Subgroups — C₂×C₈₉×AGL(1,ℤ/16) #36411315

Order 22784.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#509×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#444×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#442×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×AGL(1,ℤ/16)	C₂	1	8	yes	maximal, direct product factor
5	C₂×#365×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#361×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#360×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#347×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
10	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#131×C₈₉	—	2	1	no	—
12	C₂×C₄×D₄×C₈₉	—	2	1	no	—
13	#509×C₈₉	C₄	1	4	yes	complemented
14	#509×C₈₉	C₂²	1	4	yes	—
15	C₂×SD₃₂×C₈₉	C₄	1	2	yes	complemented
16	C₂×D₁₆×C₈₉	C₄	1	2	yes	complemented
17	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
19	#444×C₈₉	—	2	2	no	—
20	#444×C₈₉	C₂²	1	4	yes	complemented
21	#442×C₈₉	—	2	2	no	—
22	#442×C₈₉	C₂²	1	4	yes	complemented
23	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#104×C₈₉	—	2	1	no	—
26	C₂×#102×C₈₉	—	2	1	no	—
27	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
28	#365×C₈₉	C₂²	1	4	yes	complemented
29	#361×C₈₉	C₂²	1	4	yes	complemented
30	#360×C₈₉	C₂²	1	4	yes	complemented
31	#347×C₈₉	C₂²	1	4	yes	complemented
32	C₂×#41×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	—	2	1	no	—
34	C₂³×C₄×C₈₉	—	4	1	no	—
35	#135×C₈₉	—	2	1	no	—
36	#135×C₈₉	—	2	1	no	—
37	#135×C₈₉	C₂×C₄	1	2	yes	complemented
38	#135×C₈₉	C₂³	1	2	yes	—
39	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×SD₁₆×C₈₉	—	2	1	no	—
41	C₂×D₈×C₈₉	—	2	1	no	—
42	C₂×D₈×C₈₉	—	2	1	no	—
43	C₂×D₈×C₈₉	—	2	1	no	—
44	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
45	C₂×D₈×C₈₉	C₂×C₄	1	2	yes	—
46	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
47	C₂×D₈×C₈₉	C₂³	1	2	yes	—
48	#131×C₈₉	—	2	4	no	—
49	#131×C₈₉	—	4	2	no	—
50	C₂×M₁₆×C₈₉	—	2	1	no	—
51	C₂×M₁₆×C₈₉	—	4	1	no	—
52	C₂²×C₈×C₈₉	—	4	1	no	—
53	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
55	C₄×D₄×C₈₉	—	2	4	no	—
56	C₄×D₄×C₈₉	—	4	2	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₈₉	—	4	1	no	—
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	SD₃₂×C₈₉	C₂×C₄	1	8	yes	complemented
61	D₁₆×C₈₉	C₂×C₄	1	8	yes	complemented
62	M₃₂×C₈₉	—	2	1	no	—
63	M₃₂×C₈₉	C₂×C₄	1	2	yes	complemented
64	M₃₂×C₈₉	C₂³	1	2	yes	—
65	M₃₂×C₈₉	C₂³	1	2	yes	—
66	C₂×C₁₆×C₈₉	—	2	1	no	—
67	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
68	#108×C₈₉	—	2	1	no	—
69	#108×C₈₉	C₂³	1	2	yes	—
70	#106×C₈₉	—	2	1	no	—
71	#106×C₈₉	C₂³	1	2	yes	—
72	#104×C₈₉	—	2	4	no	—
73	#102×C₈₉	—	2	4	no	—
74	#97×C₈₉	D₄	1	2	yes	—
75	#97×C₈₉	C₂³	1	2	yes	—
76	C₂⁴×C₈₉	—	4	1	no	—
