Subgroups — #36613591

Order 22784.

708 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26025283	C₂	1	1	yes	maximal, characteristic, complemented
2	#26021785	C₂	1	1	yes	maximal, characteristic
3	#26021780	C₂	1	1	yes	maximal, characteristic
4	#26021640	C₂	1	1	yes	maximal, characteristic
5	#26021626	C₂	1	1	yes	maximal, characteristic
6	#26021018	C₂	1	1	yes	maximal, characteristic, complemented
7	#26021015	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021010	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020976	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020844	C₂	1	1	yes	maximal, characteristic, complemented
11	#26020830	C₂	1	1	yes	maximal, characteristic, complemented
12	#26020421	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×#2357	C₂	1	1	yes	maximal, characteristic
16	C₂×#15668003	—	2	1	no	—
17	C₂×#15667945	C₂²	1	1	yes	characteristic
18	C₂×#15667945	C₂²	1	1	yes	characteristic
19	C₂×#15667945	C₂²	1	1	yes	characteristic
20	C₂×#15667943	C₂²	1	1	yes	characteristic
21	C₂×#15667943	C₂²	1	1	yes	characteristic
22	C₂×#15667943	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
26	C₂×#15667933	C₂²	1	1	yes	characteristic
27	C₂×#15667933	C₂²	1	1	yes	characteristic
28	C₂×#15667933	C₂²	1	1	yes	characteristic
29	C₂×#15667933	C₂²	1	1	yes	characteristic
30	C₂×#15667923	C₂²	1	1	yes	characteristic
31	#19151530	—	2	1	no	—
32	#19151530	—	2	1	no	—
33	#19151497	—	2	1	no	—
34	#19151496	C₂²	1	1	yes	characteristic
35	#19151496	C₂²	1	1	yes	characteristic
36	#19151468	C₂²	1	1	yes	characteristic
37	#19151468	C₂²	1	1	yes	characteristic
38	#19151468	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₈₉	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	#19151360	C₂²	1	1	yes	characteristic
45	#19151360	C₂²	1	1	yes	characteristic
46	#19151353	C₂²	1	1	yes	characteristic
47	#19151353	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
49	#390×C₈₉	C₂²	1	1	yes	characteristic
50	#390×C₈₉	C₂²	1	1	yes	characteristic
51	#388×C₈₉	—	2	1	no	—
52	#388×C₈₉	—	2	1	no	—
53	#382×C₈₉	C₂²	1	1	yes	characteristic
54	#381×C₈₉	—	2	1	no	—
55	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
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	#15668003	—	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×#13083553	—	2	1	no	—
75	C₂×#13083553	—	2	1	no	—
76	C₂×C₄×Dic₈₉	—	2	1	no	—
77	#15667945	—	2	2	no	—
78	#15667945	—	4	1	no	—
79	#15667945	—	4	1	no	—
80	#15667943	—	2	2	no	—
81	#15667943	—	4	1	no	—
82	#15667943	—	4	1	no	—
83	C₄⋊#10623494	—	2	2	no	—
84	C₄⋊#10623494	—	2	2	no	—
85	C₄⋊#10623494	—	2	2	no	—
86	#15667933	—	2	2	no	—
87	#15667933	—	2	2	no	—
88	#15667933	—	4	1	no	—
89	#15667933	—	4	1	no	—
90	#15667923	—	2	2	no	—
91	#15667919	—	2	1	no	—
92	#15667919	—	2	1	no	—
93	#15667919	—	2	1	no	—
94	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₈₉	—	2	1	no	—
96	C₄×D₄×C₈₉	—	2	2	no	—
97	C₄×D₄×C₈₉	Q₈	1	4	yes	—
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	—	2	1	no	—
109	C₂×C₄²×C₈₉	—	2	1	no	—
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	#95×C₈₉	—	2	1	no	—
114	#95×C₈₉	—	2	1	no	—
115	#95×C₈₉	—	2	1	no	—
116	#95×C₈₉	—	2	1	no	—
117	#95×C₈₉	D₄	1	1	yes	characteristic
118	#95×C₈₉	D₄	1	1	yes	characteristic
119	C₂²×Dic₈₉	—	2	1	no	—
120	C₂²×Dic₈₉	—	2	1	no	—
