Finite Group Databasebeta

← #30610147

Subgroups — #30610147

Order 15616.

1450 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C212yesmaximal, complemented
2#21461084C218yesmaximal, complemented
3#21461069C212yesmaximal, complemented
4#21461064C212yesmaximal, complemented
5C22×#14519758C211yesmaximal, characteristic
6C22×#11758217—22no—
7#16840732—22no—
8#16840732—22no—
9#16840732C2214yes—
10#16840732C2214yescomplemented
11C2×C22⋊#92420—22no—
12C2×C22⋊#92420C2214yescomplemented
13#16840608C2218yescomplemented
14#16840605C2218yescomplemented
15C24×Dic61C2211yescharacteristic
16C2×#14519758—22no—
17C2×#14519758—22no—
18C2×#14519758—22no—
19C2×#14519758—22no—
20C2×#14519758C414yes—
21C2×#14519758C2214yes—
22C22×#11758196C411yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C411yescharacteristic
25C22×C22⋊Dic61C411yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C23×D4×C61C411yescharacteristic
28C2×#11758217—24no—
29C2×#11758217—24no—
30C2×#11758217—48no—
31C22×#92420—24no—
32C22⋊#92420—24no—
33C22⋊#92420—24no—
34C22⋊#92420—24no—
35C22⋊#92420C2318yes—
36C23×Dic61—44no—
37C23×Dic61C2×C411yescharacteristic
38C23×Dic61C2×C411yescharacteristic
39C23×Dic61C2×C411yescharacteristic
40C23×Dic61C2×C412yes—
41C23×Dic61D412yes—
42C23×Dic61D412yes—
43C23×Dic61D412yes—
44C23×Dic61D412yes—
45C23×Dic61C2311yescharacteristic
46C23×Dic61C2312yes—
47#14519758—24no—
48#14519758—24no—
49#14519758—24no—
50#14519758—24no—
51#14519758—24no—
52#14519758—24no—
53#14519758—24no—
54#14519758—24no—
55C2×#11758196—22no—
56C2×#11758196—21no—
57C2×#11758196—21no—
58C2×#11758196—22no—
59C2×#11758196—22no—
60C2×#11758196C2×C414yes—
61C2×#11758196C2×C412yes—
62C2×#11758196C2312yes—
63C2×C22⋊Dic61—22no—
64C2×C22⋊Dic61—21no—
65C2×C22⋊Dic61—21no—
66C2×C22⋊Dic61—22no—
67C2×C22⋊Dic61—21no—
68C2×C22⋊Dic61—21no—
69C2×C22⋊Dic61—22no—
70C2×C22⋊Dic61—22no—
71C2×C22⋊Dic61C2×C414yes—
72C2×C22⋊Dic61C2×C414yes—
73C2×C22⋊Dic61C2×C412yes—
74C2×C22⋊Dic61C2312yes—
75C25×C61C2×C411yescharacteristic
76C25×C61C2×C411yescharacteristic
77C22×D4×C61—22no—
78C22×D4×C61—21no—
79C22×D4×C61—21no—
80C22×D4×C61—44no—
81C22×D4×C61C2×C414yes—
82C23×C4×C61C2×C411yescharacteristic
83C24×C61—24no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61—42no—
89C24×C61—42no—
90C24×C61—42no—
91C24×C61C22⋊C412yes—
92C24×C61C22⋊C411yescharacteristic
93C24×C61C22⋊C411yescharacteristic
94C24×C61C22×C411yescharacteristic
95C24×C61C22×C412yes—
96C24×C61C22×C412yes—
97C2×D4×C61—24no—
98C2×D4×C61—24no—
99C2×D4×C61—48no—
100C2×D4×C61—44no—
101C2×D4×C61—44no—
102C2×D4×C61—48no—
103C22×C4×C61—21no—
104C22×C4×C61—21no—
105C22×C4×C61—42no—
106C22×C4×C61C22×C412yes—
107C22×Dic61—28no—
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—42no—
113C22×Dic61—44no—
114C22×Dic61—44no—
115C22×Dic61—44no—
116C22×Dic61—44no—
117C22×Dic61—44no—
118C22×Dic61—42no—
119C22×Dic61—42no—
120C22×Dic61—42no—
121C22×Dic61C22⋊C412yes—
122C22×Dic61C22⋊C412yes—
123C22×Dic61C22⋊C412yes—
124C22×Dic61C22⋊C411yescharacteristic
125C22×Dic61C22⋊C411yescharacteristic
126C22×Dic61C22⋊C412yes—
127C22×Dic61C22⋊C412yes—
128C22×Dic61C22×C412yes—
129C22×Dic61C22×C412yes—
130C22×Dic61C22×C412yes—
131C22×Dic61C22×C411yescharacteristic
132C22×Dic61C2×D412yes—
133C22×Dic61C2×D412yes—
134C22×Dic61C2×D412yes—
135C22×Dic61C2×D412yes—
136C22×Dic61C2×D412yes—
137C22×Dic61C2×D412yes—
138C22×Dic61C2411yescharacteristic
139#11758217—48no—
140#11758217—48no—
141C2×#92420—28no—
142C2×#92420—48no—
143C22⋊Dic61—24no—
144C22⋊Dic61—24no—
145C22⋊Dic61—24no—
146C22⋊Dic61—24no—
147C22⋊Dic61—24no—
