Finite Group Databasebeta

← #21430426

Subgroups — #21430426

Order 7552.

802 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14273712C211yesmaximal, characteristic, complemented
2C2×#14273702C211yesmaximal, characteristic, complemented
3C2×#14273697C211yesmaximal, characteristic, complemented
4C2×#14273697C211yesmaximal, characteristic, complemented
5#16837331C211yesmaximal, characteristic, complemented
6#16837319C211yesmaximal, characteristic, complemented
7#16837319C211yesmaximal, characteristic, complemented
8#16837312C211yesmaximal, characteristic, complemented
9#16837311C211yesmaximal, characteristic, complemented
10#16837303C211yesmaximal, characteristic, complemented
11#16837302C211yesmaximal, characteristic, complemented
12#16837292C211yesmaximal, characteristic, complemented
13#16837278C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C59×#396C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×D236C2211yescharacteristic
20C22×D236C2211yescharacteristic
21C22×D236C2211yescharacteristic, complemented
22C22×C22⋊D59C2211yescharacteristic
23C22×C22⋊D59C2211yescharacteristic
24C22×C4×D59C2211yescharacteristic, complemented
25#14273712—24no—
26#14273702—24no—
27#14273697—24no—
28#14273697—24no—
29C2×Dic59⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic59C2211yescharacteristic
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
38C2×(C2×D59)⋊C4C2211yescharacteristic
39C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D59)⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic59C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C59⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C59C2211yescharacteristic, complemented
49C2×C4⋊C4×C59C2211yescharacteristic, complemented
50C2×C4⋊C4×C59C2211yescharacteristic, complemented
51C2×C22⋊C4×C59C2211yescharacteristic
52C2×C22⋊C4×C59C2211yescharacteristic
53C2×C22⋊C4×C59C2211yescharacteristic
54#95×C59C2211yescharacteristic, complemented
55C24×C59C2311yescharacteristic
56C23×D59—22no—
57C23×D59—22no—
58C23×D59—22no—
59C23×D59—41no—
60C23×D59—41no—
61C23×D59—41no—
62C23×D59—41no—
63C23×D59C2311yescharacteristic
64C23×D59C2311yescharacteristic
65C23×D59C2311yescharacteristic
66C23×D59C2311yescharacteristic
67C22×C4×C59C2311yescharacteristic
68C22×C4×C59C2311yescharacteristic
69C22×C4×C59C2311yescharacteristic
70C22×C4×C59C2311yescharacteristic
71C22×C4×C59C2311yescharacteristic
72C22×C4×C59C2311yescharacteristic
73C2×C22⋊D59—22no—
74C2×C22⋊D59—22no—
75C2×C22⋊D59—22no—
76C2×C22⋊D59—22no—
77C2×C22⋊D59—41no—
78C2×C22⋊D59—41no—
79C22×Dic59C2311yescharacteristic
80C22×Dic59C2311yescharacteristic
81C22×Dic59C2311yescharacteristic
82C22×Dic59C2311yescharacteristic
83C2×D236—22no—
84C2×D236—22no—
85C2×D236—22no—
86C2×D236—22no—
87C2×D236—22no—
88C2×D236—22no—
89C2×D236—41no—
90C2×D236—41no—
91C2×D236—41no—
92C2×D236—41no—
93C2×D236—41no—
94C2×D236—41no—
95C2×D236—41no—
96C2×D236—41no—
97C2×D236D414yescomplemented
98C2×C4×D59—22no—
99C2×C4×D59—22no—
100C2×C4×D59—41no—
101C4⋊C4×C59—22no—
102C4⋊C4×C59—22no—
103C4⋊C4×C59—41no—
104C22⋊C4×C59—22no—
105C22⋊C4×C59—22no—
106C22⋊C4×C59—41no—
107C22⋊Dic59—41no—
108(C2×D59)⋊C4—22no—
109(C2×D59)⋊C4—22no—
110(C2×D59)⋊C4—22no—
111(C2×D59)⋊C4—22no—
112(C2×D59)⋊C4—22no—
113(C2×D59)⋊C4—22no—
114(C2×D59)⋊C4—22no—
115(C2×D59)⋊C4—41no—
116(C2×D59)⋊C4—41no—
117(C2×D59)⋊C4—41no—
118(C2×D59)⋊C4—41no—
119(C2×D59)⋊C4—41no—
120(C2×D59)⋊C4D414yescomplemented
121Dic59⋊C4—22no—
122C4×Dic59—41no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59#4112yes—
130C23×C59C2411yescharacteristic
131C22×D59—21no—
132C22×D59—21no—
133C22×D59—21no—
134C22×D59—21no—
