Subgroups — C₈₉×#29192 #36407040

Order 22784.

906 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2067	C₂	1	4	yes	maximal, complemented
4	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1862	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#125×C₈₉	—	2	1	no	—
12	C₂×C₄×D₄×C₈₉	—	2	1	no	—
13	C₂×C₄×D₄×C₈₉	—	2	1	no	—
14	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
15	C₂×#107×C₈₉	C₂²	1	4	yes	—
16	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#102×C₈₉	C₂²	1	4	yes	—
18	C₂×#102×C₈₉	C₂²	1	4	yes	—
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
21	#390×C₈₉	—	2	1	no	—
22	#390×C₈₉	—	2	1	no	—
23	#390×C₈₉	C₂²	1	2	yes	—
24	#389×C₈₉	—	2	1	no	—
25	#389×C₈₉	—	2	1	no	—
26	#389×C₈₉	C₂²	1	2	yes	—
27	#389×C₈₉	C₂²	1	2	yes	—
28	#384×C₈₉	C₂²	1	1	yes	characteristic
29	#384×C₈₉	C₂²	1	1	yes	characteristic
30	#384×C₈₉	C₂²	1	1	yes	characteristic
31	#382×C₈₉	—	2	1	no	—
32	C₄³×C₈₉	C₂²	1	1	yes	characteristic
33	#340×C₈₉	C₂²	1	4	yes	—
34	#336×C₈₉	C₂²	1	2	yes	—
35	C₂²×D₄×C₈₉	—	2	1	no	—
36	C₂²×D₄×C₈₉	—	2	1	no	—
37	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
38	C₂³×C₄×C₈₉	—	2	2	no	—
39	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
40	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
41	#127×C₈₉	—	2	2	no	—
42	#127×C₈₉	Q₈	1	4	yes	—
43	#125×C₈₉	—	4	4	no	—
44	C₄×D₄×C₈₉	—	4	4	no	—
45	C₄×D₄×C₈₉	—	4	4	no	—
46	C₄×D₄×C₈₉	—	4	4	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
51	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
61	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	#107×C₈₉	—	4	4	no	—
69	C₄⋊C₈×C₈₉	—	2	4	no	—
70	#102×C₈₉	—	2	8	no	—
71	#102×C₈₉	—	4	4	no	—
72	C₄×C₈×C₈₉	—	2	2	no	—
73	C₄×C₈×C₈₉	—	2	2	no	—
74	#95×C₈₉	—	2	2	no	—
75	#95×C₈₉	—	2	2	no	—
76	C₂⁴×C₈₉	—	2	2	no	—
77	C₂×D₄×C₈₉	—	2	4	no	—
78	C₂×D₄×C₈₉	—	2	4	no	—
79	C₂×D₄×C₈₉	—	2	4	no	—
80	C₂×D₄×C₈₉	—	2	2	no	—
81	C₂×D₄×C₈₉	—	2	4	no	—
82	C₂×D₄×C₈₉	—	4	2	no	—
83	C₂×D₄×C₈₉	—	4	2	no	—
84	C₂×D₄×C₈₉	—	4	2	no	—
85	C₂×D₄×C₈₉	—	4	2	no	—
86	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
87	C₂²×C₄×C₈₉	—	2	2	no	—
88	C₂²×C₄×C₈₉	—	2	2	no	—
89	C₂²×C₄×C₈₉	—	2	2	no	—
90	C₂²×C₄×C₈₉	—	4	4	no	—
91	C₂²×C₄×C₈₉	—	4	4	no	—
92	C₂²×C₄×C₈₉	—	4	4	no	—
93	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
100	C₂×C₈×C₈₉	—	2	2	no	—
101	C₂×C₈×C₈₉	—	2	2	no	—
102	C₂×C₈×C₈₉	—	2	2	no	—
103	C₂×C₈×C₈₉	—	2	2	no	—
104	C₂×C₈×C₈₉	—	2	2	no	—
105	C₂×C₈×C₈₉	#41	1	4	yes	—
106	C₄⋊C₄×C₈₉	—	2	4	no	—
107	C₄⋊C₄×C₈₉	—	2	4	no	—
108	C₄⋊C₄×C₈₉	—	2	4	no	—
109	C₄⋊C₄×C₈₉	—	4	2	no	—
110	C₄⋊C₄×C₈₉	—	4	4	no	—
111	C₄⋊C₄×C₈₉	—	4	4	no	—
112	C₄⋊C₄×C₈₉	—	4	2	no	—
113	C₄⋊C₄×C₈₉	—	4	2	no	—
114	C₄⋊C₄×C₈₉	—	4	2	no	—
115	C₄⋊C₄×C₈₉	—	4	2	no	—
116	C₄⋊C₄×C₈₉	—	4	2	no	—
117	C₂²⋊C₄×C₈₉	—	4	4	no	—
118	C₂²⋊C₄×C₈₉	—	4	4	no	—
119	C₂²⋊C₄×C₈₉	—	4	4	no	—
120	C₄²×C₈₉	—	2	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	D₈	1	4	yes	—
126	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
127	C₄²×C₈₉	#41	1	2	yes	—
128	C₂³×C₈₉	—	2	4	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	—	4	2	no	—
132	C₂³×C₈₉	—	4	2	no	—
133	C₂³×C₈₉	—	4	2	no	—
134	C₂³×C₈₉	—	4	2	no	—
135	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
136	D₄×C₈₉	—	2	8	no	—
