Finite Group Databasebeta

← #30602549

Subgroups — #30602549

Order 15616.

1254 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840760C212yesmaximal
2#21461524C211yesmaximal, characteristic, complemented
3#21461518C211yesmaximal, characteristic, complemented
4#21461506C212yesmaximal, complemented
5C2×#16840241C211yesmaximal, characteristic
6C2×D61⋊M16C2212yes—
7C2×#14519856C2212yes—
8#16840760—24no—
9#16840760C418yescomplemented
10C2×#14519841—24no—
11#16840642—21no—
12#16840642—21no—
13#16840640—21no—
14#16840640—21no—
15#16840635—24no—
16C22×#11758224C2211yescharacteristic
17#16840241—24no—
18#16840241—24no—
19C2×C4×Dic122C411yescharacteristic, complemented
20C2×#14519742C411yescharacteristic, complemented
21C2×D4×Dic61C411yescharacteristic, complemented
22C2×C4×C22⋊D61—21no—
23C2×#14519737—21no—
24C2×#14519734C2211yescharacteristic
25C2×#14519733—21no—
26C22×#11758196—21no—
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C4×D4×C61C411yescharacteristic, complemented
29C2×#11758213—22no—
30D61⋊M16—22no—
31D61⋊M16—22no—
32D61⋊M16—22no—
33D61⋊M16C2×C414yescomplemented
34C2×#11758217—22no—
35C2×D61⋊C8—22no—
36#14519856—22no—
37#14519856—22no—
38#14519856—22no—
39#14519856C2×C414yescomplemented
40C2×C4⋊#6923—22no—
41C2×C22⋊#6923—22no—
42C2×C4×#6923—22no—
43#14519841—216no—
44C2×#11758224—22no—
45C2×#11758224—21no—
46C2×#11758224—21no—
47C2×#11758224—22no—
48C2×#11758224C2×C414yes—
49C2×#11758224D414yes—
50C2×#11758224D412yes—
51C2×#11758224Q812yes—
52C22×Dic122C2×C411yescharacteristic
53C22×C22⋊D61—21no—
54C23×Dic61—21no—
55C23×Dic61—21no—
56C22×C4×D61—21no—
57C22×C4×D61C2311yescharacteristic
58C4×Dic122—22no—
59C4×Dic122—22no—
60#14519742—22no—
61#14519742—22no—
62D4×Dic61—22no—
63D4×Dic61—22no—
64C4×C22⋊D61—28no—
65#14519737—28no—
66#14519734—22no—
67#14519734—22no—
68#14519733—28no—
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×#11758196—28no—
71C2×#11758196—21no—
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196D411yescharacteristic
75C2×#11758196D411yescharacteristic
76C4⋊C4×D61—22no—
77C4⋊C4×D61D414yes—
78C2×C22⋊Dic61—21no—
79C2×#11758198D411yescharacteristic
80C2×#11758198D411yescharacteristic
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61C2×C411yescharacteristic
84C22×D4×C61C2×C411yescharacteristic
85C23×C4×C61—21no—
86C4×D4×C61—22no—
87C4×D4×C61—22no—
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61—21no—
90C2×C42×C61C2×C411yescharacteristic
91C24×C61—21no—
92C23×D61C2×D411yescharacteristic
93C22×#6923—42no—
94C2×D4×C61—21no—
95C2×D4×C61—21no—
96C2×D4×C61—21no—
97C2×D4×C61C4212yes—
98C2×D4×C61C22⋊C412yes—
99C2×D4×C61C4⋊C412yes—
100C22×C4×C61—21no—
101C22×C4×C61—24no—
102C22×C4×C61—82no—
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22⋊C411yescharacteristic
105C22×C4×C61C22×C411yescharacteristic
106C2×C22⋊D61—24no—
107C2×C22⋊D61—24no—
108C2×C22⋊D61—22no—
109C2×C22⋊D61—22no—
110C22×Dic61—21no—
111C22×Dic61—24no—
112C22×Dic61—24no—
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—21no—
116C22×Dic61—24no—
117C22×Dic61—82no—
118C22×Dic61C22⋊C411yescharacteristic
