Subgroups — #36709223

Order 22784.

590 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151636	C₂	1	1	yes	maximal, characteristic, complemented
2	#26022457	C₂	1	2	yes	maximal, complemented
3	#26022452	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022447	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022440	C₂	1	2	yes	maximal, complemented
6	#26022435	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022430	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022034	C₂	1	2	yes	maximal, complemented
9	#26021959	C₂	1	2	yes	maximal, complemented
10	C₂×C₂²⋊#13083549	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
12	C₂×#15667971	—	2	1	no	—
13	C₂²×#13083549	C₂²	1	2	yes	—
14	#19151636	—	2	1	no	—
15	#19151636	—	2	1	no	—
16	#19151636	C₂²	1	2	yes	—
17	#19151636	C₂²	1	2	yes	—
18	C₂×#15667946	C₂²	1	1	yes	characteristic
19	C₂×#15667946	C₂²	1	1	yes	characteristic
20	C₂×#15667944	—	2	1	no	—
21	#19151425	C₂²	1	2	yes	complemented
22	#19151425	C₂²	1	2	yes	complemented
23	#19151423	C₂²	1	2	yes	complemented
24	#19151423	C₂²	1	2	yes	complemented
25	#19151402	C₂²	1	2	yes	complemented
26	#19151402	C₂²	1	2	yes	complemented
27	#19151399	C₂²	1	2	yes	complemented
28	#19151399	C₂²	1	2	yes	complemented
29	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
30	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
31	C₂²⋊#13083549	C₂²	1	2	yes	—
32	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
33	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
34	#525×C₈₉	—	2	1	no	—
35	#467×C₈₉	C₂²	1	1	yes	characteristic
36	#467×C₈₉	C₂²	1	1	yes	characteristic
37	#466×C₈₉	C₂²	1	1	yes	characteristic
38	#466×C₈₉	C₂²	1	1	yes	characteristic
39	#465×C₈₉	—	2	1	no	—
40	#465×C₈₉	—	2	1	no	—
41	#427×C₈₉	C₂²	1	1	yes	characteristic
42	#416×C₈₉	—	2	1	no	—
43	#15667971	—	2	2	no	—
44	#15667971	—	2	2	no	—
45	#15667971	—	4	1	no	—
46	#15667971	—	4	1	no	—
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄⋊Dic₈₉	—	2	1	no	—
49	C₂×C₂²⋊Dic₈₉	—	4	1	no	—
50	C₂×C₄×Dic₈₉	—	4	1	no	—
51	C₂×#13083549	—	2	4	no	—
52	C₂×#13083549	C₂³	1	2	yes	—
53	C₂×#13083549	C₂³	1	2	yes	—
54	#15667946	—	2	1	no	—
55	#15667946	—	2	1	no	—
56	#15667946	C₂³	1	2	yes	—
57	#15667946	C₂³	1	2	yes	—
58	#15667944	—	2	2	no	—
59	#15667944	—	2	2	no	—
60	C₂×#41×C₈₉	—	2	1	no	—
61	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
62	#135×C₈₉	—	2	4	no	—
63	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₈₉	—	2	1	no	—
65	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₈₉	—	2	4	no	—
67	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
69	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
70	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	#123×C₈₉	—	4	1	no	—
74	C₂²⋊Q₈×C₈₉	—	2	1	no	—
75	C₂²⋊Q₈×C₈₉	—	2	1	no	—
76	#121×C₈₉	—	2	1	no	—
77	#121×C₈₉	—	2	1	no	—
78	#120×C₈₉	—	4	1	no	—
79	C₄×D₄×C₈₉	—	4	1	no	—
80	C₄×D₄×C₈₉	—	4	1	no	—
81	#117×C₈₉	—	2	1	no	—
82	#107×C₈₉	C₂³	1	1	yes	characteristic
83	#107×C₈₉	C₂³	1	1	yes	characteristic
