Subgroups — C₈₉×#35350 #36413198

Order 22784.

4142 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2482	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2418	C₂	1	16	yes	maximal, complemented
5	C₈₉×#2405	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2315	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2308	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#379×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂⁶×C₈₉	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
12	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
13	C₂×#120×C₈₉	—	2	8	no	—
14	C₂×#120×C₈₉	C₂²	1	8	yes	—
15	#518×C₈₉	—	2	8	no	—
16	C₂×C₄×D₄×C₈₉	C₂²	1	8	yes	complemented
17	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
18	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
22	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
24	#399×C₈₉	C₂²	1	8	yes	complemented
25	#397×C₈₉	C₂²	1	8	yes	complemented
26	#394×C₈₉	C₂²	1	16	yes	complemented
27	#388×C₈₉	C₂²	1	16	yes	complemented
28	#386×C₈₉	C₂²	1	8	yes	complemented
29	#386×C₈₉	C₂²	1	8	yes	complemented
30	#385×C₈₉	C₂²	1	8	yes	complemented
31	#385×C₈₉	C₂²	1	8	yes	complemented
32	#381×C₈₉	C₂²	1	2	yes	complemented
33	#380×C₈₉	C₂²	1	8	yes	complemented
34	#379×C₈₉	C₂²	1	8	yes	—
35	#379×C₈₉	C₂²	1	8	yes	complemented
36	#379×C₈₉	C₂²	1	2	yes	complemented
37	C₂⁵×C₈₉	—	2	4	no	—
38	C₂⁵×C₈₉	—	2	8	no	—
39	C₂⁵×C₈₉	—	4	8	no	—
40	C₂⁵×C₈₉	C₂³	1	2	yes	—
41	C₂⁵×C₈₉	C₂³	1	4	yes	—
42	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
43	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₈₉	—	2	8	no	—
45	C₂²×D₄×C₈₉	—	2	8	no	—
46	C₂²×D₄×C₈₉	—	4	8	no	—
47	C₂²×D₄×C₈₉	D₄	1	8	yes	—
48	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
49	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
52	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
54	C₂³×C₄×C₈₉	C₂³	1	4	yes	complemented
55	#123×C₈₉	—	4	16	no	—
56	#120×C₈₉	—	2	32	no	—
57	C₄×D₄×C₈₉	—	2	32	no	—
58	#117×C₈₉	—	2	8	no	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	complemented
61	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
62	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₈₉	—	4	16	no	—
67	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
68	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	16	yes	—
75	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	complemented
76	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
77	C₂×C₄²×C₈₉	C₂³	1	4	yes	complemented
78	#95×C₈₉	C₂³	1	16	yes	complemented
79	#95×C₈₉	C₂³	1	8	yes	complemented
80	C₂⁴×C₈₉	—	2	4	no	—
81	C₂⁴×C₈₉	—	2	8	no	—
82	C₂⁴×C₈₉	—	2	16	no	—
83	C₂⁴×C₈₉	—	2	8	no	—
84	C₂⁴×C₈₉	—	2	4	no	—
85	C₂⁴×C₈₉	—	2	8	no	—
86	C₂⁴×C₈₉	—	2	8	no	—
87	C₂⁴×C₈₉	—	2	8	no	—
88	C₂⁴×C₈₉	—	4	4	no	—
89	C₂⁴×C₈₉	—	4	8	no	—
90	C₂⁴×C₈₉	—	4	4	no	—
91	C₂⁴×C₈₉	—	4	4	no	—
92	C₂⁴×C₈₉	—	4	32	no	—
93	C₂⁴×C₈₉	—	4	64	no	—
94	C₂⁴×C₈₉	—	4	16	no	—
95	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
96	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
97	C₂⁴×C₈₉	#41	1	8	yes	—
98	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
99	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
