Finite Group Databasebeta

← #30603340

Subgroups — #30603340

Order 15616.

838 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#430C211yesmaximal, characteristic
2C2×#16840755C211yesmaximal, characteristic
3C2×D61⋊#101C211yesmaximal, characteristic
4#21461529C211yesmaximal, characteristic
5#21461527C211yesmaximal, characteristic
6#21461489C211yesmaximal, characteristic
7#419×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2211yescharacteristic
9C2×D61⋊M16C2211yescharacteristic
10C2×D61⋊M16C2211yescharacteristic
11C2×#14519856C2211yescharacteristic
12#16840777—22no—
13#16840777—22no—
14D61⋊#108—22no—
15#16840755—22no—
16#16840755—22no—
17C2×#14519840—22no—
18D61⋊#101—22no—
19D61⋊#101—22no—
20C2×#14519838—22no—
21#16840644—22no—
22#16840643—22no—
23#16840629—22no—
24C22×Q8×D61C2211yescharacteristic
25C2×M16×D61C2211yescharacteristic
26#117×D61C2211yescharacteristic
27#16839772C411yescharacteristic, complemented
28#16839771C411yescharacteristic, complemented
29#16839770C411yescharacteristic, complemented
30#16839769—22no—
31#103×D61—22no—
32C61×#419C411yescharacteristic, complemented
33C2×#11758213—21no—
34C2×#11758213—21no—
35C2×#11758213—21no—
36D61⋊M16—21no—
37D61⋊M16—21no—
38D61⋊M16—21no—
39D61⋊M16—21no—
40D61⋊M16—21no—
41D61⋊M16—21no—
42D61⋊M16—21no—
43D61⋊M16—21no—
44D61⋊M16—21no—
45D61⋊M16—21no—
46D61⋊M16D412yes—
47D61⋊M16D412yes—
48C2×#11758217—21no—
49C2×#11758217—21no—
50C2×#11758217D412yes—
51C2×D61⋊C8—21no—
52C2×D61⋊C8—21no—
53C2×D61⋊C8—21no—
54#14519856—21no—
55#14519856—21no—
56#14519856—21no—
57#14519856D412yes—
58C2×C4⋊#6923—21no—
59C2×C22⋊#6923—21no—
60C2×C4×#6923—21no—
61#14519848—24no—
62#14519847—24no—
63#14519840—28no—
64#14519838—28no—
65C22×Dic122—21no—
66C22×Dic122C2×C411yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61—21no—
69C2×Q8×D61—21no—
70C2×Q8×D61—21no—
71C2×Q8×D61—21no—
72C2×Q8×D61—21no—
73C2×Q8×D61—21no—
74C2×Q8×D61—21no—
75C2×Q8×D61—21no—
76C2×Q8×D61—21no—
77C2×Q8×D61D412yes—
78C2×Q8×D61Q812yes—
79C22×C4×D61—21no—
80C22×C4×D61C2311yescharacteristic
81C2×#11758194C2×C411yescharacteristic
82C2×#11758189D412yes—
83M16×D61—21no—
84M16×D61—21no—
85M16×D61—21no—
86M16×D61—21no—
87C2×C8×D61D412yes—
88#14519736C2×C411yescharacteristic
89#14519735—21no—
90#14519734—21no—
91#14519733—21no—
92C4⋊C4×D61—21no—
93C22⋊C4×D61—21no—
94C42×D61—21no—
95#14519702—22no—
96#14519701—22no—
97#14519700—22no—
98C22×Q8×C61C2×C411yescharacteristic
99C2×M16×C61C2×C411yescharacteristic
100#117×C61C2×C411yescharacteristic
101#103×C61—22no—
102C23×D61#4111yescharacteristic
103C22×#6923—41no—
104C2×Q8×C61—21no—
105C2×Q8×C61—21no—
106C2×Q8×C61—21no—
107C2×Q8×C61—21no—
108C2×Q8×C61—21no—
109C2×Q8×C61C4⋊C412yes—
110C22×C4×C61—21no—
111C22×C4×C61C22×C411yescharacteristic
112C22×Dic61—21no—
113C22×Dic61C2×D411yescharacteristic
114Q8×D61—22no—
115Q8×D61—22no—
116Q8×D61—22no—
117Q8×D61—22no—
118Q8×D61—22no—
119Q8×D61—22no—
120Q8×D61—22no—
121Q8×D61—22no—
122Q8×D61—41no—
123Q8×D61—41no—
124Q8×D61—41no—
125Q8×D61—41no—
126Q8×D61—41no—
127Q8×D61—41no—
128Q8×D61—41no—
129Q8×D61—41no—
130C2×C4×D61—22no—
131C2×C4×D61—22no—
132C2×C4×D61—41no—
133C2×C4×D61—41no—
134C2×C4×D61—41no—
135C2×C4×D61—41no—
136C2×C4×D61—41no—
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×D411yescharacteristic
