Subgroups — #36572947

Order 22784.

812 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029167	C₂	1	2	yes	maximal
2	C₂×#19151713	C₂	1	1	yes	maximal, characteristic
3	#26028860	C₂	1	1	yes	maximal, characteristic, complemented
4	#26021039	C₂	1	2	yes	maximal, complemented
5	#26020492	C₂	1	2	yes	maximal, complemented
6	#26020489	C₂	1	2	yes	maximal, complemented
7	#26020422	C₂	1	1	yes	maximal, characteristic, complemented
8	#26020307	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020306	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020134	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2916	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668032	C₂²	1	1	yes	characteristic
13	#19152364	C₂²	1	2	yes	—
14	C₂×#15668018	C₂²	1	1	yes	characteristic
15	#19151718	—	2	4	no	—
16	#19151713	—	2	4	no	—
17	#19151713	C₄	1	2	yes	complemented
18	#19151713	C₄	1	2	yes	complemented
19	#19151713	C₄	1	2	yes	complemented
20	#19151713	C₄	1	2	yes	complemented
21	#19151646	C₂²	1	2	yes	—
22	#19151645	—	2	2	no	—
23	C₂×#15667948	C₂²	1	1	yes	characteristic
24	C₂×#15667947	C₂²	1	2	yes	—
25	C₂×#15667947	C₂²	1	1	yes	characteristic
26	#108×D₈₉	—	2	2	no	—
27	#19151636	C₂²	1	1	yes	characteristic
28	#19151621	C₂²	1	2	yes	—
29	#19151615	C₂²	1	2	yes	—
30	#19151614	C₂²	1	2	yes	—
31	C₂×#15667939	C₂²	1	1	yes	characteristic
32	C₂×#15667938	C₂²	1	1	yes	characteristic
33	#19151556	C₂²	1	2	yes	—
34	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
35	#19151370	C₂²	1	2	yes	—
36	#19151369	C₂²	1	2	yes	—
37	#19151359	C₂²	1	2	yes	—
38	#568×C₈₉	C₂²	1	2	yes	—
39	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
40	#430×C₈₉	—	2	2	no	—
41	#430×C₈₉	C₂²	1	2	yes	—
42	C₂×#108×C₈₉	—	2	2	no	—
43	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083574	C₂³	1	1	yes	characteristic
46	#15668032	C₂×C₄	1	2	yes	—
47	#15668032	C₂×C₄	1	2	yes	—
48	#15668032	D₄	1	2	yes	—
49	#15668032	D₄	1	2	yes	—
50	C₂×#13083564	Q₈	1	1	yes	characteristic
51	C₂×#13083562	Q₈	1	1	yes	characteristic
52	C₂×#13083561	Q₈	1	1	yes	characteristic
53	C₂×#13083559	Q₈	1	1	yes	characteristic
54	#15668020	—	4	2	no	—
55	#15668018	—	2	4	no	—
56	#15668018	—	2	1	no	—
57	#15668018	—	2	1	no	—
58	#15668018	C₂×C₄	1	2	yes	—
59	#15668018	C₂×C₄	1	2	yes	—
60	C₂×#13083558	C₂³	1	2	yes	—
61	C₂×#13083558	C₂³	1	1	yes	characteristic
62	C₂×#13083557	—	2	1	no	—
63	M₁₆×D₈₉	—	2	4	no	—
64	C₂²×#10623494	C₂³	1	1	yes	characteristic
65	C₂×C₈×D₈₉	—	2	1	no	—
66	#15667971	C₂³	1	2	yes	—
67	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
68	#15667948	—	2	1	no	—
69	#15667948	—	2	1	no	—
70	#15667947	—	2	2	no	—
71	#15667947	—	2	2	no	—
72	#15667947	—	2	4	no	—
73	#15667947	C₂×C₄	1	2	yes	—
74	#15667947	C₂×C₄	1	2	yes	—
75	#15667946	—	2	1	no	—
76	#15667944	—	2	1	no	—
77	#15667941	—	4	2	no	—
78	#15667939	—	2	4	no	—
79	#15667939	C₂×C₄	1	2	yes	—
80	#15667939	C₂×C₄	1	2	yes	—
81	#15667938	—	2	4	no	—
82	#15667938	C₂×C₄	1	2	yes	—
83	#15667938	C₂×C₄	1	2	yes	—
84	#15667922	—	2	2	no	—
85	C₈×Dic₈₉	—	2	2	no	—
