Subgroups — C₂×C₈₉×#3054 #36438289

Order 22784.

2918 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#525×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3054	C₂	1	16	yes	maximal, direct product factor
5	C₂×#470×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#469×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#468×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#416×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×#135×C₈₉	—	2	8	no	—
13	C₂×#135×C₈₉	C₂²	1	8	yes	complemented
14	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	complemented
16	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×M₁₆×C₈₉	—	2	8	no	—
18	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
19	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
20	C₂²×M₁₆×C₈₉	C₂²	1	8	yes	complemented
21	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	#525×C₈₉	—	2	8	no	—
24	#525×C₈₉	C₂²	1	16	yes	complemented
25	C₂×#123×C₈₉	—	2	2	no	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
27	C₂×#121×C₈₉	C₂²	1	4	yes	—
28	C₂×#120×C₈₉	—	2	2	no	—
29	C₂×C₄×D₄×C₈₉	—	2	4	no	—
30	C₂×#117×C₈₉	C₂²	1	2	yes	—
31	#470×C₈₉	C₂²	1	16	yes	complemented
32	#469×C₈₉	C₂²	1	16	yes	complemented
33	#468×C₈₉	C₂²	1	32	yes	complemented
34	#427×C₈₉	C₂²	1	8	yes	complemented
35	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
36	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
37	#416×C₈₉	C₂²	1	16	yes	complemented
38	C₂×#103×C₈₉	C₂²	1	4	yes	complemented
39	C₂×#102×C₈₉	C₂²	1	4	yes	complemented
40	C₂⁵×C₈₉	D₄	1	1	yes	characteristic
41	C₂×#41×C₈₉	—	2	4	no	—
42	C₂×#41×C₈₉	—	2	8	no	—
43	C₂×#41×C₈₉	—	2	8	no	—
44	C₂×#41×C₈₉	C₂³	1	8	yes	—
45	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₈₉	—	2	4	no	—
47	C₂²×D₄×C₈₉	—	2	2	no	—
48	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
49	C₂³×C₄×C₈₉	—	2	4	no	—
50	C₂³×C₄×C₈₉	—	2	4	no	—
51	C₂³×C₄×C₈₉	—	2	2	no	—
52	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	D₄	1	4	yes	—
54	C₂³×C₄×C₈₉	D₄	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	#135×C₈₉	—	2	32	no	—
59	C₂×Q₁₆×C₈₉	—	2	4	no	—
60	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	complemented
61	C₂×SD₁₆×C₈₉	—	2	8	no	—
62	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	complemented
63	C₂×D₈×C₈₉	—	2	4	no	—
64	C₂×D₈×C₈₉	C₂³	1	4	yes	complemented
65	C₂×M₁₆×C₈₉	—	2	8	no	—
66	C₂×M₁₆×C₈₉	—	2	8	no	—
67	C₂×M₁₆×C₈₉	—	2	32	no	—
68	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
69	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
70	C₂²×C₈×C₈₉	—	2	4	no	—
71	C₂²×C₈×C₈₉	D₄	1	8	yes	complemented
72	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
77	#123×C₈₉	—	2	16	no	—
78	C₂²⋊Q₈×C₈₉	—	2	8	no	—
79	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	C₂³	1	16	yes	—
82	#120×C₈₉	—	2	16	no	—
83	C₄×D₄×C₈₉	—	2	32	no	—
84	#117×C₈₉	—	2	4	no	—
85	#117×C₈₉	C₂³	1	8	yes	—
86	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
90	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
91	C₂×C₄²×C₈₉	—	2	2	no	—
92	#107×C₈₉	C₂³	1	8	yes	complemented
93	#106×C₈₉	C₂³	1	8	yes	complemented
94	#103×C₈₉	C₂³	1	16	yes	complemented
95	#102×C₈₉	C₂³	1	16	yes	complemented
96	C₂⁴×C₈₉	—	2	4	no	—
97	C₂⁴×C₈₉	—	2	2	no	—
98	C₂⁴×C₈₉	—	4	4	no	—
