Subgroups — #36570388

Order 22784.

1316 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029169	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029053	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028799	C₂	1	2	yes	maximal, complemented
4	#26021151	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021146	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020755	C₂	1	2	yes	maximal, complemented
7	#26020616	C₂	1	2	yes	maximal, complemented
8	#26020306	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020216	C₂	1	2	yes	maximal, complemented
10	#26020094	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3584	C₂	1	1	yes	maximal, characteristic
12	#19152365	C₂²	1	2	yes	complemented
13	#41×Dic₈₉	C₂²	1	2	yes	complemented
14	#19151720	—	2	2	no	—
15	#19151715	—	2	2	no	—
16	#19151710	—	2	1	no	—
17	#19151705	—	2	1	no	—
18	#19151699	—	2	2	no	—
19	C₂×#15667948	C₂²	1	1	yes	characteristic, complemented
20	#19151636	C₂²	1	1	yes	characteristic, complemented
21	#19151615	—	2	4	no	—
22	#19151615	C₂²	1	2	yes	—
23	#19151615	C₂²	1	2	yes	complemented
24	#19151615	C₂²	1	2	yes	complemented
25	C₂×#15667939	—	2	4	no	—
26	C₂×#15667939	C₂²	1	1	yes	characteristic
27	C₂×#15667939	C₂²	1	2	yes	complemented
28	#19151594	C₂²	1	1	yes	characteristic
29	#19151594	C₂²	1	2	yes	complemented
30	#19151572	C₂²	1	2	yes	complemented
31	#19151565	C₂²	1	2	yes	complemented
32	#19151553	C₂²	1	1	yes	characteristic, complemented
33	C₂×#15667922	C₂²	1	1	yes	characteristic, complemented
34	#19151370	C₂²	1	2	yes	complemented
35	#19151362	C₂²	1	1	yes	characteristic, complemented
36	#19151359	C₂²	1	1	yes	characteristic, complemented
37	#585×C₈₉	C₂²	1	2	yes	—
38	#578×C₈₉	—	2	1	no	—
39	#578×C₈₉	C₄	1	2	yes	complemented
40	#577×C₈₉	—	2	2	no	—
41	#577×C₈₉	C₄	1	4	yes	complemented
42	#576×C₈₉	—	2	1	no	—
43	#576×C₈₉	C₄	1	2	yes	complemented
44	#575×C₈₉	—	2	2	no	—
45	#575×C₈₉	C₂²	1	2	yes	—
46	C₂×#135×C₈₉	—	2	2	no	—
47	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
50	#15668019	—	2	4	no	—
51	#15668019	—	4	2	no	—
52	C₂×#13083558	—	2	4	no	—
53	C₂×#13083558	C₂³	1	2	yes	—
54	C₂×#13083558	C₂³	1	1	yes	characteristic
55	C₂²×#10623494	C₂³	1	1	yes	characteristic
56	Q₈×Dic₈₉	—	2	2	no	—
57	D₄×Dic₈₉	—	2	2	no	—
58	D₄×Dic₈₉	—	4	2	no	—
59	#15667971	—	2	2	no	—
60	#15667971	C₂³	1	2	yes	—
61	#15667971	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₈₉	—	2	2	no	—
63	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
64	#15667948	—	2	1	no	—
65	#15667948	—	2	1	no	—