77	#41×C₈₉	—	2	2	no	—
78	#41×C₈₉	—	2	2	no	—
79	#41×C₈₉	—	4	1	no	—
80	#41×C₈₉	—	4	1	no	—
81	C₂×Q₈×C₈₉	—	2	1	no	—
82	C₂×D₄×C₈₉	—	2	2	no	—
83	C₂×D₄×C₈₉	—	2	2	no	—
84	C₂×D₄×C₈₉	—	2	1	no	—
85	C₂×D₄×C₈₉	—	2	2	no	—
86	C₂×D₄×C₈₉	—	4	1	no	—
87	C₂×D₄×C₈₉	—	4	1	no	—
88	C₂×D₄×C₈₉	—	4	1	no	—
89	C₂×D₄×C₈₉	—	4	1	no	—
90	C₂²×C₄×C₈₉	—	2	1	no	—
91	C₂²×C₄×C₈₉	—	4	4	no	—
92	C₂²×C₄×C₈₉	—	4	1	no	—
93	C₂²×C₄×C₈₉	—	4	1	no	—
94	C₂²×C₄×C₈₉	—	8	4	no	—
95	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₈₉	—	2	1	no	—
97	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	complemented
98	SD₁₆×C₈₉	—	2	2	no	—
99	SD₁₆×C₈₉	—	2	2	no	—
100	D₈×C₈₉	—	2	2	no	—
101	D₈×C₈₉	—	2	2	no	—
102	D₈×C₈₉	—	2	1	no	—
103	D₈×C₈₉	—	2	2	no	—
104	D₈×C₈₉	C₂²×C₄	1	4	yes	—
105	D₈×C₈₉	C₂²×C₄	1	2	yes	complemented
106	M₁₆×C₈₉	—	2	2	no	—
107	M₁₆×C₈₉	—	4	4	no	—
108	M₁₆×C₈₉	—	4	1	no	—
109	C₂×C₈×C₈₉	—	2	1	no	—
110	C₂×C₈×C₈₉	—	2	1	no	—
111	C₂×C₈×C₈₉	—	4	4	no	—
112	C₂×C₈×C₈₉	—	4	1	no	—
113	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
118	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
119	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
120	C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₂²⋊C₄×C₈₉	—	4	4	no	—
123	C₄²×C₈₉	—	2	1	no	—
124	C₄²×C₈₉	C₂×D₄	1	2	yes	—
125	C₁₆×C₈₉	—	2	2	no	—
126	C₁₆×C₈₉	C₂²×C₄	1	4	yes	complemented
127	C₂³×C₈₉	—	4	2	no	—
128	C₂³×C₈₉	—	4	2	no	—
129	C₂³×C₈₉	—	4	1	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	—	8	2	no	—
132	C₂³×C₈₉	—	8	2	no	—
133	C₂³×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
134	Q₈×C₈₉	—	2	2	no	—
135	Q₈×C₈₉	—	4	1	no	—
136	D₄×C₈₉	—	2	4	no	—
137	D₄×C₈₉	—	2	2	no	—
138	D₄×C₈₉	—	4	2	no	—
139	D₄×C₈₉	—	4	2	no	—
140	D₄×C₈₉	—	4	2	no	—
141	D₄×C₈₉	—	4	2	no	—
142	D₄×C₈₉	—	4	2	no	—
143	D₄×C₈₉	—	4	1	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	2	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	—	8	8	no	—
151	C₂×C₄×C₈₉	—	8	2	no	—
152	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₈×C₈₉	—	2	2	no	—
159	C₈×C₈₉	—	4	2	no	—
160	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
161	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
162	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
163	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
164	C₂²×C₈₉	—	2	2	no	—
165	C₂²×C₈₉	—	4	2	no	—
166	C₂²×C₈₉	—	4	4	no	—
167	C₂²×C₈₉	—	8	2	no	—
168	C₂²×C₈₉	—	8	2	no	—
169	C₂²×C₈₉	—	8	4	no	—
170	C₂²×C₈₉	—	8	2	no	—
171	C₂²×C₈₉	—	8	4	no	—
172	C₂²×C₈₉	#442	1	1	yes	characteristic
173	C₂²×C₈₉	#442	1	1	yes	characteristic
174	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
175	C₄×C₈₉	—	4	2	no	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	—	8	2	no	—
178	C₄×C₈₉	#442	1	1	yes	characteristic
