Subgroups — C₂×SD₁₆×#10623494 #36523792

Order 22784.

822 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#10623494	C₂	1	1	yes	maximal, characteristic
3	SD₁₆×#10623494	C₂	1	8	yes	maximal, direct product factor
4	C₂×#19151349	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊#10623494	C₂	1	1	yes	maximal, characteristic
7	C₂×C₈×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×#10623494	—	2	1	no	—
10	Q₈×#10623494	—	2	2	no	—
11	Q₈×#10623494	C₂²	1	4	yes	complemented
12	D₄×#10623494	—	2	2	no	—
13	D₄×#10623494	C₂²	1	4	yes	—
14	C₂×C₄⋊#10623494	—	2	1	no	—
15	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊#10623494	—	2	1	no	—
18	C₂×C₄×#10623494	—	2	1	no	—
19	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
20	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
21	#19151349	C₂²	1	4	yes	complemented
22	Q₈⋊#10623494	C₂²	1	4	yes	complemented
23	D₄⋊#10623494	C₂²	1	4	yes	—
24	C₈×#10623494	C₂²	1	4	yes	complemented
25	C₂²×SD₁₆×C₈₉	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₄×SD₁₆×C₈₉	C₄	1	4	yes	—
29	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
30	C₂×#106×C₈₉	C₄	1	1	yes	characteristic
31	C₂×#103×C₈₉	C₄	1	1	yes	characteristic
32	C₂×#102×C₈₉	C₄	1	1	yes	characteristic
33	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×#10623494	—	2	4	no	—
35	C₂²×#10623494	—	2	1	no	—
36	C₂²×#10623494	—	2	1	no	—
37	C₂²×#10623494	—	2	1	no	—
38	C₂²×#10623494	—	4	4	no	—
39	C₂²×#10623494	D₄	1	1	yes	characteristic
40	C₂²×#10623494	D₄	1	1	yes	characteristic
41	C₄⋊#10623494	—	2	4	no	—
42	C₄⋊#10623494	—	2	1	no	—
43	C₄⋊#10623494	—	2	1	no	—
44	C₄⋊#10623494	C₂³	1	2	yes	—
45	C₄⋊#10623494	C₂³	1	2	yes	—
46	C₂²⋊#10623494	—	2	4	no	—
47	C₄×#10623494	—	2	4	no	—
48	C₄×#10623494	—	2	1	no	—
49	C₄×#10623494	D₄	1	2	yes	—
50	C₄×#10623494	C₂³	1	2	yes	—
51	C₄×#10623494	C₂³	1	2	yes	—
52	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂²×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₈₉	—	2	1	no	—
55	C₂×SD₁₆×C₈₉	C₈	1	8	yes	complemented
56	C₂×SD₁₆×C₈₉	C₂×C₄	1	4	yes	—
57	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄×Q₈×C₈₉	—	2	1	no	—
60	C₄×Q₈×C₈₉	—	2	1	no	—
61	C₄×Q₈×C₈₉	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
63	C₄×D₄×C₈₉	—	2	1	no	—
64	C₄×D₄×C₈₉	—	2	1	no	—
65	C₄×D₄×C₈₉	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
68	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
71	C₂×C₄²×C₈₉	—	2	1	no	—
72	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
73	#106×C₈₉	C₂×C₄	1	4	yes	—
74	#103×C₈₉	C₂×C₄	1	4	yes	—
75	#102×C₈₉	C₂×C₄	1	4	yes	—
76	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₈₉	C₂³	1	2	yes	—
78	C₂×#10623494	—	2	4	no	—
79	C₂×#10623494	—	2	2	no	—
80	C₂×#10623494	—	2	2	no	—
81	C₂×#10623494	—	2	2	no	—
82	C₂×#10623494	—	2	2	no	—
83	C₂×#10623494	—	4	2	no	—
84	C₂×#10623494	—	4	2	no	—
85	C₂×#10623494	—	4	8	no	—
86	C₂×#10623494	SD₁₆	1	4	yes	direct product factor
87	C₂×#10623494	C₂×D₄	1	2	yes	—
88	C₂×#10623494	C₂×D₄	1	2	yes	—
89	C₂⁴×C₈₉	—	2	1	no	—
90	C₂×Q₈×C₈₉	—	2	1	no	—
91	C₂×Q₈×C₈₉	—	2	2	no	—
