Subgroups — #36523591

Order 22784.

684 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028884	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151649	C₂	1	1	yes	maximal, characteristic
3	#423×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019039	C₂	1	4	yes	maximal, complemented
5	#26019034	C₂	1	4	yes	maximal, complemented
6	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019010	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019007	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1566	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₈₉	—	2	1	no	—
11	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
12	#19151654	—	2	1	no	—
13	#19151654	C₂²	1	2	yes	—
14	#19151650	—	2	1	no	—
15	#19151650	C₂²	1	2	yes	—
16	#19151649	C₄	1	2	yes	—
17	#19151649	C₄	1	2	yes	—
18	#19151649	C₂²	1	2	yes	—
19	#19151649	C₂²	1	2	yes	—
20	#19151622	C₂²	1	1	yes	characteristic
21	#19151622	C₂²	1	1	yes	characteristic
22	#19151621	—	2	1	no	—
23	#19151620	—	2	1	no	—
24	#19151620	C₂²	1	2	yes	—
25	C₂×#15667941	C₄	1	2	yes	—
26	C₄⋊C₈×D₈₉	—	2	1	no	—
27	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
28	#19151561	—	2	1	no	—
29	C₂×#15667924	C₄	1	2	yes	—
30	M₁₆×Dic₈₉	—	2	1	no	—
31	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	4	yes	complemented
33	#19151350	C₂²	1	4	yes	complemented
34	#19151348	C₂²	1	4	yes	complemented
35	#423×C₈₉	C₂²	1	1	yes	characteristic
36	#423×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	#334×C₈₉	C₂²	1	4	yes	complemented
39	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
41	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
42	C₂×#13083558	—	2	1	no	—
43	C₂×#13083558	—	2	1	no	—
44	C₂×#13083557	—	2	2	no	—
45	M₁₆×D₈₉	—	4	4	no	—
46	C₂²×#10623494	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₈₉	—	2	2	no	—
48	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
51	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₈₉	D₄	1	1	yes	characteristic
54	C₄²×D₈₉	D₄	1	1	yes	characteristic
55	C₄²×D₈₉	Q₈	1	1	yes	characteristic
56	C₄²×D₈₉	Q₈	1	1	yes	characteristic
57	C₄²×D₈₉	C₂³	1	1	yes	characteristic
58	C₄²×D₈₉	C₂³	1	1	yes	characteristic
59	C₄⋊#10623494	—	2	1	no	—
60	C₄⋊#10623494	—	2	1	no	—
61	C₄⋊#10623494	C₂³	1	2	yes	—
62	C₄⋊#10623494	C₂³	1	2	yes	—
63	#15667941	—	2	2	no	—
64	#15667941	—	2	2	no	—
65	#15667941	C₂×C₄	1	4	yes	—
66	#15667941	C₂×C₄	1	4	yes	—
67	#15667924	—	2	2	no	—
68	#15667924	—	2	2	no	—
69	#15667924	C₂×C₄	1	4	yes	—
70	#15667924	C₂×C₄	1	4	yes	—
71	#15667922	—	2	2	no	—
72	C₄×#10623494	C₂×C₄	1	2	yes	—
73	C₄×#10623494	C₂³	1	2	yes	—
74	C₈×Dic₈₉	—	2	2	no	—
75	C₂×M₁₆×C₈₉	—	2	1	no	—
76	C₂×M₁₆×C₈₉	—	2	1	no	—
77	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₈₉	—	2	1	no	—
80	C₄⋊C₈×C₈₉	—	2	1	no	—
81	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
82	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
