Finite Group Databasebeta

← #30602526

Subgroups — #30602526

Order 15616.

1180 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×#16840841C211yesmaximal, characteristic
2D61⋊#410C211yesmaximal, characteristic
3#21461500C212yesmaximal, complemented
4#21461499C212yesmaximal, complemented
5#410×D61C211yesmaximal, characteristic
6#16840841—24no—
7#16840841—24no—
8C2×#14519865—21no—
9C2×#14519864—22no—
10C2×#14519864—21no—
11C22×#11758213C412yescomplemented
12C22×#11758213C2211yescharacteristic
13C2×D61⋊M16C412yescomplemented
14C2×D61⋊M16C2211yescharacteristic
15C2×#14519856C2212yes—
16#16840743—21no—
17#16840742—21no—
18#16840741C414yescomplemented
19D61⋊#99—22no—
20#16840633—24no—
21#16840632—24no—
22C2×#41×D61C2211yescharacteristic
23#117×D61C2212yes—
24#16839736C411yescharacteristic, complemented
25#16839735C412yescomplemented
26#16839734—22no—
27#99×D61—22no—
28C61×#410C411yescharacteristic, complemented
29#14519865—28no—
30#14519864—216no—
31#14519864—28no—
32C2×#11758213—22no—
33C2×#11758213—21no—
34C2×#11758213—22no—
35C2×#11758213—24no—
36C2×#11758213—24no—
37C2×#11758213C2×C411yescharacteristic
38C2×#11758213C2×C412yes—
39C2×#11758213C2×C411yescharacteristic
40C2×#11758213D414yes—
41D61⋊M16—22no—
42D61⋊M16—24no—
43D61⋊M16—24no—
44D61⋊M16D414yes—
45C2×#11758217—22no—
46C2×#11758217—21no—
47C2×D61⋊C8—22no—
48C2×D61⋊C8—21no—
49C22×#92420—22no—
50C22×#92420—21no—
51#14519856—22no—
52#14519856—22no—
53#14519856—22no—
54#14519856C2×C414yes—
55C2×C4⋊#6923—22no—
56C2×C22⋊#6923—22no—
57C2×C4×#6923—22no—
58#14519836—24no—
59#14519835—24no—
60C2×#11758226D411yescharacteristic
61C2×#11758222C2×C411yescharacteristic
62C2×#11758222C2×C412yes—
63C2×#11758224D412yes—
64C2×#11758224D411yescharacteristic
65#41×D61—22no—
66#41×D61—22no—
67#41×D61—22no—
68#41×D61—22no—
69C2×Q8×D61Q811yescharacteristic
70C2×D4×D61D412yes—
71C2×D4×D61Q811yescharacteristic
72C22×C4×D61C2×C412yes—
73C22×C4×D61C2311yescharacteristic
74#14519736C2×C412yes—
75#14519735—22no—
76#14519734—22no—
77#14519733—22no—
78C4⋊C4×D61—22no—
79C22⋊C4×D61—22no—
80C42×D61—22no—
81#14519692—22no—
82#14519691—24no—
83C2×#41×C61C2×C411yescharacteristic
84#117×C61C2×C412yes—
85#99×C61—22no—
86C23×D61C4⋊C412yes—
87C23×D61C2×D411yescharacteristic
88C22×#6923—42no—
89#41×C61—22no—
90#41×C61—22no—
91C2×Q8×C61C4⋊C411yescharacteristic
92C2×D4×C61C22⋊C412yes—
93C2×D4×C61C4⋊C411yescharacteristic
94C22×C4×C61C4212yes—
95C22×C4×C61C22×C411yescharacteristic
96C2×C22⋊D61C22⋊C412yes—
97C2×C22⋊D61C22⋊C412yes—
98C2×C22⋊D61C4⋊C412yes—
99C22×Dic61C22⋊C412yes—
100C22×Dic61C2×D411yescharacteristic
101#11758226—22no—
102#11758226—22no—
103Q8×D61—22no—
104Q8×D61—22no—
105#11758224—24no—
106#11758224—24no—
107#11758224—22no—
108#11758224—22no—
109D4×D61—24no—
110D4×D61—24no—
111D4×D61—22no—
112D4×D61—22no—