148C22⋊Dic61—24no—
149#11758196—24no—
150#11758196—24no—
151#11758196—24no—
152#11758196—24no—
153C23×C61—22no—
154C23×C61—22no—
155C23×C61—22no—
156C23×C61—24no—
157C23×C61—24no—
158C23×C61—22no—
159C23×C61—24no—
160C23×C61—24no—
161C23×C61—22no—
162C23×C61—24no—
163C23×C61—41no—
164C23×C61—42no—
165C23×C61—41no—
166C23×C61—41no—
167C23×C61—41no—
168C23×C61—42no—
169C23×C61—416no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—42no—
173C23×C61—42no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—88no—
179C23×C61#9914yes—
180C23×C61C2×C22⋊C412yes—
181C23×C61C2×C22⋊C412yes—
182C23×C61C2×C22⋊C411yescharacteristic
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61C23×C411yescharacteristic
185D4×C61—48no—
186D4×C61—48no—
187C2×C4×C61—22no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×Dic61—24no—
192C2×Dic61—24no—
193C2×Dic61—24no—
194C2×Dic61—24no—
195C2×Dic61—24no—
196C2×Dic61—24no—
197C2×Dic61—22no—
198C2×Dic61—22no—
199C2×Dic61—24no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—41no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215C2×Dic61C2×C22⋊C412yes—
216C2×Dic61C2×C22⋊C412yes—
217C2×Dic61C2×C22⋊C412yes—
218C2×Dic61C22×D412yes—
219#92420—48no—
220#17392—611nomaximal, Sylow
221C22×C61—28no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—22no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—22no—
230C22×C61—22no—
231C22×C61—22no—
232C22×C61—22no—
233C22×C61—44no—
234C22×C61—48no—
235C22×C61—48no—
236C22×C61—44no—
237C22×C61—42no—
238C22×C61—42no—
239C22×C61—42no—
240C22×C61—84no—
241C22×C61—84no—
242C22×C61—84no—
243C22×C61C2×#9912yes—
244C22×C61C2×#9914yes—
245C22×C61#41312yes—
246C22×C61C22×C22⋊C411yescharacteristic
247C22×C61#56812yes—
248C4×C61—42no—
249Dic61—22no—
250Dic61—22no—
251Dic61—22no—
252Dic61—22no—
253Dic61—42no—
254Dic61—42no—
255C22×#123—611no—
256C2×#407—612no—
257#1468—618no—
258#1463—612no—
259#1462—612no—
260C2×C61—22no—
261C2×C61—22no—
262C2×C61—22no—
263C2×C61—24no—
264C2×C61—42no—
265C2×C61—82no—
266C2×C61#287911yescharacteristic
267C2×C61C22×#9911yescharacteristic
268C2×C61C2×#41311yescharacteristic
269C23×D4#692311yescharacteristic
270C24×C4—611no—
271C22×M16—1222no—
272C2×#123—614no—
273C2×#123—614no—
274C2×#123—1222no—
275C2×#123—1222no—
276C2×#123—1222no—
277C2×#123—1222no—
278C22×C4⋊C4—611no—
279C22×C4⋊C4—611no—
280C22×C22⋊C4—611no—
281C22×C22⋊C4—611no—
282C22×C22⋊C4—611no—
283#407—614no—
284#407—614no—
285#407—1222no—
286#407—1222no—
287C2×C22⋊C8—614no—
288C2×C22⋊C8—1222no—
289#324—618no—
290#323—618no—
291C61#1739211yescharacteristic, complemented, Sylow
292C25C2×#692311yescharacteristic
293C25C2×#692311yescharacteristic
294C22×D4—22no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—44no—
298C22×D4C2×#692314yes—
299C23×C4—612no—
300C23×C4—612no—
301C23×C4—612no—
302C23×C4—612no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—612no—
306C23×C4—612no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—2444no—
310C23×C4C2×#692311yescharacteristic
311C2×M16—1224no—
312C2×M16—1224no—
313C2×M16—2448no—
314C22×C8—1224no—
315#123—1224no—
316#123—1224no—
317#123—1224no—
318#123—1224no—
319#123—1224no—
320#123—1224no—
321#123—1224no—
322#123—1224no—
323C2×C4⋊C4—612no—
324C2×C4⋊C4—612no—
325C2×C4⋊C4—614no—
326C2×C4⋊C4—1222no—
327C2×C4⋊C4—1222no—
328C2×C4⋊C4—1222no—
329C2×C4⋊C4—1221no—
330C2×C4⋊C4—1221no—
331C2×C22⋊C4—612no—
332C2×C22⋊C4—614no—
333C2×C22⋊C4—612no—
334C2×C22⋊C4—614no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1221no—
339C2×C22⋊C4—1221no—
340C2×C22⋊C4—1222no—
