Finite Group Databasebeta

← #30601750

Subgroups — #30601750

Order 15616.

826 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#14519834C211yesmaximal, characteristic, complemented
2C2×#16840614C212yesmaximal, complemented
3C2×#16840613C212yesmaximal, complemented
4#21460997C211yesmaximal, characteristic, complemented
5#21454163C211yesmaximal, characteristic
6C22×C4⋊#6923—21no—
7C2×#14519834C2212yes—
8C2×C4×#92420—21no—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12#16840614—24no—
13#16840613—24no—
14C2×#14519773C411yescharacteristic, complemented
15C2×#14519752C2211yescharacteristic
16C2×#14519750—21no—
17C2×#14519750—21no—
18C2×#14519748C2211yescharacteristic
19C2×C42×D61C2211yescharacteristic
20#16839664C411yescharacteristic, complemented
21#16839662—21no—
22#16839662—21no—
23#16839631C411yescharacteristic, complemented
24C61×#390C411yescharacteristic, complemented
25C23×#6923—22no—
26C22×#92420—22no—
27C2×C4⋊#6923—24no—
28C2×C4⋊#6923—42no—
29C2×C4⋊#6923—42no—
30#14519834—22no—
31#14519834D414yescomplemented
32C4×#92420—42no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4—22no—
35(C2×#6923)⋊C4—42no—
36C22×D244—21no—
37C22×D244C2×C411yescharacteristic
38C22×C22⋊D61—21no—
39C22×C22⋊D61—21no—
40C22×C22⋊D61—21no—
41C22×C4×D61D411yescharacteristic
42C22×C4×D61D411yescharacteristic
43C22×C4×D61C2311yescharacteristic
44#14519773—42no—
45#14519752—22no—
46#14519752—22no—
47#14519750—42no—
48#14519750—42no—
49#14519750—42no—
50#14519750—42no—
51#14519748—22no—
52#14519748—22no—
53C2×C4⋊Dic61C2×C411yescharacteristic
54C2×#11758196—21no—
55C2×#11758196—21no—
56C2×C22⋊Dic61—21no—
57C2×#11758198—21no—
58C2×#11758198—21no—
59C2×#11758198—21no—
60C2×C4×Dic61C2×C411yescharacteristic
61C2×C4×Dic61D411yescharacteristic
62C2×C4×Dic61D411yescharacteristic
63C42×D61—42no—
64C22×D4×C61C2×C411yescharacteristic
65C2×C4⋊C4×C61C2×C411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C42×C61C2×C411yescharacteristic
69C24×C61—21no—
70C23×D61—21no—
71C23×D61C2×D411yescharacteristic
72C22×#6923—24no—
73C22×#6923—42no—
74C22×#6923—42no—
75C22×#6923—42no—
76C22×#6923—42no—
77C22×#6923—42no—
78C22×#6923—42no—
79C2×D4×C61—22no—
80C2×D4×C61—41no—
81C2×D4×C61—41no—
82C22×C4×C61—21no—
83C22×C4×C61C22⋊C411yescharacteristic
84C22×C4×C61C22⋊C411yescharacteristic
85C22×C4×C61C22×C411yescharacteristic
86C2×C22⋊D61—42no—
87C2×C22⋊D61—42no—
88C2×C22⋊D61—41no—
89C2×C22⋊D61—41no—
90C2×C22⋊D61—41no—
91C2×C22⋊D61—41no—
92C2×C22⋊D61—41no—
93C2×C22⋊D61—41no—
94C2×C22⋊D61—42no—
95C2×C22⋊D61—42no—
96C2×C22⋊D61—42no—
97C2×C22⋊D61—42no—
98C22×Dic61—21no—
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C2×D411yescharacteristic
102C2×D244—22no—
103C2×D244—41no—
104C2×D244—41no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61D812yes—
118C2×C4×D61D812yes—
119C2×C4×D61SD1612yes—
120C2×C4×D61SD1612yes—
121C2×C4×D61C2×D412yes—
122C2×C4×D61#4112yes—
123C2×#92420—24no—
124C2×#92420—42no—
125C2×#92420—42no—
126C4⋊#6923—48no—
127C4⋊C4×C61—22no—
128C22⋊C4×C61—42no—
129C22⋊C4×C61—42no—
130C42×C61—41no—
131C22⋊Dic61—42no—
132#11758198—42no—
133#11758198—42no—
134#11758198—42no—
135C4⋊Dic61—22no—
136#11758196—42no—
137#11758196—42no—
138C4×Dic61—22no—
139C4×Dic61—22no—
140C4×Dic61—41no—
141C23×C61—41no—
142C23×C61—41no—
143C23×C61—41no—
144C23×C61—41no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61—41no—
148C23×C61C2×C22⋊C411yescharacteristic
149C22×D61—21no—
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61#12411yescharacteristic
161C22×D61#12711yescharacteristic
162C22×D61C2×D811yescharacteristic
163C22×D61C2×D811yescharacteristic