113#11758222—22no—
114#11758222—22no—
115#11758222—24no—
116#11758222—24no—
117C2×D244C22⋊C412yes—
118C2×D244C4⋊C411yescharacteristic
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—22no—
123C2×C4×D61—42no—
124C2×C4×D61C4212yes—
125C2×C4×D61C22⋊C412yes—
126C2×C4×D61C4⋊C412yes—
127C2×C4×D61C22×C411yescharacteristic
128C2×C4×D61C22×C411yescharacteristic
129C2×C4×D61C2×D412yes—
130C2×C4×D61C2×D412yes—
131C2×C4×D61C2×D411yescharacteristic
132C2×C4×D61C2×Q811yescharacteristic
133C2×C4×D61#4112yes—
134C2×C4×D61#4112yes—
135C2×Dic122C4⋊C411yescharacteristic
136C2×Dic122C4⋊C412yes—
137C22⋊#6923—24no—
138C22⋊#6923—42no—
139#11758217—28no—
140#11758217—24no—
141C2×#92420—28no—
142C2×#92420—21no—
143C2×#92420—22no—
144C2×#92420—21no—
145C2×#92420—24no—
146C4⋊#6923—24no—
147C4⋊#6923—42no—
148C4×#6923—24no—
149C4×#6923—42no—
150#11758213—28no—
151#11758213—21no—
152#11758213—21no—
153#11758213—22no—
154#11758213—24no—
155#11758213C22⋊C412yes—
156#11758213C22⋊C414yes—
157#11758213C22⋊C412yes—
158D61⋊C8—28no—
159D61⋊C8—24no—
160C4⋊C4×C61—22no—
161C22⋊C4×C61—22no—
162C42×C61—22no—
163C22⋊Dic61—22no—
164#11758198—42no—
165C4⋊Dic61—22no—
166#11758196—42no—
167C4×Dic61—22no—
168C4×Dic61—42no—
169C23×C61#9512yes—
170C23×C61C2×C22⋊C411yescharacteristic
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—81no—
174C22×D61—82no—
175C22×D61#9512yes—
176C22×D61C2×C22⋊C411yescharacteristic
177C22×D61C2×C4⋊C411yescharacteristic
178C22×D61#12112yes—
179C22×D61#12112yes—
180C2×#6923—44no—
181C2×#6923—84no—
182Q8×C61—22no—
183D4×C61—24no—
184D4×C61—22no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—42no—
188C2×C4×C61#9512yes—
189C2×C4×C61C2×C4211yescharacteristic
190C2×C4×C61C2×C4⋊C411yescharacteristic
191C2×C4×C61C4×D412yes—
192C2×C4×C61C4×D412yes—
193C22⋊D61—24no—
194C22⋊D61—24no—
195C22⋊D61—24no—
196C2×Dic61—22no—
197C2×Dic61—22no—
198C2×Dic61—42no—
199C2×Dic61#9512yes—
200C2×Dic61C2×C22⋊C411yescharacteristic
201C2×Dic61C2×C4⋊C411yescharacteristic
202C2×Dic61#12012yes—
203C2×Dic61#12312yes—
204D244—24no—
205D244—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—84no—
213C4×D61C2×C22⋊C411yescharacteristic
214C4×D61C2×C22⋊C411yescharacteristic
215C4×D61#11711yescharacteristic
216C4×D61#11711yescharacteristic
217C4×D61C4×D412yes—
218C4×D61C4×D412yes—
219C4×D61#12012yes—
220C4×D61C22⋊Q812yes—
221C4×D61C22⋊Q812yes—
222C4×D61#12312yes—
223Dic122—22no—
224Dic122—24no—
225#92420—22no—
226#92420—24no—
227#92420—22no—
228#10766—611nomaximal, Sylow
229C22×C61—22no—
230C22×C61—41no—
231C22×C61—42no—
232C22×C61C2×#9511yescharacteristic
233C22×C61#38612yes—
234C2×D61—22no—
235C2×D61—42no—
236C2×D61—42no—
237C2×D61—41no—
238C2×D61—41no—
239C2×D61—42no—
240C2×D61—82no—
241C2×D61—82no—
242C2×D61#38011yescharacteristic
243C2×D61#38011yescharacteristic
