Subgroups — C₈₉×#59945 #36437793

Order 22784.

2220 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2782	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2684	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2598	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2580	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2572	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2495	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2487	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2482	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2420	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2408	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#2361	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2358	C₂	1	2	yes	maximal, complemented
13	D₄×C₂²⋊C₄×C₈₉	C₂	1	2	yes	maximal, complemented
14	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2293	C₂	1	2	yes	maximal, complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#121×C₈₉	C₂²	1	2	yes	—
19	C₂×#120×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	complemented
25	C₂×#117×C₈₉	C₂²	1	4	yes	complemented
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
28	#400×C₈₉	C₂²	1	2	yes	complemented
29	#400×C₈₉	C₂²	1	4	yes	complemented
30	#399×C₈₉	C₂²	1	2	yes	—
31	#399×C₈₉	C₂²	1	4	yes	complemented
32	#397×C₈₉	C₂²	1	4	yes	—
33	#397×C₈₉	C₂²	1	4	yes	complemented
34	#394×C₈₉	C₂²	1	2	yes	—
35	#394×C₈₉	C₂²	1	4	yes	complemented
36	#393×C₈₉	C₂²	1	4	yes	complemented
37	#392×C₈₉	C₂²	1	2	yes	—
38	#391×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	#390×C₈₉	C₂²	1	1	yes	characteristic
40	#390×C₈₉	C₂²	1	2	yes	—
41	#390×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#389×C₈₉	C₂²	1	2	yes	complemented
44	#389×C₈₉	C₂²	1	2	yes	complemented
45	#389×C₈₉	C₂²	1	2	yes	complemented
46	#388×C₈₉	C₂²	1	2	yes	—
47	#388×C₈₉	C₂²	1	4	yes	—
48	#388×C₈₉	C₂²	1	2	yes	complemented
49	#388×C₈₉	C₂²	1	4	yes	complemented
50	#388×C₈₉	C₂²	1	4	yes	complemented
51	#388×C₈₉	C₂²	1	4	yes	complemented
52	#386×C₈₉	C₂²	1	4	yes	—
53	#386×C₈₉	C₂²	1	4	yes	—
54	#386×C₈₉	C₂²	1	2	yes	—
55	#386×C₈₉	C₂²	1	4	yes	complemented
56	#386×C₈₉	C₂²	1	4	yes	complemented
57	#385×C₈₉	C₂²	1	4	yes	complemented
58	#385×C₈₉	C₂²	1	4	yes	complemented
59	#385×C₈₉	C₂²	1	2	yes	complemented
60	#385×C₈₉	C₂²	1	4	yes	complemented
61	#383×C₈₉	C₂²	1	4	yes	complemented
62	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#382×C₈₉	C₂²	1	2	yes	complemented
64	#381×C₈₉	C₂²	1	4	yes	complemented
65	#380×C₈₉	C₂²	1	2	yes	—
66	#380×C₈₉	C₂²	1	1	yes	characteristic
67	#380×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	#379×C₈₉	C₂²	1	4	yes	—
69	#379×C₈₉	C₂²	1	2	yes	—
70	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
71	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
73	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
74	C₄³×C₈₉	C₂²	1	1	yes	characteristic, complemented
75	C₂⁵×C₈₉	C₂³	1	2	yes	—
76	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₈₉	—	2	8	no	—
78	C₂²×D₄×C₈₉	—	4	2	no	—
79	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