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C22⋊C8—618no—
344C22⋊C8—1224no—
345C22⋊C8—1224no—
346C22⋊C8—1224no—
347C24—24no—
348C24—21no—
349C24—21no—
350C24—42no—
351C24—42no—
352C24—42no—
353C24—42no—
354C24—42no—
355C24C22⋊#692312yes—
356C24C22⋊#692311yescharacteristic
357C24C22⋊#692311yescharacteristic
358C24C22×#692311yescharacteristic
359C24C22×#692312yes—
360C24C22×#692312yes—
361C2×D4—24no—
362C2×D4—24no—
363C2×D4—48no—
364C2×D4—44no—
365C2×D4—44no—
366C2×D4—48no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—42no—
370C22×C4—612no—
371C22×C4—612no—
372C22×C4—612no—
373C22×C4—612no—
374C22×C4—612no—
375C22×C4—612no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—612no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—612no—
382C22×C4—612no—
383C22×C4—611no—
384C22×C4—612no—
385C22×C4—611no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—1228no—
389C22×C4—1221no—
390C22×C4—1221no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—2444no—
394C22×C4—2444no—
395C22×C4—2442no—
396C22×C4—2444no—
397C22×C4—2444no—
398C22×C4—2442no—
399C22×C4—2444no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4C22×#692312yes—
403M16—2448no—
404M16—2448no—
405C2×C8—1228no—
406C2×C8—2448no—
407C4⋊C4—1224no—
408C4⋊C4—1224no—
409C4⋊C4—1224no—
410C4⋊C4—1224no—
411C22⋊C4—1224no—
412C22⋊C4—1224no—
413C22⋊C4—1224no—
414C22⋊C4—1224no—
415C22⋊C4—1224no—
416C22⋊C4—1224no—
417C23—22no—
418C23—22no—
419C23—22no—
420C23—24no—
421C23—22no—
422C23—24no—
423C23—24no—
424C23—24no—
425C23—22no—
426C23—24no—
427C23—41no—
428C23—42no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—416no—
434C23—42no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23—42no—
440C23—42no—
441C23—42no—
442C23—88no—
443C23#1451983514yes—
444C23C2×C22⋊#692312yes—
445C23C2×C22⋊#692312yes—
446C23C2×C22⋊#692311yescharacteristic
447C23C2×C22⋊#692311yescharacteristic
448C23C23×#692311yescharacteristic
449D4—48no—
450D4—48no—
451C2×C4—22no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—612no—
456C2×C4—612no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—1224no—
460C2×C4—1224no—
461C2×C4—1224no—
462C2×C4—1224no—
463C2×C4—1224no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—1224no—
468C2×C4—2441no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2442no—
475C2×C4—2441no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C8—2448no—
484C22—28no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—44no—
497C22—48no—
498C22—48no—
499C22—44no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—84no—
504C22—84no—
505C22—84no—
506C22C2×#1451983512yes—
507C22C2×#1451983514yes—
508C22#1684074912yes—
509C22C22×C22⋊#692311yescharacteristic
510C22#1684084012yes—
511C4—42no—
512C4—1222no—
513C4—1222no—
514C4—1222no—
515C4—1222no—
516C4—2442no—
517C4—2442no—
518C2—22no—
519C2—22no—
520C2—22no—
521C2—24no—
522C2—42no—
523C2—82no—
524C2#2146240311yescharacteristic
525C2C22×#1451983511yescharacteristic
526C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
Fitting, prime radicalC23×D4×C61C4
socleC22×C61C22×C22⋊C4
cosocleC22×Dic61C24
hypercenterC23×D4#6923
hypocenterC61#17392
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C23×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16840732C2semidirect
2. #21461084C2semidirect
3. #21461069C2semidirect
4. #21461064C2semidirect
10. #16840732C22semidirect
12. C2×C22⋊#92420C22semidirect
13. #16840608C22semidirect
14. #16840605C22semidirect
291. C61#17392semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168407322
#214610842
#214610692
#214610642
C22×#145197582
#1739261