Subgroups — C₂×C₈₉×#3354 #36439095

Order 22784.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#555×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#547×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3354	C₂	1	16	yes	maximal, direct product factor
4	C₂×#498×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#481×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#482×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#476×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#474×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#469×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#436×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#428×C₈₉	C₂	1	2	yes	maximal, complemented
13	C₂²×#41×C₈₉	—	2	1	no	—
14	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
16	#555×C₈₉	—	2	4	no	—
17	#555×C₈₉	C₂²	1	8	yes	complemented
18	#547×C₈₉	—	2	4	no	—
19	#547×C₈₉	C₂²	1	8	yes	complemented
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#124×C₈₉	—	2	2	no	—
23	C₂×#123×C₈₉	—	2	2	no	—
24	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
25	C₂×#121×C₈₉	—	2	1	no	—
26	C₂×#121×C₈₉	C₂²	1	2	yes	—
27	C₂×#121×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	—	2	1	no	—
32	C₂×#117×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
34	#498×C₈₉	C₂²	1	8	yes	complemented
35	#482×C₈₉	C₂²	1	16	yes	complemented
36	#481×C₈₉	C₂²	1	16	yes	complemented
37	#476×C₈₉	C₂²	1	8	yes	complemented
38	#474×C₈₉	C₂²	1	8	yes	complemented
39	#469×C₈₉	C₂²	1	16	yes	complemented
40	C₄×D₈×C₈₉	C₂²	1	8	yes	complemented
41	#436×C₈₉	C₂²	1	8	yes	complemented
42	#428×C₈₉	C₂²	1	16	yes	complemented
43	C₂×#107×C₈₉	C₂²	1	2	yes	—
44	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#106×C₈₉	C₂²	1	2	yes	—
46	C₂×#106×C₈₉	C₂²	1	2	yes	—
47	C₂×#106×C₈₉	C₂²	1	2	yes	—
48	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#102×C₈₉	C₂²	1	2	yes	—
50	C₂×#102×C₈₉	C₂²	1	2	yes	—
51	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
54	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₈₉	—	2	8	no	—
56	C₂×#41×C₈₉	—	4	8	no	—
57	C₂²×Q₈×C₈₉	—	2	1	no	—
58	C₂²×Q₈×C₈₉	—	2	1	no	—
59	C₂²×D₄×C₈₉	—	2	2	no	—
60	C₂²×D₄×C₈₉	—	2	2	no	—
61	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	—	2	2	no	—
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	—	2	1	no	—
67	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
68	C₂×D₈×C₈₉	—	2	4	no	—
69	C₂×D₈×C₈₉	C₂³	1	4	yes	—
70	C₂×M₁₆×C₈₉	—	2	8	no	—
71	C₂×M₁₆×C₈₉	C₂³	1	8	yes	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₈₉	—	2	2	no	—
76	C₄⋊Q₈×C₈₉	—	2	2	no	—
77	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
78	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
79	#124×C₈₉	—	2	16	no	—
80	#123×C₈₉	—	2	16	no	—
81	C₂²⋊Q₈×C₈₉	—	2	8	no	—
82	#121×C₈₉	—	2	8	no	—
83	#121×C₈₉	—	2	4	no	—
84	#121×C₈₉	—	2	4	no	—
85	#121×C₈₉	C₂³	1	8	yes	—
86	#121×C₈₉	C₂³	1	8	yes	—
87	C₄×D₄×C₈₉	—	2	2	no	—
88	C₄×D₄×C₈₉	—	2	2	no	—
89	C₄×D₄×C₈₉	D₄	1	4	yes	—
90	C₄×D₄×C₈₉	C₂³	1	4	yes	—
91	C₄×D₄×C₈₉	C₂³	1	4	yes	—
92	C₄×D₄×C₈₉	C₂³	1	4	yes	—
93	#117×C₈₉	—	2	4	no	—
94	#117×C₈₉	—	2	8	no	—
95	#117×C₈₉	C₂³	1	8	yes	—
96	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
106	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
107	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
108	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
112	C₂×C₄²×C₈₉	—	2	2	no	—
113	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	#107×C₈₉	C₂³	1	4	yes	—
115	#107×C₈₉	C₂³	1	8	yes	—
116	#106×C₈₉	C₂³	1	8	yes	—
117	#106×C₈₉	C₂³	1	8	yes	—
118	#106×C₈₉	C₂³	1	8	yes	—
119	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
