Subgroups — #534×D₈₉ #26033550

Order 11392.

1984 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₈₉	C₂	1	2	yes	maximal, complemented
2	#19152160	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152159	C₂	1	4	yes	maximal, complemented
4	#19152158	C₂	1	4	yes	maximal, complemented
5	#19152157	C₂	1	2	yes	maximal, complemented
6	#19152156	C₂	1	4	yes	maximal, complemented
7	#123×D₈₉	C₂	1	4	yes	maximal, complemented
8	#121×D₈₉	C₂	1	4	yes	maximal, complemented
9	#120×D₈₉	C₂	1	4	yes	maximal, complemented
10	C₂×C₂²⋊C₄×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#534×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×D₈₉	C₂²	1	1	yes	characteristic
13	C₂⁴×D₈₉	C₂²	1	2	yes	complemented
14	C₂²×D₃₅₆	C₂²	1	2	yes	complemented
15	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
16	C₂²×C₂²⋊D₈₉	C₂²	1	2	yes	complemented
17	C₂×D₄×D₈₉	—	2	16	no	—
18	C₂×D₄×D₈₉	C₂²	1	4	yes	—
19	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
20	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
21	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
22	C₂×D₄×D₈₉	C₂²	1	4	yes	complemented
23	C₂²×C₄×D₈₉	C₂²	1	2	yes	complemented
24	C₂²×C₄×D₈₉	C₂²	1	2	yes	complemented
25	#15667997	C₂²	1	8	yes	complemented
26	#15667996	C₂²	1	4	yes	complemented
27	#15667995	C₂²	1	4	yes	complemented
28	#15667994	C₂²	1	8	yes	complemented
29	#15667993	C₂²	1	4	yes	complemented
30	#15667987	C₂²	1	4	yes	complemented
31	#15667986	C₂²	1	4	yes	complemented
32	#15667985	C₂²	1	8	yes	complemented
33	#15667984	C₂²	1	8	yes	complemented
34	#15667983	C₂²	1	4	yes	complemented
35	#15667982	C₂²	1	4	yes	complemented
36	#15667982	C₂²	1	8	yes	complemented
37	#15667981	C₂²	1	4	yes	complemented
38	#15667980	C₂²	1	4	yes	complemented
39	#15667980	C₂²	1	8	yes	complemented
40	C₄⋊C₄×D₈₉	C₂²	1	4	yes	complemented
41	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13083551	C₂²	1	2	yes	complemented
43	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	complemented
44	C₂²⋊C₄×D₈₉	C₂²	1	8	yes	complemented
45	C₂²⋊C₄×D₈₉	C₂²	1	4	yes	complemented
46	C₂²×D₄×C₈₉	C₂²	1	2	yes	complemented
47	#123×C₈₉	C₂²	1	4	yes	complemented
48	#121×C₈₉	C₂²	1	4	yes	complemented
49	#120×C₈₉	C₂²	1	4	yes	complemented
50	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	C₂³×D₈₉	—	2	8	no	—
52	C₂³×D₈₉	—	4	4	no	—
53	C₂³×D₈₉	—	4	8	no	—
54	C₂³×D₈₉	D₄	1	8	yes	complemented
55	C₂³×D₈₉	C₂³	1	4	yes	—
56	C₂³×D₈₉	C₂³	1	1	yes	characteristic
