Subgroups — C₂×C₈₉×#3205 #36438622

Order 22784.

3102 conjugacy classes of subgroups.

The subgroup lattice has 496 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×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3205	C₂	1	16	yes	maximal, direct product factor
4	C₂×#493×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#486×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#459×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂×#447×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂×#431×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₈₉	—	2	1	no	—
10	C₂³×D₄×C₈₉	—	2	1	no	—
11	C₂³×D₄×C₈₉	—	2	1	no	—
12	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
13	C₂²×D₈×C₈₉	C₂²	1	8	yes	complemented
14	#532×C₈₉	—	2	4	no	—
15	#532×C₈₉	C₂²	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#127×C₈₉	—	2	1	no	—
18	C₂×#127×C₈₉	—	2	1	no	—
19	C₂×#127×C₈₉	—	2	4	no	—
20	C₂×#127×C₈₉	C₂²	1	2	yes	—
21	C₂×#127×C₈₉	C₂²	1	2	yes	—
22	C₂×#127×C₈₉	C₂²	1	8	yes	complemented
23	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×#124×C₈₉	—	2	1	no	—
25	C₂×#121×C₈₉	—	2	1	no	—
26	C₂×#121×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₈₉	—	2	1	no	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	complemented
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#493×C₈₉	C₂²	1	16	yes	complemented
31	#486×C₈₉	C₂²	1	16	yes	complemented
32	#459×C₈₉	C₂²	1	32	yes	complemented
33	#447×C₈₉	C₂²	1	32	yes	complemented
34	#431×C₈₉	C₂²	1	8	yes	complemented
35	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#102×C₈₉	C₂²	1	8	yes	complemented
37	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	complemented
39	C₂⁵×C₈₉	—	2	2	no	—
40	C₂×#41×C₈₉	—	2	8	no	—
41	C₂×#41×C₈₉	—	4	8	no	—
42	C₂²×Q₈×C₈₉	—	2	1	no	—
43	C₂²×D₄×C₈₉	—	2	2	no	—
44	C₂²×D₄×C₈₉	—	2	1	no	—
45	C₂²×D₄×C₈₉	—	2	1	no	—
46	C₂²×D₄×C₈₉	—	2	4	no	—
47	C₂²×D₄×C₈₉	—	2	2	no	—
48	C₂²×D₄×C₈₉	—	2	2	no	—
49	C₂²×D₄×C₈₉	—	2	2	no	—
50	C₂²×D₄×C₈₉	—	2	2	no	—
51	C₂²×D₄×C₈₉	—	2	2	no	—
52	C₂²×D₄×C₈₉	—	2	8	no	—
53	C₂²×D₄×C₈₉	—	2	8	no	—
54	C₂²×D₄×C₈₉	—	4	8	no	—
55	C₂²×D₄×C₈₉	—	4	8	no	—
56	C₂²×D₄×C₈₉	—	4	8	no	—
57	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
60	C₂³×C₄×C₈₉	—	2	2	no	—
61	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×D₈×C₈₉	—	4	16	no	—
65	C₂×D₈×C₈₉	C₂³	1	32	yes	complemented
66	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
67	C₄⋊Q₈×C₈₉	—	2	2	no	—
68	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	complemented
69	#127×C₈₉	—	2	4	no	—
70	#127×C₈₉	—	2	4	no	—
71	#127×C₈₉	—	2	8	no	—
72	#127×C₈₉	—	2	8	no	—
73	#127×C₈₉	—	2	2	no	—
74	#127×C₈₉	C₂³	1	8	yes	—
75	#127×C₈₉	C₂³	1	8	yes	—
76	#127×C₈₉	C₂³	1	4	yes	complemented
77	#124×C₈₉	—	2	8	no	—
