Subgroups — #36561373

Order 22784.

868 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029973	C₂	1	1	yes	maximal, characteristic
2	#26029154	C₂	1	2	yes	maximal, complemented
3	C₂×#19151719	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028679	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021150	C₂	1	1	yes	maximal, characteristic, complemented
6	#26020920	C₂	1	2	yes	maximal, complemented
7	#26020754	C₂	1	2	yes	maximal, complemented
8	#26020307	C₂	1	1	yes	maximal, characteristic, complemented
9	#26020139	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020051	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1953	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152398	C₂²	1	2	yes	—
13	C₂×#15668034	C₂²	1	1	yes	characteristic
14	C₂×#15668020	C₂²	1	2	yes	—
15	C₂×#15668020	C₂²	1	1	yes	characteristic
16	C₂×#15668018	C₂²	1	1	yes	characteristic
17	#19152066	C₂²	1	1	yes	characteristic
18	#19151874	C₄	1	2	yes	complemented
19	#19151869	C₄	1	2	yes	complemented
20	#19151862	C₄	1	4	yes	complemented
21	#19151719	—	2	1	no	—
22	#19151719	—	2	1	no	—
23	#19151719	—	2	1	no	—
24	#19151719	—	2	1	no	—
25	#19151719	—	2	4	no	—
26	#19151714	—	2	4	no	—
27	#19151636	C₂²	1	1	yes	characteristic
28	#19151614	C₂²	1	2	yes	—
29	#19151614	C₂²	1	2	yes	—
30	C₂×#15667938	C₂²	1	2	yes	—
31	#19151580	C₂²	1	2	yes	—
32	#19151571	C₂²	1	2	yes	—
33	#19151556	C₂²	1	2	yes	—
34	#19151555	—	2	1	no	—
35	#19151554	C₂²	1	1	yes	characteristic
36	#19151552	—	2	1	no	—
37	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
38	C₄×#13083557	—	2	1	no	—
39	C₂×#15667922	C₂²	1	1	yes	characteristic
40	#97×D₈₉	—	2	1	no	—
41	#19151369	C₂²	1	2	yes	—
42	#19151359	C₂²	1	2	yes	—
43	#430×C₈₉	C₂²	1	2	yes	—
44	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
46	#405×C₈₉	C₂²	1	1	yes	characteristic
47	#344×C₈₉	C₂²	1	2	yes	—
48	C₂×#13083574	C₂³	1	2	yes	—
49	C₂×#13083574	C₂³	1	1	yes	characteristic
50	#15668045	—	2	2	no	—
51	#15668045	C₂×C₄	1	4	yes	—
52	#15668040	—	2	2	no	—
53	#15668040	C₂×C₄	1	4	yes	—
54	#15668034	—	2	4	no	—
55	#15668034	—	2	1	no	—
56	#15668034	—	2	1	no	—
57	#15668034	—	2	1	no	—
58	#15668034	—	2	1	no	—
59	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic, complemented
60	C₂×#13083563	C₂×C₄	1	2	yes	complemented
61	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic, complemented
62	#15668020	—	2	2	no	—
63	#15668020	—	2	2	no	—
64	#15668020	—	2	2	no	—
65	#15668020	—	2	2	no	—
66	#15668020	—	2	2	no	—
67	#15668020	D₄	1	4	yes	—
68	#15668018	—	2	1	no	—
69	#15668018	—	2	1	no	—
70	#15668018	C₂×C₄	1	2	yes	—
71	#15668018	C₂×C₄	1	2	yes	—
72	C₂×#13083558	C₂³	1	1	yes	characteristic
