Subgroups — C₈₉×#36572 #36414420

Order 22784.

2446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2848	C₂	1	3	yes	maximal, complemented
2	C₈₉×#2564	C₂	1	3	yes	maximal, complemented
3	C₈₉×#2549	C₂	1	3	yes	maximal, complemented
4	C₈₉×#2505	C₂	1	6	yes	maximal, complemented
5	C₈₉×#2450	C₂	1	6	yes	maximal, complemented
6	C₈₉×#2368	C₂	1	3	yes	maximal, complemented
7	C₈₉×#2349	C₂	1	3	yes	maximal, complemented
8	C₄×#120×C₈₉	C₂	1	3	yes	maximal
9	C₂²×#95×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁴×C₄×C₈₉	C₂²	1	3	yes	—
11	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	3	yes	—
12	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
13	C₂×#120×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
15	C₂×C₄×D₄×C₈₉	C₂²	1	6	yes	—
16	#400×C₈₉	C₂²	1	3	yes	complemented
17	#400×C₈₉	C₂²	1	6	yes	complemented
18	#399×C₈₉	C₂²	1	1	yes	characteristic, complemented
19	#398×C₈₉	C₂²	1	6	yes	complemented
20	#396×C₈₉	C₂²	1	2	yes	complemented
21	#395×C₈₉	C₂²	1	3	yes	complemented
22	#393×C₈₉	C₂²	1	3	yes	complemented
23	#391×C₈₉	C₂²	1	6	yes	complemented
24	#389×C₈₉	C₂²	1	6	yes	complemented
25	#387×C₈₉	C₂²	1	6	yes	complemented
26	#387×C₈₉	C₂²	1	6	yes	complemented
27	#386×C₈₉	C₂²	1	6	yes	—
28	#386×C₈₉	C₂²	1	3	yes	—
29	#385×C₈₉	C₂²	1	3	yes	—
30	#385×C₈₉	C₂²	1	6	yes	—
31	#385×C₈₉	C₂²	1	6	yes	—
32	#385×C₈₉	C₂²	1	6	yes	—
33	#385×C₈₉	C₂²	1	6	yes	—
34	#385×C₈₉	C₂²	1	6	yes	complemented
35	#382×C₈₉	C₂²	1	3	yes	complemented
36	#380×C₈₉	C₂²	1	6	yes	—
37	#380×C₈₉	C₂²	1	3	yes	—
38	#380×C₈₉	C₂²	1	3	yes	complemented
39	#379×C₈₉	C₂²	1	3	yes	—
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	complemented
41	C₄×C₂²⋊C₄×C₈₉	C₂²	1	6	yes	—
42	C₄×C₂²⋊C₄×C₈₉	C₂²	1	3	yes	—
43	C₂×#95×C₈₉	C₂²	1	3	yes	—
44	C₂×#95×C₈₉	C₂²	1	3	yes	—
45	C₂×#95×C₈₉	C₂²	1	6	yes	—
46	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₈₉	C₂³	1	3	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	3	yes	—
50	C₂³×C₄×C₈₉	—	2	12	no	—
51	C₂³×C₄×C₈₉	—	4	12	no	—
52	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
57	C₂²⋊Q₈×C₈₉	—	2	12	no	—
58	C₂²⋊Q₈×C₈₉	—	4	12	no	—
59	#120×C₈₉	Q₈	1	8	yes	complemented
60	C₄×D₄×C₈₉	—	2	12	no	—
61	C₄×D₄×C₈₉	—	4	12	no	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	3	yes	—
76	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
77	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
78	#95×C₈₉	C₂³	1	1	yes	characteristic
79	#95×C₈₉	C₂³	1	3	yes	—
80	#95×C₈₉	C₂³	1	6	yes	—
81	#95×C₈₉	C₂³	1	3	yes	—
82	#95×C₈₉	C₂³	1	1	yes	characteristic
83	#95×C₈₉	C₂³	1	2	yes	—
84	#95×C₈₉	C₂³	1	3	yes	—
85	#95×C₈₉	C₂³	1	6	yes	—
86	#95×C₈₉	C₂³	1	6	yes	—
87	#95×C₈₉	C₂³	1	6	yes	—
88	#95×C₈₉	C₂³	1	3	yes	—
89	#95×C₈₉	C₂³	1	6	yes	—
90	#95×C₈₉	C₂³	1	6	yes	—
91	C₂⁴×C₈₉	—	2	6	no	—
92	C₂⁴×C₈₉	—	2	6	no	—
93	C₂⁴×C₈₉	C₂×Q₈	1	4	yes	—
