Subgroups — C₈₉×#60809 #36438657

Order 22784.

2034 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3223	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3222	C₂	1	8	yes	maximal, complemented
5	C₈₉×#3152	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3142	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3037	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3007	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂×#137×C₈₉	C₂²	1	8	yes	complemented
12	#541×C₈₉	—	2	4	no	—
13	#541×C₈₉	C₂²	1	8	yes	complemented
14	#537×C₈₉	—	2	2	no	—
15	#536×C₈₉	C₂²	1	4	yes	—
16	#535×C₈₉	C₂²	1	4	yes	—
17	#534×C₈₉	—	2	2	no	—
18	#532×C₈₉	C₂²	1	2	yes	—
19	#532×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#126×C₈₉	—	2	2	no	—
22	C₂×#125×C₈₉	—	2	2	no	—
23	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	#525×C₈₉	—	2	4	no	—
25	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	#497×C₈₉	C₂²	1	8	yes	complemented
29	#494×C₈₉	C₂²	1	4	yes	complemented
30	#492×C₈₉	C₂²	1	4	yes	complemented
31	#491×C₈₉	C₂²	1	4	yes	complemented
32	#490×C₈₉	C₂²	1	4	yes	complemented
33	#488×C₈₉	C₂²	1	8	yes	complemented
34	#464×C₈₉	C₂²	1	16	yes	complemented
35	#462×C₈₉	C₂²	1	8	yes	complemented
36	#460×C₈₉	C₂²	1	8	yes	complemented
37	#452×C₈₉	C₂²	1	16	yes	—
38	#451×C₈₉	C₂²	1	8	yes	complemented
39	#450×C₈₉	C₂²	1	8	yes	complemented
40	#433×C₈₉	C₂²	1	8	yes	complemented
41	#423×C₈₉	C₂²	1	2	yes	complemented
42	#417×C₈₉	C₂²	1	8	yes	complemented
43	#407×C₈₉	C₂²	1	2	yes	—
44	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
45	C₂×#41×C₈₉	—	2	2	no	—
46	C₂×#41×C₈₉	—	2	2	no	—
47	C₂×#41×C₈₉	—	4	8	no	—
48	C₂×#41×C₈₉	C₂³	1	4	yes	—
49	C₂×#41×C₈₉	C₂³	1	4	yes	—
50	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
52	C₂²×D₄×C₈₉	—	2	2	no	—
53	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₈₉	—	2	2	no	—
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	#137×C₈₉	—	4	16	no	—
57	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
58	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
59	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
60	C₄⋊Q₈×C₈₉	—	2	2	no	—
61	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
62	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
63	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
64	#127×C₈₉	C₂³	1	2	yes	—
65	#127×C₈₉	C₂³	1	2	yes	—
66	#126×C₈₉	—	2	16	no	—
67	#125×C₈₉	—	2	16	no	—
68	#125×C₈₉	—	2	2	no	—
69	#125×C₈₉	C₂³	1	4	yes	—
70	#124×C₈₉	C₂³	1	4	yes	—
71	#124×C₈₉	C₂³	1	4	yes	—
72	#123×C₈₉	—	2	8	no	—
73	C₂²⋊Q₈×C₈₉	—	2	4	no	—
74	C₂²⋊Q₈×C₈₉	—	2	8	no	—
75	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
76	#121×C₈₉	—	2	4	no	—
77	#121×C₈₉	—	2	4	no	—
78	#121×C₈₉	—	2	8	no	—
79	#120×C₈₉	—	2	8	no	—
80	C₄×Q₈×C₈₉	—	2	4	no	—
81	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
82	C₄×D₄×C₈₉	—	2	4	no	—
83	C₄×D₄×C₈₉	—	2	4	no	—
84	#117×C₈₉	D₄	1	4	yes	—
85	#117×C₈₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
89	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
90	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
94	C₂×C₄²×C₈₉	—	2	2	no	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
98	#103×C₈₉	C₂³	1	16	yes	—
99	#102×C₈₉	C₂³	1	16	yes	—
100	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
101	#97×C₈₉	C₂³	1	4	yes	—
102	C₄×C₈×C₈₉	C₂³	1	4	yes	—
103	C₂⁴×C₈₉	—	2	2	no	—
104	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