66	#15667946	—	2	1	no	—
67	#15667944	—	2	1	no	—
68	#15667939	—	2	4	no	—
69	#15667939	—	2	2	no	—
70	#15667939	—	2	2	no	—
71	#15667939	—	2	4	no	—
72	#15667939	—	2	4	no	—
73	#15667939	D₄	1	4	yes	—
74	#15667936	—	2	2	no	—
75	#15667936	—	2	1	no	—
76	#15667933	—	2	2	no	—
77	#15667933	—	2	1	no	—
78	#15667927	—	4	2	no	—
79	C₂²⋊#10623494	—	4	2	no	—
80	#15667922	—	2	1	no	—
81	#15667922	—	2	1	no	—
82	#15667922	—	2	1	no	—
83	C₈×Dic₈₉	—	2	1	no	—
84	2₋¹⁺⁴×C₈₉	—	2	2	no	—
85	2₋¹⁺⁴×C₈₉	—	2	2	no	—
86	2₋¹⁺⁴×C₈₉	C₂×C₄	1	4	yes	complemented
87	H(5,𝔽₂)×C₈₉	—	2	2	no	—
88	H(5,𝔽₂)×C₈₉	—	2	2	no	—
89	H(5,𝔽₂)×C₈₉	—	4	2	no	—
90	H(5,𝔽₂)×C₈₉	C₂×C₄	1	4	yes	complemented
91	C₂×#41×C₈₉	—	2	4	no	—
92	C₂×#41×C₈₉	—	2	4	no	—
93	C₂×#41×C₈₉	—	4	2	no	—
94	C₂×#41×C₈₉	C₂³	1	2	yes	—
95	C₂×#41×C₈₉	C₂³	1	2	yes	—
96	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
97	#137×C₈₉	—	2	2	no	—
98	#137×C₈₉	—	2	4	no	—
99	#137×C₈₉	—	2	4	no	—
100	#137×C₈₉	C₂×C₄	1	4	yes	complemented
101	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
102	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
103	AGL(1,ℤ/8)×C₈₉	—	2	4	no	—
104	AGL(1,ℤ/8)×C₈₉	C₂×C₄	1	4	yes	complemented
105	#135×C₈₉	—	2	4	no	—
106	#135×C₈₉	—	2	2	no	—
107	#135×C₈₉	—	2	4	no	—
108	#135×C₈₉	—	2	2	no	—
109	#135×C₈₉	—	2	1	no	—
110	#135×C₈₉	—	2	1	no	—
111	#135×C₈₉	—	2	1	no	—
112	#135×C₈₉	—	2	1	no	—
113	#135×C₈₉	C₂×C₄	1	2	yes	—
114	#135×C₈₉	C₂×C₄	1	2	yes	—
115	#135×C₈₉	D₄	1	2	yes	—
116	#135×C₈₉	D₄	1	2	yes	—
117	C₂×Q₁₆×C₈₉	—	2	2	no	—
118	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×Q₁₆×C₈₉	D₄	1	1	yes	characteristic
120	C₂×SD₁₆×C₈₉	—	2	4	no	—
121	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
122	C₂×SD₁₆×C₈₉	D₄	1	2	yes	—
123	C₂×D₈×C₈₉	—	2	2	no	—
124	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×D₈×C₈₉	D₄	1	1	yes	characteristic
126	#131×C₈₉	—	2	1	no	—
127	#131×C₈₉	—	2	1	no	—
128	#131×C₈₉	C₂×C₄	1	2	yes	complemented
129	#131×C₈₉	C₂×C₄	1	2	yes	complemented
130	C₂×M₁₆×C₈₉	—	2	1	no	—
131	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₈₉	—	2	1	no	—
133	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂²×Dic₈₉	—	2	1	no	—
135	C₂²×Dic₈₉	—	4	2	no	—
136	#13083558	—	2	1	no	—
137	#13083558	—	2	2	no	—
138	#13083558	—	2	2	no	—
139	#13083558	—	4	4	no	—
140	#13083558	C₂×D₄	1	2	yes	—
141	C₂×#10623494	—	2	1	no	—
142	C₂×#10623494	—	2	1	no	—
143	C₂×#10623494	—	2	1	no	—
144	C₂×#10623494	—	2	1	no	—
145	C₂×#10623494	—	2	2	no	—
146	C₂×#10623494	—	4	4	no	—
147	C₄⋊Dic₈₉	—	2	2	no	—
148	C₄⋊Dic₈₉	—	2	1	no	—
149	C₄⋊Dic₈₉	—	4	2	no	—
