Subgroups — C₈₉×#35264 #36413112

Order 22784.

2654 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#535×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2861	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2858	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2641	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2640	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2491	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2490	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2472	C₂	1	8	yes	maximal, complemented
10	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	#544×C₈₉	—	2	8	no	—
18	#535×C₈₉	—	2	8	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
21	C₂×#127×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
23	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
24	C₂×#124×C₈₉	C₂²	1	2	yes	—
25	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
27	C₂×#121×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#120×C₈₉	C₂²	1	4	yes	—
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#397×C₈₉	C₂²	1	8	yes	complemented
37	#394×C₈₉	C₂²	1	8	yes	complemented
38	#394×C₈₉	C₂²	1	8	yes	complemented
39	#393×C₈₉	C₂²	1	8	yes	complemented
40	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#391×C₈₉	C₂²	1	2	yes	complemented
43	#390×C₈₉	C₂²	1	2	yes	—
44	#390×C₈₉	C₂²	1	2	yes	—
45	#390×C₈₉	C₂²	1	4	yes	—
46	#390×C₈₉	C₂²	1	2	yes	—
47	#390×C₈₉	C₂²	1	2	yes	—
48	#390×C₈₉	C₂²	1	4	yes	—
49	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#390×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#390×C₈₉	C₂²	1	2	yes	complemented
52	#390×C₈₉	C₂²	1	8	yes	complemented
53	#388×C₈₉	C₂²	1	8	yes	complemented
54	#388×C₈₉	C₂²	1	8	yes	complemented
55	#386×C₈₉	C₂²	1	4	yes	—
56	#386×C₈₉	C₂²	1	4	yes	—
57	#380×C₈₉	C₂²	1	4	yes	complemented
58	#379×C₈₉	C₂²	1	4	yes	—
59	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
60	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
61	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
62	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
63	#376×C₈₉	C₂²	1	2	yes	complemented
64	C₄³×C₈₉	C₂²	1	2	yes	complemented
65	C₂⁵×C₈₉	C₂³	1	2	yes	—
66	C₂×#41×C₈₉	—	2	4	no	—
67	C₂×#41×C₈₉	—	2	4	no	—
68	C₂×#41×C₈₉	—	2	4	no	—
69	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
71	C₂²×D₄×C₈₉	—	2	4	no	—
72	C₂²×D₄×C₈₉	—	2	4	no	—
73	C₂²×D₄×C₈₉	—	2	4	no	—
74	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
80	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₈₉	—	2	8	no	—
85	C₄⋊Q₈×C₈₉	—	2	8	no	—
86	#127×C₈₉	—	2	8	no	—
87	#125×C₈₉	—	2	8	no	—
88	#125×C₈₉	—	2	8	no	—
89	#124×C₈₉	—	2	8	no	—
90	#124×C₈₉	—	4	16	no	—
91	C₂²⋊Q₈×C₈₉	—	2	16	no	—
92	#121×C₈₉	—	2	8	no	—
93	#121×C₈₉	—	2	8	no	—
94	#120×C₈₉	—	2	16	no	—
95	#117×C₈₉	—	2	4	no	—
96	#117×C₈₉	—	2	4	no	—
97	#117×C₈₉	D₄	1	8	yes	—
98	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
110	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
115	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₈₉	—	2	4	no	—
123	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
130	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
131	#95×C₈₉	C₂³	1	4	yes	—
132	#95×C₈₉	C₂³	1	4	yes	—
133	#95×C₈₉	C₂³	1	4	yes	—
134	#95×C₈₉	C₂³	1	4	yes	—
135	#95×C₈₉	C₂³	1	8	yes	—
136	C₂⁴×C₈₉	—	2	4	no	—
137	C₂⁴×C₈₉	—	2	4	no	—
138	C₂⁴×C₈₉	—	2	4	no	—
139	C₂⁴×C₈₉	—	4	4	no	—
140	C₂⁴×C₈₉	—	4	4	no	—
141	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