179	C₄×C₈₉	#442	1	1	yes	characteristic
180	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×AGL(1,ℤ/16)	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂×C₈₉	—	2	1	no	—
184	C₂×C₈₉	—	2	1	no	—
185	C₂×C₈₉	—	8	2	no	—
186	C₂×C₈₉	—	8	4	no	—
187	C₂×C₈₉	AGL(1,ℤ/16)	1	2	yes	direct product factor
188	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
189	C₂×#509	C₂×C₈₉	1	1	yes	characteristic
190	C₂×#444	C₂×C₈₉	1	1	yes	characteristic, complemented
191	C₂×#442	C₂×C₈₉	1	1	yes	characteristic, complemented
192	AGL(1,ℤ/16)	C₂×C₈₉	1	8	yes	direct product factor
193	C₂×#365	C₂×C₈₉	1	1	yes	characteristic, complemented
194	C₂×#361	C₂×C₈₉	1	1	yes	characteristic, complemented
195	C₂×#360	C₂×C₈₉	1	1	yes	characteristic, complemented
196	C₂×#347	C₂×C₈₉	1	1	yes	characteristic, complemented
197	C₈₉	C₂×AGL(1,ℤ/16)	1	1	yes	characteristic, direct product factor, Sylow
198	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
199	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
200	C₂×#131	—	2	1	no	—
201	C₂×C₄×D₄	—	2	1	no	—
202	#509	C₄×C₈₉	1	4	yes	complemented
203	#509	C₂²×C₈₉	1	4	yes	—
204	C₂×SD₃₂	C₄×C₈₉	1	2	yes	complemented
205	C₂×D₁₆	C₄×C₈₉	1	2	yes	complemented
206	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
207	C₂×M₃₂	C₂²×C₈₉	1	1	yes	characteristic
208	#444	—	2	2	no	—
209	#444	C₂²×C₈₉	1	4	yes	complemented
210	#442	—	2	2	no	—
211	#442	C₂²×C₈₉	1	4	yes	complemented
212	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
213	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
214	C₂×#104	—	2	1	no	—
215	C₂×#102	—	2	1	no	—
216	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
217	#365	C₂²×C₈₉	1	4	yes	complemented
218	#361	C₂²×C₈₉	1	4	yes	complemented
219	#360	C₂²×C₈₉	1	4	yes	complemented
220	#347	C₂²×C₈₉	1	4	yes	complemented
221	C₂×#41	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂³×C₄	—	4	1	no	—
224	#135	—	2	1	no	—
225	#135	—	2	1	no	—
226	#135	C₂×C₄×C₈₉	1	2	yes	complemented
227	#135	C₂³×C₈₉	1	2	yes	—
228	C₂×Q₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	2	1	no	—
230	C₂×D₈	—	2	1	no	—
231	C₂×D₈	—	2	1	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	C₂×C₄×C₈₉	1	2	yes	—
234	C₂×D₈	C₂×C₄×C₈₉	1	2	yes	—
235	C₂×D₈	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
236	C₂×D₈	C₂³×C₈₉	1	2	yes	—
237	#131	—	2	4	no	—
238	#131	—	4	2	no	—
239	C₂×M₁₆	—	2	1	no	—
240	C₂×M₁₆	—	4	1	no	—
241	C₂²×C₈	—	4	1	no	—
242	C₂²×C₈	D₄×C₈₉	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
244	C₄×D₄	—	2	4	no	—
245	C₄×D₄	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₂²⋊C₄	—	4	1	no	—
248	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
249	SD₃₂	C₂×C₄×C₈₉	1	8	yes	complemented
250	D₁₆	C₂×C₄×C₈₉	1	8	yes	complemented
251	M₃₂	—	2	1	no	—
