Subgroups — C₄×SD₁₆×D₈₉ #26029005

Order 11392.

552 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#19151689	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#13083563	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
8	#19151685	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
10	#19151683	C₂	1	1	yes	maximal, characteristic, complemented
11	#106×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#103×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₈₉	C₂	1	1	yes	maximal, characteristic
14	C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₈₉	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₈₉	—	2	1	no	—
19	C₂×#13083563	C₂²	1	1	yes	characteristic
20	C₂×#13083562	C₂²	1	1	yes	characteristic
21	C₂×#13083561	C₂²	1	1	yes	characteristic
22	SD₁₆×D₈₉	C₄	1	8	yes	direct product factor
23	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₈×D₈₉	C₂²	1	1	yes	characteristic
25	Q₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₄×Dic₁₇₈	—	2	1	no	—
27	C₄×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
28	#15667977	—	2	1	no	—
29	#15667977	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₃₅₆	C₂²	1	1	yes	characteristic
31	D₄×Dic₈₉	C₂²	1	1	yes	characteristic
32	#15667974	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊D₈₉	—	2	1	no	—
34	#15667972	—	2	1	no	—
35	C₄⋊C₄×D₈₉	—	2	1	no	—
36	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₈₉	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₈₉	—	2	1	no	—
39	C₄²×D₈₉	—	2	1	no	—
40	C₄²×D₈₉	C₂²	1	1	yes	characteristic
41	#15667944	C₂²	1	1	yes	characteristic, complemented
42	#15667943	C₂²	1	1	yes	characteristic, complemented
43	#15667943	C₂²	1	1	yes	characteristic, complemented
44	#15667937	C₂²	1	1	yes	characteristic, complemented
45	#15667936	C₂²	1	1	yes	characteristic, complemented
46	#15667935	C₂²	1	1	yes	characteristic, complemented
47	#15667934	C₂²	1	1	yes	characteristic
48	#15667933	C₂²	1	1	yes	characteristic
49	#15667932	C₂²	1	1	yes	characteristic
50	C₄×#10623494	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
56	#106×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₈₉	—	2	1	no	—
61	C₂×Dic₁₇₈	—	2	1	no	—
62	C₂×Dic₁₇₈	C₂³	1	1	yes	characteristic
63	Q₈×D₈₉	—	2	2	no	—
64	Q₈×D₈₉	C₂×C₄	1	4	yes	complemented
65	C₂×D₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×C₂²⋊D₈₉	—	2	1	no	—
67	D₄×D₈₉	—	2	2	no	—
68	D₄×D₈₉	C₂×C₄	1	4	yes	—
69	C₂²×Dic₈₉	—	2	1	no	—
70	C₂×C₄×D₈₉	—	2	1	no	—
71	C₂×C₄×D₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	—	2	1	no	—
