Subgroups — C₂×C₈₉×#2605 #36412708

Order 22784.

2094 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2605	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400×C₈₉	C₂	1	2	yes	maximal
3	C₂×#395×C₈₉	C₂	1	2	yes	maximal
4	C₂×#391×C₈₉	C₂	1	2	yes	maximal
5	C₂×#391×C₈₉	C₂	1	2	yes	maximal
6	C₂×#387×C₈₉	C₂	1	2	yes	maximal
7	C₂×#387×C₈₉	C₂	1	2	yes	maximal
8	C₂×#383×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#376×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
13	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
16	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
20	#400×C₈₉	C₂²	1	16	yes	—
21	#395×C₈₉	C₂²	1	16	yes	—
22	#391×C₈₉	C₂²	1	16	yes	—
23	#391×C₈₉	C₂²	1	16	yes	—
24	#387×C₈₉	C₂²	1	16	yes	—
25	#387×C₈₉	C₂²	1	16	yes	—
26	#383×C₈₉	C₂²	1	8	yes	—
27	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
28	#376×C₈₉	C₂²	1	8	yes	—
29	C₂×#95×C₈₉	C₂²	1	2	yes	—
30	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#95×C₈₉	C₂²	1	2	yes	—
32	C₂×#95×C₈₉	C₂²	1	2	yes	—
33	C₂×#95×C₈₉	C₂²	1	2	yes	—
34	C₂×#95×C₈₉	C₂²	1	2	yes	—
35	C₂×#95×C₈₉	C₂²	1	2	yes	—
36	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#95×C₈₉	C₂²	1	2	yes	—
38	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×#95×C₈₉	C₂²	1	2	yes	—
40	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₈₉	—	2	8	no	—
42	C₂²×Q₈×C₈₉	—	2	8	no	—
43	C₂²×Q₈×C₈₉	—	4	4	no	—
44	C₂²×Q₈×C₈₉	C₂³	1	8	yes	—
45	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
56	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
57	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
62	C₂×C₄²×C₈₉	—	2	8	no	—
63	C₂×C₄²×C₈₉	—	4	2	no	—
64	C₂×C₄²×C₈₉	—	4	2	no	—
65	C₂×C₄²×C₈₉	Q₈	1	8	yes	complemented
66	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
67	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
70	#95×C₈₉	C₂³	1	8	yes	—
71	#95×C₈₉	C₂³	1	4	yes	—
72	#95×C₈₉	C₂³	1	4	yes	—
73	#95×C₈₉	C₂³	1	8	yes	—
74	#95×C₈₉	C₂³	1	4	yes	—
75	#95×C₈₉	C₂³	1	8	yes	—
76	#95×C₈₉	C₂³	1	4	yes	—
77	#95×C₈₉	C₂³	1	8	yes	—
78	#95×C₈₉	C₂³	1	8	yes	—
79	#95×C₈₉	C₂³	1	8	yes	—
80	#95×C₈₉	C₂³	1	8	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
83	C₂×Q₈×C₈₉	—	2	16	no	—
84	C₂×Q₈×C₈₉	—	2	16	no	—
85	C₂×Q₈×C₈₉	—	4	8	no	—
86	C₂×Q₈×C₈₉	—	4	32	no	—
87	C₂²×C₄×C₈₉	—	2	4	no	—
88	C₂²×C₄×C₈₉	—	2	4	no	—
89	C₂²×C₄×C₈₉	—	2	4	no	—
90	C₂²×C₄×C₈₉	—	2	4	no	—
91	C₂²×C₄×C₈₉	—	2	2	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	2	4	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	2	4	no	—
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	—	2	4	no	—
98	C₂²×C₄×C₈₉	—	2	4	no	—
99	C₂²×C₄×C₈₉	—	2	4	no	—
100	C₂²×C₄×C₈₉	—	2	4	no	—
101	C₂²×C₄×C₈₉	—	2	4	no	—
102	C₂²×C₄×C₈₉	—	2	4	no	—
103	C₂²×C₄×C₈₉	—	2	4	no	—
104	C₂²×C₄×C₈₉	—	2	4	no	—
105	C₂²×C₄×C₈₉	—	2	4	no	—
106	C₂²×C₄×C₈₉	—	2	4	no	—
107	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
108	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
109	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
110	C₂²×C₄×C₈₉	#41	1	8	yes	—
111	C₂²×C₄×C₈₉	#41	1	8	yes	—
112	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
121	C₄⋊C₄×C₈₉	—	2	16	no	—
122	C₄⋊C₄×C₈₉	—	2	16	no	—
123	C₄⋊C₄×C₈₉	—	2	16	no	—
124	C₄⋊C₄×C₈₉	—	4	8	no	—
125	C₄²×C₈₉	—	2	16	no	—
126	C₄²×C₈₉	—	4	4	no	—
127	C₄²×C₈₉	—	4	4	no	—
128	C₄²×C₈₉	C₂×Q₈	1	16	yes	complemented
129	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
130	C₂³×C₈₉	C₂×#41	1	4	yes	—
131	C₂³×C₈₉	C₂×#41	1	4	yes	—
132	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
133	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
134	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
135	Q₈×C₈₉	—	4	32	no	—
136	C₂×C₄×C₈₉	—	2	8	no	—
137	C₂×C₄×C₈₉	—	2	8	no	—
138	C₂×C₄×C₈₉	—	2	8	no	—
139	C₂×C₄×C₈₉	—	2	16	no	—
140	C₂×C₄×C₈₉	—	2	16	no	—
141	C₂×C₄×C₈₉	—	2	4	no	—
142	C₂×C₄×C₈₉	—	2	4	no	—
143	C₂×C₄×C₈₉	—	2	4	no	—
144	C₂×C₄×C₈₉	—	2	4	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	4	no	—
