Subgroups — C₂×C₈₉×#3081 #36438333

Order 22784.

2234 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3081	C₂	1	16	yes	maximal, direct product factor
4	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#476×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#474×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#418×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂²×#102×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	#544×C₈₉	—	2	4	no	—
17	#544×C₈₉	C₂²	1	8	yes	complemented
18	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
20	C₂×#125×C₈₉	—	2	1	no	—
21	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
22	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
23	#518×C₈₉	—	2	4	no	—
24	#518×C₈₉	C₂²	1	8	yes	—
25	C₂×C₄×D₄×C₈₉	—	2	1	no	—
26	C₂×C₄×D₄×C₈₉	—	2	1	no	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₈₉	—	2	2	no	—
34	#478×C₈₉	C₂²	1	16	yes	complemented
35	#478×C₈₉	C₂²	1	16	yes	complemented
36	#476×C₈₉	C₂²	1	16	yes	complemented
37	#474×C₈₉	C₂²	1	16	yes	complemented
38	#428×C₈₉	C₂²	1	8	yes	complemented
39	#427×C₈₉	C₂²	1	8	yes	complemented
40	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
42	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
45	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#424×C₈₉	C₂²	1	8	yes	complemented
47	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
48	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
49	#418×C₈₉	C₂²	1	8	yes	—
50	C₂×#102×C₈₉	C₂²	1	2	yes	—
51	C₂×#102×C₈₉	C₂²	1	2	yes	—
52	C₂×#102×C₈₉	C₂²	1	2	yes	—
53	C₂×#102×C₈₉	C₂²	1	2	yes	—
54	C₂×#102×C₈₉	C₂²	1	8	yes	—
55	C₂⁵×C₈₉	—	2	1	no	—
56	C₂²×Q₈×C₈₉	—	2	2	no	—
57	C₂²×D₄×C₈₉	—	2	1	no	—
58	C₂²×D₄×C₈₉	—	2	2	no	—
59	C₂²×D₄×C₈₉	—	2	4	no	—
60	C₂²×D₄×C₈₉	Q₈	1	8	yes	complemented
61	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	—	2	1	no	—
64	C₂³×C₄×C₈₉	—	2	2	no	—
65	C₂³×C₄×C₈₉	—	2	2	no	—
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₈₉	—	2	4	no	—
68	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
69	C₂²×C₈×C₈₉	—	2	4	no	—
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
74	C₄⋊Q₈×C₈₉	—	2	8	no	—
75	C₄⋊Q₈×C₈₉	—	2	4	no	—
76	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	complemented
77	#125×C₈₉	—	2	8	no	—
78	#125×C₈₉	—	2	4	no	—
79	#125×C₈₉	C₂³	1	8	yes	complemented
80	C₂²⋊Q₈×C₈₉	—	2	16	no	—
81	C₄×D₄×C₈₉	—	2	8	no	—
82	C₄×D₄×C₈₉	—	2	8	no	—
83	C₄×D₄×C₈₉	—	2	4	no	—
84	C₄×D₄×C₈₉	—	2	4	no	—
85	C₄×D₄×C₈₉	C₂³	1	8	yes	—
86	C₄×D₄×C₈₉	C₂³	1	8	yes	—
87	#117×C₈₉	—	2	2	no	—
88	#117×C₈₉	—	2	2	no	—
89	#117×C₈₉	D₄	1	4	yes	—
90	#117×C₈₉	C₂³	1	4	yes	—
91	#117×C₈₉	C₂³	1	4	yes	—
92	#117×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
109	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
111	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
112	C₂×C₄²×C₈₉	—	2	1	no	—
113	C₂×C₄²×C₈₉	—	2	1	no	—
114	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
115	#107×C₈₉	C₂³	1	4	yes	complemented
116	#107×C₈₉	C₂³	1	4	yes	complemented
117	#107×C₈₉	C₂³	1	8	yes	complemented
118	#106×C₈₉	C₂³	1	4	yes	complemented
119	#106×C₈₉	C₂³	1	4	yes	complemented
