Finite Group Databasebeta

← #30615935

Subgroups — #30615935

Order 15616.

1018 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519847C211yesmaximal, characteristic, complemented
2C2×#16840759C211yesmaximal, characteristic
3#21462404C211yesmaximal, characteristic
4#21462384C211yesmaximal, characteristic, complemented
5#21461902C214yesmaximal, complemented
6#21461901C214yesmaximal, complemented
7#21461499C211yesmaximal, characteristic, complemented
8#21461484C211yesmaximal, characteristic, complemented
9#416×D61C211yesmaximal, characteristic
10C22×#11758213C2211yescharacteristic
11C22×#11758213C2211yescharacteristic
12C2×D61⋊M16C2211yescharacteristic
13C2×#14519856C2211yescharacteristic
14C2×#14519847—24no—
15C2×#14519847C2214yescomplemented
16#16840759—24no—
17C2×#14519842C2212yes—
18C2×#14519841C2212yes—
19#16840737C2212yes—
20#16840736C2212yes—
21#16840735—22no—
22#16840733—22no—
23#16840727C2214yescomplemented
24#16840726—22no—
25C4×#11758213—22no—
26#16840632C2214yescomplemented
27(C2×#6923)⋊C8C2214yescomplemented
28C2×#41×D61C2211yescharacteristic
29C22×C8×D61C2211yescharacteristic
30#117×D61C2211yescharacteristic
31#16839759C411yescharacteristic, complemented
32#16839758C411yescharacteristic, complemented
33#16839757C2212yes—
34#16839756C411yescharacteristic, complemented
35#16839755C2212yes—
36#103×D61C412yescomplemented
37#102×D61C412yescomplemented
38C61×#416C411yescharacteristic, complemented
39C2×#11758213—21no—
40C2×#11758213—22no—
41C2×#11758213—22no—
42C2×#11758213—22no—
43C2×#11758213—21no—
44C2×#11758213D412yes—
45C2×#11758213D414yes—
46C2×#11758213C2312yes—
47C2×#11758213C2312yes—
48D61⋊M16—22no—
49D61⋊M16—22no—
50C2×#11758217D412yes—
51C2×D61⋊C8C2312yes—
52C22×#92420—21no—
53C22×#92420—21no—
54#14519856—22no—
55#14519856—22no—
56C2×C4⋊#6923—21no—
57C2×C22⋊#6923—21no—
58C2×C4×#6923C2312yes—
59#14519847—28no—
60#14519842—24no—
61#14519841—24no—
62#14519834—24no—
63C22⋊#92420—24no—
64#14519832—24no—
65C4×#92420—24no—
66C2×#11758226C2311yescharacteristic
67C2×#11758222—21no—
68C2×#11758222C2×C411yescharacteristic
69C2×#11758224—21no—
70C2×#11758224C2311yescharacteristic
71#41×D61—22no—
72#41×D61—22no—
73#41×D61—22no—
74#41×D61—22no—
75C2×Q8×D61C2×C411yescharacteristic
76C2×D4×D61—21no—
77C2×D4×D61C2×C411yescharacteristic
78C22×C4×D61—21no—
79C22×C4×D61C2311yescharacteristic
80C22×#92418C2×C411yescharacteristic
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61C2×C412yes—
84C2×C8×D61C2312yes—
85#14519736C2×C411yescharacteristic
86#14519735C2312yes—
87#14519734—21no—
88#14519733—21no—
89C4⋊C4×D61C2×C412yes—
90C22⋊C4×D61—21no—
91C42×D61—21no—
92#14519702C2×C412yes—
93#14519701C2×C412yes—
94#14519700C2×C412yes—
95#14519699C2×C412yes—
96#14519698C2×C412yes—
97#14519697C2×C412yes—
98C2×#41×C61C2×C411yescharacteristic
99C22×C8×C61C2×C411yescharacteristic
100#117×C61C2×C411yescharacteristic
101#103×C61C2×C412yes—
102#102×C61C2×C412yes—
103C23×D61—21no—
104C23×D61#4111yescharacteristic
105C22×#6923—22no—
106#41×C61—22no—
107#41×C61—22no—
108C2×Q8×C61C22×C411yescharacteristic
109C2×D4×C61—21no—
110C2×D4×C61C22×C411yescharacteristic
111C22×C4×C61—21no—
112C22×C4×C61C22×C411yescharacteristic
