Subgroups — C₈₉×#29207 #36407055

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2059	C₂	1	4	yes	maximal
4	C₈₉×#1990	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#1990	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#1949	C₂	1	4	yes	maximal
7	C₈₉×#1845	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1844	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×#125×C₈₉	C₂²	1	2	yes	—
12	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
13	C₂×#107×C₈₉	C₂²	1	4	yes	—
14	C₂×#106×C₈₉	C₂²	1	4	yes	—
15	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
18	#391×C₈₉	—	2	1	no	—
19	#389×C₈₉	—	2	1	no	—
20	#389×C₈₉	—	2	1	no	—
21	#389×C₈₉	—	2	1	no	—
22	#389×C₈₉	—	2	1	no	—
23	#389×C₈₉	—	2	1	no	—
24	#389×C₈₉	C₂²	1	2	yes	—
25	#384×C₈₉	C₂²	1	1	yes	characteristic
26	#384×C₈₉	C₂²	1	1	yes	characteristic
27	#384×C₈₉	C₂²	1	1	yes	characteristic
28	#382×C₈₉	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
30	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
31	C₄³×C₈₉	C₂²	1	1	yes	characteristic
32	#340×C₈₉	C₂²	1	4	yes	—
33	#340×C₈₉	C₂²	1	4	yes	—
34	#336×C₈₉	C₂²	1	2	yes	—
35	C₂²×Q₈×C₈₉	—	2	1	no	—
36	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
37	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
38	C₄⋊Q₈×C₈₉	—	2	2	no	—
39	C₄⋊Q₈×C₈₉	Q₈	1	4	yes	—
40	#125×C₈₉	—	4	4	no	—
41	C₄×Q₈×C₈₉	—	4	4	no	—
42	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
48	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
49	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
56	C₂×C₄²×C₈₉	—	2	2	no	—
57	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
64	#107×C₈₉	—	4	4	no	—
65	#106×C₈₉	—	4	4	no	—
66	C₄⋊C₈×C₈₉	Q₈	1	8	yes	complemented
67	C₄×C₈×C₈₉	—	2	2	no	—
68	C₄×C₈×C₈₉	—	2	2	no	—
69	#95×C₈₉	—	2	2	no	—
70	#95×C₈₉	—	2	2	no	—
71	#95×C₈₉	—	2	2	no	—
72	#95×C₈₉	—	2	2	no	—
73	C₂×Q₈×C₈₉	—	2	4	no	—
74	C₂×Q₈×C₈₉	—	4	2	no	—
75	C₂×Q₈×C₈₉	—	4	2	no	—
76	C₂²×C₄×C₈₉	—	2	2	no	—
77	C₂²×C₄×C₈₉	—	2	2	no	—
78	C₂²×C₄×C₈₉	—	2	2	no	—
79	C₂²×C₄×C₈₉	—	2	2	no	—
80	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
87	C₂×C₈×C₈₉	—	2	2	no	—
88	C₂×C₈×C₈₉	—	2	2	no	—
89	C₂×C₈×C₈₉	—	2	2	no	—
90	C₂×C₈×C₈₉	—	2	2	no	—
91	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
92	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	—
93	C₄⋊C₄×C₈₉	—	2	4	no	—
94	C₄⋊C₄×C₈₉	—	2	2	no	—
95	C₄⋊C₄×C₈₉	—	2	4	no	—
96	C₄⋊C₄×C₈₉	—	2	4	no	—
97	C₄⋊C₄×C₈₉	—	2	4	no	—
98	C₄⋊C₄×C₈₉	—	4	4	no	—
99	C₄⋊C₄×C₈₉	—	4	4	no	—
100	C₄⋊C₄×C₈₉	—	4	4	no	—
101	C₄⋊C₄×C₈₉	—	4	2	no	—
102	C₄⋊C₄×C₈₉	—	4	2	no	—
103	C₄⋊C₄×C₈₉	—	4	2	no	—
104	C₄⋊C₄×C₈₉	—	4	2	no	—
105	C₄⋊C₄×C₈₉	—	4	2	no	—
106	C₄⋊C₄×C₈₉	—	4	2	no	—
107	C₄⋊C₄×C₈₉	C₂×Q₈	1	4	yes	—
108	C₄²×C₈₉	—	2	2	no	—
109	C₄²×C₈₉	—	2	2	no	—
110	C₄²×C₈₉	—	2	2	no	—
111	C₄²×C₈₉	—	2	2	no	—
112	C₄²×C₈₉	—	2	2	no	—
113	C₄²×C₈₉	—	4	4	no	—
114	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
115	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
116	C₄²×C₈₉	#41	1	2	yes	—
117	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
118	Q₈×C₈₉	—	4	8	no	—
119	C₂×C₄×C₈₉	—	2	1	no	—
120	C₂×C₄×C₈₉	—	2	1	no	—
121	C₂×C₄×C₈₉	—	2	1	no	—
122	C₂×C₄×C₈₉	—	2	1	no	—
123	C₂×C₄×C₈₉	—	2	4	no	—
124	C₂×C₄×C₈₉	—	2	1	no	—
125	C₂×C₄×C₈₉	—	2	1	no	—
126	C₂×C₄×C₈₉	—	2	1	no	—