120	#106×C₈₉	C₂³	1	8	yes	complemented
121	C₄⋊C₈×C₈₉	C₂³	1	8	yes	complemented
122	C₄⋊C₈×C₈₉	C₂³	1	8	yes	complemented
123	#102×C₈₉	C₂³	1	8	yes	—
124	#102×C₈₉	C₂³	1	8	yes	—
125	#102×C₈₉	C₂³	1	8	yes	—
126	#102×C₈₉	C₂³	1	8	yes	—
127	C₂⁴×C₈₉	—	2	2	no	—
128	C₂⁴×C₈₉	—	2	8	no	—
129	C₂⁴×C₈₉	—	2	4	no	—
130	C₂⁴×C₈₉	—	8	2	no	—
131	C₂⁴×C₈₉	—	8	2	no	—
132	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₈₉	—	2	8	no	—
134	C₂×Q₈×C₈₉	—	8	4	no	—
135	C₂×D₄×C₈₉	—	2	16	no	—
136	C₂×D₄×C₈₉	—	2	8	no	—
137	C₂×D₄×C₈₉	—	2	4	no	—
138	C₂×D₄×C₈₉	—	2	2	no	—
139	C₂×D₄×C₈₉	—	2	4	no	—
140	C₂×D₄×C₈₉	—	2	8	no	—
141	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
142	C₂×D₄×C₈₉	C₂×Q₈	1	16	yes	complemented
143	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	2	no	—
149	C₂²×C₄×C₈₉	—	2	4	no	—
150	C₂²×C₄×C₈₉	—	2	8	no	—
151	C₂²×C₄×C₈₉	—	2	8	no	—
152	C₂²×C₄×C₈₉	—	8	4	no	—
153	C₂²×C₄×C₈₉	—	8	4	no	—
154	C₂²×C₄×C₈₉	—	8	2	no	—
155	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
156	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
160	C₂²×C₄×C₈₉	#41	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	M₁₆×C₈₉	—	2	8	no	—
164	C₂×C₈×C₈₉	—	2	2	no	—
165	C₂×C₈×C₈₉	—	2	2	no	—
166	C₂×C₈×C₈₉	—	2	8	no	—
167	C₂×C₈×C₈₉	—	2	4	no	—
168	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
169	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
170	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	2	no	—
173	C₄⋊C₄×C₈₉	—	2	8	no	—
174	C₄⋊C₄×C₈₉	—	2	8	no	—
175	C₄⋊C₄×C₈₉	—	2	8	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
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	2	yes	—
185	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
186	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
187	C₂²⋊C₄×C₈₉	—	2	4	no	—
188	C₂²⋊C₄×C₈₉	—	2	4	no	—
189	C₂²⋊C₄×C₈₉	—	2	8	no	—
190	C₂²⋊C₄×C₈₉	—	2	8	no	—
191	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
192	C₄²×C₈₉	—	2	4	no	—
193	C₄²×C₈₉	—	2	4	no	—
194	C₄²×C₈₉	C₂×D₄	1	4	yes	—
195	C₄²×C₈₉	C₂⁴	1	4	yes	—
196	C₂³×C₈₉	—	2	2	no	—
197	C₂³×C₈₉	—	2	2	no	—
198	C₂³×C₈₉	—	2	8	no	—
199	C₂³×C₈₉	—	2	4	no	—
200	C₂³×C₈₉	—	2	16	no	—
201	C₂³×C₈₉	—	4	4	no	—
202	C₂³×C₈₉	—	4	4	no	—
203	C₂³×C₈₉	—	8	16	no	—
204	C₂³×C₈₉	—	8	4	no	—
205	C₂³×C₈₉	—	8	4	no	—
206	C₂³×C₈₉	C₂²⋊Q₈	1	4	yes	—
207	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
208	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₈₉	—	8	8	no	—
210	D₄×C₈₉	—	2	8	no	—
211	D₄×C₈₉	—	2	16	no	—
212	D₄×C₈₉	—	2	4	no	—
213	D₄×C₈₉	C₂²×Q₈	1	8	yes	—
214	C₂×C₄×C₈₉	—	2	4	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	2	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	2	no	—
220	C₂×C₄×C₈₉	—	2	4	no	—
221	C₂×C₄×C₈₉	—	4	2	no	—
222	C₂×C₄×C₈₉	—	4	4	no	—
223	C₂×C₄×C₈₉	—	4	2	no	—
224	C₂×C₄×C₈₉	—	4	2	no	—
225	C₂×C₄×C₈₉	—	4	2	no	—
226	C₂×C₄×C₈₉	—	8	8	no	—
227	C₂×C₄×C₈₉	—	8	8	no	—
228	C₂×C₄×C₈₉	—	8	4	no	—
229	C₂×C₄×C₈₉	C₂²⋊Q₈	1	8	yes	—
230	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
231	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
232	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
233	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