75	C₂×C₄×D₈₉	—	4	4	no	—
76	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
77	C₂×C₄×D₈₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₈₉	C₂³	1	1	yes	characteristic
79	#13083563	C₂×C₄	1	4	yes	complemented
80	#13083562	C₂×C₄	1	4	yes	complemented
81	#13083561	C₂×C₄	1	4	yes	complemented
82	C₂×#10623494	C₂³	1	1	yes	characteristic
83	C₂×#10623494	C₂³	1	1	yes	characteristic
84	C₈×D₈₉	—	2	2	no	—
85	C₈×D₈₉	C₂×C₄	1	4	yes	complemented
86	C₄⋊Dic₈₉	—	2	1	no	—
87	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
89	#13083553	—	2	1	no	—
90	#13083553	—	2	1	no	—
91	#13083553	—	2	1	no	—
92	#13083553	—	2	1	no	—
93	C₂²⋊Dic₈₉	—	2	1	no	—
94	#13083551	—	2	1	no	—
95	#13083551	—	2	1	no	—
96	C₄×Dic₈₉	—	2	1	no	—
97	C₄×Dic₈₉	—	2	1	no	—
98	C₄×Dic₈₉	—	2	1	no	—
99	C₄×Dic₈₉	D₄	1	1	yes	characteristic
100	C₄×Dic₈₉	D₄	1	1	yes	characteristic
101	C₄×Dic₈₉	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	SD₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₈₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₈₉	—	2	1	no	—
109	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₈₉	—	2	1	no	—
112	C₄²×C₈₉	—	2	1	no	—
113	C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	C₂³×C₈₉	—	2	1	no	—
115	C₂²×D₈₉	—	2	1	no	—
116	C₂²×D₈₉	—	2	4	no	—
117	C₂²×D₈₉	—	4	2	no	—
118	C₂²×D₈₉	—	4	2	no	—
119	C₂²×D₈₉	C₂×D₄	1	1	yes	characteristic
120	Q₈×C₈₉	—	2	1	no	—
121	Q₈×C₈₉	C₂²×C₄	1	2	yes	complemented
122	D₄×C₈₉	—	2	1	no	—
123	D₄×C₈₉	C₂²×C₄	1	2	yes	—
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	—	4	2	no	—
128	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₈₉	—	2	4	no	—
132	C₂×Dic₈₉	—	2	1	no	—
133	C₂×Dic₈₉	—	2	1	no	—
134	C₂×Dic₈₉	—	2	1	no	—
135	C₂×Dic₈₉	—	4	2	no	—
136	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₈₉	C₂×D₄	1	1	yes	characteristic
139	D₃₅₆	—	2	1	no	—
140	D₃₅₆	C₂²×C₄	1	2	yes	—
141	C₄×D₈₉	—	2	4	no	—
142	C₄×D₈₉	—	2	2	no	—
143	C₄×D₈₉	—	4	2	no	—
144	C₄×D₈₉	—	4	2	no	—
145	C₄×D₈₉	—	4	2	no	—
146	C₄×D₈₉	—	4	2	no	—
147	C₄×D₈₉	SD₁₆	1	4	yes	direct product factor
148	C₄×D₈₉	C₂²×C₄	1	2	yes	—
149	C₄×D₈₉	#41	1	2	yes	—
150	Dic₁₇₈	—	2	1	no	—
151	Dic₁₇₈	—	2	4	no	—
152	Dic₁₇₈	C₂²×C₄	1	2	yes	complemented
153	C₈×C₈₉	—	2	1	no	—
154	C₈×C₈₉	C₂²×C₄	1	2	yes	complemented
155	#10623494	—	2	1	no	—
156	#10623494	C₂²×C₄	1	2	yes	complemented
157	C₂²×C₈₉	—	2	2	no	—
158	C₂²×C₈₉	—	4	1	no	—
159	C₂²×C₈₉	—	4	1	no	—
160	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×D₈₉	—	2	2	no	—
162	C₂×D₈₉	—	4	1	no	—
163	C₂×D₈₉	—	4	1	no	—
164	C₂×D₈₉	—	4	8	no	—
165	C₂×D₈₉	C₄×D₄	1	2	yes	—
