Subgroups — C₈₉×#35584 #36413432

Order 22784.

2842 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2561	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2491	C₂	1	8	yes	maximal, complemented
5	C₈₉×#2490	C₂	1	8	yes	maximal, complemented
6	C₈₉×#2435	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2309	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2280	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
13	#544×C₈₉	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
15	C₂×#125×C₈₉	C₂²	1	4	yes	complemented
16	C₂×#124×C₈₉	C₂²	1	8	yes	complemented
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
18	C₂×#121×C₈₉	—	2	8	no	—
19	C₂×#121×C₈₉	C₂²	1	8	yes	—
20	C₂×#117×C₈₉	C₂²	1	2	yes	—
21	C₂×#117×C₈₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
24	#397×C₈₉	C₂²	1	8	yes	complemented
25	#394×C₈₉	C₂²	1	16	yes	complemented
26	#393×C₈₉	C₂²	1	8	yes	complemented
27	#390×C₈₉	C₂²	1	4	yes	complemented
28	#390×C₈₉	C₂²	1	8	yes	complemented
29	#390×C₈₉	C₂²	1	4	yes	complemented
30	#390×C₈₉	C₂²	1	8	yes	complemented
31	#388×C₈₉	C₂²	1	16	yes	complemented
32	#381×C₈₉	C₂²	1	4	yes	—
33	#380×C₈₉	C₂²	1	4	yes	complemented
34	#380×C₈₉	C₂²	1	4	yes	complemented
35	#379×C₈₉	C₂²	1	8	yes	—
36	#379×C₈₉	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	complemented
38	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
40	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
41	C₂⁵×C₈₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
43	C₂²×D₄×C₈₉	—	2	8	no	—
44	C₂²×D₄×C₈₉	—	2	4	no	—
45	C₂²×D₄×C₈₉	—	2	8	no	—
46	C₂²×D₄×C₈₉	—	4	8	no	—
47	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
48	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
49	C₂³×C₄×C₈₉	—	2	4	no	—
50	C₂³×C₄×C₈₉	—	2	8	no	—
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	1	yes	characteristic
55	C₄⋊Q₈×C₈₉	—	2	16	no	—
56	#125×C₈₉	—	2	16	no	—
57	#124×C₈₉	—	4	16	no	—
58	C₂²⋊Q₈×C₈₉	—	2	16	no	—
59	#121×C₈₉	—	2	32	no	—
60	#117×C₈₉	—	2	8	no	—
61	#117×C₈₉	—	2	8	no	—
62	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
77	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
78	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
80	#95×C₈₉	C₂³	1	8	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	#95×C₈₉	C₂³	1	8	yes	—
83	C₂⁴×C₈₉	—	2	2	no	—
84	C₂⁴×C₈₉	—	2	4	no	—
85	C₂⁴×C₈₉	—	2	4	no	—
86	C₂⁴×C₈₉	—	2	4	no	—
87	C₂⁴×C₈₉	—	2	8	no	—
88	C₂⁴×C₈₉	—	4	2	no	—
89	C₂⁴×C₈₉	—	4	4	no	—
90	C₂⁴×C₈₉	—	4	4	no	—
91	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
92	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
93	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
94	C₂×Q₈×C₈₉	—	2	8	no	—
95	C₂×Q₈×C₈₉	—	4	8	no	—
96	C₂×D₄×C₈₉	—	2	16	no	—
97	C₂×D₄×C₈₉	—	2	16	no	—
98	C₂×D₄×C₈₉	—	2	8	no	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	8	no	—
101	C₂×D₄×C₈₉	—	4	8	no	—
102	C₂×D₄×C₈₉	—	4	32	no	—
103	C₂×D₄×C₈₉	—	4	16	no	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	—	2	4	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	—	4	4	no	—
110	C₂²×C₄×C₈₉	—	4	16	no	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₈₉	#41	1	8	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
116	C₂²×C₄×C₈₉	C₂⁴	1	4	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	C₄⋊C₄×C₈₉	—	2	4	no	—
121	C₄⋊C₄×C₈₉	—	2	4	no	—
122	C₄⋊C₄×C₈₉	—	2	8	no	—
123	C₄⋊C₄×C₈₉	—	2	16	no	—
124	C₄⋊C₄×C₈₉	—	2	8	no	—
125	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