100	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
101	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
102	C₂×D₄×C₈₉	—	2	32	no	—
103	C₂×D₄×C₈₉	—	2	8	no	—
104	C₂×D₄×C₈₉	—	2	8	no	—
105	C₂×D₄×C₈₉	—	2	16	no	—
106	C₂×D₄×C₈₉	—	2	16	no	—
107	C₂×D₄×C₈₉	—	4	8	no	—
108	C₂×D₄×C₈₉	—	4	32	no	—
109	C₂×D₄×C₈₉	C₂×D₄	1	16	yes	—
110	C₂²×C₄×C₈₉	—	2	4	no	—
111	C₂²×C₄×C₈₉	—	2	4	no	—
112	C₂²×C₄×C₈₉	—	2	8	no	—
113	C₂²×C₄×C₈₉	—	2	8	no	—
114	C₂²×C₄×C₈₉	—	2	8	no	—
115	C₂²×C₄×C₈₉	—	4	4	no	—
116	C₂²×C₄×C₈₉	—	4	8	no	—
117	C₂²×C₄×C₈₉	—	4	8	no	—
118	C₂²×C₄×C₈₉	—	4	8	no	—
119	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
122	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
124	C₄⋊C₄×C₈₉	—	2	8	no	—
125	C₄⋊C₄×C₈₉	—	4	16	no	—
126	C₂²⋊C₄×C₈₉	—	2	8	no	—
127	C₂²⋊C₄×C₈₉	—	2	8	no	—
128	C₂²⋊C₄×C₈₉	—	2	8	no	—
129	C₂²⋊C₄×C₈₉	—	2	8	no	—
130	C₂²⋊C₄×C₈₉	—	2	8	no	—
131	C₂²⋊C₄×C₈₉	—	2	8	no	—
132	C₂²⋊C₄×C₈₉	—	2	32	no	—
133	C₂²⋊C₄×C₈₉	—	2	16	no	—
134	C₂²⋊C₄×C₈₉	—	4	16	no	—
135	C₂²⋊C₄×C₈₉	—	4	8	no	—
136	C₄²×C₈₉	—	2	8	no	—
137	C₂³×C₈₉	—	2	8	no	—
138	C₂³×C₈₉	—	2	4	no	—
139	C₂³×C₈₉	—	2	16	no	—
140	C₂³×C₈₉	—	2	32	no	—
141	C₂³×C₈₉	—	2	4	no	—
142	C₂³×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	2	8	no	—
144	C₂³×C₈₉	—	2	8	no	—
145	C₂³×C₈₉	—	2	8	no	—
146	C₂³×C₈₉	—	2	4	no	—
147	C₂³×C₈₉	—	2	8	no	—
148	C₂³×C₈₉	—	4	8	no	—
149	C₂³×C₈₉	—	4	16	no	—
150	C₂³×C₈₉	—	4	8	no	—
151	C₂³×C₈₉	—	4	32	no	—
152	C₂³×C₈₉	—	4	32	no	—
153	C₂³×C₈₉	—	4	32	no	—
154	C₂³×C₈₉	—	4	8	no	—
155	C₂³×C₈₉	—	4	16	no	—
156	C₂³×C₈₉	—	4	128	no	—
157	C₂³×C₈₉	—	4	8	no	—
158	C₂³×C₈₉	—	4	16	no	—
159	C₂³×C₈₉	—	8	8	no	—
160	C₂³×C₈₉	#123	1	16	yes	complemented
161	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
162	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
163	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
164	C₂³×C₈₉	C₂×#41	1	4	yes	—
165	C₂³×C₈₉	C₂×#41	1	4	yes	—
166	C₂³×C₈₉	C₂×#41	1	4	yes	—
167	C₂³×C₈₉	H(5,𝔽₂)	1	8	yes	—
168	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
169	D₄×C₈₉	—	2	32	no	—
170	D₄×C₈₉	—	4	32	no	—
171	C₂×C₄×C₈₉	—	2	8	no	—
172	C₂×C₄×C₈₉	—	2	4	no	—
173	C₂×C₄×C₈₉	—	2	8	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	8	no	—
176	C₂×C₄×C₈₉	—	2	16	no	—
177	C₂×C₄×C₈₉	—	2	16	no	—
178	C₂×C₄×C₈₉	—	2	8	no	—
179	C₂×C₄×C₈₉	—	4	8	no	—
180	C₂×C₄×C₈₉	—	8	8	no	—
181	C₂×C₄×C₈₉	—	8	8	no	—
182	C₂×C₄×C₈₉	—	8	8	no	—
183	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
184	C₂²×C₈₉	—	2	4	no	—
185	C₂²×C₈₉	—	2	8	no	—
186	C₂²×C₈₉	—	2	8	no	—
187	C₂²×C₈₉	—	2	8	no	—
188	C₂²×C₈₉	—	2	8	no	—
189	C₂²×C₈₉	—	2	4	no	—
190	C₂²×C₈₉	—	2	8	no	—
191	C₂²×C₈₉	—	2	8	no	—
192	C₂²×C₈₉	—	2	16	no	—
193	C₂²×C₈₉	—	4	16	no	—
194	C₂²×C₈₉	—	4	32	no	—
195	C₂²×C₈₉	—	4	64	no	—
196	C₂²×C₈₉	—	4	4	no	—
197	C₂²×C₈₉	—	4	4	no	—
198	C₂²×C₈₉	—	4	8	no	—
199	C₂²×C₈₉	—	4	8	no	—
200	C₂²×C₈₉	—	8	8	no	—
201	C₂²×C₈₉	C₂×#123	1	4	yes	—
202	C₂²×C₈₉	C₂×#123	1	8	yes	—
203	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
204	C₂²×C₈₉	C₂²×#41	1	2	yes	—
205	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	4	yes	—
206	C₄×C₈₉	—	2	4	no	—
207	C₄×C₈₉	—	4	4	no	—
208	C₄×C₈₉	—	4	8	no	—
