Subgroups — C₈₉×#35278 #36413126

Order 22784.

2746 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	C₂×#540×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2867	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2856	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2641	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2619	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2445	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2428	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2328	C₂	1	2	yes	maximal, complemented
10	C₄×#127×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#540×C₈₉	—	2	16	no	—
13	C₂×#127×C₈₉	C₂²	1	2	yes	—
14	C₂×#127×C₈₉	C₂²	1	2	yes	—
15	C₂×#127×C₈₉	C₂²	1	2	yes	—
16	C₂×#127×C₈₉	C₂²	1	8	yes	—
17	C₂×#125×C₈₉	C₂²	1	2	yes	—
18	C₂×#123×C₈₉	C₂²	1	8	yes	—
19	C₂×#121×C₈₉	C₂²	1	4	yes	—
20	C₂×#121×C₈₉	C₂²	1	8	yes	—
21	C₂×#121×C₈₉	C₂²	1	8	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	—
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
27	#394×C₈₉	C₂²	1	8	yes	—
28	#394×C₈₉	C₂²	1	16	yes	—
29	#392×C₈₉	C₂²	1	8	yes	—
30	#390×C₈₉	C₂²	1	4	yes	—
31	#390×C₈₉	C₂²	1	8	yes	—
32	#390×C₈₉	C₂²	1	4	yes	—
33	#390×C₈₉	C₂²	1	8	yes	—
34	#389×C₈₉	C₂²	1	8	yes	—
35	#386×C₈₉	C₂²	1	16	yes	—
36	#384×C₈₉	C₂²	1	2	yes	—
37	#382×C₈₉	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
39	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
40	#376×C₈₉	C₂²	1	1	yes	characteristic
41	#376×C₈₉	C₂²	1	1	yes	characteristic
42	C₄³×C₈₉	C₂²	1	1	yes	characteristic
43	C₄³×C₈₉	C₂²	1	1	yes	characteristic
44	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
45	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
47	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
48	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	C₂³	1	8	yes	—
52	#127×C₈₉	—	2	8	no	—
53	#127×C₈₉	—	2	8	no	—
54	#127×C₈₉	—	2	8	no	—
55	#127×C₈₉	—	4	16	no	—
56	#125×C₈₉	—	2	8	no	—
57	#123×C₈₉	—	2	32	no	—
58	#121×C₈₉	—	2	16	no	—
59	#121×C₈₉	—	2	32	no	—
60	#121×C₈₉	—	4	16	no	—
61	C₄×D₄×C₈₉	—	2	16	no	—
62	C₄×D₄×C₈₉	—	4	16	no	—
63	#117×C₈₉	—	2	4	no	—
64	#117×C₈₉	D₄	1	8	yes	complemented
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
74	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₈₉	—	2	4	no	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
86	#95×C₈₉	C₂³	1	4	yes	—
87	#95×C₈₉	C₂³	1	4	yes	—
88	#95×C₈₉	C₂³	1	8	yes	—
89	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
90	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
91	C₂×D₄×C₈₉	—	2	16	no	—
92	C₂×D₄×C₈₉	—	2	8	no	—
93	C₂×D₄×C₈₉	—	2	16	no	—
94	C₂×D₄×C₈₉	—	2	8	no	—
95	C₂×D₄×C₈₉	—	2	8	no	—
96	C₂×D₄×C₈₉	—	2	16	no	—
97	C₂×D₄×C₈₉	—	2	16	no	—
98	C₂×D₄×C₈₉	—	2	16	no	—
99	C₂×D₄×C₈₉	—	2	16	no	—
100	C₂×D₄×C₈₉	—	4	16	no	—
101	C₂×D₄×C₈₉	—	4	16	no	—
102	C₂×D₄×C₈₉	—	4	16	no	—
103	C₂²×C₄×C₈₉	—	2	2	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	16	no	—
108	C₂²×C₄×C₈₉	—	4	16	no	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
112	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	C₄⋊C₄×C₈₉	—	2	8	no	—
120	C₄⋊C₄×C₈₉	—	2	16	no	—
121	C₄⋊C₄×C₈₉	—	2	4	no	—
122	C₄⋊C₄×C₈₉	—	2	16	no	—
123	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
124	C₂²⋊C₄×C₈₉	—	2	16	no	—
125	C₂²⋊C₄×C₈₉	—	2	16	no	—
126	C₂²⋊C₄×C₈₉	—	2	4	no	—
127	C₂²⋊C₄×C₈₉	—	4	16	no	—
128	C₂²⋊C₄×C₈₉	—	4	16	no	—
129	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
130	C₄²×C₈₉	—	2	4	no	—
131	C₄²×C₈₉	—	2	2	no	—
132	C₄²×C₈₉	—	2	2	no	—
133	C₄²×C₈₉	—	2	8	no	—
134	C₄²×C₈₉	—	2	8	no	—
135	C₄²×C₈₉	C₂×D₄	1	4	yes	—
136	C₄²×C₈₉	C₂×D₄	1	4	yes	—
137	C₄²×C₈₉	#41	1	4	yes	—
138	C₄²×C₈₉	#41	1	4	yes	—
139	C₂³×C₈₉	—	2	1	no	—
140	C₂³×C₈₉	—	2	1	no	—
141	C₂³×C₈₉	—	2	4	no	—
142	C₂³×C₈₉	—	2	8	no	—
143	C₂³×C₈₉	—	2	8	no	—
144	C₂³×C₈₉	—	2	8	no	—
145	C₂³×C₈₉	—	2	16	no	—
146	C₂³×C₈₉	—	2	16	no	—
147	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
148	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
149	D₄×C₈₉	—	4	16	no	—
150	D₄×C₈₉	—	4	32	no	—
151	D₄×C₈₉	—	8	16	no	—
152	D₄×C₈₉	—	8	16	no	—
153	D₄×C₈₉	—	8	16	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	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	8	no	—
160	C₂×C₄×C₈₉	—	2	8	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	2	16	no	—
166	C₂×C₄×C₈₉	—	4	8	no	—
167	C₂×C₄×C₈₉	—	8	16	no	—
