Subgroups — C₂×C₈₉×#2433 #36412521

Order 22784.

9422 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#127×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#120×C₈₉	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2433	C₂	1	16	yes	maximal, direct product factor
6	C₂×#392×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂×#390×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂⁶×C₈₉	C₂²	1	2	yes	—
10	C₂³×D₄×C₈₉	—	2	16	no	—
11	C₂³×D₄×C₈₉	—	2	8	no	—
12	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
13	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
14	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
15	C₂³×D₄×C₈₉	C₂²	1	8	yes	complemented
16	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄×C₈₉	C₂²	1	8	yes	complemented
18	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#127×C₈₉	—	2	16	no	—
20	C₂×#127×C₈₉	C₂²	1	16	yes	complemented
21	C₂×#121×C₈₉	—	2	8	no	—
22	C₂×#121×C₈₉	C₂²	1	8	yes	complemented
23	C₂×#120×C₈₉	—	2	32	no	—
24	C₂×#120×C₈₉	C₂²	1	32	yes	complemented
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
28	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
29	C₂²×C₄²×C₈₉	C₂²	1	2	yes	complemented
30	#392×C₈₉	C₂²	1	32	yes	complemented
31	#390×C₈₉	C₂²	1	16	yes	complemented
32	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
33	C₂×#95×C₈₉	C₂²	1	2	yes	complemented
34	C₂⁵×C₈₉	—	2	16	no	—
35	C₂⁵×C₈₉	—	2	8	no	—
36	C₂⁵×C₈₉	—	2	16	no	—
37	C₂⁵×C₈₉	—	4	8	no	—
38	C₂⁵×C₈₉	C₂³	1	2	yes	—
39	C₂⁵×C₈₉	C₂³	1	4	yes	—
40	C₂⁵×C₈₉	C₂³	1	8	yes	—
41	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₈₉	—	2	128	no	—
43	C₂²×D₄×C₈₉	—	2	16	no	—
44	C₂²×D₄×C₈₉	—	2	64	no	—
45	C₂²×D₄×C₈₉	—	2	16	no	—
46	C₂²×D₄×C₈₉	—	2	8	no	—
47	C₂²×D₄×C₈₉	—	2	32	no	—
48	C₂²×D₄×C₈₉	—	2	8	no	—
49	C₂²×D₄×C₈₉	—	2	8	no	—
50	C₂²×D₄×C₈₉	—	2	8	no	—
51	C₂²×D₄×C₈₉	—	2	4	no	—
52	C₂²×D₄×C₈₉	—	2	8	no	—
53	C₂²×D₄×C₈₉	—	2	32	no	—
54	C₂²×D₄×C₈₉	—	2	32	no	—
55	C₂²×D₄×C₈₉	—	4	16	no	—
56	C₂²×D₄×C₈₉	D₄	1	16	yes	complemented
57	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
58	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
59	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	4	yes	complemented
61	C₂²×D₄×C₈₉	C₂³	1	32	yes	complemented
62	C₂³×C₄×C₈₉	—	2	8	no	—
63	C₂³×C₄×C₈₉	D₄	1	8	yes	complemented
64	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
67	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
68	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
69	#127×C₈₉	—	2	64	no	—
70	#121×C₈₉	—	2	32	no	—
71	#120×C₈₉	—	2	128	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
74	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	32	no	—
76	C₂×C₂²⋊C₄×C₈₉	D₄	1	16	yes	complemented
77	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
78	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	complemented
79	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
80	C₂×C₄²×C₈₉	—	2	8	no	—
81	C₂×C₄²×C₈₉	C₂³	1	8	yes	complemented
82	#95×C₈₉	C₂³	1	8	yes	complemented
83	C₂⁴×C₈₉	—	2	4	no	—
84	C₂⁴×C₈₉	—	2	4	no	—
85	C₂⁴×C₈₉	—	2	64	no	—
86	C₂⁴×C₈₉	—	2	16	no	—