209	C₄×C₈₉	—	4	8	no	—
210	#35350	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂×C₈₉	—	2	4	no	—
212	C₂×C₈₉	—	2	8	no	—
213	C₂×C₈₉	—	4	8	no	—
214	C₂×C₈₉	—	4	4	no	—
215	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
216	C₂×C₈₉	#3484	1	2	yes	—
217	C₂×C₈₉	#3490	1	4	yes	—
218	C₂²×#120	C₂×C₈₉	1	1	yes	characteristic
219	C₂×#518	C₂×C₈₉	1	1	yes	characteristic, complemented
220	#2482	C₂×C₈₉	1	4	yes	complemented
221	#2418	C₂×C₈₉	1	16	yes	complemented
222	#2405	C₂×C₈₉	1	4	yes	complemented
223	#2315	C₂×C₈₉	1	2	yes	complemented
224	#2308	C₂×C₈₉	1	1	yes	characteristic, complemented
225	C₂×#379	C₂×C₈₉	1	2	yes	complemented
226	C₈₉	#35350	1	1	yes	characteristic, direct product factor, Sylow
227	C₂⁶	C₂²×C₈₉	1	1	yes	characteristic
228	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
229	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
230	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
231	C₂×#120	—	2	8	no	—
232	C₂×#120	C₂²×C₈₉	1	8	yes	—
233	#518	—	2	8	no	—
234	C₂×C₄×D₄	C₂²×C₈₉	1	8	yes	complemented
235	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
236	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
237	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
238	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
239	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
240	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
241	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
242	#399	C₂²×C₈₉	1	8	yes	complemented
243	#397	C₂²×C₈₉	1	8	yes	complemented
244	#394	C₂²×C₈₉	1	16	yes	complemented
245	#388	C₂²×C₈₉	1	16	yes	complemented
246	#386	C₂²×C₈₉	1	8	yes	complemented
247	#386	C₂²×C₈₉	1	8	yes	complemented
248	#385	C₂²×C₈₉	1	8	yes	complemented
249	#385	C₂²×C₈₉	1	8	yes	complemented
250	#381	C₂²×C₈₉	1	2	yes	complemented
251	#380	C₂²×C₈₉	1	8	yes	complemented
252	#379	C₂²×C₈₉	1	8	yes	—
253	#379	C₂²×C₈₉	1	8	yes	complemented
254	#379	C₂²×C₈₉	1	2	yes	complemented
255	C₂⁵	—	2	4	no	—
256	C₂⁵	—	2	8	no	—
257	C₂⁵	—	4	8	no	—
258	C₂⁵	C₂³×C₈₉	1	2	yes	—
259	C₂⁵	C₂³×C₈₉	1	4	yes	—
260	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
261	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
262	C₂²×D₄	—	2	8	no	—
263	C₂²×D₄	—	2	8	no	—
264	C₂²×D₄	—	4	8	no	—
265	C₂²×D₄	D₄×C₈₉	1	8	yes	—
266	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
267	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
268	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
270	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
271	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
272	C₂³×C₄	C₂³×C₈₉	1	4	yes	complemented
273	#123	—	4	16	no	—
274	#120	—	2	32	no	—
275	C₄×D₄	—	2	32	no	—
276	#117	—	2	8	no	—
277	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
278	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	complemented
279	C₂×C₂²⋊C₄	—	2	8	no	—
280	C₂×C₂²⋊C₄	—	2	4	no	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	—	2	8	no	—
283	C₂×C₂²⋊C₄	—	2	8	no	—
284	C₂×C₂²⋊C₄	—	4	16	no	—
285	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
290	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	complemented