142	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
143	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
144	#41×C₈₉	—	4	16	no	—
145	C₂×Q₈×C₈₉	—	2	2	no	—
146	C₂×Q₈×C₈₉	—	2	8	no	—
147	C₂×Q₈×C₈₉	—	2	2	no	—
148	C₂×Q₈×C₈₉	—	2	2	no	—
149	C₂×Q₈×C₈₉	—	4	8	no	—
150	C₂×D₄×C₈₉	—	2	4	no	—
151	C₂×D₄×C₈₉	—	2	4	no	—
152	C₂×D₄×C₈₉	—	2	4	no	—
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	4	no	—
155	C₂×D₄×C₈₉	—	2	2	no	—
156	C₂×D₄×C₈₉	—	2	8	no	—
157	C₂×D₄×C₈₉	—	2	8	no	—
158	C₂×D₄×C₈₉	—	2	4	no	—
159	C₂×D₄×C₈₉	—	2	4	no	—
160	C₂×D₄×C₈₉	—	2	4	no	—
161	C₂×D₄×C₈₉	—	2	4	no	—
162	C₂×D₄×C₈₉	—	2	2	no	—
163	C₂×D₄×C₈₉	—	2	2	no	—
164	C₂×D₄×C₈₉	—	4	8	no	—
165	C₂×D₄×C₈₉	—	4	8	no	—
166	C₂×D₄×C₈₉	—	4	16	no	—
167	C₂²×C₄×C₈₉	—	2	4	no	—
168	C₂²×C₄×C₈₉	—	2	4	no	—
169	C₂²×C₄×C₈₉	—	2	4	no	—
170	C₂²×C₄×C₈₉	—	2	4	no	—
171	C₂²×C₄×C₈₉	—	2	4	no	—
172	C₂²×C₄×C₈₉	—	2	4	no	—
173	C₂²×C₄×C₈₉	—	4	2	no	—
174	C₂²×C₄×C₈₉	—	4	4	no	—
175	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₈₉	#41	1	4	yes	—
177	C₂²×C₄×C₈₉	#41	1	4	yes	—
178	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₄⋊C₄×C₈₉	—	2	4	no	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	—	2	2	no	—
192	C₄⋊C₄×C₈₉	—	2	2	no	—
193	C₄⋊C₄×C₈₉	—	2	8	no	—
194	C₄⋊C₄×C₈₉	—	2	8	no	—
195	C₄⋊C₄×C₈₉	—	2	8	no	—
196	C₄⋊C₄×C₈₉	—	2	4	no	—
197	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
198	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
199	C₂²⋊C₄×C₈₉	—	2	4	no	—
200	C₂²⋊C₄×C₈₉	—	2	4	no	—
201	C₂²⋊C₄×C₈₉	—	2	8	no	—
202	C₂²⋊C₄×C₈₉	—	2	8	no	—
203	C₂²⋊C₄×C₈₉	—	2	16	no	—
204	C₂²⋊C₄×C₈₉	—	2	8	no	—
205	C₂²⋊C₄×C₈₉	—	4	8	no	—
206	C₂²⋊C₄×C₈₉	—	4	8	no	—
207	C₂²⋊C₄×C₈₉	—	4	4	no	—
208	C₂²⋊C₄×C₈₉	—	4	8	no	—
209	C₂²⋊C₄×C₈₉	—	4	8	no	—
210	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
211	C₄²×C₈₉	—	2	4	no	—
212	C₄²×C₈₉	—	2	2	no	—
213	C₄²×C₈₉	—	2	4	no	—
214	C₄²×C₈₉	—	2	2	no	—
215	C₄²×C₈₉	—	2	4	no	—
216	C₄²×C₈₉	—	2	8	no	—
217	C₄²×C₈₉	—	4	4	no	—
218	C₄²×C₈₉	C₂×D₄	1	8	yes	—
219	C₂³×C₈₉	—	2	2	no	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	4	no	—
222	C₂³×C₈₉	—	2	2	no	—
223	C₂³×C₈₉	—	2	2	no	—
224	C₂³×C₈₉	—	2	2	no	—
225	C₂³×C₈₉	—	2	4	no	—
226	C₂³×C₈₉	—	2	4	no	—
227	C₂³×C₈₉	—	2	4	no	—
228	C₂³×C₈₉	—	2	8	no	—
229	C₂³×C₈₉	—	2	4	no	—
230	C₂³×C₈₉	—	2	8	no	—
231	C₂³×C₈₉	—	4	16	no	—
232	C₂³×C₈₉	—	4	8	no	—
233	C₂³×C₈₉	—	8	8	no	—
234	C₂³×C₈₉	—	8	4	no	—
235	C₂³×C₈₉	—	8	4	no	—
236	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
237	C₂³×C₈₉	C₂×#41	1	2	yes	—
238	C₂³×C₈₉	C₂×#41	1	2	yes	—
239	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
240	Q₈×C₈₉	—	4	4	no	—
241	Q₈×C₈₉	—	8	8	no	—
242	D₄×C₈₉	—	4	8	no	—
243	D₄×C₈₉	—	4	8	no	—
244	D₄×C₈₉	—	4	8	no	—
245	D₄×C₈₉	—	4	4	no	—
246	D₄×C₈₉	—	8	8	no	—
247	D₄×C₈₉	—	8	8	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	2	2	no	—
251	C₂×C₄×C₈₉	—	2	4	no	—
252	C₂×C₄×C₈₉	—	2	2	no	—
253	C₂×C₄×C₈₉	—	2	2	no	—
254	C₂×C₄×C₈₉	—	2	2	no	—
255	C₂×C₄×C₈₉	—	2	4	no	—
256	C₂×C₄×C₈₉	—	2	2	no	—
257	C₂×C₄×C₈₉	—	2	4	no	—
258	C₂×C₄×C₈₉	—	2	2	no	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	4	no	—
261	C₂×C₄×C₈₉	—	2	8	no	—
262	C₂×C₄×C₈₉	—	2	4	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	4	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	4	8	no	—
268	C₂×C₄×C₈₉	—	4	8	no	—
269	C₂×C₄×C₈₉	—	8	4	no	—
270	C₂×C₄×C₈₉	#124	1	16	yes	complemented
271	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
272	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
273	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