84	#106×C₈₉	—	2	1	no	—
85	#103×C₈₉	—	2	1	no	—
86	#103×C₈₉	—	2	1	no	—
87	#102×C₈₉	—	2	1	no	—
88	#102×C₈₉	—	2	1	no	—
89	C₂²×Dic₈₉	—	4	1	no	—
90	C₂²×Dic₈₉	—	4	1	no	—
91	C₄⋊Dic₈₉	—	2	2	no	—
92	C₄⋊Dic₈₉	—	2	2	no	—
93	C₄⋊Dic₈₉	—	4	1	no	—
94	C₄⋊Dic₈₉	—	4	1	no	—
95	C₂²⋊Dic₈₉	—	4	2	no	—
96	C₂²⋊Dic₈₉	—	4	2	no	—
97	C₄×Dic₈₉	—	4	2	no	—
98	C₄×Dic₈₉	—	4	2	no	—
99	#13083549	—	2	2	no	—
100	#13083549	—	2	2	no	—
101	C₂⁴×C₈₉	D₈	1	1	yes	characteristic
102	#41×C₈₉	—	4	2	no	—
103	#41×C₈₉	—	4	2	no	—
104	C₂×Q₈×C₈₉	—	2	1	no	—
105	C₂×D₄×C₈₉	—	2	1	no	—
106	C₂×D₄×C₈₉	—	4	1	no	—
107	C₂×D₄×C₈₉	—	4	1	no	—
108	C₂×D₄×C₈₉	—	4	1	no	—
109	C₂²×C₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	4	1	no	—
112	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
118	Q₁₆×C₈₉	—	2	2	no	—
119	SD₁₆×C₈₉	—	4	2	no	—
120	D₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	2	no	—
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₂×C₈×C₈₉	—	2	2	no	—
125	C₂×C₈×C₈₉	—	2	2	no	—
126	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₈₉	#41	1	4	yes	—
130	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₈₉	—	2	1	no	—
132	C₄⋊C₄×C₈₉	—	2	1	no	—
133	C₄⋊C₄×C₈₉	—	4	1	no	—
134	C₄⋊C₄×C₈₉	—	4	1	no	—
135	C₂²⋊C₄×C₈₉	—	4	1	no	—
136	C₂²⋊C₄×C₈₉	—	4	1	no	—
137	C₂²⋊C₄×C₈₉	—	4	1	no	—
138	C₂²⋊C₄×C₈₉	—	4	1	no	—
139	C₂²⋊C₄×C₈₉	—	4	1	no	—
140	C₄²×C₈₉	—	4	1	no	—
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	—	2	2	no	—
143	C₂³×C₈₉	—	4	1	no	—
144	C₂³×C₈₉	—	4	1	no	—
145	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
146	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
147	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
148	Q₈×C₈₉	—	4	1	no	—
149	Q₈×C₈₉	—	4	1	no	—
150	D₄×C₈₉	—	4	1	no	—
151	D₄×C₈₉	—	4	1	no	—
152	D₄×C₈₉	—	8	2	no	—
153	D₄×C₈₉	—	8	2	no	—
154	D₄×C₈₉	—	8	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	4	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	8	2	no	—
166	C₂×C₄×C₈₉	#123	1	2	yes	—
167	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#137	1	2	yes	—
171	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×Dic₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	4	2	no	—
174	C₂×Dic₈₉	—	8	2	no	—
175	C₂×Dic₈₉	—	8	2	no	—
176	C₈×C₈₉	—	2	1	no	—
177	C₈×C₈₉	—	2	1	no	—
178	C₈×C₈₉	#123	1	2	yes	—
179	C₈×C₈₉	C₂×#41	1	2	yes	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	—	2	1	no	—
187	C₂²×C₈₉	—	4	4	no	—
188	C₂²×C₈₉	—	8	1	no	—
189	C₂²×C₈₉	—	8	1	no	—
190	C₂²×C₈₉	—	8	1	no	—
191	C₂²×C₈₉	#480	1	2	yes	—
192	C₂²×C₈₉	#508	1	2	yes	—
193	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	8	1	no	—
197	C₄×C₈₉	—	8	1	no	—
198	C₄×C₈₉	—	8	1	no	—
199	C₄×C₈₉	#480	1	2	yes	—
200	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
201	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
202	Dic₈₉	—	8	2	no	—
203	Dic₈₉	—	8	2	no	—
204	#33645	—	89	1	no	maximal, Sylow
205	C₂×C₈₉	—	2	2	no	—
206	C₂×C₈₉	—	2	2	no	—
207	C₂×C₈₉	—	4	1	no	—
208	C₂×C₈₉	—	16	1	no	—