87	C₂⁴×C₈₉	—	2	32	no	—
88	C₂⁴×C₈₉	—	2	16	no	—
89	C₂⁴×C₈₉	—	2	8	no	—
90	C₂⁴×C₈₉	—	2	8	no	—
91	C₂⁴×C₈₉	—	2	16	no	—
92	C₂⁴×C₈₉	—	2	4	no	—
93	C₂⁴×C₈₉	—	2	32	no	—
94	C₂⁴×C₈₉	—	2	8	no	—
95	C₂⁴×C₈₉	—	2	8	no	—
96	C₂⁴×C₈₉	—	2	8	no	—
97	C₂⁴×C₈₉	—	4	16	no	—
98	C₂⁴×C₈₉	—	4	128	no	—
99	C₂⁴×C₈₉	—	4	32	no	—
100	C₂⁴×C₈₉	—	4	32	no	—
101	C₂⁴×C₈₉	C₂×D₄	1	16	yes	—
102	C₂⁴×C₈₉	C₂×D₄	1	8	yes	—
103	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
104	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
105	C₂⁴×C₈₉	C₂⁴	1	8	yes	—
106	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
107	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
108	C₂×D₄×C₈₉	—	2	64	no	—
109	C₂×D₄×C₈₉	—	2	256	no	—
110	C₂×D₄×C₈₉	—	2	32	no	—
111	C₂×D₄×C₈₉	—	2	32	no	—
112	C₂×D₄×C₈₉	—	2	16	no	—
113	C₂×D₄×C₈₉	—	2	64	no	—
114	C₂×D₄×C₈₉	—	2	64	no	—
115	C₂×D₄×C₈₉	—	2	16	no	—
116	C₂×D₄×C₈₉	—	2	16	no	—
117	C₂×D₄×C₈₉	—	2	16	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	2	16	no	—
120	C₂×D₄×C₈₉	—	2	64	no	—
121	C₂×D₄×C₈₉	—	4	32	no	—
122	C₂×D₄×C₈₉	—	4	128	no	—
123	C₂×D₄×C₈₉	—	4	32	no	—
124	C₂×D₄×C₈₉	—	4	16	no	—
125	C₂×D₄×C₈₉	C₂×D₄	1	32	yes	complemented
126	C₂²×C₄×C₈₉	—	2	8	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	2	8	no	—
129	C₂²×C₄×C₈₉	—	2	32	no	—
130	C₂²×C₄×C₈₉	—	2	16	no	—
131	C₂²×C₄×C₈₉	—	2	8	no	—
132	C₂²×C₄×C₈₉	—	2	4	no	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
135	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	complemented
137	C₂²×C₄×C₈₉	C₂×D₄	1	16	yes	complemented
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
142	C₄⋊C₄×C₈₉	—	2	8	no	—
143	C₂²⋊C₄×C₈₉	—	2	16	no	—
144	C₂²⋊C₄×C₈₉	—	2	64	no	—
145	C₂²⋊C₄×C₈₉	C₂×D₄	1	32	yes	complemented
146	C₄²×C₈₉	—	2	16	no	—
147	C₂³×C₈₉	—	2	8	no	—
148	C₂³×C₈₉	—	2	8	no	—
149	C₂³×C₈₉	—	2	32	no	—
150	C₂³×C₈₉	—	2	4	no	—
151	C₂³×C₈₉	—	2	4	no	—
152	C₂³×C₈₉	—	2	64	no	—
153	C₂³×C₈₉	—	2	32	no	—
154	C₂³×C₈₉	—	2	64	no	—
155	C₂³×C₈₉	—	2	16	no	—
156	C₂³×C₈₉	—	2	8	no	—
157	C₂³×C₈₉	—	2	8	no	—
158	C₂³×C₈₉	—	2	16	no	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	2	8	no	—
161	C₂³×C₈₉	—	2	8	no	—
162	C₂³×C₈₉	—	2	8	no	—
163	C₂³×C₈₉	—	4	128	no	—
164	C₂³×C₈₉	—	4	32	no	—
165	C₂³×C₈₉	—	4	256	no	—
166	C₂³×C₈₉	—	4	16	no	—
167	C₂³×C₈₉	—	4	32	no	—
168	C₂³×C₈₉	—	4	16	no	—
169	C₂³×C₈₉	—	4	32	no	—
170	C₂³×C₈₉	—	4	8	no	—
171	C₂³×C₈₉	—	4	8	no	—
172	C₂³×C₈₉	—	4	8	no	—
173	C₂³×C₈₉	—	4	32	no	—
174	C₂³×C₈₉	#127	1	16	yes	complemented
175	C₂³×C₈₉	C₂²×D₄	1	16	yes	—
176	C₂³×C₈₉	C₂²×D₄	1	8	yes	—
177	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
178	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
179	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
180	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
181	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
182	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
183	D₄×C₈₉	—	2	64	no	—
184	D₄×C₈₉	—	2	64	no	—
185	D₄×C₈₉	—	4	128	no	—
186	D₄×C₈₉	—	4	32	no	—
187	D₄×C₈₉	—	4	16	no	—
188	C₂×C₄×C₈₉	—	2	8	no	—
189	C₂×C₄×C₈₉	—	2	32	no	—
190	C₂×C₄×C₈₉	—	2	8	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	32	no	—