73	C₂×#13083557	—	2	1	no	—
74	C₂×#13083557	—	2	2	no	—
75	C₂×#13083557	—	2	1	no	—
76	C₂²×#10623494	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₈₉	—	2	1	no	—
78	C₂×C₈×D₈₉	—	2	2	no	—
79	C₂×C₈×D₈₉	—	2	1	no	—
80	#15667977	—	2	1	no	—
81	#15667974	—	2	1	no	—
82	#15667972	—	2	2	no	—
83	#15667971	C₂³	1	2	yes	—
84	#15667969	—	2	1	no	—
85	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
86	C₄²×D₈₉	—	2	1	no	—
87	#15667946	—	2	1	no	—
88	#15667944	—	2	1	no	—
89	#15667938	—	2	4	no	—
90	#15667938	—	2	2	no	—
91	#15667938	—	2	2	no	—
92	#15667938	—	2	4	no	—
93	#15667930	C₂×C₄	1	4	yes	complemented
94	#15667928	C₂×C₄	1	4	yes	complemented
95	#15667926	—	2	4	no	—
96	#15667923	—	2	1	no	—
97	#15667922	—	2	2	no	—
98	#15667922	—	2	1	no	—
99	#15667922	D₄	1	1	yes	characteristic
100	#15667922	D₄	1	1	yes	characteristic
101	#15667922	D₄	1	1	yes	characteristic
102	#15667922	D₄	1	1	yes	characteristic
103	C₄×#10623494	—	2	1	no	—
104	C₈×Dic₈₉	—	2	2	no	—
105	C₈×Dic₈₉	—	2	1	no	—
106	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
107	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
108	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#117×C₈₉	C₂³	1	1	yes	characteristic
111	#108×C₈₉	—	2	4	no	—
112	#108×C₈₉	—	2	1	no	—
113	#108×C₈₉	—	2	1	no	—
114	#108×C₈₉	C₂×C₄	1	2	yes	complemented
115	#108×C₈₉	C₂×C₄	1	2	yes	complemented
116	#97×C₈₉	—	2	1	no	—
117	C₄×C₈×C₈₉	—	2	1	no	—
118	#13083574	—	2	1	no	—
119	#13083574	—	2	1	no	—
120	#13083574	—	2	2	no	—
121	#13083574	—	2	2	no	—
122	#13083574	—	2	2	no	—
123	#13083574	—	2	2	no	—
124	#13083574	C₂²×C₄	1	2	yes	—
125	#13083574	C₂×D₄	1	2	yes	—
126	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
127	C₂×Dic₁₇₈	#41	1	1	yes	characteristic
128	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
129	C₂×D₃₅₆	#41	1	1	yes	characteristic
130	C₂×C₂²⋊D₈₉	—	2	1	no	—
131	C₂×C₂²⋊D₈₉	—	2	2	no	—
132	C₂²×Dic₈₉	—	2	1	no	—
133	C₂×C₄×D₈₉	—	2	1	no	—
134	C₂×C₄×D₈₉	—	2	2	no	—
135	C₂×C₄×D₈₉	—	2	2	no	—
136	Dic₃₅₆	—	2	4	no	—
137	Dic₃₅₆	—	2	1	no	—
138	Dic₃₅₆	—	2	1	no	—
139	#13083563	—	2	4	no	—
140	#13083563	—	2	4	no	—
141	#13083563	—	2	2	no	—
142	#13083563	—	2	2	no	—
143	D₇₁₂	—	2	4	no	—
144	D₇₁₂	—	2	1	no	—
145	D₇₁₂	—	2	1	no	—
146	#13083558	—	2	1	no	—
147	#13083558	C₂²×C₄	1	2	yes	—
148	#13083557	—	2	2	no	—
149	#13083557	—	2	2	no	—
150	#13083557	—	2	4	no	—
151	#13083557	—	4	2	no	—
152	#13083557	—	4	2	no	—
153	C₂×#10623494	—	2	1	no	—
154	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
155	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
156	C₂×#10623494	C₂×D₄	1	2	yes	—
157	C₂×#10623494	#41	1	2	yes	—
158	C₈×D₈₉	—	2	2	no	—
