Subgroups — C₂×Q₈×SD₁₆×C₈₉ #36439200

Order 22784.

2058 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈²×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	Q₈×SD₁₆×C₈₉	C₂	1	16	yes	maximal, direct product factor
4	C₂×#498×C₈₉	C₂	1	3	yes	maximal, complemented
5	C₂×#475×C₈₉	C₂	1	3	yes	maximal, complemented
6	C₂×#476×C₈₉	C₂	1	3	yes	maximal
7	C₂×C₈×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×SD₁₆×C₈₉	C₂	1	3	yes	maximal
9	C₂³×Q₈×C₈₉	—	2	1	no	—
10	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	Q₈²×C₈₉	—	2	4	no	—
12	Q₈²×C₈₉	C₂²	1	8	yes	complemented
13	D₄×Q₈×C₈₉	—	2	4	no	—
14	D₄×Q₈×C₈₉	C₂²	1	8	yes	—
15	C₂×C₄⋊Q₈×C₈₉	—	2	3	no	—
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	—	2	3	no	—
19	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	3	yes	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
23	#498×C₈₉	C₂²	1	24	yes	complemented
24	#476×C₈₉	C₂²	1	24	yes	—
25	#475×C₈₉	C₂²	1	24	yes	complemented
26	C₈×Q₈×C₈₉	C₂²	1	8	yes	complemented
27	C₄×SD₁₆×C₈₉	C₂²	1	24	yes	—
28	C₂×#106×C₈₉	C₂²	1	6	yes	—
29	C₂×#106×C₈₉	C₂²	1	3	yes	—
30	C₂×C₄⋊C₈×C₈₉	C₂²	1	3	yes	—
31	C₂×#103×C₈₉	C₂²	1	3	yes	—
32	C₂×#102×C₈₉	C₂²	1	3	yes	—
33	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
34	C₂²×Q₈×C₈₉	—	2	8	no	—
35	C₂²×Q₈×C₈₉	—	2	3	no	—
36	C₂²×Q₈×C₈₉	—	2	3	no	—
37	C₂²×Q₈×C₈₉	—	4	8	no	—
38	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	—	2	3	no	—
42	C₂×SD₁₆×C₈₉	Q₈	1	8	yes	direct product factor
43	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
44	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
45	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
46	C₄⋊Q₈×C₈₉	—	2	24	no	—
47	C₄⋊Q₈×C₈₉	—	2	6	no	—
48	C₄⋊Q₈×C₈₉	—	2	6	no	—
49	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
50	C₄⋊Q₈×C₈₉	C₂³	1	12	yes	—
51	C₂²⋊Q₈×C₈₉	—	2	24	no	—
52	C₄×Q₈×C₈₉	—	2	8	no	—
53	C₄×Q₈×C₈₉	—	2	6	no	—
54	C₄×Q₈×C₈₉	D₄	1	4	yes	—
55	C₄×Q₈×C₈₉	C₂³	1	12	yes	—
56	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
57	C₄×D₄×C₈₉	—	2	6	no	—
58	C₄×D₄×C₈₉	C₂³	1	12	yes	—
59	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
62	C₂×C₄⋊C₄×C₈₉	D₄	1	3	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
65	C₂×C₂²⋊C₄×C₈₉	—	2	3	no	—
66	C₂×C₄²×C₈₉	—	2	3	no	—
67	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
68	#106×C₈₉	C₂³	1	12	yes	—
69	#106×C₈₉	C₂³	1	24	yes	—
70	C₄⋊C₈×C₈₉	C₂³	1	12	yes	—
71	#103×C₈₉	C₂³	1	12	yes	—
72	#102×C₈₉	C₂³	1	12	yes	—
73	C₄×C₈×C₈₉	C₂³	1	12	yes	—
74	C₂⁴×C₈₉	—	2	1	no	—
75	C₂×Q₈×C₈₉	—	2	1	no	—
76	C₂×Q₈×C₈₉	—	2	12	no	—
77	C₂×Q₈×C₈₉	—	2	12	no	—
78	C₂×Q₈×C₈₉	—	2	2	no	—
79	C₂×Q₈×C₈₉	—	4	32	no	—
80	C₂×Q₈×C₈₉	—	4	12	no	—
