Subgroups — C₈₉×#61409 #36439257

Order 22784.

2078 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3399	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3396	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3391	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3155	C₂	1	2	yes	maximal, complemented
6	C₂×#493×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#3041	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3038	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2948	C₂	1	2	yes	maximal, complemented
11	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	—
13	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
15	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
16	#559×C₈₉	C₂²	1	8	yes	complemented
17	#550×C₈₉	C₂²	1	8	yes	complemented
18	#546×C₈₉	—	2	8	no	—
19	#540×C₈₉	—	2	4	no	—
20	#535×C₈₉	C₂²	1	4	yes	—
21	#533×C₈₉	C₂²	1	1	yes	characteristic
22	#532×C₈₉	—	2	4	no	—
23	C₂×#127×C₈₉	C₂²	1	2	yes	—
24	#518×C₈₉	C₂²	1	4	yes	—
25	C₄×#41×C₈₉	C₂²	1	2	yes	—
26	#496×C₈₉	C₂²	1	8	yes	complemented
27	#495×C₈₉	C₂²	1	4	yes	complemented
28	#493×C₈₉	C₂²	1	4	yes	—
29	#493×C₈₉	C₂²	1	4	yes	—
30	#493×C₈₉	C₂²	1	4	yes	complemented
31	#463×C₈₉	C₂²	1	16	yes	complemented
32	#460×C₈₉	C₂²	1	8	yes	complemented
33	#459×C₈₉	C₂²	1	8	yes	complemented
34	#459×C₈₉	C₂²	1	16	yes	complemented
35	#446×C₈₉	C₂²	1	4	yes	complemented
36	C₈×Q₈×C₈₉	C₂²	1	4	yes	complemented
37	#442×C₈₉	C₂²	1	8	yes	complemented
38	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
39	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
40	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
41	C₄×D₈×C₈₉	C₂²	1	8	yes	complemented
42	#427×C₈₉	C₂²	1	1	yes	characteristic
43	#424×C₈₉	C₂²	1	2	yes	—
44	#423×C₈₉	C₂²	1	1	yes	characteristic
45	#418×C₈₉	C₂²	1	4	yes	—
46	#416×C₈₉	C₂²	1	2	yes	—
47	#405×C₈₉	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#41×C₈₉	—	2	8	no	—
50	C₂×#41×C₈₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₈₉	—	2	4	no	—
52	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
53	AGL(1,ℤ/8)×C₈₉	—	4	8	no	—
54	#135×C₈₉	—	2	4	no	—
55	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
56	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
57	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
58	C₂×D₈×C₈₉	—	2	8	no	—
59	C₂×D₈×C₈₉	—	4	4	no	—
60	C₂×D₈×C₈₉	C₂³	1	4	yes	—
61	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₂×D₈×C₈₉	C₂³	1	4	yes	—
63	C₂×D₈×C₈₉	C₂³	1	8	yes	—
64	C₂×D₈×C₈₉	C₂³	1	8	yes	—
65	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
66	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
69	#127×C₈₉	—	2	2	no	—
70	#127×C₈₉	—	2	2	no	—
71	#127×C₈₉	C₂³	1	8	yes	—
72	#127×C₈₉	C₂³	1	8	yes	—
73	#125×C₈₉	D₄	1	2	yes	—
74	#124×C₈₉	—	2	8	no	—
75	#124×C₈₉	C₂³	1	8	yes	—
76	#123×C₈₉	—	2	16	no	—
77	C₂²⋊Q₈×C₈₉	D₄	1	4	yes	—
78	#121×C₈₉	—	2	8	no	—
79	#121×C₈₉	—	2	8	no	—
80	#121×C₈₉	—	2	16	no	—
81	#120×C₈₉	—	2	8	no	—
82	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
83	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
84	C₄×D₄×C₈₉	—	2	4	no	—