276	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
277	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
278	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
279	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
280	C₂²×C₈₉	—	2	4	no	—
281	C₂²×C₈₉	—	2	4	no	—
282	C₂²×C₈₉	—	2	2	no	—
283	C₂²×C₈₉	—	2	2	no	—
284	C₂²×C₈₉	—	4	2	no	—
285	C₂²×C₈₉	—	4	4	no	—
286	C₂²×C₈₉	—	4	4	no	—
287	C₂²×C₈₉	—	4	8	no	—
288	C₂²×C₈₉	—	4	4	no	—
289	C₂²×C₈₉	—	4	8	no	—
290	C₂²×C₈₉	—	4	2	no	—
291	C₂²×C₈₉	—	4	4	no	—
292	C₂²×C₈₉	—	4	2	no	—
293	C₂²×C₈₉	—	4	4	no	—
294	C₂²×C₈₉	—	8	16	no	—
295	C₂²×C₈₉	C₂×#124	1	4	yes	—
296	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
297	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
298	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
299	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
300	C₂²×C₈₉	#585	1	2	yes	—
301	C₄×C₈₉	—	2	4	no	—
302	C₄×C₈₉	—	2	4	no	—
303	C₄×C₈₉	—	2	4	no	—
304	C₄×C₈₉	—	4	2	no	—
305	C₄×C₈₉	—	4	4	no	—
306	C₄×C₈₉	—	4	2	no	—
307	C₄×C₈₉	—	4	4	no	—
308	C₄×C₈₉	—	4	2	no	—
309	C₄×C₈₉	—	4	2	no	—
310	C₄×C₈₉	C₂×#124	1	4	yes	—
311	C₄×C₈₉	C₂×#124	1	4	yes	—
312	#35264	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
313	C₂×C₈₉	—	2	4	no	—
314	C₂×C₈₉	—	8	2	no	—
315	C₂×C₈₉	—	8	4	no	—
316	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
317	C₂×C₈₉	#3460	1	2	yes	—
318	C₂×C₈₉	#3494	1	2	yes	—
319	C₂×C₈₉	#3498	1	1	yes	characteristic
320	C₂×C₈₉	#3500	1	1	yes	characteristic
321	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
322	C₂×#535	C₂×C₈₉	1	1	yes	characteristic
323	#2861	C₂×C₈₉	1	2	yes	complemented
324	#2858	C₂×C₈₉	1	2	yes	complemented
325	#2641	C₂×C₈₉	1	2	yes	complemented
326	#2640	C₂×C₈₉	1	2	yes	complemented
327	#2491	C₂×C₈₉	1	4	yes	complemented
328	#2490	C₂×C₈₉	1	4	yes	complemented
329	#2472	C₂×C₈₉	1	8	yes	complemented
330	#2311	C₂×C₈₉	1	1	yes	characteristic, complemented
331	#2309	C₂×C₈₉	1	1	yes	characteristic, complemented
332	#2297	C₂×C₈₉	1	1	yes	characteristic, complemented
333	C₂×#390	C₂×C₈₉	1	1	yes	characteristic, complemented
334	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
335	C₈₉	#35264	1	1	yes	characteristic, direct product factor, Sylow
336	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
337	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
338	#544	—	2	8	no	—
339	#535	—	2	8	no	—
340	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
341	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
342	C₂×#127	C₂²×C₈₉	1	2	yes	—
343	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
344	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
345	C₂×#124	C₂²×C₈₉	1	2	yes	—
346	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
347	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
348	C₂×#121	C₂²×C₈₉	1	2	yes	—
349	C₂×#121	C₂²×C₈₉	1	2	yes	—
350	C₂×#120	C₂²×C₈₉	1	4	yes	—
351	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
352	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
353	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
354	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
356	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
357	#397	C₂²×C₈₉	1	8	yes	complemented
358	#394	C₂²×C₈₉	1	8	yes	complemented
359	#394	C₂²×C₈₉	1	8	yes	complemented
360	#393	C₂²×C₈₉	1	8	yes	complemented
361	#391	C₂²×C₈₉	1	2	yes	complemented
362	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
363	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
