Subgroups — #36599719

Order 22784.

716 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₄⋊Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#26021815	C₂	1	1	yes	maximal, characteristic, complemented
3	#26021810	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021655	C₂	1	1	yes	maximal, characteristic
5	#26021655	C₂	1	1	yes	maximal, characteristic
6	#26021193	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021018	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020876	C₂	1	1	yes	maximal, characteristic
9	#26020869	C₂	1	1	yes	maximal, characteristic
10	#26020841	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020834	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020385	C₂	1	1	yes	maximal, characteristic, complemented
13	#26020252	C₂	1	1	yes	maximal, characteristic
14	#26020077	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#2580	C₂	1	1	yes	maximal, characteristic
16	C₂×Q₈×Dic₈₉	—	2	1	no	—
17	C₂×#15667945	C₂²	1	1	yes	characteristic
18	C₂×#15667943	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
20	C₂×#15667933	C₂²	1	1	yes	characteristic
21	C₂×#15667933	C₂²	1	1	yes	characteristic
22	C₂×#15667933	C₂²	1	1	yes	characteristic
23	C₂×#15667933	C₂²	1	1	yes	characteristic
24	C₂×#15667923	C₂²	1	1	yes	characteristic
25	#19151497	—	2	1	no	—
26	#19151497	—	2	1	no	—
27	#19151497	—	2	1	no	—
28	#19151468	C₂²	1	1	yes	characteristic
29	#19151468	C₂²	1	1	yes	characteristic
30	#19151468	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
34	#19151360	C₂²	1	1	yes	characteristic
35	#19151360	C₂²	1	1	yes	characteristic
36	#19151360	C₂²	1	1	yes	characteristic
37	#19151360	C₂²	1	1	yes	characteristic
38	#19151360	C₂²	1	1	yes	characteristic
39	#19151360	C₂²	1	1	yes	characteristic
40	#19151360	C₂²	1	1	yes	characteristic
41	#19151360	C₂²	1	1	yes	characteristic
42	#19151360	C₂²	1	1	yes	characteristic
43	#19151360	C₂²	1	1	yes	characteristic
44	#19151353	C₂²	1	1	yes	characteristic
45	#19151353	C₂²	1	1	yes	characteristic
46	#19151353	C₂²	1	1	yes	characteristic
47	#19151353	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
50	#399×C₈₉	—	2	1	no	—
51	#393×C₈₉	—	2	1	no	—
52	#390×C₈₉	C₂²	1	1	yes	characteristic
53	#390×C₈₉	C₂²	1	1	yes	characteristic
54	#389×C₈₉	C₂²	1	1	yes	characteristic
55	#389×C₈₉	C₂²	1	1	yes	characteristic
56	#385×C₈₉	—	2	1	no	—
57	#385×C₈₉	—	2	1	no	—
58	#382×C₈₉	C₂²	1	1	yes	characteristic
59	C₂²×#10623494	C₂³	1	1	yes	characteristic
60	C₂²×#10623494	C₂³	1	1	yes	characteristic
61	C₂²×#10623494	C₂³	1	1	yes	characteristic
62	C₂²×#10623494	C₂³	1	1	yes	characteristic
63	Q₈×Dic₈₉	—	4	4	no	—
64	C₂×C₄⋊Dic₈₉	—	2	1	no	—
65	C₂×C₄⋊Dic₈₉	—	2	1	no	—
66	C₂×C₄⋊Dic₈₉	—	2	1	no	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄⋊Dic₈₉	—	2	1	no	—
69	C₂×C₄⋊Dic₈₉	—	2	1	no	—
70	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊Dic₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄×Dic₈₉	—	2	1	no	—
75	C₂×C₄×Dic₈₉	—	2	1	no	—
