Finite Group Databasebeta

← #21430415

Subgroups — #21430415

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×#14273701C211yesmaximal, characteristic, complemented
2C2×#14273697C211yesmaximal, characteristic, complemented
3C2×#14273695C211yesmaximal, characteristic, complemented
4#16837328C211yesmaximal, characteristic, complemented
5#16837324C211yesmaximal, characteristic, complemented
6#16837319C211yesmaximal, characteristic, complemented
7#16837317C211yesmaximal, characteristic, complemented
8#16837311C211yesmaximal, characteristic, complemented
9#16837310C211yesmaximal, characteristic, complemented
10#16837303C211yesmaximal, characteristic, complemented
11#16837302C211yesmaximal, characteristic, complemented
12#16837295C211yesmaximal, characteristic, complemented
13#16837281C211yesmaximal, characteristic, complemented
14#16837257C211yesmaximal, characteristic, complemented
15C2×#123×C59C211yesmaximal, characteristic, complemented
16C24×D59C2211yescharacteristic
17C22×D236C2211yescharacteristic
18C22×D236C2211yescharacteristic
19C22×C22⋊D59C2211yescharacteristic
20C22×C22⋊D59C2211yescharacteristic
21C22×C22⋊D59C2211yescharacteristic
22C22×C22⋊D59C2211yescharacteristic, complemented
23#14273701—24no—
24#14273697—24no—
25#14273695—24no—
26C2×C4⋊Dic59C2211yescharacteristic, complemented
27C2×Dic59⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic59C2211yescharacteristic
29C2×C22⋊Dic59C2211yescharacteristic
30C2×C22⋊Dic59C2211yescharacteristic, complemented
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×C4×Dic59C2211yescharacteristic, complemented
43C59⋊#95C2211yescharacteristic, complemented
44C59⋊#95C2211yescharacteristic, complemented
45C59⋊#95C2211yescharacteristic, complemented
46C59⋊#95C2211yescharacteristic, complemented
47C22×D4×C59C2211yescharacteristic
48C23×C4×C59C2211yescharacteristic, complemented
49#123×C59—24no—
50C2×C4⋊C4×C59C2211yescharacteristic, complemented
51C2×C4⋊C4×C59C2211yescharacteristic, complemented
52C2×C22⋊C4×C59C2211yescharacteristic
53C2×C22⋊C4×C59C2211yescharacteristic
54C2×C22⋊C4×C59C2211yescharacteristic, complemented
55C24×C59C2311yescharacteristic
56C24×C59C2311yescharacteristic
57C23×D59—22no—
58C23×D59—22no—
59C23×D59—22no—
60C23×D59—41no—
61C23×D59—41no—
62C23×D59—41no—
63C23×D59—41no—
64C23×D59C2311yescharacteristic
65C23×D59C2311yescharacteristic
66C23×D59C2311yescharacteristic
67C2×D4×C59—22no—
68C2×D4×C59—22no—
69C2×D4×C59—41no—
70C22×C4×C59—22no—
71C22×C4×C59—22no—
72C22×C4×C59—41no—
73C22×C4×C59C2311yescharacteristic
74C22×C4×C59C2311yescharacteristic
75C22×C4×C59C2311yescharacteristic
76C22×C4×C59C2311yescharacteristic
77C22×C4×C59C2311yescharacteristic
78C2×C22⋊D59—22no—
79C2×C22⋊D59—22no—
80C2×C22⋊D59—22no—
81C2×C22⋊D59—22no—
82C2×C22⋊D59—41no—
83C2×C22⋊D59—41no—
84C2×C22⋊D59—41no—
85C2×C22⋊D59—41no—
86C2×C22⋊D59—41no—
87C2×C22⋊D59—41no—
88C2×C22⋊D59—41no—
89C2×C22⋊D59D414yescomplemented
90C22×Dic59C2311yescharacteristic
91C22×Dic59C2311yescharacteristic
92C22×Dic59C2311yescharacteristic
93C22×Dic59C2311yescharacteristic
94C22×Dic59C2311yescharacteristic
95C2×D236—22no—
96C2×D236—22no—
97C2×D236—22no—
98C2×D236—22no—
99C2×D236—41no—
100C2×D236—41no—
101C4⋊C4×C59—22no—
102C4⋊C4×C59—22no—
103C22⋊C4×C59—22no—
104C22⋊C4×C59—22no—
105C22⋊C4×C59D414yescomplemented
