Finite Group Databasebeta

← #30606272

Subgroups — #30606272

Order 15616.

810 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#410C211yesmaximal, characteristic
2#21462294C211yesmaximal, characteristic
3#21460905C214yesmaximal, complemented
4#413×D61C211yesmaximal, characteristic
5C2×#14519856—21no—
6C2×#14519856C411yescharacteristic, complemented
7C22×C4⋊#6923C411yescharacteristic, complemented
8#16840743—21no—
9#16840742C412yescomplemented
10#16840741—21no—
11#16840741C412yescomplemented
12D61⋊#99—21no—
13D61⋊#99C2212yes—
14(C2×#6923)⋊Q8—21no—
15#16840714—21no—
16#16840710C412yescomplemented
17#16840710C2212yes—
18#16840704—21no—
19#16840704—21no—
20C2×#41×D61C2211yescharacteristic
21C2×M16×D61—21no—
22#16839746C411yescharacteristic, complemented
23#16839745—21no—
24#16839744—21no—
25#16839743C412yescomplemented
26#101×D61—21no—
27#100×D61C2212yes—
28C61×#413C411yescharacteristic, complemented
29C23×#6923C2×C412yes—
30#14519856—22no—
31#14519856—22no—
32#14519856—41no—
33#14519856—41no—
34#14519856—41no—
35#14519856—41no—
36C2×C4⋊#6923—21no—
37C2×C4⋊#6923—21no—
38C2×C4⋊#6923—21no—
39C2×C4⋊#6923—41no—
40C2×C4⋊#6923—41no—
41C2×C4⋊#6923—41no—
42C2×C22⋊#6923—22no—
43C2×C22⋊#6923—22no—
44C2×C22⋊#6923—22no—
45C2×C22⋊#6923C2×C412yes—
46C2×C4×#6923—21no—
47C2×C4×#6923—41no—
48#14519836—22no—
49#14519836—22no—
50#14519835—22no—
51#14519835C2×C414yes—
52(C2×#6923)⋊C4—22no—
53(C2×#6923)⋊C4—22no—
54C2×#11758226D411yescharacteristic
55C2×#11758222C2×C411yescharacteristic
56C2×#11758222D411yescharacteristic
57C2×#11758222Q811yescharacteristic
58C2×#11758224C2×C411yescharacteristic
59C2×#11758224C2×C411yescharacteristic
60C2×#11758224Q811yescharacteristic
61#41×D61—41no—
62#41×D61—41no—
63#41×D61—41no—
64#41×D61—41no—
65C2×Q8×D61D411yescharacteristic
66C2×D4×D61C2×C411yescharacteristic
67C2×D4×D61D411yescharacteristic
68C2×D4×D61C2311yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61D411yescharacteristic
71C22×C4×D61D411yescharacteristic
72C2×#11758194—21no—
73C2×#11758189—41no—
74M16×D61—22no—
75M16×D61—22no—
76M16×D61—41no—
77M16×D61—41no—
78C2×C8×D61—41no—
79#14519696—21no—
80#14519695—22no—
81#14519694C2×C412yes—
82#14519693—22no—
83C2×#41×C61C2×C411yescharacteristic
84C2×M16×C61—21no—
85#101×C61—21no—
86#100×C61C2×C412yes—
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22×C411yescharacteristic
89C23×D61C2×D411yescharacteristic
90C22×#6923—22no—
91C22×#6923—22no—
92C22×#6923—42no—
93C22×#6923—42no—
94C22×#6923—82no—
95#41×C61—41no—
96#41×C61—41no—
97C2×Q8×C61C22⋊C411yescharacteristic
98C2×D4×C61C4211yescharacteristic
99C2×D4×C61C4⋊C411yescharacteristic
100C2×D4×C61C22×C411yescharacteristic
101C22×C4×C61C4211yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C4⋊C411yescharacteristic
104C2×C22⋊D61C4211yescharacteristic
105C2×C22⋊D61C22⋊C411yescharacteristic
106C2×C22⋊D61C4⋊C411yescharacteristic
107C2×C22⋊D61C4⋊C411yescharacteristic
108C2×C22⋊D61C22×C411yescharacteristic
109C2×C22⋊D61C2×Q811yescharacteristic
110C22×Dic61C4211yescharacteristic
111C22×Dic61C4⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113#11758226—41no—
114#11758226—41no—
115Q8×D61—41no—
