Subgroups — C₂×C₈₉×#2855 #36414468

Order 22784.

3246 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄²×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2855	C₂	1	16	yes	maximal, direct product factor
4	C₂×#391×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#389×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#387×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂×#385×C₈₉	C₂	1	2	yes	maximal
8	C₂×#381×C₈₉	C₂	1	2	yes	maximal
9	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₈₉	—	2	8	no	—
15	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₈₉	—	2	8	no	—
23	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
24	C₂²×C₄²×C₈₉	C₂²	1	8	yes	—
25	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
26	#391×C₈₉	C₂²	1	16	yes	complemented
27	#389×C₈₉	C₂²	1	16	yes	complemented
28	#387×C₈₉	C₂²	1	32	yes	complemented
29	#385×C₈₉	C₂²	1	16	yes	—
30	#381×C₈₉	C₂²	1	16	yes	—
31	#380×C₈₉	C₂²	1	8	yes	—
32	C₂×#95×C₈₉	C₂²	1	4	yes	—
33	C₂×#95×C₈₉	C₂²	1	4	yes	—
34	C₂×#95×C₈₉	C₂²	1	2	yes	—
35	C₂×#95×C₈₉	C₂²	1	4	yes	—
36	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
37	C₂²×Q₈×C₈₉	—	2	4	no	—
38	C₂²×Q₈×C₈₉	—	2	8	no	—
39	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
40	C₂³×C₄×C₈₉	—	2	4	no	—
41	C₂³×C₄×C₈₉	—	2	4	no	—
42	C₂³×C₄×C₈₉	—	2	4	no	—
43	C₂³×C₄×C₈₉	—	2	8	no	—
44	C₂³×C₄×C₈₉	—	2	8	no	—
45	C₂³×C₄×C₈₉	D₄	1	8	yes	—
46	C₂³×C₄×C₈₉	Q₈	1	8	yes	complemented
47	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₈₉	—	2	32	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
67	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
68	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
70	C₂×C₄²×C₈₉	—	2	8	no	—
71	C₂×C₄²×C₈₉	—	2	32	no	—
72	C₂×C₄²×C₈₉	—	2	8	no	—
73	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
74	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
75	#95×C₈₉	C₂³	1	8	yes	—
76	#95×C₈₉	C₂³	1	16	yes	—
77	#95×C₈₉	C₂³	1	16	yes	—
78	#95×C₈₉	C₂³	1	16	yes	—
79	C₂⁴×C₈₉	—	2	4	no	—
80	C₂⁴×C₈₉	—	2	4	no	—
81	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
82	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
83	C₂⁴×C₈₉	#41	1	4	yes	—
84	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
85	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
86	C₂×Q₈×C₈₉	—	2	8	no	—
87	C₂×Q₈×C₈₉	—	2	16	no	—
88	C₂×Q₈×C₈₉	—	4	16	no	—
89	C₂²×C₄×C₈₉	—	2	32	no	—
90	C₂²×C₄×C₈₉	—	2	32	no	—
91	C₂²×C₄×C₈₉	—	2	8	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	2	8	no	—
94	C₂²×C₄×C₈₉	—	2	4	no	—
95	C₂²×C₄×C₈₉	—	2	4	no	—
96	C₂²×C₄×C₈₉	—	2	8	no	—
97	C₂²×C₄×C₈₉	—	2	4	no	—
98	C₂²×C₄×C₈₉	—	2	4	no	—
99	C₂²×C₄×C₈₉	—	2	32	no	—
100	C₂²×C₄×C₈₉	—	2	16	no	—
101	C₂²×C₄×C₈₉	—	2	16	no	—
102	C₂²×C₄×C₈₉	—	2	4	no	—
103	C₂²×C₄×C₈₉	—	2	4	no	—
104	C₂²×C₄×C₈₉	—	2	8	no	—
105	C₂²×C₄×C₈₉	—	2	8	no	—
106	C₂²×C₄×C₈₉	—	2	8	no	—
107	C₂²×C₄×C₈₉	—	2	8	no	—
108	C₂²×C₄×C₈₉	—	2	8	no	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
112	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₈₉	C₂×Q₈	1	16	yes	complemented
114	C₂²×C₄×C₈₉	#41	1	8	yes	—
115	C₂²×C₄×C₈₉	#41	1	8	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
123	C₄⋊C₄×C₈₉	—	2	8	no	—
124	C₄⋊C₄×C₈₉	—	2	16	no	—
125	C₄⋊C₄×C₈₉	—	2	32	no	—
126	C₄⋊C₄×C₈₉	—	2	16	no	—
127	C₂²⋊C₄×C₈₉	—	2	16	no	—
128	C₂²⋊C₄×C₈₉	—	2	16	no	—
129	C₄²×C₈₉	—	2	16	no	—
130	C₄²×C₈₉	—	2	16	no	—
131	C₂³×C₈₉	—	2	8	no	—