159	C₈×D₈₉	—	2	2	no	—
160	C₈×D₈₉	—	2	4	no	—
161	C₈×D₈₉	—	4	2	no	—
162	C₈×D₈₉	—	4	2	no	—
163	C₄⋊Dic₈₉	—	2	2	no	—
164	#13083553	—	2	2	no	—
165	C₂²⋊Dic₈₉	—	2	2	no	—
166	#13083551	—	2	2	no	—
167	C₄×Dic₈₉	—	2	2	no	—
168	C₄×Dic₈₉	—	2	1	no	—
169	C₄×Dic₈₉	—	2	2	no	—
170	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
171	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	M₁₆×C₈₉	—	2	1	no	—
174	M₁₆×C₈₉	—	2	2	no	—
175	M₁₆×C₈₉	—	2	2	no	—
176	M₁₆×C₈₉	—	2	2	no	—
177	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
178	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	2	no	—
181	C₂×C₈×C₈₉	—	2	2	no	—
182	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
187	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₂²⋊C₄×C₈₉	#41	1	2	yes	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
192	C₂²×D₈₉	—	2	1	no	—
193	C₂²×D₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
201	C₂²⋊D₈₉	—	2	2	no	—
202	C₂²⋊D₈₉	—	2	2	no	—
203	C₂²⋊D₈₉	—	4	2	no	—
204	C₂²⋊D₈₉	—	4	2	no	—
205	C₂×Dic₈₉	—	2	1	no	—
206	C₂×Dic₈₉	—	2	2	no	—
207	C₂×Dic₈₉	—	2	1	no	—
208	C₂×Dic₈₉	—	2	1	no	—
209	C₂×Dic₈₉	—	4	2	no	—
210	C₂×Dic₈₉	—	8	1	no	—
211	D₃₅₆	—	2	2	no	—
212	D₃₅₆	—	2	2	no	—
213	D₃₅₆	—	2	1	no	—
214	D₃₅₆	C₄×D₄	1	2	yes	—
215	C₄×D₈₉	—	2	2	no	—
216	C₄×D₈₉	—	2	2	no	—
217	C₄×D₈₉	—	4	2	no	—
218	C₄×D₈₉	—	4	2	no	—
219	C₄×D₈₉	—	8	2	no	—
220	Dic₁₇₈	—	2	1	no	—
221	Dic₁₇₈	—	2	2	no	—
222	Dic₁₇₈	—	2	2	no	—
223	Dic₁₇₈	C₄×D₄	1	2	yes	—
224	C₈×C₈₉	—	2	4	no	—
225	C₈×C₈₉	—	2	2	no	—
226	C₈×C₈₉	—	4	2	no	—
227	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
228	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
229	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
230	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
231	#10623494	—	2	2	no	—
232	#10623494	#121	1	2	yes	—
233	#10623494	#121	1	2	yes	—
234	C₂²×C₈₉	—	4	1	no	—
235	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
236	C₂²×C₈₉	#525	1	1	yes	characteristic
237	C₂²×C₈₉	#532	1	1	yes	characteristic
238	C₂×D₈₉	—	2	2	no	—
239	C₂×D₈₉	—	4	2	no	—
240	C₂×D₈₉	—	4	2	no	—
241	C₂×D₈₉	—	8	2	no	—
242	C₄×C₈₉	—	4	2	no	—
243	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
244	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
246	C₄×C₈₉	#529	1	1	yes	characteristic
247	Dic₈₉	—	2	2	no	—
248	Dic₈₉	—	4	1	no	—
249	Dic₈₉	—	4	1	no	—
250	Dic₈₉	—	4	2	no	—
251	Dic₈₉	—	8	2	no	—
252	#21559	—	89	1	no	maximal, Sylow
253	C₂×C₈₉	—	2	1	no	—
254	C₂×C₈₉	—	2	1	no	—
255	C₂×C₈₉	—	2	1	no	—
256	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
257	D₈₉	—	4	2	no	—
258	D₈₉	—	8	2	no	—
259	#3067	—	89	1	no	—
260	#2955	—	89	2	no	—
