Subgroups — C₂×C₈₉×#3403 #36439248

Order 22784.

2066 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×#559×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3403	C₂	1	16	yes	maximal, direct product factor
3	C₂×#496×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₂×#495×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#464×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#463×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#459×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#446×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#440×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
14	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
17	#559×C₈₉	—	2	8	no	—
18	#559×C₈₉	C₂²	1	16	yes	complemented
19	C₂×#127×C₈₉	C₂²	1	2	yes	—
20	C₂×#124×C₈₉	—	2	2	no	—
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#123×C₈₉	—	2	2	no	—
24	C₂×#123×C₈₉	—	2	2	no	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₈₉	—	2	2	no	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
30	#496×C₈₉	C₂²	1	16	yes	complemented
31	#495×C₈₉	C₂²	1	8	yes	complemented
32	#464×C₈₉	C₂²	1	16	yes	complemented
33	#463×C₈₉	C₂²	1	16	yes	complemented
34	#459×C₈₉	C₂²	1	16	yes	complemented
35	#446×C₈₉	C₂²	1	8	yes	complemented
36	#440×C₈₉	C₂²	1	16	yes	complemented
37	C₄×D₈×C₈₉	C₂²	1	8	yes	complemented
38	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×#103×C₈₉	C₂²	1	2	yes	—
42	C₂×#102×C₈₉	C₂²	1	2	yes	—
43	C₂×#102×C₈₉	C₂²	1	2	yes	—
44	C₂×#97×C₈₉	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×D₄×C₈₉	—	2	2	no	—
49	C₂²×D₄×C₈₉	—	2	2	no	—
50	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₈₉	—	2	2	no	—
53	C₂³×C₄×C₈₉	—	2	2	no	—
54	C₂×Q₁₆×C₈₉	—	4	2	no	—
55	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
56	C₂×SD₁₆×C₈₉	—	2	8	no	—
57	C₂×SD₁₆×C₈₉	—	4	4	no	—
58	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
59	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
60	C₂×D₈×C₈₉	—	2	4	no	—
61	C₂×D₈×C₈₉	—	4	4	no	—
62	C₂×D₈×C₈₉	—	4	2	no	—
63	C₂×D₈×C₈₉	C₂³	1	4	yes	—
64	C₂×D₈×C₈₉	C₂³	1	4	yes	—
65	C₂×D₈×C₈₉	C₂³	1	8	yes	—
66	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	#127×C₈₉	—	2	4	no	—
70	#127×C₈₉	C₂³	1	8	yes	—
71	#124×C₈₉	—	2	16	no	—
72	#124×C₈₉	—	2	4	no	—
73	#124×C₈₉	—	2	4	no	—
74	#124×C₈₉	C₂³	1	8	yes	—
75	#124×C₈₉	C₂³	1	8	yes	—
76	#123×C₈₉	—	2	16	no	—
77	#123×C₈₉	—	2	16	no	—
78	C₄×Q₈×C₈₉	—	2	4	no	—
79	C₄×Q₈×C₈₉	D₄	1	4	yes	—
80	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
81	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
82	C₄×D₄×C₈₉	—	2	16	no	—
83	C₄×D₄×C₈₉	—	2	4	no	—
84	C₄×D₄×C₈₉	—	2	4	no	—
85	C₄×D₄×C₈₉	C₂³	1	8	yes	—
86	C₄×D₄×C₈₉	C₂³	1	8	yes	—
87	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
97	C₂×C₄²×C₈₉	—	2	2	no	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
100	#107×C₈₉	C₂³	1	4	yes	—
101	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
102	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
103	#103×C₈₉	C₂³	1	8	yes	—
104	#102×C₈₉	C₂³	1	8	yes	—