236	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
237	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
238	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
239	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
240	C₈×C₈₉	—	2	2	no	—
241	C₈×C₈₉	—	2	2	no	—
242	C₈×C₈₉	—	2	4	no	—
243	C₂²×C₈₉	—	2	8	no	—
244	C₂²×C₈₉	—	2	2	no	—
245	C₂²×C₈₉	—	2	2	no	—
246	C₂²×C₈₉	—	2	8	no	—
247	C₂²×C₈₉	—	4	16	no	—
248	C₂²×C₈₉	—	4	4	no	—
249	C₂²×C₈₉	—	4	4	no	—
250	C₂²×C₈₉	—	8	16	no	—
251	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
252	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
253	C₂²×C₈₉	#576	1	2	yes	—
254	C₂²×C₈₉	#577	1	2	yes	—
255	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
256	C₄×C₈₉	—	2	4	no	—
257	C₄×C₈₉	—	2	4	no	—
258	C₄×C₈₉	—	4	2	no	—
259	C₄×C₈₉	—	4	4	no	—
260	C₄×C₈₉	—	4	2	no	—
261	C₄×C₈₉	—	4	2	no	—
262	C₄×C₈₉	—	4	2	no	—
263	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
264	C₄×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
265	C₄×C₈₉	C₂³×Q₈	1	1	yes	characteristic
266	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
267	C₂×#3081	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₈₉	—	2	4	no	—
269	C₂×C₈₉	—	4	8	no	—
270	C₂×C₈₉	#3081	1	4	yes	direct product factor
271	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
272	C₂×C₈₉	C₂×#576	1	1	yes	characteristic
273	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
274	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
275	C₂×#518	C₂×C₈₉	1	1	yes	characteristic
276	#3081	C₂×C₈₉	1	16	yes	direct product factor
277	C₂×#478	C₂×C₈₉	1	2	yes	complemented
278	C₂×#478	C₂×C₈₉	1	2	yes	complemented
279	C₂×#476	C₂×C₈₉	1	2	yes	complemented
280	C₂×#474	C₂×C₈₉	1	2	yes	complemented
281	C₂×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
282	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
283	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
284	C₂×#418	C₂×C₈₉	1	1	yes	characteristic
285	C₂²×#102	C₂×C₈₉	1	1	yes	characteristic
286	C₈₉	C₂×#3081	1	1	yes	characteristic, direct product factor, Sylow
287	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
288	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
289	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
290	#544	—	2	4	no	—
291	#544	C₂²×C₈₉	1	8	yes	complemented
292	C₂×C₄⋊Q₈	—	2	1	no	—
293	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
294	C₂×#125	—	2	1	no	—
295	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
296	C₂×C₂²⋊Q₈	—	2	2	no	—
297	#518	—	2	4	no	—
298	#518	C₂²×C₈₉	1	8	yes	—
299	C₂×C₄×D₄	—	2	1	no	—
300	C₂×C₄×D₄	—	2	1	no	—
301	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
302	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
303	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
304	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
305	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
307	C₂²×C₂²⋊C₄	—	2	2	no	—
308	#478	C₂²×C₈₉	1	16	yes	complemented
309	#478	C₂²×C₈₉	1	16	yes	complemented
310	#476	C₂²×C₈₉	1	16	yes	complemented
311	#474	C₂²×C₈₉	1	16	yes	complemented
312	#428	C₂²×C₈₉	1	8	yes	complemented