150	C₂²⋊Dic₈₉	—	2	2	no	—
151	C₂²⋊Dic₈₉	—	2	1	no	—
152	C₂²⋊Dic₈₉	—	4	2	no	—
153	C₄×Dic₈₉	—	2	1	no	—
154	C₄×Dic₈₉	—	2	2	no	—
155	C₄×Dic₈₉	—	2	1	no	—
156	C₄×Dic₈₉	—	4	2	no	—
157	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
158	#41×C₈₉	—	2	1	no	—
159	#41×C₈₉	—	2	2	no	—
160	#41×C₈₉	—	2	2	no	—
161	#41×C₈₉	—	2	1	no	—
162	#41×C₈₉	—	2	4	no	—
163	#41×C₈₉	—	2	4	no	—
164	#41×C₈₉	—	2	4	no	—
165	#41×C₈₉	—	2	4	no	—
166	#41×C₈₉	—	2	2	no	—
167	#41×C₈₉	—	2	2	no	—
168	#41×C₈₉	—	2	2	no	—
169	#41×C₈₉	—	2	2	no	—
170	#41×C₈₉	—	4	4	no	—
171	#41×C₈₉	—	4	4	no	—
172	#41×C₈₉	—	4	4	no	—
173	#41×C₈₉	—	4	4	no	—
174	#41×C₈₉	—	4	2	no	—
175	#41×C₈₉	—	4	2	no	—
176	#41×C₈₉	C₂²×C₄	1	4	yes	—
177	#41×C₈₉	C₂²×C₄	1	2	yes	—
178	#41×C₈₉	C₂×D₄	1	4	yes	—
179	#41×C₈₉	C₂×D₄	1	2	yes	—
180	C₂×Q₈×C₈₉	—	2	4	no	—
181	C₂×Q₈×C₈₉	—	2	4	no	—
182	C₂×Q₈×C₈₉	—	4	2	no	—
183	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
184	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
185	C₂×Q₈×C₈₉	#41	1	1	yes	characteristic
186	C₂×D₄×C₈₉	—	2	2	no	—
187	C₂×D₄×C₈₉	—	2	1	no	—
188	C₂×D₄×C₈₉	—	2	4	no	—
189	C₂×D₄×C₈₉	—	2	4	no	—
190	C₂×D₄×C₈₉	—	2	2	no	—
191	C₂×D₄×C₈₉	—	4	4	no	—
192	C₂×D₄×C₈₉	—	4	2	no	—
193	C₂×D₄×C₈₉	—	4	4	no	—
194	C₂×D₄×C₈₉	—	4	4	no	—
195	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
196	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
197	C₂×D₄×C₈₉	#41	1	1	yes	characteristic
198	C₂²×C₄×C₈₉	—	2	2	no	—
199	C₂²×C₄×C₈₉	—	2	1	no	—
200	C₂²×C₄×C₈₉	—	2	2	no	—
201	C₂²×C₄×C₈₉	—	4	4	no	—
202	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
203	Q₁₆×C₈₉	—	2	4	no	—
204	Q₁₆×C₈₉	—	2	1	no	—
205	Q₁₆×C₈₉	—	2	1	no	—
206	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
207	Q₁₆×C₈₉	C₂²⋊C₄	1	2	yes	—
208	SD₁₆×C₈₉	—	2	4	no	—
209	SD₁₆×C₈₉	—	2	4	no	—
210	SD₁₆×C₈₉	—	2	2	no	—
211	SD₁₆×C₈₉	—	2	2	no	—
212	SD₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
213	SD₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
214	D₈×C₈₉	—	2	4	no	—
215	D₈×C₈₉	—	2	1	no	—
216	D₈×C₈₉	—	2	1	no	—
217	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
218	D₈×C₈₉	C₂²⋊C₄	1	2	yes	—
219	M₁₆×C₈₉	—	2	1	no	—
220	M₁₆×C₈₉	—	2	2	no	—
221	M₁₆×C₈₉	—	2	2	no	—
222	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
223	C₂×C₈×C₈₉	—	2	1	no	—
224	C₂×C₈×C₈₉	—	2	2	no	—
225	C₂×C₈×C₈₉	—	2	2	no	—
226	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
227	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
228	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
231	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₈₉	—	2	2	no	—