294	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
295	C₂×C₄²	C₂³×C₈₉	1	4	yes	complemented
296	#95	C₂³×C₈₉	1	16	yes	complemented
297	#95	C₂³×C₈₉	1	8	yes	complemented
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	2	8	no	—
300	C₂⁴	—	2	16	no	—
301	C₂⁴	—	2	8	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	8	no	—
304	C₂⁴	—	2	8	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	4	4	no	—
307	C₂⁴	—	4	8	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	4	no	—
310	C₂⁴	—	4	32	no	—
311	C₂⁴	—	4	64	no	—
312	C₂⁴	—	4	16	no	—
313	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
314	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
315	C₂⁴	#41×C₈₉	1	8	yes	—
316	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
317	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
318	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
319	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
320	C₂×D₄	—	2	32	no	—
321	C₂×D₄	—	2	8	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	16	no	—
325	C₂×D₄	—	4	8	no	—
326	C₂×D₄	—	4	32	no	—
327	C₂×D₄	C₂×D₄×C₈₉	1	16	yes	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	8	no	—
335	C₂²×C₄	—	4	8	no	—
336	C₂²×C₄	—	4	8	no	—
337	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
338	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
340	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
341	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
342	C₄⋊C₄	—	2	8	no	—
343	C₄⋊C₄	—	4	16	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	32	no	—
351	C₂²⋊C₄	—	2	16	no	—
352	C₂²⋊C₄	—	4	16	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₄²	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	16	no	—
358	C₂³	—	2	32	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	8	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	2	4	no	—
365	C₂³	—	2	8	no	—
366	C₂³	—	4	8	no	—
367	C₂³	—	4	16	no	—
368	C₂³	—	4	8	no	—
369	C₂³	—	4	32	no	—
370	C₂³	—	4	32	no	—
371	C₂³	—	4	32	no	—
372	C₂³	—	4	8	no	—
373	C₂³	—	4	16	no	—
374	C₂³	—	4	128	no	—
375	C₂³	—	4	8	no	—
376	C₂³	—	4	16	no	—
377	C₂³	—	8	8	no	—
378	C₂³	#123×C₈₉	1	16	yes	complemented
379	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
380	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
381	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
382	C₂³	C₂×#41×C₈₉	1	4	yes	—
383	C₂³	C₂×#41×C₈₉	1	4	yes	—
384	C₂³	C₂×#41×C₈₉	1	4	yes	—
385	C₂³	H(5,𝔽₂)×C₈₉	1	8	yes	—
386	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
387	D₄	—	2	32	no	—
388	D₄	—	4	32	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	16	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	8	8	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	—	8	8	no	—
401	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	8	no	—
406	C₂²	—	2	8	no	—
407	C₂²	—	2	4	no	—
408	C₂²	—	2	8	no	—
409	C₂²	—	2	8	no	—
410	C₂²	—	2	16	no	—
411	C₂²	—	4	16	no	—
412	C₂²	—	4	32	no	—
413	C₂²	—	4	64	no	—
414	C₂²	—	4	4	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₂×#123×C₈₉	1	4	yes	—
420	C₂²	C₂×#123×C₈₉	1	8	yes	—
421	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