135C22×D59—21no—
136C22×D59—21no—
137C22×D59—21no—
138C22×D59—21no—
139C22×D59—21no—
140C22×D59—21no—
141C22×D59—21no—
142C22×D59—21no—
143C22×D59—21no—
144C22×D59—21no—
145C22×D59—21no—
146C22×D59—21no—
147C22×D59—21no—
148C22×D59—21no—
149C22×D59—21no—
150C22×D59—21no—
151C22×D59—21no—
152C22×D59—21no—
153C22×D59—21no—
154C22×D59—21no—
155C22×D59—21no—
156C22×D59—44no—
157C22×D59—44no—
158C22×D59—44no—
159C22×D59—44no—
160C22×D59—44no—
161C22×D59—44no—
162C22×D59—44no—
163C22×D59C2×D412yes—
164C22×D59C2×D412yes—
165C22×D59C2×D412yes—
166C2×C4×C59—21no—
167C2×C4×C59—21no—
168C2×C4×C59—21no—
169C2×C4×C59—21no—
170C2×C4×C59—21no—
171C2×C4×C59—21no—
172C2×C4×C59—21no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—21no—
181C2×C4×C59—21no—
182C2×C4×C59C2×D412yes—
183C2×C4×C59C2×D412yes—
184C22⋊D59—44no—
185C22⋊D59—44no—
186C2×Dic59—21no—
187C2×Dic59—21no—
188C2×Dic59—21no—
189C2×Dic59—21no—
190C2×Dic59—21no—
191C2×Dic59—21no—
192C2×Dic59—21no—
193C2×Dic59—21no—
194C2×Dic59—21no—
195C2×Dic59—21no—
196C2×Dic59—21no—
197C2×Dic59C2×D412yes—
198D236—44no—
199D236—44no—
200D236—44no—
201D236—44no—
202D236—44no—
203C4×D59—44no—
204C22×C59—22no—
205C22×C59—22no—
206C22×C59—22no—
207C22×C59—41no—
208C22×C59—41no—
209C22×C59—41no—
210C22×C59—41no—
211C22×C59C22×D411yescharacteristic
212C22×C59C22×D411yescharacteristic
213C22×C59C2×#4111yescharacteristic
214C22×C59H(5,𝔽2)11yescharacteristic
215C22×C59H(5,𝔽2)11yescharacteristic
216C22×C59H(5,𝔽2)11yescharacteristic
217C22×C59H(5,𝔽2)11yescharacteristic
218C2×D59—22no—
219C2×D59—22no—
220C2×D59—22no—
221C2×D59—22no—
222C2×D59—22no—
223C2×D59—22no—
224C2×D59—22no—
225C2×D59—22no—
226C2×D59—22no—
227C2×D59—416no—
228C2×D59—41no—
229C2×D59—41no—
230C2×D59—41no—
231C2×D59—41no—
232C2×D59—41no—
233C2×D59—41no—
234C2×D59—41no—
235C2×D59—41no—
236C2×D59—41no—
237C2×D59—41no—
238C2×D59—41no—
239C2×D59—41no—
240C2×D59—41no—
241C2×D59—41no—
242C2×D59—41no—
243C2×D59—41no—
244C2×D59—41no—
245C2×D59—41no—
246C2×D59—41no—
247C4×C59—22no—
248C4×C59—22no—
249C4×C59—41no—
250C4×C59—41no—
251C4×C59—41no—
252C4×C59—41no—
253Dic59—22no—
254Dic59—41no—
255Dic59—41no—
256Dic59—41no—
257#2678—591nomaximal, Sylow
258C2×C59—42no—
259C2×C59#53411yescharacteristic
260C2×C59#53511yescharacteristic
261C2×C59#53811yescharacteristic
262C2×C59D4211yescharacteristic
263C2×C59#54611yescharacteristic
264C2×C59#54611yescharacteristic
265C2×C59#56011yescharacteristic
266D59—42no—
267D59—42no—
268D59—42no—
269D59—81no—
270C2×#123—591no—
271C2×#121—591no—
272C2×#120—591no—
273C2×#120—591no—
274#397—591no—
275#396D5911yescharacteristic, complemented
276#394—591no—
277#394—591no—
278#392—591no—
279#392—591no—
280#390—591no—
281#390—591no—
282#388—591no—
283#386—591no—
284#379—591no—
285C59#267811yescharacteristic, complemented, Sylow
286C25—591no—
287C22×D4—591no—
288C22×D4—591no—
289C22×D4—591no—
290C22×D4—591no—
291C22×D4—591no—
292C22×D4—591no—
293C22×D4—591no—
294C23×C4—591no—
295#123—1184no—
296#121—1184no—
297#120—1184no—
298#120—1184no—
299C2×C4⋊C4—591no—
300C2×C4⋊C4C2×D5911yescharacteristic, complemented
301C2×C4⋊C4C2×D5911yescharacteristic, complemented
302C2×C4⋊C4C2×D5911yescharacteristic, complemented
303C2×C22⋊C4—591no—
304C2×C22⋊C4—591no—
305C2×C22⋊C4—591no—
306C2×C22⋊C4—591no—
307C2×C22⋊C4—591no—
308C2×C22⋊C4—591no—
309C2×C22⋊C4—591no—
310C2×C22⋊C4—591no—
311C2×C22⋊C4—591no—
312C2×C22⋊C4—591no—
313C2×C22⋊C4—591no—
314C2×C22⋊C4—591no—
315C2×C22⋊C4—591no—
316C2×C22⋊C4—591no—
317C2×C22⋊C4C2×D5911yescharacteristic
318C2×C22⋊C4C2×D5911yescharacteristic
319C2×C22⋊C4C2×D5911yescharacteristic
320C2×C42—591no—
321#95—591no—
