Subgroups — C₈₉×#23556 #36401404

Order 22784.

1110 conjugacy classes of subgroups.

The subgroup lattice has 424 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
2	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×#106×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2059	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2058	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1736	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1735	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1729	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
12	#544×C₈₉	—	2	4	no	—
13	#544×C₈₉	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₈₉	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×#125×C₈₉	—	2	1	no	—
17	C₂×#125×C₈₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	—	2	2	no	—
19	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	#428×C₈₉	—	2	4	no	—
25	C₂×#107×C₈₉	C₂²	1	2	yes	—
26	C₂×#106×C₈₉	—	2	4	no	—
27	C₂×#106×C₈₉	C₂²	1	2	yes	—
28	C₂×#106×C₈₉	C₂²	1	4	yes	—
29	#389×C₈₉	C₂²	1	4	yes	—
30	#385×C₈₉	—	2	2	no	—
31	#384×C₈₉	—	2	1	no	—
32	#382×C₈₉	—	2	1	no	—
33	#340×C₈₉	C₂²	1	2	yes	—
34	#340×C₈₉	C₂²	1	4	yes	—
35	#340×C₈₉	C₂²	1	2	yes	—
36	#336×C₈₉	C₂²	1	4	yes	—
37	C₂²×Q₈×C₈₉	—	2	2	no	—
38	C₂³×C₄×C₈₉	—	2	1	no	—
39	C₂³×C₄×C₈₉	—	2	1	no	—
40	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
41	C₂×M₁₆×C₈₉	—	2	2	no	—
42	C₂×M₁₆×C₈₉	—	2	2	no	—
43	C₂×M₁₆×C₈₉	Q₈	1	4	yes	complemented
44	C₂²×C₈×C₈₉	—	2	2	no	—
45	C₂²×C₈×C₈₉	—	2	2	no	—
46	C₂²×C₈×C₈₉	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₈₉	—	2	8	no	—
50	C₄⋊Q₈×C₈₉	—	2	4	no	—
51	C₄⋊Q₈×C₈₉	—	2	4	no	—
52	#125×C₈₉	—	2	8	no	—
53	#125×C₈₉	—	2	4	no	—
54	#125×C₈₉	—	2	4	no	—
55	C₂²⋊Q₈×C₈₉	—	2	16	no	—
56	#117×C₈₉	—	2	2	no	—
57	#117×C₈₉	—	2	2	no	—
58	#117×C₈₉	—	2	2	no	—
59	#117×C₈₉	—	2	2	no	—
60	#117×C₈₉	D₄	1	4	yes	—
61	#117×C₈₉	Q₈	1	4	yes	complemented
62	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₈₉	D₄	1	4	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
82	C₂×C₄²×C₈₉	—	2	1	no	—
83	C₂×C₄²×C₈₉	—	2	1	no	—
84	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
85	#107×C₈₉	—	2	4	no	—
86	#106×C₈₉	—	2	8	no	—
87	#106×C₈₉	—	2	4	no	—
88	#95×C₈₉	—	2	4	no	—
89	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
90	C₂×Q₈×C₈₉	—	2	8	no	—
91	C₂×Q₈×C₈₉	—	8	4	no	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
93	C₂²×C₄×C₈₉	—	2	1	no	—
94	C₂²×C₄×C₈₉	—	2	1	no	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	2	4	no	—
97	C₂²×C₄×C₈₉	—	2	2	no	—
98	C₂²×C₄×C₈₉	—	4	2	no	—
99	C₂²×C₄×C₈₉	—	8	2	no	—
100	C₂²×C₄×C₈₉	—	8	2	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
107	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₈₉	#41	1	2	yes	—
110	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
111	M₁₆×C₈₉	—	2	8	no	—
112	C₂×C₈×C₈₉	—	2	8	no	—
113	C₂×C₈×C₈₉	—	2	2	no	—
114	C₂×C₈×C₈₉	—	2	2	no	—
115	C₂×C₈×C₈₉	—	2	2	no	—
116	C₂×C₈×C₈₉	—	2	2	no	—
117	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
118	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
119	C₄⋊C₄×C₈₉	—	2	8	no	—
120	C₄⋊C₄×C₈₉	—	2	8	no	—
121	C₄⋊C₄×C₈₉	—	2	8	no	—
122	C₄⋊C₄×C₈₉	—	2	4	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	2	2	no	—
125	C₄⋊C₄×C₈₉	—	2	2	no	—
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	2	2	no	—
131	C₄⋊C₄×C₈₉	—	4	2	no	—
132	C₄⋊C₄×C₈₉	—	8	4	no	—
133	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
137	C₂²⋊C₄×C₈₉	—	2	4	no	—
138	C₂²⋊C₄×C₈₉	—	2	4	no	—
139	C₂²⋊C₄×C₈₉	—	2	4	no	—
140	C₄²×C₈₉	—	2	4	no	—