164C22×D61C2×SD1611yescharacteristic
165C22×D61C2×SD1611yescharacteristic
166C2×#6923—44no—
167C2×#6923—44no—
168C2×#6923—44no—
169C2×#6923—82no—
170C2×#6923—82no—
171C2×#6923—82no—
172C2×#6923—82no—
173D4×C61—82no—
174C2×C4×C61—21no—
175C2×C4×C61—21no—
176C2×C4×C61—21no—
177C2×C4×C61—21no—
178C2×C4×C61—21no—
179C2×C4×C61—21no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61#10212yes—
184C2×C4×C61#10212yes—
185C2×C4×C61C4×D412yes—
186C22⋊D61—84no—
187C22⋊D61—81no—
188C22⋊D61—81no—
189C22⋊D61—81no—
190C22⋊D61—81no—
191C22⋊D61—84no—
192C2×Dic61—21no—
193C2×Dic61—21no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61#9912yes—
200C2×Dic61#10212yes—
201C2×Dic61#10212yes—
202C2×Dic61#10412yes—
203C2×Dic61#12112yes—
204D244—82no—
205D244—81no—
206D244—81no—
207D244—81no—
208D244—81no—
209C4×D61—24no—
210C4×D61—24no—
211C4×D61—42no—
212C4×D61—42no—
213C4×D61—42no—
214C4×D61—42no—
215#92420—44no—
216#9680—611nomaximal, Sylow
217C22×C61—81no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61#39011yescharacteristic
225C22×C61C2×#9911yescharacteristic
226C22×C61#41011yescharacteristic
227C22×C61C2×#10211yescharacteristic
228C22×C61C2×#10211yescharacteristic
229C22×C61C2×#10411yescharacteristic
230C22×C61#42111yescharacteristic
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—21no—
242C2×D61—21no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61#48611yescharacteristic
251C2×D61#48611yescharacteristic
252C2×D61#49211yescharacteristic
253C2×D61#49311yescharacteristic
254#6923—84no—
255C4×C61—22no—
256C4×C61—22no—
257C4×C61—22no—
258C4×C61—81no—
259Dic61—22no—
260Dic61—22no—
261Dic61—81no—
262Dic61#32714yescomplemented
263#2856—611no—
264C4×C22⋊C8—611no—
265C2×#327—612no—
266C2×#327—612no—
267C4⋊#95—611no—
268C2×C61—161no—
269C2×C61C2×#32711yescharacteristic
270C2×C61#150211yescharacteristic
271C2×C61#151711yescharacteristic
272C2×C61#151911yescharacteristic
273C2×C61#195711yescharacteristic
274C2×C61#196411yescharacteristic
275C2×C61#198011yescharacteristic
276D61—21no—
277D61—21no—
278D61—21no—
279D61—21no—
280D61—161no—
281C2×#127—611no—
282C2×#121—611no—
283C2×#121—611no—
284C2×#121—1221no—
285C2×#121—1221no—
286C22×C4⋊C4—1221no—
287C22×C42—611no—
288C2×C22⋊C8—612no—
289C2×C4×C8—1221no—
290#390—611no—
291#390—1221no—
292#390—1221no—
293#390#692311yescharacteristic, complemented
294#384—611no—
295C2×#95—612no—
296C2×#95—1221no—
297#336—1221no—
298#327—1224no—
299#327—1224no—
300C61#968011yescharacteristic, complemented, Sylow
301C22×D4—611no—
302C22×D4—1221no—
303C22×D4—1221no—
304C22×D4—1221no—
305C22×D4—1221no—
306C22×D4C2×#692311yescharacteristic
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—1222no—
311C22×C8—1222no—
312#127—2442no—
313#121—1222no—
314#121—1222no—
315#121—1222no—
316#121—1222no—
317#121—2442no—
318#121—2442no—
319#121—2442no—
320#121—2442no—
321C2×C4⋊C4—611no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—1224no—
325C2×C4⋊C4—2442no—
326C2×C4⋊C4—2442no—
327C2×C4⋊C4C2×#692311yescharacteristic
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C22⋊C4—1221no—
334C2×C42—611no—
335C2×C42—611no—
336C2×C42—611no—
337C2×C42—2442no—
338C2×C42C2×#692311yescharacteristic
339C22⋊C8—614no—
340C22⋊C8—1222no—
341C4×C8—2442no—
342#95—1222no—
343#95—1222no—
344#95—2442no—
345C24—21no—
346C24—611no—
347C24—1221no—
348C2×D4—22no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—1222no—
352C2×D4—2441no—
353C2×D4—2441no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C2×D4—2442no—
361C2×D4—2442no—
362C2×D4—2442no—
363C2×D4—2442no—
364C2×D4—2442no—
