Subgroups — #36561360

Order 22784.

876 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029972	C₂	1	1	yes	maximal, characteristic
2	#26029151	C₂	1	2	yes	maximal, complemented
3	C₂×#19151714	C₂	1	1	yes	maximal, characteristic, complemented
4	#131×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021148	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021040	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020919	C₂	1	2	yes	maximal, complemented
8	#26020751	C₂	1	2	yes	maximal, complemented
9	#26020133	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020051	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1814	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152396	C₂²	1	2	yes	—
13	C₂×#15668034	C₂²	1	1	yes	characteristic
14	C₂×#15668020	C₂²	1	2	yes	—
15	C₂×#15668019	C₂²	1	1	yes	characteristic
16	#41×Dic₈₉	C₂²	1	1	yes	characteristic
17	#19151873	C₄	1	2	yes	complemented
18	#19151868	C₄	1	2	yes	complemented
19	#19151861	C₄	1	4	yes	complemented
20	#19151717	—	2	4	no	—
21	#19151714	—	2	1	no	—
22	#19151714	—	2	1	no	—
23	#19151714	—	2	1	no	—
24	#19151714	—	2	1	no	—
25	#19151712	—	2	4	no	—
26	#19151646	C₂²	1	2	yes	—
27	C₂×#15667948	C₂²	1	1	yes	characteristic
28	#19151616	C₂²	1	2	yes	—
29	C₂×#15667938	C₂²	1	2	yes	—
30	#19151580	C₂²	1	2	yes	—
31	#19151571	C₂²	1	2	yes	—
32	#19151556	—	2	1	no	—
33	#19151556	C₂²	1	1	yes	characteristic
34	#19151554	C₂²	1	2	yes	—
35	#19151553	—	2	1	no	—
36	#19151553	C₂²	1	1	yes	characteristic
37	M₁₆×Dic₈₉	—	2	1	no	—
38	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₈₉	—	2	1	no	—
40	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
41	#19151369	C₂²	1	2	yes	—
42	#19151357	C₂²	1	2	yes	—
43	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
45	#427×C₈₉	C₂²	1	1	yes	characteristic
46	#421×C₈₉	C₂²	1	2	yes	—
47	#344×C₈₉	C₂²	1	2	yes	—
48	C₂×#13083574	C₂³	1	2	yes	—
49	#15668043	—	2	2	no	—
50	#15668042	C₂×C₄	1	4	yes	—
51	#15668038	—	2	2	no	—
52	#15668037	C₂×C₄	1	4	yes	—
53	#15668034	—	2	1	no	—
54	#15668034	—	2	1	no	—
55	#15668034	—	2	1	no	—
56	#15668034	—	2	1	no	—
57	#15668032	—	2	4	no	—
58	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic, complemented
59	C₂×#13083563	C₂×C₄	1	2	yes	complemented
60	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic, complemented
61	#15668020	—	2	2	no	—
62	#15668020	—	2	2	no	—
63	#15668020	—	2	2	no	—
64	#15668020	—	2	2	no	—
65	#15668019	—	2	1	no	—
66	#15668019	—	2	1	no	—
67	#15668019	D₄	1	2	yes	—
68	#15668019	D₄	1	2	yes	—
69	C₂×#13083558	—	2	1	no	—
70	C₂×#13083558	C₂³	1	2	yes	—
71	C₂×#13083558	C₂³	1	1	yes	characteristic
72	C₂×#13083557	—	2	2	no	—
73	C₂²×#10623494	—	2	1	no	—
74	C₂²×#10623494	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₈₉	—	2	2	no	—