99	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
100	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
102	#41×C₈₉	—	2	16	no	—
103	#41×C₈₉	—	2	16	no	—
104	#41×C₈₉	—	4	16	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×Q₈×C₈₉	—	2	4	no	—
107	C₂×Q₈×C₈₉	—	2	4	no	—
108	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
109	C₂×D₄×C₈₉	—	2	16	no	—
110	C₂×D₄×C₈₉	—	2	8	no	—
111	C₂×D₄×C₈₉	—	2	4	no	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	4	no	—
114	C₂×D₄×C₈₉	—	4	16	no	—
115	C₂×D₄×C₈₉	—	4	8	no	—
116	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
117	C₂²×C₄×C₈₉	—	2	4	no	—
118	C₂²×C₄×C₈₉	—	2	8	no	—
119	C₂²×C₄×C₈₉	—	2	16	no	—
120	C₂²×C₄×C₈₉	—	2	4	no	—
121	C₂²×C₄×C₈₉	—	2	8	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	8	no	—
124	C₂²×C₄×C₈₉	—	2	4	no	—
125	C₂²×C₄×C₈₉	—	2	2	no	—
126	C₂²×C₄×C₈₉	—	2	8	no	—
127	C₂²×C₄×C₈₉	—	4	8	no	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
139	Q₁₆×C₈₉	—	2	8	no	—
140	SD₁₆×C₈₉	—	2	16	no	—
141	D₈×C₈₉	—	2	8	no	—
142	M₁₆×C₈₉	—	2	16	no	—
143	M₁₆×C₈₉	—	2	16	no	—
144	C₂×C₈×C₈₉	—	2	4	no	—
145	C₂×C₈×C₈₉	—	2	8	no	—
146	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₈₉	C₂×D₄	1	16	yes	complemented
149	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
150	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
151	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	16	no	—
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₂²⋊C₄×C₈₉	—	2	16	no	—
157	C₂²⋊C₄×C₈₉	—	2	16	no	—
158	C₄²×C₈₉	—	2	8	no	—
159	C₂³×C₈₉	—	2	4	no	—
160	C₂³×C₈₉	—	2	8	no	—
161	C₂³×C₈₉	—	2	4	no	—
162	C₂³×C₈₉	—	2	8	no	—
163	C₂³×C₈₉	—	2	4	no	—
164	C₂³×C₈₉	—	4	8	no	—
165	C₂³×C₈₉	—	4	16	no	—
166	C₂³×C₈₉	—	4	4	no	—
167	C₂³×C₈₉	—	4	8	no	—
168	C₂³×C₈₉	#121	1	4	yes	—
169	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
170	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
171	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₈₉	—	2	4	no	—
173	Q₈×C₈₉	—	2	4	no	—
174	Q₈×C₈₉	—	4	4	no	—
175	D₄×C₈₉	—	2	4	no	—
176	D₄×C₈₉	—	2	4	no	—
177	D₄×C₈₉	—	4	32	no	—
178	D₄×C₈₉	—	4	16	no	—
179	D₄×C₈₉	—	4	4	no	—
180	C₂×C₄×C₈₉	—	2	8	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	2	16	no	—
183	C₂×C₄×C₈₉	—	2	8	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	8	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	4	4	no	—
189	C₂×C₄×C₈₉	—	4	8	no	—
190	C₂×C₄×C₈₉	—	4	16	no	—
191	C₂×C₄×C₈₉	#121	1	4	yes	—
192	C₂×C₄×C₈₉	#121	1	8	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
198	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
199	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
200	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
201	C₈×C₈₉	—	2	4	no	—
202	C₈×C₈₉	C₂²×D₄	1	4	yes	—
203	C₈×C₈₉	C₂²×D₄	1	4	yes	—
204	C₂²×C₈₉	—	2	8	no	—
205	C₂²×C₈₉	—	2	4	no	—
206	C₂²×C₈₉	—	2	4	no	—
207	C₂²×C₈₉	—	2	8	no	—
208	C₂²×C₈₉	—	4	16	no	—
209	C₂²×C₈₉	—	4	8	no	—
210	C₂²×C₈₉	—	4	4	no	—
211	C₂²×C₈₉	—	4	8	no	—
212	C₂²×C₈₉	—	8	8	no	—
213	C₂²×C₈₉	C₂×#121	1	4	yes	—
214	C₂²×C₈₉	C₂×#121	1	2	yes	—
215	C₂²×C₈₉	#575	1	4	yes	—
216	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
217	C₄×C₈₉	—	2	4	no	—
218	C₄×C₈₉	—	4	4	no	—
219	C₄×C₈₉	—	4	8	no	—
220	C₄×C₈₉	C₂×#121	1	4	yes	—
221	C₄×C₈₉	C₂×#121	1	2	yes	—