233	C₂³×C₈₉	—	2	1	no	—
234	C₂³×C₈₉	—	2	2	no	—
235	C₂³×C₈₉	—	4	4	no	—
236	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
237	Q₈×C₈₉	—	2	1	no	—
238	Q₈×C₈₉	—	2	2	no	—
239	Q₈×C₈₉	—	2	2	no	—
240	Q₈×C₈₉	—	2	2	no	—
241	Q₈×C₈₉	—	4	4	no	—
242	Q₈×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
243	Q₈×C₈₉	C₄×D₄	1	2	yes	—
244	D₄×C₈₉	—	2	2	no	—
245	D₄×C₈₉	—	2	4	no	—
246	D₄×C₈₉	—	2	2	no	—
247	D₄×C₈₉	—	2	4	no	—
248	D₄×C₈₉	—	2	2	no	—
249	D₄×C₈₉	—	2	2	no	—
250	D₄×C₈₉	—	2	1	no	—
251	D₄×C₈₉	—	2	2	no	—
252	D₄×C₈₉	—	4	4	no	—
253	D₄×C₈₉	—	4	4	no	—
254	D₄×C₈₉	—	4	4	no	—
255	D₄×C₈₉	—	4	2	no	—
256	D₄×C₈₉	—	4	2	no	—
257	D₄×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
258	D₄×C₈₉	C₄×D₄	1	2	yes	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	1	no	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	—	2	4	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	4	4	no	—
267	C₂×C₄×C₈₉	—	4	4	no	—
268	C₂×C₄×C₈₉	—	4	4	no	—
269	C₂×C₄×C₈₉	—	4	2	no	—
270	C₂×C₄×C₈₉	—	4	2	no	—
271	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
272	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
277	C₂×Dic₈₉	—	2	2	no	—
278	C₂×Dic₈₉	—	4	2	no	—
279	C₂×Dic₈₉	—	4	1	no	—
280	C₂×Dic₈₉	—	8	1	no	—
281	C₂×Dic₈₉	—	8	4	no	—
282	C₈×C₈₉	—	2	2	no	—
283	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	#10623494	—	2	2	no	—
288	#10623494	—	4	2	no	—
289	#10623494	—	4	1	no	—
290	C₂²×C₈₉	—	2	2	no	—
291	C₂²×C₈₉	—	2	4	no	—
292	C₂²×C₈₉	—	4	1	no	—
293	C₂²×C₈₉	—	4	2	no	—
294	C₂²×C₈₉	—	8	2	no	—
295	C₂²×C₈₉	—	8	1	no	—
296	C₂²×C₈₉	—	8	2	no	—
297	C₂²×C₈₉	—	16	4	no	—
298	C₂²×C₈₉	#518	1	1	yes	characteristic
299	C₂²×C₈₉	D₄²	1	1	yes	characteristic
300	C₂²×C₈₉	#546	1	1	yes	characteristic
301	C₄×C₈₉	—	2	2	no	—
302	C₄×C₈₉	—	2	4	no	—
303	C₄×C₈₉	—	4	2	no	—
304	C₄×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
305	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
306	C₄×C₈₉	D₄²	1	1	yes	characteristic
307	C₄×C₈₉	#546	1	1	yes	characteristic
308	Dic₈₉	—	4	2	no	—
309	Dic₈₉	—	8	1	no	—
310	Dic₈₉	—	8	2	no	—
311	#22461	—	89	1	no	maximal, Sylow
312	C₂×C₈₉	—	2	1	no	—
313	C₂×C₈₉	—	2	1	no	—
314	C₂×C₈₉	—	2	1	no	—
315	C₂×C₈₉	—	4	4	no	—
316	C₂×C₈₉	—	4	2	no	—
317	C₂×C₈₉	—	8	2	no	—
318	C₂×C₈₉	D₄×C₂²⋊C₄	1	1	yes	characteristic
319	#3584	D₈₉	1	1	yes	characteristic
320	#2957	—	89	1	no	—
321	#2943	—	89	1	no	—
322	#2901	—	89	2	no	—
323	#1976	—	89	1	no	—
324	#1975	—	89	1	no	—
325	#1906	—	89	2	no	—
326	#1881	—	89	2	no	—
327	#1814	—	89	1	no	—
328	#1794	—	89	2	no	—