76	Q₈×Dic₈₉	—	2	1	no	—
77	D₄×Dic₈₉	—	2	2	no	—
78	D₄×Dic₈₉	—	2	1	no	—
79	#15667971	—	2	1	no	—
80	#15667971	C₂³	1	1	yes	characteristic
81	C₂×C₄×Dic₈₉	—	2	1	no	—
82	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
83	#15667948	C₂×C₄	1	2	yes	complemented
84	#15667948	C₂×C₄	1	2	yes	complemented
85	#15667947	—	2	4	no	—
86	#15667940	—	2	4	no	—
87	#15667938	—	2	2	no	—
88	#15667938	—	2	2	no	—
89	#15667930	C₂×C₄	1	4	yes	complemented
90	#15667928	C₂×C₄	1	4	yes	complemented
91	#15667926	—	2	4	no	—
92	#15667923	—	2	2	no	—
93	#15667922	—	2	1	no	—
94	#15667922	—	2	1	no	—
95	#15667922	—	2	1	no	—
96	C₄×#10623494	—	2	2	no	—
97	C₈×Dic₈₉	—	2	1	no	—
98	C₈×Dic₈₉	—	2	1	no	—
99	C₈×Dic₈₉	—	2	1	no	—
100	C₈×Dic₈₉	D₄	1	1	yes	characteristic
101	C₈×Dic₈₉	D₄	1	1	yes	characteristic
102	C₈×Dic₈₉	D₄	1	1	yes	characteristic
103	C₈×Dic₈₉	D₄	1	1	yes	characteristic
104	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
105	#131×C₈₉	—	2	1	no	—
106	#131×C₈₉	—	2	1	no	—
107	#131×C₈₉	C₂×C₄	1	2	yes	—
108	#131×C₈₉	C₂×C₄	1	2	yes	—
109	C₂×M₁₆×C₈₉	—	2	1	no	—
110	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
111	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₈₉	—	2	1	no	—
113	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
114	#117×C₈₉	C₂³	1	2	yes	—
115	#108×C₈₉	—	2	1	no	—
116	#108×C₈₉	—	2	1	no	—
117	#107×C₈₉	—	2	1	no	—
118	#106×C₈₉	—	2	1	no	—
119	#104×C₈₉	—	2	4	no	—
120	#13083574	—	2	2	no	—
121	#13083574	—	2	2	no	—
122	#13083574	—	2	2	no	—
123	#13083574	—	2	2	no	—
124	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
125	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
126	C₂×C₂²⋊D₈₉	—	2	2	no	—
127	C₂²×Dic₈₉	—	2	2	no	—
128	C₂²×Dic₈₉	—	2	1	no	—
129	C₂×C₄×D₈₉	—	2	2	no	—
130	Dic₃₅₆	—	2	1	no	—
131	Dic₃₅₆	—	2	1	no	—
132	#13083564	—	2	4	no	—
133	#13083563	—	2	2	no	—
134	#13083563	—	2	2	no	—
135	#13083562	—	2	4	no	—
136	#13083561	—	2	4	no	—
137	D₇₁₂	—	2	1	no	—
138	D₇₁₂	—	2	1	no	—
139	#13083559	—	2	4	no	—
140	#13083558	—	2	1	no	—
141	#13083558	—	2	2	no	—
142	#13083558	—	2	2	no	—
143	#13083558	—	2	2	no	—
144	#13083558	C₂²×C₄	1	4	yes	—
145	#13083558	C₂×D₄	1	2	yes	—
146	#13083557	—	4	2	no	—
147	#13083557	—	4	2	no	—
148	C₂×#10623494	—	2	1	no	—
149	C₂×#10623494	—	2	2	no	—
150	C₂×#10623494	—	2	2	no	—
151	C₂×#10623494	—	2	2	no	—
152	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
153	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
154	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
155	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
156	C₂×#10623494	#41	1	1	yes	characteristic
157	C₂×#10623494	#41	1	1	yes	characteristic
158	C₈×D₈₉	—	4	2	no	—
159	C₈×D₈₉	—	4	2	no	—
160	C₄⋊Dic₈₉	—	2	2	no	—
161	C₄⋊Dic₈₉	—	2	1	no	—
