Finite Group Databasebeta

← #21428337

Subgroups — #21428337

Order 7552.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273720C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D59C211yesmaximal, characteristic
3#16837331C211yesmaximal, characteristic, complemented
4#16837330C211yesmaximal, characteristic, complemented
5#16837326C211yesmaximal, characteristic, complemented
6#16837296C211yesmaximal, characteristic, complemented
7#16837294C211yesmaximal, characteristic, complemented
8#16837292C211yesmaximal, characteristic, complemented
9#16837276C211yesmaximal, characteristic, complemented
10#16837273C211yesmaximal, characteristic, complemented
11#16837261C211yesmaximal, characteristic, complemented
12#16837257C211yesmaximal, characteristic
13#16837257C211yesmaximal, characteristic
14#16837249C211yesmaximal, characteristic, complemented
15C59×#397C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×C4×D59C2211yescharacteristic
18C22×C4×D59C2211yescharacteristic
19#14273720—24no—
20C2×C4⋊Dic59C2211yescharacteristic, complemented
21C2×Dic59⋊C4C2211yescharacteristic, complemented
22C2×Dic59⋊C4C2211yescharacteristic, complemented
23C2×Dic59⋊C4C2211yescharacteristic, complemented
24C2×Dic59⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic59C2211yescharacteristic
26C2×C22⋊Dic59C2211yescharacteristic
27C2×C22⋊Dic59C2211yescharacteristic
28C2×(C2×D59)⋊C4C2211yescharacteristic
29C2×(C2×D59)⋊C4C2211yescharacteristic
30C2×(C2×D59)⋊C4C2211yescharacteristic
31C2×(C2×D59)⋊C4C2211yescharacteristic
32C2×(C2×D59)⋊C4C2211yescharacteristic
33C2×(C2×D59)⋊C4C2211yescharacteristic
34C2×(C2×D59)⋊C4C2211yescharacteristic
35C2×(C2×D59)⋊C4C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic
37C2×(C2×D59)⋊C4C2211yescharacteristic
38C22⋊C4×D59—24no—
39C2×C4×Dic59C2211yescharacteristic, complemented
40C2×C4×Dic59C2211yescharacteristic, complemented
41C59⋊#95C2211yescharacteristic, complemented
42C59⋊#95C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C2×C4⋊C4×C59C2211yescharacteristic, complemented
47C2×C22⋊C4×C59C2211yescharacteristic
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50#95×C59C2211yescharacteristic, complemented
51#95×C59C2211yescharacteristic, complemented
52#95×C59C2211yescharacteristic, complemented
53C24×C59C2311yescharacteristic
54C23×D59—22no—
55C23×D59—22no—
56C23×D59—22no—
57C23×D59—22no—
58C23×D59—22no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59C2311yescharacteristic
62C23×D59C2311yescharacteristic
63C22×C4×C59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×Dic59C2311yescharacteristic
70C22×Dic59C2311yescharacteristic
71C22×Dic59C2311yescharacteristic
72C22×Dic59C2311yescharacteristic
73C22×Dic59C2311yescharacteristic
74C22×Dic59C2311yescharacteristic
75C2×C4×D59—22no—
76C2×C4×D59—22no—
77C2×C4×D59—22no—
78C2×C4×D59—22no—
79C2×C4×D59—41no—
80C2×C4×D59—41no—
81C4⋊C4×C59—41no—
82C22⋊C4×C59—22no—
83C22⋊C4×C59—22no—
84C22⋊C4×C59—41no—
85C22⋊Dic59—22no—
86C22⋊Dic59—41no—
87C22⋊Dic59D414yes—
88(C2×D59)⋊C4—22no—
89(C2×D59)⋊C4—22no—
90(C2×D59)⋊C4—22no—
91(C2×D59)⋊C4—22no—
92(C2×D59)⋊C4—22no—
93(C2×D59)⋊C4—22no—
94(C2×D59)⋊C4—22no—
95(C2×D59)⋊C4—22no—
96(C2×D59)⋊C4—41no—
97(C2×D59)⋊C4—41no—
98C4⋊Dic59—22no—
99Dic59⋊C4—22no—
100Dic59⋊C4—22no—
101Dic59⋊C4—41no—
102Dic59⋊C4—41no—
103C4×Dic59—22no—
104C4×Dic59—41no—
105C23×C59—21no—
106C23×C59—21no—
107C23×C59—21no—
108C23×C59—21no—
109C23×C59—21no—
110C23×C59—21no—
111C23×C59C2×D412yes—
112C23×C59C2411yescharacteristic
113C22×D59—21no—
