Finite Group Databasebeta

← #30602995

Subgroups — #30602995

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#104C211yesmaximal, characteristic
2#21462280C211yesmaximal, characteristic
3C2×#16840698C211yesmaximal, characteristic, complemented
4C2×#16840634C211yesmaximal, characteristic, complemented
5C2×#16840633C211yesmaximal, characteristic, complemented
6#21461481C211yesmaximal, characteristic, complemented
7C2×#104×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2211yescharacteristic
9C2×#14519856C2211yescharacteristic
10C22×C4×#6923C2211yescharacteristic
11C22×C4×#6923C2211yescharacteristic
12C2×#14519842C412yescomplemented
13D61⋊#104—22no—
14D61⋊#104—22no—
15C2×#14519841C412yescomplemented
16(C2×#6923)⋊Q8C412yescomplemented
17#16840714C412yescomplemented
18#16840710—22no—
19C4×C22⋊#6923—22no—
20#16840698—22no—
21#16840698—22no—
22C2×(C2×#6923)⋊C4—22no—
23#16840634—22no—
24#16840633—22no—
25(C2×#6923)⋊C8—22no—
26C2×#41×D61C2211yescharacteristic
27C2×M16×D61C2211yescharacteristic
28C2×C42×D61C2211yescharacteristic
29C2×#14519705C411yescharacteristic, complemented
30C2×#14519704C411yescharacteristic, complemented
31C2×#14519703C411yescharacteristic, complemented
32#104×D61—22no—
33#104×D61—22no—
34C2×#104×C61C411yescharacteristic, complemented
35C23×#6923—21no—
36C23×#6923D412yes—
37C2×#11758213C2×C412yes—
38D61⋊M16—21no—
39D61⋊M16—21no—
40D61⋊M16—21no—
41D61⋊M16—21no—
42C2×#11758217—21no—
43C2×D61⋊C8—21no—
44#14519856—21no—
45#14519856—21no—
46#14519856—21no—
47#14519856—21no—
48C2×C4⋊#6923C2×C412yes—
49C2×C22⋊#6923—21no—
50C2×C22⋊#6923—24no—
51C2×C4×#6923—21no—
52C2×C4×#6923—21no—
53C2×C4×#6923—21no—
54C2×C4×#6923—21no—
55C2×C4×#6923—21no—
56C2×C4×#6923—21no—
57C2×C4×#6923—21no—
58C2×C4×#6923—21no—
59C2×C4×#6923C2×C412yes—
60C2×C4×#6923C2×C412yes—
61C2×C4×#6923D412yes—
62C2×C4×#6923D412yes—
63C2×C4×#6923D412yes—
64#14519842—24no—
65#14519841—24no—
66(C2×#6923)⋊C4—28no—
67(C2×#6923)⋊C4—24no—
68C2×#11758226C2×C411yescharacteristic
69C2×#11758222—21no—
70C2×#11758222C2×C411yescharacteristic
71C2×#11758224—21no—
72C2×#11758224C2×C411yescharacteristic
73#41×D61—21no—
74#41×D61—21no—
75#41×D61—21no—
76#41×D61—21no—
77#41×D61—21no—
78#41×D61—21no—
79#41×D61—21no—
80#41×D61—21no—
81C2×Q8×D61C2×C411yescharacteristic
82C2×D4×D61—21no—
83C2×D4×D61C2×C411yescharacteristic
84C22×C4×D61—21no—
85C22×C4×D61—21no—
86C22×C4×D61C2311yescharacteristic
87C2×#11758194C2×C411yescharacteristic
88C2×#11758189—21no—
89M16×D61—21no—
90M16×D61—21no—
91M16×D61—21no—
92M16×D61—21no—
93C2×C8×D61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2×C411yescharacteristic
96C42×D61—21no—
97C42×D61—21no—
98C42×D61D412yes—
99C42×D61D412yes—
100#14519705—22no—
