Subgroups — M₁₆×C₄⋊Dic₈₉ #36552419

Order 22784.

1242 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151622	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₈₉	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic
4	#26020124	C₂	1	4	yes	maximal, complemented
5	#26020119	C₂	1	2	yes	maximal, complemented
6	C₈×C₄⋊Dic₈₉	C₂	1	2	yes	maximal, complemented
7	#26019945	C₂	1	2	yes	maximal
8	C₂×C₄×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂²×#13083558	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₈₉	C₄	1	2	yes	—
11	C₂²×C₄×Dic₈₉	C₂²	1	2	yes	—
12	#19151622	C₄	1	8	yes	complemented
13	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
14	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
15	M₁₆×Dic₈₉	—	2	8	no	—
16	C₂×#15667922	C₂²	1	4	yes	—
17	C₂×C₈×Dic₈₉	C₂²	1	4	yes	—
18	C₄×C₄⋊Dic₈₉	C₄	1	2	yes	—
19	C₄×C₄⋊Dic₈₉	C₄	1	2	yes	—
20	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
23	C₂×#15667919	C₄	1	2	yes	—
24	#19151352	C₂²	1	4	yes	—
25	#19151352	C₂²	1	4	yes	—
26	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
29	C₄×M₁₆×C₈₉	C₄	1	8	yes	complemented
30	C₂×#97×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
32	C₂³×Dic₈₉	C₂×C₄	1	4	yes	—
33	C₂×#13083558	—	2	4	no	—
34	C₂×#13083558	—	2	4	no	—
35	C₂×#13083558	C₂×C₄	1	8	yes	—
36	C₂²×#10623494	C₂³	1	4	yes	—
37	C₂×C₄⋊Dic₈₉	—	2	8	no	—
38	C₂×C₄⋊Dic₈₉	C₂×C₄	1	4	yes	—
39	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
40	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₈₉	—	2	4	no	—
42	C₂×C₄×Dic₈₉	—	2	4	no	—
43	C₂×C₄×Dic₈₉	C₂×C₄	1	4	yes	—
44	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
45	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
46	C₄⋊#10623494	C₂×C₄	1	8	yes	complemented
47	C₄⋊#10623494	C₂×C₄	1	8	yes	complemented
48	#15667922	—	2	8	no	—
49	C₈×Dic₈₉	—	2	8	no	—
50	#15667919	C₂×C₄	1	2	yes	—
51	#15667919	C₂×C₄	1	4	yes	—
52	#15667919	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₈₉	—	2	2	no	—
57	C₂×M₁₆×C₈₉	—	2	2	no	—
58	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
59	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
60	C₂×M₁₆×C₈₉	D₄	1	4	yes	—
61	C₂×M₁₆×C₈₉	Q₈	1	4	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
63	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₈₉	C₂×C₄	1	4	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	#97×C₈₉	C₂×C₄	1	8	yes	complemented
71	C₄×C₈×C₈₉	C₂×C₄	1	8	yes	complemented
72	C₂²×Dic₈₉	—	2	8	no	—
73	C₂²×Dic₈₉	—	2	8	no	—
74	C₂²×Dic₈₉	—	4	4	no	—
75	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
76	C₂²×Dic₈₉	C₂²×C₄	1	4	yes	—
77	#13083558	—	2	16	no	—
78	C₂×#10623494	—	2	4	no	—
79	C₂×#10623494	—	2	4	no	—
80	C₂×#10623494	C₂²×C₄	1	8	yes	—
81	C₄⋊Dic₈₉	—	2	4	no	—
82	C₄⋊Dic₈₉	—	2	8	no	—
83	C₄⋊Dic₈₉	M₁₆	1	8	yes	direct product factor
84	C₄×Dic₈₉	—	2	8	no	—
85	C₄×Dic₈₉	—	2	2	no	—
86	C₄×Dic₈₉	—	2	2	no	—
87	C₄×Dic₈₉	—	2	2	no	—
88	C₄×Dic₈₉	—	2	2	no	—
89	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₈₉	—	2	4	no	—
91	C₂²×C₄×C₈₉	—	4	2	no	—
92	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
93	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
