Subgroups — #36523438

Order 22784.

762 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028882	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019015	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019013	C₂	1	2	yes	maximal, complemented
5	#26019009	C₂	1	2	yes	maximal, complemented
6	#26019006	C₂	1	2	yes	maximal, complemented
7	#26018999	C₂	1	2	yes	maximal, complemented
8	#26018997	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₈₉	C₄	1	1	yes	characteristic
11	C₂²×C₈×D₈₉	C₄	1	1	yes	characteristic
12	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
13	#19151655	C₂²	1	2	yes	—
14	#19151653	—	2	2	no	—
15	#19151650	C₂²	1	4	yes	—
16	#19151648	—	2	2	no	—
17	#19151620	C₂²	1	4	yes	—
18	#19151560	—	2	2	no	—
19	#19151550	—	2	2	no	—
20	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₈₉	C₄	1	1	yes	characteristic
23	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
24	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
25	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
26	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
27	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
28	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
31	#19151351	C₂²	1	2	yes	complemented
32	#19151350	C₂²	1	4	yes	complemented
33	#19151349	C₂²	1	2	yes	complemented
34	#19151348	C₂²	1	4	yes	complemented
35	#432×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	#335×C₈₉	C₂²	1	2	yes	complemented
38	#334×C₈₉	C₂²	1	2	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×#13083557	—	2	4	no	—
43	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
44	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₈₉	—	2	4	no	—
46	C₂×C₈×D₈₉	—	2	4	no	—
47	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
58	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₈₉	D₄	1	1	yes	characteristic
61	C₄²×D₈₉	D₄	1	1	yes	characteristic
62	C₄²×D₈₉	Q₈	1	1	yes	characteristic
63	C₄²×D₈₉	Q₈	1	1	yes	characteristic
64	C₄²×D₈₉	C₂³	1	1	yes	characteristic
65	C₄²×D₈₉	C₂³	1	1	yes	characteristic
66	C₄⋊#10623494	C₂³	1	4	yes	—
67	#15667941	—	2	4	no	—
68	C₂²⋊#10623494	—	2	2	no	—
69	#15667924	—	2	4	no	—
70	#15667923	—	2	2	no	—
71	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
72	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
73	C₄×#10623494	C₂³	1	1	yes	characteristic
74	C₄×#10623494	C₂³	1	1	yes	characteristic
75	C₈×Dic₈₉	—	2	4	no	—
76	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
88	C₂²⋊C₈×C₈₉	—	2	2	no	—
89	#97×C₈₉	—	2	2	no	—
90	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₈₉	—	2	4	no	—
99	C₂×C₄×D₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	4	no	—
102	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
114	#13083557	—	4	8	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	4	no	—
118	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₈×D₈₉	—	2	2	no	—
123	C₈×D₈₉	—	2	2	no	—
124	C₈×D₈₉	—	2	2	no	—
125	C₈×D₈₉	—	2	2	no	—
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	—	2	2	no	—