261	C₂×#444	—	89	1	no	—
262	#2875	—	89	1	no	—
263	#1976	—	89	1	no	—
264	#1953	D₈₉	1	1	yes	characteristic, complemented
265	#1932	—	89	2	no	—
266	#1906	—	89	2	no	—
267	#1814	—	89	1	no	—
268	#1773	—	89	1	no	—
269	#1757	—	89	2	no	—
270	C₈₉	#21559	1	1	yes	characteristic, complemented, Sylow
271	#575	—	89	2	no	—
272	C₂×#135	—	89	1	no	—
273	C₂×#131	—	89	1	no	—
274	C₂×#131	—	89	2	no	—
275	C₂×#131	—	89	1	no	—
276	C₄×#41	—	89	1	no	—
277	#473	—	89	2	no	—
278	#472	—	89	2	no	—
279	#471	—	89	4	no	—
280	#444	—	178	1	no	—
281	#444	—	178	1	no	—
282	#444	—	178	1	no	—
283	#444	—	178	1	no	—
284	#444	—	178	4	no	—
285	#443	—	178	4	no	—
286	#430	C₂×D₈₉	1	2	yes	—
287	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
288	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
289	#427	—	89	1	no	—
290	#421	—	89	2	no	—
291	#421	—	89	2	no	—
292	C₂×#104	—	89	2	no	—
293	#413	—	89	2	no	—
294	#410	—	89	2	no	—
295	#405	—	89	2	no	—
296	#405	—	89	1	no	—
297	#405	—	178	1	no	—
298	#405	—	178	1	no	—
299	#405	C₂×D₈₉	1	1	yes	characteristic
300	C₄×M₁₆	—	89	1	no	—
301	C₄×M₁₆	—	178	1	no	—
302	C₂×#97	—	89	1	no	—
303	C₂×#97	—	178	1	no	—
304	#344	—	89	2	no	—
305	#344	C₂×D₈₉	1	2	yes	—
306	#339	—	89	2	no	—
307	C₂×#41	—	89	1	no	—
308	C₂×#41	—	89	2	no	—
309	#137	—	89	4	no	—
310	#137	—	178	2	no	—
311	AGL(1,ℤ/8)	—	89	4	no	—
312	AGL(1,ℤ/8)	—	178	2	no	—
313	#135	—	178	4	no	—
314	#135	—	178	1	no	—
315	#135	—	178	1	no	—
316	#135	—	178	1	no	—
317	#135	—	178	1	no	—
318	C₂×Q₁₆	—	89	1	no	—
319	C₂×SD₁₆	—	89	2	no	—
320	C₂×D₈	—	89	1	no	—
321	#131	—	89	4	no	—
322	#131	—	89	2	no	—
323	#131	—	89	2	no	—
324	#131	—	178	2	no	—
325	#131	—	178	2	no	—
326	#131	—	178	2	no	—
327	#131	—	178	2	no	—
328	#131	—	178	2	no	—
329	#131	—	178	1	no	—
330	#131	—	178	1	no	—
331	C₂×M₁₆	—	89	1	no	—
332	C₂×M₁₆	—	178	2	no	—
333	C₂×M₁₆	—	178	1	no	—
334	C₂×M₁₆	—	178	1	no	—
335	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
336	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
337	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
338	C₂²×C₈	—	89	1	no	—
339	C₂²×C₈	—	178	2	no	—
340	C₂²×C₈	—	178	1	no	—
341	C₂²×C₈	—	178	1	no	—
342	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
343	C₄×Q₈	—	178	1	no	—
344	C₄×D₄	—	178	1	no	—
345	C₄×D₄	—	178	2	no	—
346	#117	—	89	2	no	—
347	#117	—	178	1	no	—
348	#117	C₂²×D₈₉	1	1	yes	characteristic
349	C₂×C₄²	—	89	1	no	—
350	C₂×C₄²	—	178	1	no	—
351	#108	—	2	4	no	—
352	#108	—	2	1	no	—
353	#108	—	2	1	no	—
354	#108	C₄×D₈₉	1	2	yes	complemented
355	#108	C₄×D₈₉	1	2	yes	complemented
356	#107	—	178	1	no	—
357	#106	—	178	1	no	—
358	#104	—	178	2	no	—
359	#104	—	178	2	no	—
360	#104	—	178	4	no	—
