C₂	semidirect
10. C₈₉×#2404	C₂	semidirect
11. C₈₉×#2328	C₂	semidirect
12. C₈₉×#2283	C₂	semidirect
17. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
19. C₂×#127×C₈₉	C₂²	semidirect
20. C₂×#124×C₈₉	C₂²	semidirect
23. C₂×#121×C₈₉	C₂²	semidirect
30. C₂×C₄×D₄×C₈₉	C₂²	semidirect
31. C₂×C₄×D₄×C₈₉	C₂²	semidirect
35. #397×C₈₉	C₂²	semidirect
36. #393×C₈₉	C₂²	semidirect
38. #392×C₈₉	C₂²	semidirect
40. #390×C₈₉	C₂²	semidirect
42. #386×C₈₉	C₂²	semidirect
43. #386×C₈₉	C₂²	semidirect
44. #383×C₈₉	C₂²	semidirect
45. #382×C₈₉	C₂²	semidirect
46. #382×C₈₉	C₂²	semidirect
49. #380×C₈₉	C₂²	semidirect
50. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
52. #376×C₈₉	C₂²	semidirect
103. C₂×C₄²×C₈₉	D₄	semidirect
140. C₂×D₄×C₈₉	#41	semidirect
261. #35237	C₈₉	direct (N × H)
269. C₂×#532	C₂×C₈₉	semidirect
270. C₂²×C₄×D₄	C₂×C₈₉	semidirect
271. #2847	C₂×C₈₉	semidirect
272. #2631	C₂×C₈₉	semidirect
273. #2563	C₂×C₈₉	semidirect
274. #2541	C₂×C₈₉	semidirect
275. #2535	C₂×C₈₉	semidirect
276. #2504	C₂×C₈₉	semidirect
277. #2433	C₂×C₈₉	semidirect
278. #2404	C₂×C₈₉	semidirect
279. #2328	C₂×C₈₉	semidirect
280. #2283	C₂×C₈₉	semidirect
281. C₈₉	#35237	direct (N × H)
286. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
288. C₂×#127	C₂²×C₈₉	semidirect
289. C₂×#124	C₂²×C₈₉	semidirect
292. C₂×#121	C₂²×C₈₉	semidirect
299. C₂×C₄×D₄	C₂²×C₈₉	semidirect
300. C₂×C₄×D₄	C₂²×C₈₉	semidirect
304. #397	C₂²×C₈₉	semidirect
305. #393	C₂²×C₈₉	semidirect
307. #392	C₂²×C₈₉	semidirect
309. #390	C₂²×C₈₉	semidirect
311. #386	C₂²×C₈₉	semidirect
312. #386	C₂²×C₈₉	semidirect
313. #383	C₂²×C₈₉	semidirect
314. #382	C₂²×C₈₉	semidirect
315. #382	C₂²×C₈₉	semidirect
318. #380	C₂²×C₈₉	semidirect
319. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
321. #376	C₂²×C₈₉	semidirect
372. C₂×C₄²	D₄×C₈₉	semidirect
409. C₂×D₄	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₈₉	2
C₂²×C₄×D₄×C₈₉	2
C₈₉×#2847	2
C₈₉×#2631	2
C₈₉×#2563	2
C₈₉×#2541	2
C₈₉×#2535	2
C₈₉×#2504	2
C₈₉×#2433	2
C₈₉×#2404	2
C₈₉×#2328	2
C₈₉×#2283	2
#35237	89

Subgroups — C89×#35237 #36413085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35237 #36413085