Subgroups — C₈₉×#35334 #36413182

Order 22784.

2326 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	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2851	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2628	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2581	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2580	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2564	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2316	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2311	C₂	1	2	yes	maximal
10	C₂×#382×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
12	#533×C₈₉	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
14	C₂×#125×C₈₉	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
16	C₄×#41×C₈₉	—	2	8	no	—
17	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
20	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
21	C₂×#117×C₈₉	C₂²	1	2	yes	—
22	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#117×C₈₉	C₂²	1	2	yes	—
24	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
27	#400×C₈₉	C₂²	1	8	yes	—
28	#399×C₈₉	C₂²	1	8	yes	—
29	#395×C₈₉	C₂²	1	8	yes	—
30	#393×C₈₉	C₂²	1	8	yes	—
31	#391×C₈₉	C₂²	1	4	yes	—
32	#390×C₈₉	C₂²	1	4	yes	—
33	#389×C₈₉	C₂²	1	8	yes	—
34	#389×C₈₉	C₂²	1	8	yes	—
35	#387×C₈₉	C₂²	1	16	yes	—
36	#386×C₈₉	C₂²	1	8	yes	—
37	#385×C₈₉	C₂²	1	16	yes	—
38	#382×C₈₉	C₂²	1	4	yes	—
39	#382×C₈₉	C₂²	1	2	yes	—
40	#382×C₈₉	C₂²	1	2	yes	—
41	#380×C₈₉	C₂²	1	8	yes	—
42	#380×C₈₉	C₂²	1	8	yes	—
43	C₂×#95×C₈₉	C₂²	1	4	yes	—
44	C₂×#41×C₈₉	—	2	4	no	—
45	C₂×#41×C₈₉	—	2	4	no	—
46	C₂×#41×C₈₉	Q₈	1	8	yes	complemented
47	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
50	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	—	2	8	no	—
57	#125×C₈₉	—	2	8	no	—
58	C₂²⋊Q₈×C₈₉	—	2	16	no	—
59	C₄×Q₈×C₈₉	—	2	8	no	—
60	C₄×Q₈×C₈₉	—	2	16	no	—
61	C₄×D₄×C₈₉	—	2	16	no	—
62	C₄×D₄×C₈₉	—	2	8	no	—
63	#117×C₈₉	—	2	4	no	—
64	#117×C₈₉	—	2	8	no	—
65	#117×C₈₉	—	2	8	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
79	C₂×C₄²×C₈₉	—	2	8	no	—
80	C₂×C₄²×C₈₉	D₄	1	8	yes	—
81	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
87	#95×C₈₉	C₂³	1	8	yes	—
88	#95×C₈₉	C₂³	1	8	yes	—
89	#95×C₈₉	C₂³	1	16	yes	—
90	#95×C₈₉	C₂³	1	16	yes	—
91	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
92	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
93	#41×C₈₉	—	2	32	no	—
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	8	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	4	8	no	—
98	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
99	C₂×D₄×C₈₉	—	2	4	no	—
100	C₂×D₄×C₈₉	—	2	4	no	—
101	C₂×D₄×C₈₉	—	2	2	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
104	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
105	C₂²×C₄×C₈₉	—	2	4	no	—
106	C₂²×C₄×C₈₉	—	2	4	no	—
107	C₂²×C₄×C₈₉	—	2	8	no	—
108	C₂²×C₄×C₈₉	—	2	8	no	—
109	C₂²×C₄×C₈₉	—	4	4	no	—
110	C₂²×C₄×C₈₉	—	4	8	no	—
111	C₂²×C₄×C₈₉	—	4	8	no	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
115	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
116	C₂²×C₄×C₈₉	#41	1	4	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
123	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
125	C₄⋊C₄×C₈₉	—	2	8	no	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	2	8	no	—
128	C₄⋊C₄×C₈₉	—	2	16	no	—
129	C₄⋊C₄×C₈₉	—	2	8	no	—
130	C₄⋊C₄×C₈₉	—	2	8	no	—
131	C₄⋊C₄×C₈₉	—	2	8	no	—
132	C₄⋊C₄×C₈₉	—	4	16	no	—
133	C₂²⋊C₄×C₈₉	—	2	4	no	—
134	C₂²⋊C₄×C₈₉	—	2	8	no	—
135	C₂²⋊C₄×C₈₉	—	2	8	no	—
136	C₂²⋊C₄×C₈₉	—	4	16	no	—
137	C₄²×C₈₉	—	2	4	no	—
138	C₄²×C₈₉	—	2	8	no	—
139	C₄²×C₈₉	—	2	8	no	—
140	C₄²×C₈₉	C₂×D₄	1	4	yes	—
141	C₄²×C₈₉	C₂×D₄	1	4	yes	—
142	C₄²×C₈₉	C₂×D₄	1	8	yes	—
143	C₂³×C₈₉	—	2	4	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	—	2	2	no	—
146	C₂³×C₈₉	—	2	8	no	—
147	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
148	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
149	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
150	C₂³×C₈₉	C₂×#41	1	2	yes	—
151	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
152	Q₈×C₈₉	—	2	8	no	—
153	Q₈×C₈₉	—	4	16	no	—
154	D₄×C₈₉	—	2	16	no	—
155	D₄×C₈₉	—	2	8	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	16	no	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	8	no	—