105	#41×C₈₉	—	2	16	no	—
106	#41×C₈₉	—	4	8	no	—
107	#41×C₈₉	—	4	8	no	—
108	#41×C₈₉	—	4	8	no	—
109	C₂×Q₈×C₈₉	—	2	2	no	—
110	C₂×Q₈×C₈₉	—	2	2	no	—
111	C₂×Q₈×C₈₉	—	2	8	no	—
112	C₂×Q₈×C₈₉	—	4	4	no	—
113	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
114	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
115	C₂×D₄×C₈₉	—	2	4	no	—
116	C₂×D₄×C₈₉	—	2	4	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	4	no	—
119	C₂×D₄×C₈₉	—	2	4	no	—
120	C₂×D₄×C₈₉	—	4	4	no	—
121	C₂×D₄×C₈₉	—	4	8	no	—
122	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	2	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	2	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	2	4	no	—
129	C₂²×C₄×C₈₉	—	4	8	no	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₈₉	—	4	16	no	—
137	SD₁₆×C₈₉	—	4	16	no	—
138	M₁₆×C₈₉	—	2	8	no	—
139	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
140	C₄⋊C₄×C₈₉	—	2	8	no	—
141	C₄⋊C₄×C₈₉	—	2	8	no	—
142	C₄⋊C₄×C₈₉	—	2	8	no	—
143	C₄⋊C₄×C₈₉	—	2	8	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	4	no	—
147	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
148	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
149	C₂²⋊C₄×C₈₉	—	2	8	no	—
150	C₂²⋊C₄×C₈₉	—	2	8	no	—
151	C₂²⋊C₄×C₈₉	—	2	8	no	—
152	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
153	C₄²×C₈₉	—	2	8	no	—
154	C₄²×C₈₉	C₂×D₄	1	2	yes	—
155	C₄²×C₈₉	C₂×D₄	1	2	yes	—
156	C₄²×C₈₉	C₂⁴	1	2	yes	—
157	C₄²×C₈₉	C₂⁴	1	2	yes	—
158	C₂³×C₈₉	—	2	2	no	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	4	2	no	—
161	C₂³×C₈₉	—	4	4	no	—
162	C₂³×C₈₉	—	8	4	no	—
163	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
164	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₈₉	—	2	8	no	—
166	Q₈×C₈₉	—	2	8	no	—
167	Q₈×C₈₉	—	4	4	no	—
168	Q₈×C₈₉	—	4	4	no	—
169	D₄×C₈₉	—	2	8	no	—
170	D₄×C₈₉	—	4	4	no	—
171	D₄×C₈₉	—	4	8	no	—
172	D₄×C₈₉	—	4	8	no	—
173	D₄×C₈₉	—	8	4	no	—
174	D₄×C₈₉	—	8	4	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	4	no	—
179	C₂×C₄×C₈₉	—	2	4	no	—
180	C₂×C₄×C₈₉	—	2	4	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	—	4	8	no	—
184	C₂×C₄×C₈₉	—	4	4	no	—
185	C₂×C₄×C₈₉	—	4	4	no	—
186	C₂×C₄×C₈₉	—	4	4	no	—
187	C₂×C₄×C₈₉	—	4	8	no	—
188	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
193	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
194	C₈×C₈₉	—	2	8	no	—
195	C₂²×C₈₉	—	2	2	no	—
196	C₂²×C₈₉	—	2	4	no	—
197	C₂²×C₈₉	—	2	2	no	—
198	C₂²×C₈₉	—	4	8	no	—
199	C₂²×C₈₉	—	4	4	no	—
200	C₂²×C₈₉	—	8	2	no	—
201	C₂²×C₈₉	—	8	8	no	—
202	C₂²×C₈₉	#535	1	2	yes	—
203	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₈₉	—	2	4	no	—
205	C₄×C₈₉	—	2	4	no	—
206	C₄×C₈₉	—	2	2	no	—
207	C₄×C₈₉	—	4	4	no	—
208	C₄×C₈₉	—	4	4	no	—
209	C₄×C₈₉	—	4	4	no	—
210	C₄×C₈₉	#535	1	2	yes	—
211	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
212	#60809	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂×C₈₉	—	2	2	no	—
214	C₂×C₈₉	—	4	2	no	—
215	C₂×C₈₉	—	8	4	no	—
216	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
217	C₂×C₈₉	#3586	1	2	yes	—
218	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
219	#3449	C₂×C₈₉	1	1	yes	characteristic
220	#3223	C₂×C₈₉	1	8	yes	complemented
221	#3222	C₂×C₈₉	1	8	yes	complemented
222	#3152	C₂×C₈₉	1	2	yes	complemented
223	#3142	C₂×C₈₉	1	2	yes	complemented
224	#3037	C₂×C₈₉	1	4	yes	complemented
225	#3007	C₂×C₈₉	1	4	yes	complemented
226	#2921	C₂×C₈₉	1	1	yes	characteristic, complemented
