Subgroups — C₂×C₈₉×#3084 #36438336

Order 22784.

2094 conjugacy classes of subgroups.

The subgroup lattice has 546 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×#520×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3084	C₂	1	16	yes	maximal, direct product factor
4	C₂×#479×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#475×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#478×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#476×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#106×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#424×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#416×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂²×#41×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	—
20	C₂×#125×C₈₉	—	2	1	no	—
21	C₂×#125×C₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
23	#520×C₈₉	—	2	4	no	—
24	#520×C₈₉	C₂²	1	8	yes	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₈₉	—	2	2	no	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	—	2	1	no	—
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₈₉	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	#479×C₈₉	C₂²	1	16	yes	complemented
35	#478×C₈₉	C₂²	1	16	yes	complemented
36	#476×C₈₉	C₂²	1	16	yes	complemented
37	#475×C₈₉	C₂²	1	16	yes	complemented
38	#428×C₈₉	C₂²	1	8	yes	complemented
39	C₂×#107×C₈₉	C₂²	1	2	yes	—
40	C₂×#106×C₈₉	C₂²	1	2	yes	—
41	C₂×#106×C₈₉	C₂²	1	2	yes	—
42	C₂×#106×C₈₉	C₂²	1	2	yes	—
43	C₂×#106×C₈₉	C₂²	1	8	yes	complemented
44	#424×C₈₉	C₂²	1	8	yes	complemented
45	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
47	#417×C₈₉	C₂²	1	8	yes	—
48	#416×C₈₉	C₂²	1	8	yes	—
49	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
50	C₂×#103×C₈₉	C₂²	1	2	yes	—
51	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
52	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#102×C₈₉	C₂²	1	2	yes	—
54	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
55	C₂×#41×C₈₉	—	2	2	no	—
56	C₂×#41×C₈₉	—	2	4	no	—
57	C₂×#41×C₈₉	Q₈	1	8	yes	complemented
58	C₂×#41×C₈₉	C₂³	1	4	yes	—
59	C₂²×Q₈×C₈₉	—	2	2	no	—
60	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₈₉	—	2	1	no	—
62	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	—	2	1	no	—
64	C₂³×C₄×C₈₉	—	2	1	no	—
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	—	2	2	no	—
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₈₉	—	2	4	no	—
69	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
70	C₂²×C₈×C₈₉	—	2	4	no	—
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
75	C₄⋊Q₈×C₈₉	—	2	8	no	—
76	C₄⋊Q₈×C₈₉	—	2	4	no	—
77	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
78	#125×C₈₉	—	2	8	no	—
79	#125×C₈₉	—	2	4	no	—
80	#125×C₈₉	C₂³	1	8	yes	—
81	C₂²⋊Q₈×C₈₉	—	2	16	no	—
82	C₄×Q₈×C₈₉	—	2	4	no	—
83	C₄×Q₈×C₈₉	C₂³	1	8	yes	—
84	C₄×D₄×C₈₉	—	2	16	no	—
85	C₄×D₄×C₈₉	—	2	4	no	—
86	C₄×D₄×C₈₉	C₂³	1	8	yes	—
87	#117×C₈₉	—	2	2	no	—
88	#117×C₈₉	—	2	8	no	—
89	#117×C₈₉	D₄	1	4	yes	—
90	#117×C₈₉	C₂³	1	4	yes	—
91	#117×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
93	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
97	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
98	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
101	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	D₄	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	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
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	—	2	1	no	—
114	C₂×C₄²×C₈₉	C₂³	1	2	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	8	yes	—
120	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
121	#103×C₈₉	C₂³	1	4	yes	—
122	#103×C₈₉	C₂³	1	4	yes	—
123	#103×C₈₉	C₂³	1	8	yes	—
124	#102×C₈₉	C₂³	1	4	yes	—
125	#102×C₈₉	C₂³	1	4	yes	—
126	#102×C₈₉	C₂³	1	8	yes	—
127	C₂⁴×C₈₉	—	2	1	no	—
128	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
129	#41×C₈₉	—	2	16	no	—
130	#41×C₈₉	—	2	8	no	—
131	#41×C₈₉	C₂×Q₈	1	16	yes	complemented
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	8	no	—
134	C₂×Q₈×C₈₉	—	2	2	no	—
135	C₂×Q₈×C₈₉	—	8	4	no	—
136	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
137	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
138	C₂×D₄×C₈₉	—	2	8	no	—
139	C₂×D₄×C₈₉	—	2	4	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