86	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
91	#131×C₈₉	—	2	1	no	—
92	#131×C₈₉	—	2	1	no	—
93	#131×C₈₉	—	2	4	no	—
94	#131×C₈₉	—	4	2	no	—
95	#131×C₈₉	C₂×C₄	1	2	yes	—
96	#131×C₈₉	C₂×C₄	1	2	yes	—
97	C₂×M₁₆×C₈₉	—	2	1	no	—
98	C₂×M₁₆×C₈₉	—	2	4	no	—
99	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
100	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
102	C₂²×C₈×C₈₉	—	2	1	no	—
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	#108×C₈₉	—	2	4	no	—
105	#108×C₈₉	—	2	1	no	—
106	#108×C₈₉	—	2	1	no	—
107	#108×C₈₉	D₄	1	2	yes	—
108	#108×C₈₉	D₄	1	2	yes	—
109	#13083574	—	2	1	no	—
110	#13083574	—	2	1	no	—
111	#13083574	C₂²×C₄	1	2	yes	—
112	#13083574	C₂×D₄	1	2	yes	—
113	C₂×Dic₁₇₈	C₂×Q₈	1	1	yes	characteristic
114	C₂×D₃₅₆	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₂²⋊D₈₉	—	2	1	no	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	1	no	—
118	#13083564	C₄⋊C₄	1	2	yes	—
119	#13083564	C₄⋊C₄	1	2	yes	—
120	#13083562	C₄⋊C₄	1	2	yes	—
121	#13083562	C₄⋊C₄	1	2	yes	—
122	#13083561	C₄⋊C₄	1	2	yes	—
123	#13083561	C₄⋊C₄	1	2	yes	—
124	#13083559	C₄⋊C₄	1	2	yes	—
125	#13083559	C₄⋊C₄	1	2	yes	—
126	#13083558	—	2	1	no	—
127	#13083558	—	2	2	no	—
128	#13083558	—	2	2	no	—
129	#13083558	C₂²×C₄	1	2	yes	—
130	#13083557	—	2	2	no	—
131	#13083557	—	2	2	no	—
132	#13083557	—	4	4	no	—
133	C₂×#10623494	—	2	1	no	—
134	C₂×#10623494	—	2	2	no	—
135	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
136	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
137	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
138	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
139	C₂×#10623494	C₂×Q₈	1	1	yes	characteristic
140	C₂×#10623494	C₂×Q₈	1	1	yes	characteristic
141	C₈×D₈₉	—	2	2	no	—
142	C₈×D₈₉	—	2	2	no	—
143	C₈×D₈₉	—	4	4	no	—
144	C₄⋊Dic₈₉	—	2	2	no	—
145	C₂²⋊Dic₈₉	—	2	2	no	—
146	C₄×Dic₈₉	—	2	1	no	—
147	C₄×Dic₈₉	—	2	2	no	—
148	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
150	#41×C₈₉	—	2	1	no	—
151	#41×C₈₉	—	2	1	no	—
152	#41×C₈₉	C₂²×C₄	1	2	yes	—
153	#41×C₈₉	C₂×D₄	1	2	yes	—
154	C₂×Q₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
155	C₂×D₄×C₈₉	—	2	1	no	—
156	C₂×D₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	—	2	1	no	—
158	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₈₉	—	2	1	no	—
160	M₁₆×C₈₉	—	2	2	no	—
161	M₁₆×C₈₉	—	2	2	no	—
162	M₁₆×C₈₉	—	2	2	no	—
163	M₁₆×C₈₉	—	2	2	no	—
164	M₁₆×C₈₉	—	2	2	no	—
165	M₁₆×C₈₉	—	4	4	no	—
166	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
167	M₁₆×C₈₉	C₂×D₄	1	4	yes	—
168	C₂×C₈×C₈₉	—	2	2	no	—
169	C₂×C₈×C₈₉	—	2	1	no	—
170	C₂×C₈×C₈₉	—	2	2	no	—
171	C₂×C₈×C₈₉	—	2	2	no	—
172	C₂×C₈×C₈₉	—	2	2	no	—
173	C₂×C₈×C₈₉	—	4	4	no	—
174	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
179	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
180	C₂³×C₈₉	—	2	1	no	—
181	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
182	C₂²×D₈₉	—	2	1	no	—
183	Q₈×C₈₉	—	2	1	no	—
184	Q₈×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
185	D₄×C₈₉	—	2	2	no	—
186	D₄×C₈₉	—	2	2	no	—