82	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
86	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
87	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
88	#124×C₈₉	—	2	4	no	—
89	#121×C₈₉	—	2	8	no	—
90	#120×C₈₉	—	2	8	no	—
91	C₄×Q₈×C₈₉	—	4	2	no	—
92	C₄×D₄×C₈₉	—	2	8	no	—
93	C₄×D₄×C₈₉	—	4	8	no	—
94	C₄×D₄×C₈₉	—	4	4	no	—
95	C₄×D₄×C₈₉	—	4	2	no	—
96	#117×C₈₉	—	4	8	no	—
97	C₂×C₄⋊C₄×C₈₉	—	4	2	no	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
109	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	#95×C₈₉	C₂³	1	2	yes	—
135	#95×C₈₉	C₂³	1	2	yes	—
136	#95×C₈₉	C₂³	1	2	yes	—
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	2	yes	—
139	#95×C₈₉	C₂³	1	4	yes	—
140	#95×C₈₉	C₂³	1	4	yes	—
141	#95×C₈₉	C₂³	1	2	yes	—
142	#95×C₈₉	C₂³	1	4	yes	—
143	#95×C₈₉	C₂³	1	2	yes	—
144	#95×C₈₉	C₂³	1	4	yes	—
145	#95×C₈₉	C₂³	1	4	yes	—
146	#95×C₈₉	C₂³	1	4	yes	—
147	C₂⁴×C₈₉	—	2	4	no	—
148	C₂⁴×C₈₉	—	2	8	no	—
149	C₂⁴×C₈₉	—	4	4	no	—
150	C₂⁴×C₈₉	—	4	2	no	—
151	C₂⁴×C₈₉	—	4	2	no	—
152	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
154	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂×Q₈×C₈₉	—	2	2	no	—
156	C₂×Q₈×C₈₉	—	4	1	no	—
157	C₂×Q₈×C₈₉	—	4	1	no	—
158	C₂×D₄×C₈₉	—	2	8	no	—
159	C₂×D₄×C₈₉	—	2	8	no	—
160	C₂×D₄×C₈₉	—	2	8	no	—
161	C₂×D₄×C₈₉	—	2	4	no	—
162	C₂×D₄×C₈₉	—	2	4	no	—
163	C₂×D₄×C₈₉	—	4	1	no	—
164	C₂×D₄×C₈₉	—	4	4	no	—
165	C₂×D₄×C₈₉	—	4	2	no	—
166	C₂×D₄×C₈₉	—	4	1	no	—
167	C₂×D₄×C₈₉	—	4	16	no	—
168	C₂×D₄×C₈₉	#41	1	8	yes	—
169	C₂×D₄×C₈₉	#41	1	4	yes	—
170	C₂²×C₄×C₈₉	—	2	8	no	—
171	C₂²×C₄×C₈₉	—	2	4	no	—
172	C₂²×C₄×C₈₉	—	2	4	no	—
173	C₂²×C₄×C₈₉	—	2	8	no	—
174	C₂²×C₄×C₈₉	—	2	2	no	—
175	C₂²×C₄×C₈₉	—	2	2	no	—
176	C₂²×C₄×C₈₉	—	4	4	no	—
177	C₂²×C₄×C₈₉	—	4	4	no	—
178	C₂²×C₄×C₈₉	—	4	2	no	—
179	C₂²×C₄×C₈₉	—	4	4	no	—
180	C₂²×C₄×C₈₉	—	4	4	no	—
181	C₂²×C₄×C₈₉	—	4	4	no	—
182	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	—	2	4	no	—
197	C₄⋊C₄×C₈₉	—	4	2	no	—
198	C₄⋊C₄×C₈₉	—	4	4	no	—
199	C₄⋊C₄×C₈₉	—	4	4	no	—
200	C₄⋊C₄×C₈₉	—	4	1	no	—
201	C₄⋊C₄×C₈₉	—	4	4	no	—
202	C₄⋊C₄×C₈₉	—	4	1	no	—
203	C₄⋊C₄×C₈₉	—	4	2	no	—
204	C₂²⋊C₄×C₈₉	—	2	8	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	2	8	no	—
207	C₂²⋊C₄×C₈₉	—	2	4	no	—
208	C₂²⋊C₄×C₈₉	—	2	4	no	—
209	C₂²⋊C₄×C₈₉	—	2	8	no	—
210	C₂²⋊C₄×C₈₉	—	2	4	no	—
211	C₂²⋊C₄×C₈₉	—	2	8	no	—
212	C₂²⋊C₄×C₈₉	—	2	4	no	—
213	C₂²⋊C₄×C₈₉	—	4	4	no	—
214	C₂²⋊C₄×C₈₉	—	4	4	no	—
215	C₂²⋊C₄×C₈₉	—	4	2	no	—
216	C₂²⋊C₄×C₈₉	—	4	4	no	—
217	C₂²⋊C₄×C₈₉	—	4	4	no	—
218	C₂²⋊C₄×C₈₉	—	4	4	no	—
219	C₂²⋊C₄×C₈₉	—	4	1	no	—
220	C₂²⋊C₄×C₈₉	—	4	1	no	—
221	C₂²⋊C₄×C₈₉	—	4	4	no	—
222	C₄²×C₈₉	—	2	4	no	—
223	C₄²×C₈₉	—	2	2	no	—
224	C₄²×C₈₉	—	2	4	no	—
225	C₄²×C₈₉	—	2	8	no	—
226	C₄²×C₈₉	—	2	2	no	—
227	C₄²×C₈₉	—	2	4	no	—
228	C₄²×C₈₉	—	4	1	no	—
229	C₂³×C₈₉	—	2	4	no	—
230	C₂³×C₈₉	—	2	2	no	—
231	C₂³×C₈₉	—	2	2	no	—
232	C₂³×C₈₉	—	2	4	no	—
233	C₂³×C₈₉	—	2	2	no	—
234	C₂³×C₈₉	—	2	4	no	—
235	C₂³×C₈₉	—	2	2	no	—
236	C₂³×C₈₉	—	2	4	no	—
237	C₂³×C₈₉	—	2	1	no	—
238	C₂³×C₈₉	—	2	1	no	—
239	C₂³×C₈₉	—	2	4	no	—
240	C₂³×C₈₉	—	2	1	no	—
241	C₂³×C₈₉	—	2	4	no	—
242	C₂³×C₈₉	—	2	1	no	—