76	C₂×C₄×Dic₈₉	—	2	1	no	—
77	#15667945	—	2	2	no	—
78	#15667943	—	2	2	no	—
79	C₄⋊#10623494	—	2	2	no	—
80	#15667933	—	2	2	no	—
81	#15667933	—	2	2	no	—
82	#15667933	—	2	2	no	—
83	#15667933	—	2	2	no	—
84	#15667923	—	2	2	no	—
85	#15667919	—	2	1	no	—
86	#15667919	—	2	1	no	—
87	#15667919	—	2	1	no	—
88	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
89	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	—	2	2	no	—
92	C₄×Q₈×C₈₉	—	2	2	no	—
93	C₄×D₄×C₈₉	—	2	2	no	—
94	C₄×D₄×C₈₉	—	2	2	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	#95×C₈₉	—	2	1	no	—
112	#95×C₈₉	—	2	1	no	—
113	#95×C₈₉	—	2	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂²×Dic₈₉	—	2	1	no	—
118	C₂²×Dic₈₉	—	2	1	no	—
119	C₂×#10623494	—	2	1	no	—
120	C₂×#10623494	—	2	1	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	1	no	—
124	C₂×#10623494	—	2	1	no	—
125	C₂×#10623494	—	2	1	no	—
126	C₂×#10623494	—	2	1	no	—
127	C₂×#10623494	—	2	1	no	—
128	C₂×#10623494	—	2	1	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	—	2	1	no	—
138	C₄⋊Dic₈₉	—	4	2	no	—
139	C₄⋊Dic₈₉	—	4	2	no	—
140	C₄⋊Dic₈₉	—	4	2	no	—
141	C₄⋊Dic₈₉	—	8	1	no	—
142	C₄⋊Dic₈₉	—	8	1	no	—
143	C₄⋊Dic₈₉	—	8	1	no	—
144	C₄⋊Dic₈₉	#41	1	2	yes	—
145	C₄×Dic₈₉	—	4	2	no	—
146	C₄×Dic₈₉	—	4	2	no	—
147	C₄×Dic₈₉	—	4	2	no	—
148	C₂⁴×C₈₉	—	2	1	no	—
149	C₂×Q₈×C₈₉	—	2	2	no	—
150	C₂×Q₈×C₈₉	—	2	2	no	—
151	C₂×Q₈×C₈₉	—	2	2	no	—
152	C₂×D₄×C₈₉	—	2	1	no	—
153	C₂×D₄×C₈₉	—	2	1	no	—
154	C₂×D₄×C₈₉	—	2	1	no	—
155	C₂×D₄×C₈₉	—	2	1	no	—
156	C₂×D₄×C₈₉	—	2	1	no	—
157	C₂×D₄×C₈₉	#41	1	2	yes	—
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	4	2	no	—
162	C₂²×C₄×C₈₉	—	8	1	no	—
163	C₂²×C₄×C₈₉	—	8	1	no	—
164	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₄⋊C₄×C₈₉	—	2	2	no	—
172	C₄⋊C₄×C₈₉	—	2	2	no	—
173	C₄⋊C₄×C₈₉	—	2	2	no	—
174	C₄⋊C₄×C₈₉	—	2	1	no	—
175	C₄⋊C₄×C₈₉	—	2	1	no	—
176	C₄⋊C₄×C₈₉	—	2	1	no	—
177	C₄⋊C₄×C₈₉	—	2	1	no	—
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	8	1	no	—
181	C₄⋊C₄×C₈₉	—	8	1	no	—
182	C₂²⋊C₄×C₈₉	—	4	2	no	—
183	C₂²⋊C₄×C₈₉	—	4	2	no	—
184	C₂²⋊C₄×C₈₉	—	4	2	no	—
185	C₂²⋊C₄×C₈₉	—	8	1	no	—
186	C₂²⋊C₄×C₈₉	—	8	1	no	—
187	C₄²×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	2	1	no	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	#41	1	2	yes	—
192	C₄²×C₈₉	#41	1	2	yes	—
193	C₂³×C₈₉	—	2	2	no	—
194	C₂³×C₈₉	—	4	1	no	—
195	C₂³×C₈₉	—	4	1	no	—
196	C₂³×C₈₉	—	4	1	no	—
197	C₂³×C₈₉	—	4	1	no	—
198	C₂³×C₈₉	—	4	1	no	—
199	C₂³×C₈₉	—	4	1	no	—
200	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	Q₈×C₈₉	—	2	8	no	—
202	D₄×C₈₉	—	2	2	no	—
203	D₄×C₈₉	—	2	2	no	—
204	D₄×C₈₉	—	4	1	no	—
205	D₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	1	no	—
208	C₂×C₄×C₈₉	—	2	1	no	—
209	C₂×C₄×C₈₉	—	2	1	no	—
210	C₂×C₄×C₈₉	—	2	1	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	4	1	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	—	4	1	no	—
223	C₂×C₄×C₈₉	—	4	1	no	—
224	C₂×C₄×C₈₉	—	4	1	no	—