187	D₄×C₈₉	—	2	1	no	—
188	D₄×C₈₉	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂²⋊D₈₉	—	2	2	no	—
199	C₂²⋊D₈₉	—	2	2	no	—
200	C₂×Dic₈₉	—	2	1	no	—
201	C₂×Dic₈₉	—	2	1	no	—
202	C₂×Dic₈₉	—	2	1	no	—
203	C₂×Dic₈₉	—	4	2	no	—
204	C₂×Dic₈₉	—	4	2	no	—
205	D₃₅₆	—	2	1	no	—
206	D₃₅₆	C₂×C₄⋊C₄	1	2	yes	—
207	C₄×D₈₉	—	2	2	no	—
208	C₄×D₈₉	—	2	2	no	—
209	Dic₁₇₈	—	2	1	no	—
210	Dic₁₇₈	C₂×C₄⋊C₄	1	2	yes	—
211	C₈×C₈₉	—	2	2	no	—
212	C₈×C₈₉	—	2	4	no	—
213	C₈×C₈₉	—	4	2	no	—
214	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
215	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
216	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
217	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
218	#10623494	—	2	2	no	—
219	#10623494	—	4	2	no	—
220	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
221	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
222	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
223	#10623494	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₈₉	—	2	2	no	—
225	C₂²×C₈₉	—	4	1	no	—
226	C₂²×C₈₉	—	8	1	no	—
227	C₂²×C₈₉	#520	1	1	yes	characteristic
228	C₂²×C₈₉	#547	1	1	yes	characteristic
229	C₂²×C₈₉	D₄×Q₈	1	1	yes	characteristic
230	C₂×D₈₉	—	2	2	no	—
231	C₂×D₈₉	—	8	1	no	—
232	C₄×C₈₉	—	2	2	no	—
233	C₄×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
234	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₈₉	D₄²	1	1	yes	characteristic
236	C₄×C₈₉	#554	1	1	yes	characteristic
237	Dic₈₉	—	2	2	no	—
238	Dic₈₉	—	2	2	no	—
239	Dic₈₉	—	4	1	no	—
240	Dic₈₉	—	8	2	no	—
241	#22694	—	89	1	no	maximal, Sylow
242	C₂×C₈₉	—	2	1	no	—
243	C₂×C₈₉	—	2	1	no	—
244	C₂×C₈₉	—	2	1	no	—
245	C₂×C₈₉	—	4	2	no	—
246	C₂×C₈₉	D₄×C₄⋊C₄	1	1	yes	characteristic
247	D₈₉	—	4	2	no	—
248	#2957	—	89	2	no	—
249	C₂×#443	—	89	1	no	—
250	#2916	—	89	1	no	—
251	#2916	D₈₉	1	1	yes	characteristic, complemented
252	#1953	—	89	2	no	—
253	#1861	—	89	2	no	—
254	#1861	—	89	2	no	—
255	#1848	—	89	1	no	—
256	#1814	—	89	1	no	—
257	#1814	—	89	1	no	—
258	#1772	—	89	1	no	—
259	C₈₉	#22694	1	1	yes	characteristic, complemented, Sylow
260	C₂×#135	—	89	1	no	—
261	#568	—	89	2	no	—
262	#568	C₂×D₈₉	1	2	yes	—
263	C₂×#131	—	89	1	no	—
264	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
265	#444	—	178	4	no	—
266	#443	—	89	2	no	—
267	#443	—	89	2	no	—
268	#443	—	89	2	no	—
269	#443	—	89	2	no	—
270	#443	—	178	4	no	—
271	#430	—	2	2	no	—
272	#430	—	89	2	no	—
273	#430	—	178	2	no	—
274	#430	C₂×D₈₉	1	2	yes	—
275	C₂×#108	—	2	2	no	—
276	C₂×#108	—	89	1	no	—
277	C₂×#108	—	89	2	no	—
278	C₂×#108	—	89	1	no	—
279	C₂×#108	—	178	2	no	—
280	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
281	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
282	#427	—	89	1	no	—
283	#423	—	89	2	no	—
284	#421	—	89	2	no	—
285	#421	—	89	2	no	—
286	C₂×#104	—	89	1	no	—
287	C₂×#104	—	89	1	no	—
288	#405	—	89	2	no	—
289	C₂×C₄×C₈	—	89	1	no	—
290	#344	—	89	2	no	—
291	#344	—	89	2	no	—
292	#339	—	89	2	no	—
293	C₂×#41	—	89	1	no	—
294	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