243	C₂³×C₈₉	—	4	8	no	—
244	C₂³×C₈₉	—	4	16	no	—
245	C₂³×C₈₉	—	8	4	no	—
246	C₂³×C₈₉	—	8	8	no	—
247	C₂³×C₈₉	—	8	4	no	—
248	C₂³×C₈₉	C₂×#41	1	2	yes	—
249	C₂³×C₈₉	C₂×#41	1	8	yes	—
250	C₂³×C₈₉	C₂×#41	1	2	yes	—
251	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
252	Q₈×C₈₉	—	4	4	no	—
253	D₄×C₈₉	—	2	16	no	—
254	D₄×C₈₉	—	4	4	no	—
255	D₄×C₈₉	—	4	16	no	—
256	D₄×C₈₉	—	4	8	no	—
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	1	no	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	1	no	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	—	2	2	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	4	no	—
267	C₂×C₄×C₈₉	—	2	4	no	—
268	C₂×C₄×C₈₉	—	2	2	no	—
269	C₂×C₄×C₈₉	—	2	2	no	—
270	C₂×C₄×C₈₉	—	2	1	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	2	2	no	—
273	C₂×C₄×C₈₉	—	2	4	no	—
274	C₂×C₄×C₈₉	—	2	4	no	—
275	C₂×C₄×C₈₉	—	2	2	no	—
276	C₂×C₄×C₈₉	—	2	2	no	—
277	C₂×C₄×C₈₉	—	2	4	no	—
278	C₂×C₄×C₈₉	—	2	2	no	—
279	C₂×C₄×C₈₉	—	2	4	no	—
280	C₂×C₄×C₈₉	—	2	4	no	—
281	C₂×C₄×C₈₉	—	2	1	no	—
282	C₂×C₄×C₈₉	—	2	1	no	—
283	C₂×C₄×C₈₉	—	2	4	no	—
284	C₂×C₄×C₈₉	—	2	2	no	—
285	C₂×C₄×C₈₉	—	4	16	no	—
286	C₂×C₄×C₈₉	—	4	4	no	—
287	C₂×C₄×C₈₉	—	4	4	no	—
288	C₂×C₄×C₈₉	—	8	4	no	—
289	C₂×C₄×C₈₉	—	8	8	no	—
290	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
291	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
292	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
293	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
294	C₂²×C₈₉	—	2	8	no	—
295	C₂²×C₈₉	—	2	4	no	—
296	C₂²×C₈₉	—	2	8	no	—
297	C₂²×C₈₉	—	2	4	no	—
298	C₂²×C₈₉	—	2	2	no	—
299	C₂²×C₈₉	—	2	2	no	—
300	C₂²×C₈₉	—	2	8	no	—
301	C₂²×C₈₉	—	4	1	no	—
302	C₂²×C₈₉	—	4	1	no	—
303	C₂²×C₈₉	—	4	4	no	—
304	C₂²×C₈₉	—	4	4	no	—
305	C₂²×C₈₉	—	4	2	no	—
306	C₂²×C₈₉	—	4	4	no	—
307	C₂²×C₈₉	—	4	2	no	—
308	C₂²×C₈₉	—	4	1	no	—
309	C₂²×C₈₉	—	4	4	no	—
310	C₂²×C₈₉	—	4	1	no	—
311	C₂²×C₈₉	—	8	16	no	—
312	C₂²×C₈₉	C₂²×#41	1	2	yes	—
313	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
314	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
315	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
316	C₂²×C₈₉	#585	1	1	yes	characteristic
317	C₄×C₈₉	—	2	2	no	—
318	C₄×C₈₉	—	2	4	no	—
319	C₄×C₈₉	—	4	1	no	—
320	C₄×C₈₉	—	4	1	no	—
321	C₄×C₈₉	—	4	2	no	—
322	C₄×C₈₉	—	4	4	no	—
323	C₄×C₈₉	—	4	2	no	—
324	C₄×C₈₉	—	4	4	no	—
325	C₄×C₈₉	—	4	1	no	—
326	C₄×C₈₉	—	4	4	no	—
327	C₄×C₈₉	—	4	2	no	—
328	C₄×C₈₉	#551	1	4	yes	—
329	#59945	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₈₉	—	4	2	no	—
331	C₂×C₈₉	—	4	8	no	—
332	C₂×C₈₉	—	4	2	no	—
333	C₂×C₈₉	C₂×#551	1	1	yes	characteristic
334	C₂×C₈₉	#3481	1	2	yes	—
335	C₂×C₈₉	#3505	1	1	yes	characteristic
336	C₂×C₈₉	#3513	1	2	yes	—
337	C₂×C₈₉	#3549	1	1	yes	characteristic
338	#2782	C₂×C₈₉	1	2	yes	complemented
339	#2684	C₂×C₈₉	1	2	yes	complemented
340	#2598	C₂×C₈₉	1	4	yes	complemented
341	#2580	C₂×C₈₉	1	2	yes	complemented
342	#2572	C₂×C₈₉	1	2	yes	complemented
343	#2495	C₂×C₈₉	1	2	yes	complemented
344	#2487	C₂×C₈₉	1	1	yes	characteristic, complemented
345	#2482	C₂×C₈₉	1	4	yes	complemented
346	#2420	C₂×C₈₉	1	2	yes	complemented