166	C₂×D₈₉	C₂×SD₁₆	1	2	yes	—
167	C₂×D₈₉	#135	1	2	yes	—
168	C₄×C₈₉	—	2	2	no	—
169	C₄×C₈₉	—	2	1	no	—
170	C₄×C₈₉	—	4	1	no	—
171	C₄×C₈₉	—	4	1	no	—
172	C₄×C₈₉	C₂×SD₁₆	1	2	yes	complemented
173	C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	Dic₈₉	—	2	2	no	—
176	Dic₈₉	—	2	1	no	—
177	Dic₈₉	—	4	1	no	—
178	Dic₈₉	—	4	1	no	—
179	Dic₈₉	C₄×D₄	1	2	yes	—
180	Dic₈₉	C₂×SD₁₆	1	2	yes	complemented
181	C₂×C₈₉	—	4	2	no	—
182	C₂×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
184	C₂×C₈₉	C₂×#135	1	1	yes	characteristic
185	D₈₉	—	4	2	no	—
186	D₈₉	C₄×SD₁₆	1	4	yes	direct product factor
187	C₂×C₄×SD₁₆	—	89	1	no	maximal, Sylow
188	C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
189	C₂²×SD₁₆	—	89	1	no	—
190	C₂×C₄×Q₈	—	89	1	no	—
191	C₂×C₄×D₄	—	89	1	no	—
192	C₄×SD₁₆	—	89	1	no	—
193	C₄×SD₁₆	—	89	1	no	—
194	C₄×SD₁₆	—	89	1	no	—
195	C₄×SD₁₆	—	89	1	no	—
196	C₄×SD₁₆	—	89	1	no	—
197	C₄×SD₁₆	—	89	1	no	—
198	C₄×SD₁₆	—	89	1	no	—
199	C₄×SD₁₆	D₈₉	1	1	yes	characteristic, direct product factor
200	C₂×#106	—	89	1	no	—
201	C₂×#103	—	89	1	no	—
202	C₂×#102	—	89	1	no	—
203	C₂×C₄×C₈	—	89	1	no	—
204	C₂²×Q₈	—	89	1	no	—
205	C₂²×D₄	—	89	1	no	—
206	C₂³×C₄	—	178	1	no	—
207	C₂×SD₁₆	—	89	1	no	—
208	C₂×SD₁₆	—	89	1	no	—
209	C₂×SD₁₆	—	89	8	no	—
210	C₂×SD₁₆	—	89	1	no	—
211	C₂×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
212	C₂²×C₈	—	89	1	no	—
213	C₂²×C₈	—	89	1	no	—
214	C₄×Q₈	—	89	1	no	—
215	C₄×Q₈	—	89	1	no	—
216	C₄×Q₈	—	89	1	no	—
217	C₄×Q₈	—	178	1	no	—
218	C₄×Q₈	—	178	1	no	—
219	C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
220	C₄×D₄	—	89	1	no	—
221	C₄×D₄	—	89	1	no	—
222	C₄×D₄	—	89	1	no	—
223	C₄×D₄	—	178	1	no	—
224	C₄×D₄	—	178	1	no	—
225	C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
226	C₂×C₄⋊C₄	—	89	1	no	—
227	C₂×C₄⋊C₄	—	89	1	no	—
228	C₂×C₄⋊C₄	—	178	1	no	—
229	C₂×C₂²⋊C₄	—	178	1	no	—
230	C₂×C₄²	—	89	1	no	—
231	C₂×C₄²	—	178	1	no	—
232	#106	—	89	1	no	—
233	#106	—	89	1	no	—
234	#106	—	89	1	no	—
235	#106	C₂×D₈₉	1	1	yes	characteristic, complemented
236	#103	—	89	1	no	—
237	#103	—	89	1	no	—
238	#103	—	89	1	no	—
239	#103	C₂×D₈₉	1	1	yes	characteristic, complemented
240	#102	—	89	1	no	—
241	#102	—	89	1	no	—
242	#102	—	89	1	no	—
243	#102	C₂×D₈₉	1	1	yes	characteristic
244	C₄×C₈	—	89	1	no	—
245	C₄×C₈	—	89	1	no	—
246	C₄×C₈	—	89	1	no	—
247	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
248	C₂⁴	—	178	1	no	—
249	C₂×Q₈	—	89	4	no	—
250	C₂×Q₈	—	89	1	no	—
251	C₂×Q₈	—	178	1	no	—
252	C₂×Q₈	—	178	2	no	—
253	C₂×Q₈	C₂²×D₈₉	1	1	yes	characteristic
254	C₂×D₄	—	89	4	no	—