126	C₂²⋊C₄×C₈₉	—	2	8	no	—
127	C₂²⋊C₄×C₈₉	—	2	8	no	—
128	C₂²⋊C₄×C₈₉	—	2	16	no	—
129	C₂²⋊C₄×C₈₉	—	2	16	no	—
130	C₂²⋊C₄×C₈₉	—	4	8	no	—
131	C₂²⋊C₄×C₈₉	—	4	16	no	—
132	C₂²⋊C₄×C₈₉	—	4	16	no	—
133	C₄²×C₈₉	—	2	8	no	—
134	C₄²×C₈₉	—	2	8	no	—
135	C₄²×C₈₉	—	4	8	no	—
136	C₂³×C₈₉	—	2	2	no	—
137	C₂³×C₈₉	—	2	2	no	—
138	C₂³×C₈₉	—	2	8	no	—
139	C₂³×C₈₉	—	2	2	no	—
140	C₂³×C₈₉	—	2	4	no	—
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	2	4	no	—
144	C₂³×C₈₉	—	2	8	no	—
145	C₂³×C₈₉	—	2	8	no	—
146	C₂³×C₈₉	—	2	8	no	—
147	C₂³×C₈₉	—	4	16	no	—
148	C₂³×C₈₉	—	4	4	no	—
149	C₂³×C₈₉	—	4	8	no	—
150	C₂³×C₈₉	—	4	8	no	—
151	C₂³×C₈₉	—	4	4	no	—
152	C₂³×C₈₉	—	4	8	no	—
153	C₂³×C₈₉	—	8	16	no	—
154	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
155	C₂³×C₈₉	C₂×#41	1	4	yes	—
156	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
157	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
158	Q₈×C₈₉	—	8	8	no	—
159	D₄×C₈₉	—	4	32	no	—
160	D₄×C₈₉	—	4	16	no	—
161	C₂×C₄×C₈₉	—	2	8	no	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	8	no	—
166	C₂×C₄×C₈₉	—	2	4	no	—
167	C₂×C₄×C₈₉	—	2	8	no	—
168	C₂×C₄×C₈₉	—	2	8	no	—
169	C₂×C₄×C₈₉	—	2	8	no	—
170	C₂×C₄×C₈₉	—	2	8	no	—
171	C₂×C₄×C₈₉	—	4	8	no	—
172	C₂×C₄×C₈₉	—	4	4	no	—
173	C₂×C₄×C₈₉	—	4	16	no	—
174	C₂×C₄×C₈₉	#124	1	16	yes	complemented
175	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
176	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
177	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
178	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
179	C₂²×C₈₉	—	2	2	no	—
180	C₂²×C₈₉	—	2	2	no	—
181	C₂²×C₈₉	—	2	8	no	—
182	C₂²×C₈₉	—	2	4	no	—
183	C₂²×C₈₉	—	2	8	no	—
184	C₂²×C₈₉	—	4	16	no	—
185	C₂²×C₈₉	—	4	2	no	—
186	C₂²×C₈₉	—	4	2	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	—	4	4	no	—
189	C₂²×C₈₉	—	4	4	no	—
190	C₂²×C₈₉	—	4	4	no	—
191	C₂²×C₈₉	—	4	16	no	—
192	C₂²×C₈₉	—	8	16	no	—
193	C₂²×C₈₉	C₂×#124	1	4	yes	—
194	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
195	C₂²×C₈₉	C₂²×#41	1	2	yes	—
196	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
197	C₂²×C₈₉	#585	1	2	yes	—
198	C₄×C₈₉	—	2	8	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	—	4	4	no	—
201	C₄×C₈₉	—	4	4	no	—
202	C₄×C₈₉	—	4	8	no	—
203	C₄×C₈₉	C₂×#124	1	8	yes	—
204	#35584	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₈₉	—	2	4	no	—
206	C₂×C₈₉	—	4	4	no	—
207	C₂×C₈₉	—	8	4	no	—
208	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
209	C₂×C₈₉	#3484	1	1	yes	characteristic
210	C₂×C₈₉	#3487	1	1	yes	characteristic
211	C₂×C₈₉	#3494	1	4	yes	—
212	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
213	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic
214	#2561	C₂×C₈₉	1	4	yes	complemented
215	#2491	C₂×C₈₉	1	8	yes	complemented
216	#2490	C₂×C₈₉	1	8	yes	complemented
217	#2435	C₂×C₈₉	1	4	yes	complemented
218	#2309	C₂×C₈₉	1	2	yes	complemented
219	#2280	C₂×C₈₉	1	2	yes	complemented
220	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
221	C₈₉	#35584	1	1	yes	characteristic, direct product factor, Sylow
222	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
223	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
224	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
225	#544	—	2	8	no	—
226	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
227	C₂×#125	C₂²×C₈₉	1	4	yes	complemented
228	C₂×#124	C₂²×C₈₉	1	8	yes	complemented
229	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
230	C₂×#121	—	2	8	no	—
231	C₂×#121	C₂²×C₈₉	1	8	yes	—
