Finite Group Databasebeta

← #30606335

Subgroups — #30606335

Order 15616.

752 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#413C211yesmaximal, characteristic
2D61⋊#410C211yesmaximal, characteristic
3#21460920C212yesmaximal, complemented
4#21460919C212yesmaximal, complemented
5#21454261C211yesmaximal, characteristic
6C2×D61⋊M16—21no—
7C2×#14519856—21no—
8#16840749—21no—
9#16840749C412yescomplemented
10#16840748—21no—
11#16840748C2212yes—
12D61⋊#101C412yescomplemented
13D61⋊#100—21no—
14#16840743C412yes—
15#16840742—21no—
16#16840741—21no—
17#16840741C2212yes—
18D61⋊#99—21no—
19D61⋊#99C412yes—
20C2×#41×D61C2211yescharacteristic
21C22×#11758189C411yescharacteristic, complemented
22C2×M16×D61C411yescharacteristic, complemented
23#16839730C2211yescharacteristic
24#16839729C411yescharacteristic, complemented
25#16839728C2211yescharacteristic
26#16839727—21no—
27#16839727—21no—
28#16839724—21no—
29#16839724—21no—
30C61×#408C411yescharacteristic, complemented
31C2×#11758213—41no—
32D61⋊M16—22no—
33D61⋊M16—22no—
34D61⋊M16—41no—
35D61⋊M16—41no—
36C2×#11758217—22no—
37C2×D61⋊C8—41no—
38#14519856—22no—
39#14519856—22no—
40#14519856—41no—
41#14519856—41no—
42C2×C4⋊#6923—41no—
43C2×C22⋊#6923—22no—
44C2×C4×#6923—41no—
45#14519838—22no—
46#14519838C2×C414yescomplemented
47#14519837—22no—
48#14519837—22no—
49#14519836—22no—
50#14519836C2×C414yes—
51#14519835—22no—
52#14519835—22no—
53C2×#11758226C2×C411yescharacteristic
54C2×#11758222D411yescharacteristic
55C2×#11758222D411yescharacteristic
56C2×#11758222C2311yescharacteristic
57C2×#11758224C2×C411yescharacteristic
58C2×#11758224D411yescharacteristic
59C2×#11758224Q811yescharacteristic
60#41×D61—41no—
61#41×D61—41no—
62#41×D61—41no—
63#41×D61—41no—
64C2×Q8×D61C2×C411yescharacteristic
65C2×D4×D61C2×C411yescharacteristic
66C2×D4×D61D411yescharacteristic
67C2×D4×D61Q811yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C2×#11758194C2×C411yescharacteristic, complemented
72C2×#11758189—21no—
73C2×#11758189—21no—
74C2×#11758189—21no—
75C2×#11758189—41no—
76C2×#11758189—41no—
77M16×D61—41no—
78M16×D61—41no—
79C22×#92418C2×C411yescharacteristic, complemented
80C2×C8×D61—21no—
81C22⋊#92418—21no—
82C22⋊#92418—21no—
83#14519689—21no—
84#14519689—21no—
85#14519689—21no—
86#14519689—21no—
87C2×#41×C61C2×C411yescharacteristic
88C2×M16×C61C2×C411yescharacteristic, complemented
89C22×C8×C61C2×C411yescharacteristic, complemented
90C22⋊C8×C61—21no—
91C22⋊C8×C61—21no—
92C23×D61C22⋊C411yescharacteristic
93C23×D61C4⋊C411yescharacteristic
94C23×D61C4⋊C411yescharacteristic
95C22×#6923—42no—
96#41×C61—41no—
97#41×C61—41no—
98C2×Q8×C61C4211yescharacteristic
99C2×D4×C61C4211yescharacteristic
100C2×D4×C61C4⋊C411yescharacteristic
101C2×D4×C61C4⋊C411yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C22⋊C411yescharacteristic
104C22×C4×C61C22×C411yescharacteristic
105C2×C22⋊D61C22⋊C411yescharacteristic
106C2×C22⋊D61C22⋊C411yescharacteristic
107C2×C22⋊D61C4⋊C411yescharacteristic
108C2×C22⋊D61C4⋊C411yescharacteristic
109C2×C22⋊D61C2×D411yescharacteristic
110C2×C22⋊D61C2×Q811yescharacteristic
111C22×Dic61C22⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113C22×Dic61C4⋊C411yescharacteristic
