Subgroups — C₂×C₈₉×#2943 #36438003

Order 22784.

2854 conjugacy classes of subgroups.

The subgroup lattice has 394 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
2	C₂×C₄×#41×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2943	C₂	1	16	yes	maximal, direct product factor
4	C₂×#442×C₈₉	C₂	1	2	yes	maximal, complemented
5	C₂×#441×C₈₉	C₂	1	2	yes	maximal, complemented
6	C₂×#440×C₈₉	C₂	1	4	yes	maximal, complemented
7	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#416×C₈₉	C₂	1	2	yes	maximal, complemented
9	C₂²×#97×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂×#135×C₈₉	C₄	1	16	yes	complemented
12	C₂×#135×C₈₉	C₂²	1	8	yes	—
13	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₈₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₄×#41×C₈₉	—	2	8	no	—
19	C₄×#41×C₈₉	C₂²	1	16	yes	complemented
20	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₈₉	—	2	4	no	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂×#117×C₈₉	—	2	2	no	—
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₈₉	—	2	2	no	—
26	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
27	#442×C₈₉	C₂²	1	16	yes	complemented
28	#441×C₈₉	C₂²	1	16	yes	complemented
29	#440×C₈₉	C₂²	1	32	yes	complemented
30	#427×C₈₉	C₂²	1	8	yes	complemented
31	C₂×#107×C₈₉	C₂²	1	2	yes	—
32	C₂×#106×C₈₉	C₂²	1	2	yes	—
33	#416×C₈₉	C₂²	1	16	yes	complemented
34	C₂×#103×C₈₉	C₂²	1	4	yes	—
35	C₂×#102×C₈₉	C₂²	1	4	yes	—
36	C₂×#97×C₈₉	C₂²	1	2	yes	—
37	C₂×#97×C₈₉	C₂²	1	2	yes	—
38	C₂×#97×C₈₉	C₂²	1	8	yes	complemented
39	C₂×#41×C₈₉	—	2	4	no	—
40	C₂×#41×C₈₉	—	2	8	no	—
41	C₂×#41×C₈₉	C₂×C₄	1	16	yes	complemented
42	C₂×#41×C₈₉	C₂³	1	8	yes	—
43	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₈₉	—	2	2	no	—
45	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₈₉	—	2	2	no	—
47	C₂³×C₄×C₈₉	—	2	4	no	—
48	C₂³×C₄×C₈₉	D₄	1	2	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
50	#135×C₈₉	C₂×C₄	1	64	yes	complemented
51	C₂×Q₁₆×C₈₉	C₂×C₄	1	8	yes	complemented
52	C₂×Q₁₆×C₈₉	C₂³	1	4	yes	—
53	C₂×SD₁₆×C₈₉	C₂×C₄	1	16	yes	complemented
54	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
55	C₂×D₈×C₈₉	C₂×C₄	1	8	yes	complemented
56	C₂×D₈×C₈₉	C₂³	1	4	yes	—
57	C₂²×C₈×C₈₉	—	2	4	no	—
58	C₂²×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
59	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
60	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
61	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
64	C₄×Q₈×C₈₉	—	2	8	no	—
65	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
66	C₄×D₄×C₈₉	—	2	32	no	—
67	C₄×D₄×C₈₉	—	2	8	no	—
68	C₄×D₄×C₈₉	C₂³	1	16	yes	—
69	#117×C₈₉	—	2	4	no	—
70	#117×C₈₉	—	2	16	no	—
71	#117×C₈₉	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
74	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
76	C₂×C₄²×C₈₉	—	2	4	no	—
77	C₂×C₄²×C₈₉	—	2	2	no	—
78	C₂×C₄²×C₈₉	—	2	16	no	—
79	C₂×C₄²×C₈₉	D₄	1	4	yes	—
80	C₂×C₄²×C₈₉	D₄	1	2	yes	—
81	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
83	#107×C₈₉	C₂³	1	8	yes	—
84	#106×C₈₉	C₂³	1	8	yes	—
85	#103×C₈₉	C₂³	1	16	yes	—