232	C₂×#117	C₂²×C₈₉	1	2	yes	—
233	C₂×#117	C₂²×C₈₉	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
235	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
236	#397	C₂²×C₈₉	1	8	yes	complemented
237	#394	C₂²×C₈₉	1	16	yes	complemented
238	#393	C₂²×C₈₉	1	8	yes	complemented
239	#390	C₂²×C₈₉	1	4	yes	complemented
240	#390	C₂²×C₈₉	1	8	yes	complemented
241	#390	C₂²×C₈₉	1	4	yes	complemented
242	#390	C₂²×C₈₉	1	8	yes	complemented
243	#388	C₂²×C₈₉	1	16	yes	complemented
244	#381	C₂²×C₈₉	1	4	yes	—
245	#380	C₂²×C₈₉	1	4	yes	complemented
246	#380	C₂²×C₈₉	1	4	yes	complemented
247	#379	C₂²×C₈₉	1	8	yes	—
248	#379	C₂²×C₈₉	1	4	yes	—
249	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	complemented
250	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
251	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
252	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
253	C₂⁵	C₂³×C₈₉	1	2	yes	—
254	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
255	C₂²×D₄	—	2	8	no	—
256	C₂²×D₄	—	2	4	no	—
257	C₂²×D₄	—	2	8	no	—
258	C₂²×D₄	—	4	8	no	—
259	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
260	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
261	C₂³×C₄	—	2	4	no	—
262	C₂³×C₄	—	2	8	no	—
263	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
264	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
265	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
266	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
267	C₄⋊Q₈	—	2	16	no	—
268	#125	—	2	16	no	—
269	#124	—	4	16	no	—
270	C₂²⋊Q₈	—	2	16	no	—
271	#121	—	2	32	no	—
272	#117	—	2	8	no	—
273	#117	—	2	8	no	—
274	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
280	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
289	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
290	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
291	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
292	#95	C₂³×C₈₉	1	8	yes	—
293	#95	C₂³×C₈₉	1	8	yes	—
294	#95	C₂³×C₈₉	1	8	yes	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	4	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	4	2	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
304	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
305	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
306	C₂×Q₈	—	2	8	no	—
307	C₂×Q₈	—	4	8	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	16	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	8	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	32	no	—
315	C₂×D₄	—	4	16	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	8	no	—
319	C₂²×C₄	—	2	8	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	4	4	no	—
322	C₂²×C₄	—	4	16	no	—
323	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
324	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
325	C₂²×C₄	#41×C₈₉	1	8	yes	—
326	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
328	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	16	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	16	no	—
341	C₂²⋊C₄	—	2	16	no	—
342	C₂²⋊C₄	—	4	16	no	—
343	C₂²⋊C₄	—	4	8	no	—
344	C₂²⋊C₄	—	4	16	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	4	8	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	2	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	4	16	no	—
360	C₂³	—	4	4	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	8	no	—
365	C₂³	—	8	16	no	—
366	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