81	C₂×Q₈×C₈₉	—	8	6	no	—
82	C₂×Q₈×C₈₉	SD₁₆	1	8	yes	direct product factor
83	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
84	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	complemented
85	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
86	C₂×D₄×C₈₉	—	2	1	no	—
87	C₂×D₄×C₈₉	—	2	2	no	—
88	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
89	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
90	C₂²×C₄×C₈₉	—	2	1	no	—
91	C₂²×C₄×C₈₉	—	2	3	no	—
92	C₂²×C₄×C₈₉	—	2	3	no	—
93	C₂²×C₄×C₈₉	—	2	12	no	—
94	C₂²×C₄×C₈₉	—	4	12	no	—
95	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
96	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
98	SD₁₆×C₈₉	C₂×Q₈	1	16	yes	direct product factor
99	C₂×C₈×C₈₉	—	2	6	no	—
100	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	complemented
101	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
102	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
103	C₄⋊C₄×C₈₉	—	2	12	no	—
104	C₄⋊C₄×C₈₉	—	2	12	no	—
105	C₄⋊C₄×C₈₉	—	2	12	no	—
106	C₄⋊C₄×C₈₉	—	2	3	no	—
107	C₄⋊C₄×C₈₉	—	2	3	no	—
108	C₄⋊C₄×C₈₉	C₂×D₄	1	12	yes	—
109	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
110	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
111	C₂²⋊C₄×C₈₉	—	2	12	no	—
112	C₄²×C₈₉	—	2	12	no	—
113	C₄²×C₈₉	C₂×D₄	1	6	yes	—
114	C₄²×C₈₉	C₂⁴	1	6	yes	—
115	C₂³×C₈₉	—	2	4	no	—
116	C₂³×C₈₉	—	2	2	no	—
117	C₂³×C₈₉	—	4	2	no	—
118	C₂³×C₈₉	—	4	2	no	—
119	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
120	Q₈×C₈₉	—	2	4	no	—
121	Q₈×C₈₉	—	2	2	no	—
122	Q₈×C₈₉	—	4	24	no	—
123	Q₈×C₈₉	—	8	12	no	—
124	Q₈×C₈₉	C₂×SD₁₆	1	16	yes	direct product factor
125	Q₈×C₈₉	C₂²×Q₈	1	4	yes	complemented
126	D₄×C₈₉	—	2	4	no	—
127	D₄×C₈₉	—	2	2	no	—
128	D₄×C₈₉	C₂²×Q₈	1	4	yes	—
129	C₂×C₄×C₈₉	—	2	4	no	—
130	C₂×C₄×C₈₉	—	2	6	no	—
131	C₂×C₄×C₈₉	—	2	2	no	—
132	C₂×C₄×C₈₉	—	2	6	no	—
133	C₂×C₄×C₈₉	—	2	6	no	—
134	C₂×C₄×C₈₉	—	4	6	no	—
135	C₂×C₄×C₈₉	—	4	6	no	—
136	C₂×C₄×C₈₉	—	4	24	no	—
137	C₂×C₄×C₈₉	C₂×SD₁₆	1	12	yes	—
138	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
139	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
141	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
142	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
143	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
144	C₈×C₈₉	—	2	6	no	—
145	C₈×C₈₉	C₂²×Q₈	1	4	yes	complemented
146	C₂²×C₈₉	—	2	4	no	—
147	C₂²×C₈₉	—	4	8	no	—
148	C₂²×C₈₉	—	4	2	no	—
149	C₂²×C₈₉	—	4	2	no	—
150	C₂²×C₈₉	D₄×Q₈	1	2	yes	—
151	C₂²×C₈₉	C₂²×SD₁₆	1	2	yes	—
152	C₂²×C₈₉	#577	1	2	yes	—
153	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
154	C₄×C₈₉	—	2	4	no	—
155	C₄×C₈₉	—	2	6	no	—
156	C₄×C₈₉	—	4	6	no	—