101#14519704—22no—
102#14519703—22no—
103C2×#41×C61C2×C411yescharacteristic
104C2×M16×C61C2×C411yescharacteristic
105C2×C42×C61C2×C411yescharacteristic
106#104×C61—22no—
107C23×D61—21no—
108C23×D61C2×D411yescharacteristic
109C22×#6923—22no—
110C22×#6923—22no—
111C22×#6923—22no—
112C22×#6923—22no—
113C22×#6923—22no—
114C22×#6923—22no—
115C22×#6923—44no—
116C22×#6923—44no—
117C22×#6923C22⋊C414yes—
118#41×C61—21no—
119#41×C61—21no—
120#41×C61—21no—
121#41×C61—21no—
122C2×Q8×C61C4211yescharacteristic
123C2×D4×C61—21no—
124C2×D4×C61C4211yescharacteristic
125C22×C4×C61—21no—
126C22×C4×C61—21no—
127C22×C4×C61C22×C411yescharacteristic
128C2×C22⋊D61—21no—
129C2×C22⋊D61—21no—
130C2×C22⋊D61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61#4111yescharacteristic
134#11758226—21no—
135#11758226—21no—
136#11758226—21no—
137#11758226—21no—
138Q8×D61—21no—
139Q8×D61—21no—
140Q8×D61—21no—
141Q8×D61—21no—
142#11758224—21no—
143#11758224—21no—
144#11758224—21no—
145#11758224—21no—
146#11758224—41no—
147#11758224—41no—
148#11758224—41no—
149#11758224—41no—
150D4×D61—21no—
151D4×D61—21no—
152D4×D61—21no—
153D4×D61—21no—
154D4×D61—41no—
155D4×D61—41no—
156D4×D61—41no—
157D4×D61—41no—
158#11758222—21no—
159#11758222—21no—
160#11758222—21no—
161#11758222—21no—
162#11758222—41no—
163#11758222—41no—
164#11758222—41no—
165#11758222—41no—
166C2×D244—21no—
167C2×D244C4211yescharacteristic
168C2×C4×D61—21no—
169C2×C4×D61—22no—
170C2×C4×D61—22no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—44no—
174C2×C4×D61—41no—
175C2×C4×D61—41no—
176C2×C4×D61—41no—
177C2×C4×D61—41no—
178C2×C4×D61C22×C411yescharacteristic
179C2×C4×D61C22×C411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×C4×D61C2×D411yescharacteristic
182C2×C4×D61C2×D411yescharacteristic
183C2×C4×D61C2×D411yescharacteristic
184C2×C4×D61C2×D411yescharacteristic
185C2×C4×D61#4111yescharacteristic
186C2×C4×D61#4111yescharacteristic
187C2×C4×D61#4111yescharacteristic
188C2×C4×D61#4111yescharacteristic
189C2×C4×D61#4111yescharacteristic
190C2×Dic122—21no—
191C2×Dic122C4211yescharacteristic
192C22⋊#6923—48no—
193C22⋊#6923—41no—
194C22⋊#6923—41no—
195#11758217—41no—
196#11758217—41no—
197C2×#92420—22no—
198C4⋊#6923—22no—
199C4⋊#6923—22no—
200C4×#6923—22no—
201C4×#6923—22no—
202C4×#6923—22no—
203C4×#6923—22no—
204C4×#6923—22no—
205C4×#6923—22no—
206C4×#6923—22no—
207C4×#6923—41no—
208C4×#6923—41no—
209C4×#6923C22⋊C414yescomplemented
210#11758213—22no—
211#11758213—22no—
212D61⋊C8—41no—
213D61⋊C8—41no—
214M16×C61—21no—
215M16×C61—21no—
216C2×C8×C61—21no—
217C42×C61—21no—
218C42×C61C22⋊C412yescomplemented
219C4×Dic61—21no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61C22⋊C412yescomplemented