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	4	2	no	—
131	C₂×C₄×C₈₉	—	4	2	no	—
132	C₂×C₄×C₈₉	—	4	2	no	—
133	C₂×C₄×C₈₉	—	4	2	no	—
134	C₂×C₄×C₈₉	—	4	2	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	—	4	2	no	—
140	C₂×C₄×C₈₉	—	4	2	no	—
141	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
144	C₂×C₄×C₈₉	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₈₉	#135	1	2	yes	—
146	C₂×C₄×C₈₉	#135	1	2	yes	—
147	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
148	C₂×C₄×C₈₉	#137	1	2	yes	—
149	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
150	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
153	C₈×C₈₉	—	2	4	no	—
154	C₈×C₈₉	—	2	4	no	—
155	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
156	C₂²×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
157	C₂²×C₈₉	#535	1	1	yes	characteristic
158	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
159	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
160	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
162	C₄×C₈₉	—	2	2	no	—
163	C₄×C₈₉	—	2	2	no	—
164	C₄×C₈₉	—	4	4	no	—
165	C₄×C₈₉	—	4	1	no	—
166	C₄×C₈₉	—	4	1	no	—
167	C₄×C₈₉	—	8	2	no	—
168	C₄×C₈₉	—	8	2	no	—
169	C₄×C₈₉	—	8	2	no	—
170	C₄×C₈₉	#478	1	4	yes	—
171	C₄×C₈₉	#479	1	4	yes	—
172	C₄×C₈₉	#554	1	2	yes	—
173	C₄×C₈₉	Q₈²	1	2	yes	—
174	#29207	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂×C₈₉	#2567	1	1	yes	characteristic
176	C₂×C₈₉	C₂×#478	1	1	yes	characteristic
177	C₂×C₈₉	C₂×#479	1	1	yes	characteristic
178	C₂×C₈₉	#3160	1	1	yes	characteristic
179	C₂×C₈₉	#3165	1	1	yes	characteristic
180	C₂×C₈₉	#3207	1	1	yes	characteristic
181	C₂×C₈₉	#3210	1	1	yes	characteristic
182	#2859	C₂×C₈₉	1	1	yes	characteristic
183	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
184	#2059	C₂×C₈₉	1	4	yes	—
185	#1990	C₂×C₈₉	1	1	yes	characteristic
186	#1990	C₂×C₈₉	1	1	yes	characteristic
187	#1949	C₂×C₈₉	1	4	yes	—
188	#1845	C₂×C₈₉	1	1	yes	characteristic
189	#1844	C₂×C₈₉	1	1	yes	characteristic
190	C₄×C₄⋊C₈	C₂×C₈₉	1	1	yes	characteristic
191	C₈₉	#29207	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
193	C₂×#125	C₂²×C₈₉	1	2	yes	—
194	C₂×C₄×Q₈	—	2	1	no	—
195	C₂×#107	C₂²×C₈₉	1	4	yes	—
196	C₂×#106	C₂²×C₈₉	1	4	yes	—
197	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
198	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
199	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
200	#391	—	2	1	no	—
201	#389	—	2	1	no	—
202	#389	—	2	1	no	—
203	#389	—	2	1	no	—
204	#389	—	2	1	no	—
205	#389	—	2	1	no	—
206	#389	C₂²×C₈₉	1	2	yes	—
207	#384	C₂²×C₈₉	1	1	yes	characteristic
208	#384	C₂²×C₈₉	1	1	yes	characteristic
209	#384	C₂²×C₈₉	1	1	yes	characteristic
210	#382	C₂²×C₈₉	1	2	yes	—
211	C₄×C₄⋊C₄	—	2	1	no	—
212	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
213	C₄³	C₂²×C₈₉	1	1	yes	characteristic
214	#340	C₂²×C₈₉	1	4	yes	—
215	#340	C₂²×C₈₉	1	4	yes	—
216	#336	C₂²×C₈₉	1	2	yes	—
217	C₂²×Q₈	—	2	1	no	—
218	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
219	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
220	C₄⋊Q₈	—	2	2	no	—
221	C₄⋊Q₈	Q₈×C₈₉	1	4	yes	—
222	#125	—	4	4	no	—
223	C₄×Q₈	—	4	4	no	—
224	C₂×C₄⋊C₄	—	2	1	no	—
225	C₂×C₄⋊C₄	—	2	1	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₄⋊C₄	—	2	2	no	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