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C2×D411yescharacteristic
121#11758224—24no—
122#11758224—24no—
123#11758224—24no—
124#11758224—24no—
125#11758224—24no—
126#11758224—24no—
127#11758224C22⋊C418yes—
128#11758224C4⋊C418yes—
129C2×C4×D61—24no—
130C2×C4×D61—82no—
131C2×C4×D61C22×C412yes—
132C2×C4×D61C2×D411yescharacteristic
133C2×C4×D61C2×D412yes—
134C2×C4×D61C2×D412yes—
135C2×C4×D61C2×Q811yescharacteristic
136C2×C4×D61#4111yescharacteristic
137C2×C4×D61#4111yescharacteristic
138C2×C4×D61#4112yes—
139C2×Dic122—21no—
140C2×Dic122—21no—
141C2×Dic122—21no—
142C2×Dic122C4212yes—
143C2×Dic122C22⋊C412yes—
144C2×Dic122C4⋊C412yes—
145C22⋊#6923—24no—
146C22⋊#6923—42no—
147#11758217—24no—
148#11758217—42no—
149C2×#92420—42no—
150C4⋊#6923—24no—
151C4⋊#6923—42no—
152C4×#6923—24no—
153C4×#6923—42no—
154#11758213—24no—
155#11758213—42no—
156D61⋊C8—24no—
157D61⋊C8—42no—
158C4⋊C4×C61—21no—
159C4⋊C4×C61C22⋊C412yes—
160C22⋊C4×C61—24no—
161C42×C61—21no—
162C42×C61—21no—
163C22⋊Dic61—24no—
164#11758198—22no—
165#11758198—22no—
166C4⋊Dic61—21no—
167C4⋊Dic61C22⋊C412yes—
168#11758196—24no—
169#11758196—24no—
170#11758196—24no—
171#11758196—22no—
172#11758196—22no—
173C4×Dic61—24no—
174C4×Dic61—24no—
175C4×Dic61—21no—
176C4×Dic61—21no—
177C23×C61—22no—
178C23×C61—22no—
179C23×C61—22no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61C2×C22⋊C411yescharacteristic
183C22×D61—41no—
184C22×D61—41no—
185C22×D61C4×D412yes—
186C22×D61#12012yes—
187C22×D61#12111yescharacteristic
188C22×D61C22⋊Q811yescharacteristic
189C2×#6923—44no—
190C2×#6923—82no—
191C2×#6923—82no—
192D4×C61—22no—
193D4×C61—22no—
194D4×C61—22no—
195D4×C61#9514yes—
196C2×C4×C61—21no—
197C2×C4×C61—22no—
198C2×C4×C61—21no—
199C2×C4×C61—42no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—84no—
203C2×C4×C61C2×C4211yescharacteristic
204C2×C4×C61C2×C22⋊C411yescharacteristic
205C2×C4×C61C2×C22⋊C411yescharacteristic
206C2×C4×C61C2×C4⋊C411yescharacteristic
207C2×C4×C61#11711yescharacteristic
208C2×C4×C61#11711yescharacteristic
209C22⋊D61—28no—
210C22⋊D61—28no—
211C2×Dic61—22no—
212C2×Dic61—22no—
213C2×Dic61—22no—
214C2×Dic61—28no—
215C2×Dic61—28no—
216C2×Dic61—21no—
217C2×Dic61—21no—
218C2×Dic61—22no—
219C2×Dic61—42no—
220C2×Dic61—41no—
221C2×Dic61—41no—
222C2×Dic61—84no—
223C2×Dic61C4×D412yes—
224C2×Dic61#12012yes—
225C2×Dic61#12111yescharacteristic
226C2×Dic61C22⋊Q811yescharacteristic
227C4×D61—84no—
228C4×D61C2×C22⋊C412yes—
229C4×D61C2×C4⋊C412yes—
230C4×D61C4×D412yes—
231C4×D61C4×D412yes—
232C4×D61#12112yes—
233C4×D61C22⋊Q812yes—
234C4×D61#12312yes—
235C4×D61#12312yes—
236Dic122—22no—
237Dic122—22no—
238Dic122—22no—
239Dic122#9514yes—
240#92420—44no—
241#10775—611nomaximal, Sylow
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—24no—
245C22×C61—44no—
246C22×C61—44no—
247C22×C61—42no—
248C22×C61—42no—
249C22×C61C4×C22⋊C411yescharacteristic
250C22×C61#37911yescharacteristic
251C22×C61#38011yescharacteristic
252C2×D61—22no—
253C2×D61—22no—
254C2×D61—42no—
255C2×D61—41no—
256C2×D61—41no—
257C2×D61#38512yes—
258C2×D61#38612yes—
259#6923—84no—
260C4×C61—42no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61C2×#9511yescharacteristic