222	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
223	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
224	C₂×#3054	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂×C₈₉	—	2	4	no	—
226	C₂×C₈₉	—	4	4	no	—
227	C₂×C₈₉	—	8	4	no	—
228	C₂×C₈₉	#3054	1	4	yes	direct product factor
229	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
230	C₂×C₈₉	C₂×#575	1	2	yes	—
231	C₂²×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
232	C₂³×M₁₆	C₂×C₈₉	1	1	yes	characteristic, complemented
233	C₂×#525	C₂×C₈₉	1	2	yes	complemented
234	#3054	C₂×C₈₉	1	16	yes	direct product factor
235	C₂×#470	C₂×C₈₉	1	2	yes	complemented
236	C₂×#469	C₂×C₈₉	1	2	yes	complemented
237	C₂×#468	C₂×C₈₉	1	4	yes	complemented
238	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
239	C₂×#416	C₂×C₈₉	1	2	yes	complemented
240	C₈₉	C₂×#3054	1	1	yes	characteristic, direct product factor, Sylow
241	C₂²×#41	C₂²×C₈₉	1	2	yes	—
242	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
243	C₂×#135	—	2	8	no	—
244	C₂×#135	C₂²×C₈₉	1	8	yes	complemented
245	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic, complemented
246	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	complemented
247	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
248	C₂²×M₁₆	—	2	8	no	—
249	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
250	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
251	C₂²×M₁₆	C₂²×C₈₉	1	8	yes	complemented
252	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
253	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
254	#525	—	2	8	no	—
255	#525	C₂²×C₈₉	1	16	yes	complemented
256	C₂×#123	—	2	2	no	—
257	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
258	C₂×#121	C₂²×C₈₉	1	4	yes	—
259	C₂×#120	—	2	2	no	—
260	C₂×C₄×D₄	—	2	4	no	—
261	C₂×#117	C₂²×C₈₉	1	2	yes	—
262	#470	C₂²×C₈₉	1	16	yes	complemented
263	#469	C₂²×C₈₉	1	16	yes	complemented
264	#468	C₂²×C₈₉	1	32	yes	complemented
265	#427	C₂²×C₈₉	1	8	yes	complemented
266	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
267	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
268	#416	C₂²×C₈₉	1	16	yes	complemented
269	C₂×#103	C₂²×C₈₉	1	4	yes	complemented
270	C₂×#102	C₂²×C₈₉	1	4	yes	complemented
271	C₂⁵	D₄×C₈₉	1	1	yes	characteristic
272	C₂×#41	—	2	4	no	—
273	C₂×#41	—	2	8	no	—
274	C₂×#41	—	2	8	no	—
275	C₂×#41	C₂³×C₈₉	1	8	yes	—
276	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	D₄×C₈₉	1	2	yes	—
284	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
285	C₂³×C₄	D₄×C₈₉	1	4	yes	—
286	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
288	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
289	#135	—	2	32	no	—
290	C₂×Q₁₆	—	2	4	no	—
291	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	complemented
292	C₂×SD₁₆	—	2	8	no	—
293	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	complemented
294	C₂×D₈	—	2	4	no	—
295	C₂×D₈	C₂³×C₈₉	1	4	yes	complemented
296	C₂×M₁₆	—	2	8	no	—
297	C₂×M₁₆	—	2	8	no	—
298	C₂×M₁₆	—	2	32	no	—
299	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
300	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
301	C₂²×C₈	—	2	4	no	—
302	C₂²×C₈	D₄×C₈₉	1	8	yes	complemented
303	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