86	#102×C₈₉	C₂³	1	16	yes	—
87	#97×C₈₉	C₂³	1	8	yes	—
88	#97×C₈₉	C₂³	1	8	yes	—
89	C₂⁴×C₈₉	—	2	2	no	—
90	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
91	#41×C₈₉	—	2	32	no	—
92	#41×C₈₉	—	2	16	no	—
93	#41×C₈₉	C₂²×C₄	1	32	yes	complemented
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	4	no	—
96	C₂×Q₈×C₈₉	C₂²×C₄	1	8	yes	—
97	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
98	C₂×D₄×C₈₉	—	2	16	no	—
99	C₂×D₄×C₈₉	—	2	8	no	—
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	4	no	—
102	C₂×D₄×C₈₉	C₂²×C₄	1	8	yes	—
103	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	—	2	16	no	—
106	C₂²×C₄×C₈₉	—	2	8	no	—
107	C₂²×C₄×C₈₉	—	2	4	no	—
108	C₂²×C₄×C₈₉	—	2	16	no	—
109	C₂²×C₄×C₈₉	—	4	4	no	—
110	C₂²×C₄×C₈₉	—	4	16	no	—
111	C₂²×C₄×C₈₉	C₂²×C₄	1	4	yes	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	#41	1	4	yes	—
117	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
119	Q₁₆×C₈₉	C₂²×C₄	1	16	yes	complemented
120	SD₁₆×C₈₉	C₂²×C₄	1	32	yes	complemented
121	D₈×C₈₉	C₂²×C₄	1	16	yes	complemented
122	C₂×C₈×C₈₉	—	2	4	no	—
123	C₂×C₈×C₈₉	—	2	8	no	—
124	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
126	C₂×C₈×C₈₉	C₂²×C₄	1	16	yes	complemented
127	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
128	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
129	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
130	C₄⋊C₄×C₈₉	—	2	16	no	—
131	C₄⋊C₄×C₈₉	—	2	4	no	—
132	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
133	C₂²⋊C₄×C₈₉	—	2	8	no	—
134	C₂²⋊C₄×C₈₉	—	2	16	no	—
135	C₄²×C₈₉	—	2	8	no	—
136	C₄²×C₈₉	—	2	16	no	—
137	C₄²×C₈₉	C₂×D₄	1	8	yes	—
138	C₄²×C₈₉	C₂×D₄	1	4	yes	—
139	C₄²×C₈₉	C₂⁴	1	4	yes	—
140	C₂³×C₈₉	—	2	4	no	—
141	C₂³×C₈₉	—	2	8	no	—
142	C₂³×C₈₉	—	2	4	no	—
143	C₂³×C₈₉	—	4	8	no	—
144	C₂³×C₈₉	C₄×D₄	1	4	yes	—
145	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
146	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₈₉	—	2	8	no	—
148	Q₈×C₈₉	—	2	4	no	—
149	Q₈×C₈₉	C₂³×C₄	1	8	yes	—
150	D₄×C₈₉	—	2	32	no	—
151	D₄×C₈₉	—	2	8	no	—
152	D₄×C₈₉	—	2	4	no	—
153	D₄×C₈₉	C₂³×C₄	1	8	yes	—
154	C₂×C₄×C₈₉	—	2	8	no	—
155	C₂×C₄×C₈₉	—	2	8	no	—
156	C₂×C₄×C₈₉	—	2	4	no	—
157	C₂×C₄×C₈₉	—	2	32	no	—
158	C₂×C₄×C₈₉	—	2	8	no	—
159	C₂×C₄×C₈₉	—	4	8	no	—
160	C₂×C₄×C₈₉	—	4	32	no	—
161	C₂×C₄×C₈₉	—	4	8	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
163	C₂×C₄×C₈₉	C₄×D₄	1	8	yes	—
164	C₂×C₄×C₈₉	C₂³×C₄	1	2	yes	—
165	C₂×C₄×C₈₉	C₂³×C₄	1	4	yes	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
167	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
170	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
171	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
172	C₈×C₈₉	—	2	4	no	—
173	C₈×C₈₉	C₂³×C₄	1	4	yes	—
174	C₈×C₈₉	C₂³×C₄	1	4	yes	—
175	C₂²×C₈₉	—	2	8	no	—
176	C₂²×C₈₉	—	2	4	no	—
177	C₂²×C₈₉	—	2	8	no	—
178	C₂²×C₈₉	—	4	16	no	—
179	C₂²×C₈₉	—	4	8	no	—
180	C₂²×C₈₉	C₂×C₄×D₄	1	4	yes	—
181	C₂²×C₈₉	C₂×C₄×D₄	1	2	yes	—
182	C₂²×C₈₉	#575	1	4	yes	—
183	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
184	C₄×C₈₉	—	2	8	no	—
185	C₄×C₈₉	—	2	8	no	—