347	#2408	C₂×C₈₉	1	1	yes	characteristic
348	#2361	C₂×C₈₉	1	2	yes	complemented
349	#2358	C₂×C₈₉	1	2	yes	complemented
350	D₄×C₂²⋊C₄	C₂×C₈₉	1	2	yes	complemented
351	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
352	#2293	C₂×C₈₉	1	2	yes	complemented
353	C₈₉	#59945	1	1	yes	characteristic, direct product factor, Sylow
354	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
355	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
356	C₂×#121	C₂²×C₈₉	1	2	yes	—
357	C₂×#120	C₂²×C₈₉	1	2	yes	—
358	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
359	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
362	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	complemented
363	C₂×#117	C₂²×C₈₉	1	4	yes	complemented
364	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
365	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
366	#400	C₂²×C₈₉	1	2	yes	complemented
367	#400	C₂²×C₈₉	1	4	yes	complemented
368	#399	C₂²×C₈₉	1	2	yes	—
369	#399	C₂²×C₈₉	1	4	yes	complemented
370	#397	C₂²×C₈₉	1	4	yes	—
371	#397	C₂²×C₈₉	1	4	yes	complemented
372	#394	C₂²×C₈₉	1	2	yes	—
373	#394	C₂²×C₈₉	1	4	yes	complemented
374	#393	C₂²×C₈₉	1	4	yes	complemented
375	#392	C₂²×C₈₉	1	2	yes	—
376	#391	C₂²×C₈₉	1	1	yes	characteristic, complemented
377	#390	C₂²×C₈₉	1	2	yes	—
378	#390	C₂²×C₈₉	1	2	yes	—
379	#390	C₂²×C₈₉	1	2	yes	—
380	#390	C₂²×C₈₉	1	1	yes	characteristic
381	#389	C₂²×C₈₉	1	2	yes	complemented
382	#389	C₂²×C₈₉	1	2	yes	complemented
383	#389	C₂²×C₈₉	1	2	yes	complemented
384	#388	C₂²×C₈₉	1	4	yes	—
385	#388	C₂²×C₈₉	1	2	yes	—
386	#388	C₂²×C₈₉	1	4	yes	complemented
387	#388	C₂²×C₈₉	1	2	yes	complemented
388	#388	C₂²×C₈₉	1	4	yes	complemented
389	#388	C₂²×C₈₉	1	4	yes	complemented
390	#386	C₂²×C₈₉	1	4	yes	—
391	#386	C₂²×C₈₉	1	4	yes	—
392	#386	C₂²×C₈₉	1	2	yes	—
393	#386	C₂²×C₈₉	1	4	yes	complemented
394	#386	C₂²×C₈₉	1	4	yes	complemented
395	#385	C₂²×C₈₉	1	4	yes	complemented
396	#385	C₂²×C₈₉	1	4	yes	complemented
397	#385	C₂²×C₈₉	1	2	yes	complemented
398	#385	C₂²×C₈₉	1	4	yes	complemented
399	#383	C₂²×C₈₉	1	4	yes	complemented
400	#382	C₂²×C₈₉	1	2	yes	complemented
401	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
402	#381	C₂²×C₈₉	1	4	yes	complemented
403	#380	C₂²×C₈₉	1	2	yes	—
404	#380	C₂²×C₈₉	1	1	yes	characteristic
405	#380	C₂²×C₈₉	1	1	yes	characteristic, complemented
406	#379	C₂²×C₈₉	1	4	yes	—
407	#379	C₂²×C₈₉	1	2	yes	—
408	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
409	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
410	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
411	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
412	C₄³	C₂²×C₈₉	1	1	yes	characteristic, complemented
413	C₂⁵	C₂³×C₈₉	1	2	yes	—
414	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
415	C₂²×D₄	—	2	8	no	—
416	C₂²×D₄	—	4	2	no	—
417	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
418	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
419	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
420	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
