Finite Group Databasebeta

← #21430659

Subgroups — #21430659

Order 7552.

680 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273709C211yesmaximal, characteristic, complemented
2C2×#14273696C211yesmaximal, characteristic
3#16837330C211yesmaximal, characteristic, complemented
4#16837327C211yesmaximal, characteristic, complemented
5#16837325C211yesmaximal, characteristic, complemented
6#16837325C211yesmaximal, characteristic, complemented
7#16837318C211yesmaximal, characteristic, complemented
8#16837317C211yesmaximal, characteristic, complemented
9#16837302C211yesmaximal, characteristic, complemented
10#16837295C211yesmaximal, characteristic, complemented
11#16837290C211yesmaximal, characteristic, complemented
12#16837278C211yesmaximal, characteristic, complemented
13#16837278C211yesmaximal, characteristic, complemented
14#16837258C211yesmaximal, characteristic, complemented
15C59×#379C211yesmaximal, characteristic, complemented
16C22×C22⋊D59C2211yescharacteristic
17C22×C22⋊D59C2211yescharacteristic
18C22×C22⋊D59C2211yescharacteristic
19C22×C4×D59C2211yescharacteristic, complemented
20#14273709—24no—
21#14273696—24no—
22C2×C4⋊Dic59C2211yescharacteristic, complemented
23C2×C4⋊Dic59C2211yescharacteristic, complemented
24C2×Dic59⋊C4C2211yescharacteristic, complemented
25C2×Dic59⋊C4C2211yescharacteristic, complemented
26C2×Dic59⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic59C2211yescharacteristic
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×C22⋊Dic59C2211yescharacteristic
31C2×C22⋊Dic59C2211yescharacteristic
32C2×C22⋊Dic59C2211yescharacteristic
33C2×C22⋊Dic59C2211yescharacteristic
34C2×C22⋊Dic59C2211yescharacteristic
35C2×C22⋊Dic59C2211yescharacteristic
36C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
37C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
38C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
39C2×C4×Dic59C2211yescharacteristic, complemented
40C59⋊#95C2211yescharacteristic, complemented
41C59⋊#95C2211yescharacteristic, complemented
42C59⋊#95C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C25×C59C2211yescharacteristic
47C2×C22⋊C4×C59C2211yescharacteristic
48C2×C22⋊C4×C59C2211yescharacteristic
49C2×C22⋊C4×C59C2211yescharacteristic
50C2×C22⋊C4×C59C2211yescharacteristic
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic
53C24×C59—22no—
54C24×C59—22no—
55C24×C59—22no—
56C24×C59—41no—
57C24×C59—41no—
58C24×C59—41no—
59C24×C59—41no—
60C24×C59C2311yescharacteristic
61C24×C59C2311yescharacteristic
62C24×C59C2311yescharacteristic
63C23×D59C2311yescharacteristic
64C22×C4×C59C2311yescharacteristic
65C22×C4×C59C2311yescharacteristic
66C22×C4×C59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C2×C22⋊D59—22no—
69C2×C22⋊D59—22no—
70C2×C22⋊D59—22no—
71C2×C22⋊D59—22no—
72C2×C22⋊D59—41no—
73C2×C22⋊D59—41no—
74C2×C22⋊D59—41no—
75C2×C22⋊D59—41no—
76C2×C22⋊D59D414yes—
77C22×Dic59C2311yescharacteristic
78C22×Dic59C2311yescharacteristic
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C22×Dic59C2311yescharacteristic
84C2×C4×D59—22no—
85C2×C4×D59—41no—
86C2×C4×D59—41no—
87C22⋊C4×C59—22no—
88C22⋊C4×C59—22no—
89C22⋊C4×C59—41no—
90C22⋊C4×C59—41no—
91C22⋊C4×C59—41no—
92C22⋊C4×C59—41no—
93C22⋊Dic59—22no—
94C22⋊Dic59—22no—
95C22⋊Dic59—22no—
96C22⋊Dic59—22no—
97C22⋊Dic59—22no—
98C22⋊Dic59—41no—
99C22⋊Dic59—41no—
100C22⋊Dic59—41no—
101C22⋊Dic59—41no—
102(C2×D59)⋊C4—22no—
103(C2×D59)⋊C4—41no—
104(C2×D59)⋊C4—41no—
105C4⋊Dic59—22no—
106C4⋊Dic59—41no—
107Dic59⋊C4—22no—
108Dic59⋊C4—41no—
109Dic59⋊C4—41no—
110C4×Dic59—41no—
111C23×C59—21no—
112C23×C59—21no—
113C23×C59—21no—
114C23×C59—21no—