78	#121×C₈₉	—	2	8	no	—
79	#121×C₈₉	—	2	4	no	—
80	#121×C₈₉	C₂³	1	8	yes	—
81	C₄×D₄×C₈₉	—	2	8	no	—
82	C₄×D₄×C₈₉	—	2	4	no	—
83	C₄×D₄×C₈₉	C₂³	1	8	yes	complemented
84	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
88	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₈₉	D₄	1	4	yes	—
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
94	C₄⋊C₈×C₈₉	C₂³	1	8	yes	complemented
95	#102×C₈₉	C₂³	1	32	yes	complemented
96	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
97	C₄×C₈×C₈₉	C₂³	1	8	yes	complemented
98	C₂⁴×C₈₉	—	2	8	no	—
99	C₂⁴×C₈₉	—	2	2	no	—
100	C₂⁴×C₈₉	—	2	4	no	—
101	C₂⁴×C₈₉	—	4	8	no	—
102	C₂⁴×C₈₉	—	4	8	no	—
103	C₂⁴×C₈₉	—	4	8	no	—
104	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₈₉	—	4	32	no	—
106	C₂×Q₈×C₈₉	—	2	4	no	—
107	C₂×Q₈×C₈₉	—	4	4	no	—
108	C₂×D₄×C₈₉	—	2	8	no	—
109	C₂×D₄×C₈₉	—	2	2	no	—
110	C₂×D₄×C₈₉	—	2	4	no	—
111	C₂×D₄×C₈₉	—	2	4	no	—
112	C₂×D₄×C₈₉	—	2	8	no	—
113	C₂×D₄×C₈₉	—	2	4	no	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	8	no	—
116	C₂×D₄×C₈₉	—	2	8	no	—
117	C₂×D₄×C₈₉	—	2	8	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	16	no	—
120	C₂×D₄×C₈₉	—	4	16	no	—
121	C₂×D₄×C₈₉	—	4	8	no	—
122	C₂×D₄×C₈₉	—	4	8	no	—
123	C₂×D₄×C₈₉	—	4	16	no	—
124	C₂×D₄×C₈₉	—	4	32	no	—
125	C₂×D₄×C₈₉	—	4	8	no	—
126	C₂×D₄×C₈₉	—	4	8	no	—
127	C₂×D₄×C₈₉	—	4	8	no	—
128	C₂×D₄×C₈₉	—	4	4	no	—
129	C₂×D₄×C₈₉	—	4	32	no	—
130	C₂×D₄×C₈₉	—	4	4	no	—
131	C₂×D₄×C₈₉	—	4	8	no	—
132	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
133	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₈₉	—	2	4	no	—
135	C₂²×C₄×C₈₉	—	2	4	no	—
136	C₂²×C₄×C₈₉	—	2	2	no	—
137	C₂²×C₄×C₈₉	—	2	8	no	—
138	C₂²×C₄×C₈₉	—	4	8	no	—
139	C₂²×C₄×C₈₉	D₈	1	8	yes	complemented
140	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
150	D₈×C₈₉	—	4	32	no	—
151	C₂×C₈×C₈₉	—	2	8	no	—
152	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₄²×C₈₉	C₂×D₄	1	4	yes	—
159	C₄²×C₈₉	C₂×D₄	1	2	yes	—
160	C₄²×C₈₉	C₂×D₄	1	4	yes	—
161	C₄²×C₈₉	C₂×D₄	1	2	yes	—
162	C₄²×C₈₉	C₂⁴	1	2	yes	—
163	C₄²×C₈₉	C₂⁴	1	2	yes	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	2	no	—
166	C₂³×C₈₉	—	2	4	no	—
167	C₂³×C₈₉	—	2	8	no	—
168	C₂³×C₈₉	—	4	16	no	—
169	C₂³×C₈₉	—	4	16	no	—
170	C₂³×C₈₉	—	4	8	no	—
171	C₂³×C₈₉	—	4	4	no	—
172	C₂³×C₈₉	—	4	4	no	—
173	C₂³×C₈₉	—	4	16	no	—
174	C₂³×C₈₉	—	4	8	no	—
175	C₂³×C₈₉	—	4	8	no	—
176	C₂³×C₈₉	—	4	4	no	—
177	C₂³×C₈₉	—	8	32	no	—
178	C₂³×C₈₉	C₂×D₈	1	4	yes	—
179	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
180	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	Q₈×C₈₉	—	4	8	no	—
182	D₄×C₈₉	—	2	8	no	—
183	D₄×C₈₉	—	2	16	no	—
184	D₄×C₈₉	—	4	16	no	—
185	D₄×C₈₉	—	4	16	no	—
186	D₄×C₈₉	—	4	16	no	—
187	D₄×C₈₉	—	4	4	no	—
188	D₄×C₈₉	—	4	8	no	—
189	D₄×C₈₉	—	4	16	no	—
190	D₄×C₈₉	—	4	16	no	—