322#95—591no—
323#95—591no—
324#95C2×D5911yescharacteristic, complemented
325C24—591no—
326C24—591no—
327C24—591no—
328C24—591no—
329C24—1182no—
330C24—1182no—
331C24—1182no—
332C24—2361no—
333C24—2361no—
334C24—2361no—
335C24—2361no—
336C24C22×D5911yescharacteristic
337C2×D4—594no—
338C2×D4—1182no—
339C2×D4—1182no—
340C2×D4—1182no—
341C2×D4—1182no—
342C2×D4—1182no—
343C2×D4—1182no—
344C2×D4—1182no—
345C2×D4—1182no—
346C2×D4—1182no—
347C2×D4—1182no—
348C2×D4—2361no—
349C2×D4—2361no—
350C2×D4—2361no—
351C2×D4—2361no—
352C2×D4—2361no—
353C2×D4—2361no—
354C2×D4—2361no—
355C2×D4—2361no—
356C2×D4—2361no—
357C2×D4—2361no—
358C22×C4—591no—
359C22×C4—591no—
360C22×C4—591no—
361C22×C4—591no—
362C22×C4—1182no—
363C22×C4—1182no—
364C22×C4—2361no—
365C22×C4C22×D5911yescharacteristic
366C22×C4C22×D5911yescharacteristic
367C22×C4C22×D5911yescharacteristic
368C22×C4C22×D5911yescharacteristic
369C22×C4C22×D5911yescharacteristic
370C22×C4C22×D5911yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—1182no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—594no—
379C22⋊C4—1182no—
380C22⋊C4—1182no—
381C22⋊C4—1182no—
382C22⋊C4—1182no—
383C22⋊C4—1182no—
384C22⋊C4—1182no—
385C22⋊C4—1182no—
386C22⋊C4—2361no—
387C22⋊C4—2361no—
388C22⋊C4—2361no—
389C22⋊C4—2361no—
390C22⋊C4—2361no—
391C22⋊C4—2361no—
392C42—2361no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—592no—
400C23—592no—
401C23—592no—
402C23—1181no—
403C23—1181no—
404C23—1181no—
405C23—1181no—
406C23—1181no—
407C23—1181no—
408C23—1181no—
409C23—1181no—
410C23—1181no—
411C23—1181no—
412C23—1181no—
413C23—1181no—
414C23—1181no—
415C23—1181no—
416C23—1181no—
417C23—1181no—
418C23—1181no—
419C23—1181no—
420C23—1181no—
421C23—1181no—
422C23—1181no—
423C23—1181no—
424C23—1181no—
425C23—1181no—
426C23—1181no—
427C23—2364no—
428C23—2364no—
429C23—2364no—
430C23—2364no—
431C23—2364no—
432C23—2364no—
433C23—2364no—
434C23#1174568912yes—
435C23C23×D5911yescharacteristic
436D4—2364no—
437D4—2364no—
438D4—2364no—
439D4—2364no—
440D4—2364no—
441D4—2364no—
442D4—2364no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—592no—
460C2×C4—1181no—
461C2×C4—1181no—
462C2×C4—1181no—
463C2×C4—1181no—
464C2×C4—1181no—
465C2×C4—1181no—
466C2×C4—1181no—
467C2×C4—1181no—
468C2×C4—1181no—
469C2×C4—1181no—
470C2×C4—1181no—
471C2×C4—2364no—
472C2×C4D4×D5912yes—
473C2×C4D4×D5912yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—1182no—
482C22—1182no—
483C22—1182no—
484C22—1182no—
485C22—1182no—
486C22—1182no—
487C22—1182no—
488C22—1182no—
489C22—1182no—
490C22—23616no—
491C22—2361no—
492C22—2361no—
493C22—2361no—
494C22—2361no—
495C22—2361no—
496C22—2361no—
497C22—2361no—
498C22—2361no—
499C22—2361no—
500C22—2361no—
501C22—2361no—
502C22—2361no—
503C22—2361no—
504C22—2361no—
505C22—2361no—
506C22—2361no—
507C22—2361no—
508C22—2361no—
509C22—2361no—
510C22C2×D4×D5911yescharacteristic
511C22C2×D4×D5911yescharacteristic
512C22C2×#1174568911yescharacteristic
513C22#1427377211yescharacteristic
514C22#1427377311yescharacteristic
515C22#1427377311yescharacteristic
516C22#1427377311yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—1182no—
524C4—2361no—
525C4—2361no—
526C4—2361no—
527C2—42no—
528C2—4721no—
529C2—2362no—
530C2—2362no—
531C2—2362no—
532C2#1683796011yescharacteristic
533C2#1683796811yescharacteristic
534C2#1683799211yescharacteristic
535C2#1683803611yescharacteristic
536C2#1683804311yescharacteristic
537C2#1683804311yescharacteristic
538C2#1683814311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC59×#396C2
hypercenter#396D59
hypocenterC59#2678
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ #396