105	#102×C₈₉	C₂³	1	8	yes	—
106	#97×C₈₉	C₂³	1	8	yes	—
107	C₄×C₈×C₈₉	C₂³	1	4	yes	—
108	C₂⁴×C₈₉	—	2	2	no	—
109	C₂⁴×C₈₉	—	2	2	no	—
110	C₂×Q₈×C₈₉	—	2	2	no	—
111	C₂×Q₈×C₈₉	—	2	4	no	—
112	C₂×Q₈×C₈₉	—	2	4	no	—
113	C₂×Q₈×C₈₉	—	4	2	no	—
114	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
115	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
116	C₂×D₄×C₈₉	—	2	2	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	4	no	—
121	C₂×D₄×C₈₉	—	2	4	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	4	no	—
124	C₂×D₄×C₈₉	—	4	8	no	—
125	C₂×D₄×C₈₉	—	8	4	no	—
126	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
127	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₈₉	—	2	2	no	—
129	C₂²×C₄×C₈₉	—	2	2	no	—
130	C₂²×C₄×C₈₉	—	2	8	no	—
131	C₂²×C₄×C₈₉	—	2	8	no	—
132	C₂²×C₄×C₈₉	—	8	4	no	—
133	C₂²×C₄×C₈₉	—	8	4	no	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	Q₁₆×C₈₉	—	4	4	no	—
140	SD₁₆×C₈₉	—	2	16	no	—
141	SD₁₆×C₈₉	—	4	8	no	—
142	D₈×C₈₉	—	2	8	no	—
143	D₈×C₈₉	—	4	8	no	—
144	D₈×C₈₉	—	4	4	no	—
145	C₂×C₈×C₈₉	—	2	4	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	#41	1	4	yes	—
148	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
149	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
150	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
151	C₄⋊C₄×C₈₉	—	2	8	no	—
152	C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
154	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
155	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₂²⋊C₄×C₈₉	—	2	8	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	—	2	8	no	—
162	C₄²×C₈₉	—	2	8	no	—
163	C₄²×C₈₉	C₂×D₄	1	2	yes	—
164	C₄²×C₈₉	C₂×D₄	1	4	yes	—
165	C₄²×C₈₉	C₂⁴	1	2	yes	—
166	C₄²×C₈₉	C₂⁴	1	4	yes	—
167	C₂³×C₈₉	—	2	4	no	—
168	C₂³×C₈₉	—	2	4	no	—
169	C₂³×C₈₉	—	4	4	no	—
170	C₂³×C₈₉	—	4	4	no	—
171	C₂³×C₈₉	—	4	4	no	—
172	C₂³×C₈₉	—	4	4	no	—
173	C₂³×C₈₉	—	4	4	no	—
174	C₂³×C₈₉	—	4	4	no	—
175	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₈₉	—	2	4	no	—
177	Q₈×C₈₉	—	2	4	no	—
178	Q₈×C₈₉	—	4	4	no	—
179	Q₈×C₈₉	—	4	4	no	—
180	D₄×C₈₉	—	2	4	no	—
181	D₄×C₈₉	—	2	4	no	—
182	D₄×C₈₉	—	2	4	no	—
183	D₄×C₈₉	—	2	4	no	—
184	D₄×C₈₉	—	4	16	no	—
185	D₄×C₈₉	—	4	4	no	—
186	D₄×C₈₉	—	4	4	no	—
187	D₄×C₈₉	—	8	8	no	—
188	C₂×C₄×C₈₉	—	2	4	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	4	no	—
193	C₂×C₄×C₈₉	—	2	4	no	—
194	C₂×C₄×C₈₉	—	4	4	no	—
195	C₂×C₄×C₈₉	—	4	4	no	—
196	C₂×C₄×C₈₉	—	8	8	no	—
197	C₂×C₄×C₈₉	—	8	8	no	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	4	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	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
204	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
205	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
206	C₈×C₈₉	—	2	4	no	—
207	C₈×C₈₉	—	2	2	no	—
208	C₈×C₈₉	C₂×#41	1	4	yes	—
209	C₂²×C₈₉	—	4	4	no	—
210	C₂²×C₈₉	—	4	4	no	—
211	C₂²×C₈₉	—	4	4	no	—
212	C₂²×C₈₉	—	4	4	no	—
213	C₂²×C₈₉	—	4	4	no	—
214	C₂²×C₈₉	—	4	4	no	—
215	C₂²×C₈₉	—	8	8	no	—
216	C₂²×C₈₉	—	8	8	no	—
217	C₂²×C₈₉	#550	1	2	yes	—