114C22×D59—21no—
115C22×D59—21no—
116C22×D59—21no—
117C22×D59—28no—
118C22×D59—21no—
119C22×D59—21no—
120C22×D59—21no—
121C22×D59—21no—
122C22×D59—21no—
123C22×D59—21no—
124C22×D59—44no—
125C22×D59—44no—
126C22×D59—44no—
127C22×D59—44no—
128C22×D59—44no—
129C22×D59—44no—
130C22×D59#4112yes—
131C22×D59#4112yes—
132C22×D59#4112yes—
133C22×D59#4112yes—
134C2×C4×C59—21no—
135C2×C4×C59—21no—
136C2×C4×C59—21no—
137C2×C4×C59—21no—
138C2×C4×C59—21no—
139C2×C4×C59—21no—
140C2×C4×C59—21no—
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—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×Dic59—21no—
153C2×Dic59—21no—
154C2×Dic59—21no—
155C2×Dic59—21no—
156C2×Dic59—21no—
157C2×Dic59—21no—
158C2×Dic59—21no—
159C2×Dic59—21no—
160C2×Dic59—21no—
161C2×Dic59—21no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—21no—
165C2×Dic59—21no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59C2×D412yes—
169C2×Dic59C2×D412yes—
170C4×D59—44no—
171C4×D59—44no—
172C22×C59—22no—
173C22×C59—22no—
174C22×C59—22no—
175C22×C59—41no—
176C22×C59—41no—
177C22×C59—41no—
178C22×C59—41no—
179C22×C59C22×D411yescharacteristic
180C22×C59C2×#4111yescharacteristic
181C22×C59C2×#4111yescharacteristic
182C22×C59C2×#4111yescharacteristic
183C22×C59C2×#4111yescharacteristic
184C22×C59H(5,𝔽2)11yescharacteristic
185C22×C59H(5,𝔽2)11yescharacteristic
186C2×D59—22no—
187C2×D59—22no—
188C2×D59—22no—
189C2×D59—22no—
190C2×D59—22no—
191C2×D59—22no—
192C2×D59—22no—
193C2×D59—22no—
194C2×D59—22no—
195C2×D59—416no—
196C2×D59—41no—
197C2×D59—41no—
198C2×D59—41no—
199C2×D59—41no—
200C2×D59#12614yescomplemented
201C4×C59—41no—
202C4×C59—41no—
203C4×C59—41no—
204C4×C59—41no—
205C4×C59—41no—
206C4×C59—41no—
207Dic59—22no—
208Dic59—22no—
209Dic59—41no—
210Dic59—41no—
211Dic59—41no—
212Dic59—41no—
213#2480—591nomaximal, Sylow
214C2×C59—42no—
215C2×C59#52511yescharacteristic
216C2×C59C2×#12611yescharacteristic
217C2×C59#53811yescharacteristic
218C2×C59#54611yescharacteristic
219C2×C59#54611yescharacteristic
220C2×C59#55111yescharacteristic
221C2×C59#55111yescharacteristic
222D59—24no—
223D59—42no—
224C2×#126—591no—
225C22×C22⋊C4—591no—
226#397—591no—
227#397—591no—
228#397D5911yescharacteristic, complemented
229#396—591no—
230#388—591no—
231#388—591no—
232#388—591no—
233#385—591no—
234#385—591no—
235#380—591no—
236#379—591no—
237#379—591no—
238C4×C22⋊C4—591no—
239C59#248011yescharacteristic, complemented, Sylow
240C25—591no—
241C23×C4—591no—
242C23×C4—591no—
243#126—1184no—
244C2×C4⋊C4—591no—
245C2×C4⋊C4—591no—
246C2×C4⋊C4—591no—
247C2×C4⋊C4—591no—
248C2×C4⋊C4—591no—
249C2×C4⋊C4C2×D5911yescharacteristic, complemented
250C2×C22⋊C4—591no—
251C2×C22⋊C4—591no—
252C2×C22⋊C4—591no—
253C2×C22⋊C4—591no—
254C2×C22⋊C4—591no—
255C2×C22⋊C4—591no—
256C2×C22⋊C4—591no—
257C2×C22⋊C4—591no—
258C2×C22⋊C4—591no—
259C2×C22⋊C4—591no—
260C2×C22⋊C4—591no—
261C2×C22⋊C4—591no—
262C2×C22⋊C4—591no—
263C2×C22⋊C4—1184no—
264C2×C22⋊C4C2×D5911yescharacteristic
265C2×C22⋊C4C2×D5911yescharacteristic
266C2×C22⋊C4C2×D5911yescharacteristic
267C2×C42—591no—
268C2×C42—591no—
269#95—591no—
270#95—591no—
271#95—591no—
272#95—591no—
273#95—591no—
274#95C2×D5911yescharacteristic, complemented
275#95C2×D5911yescharacteristic, complemented
276#95C2×D5911yescharacteristic, complemented
277C24—591no—
278C24—591no—
279C24—1182no—
280C24—1182no—
281C24—1182no—
282C24—1182no—
283C24—1182no—
284C24—2361no—
285C24—2361no—
286C24C22×D5911yescharacteristic
287C22×C4—591no—
288C22×C4—591no—
289C22×C4—591no—
290C22×C4—591no—