141	C₄²×C₈₉	—	2	4	no	—
142	C₄²×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	—	2	2	no	—
144	C₂³×C₈₉	—	2	2	no	—
145	C₂³×C₈₉	—	2	2	no	—
146	C₂³×C₈₉	#120	1	2	yes	—
147	C₂³×C₈₉	C₂²⋊Q₈	1	2	yes	—
148	C₂³×C₈₉	C₄⋊Q₈	1	2	yes	—
149	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₈₉	—	8	8	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	4	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	2	4	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	4	4	no	—
163	C₂×C₄×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	4	no	—
166	C₂×C₄×C₈₉	—	8	4	no	—
167	C₂×C₄×C₈₉	—	8	4	no	—
168	C₂×C₄×C₈₉	#120	1	2	yes	—
169	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
171	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
172	C₂×C₄×C₈₉	C₄⋊Q₈	1	4	yes	—
173	C₂×C₄×C₈₉	C₄⋊Q₈	1	4	yes	—
174	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
175	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₈×C₈₉	—	2	4	no	—
182	C₈×C₈₉	—	2	4	no	—
183	C₂²×C₈₉	—	2	4	no	—
184	C₂²×C₈₉	—	2	4	no	—
185	C₂²×C₈₉	—	2	2	no	—
186	C₂²×C₈₉	—	2	2	no	—
187	C₂²×C₈₉	#395	1	4	yes	—
188	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
189	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
190	C₂²×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
191	C₂²×C₈₉	#577	1	2	yes	—
192	C₂²×C₈₉	#577	1	2	yes	—
193	C₄×C₈₉	—	4	4	no	—
194	C₄×C₈₉	—	4	2	no	—
195	C₄×C₈₉	—	4	4	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	8	2	no	—
200	C₄×C₈₉	#395	1	4	yes	—
201	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
204	C₄×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
205	#23556	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₈₉	—	2	4	no	—
207	C₂×C₈₉	C₂×#395	1	1	yes	characteristic
208	C₂×C₈₉	#3009	1	1	yes	characteristic
209	C₂×C₈₉	#3010	1	1	yes	characteristic
210	C₂×C₈₉	#3084	1	2	yes	—
211	C₂×C₈₉	#3163	1	2	yes	—
212	C₂×#544	C₂×C₈₉	1	1	yes	characteristic
213	C₂×#428	C₂×C₈₉	1	1	yes	characteristic
214	C₂²×#106	C₂×C₈₉	1	1	yes	characteristic
215	#2317	C₂×C₈₉	1	1	yes	characteristic
216	#2059	C₂×C₈₉	1	4	yes	complemented
217	#2058	C₂×C₈₉	1	4	yes	complemented
218	#1736	C₂×C₈₉	1	1	yes	characteristic
219	#1735	C₂×C₈₉	1	1	yes	characteristic
220	#1729	C₂×C₈₉	1	1	yes	characteristic
221	C₈₉	#23556	1	1	yes	characteristic, direct product factor, Sylow
222	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
224	#544	—	2	4	no	—
225	#544	—	2	4	no	—
226	C₂×C₄⋊Q₈	—	2	1	no	—
227	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
228	C₂×#125	—	2	1	no	—
229	C₂×#125	C₂²×C₈₉	1	2	yes	—
230	C₂×C₂²⋊Q₈	—	2	2	no	—
231	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
233	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
235	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
236	#428	—	2	4	no	—
237	C₂×#107	C₂²×C₈₉	1	2	yes	—
238	C₂×#106	—	2	4	no	—
239	C₂×#106	C₂²×C₈₉	1	2	yes	—
240	C₂×#106	C₂²×C₈₉	1	4	yes	—
241	#389	C₂²×C₈₉	1	4	yes	—
242	#385	—	2	2	no	—
243	#384	—	2	1	no	—
244	#382	—	2	1	no	—
245	#340	C₂²×C₈₉	1	2	yes	—
246	#340	C₂²×C₈₉	1	4	yes	—
247	#340	C₂²×C₈₉	1	2	yes	—
248	#336	C₂²×C₈₉	1	4	yes	—
249	C₂²×Q₈	—	2	2	no	—
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	—	2	2	no	—
255	C₂×M₁₆	Q₈×C₈₉	1	4	yes	complemented
256	C₂²×C₈	—	2	2	no	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	Q₈×C₈₉	1	4	yes	complemented
259	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
260	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
261	C₄⋊Q₈	—	2	8	no	—
262	C₄⋊Q₈	—	2	4	no	—
263	C₄⋊Q₈	—	2	4	no	—
264	#125	—	2	8	no	—