424	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
425	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
426	#124	—	2	4	no	—
427	#121	—	2	8	no	—
428	#120	—	2	8	no	—
429	C₄×Q₈	—	4	2	no	—
430	C₄×D₄	—	2	8	no	—
431	C₄×D₄	—	4	8	no	—
432	C₄×D₄	—	4	4	no	—
433	C₄×D₄	—	4	2	no	—
434	#117	—	4	8	no	—
435	C₂×C₄⋊C₄	—	4	2	no	—
436	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
437	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
438	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
444	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
446	C₂×C₂²⋊C₄	—	4	8	no	—
447	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
456	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
457	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
458	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
459	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
460	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
465	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
466	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
467	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
469	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
470	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
471	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
472	#95	C₂³×C₈₉	1	2	yes	—
473	#95	C₂³×C₈₉	1	2	yes	—
474	#95	C₂³×C₈₉	1	2	yes	—
475	#95	C₂³×C₈₉	1	4	yes	—
476	#95	C₂³×C₈₉	1	2	yes	—
477	#95	C₂³×C₈₉	1	4	yes	—
478	#95	C₂³×C₈₉	1	4	yes	—
479	#95	C₂³×C₈₉	1	2	yes	—
480	#95	C₂³×C₈₉	1	4	yes	—
481	#95	C₂³×C₈₉	1	2	yes	—
482	#95	C₂³×C₈₉	1	4	yes	—
483	#95	C₂³×C₈₉	1	4	yes	—
484	#95	C₂³×C₈₉	1	4	yes	—
485	C₂⁴	—	2	4	no	—
486	C₂⁴	—	2	8	no	—
487	C₂⁴	—	4	4	no	—
488	C₂⁴	—	4	2	no	—
489	C₂⁴	—	4	2	no	—
490	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
492	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	4	1	no	—
495	C₂×Q₈	—	4	1	no	—
496	C₂×D₄	—	2	8	no	—
497	C₂×D₄	—	2	8	no	—
498	C₂×D₄	—	2	8	no	—
499	C₂×D₄	—	2	4	no	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	1	no	—
502	C₂×D₄	—	4	4	no	—
503	C₂×D₄	—	4	2	no	—
504	C₂×D₄	—	4	1	no	—
505	C₂×D₄	—	4	16	no	—
506	C₂×D₄	#41×C₈₉	1	8	yes	—
507	C₂×D₄	#41×C₈₉	1	4	yes	—
508	C₂²×C₄	—	2	8	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	4	no	—
511	C₂²×C₄	—	2	8	no	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	4	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	4	4	no	—
518	C₂²×C₄	—	4	4	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
522	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
523	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
524	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
525	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
527	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
528	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
529	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
530	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
532	C₄⋊C₄	—	2	4	no	—
533	C₄⋊C₄	—	2	4	no	—
534	C₄⋊C₄	—	2	4	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	4	no	—
537	C₄⋊C₄	—	4	4	no	—