194	C₂×C₄×C₈₉	—	2	8	no	—
195	C₂×C₄×C₈₉	—	2	4	no	—
196	C₂×C₄×C₈₉	—	4	8	no	—
197	C₂×C₄×C₈₉	#120	1	16	yes	complemented
198	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	complemented
202	C₂²×C₈₉	—	2	4	no	—
203	C₂²×C₈₉	—	2	4	no	—
204	C₂²×C₈₉	—	2	32	no	—
205	C₂²×C₈₉	—	2	16	no	—
206	C₂²×C₈₉	—	2	16	no	—
207	C₂²×C₈₉	—	2	32	no	—
208	C₂²×C₈₉	—	4	128	no	—
209	C₂²×C₈₉	—	4	8	no	—
210	C₂²×C₈₉	—	4	8	no	—
211	C₂²×C₈₉	—	4	64	no	—
212	C₂²×C₈₉	—	4	16	no	—
213	C₂²×C₈₉	—	4	4	no	—
214	C₂²×C₈₉	—	4	4	no	—
215	C₂²×C₈₉	—	4	4	no	—
216	C₂²×C₈₉	—	4	16	no	—
217	C₂²×C₈₉	—	8	16	no	—
218	C₂²×C₈₉	C₂×#120	1	4	yes	—
219	C₂²×C₈₉	C₂×#127	1	4	yes	—
220	C₂²×C₈₉	C₂×#127	1	8	yes	complemented
221	C₂²×C₈₉	#535	1	4	yes	—
222	C₂²×C₈₉	D₄²	1	16	yes	—
223	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
224	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
225	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
226	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
227	C₄×C₈₉	—	2	4	no	—
228	C₄×C₈₉	—	2	16	no	—
229	C₄×C₈₉	—	4	4	no	—
230	C₄×C₈₉	C₂×#120	1	8	yes	complemented
231	C₂×#2433	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₈₉	—	2	8	no	—
233	C₂×C₈₉	—	4	16	no	—
234	C₂×C₈₉	—	8	4	no	—
235	C₂×C₈₉	#2433	1	8	yes	direct product factor
236	C₂×C₈₉	C₂²×#120	1	1	yes	characteristic
237	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
238	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
239	C₂×C₈₉	C₂×D₄²	1	4	yes	—
240	C₂⁴×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
241	C₂²×#127	C₂×C₈₉	1	2	yes	complemented
242	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic, complemented
243	C₂²×#120	C₂×C₈₉	1	4	yes	complemented
244	#2433	C₂×C₈₉	1	16	yes	direct product factor
245	C₂×#392	C₂×C₈₉	1	4	yes	complemented
246	C₂×#390	C₂×C₈₉	1	2	yes	complemented
247	C₂×C₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
248	C₈₉	C₂×#2433	1	1	yes	characteristic, direct product factor, Sylow
249	C₂⁶	C₂²×C₈₉	1	2	yes	—
250	C₂³×D₄	—	2	16	no	—
251	C₂³×D₄	—	2	8	no	—
252	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
253	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
254	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
255	C₂³×D₄	C₂²×C₈₉	1	8	yes	complemented
256	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
257	C₂³×D₄	C₂²×C₈₉	1	8	yes	complemented
258	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×#127	—	2	16	no	—
260	C₂×#127	C₂²×C₈₉	1	16	yes	complemented
261	C₂×#121	—	2	8	no	—
262	C₂×#121	C₂²×C₈₉	1	8	yes	complemented
263	C₂×#120	—	2	32	no	—
264	C₂×#120	C₂²×C₈₉	1	32	yes	complemented
265	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
266	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
267	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
268	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
269	C₂²×C₄²	C₂²×C₈₉	1	2	yes	complemented
270	#392	C₂²×C₈₉	1	32	yes	complemented
271	#390	C₂²×C₈₉	1	16	yes	complemented
272	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
273	C₂×#95	C₂²×C₈₉	1	2	yes	complemented
274	C₂⁵	—	2	16	no	—