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61C2×D411yescharacteristic
141C2×C4×D61C2×D411yescharacteristic
142C2×C4×D61C2×D411yescharacteristic
143C2×C4×D61C2×Q811yescharacteristic
144C2×C4×D61#4111yescharacteristic
145C2×C4×D61#4111yescharacteristic
146C2×C4×D61#4111yescharacteristic
147C2×C4×D61#4111yescharacteristic
148C2×C4×D61#4111yescharacteristic
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—21no—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122—41no—
157C2×Dic122—41no—
158C2×Dic122—41no—
159C2×Dic122—41no—
160C2×Dic122C4⋊C412yes—
161C22⋊#6923—22no—
162C22⋊#6923—41no—
163#11758217—22no—
164#11758217—22no—
165#11758217—22no—
166#11758217—22no—
167#11758217—41no—
168#11758217—41no—
169C2×#92420—22no—
170C2×#92420—41no—
171C2×#92420—41no—
172C4⋊#6923—22no—
173C4⋊#6923—41no—
174C4×#6923—22no—
175C4×#6923—41no—
176#11758213—22no—
177#11758213—22no—
178#11758213—41no—
179#11758213—41no—
180#11758213—41no—
181#11758213—41no—
182D61⋊C8—22no—
183D61⋊C8—22no—
184D61⋊C8—41no—
185D61⋊C8—41no—
186D61⋊C8—41no—
187D61⋊C8—41no—
188M16×C61—21no—
189M16×C61—21no—
190C2×C8×C61C22⋊C412yes—
191C4⋊C4×C61—21no—
192C22⋊C4×C61—21no—
193C42×C61—21no—
194C22⋊Dic61—21no—
195#11758198—41no—
196C4⋊Dic61—21no—
197#11758196—41no—
198C4×Dic61—21no—
199C4×Dic61—41no—
200#11758194—21no—
201#11758194—21no—
202C2×#92418C22⋊C412yes—
203#11758189—22no—
204#11758189—22no—
205C8×D61—22no—
206C8×D61—22no—
207C23×C61C4×D411yescharacteristic
208C22×D61—42no—
209C22×D61#12111yescharacteristic
210C22×D61C22⋊Q811yescharacteristic
211C22×D61#12311yescharacteristic
212C22×D61#12411yescharacteristic
213C22×D61#12411yescharacteristic
214C22×D61#12611yescharacteristic
215C2×#6923—42no—
216C2×#6923—82no—
217Q8×C61—22no—
218Q8×C61—22no—
219Q8×C61—41no—
220Q8×C61—41no—
221C2×C4×C61—22no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61C2×C22⋊C411yescharacteristic
226C2×C4×C61C2×C4⋊C411yescharacteristic
227C2×C4×C61#11711yescharacteristic
228C2×C4×C61C4×D411yescharacteristic
229C2×C4×C61C4×D411yescharacteristic
230C2×C4×C61C4×D411yescharacteristic
231C2×Dic61—22no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61#12011yescharacteristic
236C2×Dic61#12111yescharacteristic
237C2×Dic61#12111yescharacteristic
238C2×Dic61C22⋊Q811yescharacteristic
239C2×Dic61#12311yescharacteristic
240C2×Dic61#12711yescharacteristic
241C4×D61—42no—
242C4×D61—42no—
243C4×D61—42no—
244C4×D61—42no—
245C4×D61—82no—
246C4×D61#12011yescharacteristic
247C4×D61#12011yescharacteristic
248C4×D61#12111yescharacteristic
249C4×D61#12111yescharacteristic
250C4×D61#12111yescharacteristic
251C4×D61#12111yescharacteristic
252C4×D61#12111yescharacteristic
253C4×D61C22⋊Q811yescharacteristic
254C4×D61C22⋊Q811yescharacteristic
255C4×D61C22⋊Q811yescharacteristic
256C4×D61C22⋊Q811yescharacteristic
257C4×D61#12311yescharacteristic
258C4×D61#12311yescharacteristic
259C4×D61#12311yescharacteristic
260C4×D61#12411yescharacteristic
261C4×D61#12611yescharacteristic
262Dic122—22no—
263Dic122—22no—
264Dic122—41no—
265Dic122—41no—
266Dic122—42no—
267Dic122—42no—
268Dic122—42no—
269Dic122—42no—
270#92420—42no—
271#92420—42no—
272#92420—42no—
273C8×C61—22no—
274#92418—22no—
275#11134—611nomaximal, Sylow
276C22×C61—41no—
277C22×C61#38511yescharacteristic