120	#102×C₈₉	C₂³	1	4	yes	—
121	#102×C₈₉	C₂³	1	4	yes	—
122	#102×C₈₉	C₂³	1	8	yes	—
123	#102×C₈₉	C₂³	1	8	yes	—
124	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
125	C₄×C₈×C₈₉	C₂³	1	4	yes	—
126	C₂⁴×C₈₉	—	2	1	no	—
127	C₂⁴×C₈₉	—	2	1	no	—
128	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
129	#41×C₈₉	—	4	32	no	—
130	C₂×Q₈×C₈₉	—	2	4	no	—
131	C₂×Q₈×C₈₉	—	2	4	no	—
132	C₂×Q₈×C₈₉	—	4	4	no	—
133	C₂×Q₈×C₈₉	—	8	2	no	—
134	C₂×D₄×C₈₉	—	2	8	no	—
135	C₂×D₄×C₈₉	—	2	8	no	—
136	C₂×D₄×C₈₉	—	2	4	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	—	2	1	no	—
139	C₂×D₄×C₈₉	—	2	2	no	—
140	C₂×D₄×C₈₉	—	2	2	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	—	2	2	no	—
143	C₂×D₄×C₈₉	—	4	8	no	—
144	C₂×D₄×C₈₉	—	8	4	no	—
145	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
146	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₈₉	—	2	4	no	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	8	no	—
151	C₂²×C₄×C₈₉	—	2	1	no	—
152	C₂²×C₄×C₈₉	—	2	2	no	—
153	C₂²×C₄×C₈₉	—	2	1	no	—
154	C₂²×C₄×C₈₉	—	2	2	no	—
155	C₂²×C₄×C₈₉	—	2	4	no	—
156	C₂²×C₄×C₈₉	—	2	4	no	—
157	C₂²×C₄×C₈₉	—	4	8	no	—
158	C₂²×C₄×C₈₉	—	4	4	no	—
159	C₂²×C₄×C₈₉	—	4	4	no	—
160	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
166	D₈×C₈₉	—	2	8	no	—
167	M₁₆×C₈₉	—	2	16	no	—
168	C₂×C₈×C₈₉	—	2	4	no	—
169	C₂×C₈×C₈₉	—	2	2	no	—
170	C₂×C₈×C₈₉	#41	1	4	yes	complemented
171	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
172	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
173	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
174	C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₄⋊C₄×C₈₉	—	2	2	no	—
176	C₄⋊C₄×C₈₉	—	2	8	no	—
177	C₄⋊C₄×C₈₉	—	2	4	no	—
178	C₄⋊C₄×C₈₉	—	2	4	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
182	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
183	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
184	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
186	C₂²⋊C₄×C₈₉	—	2	8	no	—
187	C₂²⋊C₄×C₈₉	—	2	8	no	—
188	C₂²⋊C₄×C₈₉	—	2	4	no	—
189	C₂²⋊C₄×C₈₉	—	2	4	no	—
190	C₂²⋊C₄×C₈₉	—	2	8	no	—
191	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
192	C₄²×C₈₉	—	2	8	no	—
193	C₄²×C₈₉	C₂×D₄	1	2	yes	—
194	C₄²×C₈₉	C₂⁴	1	2	yes	—
195	C₂³×C₈₉	—	2	4	no	—
196	C₂³×C₈₉	—	2	4	no	—
197	C₂³×C₈₉	—	2	4	no	—
198	C₂³×C₈₉	—	2	2	no	—
199	C₂³×C₈₉	—	2	2	no	—
200	C₂³×C₈₉	—	4	2	no	—
201	C₂³×C₈₉	—	4	2	no	—
202	C₂³×C₈₉	—	4	2	no	—
203	C₂³×C₈₉	—	4	2	no	—
204	C₂³×C₈₉	—	4	2	no	—
205	C₂³×C₈₉	—	4	2	no	—
206	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
207	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₈₉	—	4	8	no	—
209	Q₈×C₈₉	—	8	4	no	—
210	D₄×C₈₉	—	2	8	no	—
211	D₄×C₈₉	—	2	2	no	—
212	D₄×C₈₉	—	2	2	no	—
213	D₄×C₈₉	—	2	2	no	—
214	D₄×C₈₉	—	2	2	no	—
215	D₄×C₈₉	—	4	16	no	—
216	D₄×C₈₉	—	4	2	no	—
217	D₄×C₈₉	—	4	2	no	—
218	D₄×C₈₉	—	8	8	no	—
219	C₂×C₄×C₈₉	—	2	4	no	—
220	C₂×C₄×C₈₉	—	2	2	no	—
221	C₂×C₄×C₈₉	—	2	8	no	—
222	C₂×C₄×C₈₉	—	2	4	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	2	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	4	no	—
228	C₂×C₄×C₈₉	—	4	16	no	—
229	C₂×C₄×C₈₉	—	4	2	no	—
230	C₂×C₄×C₈₉	—	4	2	no	—
231	C₂×C₄×C₈₉	—	4	4	no	—
232	C₂×C₄×C₈₉	—	4	4	no	—
233	C₂×C₄×C₈₉	—	4	8	no	—
234	C₂×C₄×C₈₉	—	4	8	no	—
235	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
236	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
237	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
238	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
240	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
241	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
242	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
243	C₈×C₈₉	—	2	4	no	—
244	C₈×C₈₉	—	2	2	no	—