94	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₈₉	#41	1	2	yes	—
104	C₂²×C₄×C₈₉	#41	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
106	M₁₆×C₈₉	—	2	8	no	—
107	M₁₆×C₈₉	C₄⋊C₄	1	16	yes	complemented
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
111	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
113	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
114	C₄²×C₈₉	C₄²	1	4	yes	—
115	C₄²×C₈₉	C₄²	1	4	yes	—
116	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
117	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
118	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
119	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
120	C₂³×C₈₉	—	2	2	no	—
121	C₂³×C₈₉	—	2	2	no	—
122	C₂³×C₈₉	C₂×C₄²	1	2	yes	—
123	C₂³×C₈₉	C₄×D₄	1	2	yes	—
124	C₂³×C₈₉	C₄×Q₈	1	2	yes	—
125	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₈₉	—	2	2	no	—
127	C₂×C₄×C₈₉	—	2	2	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	2	8	no	—
130	C₂×C₄×C₈₉	—	4	4	no	—
131	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
132	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
133	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
134	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
135	C₂×C₄×C₈₉	C₂×C₄²	1	2	yes	—
136	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	4	yes	—
137	C₂×C₄×C₈₉	#117	1	4	yes	—
138	C₂×C₄×C₈₉	C₄×D₄	1	4	yes	—
139	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
140	C₂×C₄×C₈₉	C₄×Q₈	1	4	yes	—
141	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
142	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
143	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₈₉	—	2	4	no	—
150	C₂×Dic₈₉	—	2	4	no	—
151	C₂×Dic₈₉	—	2	4	no	—
152	C₂×Dic₈₉	—	2	4	no	—
153	C₂×Dic₈₉	—	2	4	no	—
154	C₂×Dic₈₉	—	4	16	no	—
155	C₂×Dic₈₉	C₂×M₁₆	1	8	yes	—
156	C₈×C₈₉	—	2	4	no	—
157	C₈×C₈₉	C₂×C₄⋊C₄	1	8	yes	complemented
158	#10623494	—	2	8	no	—
159	C₂²×C₈₉	—	2	2	no	—
160	C₂²×C₈₉	—	2	2	no	—
161	C₂²×C₈₉	—	2	4	no	—
162	C₂²×C₈₉	—	2	4	no	—
163	C₂²×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
164	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
165	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₂²×C₈₉	C₂²×M₁₆	1	2	yes	—
168	C₂²×C₈₉	#568	1	2	yes	—
169	C₄×C₈₉	—	2	2	no	—
170	C₄×C₈₉	—	2	2	no	—
171	C₄×C₈₉	—	2	2	no	—
172	C₄×C₈₉	C₄×C₄⋊C₄	1	4	yes	—
173	C₄×C₈₉	C₄×M₁₆	1	4	yes	complemented
174	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
176	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
177	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
178	Dic₈₉	—	2	8	no	—
179	Dic₈₉	—	4	4	no	—
180	C₄⋊C₄×M₁₆	—	89	1	no	maximal, Sylow
181	C₂×C₈₉	—	2	4	no	—
182	C₂×C₈₉	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
184	C₂×C₈₉	#2873	1	1	yes	characteristic
185	C₂×C₈₉	D₄×M₁₆	1	2	yes	—
186	C₂×C₈₉	Q₈×M₁₆	1	2	yes	—
187	C₂×#423	—	89	1	no	—
188	C₂×C₄×M₁₆	—	89	2	no	—
189	C₂×C₄×M₁₆	D₈₉	1	1	yes	characteristic
190	C₂×C₄×C₄⋊C₄	—	89	1	no	—
191	#1771	—	89	4	no	—
192	#1770	—	89	2	no	—
193	C₈×C₄⋊C₄	—	89	2	no	—
194	#1728	—	89	2	no	—
195	C₈₉	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂²×M₁₆	—	89	2	no	—
197	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