157	C₄×C₈₉	—	4	6	no	—
158	C₄×C₈₉	D₄×Q₈	1	2	yes	—
159	C₄×C₈₉	C₂²×SD₁₆	1	12	yes	—
160	C₄×C₈₉	C₂³×Q₈	1	1	yes	characteristic
161	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×Q₈×SD₁₆	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂×C₈₉	—	4	4	no	—
164	C₂×C₈₉	Q₈×SD₁₆	1	4	yes	direct product factor
165	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
166	C₂×C₈₉	C₂³×SD₁₆	1	1	yes	characteristic
167	C₂×C₈₉	C₂×#577	1	1	yes	characteristic
168	C₂×Q₈²	C₂×C₈₉	1	1	yes	characteristic, complemented
169	C₂×D₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
170	Q₈×SD₁₆	C₂×C₈₉	1	16	yes	direct product factor
171	C₂×#498	C₂×C₈₉	1	3	yes	complemented
172	C₂×#475	C₂×C₈₉	1	3	yes	complemented
173	C₂×#476	C₂×C₈₉	1	3	yes	—
174	C₂×C₈×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
175	C₂×C₄×SD₁₆	C₂×C₈₉	1	3	yes	—
176	C₈₉	C₂×Q₈×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
177	C₂³×Q₈	—	2	1	no	—
178	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
179	Q₈²	—	2	4	no	—
180	Q₈²	C₂²×C₈₉	1	8	yes	complemented
181	D₄×Q₈	—	2	4	no	—
182	D₄×Q₈	C₂²×C₈₉	1	8	yes	—
183	C₂×C₄⋊Q₈	—	2	3	no	—
184	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
185	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
186	C₂×C₂²⋊Q₈	—	2	3	no	—
187	C₂×C₄×Q₈	—	2	1	no	—
188	C₂×C₄×Q₈	C₂²×C₈₉	1	3	yes	—
189	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
190	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
191	#498	C₂²×C₈₉	1	24	yes	complemented
192	#476	C₂²×C₈₉	1	24	yes	—
193	#475	C₂²×C₈₉	1	24	yes	complemented
194	C₈×Q₈	C₂²×C₈₉	1	8	yes	complemented
195	C₄×SD₁₆	C₂²×C₈₉	1	24	yes	—
196	C₂×#106	C₂²×C₈₉	1	6	yes	—
197	C₂×#106	C₂²×C₈₉	1	3	yes	—
198	C₂×C₄⋊C₈	C₂²×C₈₉	1	3	yes	—
199	C₂×#103	C₂²×C₈₉	1	3	yes	—
200	C₂×#102	C₂²×C₈₉	1	3	yes	—
201	C₂×C₄×C₈	C₂²×C₈₉	1	3	yes	—
202	C₂²×Q₈	—	2	8	no	—
203	C₂²×Q₈	—	2	3	no	—
204	C₂²×Q₈	—	2	3	no	—
205	C₂²×Q₈	—	4	8	no	—
206	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
207	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
208	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
209	C₂³×C₄	—	2	3	no	—
210	C₂×SD₁₆	Q₈×C₈₉	1	8	yes	direct product factor
211	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
212	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
213	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
214	C₄⋊Q₈	—	2	24	no	—
215	C₄⋊Q₈	—	2	6	no	—
216	C₄⋊Q₈	—	2	6	no	—
217	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
218	C₄⋊Q₈	C₂³×C₈₉	1	12	yes	—
219	C₂²⋊Q₈	—	2	24	no	—
220	C₄×Q₈	—	2	8	no	—
221	C₄×Q₈	—	2	6	no	—
222	C₄×Q₈	D₄×C₈₉	1	4	yes	—
223	C₄×Q₈	C₂³×C₈₉	1	12	yes	—
224	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