186	C₄×C₈₉	—	4	8	no	—
187	C₄×C₈₉	C₂×C₄×D₄	1	4	yes	—
188	C₄×C₈₉	C₂×C₄×D₄	1	2	yes	—
189	C₄×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
190	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
191	C₂×#2943	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂×C₈₉	—	2	4	no	—
193	C₂×C₈₉	—	4	8	no	—
194	C₂×C₈₉	#2943	1	4	yes	direct product factor
195	C₂×C₈₉	C₂²×C₄×D₄	1	1	yes	characteristic
196	C₂×C₈₉	C₂×#575	1	2	yes	—
197	C₂²×#135	C₂×C₈₉	1	1	yes	characteristic
198	C₂×C₄×#41	C₂×C₈₉	1	2	yes	complemented
199	#2943	C₂×C₈₉	1	16	yes	direct product factor
200	C₂×#442	C₂×C₈₉	1	2	yes	complemented
201	C₂×#441	C₂×C₈₉	1	2	yes	complemented
202	C₂×#440	C₂×C₈₉	1	4	yes	complemented
203	C₂×#427	C₂×C₈₉	1	1	yes	characteristic, complemented
204	C₂×#416	C₂×C₈₉	1	2	yes	complemented
205	C₂²×#97	C₂×C₈₉	1	1	yes	characteristic, complemented
206	C₈₉	C₂×#2943	1	1	yes	characteristic, direct product factor, Sylow
207	C₂²×#41	C₂²×C₈₉	1	2	yes	—
208	C₂×#135	C₄×C₈₉	1	16	yes	complemented
209	C₂×#135	C₂²×C₈₉	1	8	yes	—
210	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₈₉	1	2	yes	—
212	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
213	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
215	C₄×#41	—	2	8	no	—
216	C₄×#41	C₂²×C₈₉	1	16	yes	complemented
217	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	—
218	C₂×C₄×D₄	—	2	4	no	—
219	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
220	C₂×#117	—	2	2	no	—
221	C₂×#117	C₂²×C₈₉	1	2	yes	—
222	C₂²×C₄²	—	2	2	no	—
223	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
224	#442	C₂²×C₈₉	1	16	yes	complemented
225	#441	C₂²×C₈₉	1	16	yes	complemented
226	#440	C₂²×C₈₉	1	32	yes	complemented
227	#427	C₂²×C₈₉	1	8	yes	complemented
228	C₂×#107	C₂²×C₈₉	1	2	yes	—
229	C₂×#106	C₂²×C₈₉	1	2	yes	—
230	#416	C₂²×C₈₉	1	16	yes	complemented
231	C₂×#103	C₂²×C₈₉	1	4	yes	—
232	C₂×#102	C₂²×C₈₉	1	4	yes	—
233	C₂×#97	C₂²×C₈₉	1	2	yes	—
234	C₂×#97	C₂²×C₈₉	1	2	yes	—
235	C₂×#97	C₂²×C₈₉	1	8	yes	complemented
236	C₂×#41	—	2	4	no	—
237	C₂×#41	—	2	8	no	—
238	C₂×#41	C₂×C₄×C₈₉	1	16	yes	complemented
239	C₂×#41	C₂³×C₈₉	1	8	yes	—
240	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
243	C₂³×C₄	—	2	2	no	—
244	C₂³×C₄	—	2	4	no	—
245	C₂³×C₄	D₄×C₈₉	1	2	yes	—
246	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
247	#135	C₂×C₄×C₈₉	1	64	yes	complemented
248	C₂×Q₁₆	C₂×C₄×C₈₉	1	8	yes	complemented
249	C₂×Q₁₆	C₂³×C₈₉	1	4	yes	—
250	C₂×SD₁₆	C₂×C₄×C₈₉	1	16	yes	complemented
251	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
252	C₂×D₈	C₂×C₄×C₈₉	1	8	yes	complemented
253	C₂×D₈	C₂³×C₈₉	1	4	yes	—
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	C₂×C₄×C₈₉	1	8	yes	complemented
256	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
257	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
258	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
261	C₄×Q₈	—	2	8	no	—
262	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
263	C₄×D₄	—	2	32	no	—
264	C₄×D₄	—	2	8	no	—
265	C₄×D₄	C₂³×C₈₉	1	16	yes	—
266	#117	—	2	4	no	—
267	#117	—	2	16	no	—
