Subgroups — #36575298

Order 22784.

996 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029162	C₂	1	2	yes	maximal, complemented
2	#26028799	C₂	1	2	yes	maximal, complemented
3	#26021085	C₂	1	1	yes	maximal, characteristic, complemented
4	#26020923	C₂	1	2	yes	maximal, complemented
5	#26020755	C₂	1	2	yes	maximal, complemented
6	#26020636	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020494	C₂	1	2	yes	maximal, complemented
8	#26020064	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3018	C₂	1	1	yes	maximal, characteristic
10	#19152365	C₂²	1	2	yes	—
11	#19152365	C₂²	1	1	yes	characteristic, complemented
12	#41×Dic₈₉	C₂²	1	2	yes	—
13	#19151720	—	2	4	no	—
14	#19151715	—	2	4	no	—
15	#19151647	C₂²	1	2	yes	complemented
16	#19151622	C₂²	1	1	yes	characteristic, complemented
17	#19151615	—	2	4	no	—
18	#19151615	C₂²	1	2	yes	—
19	#19151615	C₂²	1	2	yes	—
20	C₂×#15667939	—	2	4	no	—
21	C₂×#15667939	C₂²	1	2	yes	—
22	C₂×#15667939	C₂²	1	2	yes	—
23	C₂×#15667939	C₂²	1	2	yes	complemented
24	#19151572	C₂²	1	1	yes	characteristic, complemented
25	M₁₆×Dic₈₉	C₂²	1	2	yes	complemented
26	#19151444	C₂²	1	1	yes	characteristic, complemented
27	#19151370	C₂²	1	2	yes	complemented
28	#19151359	C₂²	1	2	yes	complemented
29	#19151358	C₂²	1	2	yes	complemented
30	#585×C₈₉	C₂²	1	1	yes	characteristic
31	#575×C₈₉	C₂²	1	2	yes	—
32	#532×C₈₉	C₂²	1	1	yes	characteristic
33	#456×C₈₉	C₄	1	2	yes	complemented
34	#455×C₈₉	C₄	1	2	yes	complemented
35	#454×C₈₉	C₄	1	2	yes	complemented
36	#453×C₈₉	C₄	1	2	yes	complemented
37	C₂×#104×C₈₉	C₂²	1	2	yes	—
38	#413×C₈₉	C₂²	1	1	yes	characteristic
39	#15668019	—	2	4	no	—
40	#15668019	—	2	4	no	—
41	#15668019	—	4	2	no	—
42	C₂×#13083558	—	2	4	no	—
43	C₂×#13083558	—	4	1	no	—
44	C₂×#13083558	C₂³	1	2	yes	—
45	C₂×#13083558	C₂³	1	2	yes	—
46	Q₈×Dic₈₉	—	2	2	no	—
47	D₄×Dic₈₉	—	2	2	no	—
48	D₄×Dic₈₉	—	4	2	no	—
49	#15667971	—	2	2	no	—
50	#15667971	C₂³	1	2	yes	—
51	C₂×C₄×Dic₈₉	—	2	2	no	—
52	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
53	#15667948	—	2	4	no	—
54	C₄⋊#10623494	—	4	1	no	—
55	#15667939	—	2	4	no	—
56	#15667939	—	2	2	no	—
57	#15667939	—	2	2	no	—
58	#15667939	—	2	2	no	—
59	#15667939	—	2	2	no	—
60	#15667939	—	2	4	no	—
61	#15667939	D₄	1	4	yes	complemented
62	#15667939	D₄	1	4	yes	complemented
63	#15667927	—	4	1	no	—
64	#15667922	—	2	2	no	—
65	C₈×Dic₈₉	—	2	2	no	—
66	#15667919	—	4	1	no	—
67	2₋¹⁺⁴×C₈₉	—	2	2	no	—
68	2₋¹⁺⁴×C₈₉	C₂×C₄	1	2	yes	—
69	H(5,𝔽₂)×C₈₉	—	2	2	no	—
70	H(5,𝔽₂)×C₈₉	—	4	1	no	—
71	H(5,𝔽₂)×C₈₉	C₂×C₄	1	2	yes	—
72	C₂×#41×C₈₉	—	2	4	no	—
73	C₂×#41×C₈₉	—	4	1	no	—
74	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	C₂³	1	2	yes	—
77	#137×C₈₉	—	2	2	no	—
78	#137×C₈₉	C₂×C₄	1	4	yes	complemented
79	AGL(1,ℤ/8)×C₈₉	—	2	2	no	—
80	AGL(1,ℤ/8)×C₈₉	C₂×C₄	1	4	yes	complemented
81	#135×C₈₉	—	2	4	no	—
82	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
83	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