198	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
199	C₂²×C₄⋊C₄	—	89	2	no	—
200	C₂²×C₄²	—	89	2	no	—
201	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
202	#423	—	89	8	no	—
203	C₂×C₄⋊C₈	—	89	2	no	—
204	C₂×C₄⋊C₈	—	89	2	no	—
205	C₄×M₁₆	—	178	8	no	—
206	C₄×M₁₆	Dic₈₉	1	8	yes	complemented
207	C₂×#97	—	89	4	no	—
208	C₂×#97	C₂×D₈₉	1	2	yes	—
209	C₂×C₄×C₈	—	89	4	no	—
210	C₂×C₄×C₈	C₂×D₈₉	1	2	yes	—
211	C₄×C₄⋊C₄	—	89	2	no	—
212	C₄×C₄⋊C₄	—	89	2	no	—
213	C₄×C₄⋊C₄	—	89	1	no	—
214	C₄×C₄⋊C₄	—	89	1	no	—
215	C₄×C₄⋊C₄	—	89	2	no	—
216	C₂×#95	—	89	2	no	—
217	#336	—	89	4	no	—
218	#336	—	89	4	no	—
219	C₂³×C₄	—	89	4	no	—
220	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
221	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	89	8	no	—
226	C₂×M₁₆	—	178	4	no	—
227	C₂×M₁₆	—	178	4	no	—
228	C₂×M₁₆	Dic₁₇₈	1	4	yes	—
229	C₂×M₁₆	D₃₅₆	1	4	yes	—
230	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
231	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
232	C₂²×C₈	—	89	4	no	—
233	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
234	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
235	C₂×C₄⋊C₄	—	89	2	no	—
236	C₂×C₄⋊C₄	—	89	4	no	—
237	C₂×C₄⋊C₄	—	89	2	no	—
238	C₂×C₄⋊C₄	—	178	8	no	—
239	C₂×C₄²	—	89	4	no	—
240	C₂×C₄²	—	89	2	no	—
241	C₂×C₄²	—	89	2	no	—
242	C₂×C₄²	—	178	4	no	—
243	C₂×C₄²	—	178	4	no	—
244	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
245	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
246	C₂×C₄²	C₄×D₈₉	1	4	yes	—
247	C₂×C₄²	C₂×Dic₈₉	1	4	yes	—
248	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
250	C₄⋊C₈	—	89	8	no	—
251	C₄⋊C₈	—	89	8	no	—
252	#97	—	178	8	no	—
253	#97	C₂×Dic₈₉	1	8	yes	complemented
254	C₄×C₈	—	178	8	no	—
255	C₄×C₈	C₂×Dic₈₉	1	8	yes	complemented
256	#95	—	89	2	no	—
257	#95	—	89	4	no	—
258	#95	—	89	2	no	—
259	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	89	4	no	—
263	C₂²×C₄	—	89	4	no	—
264	C₂²×C₄	—	356	4	no	—
265	C₂²×C₄	—	178	8	no	—
266	C₂²×C₄	—	178	8	no	—
267	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
268	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
269	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
273	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₈₉	1	2	yes	—
276	C₂²×C₄	C₂×D₃₅₆	1	2	yes	—
277	C₂²×C₄	C₂×Dic₁₇₈	1	2	yes	—
278	C₂²×C₄	#13083574	1	2	yes	—
279	C₂²×C₄	#13083574	1	2	yes	—
280	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
281	M₁₆	—	2	8	no	—
282	M₁₆	—	178	16	no	—
283	M₁₆	C₄⋊Dic₈₉	1	16	yes	direct product factor
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	89	8	no	—
287	C₂×C₈	—	178	4	no	—
288	C₂×C₈	—	178	4	no	—
289	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
290	C₂×C₈	C₂²×Dic₈₉	1	4	yes	—
291	C₂×C₈	C₂×D₃₅₆	1	4	yes	—
292	C₂×C₈	C₂×Dic₁₇₈	1	4	yes	—
293	C₄⋊C₄	—	89	8	no	—
294	C₄⋊C₄	—	178	8	no	—
295	C₄⋊C₄	—	178	4	no	—
296	C₄²	—	178	8	no	—
297	C₄²	—	178	2	no	—
298	C₄²	—	178	2	no	—
299	C₄²	—	178	2	no	—
300	C₄²	—	178	2	no	—
301	C₄²	C₄×Dic₈₉	1	4	yes	—
302	C₄²	C₄×Dic₈₉	1	4	yes	—
303	C₄²	C₂×C₄×D₈₉	1	2	yes	—
304	C₄²	C₂×C₄×D₈₉	1	2	yes	—
305	C₄²	C₂²×Dic₈₉	1	2	yes	—