191	D₄×C₈₉	—	4	8	no	—
192	D₄×C₈₉	—	4	8	no	—
193	D₄×C₈₉	—	4	16	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	4	no	—
197	C₂×C₄×C₈₉	—	2	8	no	—
198	C₂×C₄×C₈₉	—	2	4	no	—
199	C₂×C₄×C₈₉	—	2	4	no	—
200	C₂×C₄×C₈₉	—	4	4	no	—
201	C₂×C₄×C₈₉	—	4	16	no	—
202	C₂×C₄×C₈₉	C₂×D₈	1	4	yes	—
203	C₂×C₄×C₈₉	C₂×D₈	1	4	yes	—
204	C₂×C₄×C₈₉	C₂×D₈	1	16	yes	complemented
205	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
206	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
213	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
214	C₈×C₈₉	—	2	8	no	—
215	C₂²×C₈₉	—	2	2	no	—
216	C₂²×C₈₉	—	2	8	no	—
217	C₂²×C₈₉	—	2	2	no	—
218	C₂²×C₈₉	—	4	8	no	—
219	C₂²×C₈₉	—	4	4	no	—
220	C₂²×C₈₉	—	4	4	no	—
221	C₂²×C₈₉	—	4	8	no	—
222	C₂²×C₈₉	—	4	8	no	—
223	C₂²×C₈₉	—	4	4	no	—
224	C₂²×C₈₉	—	8	32	no	—
225	C₂²×C₈₉	—	8	8	no	—
226	C₂²×C₈₉	—	8	16	no	—
227	C₂²×C₈₉	#535	1	2	yes	—
228	C₂²×C₈₉	C₂²×D₈	1	4	yes	—
229	C₂²×C₈₉	C₂²×D₈	1	2	yes	—
230	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
231	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
232	C₄×C₈₉	—	2	2	no	—
233	C₄×C₈₉	—	2	2	no	—
234	C₄×C₈₉	—	4	4	no	—
235	C₄×C₈₉	#535	1	2	yes	—
236	C₄×C₈₉	C₂²×D₈	1	4	yes	—
237	C₄×C₈₉	C₂²×D₈	1	4	yes	—
238	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
239	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
240	C₂×#3205	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₈₉	—	2	4	no	—
242	C₂×C₈₉	—	8	4	no	—
243	C₂×C₈₉	—	8	8	no	—
244	C₂×C₈₉	#3205	1	4	yes	direct product factor
245	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
246	C₂×C₈₉	C₂³×D₈	1	1	yes	characteristic
247	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
248	C₂×#532	C₂×C₈₉	1	1	yes	characteristic, complemented
249	C₂²×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#3205	C₂×C₈₉	1	16	yes	direct product factor
251	C₂×#493	C₂×C₈₉	1	2	yes	complemented
252	C₂×#486	C₂×C₈₉	1	2	yes	complemented
253	C₂×#459	C₂×C₈₉	1	4	yes	complemented
254	C₂×#447	C₂×C₈₉	1	4	yes	complemented
255	C₂×#431	C₂×C₈₉	1	1	yes	characteristic, complemented
256	C₈₉	C₂×#3205	1	1	yes	characteristic, direct product factor, Sylow
257	C₂²×#41	—	2	1	no	—
258	C₂³×D₄	—	2	1	no	—
259	C₂³×D₄	—	2	1	no	—
260	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
261	C₂²×D₈	C₂²×C₈₉	1	8	yes	complemented
262	#532	—	2	4	no	—
263	#532	C₂²×C₈₉	1	8	yes	complemented
264	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
265	C₂×#127	—	2	1	no	—
266	C₂×#127	—	2	1	no	—
267	C₂×#127	—	2	4	no	—
268	C₂×#127	C₂²×C₈₉	1	2	yes	—
269	C₂×#127	C₂²×C₈₉	1	2	yes	—
270	C₂×#127	C₂²×C₈₉	1	8	yes	complemented
271	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic, complemented
272	C₂×#124	—	2	1	no	—
273	C₂×#121	—	2	1	no	—
274	C₂×#121	C₂²×C₈₉	1	2	yes	—
