Subgroups — Q₈×#124×C₈₉ #36414396

Order 22784.

2326 conjugacy classes of subgroups.

The subgroup lattice has 346 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	C₈₉×#2862	C₂	1	3	yes	maximal, complemented
4	C₈₉×#2568	C₂	1	3	yes	maximal, complemented
5	C₈₉×#2563	C₂	1	3	yes	maximal
6	C₈₉×#2492	C₂	1	12	yes	maximal, complemented
7	Q₈×C₂²⋊C₄×C₈₉	C₂	1	4	yes	maximal, complemented
8	C₄×#124×C₈₉	C₂	1	3	yes	maximal
9	C₄²×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
11	Q₈²×C₈₉	—	2	8	no	—
12	D₄×Q₈×C₈₉	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
14	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	6	yes	—
16	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
18	C₂×C₄×Q₈×C₈₉	C₂²	1	3	yes	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	3	yes	—
23	#400×C₈₉	C₂²	1	12	yes	—
24	#393×C₈₉	C₂²	1	12	yes	—
25	#391×C₈₉	C₂²	1	3	yes	—
26	#391×C₈₉	C₂²	1	12	yes	—
27	#391×C₈₉	C₂²	1	12	yes	—
28	#391×C₈₉	C₂²	1	12	yes	—
29	#390×C₈₉	C₂²	1	3	yes	—
30	#388×C₈₉	C₂²	1	12	yes	—
31	#382×C₈₉	C₂²	1	3	yes	—
32	#382×C₈₉	C₂²	1	6	yes	—
33	#380×C₈₉	C₂²	1	12	yes	—
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	3	yes	—
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	6	yes	—
36	C₄×C₂²⋊C₄×C₈₉	C₂²	1	12	yes	—
37	C₄³×C₈₉	C₂²	1	3	yes	—
38	C₂²×Q₈×C₈₉	—	2	8	no	—
39	C₂²×Q₈×C₈₉	—	2	16	no	—
40	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
41	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
42	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
43	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	6	yes	—
46	C₄⋊Q₈×C₈₉	—	2	24	no	—
47	C₄⋊Q₈×C₈₉	—	2	12	no	—
48	C₄⋊Q₈×C₈₉	—	2	12	no	—
49	#124×C₈₉	Q₈	1	8	yes	direct product factor
50	C₂²⋊Q₈×C₈₉	—	2	24	no	—
51	C₄×Q₈×C₈₉	—	2	8	no	—
52	C₄×Q₈×C₈₉	—	2	8	no	—
53	C₄×Q₈×C₈₉	—	2	12	no	—
54	C₄×Q₈×C₈₉	D₄	1	8	yes	—
55	C₄×D₄×C₈₉	—	2	12	no	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	3	yes	—
63	C₂×C₂²⋊C₄×C₈₉	C₂³	1	6	yes	—
64	C₂×C₂²⋊C₄×C₈₉	C₂³	1	12	yes	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
67	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	6	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
71	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	#95×C₈₉	C₂³	1	12	yes	—
73	#95×C₈₉	C₂³	1	12	yes	—
74	#95×C₈₉	C₂³	1	6	yes	—
75	#95×C₈₉	C₂³	1	24	yes	—
76	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
77	C₂×Q₈×C₈₉	—	2	2	no	—
78	C₂×Q₈×C₈₉	—	2	12	no	—
79	C₂×Q₈×C₈₉	—	2	12	no	—
80	C₂×Q₈×C₈₉	—	2	24	no	—
81	C₂×Q₈×C₈₉	—	2	2	no	—
82	C₂×Q₈×C₈₉	—	4	12	no	—
83	C₂×Q₈×C₈₉	—	4	32	no	—
84	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
85	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	complemented
86	C₂×Q₈×C₈₉	#41	1	8	yes	—
87	C₂×D₄×C₈₉	—	2	2	no	—
88	C₂×D₄×C₈₉	—	2	2	no	—
89	C₂×D₄×C₈₉	C₂×Q₈	1	4	yes	—
90	C₂²×C₄×C₈₉	—	2	12	no	—
91	C₂²×C₄×C₈₉	—	2	24	no	—
92	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
94	C₂²×C₄×C₈₉	C₂⁴	1	6	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
96	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
99	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
100	C₄⋊C₄×C₈₉	—	2	6	no	—
101	C₄⋊C₄×C₈₉	—	2	12	no	—
102	C₄⋊C₄×C₈₉	—	2	12	no	—
