Subgroups — #26035037

Order 11392.

1412 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152435	C₂	1	1	yes	maximal, characteristic, complemented
2	2₋¹⁺⁴×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#19152414	C₂	1	3	yes	maximal, complemented
4	#19152413	C₂	1	1	yes	maximal, characteristic, complemented
5	#19152411	C₂	1	3	yes	maximal, complemented
6	#19152410	C₂	1	1	yes	maximal, characteristic, complemented
7	#19152407	C₂	1	3	yes	maximal, complemented
8	#19152406	C₂	1	1	yes	maximal, characteristic, complemented
9	#19152405	C₂	1	3	yes	maximal, complemented
10	#19152397	C₂	1	3	yes	maximal, complemented
11	#19152395	C₂	1	3	yes	maximal, complemented
12	C₂×#15668044	C₂	1	3	yes	maximal, complemented
13	#137×D₈₉	C₂	1	3	yes	maximal, complemented
14	#19152363	C₂	1	1	yes	maximal, characteristic, complemented
15	#578×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#15668060	—	2	1	no	—
17	#15668060	—	2	1	no	—
18	#15668060	C₂²	1	3	yes	complemented
19	#15668060	C₂²	1	3	yes	complemented
20	#15668059	—	2	3	no	—
21	#15668059	C₂²	1	1	yes	characteristic, complemented
22	#15668059	C₂²	1	3	yes	complemented
23	#15668058	—	2	3	no	—
24	#15668058	C₂²	1	1	yes	characteristic, complemented
25	#15668058	C₂²	1	3	yes	complemented
26	C₂×#13083575	—	2	1	no	—
27	C₂×#13083575	C₂²	1	3	yes	—
28	#41×D₈₉	—	2	3	no	—
29	#41×D₈₉	—	2	3	no	—
30	#41×D₈₉	C₂²	1	3	yes	—
31	#41×D₈₉	C₂²	1	1	yes	characteristic
32	#41×D₈₉	C₂²	1	3	yes	complemented
33	C₂×Q₈×D₈₉	—	2	1	no	—
34	C₂×Q₈×D₈₉	C₂²	1	3	yes	complemented
35	#15668045	C₂²	1	3	yes	complemented
36	#15668044	C₂²	1	6	yes	complemented
37	#15668044	C₂²	1	3	yes	complemented
38	#15668044	C₂²	1	6	yes	complemented
39	#15668044	C₂²	1	6	yes	complemented
40	#15668044	C₂²	1	3	yes	complemented
41	#15668043	C₂²	1	3	yes	complemented
42	#15668043	C₂²	1	3	yes	complemented
43	#15668042	C₂²	1	3	yes	complemented
44	#15668041	C₂²	1	3	yes	complemented
45	#15668041	C₂²	1	3	yes	complemented
46	#15668040	C₂²	1	3	yes	complemented
47	#15668039	C₂²	1	3	yes	complemented
48	#15668039	C₂²	1	3	yes	complemented