162	C₂²⋊Dic₈₉	—	2	2	no	—
163	C₂²⋊Dic₈₉	#41	1	2	yes	—
164	C₄×Dic₈₉	—	2	2	no	—
165	C₄×Dic₈₉	—	2	1	no	—
166	C₄×Dic₈₉	—	2	1	no	—
167	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
169	#41×C₈₉	—	2	1	no	—
170	#41×C₈₉	—	2	1	no	—
171	#41×C₈₉	C₂²×C₄	1	2	yes	—
172	#41×C₈₉	C₂×D₄	1	2	yes	—
173	C₂×Q₈×C₈₉	#41	1	1	yes	characteristic
174	C₂×D₄×C₈₉	—	2	1	no	—
175	C₂×D₄×C₈₉	#41	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	—	2	1	no	—
177	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	M₁₆×C₈₉	—	2	1	no	—
179	M₁₆×C₈₉	—	2	2	no	—
180	M₁₆×C₈₉	—	2	2	no	—
181	M₁₆×C₈₉	—	2	2	no	—
182	M₁₆×C₈₉	—	2	2	no	—
183	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	2	no	—
186	C₂×C₈×C₈₉	—	2	2	no	—
187	C₂×C₈×C₈₉	—	2	2	no	—
188	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
192	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
193	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	2	no	—
195	C₂²⋊C₄×C₈₉	—	2	2	no	—
196	C₄²×C₈₉	—	2	2	no	—
197	C₂³×C₈₉	—	2	1	no	—
198	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂²×D₈₉	—	2	2	no	—
200	Q₈×C₈₉	—	2	1	no	—
201	Q₈×C₈₉	C₄×D₄	1	2	yes	—
202	D₄×C₈₉	—	2	2	no	—
203	D₄×C₈₉	—	2	2	no	—
204	D₄×C₈₉	—	2	1	no	—
205	D₄×C₈₉	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	2	no	—
208	C₂×C₄×C₈₉	—	2	2	no	—
209	C₂×C₄×C₈₉	—	4	2	no	—
210	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
216	C₂²⋊D₈₉	—	4	2	no	—
217	C₂²⋊D₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	2	1	no	—
219	C₂×Dic₈₉	—	2	2	no	—
220	C₂×Dic₈₉	—	2	2	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	4	2	no	—
223	C₂×Dic₈₉	—	4	4	no	—
224	D₃₅₆	—	2	2	no	—
225	D₃₅₆	—	2	2	no	—
226	C₄×D₈₉	—	4	2	no	—
227	C₄×D₈₉	—	4	2	no	—
228	Dic₁₇₈	—	2	2	no	—
229	Dic₁₇₈	—	2	2	no	—
230	C₈×C₈₉	—	2	2	no	—
231	C₈×C₈₉	—	4	2	no	—
232	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
233	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
234	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
235	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
236	#10623494	—	2	4	no	—
237	#10623494	—	2	2	no	—
238	#10623494	#121	1	1	yes	characteristic
239	#10623494	#121	1	1	yes	characteristic
240	#10623494	#121	1	1	yes	characteristic
241	#10623494	#121	1	1	yes	characteristic
242	C₂²×C₈₉	—	2	2	no	—
243	C₂²×C₈₉	—	4	1	no	—
244	C₂²×C₈₉	—	4	2	no	—
245	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
246	C₂²×C₈₉	#525	1	1	yes	characteristic
247	C₂²×C₈₉	#532	1	1	yes	characteristic
248	C₂×D₈₉	—	4	2	no	—
249	C₂×D₈₉	—	8	2	no	—
250	C₄×C₈₉	—	2	2	no	—
251	C₄×C₈₉	—	8	2	no	—
252	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
255	C₄×C₈₉	#529	1	1	yes	characteristic
256	Dic₈₉	—	2	2	no	—
257	Dic₈₉	—	4	2	no	—
258	Dic₈₉	—	4	1	no	—
259	Dic₈₉	—	4	2	no	—