304	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
305	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
307	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
308	#123	—	2	16	no	—
309	C₂²⋊Q₈	—	2	8	no	—
310	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
311	#121	—	2	8	no	—
312	#121	C₂³×C₈₉	1	16	yes	—
313	#120	—	2	16	no	—
314	C₄×D₄	—	2	32	no	—
315	#117	—	2	4	no	—
316	#117	C₂³×C₈₉	1	8	yes	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	—	2	4	no	—
321	C₂×C₂²⋊C₄	—	2	4	no	—
322	C₂×C₄²	—	2	2	no	—
323	#107	C₂³×C₈₉	1	8	yes	complemented
324	#106	C₂³×C₈₉	1	8	yes	complemented
325	#103	C₂³×C₈₉	1	16	yes	complemented
326	#102	C₂³×C₈₉	1	16	yes	complemented
327	C₂⁴	—	2	4	no	—
328	C₂⁴	—	2	2	no	—
329	C₂⁴	—	4	4	no	—
330	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
331	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
332	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
333	#41	—	2	16	no	—
334	#41	—	2	16	no	—
335	#41	—	4	16	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
340	C₂×D₄	—	2	16	no	—
341	C₂×D₄	—	2	8	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	4	16	no	—
346	C₂×D₄	—	4	8	no	—
347	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	8	no	—
350	C₂²×C₄	—	2	16	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	4	8	no	—
359	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
361	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
362	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
363	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
366	C₂²×C₄	#41×C₈₉	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
368	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
370	Q₁₆	—	2	8	no	—
371	SD₁₆	—	2	16	no	—
372	D₈	—	2	8	no	—
373	M₁₆	—	2	16	no	—
374	M₁₆	—	2	16	no	—
375	C₂×C₈	—	2	4	no	—
376	C₂×C₈	—	2	8	no	—
377	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
378	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
379	C₂×C₈	C₂×D₄×C₈₉	1	16	yes	complemented
380	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
381	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
382	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
383	C₄⋊C₄	—	2	16	no	—
384	C₄⋊C₄	—	2	4	no	—
385	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	16	no	—
388	C₂²⋊C₄	—	2	16	no	—
389	C₄²	—	2	8	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	2	8	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	4	no	—
395	C₂³	—	4	8	no	—
396	C₂³	—	4	16	no	—
397	C₂³	—	4	4	no	—
398	C₂³	—	4	8	no	—
399	C₂³	#121×C₈₉	1	4	yes	—
400	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
401	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
402	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	4	32	no	—
409	D₄	—	4	16	no	—
410	D₄	—	4	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	4	no	—
420	C₂×C₄	—	4	8	no	—
421	C₂×C₄	—	4	16	no	—
422	C₂×C₄	#121×C₈₉	1	4	yes	—
423	C₂×C₄	#121×C₈₉	1	8	yes	—
424	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
429	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
430	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
431	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
432	C₈	—	2	4	no	—
433	C₈	C₂²×D₄×C₈₉	1	4	yes	—