278C22×C61#38811yescharacteristic
279C22×C61#39011yescharacteristic
280C2×D61—22no—
281C2×D61—22no—
282C2×D61—22no—
283C2×D61—41no—
284C2×D61—41no—
285C2×D61—41no—
286C2×D61#39311yescharacteristic
287C2×D61#39411yescharacteristic
288C2×D61#39611yescharacteristic
289C2×D61#39711yescharacteristic
290#6923—82no—
291C4×C61—42no—
292C4×C61—81no—
293C4×C61#38011yescharacteristic
294C4×C61#38511yescharacteristic
295C4×C61#38611yescharacteristic
296C4×C61#38811yescharacteristic
297Dic61—42no—
298Dic61—81no—
299Dic61#39211yescharacteristic
300Dic61#39411yescharacteristic
301Dic61#39611yescharacteristic
302Dic61#39911yescharacteristic
303C2×#430—611no—
304C2×#419—611no—
305C2×#419—611no—
306C22×#101—611no—
307C2×#344—611no—
308C2×#344—611no—
309C2×H(3,ℤ/4)—611no—
310C2×C61—21no—
311C2×C61—21no—
312C2×C61—21no—
313C2×C61#143911yescharacteristic
314D61—21no—
315D61—21no—
316D61—21no—
317D61#208212yes—
318C23×Q8—611no—
319C22×M16—611no—
320C22×M16—611no—
321C22×M16—611no—
322C22×M16—611no—
323C2×#117—611no—
324C2×#117—611no—
325#430—1222no—
326#430—1222no—
327C2×#108—1222no—
328#419—611no—
329#419—611no—
330#419—611no—
331#419—1222no—
332#419—1222no—
333#419—1222no—
334#419#692311yescharacteristic, complemented
335C2×#103—1222no—
336C2×#103—1222no—
337C2×#101—1222no—
338C2×#101—1222no—
339C2×#101—1222no—
340#344—1222no—
341#344—1222no—
342H(3,ℤ/4)—1222no—
343C61#1113411yescharacteristic, complemented, Sylow
344C22×Q8—612no—
345C22×Q8—612no—
346C22×Q8—611no—
347C22×Q8—1221no—
348C22×Q8—1221no—
349C22×Q8—1221no—
350C22×Q8—1221no—
351C22×Q8—1221no—
352C22×Q8—1221no—
353C22×Q8—1221no—
354C22×Q8—1221no—
355C22×Q8—1221no—
356C22×Q8—1221no—
357C22×Q8—1221no—
358C22×Q8C2×#692311yescharacteristic
359C23×C4—611no—
360C23×C4—1221no—
361C2×M16—611no—
362C2×M16—612no—
363C2×M16—612no—
364C2×M16—612no—
365C2×M16—612no—
366C2×M16—1221no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1221no—
371C2×M16—1221no—
372C2×M16—1221no—
373C2×M16—1221no—
374C2×M16—1221no—
375C2×M16—1221no—
376C2×M16—1221no—
377C2×M16—1221no—
378C2×M16—1221no—
379C2×M16—1221no—
380C2×M16—1221no—
381C2×M16—1221no—
382C2×M16—1221no—
383C2×M16—1221no—
384C2×M16—1221no—
385C2×M16C2×#692311yescharacteristic
386C22×C8—612no—
387C22×C8—1221no—
388C22×C8—1221no—
389C22×C8—1221no—
390#117—612no—
391#117—611no—
392#117—1221no—
393#117—1221no—
394#117—1221no—
395#117—1221no—
396#117—1221no—
397#117—1221no—
398#117C2×#692311yescharacteristic
399C2×C4⋊C4—1221no—
400C2×C4⋊C4—1221no—
401C2×C22⋊C4—1221no—
402C2×C22⋊C4—1221no—
403C2×C42—1221no—
404C2×C42—1221no—
405#108—1224no—
406#108—1224no—
407#103—22no—
408#103—1222no—
409#103—1222no—
410#103—1228no—
411#103—1222no—
412#101—1228no—
413C24—611no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—612no—
420C2×Q8—1222no—
421C2×Q8—1222no—
422C2×Q8—1222no—
423C2×Q8—1222no—
424C2×Q8—1222no—
425C2×Q8—1222no—
426C2×Q8—1222no—
427C2×Q8—1222no—
428C2×Q8—1222no—
429C2×Q8—1222no—
430C2×Q8—1221no—
431C2×Q8—1221no—
432C2×Q8—1221no—
433C2×Q8—1221no—
434C2×Q8—1221no—
435C2×Q8—2441no—
436C2×Q8—2441no—
437C2×Q8—2441no—
438C2×Q8—2441no—
439C2×Q8—2441no—
440C2×Q8—2441no—
441C2×Q8—2441no—
442C2×Q8—2441no—
443C2×Q8—2441no—
444C2×Q8—2441no—
445C2×Q8—2441no—
446C2×Q8—2441no—
447C2×Q8C4⋊#692312yes—
448C22×C4—21no—
449C22×C4—611no—
450C22×C4—611no—