209	C₂×C₈₉	C₂×#480	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#508	1	1	yes	characteristic
211	C₂×C₈₉	#3414	1	1	yes	characteristic
212	#3050	D₈₉	1	1	yes	characteristic
213	C₂×#427	—	89	1	no	—
214	#2237	—	89	2	no	—
215	#2236	—	89	1	no	—
216	#2235	—	89	1	no	—
217	#2234	—	89	2	no	—
218	#2233	—	89	1	no	—
219	#2232	—	89	1	no	—
220	#2158	—	89	2	no	—
221	#2138	—	89	2	no	—
222	C₂×C₂²⋊C₁₆	—	89	1	no	—
223	C₈₉	#33645	1	1	yes	characteristic, complemented, Sylow
224	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
225	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
226	#525	—	2	1	no	—
227	C₂×#117	—	178	1	no	—
228	C₂²×C₁₆	—	89	2	no	—
229	#467	C₂×D₈₉	1	1	yes	characteristic
230	#467	C₂×D₈₉	1	1	yes	characteristic
231	#466	C₂×D₈₉	1	1	yes	characteristic
232	#466	C₂×D₈₉	1	1	yes	characteristic
233	#465	—	2	1	no	—
234	#465	—	2	1	no	—
235	#427	—	89	2	no	—
236	#427	—	89	2	no	—
237	#427	—	178	1	no	—
238	#427	—	178	1	no	—
239	#427	C₂×D₈₉	1	1	yes	characteristic
240	C₂×#107	—	89	1	no	—
241	C₂×#107	—	89	1	no	—
242	C₂×#106	—	178	1	no	—
243	#416	—	2	1	no	—
244	#367	—	89	2	no	—
245	#367	—	89	2	no	—
246	#366	—	89	2	no	—
247	#366	—	89	2	no	—
248	#358	—	89	2	no	—
249	#358	—	89	2	no	—
250	#357	—	89	2	no	—
251	#357	—	89	2	no	—
252	C₂²⋊C₁₆	—	89	1	no	—
253	C₂²⋊C₁₆	—	89	1	no	—
254	C₂²⋊C₁₆	—	89	2	no	—
255	C₂×#41	—	2	1	no	—
256	C₂³×C₄	C₂²⋊D₈₉	1	1	yes	characteristic
257	#135	—	2	4	no	—
258	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
259	C₂×SD₁₆	—	2	1	no	—
260	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
261	C₂²×C₈	—	2	4	no	—
262	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
263	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
264	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
268	#123	—	4	1	no	—
269	C₂²⋊Q₈	—	2	1	no	—
270	C₂²⋊Q₈	—	2	1	no	—
271	#121	—	2	1	no	—
272	#121	—	2	1	no	—
273	#120	—	4	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	4	1	no	—
276	#117	—	2	1	no	—
277	#117	—	356	1	no	—
278	#117	—	356	1	no	—
279	#117	—	178	2	no	—
280	#117	—	178	2	no	—
281	C₂×C₄⋊C₄	—	178	1	no	—
282	C₂×C₄⋊C₄	—	178	1	no	—
283	C₂×C₂²⋊C₄	—	356	1	no	—
284	C₂×C₄²	—	356	1	no	—
285	C₂×C₁₆	—	89	2	no	—
286	C₂×C₁₆	—	89	2	no	—
287	C₂×C₁₆	—	178	4	no	—
288	#107	—	89	2	no	—
289	#107	—	89	2	no	—
290	#107	—	178	1	no	—
291	#107	—	178	1	no	—
292	#107	C₂²×D₈₉	1	1	yes	characteristic
293	#107	C₂²×D₈₉	1	1	yes	characteristic
294	#106	—	2	1	no	—
295	#106	—	178	2	no	—
296	#106	—	178	2	no	—
297	#103	—	2	1	no	—
298	#103	—	2	1	no	—
299	#102	—	2	1	no	—
300	#102	—	2	1	no	—
301	C₂⁴	#13083559	1	1	yes	characteristic
302	#41	—	4	2	no	—
303	#41	—	4	2	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	356	1	no	—
313	C₂²×C₄	—	356	1	no	—
314	C₂²×C₄	#13083559	1	1	yes	characteristic
315	C₂²×C₄	#13083559	1	1	yes	characteristic
316	C₂²×C₄	#13083559	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
320	Q₁₆	—	2	2	no	—
321	SD₁₆	—	4	2	no	—
322	D₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
