Subgroups — C₈₉×#22971 #36400819

Order 22784.

782 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#477×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2369	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1990	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1948	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1943	C₂	1	2	yes	maximal
7	C₈₉×#1918	C₂	1	2	yes	maximal
8	C₈₉×#1865	C₂	1	2	yes	maximal
9	C₈₉×#1770	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1763	C₂	1	2	yes	maximal
11	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	#477×C₈₉	C₄	1	8	yes	complemented
16	C₂×#107×C₈₉	C₂²	1	2	yes	—
17	C₂×#106×C₈₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#103×C₈₉	C₂²	1	2	yes	—
21	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#97×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
24	#391×C₈₉	—	2	2	no	—
25	#389×C₈₉	—	2	1	no	—
26	#389×C₈₉	—	2	2	no	—
27	#389×C₈₉	C₂²	1	2	yes	—
28	#389×C₈₉	C₂²	1	2	yes	—
29	#384×C₈₉	—	2	1	no	—
30	#384×C₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
32	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	#340×C₈₉	C₂²	1	2	yes	—
37	#340×C₈₉	C₂²	1	1	yes	characteristic
38	#340×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	2	yes	—
41	#336×C₈₉	C₂²	1	2	yes	—
42	C₂²×Q₈×C₈₉	—	2	1	no	—
43	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
46	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₈₉	—	2	2	no	—
48	C₄⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₈₉	—	2	2	no	—
50	C₄×Q₈×C₈₉	—	2	4	no	—
51	C₄×Q₈×C₈₉	—	4	2	no	—
52	C₄×Q₈×C₈₉	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	—	2	1	no	—
68	C₂×C₄²×C₈₉	—	2	1	no	—
69	C₂×C₄²×C₈₉	—	2	2	no	—
70	C₂×C₄²×C₈₉	—	2	2	no	—
71	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
72	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
73	#107×C₈₉	C₂×C₄	1	8	yes	—
74	#106×C₈₉	—	4	2	no	—
75	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
76	#103×C₈₉	—	2	2	no	—
77	#103×C₈₉	C₂×C₄	1	8	yes	—
78	#103×C₈₉	Q₈	1	4	yes	complemented
79	#97×C₈₉	—	4	2	no	—
80	C₄×C₈×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	2	no	—
82	#95×C₈₉	—	2	2	no	—
83	#95×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	1	no	—
85	#95×C₈₉	D₄	1	2	yes	—
86	C₂×Q₈×C₈₉	—	2	4	no	—
87	C₂×Q₈×C₈₉	—	2	1	no	—
88	C₂×Q₈×C₈₉	—	2	1	no	—
89	C₂×Q₈×C₈₉	—	2	1	no	—
90	C₂×Q₈×C₈₉	—	8	1	no	—
91	C₂×Q₈×C₈₉	—	8	1	no	—
92	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
93	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
94	C₂×Q₈×C₈₉	#41	1	2	yes	—
95	C₂²×C₄×C₈₉	—	2	1	no	—
96	C₂²×C₄×C₈₉	—	2	1	no	—
97	C₂²×C₄×C₈₉	—	2	1	no	—
98	C₂²×C₄×C₈₉	—	2	2	no	—
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	2	2	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₈₉	—	2	1	no	—
107	C₂×C₈×C₈₉	—	2	1	no	—
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	2	1	no	—
112	C₂×C₈×C₈₉	—	2	1	no	—
113	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
115	C₄⋊C₄×C₈₉	—	2	4	no	—
116	C₄⋊C₄×C₈₉	—	2	4	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	—	2	2	no	—
119	C₄⋊C₄×C₈₉	—	2	1	no	—
120	C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₄⋊C₄×C₈₉	—	2	1	no	—
122	C₄⋊C₄×C₈₉	—	2	1	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	4	4	no	—
127	C₄⋊C₄×C₈₉	—	4	2	no	—
128	C₄⋊C₄×C₈₉	—	8	1	no	—
129	C₄⋊C₄×C₈₉	—	8	2	no	—
130	C₄⋊C₄×C₈₉	—	8	2	no	—
131	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