163	C₂×C₄×C₈₉	—	2	8	no	—
164	C₂×C₄×C₈₉	—	2	8	no	—
165	C₂×C₄×C₈₉	—	2	16	no	—
166	C₂×C₄×C₈₉	—	2	8	no	—
167	C₂×C₄×C₈₉	—	2	8	no	—
168	C₂×C₄×C₈₉	—	4	8	no	—
169	C₂×C₄×C₈₉	—	4	16	no	—
170	C₂×C₄×C₈₉	—	8	8	no	—
171	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	—
172	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
173	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
174	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
177	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
178	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
179	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
180	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
181	C₂²×C₈₉	—	2	4	no	—
182	C₂²×C₈₉	—	2	4	no	—
183	C₂²×C₈₉	—	2	4	no	—
184	C₂²×C₈₉	—	2	4	no	—
185	C₂²×C₈₉	—	2	8	no	—
186	C₂²×C₈₉	—	4	4	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
189	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
190	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
191	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
192	C₂²×C₈₉	#585	1	4	yes	—
193	C₄×C₈₉	—	2	4	no	—
194	C₄×C₈₉	—	2	4	no	—
195	C₄×C₈₉	—	2	4	no	—
196	C₄×C₈₉	—	4	4	no	—
197	C₄×C₈₉	—	4	8	no	—
198	C₄×C₈₉	—	4	8	no	—
199	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
200	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
201	#35334	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₈₉	—	2	4	no	—
203	C₂×C₈₉	—	4	4	no	—
204	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
205	C₂×C₈₉	#3449	1	2	yes	—
206	C₂×C₈₉	#3504	1	2	yes	—
207	C₂×C₈₉	#3510	1	2	yes	—
208	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
209	C₂×C₄×#41	C₂×C₈₉	1	1	yes	characteristic
210	#2851	C₂×C₈₉	1	4	yes	complemented
211	#2628	C₂×C₈₉	1	4	yes	complemented
212	#2581	C₂×C₈₉	1	4	yes	complemented
213	#2580	C₂×C₈₉	1	4	yes	complemented
214	#2564	C₂×C₈₉	1	8	yes	complemented
215	#2316	C₂×C₈₉	1	2	yes	complemented
216	#2311	C₂×C₈₉	1	2	yes	—
217	C₂×#382	C₂×C₈₉	1	1	yes	characteristic, complemented
218	C₈₉	#35334	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
220	#533	—	2	8	no	—
221	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
222	C₂×#125	C₂²×C₈₉	1	2	yes	—
223	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
224	C₄×#41	—	2	8	no	—
225	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
226	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
227	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
228	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
229	C₂×#117	C₂²×C₈₉	1	2	yes	—
230	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
231	C₂×#117	C₂²×C₈₉	1	2	yes	—
232	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
233	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
234	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
235	#400	C₂²×C₈₉	1	8	yes	—
236	#399	C₂²×C₈₉	1	8	yes	—
237	#395	C₂²×C₈₉	1	8	yes	—
238	#393	C₂²×C₈₉	1	8	yes	—
239	#391	C₂²×C₈₉	1	4	yes	—
240	#390	C₂²×C₈₉	1	4	yes	—
241	#389	C₂²×C₈₉	1	8	yes	—
242	#389	C₂²×C₈₉	1	8	yes	—
243	#387	C₂²×C₈₉	1	16	yes	—
244	#386	C₂²×C₈₉	1	8	yes	—
245	#385	C₂²×C₈₉	1	16	yes	—
246	#382	C₂²×C₈₉	1	4	yes	—
247	#382	C₂²×C₈₉	1	2	yes	—
248	#382	C₂²×C₈₉	1	2	yes	—
249	#380	C₂²×C₈₉	1	8	yes	—
250	#380	C₂²×C₈₉	1	8	yes	—
251	C₂×#95	C₂²×C₈₉	1	4	yes	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	Q₈×C₈₉	1	8	yes	complemented
255	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
257	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
258	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
261	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
262	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
263	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
264	C₄⋊Q₈	—	2	8	no	—
265	#125	—	2	8	no	—
266	C₂²⋊Q₈	—	2	16	no	—
267	C₄×Q₈	—	2	8	no	—
268	C₄×Q₈	—	2	16	no	—
269	C₄×D₄	—	2	16	no	—
270	C₄×D₄	—	2	8	no	—
271	#117	—	2	4	no	—
272	#117	—	2	8	no	—
273	#117	—	2	8	no	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
287	C₂×C₄²	—	2	8	no	—
288	C₂×C₄²	D₄×C₈₉	1	8	yes	—
289	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
291	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
292	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