268	#117	C₂³×C₈₉	1	8	yes	—
269	C₂×C₄⋊C₄	—	2	4	no	—
270	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	4	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	2	4	no	—
275	C₂×C₄²	—	2	16	no	—
276	C₂×C₄²	D₄×C₈₉	1	2	yes	—
277	C₂×C₄²	D₄×C₈₉	1	4	yes	—
278	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
279	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
280	#107	C₂³×C₈₉	1	8	yes	—
281	#106	C₂³×C₈₉	1	8	yes	—
282	#103	C₂³×C₈₉	1	16	yes	—
283	#102	C₂³×C₈₉	1	16	yes	—
284	#97	C₂³×C₈₉	1	8	yes	—
285	#97	C₂³×C₈₉	1	8	yes	—
286	C₂⁴	—	2	2	no	—
287	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
288	#41	—	2	32	no	—
289	#41	—	2	16	no	—
290	#41	C₂²×C₄×C₈₉	1	32	yes	complemented
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂²×C₄×C₈₉	1	8	yes	—
294	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
295	C₂×D₄	—	2	16	no	—
296	C₂×D₄	—	2	8	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	C₂²×C₄×C₈₉	1	8	yes	—
300	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	16	no	—
303	C₂²×C₄	—	2	8	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	16	no	—
306	C₂²×C₄	—	4	4	no	—
307	C₂²×C₄	—	4	16	no	—
308	C₂²×C₄	C₂²×C₄×C₈₉	1	4	yes	—
309	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
310	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
311	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
313	C₂²×C₄	#41×C₈₉	1	4	yes	—
314	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
316	Q₁₆	C₂²×C₄×C₈₉	1	16	yes	complemented
317	SD₁₆	C₂²×C₄×C₈₉	1	32	yes	complemented
318	D₈	C₂²×C₄×C₈₉	1	16	yes	complemented
319	C₂×C₈	—	2	4	no	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
322	C₂×C₈	C₂²×C₄×C₈₉	1	4	yes	—
323	C₂×C₈	C₂²×C₄×C₈₉	1	16	yes	complemented
324	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
325	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
326	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
327	C₄⋊C₄	—	2	16	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	2	16	no	—
332	C₄²	—	2	8	no	—
333	C₄²	—	2	16	no	—
334	C₄²	C₂×D₄×C₈₉	1	8	yes	—
335	C₄²	C₂×D₄×C₈₉	1	4	yes	—
336	C₄²	C₂⁴×C₈₉	1	4	yes	—
337	C₂³	—	2	4	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	4	no	—
340	C₂³	—	4	8	no	—
341	C₂³	C₄×D₄×C₈₉	1	4	yes	—
342	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
343	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
344	Q₈	—	2	8	no	—
345	Q₈	—	2	4	no	—
346	Q₈	C₂³×C₄×C₈₉	1	8	yes	—
347	D₄	—	2	32	no	—
348	D₄	—	2	8	no	—
349	D₄	—	2	4	no	—
350	D₄	C₂³×C₄×C₈₉	1	8	yes	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	8	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	32	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	4	8	no	—
357	C₂×C₄	—	4	32	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	C₄×D₄×C₈₉	1	4	yes	—
360	C₂×C₄	C₄×D₄×C₈₉	1	8	yes	—
361	C₂×C₄	C₂³×C₄×C₈₉	1	2	yes	—
362	C₂×C₄	C₂³×C₄×C₈₉	1	4	yes	—
363	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
364	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
367	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