223#11758194—21no—
224#11758194—21no—
225C2×#92418—21no—
226#11758189—41no—
227#11758189—41no—
228C8×D61—41no—
229C8×D61—41no—
230C23×C61—21no—
231C23×C61C4×D411yescharacteristic
232C22×D61—24no—
233C22×D61—21no—
234C22×D61—41no—
235C22×D61—41no—
236C22×D61—44no—
237C22×D61C2×C22⋊C411yescharacteristic
238C22×D61C4×D411yescharacteristic
239C22×D61#12011yescharacteristic
240C22×D61#12111yescharacteristic
241C22×D61#12111yescharacteristic
242C22×D61#12311yescharacteristic
243C2×#6923—24no—
244C2×#6923—24no—
245C2×#6923—24no—
246C2×#6923—24no—
247C2×#6923—44no—
248C2×#6923—44no—
249C2×#6923—44no—
250C2×#6923—44no—
251C2×#6923—44no—
252C2×#6923—42no—
253C2×#6923—44no—
254Q8×C61—21no—
255Q8×C61—21no—
256D4×C61—21no—
257D4×C61—21no—
258D4×C61—41no—
259D4×C61—41no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61C2×C4211yescharacteristic
266C2×C4×C61C2×C22⋊C411yescharacteristic
267C2×C4×C61#11711yescharacteristic
268C2×C4×C61C4×D411yescharacteristic
269C2×C4×C61C4×D411yescharacteristic
270C2×C4×C61C4×D411yescharacteristic
271C22⋊D61—41no—
272C22⋊D61—41no—
273C22⋊D61—41no—
274C22⋊D61—41no—
275C22⋊D61—41no—
276C22⋊D61—41no—
277C2×Dic61—21no—
278C2×Dic61—22no—
279C2×Dic61—42no—
280C2×Dic61—41no—
281C2×Dic61—41no—
282C2×Dic61#11711yescharacteristic
283C2×Dic61C4×D411yescharacteristic
284C2×Dic61#12111yescharacteristic
285C2×Dic61#12311yescharacteristic
286C2×Dic61#12411yescharacteristic
287C2×Dic61#12611yescharacteristic
288D244—21no—
289D244—21no—
290D244—41no—
291D244—41no—
292C4×D61—44no—
293C4×D61—44no—
294C4×D61—41no—
295C4×D61—41no—
296C4×D61—41no—
297C4×D61—41no—
298C4×D61—41no—
299C4×D61—41no—
300C4×D61C2×C22⋊C411yescharacteristic
301C4×D61#11711yescharacteristic
302C4×D61C4×D411yescharacteristic
303C4×D61C4×D411yescharacteristic
304C4×D61C4×D411yescharacteristic
305C4×D61C4×D411yescharacteristic
306C4×D61C4×D411yescharacteristic
307C4×D61C4×D411yescharacteristic
308C4×D61#12111yescharacteristic
309C4×D61#12111yescharacteristic
310C4×D61#12111yescharacteristic
311C4×D61#12311yescharacteristic
312C4×D61#12411yescharacteristic
313C4×D61#12411yescharacteristic
314C4×D61#12611yescharacteristic
315C4×D61#12711yescharacteristic
316Dic122—21no—
317Dic122—21no—
318Dic122—41no—
319Dic122—41no—
320#92420—42no—
321C8×C61—41no—
322#92418—41no—
323#10924—611nomaximal, Sylow
324C22×C61—22no—
325C22×C61—41no—
326C22×C61—42no—
327C22×C61C4×C22⋊C411yescharacteristic
328C22×C61#38611yescharacteristic
329C22×C61#38811yescharacteristic
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—41no—
336C2×D61—42no—
337C2×D61—82no—
338C2×D61—82no—
339C2×D61#38611yescharacteristic
340C2×D61#38611yescharacteristic
341C2×D61#38811yescharacteristic
342C2×D61#39011yescharacteristic