293	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
295	#95	C₂³×C₈₉	1	8	yes	—
296	#95	C₂³×C₈₉	1	8	yes	—
297	#95	C₂³×C₈₉	1	16	yes	—
298	#95	C₂³×C₈₉	1	16	yes	—
299	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
300	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
301	#41	—	2	32	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	8	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	8	no	—
306	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
312	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	8	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	—	4	4	no	—
318	C₂²×C₄	—	4	8	no	—
319	C₂²×C₄	—	4	8	no	—
320	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
321	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
322	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
323	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
324	C₂²×C₄	#41×C₈₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
326	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
328	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
330	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	16	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	8	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	4	16	no	—
341	C₂²⋊C₄	—	2	4	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	4	16	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	2	8	no	—
348	C₄²	C₂×D₄×C₈₉	1	4	yes	—
349	C₄²	C₂×D₄×C₈₉	1	4	yes	—
350	C₄²	C₂×D₄×C₈₉	1	8	yes	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	8	no	—
355	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
356	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
357	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
358	C₂³	C₂×#41×C₈₉	1	2	yes	—
359	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
360	Q₈	—	2	8	no	—
361	Q₈	—	4	16	no	—
362	D₄	—	2	16	no	—
363	D₄	—	2	8	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	16	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	8	no	—
373	C₂×C₄	—	2	16	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	8	no	—
377	C₂×C₄	—	4	16	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	—
380	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
381	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
382	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
383	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
384	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
385	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
386	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
387	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
388	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	8	no	—
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
397	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
398	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
399	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
400	C₂²	#585×C₈₉	1	4	yes	—
401	C₄	—	2	4	no	—
402	C₄	—	2	4	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	8	no	—
406	C₄	—	4	8	no	—
407	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
408	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
409	C₂	—	2	4	no	—
410	C₂	—	4	4	no	—
411	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
412	C₂	C₈₉×#3449	1	2	yes	—
413	C₂	C₈₉×#3504	1	2	yes	—
414	C₂	C₈₉×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#2851	C₂	semidirect
4. C₈₉×#2628	C₂	semidirect
5. C₈₉×#2581	C₂	semidirect
6. C₈₉×#2580	C₂	semidirect
7. C₈₉×#2564	C₂	semidirect
8. C₈₉×#2316	C₂	semidirect
10. C₂×#382×C₈₉	C₂	semidirect
46. C₂×#41×C₈₉	Q₈	semidirect
201. #35334	C₈₉	direct (N × H)
208. C₂×#533	C₂×C₈₉	semidirect
210. #2851	C₂×C₈₉	semidirect
211. #2628	C₂×C₈₉	semidirect
212. #2581	C₂×C₈₉	semidirect
213. #2580	C₂×C₈₉	semidirect
214. #2564	C₂×C₈₉	semidirect
215. #2316	C₂×C₈₉	semidirect
217. C₂×#382	C₂×C₈₉	semidirect
218. C₈₉	#35334	direct (N × H)
254. C₂×#41	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×#533×C₈₉	2
C₂×C₄×#41×C₈₉	2
C₈₉×#2851	2
C₈₉×#2628	2
C₈₉×#2581	2
C₈₉×#2580	2
C₈₉×#2564	2
C₈₉×#2316	2
C₈₉×#2311	2
C₂×#382×C₈₉	2
#35334	89

Subgroups — C89×#35334 #36413182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35334 #36413182