329	#1765	—	89	1	no	—
330	C₈₉	#22461	1	1	yes	characteristic, complemented, Sylow
331	#585	C₂×D₈₉	1	2	yes	—
332	#578	—	2	1	no	—
333	#578	Dic₈₉	1	2	yes	complemented
334	#577	—	2	2	no	—
335	#577	Dic₈₉	1	4	yes	complemented
336	#576	—	2	1	no	—
337	#576	Dic₈₉	1	2	yes	complemented
338	#575	—	2	2	no	—
339	#575	C₂×D₈₉	1	2	yes	—
340	C₂×#135	—	2	2	no	—
341	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
342	C₂×#135	C₂×D₈₉	1	1	yes	characteristic
343	#568	—	89	2	no	—
344	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
345	C₄×#41	—	89	2	no	—
346	#444	—	178	2	no	—
347	#443	—	178	2	no	—
348	#442	—	178	1	no	—
349	#441	—	178	1	no	—
350	#440	—	178	2	no	—
351	C₂×#108	—	89	1	no	—
352	#427	—	89	1	no	—
353	#421	—	89	2	no	—
354	#421	—	89	2	no	—
355	#421	—	89	2	no	—
356	#421	—	178	4	no	—
357	C₂×#104	—	89	1	no	—
358	C₂×#104	—	89	2	no	—
359	C₂×#104	—	178	4	no	—
360	#416	—	89	1	no	—
361	#416	—	89	2	no	—
362	#410	—	89	2	no	—
363	#408	—	89	2	no	—
364	#405	—	89	1	no	—
365	C₂×#97	—	89	1	no	—
366	#344	—	89	2	no	—
367	#341	—	89	1	no	—
368	#339	—	89	1	no	—
369	2₋¹⁺⁴	—	2	2	no	—
370	2₋¹⁺⁴	—	2	2	no	—
371	2₋¹⁺⁴	C₂×Dic₈₉	1	4	yes	complemented
372	H(5,𝔽₂)	—	2	2	no	—
373	H(5,𝔽₂)	—	2	2	no	—
374	H(5,𝔽₂)	—	4	2	no	—
375	H(5,𝔽₂)	C₂×Dic₈₉	1	4	yes	complemented
376	C₂×#41	—	2	4	no	—
377	C₂×#41	—	2	4	no	—
378	C₂×#41	—	4	2	no	—
379	C₂×#41	C₂²×D₈₉	1	2	yes	—
380	C₂×#41	C₂²×D₈₉	1	2	yes	—
381	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
382	#137	—	2	2	no	—
383	#137	—	2	4	no	—
384	#137	—	2	4	no	—
385	#137	C₂×Dic₈₉	1	4	yes	complemented
386	AGL(1,ℤ/8)	—	2	2	no	—
387	AGL(1,ℤ/8)	—	2	4	no	—
388	AGL(1,ℤ/8)	—	2	4	no	—
389	AGL(1,ℤ/8)	C₂×Dic₈₉	1	4	yes	complemented
390	#135	—	2	4	no	—
391	#135	—	2	2	no	—
392	#135	—	2	4	no	—
393	#135	—	2	2	no	—
394	#135	—	2	1	no	—
395	#135	—	2	1	no	—
396	#135	—	2	1	no	—
397	#135	—	2	1	no	—
398	#135	C₂×Dic₈₉	1	2	yes	—
399	#135	C₂×Dic₈₉	1	2	yes	—
400	#135	C₂²⋊D₈₉	1	2	yes	—
401	#135	C₂²⋊D₈₉	1	2	yes	—
402	C₂×Q₁₆	—	2	2	no	—
403	C₂×Q₁₆	C₂×Dic₈₉	1	1	yes	characteristic, complemented
404	C₂×Q₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
405	C₂×SD₁₆	—	2	4	no	—
406	C₂×SD₁₆	C₂×Dic₈₉	1	2	yes	complemented
407	C₂×SD₁₆	C₂²⋊D₈₉	1	2	yes	—
408	C₂×D₈	—	2	2	no	—
409	C₂×D₈	C₂×Dic₈₉	1	1	yes	characteristic, complemented
410	C₂×D₈	C₂²⋊D₈₉	1	1	yes	characteristic
411	#131	—	2	1	no	—
412	#131	—	2	1	no	—
413	#131	—	356	2	no	—
414	#131	—	178	4	no	—
415	#131	C₂×Dic₈₉	1	2	yes	complemented
416	#131	C₂×Dic₈₉	1	2	yes	complemented
417	C₂×M₁₆	—	2	1	no	—
418	C₂×M₁₆	—	89	1	no	—