49	#15668037	C₂²	1	3	yes	complemented
50	#15668036	C₂²	1	1	yes	characteristic, complemented
51	#15668036	C₂²	1	3	yes	complemented
52	#15668035	C₂²	1	6	yes	complemented
53	#15668034	C₂²	1	3	yes	complemented
54	#15668033	C₂²	1	6	yes	complemented
55	#15668032	C₂²	1	3	yes	complemented
56	#15668032	C₂²	1	3	yes	complemented
57	C₂×#13083564	C₂²	1	3	yes	complemented
58	Q₁₆×D₈₉	C₂²	1	6	yes	complemented
59	C₂×#13083563	C₂²	1	3	yes	complemented
60	C₂×#13083561	C₂²	1	3	yes	complemented
61	SD₁₆×D₈₉	C₂²	1	6	yes	complemented
62	#15668020	C₂²	1	3	yes	complemented
63	#15668019	C₂²	1	1	yes	characteristic, complemented
64	#15668018	C₂²	1	3	yes	complemented
65	C₂×#13083557	C₂²	1	3	yes	complemented
66	M₁₆×D₈₉	C₂²	1	3	yes	complemented
67	2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
68	2₋¹⁺⁴×C₈₉	C₂²	1	1	yes	characteristic, complemented
69	#137×C₈₉	C₂²	1	3	yes	complemented
70	#137×C₈₉	C₂²	1	3	yes	complemented
71	#135×C₈₉	C₂²	1	3	yes	complemented
72	C₂×Q₁₆×C₈₉	C₂²	1	3	yes	complemented
73	#131×C₈₉	C₂²	1	1	yes	characteristic, complemented
74	#13083575	—	2	1	no	—
75	#13083575	—	2	3	no	—
76	#13083575	—	2	3	no	—
77	#13083575	—	2	3	no	—
78	#13083575	—	2	3	no	—
79	#13083575	D₄	1	1	yes	characteristic
80	#13083575	C₂³	1	6	yes	—
81	#13083575	C₂³	1	3	yes	—
82	#13083575	C₂³	1	3	yes	—
83	#13083574	—	2	6	no	—
84	#13083574	—	2	6	no	—
85	#13083574	—	2	3	no	—
86	#13083574	—	2	3	no	—
87	#13083574	—	2	3	no	—
88	#13083574	—	2	3	no	—
89	#13083574	C₂³	1	3	yes	—
90	#13083574	C₂³	1	3	yes	—
91	#13083574	C₂³	1	3	yes	—
92	#13083573	—	2	3	no	—
93	#13083573	—	2	6	no	—
94	#13083573	—	2	3	no	—
95	#13083573	—	2	3	no	—
96	#13083573	D₄	1	3	yes	—
97	#13083573	C₂³	1	3	yes	—
98	#13083573	C₂³	1	1	yes	characteristic
99	C₂×Dic₁₇₈	—	2	3	no	—
100	C₂×Dic₁₇₈	—	2	3	no	—
101	C₂×Dic₁₇₈	C₂³	1	3	yes	—
102	Q₈×D₈₉	—	2	1	no	—
103	Q₈×D₈₉	—	2	3	no	—
104	Q₈×D₈₉	—	2	3	no	—
105	Q₈×D₈₉	—	2	3	no	—
106	Q₈×D₈₉	—	2	3	no	—
107	Q₈×D₈₉	D₄	1	1	yes	characteristic
108	Q₈×D₈₉	C₂³	1	6	yes	—
109	Q₈×D₈₉	C₂³	1	3	yes	—
110	Q₈×D₈₉	C₂³	1	3	yes	—
111	C₂×D₃₅₆	—	2	3	no	—
112	C₂×D₃₅₆	—	2	3	no	—