128	C₈×D₈₉	M₁₆	1	4	yes	complemented
129	C₈×D₈₉	M₁₆	1	4	yes	complemented
130	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
135	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
139	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
141	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
145	C₂×C₈×C₈₉	—	2	2	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	—	2	4	no	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
155	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂²×D₈₉	—	2	2	no	—
158	C₂²×D₈₉	—	2	2	no	—
159	C₂²×D₈₉	—	2	2	no	—
160	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
172	C₂×Dic₈₉	—	2	2	no	—
173	C₂×Dic₈₉	—	2	2	no	—
174	C₂×Dic₈₉	#108	1	4	yes	—
175	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₄×D₈₉	—	2	2	no	—
182	C₄×D₈₉	—	2	2	no	—
183	C₄×D₈₉	—	2	1	no	—
184	C₄×D₈₉	—	2	1	no	—
185	C₄×D₈₉	—	2	2	no	—
186	C₄×D₈₉	—	2	2	no	—
187	C₄×D₈₉	—	2	2	no	—
188	C₄×D₈₉	—	2	2	no	—
189	C₄×D₈₉	—	2	2	no	—
190	C₄×D₈₉	—	2	2	no	—
191	C₄×D₈₉	—	2	2	no	—
192	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
193	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
194	C₄×D₈₉	#135	1	4	yes	—
195	C₈×C₈₉	—	2	1	no	—
196	C₈×C₈₉	—	2	1	no	—
197	C₈×C₈₉	—	4	4	no	—
198	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
199	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
200	#10623494	—	2	1	no	—
201	#10623494	—	2	1	no	—
202	#10623494	—	4	4	no	—
203	#10623494	C₂×M₁₆	1	2	yes	—
204	#10623494	C₂×M₁₆	1	2	yes	—
205	C₂²×C₈₉	—	2	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	C₂×#108	1	2	yes	—
208	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₂×D₈₉	—	2	8	no	—
210	C₂×D₈₉	—	2	1	no	—
211	C₂×D₈₉	—	2	1	no	—
212	C₂×D₈₉	—	2	1	no	—
213	C₂×D₈₉	—	2	1	no	—
214	C₂×D₈₉	#423	1	2	yes	—
215	C₂×D₈₉	#427	1	2	yes	—
216	C₄×C₈₉	—	2	1	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
221	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
222	C₄×C₈₉	C₂×#135	1	2	yes	—
223	Dic₈₉	—	2	1	no	—
224	Dic₈₉	—	2	1	no	—
225	Dic₈₉	#423	1	2	yes	—
226	Dic₈₉	#427	1	2	yes	—
227	Dic₈₉	C₂×#108	1	2	yes	—
228	Dic₈₉	C₂×#108	1	2	yes	—
229	#17793	—	89	1	no	maximal, Sylow
230	C₂×C₈₉	—	2	2	no	—
231	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
232	C₂×C₈₉	C₂×#427	1	1	yes	characteristic
233	C₂×C₈₉	C₂²×#108	1	1	yes	characteristic
234	D₈₉	—	2	2	no	—
235	D₈₉	—	2	2	no	—
236	#2920	—	89	2	no	—
237	C₂²×C₄×C₈	—	89	1	no	—
238	#1568	—	89	2	no	—
239	#1568	—	89	1	no	—
240	#1568	D₈₉	1	1	yes	characteristic, complemented
241	#1567	—	89	2	no	—
242	#1566	—	89	2	no	—
243	#1564	—	89	2	no	—
244	#1564	—	89	2	no	—
245	C₈₉	#17793	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₈	—	89	1	no	—
247	C₂³×C₈	—	89	1	no	—
248	C₂²×C₄²	—	89	1	no	—
249	#432	—	89	2	no	—
250	#432	—	178	2	no	—
251	#432	C₂×D₈₉	1	2	yes	—
252	#431	—	89	4	no	—
253	#431	—	178	2	no	—
254	#423	—	89	4	no	—
255	#407	—	178	2	no	—
256	C₄×M₁₆	—	178	2	no	—
257	C₂×C₄×C₈	—	89	1	no	—
258	C₂×C₄×C₈	—	89	1	no	—
259	C₂×C₄×C₈	—	89	1	no	—
260	C₂×C₄×C₈	—	89	1	no	—