113C2×C22⋊D61—21no—
114C2×C22⋊D61—21no—
115C2×C22⋊D61—21no—
116C22×Dic61—21no—
117C22×Dic61C2×D411yescharacteristic
118#11758226—21no—
119#11758226—21no—
120#11758226—21no—
121#11758226—21no—
122Q8×D61—22no—
123Q8×D61—22no—
124#11758224—21no—
125#11758224—21no—
126#11758224—21no—
127#11758224—21no—
128#11758224—42no—
129#11758224—42no—
130D4×D61—22no—
131D4×D61—22no—
132D4×D61—42no—
133D4×D61—42no—
134#11758222—22no—
135#11758222—22no—
136#11758222—42no—
137#11758222—42no—
138C2×D244—21no—
139C2×D244C22×C411yescharacteristic
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—22no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×C4×D61C22×C411yescharacteristic
147C2×C4×D61C2×D412yes—
148C2×C4×D61C2×D411yescharacteristic
149C2×C4×D61#4112yes—
150C2×C4×D61#4112yes—
151C2×C4×D61#4112yes—
152C2×C4×D61#4111yescharacteristic
153C2×C4×D61C2411yescharacteristic
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C22⋊#6923—42no—
157#11758217—24no—
158C2×#92420—24no—
159C2×#92420—22no—
160C2×#92420—22no—
161C2×#92420—42no—
162C2×#92420C2×D414yes—
163C4⋊#6923—42no—
164C4×#6923—22no—
165C4×#6923—22no—
166#11758213—24no—
167#11758213—24no—
168#11758213—22no—
169#11758213—22no—
170#11758213—22no—
171#11758213—42no—
172#11758213C2×D414yes—
173D61⋊C8—22no—
174D61⋊C8—22no—
175C2×C8×C61—22no—
176C2×C8×C61C22×C412yes—
177C4⋊C4×C61C22×C412yes—
178C22⋊C4×C61—21no—
179C42×C61—21no—
180C22⋊Dic61—21no—
181#11758198—22no—
182C4⋊Dic61C22×C412yes—
183#11758196—22no—
184C4×Dic61—21no—
185C4×Dic61—22no—
186C2×#92418—22no—
187C2×#92418C22×C412yes—
188C8×D61—24no—
189C8×D61—22no—
190C8×D61—22no—
191C23×C61—21no—
192C23×C61C4×D411yescharacteristic
193C22×D61—21no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—82no—
197C22×D61C4×D411yescharacteristic
198C22×D61#12412yes—
199C22×D61#12612yes—
200C22×D61C2×#4111yescharacteristic
201C2×#6923—44no—
202C2×#6923—42no—
203Q8×C61—21no—
204Q8×C61—21no—
205D4×C61—21no—
206D4×C61—21no—
207D4×C61—42no—
208C2×C4×C61—22no—
209C2×C4×C61—21no—
210C2×C4×C61—42no—
211C2×C4×C61#11712yes—
212C2×C4×C61C4×D412yes—
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C23×C411yescharacteristic
215C22⋊D61—42no—
216C22⋊D61—41no—
217C22⋊D61—41no—
218C22⋊D61—42no—
219C2×Dic61—22no—
220C2×Dic61—21no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61C4×D411yescharacteristic
224C2×Dic61#12112yes—
225C2×Dic61#12312yes—
226C2×Dic61C22×D411yescharacteristic
227D244—21no—
228D244—21no—
229D244—41no—
230D244—41no—
231C4×D61—42no—
232C4×D61—42no—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—82no—
236C4×D61#11712yes—
237C4×D61C4×D412yes—
238C4×D61#12112yes—
239C4×D61#12312yes—
240C4×D61#12412yes—
241C4×D61#12612yes—
242C4×D61C22×D411yescharacteristic
243C4×D61C2×#4111yescharacteristic
244C4×D61C2×#4111yescharacteristic
245C4×D61C2×#4111yescharacteristic
246Dic122—21no—
247Dic122—21no—
248Dic122—42no—
249#92420—24no—
250#92420—24no—
251#92420—42no—
252C8×C61—22no—
253#92418—22no—
254#21072—611nomaximal, Sylow
255C22×C61—22no—
256C22×C61—42no—
257C22×C61—41no—
258C22×C61#38812yes—
259C22×C61C2×C4×D411yescharacteristic
260C2×D61—22no—
261C2×D61—22no—
262C2×D61—42no—
263C2×D61—42no—
264C2×D61—42no—
265C2×D61—41no—