113	C₂×D₃₅₆	C₂³	1	3	yes	—
114	D₄×D₈₉	—	2	3	no	—
115	D₄×D₈₉	—	2	3	no	—
116	D₄×D₈₉	—	2	3	no	—
117	D₄×D₈₉	—	2	6	no	—
118	D₄×D₈₉	D₄	1	3	yes	—
119	D₄×D₈₉	C₂³	1	3	yes	—
120	D₄×D₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄×D₈₉	—	2	3	no	—
122	C₂×C₄×D₈₉	—	2	3	no	—
123	C₂×C₄×D₈₉	—	2	3	no	—
124	C₂×C₄×D₈₉	—	2	3	no	—
125	C₂×C₄×D₈₉	C₂³	1	3	yes	—
126	Dic₃₅₆	C₂³	1	3	yes	—
127	#13083564	C₂³	1	3	yes	—
128	#13083564	C₂³	1	6	yes	—
129	#13083564	C₂³	1	3	yes	—
130	#13083563	C₂³	1	6	yes	—
131	#13083563	C₂³	1	3	yes	—
132	#13083563	C₂³	1	1	yes	characteristic
133	#13083562	C₂³	1	3	yes	—
134	#13083562	C₂³	1	1	yes	characteristic
135	#13083561	C₂³	1	6	yes	—
136	#13083561	C₂³	1	3	yes	—
137	#13083561	C₂³	1	3	yes	—
138	D₇₁₂	C₂³	1	3	yes	—
139	#13083559	C₂³	1	1	yes	characteristic
140	#13083559	C₂³	1	3	yes	—
141	#13083558	C₂³	1	3	yes	—
142	#13083557	C₂³	1	3	yes	—
143	#13083557	C₂³	1	1	yes	characteristic
144	#13083557	C₂³	1	3	yes	—
145	#13083557	C₂³	1	3	yes	—
146	C₂×#10623494	C₂³	1	3	yes	—
147	C₈×D₈₉	C₂³	1	6	yes	—
148	#41×C₈₉	—	2	3	no	—
149	#41×C₈₉	—	2	3	no	—
150	#41×C₈₉	C₂³	1	3	yes	—
151	#41×C₈₉	C₂³	1	3	yes	—
152	#41×C₈₉	C₂³	1	1	yes	characteristic
153	C₂×Q₈×C₈₉	—	2	1	no	—
154	C₂×Q₈×C₈₉	—	2	1	no	—
155	C₂×Q₈×C₈₉	C₂³	1	3	yes	—
156	C₂×Q₈×C₈₉	C₂³	1	3	yes	—
157	Q₁₆×C₈₉	C₂³	1	6	yes	—
158	Q₁₆×C₈₉	C₂³	1	3	yes	—
159	SD₁₆×C₈₉	C₂³	1	3	yes	—
160	SD₁₆×C₈₉	C₂³	1	3	yes	—
161	D₈×C₈₉	C₂³	1	1	yes	characteristic
162	M₁₆×C₈₉	C₂³	1	3	yes	—
163	C₂×C₈×C₈₉	C₂³	1	3	yes	—
164	C₂²×D₈₉	—	2	3	no	—
165	C₂²×D₈₉	—	2	1	no	—
166	C₂²×D₈₉	—	2	3	no	—
167	C₂²×D₈₉	C₂×D₄	1	3	yes	—
168	Q₈×C₈₉	—	2	3	no	—
169	Q₈×C₈₉	—	2	3	no	—
170	Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
171	Q₈×C₈₉	C₂⁴	1	3	yes	—
172	Q₈×C₈₉	C₂⁴	1	3	yes	—
173	D₄×C₈₉	—	2	3	no	—
174	D₄×C₈₉	—	2	3	no	—
175	D₄×C₈₉	C₂×D₄	1	3	yes	—
176	D₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	D₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₈₉	—	2	3	no	—
179	C₂×C₄×C₈₉	—	2	3	no	—
180	C₂×C₄×C₈₉	—	2	3	no	—
181	C₂×C₄×C₈₉	—	2	3	no	—
182	C₂×C₄×C₈₉	C₂⁴	1	3	yes	—
183	C₂²⋊D₈₉	—	2	3	no	—