106C22⋊Dic59—22no—
107C22⋊Dic59—41no—
108C22⋊Dic59—41no—
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—
120C4⋊Dic59—22no—
121Dic59⋊C4—41no—
122C4×Dic59—41no—
123C23×C59—21no—
124C23×C59—21no—
125C23×C59—21no—
126C23×C59—21no—
127C23×C59—21no—
128C23×C59—21no—
129C23×C59—21no—
130C23×C59—21no—
131C23×C59—21no—
132C23×C59—21no—
133C23×C59—21no—
134C23×C59—21no—
135C23×C59C2×D412yes—
136C23×C59C2×D412yes—
137C23×C59C2411yescharacteristic
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—21no—
157C22×D59—44no—
158C22×D59—44no—
159C22×D59—44no—
160C22×D59—44no—
161C22×D59—44no—
162C22×D59—44no—
163C22×D59—44no—
164C22×D59C2×D412yes—
165C22×D59#4112yes—
166D4×C59—44no—
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—44no—
181C2×C4×C59C2×D412yes—
182C2×C4×C59C2×D412yes—
183C22⋊D59—44no—
184C22⋊D59—44no—
185C22⋊D59—44no—
186C22⋊D59—44no—
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×Dic59—21no—
198C2×Dic59—21no—
199C2×Dic59—21no—
200C2×Dic59—21no—
201C2×Dic59C2×D412yes—
202D236—44no—
203D236—44no—
204C22×C59—22no—
205C22×C59—22no—
206C22×C59—22no—
207C22×C59—22no—
208C22×C59—22no—
209C22×C59—22no—
210C22×C59—41no—
211C22×C59—41no—
212C22×C59—41no—
213C22×C59—41no—
214C22×C59—41no—
215C22×C59—41no—
216C22×C59—41no—
217C22×C59—41no—
218C22×C59C22×D411yescharacteristic
219C22×C59C22×D411yescharacteristic
220C22×C59C2×#4111yescharacteristic
221C22×C59H(5,𝔽2)11yescharacteristic
222C22×C59H(5,𝔽2)11yescharacteristic
223C22×C59H(5,𝔽2)11yescharacteristic
224C22×C59H(5,𝔽2)11yescharacteristic
225C2×D59—22no—
226C2×D59—22no—
227C2×D59—22no—
228C2×D59—22no—
229C2×D59—22no—
230C2×D59—22no—
231C2×D59—416no—
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—
252Dic59—22no—
253Dic59—41no—
254Dic59—41no—
255Dic59—41no—
256Dic59—41no—
257#2678—591nomaximal, Sylow
258C2×C59—42no—
259C2×C59—42no—
260C2×C59#53411yescharacteristic
261C2×C59#53511yescharacteristic
262C2×C59#53811yescharacteristic
263C2×C59D4211yescharacteristic
264C2×C59#54611yescharacteristic
265C2×C59#54611yescharacteristic
266C2×C59#56011yescharacteristic
267D59—42no—
268D59—42no—
269D59—81no—
270C2×#123D5911yescharacteristic, complemented
271C2×#121—591no—
272C2×#120—591no—
273C2×#120—591no—
274#397—591no—
275#396—591no—
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×D4C2×D5911yescharacteristic
294C23×C4C2×D5911yescharacteristic, complemented
295#123—24no—
296#121—1184no—
297#120—1184no—
298#120—1184no—
299C2×C4⋊C4—591no—
300C2×C4⋊C4—591no—
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, complemented
320C2×C42—591no—
321#95—591no—
322#95—591no—
323#95—591no—
324#95—591no—
325C24—591no—
326C24—591no—
327C24—591no—
328C24—1182no—
329C24—1182no—
330C24—1182no—
331C24—2361no—
332C24—2361no—
333C24—2361no—
334C24—2361no—
335C24C22×D5911yescharacteristic
336C24C22×D5911yescharacteristic
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—41no—
340C2×D4—594no—
341C2×D4—1182no—
342C2×D4—1182no—
343C2×D4—1182no—
344C2×D4—1182no—
345C2×D4—1182no—
346C2×D4—1182no—
347C2×D4—1182no—
348C2×D4—1182no—
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—22no—
359C22×C4—22no—
360C22×C4—41no—
361C22×C4—591no—
362C22×C4—591no—
363C22×C4—591no—
364C22×C4—591no—
365C22×C4—591no—
366C22×C4C22×D5911yescharacteristic
367C22×C4C22×D5911yescharacteristic