85	C₄×D₄×C₈₉	—	2	8	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	C₄×D₄×C₈₉	C₂³	1	4	yes	—
88	C₄×D₄×C₈₉	C₂³	1	16	yes	—
89	#117×C₈₉	—	2	2	no	—
90	#117×C₈₉	C₂³	1	2	yes	—
91	#117×C₈₉	C₂³	1	2	yes	—
92	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
93	C₂×C₄²×C₈₉	—	2	2	no	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	#107×C₈₉	C₂³	1	2	yes	—
96	#106×C₈₉	C₂³	1	2	yes	—
97	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
98	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
99	#103×C₈₉	C₂³	1	4	yes	—
100	#102×C₈₉	C₂³	1	4	yes	—
101	#102×C₈₉	C₂³	1	16	yes	—
102	#97×C₈₉	C₂³	1	4	yes	—
103	C₄×C₈×C₈₉	C₂³	1	2	yes	—
104	C₄×C₈×C₈₉	C₂³	1	2	yes	—
105	C₄×C₈×C₈₉	C₂³	1	4	yes	—
106	C₂⁴×C₈₉	—	2	4	no	—
107	#41×C₈₉	—	2	4	no	—
108	#41×C₈₉	—	2	4	no	—
109	#41×C₈₉	—	8	16	no	—
110	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
111	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
112	C₂×D₄×C₈₉	—	2	2	no	—
113	C₂×D₄×C₈₉	—	2	4	no	—
114	C₂×D₄×C₈₉	—	2	8	no	—
115	C₂×D₄×C₈₉	—	2	16	no	—
116	C₂×D₄×C₈₉	—	2	8	no	—
117	C₂×D₄×C₈₉	—	2	8	no	—
118	C₂×D₄×C₈₉	—	2	8	no	—
119	C₂×D₄×C₈₉	—	8	8	no	—
120	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
121	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₈₉	—	2	2	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	16	no	—
125	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
127	Q₁₆×C₈₉	—	2	2	no	—
128	SD₁₆×C₈₉	—	2	4	no	—
129	SD₁₆×C₈₉	—	4	8	no	—
130	D₈×C₈₉	—	2	8	no	—
131	D₈×C₈₉	—	2	8	no	—
132	D₈×C₈₉	—	2	2	no	—
133	D₈×C₈₉	—	4	8	no	—
134	D₈×C₈₉	—	4	8	no	—
135	M₁₆×C₈₉	—	2	4	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	#41	1	4	yes	complemented
138	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
139	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
140	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	—	2	4	no	—
143	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
144	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
145	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
146	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₂²⋊C₄×C₈₉	—	2	16	no	—
149	C₂²⋊C₄×C₈₉	—	2	4	no	—
150	C₂²⋊C₄×C₈₉	—	2	16	no	—
151	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
152	C₄²×C₈₉	—	2	2	no	—
153	C₄²×C₈₉	—	2	4	no	—
154	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂⁴	1	2	yes	—
157	C₄²×C₈₉	C₂⁴	1	4	yes	—
158	C₂³×C₈₉	—	2	8	no	—
159	C₂³×C₈₉	—	2	2	no	—
160	C₂³×C₈₉	—	4	8	no	—
161	C₂³×C₈₉	—	8	8	no	—
162	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₈₉	—	2	8	no	—
164	Q₈×C₈₉	—	2	2	no	—
165	Q₈×C₈₉	—	2	2	no	—
166	D₄×C₈₉	—	2	8	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	2	2	no	—
169	D₄×C₈₉	—	2	8	no	—
170	D₄×C₈₉	—	4	4	no	—
171	D₄×C₈₉	—	4	8	no	—
172	D₄×C₈₉	—	4	16	no	—
173	D₄×C₈₉	—	8	8	no	—
174	D₄×C₈₉	—	8	16	no	—
175	C₂×C₄×C₈₉	—	2	4	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	4	4	no	—
179	C₂×C₄×C₈₉	—	4	8	no	—
180	C₂×C₄×C₈₉	—	8	16	no	—
181	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
186	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
187	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
188	C₈×C₈₉	—	2	2	no	—
189	C₈×C₈₉	—	2	4	no	—