275	C₂⁵	—	2	8	no	—
276	C₂⁵	—	2	16	no	—
277	C₂⁵	—	4	8	no	—
278	C₂⁵	C₂³×C₈₉	1	2	yes	—
279	C₂⁵	C₂³×C₈₉	1	4	yes	—
280	C₂⁵	C₂³×C₈₉	1	8	yes	—
281	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
282	C₂²×D₄	—	2	128	no	—
283	C₂²×D₄	—	2	16	no	—
284	C₂²×D₄	—	2	64	no	—
285	C₂²×D₄	—	2	16	no	—
286	C₂²×D₄	—	2	8	no	—
287	C₂²×D₄	—	2	32	no	—
288	C₂²×D₄	—	2	8	no	—
289	C₂²×D₄	—	2	8	no	—
290	C₂²×D₄	—	2	8	no	—
291	C₂²×D₄	—	2	4	no	—
292	C₂²×D₄	—	2	8	no	—
293	C₂²×D₄	—	2	32	no	—
294	C₂²×D₄	—	2	32	no	—
295	C₂²×D₄	—	4	16	no	—
296	C₂²×D₄	D₄×C₈₉	1	16	yes	complemented
297	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
298	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
299	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
300	C₂²×D₄	C₂³×C₈₉	1	4	yes	complemented
301	C₂²×D₄	C₂³×C₈₉	1	32	yes	complemented
302	C₂³×C₄	—	2	8	no	—
303	C₂³×C₄	D₄×C₈₉	1	8	yes	complemented
304	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
305	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
307	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
308	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
309	#127	—	2	64	no	—
310	#121	—	2	32	no	—
311	#120	—	2	128	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	complemented
314	C₂×C₂²⋊C₄	—	2	8	no	—
315	C₂×C₂²⋊C₄	—	2	32	no	—
316	C₂×C₂²⋊C₄	D₄×C₈₉	1	16	yes	complemented
317	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	complemented
319	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	complemented
320	C₂×C₄²	—	2	8	no	—
321	C₂×C₄²	C₂³×C₈₉	1	8	yes	complemented
322	#95	C₂³×C₈₉	1	8	yes	complemented
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	4	no	—
325	C₂⁴	—	2	64	no	—
326	C₂⁴	—	2	16	no	—
327	C₂⁴	—	2	32	no	—
328	C₂⁴	—	2	16	no	—
329	C₂⁴	—	2	8	no	—
330	C₂⁴	—	2	8	no	—
331	C₂⁴	—	2	16	no	—
332	C₂⁴	—	2	4	no	—
333	C₂⁴	—	2	32	no	—
334	C₂⁴	—	2	8	no	—
335	C₂⁴	—	2	8	no	—
336	C₂⁴	—	2	8	no	—
337	C₂⁴	—	4	16	no	—
338	C₂⁴	—	4	128	no	—
339	C₂⁴	—	4	32	no	—
340	C₂⁴	—	4	32	no	—
341	C₂⁴	C₂×D₄×C₈₉	1	16	yes	—
342	C₂⁴	C₂×D₄×C₈₉	1	8	yes	—
343	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
344	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
345	C₂⁴	C₂⁴×C₈₉	1	8	yes	—
346	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
347	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
348	C₂×D₄	—	2	64	no	—
349	C₂×D₄	—	2	256	no	—
350	C₂×D₄	—	2	32	no	—
351	C₂×D₄	—	2	32	no	—
352	C₂×D₄	—	2	16	no	—
353	C₂×D₄	—	2	64	no	—
354	C₂×D₄	—	2	64	no	—
355	C₂×D₄	—	2	16	no	—
356	C₂×D₄	—	2	16	no	—
357	C₂×D₄	—	2	16	no	—
358	C₂×D₄	—	2	8	no	—
359	C₂×D₄	—	2	16	no	—
360	C₂×D₄	—	2	64	no	—
361	C₂×D₄	—	4	32	no	—
362	C₂×D₄	—	4	128	no	—
363	C₂×D₄	—	4	32	no	—
364	C₂×D₄	—	4	16	no	—
365	C₂×D₄	C₂×D₄×C₈₉	1	32	yes	complemented
366	C₂²×C₄	—	2	8	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	8	no	—
369	C₂²×C₄	—	2	32	no	—
370	C₂²×C₄	—	2	16	no	—
371	C₂²×C₄	—	2	8	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
374	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
375	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	complemented
377	C₂²×C₄	C₂×D₄×C₈₉	1	16	yes	complemented