225	C₂×C₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	4	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	8	4	no	—
230	C₂×C₄×C₈₉	#123	1	2	yes	—
231	C₂×C₄×C₈₉	#123	1	2	yes	—
232	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
233	C₂×C₄×C₈₉	#137	1	2	yes	—
234	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂×Dic₈₉	—	2	2	no	—
241	C₂×Dic₈₉	—	4	1	no	—
242	C₂×Dic₈₉	—	4	1	no	—
243	C₂×Dic₈₉	—	4	1	no	—
244	C₂×Dic₈₉	—	4	1	no	—
245	C₂×Dic₈₉	—	4	1	no	—
246	C₂×Dic₈₉	—	4	1	no	—
247	C₂×Dic₈₉	—	4	1	no	—
248	C₂×Dic₈₉	—	4	1	no	—
249	C₂×Dic₈₉	—	4	1	no	—
250	C₂×Dic₈₉	—	4	1	no	—
251	C₂×Dic₈₉	—	4	1	no	—
252	#10623494	—	4	1	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	#10623494	—	4	1	no	—
256	C₂²×C₈₉	—	4	2	no	—
257	C₂²×C₈₉	—	4	2	no	—
258	C₂²×C₈₉	—	4	2	no	—
259	C₂²×C₈₉	—	8	1	no	—
260	C₂²×C₈₉	—	8	1	no	—
261	C₂²×C₈₉	—	8	1	no	—
262	C₂²×C₈₉	—	8	1	no	—
263	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
264	C₂²×C₈₉	#548	1	1	yes	characteristic
265	C₂²×C₈₉	#548	1	1	yes	characteristic
266	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
267	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
268	C₂²×C₈₉	#576	1	1	yes	characteristic
269	C₂²×C₈₉	#577	1	1	yes	characteristic
270	C₄×C₈₉	—	2	2	no	—
271	C₄×C₈₉	—	2	2	no	—
272	C₄×C₈₉	—	2	2	no	—
273	C₄×C₈₉	—	2	2	no	—
274	C₄×C₈₉	—	4	1	no	—
275	C₄×C₈₉	—	4	1	no	—
276	C₄×C₈₉	—	8	1	no	—
277	C₄×C₈₉	—	8	1	no	—
278	C₄×C₈₉	—	8	1	no	—
279	C₄×C₈₉	#529	1	1	yes	characteristic
280	C₄×C₈₉	#541	1	1	yes	characteristic
281	C₄×C₈₉	#552	1	1	yes	characteristic
282	C₄×C₈₉	#556	1	1	yes	characteristic
283	Dic₈₉	—	4	2	no	—
284	Dic₈₉	—	8	1	no	—
285	Dic₈₉	—	8	1	no	—
286	Dic₈₉	—	8	1	no	—
287	#25002	—	89	1	no	maximal, Sylow
288	C₂×C₈₉	—	8	2	no	—
289	C₂×C₈₉	#2421	1	1	yes	characteristic
290	C₂×C₈₉	#3092	1	1	yes	characteristic
291	C₂×C₈₉	#3096	1	1	yes	characteristic
292	C₂×C₈₉	#3366	1	1	yes	characteristic
293	C₂×C₈₉	#3372	1	1	yes	characteristic
294	C₂×C₈₉	#3373	1	1	yes	characteristic
295	C₂×C₈₉	#3375	1	1	yes	characteristic
296	#2580	D₈₉	1	1	yes	characteristic
297	Q₈×C₄⋊C₄	—	89	1	no	—
298	#2100	—	89	1	no	—
299	#2099	—	89	1	no	—
300	#2071	—	89	1	no	—
301	#2071	—	89	1	no	—
302	#1985	—	89	1	no	—
303	#1949	—	89	1	no	—
304	#1926	—	89	1	no	—
305	#1925	—	89	1	no	—
306	#1921	—	89	1	no	—
307	#1920	—	89	1	no	—
308	#1836	—	89	1	no	—
309	#1802	—	89	1	no	—
310	#1762	—	89	1	no	—
311	C₈₉	#25002	1	1	yes	characteristic, complemented, Sylow
312	C₂×C₄×Q₈	—	178	1	no	—
313	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
314	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
315	C₂×#107	—	89	1	no	—
316	C₂×#106	—	89	1	no	—
317	C₂×C₄⋊C₈	—	89	1	no	—
318	C₂×#102	—	89	1	no	—
319	C₂×#102	—	89	1	no	—
320	C₂×#102	—	89	1	no	—
321	C₂×#102	—	89	1	no	—
322	C₂×#97	—	89	1	no	—
323	#399	—	2	1	no	—
324	#393	—	2	1	no	—
325	#390	C₂×D₈₉	1	1	yes	characteristic
326	#390	C₂×D₈₉	1	1	yes	characteristic
327	#389	—	178	1	no	—
328	#389	—	178	1	no	—
329	#389	—	178	1	no	—