260	#21558	—	89	1	no	maximal, Sylow
261	C₂×C₈₉	—	2	1	no	—
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	2	1	no	—
264	C₂×C₈₉	—	4	2	no	—
265	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
266	D₈₉	—	8	2	no	—
267	#3067	—	89	1	no	—
268	#2955	—	89	2	no	—
269	C₂×#443	—	89	1	no	—
270	C₄×#131	—	89	1	no	—
271	#1976	—	89	1	no	—
272	#1953	—	89	1	no	—
273	#1932	—	89	2	no	—
274	#1906	—	89	2	no	—
275	#1814	D₈₉	1	1	yes	characteristic, complemented
276	#1772	—	89	1	no	—
277	#1757	—	89	2	no	—
278	C₈₉	#21558	1	1	yes	characteristic, complemented, Sylow
279	#575	—	89	2	no	—
280	C₂×#135	—	89	1	no	—
281	C₂×#131	—	89	1	no	—
282	C₂×#131	—	89	2	no	—
283	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
284	C₄×#41	—	89	1	no	—
285	#473	—	89	2	no	—
286	#472	—	89	2	no	—
287	#471	—	89	4	no	—
288	#444	—	178	4	no	—
289	#443	—	178	1	no	—
290	#443	—	178	1	no	—
291	#443	—	178	1	no	—
292	#443	—	178	1	no	—
293	#443	—	178	4	no	—
294	#430	—	89	2	no	—
295	C₂×#108	—	89	1	no	—
296	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
297	#427	C₂×D₈₉	1	1	yes	characteristic
298	#421	—	89	2	no	—
299	#421	C₂×D₈₉	1	2	yes	—
300	C₂×#104	—	89	2	no	—
301	#413	—	89	2	no	—
302	#410	—	89	2	no	—
303	#405	—	89	1	no	—
304	#405	—	89	1	no	—
305	#405	—	89	2	no	—
306	#405	—	178	1	no	—
307	#405	—	178	1	no	—
308	C₄×M₁₆	—	89	1	no	—
309	C₄×M₁₆	—	178	1	no	—
310	C₂×C₄×C₈	—	89	1	no	—
311	C₂×C₄×C₈	—	178	1	no	—
312	#344	—	89	2	no	—
313	#344	C₂×D₈₉	1	2	yes	—
314	#339	—	89	2	no	—
315	C₂×#41	—	89	2	no	—
316	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
317	#137	—	89	4	no	—
318	#137	—	178	2	no	—
319	AGL(1,ℤ/8)	—	89	4	no	—
320	AGL(1,ℤ/8)	—	178	2	no	—
321	#135	—	178	4	no	—
322	#135	—	178	1	no	—
323	#135	—	178	1	no	—
324	#135	—	178	1	no	—
325	#135	—	178	1	no	—
326	C₂×Q₁₆	—	89	1	no	—
327	C₂×SD₁₆	—	89	2	no	—
328	C₂×D₈	—	89	1	no	—
329	#131	—	2	1	no	—
330	#131	—	2	1	no	—
331	#131	—	89	2	no	—
332	#131	—	89	2	no	—
333	#131	—	178	2	no	—
334	#131	—	178	2	no	—
335	#131	—	178	2	no	—
336	#131	—	178	2	no	—
337	#131	—	178	1	no	—
338	#131	—	178	1	no	—
339	#131	C₄×D₈₉	1	2	yes	—
340	#131	C₄×D₈₉	1	2	yes	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	89	1	no	—
343	C₂×M₁₆	—	89	2	no	—
344	C₂×M₁₆	—	178	2	no	—
345	C₂×M₁₆	—	178	1	no	—
346	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
347	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	89	1	no	—
350	C₂²×C₈	—	178	2	no	—
351	C₂²×C₈	—	178	1	no	—
352	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
353	C₄×Q₈	—	178	1	no	—
354	C₄×D₄	—	178	2	no	—
355	C₄×D₄	—	178	1	no	—
356	#117	—	89	1	no	—
357	#117	—	178	1	no	—
358	#117	C₂²×D₈₉	1	2	yes	—
359	C₂×C₄²	—	89	1	no	—
360	C₂×C₄²	—	178	1	no	—
361	#108	—	2	1	no	—
362	#108	—	2	1	no	—