291C22×C4—591no—
292C22×C4—591no—
293C22×C4—1182no—
294C22×C4—1182no—
295C22×C4—1182no—
296C22×C4—1182no—
297C22×C4—2361no—
298C22×C4—2361no—
299C22×C4C22×D5911yescharacteristic
300C22×C4C22×D5911yescharacteristic
301C22×C4C22×D5911yescharacteristic
302C22×C4C22×D5911yescharacteristic
303C22×C4C22×D5911yescharacteristic
304C22×C4C22×D5911yescharacteristic
305C4⋊C4—41no—
306C4⋊C4—1182no—
307C4⋊C4—1182no—
308C4⋊C4—1182no—
309C4⋊C4—2361no—
310C4⋊C4—2361no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—41no—
314C22⋊C4—594no—
315C22⋊C4—1182no—
316C22⋊C4—1182no—
317C22⋊C4—1182no—
318C22⋊C4—1182no—
319C22⋊C4—1182no—
320C22⋊C4—1182no—
321C22⋊C4—1182no—
322C22⋊C4—1182no—
323C22⋊C4—1182no—
324C22⋊C4—2361no—
325C22⋊C4—2361no—
326C22⋊C4—2361no—
327C42—1182no—
328C42—2361no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—21no—
335C23—592no—
336C23—592no—
337C23—592no—
338C23—592no—
339C23—1188no—
340C23—1181no—
341C23—1181no—
342C23—1181no—
343C23—1181no—
344C23—1181no—
345C23—1181no—
346C23—1181no—
347C23—1181no—
348C23—1181no—
349C23—1181no—
350C23—2364no—
351C23—2364no—
352C23—2364no—
353C23—2364no—
354C23—2364no—
355C23—2364no—
356C23D4×D5912yes—
357C23C23×D5911yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—592no—
377C2×C4—592no—
378C2×C4—1181no—
379C2×C4—1181no—
380C2×C4—1181no—
381C2×C4—1181no—
382C2×C4—1181no—
383C2×C4—1181no—
384C2×C4—1181no—
385C2×C4—1181no—
386C2×C4—1181no—
387C2×C4—1181no—
388C2×C4—1181no—
389C2×C4—1181no—
390C2×C4—1181no—
391C2×C4—1181no—
392C2×C4—1181no—
393C2×C4—1181no—
394C2×C4—2364no—
395C2×C4—2364no—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—594no—
404C22—1182no—
405C22—1182no—
406C22—1182no—
407C22—1182no—
408C22—1182no—
409C22—1182no—
410C22—1182no—
411C22—1182no—
412C22—1182no—
413C22—23616no—
414C22—2361no—
415C22—2361no—
416C22—2361no—
417C22—2361no—
418C22C2×D4×D5911yescharacteristic
419C22#41×D5911yescharacteristic
420C22#41×D5911yescharacteristic
421C22#41×D5911yescharacteristic
422C22#41×D5911yescharacteristic
423C22#1427377211yescharacteristic
424C22#1427377311yescharacteristic
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—1182no—
432C4—1182no—
433C4—2361no—
434C4—2361no—
435C4—2361no—
436C4—2361no—
437C2—42no—
438C2—1184no—
439C2—2362no—
440C2#1683791011yescharacteristic
441C2#126×D5911yescharacteristic
442C2#1683798611yescharacteristic
443C2#1683804111yescharacteristic
444C2#1683804411yescharacteristic
445C2#1683807711yescharacteristic
446C2#1683808011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#397C2
hypercenter#397D59
hypocenterC59#2480
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#14273720C2semidirect
3. #16837331C2semidirect
4. #16837330C2semidirect
5. #16837326C2semidirect
6. #16837296C2semidirect
7. #16837294C2semidirect
8. #16837292C2semidirect
9. #16837276C2semidirect
10. #16837273C2semidirect
11. #16837261C2semidirect
14. #16837249C2semidirect
15. C59×#397C2semidirect
20. C2×C4⋊Dic59C22semidirect
21. C2×Dic59⋊C4C22semidirect
22. C2×Dic59⋊C4C22semidirect
23. C2×Dic59⋊C4C22semidirect
24. C2×Dic59⋊C4C22semidirect
39. C2×C4×Dic59C22semidirect
40. C2×C4×Dic59C22semidirect
41. C59⋊#95C22semidirect
42. C59⋊#95C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
46. C2×C4⋊C4×C59C22semidirect
50. #95×C59C22semidirect
51. #95×C59C22semidirect
52. #95×C59C22semidirect
200. C2×D59#126semidirect
228. #397D59semidirect
239. C59#2480semidirect
249. C2×C4⋊C4C2×D59semidirect
274. #95C2×D59semidirect
275. #95C2×D59semidirect
276. #95C2×D59semidirect