378	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
379	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
382	C₄⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	16	no	—
384	C₂²⋊C₄	—	2	64	no	—
385	C₂²⋊C₄	C₂×D₄×C₈₉	1	32	yes	complemented
386	C₄²	—	2	16	no	—
387	C₂³	—	2	8	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	2	32	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	64	no	—
393	C₂³	—	2	32	no	—
394	C₂³	—	2	64	no	—
395	C₂³	—	2	16	no	—
396	C₂³	—	2	8	no	—
397	C₂³	—	2	8	no	—
398	C₂³	—	2	16	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	2	8	no	—
401	C₂³	—	2	8	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	4	128	no	—
404	C₂³	—	4	32	no	—
405	C₂³	—	4	256	no	—
406	C₂³	—	4	16	no	—
407	C₂³	—	4	32	no	—
408	C₂³	—	4	16	no	—
409	C₂³	—	4	32	no	—
410	C₂³	—	4	8	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	8	no	—
413	C₂³	—	4	32	no	—
414	C₂³	#127×C₈₉	1	16	yes	complemented
415	C₂³	C₂²×D₄×C₈₉	1	16	yes	—
416	C₂³	C₂²×D₄×C₈₉	1	8	yes	—
417	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
418	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
419	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
420	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
421	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
422	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
423	D₄	—	2	64	no	—
424	D₄	—	2	64	no	—
425	D₄	—	4	128	no	—
426	D₄	—	4	32	no	—
427	D₄	—	4	16	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	32	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	32	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	#120×C₈₉	1	16	yes	complemented
438	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
440	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
441	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	complemented
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	32	no	—
445	C₂²	—	2	16	no	—
446	C₂²	—	2	16	no	—
447	C₂²	—	2	32	no	—
448	C₂²	—	4	128	no	—
449	C₂²	—	4	8	no	—
450	C₂²	—	4	8	no	—
451	C₂²	—	4	64	no	—
452	C₂²	—	4	16	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	16	no	—
457	C₂²	—	8	16	no	—
458	C₂²	C₂×#120×C₈₉	1	4	yes	—
459	C₂²	C₂×#127×C₈₉	1	4	yes	—
460	C₂²	C₂×#127×C₈₉	1	8	yes	complemented
461	C₂²	#535×C₈₉	1	4	yes	—
462	C₂²	D₄²×C₈₉	1	16	yes	—
463	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
464	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
465	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
466	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
467	C₄	—	2	4	no	—
468	C₄	—	2	16	no	—
469	C₄	—	4	4	no	—
470	C₄	C₂×#120×C₈₉	1	8	yes	complemented
471	C₂	—	2	8	no	—
472	C₂	—	4	16	no	—
473	C₂	—	8	4	no	—
474	C₂	C₈₉×#2433	1	8	yes	direct product factor
475	C₂	C₂²×#120×C₈₉	1	1	yes	characteristic
476	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
477	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
478	C₂	C₂×D₄²×C₈₉	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂⁴×D₄×C₈₉	C₂	semidirect
2. C₂²×#127×C₈₉	C₂	semidirect
3. C₂²×#121×C₈₉	C₂	semidirect