57	C₂³×D₈₉	C₂³	1	2	yes	—
58	C₂³×D₈₉	C₂³	1	1	yes	characteristic
59	C₂³×D₈₉	C₂³	1	2	yes	—
60	C₂³×D₈₉	C₂³	1	4	yes	complemented
61	C₂³×D₈₉	C₂³	1	2	yes	complemented
62	C₂×D₃₅₆	—	2	8	no	—
63	C₂×D₃₅₆	C₂³	1	4	yes	—
64	C₂×D₃₅₆	C₂³	1	4	yes	complemented
65	C₂×D₃₅₆	C₂³	1	4	yes	complemented
66	C₂×C₂²⋊D₈₉	—	2	8	no	—
67	C₂×C₂²⋊D₈₉	—	2	8	no	—
68	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
69	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
70	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	complemented
71	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	complemented
72	C₂×C₂²⋊D₈₉	C₂³	1	8	yes	complemented
73	D₄×D₈₉	—	2	16	no	—
74	D₄×D₈₉	—	2	16	no	—
75	D₄×D₈₉	—	2	16	no	—
76	D₄×D₈₉	—	2	16	no	—
77	D₄×D₈₉	—	4	8	no	—
78	C₂²×Dic₈₉	C₂³	1	2	yes	complemented
79	C₂²×Dic₈₉	C₂³	1	2	yes	complemented
80	C₂×C₄×D₈₉	—	2	8	no	—
81	C₂×C₄×D₈₉	—	4	4	no	—
82	C₂×C₄×D₈₉	C₂³	1	4	yes	—
83	C₂×C₄×D₈₉	C₂³	1	4	yes	—
84	C₂×C₄×D₈₉	C₂³	1	4	yes	complemented
85	C₂×C₄×D₈₉	C₂³	1	4	yes	complemented
86	C₄⋊Dic₈₉	C₂³	1	4	yes	complemented
87	#13083553	C₂³	1	8	yes	complemented
88	C₂²⋊Dic₈₉	C₂³	1	8	yes	complemented
89	C₂²⋊Dic₈₉	C₂³	1	4	yes	complemented
90	#13083551	C₂³	1	8	yes	complemented
91	#13083551	C₂³	1	8	yes	complemented
92	#13083551	C₂³	1	8	yes	complemented
93	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
94	C₂⁴×C₈₉	C₂³	1	2	yes	complemented
95	C₂×D₄×C₈₉	—	2	8	no	—
96	C₂×D₄×C₈₉	C₂³	1	4	yes	—
97	C₂×D₄×C₈₉	C₂³	1	4	yes	complemented
98	C₂×D₄×C₈₉	C₂³	1	4	yes	complemented
99	C₂²×C₄×C₈₉	C₂³	1	2	yes	complemented
100	C₂²×C₄×C₈₉	C₂³	1	2	yes	complemented
101	C₄⋊C₄×C₈₉	C₂³	1	4	yes	complemented
102	C₂²⋊C₄×C₈₉	C₂³	1	8	yes	complemented
103	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	complemented
104	C₂³×C₈₉	—	2	4	no	—
105	C₂³×C₈₉	—	4	2	no	—
106	C₂³×C₈₉	—	4	4	no	—
107	C₂³×C₈₉	C₂×D₄	1	4	yes	complemented
108	C₂³×C₈₉	C₂⁴	1	4	yes	—
109	C₂³×C₈₉	C₂⁴	1	2	yes	—
110	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
111	C₂²×D₈₉	—	2	4	no	—
112	C₂²×D₈₉	—	2	8	no	—
113	C₂²×D₈₉	—	2	4	no	—
114	C₂²×D₈₉	—	2	8	no	—
115	C₂²×D₈₉	—	2	8	no	—
116	C₂²×D₈₉	—	2	16	no	—
117	C₂²×D₈₉	—	4	16	no	—
118	C₂²×D₈₉	—	4	4	no	—
119	C₂²×D₈₉	—	4	2	no	—
120	C₂²×D₈₉	—	4	8	no	—
121	C₂²×D₈₉	—	4	4	no	—
122	C₂²×D₈₉	—	4	32	no	—
123	C₂²×D₈₉	C₂×D₄	1	8	yes	—
124	C₂²×D₈₉	C₂×D₄	1	4	yes	—
125	C₂²×D₈₉	C₂×D₄	1	4	yes	complemented
126	C₂²×D₈₉	C₂×D₄	1	8	yes	complemented
127	C₂²×D₈₉	C₂⁴	1	4	yes	—
