Finite Group Databasebeta

← #21435617

Subgroups — #21435617

Order 7552.

500 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273753C211yesmaximal, characteristic, complemented
2C2×#14273747C211yesmaximal, characteristic, complemented
3#16838057C211yesmaximal, characteristic, complemented
4#16837797C211yesmaximal, characteristic, complemented
5#16837658C211yesmaximal, characteristic, complemented
6#16837629C211yesmaximal, characteristic, complemented
7#16837614C211yesmaximal, characteristic, complemented
8#16837607C211yesmaximal, characteristic, complemented
9#16837564C211yesmaximal, characteristic, complemented
10#16837562C211yesmaximal, characteristic, complemented
11#16837553C211yesmaximal, characteristic, complemented
12#16837545C211yesmaximal, characteristic, complemented
13#16837512C211yesmaximal, characteristic, complemented
14#16837474C211yesmaximal, characteristic, complemented
15C59×#546C211yesmaximal, characteristic, complemented
16C2×#11745685C2211yescharacteristic
17C2×#11745685C2211yescharacteristic, complemented
18#14273753—24no—
19#14273747—24no—
20C2×#11745672C2211yescharacteristic, complemented
21C2×#11745672C2211yescharacteristic, complemented
22C2×#11745670C2211yescharacteristic
23C2×#11745670C2211yescharacteristic
24C2×#11745670C2211yescharacteristic
25C2×#11745670C2211yescharacteristic
26C2×#11745671C2211yescharacteristic, complemented
27C2×#11745669C2211yescharacteristic
28C2×#11745669C2211yescharacteristic
29C2×#11745664C2211yescharacteristic
30C22×C59⋊C8C2211yescharacteristic, complemented
31#14273727C2211yescharacteristic, complemented
32#14273709—21no—
33#14273709—21no—
34#14273706C2211yescharacteristic
35#14273706C2211yescharacteristic, complemented
36#14273698—21no—
37C4×D236C2211yescharacteristic, complemented
38C4⋊C4×D59—21no—
39#14273658C2211yescharacteristic, complemented
40C4⋊(C59⋊C8)C2211yescharacteristic, complemented
41#14273651C2211yescharacteristic, complemented
42#14273650C2211yescharacteristic, complemented
43#14273650C2211yescharacteristic, complemented
44#14273648C2211yescharacteristic
45#14273648C2211yescharacteristic
46#14273647C2211yescharacteristic, complemented
47C22⋊(C59⋊C8)C2211yescharacteristic
48C22⋊(C59⋊C8)C2211yescharacteristic, complemented
49#14273638C2211yescharacteristic, complemented
50C2×#41×C59C2211yescharacteristic
51C22×D4×C59C2211yescharacteristic
52#124×C59C2211yescharacteristic
53#123×C59—21no—
54C22⋊Q8×C59C2211yescharacteristic
55#121×C59—21no—
56#121×C59C2211yescharacteristic
57#120×C59—21no—
58C4×D4×C59C2211yescharacteristic
59C4×D4×C59C2211yescharacteristic
60C2×C22⋊C4×C59—21no—
61C24×C59—21no—
62#41×C59—22no—
63#41×C59—41no—
64C2×Q8×C59C2311yescharacteristic
65C2×D4×C59—22no—
66C2×D4×C59—21no—
67C2×D4×C59—21no—
68C2×D4×C59—21no—
69C2×D4×C59—41no—
70C2×D4×C59D411yescharacteristic
71C2×D4×C59C2311yescharacteristic
72C2×D4×C59C2311yescharacteristic
73C22×C4×C59—21no—
74C22×C4×C59—21no—
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C2×C22⋊D59—21no—
78C2×C22⋊D59—21no—
79#11745685—22no—
80#11745685—22no—
81#11745685—41no—
82#11745685—41no—
83C2×D236C2311yescharacteristic
84C2×C4×D59—21no—
85C2×C4×D59—21no—
86C2×C4×D59—21no—
87C2×Dic118C2311yescharacteristic
88C2×Dic118C2311yescharacteristic
89C4⋊C4×C59—21no—
90C4⋊C4×C59D411yescharacteristic
91C4⋊C4×C59C2311yescharacteristic
92C22⋊C4×C59—21no—
93C22⋊C4×C59—21no—
94C22⋊C4×C59—21no—
95C22⋊C4×C59—21no—
96C22⋊C4×C59—21no—
97C22⋊C4×C59D411yescharacteristic
98C22⋊C4×C59D411yescharacteristic
99C42×C59C2311yescharacteristic
100C22⋊Dic59—21no—
101C22⋊Dic59—21no—