4. C₂²×#120×C₈₉	C₂	semidirect
5. C₈₉×#2433	C₂	direct (N × H)
6. C₂×#392×C₈₉	C₂	semidirect
7. C₂×#390×C₈₉	C₂	semidirect
8. C₂×C₄×C₂²⋊C₄×C₈₉	C₂	semidirect
15. C₂³×D₄×C₈₉	C₂²	semidirect
16. C₂³×D₄×C₈₉	C₂²	semidirect
17. C₂³×D₄×C₈₉	C₂²	semidirect
20. C₂×#127×C₈₉	C₂²	semidirect
22. C₂×#121×C₈₉	C₂²	semidirect
24. C₂×#120×C₈₉	C₂²	semidirect
25. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
28. C₂²×C₂²⋊C₄×C₈₉	C₂²	semidirect
29. C₂²×C₄²×C₈₉	C₂²	semidirect
30. #392×C₈₉	C₂²	semidirect
31. #390×C₈₉	C₂²	semidirect
32. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
33. C₂×#95×C₈₉	C₂²	semidirect
56. C₂²×D₄×C₈₉	D₄	semidirect
60. C₂²×D₄×C₈₉	C₂³	semidirect
61. C₂²×D₄×C₈₉	C₂³	semidirect
63. C₂³×C₄×C₈₉	D₄	semidirect
73. C₂×C₄⋊C₄×C₈₉	C₂³	semidirect
76. C₂×C₂²⋊C₄×C₈₉	D₄	semidirect
78. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
79. C₂×C₂²⋊C₄×C₈₉	C₂³	semidirect
81. C₂×C₄²×C₈₉	C₂³	semidirect
82. #95×C₈₉	C₂³	semidirect
125. C₂×D₄×C₈₉	C₂×D₄	semidirect
136. C₂²×C₄×C₈₉	C₂×D₄	semidirect
137. C₂²×C₄×C₈₉	C₂×D₄	semidirect
145. C₂²⋊C₄×C₈₉	C₂×D₄	semidirect
174. C₂³×C₈₉	#127	semidirect
197. C₂×C₄×C₈₉	#120	semidirect
201. C₂×C₄×C₈₉	C₂²×D₄	semidirect
220. C₂²×C₈₉	C₂×#127	semidirect
230. C₄×C₈₉	C₂×#120	semidirect
231. C₂×#2433	C₈₉	direct (N × H)
235. C₂×C₈₉	#2433	direct (N × H)
240. C₂⁴×D₄	C₂×C₈₉	semidirect
241. C₂²×#127	C₂×C₈₉	semidirect
242. C₂²×#121	C₂×C₈₉	semidirect
243. C₂²×#120	C₂×C₈₉	semidirect
244. #2433	C₂×C₈₉	direct (N × H)
245. C₂×#392	C₂×C₈₉	semidirect
246. C₂×#390	C₂×C₈₉	semidirect
247. C₂×C₄×C₂²⋊C₄	C₂×C₈₉	semidirect
248. C₈₉	C₂×#2433	direct (N × H)
255. C₂³×D₄	C₂²×C₈₉	semidirect
256. C₂³×D₄	C₂²×C₈₉	semidirect
257. C₂³×D₄	C₂²×C₈₉	semidirect
260. C₂×#127	C₂²×C₈₉	semidirect
262. C₂×#121	C₂²×C₈₉	semidirect
264. C₂×#120	C₂²×C₈₉	semidirect
265. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
267. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
268. C₂²×C₂²⋊C₄	C₂²×C₈₉	semidirect
269. C₂²×C₄²	C₂²×C₈₉	semidirect
270. #392	C₂²×C₈₉	semidirect
271. #390	C₂²×C₈₉	semidirect
272. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
273. C₂×#95	C₂²×C₈₉	semidirect
296. C₂²×D₄	D₄×C₈₉	semidirect
300. C₂²×D₄	C₂³×C₈₉	semidirect
301. C₂²×D₄	C₂³×C₈₉	semidirect
303. C₂³×C₄	D₄×C₈₉	semidirect
313. C₂×C₄⋊C₄	C₂³×C₈₉	semidirect
316. C₂×C₂²⋊C₄	D₄×C₈₉	semidirect
318. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
319. C₂×C₂²⋊C₄	C₂³×C₈₉	semidirect
321. C₂×C₄²	C₂³×C₈₉	semidirect
322. #95	C₂³×C₈₉	semidirect
365. C₂×D₄	C₂×D₄×C₈₉	semidirect
376. C₂²×C₄	C₂×D₄×C₈₉	semidirect
377. C₂²×C₄	C₂×D₄×C₈₉	semidirect
385. C₂²⋊C₄	C₂×D₄×C₈₉	semidirect
414. C₂³	#127×C₈₉	semidirect
437. C₂×C₄	#120×C₈₉	semidirect
441. C₂×C₄	C₂²×D₄×C₈₉	semidirect
460. C₂²	C₂×#127×C₈₉	semidirect
470. C₄	C₂×#120×C₈₉	semidirect
474. C₂	C₈₉×#2433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₈₉	2
C₂²×#127×C₈₉	2
C₂²×#121×C₈₉	2
C₂²×#120×C₈₉	2
C₈₉×#2433	2
C₂×#392×C₈₉	2
C₂×#390×C₈₉	2
C₂×C₄×C₂²⋊C₄×C₈₉	2
C₂×#2433	89

Subgroups — C2×C89×#2433 #36412521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2433 #36412521