245	C₈×C₈₉	C₂×#41	1	4	yes	complemented
246	C₂²×C₈₉	—	2	4	no	—
247	C₂²×C₈₉	—	2	4	no	—
248	C₂²×C₈₉	—	2	4	no	—
249	C₂²×C₈₉	—	4	8	no	—
250	C₂²×C₈₉	—	4	2	no	—
251	C₂²×C₈₉	—	4	2	no	—
252	C₂²×C₈₉	—	4	2	no	—
253	C₂²×C₈₉	—	4	2	no	—
254	C₂²×C₈₉	—	4	2	no	—
255	C₂²×C₈₉	—	4	2	no	—
256	C₂²×C₈₉	—	8	4	no	—
257	C₂²×C₈₉	—	8	4	no	—
258	C₂²×C₈₉	#547	1	2	yes	—
259	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
260	C₂²×C₈₉	#577	1	2	yes	—
261	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
262	C₄×C₈₉	—	2	4	no	—
263	C₄×C₈₉	—	2	2	no	—
264	C₄×C₈₉	—	4	2	no	—
265	C₄×C₈₉	—	4	2	no	—
266	C₄×C₈₉	—	4	4	no	—
267	C₄×C₈₉	—	4	4	no	—
268	C₄×C₈₉	#547	1	2	yes	—
269	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	4	yes	—
270	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
271	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
272	C₂×#3354	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂×C₈₉	—	4	4	no	—
274	C₂×C₈₉	—	8	2	no	—
275	C₂×C₈₉	—	8	2	no	—
276	C₂×C₈₉	#3354	1	4	yes	direct product factor
277	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
278	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
279	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
280	C₂×#555	C₂×C₈₉	1	1	yes	characteristic, complemented
281	C₂×#547	C₂×C₈₉	1	1	yes	characteristic, complemented
282	#3354	C₂×C₈₉	1	16	yes	direct product factor
283	C₂×#498	C₂×C₈₉	1	1	yes	characteristic, complemented
284	C₂×#481	C₂×C₈₉	1	2	yes	complemented
285	C₂×#482	C₂×C₈₉	1	2	yes	complemented
286	C₂×#476	C₂×C₈₉	1	1	yes	characteristic, complemented
287	C₂×#474	C₂×C₈₉	1	1	yes	characteristic, complemented
288	C₂×#469	C₂×C₈₉	1	2	yes	complemented
289	C₂×C₄×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
290	C₂×#436	C₂×C₈₉	1	1	yes	characteristic, complemented
291	C₂×#428	C₂×C₈₉	1	2	yes	complemented
292	C₈₉	C₂×#3354	1	1	yes	characteristic, direct product factor, Sylow
293	C₂²×#41	—	2	1	no	—
294	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
295	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
296	#555	—	2	4	no	—
297	#555	C₂²×C₈₉	1	8	yes	complemented
298	#547	—	2	4	no	—
299	#547	C₂²×C₈₉	1	8	yes	complemented
300	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
301	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
302	C₂×#124	—	2	2	no	—
303	C₂×#123	—	2	2	no	—
304	C₂×C₂²⋊Q₈	—	2	1	no	—
305	C₂×#121	—	2	1	no	—
306	C₂×#121	C₂²×C₈₉	1	2	yes	—
307	C₂×#121	C₂²×C₈₉	1	2	yes	—
308	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
309	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
310	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
311	C₂×#117	—	2	1	no	—
312	C₂×#117	C₂²×C₈₉	1	2	yes	—
313	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
314	#498	C₂²×C₈₉	1	8	yes	complemented
315	#482	C₂²×C₈₉	1	16	yes	complemented
316	#481	C₂²×C₈₉	1	16	yes	complemented
317	#476	C₂²×C₈₉	1	8	yes	complemented
318	#474	C₂²×C₈₉	1	8	yes	complemented
319	#469	C₂²×C₈₉	1	16	yes	complemented
320	C₄×D₈	C₂²×C₈₉	1	8	yes	complemented
321	#436	C₂²×C₈₉	1	8	yes	complemented
322	#428	C₂²×C₈₉	1	16	yes	complemented
323	C₂×#107	C₂²×C₈₉	1	2	yes	—
324	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
325	C₂×#106	C₂²×C₈₉	1	2	yes	—
326	C₂×#106	C₂²×C₈₉	1	2	yes	—
327	C₂×#106	C₂²×C₈₉	1	2	yes	—
328	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
329	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
330	C₂×#102	C₂²×C₈₉	1	2	yes	—
331	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
332	C₂×#102	C₂²×C₈₉	1	2	yes	—
333	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
334	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×#41	—	2	8	no	—