143	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₈₉	—	2	1	no	—
145	C₂²×C₄×C₈₉	—	2	8	no	—
146	C₂²×C₄×C₈₉	—	2	4	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	2	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	—	2	2	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	4	no	—
153	C₂²×C₄×C₈₉	—	2	8	no	—
154	C₂²×C₄×C₈₉	—	8	4	no	—
155	C₂²×C₄×C₈₉	—	8	2	no	—
156	C₂²×C₄×C₈₉	—	8	2	no	—
157	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
162	C₂²×C₄×C₈₉	#41	1	4	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	M₁₆×C₈₉	—	2	8	no	—
166	C₂×C₈×C₈₉	—	2	2	no	—
167	C₂×C₈×C₈₉	—	2	2	no	—
168	C₂×C₈×C₈₉	—	2	8	no	—
169	C₂×C₈×C₈₉	—	2	4	no	—
170	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
171	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
172	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
173	C₄⋊C₄×C₈₉	—	2	4	no	—
174	C₄⋊C₄×C₈₉	—	2	8	no	—
175	C₄⋊C₄×C₈₉	—	2	2	no	—
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	—	2	8	no	—
179	C₄⋊C₄×C₈₉	—	2	8	no	—
180	C₄⋊C₄×C₈₉	—	2	8	no	—
181	C₄⋊C₄×C₈₉	—	2	1	no	—
182	C₄⋊C₄×C₈₉	—	2	1	no	—
183	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
185	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
186	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
187	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
188	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
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	—	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	4	no	—
199	C₂³×C₈₉	—	2	2	no	—
200	C₂³×C₈₉	—	4	2	no	—
201	C₂³×C₈₉	—	4	2	no	—
202	C₂³×C₈₉	C₂²⋊Q₈	1	4	yes	—
203	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
204	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₈₉	—	2	4	no	—
206	Q₈×C₈₉	—	2	2	no	—
207	Q₈×C₈₉	—	8	8	no	—
208	Q₈×C₈₉	C₂²×Q₈	1	4	yes	—
209	D₄×C₈₉	—	2	16	no	—
210	D₄×C₈₉	—	2	4	no	—
211	D₄×C₈₉	—	2	2	no	—
212	D₄×C₈₉	C₂²×Q₈	1	4	yes	—
213	C₂×C₄×C₈₉	—	2	4	no	—
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	16	no	—
218	C₂×C₄×C₈₉	—	2	2	no	—
219	C₂×C₄×C₈₉	—	2	4	no	—
220	C₂×C₄×C₈₉	—	2	2	no	—
221	C₂×C₄×C₈₉	—	2	4	no	—
222	C₂×C₄×C₈₉	—	4	2	no	—
223	C₂×C₄×C₈₉	—	4	4	no	—
224	C₂×C₄×C₈₉	—	4	4	no	—
225	C₂×C₄×C₈₉	—	4	2	no	—
226	C₂×C₄×C₈₉	—	8	8	no	—
227	C₂×C₄×C₈₉	—	8	4	no	—
228	C₂×C₄×C₈₉	—	8	4	no	—
229	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
230	C₂×C₄×C₈₉	C₂²⋊Q₈	1	8	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	4	no	—
247	C₂²×C₈₉	—	4	8	no	—
248	C₂²×C₈₉	—	4	2	no	—
249	C₂²×C₈₉	—	4	2	no	—
250	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
251	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
252	C₂²×C₈₉	#577	1	2	yes	—
253	C₂²×C₈₉	#577	1	2	yes	—
254	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₈₉	—	2	4	no	—
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	4	no	—
261	C₄×C₈₉	—	4	2	no	—
262	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
263	C₄×C₈₉	C₂×C₂²⋊Q₈	1	2	yes	—
264	C₄×C₈₉	C₂³×Q₈	1	1	yes	characteristic
265	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
266	C₂×#3084	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
267	C₂×C₈₉	—	2	4	no	—
268	C₂×C₈₉	—	4	4	no	—
269	C₂×C₈₉	#3084	1	4	yes	direct product factor
270	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
271	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
272	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
273	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
274	C₂×#520	C₂×C₈₉	1	1	yes	characteristic
275	#3084	C₂×C₈₉	1	16	yes	direct product factor
276	C₂×#479	C₂×C₈₉	1	2	yes	complemented
277	C₂×#475	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×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
281	C₂²×#106	C₂×C₈₉	1	1	yes	characteristic, complemented
282	C₂×#424	C₂×C₈₉	1	1	yes	characteristic, complemented
283	C₂×#417	C₂×C₈₉	1	1	yes	characteristic
284	C₂×#416	C₂×C₈₉	1	1	yes	characteristic
285	C₈₉	C₂×#3084	1	1	yes	characteristic, direct product factor, Sylow
286	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
287	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
288	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
289	#544	—	2	4	no	—
290	#544	C₂²×C₈₉	1	8	yes	complemented
291	C₂×C₄⋊Q₈	—	2	1	no	—
292	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