364	#390	C₂²×C₈₉	1	2	yes	—
365	#390	C₂²×C₈₉	1	2	yes	—
366	#390	C₂²×C₈₉	1	4	yes	—
367	#390	C₂²×C₈₉	1	2	yes	—
368	#390	C₂²×C₈₉	1	2	yes	—
369	#390	C₂²×C₈₉	1	4	yes	—
370	#390	C₂²×C₈₉	1	2	yes	complemented
371	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
372	#390	C₂²×C₈₉	1	8	yes	complemented
373	#390	C₂²×C₈₉	1	1	yes	characteristic, complemented
374	#388	C₂²×C₈₉	1	8	yes	complemented
375	#388	C₂²×C₈₉	1	8	yes	complemented
376	#386	C₂²×C₈₉	1	4	yes	—
377	#386	C₂²×C₈₉	1	4	yes	—
378	#380	C₂²×C₈₉	1	4	yes	complemented
379	#379	C₂²×C₈₉	1	4	yes	—
380	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
381	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
382	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
384	#376	C₂²×C₈₉	1	2	yes	complemented
385	C₄³	C₂²×C₈₉	1	2	yes	complemented
386	C₂⁵	C₂³×C₈₉	1	2	yes	—
387	C₂×#41	—	2	4	no	—
388	C₂×#41	—	2	4	no	—
389	C₂×#41	—	2	4	no	—
390	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
391	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
392	C₂²×D₄	—	2	4	no	—
393	C₂²×D₄	—	2	4	no	—
394	C₂²×D₄	—	2	4	no	—
395	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
396	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
397	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
398	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
400	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
401	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
402	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
403	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
404	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
405	C₄⋊Q₈	—	2	8	no	—
406	C₄⋊Q₈	—	2	8	no	—
407	#127	—	2	8	no	—
408	#125	—	2	8	no	—
409	#125	—	2	8	no	—
410	#124	—	2	8	no	—
411	#124	—	4	16	no	—
412	C₂²⋊Q₈	—	2	16	no	—
413	#121	—	2	8	no	—
414	#121	—	2	8	no	—
415	#120	—	2	16	no	—
416	#117	—	2	4	no	—
417	#117	—	2	4	no	—
418	#117	D₄×C₈₉	1	8	yes	—
419	C₂×C₄⋊C₄	—	2	4	no	—
420	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
425	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
426	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
427	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
428	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	4	8	no	—
431	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
433	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
434	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
435	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
443	C₂×C₄²	—	2	4	no	—
444	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
445	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
446	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
447	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
449	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
450	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
451	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
452	#95	C₂³×C₈₉	1	4	yes	—
453	#95	C₂³×C₈₉	1	4	yes	—
454	#95	C₂³×C₈₉	1	4	yes	—
455	#95	C₂³×C₈₉	1	4	yes	—
456	#95	C₂³×C₈₉	1	8	yes	—
457	C₂⁴	—	2	4	no	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	4	no	—
460	C₂⁴	—	4	4	no	—
461	C₂⁴	—	4	4	no	—
462	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
463	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
464	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
465	#41	—	4	16	no	—
466	C₂×Q₈	—	2	2	no	—
467	C₂×Q₈	—	2	8	no	—
468	C₂×Q₈	—	2	2	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	4	8	no	—