128	C₂²×D₈₉	C₂⁴	1	2	yes	—
129	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
130	C₂²×D₈₉	C₂⁴	1	1	yes	characteristic
131	D₄×C₈₉	—	2	8	no	—
132	D₄×C₈₉	—	2	8	no	—
133	D₄×C₈₉	—	4	4	no	—
134	C₂×C₄×C₈₉	—	2	4	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂×C₄×C₈₉	C₂⁴	1	4	yes	—
138	C₂²⋊D₈₉	—	2	8	no	—
139	C₂²⋊D₈₉	—	2	8	no	—
140	C₂²⋊D₈₉	—	2	8	no	—
141	C₂²⋊D₈₉	—	2	8	no	—
142	C₂²⋊D₈₉	—	4	8	no	—
143	C₂×Dic₈₉	—	2	4	no	—
144	C₂×Dic₈₉	—	4	2	no	—
145	C₂×Dic₈₉	C₂⁴	1	4	yes	—
146	C₂×Dic₈₉	C₂⁴	1	4	yes	—
147	D₃₅₆	—	2	8	no	—
148	D₃₅₆	—	2	8	no	—
149	D₃₅₆	—	4	4	no	—
150	C₄×D₈₉	—	2	8	no	—
151	C₄×D₈₉	—	2	8	no	—
152	C₄×D₈₉	—	2	8	no	—
153	C₄×D₈₉	—	4	4	no	—
154	C₂²×C₈₉	—	2	2	no	—
155	C₂²×C₈₉	—	2	4	no	—
156	C₂²×C₈₉	—	2	4	no	—
157	C₂²×C₈₉	—	2	8	no	—
158	C₂²×C₈₉	—	4	4	no	—
159	C₂²×C₈₉	—	4	8	no	—
160	C₂²×C₈₉	C₂²×D₄	1	4	yes	—
161	C₂²×C₈₉	C₂²×D₄	1	2	yes	—
162	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
163	C₂×D₈₉	—	2	2	no	—
164	C₂×D₈₉	—	2	4	no	—
165	C₂×D₈₉	—	2	16	no	—
166	C₂×D₈₉	—	2	8	no	—
167	C₂×D₈₉	—	2	4	no	—
168	C₂×D₈₉	—	2	8	no	—
169	C₂×D₈₉	—	4	4	no	—
170	C₂×D₈₉	—	4	8	no	—
171	C₂×D₈₉	—	4	16	no	—
172	C₂×D₈₉	—	4	8	no	—
173	C₂×D₈₉	—	4	16	no	—
174	C₂×D₈₉	C₂²×D₄	1	4	yes	—
175	C₂×D₈₉	C₂²×D₄	1	2	yes	—
176	C₂×D₈₉	C₂²×D₄	1	2	yes	—
177	C₂×D₈₉	H(5,𝔽₂)	1	4	yes	—
178	C₄×C₈₉	—	2	4	no	—
179	C₄×C₈₉	—	2	4	no	—
180	Dic₈₉	—	2	4	no	—
181	Dic₈₉	—	2	4	no	—
182	C₂×C₈₉	—	2	4	no	—
183	C₂×C₈₉	—	2	2	no	—
184	C₂×C₈₉	—	4	4	no	—
185	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
186	C₂×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
187	D₈₉	—	2	4	no	—
188	D₈₉	—	2	2	no	—
189	D₈₉	—	4	4	no	—
190	D₈₉	#534	1	4	yes	direct product factor
191	C₂×#534	—	89	1	no	maximal, Sylow
192	C₈₉	C₂×#534	1	1	yes	characteristic, complemented, Sylow
193	C₂³×D₄	—	89	2	no	—
194	#534	—	89	2	no	—
195	#534	—	89	4	no	—
196	#534	—	89	4	no	—
197	#534	—	89	4	no	—
198	#534	—	89	1	no	—
199	#534	D₈₉	1	1	yes	characteristic, direct product factor
200	C₂×#123	—	89	4	no	—
201	C₂×#121	—	89	4	no	—
202	C₂×#120	—	89	4	no	—
203	C₂²×C₂²⋊C₄	—	89	1	no	—
204	C₂⁵	—	89	1	no	—
205	C₂⁵	—	89	2	no	—
206	C₂²×D₄	—	89	2	no	—
207	C₂²×D₄	—	89	2	no	—
208	C₂²×D₄	—	89	4	no	—
209	C₂²×D₄	—	89	4	no	—
210	C₂²×D₄	—	89	4	no	—
211	C₂²×D₄	—	89	4	no	—
212	C₂²×D₄	—	89	4	no	—
213	C₂²×D₄	—	89	2	no	—
214	C₂²×D₄	—	178	16	no	—
215	C₂²×D₄	C₂×D₈₉	1	2	yes	complemented
216	C₂³×C₄	—	89	2	no	—
217	C₂³×C₄	—	89	2	no	—
218	#123	—	89	4	no	—
219	#123	—	89	4	no	—
