Subgroups — C₈₉×#25294 #36403142

Order 22784.

782 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#462×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2582	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2568	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2068	C₂	1	2	yes	maximal
6	C₈₉×#2056	C₂	1	2	yes	maximal
7	C₈₉×#1969	C₂	1	2	yes	maximal
8	C₈₉×#1956	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1947	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1933	C₂	1	2	yes	maximal
11	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	#462×C₈₉	—	2	4	no	—
17	C₈×Q₈×C₈₉	—	2	4	no	—
18	C₂×#107×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₈₉	C₂²	1	2	yes	—
23	C₂×#103×C₈₉	C₂²	1	2	yes	—
24	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
28	#400×C₈₉	—	2	2	no	—
29	#398×C₈₉	—	2	2	no	—
30	#391×C₈₉	—	2	1	no	—
31	#391×C₈₉	—	2	1	no	—
32	#391×C₈₉	C₂²	1	2	yes	—
33	#391×C₈₉	C₂²	1	2	yes	—
34	#391×C₈₉	C₂²	1	2	yes	—
35	#389×C₈₉	—	2	1	no	—
36	#389×C₈₉	C₂²	1	2	yes	—
37	#384×C₈₉	C₂²	1	1	yes	characteristic
38	#382×C₈₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	2	yes	—
41	#340×C₈₉	C₂²	1	1	yes	characteristic
42	#340×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
44	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
45	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₈₉	—	2	4	no	—
47	C₂×Q₁₆×C₈₉	—	2	4	no	—
48	C₂×Q₁₆×C₈₉	—	4	2	no	—
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
51	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
52	C₄⋊Q₈×C₈₉	—	2	2	no	—
53	C₄⋊Q₈×C₈₉	—	2	2	no	—
54	C₄×Q₈×C₈₉	—	2	2	no	—
55	C₄×Q₈×C₈₉	—	2	2	no	—
56	C₄×Q₈×C₈₉	—	2	2	no	—
57	C₄×Q₈×C₈₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	—	2	1	no	—
71	C₂×C₄²×C₈₉	—	2	1	no	—
72	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
74	#107×C₈₉	—	4	2	no	—
75	C₄⋊C₈×C₈₉	—	2	4	no	—
76	C₄⋊C₈×C₈₉	D₄	1	4	yes	—
77	#103×C₈₉	—	2	2	no	—
78	#103×C₈₉	—	2	4	no	—
79	#103×C₈₉	—	2	2	no	—
80	#103×C₈₉	—	2	4	no	—
81	#103×C₈₉	—	4	2	no	—
82	C₄×C₈×C₈₉	—	2	4	no	—
83	C₄×C₈×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	1	no	—
85	#95×C₈₉	—	2	2	no	—
86	#95×C₈₉	—	2	2	no	—
87	#95×C₈₉	—	2	2	no	—
88	#95×C₈₉	—	2	2	no	—
89	#95×C₈₉	—	2	2	no	—
90	#95×C₈₉	—	2	2	no	—
91	#95×C₈₉	—	2	2	no	—
92	C₂×Q₈×C₈₉	—	2	2	no	—
93	C₂×Q₈×C₈₉	—	2	2	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	2	1	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	1	no	—
98	C₂×Q₈×C₈₉	—	2	1	no	—
99	C₂×Q₈×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	—	2	2	no	—
101	C₂×Q₈×C₈₉	—	2	2	no	—
102	C₂×Q₈×C₈₉	—	2	1	no	—
103	C₂×Q₈×C₈₉	—	2	2	no	—
104	C₂×Q₈×C₈₉	—	2	2	no	—
105	C₂×Q₈×C₈₉	Q₁₆	1	4	yes	complemented
106	C₂×Q₈×C₈₉	#41	1	2	yes	—
107	C₂²×C₄×C₈₉	—	2	1	no	—
108	C₂²×C₄×C₈₉	—	2	1	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	1	no	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
118	Q₁₆×C₈₉	—	4	8	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₂×C₈×C₈₉	—	2	1	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
127	C₂×C₈×C₈₉	#41	1	2	yes	—
128	C₄⋊C₄×C₈₉	—	2	4	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	1	no	—
131	C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₄⋊C₄×C₈₉	—	2	2	no	—
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₄⋊C₄×C₈₉	—	4	2	no	—
139	C₄⋊C₄×C₈₉	—	4	2	no	—
140	C₄⋊C₄×C₈₉	—	4	2	no	—
141	C₄⋊C₄×C₈₉	—	4	2	no	—
142	C₄⋊C₄×C₈₉	—	8	1	no	—
143	C₄⋊C₄×C₈₉	—	8	2	no	—