184	C₂²⋊D₈₉	—	2	3	no	—
185	C₂²⋊D₈₉	—	2	1	no	—
186	C₂²⋊D₈₉	—	2	3	no	—
187	C₂²⋊D₈₉	—	2	3	no	—
188	C₂²⋊D₈₉	—	2	1	no	—
189	C₂²⋊D₈₉	C₂×D₄	1	6	yes	—
190	C₂×Dic₈₉	—	2	3	no	—
191	C₂×Dic₈₉	—	2	1	no	—
192	C₂×Dic₈₉	—	2	3	no	—
193	C₂×Dic₈₉	C₂×D₄	1	3	yes	—
194	D₃₅₆	—	2	3	no	—
195	D₃₅₆	—	2	6	no	—
196	D₃₅₆	—	2	3	no	—
197	D₃₅₆	—	2	3	no	—
198	D₃₅₆	C₂×D₄	1	3	yes	—
199	D₃₅₆	C₂⁴	1	1	yes	characteristic
200	D₃₅₆	C₂⁴	1	3	yes	—
201	C₄×D₈₉	—	2	3	no	—
202	C₄×D₈₉	—	2	3	no	—
203	C₄×D₈₉	—	2	6	no	—
204	C₄×D₈₉	—	2	3	no	—
205	C₄×D₈₉	—	2	3	no	—
206	C₄×D₈₉	—	2	3	no	—
207	C₄×D₈₉	—	2	6	no	—
208	C₄×D₈₉	—	2	3	no	—
209	C₄×D₈₉	C₂×D₄	1	3	yes	—
210	C₄×D₈₉	C₂×D₄	1	3	yes	—
211	C₄×D₈₉	C₂⁴	1	3	yes	—
212	C₄×D₈₉	C₂⁴	1	1	yes	characteristic
213	Dic₁₇₈	—	2	3	no	—
214	Dic₁₇₈	—	2	6	no	—
215	Dic₁₇₈	—	2	3	no	—
216	Dic₁₇₈	—	2	3	no	—
217	Dic₁₇₈	C₂×D₄	1	3	yes	—
218	Dic₁₇₈	C₂⁴	1	3	yes	—
219	Dic₁₇₈	C₂⁴	1	1	yes	characteristic
220	C₈×C₈₉	C₂⁴	1	1	yes	characteristic
221	C₈×C₈₉	C₂⁴	1	3	yes	—
222	#10623494	C₂⁴	1	3	yes	—
223	#10623494	C₂⁴	1	1	yes	characteristic
224	C₂²×C₈₉	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	C₂²×D₄	1	3	yes	—
227	C₂×D₈₉	—	2	1	no	—
228	C₂×D₈₉	—	2	3	no	—
229	C₂×D₈₉	—	4	3	no	—
230	C₂×D₈₉	—	4	2	no	—
231	C₂×D₈₉	—	8	3	no	—
232	C₂×D₈₉	—	8	3	no	—
233	C₂×D₈₉	C₂²×D₄	1	1	yes	characteristic
234	C₂×D₈₉	C₂²×D₄	1	3	yes	—
235	C₄×C₈₉	—	2	3	no	—
236	C₄×C₈₉	—	2	3	no	—
237	C₄×C₈₉	C₂²×D₄	1	3	yes	—
238	C₄×C₈₉	C₂⁵	1	1	yes	characteristic
239	Dic₈₉	—	2	3	no	—
240	Dic₈₉	—	2	1	no	—
241	Dic₈₉	C₂²×D₄	1	3	yes	—
242	Dic₈₉	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₈₉	—	2	3	no	—
244	C₂×C₈₉	—	4	1	no	—
245	C₂×C₈₉	—	4	1	no	—
246	C₂×C₈₉	C₂³×D₄	1	1	yes	characteristic
247	D₈₉	—	2	1	no	—
248	D₈₉	—	2	3	no	—
249	D₈₉	—	4	1	no	—
250	D₈₉	—	4	3	no	—
251	#3586	—	89	1	no	maximal, Sylow
252	C₈₉	#3586	1	1	yes	characteristic, complemented, Sylow
253	#585	—	89	1	no	—
254	C₂×2₋¹⁺⁴	—	89	1	no	—
255	#578	—	89	1	no	—
256	#578	—	89	3	no	—
257	#578	—	89	3	no	—
258	#578	D₈₉	1	1	yes	characteristic, complemented
259	#577	—	89	1	no	—
260	#577	—	89	3	no	—
261	#577	—	89	3	no	—
262	#577	—	89	1	no	—