220	#123	—	89	8	no	—
221	#123	—	89	8	no	—
222	#123	—	89	4	no	—
223	#123	C₂×D₈₉	1	4	yes	complemented
224	#121	—	89	4	no	—
225	#121	—	89	8	no	—
226	#121	—	89	4	no	—
227	#121	—	89	4	no	—
228	#121	—	89	8	no	—
229	#121	C₂×D₈₉	1	4	yes	complemented
230	#120	—	89	4	no	—
231	#120	—	89	4	no	—
232	#120	—	89	8	no	—
233	#120	—	89	8	no	—
234	#120	—	89	4	no	—
235	#120	C₂×D₈₉	1	4	yes	complemented
236	C₂×C₄⋊C₄	—	89	4	no	—
237	C₂×C₂²⋊C₄	—	89	1	no	—
238	C₂×C₂²⋊C₄	—	89	2	no	—
239	C₂×C₂²⋊C₄	—	89	4	no	—
240	C₂×C₂²⋊C₄	—	89	4	no	—
241	C₂×C₂²⋊C₄	—	89	8	no	—
242	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic, complemented
243	C₂⁴	—	89	8	no	—
244	C₂⁴	—	89	1	no	—
245	C₂⁴	—	89	2	no	—
246	C₂⁴	—	89	2	no	—
247	C₂⁴	—	89	1	no	—
248	C₂⁴	—	89	4	no	—
249	C₂⁴	—	89	2	no	—
250	C₂⁴	—	89	4	no	—
251	C₂⁴	—	356	4	no	—
252	C₂⁴	—	356	8	no	—
253	C₂⁴	—	178	8	no	—
254	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
255	C₂⁴	C₂²×D₈₉	1	2	yes	complemented
256	C₂×D₄	—	2	8	no	—
257	C₂×D₄	—	89	8	no	—
258	C₂×D₄	—	89	4	no	—
259	C₂×D₄	—	89	4	no	—
260	C₂×D₄	—	89	4	no	—
261	C₂×D₄	—	89	4	no	—
262	C₂×D₄	—	89	4	no	—
263	C₂×D₄	—	89	4	no	—
264	C₂×D₄	—	89	4	no	—
265	C₂×D₄	—	356	8	no	—
266	C₂×D₄	—	178	8	no	—
267	C₂×D₄	—	178	16	no	—
268	C₂×D₄	—	178	16	no	—
269	C₂×D₄	—	178	16	no	—
270	C₂×D₄	—	178	16	no	—
271	C₂×D₄	—	178	8	no	—
272	C₂×D₄	—	178	8	no	—
273	C₂×D₄	C₂²×D₈₉	1	4	yes	—
274	C₂×D₄	C₂²×D₈₉	1	4	yes	complemented
275	C₂×D₄	C₂²×D₈₉	1	4	yes	complemented
276	C₂²×C₄	—	89	2	no	—
277	C₂²×C₄	—	89	2	no	—
278	C₂²×C₄	—	89	4	no	—
279	C₂²×C₄	—	89	4	no	—
280	C₂²×C₄	—	89	4	no	—
281	C₂²×C₄	—	89	4	no	—
282	C₂²×C₄	—	356	4	no	—
283	C₂²×C₄	—	178	8	no	—
284	C₂²×C₄	C₂²×D₈₉	1	2	yes	complemented
285	C₂²×C₄	C₂²×D₈₉	1	2	yes	complemented
286	C₄⋊C₄	—	89	8	no	—
287	C₄⋊C₄	—	89	4	no	—
288	C₄⋊C₄	C₂²×D₈₉	1	4	yes	complemented
289	C₂²⋊C₄	—	89	4	no	—
290	C₂²⋊C₄	—	89	8	no	—
291	C₂²⋊C₄	—	89	8	no	—
292	C₂²⋊C₄	—	89	8	no	—
293	C₂²⋊C₄	—	89	8	no	—
294	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	complemented
295	C₂²⋊C₄	C₂²×D₈₉	1	8	yes	complemented
296	C₂³	—	2	4	no	—
297	C₂³	—	4	2	no	—
298	C₂³	—	4	4	no	—
299	C₂³	—	89	1	no	—
300	C₂³	—	89	4	no	—
301	C₂³	—	89	8	no	—
302	C₂³	—	89	8	no	—
303	C₂³	—	89	4	no	—
304	C₂³	—	89	2	no	—
305	C₂³	—	89	1	no	—
306	C₂³	—	89	4	no	—
307	C₂³	—	356	2	no	—
308	C₂³	—	356	4	no	—
309	C₂³	—	356	4	no	—
310	C₂³	—	356	8	no	—
311	C₂³	—	356	32	no	—
312	C₂³	—	356	16	no	—
313	C₂³	—	178	16	no	—
314	C₂³	—	178	8	no	—