293	C₂×#125	—	2	1	no	—
294	C₂×#125	C₂²×C₈₉	1	2	yes	—
295	C₂×C₂²⋊Q₈	—	2	2	no	—
296	#520	—	2	4	no	—
297	#520	C₂²×C₈₉	1	8	yes	—
298	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
299	C₂×C₄×D₄	—	2	2	no	—
300	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
301	C₂×#117	—	2	1	no	—
302	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
303	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	—	2	1	no	—
305	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
306	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
307	#479	C₂²×C₈₉	1	16	yes	complemented
308	#478	C₂²×C₈₉	1	16	yes	complemented
309	#476	C₂²×C₈₉	1	16	yes	complemented
310	#475	C₂²×C₈₉	1	16	yes	complemented
311	#428	C₂²×C₈₉	1	8	yes	complemented
312	C₂×#107	C₂²×C₈₉	1	2	yes	—
313	C₂×#106	C₂²×C₈₉	1	2	yes	—
314	C₂×#106	C₂²×C₈₉	1	2	yes	—
315	C₂×#106	C₂²×C₈₉	1	2	yes	—
316	C₂×#106	C₂²×C₈₉	1	8	yes	complemented
317	#424	C₂²×C₈₉	1	8	yes	complemented
318	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
319	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
320	#417	C₂²×C₈₉	1	8	yes	—
321	#416	C₂²×C₈₉	1	8	yes	—
322	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×#103	C₂²×C₈₉	1	2	yes	—
324	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
325	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
326	C₂×#102	C₂²×C₈₉	1	2	yes	—
327	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×#41	—	2	2	no	—
329	C₂×#41	—	2	4	no	—
330	C₂×#41	Q₈×C₈₉	1	8	yes	complemented
331	C₂×#41	C₂³×C₈₉	1	4	yes	—
332	C₂²×Q₈	—	2	2	no	—
333	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
334	C₂²×D₄	—	2	1	no	—
335	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	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	—
351	#125	—	2	8	no	—
352	#125	—	2	4	no	—
353	#125	C₂³×C₈₉	1	8	yes	—
354	C₂²⋊Q₈	—	2	16	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	C₂³×C₈₉	1	8	yes	—
357	C₄×D₄	—	2	16	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	C₂³×C₈₉	1	8	yes	—
360	#117	—	2	2	no	—
361	#117	—	2	8	no	—
362	#117	D₄×C₈₉	1	4	yes	—
363	#117	C₂³×C₈₉	1	4	yes	—
364	#117	C₂³×C₈₉	1	4	yes	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	1	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	—	2	2	no	—
373	C₂×C₄⋊C₄	—	2	8	no	—
374	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
375	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
377	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
378	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
379	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
380	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
388	#107	C₂³×C₈₉	1	8	yes	—
389	#106	C₂³×C₈₉	1	8	yes	—
390	#106	C₂³×C₈₉	1	8	yes	—
391	#106	C₂³×C₈₉	1	8	yes	—
392	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
393	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
394	#103	C₂³×C₈₉	1	4	yes	—
395	#103	C₂³×C₈₉	1	4	yes	—
396	#103	C₂³×C₈₉	1	8	yes	—
397	#102	C₂³×C₈₉	1	4	yes	—
398	#102	C₂³×C₈₉	1	4	yes	—
399	#102	C₂³×C₈₉	1	8	yes	—
400	C₂⁴	—	2	1	no	—
401	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
402	#41	—	2	16	no	—
403	#41	—	2	8	no	—
404	#41	C₂×Q₈×C₈₉	1	16	yes	complemented
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	8	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	8	4	no	—
409	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
410	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
416	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	8	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	4	no	—
425	C₂²×C₄	—	2	4	no	—
426	C₂²×C₄	—	2	8	no	—
427	C₂²×C₄	—	8	4	no	—
428	C₂²×C₄	—	8	2	no	—
429	C₂²×C₄	—	8	2	no	—
430	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
434	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
435	C₂²×C₄	#41×C₈₉	1	4	yes	—
436	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
438	M₁₆	—	2	8	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	8	no	—
442	C₂×C₈	—	2	4	no	—
443	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
444	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
445	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	4	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	8	no	—
452	C₄⋊C₄	—	2	8	no	—
453	C₄⋊C₄	—	2	8	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