263	#575	—	89	3	no	—
264	#575	—	89	3	no	—
265	C₂×#137	—	89	3	no	—
266	C₂×#137	—	89	3	no	—
267	#568	—	89	1	no	—
268	2₋¹⁺⁴	—	89	3	no	—
269	2₋¹⁺⁴	—	89	1	no	—
270	2₋¹⁺⁴	—	89	3	no	—
271	2₋¹⁺⁴	—	89	3	no	—
272	2₋¹⁺⁴	—	178	1	no	—
273	2₋¹⁺⁴	—	178	1	no	—
274	2₋¹⁺⁴	—	178	3	no	—
275	2₋¹⁺⁴	C₂×D₈₉	1	1	yes	characteristic, complemented
276	2₋¹⁺⁴	C₂×D₈₉	1	1	yes	characteristic, complemented
277	H(5,𝔽₂)	—	89	3	no	—
278	H(5,𝔽₂)	—	89	1	no	—
279	H(5,𝔽₂)	—	178	3	no	—
280	C₂×#41	—	89	1	no	—
281	C₂×#41	—	89	3	no	—
282	C₂×#41	—	89	3	no	—
283	C₂×#41	—	89	3	no	—
284	C₂×#41	—	178	3	no	—
285	C₂×#41	—	178	1	no	—
286	C₂×#41	—	178	3	no	—
287	C₂²×Q₈	—	89	3	no	—
288	C₂²×Q₈	—	178	1	no	—
289	#137	—	89	3	no	—
290	#137	—	89	3	no	—
291	#137	—	89	3	no	—
292	#137	—	89	6	no	—
293	#137	—	89	3	no	—
294	#137	—	89	6	no	—
295	#137	—	89	6	no	—
296	#137	—	89	3	no	—
297	#137	—	89	3	no	—
298	#137	—	89	3	no	—
299	#137	—	89	3	no	—
300	#137	C₂×D₈₉	1	3	yes	complemented
301	#137	C₂×D₈₉	1	3	yes	complemented
302	AGL(1,ℤ/8)	—	89	3	no	—
303	AGL(1,ℤ/8)	—	89	3	no	—
304	AGL(1,ℤ/8)	—	89	3	no	—
305	AGL(1,ℤ/8)	—	89	1	no	—
306	AGL(1,ℤ/8)	—	89	3	no	—
307	AGL(1,ℤ/8)	—	89	3	no	—
308	#135	—	89	3	no	—
309	#135	—	89	3	no	—
310	#135	—	89	6	no	—
311	#135	—	89	6	no	—
312	#135	—	89	3	no	—
313	#135	C₂×D₈₉	1	3	yes	complemented
314	C₂×Q₁₆	—	89	3	no	—
315	C₂×Q₁₆	—	89	6	no	—
316	C₂×Q₁₆	C₂×D₈₉	1	3	yes	complemented
317	C₂×SD₁₆	—	89	3	no	—
318	C₂×SD₁₆	—	89	6	no	—
319	C₂×SD₁₆	—	89	3	no	—
320	#131	—	89	1	no	—
321	#131	—	89	3	no	—
322	#131	—	89	3	no	—
323	#131	C₂×D₈₉	1	1	yes	characteristic, complemented
324	C₂×M₁₆	—	89	3	no	—
325	C₂×M₁₆	—	89	3	no	—
326	#41	—	2	3	no	—
327	#41	—	2	3	no	—
328	#41	—	89	1	no	—
329	#41	—	89	3	no	—
330	#41	—	89	3	no	—
331	#41	—	89	3	no	—
332	#41	—	89	6	no	—
333	#41	—	89	3	no	—
334	#41	—	89	3	no	—
335	#41	—	89	1	no	—
336	#41	—	89	3	no	—
337	#41	—	89	3	no	—
338	#41	—	178	3	no	—
339	#41	—	178	3	no	—
340	#41	—	178	6	no	—
341	#41	—	178	6	no	—
342	#41	—	178	3	no	—
343	#41	—	178	3	no	—
344	#41	—	178	3	no	—
345	#41	—	178	3	no	—
346	#41	—	178	3	no	—
347	#41	—	178	3	no	—