144	C₄²×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	—	4	2	no	—
147	C₄²×C₈₉	—	4	2	no	—
148	C₄²×C₈₉	C₂×D₄	1	2	yes	—
149	C₄²×C₈₉	#41	1	2	yes	—
150	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₈₉	—	2	8	no	—
152	Q₈×C₈₉	—	2	2	no	—
153	Q₈×C₈₉	—	2	2	no	—
154	Q₈×C₈₉	—	4	1	no	—
155	Q₈×C₈₉	—	4	1	no	—
156	Q₈×C₈₉	—	4	2	no	—
157	Q₈×C₈₉	—	4	2	no	—
158	Q₈×C₈₉	—	4	2	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	2	2	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	4	1	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	1	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	1	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	4	1	no	—
185	C₂×C₄×C₈₉	#121	1	2	yes	—
186	C₂×C₄×C₈₉	#121	1	2	yes	—
187	C₂×C₄×C₈₉	C₂×Q₁₆	1	4	yes	—
188	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
189	C₂×C₄×C₈₉	#135	1	2	yes	—
190	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
196	C₈×C₈₉	—	2	4	no	—
197	C₈×C₈₉	—	2	2	no	—
198	C₈×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
200	C₂²×C₈₉	#548	1	1	yes	characteristic
201	C₂²×C₈₉	#550	1	1	yes	characteristic
202	C₂²×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
203	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
204	C₂²×C₈₉	#577	1	1	yes	characteristic
205	C₂²×C₈₉	#578	1	1	yes	characteristic
206	C₄×C₈₉	—	2	4	no	—
207	C₄×C₈₉	—	2	2	no	—
208	C₄×C₈₉	—	4	2	no	—
209	C₄×C₈₉	—	4	2	no	—
210	C₄×C₈₉	—	8	1	no	—
211	C₄×C₈₉	—	8	1	no	—
212	C₄×C₈₉	—	8	2	no	—
213	C₄×C₈₉	—	8	2	no	—
214	C₄×C₈₉	—	8	1	no	—
215	C₄×C₈₉	#467	1	4	yes	—
216	C₄×C₈₉	#529	1	1	yes	characteristic
217	C₄×C₈₉	#542	1	1	yes	characteristic
218	C₄×C₈₉	#546	1	1	yes	characteristic
219	C₄×C₈₉	#548	1	1	yes	characteristic
220	#25294	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₈₉	#2426	1	1	yes	characteristic
222	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
223	C₂×C₈₉	#3063	1	1	yes	characteristic
224	C₂×C₈₉	#3363	1	1	yes	characteristic
225	C₂×C₈₉	#3364	1	1	yes	characteristic
226	C₂×C₈₉	#3394	1	1	yes	characteristic
227	C₂×C₈₉	#3395	1	1	yes	characteristic
228	C₂×#462	C₂×C₈₉	1	1	yes	characteristic
229	C₂×C₈×Q₈	C₂×C₈₉	1	1	yes	characteristic
230	#2582	C₂×C₈₉	1	1	yes	characteristic
231	#2568	C₂×C₈₉	1	1	yes	characteristic
232	#2068	C₂×C₈₉	1	2	yes	—
233	#2056	C₂×C₈₉	1	2	yes	—
234	#1969	C₂×C₈₉	1	2	yes	—
235	#1956	C₂×C₈₉	1	1	yes	characteristic
236	#1947	C₂×C₈₉	1	1	yes	characteristic
237	#1933	C₂×C₈₉	1	2	yes	—
238	C₄×#103	C₂×C₈₉	1	1	yes	characteristic
239	C₈₉	#25294	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
241	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
242	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
244	#462	—	2	4	no	—
245	C₈×Q₈	—	2	4	no	—
246	C₂×#107	C₂²×C₈₉	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
249	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×#103	C₂²×C₈₉	1	2	yes	—
251	C₂×#103	C₂²×C₈₉	1	2	yes	—
252	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×#103	C₂²×C₈₉	1	2	yes	—
254	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
256	#400	—	2	2	no	—
257	#398	—	2	2	no	—
258	#391	—	2	1	no	—
259	#391	—	2	1	no	—
260	#391	C₂²×C₈₉	1	2	yes	—
261	#391	C₂²×C₈₉	1	2	yes	—
262	#391	C₂²×C₈₉	1	2	yes	—
263	#389	—	2	1	no	—
264	#389	C₂²×C₈₉	1	2	yes	—
265	#384	C₂²×C₈₉	1	1	yes	characteristic
266	#382	—	2	1	no	—
267	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
268	#340	C₂²×C₈₉	1	2	yes	—
269	#340	C₂²×C₈₉	1	1	yes	characteristic
270	#340	C₂²×C₈₉	1	1	yes	characteristic