295	#135	—	89	2	no	—
296	#135	—	89	2	no	—
297	#135	—	89	2	no	—
298	#135	—	89	2	no	—
299	C₂×Q₁₆	—	89	1	no	—
300	C₂×SD₁₆	—	89	1	no	—
301	C₂×SD₁₆	—	89	1	no	—
302	C₂×D₈	—	89	1	no	—
303	#131	—	2	1	no	—
304	#131	—	2	1	no	—
305	#131	—	2	4	no	—
306	#131	—	4	2	no	—
307	#131	—	89	2	no	—
308	#131	—	89	2	no	—
309	#131	—	356	2	no	—
310	#131	—	178	4	no	—
311	#131	—	178	1	no	—
312	#131	—	178	1	no	—
313	#131	C₄×D₈₉	1	2	yes	—
314	#131	C₄×D₈₉	1	2	yes	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	4	no	—
317	C₂×M₁₆	—	89	1	no	—
318	C₂×M₁₆	—	89	2	no	—
319	C₂×M₁₆	—	178	4	no	—
320	C₂×M₁₆	—	178	1	no	—
321	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
322	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
323	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	89	1	no	—
326	C₂²×C₈	—	178	1	no	—
327	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
328	#117	—	89	2	no	—
329	C₂×C₄²	—	89	1	no	—
330	#108	—	2	4	no	—
331	#108	—	2	1	no	—
332	#108	—	2	1	no	—
333	#108	—	89	2	no	—
334	#108	—	89	2	no	—
335	#108	—	178	2	no	—
336	#108	—	178	2	no	—
337	#108	—	178	4	no	—
338	#108	—	178	1	no	—
339	#108	—	178	1	no	—
340	#108	C₂²⋊D₈₉	1	2	yes	—
341	#108	C₂²⋊D₈₉	1	2	yes	—
342	#107	—	178	1	no	—
343	#106	—	178	1	no	—
344	C₄⋊C₈	—	356	2	no	—
345	#104	—	89	2	no	—
346	#104	—	89	2	no	—
347	#104	—	89	2	no	—
348	#104	—	89	2	no	—
349	#104	—	178	4	no	—
350	#104	—	178	4	no	—
351	#97	—	178	2	no	—
352	C₄×C₈	—	89	1	no	—
353	C₄×C₈	—	89	1	no	—
354	C₄×C₈	—	89	1	no	—
355	C₄×C₈	—	89	1	no	—
356	C₄×C₈	—	178	2	no	—
357	#41	—	2	1	no	—
358	#41	—	2	1	no	—
359	#41	—	89	2	no	—
360	#41	—	89	2	no	—
361	#41	—	178	1	no	—
362	#41	—	178	1	no	—
363	#41	C₂×C₄×D₈₉	1	2	yes	—
364	#41	D₄×D₈₉	1	2	yes	—
365	C₂×Q₈	—	89	1	no	—
366	C₂×Q₈	Q₈×D₈₉	1	1	yes	characteristic
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	89	1	no	—
369	C₂×D₄	—	178	1	no	—
370	C₂×D₄	Q₈×D₈₉	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	178	1	no	—
373	C₂²×C₄	—	178	1	no	—
374	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
375	Q₁₆	—	89	2	no	—
376	Q₁₆	—	89	2	no	—
377	SD₁₆	—	89	2	no	—
378	SD₁₆	—	89	2	no	—
379	SD₁₆	—	89	2	no	—
380	SD₁₆	—	89	2	no	—
381	D₈	—	89	2	no	—
382	D₈	—	89	2	no	—
383	M₁₆	—	2	1	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	2	2	no	—
388	M₁₆	—	2	2	no	—
389	M₁₆	—	4	4	no	—
390	M₁₆	—	89	2	no	—
391	M₁₆	—	356	4	no	—
392	M₁₆	—	178	2	no	—
393	M₁₆	—	178	2	no	—
394	M₁₆	—	178	1	no	—
395	M₁₆	—	178	2	no	—
396	M₁₆	—	178	2	no	—
397	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
398	M₁₆	C₂×C₂²⋊D₈₉	1	4	yes	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	4	4	no	—
405	C₂×C₈	—	89	1	no	—
406	C₂×C₈	—	89	1	no	—
407	C₂×C₈	—	89	1	no	—
408	C₂×C₈	—	89	1	no	—
409	C₂×C₈	—	89	1	no	—
410	C₂×C₈	—	89	1	no	—
411	C₂×C₈	—	356	4	no	—
412	C₂×C₈	—	178	2	no	—
413	C₂×C₈	—	178	1	no	—
414	C₂×C₈	—	178	2	no	—
415	C₂×C₈	—	178	2	no	—
416	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
417	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