315	C₂³	—	178	8	no	—
316	C₂³	—	178	4	no	—
317	C₂³	—	178	8	no	—
318	C₂³	—	178	4	no	—
319	C₂³	D₄×D₈₉	1	4	yes	complemented
320	C₂³	C₂³×D₈₉	1	4	yes	—
321	C₂³	C₂³×D₈₉	1	2	yes	—
322	C₂³	C₂³×D₈₉	1	1	yes	characteristic
323	D₄	—	2	8	no	—
324	D₄	—	2	8	no	—
325	D₄	—	4	4	no	—
326	D₄	—	356	4	no	—
327	D₄	—	356	8	no	—
328	D₄	—	178	8	no	—
329	D₄	—	178	8	no	—
330	D₄	—	178	8	no	—
331	D₄	—	178	8	no	—
332	D₄	—	178	8	no	—
333	D₄	—	178	8	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	89	4	no	—
337	C₂×C₄	—	89	4	no	—
338	C₂×C₄	—	356	4	no	—
339	C₂×C₄	—	356	2	no	—
340	C₂×C₄	—	178	8	no	—
341	C₂×C₄	—	178	8	no	—
342	C₂×C₄	—	178	8	no	—
343	C₂×C₄	—	178	4	no	—
344	C₂×C₄	C₂³×D₈₉	1	4	yes	—
345	C₂×C₄	C₂³×D₈₉	1	4	yes	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	8	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	8	no	—
352	C₂²	—	89	2	no	—
353	C₂²	—	89	4	no	—
354	C₂²	—	89	4	no	—
355	C₂²	—	89	2	no	—
356	C₂²	—	356	8	no	—
357	C₂²	—	356	8	no	—
358	C₂²	—	356	4	no	—
359	C₂²	—	356	16	no	—
360	C₂²	—	356	16	no	—
361	C₂²	—	178	16	no	—
362	C₂²	—	178	8	no	—
363	C₂²	—	178	4	no	—
364	C₂²	—	178	8	no	—
365	C₂²	—	178	2	no	—
366	C₂²	—	178	4	no	—
367	C₂²	C₂×D₄×D₈₉	1	4	yes	—
368	C₂²	C₂×D₄×D₈₉	1	2	yes	—
369	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
370	C₄	—	2	4	no	—
371	C₄	—	2	4	no	—
372	C₄	—	178	4	no	—
373	C₄	—	178	4	no	—
374	C₂	—	2	4	no	—
375	C₂	—	2	2	no	—
376	C₂	—	4	4	no	—
377	C₂	—	89	4	no	—
378	C₂	—	356	4	no	—
379	C₂	—	178	4	no	—
380	C₂	—	178	2	no	—
381	C₂	C₂²×D₄×D₈₉	1	1	yes	characteristic
382	C₂	H(5,𝔽₂)×D₈₉	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₈₉
commutator, socle, cosocle	C₂²×C₈₉	C₂⁵
Fitting	#534×C₈₉	C₂
hypercenter	#534	D₈₉
hypocenter	C₈₉	C₂×#534
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₈₉	C₂	semidirect
2. #19152160	C₂	semidirect
3. #19152159	C₂	semidirect
4. #19152158	C₂	semidirect
5. #19152157	C₂	semidirect
6. #19152156	C₂	semidirect
7. #123×D₈₉	C₂	semidirect
8. #121×D₈₉	C₂	semidirect
9. #120×D₈₉	C₂	semidirect
10. C₂×C₂²⋊C₄×D₈₉	C₂	semidirect
11. #534×C₈₉	C₂	semidirect
13. C₂⁴×D₈₉	C₂²	semidirect
14. C₂²×D₃₅₆	C₂²	semidirect
15. C₂²×C₂²⋊D₈₉	C₂²	semidirect
16. C₂²×C₂²⋊D₈₉	C₂²	semidirect
19. C₂×D₄×D₈₉	C₂²	semidirect
20. C₂×D₄×D₈₉	C₂²	semidirect
21. C₂×D₄×D₈₉	C₂²	semidirect
22. C₂×D₄×D₈₉	C₂²	semidirect
23. C₂²×C₄×D₈₉	C₂²	semidirect
24. C₂²×C₄×D₈₉	C₂²	semidirect
25. #15667997	C₂²	semidirect
26. #15667996	C₂²	semidirect