261	C₂×C₄×C₈	—	89	1	no	—
262	C₂×C₄×C₈	—	89	1	no	—
263	C₂×C₄×C₈	—	89	1	no	—
264	C₂×C₄×C₈	—	89	1	no	—
265	C₂×C₄×C₈	—	89	1	no	—
266	C₂×C₄×C₈	—	89	1	no	—
267	C₂×C₄×C₈	—	89	1	no	—
268	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
269	#335	—	89	4	no	—
270	#335	—	89	2	no	—
271	#335	C₂×D₈₉	1	2	yes	complemented
272	#334	—	89	4	no	—
273	#334	—	89	2	no	—
274	#334	C₂×D₈₉	1	2	yes	complemented
275	C₂³×C₄	—	89	1	no	—
276	C₂³×C₄	—	89	1	no	—
277	C₂³×C₄	—	89	1	no	—
278	C₂×M₁₆	—	178	4	no	—
279	C₂²×C₈	—	89	1	no	—
280	C₂²×C₈	—	89	1	no	—
281	C₂²×C₈	—	89	1	no	—
282	C₂²×C₈	—	89	1	no	—
283	C₂²×C₈	—	89	1	no	—
284	C₂²×C₈	—	89	1	no	—
285	C₂²×C₈	—	89	1	no	—
286	C₂²×C₈	—	89	1	no	—
287	C₂²×C₈	—	89	1	no	—
288	C₂²×C₈	—	89	1	no	—
289	C₂²×C₈	—	178	4	no	—
290	C₂²×C₈	—	178	4	no	—
291	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
292	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
293	C₂×C₄²	—	89	1	no	—
294	C₂×C₄²	—	89	1	no	—
295	C₂×C₄²	—	89	1	no	—
296	C₂×C₄²	—	89	1	no	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	89	1	no	—
299	C₂×C₄²	—	89	1	no	—
300	C₂×C₄²	—	89	1	no	—
301	C₂×C₄²	—	89	1	no	—
302	C₂×C₄²	—	89	1	no	—
303	C₂×C₄²	—	89	1	no	—
304	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
305	C₄⋊C₈	—	89	4	no	—
306	C₄⋊C₈	—	178	4	no	—
307	C₄⋊C₈	C₂²×D₈₉	1	4	yes	—
308	C₂²⋊C₈	—	2	2	no	—
309	C₂²⋊C₈	—	178	4	no	—
310	C₂²⋊C₈	—	178	2	no	—
311	#97	—	2	2	no	—
312	#97	—	178	2	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	1	no	—
315	C₄×C₈	—	89	1	no	—
316	C₄×C₈	—	89	1	no	—
317	C₄×C₈	—	89	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	1	no	—
321	C₄×C₈	—	89	1	no	—
322	C₄×C₈	—	89	1	no	—
323	C₄×C₈	—	89	1	no	—
324	C₄×C₈	—	89	1	no	—
325	C₄×C₈	—	178	4	no	—
326	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
327	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
328	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₂⁴	—	89	1	no	—
331	C₂²×C₄	—	89	1	no	—
332	C₂²×C₄	—	89	1	no	—
333	C₂²×C₄	—	89	1	no	—
334	C₂²×C₄	—	89	1	no	—
335	C₂²×C₄	—	89	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	C₂²×C₄	—	89	1	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	—	89	1	no	—
342	C₂²×C₄	—	89	1	no	—
343	C₂²×C₄	—	89	1	no	—
344	C₂²×C₄	—	89	1	no	—
345	C₂²×C₄	—	89	1	no	—
346	C₂²×C₄	—	178	2	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	—	178	4	no	—
349	C₂²×C₄	—	178	4	no	—
350	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
351	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
353	M₁₆	—	356	8	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	4	no	—
357	C₂×C₈	—	89	1	no	—
358	C₂×C₈	—	89	1	no	—
359	C₂×C₈	—	89	4	no	—
360	C₂×C₈	—	89	4	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	—	89	1	no	—
363	C₂×C₈	—	178	2	no	—
364	C₂×C₈	—	178	2	no	—
365	C₂×C₈	—	178	2	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	2	no	—
369	C₂×C₈	—	178	4	no	—
370	C₂×C₈	—	178	2	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
373	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