361	#104	—	178	4	no	—
362	#101	—	89	4	no	—
363	#100	—	89	4	no	—
364	#99	—	178	4	no	—
365	#97	—	2	1	no	—
366	#97	—	89	1	no	—
367	#97	—	89	1	no	—
368	#97	—	89	1	no	—
369	#97	—	89	1	no	—
370	#97	—	178	1	no	—
371	#97	—	178	1	no	—
372	#97	—	178	2	no	—
373	C₄×C₈	—	2	1	no	—
374	C₄×C₈	—	178	1	no	—
375	C₄×C₈	—	178	1	no	—
376	C₄×C₈	—	178	2	no	—
377	#41	—	89	2	no	—
378	#41	—	89	2	no	—
379	#41	—	178	2	no	—
380	#41	—	178	2	no	—
381	#41	—	178	2	no	—
382	#41	—	178	2	no	—
383	#41	—	178	1	no	—
384	#41	—	178	1	no	—
385	C₂×Q₈	—	89	2	no	—
386	C₂×Q₈	—	89	1	no	—
387	C₂×D₄	—	89	2	no	—
388	C₂×D₄	—	89	1	no	—
389	C₂×D₄	—	178	2	no	—
390	C₂×D₄	—	178	1	no	—
391	C₂²×C₄	—	178	2	no	—
392	C₂²×C₄	—	178	2	no	—
393	C₂²×C₄	—	178	1	no	—
394	C₂²×C₄	—	178	1	no	—
395	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
396	Q₁₆	—	178	4	no	—
397	Q₁₆	—	178	1	no	—
398	Q₁₆	—	178	1	no	—
399	SD₁₆	—	178	4	no	—
400	SD₁₆	—	178	4	no	—
401	SD₁₆	—	178	2	no	—
402	SD₁₆	—	178	2	no	—
403	D₈	—	178	4	no	—
404	D₈	—	178	1	no	—
405	D₈	—	178	1	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	89	2	no	—
411	M₁₆	—	356	2	no	—
412	M₁₆	—	356	2	no	—
413	M₁₆	—	178	4	no	—
414	M₁₆	—	178	1	no	—
415	M₁₆	—	178	2	no	—
416	M₁₆	—	178	2	no	—
417	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
418	M₁₆	D₄×D₈₉	1	2	yes	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	89	1	no	—
423	C₂×C₈	—	89	2	no	—
424	C₂×C₈	—	89	1	no	—
425	C₂×C₈	—	89	2	no	—
426	C₂×C₈	—	356	2	no	—
427	C₂×C₈	—	356	2	no	—
428	C₂×C₈	—	178	4	no	—
429	C₂×C₈	—	178	1	no	—
430	C₂×C₈	—	178	2	no	—
431	C₂×C₈	—	178	2	no	—
432	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
433	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
434	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
435	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
436	C₂×C₈	#13083575	1	1	yes	characteristic
437	C₂×C₈	#13083575	1	1	yes	characteristic
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	178	2	no	—
440	C₄⋊C₄	—	178	2	no	—
441	C₂²⋊C₄	—	178	2	no	—
442	C₂²⋊C₄	—	178	2	no	—
443	C₂²⋊C₄	#13083575	1	2	yes	—
444	C₄²	—	2	1	no	—
445	C₄²	—	89	1	no	—
446	C₄²	—	89	1	no	—
447	C₄²	—	178	2	no	—
448	C₄²	—	178	2	no	—
449	C₄²	—	178	1	no	—
450	C₂³	—	178	1	no	—
451	C₂³	—	178	2	no	—
452	C₂³	C₂×#13083575	1	1	yes	characteristic
453	Q₈	—	89	2	no	—
454	Q₈	—	178	2	no	—
455	Q₈	—	178	2	no	—
456	Q₈	—	178	1	no	—
457	D₄	—	89	2	no	—
458	D₄	—	356	2	no	—
459	D₄	—	356	2	no	—
460	D₄	—	178	2	no	—
461	D₄	—	178	2	no	—
462	D₄	—	178	1	no	—
463	D₄	—	178	2	no	—
464	D₄	—	178	2	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	356	2	no	—
467	C₂×C₄	—	356	2	no	—
468	C₂×C₄	—	356	2	no	—
469	C₂×C₄	—	178	2	no	—