264C4×C61C4×C22⋊C411yescharacteristic
265C4×C61#38011yescharacteristic
266C4×C61#38111yescharacteristic
267Dic61—24no—
268Dic61—42no—
269Dic61—41no—
270Dic61—41no—
271Dic61#38512yes—
272Dic61#38612yes—
273C2×#520—611no—
274C2×#421—612no—
275#1742—611no—
276#1740—611no—
277#1736—612no—
278C2×C61—21no—
279C2×C61—21no—
280C2×C61—44no—
281C2×C61C22⋊#9511yescharacteristic
282C2×C61#179511yescharacteristic
283C2×C61#179611yescharacteristic
284D61—22no—
285D61—22no—
286C22×#41—611no—
287C22×M16—612no—
288#520—1224no—
289#520—1224no—
290C2×C4×Q8—611no—
291C2×C4×Q8—611no—
292C2×C4×D4—611no—
293C2×C4×D4—1221no—
294C2×C4×D4—1221no—
295C2×C4×D4#692311yescharacteristic, complemented
296C2×#117—611no—
297C2×#117—612no—
298C2×#117—1221no—
299C22×C4⋊C4—611no—
300C22×C4⋊C4—1221no—
301#421—618no—
302#421—1224no—
303C2×#104—1224no—
304#343—1221no—
305#343—1221no—
306#342—1221no—
307#342—1221no—
308#340—1224no—
309C61#1077511yescharacteristic, complemented, Sylow
310C2×#41—614no—
311C2×#41—612no—
312C2×#41—612no—
313C2×#41—614no—
314C2×#41—1222no—
315C2×#41—1221no—
316C2×#41—1222no—
317C2×#41—1221no—
318C22×Q8—611no—
319C22×D4—1221no—
320C22×D4C2×#692311yescharacteristic
321C23×C4—21no—
322C23×C4—611no—
323C23×C4—1221no—
324C23×C4—1221no—
325C23×C4—1221no—
326C2×M16—614no—
327C2×M16—1222no—
328C2×M16—1222no—
329C2×M16—1222no—
330C2×M16—1222no—
331C2×M16—1222no—
332C22×C8—1222no—
333C4×Q8—1222no—
334C4×Q8—1222no—
335C4×Q8—1222no—
336C4×Q8—1222no—
337C4×D4—22no—
338C4×D4—22no—
339C4×D4—1228no—
340C4×D4—1222no—
341C4×D4—1228no—
342C4×D4—1222no—
343#117—614no—
344#117—1222no—
345#117—1222no—
346#117—1228no—
347#117—1222no—
348#117—1222no—
349#117—1222no—
350C2×C4⋊C4—611no—
351C2×C4⋊C4—614no—
352C2×C4⋊C4—611no—
353C2×C4⋊C4—611no—
354C2×C4⋊C4—1222no—
355C2×C4⋊C4—1221no—
356C2×C4⋊C4—1221no—
357C2×C4⋊C4—1228no—
358C2×C4⋊C4—1221no—
359C2×C4⋊C4—1222no—
360C2×C4⋊C4C2×#692311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—611no—
363C2×C22⋊C4—611no—
364C2×C22⋊C4—1221no—
365C2×C22⋊C4—1222no—
366C2×C42—611no—
367C2×C42—1221no—
368C2×C42—1221no—
369C2×C42—1222no—
370C2×C42C2×#692311yescharacteristic
371#104—12216no—
372C24—21no—
373C24—611no—
374#41—618no—
375#41—618no—
376#41—1224no—
377#41—1224no—
378#41—1224no—
379#41—1224no—
380#41—1224no—
381#41—1224no—
382C2×Q8—612no—
383C2×Q8—612no—
384C2×Q8—612no—
385C2×Q8—1221no—
386C2×Q8—1221no—
387C2×Q8—1221no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—1224no—
392C2×D4—1222no—
393C2×D4—1222no—
394C2×D4—1224no—
395C2×D4C4×#692312yes—
396C2×D4C4⋊#692312yes—
397C2×D4C22⋊#692312yes—
398C22×C4—21no—
399C22×C4—24no—
400C22×C4—82no—
401C22×C4—611no—
402C22×C4—612no—
403C22×C4—612no—
404C22×C4—612no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—612no—
409C22×C4—611no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—1224no—
413C22×C4—1224no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1224no—
417C22×C4—1221no—
418C22×C4—1224no—
419C22×C4—1221no—
420C22×C4—4882no—
421C22×C4—4882no—
422C22×C4—2442no—
423C22×C4C22⋊#692311yescharacteristic
424C22×C4C22⋊#692311yescharacteristic
425C22×C4C22×#692311yescharacteristic
