Subgroups — C₈₉×#29148 #36406996

Order 22784.

830 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2868	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2024	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2023	C₂	1	2	yes	maximal
5	C₈₉×#1959	C₂	1	2	yes	maximal
6	C₈₉×#1836	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1803	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1802	C₂	1	2	yes	maximal
9	C₈₉×#1767	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
11	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
13	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#103×C₈₉	C₂²	1	4	yes	—
18	C₂×#102×C₈₉	C₂²	1	4	yes	—
19	C₂×#97×C₈₉	C₂²	1	2	yes	—
20	#391×C₈₉	C₂²	1	1	yes	characteristic
21	#390×C₈₉	C₂²	1	1	yes	characteristic
22	#388×C₈₉	—	2	1	no	—
23	#388×C₈₉	—	2	1	no	—
24	#384×C₈₉	—	2	1	no	—
25	#384×C₈₉	—	2	1	no	—
26	#384×C₈₉	C₂²	1	2	yes	—
27	#384×C₈₉	C₂²	1	2	yes	—
28	#382×C₈₉	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
30	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
31	C₄³×C₈₉	C₂²	1	1	yes	characteristic
32	#340×C₈₉	C₂²	1	4	yes	—
33	#340×C₈₉	C₂²	1	4	yes	—
34	#336×C₈₉	C₂²	1	2	yes	—
35	C₂²×Q₈×C₈₉	—	2	2	no	—
36	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₈₉	—	2	1	no	—
39	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₈₉	—	4	4	no	—
41	C₄⋊Q₈×C₈₉	—	4	4	no	—
42	C₄⋊Q₈×C₈₉	—	4	4	no	—
43	#124×C₈₉	—	2	2	no	—
44	#124×C₈₉	Q₈	1	4	yes	complemented
45	C₄×Q₈×C₈₉	—	2	4	no	—
46	C₄×D₄×C₈₉	—	2	4	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
56	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
59	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
61	C₂×C₄²×C₈₉	—	2	1	no	—
62	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₈₉	—	2	4	no	—
70	#103×C₈₉	—	4	4	no	—
71	#102×C₈₉	—	4	4	no	—
72	#97×C₈₉	—	2	4	no	—
73	#95×C₈₉	—	2	1	no	—
74	#95×C₈₉	—	2	1	no	—
75	#95×C₈₉	—	2	1	no	—
76	#95×C₈₉	—	2	1	no	—
77	C₂⁴×C₈₉	—	2	1	no	—
78	C₂×Q₈×C₈₉	—	2	1	no	—
79	C₂×Q₈×C₈₉	—	2	2	no	—
80	C₂×Q₈×C₈₉	—	2	2	no	—
81	C₂×Q₈×C₈₉	—	4	4	no	—
82	C₂×Q₈×C₈₉	—	4	4	no	—
83	C₂×Q₈×C₈₉	—	4	4	no	—
84	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
85	C₂×D₄×C₈₉	—	2	2	no	—
86	C₂×D₄×C₈₉	—	2	1	no	—
87	C₂×D₄×C₈₉	—	2	2	no	—
88	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₈₉	—	2	1	no	—
90	C₂²×C₄×C₈₉	—	2	1	no	—
91	C₂²×C₄×C₈₉	—	2	1	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	4	2	no	—
94	C₂²×C₄×C₈₉	—	4	2	no	—
95	C₂²×C₄×C₈₉	—	4	2	no	—
96	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₈₉	—	2	4	no	—
104	C₂×C₈×C₈₉	—	2	4	no	—
105	C₂×C₈×C₈₉	—	2	4	no	—
106	C₄⋊C₄×C₈₉	—	2	2	no	—
107	C₄⋊C₄×C₈₉	—	2	2	no	—
108	C₄⋊C₄×C₈₉	—	2	4	no	—
109	C₄⋊C₄×C₈₉	—	2	4	no	—
110	C₄⋊C₄×C₈₉	—	4	4	no	—
111	C₄⋊C₄×C₈₉	—	4	4	no	—
112	C₄⋊C₄×C₈₉	—	4	4	no	—
113	C₄⋊C₄×C₈₉	—	4	4	no	—
114	C₄⋊C₄×C₈₉	—	4	2	no	—
115	C₄⋊C₄×C₈₉	—	4	4	no	—
116	C₂²⋊C₄×C₈₉	—	2	4	no	—
117	C₂²⋊C₄×C₈₉	—	2	4	no	—
118	C₂²⋊C₄×C₈₉	—	4	2	no	—
119	C₂²⋊C₄×C₈₉	—	4	2	no	—
120	C₂²⋊C₄×C₈₉	—	4	2	no	—
121	C₄²×C₈₉	—	2	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	—	2	2	no	—
124	C₄²×C₈₉	—	2	2	no	—
125	C₄²×C₈₉	—	2	2	no	—
126	C₄²×C₈₉	—	4	2	no	—
127	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
128	C₄²×C₈₉	#41	1	2	yes	—
129	C₄²×C₈₉	#41	1	4	yes	—
130	C₂³×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	—	4	1	no	—
132	C₂³×C₈₉	—	4	1	no	—
133	C₂³×C₈₉	—	4	1	no	—
134	C₂³×C₈₉	—	4	1	no	—
135	C₂³×C₈₉	—	4	1	no	—
136	C₂³×C₈₉	—	4	1	no	—
137	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
138	Q₈×C₈₉	—	2	4	no	—
