Subgroups — #1690×D₈₉ #36537030

Order 22784.

682 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#475×D₈₉	C₂	1	2	yes	maximal
3	#446×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019747	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019746	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019745	C₂	1	2	yes	maximal, complemented
7	#26019744	C₂	1	2	yes	maximal, complemented
8	#26019743	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₈₉	C₂	1	1	yes	maximal, characteristic
10	#332×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#1690	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	—	2	1	no	—
13	C₂×Q₁₆×D₈₉	—	2	1	no	—
14	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
15	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
16	#19151978	C₂²	1	1	yes	characteristic
17	#19151977	C₂²	1	2	yes	—
18	#19151976	—	2	1	no	—
19	#19151976	—	2	1	no	—
20	#19151884	C₂²	1	2	yes	—
21	#19151883	C₂²	1	2	yes	—
22	#19151882	—	2	2	no	—
23	#19151881	—	2	2	no	—
24	#19151880	C₂²	1	2	yes	—
25	#19151729	C₂²	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151727	—	2	1	no	—
28	#19151726	—	2	1	no	—
29	#19151725	C₂²	1	1	yes	characteristic
30	#106×D₈₉	—	2	2	no	—
31	C₄⋊C₈×D₈₉	—	2	1	no	—
32	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
34	#103×D₈₉	—	2	2	no	—
35	#97×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151349	C₂²	1	1	yes	characteristic
38	#19151348	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151344	C₂²	1	2	yes	—
41	#19151343	C₂²	1	2	yes	—
42	#494×C₈₉	C₂²	1	1	yes	characteristic
43	#475×C₈₉	C₂²	1	2	yes	—
44	#446×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	2	yes	—
47	C₂×Q₈×D₈₉	—	2	2	no	—
48	C₂×Q₈×D₈₉	D₄	1	1	yes	characteristic
49	C₂×Dic₃₅₆	—	2	1	no	—
50	C₂×Dic₃₅₆	—	2	1	no	—
51	C₂×#13083564	—	2	2	no	—
52	C₂×#13083564	—	2	2	no	—
53	Q₁₆×D₈₉	—	4	4	no	—
54	Q₁₆×D₈₉	—	4	4	no	—
55	C₂×C₈×D₈₉	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	2	no	—
57	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
59	#15668012	C₂³	1	2	yes	—
60	#15668011	—	2	2	no	—
61	#15668011	—	2	2	no	—
62	#15668010	—	2	2	no	—
63	Q₈×Dic₈₉	D₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	#15667977	—	2	1	no	—
67	#15667977	D₄	1	1	yes	characteristic
68	C₄⋊C₄×D₈₉	—	2	1	no	—
69	C₄⋊C₄×D₈₉	—	2	2	no	—
70	C₄⋊C₄×D₈₉	—	2	2	no	—
71	C₄⋊C₄×D₈₉	D₄	1	1	yes	characteristic
72	C₄²×D₈₉	—	2	1	no	—
73	C₄²×D₈₉	C₂³	1	1	yes	characteristic
74	#15667944	—	2	2	no	—
75	#15667943	—	2	2	no	—
76	#15667943	—	2	2	no	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	#15667941	—	2	1	no	—
81	#15667941	—	2	2	no	—
82	#15667941	—	2	1	no	—
83	#15667941	—	2	1	no	—
84	#15667937	—	2	2	no	—
85	#15667936	—	2	2	no	—
86	#15667935	—	2	2	no	—
87	#15667923	—	2	1	no	—
88	#15667922	—	2	1	no	—
89	#15667922	—	2	1	no	—
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₈×Dic₈₉	D₄	1	1	yes	characteristic
92	C₈×Dic₈₉	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₈₉	—	2	1	no	—