237	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
240	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
241	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
246	#107	—	4	4	no	—
247	#106	—	4	4	no	—
248	C₄⋊C₈	Q₈×C₈₉	1	8	yes	complemented
249	C₄×C₈	—	2	2	no	—
250	C₄×C₈	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	4	2	no	—
257	C₂×Q₈	—	4	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
263	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
265	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
266	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
268	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	—
274	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	4	no	—
282	C₄⋊C₄	—	4	4	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₄⋊C₄	—	4	2	no	—
287	C₄⋊C₄	—	4	2	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	C₂×Q₈×C₈₉	1	4	yes	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	C₂×Q₈×C₈₉	1	2	yes	—
297	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
298	C₄²	#41×C₈₉	1	2	yes	—
299	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
300	Q₈	—	4	8	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	—	2	1	no	—
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	4	no	—
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
324	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
325	C₂×C₄	C₄⋊Q₈×C₈₉	1	2	yes	—
326	C₂×C₄	C₄⋊Q₈×C₈₉	1	2	yes	—
327	C₂×C₄	#135×C₈₉	1	2	yes	—
328	C₂×C₄	#135×C₈₉	1	2	yes	—
329	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
330	C₂×C₄	#137×C₈₉	1	2	yes	—
331	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
332	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
333	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
334	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
335	C₈	—	2	4	no	—
336	C₈	—	2	4	no	—
337	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
338	C₂²	C₂×C₄⋊Q₈×C₈₉	1	1	yes	characteristic
339	C₂²	#535×C₈₉	1	1	yes	characteristic
340	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
341	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
342	C₂²	C₂×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
343	C₂²	C₂×#137×C₈₉	1	1	yes	characteristic
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	4	4	no	—
347	C₄	—	4	1	no	—
348	C₄	—	4	1	no	—
349	C₄	—	8	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	#478×C₈₉	1	4	yes	—
353	C₄	#479×C₈₉	1	4	yes	—
354	C₄	#554×C₈₉	1	2	yes	—
355	C₄	Q₈²×C₈₉	1	2	yes	—
356	C₂	C₈₉×#2567	1	1	yes	characteristic
357	C₂	C₂×#478×C₈₉	1	1	yes	characteristic
358	C₂	C₂×#479×C₈₉	1	1	yes	characteristic
359	C₂	C₈₉×#3160	1	1	yes	characteristic
360	C₂	C₈₉×#3165	1	1	yes	characteristic
361	C₂	C₈₉×#3207	1	1	yes	characteristic
362	C₂	C₈₉×#3210	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
66. C₄⋊C₈×C₈₉	Q₈	semidirect
174. #29207	C₈₉	direct (N × H)
191. C₈₉	#29207	direct (N × H)
248. C₄⋊C₈	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2859	2
C₄×C₄⋊Q₈×C₈₉	2
C₈₉×#2059	2
C₈₉×#1990	2
C₈₉×#1949	2
C₈₉×#1845	2
C₈₉×#1844	2
C₄×C₄⋊C₈×C₈₉	2
#29207	89

Subgroups — C89×#29207 #36407055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#29207 #36407055