114#11758226—41no—
115#11758226—41no—
116Q8×D61—41no—
117Q8×D61—41no—
118#11758224—41no—
119#11758224—41no—
120#11758224—41no—
121#11758224—41no—
122#11758224—41no—
123#11758224—41no—
124D4×D61—41no—
125D4×D61—41no—
126D4×D61—41no—
127D4×D61—41no—
128D4×D61—41no—
129D4×D61—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135#11758222—41no—
136C2×D244C22⋊C411yescharacteristic
137C2×D244C4⋊C411yescharacteristic
138C2×D244C22×C411yescharacteristic
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—21no—
143C2×C4×D61—21no—
144C2×C4×D61—21no—
145C2×C4×D61—21no—
146C2×C4×D61—21no—
147C2×C4×D61—21no—
148C2×C4×D61—21no—
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61C4211yescharacteristic
152C2×C4×D61C4211yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C4⋊C411yescharacteristic
158C2×C4×D61C4⋊C411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×C4×D61C2×D411yescharacteristic
161C2×Dic122C22⋊C411yescharacteristic
162C2×Dic122C4⋊C411yescharacteristic
163C2×Dic122C22×C411yescharacteristic
164C22⋊#6923—24no—
165C22⋊#6923—42no—
166#11758217—24no—
167#11758217—42no—
168C2×#92420—42no—
169C4⋊#6923—42no—
170C4⋊#6923—42no—
171C4×#6923—42no—
172C4×#6923—42no—
173#11758213—42no—
174#11758213—42no—
175D61⋊C8—42no—
176D61⋊C8—42no—
177M16×C61—41no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—41no—
181#11758194—41no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—41no—
185#11758189—42no—
186#11758189—41no—
187#11758189—41no—
188#11758189—41no—
189#11758189—41no—
190C8×D61—42no—
191C23×C61#9511yescharacteristic
192C23×C61#9511yescharacteristic
193C23×C61C2×C4⋊C411yescharacteristic
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—81no—
201C22×D61—81no—
202C22×D61—81no—
203C22×D61#9511yescharacteristic
204C22×D61#9511yescharacteristic
205C22×D61C2×C22⋊C411yescharacteristic
206C22×D61C2×C4⋊C411yescharacteristic
207C2×#6923—44no—
208C2×#6923—84no—
209Q8×C61—41no—
210D4×C61—41no—
211D4×C61—41no—
212D4×C61—41no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61#9511yescharacteristic
220C2×C4×C61#9511yescharacteristic
221C2×C4×C61C2×C4211yescharacteristic
222C2×C4×C61C2×C22⋊C411yescharacteristic
223C22⋊D61—41no—
224C22⋊D61—41no—
225C22⋊D61—41no—
226C22⋊D61—41no—
227C22⋊D61—41no—
228C22⋊D61—41no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61#9511yescharacteristic
236C2×Dic61#9511yescharacteristic
237C2×Dic61C2×C22⋊C411yescharacteristic
238C2×Dic61C2×C4⋊C411yescharacteristic
239D244—41no—
240D244—41no—
241D244—41no—
242C4×D61—21no—
243C4×D61—21no—
244C4×D61—21no—
245C4×D61—21no—
246C4×D61—21no—
247C4×D61—21no—
248C4×D61—21no—
249C4×D61—21no—
250C4×D61—21no—
251C4×D61—21no—
252C4×D61—21no—
253C4×D61—21no—
254C4×D61—21no—
255C4×D61—21no—
256C4×D61—21no—
257C4×D61—21no—
258C4×D61—21no—
259C4×D61—21no—
260C4×D61#9911yescharacteristic
261C4×D61#9911yescharacteristic
262C4×D61#9911yescharacteristic
263C4×D61#9911yescharacteristic
264Dic122—41no—
265Dic122—41no—
266Dic122—41no—
267#92420—44no—
268C8×C61—41no—
269C8×C61—41no—
270#92418—41no—
271#92418—41no—
272#12589—611nomaximal, Sylow
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—41no—
277C22×C61—41no—
278C22×C61—41no—