94	C₂×Q₁₆×C₈₉	—	2	1	no	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	2	no	—
98	C₄⋊C₈×C₈₉	—	2	1	no	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	#103×C₈₉	—	2	2	no	—
102	#97×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×Dic₁₇₈	—	2	2	no	—
106	C₂×Dic₁₇₈	—	4	2	no	—
107	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₈₉	—	2	4	no	—
109	Q₈×D₈₉	—	4	4	no	—
110	Q₈×D₈₉	—	4	4	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	C₂×C₄×D₈₉	—	2	1	no	—
113	C₂×C₄×D₈₉	—	4	2	no	—
114	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
117	Dic₃₅₆	—	4	2	no	—
118	Dic₃₅₆	—	4	2	no	—
119	#13083564	—	4	4	no	—
120	#13083564	—	4	4	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₈×D₈₉	—	2	2	no	—
126	C₈×D₈₉	—	4	2	no	—
127	C₈×D₈₉	—	4	4	no	—
128	C₈×D₈₉	SD₁₆	1	4	yes	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	C₄⋊Dic₈₉	—	2	2	no	—
131	C₄⋊Dic₈₉	—	2	2	no	—
132	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
133	#13083553	—	2	1	no	—
134	#13083553	—	2	1	no	—
135	#13083553	—	2	1	no	—
136	#13083553	—	4	2	no	—
137	#13083553	—	4	2	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₈₉	#41	1	1	yes	characteristic
144	C₂×Q₈×C₈₉	—	2	2	no	—
145	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₈₉	—	4	2	no	—
147	Q₁₆×C₈₉	—	4	2	no	—
148	C₂×C₈×C₈₉	—	2	1	no	—
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₈₉	—	2	1	no	—
157	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
158	C₂²×D₈₉	#121	1	1	yes	characteristic
159	Q₈×C₈₉	—	2	2	no	—
160	Q₈×C₈₉	—	4	2	no	—
161	Q₈×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	#121	1	1	yes	characteristic
172	C₂×Dic₈₉	#121	1	1	yes	characteristic
173	C₂×Dic₈₉	#121	1	1	yes	characteristic
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	4	2	no	—
176	C₄×D₈₉	—	4	2	no	—
177	C₄×D₈₉	—	8	4	no	—
178	C₄×D₈₉	C₂×SD₁₆	1	2	yes	—
179	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
180	C₄×D₈₉	#137	1	4	yes	—
181	Dic₁₇₈	—	2	2	no	—
182	Dic₁₇₈	—	4	2	no	—
183	Dic₁₇₈	—	4	2	no	—
184	Dic₁₇₈	—	4	2	no	—
185	Dic₁₇₈	—	8	4	no	—
186	C₈×C₈₉	—	2	1	no	—
187	C₈×C₈₉	—	4	1	no	—
188	C₈×C₈₉	—	4	2	no	—
189	C₈×C₈₉	C₂×SD₁₆	1	2	yes	—
190	#10623494	—	2	1	no	—
191	#10623494	—	4	1	no	—
192	#10623494	—	4	2	no	—
193	#10623494	C₂×SD₁₆	1	2	yes	—
194	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
195	C₂×D₈₉	#460	1	2	yes	—
196	C₂×D₈₉	#470	1	2	yes	—
197	C₂×D₈₉	#473	1	2	yes	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	—	4	1	no	—
201	C₄×C₈₉	—	8	2	no	—
202	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
203	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#137	1	2	yes	—
205	Dic₈₉	—	2	1	no	—
206	Dic₈₉	—	4	1	no	—
207	Dic₈₉	—	4	1	no	—
208	Dic₈₉	—	8	2	no	—
209	Dic₈₉	#460	1	2	yes	—
210	Dic₈₉	#470	1	2	yes	—
211	C₂×#1690	—	89	1	no	maximal, Sylow
212	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#470	1	1	yes	characteristic
214	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
215	D₈₉	#1690	1	4	yes	direct product factor
216	C₂×#494	—	89	1	no	—
217	C₂×#475	—	89	2	no	—