115C23×C59—21no—
116C23×C59—21no—
117C23×C59—21no—
118C23×C59—21no—
119C23×C59—21no—
120C23×C59—21no—
121C23×C59—21no—
122C23×C59—21no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59—44no—
130C23×C59—44no—
131C23×C59—44no—
132C23×C59—44no—
133C23×C59—44no—
134C23×C59—44no—
135C23×C59—44no—
136C23×C59C2×D412yes—
137C23×C59#4112yes—
138C23×C59#4112yes—
139C23×C59C2411yescharacteristic
140C22×D59—21no—
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
145C22×D59—21no—
146C22×D59C2×D412yes—
147C2×C4×C59—21no—
148C2×C4×C59—21no—
149C2×C4×C59—21no—
150C2×C4×C59—21no—
151C2×C4×C59—21no—
152C2×C4×C59—21no—
153C2×C4×C59—21no—
154C2×C4×C59—21no—
155C2×C4×C59—21no—
156C2×C4×C59—21no—
157C2×C4×C59—21no—
158C2×C4×C59—21no—
159C22⋊D59—44no—
160C22⋊D59—44no—
161C22⋊D59—44no—
162C2×Dic59—21no—
163C2×Dic59—21no—
164C2×Dic59—21no—
165C2×Dic59—21no—
166C2×Dic59—21no—
167C2×Dic59—21no—
168C2×Dic59—21no—
169C2×Dic59—21no—
170C2×Dic59—21no—
171C2×Dic59—21no—
172C2×Dic59—21no—
173C2×Dic59—21no—
174C2×Dic59—21no—
175C2×Dic59—21no—
176C2×Dic59—21no—
177C2×Dic59—21no—
178C2×Dic59—21no—
179C2×Dic59—21no—
180C2×Dic59—21no—
181C2×Dic59—21no—
182C2×Dic59C2×D412yes—
183C4×D59—44no—
184C22×C59—22no—
185C22×C59—22no—
186C22×C59—22no—
187C22×C59—22no—
188C22×C59—22no—
189C22×C59—22no—
190C22×C59—22no—
191C22×C59—22no—
192C22×C59—22no—
193C22×C59—416no—
194C22×C59—41no—
195C22×C59—41no—
196C22×C59—41no—
197C22×C59—41no—
198C22×C59—41no—
199C22×C59—41no—
200C22×C59—41no—
201C22×C59—41no—
202C22×C59—41no—
203C22×C59—41no—
204C22×C59—41no—
205C22×C59—41no—
206C22×C59C22×D411yescharacteristic
207C22×C59C2×#4111yescharacteristic
208C22×C59C2×#4111yescharacteristic
209C22×C59H(5,𝔽2)11yescharacteristic
210C22×C59H(5,𝔽2)11yescharacteristic
211C22×C59H(5,𝔽2)11yescharacteristic
212C22×C59H(5,𝔽2)11yescharacteristic
213C2×D59—22no—
214C2×D59—22no—
215C2×D59—22no—
216C2×D59—41no—
217C2×D59—41no—
218C2×D59—41no—
219C2×D59—41no—
220C4×C59—41no—
221C4×C59—41no—
222C4×C59—41no—
223C4×C59—41no—
224Dic59—22no—
225Dic59—41no—
226Dic59—41no—
227Dic59—41no—
228Dic59—41no—
229Dic59—41no—
230Dic59—41no—
231#2697—591nomaximal, Sylow
232C2×C59—42no—
233C2×C59—42no—
234C2×C59—42no—
235C2×C59#53411yescharacteristic
236C2×C59#53811yescharacteristic
237C2×C59#53811yescharacteristic
238C2×C59#54611yescharacteristic
239C2×C59#54611yescharacteristic
240C2×C59#55111yescharacteristic
241C2×C59#56011yescharacteristic
242D59—42no—
243C2×#123—591no—
244C2×#120—591no—
245#397—591no—
246#397—591no—
247#396—591no—
248#396—591no—
249#394—591no—
250#394—591no—
251#390—591no—
252#388—591no—
253#388—591no—
254#386—591no—
255#386—591no—
256#379—591no—
257#379D5911yescharacteristic, complemented
258C59#269711yescharacteristic, complemented, Sylow
259C25C2×D5911yescharacteristic
260C22×D4—591no—
261C22×D4—591no—
262C22×D4—591no—
263C23×C4—591no—
264#123—1184no—
265#120—1184no—
266C2×C4⋊C4—591no—
267C2×C4⋊C4—591no—
268C2×C4⋊C4—591no—
269C2×C4⋊C4—591no—
270C2×C4⋊C4—591no—
271C2×C22⋊C4—591no—
272C2×C22⋊C4—591no—
273C2×C22⋊C4—591no—
274C2×C22⋊C4—591no—
275C2×C22⋊C4—591no—
276C2×C22⋊C4—591no—
277C2×C22⋊C4—591no—
278C2×C22⋊C4—591no—
279C2×C22⋊C4—591no—
280C2×C22⋊C4—591no—
281C2×C22⋊C4—591no—
282C2×C22⋊C4—591no—
283C2×C22⋊C4C2×D5911yescharacteristic
284C2×C22⋊C4C2×D5911yescharacteristic
285C2×C22⋊C4C2×D5911yescharacteristic
286C2×C22⋊C4C2×D5911yescharacteristic
287C2×C22⋊C4C2×D5911yescharacteristic
288C2×C22⋊C4C2×D5911yescharacteristic
289C2×C42—591no—
290#95—591no—
291#95—591no—
292#95—591no—
293#95—591no—
294#95—591no—
295#95—591no—
296C24—22no—
297C24—22no—
298C24—22no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—591no—