279C22×C61C2×#9511yescharacteristic
280C2×D61—21no—
281C2×D61—21no—
282C2×D61—21no—
283C2×D61—41no—
284C2×D61—42no—
285C2×D61—42no—
286C2×D61—41no—
287C2×D61—41no—
288C2×D61—41no—
289C2×D61—81no—
290C2×D61—81no—
291C2×D61—81no—
292C2×D61—81no—
293C2×D61#34211yescharacteristic
294C2×D61#34211yescharacteristic
295#6923—84no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61C2×#9911yescharacteristic
300C4×C61C2×#9911yescharacteristic
301Dic61—21no—
302Dic61—21no—
303Dic61—21no—
304Dic61#34211yescharacteristic
305Dic61#34211yescharacteristic
306C2×#413—611no—
307C2×#410—611no—
308#2879—611no—
309#1395—612no—
310#1395—612no—
311C2×C61—21no—
312C2×C61—41no—
313C2×C61—41no—
314C2×C61—41no—
315C2×C61C2×#34211yescharacteristic
316D61—21no—
317D61—21no—
318D61—41no—
319D61—41no—
320D61—41no—
321C22×#41—611no—
322C22×M16—611no—
323C22×M16—611no—
324C22×M16—1221no—
325C2×#117—1221no—
326#413—612no—
327#413—612no—
328#413—1221no—
329#413—1221no—
330C2×#101—612no—
331C2×#100—1221no—
332#410—612no—
333#410—612no—
334#410—1221no—
335#410—1221no—
336C2×#99—612no—
337C2×#99—1221no—
338#408—611no—
339#408—611no—
340#408—611no—
341#408—1221no—
342#408—1221no—
343#408#692311yescharacteristic, complemented
344#407—1221no—
345#407—1221no—
346C61#1258911yescharacteristic, complemented, Sylow
347C2×#41—611no—
348C2×#41—611no—
349C2×#41—611no—
350C2×#41—611no—
351C2×#41—611no—
352C2×#41—611no—
353C2×#41—611no—
354C2×#41—2441no—
355C2×#41—2441no—
356C2×#41—2441no—
357C2×#41—2441no—
358C2×#41C2×#692311yescharacteristic
359C22×Q8—611no—
360C22×D4—611no—
361C22×D4—611no—
362C22×D4—611no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C2×M16—611no—
367C2×M16—1221no—
368C2×M16—1221no—
369C2×M16—1221no—
370C2×M16—1222no—
371C2×M16—1222no—
372C2×M16—1222no—
373C2×M16—2441no—
374C2×M16—2441no—
375C2×M16—2441no—
376C2×M16—2441no—
377C2×M16—2441no—
378C2×M16—2441no—
379C2×M16—2441no—
380C2×M16C2×#692311yescharacteristic, complemented
381C22×C8—611no—
382C22×C8—1221no—
383C22×C8—2441no—
384C22×C8C2×#692311yescharacteristic, complemented
385#117—1222no—
386#117—1222no—
387#117—2441no—
388#117—2441no—
389C2×C4⋊C4—2441no—
390C2×C22⋊C4—1222no—
391C2×C42—2441no—
392#101—614no—
393#101—1222no—
394#100—1222no—
395#100—1222no—
396#99—614no—
397#99—1222no—
398#99—1222no—
399#99—1222no—
400C22⋊C8—21no—
401C22⋊C8—21no—
402C22⋊C8—1221no—
403C22⋊C8—1221no—
404C22⋊C8—1221no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C24—611no—
409C24—611no—
410C24—611no—
411#41—41no—
412#41—41no—
413#41—2441no—
414#41—2441no—
415#41—2441no—
416#41—2441no—
417#41—2441no—
418#41—2441no—
419#41—2441no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—2441no—
431C2×Q8—2441no—
432C2×Q8C4×#692311yescharacteristic
433C2×D4—611no—
434C2×D4—611no—
435C2×D4—611no—
436C2×D4—611no—
437C2×D4—611no—
438C2×D4—611no—
439C2×D4—611no—
440C2×D4—611no—
441C2×D4—611no—
442C2×D4—2441no—
443C2×D4—2441no—
444C2×D4—2441no—
445C2×D4—2441no—
446C2×D4—2441no—
447C2×D4—2441no—
448C2×D4C4×#692311yescharacteristic
449C2×D4C4⋊#692311yescharacteristic
450C2×D4C4⋊#692311yescharacteristic
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—611no—
463C22×C4—611no—
464C22×C4—1221no—