218	C₂×#446	—	89	1	no	—
219	#1690	—	89	1	no	—
220	#1690	—	89	2	no	—
221	#1690	—	89	1	no	—
222	#1690	—	89	1	no	—
223	#1690	—	89	2	no	—
224	#1690	D₈₉	1	1	yes	characteristic, direct product factor
225	C₂×#334	—	89	1	no	—
226	C₂×#332	—	89	2	no	—
227	C₈₉	C₂×#1690	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₁₆	—	178	1	no	—
229	C₂²×Q₁₆	—	178	1	no	—
230	C₂×C₄⋊Q₈	—	89	2	no	—
231	C₂×C₄×Q₈	—	89	1	no	—
232	#494	—	89	2	no	—
233	#494	—	89	1	no	—
234	#494	—	178	1	no	—
235	#494	—	178	1	no	—
236	#494	C₂×D₈₉	1	1	yes	characteristic
237	#475	—	89	2	no	—
238	#475	—	89	2	no	—
239	#475	—	89	2	no	—
240	#475	—	178	2	no	—
241	#475	—	178	2	no	—
242	#475	C₂×D₈₉	1	2	yes	—
243	#446	—	89	1	no	—
244	#446	—	89	1	no	—
245	#446	—	89	1	no	—
246	#446	—	178	1	no	—
247	#446	—	178	1	no	—
248	#446	C₂×D₈₉	1	1	yes	characteristic
249	C₂×#106	—	178	2	no	—
250	C₂×C₄⋊C₈	—	89	2	no	—
251	C₂×C₄⋊C₈	—	89	1	no	—
252	C₂×C₄⋊C₈	—	178	1	no	—
253	C₂×#103	—	178	2	no	—
254	C₂×#97	—	178	1	no	—
255	C₂×C₄×C₈	—	89	1	no	—
256	#334	—	89	2	no	—
257	#334	—	89	1	no	—
258	#334	C₂×D₈₉	1	1	yes	characteristic
259	#332	—	89	2	no	—
260	#332	—	89	2	no	—
261	#332	—	89	2	no	—
262	#332	C₂×D₈₉	1	2	yes	—
263	C₂²×Q₈	—	89	1	no	—
264	C₂²×Q₈	—	178	2	no	—
265	C₂×Q₁₆	—	2	1	no	—
266	C₂×Q₁₆	—	2	1	no	—
267	C₂×Q₁₆	—	356	4	no	—
268	C₂×Q₁₆	—	356	4	no	—
269	C₂×Q₁₆	—	178	2	no	—
270	C₂×Q₁₆	—	178	2	no	—
271	C₂×Q₁₆	—	178	1	no	—
272	C₂×Q₁₆	—	178	1	no	—
273	C₂²×C₈	—	89	1	no	—
274	C₂²×C₈	—	89	1	no	—
275	C₂²×C₈	—	178	1	no	—
276	C₂²×C₈	—	178	2	no	—
277	C₄⋊Q₈	—	89	2	no	—
278	C₄⋊Q₈	—	178	2	no	—
279	C₄⋊Q₈	—	178	2	no	—
280	C₄⋊Q₈	—	178	2	no	—
281	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
282	C₄×Q₈	—	89	1	no	—
283	C₄×Q₈	—	89	1	no	—
284	C₄×Q₈	—	89	1	no	—
285	C₄×Q₈	—	178	1	no	—
286	C₄×Q₈	—	178	1	no	—
287	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	—	89	1	no	—
289	C₂×C₄⋊C₄	—	178	2	no	—
290	C₂×C₄⋊C₄	—	178	2	no	—
291	C₂×C₄⋊C₄	—	178	1	no	—
292	C₂×C₄²	—	89	1	no	—
293	C₂×C₄²	—	178	1	no	—
294	#106	—	2	2	no	—
295	#106	—	178	2	no	—
296	#106	—	178	2	no	—
297	#106	—	178	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	89	1	no	—
300	C₄⋊C₈	—	89	2	no	—
301	C₄⋊C₈	—	178	1	no	—
302	C₄⋊C₈	—	178	1	no	—
303	C₄⋊C₈	—	178	2	no	—
304	C₄⋊C₈	—	178	1	no	—
305	C₄⋊C₈	—	178	1	no	—
306	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
308	#103	—	2	2	no	—
309	#103	—	178	2	no	—
310	#103	—	178	2	no	—
311	#103	—	178	2	no	—
312	#97	—	2	1	no	—
313	#97	—	178	1	no	—
314	#97	—	178	1	no	—
315	#97	—	178	1	no	—
316	C₄×C₈	—	89	1	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	89	1	no	—
322	C₂×Q₈	—	356	2	no	—
323	C₂×Q₈	—	356	4	no	—
324	C₂×Q₈	—	356	4	no	—
325	C₂×Q₈	—	178	1	no	—
326	C₂×Q₈	—	178	4	no	—
327	C₂×Q₈	—	178	2	no	—
328	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	89	1	no	—
331	C₂²×C₄	—	89	1	no	—
332	C₂²×C₄	—	356	2	no	—
333	C₂²×C₄	—	178	1	no	—
334	C₂²×C₄	—	178	1	no	—
335	Q₁₆	—	4	2	no	—
336	Q₁₆	—	4	2	no	—
337	Q₁₆	—	356	2	no	—
338	Q₁₆	—	356	4	no	—
339	Q₁₆	—	356	4	no	—