244C2×D61#38612yes—
245#6923—84no—
246C4×C61—22no—
247C4×C61—82no—
248C4×C61C4×C22⋊C411yescharacteristic
249C4×C61C4×C22⋊C411yescharacteristic
250C4×C61#38512yes—
251Dic61—22no—
252Dic61—82no—
253Dic61#37911yescharacteristic
254Dic61#38111yescharacteristic
255Dic61#38512yes—
256C2×#568—611no—
257C2×#410—611no—
258C2×#410—611no—
259#1733—612no—
260#1733—612no—
261C2×C61—22no—
262C2×C61—21no—
263C2×C61—42no—
264C2×C61C22⋊#9511yescharacteristic
265D61—22no—
266D61—21no—
267D61—21no—
268D61—42no—
269C22×#41—611no—
270#568—1224no—
271#568—1224no—
272C2×#131—1221no—
273C2×#131—1222no—
274C2×#131—1221no—
275C22×M16—611no—
276C22×M16—611no—
277C22×M16—612no—
278C22×M16—612no—
279C2×#117—612no—
280C2×#117—612no—
281#410—614no—
282#410—611no—
283#410—612no—
284#410—1222no—
285#410—1221no—
286#410—1221no—
287#410#692311yescharacteristic, complemented
288C2×#99—1222no—
289C2×#99—1222no—
290#339—1224no—
291#339—1224no—
292C61#1076611yescharacteristic, complemented, Sylow
293C2×#41—611no—
294C2×#41—611no—
295C2×#41—612no—
296C2×#41—612no—
297C2×#41—611no—
298C2×#41—1222no—
299C2×#41—1222no—
300C2×#41—1222no—
301C2×#41—1222no—
302C2×#41C2×#692311yescharacteristic
303C22×Q8—611no—
304C22×D4—611no—
305C22×D4—612no—
306C23×C4—611no—
307C23×C4—612no—
308#131—1228no—
309#131—12216no—
310#131—1228no—
311C2×M16—611no—
312C2×M16—611no—
313C2×M16—612no—
314C2×M16—614no—
315C2×M16—614no—
316C2×M16—1224no—
317C2×M16—1224no—
318C2×M16—1224no—
319C2×M16—1224no—
320C2×M16—1221no—
321C2×M16—1222no—
322C2×M16—1222no—
323C2×M16—1221no—
324C2×M16—1222no—
325C2×M16—1222no—
326C22×C8—1221no—
327C22×C8—1222no—
328C22×C8—1221no—
329C22×C8—1222no—
330#117—614no—
331#117—612no—
332#117—1222no—
333#117—1222no—
334#117—1222no—
335#117—1222no—
336#117—1222no—
337#117—1222no—
338#117C2×#692312yes—
339C2×C4⋊C4—1222no—
340C2×C4⋊C4—1222no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C42—1222no—
344C2×C42—1222no—
345#99—22no—
346#99—1224no—
347#99—1224no—
348#99—1224no—
349#99—1222no—
350C24—611no—
351C24—612no—
352#41—22no—
353#41—22no—
354#41—1224no—
355#41—1224no—
356#41—1224no—
357#41—1222no—
358#41—1224no—
359#41—1222no—
360#41—1222no—
361#41—1222no—
362#41—1222no—
363#41—1222no—
364C2×Q8—612no—
365C2×Q8—611no—
366C2×Q8—1222no—
367C2×Q8—1222no—
368C2×Q8C4⋊#692311yescharacteristic
369C2×D4—612no—
370C2×D4—612no—
371C2×D4—612no—
372C2×D4—612no—
373C2×D4—611no—
374C2×D4—1222no—
375C2×D4—1222no—
376C2×D4—1224no—
377C2×D4—1224no—
378C2×D4C4⋊#692311yescharacteristic
379C2×D4C22⋊#692312yes—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—612no—
386C22×C4—612no—
387C22×C4—612no—
388C22×C4—612no—
389C22×C4—612no—
390C22×C4—612no—
391C22×C4—612no—
392C22×C4—612no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4—1222no—