465C22×C4—1221no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—2442no—
477C22×C4C22⋊#692311yescharacteristic
478C22×C4C22⋊#692311yescharacteristic
479C22×C4C22×#692311yescharacteristic
480M16—41no—
481M16—1224no—
482M16—2441no—
483M16—2441no—
484M16—2441no—
485M16—2441no—
486M16—2442no—
487M16—2442no—
488M16—2442no—
489M16—2442no—
490M16—2441no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—41no—
494C2×C8—1221no—
495C2×C8—1221no—
496C2×C8—2442no—
497C2×C8—2442no—
498C2×C8—2442no—
499C2×C8—2442no—
500C2×C8—2441no—
501C4⋊C4—2442no—
502C4⋊C4—2442no—
503C22⋊C4—1224no—
504C22⋊C4—2442no—
505C42—2442no—
506C42—2442no—
507C23—611no—
508C23—611no—
509C23—611no—
510C23—611no—
511C23—1221no—
512C23—1221no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—4881no—
518C23—4881no—
519C23—4881no—
520C23(C2×#6923)⋊C411yescharacteristic
521C23(C2×#6923)⋊C411yescharacteristic
522C23C2×C4⋊#692311yescharacteristic
523Q8—41no—
524Q8—2441no—
525Q8—2441no—
526Q8—2441no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—2441no—
531D4—2441no—
532D4—2441no—
533D4—2441no—
534D4—2441no—
535D4—2441no—
536D4—2441no—
537D4—2441no—
538D4—2441no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
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—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—1221no—
559C2×C4—1221no—
560C2×C4—1221no—
561C2×C4—1221no—
562C2×C4—1221no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—1221no—
576C2×C4—1221no—
577C2×C4—4884no—
578C2×C4—2444no—
579C2×C4(C2×#6923)⋊C411yescharacteristic
580C2×C4(C2×#6923)⋊C411yescharacteristic
581C2×C4C2×C4×#692311yescharacteristic
582C2×C4C2×C22⋊#692311yescharacteristic
583C8—41no—
584C8—41no—
585C8—2444no—
586C8—2441no—
587C8—2441no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—611no—
595C22—611no—
596C22—1221no—
597C22—1221no—
598C22—1221no—
599C22—4881no—
600C22—4881no—
601C22—4881no—
602C22—4881no—
603C22—2441no—
604C22—2441no—
605C22—2441no—
606C22—2441no—
607C22—2442no—
608C22—2442no—
609C22C2×(C2×#6923)⋊C411yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—611no—
614C4—611no—
615C4—1221no—
616C4—1221no—
617C4—1221no—
618C4—4884no—
619C4D61⋊#9911yescharacteristic
620C4D61⋊#9911yescharacteristic
621C2—21no—
622C2—41no—
623C2—41no—
624C2—41no—
625C2—1221no—
626C2—1221no—
627C2—2441no—
628C2—2441no—
629C2—2441no—
630C2#2146151611yescharacteristic
subgroupG/H
centerC4D61⋊#99
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#408C4
socleC2×C61C2×#342
prime radicalC2×#41×D61C22
cosocleC2×#11758222C23
hypercenter#408#6923
hypocenterC61#12589
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #21460920C2semidirect
4. #21460919C2semidirect
9. #16840749C4semidirect
12. D61⋊#101C4semidirect
21. C22×#11758189C4semidirect
22. C2×M16×D61C4semidirect
24. #16839729C4semidirect
30. C61×#408C4semidirect
46. #14519838C2×C4semidirect
71. C2×#11758194C2×C4semidirect
79. C22×#92418C2×C4semidirect
88. C2×M16×C61C2×C4semidirect
89. C22×C8×C61C2×C4semidirect
343. #408#6923semidirect
346. C61#12589semidirect
380. C2×M16C2×#6923semidirect
384. C22×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4132
D61⋊#4102
#214609202
#214609192
#214542612
#1258961