116Q8×D61—41no—
117#11758224—41no—
118#11758224—41no—
119#11758224—41no—
120#11758224—41no—
121#11758224—41no—
122#11758224—41no—
123D4×D61—41no—
124D4×D61—41no—
125D4×D61—41no—
126D4×D61—41no—
127D4×D61—41no—
128D4×D61—41no—
129#11758222—41no—
130#11758222—41no—
131#11758222—41no—
132#11758222—41no—
133#11758222—41no—
134#11758222—41no—
135C2×D244C22⋊C411yescharacteristic
136C2×D244C4⋊C411yescharacteristic
137C2×D244C2×D411yescharacteristic
138C2×C4×D61—21no—
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×D61C22⋊C411yescharacteristic
151C2×C4×D61C22⋊C411yescharacteristic
152C2×C4×D61C22⋊C411yescharacteristic
153C2×C4×D61C22⋊C411yescharacteristic
154C2×C4×D61C22⋊C411yescharacteristic
155C2×C4×D61C22⋊C411yescharacteristic
156C2×C4×D61C4⋊C411yescharacteristic
157C2×C4×D61C4⋊C411yescharacteristic
158C2×C4×D61C4⋊C411yescharacteristic
159C2×C4×D61C2×D411yescharacteristic
160C2×Dic122C22⋊C411yescharacteristic
161C2×Dic122C4⋊C411yescharacteristic
162C2×Dic122C4⋊C411yescharacteristic
163C22⋊#6923—24no—
164C22⋊#6923—42no—
165C22⋊#6923—42no—
166C22⋊#6923—82no—
167C22⋊#6923—82no—
168C4⋊#6923—42no—
169C4⋊#6923—42no—
170C4⋊#6923—42no—
171C4⋊#6923—41no—
172C4⋊#6923—41no—
173C4⋊#6923—41no—
174C4⋊#6923—41no—
175C4×#6923—42no—
176C4×#6923—42no—
177C4×#6923—42no—
178M16×C61—22no—
179M16×C61—41no—
180C2×C8×C61—41no—
181#11758194—22no—
182#11758194—41no—
183C2×#92418—41no—
184#11758189—42no—
185#11758189—42no—
186C8×D61—42no—
187C8×D61—42no—
188C23×C61#9511yescharacteristic
189C23×C61C2×C4211yescharacteristic
190C23×C61C2×C4⋊C411yescharacteristic
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61#9511yescharacteristic
204C22×D61C2×C22⋊C411yescharacteristic
205C22×D61C2×C22⋊C411yescharacteristic
206C22×D61C2×C4⋊C411yescharacteristic
207C2×#6923—44no—
208C2×#6923—42no—
209C2×#6923—42no—
210C2×#6923—42no—
211C2×#6923—42no—
212C2×#6923—42no—
213C2×#6923—42no—
214C2×#6923—82no—
215C2×#6923—82no—
216C2×#6923—84no—
217Q8×C61—41no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61#9511yescharacteristic
228C2×C4×C61#9511yescharacteristic
229C2×C4×C61#9511yescharacteristic
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C22⋊D61—41no—
232C22⋊D61—41no—
233C22⋊D61—41no—
234C22⋊D61—41no—
235C22⋊D61—41no—
236C22⋊D61—41no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—21no—
240C2×Dic61—21no—
241C2×Dic61—21no—
242C2×Dic61—21no—
243C2×Dic61#9511yescharacteristic
244C2×Dic61#9511yescharacteristic
245C2×Dic61#9511yescharacteristic
246C2×Dic61C2×C4⋊C411yescharacteristic
247D244—41no—
248D244—41no—
249D244—41no—
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—21no—
261C4×D61—21no—
262C4×D61—21no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—21no—
267C4×D61—21no—
268C4×D61#9911yescharacteristic
269C4×D61#9911yescharacteristic
270C4×D61#9911yescharacteristic
271C4×D61#9911yescharacteristic
272Dic122—41no—
273Dic122—41no—
274Dic122—41no—
275C8×C61—42no—
276#92418—42no—
277#12575—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—41no—
282C22×C61—41no—
283C22×C61—41no—
284C22×C61C2×#9511yescharacteristic
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—42no—
291C2×D61—41no—