396C22×C4—1222no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4C4×#692312yes—
400C22×C4C22×#692311yescharacteristic
401M16—612no—
402M16—612no—
403M16—614no—
404M16—1221no—
405M16—1222no—
406M16—1221no—
407M16—1224no—
408M16—1224no—
409M16—1228no—
410M16—1228no—
411C2×C8—1221no—
412C2×C8—1222no—
413C2×C8—1221no—
414C2×C8—1224no—
415C2×C8—1224no—
416C2×C8—1228no—
417C2×C8—1228no—
418C4⋊C4—22no—
419C4⋊C4—1224no—
420C4⋊C4—1222no—
421C4⋊C4—2442no—
422C4⋊C4—2442no—
423C22⋊C4—22no—
424C22⋊C4—1224no—
425C22⋊C4—1222no—
426C22⋊C4—2442no—
427C22⋊C4—2442no—
428C42—22no—
429C42—1224no—
430C42—1222no—
431C42—2442no—
432C42—2442no—
433C23—612no—
434C23—612no—
435C23—611no—
436C23—611no—
437C23—612no—
438C23—1222no—
439C23—1222no—
440C23—4882no—
441C23—4881no—
442C23(C2×#6923)⋊C412yes—
443C23C2×C22⋊#692311yescharacteristic
444Q8—22no—
445Q8—1224no—
446Q8—1222no—
447D4—24no—
448D4—22no—
449D4—1224no—
450D4—1224no—
451D4—1224no—
452D4—1224no—
453D4—1222no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—42no—
457C2×C4—612no—
458C2×C4—612no—
459C2×C4—611no—
460C2×C4—611no—
461C2×C4—612no—
462C2×C4—612no—
463C2×C4—612no—
464C2×C4—612no—
465C2×C4—611no—
466C2×C4—611no—
467C2×C4—611no—
468C2×C4—611no—
469C2×C4—612no—
470C2×C4—612no—
471C2×C4—612no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—4884no—
481C2×C4—4884no—
482C2×C4—2444no—
483C2×C4—2442no—
484C2×C4(C2×#6923)⋊C412yes—
485C2×C4C2×C4×#692311yescharacteristic
486C2×C4C2×C4⋊#692311yescharacteristic
487C2×C4D4×#692312yes—
488C2×C4D4×#692312yes—
489C8—1222no—
490C8—1222no—
491C8—1224no—
492C22—22no—
493C22—41no—
494C22—42no—
495C22—611no—
496C22—611no—
497C22—612no—
498C22—1222no—
499C22—4882no—
500C22—4882no—
501C22—2442no—
502C22—2442no—
503C22—2441no—
504C22—2441no—
505C22—2442no—
506C22C2×(C2×#6923)⋊C411yescharacteristic
507C22#1684071012yes—
508C4—22no—
509C4—82no—
510C4—611no—
511C4—611no—
512C4—612no—
513C4—1222no—
514C4—4882no—
515C4—4884no—
516C4C22⋊C4×#692311yescharacteristic
517C4C22⋊C4×#692311yescharacteristic
518C4#1684070912yes—
519C2—22no—
520C2—21no—
521C2—42no—
522C2—1222no—
523C2—1221no—
524C2—1221no—
525C2—2442no—
526C2#2146099211yescharacteristic
subgroupG/H
centerC2#21460992
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#410C4
socleC2×C61C22⋊#95
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenter#410#6923
hypocenterC61#10766
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
3. #21461500C2semidirect
4. #21461499C2semidirect
11. C22×#11758213C4semidirect
13. C2×D61⋊M16C4semidirect
18. #16840741C4semidirect
24. #16839736C4semidirect
25. #16839735C4semidirect
28. C61×#410C4semidirect
287. #410#6923semidirect
292. C61#10766semidirect

Maximal subgroups

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

subgroupindex
C2×#168408412
D61⋊#4102
#214615002
#214614992
#410×D612
#1076661