190	C₈×C₈₉	C₂×#41	1	2	yes	—
191	C₈×C₈₉	C₂×#41	1	2	yes	—
192	C₂²×C₈₉	—	2	2	no	—
193	C₂²×C₈₉	—	4	2	no	—
194	C₂²×C₈₉	—	4	8	no	—
195	C₂²×C₈₉	—	4	4	no	—
196	C₂²×C₈₉	—	4	16	no	—
197	C₂²×C₈₉	—	16	8	no	—
198	C₂²×C₈₉	#550	1	2	yes	—
199	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	2	8	no	—
202	C₄×C₈₉	—	4	2	no	—
203	C₄×C₈₉	—	4	4	no	—
204	C₄×C₈₉	#550	1	2	yes	—
205	C₄×C₈₉	#576	1	4	yes	—
206	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
207	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
208	#61409	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₈₉	—	2	2	no	—
210	C₂×C₈₉	—	8	2	no	—
211	C₂×C₈₉	—	8	8	no	—
212	C₂×C₈₉	C₂×#550	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#576	1	2	yes	—
214	#3508	C₂×C₈₉	1	2	yes	complemented
215	#3399	C₂×C₈₉	1	8	yes	complemented
216	#3396	C₂×C₈₉	1	4	yes	complemented
217	#3391	C₂×C₈₉	1	4	yes	complemented
218	#3155	C₂×C₈₉	1	2	yes	complemented
219	C₂×#493	C₂×C₈₉	1	1	yes	characteristic, complemented
220	#3041	C₂×C₈₉	1	4	yes	complemented
221	#3038	C₂×C₈₉	1	2	yes	complemented
222	#2960	C₂×C₈₉	1	1	yes	characteristic, complemented
223	#2948	C₂×C₈₉	1	2	yes	complemented
224	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
225	C₈₉	#61409	1	1	yes	characteristic, direct product factor, Sylow
226	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	—
227	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
228	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
229	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
230	#559	C₂²×C₈₉	1	8	yes	complemented
231	#550	C₂²×C₈₉	1	8	yes	complemented
232	#546	—	2	8	no	—
233	#540	—	2	4	no	—
234	#535	C₂²×C₈₉	1	4	yes	—
235	#533	C₂²×C₈₉	1	1	yes	characteristic
236	#532	—	2	4	no	—
237	C₂×#127	C₂²×C₈₉	1	2	yes	—
238	#518	C₂²×C₈₉	1	4	yes	—
239	C₄×#41	C₂²×C₈₉	1	2	yes	—
240	#496	C₂²×C₈₉	1	8	yes	complemented
241	#495	C₂²×C₈₉	1	4	yes	complemented
242	#493	C₂²×C₈₉	1	4	yes	—
243	#493	C₂²×C₈₉	1	4	yes	—
244	#493	C₂²×C₈₉	1	4	yes	complemented
245	#463	C₂²×C₈₉	1	16	yes	complemented
246	#460	C₂²×C₈₉	1	8	yes	complemented
247	#459	C₂²×C₈₉	1	8	yes	complemented
248	#459	C₂²×C₈₉	1	16	yes	complemented
249	#446	C₂²×C₈₉	1	4	yes	complemented
250	C₈×Q₈	C₂²×C₈₉	1	4	yes	complemented
251	#442	C₂²×C₈₉	1	8	yes	complemented
252	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
253	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
254	C₄×D₈	C₂²×C₈₉	1	2	yes	complemented
255	C₄×D₈	C₂²×C₈₉	1	8	yes	complemented
256	#427	C₂²×C₈₉	1	1	yes	characteristic
257	#424	C₂²×C₈₉	1	2	yes	—
258	#423	C₂²×C₈₉	1	1	yes	characteristic
259	#418	C₂²×C₈₉	1	4	yes	—
260	#416	C₂²×C₈₉	1	2	yes	—
261	#405	C₂²×C₈₉	1	2	yes	—
262	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
263	C₂×#41	—	2	8	no	—
264	C₂×#41	C₂³×C₈₉	1	2	yes	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
267	AGL(1,ℤ/8)	—	4	8	no	—
268	#135	—	2	4	no	—
269	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
270	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
271	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
272	C₂×D₈	—	2	8	no	—
273	C₂×D₈	—	4	4	no	—
274	C₂×D₈	C₂³×C₈₉	1	4	yes	—
275	C₂×D₈	C₂³×C₈₉	1	4	yes	—