Complements

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

NH ≅ G/Ntype
1. C2×#14273712C2semidirect
2. C2×#14273702C2semidirect
3. C2×#14273697C2semidirect
4. C2×#14273697C2semidirect
5. #16837331C2semidirect
6. #16837319C2semidirect
7. #16837319C2semidirect
8. #16837312C2semidirect
9. #16837311C2semidirect
10. #16837303C2semidirect
11. #16837302C2semidirect
12. #16837292C2semidirect
13. #16837278C2semidirect
14. #16837257C2semidirect
15. C59×#396C2semidirect
21. C22×D236C22semidirect
24. C22×C4×D59C22semidirect
29. C2×Dic59⋊C4C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
42. C2×(C2×D59)⋊C4C22semidirect
43. C2×(C2×D59)⋊C4C22semidirect
44. C2×C4×Dic59C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
47. C59⋊#95C22semidirect
48. C2×C4⋊C4×C59C22semidirect
49. C2×C4⋊C4×C59C22semidirect
50. C2×C4⋊C4×C59C22semidirect
54. #95×C59C22semidirect
97. C2×D236D4semidirect
120. (C2×D59)⋊C4D4semidirect
275. #396D59semidirect
285. C59#2678semidirect
300. C2×C4⋊C4C2×D59semidirect
301. C2×C4⋊C4C2×D59semidirect
302. C2×C4⋊C4C2×D59semidirect
324. #95C2×D59semidirect