83	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
84	C₄×C₈×C₈₉	C₂³	1	2	yes	—
85	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₈₉	—	2	2	no	—
90	C₂×C₄×D₈₉	—	2	2	no	—
91	C₂×C₄×D₈₉	—	2	4	no	—
92	C₂×C₄×D₈₉	—	4	2	no	—
93	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
105	#13083558	—	4	2	no	—
106	#13083558	—	4	2	no	—
107	#13083557	—	4	4	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	4	2	no	—
111	C₂×#10623494	C₂²×C₄	1	4	yes	—
112	C₈×D₈₉	—	4	4	no	—
113	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
114	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
115	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
116	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
123	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
124	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
128	M₁₆×C₈₉	—	4	2	no	—
129	M₁₆×C₈₉	—	4	2	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	4	2	no	—
133	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
134	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
137	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	2	2	no	—
141	C₂²×D₈₉	—	4	1	no	—
142	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₈₉	#137	1	2	yes	—
151	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
154	C₂×Dic₈₉	—	2	2	no	—
155	C₂×Dic₈₉	—	2	2	no	—
156	C₂×Dic₈₉	—	4	1	no	—
157	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
160	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₄×D₈₉	—	2	2	no	—
164	C₄×D₈₉	—	2	2	no	—
165	C₄×D₈₉	—	2	2	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	2	1	no	—
168	C₄×D₈₉	—	2	1	no	—
169	C₄×D₈₉	—	2	1	no	—
170	C₄×D₈₉	—	2	2	no	—
171	C₄×D₈₉	—	2	2	no	—
172	C₄×D₈₉	—	2	2	no	—
173	C₄×D₈₉	—	2	2	no	—
174	C₄×D₈₉	—	4	1	no	—
175	C₄×D₈₉	—	4	1	no	—
176	C₄×D₈₉	#108	1	4	yes	—
177	C₈×C₈₉	—	2	4	no	—
178	C₈×C₈₉	—	4	2	no	—
179	C₈×C₈₉	—	4	2	no	—
180	#10623494	—	2	4	no	—
181	#10623494	—	4	2	no	—
182	#10623494	—	4	2	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	#428	1	2	yes	—
186	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₂×D₈₉	—	2	1	no	—
188	C₂×D₈₉	—	2	1	no	—
189	C₂×D₈₉	—	2	1	no	—
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	4	4	no	—
193	C₂×D₈₉	C₂×#108	1	2	yes	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	#428	1	2	yes	—
197	C₄×C₈₉	C₂×#108	1	2	yes	—
198	C₄×C₈₉	#568	1	2	yes	—
199	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
201	Dic₈₉	—	2	1	no	—
202	Dic₈₉	—	2	1	no	—
203	Dic₈₉	—	2	1	no	—
204	Dic₈₉	—	2	1	no	—
205	Dic₈₉	—	2	1	no	—
206	Dic₈₉	C₂×#108	1	2	yes	—
207	#17817	—	89	1	no	maximal, Sylow
208	C₂×C₈₉	—	2	2	no	—
209	C₂×C₈₉	#2905	1	1	yes	characteristic
210	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
211	C₂×C₈₉	C₂²×#108	1	1	yes	characteristic
212	D₈₉	—	2	2	no	—
213	D₈₉	—	4	1	no	—
214	#2920	—	89	1	no	—
215	C₂×#431	—	89	1	no	—