276	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
277	C₂×D₈	C₂³×C₈₉	1	8	yes	—
278	C₂×D₈	C₂³×C₈₉	1	8	yes	—
279	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
280	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
282	C₄⋊Q₈	D₄×C₈₉	1	2	yes	—
283	#127	—	2	2	no	—
284	#127	—	2	2	no	—
285	#127	C₂³×C₈₉	1	8	yes	—
286	#127	C₂³×C₈₉	1	8	yes	—
287	#125	D₄×C₈₉	1	2	yes	—
288	#124	—	2	8	no	—
289	#124	C₂³×C₈₉	1	8	yes	—
290	#123	—	2	16	no	—
291	C₂²⋊Q₈	D₄×C₈₉	1	4	yes	—
292	#121	—	2	8	no	—
293	#121	—	2	8	no	—
294	#121	—	2	16	no	—
295	#120	—	2	8	no	—
296	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
297	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
298	C₄×D₄	—	2	4	no	—
299	C₄×D₄	—	2	8	no	—
300	C₄×D₄	—	2	8	no	—
301	C₄×D₄	C₂³×C₈₉	1	4	yes	—
302	C₄×D₄	C₂³×C₈₉	1	16	yes	—
303	#117	—	2	2	no	—
304	#117	C₂³×C₈₉	1	2	yes	—
305	#117	C₂³×C₈₉	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	8	no	—
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
309	#107	C₂³×C₈₉	1	2	yes	—
310	#106	C₂³×C₈₉	1	2	yes	—
311	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
312	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
313	#103	C₂³×C₈₉	1	4	yes	—
314	#102	C₂³×C₈₉	1	4	yes	—
315	#102	C₂³×C₈₉	1	16	yes	—
316	#97	C₂³×C₈₉	1	4	yes	—
317	C₄×C₈	C₂³×C₈₉	1	2	yes	—
318	C₄×C₈	C₂³×C₈₉	1	2	yes	—
319	C₄×C₈	C₂³×C₈₉	1	4	yes	—
320	C₂⁴	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	2	4	no	—
323	#41	—	8	16	no	—
324	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
325	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	4	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	16	no	—
330	C₂×D₄	—	2	8	no	—
331	C₂×D₄	—	2	8	no	—
332	C₂×D₄	—	2	8	no	—
333	C₂×D₄	—	8	8	no	—
334	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
335	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	SD₁₆	—	4	8	no	—
344	D₈	—	2	8	no	—
345	D₈	—	2	8	no	—
346	D₈	—	2	2	no	—
347	D₈	—	4	8	no	—
348	D₈	—	4	8	no	—
349	M₁₆	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	#41×C₈₉	1	4	yes	complemented
352	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
353	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
354	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
355	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
358	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
359	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
360	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₂²⋊C₄	—	2	16	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	16	no	—
365	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	4	no	—
368	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
370	C₄²	C₂⁴×C₈₉	1	2	yes	—
371	C₄²	C₂⁴×C₈₉	1	4	yes	—
372	C₂³	—	2	8	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	4	8	no	—
375	C₂³	—	8	8	no	—
376	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
377	Q₈	—	2	8	no	—
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	D₄	—	2	8	no	—
381	D₄	—	2	2	no	—
382	D₄	—	2	2	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	8	no	—
386	D₄	—	4	16	no	—
387	D₄	—	8	8	no	—