132	C₂³×C₈₉	—	2	8	no	—
133	C₂³×C₈₉	—	2	16	no	—
134	C₂³×C₈₉	—	2	16	no	—
135	C₂³×C₈₉	—	2	4	no	—
136	C₂³×C₈₉	—	2	4	no	—
137	C₂³×C₈₉	C₂²⋊Q₈	1	16	yes	—
138	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
139	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
140	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
141	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
142	C₂³×C₈₉	C₂×#41	1	4	yes	—
143	C₂³×C₈₉	C₂×#41	1	2	yes	—
144	C₂³×C₈₉	C₂×#41	1	4	yes	—
145	C₂³×C₈₉	C₂×#41	1	4	yes	—
146	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
147	Q₈×C₈₉	—	4	16	no	—
148	C₂×C₄×C₈₉	—	2	32	no	—
149	C₂×C₄×C₈₉	—	2	16	no	—
150	C₂×C₄×C₈₉	—	2	32	no	—
151	C₂×C₄×C₈₉	—	2	8	no	—
152	C₂×C₄×C₈₉	—	2	16	no	—
153	C₂×C₄×C₈₉	—	2	4	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	4	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	2	32	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	4	no	—
161	C₂×C₄×C₈₉	—	2	8	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	8	no	—
166	C₂×C₄×C₈₉	—	4	8	no	—
167	C₂×C₄×C₈₉	—	4	8	no	—
168	C₂×C₄×C₈₉	—	4	16	no	—
169	C₂×C₄×C₈₉	#123	1	16	yes	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
171	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
172	C₂×C₄×C₈₉	C₂²×Q₈	1	8	yes	—
173	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
174	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
175	C₂²×C₈₉	—	2	32	no	—
176	C₂²×C₈₉	—	2	4	no	—
177	C₂²×C₈₉	—	2	4	no	—
178	C₂²×C₈₉	—	2	8	no	—
179	C₂²×C₈₉	—	2	8	no	—
180	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	8	yes	—
181	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
182	C₂²×C₈₉	C₂×#123	1	4	yes	—
183	C₂²×C₈₉	#525	1	4	yes	—
184	C₂²×C₈₉	#529	1	8	yes	—
185	C₂²×C₈₉	#533	1	8	yes	—
186	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
187	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
188	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
189	C₂²×C₈₉	C₂²×#41	1	2	yes	—
190	C₂²×C₈₉	C₂²×#41	1	2	yes	—
191	C₄×C₈₉	—	2	8	no	—
192	C₄×C₈₉	—	2	4	no	—
193	C₄×C₈₉	—	2	8	no	—
194	C₄×C₈₉	—	4	4	no	—
195	C₄×C₈₉	—	4	4	no	—
196	C₄×C₈₉	—	4	8	no	—
197	C₄×C₈₉	C₂×#123	1	8	yes	—
198	C₂×#2855	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₈₉	—	2	8	no	—
200	C₂×C₈₉	#2855	1	8	yes	direct product factor
201	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
202	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
203	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
204	C₂×C₈₉	C₂×#529	1	2	yes	—
205	C₂×C₈₉	C₂×#533	1	2	yes	—
206	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
207	C₂³×C₄²	C₂×C₈₉	1	1	yes	characteristic
208	#2855	C₂×C₈₉	1	16	yes	direct product factor
209	C₂×#391	C₂×C₈₉	1	2	yes	complemented
210	C₂×#389	C₂×C₈₉	1	2	yes	complemented
211	C₂×#387	C₂×C₈₉	1	4	yes	complemented
212	C₂×#385	C₂×C₈₉	1	2	yes	—
213	C₂×#381	C₂×C₈₉	1	2	yes	—
214	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
215	C₈₉	C₂×#2855	1	1	yes	characteristic, direct product factor, Sylow
216	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
217	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
218	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
219	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	—	2	8	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	—
222	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