275	C₂×C₄×D₄	—	2	1	no	—
276	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	complemented
277	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
278	#493	C₂²×C₈₉	1	16	yes	complemented
279	#486	C₂²×C₈₉	1	16	yes	complemented
280	#459	C₂²×C₈₉	1	32	yes	complemented
281	#447	C₂²×C₈₉	1	32	yes	complemented
282	#431	C₂²×C₈₉	1	8	yes	complemented
283	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
284	C₂×#102	C₂²×C₈₉	1	8	yes	complemented
285	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
286	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
287	C₂⁵	—	2	2	no	—
288	C₂×#41	—	2	8	no	—
289	C₂×#41	—	4	8	no	—
290	C₂²×Q₈	—	2	1	no	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	—	2	2	no	—
295	C₂²×D₄	—	2	4	no	—
296	C₂²×D₄	—	2	2	no	—
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	2	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	—	2	8	no	—
302	C₂²×D₄	—	4	8	no	—
303	C₂²×D₄	—	4	8	no	—
304	C₂²×D₄	—	4	8	no	—
305	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
306	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
307	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
308	C₂³×C₄	—	2	2	no	—
309	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
310	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
312	C₂×D₈	—	4	16	no	—
313	C₂×D₈	C₂³×C₈₉	1	32	yes	complemented
314	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
315	C₄⋊Q₈	—	2	2	no	—
316	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	complemented
317	#127	—	2	4	no	—
318	#127	—	2	4	no	—
319	#127	—	2	8	no	—
320	#127	—	2	8	no	—
321	#127	—	2	2	no	—
322	#127	C₂³×C₈₉	1	8	yes	—
323	#127	C₂³×C₈₉	1	8	yes	—
324	#127	C₂³×C₈₉	1	4	yes	complemented
325	#124	—	2	8	no	—
326	#121	—	2	8	no	—
327	#121	—	2	4	no	—
328	#121	C₂³×C₈₉	1	8	yes	—
329	C₄×D₄	—	2	8	no	—
330	C₄×D₄	—	2	4	no	—
331	C₄×D₄	C₂³×C₈₉	1	8	yes	complemented
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
337	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₈₉	1	4	yes	—
339	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
342	C₄⋊C₈	C₂³×C₈₉	1	8	yes	complemented
343	#102	C₂³×C₈₉	1	32	yes	complemented
344	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
345	C₄×C₈	C₂³×C₈₉	1	8	yes	complemented
346	C₂⁴	—	2	2	no	—
347	C₂⁴	—	2	8	no	—
348	C₂⁴	—	2	4	no	—
349	C₂⁴	—	4	8	no	—
350	C₂⁴	—	4	8	no	—
351	C₂⁴	—	4	8	no	—
352	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
353	#41	—	4	32	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	4	4	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	8	no	—
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	8	no	—
364	C₂×D₄	—	2	8	no	—
365	C₂×D₄	—	2	8	no	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	16	no	—