330	#389	C₂×D₈₉	1	1	yes	characteristic
331	#389	C₂×D₈₉	1	1	yes	characteristic
332	#385	—	2	1	no	—
333	#385	—	2	1	no	—
334	#384	—	89	1	no	—
335	#384	—	89	1	no	—
336	#384	—	89	1	no	—
337	#382	C₂×D₈₉	1	1	yes	characteristic
338	C₄×C₄⋊C₄	—	89	1	no	—
339	C₄×C₄⋊C₄	—	89	1	no	—
340	C₄×C₄⋊C₄	—	89	1	no	—
341	#340	—	89	1	no	—
342	#340	—	89	1	no	—
343	#340	—	89	1	no	—
344	#340	—	89	1	no	—
345	#340	—	89	1	no	—
346	#340	—	89	1	no	—
347	#340	—	89	1	no	—
348	#340	—	89	1	no	—
349	#340	—	89	1	no	—
350	#340	—	89	1	no	—
351	#336	—	89	1	no	—
352	#336	—	89	1	no	—
353	#336	—	89	1	no	—
354	#336	—	89	1	no	—
355	C₂²×Q₈	C₂²⋊D₈₉	1	1	yes	characteristic
356	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
357	C₂³×C₄	—	2	1	no	—
358	C₂²×C₈	—	89	1	no	—
359	C₂²×C₈	—	89	1	no	—
360	C₂²×C₈	—	89	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	356	4	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	89	1	no	—
370	C₂×C₄⋊C₄	—	89	1	no	—
371	C₂×C₄⋊C₄	—	89	1	no	—
372	C₂×C₄⋊C₄	—	89	1	no	—
373	C₂×C₄⋊C₄	—	178	1	no	—
374	C₂×C₄⋊C₄	—	178	1	no	—
375	C₂×C₄⋊C₄	—	178	1	no	—
376	C₂×C₄⋊C₄	—	178	1	no	—
377	C₂×C₄⋊C₄	—	178	1	no	—
378	C₂×C₄⋊C₄	—	178	1	no	—
379	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
381	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
382	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
384	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	—	178	1	no	—
391	C₂×C₄²	—	178	1	no	—
392	C₂×C₄²	—	178	1	no	—
393	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
394	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
396	#107	—	178	2	no	—
397	#106	—	178	2	no	—
398	C₄⋊C₈	—	178	2	no	—
399	#102	—	178	2	no	—
400	#102	—	178	2	no	—
401	#102	—	178	2	no	—
402	#102	—	178	2	no	—
403	#97	—	178	2	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	178	1	no	—
409	#95	—	178	1	no	—
410	#95	—	178	1	no	—
411	C₂⁴	—	2	1	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	#13083575	1	2	yes	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	8	1	no	—
426	C₂²×C₄	—	8	1	no	—
427	C₂²×C₄	—	178	1	no	—
428	C₂²×C₄	—	178	1	no	—
429	C₂²×C₄	—	178	1	no	—
430	C₂²×C₄	—	178	1	no	—
431	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
438	C₂×C₈	—	178	1	no	—
439	C₂×C₈	—	178	1	no	—
440	C₂×C₈	—	178	1	no	—
441	C₂×C₈	—	178	1	no	—
442	C₂×C₈	—	178	1	no	—
443	C₂×C₈	—	178	1	no	—
444	C₂×C₈	—	178	1	no	—
445	C₂×C₈	—	178	1	no	—
446	C₂×C₈	—	178	1	no	—
447	C₂×C₈	—	178	1	no	—
448	C₂×C₈	—	178	1	no	—
449	C₂×C₈	—	178	1	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	8	1	no	—
460	C₄⋊C₄	—	8	1	no	—
461	C₄⋊C₄	—	89	2	no	—
462	C₄⋊C₄	—	356	2	no	—
463	C₄⋊C₄	—	356	2	no	—
464	C₄⋊C₄	—	356	2	no	—
465	C₄⋊C₄	—	178	1	no	—
466	C₄⋊C₄	—	178	1	no	—
467	C₄⋊C₄	—	178	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	1	no	—
472	C₄⋊C₄	—	712	1	no	—
473	C₄⋊C₄	—	712	1	no	—
474	C₄⋊C₄	—	712	1	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	4	2	no	—
478	C₂²⋊C₄	—	8	1	no	—