365C2×D4—2442no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C22×C4—21no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—612no—
377C22×C4—612no—
378C22×C4—612no—
379C22×C4—612no—
380C22×C4—612no—
381C22×C4—612no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1224no—
385C22×C4—1221no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2442no—
391C22×C4—2442no—
392C22×C4—2442no—
393C22×C4—2442no—
394C22×C4—2442no—
395C22×C4—2442no—
396C22×C4C22⋊#692311yescharacteristic
397C22×C4C22⋊#692311yescharacteristic
398C22×C4C22×#692311yescharacteristic
399C2×C8—1224no—
400C2×C8—2442no—
401C2×C8—2442no—
402C4⋊C4—22no—
403C4⋊C4—1222no—
404C4⋊C4—2442no—
405C4⋊C4—2442no—
406C4⋊C4—2448no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—2442no—
410C22⋊C4—2442no—
411C22⋊C4—2442no—
412C22⋊C4—2442no—
413C42—41no—
414C42—1222no—
415C42—1222no—
416C42—2441no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—611no—
425C23—611no—
426C23—611no—
427C23—611no—
428C23—611no—
429C23—611no—
430C23—1221no—
431C23—1221no—
432C23—1221no—
433C23—1221no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23C2×C22⋊#692311yescharacteristic
442D4—82no—
443D4—4882no—
444D4—4881no—
445D4—4881no—
446D4—4881no—
447D4—4881no—
448D4—4884no—
449D4—4884no—
450D4—4881no—
451D4—4881no—
452D4—4881no—
453D4—4881no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—612no—
466C2×C4—612no—
467C2×C4—612no—
468C2×C4—1224no—
469C2×C4—1224no—
470C2×C4—1221no—
471C2×C4—1221no—
472C2×C4—1221no—
473C2×C4—1221no—
474C2×C4—4882no—
475C2×C4—4882no—
476C2×C4—4882no—
477C2×C4—4882no—
478C2×C4—2442no—
479C2×C4—2442no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2444no—
483C2×C4—2444no—
484C2×C4—2444no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4#1451983912yes—
489C2×C4#1451983912yes—
490C2×C4D4×#692312yes—
491C8—2444no—
492C22—81no—
493C22—81no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—81no—
499C22—611no—
500C22—611no—
501C22—611no—
502C22—611no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—1221no—
509C22—1221no—
510C22—1221no—
511C22—1221no—
512C22—1221no—
513C22—1221no—
514C22—1221no—
515C22—4881no—
516C22—4881no—
517C22—4881no—
518C22—4881no—
519C22—4881no—
520C22—4881no—
521C22—4881no—
522C22#1684071411yescharacteristic
523C22D61⋊#9911yescharacteristic
524C22#1684074111yescharacteristic
525C22C2×#1451983911yescharacteristic
526C22C2×#1451983911yescharacteristic
527C22D61⋊#10411yescharacteristic
528C22#1684075911yescharacteristic
529C4—22no—
530C4—22no—
531C4—22no—
532C4—81no—
533C4—614no—
534C4—1222no—
535C4—1222no—
536C4—4884no—
537C4—4881no—
538C2—161no—
539C2—1221no—
540C2—1221no—
541C2—1221no—
542C2—1221no—
543C2—9761no—
544C2D61⋊#32711yescharacteristic
545C2#2146119811yescharacteristic
546C2#2146124911yescharacteristic
547C2#2146125411yescharacteristic
548C2#2146194711yescharacteristic
549C2#2146196011yescharacteristic
550C2#2146198411yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#390C4
socleC23×C61C2×C22⋊C4
prime radical#21454163C2
cosocleC22×C4×D61C23
hypercenter#390#6923
hypocenterC61#9680
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C4×#14519834C2semidirect
2. C2×#16840614C2semidirect
3. C2×#16840613C2semidirect
4. #21460997C2semidirect
14. C2×#14519773C4semidirect
20. #16839664C4semidirect
23. #16839631C4semidirect
24. C61×#390C4semidirect
31. #14519834D4semidirect
262. Dic61#327semidirect
293. #390#6923semidirect
300. C61#9680semidirect

Maximal subgroups

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

subgroupindex
C4×#145198342
C2×#168406142
C2×#168406132
#214609972
#214541632
#968061