292C2×D61—41no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—81no—
301C2×D61—81no—
302C2×D61C2×#9911yescharacteristic
303C2×D61C2×#9911yescharacteristic
304#6923—82no—
305#6923—84no—
306#6923—82no—
307C4×C61—21no—
308C4×C61—21no—
309C4×C61—21no—
310C4×C61#34211yescharacteristic
311C4×C61#34211yescharacteristic
312Dic61—21no—
313Dic61—21no—
314Dic61—21no—
315Dic61#34211yescharacteristic
316Dic61#34211yescharacteristic
317C2×#413—611no—
318C2×#410—611no—
319#2311—611no—
320#1390—614no—
321C2×C61—21no—
322C2×C61—41no—
323C2×C61—41no—
324C2×C61—41no—
325C2×C61C2×#34211yescharacteristic
326D61—21no—
327D61—41no—
328D61—41no—
329D61—41no—
330D61#212211yescharacteristic
331D61#212311yescharacteristic
332C22×#41—611no—
333C22×M16—1221no—
334C2×#117—611no—
335C2×#117—1221no—
336C22×C4⋊C4—611no—
337#413—611no—
338#413—612no—
339#413—1221no—
340#413—1221no—
341#413#692311yescharacteristic, complemented
342C2×#101—1221no—
343C2×#100—612no—
344#410—612no—
345#410—612no—
346#410—1221no—
347#410—1221no—
348C2×#99—612no—
349C2×#99—1221no—
350#391—1221no—
351#390—1221no—
352#386—612no—
353#386—612no—
354#380—1221no—
355#380—1221no—
356C61#1257511yescharacteristic, complemented, Sylow
357C2×#41—611no—
358C2×#41—611no—
359C2×#41—611no—
360C2×#41—611no—
361C2×#41—611no—
362C2×#41—611no—
363C2×#41—611no—
364C2×#41—2441no—
365C2×#41—2441no—
366C2×#41—2441no—
367C2×#41—2441no—
368C2×#41C2×#692311yescharacteristic
369C22×Q8—611no—
370C22×D4—611no—
371C22×D4—611no—
372C22×D4—611no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—612no—
377C2×M16—21no—
378C2×M16—1222no—
379C2×M16—1222no—
380C2×M16—1221no—
381C2×M16—2441no—
382C2×M16—2441no—
383C2×M16—2441no—
384C22×C8—2441no—
385#117—1222no—
386#117—1222no—
387#117—2441no—
388#117—2441no—
389#117—2441no—
390#117—2441no—
391C2×C4⋊C4—1221no—
392C2×C4⋊C4—1221no—
393C2×C4⋊C4—1221no—
394C2×C4⋊C4—2441no—
395C2×C4⋊C4—2441no—
396C2×C4⋊C4—2441no—
397C2×C22⋊C4—612no—
398C2×C22⋊C4—1222no—
399C2×C22⋊C4—1222no—
400C2×C22⋊C4—1222no—
401C2×C42—1221no—
402C2×C42—2441no—
403#101—21no—
404#101—1222no—
405#101—1221no—
406#100—612no—
407#100—1222no—
408#100C2×#692312yes—
409#99—614no—
410#99—1222no—
411#99—1222no—
412#99—1222no—
413#95—1222no—
414#95—1222no—
415C24—611no—
416C24—611no—
417C24—611no—
418#41—41no—
419#41—41no—
420#41—2441no—
421#41—2441no—
422#41—2441no—
423#41—2441no—
424#41—2441no—
425#41—2441no—
426#41—2441no—
427#41—2441no—
428#41—2441no—
429#41—2441no—
430#41—2441no—
431#41—2441no—
432#41—2441no—
433#41—2441no—
434C2×Q8—611no—
435C2×Q8—611no—
436C2×Q8—611no—
437C2×Q8—2441no—
438C2×Q8—2441no—
439C2×Q8C22⋊#692311yescharacteristic
440C2×D4—611no—
441C2×D4—611no—
442C2×D4—611no—
443C2×D4—611no—
444C2×D4—611no—
445C2×D4—611no—
446C2×D4—611no—
447C2×D4—611no—
448C2×D4—611no—
449C2×D4—2441no—
450C2×D4—2441no—
451C2×D4—2441no—
452C2×D4—2441no—
453C2×D4—2441no—
454C2×D4—2441no—
455C2×D4C4×#692311yescharacteristic
456C2×D4C4⋊#692311yescharacteristic
457C2×D4C22×#692311yescharacteristic
458C22×C4—611no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1221no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1222no—
484C22×C4—1222no—