479	C₂²⋊C₄	—	8	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	356	2	no	—
485	C₄²	—	356	2	no	—
486	C₄²	—	356	2	no	—
487	C₄²	#13083573	1	2	yes	—
488	C₄²	#13083573	1	2	yes	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
497	Q₈	—	2	8	no	—
498	D₄	—	2	2	no	—
499	D₄	—	2	2	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	8	4	no	—
526	C₂×C₄	—	356	1	no	—
527	C₂×C₄	—	356	1	no	—
528	C₂×C₄	—	356	1	no	—
529	C₂×C₄	—	356	1	no	—
530	C₂×C₄	—	356	1	no	—
531	C₂×C₄	—	356	1	no	—
532	C₂×C₄	—	356	1	no	—
533	C₂×C₄	—	356	1	no	—
534	C₂×C₄	—	356	1	no	—
535	C₂×C₄	—	356	1	no	—
536	C₂×C₄	—	356	1	no	—
537	C₂×C₄	—	178	2	no	—
538	C₂×C₄	#15667993	1	2	yes	—
539	C₂×C₄	#15667993	1	2	yes	—
540	C₂×C₄	#15668037	1	2	yes	—
541	C₂×C₄	#15668042	1	2	yes	—
542	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
543	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
544	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
545	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
546	C₂×C₄	#15668059	1	1	yes	characteristic
547	C₂×C₄	#15668060	1	1	yes	characteristic
548	C₈	—	356	1	no	—
549	C₈	—	356	1	no	—
550	C₈	—	356	1	no	—
551	C₈	—	356	1	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	—	8	1	no	—
559	C₂²	C₂×#15667993	1	1	yes	characteristic
560	C₂²	#19152255	1	1	yes	characteristic
561	C₂²	#19152259	1	1	yes	characteristic
562	C₂²	C₂×#15668037	1	1	yes	characteristic
563	C₂²	C₂×#15668042	1	1	yes	characteristic
564	C₂²	#19152401	1	1	yes	characteristic
565	C₂²	#19152409	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	356	2	no	—
576	C₄	—	712	1	no	—
577	C₄	—	712	1	no	—
578	C₄	—	712	1	no	—
579	C₄	#19152134	1	1	yes	characteristic
580	C₄	#19152208	1	1	yes	characteristic
581	C₄	#19152290	1	1	yes	characteristic
582	C₄	#19152319	1	1	yes	characteristic
583	C₂	—	8	2	no	—
584	C₂	#26023751	1	1	yes	characteristic
585	C₂	#26030172	1	1	yes	characteristic
586	C₂	#26030204	1	1	yes	characteristic
587	C₂	#26032959	1	1	yes	characteristic
588	C₂	#26033033	1	1	yes	characteristic
589	C₂	#26033040	1	1	yes	characteristic
590	C₂	#26033062	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₈₉
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2580	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×D₄×C₈₉	C₂³
hypercenter	#2580	D₈₉
hypocenter	C₈₉	#25002
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ #2580

Complements

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

N	H ≅ G/N	type
1. Q₈×C₄⋊Dic₈₉	C₂	semidirect
2. #26021815	C₂	semidirect
3. #26021810	C₂	semidirect
6. #26021193	C₂	semidirect
7. #26021018	C₂	semidirect
10. #26020841	C₂	semidirect
11. #26020834	C₂	semidirect
12. #26020385	C₂	semidirect
311. C₈₉	#25002	semidirect

Maximal subgroups

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

subgroup	index
Q₈×C₄⋊Dic₈₉	2
#26021815	2
#26021810	2
#26021655	2
#26021193	2
#26021018	2
#26020876	2
#26020869	2
#26020841	2
#26020834	2
#26020385	2
#26020252	2
#26020077	2
C₈₉×#2580	2
#25002	89