224	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
226	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
228	C₂²×C₄²	—	2	8	no	—
229	C₂²×C₄²	C₂²×C₈₉	1	8	yes	—
230	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
231	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
232	#391	C₂²×C₈₉	1	16	yes	complemented
233	#389	C₂²×C₈₉	1	16	yes	complemented
234	#387	C₂²×C₈₉	1	32	yes	complemented
235	#385	C₂²×C₈₉	1	16	yes	—
236	#381	C₂²×C₈₉	1	16	yes	—
237	#380	C₂²×C₈₉	1	8	yes	—
238	C₂×#95	C₂²×C₈₉	1	2	yes	—
239	C₂×#95	C₂²×C₈₉	1	4	yes	—
240	C₂×#95	C₂²×C₈₉	1	4	yes	—
241	C₂×#95	C₂²×C₈₉	1	4	yes	—
242	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
243	C₂²×Q₈	—	2	4	no	—
244	C₂²×Q₈	—	2	8	no	—
245	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	4	no	—
249	C₂³×C₄	—	2	8	no	—
250	C₂³×C₄	—	2	8	no	—
251	C₂³×C₄	D₄×C₈₉	1	8	yes	—
252	C₂³×C₄	Q₈×C₈₉	1	8	yes	complemented
253	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
254	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
255	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
257	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
259	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
261	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
262	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
263	C₂²⋊Q₈	—	2	32	no	—
264	C₂×C₄⋊C₄	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	8	no	—
266	C₂×C₄⋊C₄	—	2	16	no	—
267	C₂×C₄⋊C₄	—	2	8	no	—
268	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
269	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
271	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
272	C₂×C₂²⋊C₄	—	2	8	no	—
273	C₂×C₂²⋊C₄	—	2	8	no	—
274	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
275	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
276	C₂×C₄²	—	2	8	no	—
277	C₂×C₄²	—	2	32	no	—
278	C₂×C₄²	—	2	8	no	—
279	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
280	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
281	#95	C₂³×C₈₉	1	8	yes	—
282	#95	C₂³×C₈₉	1	16	yes	—
283	#95	C₂³×C₈₉	1	16	yes	—
284	#95	C₂³×C₈₉	1	16	yes	—
285	C₂⁴	—	2	4	no	—
286	C₂⁴	—	2	4	no	—
287	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
288	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
289	C₂⁴	#41×C₈₉	1	4	yes	—
290	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
291	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	4	16	no	—
295	C₂²×C₄	—	2	32	no	—
296	C₂²×C₄	—	2	32	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	8	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	32	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	16	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	8	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	8	no	—
314	C₂²×C₄	—	2	8	no	—
315	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
316	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	—
317	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
318	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
319	C₂²×C₄	C₂×Q₈×C₈₉	1	16	yes	complemented
320	C₂²×C₄	#41×C₈₉	1	8	yes	—
321	C₂²×C₄	#41×C₈₉	1	8	yes	—
322	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
323	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
324	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
328	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	16	no	—