94	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
95	C₂⁴×C₈₉	C₂⁴	1	3	yes	—
96	C₂×Q₈×C₈₉	—	2	6	no	—
97	C₂×Q₈×C₈₉	—	4	6	no	—
98	C₂×D₄×C₈₉	—	2	6	no	—
99	C₂×D₄×C₈₉	—	2	6	no	—
100	C₂×D₄×C₈₉	C₂×Q₈	1	12	yes	—
101	C₂²×C₄×C₈₉	—	2	6	no	—
102	C₂²×C₄×C₈₉	—	2	12	no	—
103	C₂²×C₄×C₈₉	—	2	12	no	—
104	C₂²×C₄×C₈₉	—	2	12	no	—
105	C₂²×C₄×C₈₉	—	2	12	no	—
106	C₂²×C₄×C₈₉	—	2	6	no	—
107	C₂²×C₄×C₈₉	—	4	6	no	—
108	C₂²×C₄×C₈₉	—	4	6	no	—
109	C₂²×C₄×C₈₉	—	4	6	no	—
110	C₂²×C₄×C₈₉	—	4	6	no	—
111	C₂²×C₄×C₈₉	—	4	6	no	—
112	C₂²×C₄×C₈₉	—	4	48	no	—
113	C₂²×C₄×C₈₉	#41	1	12	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
118	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
119	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
121	C₄⋊C₄×C₈₉	—	2	6	no	—
122	C₄⋊C₄×C₈₉	—	2	6	no	—
123	C₄⋊C₄×C₈₉	—	2	12	no	—
124	C₄⋊C₄×C₈₉	—	4	6	no	—
125	C₄⋊C₄×C₈₉	—	4	6	no	—
126	C₄⋊C₄×C₈₉	—	4	6	no	—
127	C₄⋊C₄×C₈₉	—	4	6	no	—
128	C₂²⋊C₄×C₈₉	—	2	6	no	—
129	C₂²⋊C₄×C₈₉	—	2	12	no	—
130	C₂²⋊C₄×C₈₉	—	2	12	no	—
131	C₂²⋊C₄×C₈₉	—	2	6	no	—
132	C₂²⋊C₄×C₈₉	—	2	6	no	—
133	C₂²⋊C₄×C₈₉	—	4	6	no	—
134	C₂²⋊C₄×C₈₉	C₂×Q₈	1	12	yes	—
135	C₄²×C₈₉	—	2	6	no	—
136	C₄²×C₈₉	—	4	6	no	—
137	C₂³×C₈₉	—	2	24	no	—
138	C₂³×C₈₉	—	2	8	no	—
139	C₂³×C₈₉	—	2	24	no	—
140	C₂³×C₈₉	—	2	6	no	—
141	C₂³×C₈₉	—	2	6	no	—
142	C₂³×C₈₉	—	2	3	no	—
143	C₂³×C₈₉	—	2	3	no	—
144	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
145	C₂³×C₈₉	C₂²×Q₈	1	6	yes	—
146	C₂³×C₈₉	C₂×#41	1	6	yes	—
147	C₂³×C₈₉	H(5,𝔽₂)	1	6	yes	—
148	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
149	Q₈×C₈₉	—	8	6	no	—
150	D₄×C₈₉	—	2	24	no	—
151	C₂×C₄×C₈₉	—	2	3	no	—
152	C₂×C₄×C₈₉	—	2	3	no	—
153	C₂×C₄×C₈₉	—	2	6	no	—
154	C₂×C₄×C₈₉	—	2	6	no	—
155	C₂×C₄×C₈₉	—	2	3	no	—
156	C₂×C₄×C₈₉	—	2	6	no	—
157	C₂×C₄×C₈₉	—	2	3	no	—
158	C₂×C₄×C₈₉	—	2	6	no	—
159	C₂×C₄×C₈₉	—	2	6	no	—
160	C₂×C₄×C₈₉	—	2	6	no	—
161	C₂×C₄×C₈₉	—	2	6	no	—
162	C₂×C₄×C₈₉	—	2	6	no	—
163	C₂×C₄×C₈₉	—	2	6	no	—
164	C₂×C₄×C₈₉	—	2	6	no	—
165	C₂×C₄×C₈₉	—	4	12	no	—
166	C₂×C₄×C₈₉	—	4	24	no	—
167	C₂×C₄×C₈₉	—	4	24	no	—
168	C₂×C₄×C₈₉	—	4	12	no	—
169	C₂×C₄×C₈₉	—	8	6	no	—
170	C₂×C₄×C₈₉	C₂²×Q₈	1	6	yes	—
171	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
172	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
173	C₂²×C₈₉	—	2	32	no	—
174	C₂²×C₈₉	—	2	6	no	—
175	C₂²×C₈₉	—	2	12	no	—
176	C₂²×C₈₉	—	2	6	no	—
177	C₂²×C₈₉	—	2	12	no	—
178	C₂²×C₈₉	—	2	6	no	—
179	C₂²×C₈₉	—	4	1	no	—
180	C₂²×C₈₉	—	4	3	no	—
181	C₂²×C₈₉	#554	1	12	yes	—
182	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
183	C₂²×C₈₉	C₂²×#41	1	3	yes	—
184	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	3	yes	—
185	C₄×C₈₉	—	2	6	no	—
186	C₄×C₈₉	—	2	6	no	—
187	C₄×C₈₉	—	2	6	no	—
188	C₄×C₈₉	—	4	3	no	—
189	C₄×C₈₉	—	4	6	no	—
190	C₄×C₈₉	—	4	3	no	—
191	C₄×C₈₉	—	4	6	no	—
192	#36572	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₈₉	—	2	12	no	—