265	#125	—	2	4	no	—
266	#125	—	2	4	no	—
267	C₂²⋊Q₈	—	2	16	no	—
268	#117	—	2	2	no	—
269	#117	—	2	2	no	—
270	#117	—	2	2	no	—
271	#117	—	2	2	no	—
272	#117	D₄×C₈₉	1	4	yes	—
273	#117	Q₈×C₈₉	1	4	yes	complemented
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	4	no	—
283	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
285	C₂×C₄⋊C₄	D₄×C₈₉	1	4	yes	—
286	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
297	#107	—	2	4	no	—
298	#106	—	2	8	no	—
299	#106	—	2	4	no	—
300	#95	—	2	4	no	—
301	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
302	C₂×Q₈	—	2	8	no	—
303	C₂×Q₈	—	8	4	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	—	8	2	no	—
313	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
317	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
318	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
319	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
320	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
321	C₂²×C₄	#41×C₈₉	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
323	M₁₆	—	2	8	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	—
330	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	8	4	no	—
345	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
346	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
347	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
348	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₄²	—	2	4	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₂³	—	2	2	no	—
357	C₂³	—	2	2	no	—
358	C₂³	#120×C₈₉	1	2	yes	—
359	C₂³	C₂²⋊Q₈×C₈₉	1	2	yes	—
360	C₂³	C₄⋊Q₈×C₈₉	1	2	yes	—
361	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
362	Q₈	—	8	8	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	#120×C₈₉	1	2	yes	—
381	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
382	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
383	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
384	C₂×C₄	C₄⋊Q₈×C₈₉	1	2	yes	—
385	C₂×C₄	C₄⋊Q₈×C₈₉	1	4	yes	—
386	C₂×C₄	C₄⋊Q₈×C₈₉	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	#395×C₈₉	1	4	yes	—
400	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
401	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
402	C₂²	C₂×C₄⋊Q₈×C₈₉	1	1	yes	characteristic
403	C₂²	#577×C₈₉	1	2	yes	—
404	C₂²	#577×C₈₉	1	2	yes	—
405	C₄	—	4	4	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	8	2	no	—
412	C₄	#395×C₈₉	1	4	yes	—
413	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
414	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
415	C₄	C₂×C₄⋊Q₈×C₈₉	1	1	yes	characteristic
416	C₄	C₂×C₄⋊Q₈×C₈₉	1	1	yes	characteristic
417	C₂	—	2	4	no	—
418	C₂	C₂×#395×C₈₉	1	1	yes	characteristic
419	C₂	C₈₉×#3009	1	1	yes	characteristic
420	C₂	C₈₉×#3010	1	1	yes	characteristic
421	C₂	C₈₉×#3084	1	2	yes	—
422	C₂	C₈₉×#3163	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂²×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
5. C₈₉×#2059	C₂	semidirect
6. C₈₉×#2058	C₂	semidirect
43. C₂×M₁₆×C₈₉	Q₈	semidirect
46. C₂²×C₈×C₈₉	Q₈	semidirect
61. #117×C₈₉	Q₈	semidirect
205. #23556	C₈₉	direct (N × H)
216. #2059	C₂×C₈₉	semidirect
217. #2058	C₂×C₈₉	semidirect
221. C₈₉	#23556	direct (N × H)
255. C₂×M₁₆	Q₈×C₈₉	semidirect
258. C₂²×C₈	Q₈×C₈₉	semidirect
273. #117	Q₈×C₈₉	semidirect

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×#428×C₈₉	2
C₂²×#106×C₈₉	2
C₈₉×#2317	2
C₈₉×#2059	2
C₈₉×#2058	2
C₈₉×#1736	2
C₈₉×#1735	2
C₈₉×#1729	2
#23556	89

Subgroups — C89×#23556 #36401404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23556 #36401404