216	C₂×#423	—	89	1	no	—
217	#1574	—	89	4	no	—
218	#1573	—	89	4	no	—
219	#1567	—	89	1	no	—
220	#1567	—	89	1	no	—
221	#1566	—	89	1	no	—
222	#1566	D₈₉	1	1	yes	characteristic, complemented
223	C₈₉	#17817	1	1	yes	characteristic, complemented, Sylow
224	C₂²×M₁₆	—	178	1	no	—
225	C₂²×C₄²	—	89	1	no	—
226	#432	—	89	2	no	—
227	#432	—	178	1	no	—
228	#431	—	89	2	no	—
229	#431	—	89	2	no	—
230	#431	—	89	2	no	—
231	#431	—	89	2	no	—
232	#431	—	89	2	no	—
233	#431	—	178	1	no	—
234	#423	—	89	1	no	—
235	#423	—	89	1	no	—
236	#423	—	89	2	no	—
237	#423	—	178	1	no	—
238	#423	—	178	1	no	—
239	#423	C₂×D₈₉	1	1	yes	characteristic
240	#423	C₂×D₈₉	1	1	yes	characteristic
241	C₂×C₄⋊C₈	—	89	2	no	—
242	C₂×C₄⋊C₈	—	89	2	no	—
243	C₂×C₄⋊C₈	—	178	1	no	—
244	#407	—	178	1	no	—
245	C₂×C₂²⋊C₈	—	89	2	no	—
246	C₄×M₁₆	—	178	1	no	—
247	C₂×C₄×C₈	—	89	1	no	—
248	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
249	#335	—	89	4	no	—
250	#335	—	89	4	no	—
251	#334	—	89	4	no	—
252	#334	C₂×D₈₉	1	4	yes	complemented
253	C₂³×C₄	—	89	1	no	—
254	C₂³×C₄	—	89	1	no	—
255	C₂³×C₄	—	89	1	no	—
256	C₂×M₁₆	—	2	1	no	—
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	356	4	no	—
259	C₂×M₁₆	—	178	2	no	—
260	C₂×M₁₆	—	178	1	no	—
261	C₂×M₁₆	—	178	1	no	—
262	C₂²×C₈	—	89	2	no	—
263	C₂²×C₈	—	178	2	no	—
264	C₂²×C₈	C₄×D₈₉	1	2	yes	—
265	C₂×C₄²	—	89	1	no	—
266	C₂×C₄²	—	89	1	no	—
267	C₂×C₄²	—	89	1	no	—
268	C₂×C₄²	—	89	1	no	—
269	C₂×C₄²	—	89	1	no	—
270	C₂×C₄²	—	89	1	no	—
271	C₂×C₄²	—	89	1	no	—
272	C₂×C₄²	—	89	1	no	—
273	C₂×C₄²	—	89	1	no	—
274	C₂×C₄²	—	89	1	no	—
275	C₂×C₄²	—	89	1	no	—
276	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
277	C₄⋊C₈	—	2	1	no	—
278	C₄⋊C₈	—	2	1	no	—
279	C₄⋊C₈	—	89	4	no	—
280	C₄⋊C₈	—	89	4	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	2	yes	—
288	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
289	C₂²⋊C₈	—	89	4	no	—
290	C₂²⋊C₈	—	89	4	no	—
291	C₂²⋊C₈	—	178	2	no	—
292	C₂²⋊C₈	—	178	2	no	—
293	#97	—	178	2	no	—
294	C₄×C₈	—	89	2	no	—
295	C₄×C₈	—	89	2	no	—
296	C₄×C₈	—	178	2	no	—
297	C₄×C₈	C₄×D₈₉	1	2	yes	—
298	C₄×C₈	C₂²×D₈₉	1	2	yes	—
299	C₂⁴	—	89	1	no	—
300	C₂²×C₄	—	89	1	no	—
301	C₂²×C₄	—	89	1	no	—
302	C₂²×C₄	—	89	1	no	—
303	C₂²×C₄	—	89	1	no	—
304	C₂²×C₄	—	89	1	no	—
305	C₂²×C₄	—	89	1	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	89	1	no	—
311	C₂²×C₄	—	89	1	no	—
312	C₂²×C₄	—	89	1	no	—
313	C₂²×C₄	—	89	1	no	—
314	C₂²×C₄	—	89	1	no	—
315	C₂²×C₄	—	356	2	no	—
316	C₂²×C₄	—	178	4	no	—
317	C₂²×C₄	—	178	2	no	—
318	C₂²×C₄	—	178	2	no	—
319	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
321	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
322	M₁₆	—	4	2	no	—
323	M₁₆	—	4	2	no	—
324	M₁₆	—	356	4	no	—
325	M₁₆	—	356	2	no	—
326	M₁₆	—	356	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	4	2	no	—
330	C₂×C₈	—	89	4	no	—
331	C₂×C₈	—	356	4	no	—
332	C₂×C₈	—	356	2	no	—
333	C₂×C₈	—	178	2	no	—
