Subgroups — #36523676

Order 22784.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029218	C₂	1	1	yes	maximal, characteristic
2	#26028917	C₂	1	1	yes	maximal, characteristic
3	#26028817	C₂	1	1	yes	maximal, characteristic
4	#26019039	C₂	1	2	yes	maximal, complemented
5	#26019034	C₂	1	2	yes	maximal, complemented
6	#26019026	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019022	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019016	C₂	1	2	yes	maximal, complemented
9	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019001	C₂	1	2	yes	maximal, complemented
11	C₂×#334×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	1	no	—
13	C₄×#13083574	C₂²	1	1	yes	characteristic
14	#19151728	C₄	1	1	yes	characteristic
15	#19151728	C₄	1	1	yes	characteristic
16	#19151677	C₄	1	1	yes	characteristic
17	#19151677	C₄	1	1	yes	characteristic
18	#19151669	C₄	1	2	yes	—
19	#19151669	C₄	1	2	yes	—
20	#19151658	—	2	2	no	—
21	#19151654	C₂²	1	2	yes	—
22	#19151651	C₂²	1	1	yes	characteristic
23	#19151650	C₂²	1	2	yes	—
24	#19151649	C₂²	1	2	yes	—
25	#19151624	—	2	1	no	—
26	#19151623	—	2	2	no	—
27	#19151622	C₂²	1	1	yes	characteristic
28	#19151622	C₂²	1	1	yes	characteristic
29	#19151620	C₂²	1	2	yes	—
30	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
31	#19151564	—	2	1	no	—
32	#19151553	—	2	1	no	—
33	C₄×#13083557	C₂²	1	2	yes	—
34	#19151351	C₂²	1	2	yes	—
35	#19151351	C₂²	1	2	yes	—
36	#19151350	C₂²	1	2	yes	—
37	#19151350	C₂²	1	2	yes	—
38	#19151348	C₂²	1	2	yes	—
39	#19151348	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#334×C₈₉	C₂²	1	1	yes	characteristic
44	#334×C₈₉	C₂²	1	1	yes	characteristic
45	#334×C₈₉	C₂²	1	1	yes	characteristic
46	#334×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	D₄	1	1	yes	characteristic
48	#15668018	—	4	4	no	—
49	C₂×#13083558	—	2	1	no	—
50	C₂×#13083558	—	2	1	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂×#13083557	C₂×C₄	1	2	yes	—
53	C₂×#13083557	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₁₇₈	Q₈	1	1	yes	characteristic
57	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
58	C₄×D₃₅₆	Q₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
60	C₄×C₂²⋊D₈₉	Q₈	1	2	yes	—
61	#15667971	D₄	1	1	yes	characteristic
62	#15667969	D₄	1	2	yes	—
63	C₄²×D₈₉	C₂³	1	2	yes	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667941	—	2	2	no	—
71	#15667941	—	2	2	no	—
72	#15667941	C₂×C₄	1	2	yes	—
73	#15667941	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	#15667924	C₂×C₄	1	2	yes	—
78	#15667924	C₂×C₄	1	2	yes	—
79	#15667922	—	2	2	no	—
80	#15667922	C₂×C₄	1	2	yes	—
81	#15667922	C₂×C₄	1	2	yes	—
82	C₄×#10623494	C₂³	1	2	yes	—
83	C₈×Dic₈₉	—	2	2	no	—
84	C₂²×C₈×C₈₉	—	2	1	no	—
85	C₂²×C₈×C₈₉	—	2	1	no	—
86	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	—	2	1	no	—
90	C₄⋊C₈×C₈₉	—	2	1	no	—
91	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	#13083574	—	2	2	no	—
100	#13083574	—	2	2	no	—
101	C₂×Dic₁₇₈	C₄⋊C₄	1	1	yes	characteristic
102	C₂×D₃₅₆	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₂²⋊D₈₉	C₄⋊C₄	1	2	yes	—
104	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₈₉	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₈₉	C₂×Q₈	1	2	yes	—
107	#13083558	—	4	2	no	—
108	#13083558	—	4	2	no	—
109	#13083557	—	2	4	no	—
110	#13083557	—	4	2	no	—
111	#13083557	—	4	4	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	C₂²×C₄	1	2	yes	—
115	C₂×#10623494	C₂²×C₄	1	2	yes	—
116	C₈×D₈₉	—	4	4	no	—
117	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄⋊Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
119	#13083553	C₄⋊C₄	1	2	yes	—
120	#13083553	C₄⋊C₄	1	2	yes	—
121	C₂²⋊Dic₈₉	C₄⋊C₄	1	2	yes	—
122	#13083551	C₄⋊C₄	1	2	yes	—
123	#13083551	C₄⋊C₄	1	2	yes	—
124	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
125	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