368	C₂×D₄	—	4	16	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	16	no	—
372	C₂×D₄	—	4	32	no	—
373	C₂×D₄	—	4	8	no	—
374	C₂×D₄	—	4	8	no	—
375	C₂×D₄	—	4	8	no	—
376	C₂×D₄	—	4	4	no	—
377	C₂×D₄	—	4	32	no	—
378	C₂×D₄	—	4	8	no	—
379	C₂×D₄	—	4	4	no	—
380	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
381	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	4	8	no	—
387	C₂²×C₄	D₈×C₈₉	1	8	yes	complemented
388	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
392	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
396	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
398	D₈	—	4	32	no	—
399	C₂×C₈	—	2	8	no	—
400	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₄²	C₂×D₄×C₈₉	1	4	yes	—
407	C₄²	C₂×D₄×C₈₉	1	2	yes	—
408	C₄²	C₂×D₄×C₈₉	1	4	yes	—
409	C₄²	C₂×D₄×C₈₉	1	2	yes	—
410	C₄²	C₂⁴×C₈₉	1	2	yes	—
411	C₄²	C₂⁴×C₈₉	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	4	no	—
415	C₂³	—	2	8	no	—
416	C₂³	—	4	16	no	—
417	C₂³	—	4	16	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	—	4	16	no	—
422	C₂³	—	4	8	no	—
423	C₂³	—	4	8	no	—
424	C₂³	—	4	4	no	—
425	C₂³	—	8	32	no	—
426	C₂³	C₂×D₈×C₈₉	1	4	yes	—
427	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
428	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
429	Q₈	—	4	8	no	—
430	D₄	—	2	8	no	—
431	D₄	—	2	16	no	—
432	D₄	—	4	16	no	—
433	D₄	—	4	16	no	—
434	D₄	—	4	16	no	—
435	D₄	—	4	4	no	—
436	D₄	—	4	8	no	—
437	D₄	—	4	16	no	—
438	D₄	—	4	16	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	8	no	—
441	D₄	—	4	16	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	8	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	16	no	—
450	C₂×C₄	C₂×D₈×C₈₉	1	4	yes	—
451	C₂×C₄	C₂×D₈×C₈₉	1	4	yes	—
452	C₂×C₄	C₂×D₈×C₈₉	1	16	yes	complemented
453	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
454	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
455	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
460	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
461	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
462	C₈	—	2	8	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	8	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	4	8	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	4	no	—
470	C₂²	—	4	8	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	32	no	—
473	C₂²	—	8	16	no	—
474	C₂²	—	8	8	no	—
475	C₂²	#535×C₈₉	1	2	yes	—
476	C₂²	C₂²×D₈×C₈₉	1	4	yes	—
477	C₂²	C₂²×D₈×C₈₉	1	2	yes	—
478	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
479	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	4	4	no	—
483	C₄	#535×C₈₉	1	2	yes	—
484	C₄	C₂²×D₈×C₈₉	1	4	yes	—
485	C₄	C₂²×D₈×C₈₉	1	4	yes	—
486	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
487	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