313	#427	C₂²×C₈₉	1	8	yes	complemented
314	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
315	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
316	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic, complemented
317	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
318	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
319	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic, complemented
320	#424	C₂²×C₈₉	1	8	yes	complemented
321	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
322	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	complemented
323	#418	C₂²×C₈₉	1	8	yes	—
324	C₂×#102	C₂²×C₈₉	1	2	yes	—
325	C₂×#102	C₂²×C₈₉	1	2	yes	—
326	C₂×#102	C₂²×C₈₉	1	2	yes	—
327	C₂×#102	C₂²×C₈₉	1	8	yes	—
328	C₂×#102	C₂²×C₈₉	1	2	yes	—
329	C₂⁵	—	2	1	no	—
330	C₂²×Q₈	—	2	2	no	—
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	4	no	—
334	C₂²×D₄	Q₈×C₈₉	1	8	yes	complemented
335	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
336	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	2	no	—
339	C₂³×C₄	—	2	2	no	—
340	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
341	C₂×M₁₆	—	2	4	no	—
342	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
343	C₂²×C₈	—	2	4	no	—
344	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
347	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
348	C₄⋊Q₈	—	2	8	no	—
349	C₄⋊Q₈	—	2	4	no	—
350	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	complemented
351	#125	—	2	8	no	—
352	#125	—	2	4	no	—
353	#125	C₂³×C₈₉	1	8	yes	complemented
354	C₂²⋊Q₈	—	2	16	no	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	8	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	C₂³×C₈₉	1	8	yes	—
360	C₄×D₄	C₂³×C₈₉	1	8	yes	—
361	#117	—	2	2	no	—
362	#117	—	2	2	no	—
363	#117	D₄×C₈₉	1	4	yes	—
364	#117	C₂³×C₈₉	1	4	yes	—
365	#117	C₂³×C₈₉	1	4	yes	—
366	#117	C₂³×C₈₉	1	4	yes	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	2	no	—
371	C₂×C₄⋊C₄	—	2	2	no	—
372	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
373	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
375	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
376	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	16	no	—
385	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
389	#107	C₂³×C₈₉	1	4	yes	complemented
390	#107	C₂³×C₈₉	1	4	yes	complemented
391	#107	C₂³×C₈₉	1	8	yes	complemented
392	#106	C₂³×C₈₉	1	4	yes	complemented
393	#106	C₂³×C₈₉	1	4	yes	complemented
394	#106	C₂³×C₈₉	1	8	yes	complemented
395	C₄⋊C₈	C₂³×C₈₉	1	8	yes	complemented
396	C₄⋊C₈	C₂³×C₈₉	1	8	yes	complemented
397	#102	C₂³×C₈₉	1	8	yes	—
398	#102	C₂³×C₈₉	1	8	yes	—
399	#102	C₂³×C₈₉	1	8	yes	—
400	#102	C₂³×C₈₉	1	8	yes	—
401	C₂⁴	—	2	2	no	—
402	C₂⁴	—	2	8	no	—
403	C₂⁴	—	2	4	no	—
404	C₂⁴	—	8	2	no	—
405	C₂⁴	—	8	2	no	—
406	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	—	8	4	no	—
409	C₂×D₄	—	2	16	no	—
410	C₂×D₄	—	2	8	no	—
411	C₂×D₄	—	2	4	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
416	C₂×D₄	C₂×Q₈×C₈₉	1	16	yes	complemented
417	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	4	no	—
424	C₂²×C₄	—	2	8	no	—