471	C₂×D₄	—	2	4	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	4	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	4	no	—
476	C₂×D₄	—	2	2	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	4	8	no	—
486	C₂×D₄	—	4	8	no	—
487	C₂×D₄	—	4	16	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	4	no	—
496	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
497	C₂²×C₄	#41×C₈₉	1	4	yes	—
498	C₂²×C₄	#41×C₈₉	1	4	yes	—
499	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
500	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
501	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
502	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
503	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
504	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
505	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
506	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
510	C₄⋊C₄	—	2	4	no	—
511	C₄⋊C₄	—	2	4	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	8	no	—
515	C₄⋊C₄	—	2	8	no	—
516	C₄⋊C₄	—	2	8	no	—
517	C₄⋊C₄	—	2	4	no	—
518	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
519	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
520	C₂²⋊C₄	—	2	4	no	—
521	C₂²⋊C₄	—	2	4	no	—
522	C₂²⋊C₄	—	2	8	no	—
523	C₂²⋊C₄	—	2	8	no	—
524	C₂²⋊C₄	—	2	16	no	—
525	C₂²⋊C₄	—	2	8	no	—
526	C₂²⋊C₄	—	4	8	no	—
527	C₂²⋊C₄	—	4	8	no	—
528	C₂²⋊C₄	—	4	8	no	—
529	C₂²⋊C₄	—	4	8	no	—
530	C₂²⋊C₄	—	4	4	no	—
531	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	2	no	—
534	C₄²	—	2	4	no	—
535	C₄²	—	2	2	no	—
536	C₄²	—	2	4	no	—
537	C₄²	—	2	8	no	—
538	C₄²	—	4	4	no	—
539	C₄²	C₂×D₄×C₈₉	1	8	yes	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	2	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	2	4	no	—
549	C₂³	—	2	8	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	8	no	—
552	C₂³	—	4	16	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	8	8	no	—
555	C₂³	—	8	4	no	—
556	C₂³	—	8	4	no	—
557	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
558	C₂³	C₂×#41×C₈₉	1	2	yes	—
559	C₂³	C₂×#41×C₈₉	1	2	yes	—
560	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
561	Q₈	—	4	4	no	—
562	Q₈	—	8	8	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	8	no	—
565	D₄	—	4	8	no	—
566	D₄	—	4	4	no	—
567	D₄	—	8	8	no	—
568	D₄	—	8	8	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	4	8	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	—	8	4	no	—
591	C₂×C₄	#124×C₈₉	1	16	yes	complemented
592	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
594	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
596	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
597	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
598	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
599	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
600	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	4	2	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	8	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	8	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	2	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	8	16	no	—
616	C₂²	C₂×#124×C₈₉	1	4	yes	—
617	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
618	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
619	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
620	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
621	C₂²	#585×C₈₉	1	2	yes	—
622	C₄	—	2	4	no	—
623	C₄	—	2	4	no	—