419	C₂×M₁₆	—	89	2	no	—
420	C₂×M₁₆	—	178	4	no	—
421	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	—	89	1	no	—
424	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
425	C₄×Q₈	—	178	2	no	—
426	C₄×D₄	—	356	2	no	—
427	C₄×D₄	—	178	2	no	—
428	#117	—	89	2	no	—
429	#117	—	89	1	no	—
430	#117	—	178	2	no	—
431	C₂×C₄²	—	89	1	no	—
432	C₂×C₄²	—	178	2	no	—
433	#108	—	178	1	no	—
434	#108	—	178	1	no	—
435	#107	—	178	1	no	—
436	#106	—	178	1	no	—
437	#104	—	89	4	no	—
438	#104	—	178	2	no	—
439	#104	—	178	2	no	—
440	#104	—	178	4	no	—
441	#104	—	178	4	no	—
442	#104	—	178	4	no	—
443	#103	—	178	2	no	—
444	#103	—	178	1	no	—
445	#102	—	178	2	no	—
446	#102	—	178	1	no	—
447	#99	—	356	2	no	—
448	C₂²⋊C₈	—	356	2	no	—
449	#97	—	178	1	no	—
450	#97	—	178	1	no	—
451	#97	—	178	1	no	—
452	C₄×C₈	—	178	1	no	—
453	#41	—	2	1	no	—
454	#41	—	2	2	no	—
455	#41	—	2	2	no	—
456	#41	—	2	1	no	—
457	#41	—	2	4	no	—
458	#41	—	2	4	no	—
459	#41	—	2	4	no	—
460	#41	—	2	4	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	#41	—	2	2	no	—
464	#41	—	2	2	no	—
465	#41	—	4	4	no	—
466	#41	—	4	4	no	—
467	#41	—	4	4	no	—
468	#41	—	4	4	no	—
469	#41	—	4	2	no	—
470	#41	—	4	2	no	—
471	#41	C₂²×Dic₈₉	1	2	yes	—
472	#41	C₂²×Dic₈₉	1	4	yes	—
473	#41	D₄×D₈₉	1	2	yes	—
474	#41	C₂×C₂²⋊D₈₉	1	4	yes	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	—	2	4	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	C₂²×Dic₈₉	1	2	yes	—
479	C₂×Q₈	C₂×C₂²⋊D₈₉	1	2	yes	—
480	C₂×Q₈	#13083573	1	1	yes	characteristic
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	—	4	2	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	C₂²×Dic₈₉	1	2	yes	—
491	C₂×D₄	C₂×C₂²⋊D₈₉	1	2	yes	—
492	C₂×D₄	#13083573	1	1	yes	characteristic
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	4	4	no	—
497	C₂²×C₄	—	356	2	no	—
498	C₂²×C₄	—	178	1	no	—
499	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
500	Q₁₆	—	2	4	no	—
501	Q₁₆	—	2	1	no	—
502	Q₁₆	—	2	1	no	—
503	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
504	Q₁₆	C₂²⋊Dic₈₉	1	2	yes	—
505	SD₁₆	—	2	4	no	—
506	SD₁₆	—	2	4	no	—
507	SD₁₆	—	2	2	no	—
508	SD₁₆	—	2	2	no	—
509	SD₁₆	C₂²⋊Dic₈₉	1	4	yes	—
510	SD₁₆	C₂²⋊Dic₈₉	1	4	yes	—
511	D₈	—	2	4	no	—
512	D₈	—	2	1	no	—
513	D₈	—	2	1	no	—
514	D₈	C₂²⋊Dic₈₉	1	2	yes	—
515	D₈	C₂²⋊Dic₈₉	1	2	yes	—
516	M₁₆	—	2	1	no	—
517	M₁₆	—	2	2	no	—
518	M₁₆	—	2	2	no	—
519	M₁₆	—	89	2	no	—
520	M₁₆	—	356	4	no	—
521	M₁₆	—	178	2	no	—
522	M₁₆	—	178	2	no	—
523	M₁₆	—	178	1	no	—
524	M₁₆	C₂²×Dic₈₉	1	2	yes	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	2	no	—