84	#127×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
85	#124×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
86	#124×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
87	#121×C₈₉	—	4	1	no	—
88	C₄×D₄×C₈₉	—	4	1	no	—
89	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
90	#104×C₈₉	C₂×C₄	1	4	yes	complemented
91	#104×C₈₉	C₂×C₄	1	4	yes	complemented
92	#101×C₈₉	C₂×C₄	1	2	yes	complemented
93	#100×C₈₉	C₂×C₄	1	2	yes	complemented
94	C₂²×Dic₈₉	—	2	2	no	—
95	C₂²×Dic₈₉	—	4	2	no	—
96	#13083558	—	2	2	no	—
97	#13083558	—	2	2	no	—
98	#13083558	—	2	2	no	—
99	#13083558	—	4	2	no	—
100	#13083558	—	4	4	no	—
101	#13083558	C₂×D₄	1	4	yes	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	—	4	2	no	—
105	C₂×#10623494	—	4	4	no	—
106	C₄⋊Dic₈₉	—	2	2	no	—
107	C₄⋊Dic₈₉	—	4	2	no	—
108	C₂²⋊Dic₈₉	—	2	2	no	—
109	C₂²⋊Dic₈₉	—	4	2	no	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₄×Dic₈₉	—	2	2	no	—
112	C₄×Dic₈₉	—	4	2	no	—
113	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
114	C₄×Dic₈₉	C₂×D₄	1	2	yes	—
115	#41×C₈₉	—	2	2	no	—
116	#41×C₈₉	—	2	2	no	—
117	#41×C₈₉	—	2	4	no	—
118	#41×C₈₉	—	2	4	no	—
119	#41×C₈₉	—	2	2	no	—
120	#41×C₈₉	—	2	2	no	—
121	#41×C₈₉	—	2	2	no	—
122	#41×C₈₉	—	2	2	no	—
123	#41×C₈₉	—	4	2	no	—
124	#41×C₈₉	—	4	2	no	—
125	#41×C₈₉	—	4	4	no	—
126	#41×C₈₉	—	4	2	no	—
127	#41×C₈₉	C₂²×C₄	1	4	yes	—
128	#41×C₈₉	C₂×D₄	1	4	yes	—
129	C₂×Q₈×C₈₉	—	2	4	no	—
130	C₂×Q₈×C₈₉	—	4	1	no	—
131	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×Q₈×C₈₉	#41	1	2	yes	—
134	C₂×D₄×C₈₉	—	2	2	no	—
135	C₂×D₄×C₈₉	—	2	4	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	—	4	1	no	—
139	C₂×D₄×C₈₉	—	4	2	no	—
140	C₂×D₄×C₈₉	—	4	1	no	—
141	C₂×D₄×C₈₉	—	4	4	no	—
142	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₈₉	#41	1	2	yes	—
145	C₂²×C₄×C₈₉	—	2	2	no	—
146	C₂²×C₄×C₈₉	—	2	1	no	—
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	4	2	no	—
150	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	Q₁₆×C₈₉	—	2	4	no	—
152	SD₁₆×C₈₉	—	2	4	no	—
153	SD₁₆×C₈₉	—	2	4	no	—
154	D₈×C₈₉	—	2	4	no	—
155	M₁₆×C₈₉	—	2	2	no	—
156	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₈₉	—	2	2	no	—
158	C₄⋊C₄×C₈₉	—	4	1	no	—
159	C₂²⋊C₄×C₈₉	—	4	1	no	—
160	C₂²⋊C₄×C₈₉	—	4	1	no	—
161	C₄²×C₈₉	—	2	1	no	—
162	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	1	no	—
166	C₂³×C₈₉	—	2	1	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
169	Q₈×C₈₉	—	2	2	no	—
170	Q₈×C₈₉	—	2	2	no	—
171	Q₈×C₈₉	—	2	2	no	—
172	Q₈×C₈₉	—	4	2	no	—
173	Q₈×C₈₉	C₄×D₄	1	4	yes	—
174	D₄×C₈₉	—	2	4	no	—
175	D₄×C₈₉	—	2	4	no	—
176	D₄×C₈₉	—	2	2	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	2	2	no	—
179	D₄×C₈₉	—	4	4	no	—
180	D₄×C₈₉	—	4	2	no	—
181	D₄×C₈₉	—	4	2	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	8	2	no	—
184	D₄×C₈₉	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	4	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	2	1	no	—
192	C₂×C₄×C₈₉	—	4	2	no	—
193	C₂×C₄×C₈₉	—	4	4	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	8	1	no	—