343C2×D61#42114yes—
344#6923—44no—
345#6923—44no—
346#6923—82no—
347C4×C61—42no—
348C4×C61—41no—
349C4×C61C4×C22⋊C411yescharacteristic
350C4×C61C4×C22⋊C411yescharacteristic
351C4×C61#38811yescharacteristic
352C4×C61#39011yescharacteristic
353Dic61—42no—
354Dic61—41no—
355Dic61#38811yescharacteristic
356Dic61#38811yescharacteristic
357Dic61#38811yescharacteristic
358Dic61#39011yescharacteristic
359C22×#104—611no—
360C22×#104—611no—
361#2297—611no—
362C2×#376—611no—
363C2×#339—611no—
364C2×#339—611no—
365#1728—611no—
366C2×C61—21no—
367C2×C61—21no—
368C2×C61—81no—
369C2×C61#143711yescharacteristic
370C2×C61#175912yes—
371D61—21no—
372D61—21no—
373D61—81no—
374D61#189712yes—
375D61#196312yes—
376C22×#41—611no—
377C22×M16—611no—
378C22×M16—611no—
379C2×#117—611no—
380C22×C42—611no—
381C22×C42—611no—
382C22×C42—611no—
383C2×#104—612no—
384C2×#104—612no—
385C2×#104—611no—
386C2×#104—611no—
387C2×#104—611no—
388C2×#104—1222no—
389C2×#104—1222no—
390C2×#104—1222no—
391C2×#104—1222no—
392C2×#104#692311yescharacteristic, complemented
393#391—612no—
394#390—612no—
395#386—1222no—
396C4×C22⋊C4—1222no—
397#376—1222no—
398#376—1222no—
399C2×#95—1222no—
400#339—1222no—
401#339—1222no—
402#336—1222no—
403C61#1092411yescharacteristic, complemented, Sylow
404C2×#41—611no—
405C2×#41—611no—
406C2×#41—611no—
407C2×#41—1221no—
408C2×#41—1221no—
409C2×#41—1221no—
410C2×#41—1221no—
411C2×#41—1221no—
412C2×#41—1221no—
413C2×#41—1221no—
414C2×#41—1221no—
415C2×#41—1221no—
416C2×#41—1221no—
417C2×#41C2×#692311yescharacteristic
418C22×Q8—611no—
419C22×D4—611no—
420C22×D4—1221no—
421C23×C4—611no—
422C23×C4—612no—
423C23×C4—1221no—
424C23×C4—1221no—
425C23×C4—1221no—
426C2×M16—612no—
427C2×M16—611no—
428C2×M16—1221no—
429C2×M16—1221no—
430C2×M16—1221no—
431C2×M16—1221no—
432C2×M16—1221no—
433C2×M16—1221no—
434C2×M16—1221no—
435C2×M16—1221no—
436C2×M16—1221no—
437C2×M16—1221no—
438C2×M16C2×#692311yescharacteristic
439C22×C8—1221no—
440C22×C8—1221no—
441#117—1221no—
442#117—1221no—
443#117—1221no—
444#117—1221no—
445C2×C4⋊C4—612no—
446C2×C22⋊C4—1224no—
447C2×C22⋊C4—1221no—
448C2×C42—612no—
449C2×C42—612no—
450C2×C42—612no—
451C2×C42—611no—
452C2×C42—612no—
453C2×C42—612no—
454C2×C42—612no—
455C2×C42—612no—
456C2×C42—1221no—
457C2×C42—1221no—
458C2×C42—1221no—
459C2×C42—1221no—
460C2×C42—1221no—
461C2×C42—1221no—
462C2×C42—1221no—
463C2×C42—1221no—
464C2×C42—1221no—
465C2×C42—1221no—
466C2×C42—1221no—
467C2×C42C2×#692311yescharacteristic
468#104—22no—
469#104—1222no—
470#104—1222no—
471#104—1224no—
472#104—1224no—
473#104—1222no—
474#95—1224no—
475#95—1228no—
476C24—611no—
477C24—1221no—
478#41—21no—
479#41—21no—
480#41—21no—
481#41—21no—
482#41—1221no—