306	C₄²	C₂²×Dic₈₉	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₄×Dic₈₉	1	2	yes	—
310	C₂³	C₄×D₃₅₆	1	2	yes	—
311	C₂³	C₄×Dic₁₇₈	1	2	yes	—
312	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	89	8	no	—
319	C₂×C₄	—	356	16	no	—
320	C₂×C₄	—	178	4	no	—
321	C₂×C₄	—	178	4	no	—
322	C₂×C₄	—	178	4	no	—
323	C₂×C₄	—	178	4	no	—
324	C₂×C₄	—	178	4	no	—
325	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
326	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
327	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
328	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
329	C₂×C₄	C₂×C₄×Dic₈₉	1	2	yes	—
330	C₂×C₄	C₂×C₄⋊Dic₈₉	1	4	yes	—
331	C₂×C₄	#15667971	1	4	yes	—
332	C₂×C₄	C₄×D₃₅₆	1	2	yes	—
333	C₂×C₄	C₄×D₃₅₆	1	4	yes	—
334	C₂×C₄	C₄×Dic₁₇₈	1	2	yes	—
335	C₂×C₄	C₄×Dic₁₇₈	1	4	yes	—
336	C₂×C₄	M₁₆×D₈₉	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
338	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
339	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
340	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
341	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
342	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
343	C₈	—	2	4	no	—
344	C₈	—	178	8	no	—
345	C₈	C₂×C₄⋊Dic₈₉	1	8	yes	complemented
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	C₄×C₄⋊Dic₈₉	1	4	yes	—
351	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
352	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
353	C₂²	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
354	C₂²	C₂×M₁₆×D₈₉	1	2	yes	—
355	C₂²	#19152364	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	356	4	no	—
360	C₄	—	178	8	no	—
361	C₄	C₄×C₄⋊Dic₈₉	1	4	yes	—
362	C₄	M₁₆×Dic₈₉	1	4	yes	complemented
363	C₄	C₂²×C₄⋊Dic₈₉	1	1	yes	characteristic
364	C₄	C₂×#15667971	1	1	yes	characteristic
365	C₄	C₂×C₄×D₃₅₆	1	1	yes	characteristic
366	C₄	C₂×C₄×Dic₁₇₈	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
369	C₂	C₂×M₁₆×Dic₈₉	1	1	yes	characteristic
370	C₂	#26028670	1	1	yes	characteristic
371	C₂	M₁₆×D₃₅₆	1	2	yes	—
372	C₂	M₁₆×Dic₁₇₈	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator	C₂²×C₈₉	C₂²×C₄²
Fitting	C₂×C₄×M₁₆×C₈₉	C₂
socle	C₂³×C₈₉	C₂³×C₄
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₈₉
hypocenter	C₈₉	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #26020124	C₂	semidirect
5. #26020119	C₂	semidirect
6. C₈×C₄⋊Dic₈₉	C₂	semidirect
12. #19151622	C₄	semidirect
29. C₄×M₁₆×C₈₉	C₄	semidirect
46. C₄⋊#10623494	C₂×C₄	semidirect
47. C₄⋊#10623494	C₂×C₄	semidirect
70. #97×C₈₉	C₂×C₄	semidirect
71. C₄×C₈×C₈₉	C₂×C₄	semidirect
83. C₄⋊Dic₈₉	M₁₆	direct (N × H)
107. M₁₆×C₈₉	C₄⋊C₄	semidirect
157. C₈×C₈₉	C₂×C₄⋊C₄	semidirect
173. C₄×C₈₉	C₄×M₁₆	semidirect
195. C₈₉	C₄⋊C₄×M₁₆	semidirect
206. C₄×M₁₆	Dic₈₉	semidirect
253. #97	C₂×Dic₈₉	semidirect
255. C₄×C₈	C₂×Dic₈₉	semidirect
283. M₁₆	C₄⋊Dic₈₉	direct (N × H)
345. C₈	C₂×C₄⋊Dic₈₉	semidirect
362. C₄	M₁₆×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151622	2
C₂×M₁₆×Dic₈₉	2
C₂×C₄×C₄⋊Dic₈₉	2
#26020124	2
#26020119	2
C₈×C₄⋊Dic₈₉	2
#26019945	2
C₂×C₄×M₁₆×C₈₉	2
C₄⋊C₄×M₁₆	89

Subgroups — M16×C4⋊Dic89 #36552419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₁₆×C₄⋊Dic₈₉ #36552419