252	M₃₂	C₂×C₄×C₈₉	1	2	yes	complemented
253	M₃₂	C₂³×C₈₉	1	2	yes	—
254	M₃₂	C₂³×C₈₉	1	2	yes	—
255	C₂×C₁₆	—	2	1	no	—
256	C₂×C₁₆	C₂×C₄×C₈₉	1	2	yes	complemented
257	#108	—	2	1	no	—
258	#108	C₂³×C₈₉	1	2	yes	—
259	#106	—	2	1	no	—
260	#106	C₂³×C₈₉	1	2	yes	—
261	#104	—	2	4	no	—
262	#102	—	2	4	no	—
263	#97	D₄×C₈₉	1	2	yes	—
264	#97	C₂³×C₈₉	1	2	yes	—
265	C₂⁴	—	4	1	no	—
266	#41	—	2	2	no	—
267	#41	—	2	2	no	—
268	#41	—	4	1	no	—
269	#41	—	4	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×D₄	—	2	2	no	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	1	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	4	4	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	8	4	no	—
284	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
285	Q₁₆	—	2	1	no	—
286	Q₁₆	C₂²×C₄×C₈₉	1	2	yes	complemented
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	2	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	D₈	—	2	1	no	—
292	D₈	—	2	2	no	—
293	D₈	C₂²×C₄×C₈₉	1	4	yes	—
294	D₈	C₂²×C₄×C₈₉	1	2	yes	complemented
295	M₁₆	—	2	2	no	—
296	M₁₆	—	4	4	no	—
297	M₁₆	—	4	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	4	4	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
304	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
305	C₂×C₈	C₂×D₄×C₈₉	1	1	yes	characteristic
306	C₂×C₈	#41×C₈₉	1	1	yes	characteristic
307	C₂×C₈	#41×C₈₉	1	1	yes	characteristic
308	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₄²	—	2	1	no	—
313	C₄²	C₂×D₄×C₈₉	1	2	yes	—
314	C₁₆	—	2	2	no	—
315	C₁₆	C₂²×C₄×C₈₉	1	4	yes	complemented
316	C₂³	—	4	1	no	—
317	C₂³	—	4	2	no	—
318	C₂³	—	4	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	8	2	no	—
321	C₂³	—	8	2	no	—
322	C₂³	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
323	Q₈	—	2	2	no	—
324	Q₈	—	4	1	no	—
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	1	no	—
332	D₄	—	4	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	8	8	no	—
340	C₂×C₄	—	8	2	no	—
341	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
342	C₂×C₄	C₄×D₄×C₈₉	1	1	yes	characteristic
343	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
344	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
345	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
347	C₈	—	2	2	no	—
348	C₈	—	4	2	no	—
349	C₈	C₄×D₄×C₈₉	1	1	yes	characteristic
350	C₈	C₄×D₄×C₈₉	1	1	yes	characteristic
351	C₈	C₂³×C₄×C₈₉	1	1	yes	characteristic
352	C₈	C₂×#41×C₈₉	1	1	yes	characteristic
353	C₂²	—	2	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	4	4	no	—
356	C₂²	—	8	2	no	—
357	C₂²	—	8	2	no	—
358	C₂²	—	8	4	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	2	no	—
361	C₂²	#442×C₈₉	1	1	yes	characteristic
362	C₂²	#442×C₈₉	1	1	yes	characteristic