218	C₂²×C₈₉	#575	1	2	yes	—
219	C₂²×C₈₉	#576	1	2	yes	—
220	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
221	C₄×C₈₉	—	2	4	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	—	2	4	no	—
225	C₄×C₈₉	—	4	4	no	—
226	C₄×C₈₉	—	4	4	no	—
227	C₄×C₈₉	#550	1	2	yes	—
228	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
229	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×#3403	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₈₉	—	8	4	no	—
232	C₂×C₈₉	—	8	4	no	—
233	C₂×C₈₉	#3403	1	4	yes	direct product factor
234	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
235	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
236	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
237	C₂×#559	C₂×C₈₉	1	2	yes	complemented
238	#3403	C₂×C₈₉	1	16	yes	direct product factor
239	C₂×#496	C₂×C₈₉	1	2	yes	complemented
240	C₂×#495	C₂×C₈₉	1	1	yes	characteristic, complemented
241	C₂×#464	C₂×C₈₉	1	2	yes	complemented
242	C₂×#463	C₂×C₈₉	1	2	yes	complemented
243	C₂×#459	C₂×C₈₉	1	2	yes	complemented
244	C₂×#446	C₂×C₈₉	1	1	yes	characteristic, complemented
245	C₂×#440	C₂×C₈₉	1	2	yes	complemented
246	C₂×C₄×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
247	C₈₉	C₂×#3403	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
249	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
250	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
251	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
252	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
253	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
254	#559	—	2	8	no	—
255	#559	C₂²×C₈₉	1	16	yes	complemented
256	C₂×#127	C₂²×C₈₉	1	2	yes	—
257	C₂×#124	—	2	2	no	—
258	C₂×#124	C₂²×C₈₉	1	2	yes	—
259	C₂×#124	C₂²×C₈₉	1	2	yes	—
260	C₂×#123	—	2	2	no	—
261	C₂×#123	—	2	2	no	—
262	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
264	C₂×C₄×D₄	—	2	2	no	—
265	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
266	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
267	#496	C₂²×C₈₉	1	16	yes	complemented
268	#495	C₂²×C₈₉	1	8	yes	complemented
269	#464	C₂²×C₈₉	1	16	yes	complemented
270	#463	C₂²×C₈₉	1	16	yes	complemented
271	#459	C₂²×C₈₉	1	16	yes	complemented
272	#446	C₂²×C₈₉	1	8	yes	complemented
273	#440	C₂²×C₈₉	1	16	yes	complemented
274	C₄×D₈	C₂²×C₈₉	1	8	yes	complemented
275	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
276	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
277	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
278	C₂×#103	C₂²×C₈₉	1	2	yes	—
279	C₂×#102	C₂²×C₈₉	1	2	yes	—
280	C₂×#102	C₂²×C₈₉	1	2	yes	—
281	C₂×#97	C₂²×C₈₉	1	2	yes	—
282	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
283	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
284	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
285	C₂²×D₄	—	2	2	no	—
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
288	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
289	C₂³×C₄	—	2	2	no	—
290	C₂³×C₄	—	2	2	no	—
291	C₂×Q₁₆	—	4	2	no	—
292	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