488	C₂	—	2	4	no	—
489	C₂	—	8	4	no	—
490	C₂	—	8	8	no	—
491	C₂	C₈₉×#3205	1	4	yes	direct product factor
492	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
493	C₂	C₂³×D₈×C₈₉	1	1	yes	characteristic
494	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂²×C₄²×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×#127×C₈₉	C₂	semidirect
3. C₈₉×#3205	C₂	direct (N × H)
4. C₂×#493×C₈₉	C₂	semidirect
5. C₂×#486×C₈₉	C₂	semidirect
6. C₂×#459×C₈₉	C₂	semidirect
7. C₂×#447×C₈₉	C₂	semidirect
8. C₂×#431×C₈₉	C₂	semidirect
13. C₂²×D₈×C₈₉	C₂²	semidirect
15. #532×C₈₉	C₂²	semidirect
16. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
22. C₂×#127×C₈₉	C₂²	semidirect
23. C₂×#127×C₈₉	C₂²	semidirect
28. C₂×C₄×D₄×C₈₉	C₂²	semidirect
30. #493×C₈₉	C₂²	semidirect
31. #486×C₈₉	C₂²	semidirect
32. #459×C₈₉	C₂²	semidirect
33. #447×C₈₉	C₂²	semidirect
34. #431×C₈₉	C₂²	semidirect
35. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
36. C₂×#102×C₈₉	C₂²	semidirect
38. C₂×C₄×C₈×C₈₉	C₂²	semidirect
65. C₂×D₈×C₈₉	C₂³	semidirect
68. C₄⋊Q₈×C₈₉	C₂³	semidirect
76. #127×C₈₉	C₂³	semidirect
83. C₄×D₄×C₈₉	C₂³	semidirect
94. C₄⋊C₈×C₈₉	C₂³	semidirect
95. #102×C₈₉	C₂³	semidirect
97. C₄×C₈×C₈₉	C₂³	semidirect
139. C₂²×C₄×C₈₉	D₈	semidirect
204. C₂×C₄×C₈₉	C₂×D₈	semidirect
240. C₂×#3205	C₈₉	direct (N × H)
244. C₂×C₈₉	#3205	direct (N × H)
248. C₂×#532	C₂×C₈₉	semidirect
249. C₂²×#127	C₂×C₈₉	semidirect
250. #3205	C₂×C₈₉	direct (N × H)
251. C₂×#493	C₂×C₈₉	semidirect
252. C₂×#486	C₂×C₈₉	semidirect
253. C₂×#459	C₂×C₈₉	semidirect
254. C₂×#447	C₂×C₈₉	semidirect
255. C₂×#431	C₂×C₈₉	semidirect
256. C₈₉	C₂×#3205	direct (N × H)
261. C₂²×D₈	C₂²×C₈₉	semidirect
263. #532	C₂²×C₈₉	semidirect
264. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
270. C₂×#127	C₂²×C₈₉	semidirect
271. C₂×#127	C₂²×C₈₉	semidirect
276. C₂×C₄×D₄	C₂²×C₈₉	semidirect
278. #493	C₂²×C₈₉	semidirect
279. #486	C₂²×C₈₉	semidirect
280. #459	C₂²×C₈₉	semidirect
281. #447	C₂²×C₈₉	semidirect
282. #431	C₂²×C₈₉	semidirect
283. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
284. C₂×#102	C₂²×C₈₉	semidirect
286. C₂×C₄×C₈	C₂²×C₈₉	semidirect
313. C₂×D₈	C₂³×C₈₉	semidirect
316. C₄⋊Q₈	C₂³×C₈₉	semidirect
324. #127	C₂³×C₈₉	semidirect
331. C₄×D₄	C₂³×C₈₉	semidirect
342. C₄⋊C₈	C₂³×C₈₉	semidirect
343. #102	C₂³×C₈₉	semidirect
345. C₄×C₈	C₂³×C₈₉	semidirect
387. C₂²×C₄	D₈×C₈₉	semidirect
452. C₂×C₄	C₂×D₈×C₈₉	semidirect
491. C₂	C₈₉×#3205	direct (N × H)

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×#127×C₈₉	2
C₈₉×#3205	2
C₂×#493×C₈₉	2
C₂×#486×C₈₉	2
C₂×#459×C₈₉	2
C₂×#447×C₈₉	2
C₂×#431×C₈₉	2
C₂×#3205	89

Subgroups — C2×C89×#3205 #36438622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3205 #36438622