137	D₄×C₈₉	—	4	4	no	—
138	D₄×C₈₉	—	4	8	no	—
139	D₄×C₈₉	—	4	8	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	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	—	4	2	no	—
151	C₂×C₄×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	—	4	2	no	—
155	C₂×C₄×C₈₉	—	4	2	no	—
156	C₂×C₄×C₈₉	—	4	2	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	8	8	no	—
160	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
162	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₈₉	#135	1	2	yes	—
166	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×C₄×C₈₉	#137	1	2	yes	—
168	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
171	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
172	C₈×C₈₉	—	2	4	no	—
173	C₈×C₈₉	—	4	2	no	—
174	C₂²×C₈₉	—	4	4	no	—
175	C₂²×C₈₉	—	4	4	no	—
176	C₂²×C₈₉	—	4	4	no	—
177	C₂²×C₈₉	—	8	2	no	—
178	C₂²×C₈₉	—	8	2	no	—
179	C₂²×C₈₉	—	8	2	no	—
180	C₂²×C₈₉	—	8	2	no	—
181	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₂²×C₈₉	#532	1	1	yes	characteristic
183	C₂²×C₈₉	#535	1	1	yes	characteristic
184	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
185	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
186	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	4	1	no	—
191	C₄×C₈₉	—	4	1	no	—
192	C₄×C₈₉	—	8	2	no	—
193	C₄×C₈₉	—	8	2	no	—
194	C₄×C₈₉	—	8	2	no	—
195	C₄×C₈₉	#474	1	4	yes	—
196	C₄×C₈₉	#478	1	4	yes	—
197	C₄×C₈₉	#553	1	2	yes	—
198	C₄×C₈₉	#554	1	2	yes	—
199	#29192	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₈₉	—	8	4	no	—
201	C₂×C₈₉	#2566	1	1	yes	characteristic
202	C₂×C₈₉	C₂×#474	1	1	yes	characteristic
203	C₂×C₈₉	C₂×#478	1	1	yes	characteristic
204	C₂×C₈₉	#3169	1	1	yes	characteristic
205	C₂×C₈₉	#3182	1	1	yes	characteristic
206	C₂×C₈₉	#3205	1	1	yes	characteristic
207	C₂×C₈₉	#3210	1	1	yes	characteristic
208	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
209	C₄×#127	C₂×C₈₉	1	1	yes	characteristic
210	#2067	C₂×C₈₉	1	4	yes	complemented
211	#1957	C₂×C₈₉	1	1	yes	characteristic
212	#1957	C₂×C₈₉	1	1	yes	characteristic
213	#1862	C₂×C₈₉	1	4	yes	complemented
214	#1845	C₂×C₈₉	1	1	yes	characteristic, complemented
215	#1834	C₂×C₈₉	1	1	yes	characteristic, complemented
216	C₄×C₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic, complemented
217	C₈₉	#29192	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
219	C₂×#125	—	2	1	no	—
220	C₂×C₄×D₄	—	2	1	no	—
221	C₂×C₄×D₄	—	2	1	no	—
222	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
223	C₂×#107	C₂²×C₈₉	1	4	yes	—
224	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
225	C₂×#102	C₂²×C₈₉	1	4	yes	—
226	C₂×#102	C₂²×C₈₉	1	4	yes	—
227	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
229	#390	—	2	1	no	—
230	#390	—	2	1	no	—
231	#390	C₂²×C₈₉	1	2	yes	—
232	#389	—	2	1	no	—
233	#389	—	2	1	no	—
234	#389	C₂²×C₈₉	1	2	yes	—
235	#389	C₂²×C₈₉	1	2	yes	—
236	#384	C₂²×C₈₉	1	1	yes	characteristic
237	#384	C₂²×C₈₉	1	1	yes	characteristic
238	#384	C₂²×C₈₉	1	1	yes	characteristic
239	#382	—	2	1	no	—
240	C₄³	C₂²×C₈₉	1	1	yes	characteristic
241	#340	C₂²×C₈₉	1	4	yes	—
242	#336	C₂²×C₈₉	1	2	yes	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
246	C₂³×C₄	—	2	2	no	—