227	C₈₉	#60809	1	1	yes	characteristic, direct product factor, Sylow
228	C₂²×#41	C₂²×C₈₉	1	2	yes	—
229	C₂×#137	C₂²×C₈₉	1	8	yes	complemented
230	#541	—	2	4	no	—
231	#541	C₂²×C₈₉	1	8	yes	complemented
232	#537	—	2	2	no	—
233	#536	C₂²×C₈₉	1	4	yes	—
234	#535	C₂²×C₈₉	1	4	yes	—
235	#534	—	2	2	no	—
236	#532	C₂²×C₈₉	1	2	yes	—
237	#532	C₂²×C₈₉	1	2	yes	—
238	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
239	C₂×#126	—	2	2	no	—
240	C₂×#125	—	2	2	no	—
241	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
242	#525	—	2	4	no	—
243	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
244	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
245	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
246	#497	C₂²×C₈₉	1	8	yes	complemented
247	#494	C₂²×C₈₉	1	4	yes	complemented
248	#492	C₂²×C₈₉	1	4	yes	complemented
249	#491	C₂²×C₈₉	1	4	yes	complemented
250	#490	C₂²×C₈₉	1	4	yes	complemented
251	#488	C₂²×C₈₉	1	8	yes	complemented
252	#464	C₂²×C₈₉	1	16	yes	complemented
253	#462	C₂²×C₈₉	1	8	yes	complemented
254	#460	C₂²×C₈₉	1	8	yes	complemented
255	#452	C₂²×C₈₉	1	16	yes	—
256	#451	C₂²×C₈₉	1	8	yes	complemented
257	#450	C₂²×C₈₉	1	8	yes	complemented
258	#433	C₂²×C₈₉	1	8	yes	complemented
259	#423	C₂²×C₈₉	1	2	yes	complemented
260	#417	C₂²×C₈₉	1	8	yes	complemented
261	#407	C₂²×C₈₉	1	2	yes	—
262	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
263	C₂×#41	—	2	2	no	—
264	C₂×#41	—	2	2	no	—
265	C₂×#41	—	4	8	no	—
266	C₂×#41	C₂³×C₈₉	1	4	yes	—
267	C₂×#41	C₂³×C₈₉	1	4	yes	—
268	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
269	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
274	#137	—	4	16	no	—
275	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
276	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
277	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
280	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
282	#127	C₂³×C₈₉	1	2	yes	—
283	#127	C₂³×C₈₉	1	2	yes	—
284	#126	—	2	16	no	—
285	#125	—	2	16	no	—
286	#125	—	2	2	no	—
287	#125	C₂³×C₈₉	1	4	yes	—
288	#124	C₂³×C₈₉	1	4	yes	—
289	#124	C₂³×C₈₉	1	4	yes	—
290	#123	—	2	8	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	8	no	—
293	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
294	#121	—	2	4	no	—
295	#121	—	2	4	no	—
296	#121	—	2	8	no	—
297	#120	—	2	8	no	—
298	C₄×Q₈	—	2	4	no	—
299	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	#117	D₄×C₈₉	1	4	yes	—
303	#117	C₂³×C₈₉	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
312	C₂×C₄²	—	2	2	no	—
313	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
316	#103	C₂³×C₈₉	1	16	yes	—
317	#102	C₂³×C₈₉	1	16	yes	—
318	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
319	#97	C₂³×C₈₉	1	4	yes	—
320	C₄×C₈	C₂³×C₈₉	1	4	yes	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
323	#41	—	2	16	no	—
324	#41	—	4	8	no	—
325	#41	—	4	8	no	—
326	#41	—	4	8	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	8	no	—
330	C₂×Q₈	—	4	4	no	—
331	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
332	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	8	no	—
340	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	4	8	no	—
348	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
354	Q₁₆	—	4	16	no	—
355	SD₁₆	—	4	16	no	—
356	M₁₆	—	2	8	no	—
357	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
358	C₄⋊C₄	—	2	8	no	—
359	C₄⋊C₄	—	2	8	no	—
360	C₄⋊C₄	—	2	8	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