194	C₂×C₈₉	—	4	2	no	—
195	C₂×C₈₉	#3444	1	1	yes	characteristic
196	C₂×C₈₉	C₂×#554	1	3	yes	—
197	C₂×C₈₉	#3490	1	3	yes	—
198	#2848	C₂×C₈₉	1	3	yes	complemented
199	#2564	C₂×C₈₉	1	3	yes	complemented
200	#2549	C₂×C₈₉	1	3	yes	complemented
201	#2505	C₂×C₈₉	1	6	yes	complemented
202	#2450	C₂×C₈₉	1	6	yes	complemented
203	#2368	C₂×C₈₉	1	3	yes	complemented
204	#2349	C₂×C₈₉	1	3	yes	complemented
205	C₄×#120	C₂×C₈₉	1	3	yes	—
206	C₂²×#95	C₂×C₈₉	1	1	yes	characteristic, complemented
207	C₈₉	#36572	1	1	yes	characteristic, direct product factor, Sylow
208	C₂⁴×C₄	C₂²×C₈₉	1	3	yes	—
209	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	3	yes	—
210	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
211	C₂×#120	C₂²×C₈₉	1	1	yes	characteristic
212	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
213	C₂×C₄×D₄	C₂²×C₈₉	1	6	yes	—
214	#400	C₂²×C₈₉	1	3	yes	complemented
215	#400	C₂²×C₈₉	1	6	yes	complemented
216	#399	C₂²×C₈₉	1	1	yes	characteristic, complemented
217	#398	C₂²×C₈₉	1	6	yes	complemented
218	#396	C₂²×C₈₉	1	2	yes	complemented
219	#395	C₂²×C₈₉	1	3	yes	complemented
220	#393	C₂²×C₈₉	1	3	yes	complemented
221	#391	C₂²×C₈₉	1	6	yes	complemented
222	#389	C₂²×C₈₉	1	6	yes	complemented
223	#387	C₂²×C₈₉	1	6	yes	complemented
224	#387	C₂²×C₈₉	1	6	yes	complemented
225	#386	C₂²×C₈₉	1	6	yes	—
226	#386	C₂²×C₈₉	1	3	yes	—
227	#385	C₂²×C₈₉	1	6	yes	—
228	#385	C₂²×C₈₉	1	6	yes	—
229	#385	C₂²×C₈₉	1	6	yes	—
230	#385	C₂²×C₈₉	1	3	yes	—
231	#385	C₂²×C₈₉	1	6	yes	—
232	#385	C₂²×C₈₉	1	6	yes	complemented
233	#382	C₂²×C₈₉	1	3	yes	complemented
234	#380	C₂²×C₈₉	1	6	yes	—
235	#380	C₂²×C₈₉	1	3	yes	—
236	#380	C₂²×C₈₉	1	3	yes	complemented
237	#379	C₂²×C₈₉	1	3	yes	—
238	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	complemented
239	C₄×C₂²⋊C₄	C₂²×C₈₉	1	6	yes	—
240	C₄×C₂²⋊C₄	C₂²×C₈₉	1	3	yes	—
241	C₂×#95	C₂²×C₈₉	1	3	yes	—
242	C₂×#95	C₂²×C₈₉	1	3	yes	—
243	C₂×#95	C₂²×C₈₉	1	6	yes	—
244	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
245	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
246	C₂²×Q₈	C₂³×C₈₉	1	3	yes	—
247	C₂²×D₄	C₂³×C₈₉	1	3	yes	—
248	C₂³×C₄	—	2	12	no	—
249	C₂³×C₄	—	4	12	no	—
250	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
251	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
252	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
253	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
254	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
255	C₂²⋊Q₈	—	2	12	no	—
256	C₂²⋊Q₈	—	4	12	no	—
257	#120	Q₈×C₈₉	1	8	yes	complemented
258	C₄×D₄	—	2	12	no	—
259	C₄×D₄	—	4	12	no	—
260	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
261	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
262	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
263	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
264	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