225	C₄×D₄	—	2	6	no	—
226	C₄×D₄	C₂³×C₈₉	1	12	yes	—
227	C₂×C₄⋊C₄	—	2	3	no	—
228	C₂×C₄⋊C₄	—	2	3	no	—
229	C₂×C₄⋊C₄	—	2	3	no	—
230	C₂×C₄⋊C₄	D₄×C₈₉	1	3	yes	—
231	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
232	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
233	C₂×C₂²⋊C₄	—	2	3	no	—
234	C₂×C₄²	—	2	3	no	—
235	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
236	#106	C₂³×C₈₉	1	12	yes	—
237	#106	C₂³×C₈₉	1	24	yes	—
238	C₄⋊C₈	C₂³×C₈₉	1	12	yes	—
239	#103	C₂³×C₈₉	1	12	yes	—
240	#102	C₂³×C₈₉	1	12	yes	—
241	C₄×C₈	C₂³×C₈₉	1	12	yes	—
242	C₂⁴	—	2	1	no	—
243	C₂×Q₈	—	2	1	no	—
244	C₂×Q₈	—	2	12	no	—
245	C₂×Q₈	—	2	12	no	—
246	C₂×Q₈	—	2	2	no	—
247	C₂×Q₈	—	4	32	no	—
248	C₂×Q₈	—	4	12	no	—
249	C₂×Q₈	—	8	6	no	—
250	C₂×Q₈	SD₁₆×C₈₉	1	8	yes	direct product factor
251	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
252	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	complemented
253	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
254	C₂×D₄	—	2	1	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
257	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
258	C₂²×C₄	—	2	1	no	—
259	C₂²×C₄	—	2	3	no	—
260	C₂²×C₄	—	2	3	no	—
261	C₂²×C₄	—	2	12	no	—
262	C₂²×C₄	—	4	12	no	—
263	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
264	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
265	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
266	SD₁₆	C₂×Q₈×C₈₉	1	16	yes	direct product factor
267	C₂×C₈	—	2	6	no	—
268	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	complemented
269	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
270	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
271	C₄⋊C₄	—	2	12	no	—
272	C₄⋊C₄	—	2	12	no	—
273	C₄⋊C₄	—	2	12	no	—
274	C₄⋊C₄	—	2	3	no	—
275	C₄⋊C₄	—	2	3	no	—
276	C₄⋊C₄	C₂×D₄×C₈₉	1	12	yes	—
277	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
278	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
279	C₂²⋊C₄	—	2	12	no	—
280	C₄²	—	2	12	no	—
281	C₄²	C₂×D₄×C₈₉	1	6	yes	—
282	C₄²	C₂⁴×C₈₉	1	6	yes	—
283	C₂³	—	2	4	no	—
284	C₂³	—	2	2	no	—
285	C₂³	—	4	2	no	—
286	C₂³	—	4	2	no	—
287	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
288	Q₈	—	2	4	no	—
289	Q₈	—	2	2	no	—
290	Q₈	—	4	24	no	—
291	Q₈	—	8	12	no	—
292	Q₈	C₂×SD₁₆×C₈₉	1	16	yes	direct product factor
293	Q₈	C₂²×Q₈×C₈₉	1	4	yes	complemented
294	D₄	—	2	4	no	—
295	D₄	—	2	2	no	—
296	D₄	C₂²×Q₈×C₈₉	1	4	yes	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	6	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	6	no	—
301	C₂×C₄	—	2	6	no	—
302	C₂×C₄	—	4	6	no	—
303	C₂×C₄	—	4	6	no	—
304	C₂×C₄	—	4	24	no	—