121	C₂²×Dic₈₉	—	2	1	no	—
122	C₂²×Dic₈₉	—	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	C₂×#10623494	—	2	1	no	—
132	C₂×#10623494	—	2	1	no	—
133	C₂×#10623494	#41	1	2	yes	—
134	C₂×#10623494	#41	1	2	yes	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	—	2	1	no	—
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	—	2	1	no	—
140	C₄⋊Dic₈₉	—	2	1	no	—
141	C₄⋊Dic₈₉	—	2	1	no	—
142	C₄⋊Dic₈₉	—	2	1	no	—
143	C₄⋊Dic₈₉	—	4	2	no	—
144	C₄⋊Dic₈₉	—	4	2	no	—
145	C₄⋊Dic₈₉	—	4	2	no	—
146	C₄⋊Dic₈₉	—	8	1	no	—
147	C₄⋊Dic₈₉	—	8	1	no	—
148	C₄⋊Dic₈₉	—	8	1	no	—
149	#13083553	—	4	2	no	—
150	#13083553	—	4	2	no	—
151	C₄×Dic₈₉	—	4	2	no	—
152	C₂⁴×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	—	2	1	no	—
158	C₂×D₄×C₈₉	C₂×Q₈	1	2	yes	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	1	no	—
162	C₂²×C₄×C₈₉	—	2	1	no	—
163	C₂²×C₄×C₈₉	—	8	1	no	—
164	C₂²×C₄×C₈₉	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	C₂×Q₈	1	2	yes	—
180	C₂²⋊C₄×C₈₉	—	2	4	no	—
181	C₂²⋊C₄×C₈₉	—	4	2	no	—
182	C₂²⋊C₄×C₈₉	—	4	2	no	—
183	C₂²⋊C₄×C₈₉	—	8	1	no	—
184	C₂²⋊C₄×C₈₉	—	8	1	no	—
185	C₄²×C₈₉	—	2	1	no	—
186	C₄²×C₈₉	—	2	1	no	—
187	C₄²×C₈₉	—	2	1	no	—
188	C₄²×C₈₉	—	2	1	no	—
189	C₄²×C₈₉	—	8	1	no	—
190	C₄²×C₈₉	—	8	1	no	—
191	C₄²×C₈₉	C₂×Q₈	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	D₄×C₈₉	—	2	2	no	—
202	D₄×C₈₉	—	2	2	no	—
203	D₄×C₈₉	—	4	1	no	—
204	D₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	2	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	2	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	—	8	4	no	—
229	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
230	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
231	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₈₉	#137	1	2	yes	—
233	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
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	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×Dic₈₉	—	4	1	no	—
240	C₂×Dic₈₉	—	4	1	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	#10623494	—	2	2	no	—
252	#10623494	—	2	2	no	—
253	#10623494	—	4	1	no	—
254	#10623494	—	4	1	no	—
255	C₂²×C₈₉	—	4	2	no	—
256	C₂²×C₈₉	—	4	2	no	—
257	C₂²×C₈₉	—	4	2	no	—
258	C₂²×C₈₉	—	8	1	no	—
259	C₂²×C₈₉	—	8	1	no	—
260	C₂²×C₈₉	—	8	1	no	—
261	C₂²×C₈₉	—	8	1	no	—
262	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
263	C₂²×C₈₉	#547	1	1	yes	characteristic
264	C₂²×C₈₉	#550	1	1	yes	characteristic
265	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
266	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
267	C₂²×C₈₉	#576	1	1	yes	characteristic
268	C₂²×C₈₉	#577	1	1	yes	characteristic
269	C₄×C₈₉	—	2	2	no	—
270	C₄×C₈₉	—	2	2	no	—
271	C₄×C₈₉	—	2	2	no	—
272	C₄×C₈₉	—	2	2	no	—
273	C₄×C₈₉	—	4	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	#533	1	1	yes	characteristic
279	C₄×C₈₉	#544	1	1	yes	characteristic
280	C₄×C₈₉	#552	1	1	yes	characteristic
281	C₄×C₈₉	#553	1	1	yes	characteristic
282	Dic₈₉	—	8	1	no	—
283	Dic₈₉	—	8	1	no	—
284	Dic₈₉	—	8	1	no	—
285	Dic₈₉	—	8	1	no	—
286	#26102	—	89	1	no	maximal, Sylow
287	C₂×C₈₉	—	8	2	no	—
288	C₂×C₈₉	#2441	1	1	yes	characteristic
289	C₂×C₈₉	#3079	1	1	yes	characteristic
290	C₂×C₈₉	#3081	1	1	yes	characteristic
291	C₂×C₈₉	#3345	1	1	yes	characteristic
292	C₂×C₈₉	#3346	1	1	yes	characteristic