265	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
266	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
272	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
273	C₂×C₂²⋊C₄	C₂³×C₈₉	1	3	yes	—
274	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
275	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
276	#95	C₂³×C₈₉	1	1	yes	characteristic
277	#95	C₂³×C₈₉	1	3	yes	—
278	#95	C₂³×C₈₉	1	6	yes	—
279	#95	C₂³×C₈₉	1	3	yes	—
280	#95	C₂³×C₈₉	1	1	yes	characteristic
281	#95	C₂³×C₈₉	1	2	yes	—
282	#95	C₂³×C₈₉	1	3	yes	—
283	#95	C₂³×C₈₉	1	6	yes	—
284	#95	C₂³×C₈₉	1	6	yes	—
285	#95	C₂³×C₈₉	1	6	yes	—
286	#95	C₂³×C₈₉	1	3	yes	—
287	#95	C₂³×C₈₉	1	6	yes	—
288	#95	C₂³×C₈₉	1	6	yes	—
289	C₂⁴	—	2	6	no	—
290	C₂⁴	—	2	6	no	—
291	C₂⁴	C₂×Q₈×C₈₉	1	4	yes	—
292	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
293	C₂⁴	C₂⁴×C₈₉	1	3	yes	—
294	C₂×Q₈	—	2	6	no	—
295	C₂×Q₈	—	4	6	no	—
296	C₂×D₄	—	2	6	no	—
297	C₂×D₄	—	2	6	no	—
298	C₂×D₄	C₂×Q₈×C₈₉	1	12	yes	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	2	12	no	—
301	C₂²×C₄	—	2	12	no	—
302	C₂²×C₄	—	2	12	no	—
303	C₂²×C₄	—	2	12	no	—
304	C₂²×C₄	—	2	6	no	—
305	C₂²×C₄	—	4	6	no	—
306	C₂²×C₄	—	4	6	no	—
307	C₂²×C₄	—	4	6	no	—
308	C₂²×C₄	—	4	6	no	—
309	C₂²×C₄	—	4	6	no	—
310	C₂²×C₄	—	4	48	no	—
311	C₂²×C₄	#41×C₈₉	1	12	yes	—
312	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
313	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
314	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
315	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
316	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
317	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
318	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
319	C₄⋊C₄	—	2	6	no	—
320	C₄⋊C₄	—	2	6	no	—
321	C₄⋊C₄	—	2	12	no	—
322	C₄⋊C₄	—	4	6	no	—
323	C₄⋊C₄	—	4	6	no	—
324	C₄⋊C₄	—	4	6	no	—
325	C₄⋊C₄	—	4	6	no	—
326	C₂²⋊C₄	—	2	6	no	—
327	C₂²⋊C₄	—	2	12	no	—
328	C₂²⋊C₄	—	2	12	no	—
329	C₂²⋊C₄	—	2	6	no	—
330	C₂²⋊C₄	—	2	6	no	—
331	C₂²⋊C₄	—	4	6	no	—
332	C₂²⋊C₄	C₂×Q₈×C₈₉	1	12	yes	—
333	C₄²	—	2	6	no	—
334	C₄²	—	4	6	no	—
335	C₂³	—	2	24	no	—
336	C₂³	—	2	8	no	—
337	C₂³	—	2	24	no	—
338	C₂³	—	2	6	no	—
339	C₂³	—	2	6	no	—
340	C₂³	—	2	3	no	—
341	C₂³	—	2	3	no	—
342	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
343	C₂³	C₂²×Q₈×C₈₉	1	6	yes	—
344	C₂³	C₂×#41×C₈₉	1	6	yes	—
345	C₂³	H(5,𝔽₂)×C₈₉	1	6	yes	—
346	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
347	Q₈	—	8	6	no	—
348	D₄	—	2	24	no	—
349	C₂×C₄	—	2	3	no	—
350	C₂×C₄	—	2	3	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	2	6	no	—
353	C₂×C₄	—	2	3	no	—
354	C₂×C₄	—	2	6	no	—
355	C₂×C₄	—	2	3	no	—
356	C₂×C₄	—	2	6	no	—
357	C₂×C₄	—	2	6	no	—
358	C₂×C₄	—	2	6	no	—
359	C₂×C₄	—	2	6	no	—
360	C₂×C₄	—	2	6	no	—
361	C₂×C₄	—	2	6	no	—
362	C₂×C₄	—	2	6	no	—
363	C₂×C₄	—	4	12	no	—