368C22×C4C22×D5911yescharacteristic
369C22×C4C22×D5911yescharacteristic
370C22×C4C22×D5911yescharacteristic
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—1182no—
374C4⋊C4—2361no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—1182no—
378C22⋊C4—1182no—
379C22⋊C4—1182no—
380C22⋊C4—1182no—
381C22⋊C4—1182no—
382C22⋊C4—1182no—
383C22⋊C4—1182no—
384C22⋊C4—2361no—
385C22⋊C4—2361no—
386C22⋊C4—2361no—
387C22⋊C4—2361no—
388C22⋊C4—2361no—
389C22⋊C4—2361no—
390C22⋊C4—2361no—
391C22⋊C4C22⋊D5914yescomplemented
392C42—2361no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—592no—
406C23—592no—
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—2364no—
427C23—2364no—
428C23—2364no—
429C23—2364no—
430C23—2364no—
431C23—2364no—
432C23—2364no—
433C23D4×D5912yes—
434C23C2×C22⋊D5912yes—
435C23C23×D5911yescharacteristic
436D4—44no—
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—44no—
457C2×C4—592no—
458C2×C4—1181no—
459C2×C4—1181no—
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—1181no—
472C2×C4C2×C22⋊D5912yes—
473C2×C4C2×C22⋊D5912yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—22no—
478C22—22no—
479C22—22no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—1182no—
489C22—1182no—
490C22—1182no—
491C22—1182no—
492C22—1182no—
493C22—1182no—
494C22—23616no—
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
511C22C22×C22⋊D5911yescharacteristic
512C22#41×D5911yescharacteristic
513C22#1427377211yescharacteristic
514C22#1427377311yescharacteristic
515C22#1427377311yescharacteristic
516C22#1427377311yescharacteristic
517C4—22no—
518C4—22no—
519C4—41no—
520C4—41no—
521C4—41no—
522C4—1182no—
523C4—2361no—
524C4—2361no—
525C4—2361no—
526C4—2361no—
527C2—42no—
528C2—42no—
529C2—4721no—
530C2—2362no—
531C2—2362no—
532C2#1683796311yescharacteristic
533C2#1683796611yescharacteristic
534C2#1683798811yescharacteristic
535C2D4×C22⋊D5911yescharacteristic
536C2#1683804011yescharacteristic
537C2#1683804411yescharacteristic
538C2#1683814211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D59
commutator, socleC23×C59C24
FittingC2×#123×C59C2
hypercenterC2×#123D59
hypocenterC59#2678
LCSG ▷ C23×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×#14273701C2semidirect
2. C2×#14273697C2semidirect
3. C2×#14273695C2semidirect
4. #16837328C2semidirect
5. #16837324C2semidirect
6. #16837319C2semidirect
7. #16837317C2semidirect
8. #16837311C2semidirect
9. #16837310C2semidirect
10. #16837303C2semidirect
11. #16837302C2semidirect
12. #16837295C2semidirect
13. #16837281C2semidirect
14. #16837257C2semidirect
15. C2×#123×C59C2semidirect
22. C22×C22⋊D59C22semidirect
26. C2×C4⋊Dic59C22semidirect
27. C2×Dic59⋊C4C22semidirect
30. C2×C22⋊Dic59C22semidirect
39. C2×(C2×D59)⋊C4C22semidirect
40. C2×(C2×D59)⋊C4C22semidirect
41. C2×(C2×D59)⋊C4C22semidirect
42. C2×C4×Dic59C22semidirect
43. C59⋊#95C22semidirect
44. C59⋊#95C22semidirect
45. C59⋊#95C22semidirect
46. C59⋊#95C22semidirect
48. C23×C4×C59C22semidirect
50. C2×C4⋊C4×C59C22semidirect
51. C2×C4⋊C4×C59C22semidirect
54. C2×C22⋊C4×C59C22semidirect
89. C2×C22⋊D59D4semidirect
105. C22⋊C4×C59D4semidirect
270. C2×#123D59semidirect
285. C59#2678semidirect
294. C23×C4C2×D59semidirect
301. C2×C4⋊C4C2×D59semidirect
302. C2×C4⋊C4C2×D59semidirect
319. C2×C22⋊C4C2×D59semidirect
391. C22⋊C4C22⋊D59semidirect