451C22×C4—611no—
452C22×C4—611no—
453C22×C4—611no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—611no—
457C22×C4—611no—
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1221no—
465C22×C4—2441no—
466C22×C4—2441no—
467C22×C4—2441no—
468C22×C4—2441no—
469C22×C4—2441no—
470C22×C4—2441no—
471C22×C4C22×#692311yescharacteristic
472M16—21no—
473M16—21no—
474M16—1222no—
475M16—1222no—
476M16—1221no—
477M16—1221no—
478M16—1222no—
479M16—1222no—
480M16—1222no—
481M16—1222no—
482M16—1222no—
483M16—1222no—
484M16—2441no—
485M16—2441no—
486M16—2441no—
487M16—2441no—
488M16—2441no—
489M16—2441no—
490C2×C8—612no—
491C2×C8—1222no—
492C2×C8—1222no—
493C2×C8—1222no—
494C2×C8—1222no—
495C2×C8—1222no—
496C2×C8—2441no—
497C2×C8—2441no—
498C2×C8—2441no—
499C2×C8—2441no—
500C2×C8—2441no—
501C2×C8—2441no—
502C2×C8C22⋊#692312yes—
503C4⋊C4—21no—
504C4⋊C4—1222no—
505C4⋊C4—1221no—
506C4⋊C4—2441no—
507C4⋊C4—2441no—
508C22⋊C4—21no—
509C22⋊C4—1222no—
510C22⋊C4—1221no—
511C22⋊C4—2441no—
512C22⋊C4—2441no—
513C42—21no—
514C42—1222no—
515C42—1221no—
516C42—2441no—
517C42—2441no—
518C23—611no—
519C23—611no—
520C23—611no—
521C23—611no—
522C23—611no—
523C23—611no—
524C23—2442no—
525C23D4×#692311yescharacteristic
526Q8—22no—
527Q8—22no—
528Q8—41no—
529Q8—41no—
530Q8—1222no—
531Q8—1222no—
532Q8—2442no—
533Q8—2442no—
534Q8—2442no—
535Q8—2442no—
536Q8—2441no—
537Q8—2441no—
538C2×C4—22no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—611no—
543C2×C4—611no—
544C2×C4—611no—
545C2×C4—611no—
546C2×C4—611no—
547C2×C4—611no—
548C2×C4—611no—
549C2×C4—611no—
550C2×C4—611no—
551C2×C4—611no—
552C2×C4—611no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—611no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—1222no—
565C2×C4—4882no—
566C2×C4—4882no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4C2×C22⋊#692311yescharacteristic
576C2×C4C2×C4⋊#692311yescharacteristic
577C2×C4#1451985611yescharacteristic
578C2×C4D4×#692311yescharacteristic
579C2×C4D4×#692311yescharacteristic
580C2×C4D4×#692311yescharacteristic
581C8—22no—
582C8—1222no—
583C8—2442no—
584C8—2442no—
585C8—2442no—
586C22—41no—
587C22—611no—
588C22—611no—
589C22—611no—
590C22—611no—
591C22—1222no—
592C22—1222no—
593C22—1222no—
594C22—2441no—
595C22—2441no—
596C22—2441no—
597C22#1684070911yescharacteristic
598C22#1684071211yescharacteristic
599C22#1684071411yescharacteristic
600C4—42no—
601C4—81no—
602C4—611no—
603C4—611no—
604C4—611no—
605C4—611no—
606C4—4881no—
607C4—4882no—
608C4—2442no—
609C4#1684070411yescharacteristic
610C4#1684070911yescharacteristic
611C4#1684071011yescharacteristic
612C4#1684071211yescharacteristic
613C2—21no—
614C2—21no—
615C2—21no—
616C2—612no—
617C2—1221no—
618C2—1221no—
619C2—1221no—
620C2#2146100211yescharacteristic
subgroupG/H
centerC2#21461002
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#419C4
socleC2×C61#1439
prime radicalC23×D61#41
cosocleC22×C4×D61C23
hypercenter#419#6923
hypocenterC61#11134
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
27. #16839772C4semidirect
28. #16839771C4semidirect
29. #16839770C4semidirect
32. C61×#419C4semidirect
334. #419#6923semidirect
343. C61#11134semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4302
C2×#168407552
C2×D61⋊#1012
#214615292
#214615272
#214614892
#419×D612
#1113461