368	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	C₂³×C₄×C₈₉	1	4	yes	—
371	C₈	C₂³×C₄×C₈₉	1	4	yes	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	8	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	4	8	no	—
376	C₂²	—	4	16	no	—
377	C₂²	C₂×C₄×D₄×C₈₉	1	4	yes	—
378	C₂²	C₂×C₄×D₄×C₈₉	1	2	yes	—
379	C₂²	#575×C₈₉	1	4	yes	—
380	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
381	C₄	—	2	8	no	—
382	C₄	—	2	8	no	—
383	C₄	—	4	8	no	—
384	C₄	C₂×C₄×D₄×C₈₉	1	4	yes	—
385	C₄	C₂×C₄×D₄×C₈₉	1	2	yes	—
386	C₄	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
387	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
388	C₂	—	2	4	no	—
389	C₂	—	4	8	no	—
390	C₂	C₈₉×#2943	1	4	yes	direct product factor
391	C₂	C₂²×C₄×D₄×C₈₉	1	1	yes	characteristic
392	C₂	C₂×#575×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×#135×C₈₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×#41×C₈₉	C₂	semidirect
3. C₈₉×#2943	C₂	direct (N × H)
4. C₂×#442×C₈₉	C₂	semidirect
5. C₂×#441×C₈₉	C₂	semidirect
6. C₂×#440×C₈₉	C₂	semidirect
7. C₂×#427×C₈₉	C₂	semidirect
8. C₂×#416×C₈₉	C₂	semidirect
9. C₂²×#97×C₈₉	C₂	semidirect
11. C₂×#135×C₈₉	C₄	semidirect
19. C₄×#41×C₈₉	C₂²	semidirect
27. #442×C₈₉	C₂²	semidirect
28. #441×C₈₉	C₂²	semidirect
29. #440×C₈₉	C₂²	semidirect
30. #427×C₈₉	C₂²	semidirect
33. #416×C₈₉	C₂²	semidirect
38. C₂×#97×C₈₉	C₂²	semidirect
41. C₂×#41×C₈₉	C₂×C₄	semidirect
50. #135×C₈₉	C₂×C₄	semidirect
51. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
53. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
55. C₂×D₈×C₈₉	C₂×C₄	semidirect
58. C₂²×C₈×C₈₉	C₂×C₄	semidirect
93. #41×C₈₉	C₂²×C₄	semidirect
119. Q₁₆×C₈₉	C₂²×C₄	semidirect
120. SD₁₆×C₈₉	C₂²×C₄	semidirect
121. D₈×C₈₉	C₂²×C₄	semidirect
126. C₂×C₈×C₈₉	C₂²×C₄	semidirect
191. C₂×#2943	C₈₉	direct (N × H)
194. C₂×C₈₉	#2943	direct (N × H)
198. C₂×C₄×#41	C₂×C₈₉	semidirect
199. #2943	C₂×C₈₉	direct (N × H)
200. C₂×#442	C₂×C₈₉	semidirect
201. C₂×#441	C₂×C₈₉	semidirect
202. C₂×#440	C₂×C₈₉	semidirect
203. C₂×#427	C₂×C₈₉	semidirect
204. C₂×#416	C₂×C₈₉	semidirect
205. C₂²×#97	C₂×C₈₉	semidirect
206. C₈₉	C₂×#2943	direct (N × H)
208. C₂×#135	C₄×C₈₉	semidirect
216. C₄×#41	C₂²×C₈₉	semidirect
224. #442	C₂²×C₈₉	semidirect
225. #441	C₂²×C₈₉	semidirect
226. #440	C₂²×C₈₉	semidirect
227. #427	C₂²×C₈₉	semidirect
230. #416	C₂²×C₈₉	semidirect
235. C₂×#97	C₂²×C₈₉	semidirect
238. C₂×#41	C₂×C₄×C₈₉	semidirect
247. #135	C₂×C₄×C₈₉	semidirect
248. C₂×Q₁₆	C₂×C₄×C₈₉	semidirect
250. C₂×SD₁₆	C₂×C₄×C₈₉	semidirect
252. C₂×D₈	C₂×C₄×C₈₉	semidirect
255. C₂²×C₈	C₂×C₄×C₈₉	semidirect
290. #41	C₂²×C₄×C₈₉	semidirect
316. Q₁₆	C₂²×C₄×C₈₉	semidirect
317. SD₁₆	C₂²×C₄×C₈₉	semidirect
318. D₈	C₂²×C₄×C₈₉	semidirect
323. C₂×C₈	C₂²×C₄×C₈₉	semidirect
390. C₂	C₈₉×#2943	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
C₂×C₄×#41×C₈₉	2
C₈₉×#2943	2
C₂×#442×C₈₉	2
C₂×#441×C₈₉	2
C₂×#440×C₈₉	2
C₂×#427×C₈₉	2
C₂×#416×C₈₉	2
C₂²×#97×C₈₉	2
C₂×#2943	89

Subgroups — C2×C89×#2943 #36438003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2943 #36438003