422	C₂²	C₂²×#41×C₈₉	1	2	yes	—
423	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	4	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	4	4	no	—
426	C₄	—	4	8	no	—
427	C₄	—	4	8	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	8	no	—
430	C₂	—	4	8	no	—
431	C₂	—	4	4	no	—
432	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
433	C₂	C₈₉×#3484	1	2	yes	—
434	C₂	C₈₉×#3490	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#120×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
2. C₂×#518×C₈₉	C₂	semidirect
3. C₈₉×#2482	C₂	semidirect
4. C₈₉×#2418	C₂	semidirect
5. C₈₉×#2405	C₂	semidirect
6. C₈₉×#2315	C₂	semidirect
7. C₈₉×#2308	C₂	semidirect
8. C₂×#379×C₈₉	C₂	semidirect
12. C₂×#123×C₈₉	C₂²	semidirect
16. C₂×C₄×D₄×C₈₉	C₂²	semidirect
17. C₂×#117×C₈₉	C₂²	semidirect
22. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
23. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
24. #399×C₈₉	C₂²	semidirect
25. #397×C₈₉	C₂²	semidirect
26. #394×C₈₉	C₂²	semidirect
27. #388×C₈₉	C₂²	semidirect
28. #386×C₈₉	C₂²	semidirect
29. #386×C₈₉	C₂²	semidirect
30. #385×C₈₉	C₂²	semidirect
31. #385×C₈₉	C₂²	semidirect
32. #381×C₈₉	C₂²	semidirect
33. #380×C₈₉	C₂²	semidirect
35. #379×C₈₉	C₂²	semidirect
36. #379×C₈₉	C₂²	semidirect
54. C₂³×C₄×C₈₉	C₂³	semidirect
59. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
60. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
75. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
76. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
77. C₂×C₄²×C₈₉	C₂³	semidirect
78. #95×C₈₉	C₂³	semidirect
79. #95×C₈₉	C₂³	semidirect
160. C₂³×C₈₉	#123	semidirect
210. #35350	C₈₉	direct (N × H)
219. C₂×#518	C₂×C₈₉	semidirect
220. #2482	C₂×C₈₉	semidirect
221. #2418	C₂×C₈₉	semidirect
222. #2405	C₂×C₈₉	semidirect
223. #2315	C₂×C₈₉	semidirect
224. #2308	C₂×C₈₉	semidirect
225. C₂×#379	C₂×C₈₉	semidirect
226. C₈₉	#35350	direct (N × H)
230. C₂×#123	C₂²×C₈₉	semidirect
234. C₂×C₄×D₄	C₂²×C₈₉	semidirect
235. C₂×#117	C₂²×C₈₉	semidirect
240. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
241. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
242. #399	C₂²×C₈₉	semidirect
243. #397	C₂²×C₈₉	semidirect
244. #394	C₂²×C₈₉	semidirect
245. #388	C₂²×C₈₉	semidirect
246. #386	C₂²×C₈₉	semidirect
247. #386	C₂²×C₈₉	semidirect
248. #385	C₂²×C₈₉	semidirect
249. #385	C₂²×C₈₉	semidirect
250. #381	C₂²×C₈₉	semidirect
251. #380	C₂²×C₈₉	semidirect
253. #379	C₂²×C₈₉	semidirect
254. #379	C₂²×C₈₉	semidirect
272. C₂³×C₄	C₂³×C₈₉	semidirect
277. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
278. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
293. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
294. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
295. C₂×C₄²	C₂³×C₈₉	semidirect
296. #95	C₂³×C₈₉	semidirect
297. #95	C₂³×C₈₉	semidirect
378. C₂³	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#120×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2482	2
C₈₉×#2418	2
C₈₉×#2405	2
C₈₉×#2315	2
C₈₉×#2308	2
C₂×#379×C₈₉	2
#35350	89

Subgroups — C89×#35350 #36413198

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35350 #36413198