485C22×C4—4882no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4C4×#692311yescharacteristic
489C22×C4C4⋊#692311yescharacteristic
490C22×C4C22⋊#692311yescharacteristic
491M16—22no—
492M16—41no—
493M16—1222no—
494M16—2442no—
495M16—2442no—
496M16—2441no—
497C2×C8—41no—
498C2×C8—2442no—
499C2×C8—2442no—
500C2×C8—2441no—
501C4⋊C4—2441no—
502C4⋊C4—2441no—
503C4⋊C4—2441no—
504C4⋊C4—2441no—
505C4⋊C4—2442no—
506C4⋊C4—2442no—
507C4⋊C4—2442no—
508C22⋊C4—1224no—
509C22⋊C4—4882no—
510C22⋊C4—4882no—
511C22⋊C4—2442no—
512C22⋊C4—2442no—
513C42—2442no—
514C42—2442no—
515C42—2442no—
516C23—611no—
517C23—611no—
518C23—611no—
519C23—611no—
520C23—1221no—
521C23—1221no—
522C23—1221no—
523C23—1221no—
524C23—1221no—
525C23—1221no—
526C23—2441no—
527C23—2441no—
528C23—2441no—
529C23—2441no—
530C23—2441no—
531C23—2441no—
532C23(C2×#6923)⋊C411yescharacteristic
533C23C2×C4×#692311yescharacteristic
534C23C2×C4⋊#692311yescharacteristic
535Q8—41no—
536Q8—2441no—
537Q8—2441no—
538Q8—2441no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—2441no—
543D4—2441no—
544D4—2441no—
545D4—2441no—
546D4—2441no—
547D4—2441no—
548D4—2441no—
549D4—2441no—
550D4—2441no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—611no—
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—1221no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—1221no—
581C2×C4—1221no—
582C2×C4—1221no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1221no—
588C2×C4—1221no—
589C2×C4—4882no—
590C2×C4—4882no—
591C2×C4—4884no—
592C2×C4—2442no—
593C2×C4—2442no—
594C2×C4—2444no—
595C2×C4—2442no—
596C2×C4—2442no—
597C2×C4—2442no—
598C2×C4—2442no—
599C2×C4(C2×#6923)⋊C411yescharacteristic
600C2×C4(C2×#6923)⋊C411yescharacteristic
601C2×C4(C2×#6923)⋊C411yescharacteristic
602C2×C4C2×C22⋊#692311yescharacteristic
603C8—42no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—611no—
612C22—611no—
613C22—1221no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—4881no—
619C22—4881no—
620C22—2441no—
621C22—2441no—
622C22—2441no—
623C22—2441no—
624C22—2441no—
625C22—2441no—
626C22—2441no—
627C22—2441no—
628C22—2441no—
629C22—2442no—
630C22C2×(C2×#6923)⋊C411yescharacteristic
631C4—21no—
632C4—21no—
633C4—21no—
634C4—611no—
635C4—611no—
636C4—1221no—
637C4—1221no—
638C4—1221no—
639C4—4882no—
640C4—4882no—
641C4—4884no—
642C4#1684063911yescharacteristic
643C4#1684063911yescharacteristic
644C2—21no—
645C2—41no—
646C2—41no—
647C2—41no—
648C2—611no—
649C2—611no—
650C2—1221no—
651C2—2441no—
652C2—2441no—
653C2—2441no—
654C2C2×#1684063911yescharacteristic
subgroupG/H
centerC2C2×#16840639
commutatorC23×C61C2×C42
FrattiniC2×D4C22×#6923
FittingC61×#413C4
socleC2×C61C2×#342
prime radicalC2×#41×D61C22
cosocleC2×D4×D61C23
hypercenter#413#6923
hypocenterC61#12575
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #21460905C2semidirect
6. C2×#14519856C4semidirect
7. C22×C4⋊#6923C4semidirect
9. #16840742C4semidirect
11. #16840741C4semidirect
16. #16840710C4semidirect
22. #16839746C4semidirect
25. #16839743C4semidirect
28. C61×#413C4semidirect
341. #413#6923semidirect
356. C61#12575semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4102
#214622942
#214609052
#413×D612
#1257561