293	C₂×SD₁₆	—	2	8	no	—
294	C₂×SD₁₆	—	4	4	no	—
295	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
296	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
297	C₂×D₈	—	2	4	no	—
298	C₂×D₈	—	4	4	no	—
299	C₂×D₈	—	4	2	no	—
300	C₂×D₈	C₂³×C₈₉	1	4	yes	—
301	C₂×D₈	C₂³×C₈₉	1	4	yes	—
302	C₂×D₈	C₂³×C₈₉	1	8	yes	—
303	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
306	#127	—	2	4	no	—
307	#127	C₂³×C₈₉	1	8	yes	—
308	#124	—	2	16	no	—
309	#124	—	2	4	no	—
310	#124	—	2	4	no	—
311	#124	C₂³×C₈₉	1	8	yes	—
312	#124	C₂³×C₈₉	1	8	yes	—
313	#123	—	2	16	no	—
314	#123	—	2	16	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	D₄×C₈₉	1	4	yes	—
317	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
318	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
319	C₄×D₄	—	2	16	no	—
320	C₄×D₄	—	2	4	no	—
321	C₄×D₄	—	2	4	no	—
322	C₄×D₄	C₂³×C₈₉	1	8	yes	—
323	C₄×D₄	C₂³×C₈₉	1	8	yes	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
326	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₄²	—	2	2	no	—
335	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
337	#107	C₂³×C₈₉	1	4	yes	—
338	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
339	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
340	#103	C₂³×C₈₉	1	8	yes	—
341	#102	C₂³×C₈₉	1	8	yes	—
342	#102	C₂³×C₈₉	1	8	yes	—
343	#97	C₂³×C₈₉	1	8	yes	—
344	C₄×C₈	C₂³×C₈₉	1	4	yes	—
345	C₂⁴	—	2	2	no	—
346	C₂⁴	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
352	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	8	no	—
356	C₂×D₄	—	2	8	no	—
357	C₂×D₄	—	2	4	no	—
358	C₂×D₄	—	2	4	no	—
359	C₂×D₄	—	2	4	no	—
360	C₂×D₄	—	2	4	no	—
361	C₂×D₄	—	4	8	no	—
362	C₂×D₄	—	8	4	no	—
363	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
364	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	8	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	8	4	no	—
370	C₂²×C₄	—	8	4	no	—
371	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
376	Q₁₆	—	4	4	no	—
377	SD₁₆	—	2	16	no	—
378	SD₁₆	—	4	8	no	—
379	D₈	—	2	8	no	—
380	D₈	—	4	8	no	—
381	D₈	—	4	4	no	—
382	C₂×C₈	—	2	4	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	#41×C₈₉	1	4	yes	—
385	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
386	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
387	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
388	C₄⋊C₄	—	2	8	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
391	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
392	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
393	C₂²⋊C₄	—	2	8	no	—
394	C₂²⋊C₄	—	2	8	no	—
395	C₂²⋊C₄	—	2	8	no	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	8	no	—
398	C₂²⋊C₄	—	2	8	no	—
399	C₄²	—	2	8	no	—
400	C₄²	C₂×D₄×C₈₉	1	2	yes	—
401	C₄²	C₂×D₄×C₈₉	1	4	yes	—
402	C₄²	C₂⁴×C₈₉	1	2	yes	—
403	C₄²	C₂⁴×C₈₉	1	4	yes	—
404	C₂³	—	2	4	no	—
405	C₂³	—	2	4	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	4	no	—
408	C₂³	—	4	4	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	4	no	—
412	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	4	4	no	—