425	C₂²×C₄	—	2	8	no	—
426	C₂²×C₄	—	8	4	no	—
427	C₂²×C₄	—	8	4	no	—
428	C₂²×C₄	—	8	2	no	—
429	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
433	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
434	C₂²×C₄	#41×C₈₉	1	4	yes	—
435	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
437	M₁₆	—	2	8	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	8	no	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
443	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
444	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	—	2	8	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
455	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
456	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
457	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
458	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
459	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
460	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	—	2	8	no	—
465	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	4	no	—
468	C₄²	C₂×D₄×C₈₉	1	4	yes	—
469	C₄²	C₂⁴×C₈₉	1	4	yes	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	2	no	—
472	C₂³	—	2	8	no	—
473	C₂³	—	2	4	no	—
474	C₂³	—	2	16	no	—
475	C₂³	—	4	4	no	—
476	C₂³	—	4	4	no	—
477	C₂³	—	8	4	no	—
478	C₂³	—	8	4	no	—
479	C₂³	—	8	16	no	—
480	C₂³	C₂²⋊Q₈×C₈₉	1	4	yes	—
481	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
482	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
483	Q₈	—	8	8	no	—
484	D₄	—	2	8	no	—
485	D₄	—	2	16	no	—
486	D₄	—	2	4	no	—
487	D₄	C₂²×Q₈×C₈₉	1	8	yes	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	—	8	8	no	—
502	C₂×C₄	—	8	4	no	—
503	C₂×C₄	C₂²⋊Q₈×C₈₉	1	8	yes	—
504	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
505	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
507	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
508	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
509	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
510	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
511	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
512	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
513	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
514	C₈	—	2	2	no	—
515	C₈	—	2	2	no	—
516	C₈	—	2	4	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	8	no	—
520	C₂²	—	2	8	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	16	no	—
524	C₂²	—	8	16	no	—
525	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
526	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
527	C₂²	#576×C₈₉	1	2	yes	—
528	C₂²	#577×C₈₉	1	2	yes	—
529	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
530	C₄	—	2	4	no	—
531	C₄	—	2	4	no	—
532	C₄	—	4	2	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	2	no	—
535	C₄	—	4	2	no	—
536	C₄	—	4	2	no	—
537	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
538	C₄	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
539	C₄	C₂³×Q₈×C₈₉	1	1	yes	characteristic
540	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
541	C₂	—	2	4	no	—
542	C₂	—	4	8	no	—
543	C₂	C₈₉×#3081	1	4	yes	direct product factor