126	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	4	1	no	—
136	C₂×C₈×C₈₉	—	4	2	no	—
137	C₂×C₈×C₈₉	—	4	2	no	—
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
145	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₈₉	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₈₉	—	2	1	no	—
149	C₂×C₄×C₈₉	—	2	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
155	C₂×C₄×C₈₉	#137	1	2	yes	—
156	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂²⋊D₈₉	—	2	4	no	—
160	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₈₉	C₂×C₄⋊C₄	1	2	yes	—
163	D₃₅₆	—	2	2	no	—
164	C₄×D₈₉	—	2	2	no	—
165	C₄×D₈₉	—	2	2	no	—
166	C₄×D₈₉	—	2	2	no	—
167	C₄×D₈₉	—	2	2	no	—
168	C₄×D₈₉	—	4	2	no	—
169	Dic₁₇₈	—	2	2	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	—	2	1	no	—
173	C₈×C₈₉	—	4	1	no	—
174	C₈×C₈₉	—	4	1	no	—
175	C₈×C₈₉	—	4	1	no	—
176	C₈×C₈₉	—	4	1	no	—
177	C₈×C₈₉	#131	1	2	yes	complemented
178	#10623494	—	2	2	no	—
179	#10623494	—	2	2	no	—
180	#10623494	—	4	2	no	—
181	#10623494	—	4	2	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	#428	1	2	yes	—
185	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₂×D₈₉	—	2	2	no	—
187	C₂×D₈₉	—	2	2	no	—
188	C₂×D₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	#428	1	2	yes	—
193	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
194	C₄×C₈₉	#568	1	1	yes	characteristic
195	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
197	Dic₈₉	—	2	2	no	—
198	Dic₈₉	—	2	2	no	—
199	Dic₈₉	—	2	2	no	—
200	#17830	—	89	1	no	maximal, Sylow
201	C₂×C₈₉	—	2	2	no	—
202	C₂×C₈₉	#2906	1	1	yes	characteristic
203	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
204	C₂×C₈₉	#2916	1	1	yes	characteristic
205	D₈₉	—	4	2	no	—
206	#2965	—	89	1	no	—
207	#2925	—	89	1	no	—
208	#2906	—	89	1	no	—
209	#1574	—	89	2	no	—
210	#1573	—	89	2	no	—
211	#1571	—	89	1	no	—
212	#1570	—	89	1	no	—
213	#1569	—	89	2	no	—
214	#1567	—	89	1	no	—
215	#1565	—	89	2	no	—
216	C₂×#334	D₈₉	1	1	yes	characteristic, complemented
217	C₈₉	#17830	1	1	yes	characteristic, complemented, Sylow
218	C₂×#131	—	178	1	no	—
219	C₄×#41	—	89	1	no	—
220	#446	—	89	1	no	—
221	#446	—	89	1	no	—
222	#436	—	89	1	no	—
223	#436	—	89	1	no	—
224	#435	—	89	2	no	—
225	#435	—	89	2	no	—
226	#433	—	178	2	no	—
227	#432	—	89	2	no	—
228	#431	—	89	1	no	—
229	#431	—	89	2	no	—
230	#431	—	89	2	no	—
231	#424	—	178	2	no	—
232	#424	—	178	1	no	—
233	#423	—	89	1	no	—
234	#423	—	89	1	no	—
235	#423	—	89	2	no	—
236	C₂×C₄⋊C₈	—	89	2	no	—
237	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
239	#408	—	178	1	no	—
240	#405	—	178	1	no	—
241	C₄×M₁₆	—	89	2	no	—
242	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
243	#335	—	89	2	no	—
244	#335	—	89	2	no	—
245	#335	—	89	2	no	—
246	#335	—	89	2	no	—
247	#334	—	89	2	no	—
248	#334	—	89	2	no	—
249	#334	C₂×D₈₉	1	1	yes	characteristic
250	#334	C₂×D₈₉	1	1	yes	characteristic
251	#334	C₂×D₈₉	1	1	yes	characteristic
252	#334	C₂×D₈₉	1	1	yes	characteristic
253	C₂×#41	—	89	1	no	—
254	#131	—	356	4	no	—
255	C₂×M₁₆	—	89	2	no	—
256	C₂×M₁₆	—	89	2	no	—
257	C₂×M₁₆	—	178	2	no	—
258	C₂×M₁₆	—	178	1	no	—
259	C₂×M₁₆	—	178	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	178	2	no	—
263	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
264	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
265	C₄×Q₈	—	89	1	no	—
266	C₄×Q₈	—	89	1	no	—
267	C₄×D₄	—	89	2	no	—
268	C₄×D₄	—	89	2	no	—
269	C₄×D₄	—	89	1	no	—
270	C₄×D₄	—	89	1	no	—
271	#117	—	89	1	no	—
272	#117	—	89	2	no	—
273	C₂×C₄²	—	89	2	no	—
274	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	89	2	no	—
278	C₄⋊C₈	—	89	2	no	—
279	C₄⋊C₈	—	89	1	no	—
280	C₄⋊C₈	—	89	1	no	—
281	C₄⋊C₈	—	89	2	no	—
282	C₄⋊C₈	—	89	2	no	—
283	C₄⋊C₈	—	178	2	no	—
284	C₄⋊C₈	—	178	2	no	—
285	C₄⋊C₈	—	178	1	no	—
286	C₄⋊C₈	—	178	1	no	—
287	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