329	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
330	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
331	C₂×C₈	#13083573	1	4	yes	—
332	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	356	1	no	—
338	C₄⋊C₄	—	356	1	no	—
339	C₄⋊C₄	—	178	2	no	—
340	C₄⋊C₄	—	178	2	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	356	2	no	—
347	C₂²⋊C₄	—	356	2	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	356	2	no	—
350	C₄²	—	356	2	no	—
351	C₁₆	—	178	2	no	—
352	C₁₆	—	178	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	—	4	1	no	—
356	C₂³	—	4	1	no	—
357	C₂³	C₂×#13083559	1	1	yes	characteristic
358	C₂³	C₂×#13083559	1	1	yes	characteristic
359	C₂³	C₂×#13083559	1	1	yes	characteristic
360	Q₈	—	4	1	no	—
361	Q₈	—	4	1	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	8	2	no	—
365	D₄	—	8	2	no	—
366	D₄	—	8	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	8	2	no	—
378	C₂×C₄	—	356	2	no	—
379	C₂×C₄	—	356	2	no	—
380	C₂×C₄	—	712	2	no	—
381	C₂×C₄	—	712	2	no	—
382	C₂×C₄	#15667993	1	2	yes	—
383	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
384	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
385	C₂×C₄	C₂×#13083559	1	1	yes	characteristic
386	C₂×C₄	#15668042	1	2	yes	—
387	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	#15667993	1	2	yes	—
391	C₈	C₂×#13083573	1	2	yes	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	8	1	no	—
401	C₂²	—	8	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	#19151909	1	2	yes	—
404	C₂²	#19152028	1	2	yes	—
405	C₂²	C₂²×#13083559	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	8	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	1	no	—
411	C₄	—	712	2	no	—
412	C₄	—	712	2	no	—
413	C₄	#19151909	1	2	yes	—
414	C₄	C₂×#15667993	1	1	yes	characteristic
415	C₄	C₂×#15668042	1	1	yes	characteristic
416	C₂	—	2	2	no	—
417	C₂	—	2	2	no	—
418	C₂	—	4	1	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×#19151909	1	1	yes	characteristic
421	C₂	C₂×#19152028	1	1	yes	characteristic
422	C₂	#26033386	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#13083559
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3050	C₂
socle	C₂²×C₈₉	C₂²×D₈
hypercenter	#3050	D₈₉
hypocenter	C₈₉	#33645
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. C₂×#19151636	C₂	semidirect
2. #26022457	C₂	semidirect
3. #26022452	C₂	semidirect
4. #26022447	C₂	semidirect
5. #26022440	C₂	semidirect
6. #26022435	C₂	semidirect
7. #26022430	C₂	semidirect
8. #26022034	C₂	semidirect
9. #26021959	C₂	semidirect
10. C₂×C₂²⋊#13083549	C₂	semidirect
21. #19151425	C₂²	semidirect
22. #19151425	C₂²	semidirect
23. #19151423	C₂²	semidirect
24. #19151423	C₂²	semidirect
25. #19151402	C₂²	semidirect
26. #19151402	C₂²	semidirect
27. #19151399	C₂²	semidirect
28. #19151399	C₂²	semidirect
223. C₈₉	#33645	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151636	2
#26022457	2
#26022452	2
#26022447	2
#26022440	2
#26022435	2
#26022430	2
#26022034	2
#26021959	2
C₂×C₂²⋊#13083549	2
C₈₉×#3050	2
#33645	89