367	C₂³	C₂×#41×C₈₉	1	4	yes	—
368	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
369	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
370	Q₈	—	8	8	no	—
371	D₄	—	4	32	no	—
372	D₄	—	4	16	no	—
373	C₂×C₄	—	2	8	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	8	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	4	no	—
385	C₂×C₄	—	4	16	no	—
386	C₂×C₄	#124×C₈₉	1	16	yes	complemented
387	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
388	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
389	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
390	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	2	8	no	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	8	no	—
396	C₂²	—	4	16	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	—	4	4	no	—
403	C₂²	—	4	16	no	—
404	C₂²	—	8	16	no	—
405	C₂²	C₂×#124×C₈₉	1	4	yes	—
406	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
407	C₂²	C₂²×#41×C₈₉	1	2	yes	—
408	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
409	C₂²	#585×C₈₉	1	2	yes	—
410	C₄	—	2	8	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	4	no	—
413	C₄	—	4	4	no	—
414	C₄	—	4	8	no	—
415	C₄	C₂×#124×C₈₉	1	8	yes	—
416	C₂	—	2	4	no	—
417	C₂	—	4	4	no	—
418	C₂	—	8	4	no	—
419	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
420	C₂	C₈₉×#3484	1	1	yes	characteristic
421	C₂	C₈₉×#3487	1	1	yes	characteristic
422	C₂	C₈₉×#3494	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#121×C₈₉	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. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#2561	C₂	semidirect
4. C₈₉×#2491	C₂	semidirect
5. C₈₉×#2490	C₂	semidirect
6. C₈₉×#2435	C₂	semidirect
7. C₈₉×#2309	C₂	semidirect
8. C₈₉×#2280	C₂	semidirect
9. C₈₉×#2274	C₂	semidirect
14. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
15. C₂×#125×C₈₉	C₂²	semidirect
16. C₂×#124×C₈₉	C₂²	semidirect
24. #397×C₈₉	C₂²	semidirect
25. #394×C₈₉	C₂²	semidirect
26. #393×C₈₉	C₂²	semidirect
27. #390×C₈₉	C₂²	semidirect
28. #390×C₈₉	C₂²	semidirect
29. #390×C₈₉	C₂²	semidirect
30. #390×C₈₉	C₂²	semidirect
31. #388×C₈₉	C₂²	semidirect
33. #380×C₈₉	C₂²	semidirect
34. #380×C₈₉	C₂²	semidirect
37. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
39. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
174. C₂×C₄×C₈₉	#124	semidirect
204. #35584	C₈₉	direct (N × H)
212. C₂×#544	C₂×C₈₉	semidirect
214. #2561	C₂×C₈₉	semidirect
215. #2491	C₂×C₈₉	semidirect
216. #2490	C₂×C₈₉	semidirect
217. #2435	C₂×C₈₉	semidirect
218. #2309	C₂×C₈₉	semidirect
219. #2280	C₂×C₈₉	semidirect
220. #2274	C₂×C₈₉	semidirect
221. C₈₉	#35584	direct (N × H)
226. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
227. C₂×#125	C₂²×C₈₉	semidirect
228. C₂×#124	C₂²×C₈₉	semidirect
236. #397	C₂²×C₈₉	semidirect
237. #394	C₂²×C₈₉	semidirect
238. #393	C₂²×C₈₉	semidirect
239. #390	C₂²×C₈₉	semidirect
240. #390	C₂²×C₈₉	semidirect
241. #390	C₂²×C₈₉	semidirect
242. #390	C₂²×C₈₉	semidirect
243. #388	C₂²×C₈₉	semidirect
245. #380	C₂²×C₈₉	semidirect
246. #380	C₂²×C₈₉	semidirect
249. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
251. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
386. C₂×C₄	#124×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#544×C₈₉	2
C₂²×#121×C₈₉	2
C₈₉×#2561	2
C₈₉×#2491	2
C₈₉×#2490	2
C₈₉×#2435	2
C₈₉×#2309	2
C₈₉×#2280	2
C₈₉×#2274	2
#35584	89

Subgroups — C89×#35584 #36413432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35584 #36413432