103	C₄⋊C₄×C₈₉	—	2	6	no	—
104	C₄⋊C₄×C₈₉	—	2	12	no	—
105	C₄⋊C₄×C₈₉	—	2	12	no	—
106	C₄⋊C₄×C₈₉	C₂×D₄	1	12	yes	—
107	C₂²⋊C₄×C₈₉	—	2	12	no	—
108	C₂²⋊C₄×C₈₉	—	4	12	no	—
109	C₂²⋊C₄×C₈₉	C₂×Q₈	1	16	yes	complemented
110	C₄²×C₈₉	—	2	12	no	—
111	C₄²×C₈₉	—	2	12	no	—
112	C₄²×C₈₉	—	2	6	no	—
113	C₄²×C₈₉	—	4	6	no	—
114	C₄²×C₈₉	C₂×D₄	1	12	yes	—
115	C₄²×C₈₉	C₂×Q₈	1	4	yes	complemented
116	C₂³×C₈₉	—	2	2	no	—
117	C₂³×C₈₉	—	2	4	no	—
118	C₂³×C₈₉	—	2	2	no	—
119	C₂³×C₈₉	—	2	4	no	—
120	C₂³×C₈₉	C₂²×Q₈	1	4	yes	—
121	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
122	Q₈×C₈₉	—	2	8	no	—
123	Q₈×C₈₉	—	4	24	no	—
124	Q₈×C₈₉	—	8	12	no	—
125	Q₈×C₈₉	#124	1	16	yes	direct product factor
126	D₄×C₈₉	—	2	8	no	—
127	C₂×C₄×C₈₉	—	2	2	no	—
128	C₂×C₄×C₈₉	—	2	2	no	—
129	C₂×C₄×C₈₉	—	2	2	no	—
130	C₂×C₄×C₈₉	—	2	2	no	—
131	C₂×C₄×C₈₉	—	2	6	no	—
132	C₂×C₄×C₈₉	—	2	6	no	—
133	C₂×C₄×C₈₉	—	2	6	no	—
134	C₂×C₄×C₈₉	—	2	6	no	—
135	C₂×C₄×C₈₉	—	2	12	no	—
136	C₂×C₄×C₈₉	—	2	6	no	—
137	C₂×C₄×C₈₉	—	2	6	no	—
138	C₂×C₄×C₈₉	—	2	12	no	—
139	C₂×C₄×C₈₉	—	4	24	no	—
140	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
141	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
142	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
143	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
144	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
145	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
146	C₂×C₄×C₈₉	C₂×#41	1	12	yes	—
147	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
148	C₂²×C₈₉	—	2	4	no	—
149	C₂²×C₈₉	—	2	8	no	—
150	C₂²×C₈₉	—	4	2	no	—
151	C₂²×C₈₉	—	4	2	no	—
152	C₂²×C₈₉	—	4	4	no	—
153	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
154	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
155	C₂²×C₈₉	C₂²×#41	1	2	yes	—
156	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
157	C₂²×C₈₉	#585	1	2	yes	—
158	C₄×C₈₉	—	2	4	no	—
159	C₄×C₈₉	—	2	4	no	—
160	C₄×C₈₉	—	2	6	no	—
161	C₄×C₈₉	—	4	6	no	—
162	C₄×C₈₉	—	4	6	no	—
163	C₄×C₈₉	—	4	6	no	—
164	C₄×C₈₉	C₂×#124	1	12	yes	—
165	C₄×C₈₉	D₄×Q₈	1	4	yes	—
166	Q₈×#124	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂×C₈₉	—	4	4	no	—
168	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
169	C₂×C₈₉	C₂×D₄×Q₈	1	1	yes	characteristic
170	C₂×C₈₉	Q₈×#41	1	2	yes	—
171	C₂×C₈₉	#3500	1	1	yes	characteristic
172	C₂×C₈₉	#3518	1	2	yes	—
173	C₂×Q₈²	C₂×C₈₉	1	1	yes	characteristic, complemented
174	C₂×D₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
175	#2862	C₂×C₈₉	1	3	yes	complemented
176	#2568	C₂×C₈₉	1	3	yes	complemented
177	#2563	C₂×C₈₉	1	3	yes	—
178	#2492	C₂×C₈₉	1	12	yes	complemented
179	Q₈×C₂²⋊C₄	C₂×C₈₉	1	4	yes	complemented
180	C₄×#124	C₂×C₈₉	1	3	yes	—
181	C₄²×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
182	C₈₉	Q₈×#124	1	1	yes	characteristic, direct product factor, Sylow
183	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
184	Q₈²	—	2	8	no	—
185	D₄×Q₈	—	2	8	no	—
186	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
187	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
188	C₂×C₄⋊Q₈	C₂²×C₈₉	1	6	yes	—
189	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
190	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