304C24C22×D5911yescharacteristic
305C24C22×D5911yescharacteristic
306C24C22×D5911yescharacteristic
307C2×D4—594no—
308C2×D4—1182no—
309C2×D4—1182no—
310C2×D4—1182no—
311C2×D4—1182no—
312C2×D4—2361no—
313C2×D4—2361no—
314C2×D4—2361no—
315C2×D4—2361no—
316C22×C4—591no—
317C22×C4—591no—
318C22×C4—591no—
319C22×C4—591no—
320C22×C4—591no—
321C22×C4—591no—
322C22×C4—591no—
323C22×C4—1182no—
324C22×C4—2361no—
325C22×C4—2361no—
326C22×C4C22×D5911yescharacteristic
327C22×C4C22×D5911yescharacteristic
328C22×C4C22×D5911yescharacteristic
329C22×C4C22×D5911yescharacteristic
330C4⋊C4—1182no—
331C4⋊C4—1182no—
332C4⋊C4—2361no—
333C4⋊C4—2361no—
334C4⋊C4—2361no—
335C22⋊C4—22no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—1182no—
342C22⋊C4—1182no—
343C22⋊C4—1182no—
344C22⋊C4—1182no—
345C22⋊C4—1182no—
346C22⋊C4—1182no—
347C22⋊C4—2361no—
348C22⋊C4—2361no—
349C22⋊C4—2361no—
350C22⋊C4—2361no—
351C22⋊C4—2361no—
352C22⋊C4—2361no—
353C42—2361no—
354C23—21no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—44no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—592no—
380C23—1181no—
381C23—1181no—
382C23—1181no—
383C23—1181no—
384C23—1181no—
385C23—1181no—
386C23#1174568512yes—
387C23D4×D5912yes—
388C23#1174568712yes—
389C23C23×D5911yescharacteristic
390D4—2364no—
391D4—2364no—
392D4—2364no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—592no—
406C2×C4—1181no—
407C2×C4—1181no—
408C2×C4—1181no—
409C2×C4—1181no—
410C2×C4—1181no—
411C2×C4—1181no—
412C2×C4—1181no—
413C2×C4—1181no—
414C2×C4—1181no—
415C2×C4—1181no—
416C2×C4—1181no—
417C2×C4—1181no—
418C2×C4—1181no—
419C2×C4—1181no—
420C2×C4—1181no—
421C2×C4—1181no—
422C2×C4—1181no—
423C2×C4—1181no—
424C2×C4—1181no—
425C2×C4—1181no—
426C2×C4—2364no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—416no—
437C22—41no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—1182no—
450C22—1182no—
451C22—1182no—
452C22—2361no—
453C22—2361no—
454C22—2361no—
455C22—2361no—
456C22C2×D4×D5911yescharacteristic
457C22C2×#1174568711yescharacteristic
458C22C2×#1174568511yescharacteristic
459C22#1427377211yescharacteristic
460C22#1427377211yescharacteristic
461C22#1427377211yescharacteristic
462C22#1427377211yescharacteristic
463C4—41no—
464C4—41no—
465C4—41no—
466C4—41no—
467C4—1182no—
468C4—2361no—
469C4—2361no—
470C4—2361no—
471C4—2361no—
472C4—2361no—
473C4—2361no—
474C2—42no—
475C2—42no—
476C2—42no—
477C2—2362no—
478C2#1683796211yescharacteristic
479C2#1683798711yescharacteristic
480C2#1683799011yescharacteristic
481C2#1683803911yescharacteristic
482C2#1683804211yescharacteristic
483C2#1683807811yescharacteristic
484C2#1683814111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#379C2
hypercenter#379D59
hypocenterC59#2697
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#14273709C2semidirect
3. #16837330C2semidirect
4. #16837327C2semidirect
5. #16837325C2semidirect
6. #16837325C2semidirect
7. #16837318C2semidirect
8. #16837317C2semidirect
9. #16837302C2semidirect
10. #16837295C2semidirect
11. #16837290C2semidirect
12. #16837278C2semidirect
13. #16837278C2semidirect
14. #16837258C2semidirect
15. C59×#379C2semidirect
19. C22×C4×D59C22semidirect
22. C2×C4⋊Dic59C22semidirect
23. C2×C4⋊Dic59C22semidirect
24. C2×Dic59⋊C4C22semidirect
25. C2×Dic59⋊C4C22semidirect
26. C2×Dic59⋊C4C22semidirect
36. C2×(C2×D59)⋊C4C22semidirect
37. C2×(C2×D59)⋊C4C22semidirect
38. C2×(C2×D59)⋊C4C22semidirect
39. C2×C4×Dic59C22semidirect
40. C59⋊#95C22semidirect
41. C59⋊#95C22semidirect
42. C59⋊#95C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
257. #379D59semidirect
258. C59#2697semidirect