418	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
419	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
420	C₂×C₈	#13083574	1	1	yes	characteristic
421	C₂×C₈	#13083574	1	1	yes	characteristic
422	C₄⋊C₄	—	178	2	no	—
423	C₂²⋊C₄	—	178	2	no	—
424	C₄²	—	89	1	no	—
425	C₄²	—	89	1	no	—
426	C₄²	—	178	2	no	—
427	C₄²	—	178	1	no	—
428	C₂³	—	2	1	no	—
429	C₂³	—	178	1	no	—
430	C₂³	#15668060	1	1	yes	characteristic
431	Q₈	—	2	1	no	—
432	Q₈	—	89	2	no	—
433	Q₈	—	178	1	no	—
434	Q₈	C₄⋊C₄×D₈₉	1	2	yes	—
435	D₄	—	2	2	no	—
436	D₄	—	2	2	no	—
437	D₄	—	2	1	no	—
438	D₄	—	89	2	no	—
439	D₄	—	178	2	no	—
440	D₄	—	178	2	no	—
441	D₄	—	178	1	no	—
442	D₄	C₄⋊C₄×D₈₉	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	356	2	no	—
447	C₂×C₄	—	356	2	no	—
448	C₂×C₄	—	178	1	no	—
449	C₂×C₄	—	178	1	no	—
450	C₂×C₄	—	178	1	no	—
451	C₂×C₄	—	178	2	no	—
452	C₂×C₄	—	178	2	no	—
453	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
458	C₂×C₄	#15668057	1	1	yes	characteristic
459	C₈	—	2	4	no	—
460	C₈	—	2	2	no	—
461	C₈	—	4	2	no	—
462	C₈	—	89	1	no	—
463	C₈	—	89	1	no	—
464	C₈	—	89	1	no	—
465	C₈	—	89	1	no	—
466	C₈	—	356	2	no	—
467	C₈	—	178	2	no	—
468	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
469	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
470	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
471	C₈	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
472	C₂²	—	2	2	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	—	178	2	no	—
476	C₂²	—	712	1	no	—
477	C₂²	#19152079	1	1	yes	characteristic
478	C₂²	#19152249	1	1	yes	characteristic
479	C₂²	Q₈×C₂²⋊D₈₉	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	356	1	no	—
482	C₄	—	178	2	no	—
483	C₄	—	178	2	no	—
484	C₄	—	712	2	no	—
485	C₄	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
486	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
487	C₄	D₄×C₂²⋊D₈₉	1	1	yes	characteristic
488	C₄	#19152303	1	1	yes	characteristic
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	4	2	no	—
493	C₂	—	356	2	no	—
494	C₂	C₄⋊C₄×C₂²⋊D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#2916	C₂
socle	C₂×C₈₉	D₄×C₄⋊C₄
prime radical	C₂×#15668032	C₂²
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#2916	D₈₉
hypocenter	C₈₉	#22694
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2916

Complements

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

N	H ≅ G/N	type
3. #26028860	C₂	semidirect
4. #26021039	C₂	semidirect
5. #26020492	C₂	semidirect
6. #26020489	C₂	semidirect
7. #26020422	C₂	semidirect
8. #26020307	C₂	semidirect
9. #26020306	C₂	semidirect
10. #26020134	C₂	semidirect
11. C₈₉×#2916	C₂	semidirect
17. #19151713	C₄	semidirect
18. #19151713	C₄	semidirect
19. #19151713	C₄	semidirect
20. #19151713	C₄	semidirect
251. #2916	D₈₉	semidirect
259. C₈₉	#22694	semidirect

Maximal subgroups

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

subgroup	index
#26029167	2
C₂×#19151713	2
#26028860	2
#26021039	2
#26020492	2
#26020489	2
#26020422	2
#26020307	2
#26020306	2
#26020134	2
C₈₉×#2916	2
#22694	89