434	C₈	C₂²×D₄×C₈₉	1	4	yes	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	16	no	—
440	C₂²	—	4	8	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	8	no	—
444	C₂²	C₂×#121×C₈₉	1	4	yes	—
445	C₂²	C₂×#121×C₈₉	1	2	yes	—
446	C₂²	#575×C₈₉	1	4	yes	—
447	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
448	C₄	—	2	4	no	—
449	C₄	—	4	8	no	—
450	C₄	—	4	4	no	—
451	C₄	C₂×#121×C₈₉	1	4	yes	—
452	C₄	C₂×#121×C₈₉	1	2	yes	—
453	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
454	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
455	C₂	—	2	4	no	—
456	C₂	—	4	4	no	—
457	C₂	—	8	4	no	—
458	C₂	C₈₉×#3054	1	4	yes	direct product factor
459	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
460	C₂	C₂×#575×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂⁴×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#135×C₈₉	C₂	semidirect
2. C₂³×M₁₆×C₈₉	C₂	semidirect
3. C₂×#525×C₈₉	C₂	semidirect
4. C₈₉×#3054	C₂	direct (N × H)
5. C₂×#470×C₈₉	C₂	semidirect
6. C₂×#469×C₈₉	C₂	semidirect
7. C₂×#468×C₈₉	C₂	semidirect
8. C₂×#427×C₈₉	C₂	semidirect
9. C₂×#416×C₈₉	C₂	semidirect
13. C₂×#135×C₈₉	C₂²	semidirect
14. C₂²×Q₁₆×C₈₉	C₂²	semidirect
15. C₂²×SD₁₆×C₈₉	C₂²	semidirect
16. C₂²×D₈×C₈₉	C₂²	semidirect
20. C₂²×M₁₆×C₈₉	C₂²	semidirect
24. #525×C₈₉	C₂²	semidirect
31. #470×C₈₉	C₂²	semidirect
32. #469×C₈₉	C₂²	semidirect
33. #468×C₈₉	C₂²	semidirect
34. #427×C₈₉	C₂²	semidirect
35. C₂×#107×C₈₉	C₂²	semidirect
36. C₂×#106×C₈₉	C₂²	semidirect
37. #416×C₈₉	C₂²	semidirect
38. C₂×#103×C₈₉	C₂²	semidirect
39. C₂×#102×C₈₉	C₂²	semidirect
60. C₂×Q₁₆×C₈₉	C₂³	semidirect
62. C₂×SD₁₆×C₈₉	C₂³	semidirect
64. C₂×D₈×C₈₉	C₂³	semidirect
71. C₂²×C₈×C₈₉	D₄	semidirect
92. #107×C₈₉	C₂³	semidirect
93. #106×C₈₉	C₂³	semidirect
94. #103×C₈₉	C₂³	semidirect
95. #102×C₈₉	C₂³	semidirect
148. C₂×C₈×C₈₉	C₂×D₄	semidirect
224. C₂×#3054	C₈₉	direct (N × H)
228. C₂×C₈₉	#3054	direct (N × H)
231. C₂²×#135	C₂×C₈₉	semidirect
232. C₂³×M₁₆	C₂×C₈₉	semidirect
233. C₂×#525	C₂×C₈₉	semidirect
234. #3054	C₂×C₈₉	direct (N × H)
235. C₂×#470	C₂×C₈₉	semidirect
236. C₂×#469	C₂×C₈₉	semidirect
237. C₂×#468	C₂×C₈₉	semidirect
238. C₂×#427	C₂×C₈₉	semidirect
239. C₂×#416	C₂×C₈₉	semidirect
240. C₈₉	C₂×#3054	direct (N × H)
244. C₂×#135	C₂²×C₈₉	semidirect
245. C₂²×Q₁₆	C₂²×C₈₉	semidirect
246. C₂²×SD₁₆	C₂²×C₈₉	semidirect
247. C₂²×D₈	C₂²×C₈₉	semidirect
251. C₂²×M₁₆	C₂²×C₈₉	semidirect
255. #525	C₂²×C₈₉	semidirect
262. #470	C₂²×C₈₉	semidirect
263. #469	C₂²×C₈₉	semidirect
264. #468	C₂²×C₈₉	semidirect
265. #427	C₂²×C₈₉	semidirect
266. C₂×#107	C₂²×C₈₉	semidirect
267. C₂×#106	C₂²×C₈₉	semidirect
268. #416	C₂²×C₈₉	semidirect
269. C₂×#103	C₂²×C₈₉	semidirect
270. C₂×#102	C₂²×C₈₉	semidirect
291. C₂×Q₁₆	C₂³×C₈₉	semidirect
293. C₂×SD₁₆	C₂³×C₈₉	semidirect
295. C₂×D₈	C₂³×C₈₉	semidirect
302. C₂²×C₈	D₄×C₈₉	semidirect
323. #107	C₂³×C₈₉	semidirect
324. #106	C₂³×C₈₉	semidirect
325. #103	C₂³×C₈₉	semidirect
326. #102	C₂³×C₈₉	semidirect
379. C₂×C₈	C₂×D₄×C₈₉	semidirect
458. C₂	C₈₉×#3054	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#135×C₈₉	2
C₂³×M₁₆×C₈₉	2
C₂×#525×C₈₉	2
C₈₉×#3054	2
C₂×#470×C₈₉	2
C₂×#469×C₈₉	2
C₂×#468×C₈₉	2
C₂×#427×C₈₉	2
C₂×#416×C₈₉	2
C₂×#3054	89

Subgroups — C2×C89×#3054 #36438289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3054 #36438289