340	Q₁₆	—	356	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	89	1	no	—
344	C₂×C₈	—	89	4	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	356	4	no	—
347	C₂×C₈	—	356	2	no	—
348	C₂×C₈	—	178	2	no	—
349	C₂×C₈	—	178	1	no	—
350	C₂×C₈	—	178	2	no	—
351	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
352	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	89	1	no	—
357	C₄⋊C₄	—	356	2	no	—
358	C₄⋊C₄	—	356	2	no	—
359	C₄⋊C₄	—	178	1	no	—
360	C₄⋊C₄	—	178	1	no	—
361	C₄⋊C₄	—	178	1	no	—
362	C₄⋊C₄	—	178	2	no	—
363	C₄⋊C₄	—	178	2	no	—
364	C₄⋊C₄	—	178	1	no	—
365	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
366	C₄²	—	2	1	no	—
367	C₄²	—	89	1	no	—
368	C₄²	—	89	1	no	—
369	C₄²	—	89	1	no	—
370	C₄²	—	178	1	no	—
371	C₄²	—	178	1	no	—
372	C₄²	—	178	1	no	—
373	C₄²	C₂³×D₈₉	1	1	yes	characteristic
374	C₂³	—	89	1	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	356	2	no	—
379	Q₈	—	356	2	no	—
380	Q₈	—	356	2	no	—
381	Q₈	—	178	2	no	—
382	Q₈	—	712	4	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	89	1	no	—
387	C₂×C₄	—	89	1	no	—
388	C₂×C₄	—	89	4	no	—
389	C₂×C₄	—	89	2	no	—
390	C₂×C₄	—	89	2	no	—
391	C₂×C₄	—	89	1	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	356	2	no	—
394	C₂×C₄	—	356	2	no	—
395	C₂×C₄	—	178	2	no	—
396	C₂×C₄	—	178	1	no	—
397	C₂×C₄	—	178	1	no	—
398	C₂×C₄	—	712	4	no	—
399	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
401	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	89	2	no	—
406	C₈	—	356	2	no	—
407	C₈	—	356	1	no	—
408	C₈	—	178	1	no	—
409	C₈	SD₁₆×D₈₉	1	2	yes	—
410	C₂²	—	89	2	no	—
411	C₂²	—	89	2	no	—
412	C₂²	—	89	2	no	—
413	C₂²	#121×D₈₉	1	1	yes	characteristic
414	C₄	—	2	1	no	—
415	C₄	—	4	1	no	—
416	C₄	—	4	1	no	—
417	C₄	—	8	2	no	—
418	C₄	—	89	2	no	—
419	C₄	—	89	2	no	—
420	C₄	—	356	1	no	—
421	C₄	—	356	1	no	—
422	C₄	—	178	1	no	—
423	C₄	—	712	2	no	—
424	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
425	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
426	C₄	#137×D₈₉	1	2	yes	—
427	C₂	—	89	4	no	—
428	C₂	#460×D₈₉	1	1	yes	characteristic
429	C₂	#470×D₈₉	1	1	yes	characteristic
430	C₂	#473×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1690	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₈₉	#121
hypercenter	#1690	D₈₉
hypocenter	C₈₉	C₂×#1690
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1690

Complements

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

N	H ≅ G/N	type
4. #26019747	C₂	semidirect
5. #26019746	C₂	semidirect
6. #26019745	C₂	semidirect
7. #26019744	C₂	semidirect
8. #26019743	C₂	semidirect
11. C₈₉×#1690	C₂	semidirect
215. D₈₉	#1690	direct (N × H)
224. #1690	D₈₉	direct (N × H)
227. C₈₉	C₂×#1690	semidirect

Maximal subgroups

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

subgroup	index
#494×D₈₉	2
#475×D₈₉	2
#446×D₈₉	2
#26019747	2
#26019746	2
#26019745	2
#26019744	2
#26019743	2
#334×D₈₉	2
#332×D₈₉	2
C₈₉×#1690	2
C₂×#1690	89

Subgroups — #1690×D89 #36537030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1690×D₈₉ #36537030