199	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
202	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₂×Dic₈₉	—	2	2	no	—
204	C₂×Dic₈₉	—	2	2	no	—
205	C₂×Dic₈₉	—	4	2	no	—
206	C₂×Dic₈₉	—	8	2	no	—
207	C₂×Dic₈₉	—	8	4	no	—
208	C₈×C₈₉	—	2	4	no	—
209	#10623494	—	2	4	no	—
210	#10623494	—	4	2	no	—
211	C₂²×C₈₉	—	2	4	no	—
212	C₂²×C₈₉	—	4	1	no	—
213	C₂²×C₈₉	—	4	1	no	—
214	C₂²×C₈₉	—	4	1	no	—
215	C₂²×C₈₉	—	8	2	no	—
216	C₂²×C₈₉	—	8	1	no	—
217	C₂²×C₈₉	—	8	1	no	—
218	C₂²×C₈₉	—	16	2	no	—
219	C₂²×C₈₉	#518	1	1	yes	characteristic
220	C₂²×C₈₉	#546	1	2	yes	—
221	C₄×C₈₉	—	2	4	no	—
222	C₄×C₈₉	—	4	1	no	—
223	C₄×C₈₉	—	4	1	no	—
224	C₄×C₈₉	—	4	1	no	—
225	C₄×C₈₉	—	4	1	no	—
226	C₄×C₈₉	C₂×C₄×D₄	1	2	yes	—
227	C₄×C₈₉	D₄²	1	1	yes	characteristic
228	C₄×C₈₉	#551	1	1	yes	characteristic
229	Dic₈₉	—	4	2	no	—
230	Dic₈₉	—	4	2	no	—
231	Dic₈₉	—	8	2	no	—
232	#22898	—	89	1	no	maximal, Sylow
233	C₂×C₈₉	—	2	2	no	—
234	C₂×C₈₉	—	2	1	no	—
235	C₂×C₈₉	—	4	4	no	—
236	C₂×C₈₉	—	8	1	no	—
237	C₂×C₈₉	—	8	1	no	—
238	C₂×C₈₉	#2358	1	1	yes	characteristic
239	#3018	D₈₉	1	1	yes	characteristic
240	#2956	—	89	2	no	—
241	#2901	—	89	2	no	—
242	#1963	—	89	1	no	—
243	#1932	—	89	2	no	—
244	#1906	—	89	2	no	—
245	#1884	—	89	1	no	—
246	#1861	—	89	2	no	—
247	#1759	—	89	2	no	—
248	C₈₉	#22898	1	1	yes	characteristic, complemented, Sylow
249	#585	C₂×D₈₉	1	1	yes	characteristic
250	#575	C₂×D₈₉	1	2	yes	—
251	#568	—	89	1	no	—
252	#568	—	89	2	no	—
253	#532	C₂×D₈₉	1	1	yes	characteristic
254	C₄×#41	—	89	2	no	—
255	#456	Dic₈₉	1	2	yes	complemented
256	#455	Dic₈₉	1	2	yes	complemented
257	#454	Dic₈₉	1	2	yes	complemented
258	#453	Dic₈₉	1	2	yes	complemented
259	#444	—	178	4	no	—
260	#443	—	178	4	no	—
261	#430	—	89	2	no	—
262	#423	—	89	1	no	—
263	#421	—	89	2	no	—
264	#421	—	89	2	no	—
265	#421	—	178	4	no	—
266	C₂×#104	—	89	2	no	—
267	C₂×#104	—	89	2	no	—
268	C₂×#104	—	89	2	no	—
269	C₂×#104	—	178	4	no	—
270	C₂×#104	C₂×D₈₉	1	2	yes	—
271	#413	C₂×D₈₉	1	1	yes	characteristic
272	#410	—	89	1	no	—
273	C₄×M₁₆	—	89	2	no	—
274	#376	—	89	1	no	—
275	#344	—	89	2	no	—
276	#339	—	89	2	no	—
277	#339	—	89	2	no	—
278	2₋¹⁺⁴	—	2	2	no	—
279	2₋¹⁺⁴	C₂×Dic₈₉	1	2	yes	—
280	H(5,𝔽₂)	—	2	2	no	—
281	H(5,𝔽₂)	—	4	1	no	—
282	H(5,𝔽₂)	C₂×Dic₈₉	1	2	yes	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	4	1	no	—
285	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
286	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
287	C₂×#41	C₂²×D₈₉	1	2	yes	—
288	#137	—	2	2	no	—
289	#137	C₂×Dic₈₉	1	4	yes	complemented
290	AGL(1,ℤ/8)	—	2	2	no	—
291	AGL(1,ℤ/8)	C₂×Dic₈₉	1	4	yes	complemented
292	#135	—	2	4	no	—
293	#131	—	356	2	no	—
294	#131	—	178	4	no	—
295	#131	—	178	4	no	—
296	C₂×M₁₆	—	89	2	no	—
297	C₂×M₁₆	—	89	2	no	—
298	C₂×M₁₆	—	356	1	no	—
299	C₂×M₁₆	—	178	4	no	—
300	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
301	C₄⋊Q₈	C₂×Dic₈₉	1	1	yes	characteristic, complemented
302	#127	C₂×Dic₈₉	1	1	yes	characteristic, complemented