363	#108	—	89	2	no	—
364	#108	—	89	2	no	—
365	#108	—	178	4	no	—
366	#107	—	2	1	no	—
367	#106	—	2	1	no	—
368	#104	—	2	4	no	—
369	#104	—	178	4	no	—
370	#104	—	178	2	no	—
371	#104	—	178	2	no	—
372	#101	—	89	4	no	—
373	#100	—	89	4	no	—
374	#99	—	178	4	no	—
375	#97	—	178	2	no	—
376	#97	—	178	1	no	—
377	#97	—	178	1	no	—
378	#97	—	178	1	no	—
379	C₄×C₈	—	89	1	no	—
380	C₄×C₈	—	89	1	no	—
381	C₄×C₈	—	89	1	no	—
382	C₄×C₈	—	89	1	no	—
383	C₄×C₈	—	178	2	no	—
384	C₄×C₈	—	178	1	no	—
385	C₄×C₈	—	178	1	no	—
386	C₄×C₈	—	178	1	no	—
387	#41	—	2	1	no	—
388	#41	—	2	1	no	—
389	#41	—	178	2	no	—
390	#41	—	178	2	no	—
391	#41	—	178	2	no	—
392	#41	—	178	2	no	—
393	#41	C₂×C₄×D₈₉	1	2	yes	—
394	#41	D₄×D₈₉	1	2	yes	—
395	C₂×Q₈	—	89	2	no	—
396	C₂×Q₈	#13083575	1	1	yes	characteristic
397	C₂×D₄	—	2	1	no	—
398	C₂×D₄	—	89	2	no	—
399	C₂×D₄	—	178	2	no	—
400	C₂×D₄	#13083575	1	1	yes	characteristic
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	178	2	no	—
403	C₂²×C₄	—	178	1	no	—
404	C₂²×C₄	—	178	2	no	—
405	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
406	Q₁₆	—	178	4	no	—
407	Q₁₆	—	178	1	no	—
408	Q₁₆	—	178	1	no	—
409	SD₁₆	—	178	4	no	—
410	SD₁₆	—	178	4	no	—
411	SD₁₆	—	178	2	no	—
412	SD₁₆	—	178	2	no	—
413	D₈	—	178	4	no	—
414	D₈	—	178	1	no	—
415	D₈	—	178	1	no	—
416	M₁₆	—	2	1	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	89	4	no	—
422	M₁₆	—	89	2	no	—
423	M₁₆	—	356	2	no	—
424	M₁₆	—	356	2	no	—
425	M₁₆	—	178	2	no	—
426	M₁₆	—	178	2	no	—
427	M₁₆	—	178	1	no	—
428	M₁₆	—	178	2	no	—
429	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	89	1	no	—
435	C₂×C₈	—	89	1	no	—
436	C₂×C₈	—	89	1	no	—
437	C₂×C₈	—	89	1	no	—
438	C₂×C₈	—	89	1	no	—
439	C₂×C₈	—	89	1	no	—
440	C₂×C₈	—	356	2	no	—
441	C₂×C₈	—	356	2	no	—
442	C₂×C₈	—	178	2	no	—
443	C₂×C₈	—	178	2	no	—
444	C₂×C₈	—	178	1	no	—
445	C₂×C₈	—	178	2	no	—
446	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
447	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
448	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
449	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
450	C₂×C₈	#13083573	1	1	yes	characteristic
451	C₂×C₈	#13083573	1	1	yes	characteristic
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	178	2	no	—
454	C₄⋊C₄	—	178	1	no	—
455	C₂²⋊C₄	—	2	2	no	—
456	C₂²⋊C₄	—	89	2	no	—
457	C₂²⋊C₄	—	178	2	no	—
458	C₄²	—	2	2	no	—
459	C₄²	—	89	1	no	—
460	C₄²	—	89	1	no	—
461	C₄²	—	178	2	no	—
462	C₄²	—	178	1	no	—
463	C₄²	—	178	1	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	178	2	no	—
466	C₂³	#41×D₈₉	1	1	yes	characteristic
467	Q₈	—	2	1	no	—
468	Q₈	—	178	2	no	—
469	Q₈	—	178	2	no	—
470	Q₈	#15667974	1	2	yes	—
471	D₄	—	2	2	no	—
472	D₄	—	2	2	no	—
473	D₄	—	2	1	no	—
474	D₄	—	356	2	no	—
475	D₄	—	356	2	no	—