255	C₂×D₄	—	89	1	no	—
256	C₂×D₄	—	178	2	no	—
257	C₂×D₄	—	178	1	no	—
258	C₂×D₄	C₂²×D₈₉	1	1	yes	characteristic
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	89	1	no	—
261	C₂²×C₄	—	89	1	no	—
262	C₂²×C₄	—	89	1	no	—
263	C₂²×C₄	—	356	4	no	—
264	C₂²×C₄	—	178	1	no	—
265	C₂²×C₄	—	178	1	no	—
266	C₂²×C₄	—	178	1	no	—
267	C₂²×C₄	—	178	1	no	—
268	C₂²×C₄	—	178	1	no	—
269	C₂²×C₄	—	178	1	no	—
270	SD₁₆	—	89	4	no	—
271	SD₁₆	—	89	4	no	—
272	SD₁₆	—	89	4	no	—
273	SD₁₆	C₄×D₈₉	1	4	yes	direct product factor
274	C₂×C₈	—	89	1	no	—
275	C₂×C₈	—	89	4	no	—
276	C₂×C₈	—	89	1	no	—
277	C₂×C₈	—	178	2	no	—
278	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
279	C₂×C₈	C₂²×D₈₉	1	1	yes	characteristic
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	89	1	no	—
282	C₄⋊C₄	—	89	1	no	—
283	C₄⋊C₄	—	178	1	no	—
284	C₄⋊C₄	—	178	1	no	—
285	C₄⋊C₄	—	178	1	no	—
286	C₄⋊C₄	—	178	1	no	—
287	C₄⋊C₄	—	178	1	no	—
288	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
289	C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
290	C₂²⋊C₄	—	2	1	no	—
291	C₂²⋊C₄	—	178	1	no	—
292	C₂²⋊C₄	—	178	1	no	—
293	C₂²⋊C₄	—	178	1	no	—
294	C₄²	—	2	1	no	—
295	C₄²	—	89	1	no	—
296	C₄²	—	89	1	no	—
297	C₄²	—	89	1	no	—
298	C₄²	—	178	1	no	—
299	C₄²	—	178	1	no	—
300	C₄²	—	178	1	no	—
301	C₄²	C₂²×D₈₉	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	89	1	no	—
304	C₂³	—	356	2	no	—
305	C₂³	—	356	2	no	—
306	C₂³	—	178	4	no	—
307	C₂³	—	178	1	no	—
308	Q₈	—	2	1	no	—
309	Q₈	—	89	2	no	—
310	Q₈	—	178	4	no	—
311	Q₈	—	178	1	no	—
312	Q₈	C₂×C₄×D₈₉	1	2	yes	complemented
313	D₄	—	2	1	no	—
314	D₄	—	89	2	no	—
315	D₄	—	178	4	no	—
316	D₄	—	178	1	no	—
317	D₄	C₂×C₄×D₈₉	1	2	yes	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	89	1	no	—
323	C₂×C₄	—	89	1	no	—
324	C₂×C₄	—	89	4	no	—
325	C₂×C₄	—	89	2	no	—
326	C₂×C₄	—	89	2	no	—
327	C₂×C₄	—	89	1	no	—
328	C₂×C₄	—	356	2	no	—
329	C₂×C₄	—	356	2	no	—
330	C₂×C₄	—	356	2	no	—
331	C₂×C₄	—	356	2	no	—
332	C₂×C₄	—	356	2	no	—
333	C₂×C₄	—	178	2	no	—
334	C₂×C₄	—	178	4	no	—
335	C₂×C₄	—	178	1	no	—
336	C₂×C₄	—	178	1	no	—
337	C₂×C₄	—	178	1	no	—
338	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
339	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
340	C₂×C₄	C₂³×D₈₉	1	1	yes	characteristic
341	C₈	—	2	1	no	—
342	C₈	—	89	2	no	—
343	C₈	—	178	1	no	—
344	C₈	C₂×C₄×D₈₉	1	2	yes	complemented
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	89	2	no	—
349	C₂²	—	89	2	no	—
350	C₂²	—	89	2	no	—
351	C₂²	—	356	8	no	—
352	C₂²	—	356	1	no	—
353	C₂²	—	356	1	no	—
354	C₂²	—	178	2	no	—