364	C₂×C₄	—	4	24	no	—
365	C₂×C₄	—	4	24	no	—
366	C₂×C₄	—	4	12	no	—
367	C₂×C₄	—	8	6	no	—
368	C₂×C₄	C₂²×Q₈×C₈₉	1	6	yes	—
369	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
370	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
371	C₂²	—	2	32	no	—
372	C₂²	—	2	6	no	—
373	C₂²	—	2	12	no	—
374	C₂²	—	2	6	no	—
375	C₂²	—	2	12	no	—
376	C₂²	—	2	6	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	3	no	—
379	C₂²	#554×C₈₉	1	12	yes	—
380	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
381	C₂²	C₂²×#41×C₈₉	1	3	yes	—
382	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	3	yes	—
383	C₄	—	2	6	no	—
384	C₄	—	2	6	no	—
385	C₄	—	2	6	no	—
386	C₄	—	4	3	no	—
387	C₄	—	4	6	no	—
388	C₄	—	4	3	no	—
389	C₄	—	4	6	no	—
390	C₂	—	2	12	no	—
391	C₂	—	4	2	no	—
392	C₂	C₈₉×#3444	1	1	yes	characteristic
393	C₂	C₂×#554×C₈₉	1	3	yes	—
394	C₂	C₈₉×#3490	1	3	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#120×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. C₈₉×#2848	C₂	semidirect
2. C₈₉×#2564	C₂	semidirect
3. C₈₉×#2549	C₂	semidirect
4. C₈₉×#2505	C₂	semidirect
5. C₈₉×#2450	C₂	semidirect
6. C₈₉×#2368	C₂	semidirect
7. C₈₉×#2349	C₂	semidirect
9. C₂²×#95×C₈₉	C₂	semidirect
16. #400×C₈₉	C₂²	semidirect
17. #400×C₈₉	C₂²	semidirect
18. #399×C₈₉	C₂²	semidirect
19. #398×C₈₉	C₂²	semidirect
20. #396×C₈₉	C₂²	semidirect
21. #395×C₈₉	C₂²	semidirect
22. #393×C₈₉	C₂²	semidirect
23. #391×C₈₉	C₂²	semidirect
24. #389×C₈₉	C₂²	semidirect
25. #387×C₈₉	C₂²	semidirect
26. #387×C₈₉	C₂²	semidirect
34. #385×C₈₉	C₂²	semidirect
35. #382×C₈₉	C₂²	semidirect
38. #380×C₈₉	C₂²	semidirect
40. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
46. C₂×#95×C₈₉	C₂²	semidirect
59. #120×C₈₉	Q₈	semidirect
192. #36572	C₈₉	direct (N × H)
198. #2848	C₂×C₈₉	semidirect
199. #2564	C₂×C₈₉	semidirect
200. #2549	C₂×C₈₉	semidirect
201. #2505	C₂×C₈₉	semidirect
202. #2450	C₂×C₈₉	semidirect
203. #2368	C₂×C₈₉	semidirect
204. #2349	C₂×C₈₉	semidirect
206. C₂²×#95	C₂×C₈₉	semidirect
207. C₈₉	#36572	direct (N × H)
214. #400	C₂²×C₈₉	semidirect
215. #400	C₂²×C₈₉	semidirect
216. #399	C₂²×C₈₉	semidirect
217. #398	C₂²×C₈₉	semidirect
218. #396	C₂²×C₈₉	semidirect
219. #395	C₂²×C₈₉	semidirect
220. #393	C₂²×C₈₉	semidirect
221. #391	C₂²×C₈₉	semidirect
222. #389	C₂²×C₈₉	semidirect
223. #387	C₂²×C₈₉	semidirect
224. #387	C₂²×C₈₉	semidirect
232. #385	C₂²×C₈₉	semidirect
233. #382	C₂²×C₈₉	semidirect
236. #380	C₂²×C₈₉	semidirect
238. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
244. C₂×#95	C₂²×C₈₉	semidirect
257. #120	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×#2848	2
C₈₉×#2564	2
C₈₉×#2549	2
C₈₉×#2505	2
C₈₉×#2450	2
C₈₉×#2368	2
C₈₉×#2349	2
C₄×#120×C₈₉	2
C₂²×#95×C₈₉	2
#36572	89

Subgroups — C89×#36572 #36414420

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36572 #36414420