336	C₂×#41	—	4	8	no	—
337	C₂²×Q₈	—	2	1	no	—
338	C₂²×Q₈	—	2	1	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
343	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
344	C₂³×C₄	—	2	2	no	—
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	—	2	1	no	—
347	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
348	C₂×D₈	—	2	4	no	—
349	C₂×D₈	C₂³×C₈₉	1	4	yes	—
350	C₂×M₁₆	—	2	8	no	—
351	C₂×M₁₆	C₂³×C₈₉	1	8	yes	—
352	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
353	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
355	C₄⋊Q₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
358	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
359	#124	—	2	16	no	—
360	#123	—	2	16	no	—
361	C₂²⋊Q₈	—	2	8	no	—
362	#121	—	2	8	no	—
363	#121	—	2	4	no	—
364	#121	—	2	4	no	—
365	#121	C₂³×C₈₉	1	8	yes	—
366	#121	C₂³×C₈₉	1	8	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	D₄×C₈₉	1	4	yes	—
370	C₄×D₄	C₂³×C₈₉	1	4	yes	—
371	C₄×D₄	C₂³×C₈₉	1	4	yes	—
372	C₄×D₄	C₂³×C₈₉	1	4	yes	—
373	#117	—	2	4	no	—
374	#117	—	2	8	no	—
375	#117	C₂³×C₈₉	1	8	yes	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₄⋊C₄	—	2	4	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
383	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
384	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
386	C₂×C₂²⋊C₄	—	2	2	no	—
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
392	C₂×C₄²	—	2	2	no	—
393	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
394	#107	C₂³×C₈₉	1	4	yes	—
395	#107	C₂³×C₈₉	1	8	yes	—
396	#106	C₂³×C₈₉	1	8	yes	—
397	#106	C₂³×C₈₉	1	8	yes	—
398	#106	C₂³×C₈₉	1	8	yes	—
399	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
400	#102	C₂³×C₈₉	1	4	yes	—
401	#102	C₂³×C₈₉	1	4	yes	—
402	#102	C₂³×C₈₉	1	8	yes	—
403	#102	C₂³×C₈₉	1	8	yes	—
404	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
405	C₄×C₈	C₂³×C₈₉	1	4	yes	—
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
409	#41	—	4	32	no	—
410	C₂×Q₈	—	2	4	no	—
411	C₂×Q₈	—	2	4	no	—
412	C₂×Q₈	—	4	4	no	—
413	C₂×Q₈	—	8	2	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	2	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	4	8	no	—
424	C₂×D₄	—	8	4	no	—
425	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
426	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
427	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	2	8	no	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	4	8	no	—
438	C₂²×C₄	—	4	4	no	—
439	C₂²×C₄	—	4	4	no	—
440	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
441	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
443	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
445	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
446	D₈	—	2	8	no	—
447	M₁₆	—	2	16	no	—
448	C₂×C₈	—	2	4	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	#41×C₈₉	1	4	yes	complemented
451	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
452	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
453	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	8	no	—
457	C₄⋊C₄	—	2	4	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
462	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
463	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
464	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
465	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	8	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	8	no	—
471	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
472	C₄²	—	2	8	no	—
473	C₄²	C₂×D₄×C₈₉	1	2	yes	—
474	C₄²	C₂⁴×C₈₉	1	2	yes	—
475	C₂³	—	2	4	no	—
476	C₂³	—	2	4	no	—
477	C₂³	—	2	4	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