132	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₈₉	C₂×Q₈	1	2	yes	—
134	C₄²×C₈₉	—	2	4	no	—
135	C₄²×C₈₉	—	2	2	no	—
136	C₄²×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	—	4	4	no	—
138	C₄²×C₈₉	—	4	2	no	—
139	C₄²×C₈₉	—	8	2	no	—
140	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
141	C₄²×C₈₉	#41	1	2	yes	—
142	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
143	Q₈×C₈₉	—	2	2	no	—
144	Q₈×C₈₉	—	2	2	no	—
145	Q₈×C₈₉	—	2	2	no	—
146	Q₈×C₈₉	—	8	4	no	—
147	Q₈×C₈₉	C₄×Q₈	1	4	yes	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	1	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₈₉	#137	1	2	yes	—
177	C₂×C₄×C₈₉	#137	1	2	yes	—
178	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₈₉	—	2	4	no	—
185	C₈×C₈₉	—	2	2	no	—
186	C₈×C₈₉	—	4	1	no	—
187	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₈₉	#546	1	1	yes	characteristic
189	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
190	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
192	C₂²×C₈₉	#576	1	1	yes	characteristic
193	C₂²×C₈₉	#577	1	1	yes	characteristic
194	C₄×C₈₉	—	2	4	no	—
195	C₄×C₈₉	—	2	2	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	—	4	4	no	—
201	C₄×C₈₉	—	8	1	no	—
202	C₄×C₈₉	—	8	2	no	—
203	C₄×C₈₉	#441	1	4	yes	—
204	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₄×C₈₉	#520	1	1	yes	characteristic
206	C₄×C₈₉	#552	1	1	yes	characteristic
207	C₄×C₈₉	#554	1	1	yes	characteristic
208	#22971	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₈₉	#2360	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#441	1	1	yes	characteristic
211	C₂×C₈₉	#2946	1	1	yes	characteristic
212	C₂×C₈₉	#3329	1	1	yes	characteristic
213	C₂×C₈₉	#3333	1	1	yes	characteristic
214	C₂×C₈₉	#3385	1	1	yes	characteristic
215	C₂×C₈₉	#3387	1	1	yes	characteristic
216	C₂×#477	C₂×C₈₉	1	1	yes	characteristic
217	#2369	C₂×C₈₉	1	1	yes	characteristic
218	Q₈×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
219	#1990	C₂×C₈₉	1	1	yes	characteristic
220	#1948	C₂×C₈₉	1	1	yes	characteristic
221	#1943	C₂×C₈₉	1	2	yes	—
222	#1918	C₂×C₈₉	1	2	yes	—
223	#1865	C₂×C₈₉	1	2	yes	—
224	#1770	C₂×C₈₉	1	1	yes	characteristic
225	#1763	C₂×C₈₉	1	2	yes	—
226	C₄×#103	C₂×C₈₉	1	1	yes	characteristic
227	C₈₉	#22971	1	1	yes	characteristic, direct product factor, Sylow
228	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
230	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
231	#477	C₄×C₈₉	1	8	yes	complemented
232	C₂×#107	C₂²×C₈₉	1	2	yes	—
233	C₂×#106	C₂²×C₈₉	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
235	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
236	C₂×#103	C₂²×C₈₉	1	2	yes	—
237	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
238	C₂×#97	C₂²×C₈₉	1	2	yes	—
239	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
240	#391	—	2	2	no	—
241	#389	—	2	1	no	—
242	#389	—	2	2	no	—
243	#389	C₂²×C₈₉	1	2	yes	—
244	#389	C₂²×C₈₉	1	2	yes	—
245	#384	—	2	1	no	—
246	#384	C₂²×C₈₉	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	2	1	no	—
248	C₄×C₄⋊C₄	—	2	1	no	—
249	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
250	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
251	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
252	#340	C₂²×C₈₉	1	2	yes	—
253	#340	C₂²×C₈₉	1	1	yes	characteristic
254	#340	C₂²×C₈₉	1	2	yes	—
255	#340	C₂²×C₈₉	1	1	yes	characteristic
256	#340	C₂²×C₈₉	1	2	yes	—
257	#336	C₂²×C₈₉	1	2	yes	—