348	#41	—	178	6	no	—
349	#41	—	178	3	no	—
350	#41	—	178	3	no	—
351	#41	—	178	1	no	—
352	#41	—	178	3	no	—
353	#41	C₂²×D₈₉	1	3	yes	—
354	#41	C₂²×D₈₉	1	3	yes	—
355	#41	C₂²×D₈₉	1	1	yes	characteristic
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	89	1	no	—
359	C₂×Q₈	—	89	6	no	—
360	C₂×Q₈	—	89	3	no	—
361	C₂×Q₈	—	89	3	no	—
362	C₂×Q₈	—	89	3	no	—
363	C₂×Q₈	—	178	3	no	—
364	C₂×Q₈	—	178	3	no	—
365	C₂×Q₈	—	178	3	no	—
366	C₂×Q₈	—	178	3	no	—
367	C₂×Q₈	—	178	3	no	—
368	C₂×Q₈	—	178	3	no	—
369	C₂×Q₈	—	178	1	no	—
370	C₂×Q₈	C₂²×D₈₉	1	3	yes	—
371	C₂×Q₈	C₂²×D₈₉	1	3	yes	—
372	C₂×D₄	—	89	3	no	—
373	C₂×D₄	—	89	3	no	—
374	C₂×D₄	—	89	1	no	—
375	C₂×D₄	—	89	3	no	—
376	C₂×D₄	—	178	3	no	—
377	C₂×D₄	—	178	3	no	—
378	C₂×D₄	—	178	6	no	—
379	C₂×D₄	—	178	3	no	—
380	C₂×D₄	—	178	3	no	—
381	C₂×D₄	—	178	3	no	—
382	C₂²×C₄	—	89	3	no	—
383	C₂²×C₄	—	178	3	no	—
384	C₂²×C₄	—	178	3	no	—
385	C₂²×C₄	—	178	3	no	—
386	C₂²×C₄	—	178	3	no	—
387	Q₁₆	—	89	3	no	—
388	Q₁₆	—	89	6	no	—
389	Q₁₆	—	89	3	no	—
390	Q₁₆	—	89	3	no	—
391	Q₁₆	C₂²×D₈₉	1	6	yes	—
392	Q₁₆	C₂²×D₈₉	1	3	yes	—
393	SD₁₆	—	89	3	no	—
394	SD₁₆	—	89	6	no	—
395	SD₁₆	—	89	3	no	—
396	SD₁₆	—	89	3	no	—
397	SD₁₆	—	89	1	no	—
398	SD₁₆	—	89	6	no	—
399	SD₁₆	—	89	3	no	—
400	SD₁₆	—	89	1	no	—
401	SD₁₆	C₂²×D₈₉	1	3	yes	—
402	SD₁₆	C₂²×D₈₉	1	3	yes	—
403	D₈	—	89	1	no	—
404	D₈	—	89	3	no	—
405	D₈	—	89	3	no	—
406	D₈	C₂²×D₈₉	1	1	yes	characteristic
407	M₁₆	—	89	3	no	—
408	M₁₆	—	89	3	no	—
409	M₁₆	—	89	1	no	—
410	M₁₆	—	89	3	no	—
411	M₁₆	—	89	3	no	—
412	M₁₆	C₂²×D₈₉	1	3	yes	—
413	C₂×C₈	—	89	3	no	—
414	C₂×C₈	—	89	6	no	—
415	C₂×C₈	C₂²×D₈₉	1	3	yes	—
416	C₂³	—	89	3	no	—
417	C₂³	—	178	1	no	—
418	C₂³	—	178	3	no	—
419	C₂³	—	178	3	no	—
420	Q₈	—	2	3	no	—
421	Q₈	—	2	3	no	—
422	Q₈	—	89	3	no	—
423	Q₈	—	89	3	no	—
424	Q₈	—	89	1	no	—
425	Q₈	—	178	3	no	—
426	Q₈	—	178	6	no	—
427	Q₈	—	178	3	no	—
428	Q₈	—	178	3	no	—
429	Q₈	D₄×D₈₉	1	1	yes	characteristic
430	Q₈	C₂³×D₈₉	1	3	yes	—
431	Q₈	C₂³×D₈₉	1	3	yes	—
432	D₄	—	2	3	no	—
433	D₄	—	2	3	no	—
434	D₄	—	89	6	no	—
435	D₄	—	89	3	no	—
436	D₄	—	89	1	no	—
437	D₄	—	89	3	no	—
438	D₄	—	178	3	no	—