247	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
248	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
249	#127	—	2	2	no	—
250	#127	Q₈×C₈₉	1	4	yes	—
251	#125	—	4	4	no	—
252	C₄×D₄	—	4	4	no	—
253	C₄×D₄	—	4	4	no	—
254	C₄×D₄	—	4	4	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
271	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
272	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
276	#107	—	4	4	no	—
277	C₄⋊C₈	—	2	4	no	—
278	#102	—	2	8	no	—
279	#102	—	4	4	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	C₂⁴	—	2	2	no	—
285	C₂×D₄	—	2	4	no	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	4	4	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	#41×C₈₉	1	4	yes	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	D₈×C₈₉	1	4	yes	—
334	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
335	C₄²	#41×C₈₉	1	2	yes	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
344	D₄	—	2	8	no	—
345	D₄	—	4	8	no	—
346	D₄	—	4	8	no	—
347	D₄	—	4	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	8	no	—
368	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
369	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
370	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
371	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
372	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
373	C₂×C₄	#135×C₈₉	1	2	yes	—
374	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
375	C₂×C₄	#137×C₈₉	1	2	yes	—
376	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
377	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	2	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
390	C₂²	#532×C₈₉	1	1	yes	characteristic
391	C₂²	#535×C₈₉	1	1	yes	characteristic
392	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
393	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
394	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
395	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	4	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	2	no	—
403	C₄	#474×C₈₉	1	4	yes	—
404	C₄	#478×C₈₉	1	4	yes	—
405	C₄	#553×C₈₉	1	2	yes	—
406	C₄	#554×C₈₉	1	2	yes	—
407	C₂	—	8	4	no	—
408	C₂	C₈₉×#2566	1	1	yes	characteristic
409	C₂	C₂×#474×C₈₉	1	1	yes	characteristic
410	C₂	C₂×#478×C₈₉	1	1	yes	characteristic
411	C₂	C₈₉×#3169	1	1	yes	characteristic
412	C₂	C₈₉×#3182	1	1	yes	characteristic
413	C₂	C₈₉×#3205	1	1	yes	characteristic
414	C₂	C₈₉×#3210	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#127×C₈₉	C₂²
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×#2859	C₂	semidirect
3. C₈₉×#2067	C₂	semidirect
6. C₈₉×#1862	C₂	semidirect
7. C₈₉×#1845	C₂	semidirect
8. C₈₉×#1834	C₂	semidirect
9. C₄×C₄⋊C₈×C₈₉	C₂	semidirect
199. #29192	C₈₉	direct (N × H)
208. #2859	C₂×C₈₉	semidirect
210. #2067	C₂×C₈₉	semidirect
213. #1862	C₂×C₈₉	semidirect
214. #1845	C₂×C₈₉	semidirect
215. #1834	C₂×C₈₉	semidirect
216. C₄×C₄⋊C₈	C₂×C₈₉	semidirect
217. C₈₉	#29192	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2859	2
C₄×#127×C₈₉	2
C₈₉×#2067	2
C₈₉×#1957	2
C₈₉×#1862	2
C₈₉×#1845	2
C₈₉×#1834	2
C₄×C₄⋊C₈×C₈₉	2
#29192	89

Subgroups — C89×#29192 #36407040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29192 #36407040