271	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
272	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
273	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
274	C₂×Q₁₆	—	2	4	no	—
275	C₂×Q₁₆	—	2	4	no	—
276	C₂×Q₁₆	—	4	2	no	—
277	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
279	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	2	no	—
281	C₄⋊Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	2	2	no	—
284	C₄×Q₈	—	2	2	no	—
285	C₄×Q₈	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
301	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
302	#107	—	4	2	no	—
303	C₄⋊C₈	—	2	4	no	—
304	C₄⋊C₈	D₄×C₈₉	1	4	yes	—
305	#103	—	2	2	no	—
306	#103	—	2	4	no	—
307	#103	—	2	2	no	—
308	#103	—	2	4	no	—
309	#103	—	4	2	no	—
310	C₄×C₈	—	2	4	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	—	2	2	no	—
318	#95	—	2	2	no	—
319	#95	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	Q₁₆×C₈₉	1	4	yes	complemented
334	C₂×Q₈	#41×C₈₉	1	2	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
345	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
346	Q₁₆	—	4	8	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
355	C₂×C₈	#41×C₈₉	1	2	yes	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	4	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	2	no	—
369	C₄⋊C₄	—	4	2	no	—
370	C₄⋊C₄	—	8	1	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	4	2	no	—
375	C₄²	—	4	2	no	—
376	C₄²	C₂×D₄×C₈₉	1	2	yes	—
377	C₄²	#41×C₈₉	1	2	yes	—
378	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
379	Q₈	—	2	8	no	—
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	1	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	Q₈	—	4	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	#121×C₈₉	1	2	yes	—
414	C₂×C₄	#121×C₈₉	1	2	yes	—
415	C₂×C₄	C₂×Q₁₆×C₈₉	1	4	yes	—
416	C₂×C₄	C₂×Q₁₆×C₈₉	1	2	yes	—
417	C₂×C₄	#135×C₈₉	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
422	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
423	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
424	C₈	—	2	4	no	—
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
428	C₂²	#548×C₈₉	1	1	yes	characteristic
429	C₂²	#550×C₈₉	1	1	yes	characteristic
430	C₂²	C₂²×Q₁₆×C₈₉	1	1	yes	characteristic
431	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
432	C₂²	#577×C₈₉	1	1	yes	characteristic
433	C₂²	#578×C₈₉	1	1	yes	characteristic
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	2	no	—
442	C₄	—	8	2	no	—
443	C₄	#467×C₈₉	1	4	yes	—
444	C₄	#529×C₈₉	1	1	yes	characteristic
445	C₄	#542×C₈₉	1	1	yes	characteristic
446	C₄	#546×C₈₉	1	1	yes	characteristic
447	C₄	#548×C₈₉	1	1	yes	characteristic
448	C₂	C₈₉×#2426	1	1	yes	characteristic
449	C₂	C₂×#467×C₈₉	1	1	yes	characteristic
450	C₂	C₈₉×#3063	1	1	yes	characteristic
451	C₂	C₈₉×#3363	1	1	yes	characteristic
452	C₂	C₈₉×#3364	1	1	yes	characteristic
453	C₂	C₈₉×#3394	1	1	yes	characteristic
454	C₂	C₈₉×#3395	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×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
105. C₂×Q₈×C₈₉	Q₁₆	semidirect
220. #25294	C₈₉	direct (N × H)
239. C₈₉	#25294	direct (N × H)
333. C₂×Q₈	Q₁₆×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#462×C₈₉	2
C₂×C₈×Q₈×C₈₉	2
C₈₉×#2582	2
C₈₉×#2568	2
C₈₉×#2068	2
C₈₉×#2056	2
C₈₉×#1969	2
C₈₉×#1956	2
C₈₉×#1947	2
C₈₉×#1933	2
C₄×#103×C₈₉	2
#25294	89

Subgroups — C89×#25294 #36403142

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25294 #36403142