92	C₂×Q₈×C₈₉	C₂×C₈	1	4	yes	complemented
93	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
94	C₂×D₄×C₈₉	—	2	1	no	—
95	C₂×D₄×C₈₉	—	2	2	no	—
96	C₂×D₄×C₈₉	C₂×C₈	1	4	yes	—
97	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₈₉	—	2	1	no	—
99	C₂²×C₄×C₈₉	—	2	1	no	—
100	C₂²×C₄×C₈₉	—	2	1	no	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	—	4	2	no	—
104	C₂²×C₄×C₈₉	—	4	2	no	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
108	SD₁₆×C₈₉	C₂×C₈	1	16	yes	complemented
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	C₂×C₈	1	4	yes	complemented
111	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
112	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
113	C₄⋊C₄×C₈₉	—	2	2	no	—
114	C₄⋊C₄×C₈₉	—	2	1	no	—
115	C₄⋊C₄×C₈₉	—	2	1	no	—
116	C₄⋊C₄×C₈₉	—	2	2	no	—
117	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₈₉	—	2	2	no	—
120	C₂²⋊C₄×C₈₉	—	2	2	no	—
121	C₄²×C₈₉	—	2	2	no	—
122	C₄²×C₈₉	—	2	2	no	—
123	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₈₉	#41	1	1	yes	characteristic
126	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
127	C₂³×C₈₉	—	2	2	no	—
128	C₂³×C₈₉	—	2	4	no	—
129	C₂³×C₈₉	—	4	2	no	—
130	C₂³×C₈₉	—	4	2	no	—
131	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
132	Q₈×C₈₉	—	2	2	no	—
133	Q₈×C₈₉	—	2	4	no	—
134	Q₈×C₈₉	C₂²×C₈	1	4	yes	complemented
135	D₄×C₈₉	—	2	2	no	—
136	D₄×C₈₉	—	2	4	no	—
137	D₄×C₈₉	C₂²×C₈	1	4	yes	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	4	2	no	—
144	C₂×C₄×C₈₉	—	4	2	no	—
145	C₂×C₄×C₈₉	—	4	2	no	—
146	C₂×C₄×C₈₉	—	4	2	no	—
147	C₂×C₄×C₈₉	—	4	4	no	—
148	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
152	C₂×C₄×C₈₉	#131	1	2	yes	—
153	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
154	C₂×C₄×C₈₉	#135	1	2	yes	—
155	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
158	C₈×C₈₉	—	2	2	no	—
159	C₈×C₈₉	C₂²×C₈	1	4	yes	complemented
160	#10623494	—	2	4	no	—
161	#10623494	—	2	2	no	—
162	#10623494	—	4	2	no	—
163	#10623494	—	4	2	no	—
164	#10623494	C₂×SD₁₆	1	4	yes	direct product factor
165	C₂²×C₈₉	—	2	4	no	—
166	C₂²×C₈₉	—	4	8	no	—
167	C₂²×C₈₉	—	4	2	no	—
168	C₂²×C₈₉	—	4	2	no	—
169	C₂²×C₈₉	C₈×D₄	1	2	yes	—
170	C₂²×C₈₉	C₄×SD₁₆	1	2	yes	—
171	C₂²×C₈₉	#443	1	2	yes	—
172	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
173	C₄×C₈₉	—	2	4	no	—
174	C₄×C₈₉	—	2	1	no	—
175	C₄×C₈₉	—	2	1	no	—
176	C₄×C₈₉	—	4	2	no	—
177	C₄×C₈₉	—	4	2	no	—
178	C₄×C₈₉	C₈×D₄	1	2	yes	—
179	C₄×C₈₉	C₄×SD₁₆	1	2	yes	—
180	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
181	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
182	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
183	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
184	C₂×C₈×SD₁₆	—	89	1	no	maximal, Sylow
185	C₂×C₈₉	—	4	4	no	—
186	C₂×C₈₉	C₈×SD₁₆	1	4	yes	complemented
187	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
188	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
189	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
190	C₂×C₈×Q₈	—	89	1	no	—
191	C₂×C₄×SD₁₆	D₈₉	1	1	yes	characteristic
192	C₂×C₈×D₄	—	89	1	no	—
193	C₈×SD₁₆	—	89	8	no	—
194	C₂×#334	—	89	1	no	—