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
262	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	C₂×C₄×C₈₉	1	4	yes	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	4	2	no	—
268	C₄×Q₈	C₂×C₄×C₈₉	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
277	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	2	no	—
287	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
288	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
289	#107	C₂×C₄×C₈₉	1	8	yes	—
290	#106	—	4	2	no	—
291	C₄⋊C₈	C₂×C₄×C₈₉	1	4	yes	—
292	#103	—	2	2	no	—
293	#103	C₂×C₄×C₈₉	1	8	yes	—
294	#103	Q₈×C₈₉	1	4	yes	complemented
295	#97	—	4	2	no	—
296	C₄×C₈	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	1	no	—
301	#95	D₄×C₈₉	1	2	yes	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	8	1	no	—
307	C₂×Q₈	—	8	1	no	—
308	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
309	C₂×Q₈	C₂×Q₈×C₈₉	1	2	yes	—
310	C₂×Q₈	#41×C₈₉	1	2	yes	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
330	C₂×C₈	C₂×Q₈×C₈₉	1	2	yes	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	1	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
348	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
349	C₄⋊C₄	C₂×Q₈×C₈₉	1	2	yes	—
350	C₄²	—	2	4	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	4	4	no	—
354	C₄²	—	4	2	no	—
355	C₄²	—	8	2	no	—
356	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
357	C₄²	#41×C₈₉	1	2	yes	—
358	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	8	4	no	—
363	Q₈	C₄×Q₈×C₈₉	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
391	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
392	C₂×C₄	#137×C₈₉	1	2	yes	—
393	C₂×C₄	#137×C₈₉	1	2	yes	—
394	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
398	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
399	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
400	C₈	—	2	4	no	—
401	C₈	—	2	2	no	—
402	C₈	—	4	1	no	—
403	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
404	C₂²	#546×C₈₉	1	1	yes	characteristic
405	C₂²	D₄×Q₈×C₈₉	1	1	yes	characteristic
406	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
407	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
408	C₂²	#576×C₈₉	1	1	yes	characteristic
409	C₂²	#577×C₈₉	1	1	yes	characteristic
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	4	no	—
416	C₄	—	4	2	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	2	no	—
419	C₄	#441×C₈₉	1	4	yes	—
420	C₄	C₂×C₄×Q₈×C₈₉	1	1	yes	characteristic
421	C₄	#520×C₈₉	1	1	yes	characteristic
422	C₄	#552×C₈₉	1	1	yes	characteristic
423	C₄	#554×C₈₉	1	1	yes	characteristic
424	C₂	C₈₉×#2360	1	1	yes	characteristic
425	C₂	C₂×#441×C₈₉	1	1	yes	characteristic
426	C₂	C₈₉×#2946	1	1	yes	characteristic
427	C₂	C₈₉×#3329	1	1	yes	characteristic
428	C₂	C₈₉×#3333	1	1	yes	characteristic
429	C₂	C₈₉×#3385	1	1	yes	characteristic
430	C₂	C₈₉×#3387	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₄⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
15. #477×C₈₉	C₄	semidirect
78. #103×C₈₉	Q₈	semidirect
208. #22971	C₈₉	direct (N × H)
227. C₈₉	#22971	direct (N × H)
231. #477	C₄×C₈₉	semidirect
294. #103	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#477×C₈₉	2
C₈₉×#2369	2
Q₈×C₄⋊C₄×C₈₉	2
C₈₉×#1990	2
C₈₉×#1948	2
C₈₉×#1943	2
C₈₉×#1918	2
C₈₉×#1865	2
C₈₉×#1770	2
C₈₉×#1763	2
C₄×#103×C₈₉	2
#22971	89

Subgroups — C89×#22971 #36400819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22971 #36400819