624	C₄	—	2	4	no	—
625	C₄	—	4	2	no	—
626	C₄	—	4	4	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	4	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	2	no	—
631	C₄	C₂×#124×C₈₉	1	4	yes	—
632	C₄	C₂×#124×C₈₉	1	4	yes	—
633	C₂	—	2	4	no	—
634	C₂	—	8	2	no	—
635	C₂	—	8	4	no	—
636	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
637	C₂	C₈₉×#3460	1	2	yes	—
638	C₂	C₈₉×#3494	1	2	yes	—
639	C₂	C₈₉×#3498	1	1	yes	characteristic
640	C₂	C₈₉×#3500	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#535×C₈₉	C₂
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×#544×C₈₉	C₂	semidirect
3. C₈₉×#2861	C₂	semidirect
4. C₈₉×#2858	C₂	semidirect
5. C₈₉×#2641	C₂	semidirect
6. C₈₉×#2640	C₂	semidirect
7. C₈₉×#2491	C₂	semidirect
8. C₈₉×#2490	C₂	semidirect
9. C₈₉×#2472	C₂	semidirect
10. C₈₉×#2311	C₂	semidirect
11. C₈₉×#2309	C₂	semidirect
12. C₈₉×#2297	C₂	semidirect
13. C₂×#390×C₈₉	C₂	semidirect
14. C₄×#117×C₈₉	C₂	semidirect
19. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
20. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#125×C₈₉	C₂²	semidirect
23. C₂×#125×C₈₉	C₂²	semidirect
25. C₂×#124×C₈₉	C₂²	semidirect
36. #397×C₈₉	C₂²	semidirect
37. #394×C₈₉	C₂²	semidirect
38. #394×C₈₉	C₂²	semidirect
39. #393×C₈₉	C₂²	semidirect
40. #391×C₈₉	C₂²	semidirect
41. #391×C₈₉	C₂²	semidirect
42. #391×C₈₉	C₂²	semidirect
49. #390×C₈₉	C₂²	semidirect
50. #390×C₈₉	C₂²	semidirect
51. #390×C₈₉	C₂²	semidirect
52. #390×C₈₉	C₂²	semidirect
53. #388×C₈₉	C₂²	semidirect
54. #388×C₈₉	C₂²	semidirect
57. #380×C₈₉	C₂²	semidirect
59. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
60. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
62. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
63. #376×C₈₉	C₂²	semidirect
64. C₄³×C₈₉	C₂²	semidirect
270. C₂×C₄×C₈₉	#124	semidirect
312. #35264	C₈₉	direct (N × H)
321. C₂×#544	C₂×C₈₉	semidirect
323. #2861	C₂×C₈₉	semidirect
324. #2858	C₂×C₈₉	semidirect
325. #2641	C₂×C₈₉	semidirect
326. #2640	C₂×C₈₉	semidirect
327. #2491	C₂×C₈₉	semidirect
328. #2490	C₂×C₈₉	semidirect
329. #2472	C₂×C₈₉	semidirect
330. #2311	C₂×C₈₉	semidirect
331. #2309	C₂×C₈₉	semidirect
332. #2297	C₂×C₈₉	semidirect
333. C₂×#390	C₂×C₈₉	semidirect
334. C₄×#117	C₂×C₈₉	semidirect
335. C₈₉	#35264	direct (N × H)
340. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
341. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
343. C₂×#125	C₂²×C₈₉	semidirect
344. C₂×#125	C₂²×C₈₉	semidirect
346. C₂×#124	C₂²×C₈₉	semidirect
357. #397	C₂²×C₈₉	semidirect
358. #394	C₂²×C₈₉	semidirect
359. #394	C₂²×C₈₉	semidirect
360. #393	C₂²×C₈₉	semidirect
361. #391	C₂²×C₈₉	semidirect
362. #391	C₂²×C₈₉	semidirect
363. #391	C₂²×C₈₉	semidirect
370. #390	C₂²×C₈₉	semidirect
371. #390	C₂²×C₈₉	semidirect
372. #390	C₂²×C₈₉	semidirect
373. #390	C₂²×C₈₉	semidirect
374. #388	C₂²×C₈₉	semidirect
375. #388	C₂²×C₈₉	semidirect
378. #380	C₂²×C₈₉	semidirect
380. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
381. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
383. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
384. #376	C₂²×C₈₉	semidirect
385. C₄³	C₂²×C₈₉	semidirect
591. C₂×C₄	#124×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₈₉	2
C₂×#535×C₈₉	2
C₈₉×#2861	2
C₈₉×#2858	2
C₈₉×#2641	2
C₈₉×#2640	2
C₈₉×#2491	2
C₈₉×#2490	2
C₈₉×#2472	2
C₈₉×#2311	2
C₈₉×#2309	2
C₈₉×#2297	2
C₂×#390×C₈₉	2
C₄×#117×C₈₉	2
#35264	89

Subgroups — C89×#35264 #36413112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35264 #36413112