195	C₂×Q₈⋊C₈	—	89	1	no	—
196	C₂×D₄⋊C₈	—	89	1	no	—
197	C₂×C₈²	—	89	1	no	—
198	C₈₉	C₂×C₈×SD₁₆	1	1	yes	characteristic, complemented, Sylow
199	C₂²×SD₁₆	Dic₈₉	1	1	yes	characteristic
200	C₂³×C₈	—	178	1	no	—
201	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
202	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
203	C₈×Q₈	—	89	4	no	—
204	C₈×Q₈	—	178	2	no	—
205	C₄×SD₁₆	Dic₈₉	1	4	yes	—
206	C₄×SD₁₆	C₂×D₈₉	1	4	yes	—
207	C₈×D₄	—	89	4	no	—
208	C₈×D₄	—	178	2	no	—
209	C₂×#106	Dic₈₉	1	1	yes	characteristic
210	C₂×C₄⋊C₈	—	89	1	no	—
211	C₂×C₄⋊C₈	—	89	1	no	—
212	C₂×C₄⋊C₈	—	178	1	no	—
213	C₂×#103	Dic₈₉	1	1	yes	characteristic
214	C₂×#102	Dic₈₉	1	1	yes	characteristic
215	C₂×C₂²⋊C₈	—	178	1	no	—
216	C₂×C₄×C₈	—	89	1	no	—
217	C₂×C₄×C₈	—	89	1	no	—
218	C₂×C₄×C₈	—	178	1	no	—
219	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
220	#334	—	89	4	no	—
221	Q₈⋊C₈	—	89	4	no	—
222	D₄⋊C₈	—	89	4	no	—
223	C₈²	—	89	4	no	—
224	C₂²×Q₈	C₂×Dic₈₉	1	1	yes	characteristic
225	C₂²×D₄	C₂×Dic₈₉	1	1	yes	characteristic
226	C₂³×C₄	—	2	1	no	—
227	C₂×SD₁₆	#10623494	1	8	yes	direct product factor
228	C₂×SD₁₆	C₂×Dic₈₉	1	4	yes	—
229	C₂²×C₈	—	89	1	no	—
230	C₂²×C₈	—	89	1	no	—
231	C₂²×C₈	—	356	4	no	—
232	C₂²×C₈	—	178	4	no	—
233	C₂²×C₈	—	178	1	no	—
234	C₂²×C₈	—	178	1	no	—
235	C₂²×C₈	—	178	1	no	—
236	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
237	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₂×Dic₈₉	1	2	yes	—
241	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	C₂×Dic₈₉	1	2	yes	—
245	C₄×D₄	C₂²×D₈₉	1	2	yes	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₈₉	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
252	#106	C₂×Dic₈₉	1	4	yes	—
253	C₄⋊C₈	—	89	2	no	—
254	C₄⋊C₈	—	89	2	no	—
255	C₄⋊C₈	—	178	4	no	—
256	C₄⋊C₈	—	178	1	no	—
257	C₄⋊C₈	—	178	1	no	—
258	#103	C₂×Dic₈₉	1	4	yes	—
259	#102	C₂×Dic₈₉	1	4	yes	—
260	C₂²⋊C₈	—	178	4	no	—
261	C₄×C₈	—	89	2	no	—
262	C₄×C₈	—	89	2	no	—
263	C₄×C₈	—	89	2	no	—
264	C₄×C₈	—	178	4	no	—
265	C₄×C₈	—	178	1	no	—
266	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
267	C₄×C₈	C₂²×D₈₉	1	2	yes	—
268	C₂⁴	—	2	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	C₂×#10623494	1	4	yes	complemented
272	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	C₂×#10623494	1	4	yes	—
276	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
286	C₂²×C₄	#13083573	1	1	yes	characteristic
287	SD₁₆	C₂×#10623494	1	16	yes	direct product factor
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	89	4	no	—
290	C₂×C₈	—	89	2	no	—
291	C₂×C₈	—	89	2	no	—
292	C₂×C₈	—	356	8	no	—
293	C₂×C₈	—	356	2	no	—
294	C₂×C₈	—	356	2	no	—
295	C₂×C₈	—	178	2	no	—
296	C₂×C₈	—	178	2	no	—
297	C₂×C₈	—	178	4	no	—
298	C₂×C₈	—	178	2	no	—
299	C₂×C₈	—	178	2	no	—
300	C₂×C₈	C₂×#10623494	1	4	yes	complemented
301	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
302	C₂×C₈	C₂²×Dic₈₉	1	2	yes	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	1	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
308	C₄⋊C₄	C₂²×Dic₈₉	1	2	yes	—
309	C₂²⋊C₄	—	2	2	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