439	D₄	—	178	6	no	—
440	D₄	—	178	3	no	—
441	D₄	—	178	3	no	—
442	D₄	—	178	1	no	—
443	D₄	—	178	1	no	—
444	D₄	—	178	3	no	—
445	D₄	—	178	3	no	—
446	D₄	—	178	3	no	—
447	D₄	—	178	3	no	—
448	D₄	D₄×D₈₉	1	3	yes	—
449	D₄	C₂³×D₈₉	1	1	yes	characteristic
450	D₄	C₂³×D₈₉	1	1	yes	characteristic
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	3	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	3	no	—
455	C₂×C₄	—	89	3	no	—
456	C₂×C₄	—	89	3	no	—
457	C₂×C₄	—	89	3	no	—
458	C₂×C₄	—	89	3	no	—
459	C₂×C₄	—	89	1	no	—
460	C₂×C₄	—	178	3	no	—
461	C₂×C₄	—	178	6	no	—
462	C₂×C₄	—	178	3	no	—
463	C₂×C₄	—	178	3	no	—
464	C₂×C₄	—	178	3	no	—
465	C₂×C₄	—	178	6	no	—
466	C₂×C₄	—	178	1	no	—
467	C₂×C₄	—	178	3	no	—
468	C₂×C₄	—	178	3	no	—
469	C₂×C₄	—	178	3	no	—
470	C₂×C₄	—	178	3	no	—
471	C₂×C₄	C₂³×D₈₉	1	3	yes	—
472	C₈	—	89	3	no	—
473	C₈	—	89	1	no	—
474	C₈	C₂³×D₈₉	1	3	yes	—
475	C₈	C₂³×D₈₉	1	1	yes	characteristic
476	C₂²	—	2	1	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	89	1	no	—
479	C₂²	—	89	3	no	—
480	C₂²	—	356	3	no	—
481	C₂²	—	356	2	no	—
482	C₂²	—	178	1	no	—
483	C₂²	—	178	3	no	—
484	C₂²	—	712	3	no	—
485	C₂²	—	712	3	no	—
486	C₂²	C₂×D₄×D₈₉	1	3	yes	—
487	C₄	—	2	3	no	—
488	C₄	—	2	3	no	—
489	C₄	—	89	1	no	—
490	C₄	—	89	3	no	—
491	C₄	—	178	1	no	—
492	C₄	—	178	3	no	—
493	C₄	C₂×D₄×D₈₉	1	3	yes	—
494	C₄	C₂⁴×D₈₉	1	1	yes	characteristic
495	C₂	—	2	3	no	—
496	C₂	—	4	1	no	—
497	C₂	—	4	1	no	—
498	C₂	—	356	1	no	—
499	C₂	—	356	3	no	—
500	C₂	—	178	1	no	—
501	C₂	—	178	3	no	—
502	C₂	C₂²×D₄×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₈₉
commutator, cosocle	C₄×C₈₉	C₂⁵
Frattini	C₄	C₂⁴×D₈₉
Fitting	#578×C₈₉	C₂
socle	C₂×C₈₉	C₂³×D₄
hypercenter	#578	D₈₉
hypocenter	C₈₉	#3586
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ #41 ◁ #578

Complements

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

N	H ≅ G/N	type
1. #19152435	C₂	semidirect
2. 2₋¹⁺⁴×D₈₉	C₂	semidirect
3. #19152414	C₂	semidirect
4. #19152413	C₂	semidirect
5. #19152411	C₂	semidirect
6. #19152410	C₂	semidirect
7. #19152407	C₂	semidirect
8. #19152406	C₂	semidirect