266C2×D61—84no—
267C2×D61#38812yes—
268C2×D61C2×#12411yescharacteristic
269C2×D61C2×#12611yescharacteristic
270#6923—82no—
271C4×C61—42no—
272C4×C61—41no—
273C4×C61#38812yes—
274C4×C61C2×#11711yescharacteristic
275C4×C61C2×C4×D411yescharacteristic
276Dic61—42no—
277Dic61—41no—
278Dic61#38812yes—
279Dic61C2×#12111yescharacteristic
280Dic61C2×#12311yescharacteristic
281C22×#108—611no—
282C2×#421—611no—
283C2×#416—611no—
284#2879—611no—
285#2873—611no—
286#1929—614no—
287#1929—614no—
288#1733—611no—
289#1729—611no—
290C2×C61—22no—
291C2×C61—81no—
292C2×C61C2×#38811yescharacteristic
293C2×C61#295712yes—
294D61—21no—
295D61—22no—
296D61—21no—
297D61—81no—
298C22×#41—611no—
299C22×M16—611no—
300C22×M16—611no—
301C22×M16—611no—
302C23×C8—611no—
303C2×#117—611no—
304C2×#117—611no—
305C2×#108—614no—
306C2×#108—1224no—
307#421—1224no—
308C2×#104—612no—
309C2×#104—612no—
310#416—611no—
311#416—611no—
312#416—611no—
313#416—612no—
314#416—612no—
315#416#692311yescharacteristic, complemented
316C2×#103—612no—
317C2×#102—612no—
318#408—612no—
319#408—612no—
320#408—1222no—
321#407—1222no—
322#405—614no—
323#405—1222no—
324C4×M16—1222no—
325#339—614no—
326#336—614no—
327C61#2107211yescharacteristic, complemented, Sylow
328C2×#41—611no—
329C2×#41—611no—
330C2×#41—611no—
331C2×#41—1221no—
332C2×#41—1221no—
333C2×#41—1222no—
334C2×#41—1222no—
335C2×#41—1222no—
336C2×#41—1222no—
337C2×#41C2×#692311yescharacteristic
338C22×Q8—611no—
339C22×D4—611no—
340C22×D4—1221no—
341C23×C4—611no—
342C23×C4—1221no—
343C2×M16—612no—
344C2×M16—612no—
345C2×M16—614no—
346C2×M16—612no—
347C2×M16—612no—
348C2×M16—1222no—
349C2×M16—1222no—
350C2×M16—1222no—
351C2×M16—1221no—
352C2×M16—1221no—
353C2×M16—1222no—
354C2×M16—1222no—
355C22×C8—612no—
356C22×C8—611no—
357C22×C8—612no—
358C22×C8—612no—
359C22×C8—1222no—
360C22×C8—1222no—
361C22×C8—1221no—
362C22×C8—1221no—
363C22×C8C2×#692311yescharacteristic
364#117—611no—
365#117—612no—
366#117—1221no—
367#117—1221no—
368#117—1222no—
369#117—1222no—
370#117C2×#692311yescharacteristic
371C2×C4⋊C4—612no—
372C2×C4⋊C4—1221no—
373C2×C22⋊C4—1221no—
374C2×C22⋊C4—1221no—
375C2×C42—612no—
376C2×C42—1221no—
377#108—1228no—
378#104—1224no—
379#104—1224no—
380#103—612no—
381#103—612no—
382#103—612no—
383#103C2×#692312yes—
384#102—612no—
385#102—612no—
386#102—612no—
387#102C2×#692312yes—
388C22⋊C8—1224no—
389C22⋊C8—1224no—
390#97—1224no—
391C4×C8—1224no—
392C24—611no—
393C24—1221no—
394#41—22no—
395#41—22no—
396#41—1221no—
397#41—1221no—
398#41—1221no—
399#41—1221no—
400#41—1221no—
401#41—1221no—
402#41—1221no—
403#41—1221no—
404#41—1222no—
405#41—1222no—
406#41—2442no—
407#41—2442no—
408#41—2442no—
409#41—2442no—
410C2×Q8—611no—
411C2×Q8—1221no—
412C2×Q8—1222no—
413C2×Q8—1222no—
414C2×Q8C22×#692311yescharacteristic
415C2×D4—21no—
416C2×D4—611no—
417C2×D4—1221no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1221no—
421C2×D4—1221no—
422C2×D4—1221no—
423C2×D4—2442no—
424C2×D4—2442no—
425C2×D4C22×#692311yescharacteristic
426C22×C4—21no—
427C22×C4—611no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—1221no—
437C22×C4—1222no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1222no—
442C22×C4—2442no—
443C22×C4—2442no—