168	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
169	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
170	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
173	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
174	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
175	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
176	C₂×C₄×C₈₉	H(5,𝔽₂)	1	8	yes	—
177	C₂²×C₈₉	—	2	2	no	—
178	C₂²×C₈₉	—	2	4	no	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	—	4	8	no	—
182	C₂²×C₈₉	—	4	16	no	—
183	C₂²×C₈₉	—	4	8	no	—
184	C₂²×C₈₉	—	4	8	no	—
185	C₂²×C₈₉	—	4	16	no	—
186	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
187	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
188	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
190	C₄×C₈₉	—	2	2	no	—
191	C₄×C₈₉	—	2	4	no	—
192	C₄×C₈₉	—	2	4	no	—
193	C₄×C₈₉	—	2	4	no	—
194	C₄×C₈₉	—	4	2	no	—
195	C₄×C₈₉	—	4	8	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	#532	1	4	yes	—
198	C₄×C₈₉	#540	1	8	yes	complemented
199	#35278	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₈₉	—	4	2	no	—
201	C₂×C₈₉	—	8	8	no	—
202	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
203	C₂×C₈₉	C₂×#540	1	2	yes	—
204	C₂×C₈₉	#3498	1	2	yes	—
205	C₂×C₈₉	#3508	1	2	yes	—
206	C₂×#540	C₂×C₈₉	1	2	yes	complemented
207	#2867	C₂×C₈₉	1	1	yes	characteristic, complemented
208	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
209	#2856	C₂×C₈₉	1	2	yes	complemented
210	#2641	C₂×C₈₉	1	2	yes	complemented
211	#2619	C₂×C₈₉	1	2	yes	complemented
212	#2445	C₂×C₈₉	1	8	yes	complemented
213	#2428	C₂×C₈₉	1	8	yes	complemented
214	#2328	C₂×C₈₉	1	2	yes	complemented
215	C₄×#127	C₂×C₈₉	1	2	yes	complemented
216	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
217	C₈₉	#35278	1	1	yes	characteristic, direct product factor, Sylow
218	#540	—	2	16	no	—
219	C₂×#127	C₂²×C₈₉	1	2	yes	—
220	C₂×#127	C₂²×C₈₉	1	2	yes	—
221	C₂×#127	C₂²×C₈₉	1	2	yes	—
222	C₂×#127	C₂²×C₈₉	1	8	yes	—
223	C₂×#125	C₂²×C₈₉	1	2	yes	—
224	C₂×#123	C₂²×C₈₉	1	8	yes	—
225	C₂×#121	C₂²×C₈₉	1	4	yes	—
226	C₂×#121	C₂²×C₈₉	1	8	yes	—
227	C₂×#121	C₂²×C₈₉	1	8	yes	—
228	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
229	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	—
230	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
231	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
232	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
233	#394	C₂²×C₈₉	1	8	yes	—
234	#394	C₂²×C₈₉	1	16	yes	—
235	#392	C₂²×C₈₉	1	8	yes	—
236	#390	C₂²×C₈₉	1	4	yes	—
237	#390	C₂²×C₈₉	1	8	yes	—
238	#390	C₂²×C₈₉	1	4	yes	—
239	#390	C₂²×C₈₉	1	8	yes	—
240	#389	C₂²×C₈₉	1	8	yes	—
241	#386	C₂²×C₈₉	1	16	yes	—
242	#384	C₂²×C₈₉	1	2	yes	—
243	#382	C₂²×C₈₉	1	2	yes	—
244	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
245	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
246	#376	C₂²×C₈₉	1	1	yes	characteristic
247	#376	C₂²×C₈₉	1	1	yes	characteristic
248	C₄³	C₂²×C₈₉	1	1	yes	characteristic
249	C₄³	C₂²×C₈₉	1	1	yes	characteristic
250	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
251	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
252	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
253	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
254	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
255	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
256	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₈₉	1	8	yes	—
258	#127	—	2	8	no	—
259	#127	—	2	8	no	—
260	#127	—	2	8	no	—
261	#127	—	4	16	no	—
262	#125	—	2	8	no	—
263	#123	—	2	32	no	—
264	#121	—	2	16	no	—
265	#121	—	2	32	no	—
266	#121	—	4	16	no	—
267	C₄×D₄	—	2	16	no	—
268	C₄×D₄	—	4	16	no	—
269	#117	—	2	4	no	—
270	#117	D₄×C₈₉	1	8	yes	complemented
271	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
274	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
276	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
277	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
278	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
279	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
282	C₂×C₄²	—	2	4	no	—
283	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
285	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
286	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
288	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