457	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
458	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
459	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
460	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
461	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	8	no	—
464	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
465	C₄²	—	2	8	no	—
466	C₄²	—	2	4	no	—
467	C₄²	C₂×D₄×C₈₉	1	4	yes	—
468	C₄²	C₂⁴×C₈₉	1	4	yes	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	4	2	no	—
474	C₂³	—	4	2	no	—
475	C₂³	C₂²⋊Q₈×C₈₉	1	4	yes	—
476	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
477	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
478	Q₈	—	2	4	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	8	8	no	—
481	Q₈	C₂²×Q₈×C₈₉	1	4	yes	—
482	D₄	—	2	16	no	—
483	D₄	—	2	4	no	—
484	D₄	—	2	2	no	—
485	D₄	C₂²×Q₈×C₈₉	1	4	yes	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	2	4	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	16	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	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	4	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	8	8	no	—
500	C₂×C₄	—	8	4	no	—
501	C₂×C₄	—	8	4	no	—
502	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
503	C₂×C₄	C₂²⋊Q₈×C₈₉	1	8	yes	—
504	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
505	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
506	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
507	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
508	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
509	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
510	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
511	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
512	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
513	C₈	—	2	2	no	—
514	C₈	—	2	2	no	—
515	C₈	—	2	4	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	8	no	—
523	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
524	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
525	C₂²	#577×C₈₉	1	2	yes	—
526	C₂²	#577×C₈₉	1	2	yes	—
527	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	2	no	—
535	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
536	C₄	C₂×C₂²⋊Q₈×C₈₉	1	2	yes	—
537	C₄	C₂³×Q₈×C₈₉	1	1	yes	characteristic
538	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
539	C₂	—	2	4	no	—
540	C₂	—	4	4	no	—
541	C₂	C₈₉×#3084	1	4	yes	direct product factor
542	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
543	C₂	C₂×#577×C₈₉	1	1	yes	characteristic
544	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	C₂²×#41×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×#3084	C₂	direct (N × H)
4. C₂×#479×C₈₉	C₂	semidirect
5. C₂×#475×C₈₉	C₂	semidirect
6. C₂×#478×C₈₉	C₂	semidirect
7. C₂×#476×C₈₉	C₂	semidirect
8. C₂×#428×C₈₉	C₂	semidirect
9. C₂²×#106×C₈₉	C₂	semidirect
10. C₂×#424×C₈₉	C₂	semidirect
17. #544×C₈₉	C₂²	semidirect
34. #479×C₈₉	C₂²	semidirect
35. #478×C₈₉	C₂²	semidirect
36. #476×C₈₉	C₂²	semidirect
37. #475×C₈₉	C₂²	semidirect
38. #428×C₈₉	C₂²	semidirect
43. C₂×#106×C₈₉	C₂²	semidirect
44. #424×C₈₉	C₂²	semidirect
57. C₂×#41×C₈₉	Q₈	semidirect
131. #41×C₈₉	C₂×Q₈	semidirect
266. C₂×#3084	C₈₉	direct (N × H)
269. C₂×C₈₉	#3084	direct (N × H)
273. C₂×#544	C₂×C₈₉	semidirect
275. #3084	C₂×C₈₉	direct (N × H)
276. C₂×#479	C₂×C₈₉	semidirect
277. C₂×#475	C₂×C₈₉	semidirect
278. C₂×#478	C₂×C₈₉	semidirect
279. C₂×#476	C₂×C₈₉	semidirect
280. C₂×#428	C₂×C₈₉	semidirect
281. C₂²×#106	C₂×C₈₉	semidirect
282. C₂×#424	C₂×C₈₉	semidirect
285. C₈₉	C₂×#3084	direct (N × H)
290. #544	C₂²×C₈₉	semidirect
307. #479	C₂²×C₈₉	semidirect
308. #478	C₂²×C₈₉	semidirect
309. #476	C₂²×C₈₉	semidirect
310. #475	C₂²×C₈₉	semidirect
311. #428	C₂²×C₈₉	semidirect
316. C₂×#106	C₂²×C₈₉	semidirect
317. #424	C₂²×C₈₉	semidirect
330. C₂×#41	Q₈×C₈₉	semidirect
404. #41	C₂×Q₈×C₈₉	semidirect
541. C₂	C₈₉×#3084	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×#520×C₈₉	2
C₈₉×#3084	2
C₂×#479×C₈₉	2
C₂×#475×C₈₉	2
C₂×#478×C₈₉	2
C₂×#476×C₈₉	2
C₂×#428×C₈₉	2
C₂²×#106×C₈₉	2
C₂×#424×C₈₉	2
C₂×#417×C₈₉	2
C₂×#416×C₈₉	2
C₂×#3084	89

Subgroups — C2×C89×#3084 #36438336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#3084 #36438336