303	#124	C₂×Dic₈₉	1	1	yes	characteristic, complemented
304	#124	C₂×Dic₈₉	1	1	yes	characteristic, complemented
305	#121	—	4	1	no	—
306	C₄×Q₈	—	178	2	no	—
307	C₄×D₄	—	4	1	no	—
308	C₄×D₄	—	356	2	no	—
309	C₄×D₄	—	178	2	no	—
310	#117	—	89	2	no	—
311	#117	—	178	2	no	—
312	C₂×C₄²	—	89	2	no	—
313	C₂×C₄²	—	178	2	no	—
314	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
315	#108	—	178	4	no	—
316	C₄⋊C₈	—	356	1	no	—
317	#104	—	89	4	no	—
318	#104	—	89	4	no	—
319	#104	—	178	2	no	—
320	#104	—	178	2	no	—
321	#104	—	178	2	no	—
322	#104	—	178	2	no	—
323	#104	—	178	4	no	—
324	#104	—	178	4	no	—
325	#104	C₂×Dic₈₉	1	4	yes	complemented
326	#104	C₂×Dic₈₉	1	4	yes	complemented
327	#101	C₂×Dic₈₉	1	2	yes	complemented
328	#100	C₂×Dic₈₉	1	2	yes	complemented
329	#99	—	356	1	no	—
330	#97	—	178	2	no	—
331	C₄×C₈	—	178	2	no	—
332	#95	—	356	1	no	—
333	#41	—	2	2	no	—
334	#41	—	2	2	no	—
335	#41	—	2	4	no	—
336	#41	—	2	4	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	#41	—	4	2	no	—
342	#41	—	4	2	no	—
343	#41	—	4	4	no	—
344	#41	—	4	2	no	—
345	#41	C₂²×Dic₈₉	1	4	yes	—
346	#41	D₄×D₈₉	1	4	yes	—
347	C₂×Q₈	—	2	4	no	—
348	C₂×Q₈	—	4	1	no	—
349	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
350	C₂×Q₈	C₂²×Dic₈₉	1	1	yes	characteristic
351	C₂×Q₈	#13083573	1	2	yes	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	4	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
361	C₂×D₄	C₂²×Dic₈₉	1	1	yes	characteristic
362	C₂×D₄	#13083573	1	2	yes	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	4	2	no	—
368	C₂²×C₄	—	356	2	no	—
369	C₂²×C₄	—	178	2	no	—
370	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
371	Q₁₆	—	2	4	no	—
372	SD₁₆	—	2	4	no	—
373	SD₁₆	—	2	4	no	—
374	D₈	—	2	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	89	4	no	—
377	M₁₆	—	356	4	no	—
378	M₁₆	—	356	2	no	—
379	M₁₆	—	178	2	no	—
380	M₁₆	—	178	2	no	—
381	M₁₆	—	178	2	no	—
382	M₁₆	C₂²×Dic₈₉	1	4	yes	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	356	4	no	—
385	C₂×C₈	—	356	2	no	—
386	C₂×C₈	—	178	2	no	—
387	C₂×C₈	—	178	2	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	356	2	no	—
390	C₄⋊C₄	—	178	2	no	—
391	C₂²⋊C₄	—	4	1	no	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	356	2	no	—
394	C₂²⋊C₄	—	178	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	89	2	no	—
397	C₄²	—	89	2	no	—
398	C₄²	—	356	2	no	—
399	C₄²	—	178	2	no	—
400	C₄²	—	178	2	no	—
401	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
402	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
403	C₂³	—	2	2	no	—
404	C₂³	—	2	1	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	4	2	no	—
407	C₂³	#15668057	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	2	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	D₄×Dic₈₉	1	4	yes	—
413	D₄	—	2	4	no	—
414	D₄	—	2	4	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	2	2	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	2	no	—