191	C₂×C₄×Q₈	C₂²×C₈₉	1	3	yes	—
192	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
193	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
194	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₈₉	1	3	yes	—
196	#400	C₂²×C₈₉	1	12	yes	—
197	#393	C₂²×C₈₉	1	12	yes	—
198	#391	C₂²×C₈₉	1	3	yes	—
199	#391	C₂²×C₈₉	1	12	yes	—
200	#391	C₂²×C₈₉	1	12	yes	—
201	#391	C₂²×C₈₉	1	12	yes	—
202	#390	C₂²×C₈₉	1	3	yes	—
203	#388	C₂²×C₈₉	1	12	yes	—
204	#382	C₂²×C₈₉	1	6	yes	—
205	#382	C₂²×C₈₉	1	3	yes	—
206	#380	C₂²×C₈₉	1	12	yes	—
207	C₄×C₄⋊C₄	C₂²×C₈₉	1	3	yes	—
208	C₄×C₄⋊C₄	C₂²×C₈₉	1	6	yes	—
209	C₄×C₂²⋊C₄	C₂²×C₈₉	1	12	yes	—
210	C₄³	C₂²×C₈₉	1	3	yes	—
211	C₂²×Q₈	—	2	8	no	—
212	C₂²×Q₈	—	2	16	no	—
213	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
214	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
215	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
216	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
217	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₈₉	1	6	yes	—
219	C₄⋊Q₈	—	2	24	no	—
220	C₄⋊Q₈	—	2	12	no	—
221	C₄⋊Q₈	—	2	12	no	—
222	#124	Q₈×C₈₉	1	8	yes	direct product factor
223	C₂²⋊Q₈	—	2	24	no	—
224	C₄×Q₈	—	2	8	no	—
225	C₄×Q₈	—	2	8	no	—
226	C₄×Q₈	—	2	12	no	—
227	C₄×Q₈	D₄×C₈₉	1	8	yes	—
228	C₄×D₄	—	2	12	no	—
229	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
230	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
231	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
232	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
233	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
234	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
235	C₂×C₄⋊C₄	C₂³×C₈₉	1	3	yes	—
236	C₂×C₂²⋊C₄	C₂³×C₈₉	1	6	yes	—
237	C₂×C₂²⋊C₄	C₂³×C₈₉	1	12	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
239	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
240	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
241	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
242	C₂×C₄²	C₂³×C₈₉	1	6	yes	—
243	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
244	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
245	#95	C₂³×C₈₉	1	12	yes	—
246	#95	C₂³×C₈₉	1	12	yes	—
247	#95	C₂³×C₈₉	1	6	yes	—
248	#95	C₂³×C₈₉	1	24	yes	—
249	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	—	2	12	no	—
252	C₂×Q₈	—	2	12	no	—
253	C₂×Q₈	—	2	24	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	4	12	no	—
256	C₂×Q₈	—	4	32	no	—
257	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
258	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	complemented
259	C₂×Q₈	#41×C₈₉	1	8	yes	—
260	C₂×D₄	—	2	2	no	—
261	C₂×D₄	—	2	2	no	—
262	C₂×D₄	C₂×Q₈×C₈₉	1	4	yes	—
263	C₂²×C₄	—	2	12	no	—
264	C₂²×C₄	—	2	24	no	—
265	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
266	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
267	C₂²×C₄	C₂⁴×C₈₉	1	6	yes	—
268	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
269	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
272	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
273	C₄⋊C₄	—	2	6	no	—
274	C₄⋊C₄	—	2	12	no	—
275	C₄⋊C₄	—	2	12	no	—
276	C₄⋊C₄	—	2	6	no	—
277	C₄⋊C₄	—	2	12	no	—
278	C₄⋊C₄	—	2	12	no	—