305	C₂×C₄	C₂×SD₁₆×C₈₉	1	12	yes	—
306	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
307	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
308	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
309	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
310	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
311	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
312	C₈	—	2	6	no	—
313	C₈	C₂²×Q₈×C₈₉	1	4	yes	complemented
314	C₂²	—	2	4	no	—
315	C₂²	—	4	2	no	—
316	C₂²	—	4	2	no	—
317	C₂²	—	4	8	no	—
318	C₂²	D₄×Q₈×C₈₉	1	2	yes	—
319	C₂²	C₂²×SD₁₆×C₈₉	1	2	yes	—
320	C₂²	#577×C₈₉	1	2	yes	—
321	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
322	C₄	—	2	6	no	—
323	C₄	—	2	4	no	—
324	C₄	—	4	6	no	—
325	C₄	—	4	6	no	—
326	C₄	D₄×Q₈×C₈₉	1	2	yes	—
327	C₄	C₂²×SD₁₆×C₈₉	1	12	yes	—
328	C₄	C₂³×Q₈×C₈₉	1	1	yes	characteristic
329	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
330	C₂	—	4	4	no	—
331	C₂	Q₈×SD₁₆×C₈₉	1	4	yes	direct product factor
332	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
333	C₂	C₂³×SD₁₆×C₈₉	1	1	yes	characteristic
334	C₂	C₂×#577×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈²×C₈₉	C₂	semidirect
3. Q₈×SD₁₆×C₈₉	C₂	direct (N × H)
4. C₂×#498×C₈₉	C₂	semidirect
5. C₂×#475×C₈₉	C₂	semidirect
7. C₂×C₈×Q₈×C₈₉	C₂	semidirect
12. Q₈²×C₈₉	C₂²	semidirect
23. #498×C₈₉	C₂²	semidirect
25. #475×C₈₉	C₂²	semidirect
26. C₈×Q₈×C₈₉	C₂²	semidirect
42. C₂×SD₁₆×C₈₉	Q₈	direct (N × H)
82. C₂×Q₈×C₈₉	SD₁₆	direct (N × H)
84. C₂×Q₈×C₈₉	C₂×Q₈	semidirect
98. SD₁₆×C₈₉	C₂×Q₈	direct (N × H)
100. C₂×C₈×C₈₉	C₂×Q₈	semidirect
124. Q₈×C₈₉	C₂×SD₁₆	direct (N × H)
125. Q₈×C₈₉	C₂²×Q₈	semidirect
145. C₈×C₈₉	C₂²×Q₈	semidirect
162. C₂×Q₈×SD₁₆	C₈₉	direct (N × H)
164. C₂×C₈₉	Q₈×SD₁₆	direct (N × H)
168. C₂×Q₈²	C₂×C₈₉	semidirect
170. Q₈×SD₁₆	C₂×C₈₉	direct (N × H)
171. C₂×#498	C₂×C₈₉	semidirect
172. C₂×#475	C₂×C₈₉	semidirect
174. C₂×C₈×Q₈	C₂×C₈₉	semidirect
176. C₈₉	C₂×Q₈×SD₁₆	direct (N × H)
180. Q₈²	C₂²×C₈₉	semidirect
191. #498	C₂²×C₈₉	semidirect
193. #475	C₂²×C₈₉	semidirect
194. C₈×Q₈	C₂²×C₈₉	semidirect
210. C₂×SD₁₆	Q₈×C₈₉	direct (N × H)
250. C₂×Q₈	SD₁₆×C₈₉	direct (N × H)
252. C₂×Q₈	C₂×Q₈×C₈₉	semidirect
266. SD₁₆	C₂×Q₈×C₈₉	direct (N × H)
268. C₂×C₈	C₂×Q₈×C₈₉	semidirect
292. Q₈	C₂×SD₁₆×C₈₉	direct (N × H)
293. Q₈	C₂²×Q₈×C₈₉	semidirect
313. C₈	C₂²×Q₈×C₈₉	semidirect
331. C₂	Q₈×SD₁₆×C₈₉	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×Q₈²×C₈₉	2
C₂×D₄×Q₈×C₈₉	2
Q₈×SD₁₆×C₈₉	2
C₂×#498×C₈₉	2
C₂×#475×C₈₉	2
C₂×#476×C₈₉	2
C₂×C₈×Q₈×C₈₉	2
C₂×C₄×SD₁₆×C₈₉	2
C₂×Q₈×SD₁₆	89

Subgroups — C2×Q8×SD16×C89 #36439200

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×SD₁₆×C₈₉ #36439200