426M16—1224no—
427M16—1224no—
428M16—2442no—
429M16—2442no—
430C2×C8—1224no—
431C2×C8—2442no—
432C2×C8—2442no—
433C4⋊C4—21no—
434C4⋊C4—612no—
435C4⋊C4—1222no—
436C4⋊C4—1224no—
437C4⋊C4—1222no—
438C4⋊C4—1224no—
439C4⋊C4—1224no—
440C4⋊C4—1224no—
441C4⋊C4—1221no—
442C4⋊C4—2442no—
443C4⋊C4C22⋊#692312yes—
444C22⋊C4—24no—
445C22⋊C4—1222no—
446C22⋊C4—1222no—
447C22⋊C4—1224no—
448C22⋊C4—1224no—
449C22⋊C4—2442no—
450C42—21no—
451C42—21no—
452C42—1224no—
453C42—1224no—
454C42—1224no—
455C42—1221no—
456C42—1221no—
457C42—2442no—
458C23—22no—
459C23—22no—
460C23—22no—
461C23—42no—
462C23—42no—
463C23—612no—
464C23—611no—
465C23—611no—
466C23—612no—
467C23—2441no—
468C23—2441no—
469C23C2×C22⋊#692311yescharacteristic
470Q8—614no—
471Q8—1222no—
472Q8—1222no—
473Q8—1222no—
474D4—22no—
475D4—22no—
476D4—22no—
477D4—1228no—
478D4—1228no—
479D4(C2×#6923)⋊C414yes—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—84no—
487C2×C4—611no—
488C2×C4—611no—
489C2×C4—612no—
490C2×C4—612no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—612no—
495C2×C4—612no—
496C2×C4—612no—
497C2×C4—612no—
498C2×C4—612no—
499C2×C4—1228no—
500C2×C4—1228no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1221no—
505C2×C4—1222no—
506C2×C4—1221no—
507C2×C4—4884no—
508C2×C4—4882no—
509C2×C4—4882no—
510C2×C4—4884no—
511C2×C4—2444no—
512C2×C4—2442no—
513C2×C4—2441no—
514C2×C4—2441no—
515C2×C4C2×C4×#692311yescharacteristic
516C2×C4C2×C22⋊#692311yescharacteristic
517C2×C4C2×C22⋊#692311yescharacteristic
518C2×C4C2×C4⋊#692311yescharacteristic
519C2×C4#1451985611yescharacteristic
520C2×C4#1451985611yescharacteristic
521C8—2444no—
522C22—21no—
523C22—21no—
524C22—24no—
525C22—44no—
526C22—44no—
527C22—42no—
528C22—42no—
529C22—612no—
530C22—612no—
531C22—1222no—
532C22—1222no—
533C22—2441no—
534C22—2441no—
535C22—2442no—
536C22C4×C22⋊#692311yescharacteristic
537C22#1684070311yescharacteristic
538C22#1684070411yescharacteristic
539C4—42no—
540C4—41no—
541C4—41no—
542C4—612no—
543C4—612no—
544C4—1224no—
545C4—4884no—
546C4—2441no—
547C4—2442no—
548C4—2441no—
549C4C2×(C2×#6923)⋊C411yescharacteristic
550C4C4×C22⋊#692311yescharacteristic
551C4#1684070411yescharacteristic
552C4#1684070511yescharacteristic
553C2—21no—
554C2—21no—
555C2—44no—
556C2—1222no—
557C2—1222no—
558C2#2146099311yescharacteristic
559C2#2146166911yescharacteristic
560C2#2146167211yescharacteristic
subgroupG/H
centerC22#16840703
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×C4×D4×C61C4
socleC22×C61#379
prime radicalC22×#11758224C22
cosocleC22×C4×D61C23
hypercenterC2×C4×D4#6923
hypocenterC61#10775
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. #21461524C2semidirect
3. #21461518C2semidirect
4. #21461506C2semidirect
9. #16840760C4semidirect
19. C2×C4×Dic122C4semidirect
20. C2×#14519742C4semidirect
21. C2×D4×Dic61C4semidirect
28. C2×C4×D4×C61C4semidirect
33. D61⋊M16C2×C4semidirect
39. #14519856C2×C4semidirect
295. C2×C4×D4#6923semidirect
309. C61#10775semidirect

Maximal subgroups

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

subgroupindex
C2×#168407602
#214615242
#214615182
#214615062
C2×#168402412
#1077561