487	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
488	Q₈	—	4	8	no	—
489	Q₈	—	8	4	no	—
490	D₄	—	2	8	no	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	4	16	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	8	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	16	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	8	no	—
514	C₂×C₄	—	4	8	no	—
515	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
516	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
517	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
520	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
521	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
522	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
523	C₈	—	2	4	no	—
524	C₈	—	2	2	no	—
525	C₈	C₂×#41×C₈₉	1	4	yes	complemented
526	C₂²	—	2	4	no	—
527	C₂²	—	2	4	no	—
528	C₂²	—	2	4	no	—
529	C₂²	—	4	8	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	8	4	no	—
537	C₂²	—	8	4	no	—
538	C₂²	#547×C₈₉	1	2	yes	—
539	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	2	yes	—
540	C₂²	#577×C₈₉	1	2	yes	—
541	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	2	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	4	no	—
548	C₄	#547×C₈₉	1	2	yes	—
549	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	4	yes	—
550	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
551	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
552	C₂	—	4	4	no	—
553	C₂	—	8	2	no	—
554	C₂	—	8	2	no	—
555	C₂	C₈₉×#3354	1	4	yes	direct product factor
556	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
557	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
558	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#555×C₈₉	C₂	semidirect
2. C₂×#547×C₈₉	C₂	semidirect
3. C₈₉×#3354	C₂	direct (N × H)
4. C₂×#498×C₈₉	C₂	semidirect
5. C₂×#481×C₈₉	C₂	semidirect
6. C₂×#482×C₈₉	C₂	semidirect
7. C₂×#476×C₈₉	C₂	semidirect
8. C₂×#474×C₈₉	C₂	semidirect
9. C₂×#469×C₈₉	C₂	semidirect
10. C₂×C₄×D₈×C₈₉	C₂	semidirect
11. C₂×#436×C₈₉	C₂	semidirect
12. C₂×#428×C₈₉	C₂	semidirect
17. #555×C₈₉	C₂²	semidirect
19. #547×C₈₉	C₂²	semidirect
34. #498×C₈₉	C₂²	semidirect
35. #482×C₈₉	C₂²	semidirect
36. #481×C₈₉	C₂²	semidirect
37. #476×C₈₉	C₂²	semidirect
38. #474×C₈₉	C₂²	semidirect
39. #469×C₈₉	C₂²	semidirect
40. C₄×D₈×C₈₉	C₂²	semidirect
41. #436×C₈₉	C₂²	semidirect
42. #428×C₈₉	C₂²	semidirect
170. C₂×C₈×C₈₉	#41	semidirect
245. C₈×C₈₉	C₂×#41	semidirect
272. C₂×#3354	C₈₉	direct (N × H)
276. C₂×C₈₉	#3354	direct (N × H)
280. C₂×#555	C₂×C₈₉	semidirect
281. C₂×#547	C₂×C₈₉	semidirect
282. #3354	C₂×C₈₉	direct (N × H)
283. C₂×#498	C₂×C₈₉	semidirect
284. C₂×#481	C₂×C₈₉	semidirect
285. C₂×#482	C₂×C₈₉	semidirect
286. C₂×#476	C₂×C₈₉	semidirect
287. C₂×#474	C₂×C₈₉	semidirect
288. C₂×#469	C₂×C₈₉	semidirect
289. C₂×C₄×D₈	C₂×C₈₉	semidirect
290. C₂×#436	C₂×C₈₉	semidirect
291. C₂×#428	C₂×C₈₉	semidirect
292. C₈₉	C₂×#3354	direct (N × H)
297. #555	C₂²×C₈₉	semidirect
299. #547	C₂²×C₈₉	semidirect
314. #498	C₂²×C₈₉	semidirect
315. #482	C₂²×C₈₉	semidirect
316. #481	C₂²×C₈₉	semidirect
317. #476	C₂²×C₈₉	semidirect
318. #474	C₂²×C₈₉	semidirect
319. #469	C₂²×C₈₉	semidirect
320. C₄×D₈	C₂²×C₈₉	semidirect
321. #436	C₂²×C₈₉	semidirect
322. #428	C₂²×C₈₉	semidirect
450. C₂×C₈	#41×C₈₉	semidirect
525. C₈	C₂×#41×C₈₉	semidirect
555. C₂	C₈₉×#3354	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#555×C₈₉	2
C₂×#547×C₈₉	2
C₈₉×#3354	2
C₂×#498×C₈₉	2
C₂×#481×C₈₉	2
C₂×#482×C₈₉	2
C₂×#476×C₈₉	2
C₂×#474×C₈₉	2
C₂×#469×C₈₉	2
C₂×C₄×D₈×C₈₉	2
C₂×#436×C₈₉	2
C₂×#428×C₈₉	2
C₂×#3354	89

Subgroups — C2×C89×#3354 #36439095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3354 #36439095