314	C₄²	D₄×D₈₉	1	1	yes	characteristic
315	C₄²	#13083573	1	1	yes	characteristic
316	C₄²	C₂³×D₈₉	1	1	yes	characteristic
317	C₂³	—	2	4	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	2	no	—
321	C₂³	D₄×Dic₈₉	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	2	no	—
324	Q₈	C₂²×#10623494	1	4	yes	complemented
325	D₄	—	2	4	no	—
326	D₄	—	2	2	no	—
327	D₄	C₂²×#10623494	1	4	yes	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
339	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
341	C₂×C₄	C₂²×#10623494	1	2	yes	—
342	C₂×C₄	#15668019	1	2	yes	—
343	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
344	C₂×C₄	#15668033	1	2	yes	—
345	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
347	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
348	C₈	—	2	2	no	—
349	C₈	—	89	4	no	—
350	C₈	—	356	2	no	—
351	C₈	—	356	2	no	—
352	C₈	—	178	4	no	—
353	C₈	—	178	2	no	—
354	C₈	C₂²×#10623494	1	4	yes	complemented
355	C₂²	—	2	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	8	no	—
359	C₂²	D₄×#10623494	1	2	yes	—
360	C₂²	SD₁₆×Dic₈₉	1	2	yes	—
361	C₂²	#19151715	1	2	yes	—
362	C₂²	C₂×D₄×Dic₈₉	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	D₄×#10623494	1	2	yes	—
369	C₄	SD₁₆×Dic₈₉	1	2	yes	—
370	C₄	C₂³×#10623494	1	1	yes	characteristic
371	C₄	C₂×#15668019	1	1	yes	characteristic
372	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
373	C₄	C₂×#15668033	1	1	yes	characteristic
374	C₂	—	4	4	no	—
375	C₂	SD₁₆×#10623494	1	4	yes	direct product factor
376	C₂	C₂×D₄×#10623494	1	1	yes	characteristic
377	C₂	C₂×SD₁₆×Dic₈₉	1	1	yes	characteristic
378	C₂	C₂×#19151715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×C₄×SD₁₆×C₈₉	C₂
socle	C₂³×C₈₉	C₄×D₄
prime radical	C₂²×D₄×C₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₈₉
hypocenter	C₈₉	C₂×C₈×SD₁₆
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×#10623494	C₂	semidirect
3. SD₁₆×#10623494	C₂	direct (N × H)
4. C₂×#19151349	C₂	semidirect
5. C₂×Q₈⋊#10623494	C₂	semidirect
7. C₂×C₈×#10623494	C₂	semidirect
11. Q₈×#10623494	C₂²	semidirect
21. #19151349	C₂²	semidirect
22. Q₈⋊#10623494	C₂²	semidirect
24. C₈×#10623494	C₂²	semidirect
55. C₂×SD₁₆×C₈₉	C₈	semidirect
86. C₂×#10623494	SD₁₆	direct (N × H)
92. C₂×Q₈×C₈₉	C₂×C₈	semidirect
108. SD₁₆×C₈₉	C₂×C₈	semidirect
110. C₂×C₈×C₈₉	C₂×C₈	semidirect
134. Q₈×C₈₉	C₂²×C₈	semidirect
159. C₈×C₈₉	C₂²×C₈	semidirect
164. #10623494	C₂×SD₁₆	direct (N × H)
186. C₂×C₈₉	C₈×SD₁₆	semidirect
198. C₈₉	C₂×C₈×SD₁₆	semidirect
227. C₂×SD₁₆	#10623494	direct (N × H)
271. C₂×Q₈	C₂×#10623494	semidirect
287. SD₁₆	C₂×#10623494	direct (N × H)
300. C₂×C₈	C₂×#10623494	semidirect
324. Q₈	C₂²×#10623494	semidirect
354. C₈	C₂²×#10623494	semidirect
375. C₂	SD₁₆×#10623494	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×Q₈×#10623494	2
C₂×D₄×#10623494	2
SD₁₆×#10623494	2
C₂×#19151349	2
C₂×Q₈⋊#10623494	2
C₂×D₄⋊#10623494	2
C₂×C₈×#10623494	2
C₂×C₄×SD₁₆×C₈₉	2
C₂×C₈×SD₁₆	89

Subgroups — C2×SD16×#10623494 #36523792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×SD₁₆×#10623494 #36523792