538	C₄⋊C₄	—	4	1	no	—
539	C₄⋊C₄	—	4	4	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₂²⋊C₄	—	2	8	no	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	8	no	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	2	8	no	—
548	C₂²⋊C₄	—	2	4	no	—
549	C₂²⋊C₄	—	2	8	no	—
550	C₂²⋊C₄	—	2	4	no	—
551	C₂²⋊C₄	—	4	4	no	—
552	C₂²⋊C₄	—	4	4	no	—
553	C₂²⋊C₄	—	4	4	no	—
554	C₂²⋊C₄	—	4	4	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	4	no	—
558	C₂²⋊C₄	—	4	2	no	—
559	C₂²⋊C₄	—	4	4	no	—
560	C₄²	—	2	4	no	—
561	C₄²	—	2	2	no	—
562	C₄²	—	2	4	no	—
563	C₄²	—	2	8	no	—
564	C₄²	—	2	2	no	—
565	C₄²	—	2	4	no	—
566	C₄²	—	4	1	no	—
567	C₂³	—	2	4	no	—
568	C₂³	—	2	2	no	—
569	C₂³	—	2	2	no	—
570	C₂³	—	2	4	no	—
571	C₂³	—	2	2	no	—
572	C₂³	—	2	4	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	4	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	4	8	no	—
582	C₂³	—	4	16	no	—
583	C₂³	—	8	4	no	—
584	C₂³	—	8	8	no	—
585	C₂³	—	8	4	no	—
586	C₂³	C₂×#41×C₈₉	1	2	yes	—
587	C₂³	C₂×#41×C₈₉	1	8	yes	—
588	C₂³	C₂×#41×C₈₉	1	2	yes	—
589	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
590	Q₈	—	4	4	no	—
591	D₄	—	2	16	no	—
592	D₄	—	4	4	no	—
593	D₄	—	4	16	no	—
594	D₄	—	4	8	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	4	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	16	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	—	8	8	no	—
628	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
629	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
630	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
631	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
632	C₂²	—	2	8	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	2	8	no	—
635	C₂²	—	2	4	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	8	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	4	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	4	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	1	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	8	16	no	—
650	C₂²	C₂²×#41×C₈₉	1	2	yes	—
651	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
652	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
653	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
654	C₂²	#585×C₈₉	1	1	yes	characteristic
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	4	1	no	—
658	C₄	—	4	1	no	—
659	C₄	—	4	4	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	4	no	—
663	C₄	—	4	4	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	#551×C₈₉	1	4	yes	—
667	C₂	—	4	2	no	—
668	C₂	—	4	8	no	—
669	C₂	—	4	2	no	—
670	C₂	C₂×#551×C₈₉	1	1	yes	characteristic
671	C₂	C₈₉×#3481	1	2	yes	—
672	C₂	C₈₉×#3505	1	1	yes	characteristic
673	C₂	C₈₉×#3513	1	2	yes	—
674	C₂	C₈₉×#3549	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2408	C₂
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×#2782	C₂	semidirect
2. C₈₉×#2684	C₂	semidirect
3. C₈₉×#2598	C₂	semidirect
4. C₈₉×#2580	C₂	semidirect
5. C₈₉×#2572	C₂	semidirect
6. C₈₉×#2495	C₂	semidirect
7. C₈₉×#2487	C₂	semidirect
8. C₈₉×#2482	C₂	semidirect
9. C₈₉×#2420	C₂	semidirect