544	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
545	C₂	C₂×#576×C₈₉	1	1	yes	characteristic
546	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#544×C₈₉	C₂	semidirect
3. C₈₉×#3081	C₂	direct (N × H)
4. C₂×#478×C₈₉	C₂	semidirect
5. C₂×#478×C₈₉	C₂	semidirect
6. C₂×#476×C₈₉	C₂	semidirect
7. C₂×#474×C₈₉	C₂	semidirect
8. C₂×#428×C₈₉	C₂	semidirect
9. C₂×#427×C₈₉	C₂	semidirect
10. C₂×#424×C₈₉	C₂	semidirect
17. #544×C₈₉	C₂²	semidirect
19. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
21. C₂×#125×C₈₉	C₂²	semidirect
34. #478×C₈₉	C₂²	semidirect
35. #478×C₈₉	C₂²	semidirect
36. #476×C₈₉	C₂²	semidirect
37. #474×C₈₉	C₂²	semidirect
38. #428×C₈₉	C₂²	semidirect
39. #427×C₈₉	C₂²	semidirect
40. C₂×#107×C₈₉	C₂²	semidirect
41. C₂×#107×C₈₉	C₂²	semidirect
42. C₂×#107×C₈₉	C₂²	semidirect
43. C₂×#106×C₈₉	C₂²	semidirect
44. C₂×#106×C₈₉	C₂²	semidirect
45. C₂×#106×C₈₉	C₂²	semidirect
46. #424×C₈₉	C₂²	semidirect
47. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
48. C₂×C₄⋊C₈×C₈₉	C₂²	semidirect
60. C₂²×D₄×C₈₉	Q₈	semidirect
76. C₄⋊Q₈×C₈₉	C₂³	semidirect
79. #125×C₈₉	C₂³	semidirect
115. #107×C₈₉	C₂³	semidirect
116. #107×C₈₉	C₂³	semidirect
117. #107×C₈₉	C₂³	semidirect
118. #106×C₈₉	C₂³	semidirect
119. #106×C₈₉	C₂³	semidirect
120. #106×C₈₉	C₂³	semidirect
121. C₄⋊C₈×C₈₉	C₂³	semidirect
122. C₄⋊C₈×C₈₉	C₂³	semidirect
142. C₂×D₄×C₈₉	C₂×Q₈	semidirect
267. C₂×#3081	C₈₉	direct (N × H)
270. C₂×C₈₉	#3081	direct (N × H)
274. C₂×#544	C₂×C₈₉	semidirect
276. #3081	C₂×C₈₉	direct (N × H)
277. C₂×#478	C₂×C₈₉	semidirect
278. C₂×#478	C₂×C₈₉	semidirect
279. C₂×#476	C₂×C₈₉	semidirect
280. C₂×#474	C₂×C₈₉	semidirect
281. C₂×#428	C₂×C₈₉	semidirect
282. C₂×#427	C₂×C₈₉	semidirect
283. C₂×#424	C₂×C₈₉	semidirect
286. C₈₉	C₂×#3081	direct (N × H)
291. #544	C₂²×C₈₉	semidirect
293. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
295. C₂×#125	C₂²×C₈₉	semidirect
308. #478	C₂²×C₈₉	semidirect
309. #478	C₂²×C₈₉	semidirect
310. #476	C₂²×C₈₉	semidirect
311. #474	C₂²×C₈₉	semidirect
312. #428	C₂²×C₈₉	semidirect
313. #427	C₂²×C₈₉	semidirect
314. C₂×#107	C₂²×C₈₉	semidirect
315. C₂×#107	C₂²×C₈₉	semidirect
316. C₂×#107	C₂²×C₈₉	semidirect
317. C₂×#106	C₂²×C₈₉	semidirect
318. C₂×#106	C₂²×C₈₉	semidirect
319. C₂×#106	C₂²×C₈₉	semidirect
320. #424	C₂²×C₈₉	semidirect
321. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
322. C₂×C₄⋊C₈	C₂²×C₈₉	semidirect
334. C₂²×D₄	Q₈×C₈₉	semidirect
350. C₄⋊Q₈	C₂³×C₈₉	semidirect
353. #125	C₂³×C₈₉	semidirect
389. #107	C₂³×C₈₉	semidirect
390. #107	C₂³×C₈₉	semidirect
391. #107	C₂³×C₈₉	semidirect
392. #106	C₂³×C₈₉	semidirect
393. #106	C₂³×C₈₉	semidirect
394. #106	C₂³×C₈₉	semidirect
395. C₄⋊C₈	C₂³×C₈₉	semidirect
396. C₄⋊C₈	C₂³×C₈₉	semidirect
416. C₂×D₄	C₂×Q₈×C₈₉	semidirect
543. C₂	C₈₉×#3081	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×#544×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#3081	2
C₂×#478×C₈₉	2
C₂×#476×C₈₉	2
C₂×#474×C₈₉	2
C₂×#428×C₈₉	2
C₂×#427×C₈₉	2
C₂×#424×C₈₉	2
C₂×#418×C₈₉	2
C₂²×#102×C₈₉	2
C₂×#3081	89

Subgroups — C2×C89×#3081 #36438333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3081 #36438333