470	C₂×C₄	—	178	1	no	—
471	C₂×C₄	—	178	1	no	—
472	C₂×C₄	—	178	1	no	—
473	C₂×C₄	—	178	2	no	—
474	C₂×C₄	—	178	2	no	—
475	C₂×C₄	—	712	2	no	—
476	C₂×C₄	—	712	1	no	—
477	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
479	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
480	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
481	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
482	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
483	C₈	—	2	4	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	89	2	no	—
487	C₈	—	89	2	no	—
488	C₈	—	178	2	no	—
489	C₈	#15667974	1	1	yes	characteristic
490	C₈	#15667974	1	1	yes	characteristic
491	C₈	#15667974	1	1	yes	characteristic
492	C₈	#15667974	1	1	yes	characteristic
493	C₂²	—	4	1	no	—
494	C₂²	—	356	2	no	—
495	C₂²	—	356	2	no	—
496	C₂²	—	178	2	no	—
497	C₂²	—	712	2	no	—
498	C₂²	C₄×#13083575	1	1	yes	characteristic
499	C₂²	#19152111	1	1	yes	characteristic
500	C₂²	#19152149	1	1	yes	characteristic
501	C₄	—	4	2	no	—
502	C₄	—	356	1	no	—
503	C₄	—	356	1	no	—
504	C₄	—	356	2	no	—
505	C₄	—	178	2	no	—
506	C₄	—	712	2	no	—
507	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
508	C₄	C₂×#15667974	1	1	yes	characteristic
509	C₄	#121×D₈₉	1	1	yes	characteristic
510	C₄	#19152133	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	356	2	no	—
515	C₂	—	712	2	no	—
516	C₂	#26022760	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#121×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1953	C₂
socle	C₂×C₈₉	C₄×#121
prime radical	#26029973	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1953	D₈₉
hypocenter	C₈₉	#21559
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1953

Complements

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

N	H ≅ G/N	type
2. #26029154	C₂	semidirect
3. C₂×#19151719	C₂	semidirect
4. #26028679	C₂	semidirect
5. #26021150	C₂	semidirect
6. #26020920	C₂	semidirect
7. #26020754	C₂	semidirect
8. #26020307	C₂	semidirect
9. #26020139	C₂	semidirect
10. #26020051	C₂	semidirect
11. C₈₉×#1953	C₂	semidirect
18. #19151874	C₄	semidirect
19. #19151869	C₄	semidirect
20. #19151862	C₄	semidirect
59. C₂×Dic₃₅₆	C₂×C₄	semidirect
60. C₂×#13083563	C₂×C₄	semidirect
61. C₂×D₇₁₂	C₂×C₄	semidirect
93. #15667930	C₂×C₄	semidirect
94. #15667928	C₂×C₄	semidirect
114. #108×C₈₉	C₂×C₄	semidirect
115. #108×C₈₉	C₂×C₄	semidirect
264. #1953	D₈₉	semidirect
270. C₈₉	#21559	semidirect
354. #108	C₄×D₈₉	semidirect
355. #108	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029973	2
#26029154	2
C₂×#19151719	2
#26028679	2
#26021150	2
#26020920	2
#26020754	2
#26020307	2
#26020139	2
#26020051	2
C₈₉×#1953	2
#21559	89