363	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	—	8	2	no	—
367	C₄	#442×C₈₉	1	1	yes	characteristic
368	C₄	#442×C₈₉	1	1	yes	characteristic
369	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
370	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
371	C₂	—	2	1	no	—
372	C₂	—	2	1	no	—
373	C₂	—	8	2	no	—
374	C₂	—	8	4	no	—
375	C₂	C₈₉×AGL(1,ℤ/16)	1	2	yes	direct product factor
376	C₂	C₂×#442×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	#442
commutator	C₈	C₂³×C₄×C₈₉
Frattini, cosocle	C₂×C₈	C₂⁴×C₈₉
prime radical	C₂×#509×C₈₉	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄×C₈₉ ◁ C₂×#97×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#444×C₈₉	C₂	semidirect
3. C₂×#442×C₈₉	C₂	semidirect
4. C₈₉×AGL(1,ℤ/16)	C₂	direct (N × H)
5. C₂×#365×C₈₉	C₂	semidirect
6. C₂×#361×C₈₉	C₂	semidirect
7. C₂×#360×C₈₉	C₂	semidirect
8. C₂×#347×C₈₉	C₂	semidirect
13. #509×C₈₉	C₄	semidirect
15. C₂×SD₃₂×C₈₉	C₄	semidirect
16. C₂×D₁₆×C₈₉	C₄	semidirect
20. #444×C₈₉	C₂²	semidirect
22. #442×C₈₉	C₂²	semidirect
28. #365×C₈₉	C₂²	semidirect
29. #361×C₈₉	C₂²	semidirect
30. #360×C₈₉	C₂²	semidirect
31. #347×C₈₉	C₂²	semidirect
37. #135×C₈₉	C₂×C₄	semidirect
39. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
46. C₂×D₈×C₈₉	C₂×C₄	semidirect
60. SD₃₂×C₈₉	C₂×C₄	semidirect
61. D₁₆×C₈₉	C₂×C₄	semidirect
63. M₃₂×C₈₉	C₂×C₄	semidirect
67. C₂×C₁₆×C₈₉	C₂×C₄	semidirect
97. Q₁₆×C₈₉	C₂²×C₄	semidirect
105. D₈×C₈₉	C₂²×C₄	semidirect
126. C₁₆×C₈₉	C₂²×C₄	semidirect
182. C₂×AGL(1,ℤ/16)	C₈₉	direct (N × H)
187. C₂×C₈₉	AGL(1,ℤ/16)	direct (N × H)
190. C₂×#444	C₂×C₈₉	semidirect
191. C₂×#442	C₂×C₈₉	semidirect
192. AGL(1,ℤ/16)	C₂×C₈₉	direct (N × H)
193. C₂×#365	C₂×C₈₉	semidirect
194. C₂×#361	C₂×C₈₉	semidirect
195. C₂×#360	C₂×C₈₉	semidirect
196. C₂×#347	C₂×C₈₉	semidirect
197. C₈₉	C₂×AGL(1,ℤ/16)	direct (N × H)
202. #509	C₄×C₈₉	semidirect
204. C₂×SD₃₂	C₄×C₈₉	semidirect
205. C₂×D₁₆	C₄×C₈₉	semidirect
209. #444	C₂²×C₈₉	semidirect
211. #442	C₂²×C₈₉	semidirect
217. #365	C₂²×C₈₉	semidirect
218. #361	C₂²×C₈₉	semidirect
219. #360	C₂²×C₈₉	semidirect
220. #347	C₂²×C₈₉	semidirect
226. #135	C₂×C₄×C₈₉	semidirect
228. C₂×Q₁₆	C₂×C₄×C₈₉	semidirect
235. C₂×D₈	C₂×C₄×C₈₉	semidirect
249. SD₃₂	C₂×C₄×C₈₉	semidirect
250. D₁₆	C₂×C₄×C₈₉	semidirect
252. M₃₂	C₂×C₄×C₈₉	semidirect
256. C₂×C₁₆	C₂×C₄×C₈₉	semidirect
286. Q₁₆	C₂²×C₄×C₈₉	semidirect
294. D₈	C₂²×C₄×C₈₉	semidirect
315. C₁₆	C₂²×C₄×C₈₉	semidirect
375. C₂	C₈₉×AGL(1,ℤ/16)	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×#509×C₈₉	2
C₂×#444×C₈₉	2
C₂×#442×C₈₉	2
C₈₉×AGL(1,ℤ/16)	2
C₂×#365×C₈₉	2
C₂×#361×C₈₉	2
C₂×#360×C₈₉	2
C₂×#347×C₈₉	2
C₂×AGL(1,ℤ/16)	89

Subgroups — C2×C89×AGL(1,ℤ/16) #36411315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×AGL(1,ℤ/16) #36411315