27. #15667995	C₂²	semidirect
28. #15667994	C₂²	semidirect
29. #15667993	C₂²	semidirect
30. #15667987	C₂²	semidirect
31. #15667986	C₂²	semidirect
32. #15667985	C₂²	semidirect
33. #15667984	C₂²	semidirect
34. #15667983	C₂²	semidirect
35. #15667982	C₂²	semidirect
36. #15667982	C₂²	semidirect
37. #15667981	C₂²	semidirect
38. #15667980	C₂²	semidirect
39. #15667980	C₂²	semidirect
40. C₄⋊C₄×D₈₉	C₂²	semidirect
41. C₂×C₂²⋊Dic₈₉	C₂²	semidirect
42. C₂×#13083551	C₂²	semidirect
43. C₂²⋊C₄×D₈₉	C₂²	semidirect
44. C₂²⋊C₄×D₈₉	C₂²	semidirect
45. C₂²⋊C₄×D₈₉	C₂²	semidirect
46. C₂²×D₄×C₈₉	C₂²	semidirect
47. #123×C₈₉	C₂²	semidirect
48. #121×C₈₉	C₂²	semidirect
49. #120×C₈₉	C₂²	semidirect
50. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
54. C₂³×D₈₉	D₄	semidirect
60. C₂³×D₈₉	C₂³	semidirect
61. C₂³×D₈₉	C₂³	semidirect
64. C₂×D₃₅₆	C₂³	semidirect
65. C₂×D₃₅₆	C₂³	semidirect
70. C₂×C₂²⋊D₈₉	C₂³	semidirect
71. C₂×C₂²⋊D₈₉	C₂³	semidirect
72. C₂×C₂²⋊D₈₉	C₂³	semidirect
78. C₂²×Dic₈₉	C₂³	semidirect
79. C₂²×Dic₈₉	C₂³	semidirect
84. C₂×C₄×D₈₉	C₂³	semidirect
85. C₂×C₄×D₈₉	C₂³	semidirect
86. C₄⋊Dic₈₉	C₂³	semidirect
87. #13083553	C₂³	semidirect
88. C₂²⋊Dic₈₉	C₂³	semidirect
89. C₂²⋊Dic₈₉	C₂³	semidirect
90. #13083551	C₂³	semidirect
91. #13083551	C₂³	semidirect
92. #13083551	C₂³	semidirect
94. C₂⁴×C₈₉	C₂³	semidirect
97. C₂×D₄×C₈₉	C₂³	semidirect
98. C₂×D₄×C₈₉	C₂³	semidirect
99. C₂²×C₄×C₈₉	C₂³	semidirect
100. C₂²×C₄×C₈₉	C₂³	semidirect
101. C₄⋊C₄×C₈₉	C₂³	semidirect
102. C₂²⋊C₄×C₈₉	C₂³	semidirect
103. C₂²⋊C₄×C₈₉	C₂³	semidirect
107. C₂³×C₈₉	C₂×D₄	semidirect
125. C₂²×D₈₉	C₂×D₄	semidirect
126. C₂²×D₈₉	C₂×D₄	semidirect
190. D₈₉	#534	direct (N × H)
192. C₈₉	C₂×#534	semidirect
199. #534	D₈₉	direct (N × H)
215. C₂²×D₄	C₂×D₈₉	semidirect
223. #123	C₂×D₈₉	semidirect
229. #121	C₂×D₈₉	semidirect
235. #120	C₂×D₈₉	semidirect
242. C₂×C₂²⋊C₄	C₂×D₈₉	semidirect
255. C₂⁴	C₂²×D₈₉	semidirect
274. C₂×D₄	C₂²×D₈₉	semidirect
275. C₂×D₄	C₂²×D₈₉	semidirect
284. C₂²×C₄	C₂²×D₈₉	semidirect
285. C₂²×C₄	C₂²×D₈₉	semidirect
288. C₄⋊C₄	C₂²×D₈₉	semidirect
294. C₂²⋊C₄	C₂²×D₈₉	semidirect
295. C₂²⋊C₄	C₂²×D₈₉	semidirect
319. C₂³	D₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×D₄×D₈₉	2
#19152160	2
#19152159	2
#19152158	2
#19152157	2
#19152156	2
#123×D₈₉	2
#121×D₈₉	2
#120×D₈₉	2
C₂×C₂²⋊C₄×D₈₉	2
#534×C₈₉	2
C₂×#534	89

Subgroups — #534×D89 #26033550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #534×D₈₉ #26033550