331	C₄⋊C₄	—	2	32	no	—
332	C₄⋊C₄	—	2	16	no	—
333	C₂²⋊C₄	—	2	16	no	—
334	C₂²⋊C₄	—	2	16	no	—
335	C₄²	—	2	16	no	—
336	C₄²	—	2	16	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	16	no	—
340	C₂³	—	2	16	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	C₂²⋊Q₈×C₈₉	1	16	yes	—
344	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
345	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
346	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
347	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
348	C₂³	C₂×#41×C₈₉	1	4	yes	—
349	C₂³	C₂×#41×C₈₉	1	2	yes	—
350	C₂³	C₂×#41×C₈₉	1	4	yes	—
351	C₂³	C₂×#41×C₈₉	1	4	yes	—
352	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
353	Q₈	—	4	16	no	—
354	C₂×C₄	—	2	32	no	—
355	C₂×C₄	—	2	16	no	—
356	C₂×C₄	—	2	32	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	16	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	32	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	8	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	8	no	—
374	C₂×C₄	—	4	16	no	—
375	C₂×C₄	#123×C₈₉	1	16	yes	—
376	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
378	C₂×C₄	C₂²×Q₈×C₈₉	1	8	yes	—
379	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
380	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
381	C₂²	—	2	32	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	4	no	—
384	C₂²	—	2	8	no	—
385	C₂²	—	2	8	no	—
386	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	8	yes	—
387	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
388	C₂²	C₂×#123×C₈₉	1	4	yes	—
389	C₂²	#525×C₈₉	1	4	yes	—
390	C₂²	#529×C₈₉	1	8	yes	—
391	C₂²	#533×C₈₉	1	8	yes	—
392	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
393	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
394	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
395	C₂²	C₂²×#41×C₈₉	1	2	yes	—
396	C₂²	C₂²×#41×C₈₉	1	2	yes	—
397	C₄	—	2	8	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	8	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	4	no	—
402	C₄	—	4	8	no	—
403	C₄	C₂×#123×C₈₉	1	8	yes	—
404	C₂	—	2	8	no	—
405	C₂	C₈₉×#2855	1	8	yes	direct product factor
406	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
407	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
408	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
409	C₂	C₂×#529×C₈₉	1	2	yes	—
410	C₂	C₂×#533×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₈₉×#2855	C₂	direct (N × H)
4. C₂×#391×C₈₉	C₂	semidirect
5. C₂×#389×C₈₉	C₂	semidirect
6. C₂×#387×C₈₉	C₂	semidirect
26. #391×C₈₉	C₂²	semidirect
27. #389×C₈₉	C₂²	semidirect
28. #387×C₈₉	C₂²	semidirect
46. C₂³×C₄×C₈₉	Q₈	semidirect
113. C₂²×C₄×C₈₉	C₂×Q₈	semidirect
198. C₂×#2855	C₈₉	direct (N × H)
200. C₂×C₈₉	#2855	direct (N × H)
208. #2855	C₂×C₈₉	direct (N × H)
209. C₂×#391	C₂×C₈₉	semidirect
210. C₂×#389	C₂×C₈₉	semidirect
211. C₂×#387	C₂×C₈₉	semidirect
215. C₈₉	C₂×#2855	direct (N × H)
232. #391	C₂²×C₈₉	semidirect
233. #389	C₂²×C₈₉	semidirect
234. #387	C₂²×C₈₉	semidirect
252. C₂³×C₄	Q₈×C₈₉	semidirect
319. C₂²×C₄	C₂×Q₈×C₈₉	semidirect
405. C₂	C₈₉×#2855	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₈₉	2
C₂³×C₄²×C₈₉	2
C₈₉×#2855	2
C₂×#391×C₈₉	2
C₂×#389×C₈₉	2
C₂×#387×C₈₉	2
C₂×#385×C₈₉	2
C₂×#381×C₈₉	2
C₂×#380×C₈₉	2
C₂×#2855	89

Subgroups — C2×C89×#2855 #36414468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2855 #36414468