293	C₂×C₈₉	#3399	1	1	yes	characteristic
294	C₂×C₈₉	#3400	1	1	yes	characteristic
295	#2552	—	89	1	no	—
296	#2357	D₈₉	1	1	yes	characteristic
297	#2094	—	89	1	no	—
298	#2093	—	89	1	no	—
299	#2067	—	89	1	no	—
300	#2065	—	89	1	no	—
301	#1949	—	89	1	no	—
302	#1948	—	89	1	no	—
303	#1947	—	89	1	no	—
304	#1940	—	89	1	no	—
305	#1921	—	89	1	no	—
306	#1919	—	89	1	no	—
307	#1847	—	89	1	no	—
308	#1802	—	89	1	no	—
309	#1762	—	89	1	no	—
310	C₈₉	#26102	1	1	yes	characteristic, complemented, Sylow
311	C₂×#125	—	178	1	no	—
312	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
313	C₂×#107	—	89	1	no	—
314	C₂×#107	—	89	1	no	—
315	C₂×#107	—	89	1	no	—
316	C₂×#106	—	89	1	no	—
317	C₂×#106	—	89	1	no	—
318	C₂×#106	—	89	1	no	—
319	C₂×C₄⋊C₈	—	89	1	no	—
320	C₂×C₄⋊C₈	—	89	1	no	—
321	C₂×C₄⋊C₈	—	89	1	no	—
322	C₂×#102	—	89	1	no	—
323	C₂×#102	—	89	1	no	—
324	C₂×#102	—	89	1	no	—
325	C₂×#102	—	89	1	no	—
326	C₂×#97	—	89	1	no	—
327	#398	—	178	1	no	—
328	#398	—	178	1	no	—
329	#390	C₂×D₈₉	1	1	yes	characteristic
330	#390	C₂×D₈₉	1	1	yes	characteristic
331	#389	—	89	1	no	—
332	#389	—	89	1	no	—
333	#389	—	178	1	no	—
334	#388	—	2	1	no	—
335	#388	—	2	1	no	—
336	#384	—	89	1	no	—
337	#384	—	89	1	no	—
338	#384	—	89	1	no	—
339	#382	C₂×D₈₉	1	1	yes	characteristic
340	#381	—	2	1	no	—
341	C₄×C₄⋊C₄	—	89	1	no	—
342	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
343	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
344	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
345	C₄×C₂²⋊C₄	—	2	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	#340	—	89	1	no	—
352	#336	—	89	1	no	—
353	#336	—	89	1	no	—
354	C₂²×D₄	C₂²×D₈₉	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	C₂²×C₈	—	89	1	no	—
357	C₂²×C₈	—	89	1	no	—
358	C₂²×C₈	—	89	1	no	—
359	C₂²×C₈	—	89	1	no	—
360	#125	—	356	4	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	Dic₁₇₈	1	4	yes	—
363	C₂×C₄⋊C₄	—	89	1	no	—
364	C₂×C₄⋊C₄	—	89	1	no	—
365	C₂×C₄⋊C₄	—	89	1	no	—
366	C₂×C₄⋊C₄	—	89	1	no	—
367	C₂×C₄⋊C₄	—	178	1	no	—
368	C₂×C₄⋊C₄	—	178	1	no	—
369	C₂×C₄⋊C₄	—	178	1	no	—
370	C₂×C₄⋊C₄	—	178	1	no	—
371	C₂×C₄⋊C₄	—	178	1	no	—
372	C₂×C₄⋊C₄	—	178	1	no	—
373	C₂×C₄⋊C₄	—	178	1	no	—
374	C₂×C₄⋊C₄	—	178	1	no	—
375	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂²⋊D₈₉	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	178	1	no	—
388	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
389	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
391	#107	—	356	1	no	—
392	#107	—	356	1	no	—
393	#107	—	178	2	no	—
394	#106	—	356	1	no	—
395	#106	—	356	1	no	—
396	#106	—	178	2	no	—
397	C₄⋊C₈	—	178	2	no	—
398	C₄⋊C₈	—	178	2	no	—
399	C₄⋊C₈	—	178	2	no	—
400	#102	—	356	1	no	—
401	#102	—	356	1	no	—
402	#102	—	178	2	no	—
403	#102	—	178	2	no	—
404	#97	—	178	2	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	178	1	no	—
410	#95	—	178	1	no	—
411	#95	—	178	1	no	—
412	#95	C₂²⋊D₈₉	1	1	yes	characteristic
413	#95	C₂²⋊D₈₉	1	1	yes	characteristic
414	C₂⁴	—	2	1	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	C₂×Dic₁₇₈	1	2	yes	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	4	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	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	—	89	2	no	—
439	C₂×C₈	—	89	2	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	1	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	—	356	2	no	—