355	C₂²	C₂×D₄×D₈₉	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	1	no	—
358	C₄	—	4	1	no	—
359	C₄	—	4	1	no	—
360	C₄	—	89	2	no	—
361	C₄	—	89	2	no	—
362	C₄	—	356	1	no	—
363	C₄	—	356	1	no	—
364	C₄	—	178	2	no	—
365	C₄	—	178	1	no	—
366	C₄	SD₁₆×D₈₉	1	2	yes	direct product factor
367	C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
368	C₄	#41×D₈₉	1	1	yes	characteristic
369	C₂	—	4	2	no	—
370	C₂	—	89	4	no	—
371	C₂	—	356	2	no	—
372	C₂	C₄×D₄×D₈₉	1	1	yes	characteristic
373	C₂	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
374	C₂	#135×D₈₉	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₄×Q₈×D₈₉	C₂	semidirect
4. #19151689	C₂	semidirect
5. C₄×#13083563	C₂	semidirect
6. SD₁₆×Dic₈₉	C₂	semidirect
7. C₄×#13083561	C₂	semidirect
8. #19151685	C₂	semidirect
9. C₄×#13083562	C₂	semidirect
10. #19151683	C₂	semidirect
11. #106×D₈₉	C₂	semidirect
12. #103×D₈₉	C₂	semidirect
14. C₄×C₈×D₈₉	C₂	semidirect
15. C₄×SD₁₆×C₈₉	C₂	semidirect
22. SD₁₆×D₈₉	C₄	direct (N × H)
25. Q₈×Dic₈₉	C₂²	semidirect
27. C₄×Dic₁₇₈	C₂²	semidirect
29. #15667977	C₂²	semidirect
41. #15667944	C₂²	semidirect
42. #15667943	C₂²	semidirect
43. #15667943	C₂²	semidirect
44. #15667937	C₂²	semidirect
45. #15667936	C₂²	semidirect
46. #15667935	C₂²	semidirect
50. C₄×#10623494	C₂²	semidirect
51. C₈×Dic₈₉	C₂²	semidirect
52. C₈×Dic₈₉	C₂²	semidirect
54. C₄×Q₈×C₈₉	C₂²	semidirect
56. #106×C₈₉	C₂²	semidirect
57. #103×C₈₉	C₂²	semidirect
59. C₄×C₈×C₈₉	C₂²	semidirect
64. Q₈×D₈₉	C₂×C₄	semidirect
79. #13083563	C₂×C₄	semidirect
80. #13083562	C₂×C₄	semidirect
81. #13083561	C₂×C₄	semidirect
85. C₈×D₈₉	C₂×C₄	semidirect
105. SD₁₆×C₈₉	C₂×C₄	semidirect
121. Q₈×C₈₉	C₂²×C₄	semidirect
147. C₄×D₈₉	SD₁₆	direct (N × H)
152. Dic₁₇₈	C₂²×C₄	semidirect
154. C₈×C₈₉	C₂²×C₄	semidirect
156. #10623494	C₂²×C₄	semidirect
172. C₄×C₈₉	C₂×SD₁₆	semidirect
180. Dic₈₉	C₂×SD₁₆	semidirect
186. D₈₉	C₄×SD₁₆	direct (N × H)
188. C₈₉	C₂×C₄×SD₁₆	semidirect
199. C₄×SD₁₆	D₈₉	direct (N × H)
219. C₄×Q₈	C₂×D₈₉	semidirect
235. #106	C₂×D₈₉	semidirect
239. #103	C₂×D₈₉	semidirect
247. C₄×C₈	C₂×D₈₉	semidirect
273. SD₁₆	C₄×D₈₉	direct (N × H)
312. Q₈	C₂×C₄×D₈₉	semidirect
344. C₈	C₂×C₄×D₈₉	semidirect
366. C₄	SD₁₆×D₈₉	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×SD₁₆×D₈₉	2
C₄×Q₈×D₈₉	2
C₄×D₄×D₈₉	2
#19151689	2
C₄×#13083563	2
SD₁₆×Dic₈₉	2
C₄×#13083561	2
#19151685	2
C₄×#13083562	2
#19151683	2
#106×D₈₉	2
#103×D₈₉	2
#102×D₈₉	2
C₄×C₈×D₈₉	2
C₄×SD₁₆×C₈₉	2
C₂×C₄×SD₁₆	89

Subgroups — C4×SD16×D89 #26029005

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₁₆×D₈₉ #26029005