279	C₄⋊C₄	C₂×D₄×C₈₉	1	12	yes	—
280	C₂²⋊C₄	—	2	12	no	—
281	C₂²⋊C₄	—	4	12	no	—
282	C₂²⋊C₄	C₂×Q₈×C₈₉	1	16	yes	complemented
283	C₄²	—	2	12	no	—
284	C₄²	—	2	12	no	—
285	C₄²	—	2	6	no	—
286	C₄²	—	4	6	no	—
287	C₄²	C₂×D₄×C₈₉	1	12	yes	—
288	C₄²	C₂×Q₈×C₈₉	1	4	yes	complemented
289	C₂³	—	2	2	no	—
290	C₂³	—	2	4	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	4	no	—
293	C₂³	C₂²×Q₈×C₈₉	1	4	yes	—
294	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
295	Q₈	—	2	8	no	—
296	Q₈	—	4	24	no	—
297	Q₈	—	8	12	no	—
298	Q₈	#124×C₈₉	1	16	yes	direct product factor
299	D₄	—	2	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	6	no	—
305	C₂×C₄	—	2	6	no	—
306	C₂×C₄	—	2	6	no	—
307	C₂×C₄	—	2	6	no	—
308	C₂×C₄	—	2	12	no	—
309	C₂×C₄	—	2	6	no	—
310	C₂×C₄	—	2	6	no	—
311	C₂×C₄	—	2	12	no	—
312	C₂×C₄	—	4	24	no	—
313	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
314	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
315	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
316	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
317	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
318	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
319	C₂×C₄	C₂×#41×C₈₉	1	12	yes	—
320	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
321	C₂²	—	2	4	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	4	2	no	—
324	C₂²	—	4	2	no	—
325	C₂²	—	4	4	no	—
326	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
327	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
328	C₂²	C₂²×#41×C₈₉	1	2	yes	—
329	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
330	C₂²	#585×C₈₉	1	2	yes	—
331	C₄	—	2	4	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	6	no	—
334	C₄	—	4	6	no	—
335	C₄	—	4	6	no	—
336	C₄	—	4	6	no	—
337	C₄	C₂×#124×C₈₉	1	12	yes	—
338	C₄	D₄×Q₈×C₈₉	1	4	yes	—
339	C₂	—	4	4	no	—
340	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
341	C₂	C₂×D₄×Q₈×C₈₉	1	1	yes	characteristic
342	C₂	Q₈×#41×C₈₉	1	2	yes	—
343	C₂	C₈₉×#3500	1	1	yes	characteristic
344	C₂	C₈₉×#3518	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×D₄×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×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. C₈₉×#2862	C₂	semidirect
4. C₈₉×#2568	C₂	semidirect
6. C₈₉×#2492	C₂	semidirect
7. Q₈×C₂²⋊C₄×C₈₉	C₂	semidirect
9. C₄²×Q₈×C₈₉	C₂	semidirect
49. #124×C₈₉	Q₈	direct (N × H)
85. C₂×Q₈×C₈₉	C₂×Q₈	semidirect
109. C₂²⋊C₄×C₈₉	C₂×Q₈	semidirect
115. C₄²×C₈₉	C₂×Q₈	semidirect
125. Q₈×C₈₉	#124	direct (N × H)
166. Q₈×#124	C₈₉	direct (N × H)
173. C₂×Q₈²	C₂×C₈₉	semidirect
175. #2862	C₂×C₈₉	semidirect
176. #2568	C₂×C₈₉	semidirect
178. #2492	C₂×C₈₉	semidirect
179. Q₈×C₂²⋊C₄	C₂×C₈₉	semidirect
181. C₄²×Q₈	C₂×C₈₉	semidirect
182. C₈₉	Q₈×#124	direct (N × H)
222. #124	Q₈×C₈₉	direct (N × H)
258. C₂×Q₈	C₂×Q₈×C₈₉	semidirect
282. C₂²⋊C₄	C₂×Q₈×C₈₉	semidirect
288. C₄²	C₂×Q₈×C₈₉	semidirect
298. Q₈	#124×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
C₈₉×#2862	2
C₈₉×#2568	2
C₈₉×#2563	2
C₈₉×#2492	2
Q₈×C₂²⋊C₄×C₈₉	2
C₄×#124×C₈₉	2
C₄²×Q₈×C₈₉	2
Q₈×#124	89

Subgroups — Q8×#124×C89 #36414396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×#124×C₈₉ #36414396