423	D₄	D₄×Dic₈₉	1	4	yes	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	1	no	—
438	C₂×C₄	—	356	2	no	—
439	C₂×C₄	—	178	2	no	—
440	C₂×C₄	—	178	2	no	—
441	C₂×C₄	—	712	2	no	—
442	C₂×C₄	—	712	4	no	—
443	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₈₉	1	2	yes	—
445	C₂×C₄	C₂×#13083573	1	2	yes	—
446	C₂×C₄	#15668057	1	1	yes	characteristic
447	C₈	—	2	4	no	—
448	C₈	—	356	2	no	—
449	C₈	—	178	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	1	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	16	2	no	—
458	C₂²	#19152073	1	1	yes	characteristic
459	C₂²	#19152235	1	2	yes	—
460	C₄	—	2	4	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	356	2	no	—
466	C₄	—	356	2	no	—
467	C₄	—	712	2	no	—
468	C₄	C₂×D₄×Dic₈₉	1	2	yes	—
469	C₄	#19152230	1	1	yes	characteristic
470	C₄	#19152279	1	1	yes	characteristic
471	C₂	—	2	1	no	—
472	C₂	—	2	2	no	—
473	C₂	—	4	4	no	—
474	C₂	—	8	1	no	—
475	C₂	—	8	1	no	—
476	C₂	#26023236	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19152230
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting, prime radical	C₈₉×#3018	C₂
socle	C₂×C₈₉	#2358
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#3018	D₈₉
hypocenter	C₈₉	#22898
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #3018

Complements

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

N	H ≅ G/N	type
1. #26029162	C₂	semidirect
2. #26028799	C₂	semidirect
3. #26021085	C₂	semidirect
4. #26020923	C₂	semidirect
5. #26020755	C₂	semidirect
6. #26020636	C₂	semidirect
7. #26020494	C₂	semidirect
8. #26020064	C₂	semidirect
11. #19152365	C₂²	semidirect
15. #19151647	C₂²	semidirect
16. #19151622	C₂²	semidirect
23. C₂×#15667939	C₂²	semidirect
24. #19151572	C₂²	semidirect
25. M₁₆×Dic₈₉	C₂²	semidirect
26. #19151444	C₂²	semidirect
27. #19151370	C₂²	semidirect
28. #19151359	C₂²	semidirect
29. #19151358	C₂²	semidirect
33. #456×C₈₉	C₄	semidirect
34. #455×C₈₉	C₄	semidirect
35. #454×C₈₉	C₄	semidirect
36. #453×C₈₉	C₄	semidirect
61. #15667939	D₄	semidirect
62. #15667939	D₄	semidirect
78. #137×C₈₉	C₂×C₄	semidirect
80. AGL(1,ℤ/8)×C₈₉	C₂×C₄	semidirect
83. C₄⋊Q₈×C₈₉	C₂×C₄	semidirect
84. #127×C₈₉	C₂×C₄	semidirect
85. #124×C₈₉	C₂×C₄	semidirect
86. #124×C₈₉	C₂×C₄	semidirect
90. #104×C₈₉	C₂×C₄	semidirect
91. #104×C₈₉	C₂×C₄	semidirect
92. #101×C₈₉	C₂×C₄	semidirect
93. #100×C₈₉	C₂×C₄	semidirect
248. C₈₉	#22898	semidirect
255. #456	Dic₈₉	semidirect
256. #455	Dic₈₉	semidirect
257. #454	Dic₈₉	semidirect
258. #453	Dic₈₉	semidirect
289. #137	C₂×Dic₈₉	semidirect
291. AGL(1,ℤ/8)	C₂×Dic₈₉	semidirect
301. C₄⋊Q₈	C₂×Dic₈₉	semidirect
302. #127	C₂×Dic₈₉	semidirect
303. #124	C₂×Dic₈₉	semidirect
304. #124	C₂×Dic₈₉	semidirect
325. #104	C₂×Dic₈₉	semidirect
326. #104	C₂×Dic₈₉	semidirect
327. #101	C₂×Dic₈₉	semidirect
328. #100	C₂×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029162	2
#26028799	2
#26021085	2
#26020923	2
#26020755	2
#26020636	2
#26020494	2
#26020064	2
C₈₉×#3018	2
#22898	89