139	Q₈×C₈₉	—	4	2	no	—
140	Q₈×C₈₉	—	8	8	no	—
141	D₄×C₈₉	—	2	4	no	—
142	D₄×C₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	2	1	no	—
147	C₂×C₄×C₈₉	—	2	1	no	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	2	1	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	—	4	1	no	—
155	C₂×C₄×C₈₉	—	4	1	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	4	no	—
159	C₂×C₄×C₈₉	—	4	1	no	—
160	C₂×C₄×C₈₉	—	4	4	no	—
161	C₂×C₄×C₈₉	—	4	4	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	8	4	no	—
166	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄×C₈₉	#124	1	2	yes	—
169	C₂×C₄×C₈₉	#124	1	2	yes	—
170	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
172	C₂×C₄×C₈₉	#137	1	2	yes	—
173	C₂×C₄×C₈₉	#137	1	2	yes	—
174	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
176	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
178	C₈×C₈₉	—	4	4	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	—	4	2	no	—
182	C₂²×C₈₉	—	8	1	no	—
183	C₂²×C₈₉	—	8	1	no	—
184	C₂²×C₈₉	—	8	1	no	—
185	C₂²×C₈₉	—	8	1	no	—
186	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#124	1	1	yes	characteristic
188	C₂²×C₈₉	#535	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
192	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	2	2	no	—
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	8	1	no	—
200	C₄×C₈₉	—	8	1	no	—
201	C₄×C₈₉	—	8	4	no	—
202	C₄×C₈₉	#489	1	4	yes	—
203	C₄×C₈₉	#554	1	2	yes	—
204	C₄×C₈₉	#555	1	2	yes	—
205	#29148	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₈₉	—	8	2	no	—
207	C₂×C₈₉	#2563	1	1	yes	characteristic
208	C₂×C₈₉	#3079	1	1	yes	characteristic
209	C₂×C₈₉	#3079	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#489	1	1	yes	characteristic
211	C₂×C₈₉	#3141	1	1	yes	characteristic
212	C₂×C₈₉	#3217	1	1	yes	characteristic
213	C₂×C₈₉	#3218	1	1	yes	characteristic
214	#2868	C₂×C₈₉	1	1	yes	characteristic, complemented
215	C₄×#124	C₂×C₈₉	1	1	yes	characteristic
216	#2024	C₂×C₈₉	1	2	yes	complemented
217	#2023	C₂×C₈₉	1	2	yes	—
218	#1959	C₂×C₈₉	1	2	yes	—
219	#1836	C₂×C₈₉	1	2	yes	complemented
220	#1803	C₂×C₈₉	1	2	yes	complemented
221	#1802	C₂×C₈₉	1	2	yes	—
222	#1767	C₂×C₈₉	1	1	yes	characteristic, complemented
223	C₈₉	#29148	1	1	yes	characteristic, direct product factor, Sylow
224	C₂×C₄⋊Q₈	—	2	1	no	—
225	C₂×C₄⋊Q₈	—	2	1	no	—
226	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
227	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
231	C₂×#103	C₂²×C₈₉	1	4	yes	—
232	C₂×#102	C₂²×C₈₉	1	4	yes	—
233	C₂×#97	C₂²×C₈₉	1	2	yes	—
234	#391	C₂²×C₈₉	1	1	yes	characteristic
235	#390	C₂²×C₈₉	1	1	yes	characteristic
236	#388	—	2	1	no	—
237	#388	—	2	1	no	—
238	#384	—	2	1	no	—
239	#384	—	2	1	no	—
240	#384	C₂²×C₈₉	1	2	yes	—
241	#384	C₂²×C₈₉	1	2	yes	—
242	#382	C₂²×C₈₉	1	1	yes	characteristic
243	C₄×C₂²⋊C₄	—	2	1	no	—
244	C₄×C₂²⋊C₄	—	2	1	no	—
245	C₄³	C₂²×C₈₉	1	1	yes	characteristic
246	#340	C₂²×C₈₉	1	4	yes	—
247	#340	C₂²×C₈₉	1	4	yes	—
248	#336	C₂²×C₈₉	1	2	yes	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
251	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
252	C₂³×C₄	—	2	1	no	—
253	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
254	C₄⋊Q₈	—	4	4	no	—
255	C₄⋊Q₈	—	4	4	no	—
256	C₄⋊Q₈	—	4	4	no	—
257	#124	—	2	2	no	—
258	#124	Q₈×C₈₉	1	4	yes	complemented
259	C₄×Q₈	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
268	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
269	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	2	1	no	—
273	C₂×C₂²⋊C₄	—	2	1	no	—