527	C₂×C₈	—	2	2	no	—
528	C₂×C₈	—	356	4	no	—
529	C₂×C₈	—	178	1	no	—
530	C₂×C₈	—	178	1	no	—
531	C₂×C₈	—	178	1	no	—
532	C₂×C₈	—	178	2	no	—
533	C₂×C₈	—	178	1	no	—
534	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
535	C₂×C₈	C₂²×Dic₈₉	1	1	yes	characteristic
536	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
537	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
538	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
539	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
540	C₄⋊C₄	—	356	2	no	—
541	C₄⋊C₄	—	178	2	no	—
542	C₄⋊C₄	—	178	1	no	—
543	C₂²⋊C₄	—	356	2	no	—
544	C₂²⋊C₄	—	178	1	no	—
545	C₂²⋊C₄	—	178	2	no	—
546	C₄²	—	89	2	no	—
547	C₄²	—	356	2	no	—
548	C₄²	—	178	2	no	—
549	C₄²	—	178	1	no	—
550	C₄²	—	178	1	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	1	no	—
553	C₂³	—	2	2	no	—
554	C₂³	—	4	4	no	—
555	C₂³	#15668057	1	1	yes	characteristic
556	Q₈	—	2	1	no	—
557	Q₈	—	2	2	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	2	no	—
560	Q₈	—	4	4	no	—
561	Q₈	C₂×C₂²⋊Dic₈₉	1	4	yes	—
562	Q₈	D₄×Dic₈₉	1	2	yes	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	2	2	no	—
566	D₄	—	2	4	no	—
567	D₄	—	2	1	no	—
568	D₄	—	2	2	no	—
569	D₄	—	2	2	no	—
570	D₄	—	2	2	no	—
571	D₄	—	4	4	no	—
572	D₄	—	4	4	no	—
573	D₄	—	4	4	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	C₂×C₂²⋊Dic₈₉	1	4	yes	—
577	D₄	D₄×Dic₈₉	1	2	yes	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	4	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	2	no	—
590	C₂×C₄	—	356	2	no	—
591	C₂×C₄	—	356	1	no	—
592	C₂×C₄	—	178	2	no	—
593	C₂×C₄	—	712	1	no	—
594	C₂×C₄	—	712	4	no	—
595	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
596	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
597	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
598	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
599	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
600	C₂×C₄	#15668057	1	1	yes	characteristic
601	C₈	—	2	2	no	—
602	C₈	—	356	2	no	—
603	C₈	—	356	1	no	—
604	C₈	—	178	2	no	—
605	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
606	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
607	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
608	C₈	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
609	C₂²	—	2	2	no	—
610	C₂²	—	2	4	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	8	2	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	2	no	—
616	C₂²	—	16	4	no	—
617	C₂²	#19152073	1	1	yes	characteristic
618	C₂²	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