102#11745672—22no—
103#11745672—41no—
104#11745671—22no—
105#11745670—22no—
106#11745670—22no—
107#11745670—22no—
108#11745670—41no—
109#11745669—22no—
110#11745669D414yescomplemented
111(C2×D59)⋊C4—21no—
112C4⋊Dic59—21no—
113C4⋊Dic59—21no—
114C4⋊Dic59C2311yescharacteristic
115Dic59⋊C4—21no—
116Dic59⋊C4—21no—
117#11745664—22no—
118C2×C59⋊C8—22no—
119C2×C59⋊C8C2311yescharacteristic
120C2×C59⋊C8C2311yescharacteristic
121C2×C59⋊C8C2311yescharacteristic
122C2×C59⋊C8C2311yescharacteristic
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—42no—
126C23×C59—42no—
127C23×C59—81no—
128C23×C59C2×D411yescharacteristic
129C23×C59C2×D411yescharacteristic
130C22×D59—21no—
131Q8×C59—21no—
132Q8×C59—21no—
133D4×C59—21no—
134D4×C59—21no—
135D4×C59—21no—
136D4×C59—41no—
137D4×C59—42no—
138D4×C59—42no—
139D4×C59—81no—
140D4×C59C2×D412yes—
141C2×C4×C59—21no—
142C2×C4×C59—21no—
143C2×C4×C59—21no—
144C2×C4×C59—21no—
145C2×C4×C59—21no—
146C2×C4×C59—21no—
147C2×C4×C59—42no—
148C2×C4×C59—81no—
149C2×C4×C59C2×D411yescharacteristic
150C2×C4×C59C2×D411yescharacteristic
151C2×C4×C59C2×D411yescharacteristic
152C2×C4×C59C2×D411yescharacteristic
153C2×C4×C59C2411yescharacteristic
154C22⋊D59—42no—
155C22⋊D59—42no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159D236—21no—
160D236C2×D412yes—
161C4×D59—42no—
162C4×D59—42no—
163C4×D59—42no—
164Dic118—21no—
165Dic118—21no—
166Dic118—21no—
167Dic118—21no—
168C59⋊C8—21no—
169C59⋊C8—21no—
170C59⋊C8—21no—
171C59⋊C8C2×D412yes—
172C22×C59—21no—
173C22×C59—21no—
174C22×C59—22no—
175C22×C59—21no—
176C22×C59—21no—
177C22×C59—21no—
178C22×C59—21no—
179C22×C59—41no—
180C22×C59—41no—
181C22×C59—41no—
182C22×C59—41no—
183C22×C59—41no—
184C22×C59—84no—
185C22×C59C22×D411yescharacteristic
186C2×D59—22no—
187C2×D59—41no—
188C2×D59—41no—
189C4×C59—21no—
190C4×C59—21no—
191C4×C59—21no—
192C4×C59—21no—
193C4×C59—41no—
194C4×C59—41no—
195C4×C59C22×D411yescharacteristic
196C4×C59H(5,𝔽2)11yescharacteristic
197Dic59—41no—
198Dic59—41no—
199Dic59—41no—
200#3267—591nomaximal, Sylow
201C2×C59—41no—
202C2×C59—41no—
203C2×C59—42no—
204C2×C59—81no—
205C2×C59D4211yescharacteristic
206C2×C59#57511yescharacteristic
207C2×C59#57711yescharacteristic
208D59—42no—
209C2×AGL(1,ℤ/8)—591no—
210C2×#135—591no—
211#547—591no—
212#546D5911yescharacteristic, complemented
213#497—591no—
214#470—591no—
215#465—591no—
216#463—591no—
217#461—591no—
218#452—591no—
219#452—591no—
220#450—591no—
221#449—591no—
222#442—591no—
223#435—591no—
224C59#326711yescharacteristic, complemented, Sylow
225C2×#41—591no—
226C2×#41—591no—
227C2×#41C2×D5911yescharacteristic
228C22×D4C2×D5911yescharacteristic
229AGL(1,ℤ/8)—1184no—
230#135—1184no—
231C2×Q16—591no—
232C2×Q16—591no—
233C2×SD16—591no—
234C2×SD16—591no—
235C2×SD16—591no—
236C2×SD16—591no—
237C2×SD16—591no—
238C2×D8—591no—
239C2×D8—591no—
240C2×M16—591no—
241C22×C8—591no—
242C4⋊Q8—591no—
243#124C2×D5911yescharacteristic
244#123—21no—
245#123—1181no—
246#123—1181no—
247C22⋊Q8—591no—
248C22⋊Q8—591no—
249C22⋊Q8C2×D5911yescharacteristic
250#121—21no—
251#121—1181no—
252#121C2×D5911yescharacteristic
253#120—21no—
254C4×D4—591no—
255C4×D4C2×D5911yescharacteristic
256C4×D4C2×D5911yescharacteristic
257C2×C4⋊C4—1181no—
258C2×C22⋊C4—21no—
259#106—591no—
260C4⋊C8—591no—
261#103—591no—
262#103—591no—
263#103—591no—
264#102—591no—
265#102—591no—
266#102—591no—
267C22⋊C8—591no—
268C22⋊C8—591no—
269#97—591no—
270C24—21no—
271#41—22no—
272#41—41no—
273#41—1182no—
274#41—1182no—
275#41—2361no—
276#41—2361no—
277C2×Q8—591no—
278C2×Q8—591no—
279C2×Q8C22×D5911yescharacteristic