374	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₄²	—	89	1	no	—
377	C₄²	—	89	1	no	—
378	C₄²	—	89	1	no	—
379	C₄²	—	89	1	no	—
380	C₄²	—	89	1	no	—
381	C₄²	—	89	1	no	—
382	C₄²	—	89	1	no	—
383	C₄²	—	89	1	no	—
384	C₄²	—	89	1	no	—
385	C₄²	—	89	1	no	—
386	C₄²	—	89	1	no	—
387	C₄²	—	89	1	no	—
388	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
389	C₄²	D₄×D₈₉	1	1	yes	characteristic
390	C₄²	Q₈×D₈₉	1	1	yes	characteristic
391	C₄²	C₂³×D₈₉	1	1	yes	characteristic
392	C₂³	—	89	1	no	—
393	C₂³	—	89	1	no	—
394	C₂³	—	178	2	no	—
395	C₂³	—	178	2	no	—
396	C₂³	—	178	2	no	—
397	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	89	4	no	—
403	C₂×C₄	—	89	1	no	—
404	C₂×C₄	—	89	1	no	—
405	C₂×C₄	—	89	1	no	—
406	C₂×C₄	—	89	1	no	—
407	C₂×C₄	—	89	2	no	—
408	C₂×C₄	—	89	2	no	—
409	C₂×C₄	—	89	4	no	—
410	C₂×C₄	—	89	1	no	—
411	C₂×C₄	—	89	1	no	—
412	C₂×C₄	—	178	2	no	—
413	C₂×C₄	—	178	2	no	—
414	C₂×C₄	—	178	2	no	—
415	C₂×C₄	—	178	2	no	—
416	C₂×C₄	—	178	2	no	—
417	C₂×C₄	—	178	2	no	—
418	C₂×C₄	—	178	2	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	178	2	no	—
421	C₂×C₄	—	178	2	no	—
422	C₂×C₄	—	178	1	no	—
423	C₂×C₄	—	178	1	no	—
424	C₂×C₄	—	178	2	no	—
425	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
430	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	4	no	—
434	C₈	—	89	2	no	—
435	C₈	—	89	2	no	—
436	C₈	—	356	4	no	—
437	C₈	—	178	1	no	—
438	C₈	—	178	1	no	—
439	C₈	M₁₆×D₈₉	1	2	yes	—
440	C₈	M₁₆×D₈₉	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	89	2	no	—
444	C₂²	—	89	2	no	—
445	C₂²	—	178	8	no	—
446	C₂²	—	178	1	no	—
447	C₂²	—	178	1	no	—
448	C₂²	—	178	1	no	—
449	C₂²	—	178	1	no	—
450	C₂²	#108×D₈₉	1	2	yes	—
451	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	89	2	no	—
457	C₄	—	89	2	no	—
458	C₄	—	89	2	no	—
459	C₄	—	89	2	no	—
460	C₄	—	178	1	no	—
461	C₄	—	178	1	no	—
462	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
463	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
464	C₄	#135×D₈₉	1	2	yes	—
465	C₂	—	2	2	no	—
466	C₂	—	178	2	no	—
467	C₂	—	178	2	no	—
468	C₂	#423×D₈₉	1	1	yes	characteristic
469	C₂	#427×D₈₉	1	1	yes	characteristic
470	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×#1568	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1568	D₈₉
hypocenter	C₈₉	#17793
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
3. #26019015	C₂	semidirect
4. #26019013	C₂	semidirect
5. #26019009	C₂	semidirect
6. #26019006	C₂	semidirect
7. #26018999	C₂	semidirect
8. #26018997	C₂	semidirect
9. C₈₉×#1568	C₂	semidirect
31. #19151351	C₂²	semidirect
32. #19151350	C₂²	semidirect
33. #19151349	C₂²	semidirect
34. #19151348	C₂²	semidirect
37. #335×C₈₉	C₂²	semidirect
38. #334×C₈₉	C₂²	semidirect
128. C₈×D₈₉	M₁₆	semidirect
129. C₈×D₈₉	M₁₆	semidirect
240. #1568	D₈₉	semidirect
245. C₈₉	#17793	semidirect
271. #335	C₂×D₈₉	semidirect
274. #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
#26028882	2
C₂×C₄×C₈×D₈₉	2
#26019015	2
#26019013	2
#26019009	2
#26019006	2
#26018999	2
#26018997	2
C₈₉×#1568	2
#17793	89