147	C₂×C₄×C₈₉	—	2	4	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	4	no	—
150	C₂×C₄×C₈₉	—	2	4	no	—
151	C₂×C₄×C₈₉	—	2	4	no	—
152	C₂×C₄×C₈₉	—	2	4	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	4	no	—
159	C₂×C₄×C₈₉	—	2	4	no	—
160	C₂×C₄×C₈₉	—	2	4	no	—
161	C₂×C₄×C₈₉	—	4	8	no	—
162	C₂×C₄×C₈₉	—	4	8	no	—
163	C₂×C₄×C₈₉	—	4	8	no	—
164	C₂×C₄×C₈₉	—	4	8	no	—
165	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
166	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
167	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
168	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
169	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
170	C₂²×C₈₉	#533	1	4	yes	—
171	C₂²×C₈₉	#533	1	4	yes	—
172	C₂²×C₈₉	#544	1	4	yes	—
173	C₂²×C₈₉	#551	1	8	yes	—
174	C₂²×C₈₉	#556	1	8	yes	—
175	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
176	C₂²×C₈₉	C₂²×#41	1	2	yes	—
177	C₂²×C₈₉	C₂²×#41	1	2	yes	—
178	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
179	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
180	C₄×C₈₉	—	2	4	no	—
181	C₄×C₈₉	—	2	4	no	—
182	C₄×C₈₉	—	2	4	no	—
183	C₄×C₈₉	—	2	8	no	—
184	C₄×C₈₉	—	2	8	no	—
185	C₄×C₈₉	—	4	4	no	—
186	C₄×C₈₉	—	4	4	no	—
187	C₄×C₈₉	—	4	4	no	—
188	C₄×C₈₉	—	4	4	no	—
189	C₂×#2605	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₈₉	#2605	1	8	yes	direct product factor
191	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
192	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
193	C₂×C₈₉	C₂×#544	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#551	1	2	yes	—
195	C₂×C₈₉	C₂×#556	1	2	yes	—
196	#2605	C₂×C₈₉	1	16	yes	direct product factor
197	C₂×#400	C₂×C₈₉	1	2	yes	—
198	C₂×#395	C₂×C₈₉	1	2	yes	—
199	C₂×#391	C₂×C₈₉	1	2	yes	—
200	C₂×#391	C₂×C₈₉	1	2	yes	—
201	C₂×#387	C₂×C₈₉	1	2	yes	—
202	C₂×#387	C₂×C₈₉	1	2	yes	—
203	C₂×#383	C₂×C₈₉	1	1	yes	characteristic
204	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic
205	C₂×#376	C₂×C₈₉	1	1	yes	characteristic
206	C₈₉	C₂×#2605	1	1	yes	characteristic, direct product factor, Sylow
207	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
208	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
209	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
210	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
211	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
212	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
213	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
214	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
215	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
216	#400	C₂²×C₈₉	1	16	yes	—
217	#395	C₂²×C₈₉	1	16	yes	—
218	#391	C₂²×C₈₉	1	16	yes	—
219	#391	C₂²×C₈₉	1	16	yes	—
220	#387	C₂²×C₈₉	1	16	yes	—
221	#387	C₂²×C₈₉	1	16	yes	—
222	#383	C₂²×C₈₉	1	8	yes	—
223	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
224	#376	C₂²×C₈₉	1	8	yes	—
225	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
226	C₂×#95	C₂²×C₈₉	1	2	yes	—
227	C₂×#95	C₂²×C₈₉	1	2	yes	—
228	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
229	C₂×#95	C₂²×C₈₉	1	2	yes	—
230	C₂×#95	C₂²×C₈₉	1	2	yes	—
231	C₂×#95	C₂²×C₈₉	1	2	yes	—
232	C₂×#95	C₂²×C₈₉	1	2	yes	—
233	C₂×#95	C₂²×C₈₉	1	2	yes	—
234	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
235	C₂×#95	C₂²×C₈₉	1	2	yes	—
236	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
237	C₂²×Q₈	—	2	8	no	—
238	C₂²×Q₈	—	2	8	no	—
239	C₂²×Q₈	—	4	4	no	—
240	C₂²×Q₈	C₂³×C₈₉	1	8	yes	—
241	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
242	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
243	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
244	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
245	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
249	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
250	C₂×C₄⋊C₄	—	2	8	no	—
251	C₂×C₄⋊C₄	—	2	8	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	4	4	no	—
254	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
255	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