11. C₈₉×#2361	C₂	semidirect
12. C₈₉×#2358	C₂	semidirect
13. D₄×C₂²⋊C₄×C₈₉	C₂	semidirect
14. C₄×#124×C₈₉	C₂	semidirect
15. C₈₉×#2293	C₂	semidirect
20. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
24. C₂×C₄×D₄×C₈₉	C₂²	semidirect
25. C₂×#117×C₈₉	C₂²	semidirect
26. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
28. #400×C₈₉	C₂²	semidirect
29. #400×C₈₉	C₂²	semidirect
31. #399×C₈₉	C₂²	semidirect
33. #397×C₈₉	C₂²	semidirect
35. #394×C₈₉	C₂²	semidirect
36. #393×C₈₉	C₂²	semidirect
38. #391×C₈₉	C₂²	semidirect
43. #389×C₈₉	C₂²	semidirect
44. #389×C₈₉	C₂²	semidirect
45. #389×C₈₉	C₂²	semidirect
48. #388×C₈₉	C₂²	semidirect
49. #388×C₈₉	C₂²	semidirect
50. #388×C₈₉	C₂²	semidirect
51. #388×C₈₉	C₂²	semidirect
55. #386×C₈₉	C₂²	semidirect
56. #386×C₈₉	C₂²	semidirect
57. #385×C₈₉	C₂²	semidirect
58. #385×C₈₉	C₂²	semidirect
59. #385×C₈₉	C₂²	semidirect
60. #385×C₈₉	C₂²	semidirect
61. #383×C₈₉	C₂²	semidirect
62. #382×C₈₉	C₂²	semidirect
63. #382×C₈₉	C₂²	semidirect
64. #381×C₈₉	C₂²	semidirect
67. #380×C₈₉	C₂²	semidirect
70. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
72. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
74. C₄³×C₈₉	C₂²	semidirect
329. #59945	C₈₉	direct (N × H)
338. #2782	C₂×C₈₉	semidirect
339. #2684	C₂×C₈₉	semidirect
340. #2598	C₂×C₈₉	semidirect
341. #2580	C₂×C₈₉	semidirect
342. #2572	C₂×C₈₉	semidirect
343. #2495	C₂×C₈₉	semidirect
344. #2487	C₂×C₈₉	semidirect
345. #2482	C₂×C₈₉	semidirect
346. #2420	C₂×C₈₉	semidirect
348. #2361	C₂×C₈₉	semidirect
349. #2358	C₂×C₈₉	semidirect
350. D₄×C₂²⋊C₄	C₂×C₈₉	semidirect
351. C₄×#124	C₂×C₈₉	semidirect
352. #2293	C₂×C₈₉	semidirect
353. C₈₉	#59945	direct (N × H)
358. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
362. C₂×C₄×D₄	C₂²×C₈₉	semidirect
363. C₂×#117	C₂²×C₈₉	semidirect
364. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
366. #400	C₂²×C₈₉	semidirect
367. #400	C₂²×C₈₉	semidirect
369. #399	C₂²×C₈₉	semidirect
371. #397	C₂²×C₈₉	semidirect
373. #394	C₂²×C₈₉	semidirect
374. #393	C₂²×C₈₉	semidirect
376. #391	C₂²×C₈₉	semidirect
381. #389	C₂²×C₈₉	semidirect
382. #389	C₂²×C₈₉	semidirect
383. #389	C₂²×C₈₉	semidirect
386. #388	C₂²×C₈₉	semidirect
387. #388	C₂²×C₈₉	semidirect
388. #388	C₂²×C₈₉	semidirect
389. #388	C₂²×C₈₉	semidirect
393. #386	C₂²×C₈₉	semidirect
394. #386	C₂²×C₈₉	semidirect
395. #385	C₂²×C₈₉	semidirect
396. #385	C₂²×C₈₉	semidirect
397. #385	C₂²×C₈₉	semidirect
398. #385	C₂²×C₈₉	semidirect
399. #383	C₂²×C₈₉	semidirect
400. #382	C₂²×C₈₉	semidirect
401. #382	C₂²×C₈₉	semidirect
402. #381	C₂²×C₈₉	semidirect
405. #380	C₂²×C₈₉	semidirect
408. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
411. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
412. C₄³	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2782	2
C₈₉×#2684	2
C₈₉×#2598	2
C₈₉×#2580	2
C₈₉×#2572	2
C₈₉×#2495	2
C₈₉×#2487	2
C₈₉×#2482	2
C₈₉×#2420	2
C₈₉×#2408	2
C₈₉×#2361	2
C₈₉×#2358	2
D₄×C₂²⋊C₄×C₈₉	2
C₄×#124×C₈₉	2
C₈₉×#2293	2
#59945	89

Subgroups — C89×#59945 #36437793

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#59945 #36437793