280C2×D4—22no—
281C2×D4—21no—
282C2×D4—21no—
283C2×D4—21no—
284C2×D4—41no—
285C2×D4—591no—
286C2×D4—1181no—
287C2×D4—1181no—
288C2×D4C22⋊D5911yescharacteristic
289C2×D4C22×D5911yescharacteristic
290C2×D4C22×D5911yescharacteristic
291C22×C4—21no—
292C22×C4—21no—
293C22×C4—1181no—
294C22×C4—1181no—
295C22×C4—1181no—
296C22×C4C22×D5911yescharacteristic
297C22×C4C22×D5911yescharacteristic
298Q16—1182no—
299Q16—2361no—
300SD16—1182no—
301SD16—1182no—
302SD16—1182no—
303SD16—1182no—
304SD16—2361no—
305D8—594no—
306D8—1182no—
307M16—1182no—
308C2×C8—591no—
309C2×C8—591no—
310C2×C8—591no—
311C2×C8—591no—
312C2×C8—1182no—
313C4⋊C4—21no—
314C4⋊C4—591no—
315C4⋊C4—1181no—
316C4⋊C4—1181no—
317C4⋊C4—1181no—
318C4⋊C4—1181no—
319C4⋊C4C22⋊D5911yescharacteristic
320C4⋊C4C22×D5911yescharacteristic
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—21no—
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—1181no—
327C22⋊C4—1181no—
328C22⋊C4—1181no—
329C22⋊C4C22⋊D5911yescharacteristic
330C22⋊C4C22⋊D5911yescharacteristic
331C42C22×D5911yescharacteristic
332C23—21no—
333C23—21no—
334C23—42no—
335C23—42no—
336C23—81no—
337C23—1181no—
338C23C2×C22⋊D5911yescharacteristic
339C23C2×C22⋊D5911yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—1181no—
343Q8—1181no—
344Q8—1181no—
345Q8—1181no—
346D4—21no—
347D4—21no—
348D4—21no—
349D4—41no—
350D4—42no—
351D4—42no—
352D4—81no—
353D4—592no—
354D4—1181no—
355D4—2362no—
356D4—2362no—
357D4D4×D5912yes—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—1181no—
367C2×C4—1181no—
368C2×C4—1181no—
369C2×C4—2362no—
370C2×C4—2362no—
371C2×C4—2362no—
372C2×C4C2×C22⋊D5911yescharacteristic
373C2×C4C2×C22⋊D5911yescharacteristic
374C2×C4C2×C22⋊D5911yescharacteristic
375C2×C4C2×C22⋊D5911yescharacteristic
376C2×C4C23×D5911yescharacteristic
377C8—592no—
378C8—1181no—
379C8—1181no—
380C8—1181no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—84no—
394C22—1182no—
395C22—2361no—
396C22—2361no—
397C22C22×C22⋊D5911yescharacteristic
398C4—21no—
399C4—21no—
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—2361no—
405C4—2361no—
406C4—2361no—
407C4C2×D4×D5911yescharacteristic
408C4#1427377211yescharacteristic
409C2—41no—
410C2—41no—
411C2—42no—
412C2—81no—
413C2—2362no—
414C2D4×C22⋊D5911yescharacteristic
415C2#1683820011yescharacteristic
416C2#1683821311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D59
commutatorC2×C4×C59C24
FrattiniC2×C4C23×D59
FittingC59×#546C2
socleC22×C59C22×D4
hypercenter#546D59
hypocenterC59#3267
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C4×D4 ◁ #546

Complements

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

NH ≅ G/Ntype
1. C2×#14273753C2semidirect
2. C2×#14273747C2semidirect
3. #16838057C2semidirect
4. #16837797C2semidirect
5. #16837658C2semidirect
6. #16837629C2semidirect
7. #16837614C2semidirect
8. #16837607C2semidirect
9. #16837564C2semidirect
10. #16837562C2semidirect
11. #16837553C2semidirect
12. #16837545C2semidirect
13. #16837512C2semidirect
14. #16837474C2semidirect
15. C59×#546C2semidirect
17. C2×#11745685C22semidirect
20. C2×#11745672C22semidirect
21. C2×#11745672C22semidirect
26. C2×#11745671C22semidirect
30. C22×C59⋊C8C22semidirect
31. #14273727C22semidirect
35. #14273706C22semidirect
37. C4×D236C22semidirect
39. #14273658C22semidirect
40. C4⋊(C59⋊C8)C22semidirect
41. #14273651C22semidirect
42. #14273650C22semidirect
43. #14273650C22semidirect
46. #14273647C22semidirect
48. C22⋊(C59⋊C8)C22semidirect
49. #14273638C22semidirect
110. #11745669D4semidirect
212. #546D59semidirect
224. C59#3267semidirect