366	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
371	C₄²	—	2	8	no	—
372	C₄²	C₂×D₄×C₈₉	1	2	yes	—
373	C₄²	C₂×D₄×C₈₉	1	2	yes	—
374	C₄²	C₂⁴×C₈₉	1	2	yes	—
375	C₄²	C₂⁴×C₈₉	1	2	yes	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	4	2	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	8	4	no	—
381	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
382	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
383	Q₈	—	2	8	no	—
384	Q₈	—	2	8	no	—
385	Q₈	—	4	4	no	—
386	Q₈	—	4	4	no	—
387	D₄	—	2	8	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	8	no	—
391	D₄	—	8	4	no	—
392	D₄	—	8	4	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	—	4	8	no	—
406	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
410	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
411	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
412	C₈	—	2	8	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	8	no	—
420	C₂²	#535×C₈₉	1	2	yes	—
421	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
422	C₄	—	2	4	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	#535×C₈₉	1	2	yes	—
429	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
430	C₂	—	2	2	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	4	no	—
433	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
434	C₂	C₈₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#3223	C₂	semidirect
4. C₈₉×#3222	C₂	semidirect
5. C₈₉×#3152	C₂	semidirect
6. C₈₉×#3142	C₂	semidirect
7. C₈₉×#3037	C₂	semidirect
8. C₈₉×#3007	C₂	semidirect
9. C₈₉×#2921	C₂	semidirect
11. C₂×#137×C₈₉	C₂²	semidirect
13. #541×C₈₉	C₂²	semidirect
20. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
23. C₂×#125×C₈₉	C₂²	semidirect
26. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
28. #497×C₈₉	C₂²	semidirect
29. #494×C₈₉	C₂²	semidirect
30. #492×C₈₉	C₂²	semidirect
31. #491×C₈₉	C₂²	semidirect
32. #490×C₈₉	C₂²	semidirect
33. #488×C₈₉	C₂²	semidirect
34. #464×C₈₉	C₂²	semidirect
35. #462×C₈₉	C₂²	semidirect
36. #460×C₈₉	C₂²	semidirect
38. #451×C₈₉	C₂²	semidirect
39. #450×C₈₉	C₂²	semidirect
40. #433×C₈₉	C₂²	semidirect
41. #423×C₈₉	C₂²	semidirect
42. #417×C₈₉	C₂²	semidirect
44. C₄×M₁₆×C₈₉	C₂²	semidirect
212. #60809	C₈₉	direct (N × H)
218. C₂×#541	C₂×C₈₉	semidirect
220. #3223	C₂×C₈₉	semidirect
221. #3222	C₂×C₈₉	semidirect
222. #3152	C₂×C₈₉	semidirect
223. #3142	C₂×C₈₉	semidirect
224. #3037	C₂×C₈₉	semidirect
225. #3007	C₂×C₈₉	semidirect
226. #2921	C₂×C₈₉	semidirect
227. C₈₉	#60809	direct (N × H)
229. C₂×#137	C₂²×C₈₉	semidirect
231. #541	C₂²×C₈₉	semidirect
238. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
241. C₂×#125	C₂²×C₈₉	semidirect
244. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
246. #497	C₂²×C₈₉	semidirect
247. #494	C₂²×C₈₉	semidirect
248. #492	C₂²×C₈₉	semidirect
249. #491	C₂²×C₈₉	semidirect
250. #490	C₂²×C₈₉	semidirect
251. #488	C₂²×C₈₉	semidirect
252. #464	C₂²×C₈₉	semidirect
253. #462	C₂²×C₈₉	semidirect
254. #460	C₂²×C₈₉	semidirect
256. #451	C₂²×C₈₉	semidirect
257. #450	C₂²×C₈₉	semidirect
258. #433	C₂²×C₈₉	semidirect
259. #423	C₂²×C₈₉	semidirect
260. #417	C₂²×C₈₉	semidirect
262. C₄×M₁₆	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#541×C₈₉	2
C₈₉×#3449	2
C₈₉×#3223	2
C₈₉×#3222	2
C₈₉×#3152	2
C₈₉×#3142	2
C₈₉×#3037	2
C₈₉×#3007	2
C₈₉×#2921	2
#60809	89

Subgroups — C89×#60809 #36438657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60809 #36438657