334	C₂×C₈	—	178	2	no	—
335	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
336	C₄²	—	89	1	no	—
337	C₄²	—	89	1	no	—
338	C₄²	—	89	1	no	—
339	C₄²	—	89	1	no	—
340	C₄²	—	89	1	no	—
341	C₄²	—	89	1	no	—
342	C₄²	—	89	1	no	—
343	C₄²	—	89	1	no	—
344	C₄²	—	89	1	no	—
345	C₄²	—	89	1	no	—
346	C₄²	—	89	1	no	—
347	C₄²	—	89	1	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	1	no	—
353	C₂³	—	89	1	no	—
354	C₂³	—	356	1	no	—
355	C₂³	—	178	2	no	—
356	C₂³	—	178	2	no	—
357	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	89	1	no	—
361	C₂×C₄	—	89	4	no	—
362	C₂×C₄	—	89	1	no	—
363	C₂×C₄	—	89	1	no	—
364	C₂×C₄	—	89	1	no	—
365	C₂×C₄	—	89	1	no	—
366	C₂×C₄	—	89	1	no	—
367	C₂×C₄	—	356	1	no	—
368	C₂×C₄	—	356	1	no	—
369	C₂×C₄	—	356	1	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	2	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	178	1	no	—
375	C₂×C₄	—	178	1	no	—
376	C₂×C₄	—	178	1	no	—
377	C₂×C₄	—	178	1	no	—
378	C₂×C₄	—	178	2	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	2	no	—
381	C₂×C₄	—	178	2	no	—
382	C₂×C₄	—	178	2	no	—
383	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
385	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
386	C₂×C₄	#15668039	1	2	yes	—
387	C₂×C₄	#15668041	1	2	yes	—
388	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
390	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	356	2	no	—
395	C₈	—	356	2	no	—
396	C₈	—	178	4	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	89	2	no	—
400	C₂²	—	356	4	no	—
401	C₂²	—	178	1	no	—
402	C₂²	—	178	1	no	—
403	C₂²	—	178	1	no	—
404	C₂²	—	178	1	no	—
405	C₂²	—	178	1	no	—
406	C₂²	#19151637	1	2	yes	—
407	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	89	2	no	—
411	C₄	—	178	1	no	—
412	C₄	—	178	1	no	—
413	C₄	—	178	1	no	—
414	C₄	—	178	1	no	—
415	C₄	—	178	1	no	—
416	C₄	#19151637	1	2	yes	—
417	C₄	#108×D₈₉	1	2	yes	—
418	C₄	#19152364	1	2	yes	—
419	C₄	C₂×#15668039	1	1	yes	characteristic
420	C₄	C₂×#15668041	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	356	1	no	—
423	C₂	—	178	2	no	—
424	C₂	#26028814	1	1	yes	characteristic
425	C₂	C₂×#19151637	1	1	yes	characteristic
426	C₂	C₂×#108×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1566	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1566	D₈₉
hypocenter	C₈₉	#17817
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1566

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. #26019011	C₂	semidirect
7. #26019010	C₂	semidirect
8. #26019007	C₂	semidirect
9. C₈₉×#1566	C₂	semidirect
32. #19151351	C₂²	semidirect
33. #19151350	C₂²	semidirect
34. #19151348	C₂²	semidirect
38. #334×C₈₉	C₂²	semidirect
222. #1566	D₈₉	semidirect
223. C₈₉	#17817	semidirect
252. #334	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028884	2
C₂×#19151649	2
#423×D₈₉	2
#26019039	2
#26019034	2
#26019011	2
#26019010	2
#26019007	2
C₈₉×#1566	2
#17817	89