416	Q₈	—	4	4	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	4	no	—
419	D₄	—	2	4	no	—
420	D₄	—	2	4	no	—
421	D₄	—	4	16	no	—
422	D₄	—	4	4	no	—
423	D₄	—	4	4	no	—
424	D₄	—	8	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	8	8	no	—
434	C₂×C₄	—	8	8	no	—
435	C₂×C₄	C₂²×D₄×C₈₉	1	4	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	C₂²×D₄×C₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
441	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
442	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
443	C₈	—	2	4	no	—
444	C₈	—	2	2	no	—
445	C₈	C₂×#41×C₈₉	1	4	yes	—
446	C₂²	—	4	4	no	—
447	C₂²	—	4	4	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	8	8	no	—
453	C₂²	—	8	8	no	—
454	C₂²	#550×C₈₉	1	2	yes	—
455	C₂²	#575×C₈₉	1	2	yes	—
456	C₂²	#576×C₈₉	1	2	yes	—
457	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
458	C₄	—	2	4	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	4	no	—
462	C₄	—	4	4	no	—
463	C₄	—	4	4	no	—
464	C₄	#550×C₈₉	1	2	yes	—
465	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
466	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
467	C₂	—	8	4	no	—
468	C₂	—	8	4	no	—
469	C₂	C₈₉×#3403	1	4	yes	direct product factor
470	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
471	C₂	C₂×#575×C₈₉	1	1	yes	characteristic
472	C₂	C₂×#576×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 ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#559×C₈₉	C₂	semidirect
2. C₈₉×#3403	C₂	direct (N × H)
3. C₂×#496×C₈₉	C₂	semidirect
4. C₂×#495×C₈₉	C₂	semidirect
5. C₂×#464×C₈₉	C₂	semidirect
6. C₂×#463×C₈₉	C₂	semidirect
7. C₂×#459×C₈₉	C₂	semidirect
8. C₂×#446×C₈₉	C₂	semidirect
9. C₂×#440×C₈₉	C₂	semidirect
10. C₂×C₄×D₈×C₈₉	C₂	semidirect
18. #559×C₈₉	C₂²	semidirect
30. #496×C₈₉	C₂²	semidirect
31. #495×C₈₉	C₂²	semidirect
32. #464×C₈₉	C₂²	semidirect
33. #463×C₈₉	C₂²	semidirect
34. #459×C₈₉	C₂²	semidirect
35. #446×C₈₉	C₂²	semidirect
36. #440×C₈₉	C₂²	semidirect
37. C₄×D₈×C₈₉	C₂²	semidirect
230. C₂×#3403	C₈₉	direct (N × H)
233. C₂×C₈₉	#3403	direct (N × H)
237. C₂×#559	C₂×C₈₉	semidirect
238. #3403	C₂×C₈₉	direct (N × H)
239. C₂×#496	C₂×C₈₉	semidirect
240. C₂×#495	C₂×C₈₉	semidirect
241. C₂×#464	C₂×C₈₉	semidirect
242. C₂×#463	C₂×C₈₉	semidirect
243. C₂×#459	C₂×C₈₉	semidirect
244. C₂×#446	C₂×C₈₉	semidirect
245. C₂×#440	C₂×C₈₉	semidirect
246. C₂×C₄×D₈	C₂×C₈₉	semidirect
247. C₈₉	C₂×#3403	direct (N × H)
255. #559	C₂²×C₈₉	semidirect
267. #496	C₂²×C₈₉	semidirect
268. #495	C₂²×C₈₉	semidirect
269. #464	C₂²×C₈₉	semidirect
270. #463	C₂²×C₈₉	semidirect
271. #459	C₂²×C₈₉	semidirect
272. #446	C₂²×C₈₉	semidirect
273. #440	C₂²×C₈₉	semidirect
274. C₄×D₈	C₂²×C₈₉	semidirect
469. C₂	C₈₉×#3403	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×#559×C₈₉	2
C₈₉×#3403	2
C₂×#496×C₈₉	2
C₂×#495×C₈₉	2
C₂×#464×C₈₉	2
C₂×#463×C₈₉	2
C₂×#459×C₈₉	2
C₂×#446×C₈₉	2
C₂×#440×C₈₉	2
C₂×C₄×D₈×C₈₉	2
C₂×#3403	89

Subgroups — C2×C89×#3403 #36439248

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3403 #36439248