9. #19152405	C₂	semidirect
10. #19152397	C₂	semidirect
11. #19152395	C₂	semidirect
12. C₂×#15668044	C₂	semidirect
13. #137×D₈₉	C₂	semidirect
14. #19152363	C₂	semidirect
15. #578×C₈₉	C₂	semidirect
18. #15668060	C₂²	semidirect
19. #15668060	C₂²	semidirect
21. #15668059	C₂²	semidirect
22. #15668059	C₂²	semidirect
24. #15668058	C₂²	semidirect
25. #15668058	C₂²	semidirect
32. #41×D₈₉	C₂²	semidirect
34. C₂×Q₈×D₈₉	C₂²	semidirect
35. #15668045	C₂²	semidirect
36. #15668044	C₂²	semidirect
37. #15668044	C₂²	semidirect
38. #15668044	C₂²	semidirect
39. #15668044	C₂²	semidirect
40. #15668044	C₂²	semidirect
41. #15668043	C₂²	semidirect
42. #15668043	C₂²	semidirect
43. #15668042	C₂²	semidirect
44. #15668041	C₂²	semidirect
45. #15668041	C₂²	semidirect
46. #15668040	C₂²	semidirect
47. #15668039	C₂²	semidirect
48. #15668039	C₂²	semidirect
49. #15668037	C₂²	semidirect
50. #15668036	C₂²	semidirect
51. #15668036	C₂²	semidirect
52. #15668035	C₂²	semidirect
53. #15668034	C₂²	semidirect
54. #15668033	C₂²	semidirect
55. #15668032	C₂²	semidirect
56. #15668032	C₂²	semidirect
57. C₂×#13083564	C₂²	semidirect
58. Q₁₆×D₈₉	C₂²	semidirect
59. C₂×#13083563	C₂²	semidirect
60. C₂×#13083561	C₂²	semidirect
61. SD₁₆×D₈₉	C₂²	semidirect
62. #15668020	C₂²	semidirect
63. #15668019	C₂²	semidirect
64. #15668018	C₂²	semidirect
65. C₂×#13083557	C₂²	semidirect
66. M₁₆×D₈₉	C₂²	semidirect
67. 2₋¹⁺⁴×C₈₉	C₂²	semidirect
68. 2₋¹⁺⁴×C₈₉	C₂²	semidirect
69. #137×C₈₉	C₂²	semidirect
70. #137×C₈₉	C₂²	semidirect
71. #135×C₈₉	C₂²	semidirect
72. C₂×Q₁₆×C₈₉	C₂²	semidirect
73. #131×C₈₉	C₂²	semidirect
252. C₈₉	#3586	semidirect
258. #578	D₈₉	semidirect
275. 2₋¹⁺⁴	C₂×D₈₉	semidirect
276. 2₋¹⁺⁴	C₂×D₈₉	semidirect
300. #137	C₂×D₈₉	semidirect
301. #137	C₂×D₈₉	semidirect
313. #135	C₂×D₈₉	semidirect
316. C₂×Q₁₆	C₂×D₈₉	semidirect
323. #131	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19152435	2
2₋¹⁺⁴×D₈₉	2
#19152414	2
#19152413	2
#19152411	2
#19152410	2
#19152407	2
#19152406	2
#19152405	2
#19152397	2
#19152395	2
C₂×#15668044	2
#137×D₈₉	2
#19152363	2
#578×C₈₉	2
#3586	89