476	D₄	—	178	2	no	—
477	D₄	—	178	2	no	—
478	D₄	#15667974	1	2	yes	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	356	2	no	—
484	C₂×C₄	—	356	4	no	—
485	C₂×C₄	—	356	2	no	—
486	C₂×C₄	—	356	2	no	—
487	C₂×C₄	—	178	2	no	—
488	C₂×C₄	—	178	1	no	—
489	C₂×C₄	—	178	2	no	—
490	C₂×C₄	—	178	1	no	—
491	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
493	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
494	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
495	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
496	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	4	2	no	—
499	C₈	—	89	1	no	—
500	C₈	—	89	1	no	—
501	C₈	—	89	1	no	—
502	C₈	—	89	1	no	—
503	C₈	—	178	4	no	—
504	C₈	—	178	2	no	—
505	C₈	#15667972	1	1	yes	characteristic
506	C₈	#15667972	1	1	yes	characteristic
507	C₈	#15667972	1	1	yes	characteristic
508	C₈	#15667972	1	1	yes	characteristic
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	356	2	no	—
513	C₂²	—	712	2	no	—
514	C₂²	#19152066	1	1	yes	characteristic
515	C₂²	#19152111	1	1	yes	characteristic
516	C₂²	#19152143	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	8	2	no	—
519	C₄	—	356	1	no	—
520	C₄	—	356	2	no	—
521	C₄	—	356	2	no	—
522	C₄	—	178	2	no	—
523	C₄	C₂×#15667972	1	1	yes	characteristic
524	C₄	C₂×#15667974	1	1	yes	characteristic
525	C₄	#121×D₈₉	1	1	yes	characteristic
526	C₄	#19152134	1	1	yes	characteristic
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	2	1	no	—
530	C₂	—	4	2	no	—
531	C₂	—	712	2	no	—
532	C₂	#26022758	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1814	C₂
socle	C₂×C₈₉	C₄×#121
prime radical	#26029972	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1814	D₈₉
hypocenter	C₈₉	#21558
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1814

Complements

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

N	H ≅ G/N	type
2. #26029151	C₂	semidirect
3. C₂×#19151714	C₂	semidirect
4. #131×Dic₈₉	C₂	semidirect
5. #26021148	C₂	semidirect
6. #26021040	C₂	semidirect
7. #26020919	C₂	semidirect
8. #26020751	C₂	semidirect
9. #26020133	C₂	semidirect
10. #26020051	C₂	semidirect
11. C₈₉×#1814	C₂	semidirect
17. #19151873	C₄	semidirect
18. #19151868	C₄	semidirect
19. #19151861	C₄	semidirect
58. C₂×Dic₃₅₆	C₂×C₄	semidirect
59. C₂×#13083563	C₂×C₄	semidirect
60. C₂×D₇₁₂	C₂×C₄	semidirect
83. #15667948	C₂×C₄	semidirect
84. #15667948	C₂×C₄	semidirect
89. #15667930	C₂×C₄	semidirect
90. #15667928	C₂×C₄	semidirect
275. #1814	D₈₉	semidirect
278. C₈₉	#21558	semidirect

Maximal subgroups

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

subgroup	index
#26029972	2
#26029151	2
C₂×#19151714	2
#131×Dic₈₉	2
#26021148	2
#26021040	2
#26020919	2
#26020751	2
#26020133	2
#26020051	2
C₈₉×#1814	2
#21558	89