288	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₂²⋊C₈	—	89	2	no	—
292	C₂²⋊C₈	—	89	2	no	—
293	C₂²⋊C₈	—	89	2	no	—
294	C₂²⋊C₈	—	178	2	no	—
295	C₂²⋊C₈	—	178	2	no	—
296	#97	—	89	2	no	—
297	#97	—	89	2	no	—
298	#97	—	178	2	no	—
299	C₄×C₈	—	89	2	no	—
300	C₄×C₈	—	178	2	no	—
301	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
302	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
305	#41	—	178	2	no	—
306	#41	—	178	2	no	—
307	C₂×Q₈	—	89	1	no	—
308	C₂×D₄	—	89	2	no	—
309	C₂×D₄	—	89	1	no	—
310	C₂²×C₄	—	89	2	no	—
311	C₂²×C₄	—	89	2	no	—
312	C₂²×C₄	—	89	2	no	—
313	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
314	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
315	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
316	M₁₆	—	356	2	no	—
317	M₁₆	—	356	4	no	—
318	M₁₆	—	356	2	no	—
319	M₁₆	—	356	2	no	—
320	M₁₆	—	178	4	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	2	no	—
328	C₂×C₈	—	4	2	no	—
329	C₂×C₈	—	89	2	no	—
330	C₂×C₈	—	89	2	no	—
331	C₂×C₈	—	356	4	no	—
332	C₂×C₈	—	178	2	no	—
333	C₂×C₈	—	178	2	no	—
334	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
337	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
338	C₄⋊C₄	—	89	2	no	—
339	C₄⋊C₄	—	89	2	no	—
340	C₄⋊C₄	—	89	1	no	—
341	C₄⋊C₄	—	89	1	no	—
342	C₂²⋊C₄	—	89	2	no	—
343	C₂²⋊C₄	—	89	2	no	—
344	C₂²⋊C₄	—	89	2	no	—
345	C₄²	—	89	2	no	—
346	C₄²	—	89	2	no	—
347	C₄²	—	89	2	no	—
348	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
349	C₄²	D₄×D₈₉	1	1	yes	characteristic
350	C₄²	Q₈×D₈₉	1	1	yes	characteristic
351	C₄²	C₂³×D₈₉	1	1	yes	characteristic
352	C₂³	—	89	2	no	—
353	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
354	Q₈	—	178	2	no	—
355	D₄	—	178	4	no	—
356	D₄	—	178	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	89	2	no	—
361	C₂×C₄	—	89	2	no	—
362	C₂×C₄	—	89	2	no	—
363	C₂×C₄	—	356	2	no	—
364	C₂×C₄	—	178	2	no	—
365	C₂×C₄	—	178	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
369	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
370	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
371	C₂×C₄	#15668039	1	2	yes	—
372	C₂×C₄	#15668041	1	2	yes	—
373	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
375	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	1	no	—
380	C₈	—	4	1	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	356	2	no	—
384	C₈	—	356	2	no	—
385	C₈	—	178	2	no	—
386	C₈	—	178	2	no	—
387	C₈	#15668018	1	2	yes	complemented
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	178	2	no	—
391	C₂²	—	178	2	no	—
392	C₂²	—	178	2	no	—
393	C₂²	#19151637	1	2	yes	—
394	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	1	no	—
398	C₄	—	178	2	no	—
399	C₄	—	178	2	no	—
400	C₄	—	178	2	no	—
401	C₄	#19151637	1	2	yes	—
402	C₄	C₂×#15668018	1	1	yes	characteristic
403	C₄	#19152364	1	1	yes	characteristic
404	C₄	C₂×#15668039	1	1	yes	characteristic
405	C₄	C₂×#15668041	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	356	2	no	—
408	C₂	#26028817	1	1	yes	characteristic
409	C₂	C₂×#19151637	1	1	yes	characteristic
410	C₂	#26028860	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#334×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂×#13083574	D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#334	D₈₉
hypocenter	C₈₉	#17830
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. #26019039	C₂	semidirect
5. #26019034	C₂	semidirect
6. #26019026	C₂	semidirect
7. #26019022	C₂	semidirect
8. #26019016	C₂	semidirect
9. #26019011	C₂	semidirect
10. #26019001	C₂	semidirect
11. C₂×#334×C₈₉	C₂	semidirect
177. C₈×C₈₉	#131	semidirect
216. C₂×#334	D₈₉	semidirect
217. C₈₉	#17830	semidirect
387. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26029218	2
#26028917	2
#26028817	2
#26019039	2
#26019034	2
#26019026	2
#26019022	2
#26019016	2
#26019011	2
#26019001	2
C₂×#334×C₈₉	2
#17830	89