292	#95	C₂³×C₈₉	1	4	yes	—
293	#95	C₂³×C₈₉	1	4	yes	—
294	#95	C₂³×C₈₉	1	8	yes	—
295	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
296	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
297	C₂×D₄	—	2	16	no	—
298	C₂×D₄	—	2	8	no	—
299	C₂×D₄	—	2	16	no	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	8	no	—
302	C₂×D₄	—	2	16	no	—
303	C₂×D₄	—	2	16	no	—
304	C₂×D₄	—	2	16	no	—
305	C₂×D₄	—	2	16	no	—
306	C₂×D₄	—	4	16	no	—
307	C₂×D₄	—	4	16	no	—
308	C₂×D₄	—	4	16	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	8	no	—
313	C₂²×C₄	—	2	16	no	—
314	C₂²×C₄	—	4	16	no	—
315	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
316	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
318	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
319	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
321	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
323	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	16	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
330	C₂²⋊C₄	—	2	16	no	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₂²⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	4	16	no	—
334	C₂²⋊C₄	—	4	16	no	—
335	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	8	no	—
341	C₄²	C₂×D₄×C₈₉	1	4	yes	—
342	C₄²	C₂×D₄×C₈₉	1	4	yes	—
343	C₄²	#41×C₈₉	1	4	yes	—
344	C₄²	#41×C₈₉	1	4	yes	—
345	C₂³	—	2	1	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	8	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	2	16	no	—
353	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
354	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
355	D₄	—	4	16	no	—
356	D₄	—	4	32	no	—
357	D₄	—	8	16	no	—
358	D₄	—	8	16	no	—
359	D₄	—	8	16	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	8	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	16	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	8	16	no	—
374	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
375	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
376	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
377	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
378	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
379	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
380	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
381	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
382	C₂×C₄	H(5,𝔽₂)×C₈₉	1	8	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	8	no	—
388	C₂²	—	4	16	no	—
389	C₂²	—	4	8	no	—
390	C₂²	—	4	8	no	—
391	C₂²	—	4	16	no	—
392	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
393	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
394	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
395	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	2	4	no	—
398	C₄	—	2	4	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	8	no	—
402	C₄	—	4	2	no	—
403	C₄	#532×C₈₉	1	4	yes	—
404	C₄	#540×C₈₉	1	8	yes	complemented
405	C₂	—	4	2	no	—
406	C₂	—	8	8	no	—
407	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
408	C₂	C₂×#540×C₈₉	1	2	yes	—
409	C₂	C₈₉×#3498	1	2	yes	—
410	C₂	C₈₉×#3508	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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×#540×C₈₉	C₂	semidirect
2. C₈₉×#2867	C₂	semidirect
3. C₈₉×#2859	C₂	semidirect
4. C₈₉×#2856	C₂	semidirect
5. C₈₉×#2641	C₂	semidirect
6. C₈₉×#2619	C₂	semidirect
7. C₈₉×#2445	C₂	semidirect
8. C₈₉×#2428	C₂	semidirect
9. C₈₉×#2328	C₂	semidirect
10. C₄×#127×C₈₉	C₂	semidirect
11. C₄×#117×C₈₉	C₂	semidirect
64. #117×C₈₉	D₄	semidirect
198. C₄×C₈₉	#540	semidirect
199. #35278	C₈₉	direct (N × H)
206. C₂×#540	C₂×C₈₉	semidirect
207. #2867	C₂×C₈₉	semidirect
208. #2859	C₂×C₈₉	semidirect
209. #2856	C₂×C₈₉	semidirect
210. #2641	C₂×C₈₉	semidirect
211. #2619	C₂×C₈₉	semidirect
212. #2445	C₂×C₈₉	semidirect
213. #2428	C₂×C₈₉	semidirect
214. #2328	C₂×C₈₉	semidirect
215. C₄×#127	C₂×C₈₉	semidirect
216. C₄×#117	C₂×C₈₉	semidirect
217. C₈₉	#35278	direct (N × H)
270. #117	D₄×C₈₉	semidirect
404. C₄	#540×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₈₉	2
C₈₉×#2867	2
C₈₉×#2859	2
C₈₉×#2856	2
C₈₉×#2641	2
C₈₉×#2619	2
C₈₉×#2445	2
C₈₉×#2428	2
C₈₉×#2328	2
C₄×#127×C₈₉	2
C₄×#117×C₈₉	2
#35278	89

Subgroups — C89×#35278 #36413126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35278 #36413126