458	C₄⋊C₄	—	356	2	no	—
459	C₄⋊C₄	—	356	2	no	—
460	C₄⋊C₄	—	356	2	no	—
461	C₄⋊C₄	—	356	2	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	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	—	712	1	no	—
471	C₄⋊C₄	—	712	1	no	—
472	C₄⋊C₄	—	712	1	no	—
473	C₄⋊C₄	C₂×Dic₁₇₈	1	2	yes	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	4	2	no	—
477	C₂²⋊C₄	—	8	1	no	—
478	C₂²⋊C₄	—	8	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	2	1	no	—
483	C₄²	—	8	1	no	—
484	C₄²	—	8	1	no	—
485	C₄²	—	356	2	no	—
486	C₄²	C₂×Dic₁₇₈	1	2	yes	—
487	C₄²	#13083574	1	2	yes	—
488	C₂³	—	2	2	no	—
489	C₂³	—	4	1	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	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	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	2	no	—
515	C₂×C₄	—	4	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	—	8	4	no	—
524	C₂×C₄	—	356	1	no	—
525	C₂×C₄	—	356	1	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	#15667991	1	2	yes	—
537	C₂×C₄	#15667991	1	2	yes	—
538	C₂×C₄	#15668037	1	2	yes	—
539	C₂×C₄	#15668042	1	2	yes	—
540	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
541	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
542	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
543	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
544	C₂×C₄	#15668058	1	1	yes	characteristic
545	C₂×C₄	#15668059	1	1	yes	characteristic
546	C₈	—	356	1	no	—
547	C₈	—	356	1	no	—
548	C₈	—	178	2	no	—
549	C₈	—	178	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×#15667991	1	1	yes	characteristic
558	C₂²	#19152247	1	1	yes	characteristic
559	C₂²	#19152267	1	1	yes	characteristic
560	C₂²	C₂×#15668037	1	1	yes	characteristic
561	C₂²	C₂×#15668042	1	1	yes	characteristic
562	C₂²	#19152401	1	1	yes	characteristic
563	C₂²	#19152409	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	712	1	no	—
574	C₄	—	712	1	no	—
575	C₄	—	712	1	no	—
576	C₄	—	712	1	no	—
577	C₄	#19152151	1	1	yes	characteristic
578	C₄	#19152226	1	1	yes	characteristic
579	C₄	#19152287	1	1	yes	characteristic
580	C₄	#19152292	1	1	yes	characteristic
581	C₂	—	8	2	no	—
582	C₂	#26023959	1	1	yes	characteristic
583	C₂	#26030067	1	1	yes	characteristic
584	C₂	#26030083	1	1	yes	characteristic
585	C₂	#26032716	1	1	yes	characteristic
586	C₂	#26032737	1	1	yes	characteristic
587	C₂	#26033290	1	1	yes	characteristic
588	C₂	#26033305	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×#2357	C₂
socle	C₂³×C₈₉	C₂²×D₄
prime radical	C₂²×D₄×C₈₉	C₂³
hypercenter	#2357	D₈₉
hypocenter	C₈₉	#26102
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄×C₄⋊C₄ ◁ #2357

Complements

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

N	H ≅ G/N	type
1. #26025283	C₂	semidirect
6. #26021018	C₂	semidirect
7. #26021015	C₂	semidirect
8. #26021010	C₂	semidirect
9. #26020976	C₂	semidirect
10. #26020844	C₂	semidirect
11. #26020830	C₂	semidirect
12. #26020421	C₂	semidirect
310. C₈₉	#26102	semidirect

Maximal subgroups

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

subgroup	index
#26025283	2
#26021785	2
#26021780	2
#26021640	2
#26021626	2
#26021018	2
#26021015	2
#26021010	2
#26020976	2
#26020844	2
#26020830	2
#26020421	2
#26020252	2
#26020077	2
C₈₉×#2357	2
#26102	89