388	D₄	—	8	16	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	8	no	—
394	C₂×C₄	—	8	16	no	—
395	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
396	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
397	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
399	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
400	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
401	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	C₂×#41×C₈₉	1	2	yes	—
405	C₈	C₂×#41×C₈₉	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	4	16	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	8	no	—
411	C₂²	—	16	8	no	—
412	C₂²	#550×C₈₉	1	2	yes	—
413	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
414	C₄	—	2	2	no	—
415	C₄	—	2	8	no	—
416	C₄	—	4	4	no	—
417	C₄	—	4	2	no	—
418	C₄	#550×C₈₉	1	2	yes	—
419	C₄	#576×C₈₉	1	4	yes	—
420	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
421	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	—	8	8	no	—
425	C₂	C₂×#550×C₈₉	1	1	yes	characteristic
426	C₂	C₂×#576×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ #533×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3508	C₂	semidirect
2. C₈₉×#3399	C₂	semidirect
3. C₈₉×#3396	C₂	semidirect
4. C₈₉×#3391	C₂	semidirect
5. C₈₉×#3155	C₂	semidirect
6. C₂×#493×C₈₉	C₂	semidirect
7. C₈₉×#3041	C₂	semidirect
8. C₈₉×#3038	C₂	semidirect
9. C₈₉×#2960	C₂	semidirect
10. C₈₉×#2948	C₂	semidirect
11. C₄×#135×C₈₉	C₂	semidirect
16. #559×C₈₉	C₂²	semidirect
17. #550×C₈₉	C₂²	semidirect
26. #496×C₈₉	C₂²	semidirect
27. #495×C₈₉	C₂²	semidirect
30. #493×C₈₉	C₂²	semidirect
31. #463×C₈₉	C₂²	semidirect
32. #460×C₈₉	C₂²	semidirect
33. #459×C₈₉	C₂²	semidirect
34. #459×C₈₉	C₂²	semidirect
35. #446×C₈₉	C₂²	semidirect
36. C₈×Q₈×C₈₉	C₂²	semidirect
37. #442×C₈₉	C₂²	semidirect
38. C₄×Q₁₆×C₈₉	C₂²	semidirect
39. C₄×SD₁₆×C₈₉	C₂²	semidirect
40. C₄×D₈×C₈₉	C₂²	semidirect
41. C₄×D₈×C₈₉	C₂²	semidirect
137. C₂×C₈×C₈₉	#41	semidirect
208. #61409	C₈₉	direct (N × H)
214. #3508	C₂×C₈₉	semidirect
215. #3399	C₂×C₈₉	semidirect
216. #3396	C₂×C₈₉	semidirect
217. #3391	C₂×C₈₉	semidirect
218. #3155	C₂×C₈₉	semidirect
219. C₂×#493	C₂×C₈₉	semidirect
220. #3041	C₂×C₈₉	semidirect
221. #3038	C₂×C₈₉	semidirect
222. #2960	C₂×C₈₉	semidirect
223. #2948	C₂×C₈₉	semidirect
224. C₄×#135	C₂×C₈₉	semidirect
225. C₈₉	#61409	direct (N × H)
230. #559	C₂²×C₈₉	semidirect
231. #550	C₂²×C₈₉	semidirect
240. #496	C₂²×C₈₉	semidirect
241. #495	C₂²×C₈₉	semidirect
244. #493	C₂²×C₈₉	semidirect
245. #463	C₂²×C₈₉	semidirect
246. #460	C₂²×C₈₉	semidirect
247. #459	C₂²×C₈₉	semidirect
248. #459	C₂²×C₈₉	semidirect
249. #446	C₂²×C₈₉	semidirect
250. C₈×Q₈	C₂²×C₈₉	semidirect
251. #442	C₂²×C₈₉	semidirect
252. C₄×Q₁₆	C₂²×C₈₉	semidirect
253. C₄×SD₁₆	C₂²×C₈₉	semidirect
254. C₄×D₈	C₂²×C₈₉	semidirect
255. C₄×D₈	C₂²×C₈₉	semidirect
351. C₂×C₈	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3508	2
C₈₉×#3399	2
C₈₉×#3396	2
C₈₉×#3391	2
C₈₉×#3155	2
C₂×#493×C₈₉	2
C₈₉×#3041	2
C₈₉×#3038	2
C₈₉×#2960	2
C₈₉×#2948	2
C₄×#135×C₈₉	2
#61409	89

Subgroups — C89×#61409 #36439257

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61409 #36439257