274	C₂×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
277	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
278	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
279	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
280	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
281	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
282	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
283	C₄⋊C₈	—	2	4	no	—
284	#103	—	4	4	no	—
285	#102	—	4	4	no	—
286	#97	—	2	4	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	1	no	—
290	#95	—	2	1	no	—
291	C₂⁴	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	C₂×Q₈×C₈₉	1	2	yes	—
299	C₂×D₄	—	2	2	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	C₂×Q₈×C₈₉	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	4	no	—
319	C₂×C₈	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	4	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	4	4	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	4	no	—
327	C₄⋊C₄	—	4	4	no	—
328	C₄⋊C₄	—	4	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	2	4	no	—
331	C₂²⋊C₄	—	2	4	no	—
332	C₂²⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	4	2	no	—
341	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
342	C₄²	#41×C₈₉	1	2	yes	—
343	C₄²	#41×C₈₉	1	4	yes	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	8	8	no	—
355	D₄	—	2	4	no	—
356	D₄	—	4	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
381	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
382	C₂×C₄	#124×C₈₉	1	2	yes	—
383	C₂×C₄	#124×C₈₉	1	2	yes	—
384	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
385	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
386	C₂×C₄	#137×C₈₉	1	2	yes	—
387	C₂×C₄	#137×C₈₉	1	2	yes	—
388	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
390	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
391	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
392	C₈	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	—	8	1	no	—
400	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
401	C₂²	C₂×#124×C₈₉	1	1	yes	characteristic
402	C₂²	#535×C₈₉	1	1	yes	characteristic
403	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
404	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
405	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
406	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	2	2	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	4	no	—
416	C₄	#489×C₈₉	1	4	yes	—
417	C₄	#554×C₈₉	1	2	yes	—
418	C₄	#555×C₈₉	1	2	yes	—
419	C₂	—	8	2	no	—
420	C₂	C₈₉×#2563	1	1	yes	characteristic
421	C₂	C₈₉×#3079	1	1	yes	characteristic
422	C₂	C₈₉×#3079	1	1	yes	characteristic
423	C₂	C₂×#489×C₈₉	1	1	yes	characteristic
424	C₂	C₈₉×#3141	1	1	yes	characteristic
425	C₂	C₈₉×#3217	1	1	yes	characteristic
426	C₂	C₈₉×#3218	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2868	C₂	semidirect
3. C₈₉×#2024	C₂	semidirect
6. C₈₉×#1836	C₂	semidirect
7. C₈₉×#1803	C₂	semidirect
9. C₈₉×#1767	C₂	semidirect
44. #124×C₈₉	Q₈	semidirect
205. #29148	C₈₉	direct (N × H)
214. #2868	C₂×C₈₉	semidirect
216. #2024	C₂×C₈₉	semidirect
219. #1836	C₂×C₈₉	semidirect
220. #1803	C₂×C₈₉	semidirect
222. #1767	C₂×C₈₉	semidirect
223. C₈₉	#29148	direct (N × H)
258. #124	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2868	2
C₄×#124×C₈₉	2
C₈₉×#2024	2
C₈₉×#2023	2
C₈₉×#1959	2
C₈₉×#1836	2
C₈₉×#1803	2
C₈₉×#1802	2
C₈₉×#1767	2
#29148	89

Subgroups — C89×#29148 #36406996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29148 #36406996