256	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
257	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
258	C₂×C₄²	—	2	8	no	—
259	C₂×C₄²	—	4	2	no	—
260	C₂×C₄²	—	4	2	no	—
261	C₂×C₄²	Q₈×C₈₉	1	8	yes	complemented
262	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
263	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
264	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
265	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
266	#95	C₂³×C₈₉	1	8	yes	—
267	#95	C₂³×C₈₉	1	4	yes	—
268	#95	C₂³×C₈₉	1	4	yes	—
269	#95	C₂³×C₈₉	1	8	yes	—
270	#95	C₂³×C₈₉	1	4	yes	—
271	#95	C₂³×C₈₉	1	8	yes	—
272	#95	C₂³×C₈₉	1	4	yes	—
273	#95	C₂³×C₈₉	1	8	yes	—
274	#95	C₂³×C₈₉	1	8	yes	—
275	#95	C₂³×C₈₉	1	8	yes	—
276	#95	C₂³×C₈₉	1	8	yes	—
277	#95	C₂³×C₈₉	1	8	yes	—
278	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
279	C₂×Q₈	—	2	16	no	—
280	C₂×Q₈	—	2	16	no	—
281	C₂×Q₈	—	4	8	no	—
282	C₂×Q₈	—	4	32	no	—
283	C₂²×C₄	—	2	4	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
304	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
305	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
306	C₂²×C₄	#41×C₈₉	1	8	yes	—
307	C₂²×C₄	#41×C₈₉	1	8	yes	—
308	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
309	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
310	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
312	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
316	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
317	C₄⋊C₄	—	2	16	no	—
318	C₄⋊C₄	—	2	16	no	—
319	C₄⋊C₄	—	2	16	no	—
320	C₄⋊C₄	—	4	8	no	—
321	C₄²	—	2	16	no	—
322	C₄²	—	4	4	no	—
323	C₄²	—	4	4	no	—
324	C₄²	C₂×Q₈×C₈₉	1	16	yes	complemented
325	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
326	C₂³	C₂×#41×C₈₉	1	4	yes	—
327	C₂³	C₂×#41×C₈₉	1	4	yes	—
328	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
329	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
330	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
331	Q₈	—	4	32	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	16	no	—
336	C₂×C₄	—	2	16	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	8	no	—
360	C₂×C₄	—	4	8	no	—
361	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
362	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
363	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
364	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
365	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
366	C₂²	#533×C₈₉	1	4	yes	—
367	C₂²	#533×C₈₉	1	4	yes	—
368	C₂²	#544×C₈₉	1	4	yes	—
369	C₂²	#551×C₈₉	1	8	yes	—
370	C₂²	#556×C₈₉	1	8	yes	—
371	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
372	C₂²	C₂²×#41×C₈₉	1	2	yes	—
373	C₂²	C₂²×#41×C₈₉	1	2	yes	—
374	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
375	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
376	C₄	—	2	4	no	—
377	C₄	—	2	4	no	—
378	C₄	—	2	4	no	—
379	C₄	—	2	8	no	—
380	C₄	—	2	8	no	—
381	C₄	—	4	4	no	—
382	C₄	—	4	4	no	—
383	C₄	—	4	4	no	—
384	C₄	—	4	4	no	—
385	C₂	C₈₉×#2605	1	8	yes	direct product factor
386	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
387	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
388	C₂	C₂×#544×C₈₉	1	1	yes	characteristic
389	C₂	C₂×#551×C₈₉	1	2	yes	—
390	C₂	C₂×#556×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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
1. C₈₉×#2605	C₂	direct (N × H)
65. C₂×C₄²×C₈₉	Q₈	semidirect
128. C₄²×C₈₉	C₂×Q₈	semidirect
189. C₂×#2605	C₈₉	direct (N × H)
190. C₂×C₈₉	#2605	direct (N × H)
196. #2605	C₂×C₈₉	direct (N × H)
206. C₈₉	C₂×#2605	direct (N × H)
261. C₂×C₄²	Q₈×C₈₉	semidirect
324. C₄²	C₂×Q₈×C₈₉	semidirect
385. C₂	C₈₉×#2605	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×#2605	2
C₂×#400×C₈₉	2
C₂×#395×C₈₉	2
C₂×#391×C₈₉	2
C₂×#387×C₈₉	2
C₂×#383×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₂×#376×C₈₉	2
C₂×#2605	89

Subgroups — C2×C89×#2605 #36412708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2605 #36412708