619	C₂²	#19152242	1	1	yes	characteristic
620	C₄	—	2	2	no	—
621	C₄	—	2	4	no	—
622	C₄	—	4	2	no	—
623	C₄	—	356	2	no	—
624	C₄	—	712	2	no	—
625	C₄	—	712	1	no	—
626	C₄	C₂²×C₂²⋊Dic₈₉	1	1	yes	characteristic
627	C₄	C₂×D₄×Dic₈₉	1	1	yes	characteristic
628	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
629	C₄	#19152242	1	1	yes	characteristic
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	4	no	—
634	C₂	—	4	2	no	—
635	C₂	—	8	2	no	—
636	C₂	D₄×C₂²⋊Dic₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3584	C₂
socle	C₂×C₈₉	D₄×C₂²⋊C₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3584	D₈₉
hypocenter	C₈₉	#22461
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3584

Complements

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

N	H ≅ G/N	type
1. #26029169	C₂	semidirect
2. #26029053	C₂	semidirect
3. #26028799	C₂	semidirect
4. #26021151	C₂	semidirect
5. #26021146	C₂	semidirect
6. #26020755	C₂	semidirect
7. #26020616	C₂	semidirect
8. #26020306	C₂	semidirect
9. #26020216	C₂	semidirect
10. #26020094	C₂	semidirect
12. #19152365	C₂²	semidirect
13. #41×Dic₈₉	C₂²	semidirect
19. C₂×#15667948	C₂²	semidirect
20. #19151636	C₂²	semidirect
23. #19151615	C₂²	semidirect
24. #19151615	C₂²	semidirect
27. C₂×#15667939	C₂²	semidirect
29. #19151594	C₂²	semidirect
30. #19151572	C₂²	semidirect
31. #19151565	C₂²	semidirect
32. #19151553	C₂²	semidirect
33. C₂×#15667922	C₂²	semidirect
34. #19151370	C₂²	semidirect
35. #19151362	C₂²	semidirect
36. #19151359	C₂²	semidirect
39. #578×C₈₉	C₄	semidirect
41. #577×C₈₉	C₄	semidirect
43. #576×C₈₉	C₄	semidirect
86. 2₋¹⁺⁴×C₈₉	C₂×C₄	semidirect
90. H(5,𝔽₂)×C₈₉	C₂×C₄	semidirect
100. #137×C₈₉	C₂×C₄	semidirect
104. AGL(1,ℤ/8)×C₈₉	C₂×C₄	semidirect
118. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
121. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
124. C₂×D₈×C₈₉	C₂×C₄	semidirect
128. #131×C₈₉	C₂×C₄	semidirect
129. #131×C₈₉	C₂×C₄	semidirect
330. C₈₉	#22461	semidirect
333. #578	Dic₈₉	semidirect
335. #577	Dic₈₉	semidirect
337. #576	Dic₈₉	semidirect
371. 2₋¹⁺⁴	C₂×Dic₈₉	semidirect
375. H(5,𝔽₂)	C₂×Dic₈₉	semidirect
385. #137	C₂×Dic₈₉	semidirect
389. AGL(1,ℤ/8)	C₂×Dic₈₉	semidirect
403. C₂×Q₁₆	C₂×Dic₈₉	semidirect
406. C₂×SD₁₆	C₂×Dic₈₉	semidirect
409. C₂×D₈	C₂×Dic₈₉	semidirect
415. #131	C₂×Dic₈₉	semidirect
416. #131	C₂×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029169	2
#26029053	2
#26028799	2
#26021151	2
#26021146	2
#26020755	2
#26020616	2
#26020306	2
#26020216	2
#26020094	2
C₈₉×#3584	2
#22461	89