444C22×C4C22×#692311yescharacteristic
445M16—614no—
446M16—1224no—
447M16—1224no—
448M16—1222no—
449M16—1224no—
450M16—1222no—
451M16—1222no—
452M16—2442no—
453C2×C8—22no—
454C2×C8—614no—
455C2×C8—612no—
456C2×C8—1222no—
457C2×C8—1224no—
458C2×C8—1222no—
459C2×C8—1222no—
460C2×C8—1222no—
461C2×C8—1222no—
462C2×C8—1224no—
463C2×C8—1222no—
464C2×C8—1222no—
465C2×C8—2442no—
466C2×C8C22×#692312yes—
467C4⋊C4—612no—
468C4⋊C4—1222no—
469C4⋊C4—2442no—
470C4⋊C4C22×#692312yes—
471C22⋊C4—21no—
472C22⋊C4—1222no—
473C22⋊C4—1221no—
474C22⋊C4—2442no—
475C42—21no—
476C42—1222no—
477C42—1222no—
478C42—1222no—
479C42—1221no—
480C23—21no—
481C23—611no—
482C23—611no—
483C23—612no—
484C23—612no—
485C23—1221no—
486C23—4882no—
487C23—2442no—
488C23—2442no—
489C23D4×#692311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—1221no—
493Q8—1221no—
494Q8—2442no—
495D4—21no—
496D4—21no—
497D4—42no—
498D4—1221no—
499D4—1221no—
500D4—2441no—
501D4—2441no—
502D4—2442no—
503D4—2441no—
504D4—2441no—
505D4—2442no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—42no—
509C2×C4—612no—
510C2×C4—612no—
511C2×C4—611no—
512C2×C4—611no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—612no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—611no—
519C2×C4—611no—
520C2×C4—612no—
521C2×C4—611no—
522C2×C4—611no—
523C2×C4—1222no—
524C2×C4—1221no—
525C2×C4—4882no—
526C2×C4—2441no—
527C2×C4—2441no—
528C2×C4—2442no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2442no—
532C2×C4—2444no—
533C2×C4—2442no—
534C2×C4#1451985612yes—
535C2×C4D4×#692311yescharacteristic
536C2×C4D4×#692312yes—
537C2×C4C23×#692311yescharacteristic
538C8—22no—
539C8—1224no—
540C8—1224no—
541C8—1222no—
542C8—2442no—
543C22—22no—
544C22—41no—
545C22—42no—
546C22—611no—
547C22—612no—
548C22—611no—
549C22—1222no—
550C22—1222no—
551C22—4884no—
552C22—2442no—
553C22—2442no—
554C22—2441no—
555C22—2442no—
556C22#1684071212yes—
557C22C2×D4×#692311yescharacteristic
558C4—41no—
559C4—42no—
560C4—611no—
561C4—611no—
562C4—612no—
563C4—4882no—
564C4—2441no—
565C4—2442no—
566C4#1684071212yes—
567C4C2×#1451985611yescharacteristic
568C4C2×D4×#692311yescharacteristic
569C2—22no—
570C2—81no—
571C2—1221no—
572C2—1222no—
573C2—1221no—
574C2—4881no—
575C2C2×#1684071211yescharacteristic
576C2#2146259812yes—
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#416C4
socleC22×C61C2×C4×D4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenter#416#6923
hypocenterC61#21072
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. C22×#14519847C2semidirect
4. #21462384C2semidirect
5. #21461902C2semidirect
6. #21461901C2semidirect
7. #21461499C2semidirect
8. #21461484C2semidirect
15. C2×#14519847C22semidirect
23. #16840727C22semidirect
26. #16840632C22semidirect
27. (C2×#6923)⋊C8C22semidirect
31. #16839759C4semidirect
32. #16839758C4semidirect
34. #16839756C4semidirect
36. #103×D61C4semidirect
37. #102×D61C4semidirect
38. C61×#416C4semidirect
315. #416#6923semidirect
327. C61#21072semidirect

Maximal subgroups

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

subgroupindex
C22×#145198472
C2×#168407592
#214624042
#214623842
#214619022
#214619012
#214614992
#214614842
#416×D612
#2107261