483#41—1221no—
484#41—1221no—
485#41—1221no—
486#41—1221no—
487#41—1221no—
488#41—1221no—
489#41—1221no—
490#41—1221no—
491#41—1221no—
492#41—1221no—
493#41—1221no—
494#41—2441no—
495#41—2441no—
496#41—2441no—
497#41—2441no—
498#41—2441no—
499#41—2441no—
500#41—2441no—
501#41—2441no—
502C2×Q8—611no—
503C2×Q8—1221no—
504C2×Q8—1221no—
505C2×Q8—1221no—
506C2×Q8—1221no—
507C2×Q8—1221no—
508C2×Q8C4×#692311yescharacteristic
509C2×D4—21no—
510C2×D4—611no—
511C2×D4—1221no—
512C2×D4—1221no—
513C2×D4—1221no—
514C2×D4—1221no—
515C2×D4—1221no—
516C2×D4—1221no—
517C2×D4—1221no—
518C2×D4—1221no—
519C2×D4—2441no—
520C2×D4—2441no—
521C2×D4—2441no—
522C2×D4—2441no—
523C2×D4C4×#692311yescharacteristic
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—611no—
527C22×C4—611no—
528C22×C4—611no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—611no—
532C22×C4—611no—
533C22×C4—611no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—611no—
538C22×C4—611no—
539C22×C4—614no—
540C22×C4—1221no—
541C22×C4—1222no—
542C22×C4—1221no—
543C22×C4—1222no—
544C22×C4—1221no—
545C22×C4—1222no—
546C22×C4—1222no—
547C22×C4—1222no—
548C22×C4—1222no—
549C22×C4—1222no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—1222no—
553C22×C4—2441no—
554C22×C4—2441no—
555C22×C4—2441no—
556C22×C4—2441no—
557C22×C4—2444no—
558C22×C4—2444no—
559C22×C4—2444no—
560C22×C4C22×#692311yescharacteristic
561M16—21no—
562M16—21no—
563M16—1222no—
564M16—1222no—
565M16—1221no—
566M16—1221no—
567M16—2441no—
568M16—2441no—
569M16—2441no—
570M16—2441no—
571C2×C8—21no—
572C2×C8—1222no—
573C2×C8—1221no—
574C2×C8—2441no—
575C2×C8—2441no—
576C2×C8—2441no—
577C2×C8—2441no—
578C4⋊C4—1222no—
579C4⋊C4—1222no—
580C22⋊C4—2448no—
581C22⋊C4—2441no—
582C22⋊C4—2441no—
583C42—21no—
584C42—614no—
585C42—612no—
586C42—1222no—
587C42—1222no—
588C42—1222no—
589C42—1222no—
590C42—1222no—
591C42—1222no—
592C42—1222no—
593C42—1222no—
594C42—1222no—
595C42—1221no—
596C42—2441no—
597C42—2441no—
598C42C22⋊#692312yescomplemented
599C23—21no—
600C23—611no—
601C23—611no—
602C23—611no—
603C23—611no—
604C23—611no—
605C23—611no—
606C23—1224no—
607C23—1221no—
608C23—2444no—
609C23—2441no—
610C23—2441no—
611C23D4×#692311yescharacteristic
612Q8—21no—
613Q8—21no—
614Q8—1221no—
615Q8—1221no—
616Q8—2441no—
617Q8—2441no—
618D4—21no—
619D4—21no—
620D4—41no—
621D4—41no—
622D4—1221no—
623D4—1221no—
624D4—2441no—
625D4—2441no—
626D4—2441no—
627D4—2441no—
628D4—2441no—
629D4—2441no—
630D4—2441no—
631D4—2441no—
632C2×C4—22no—
633C2×C4—21no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—611no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—611no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—611no—
644C2×C4—611no—
645C2×C4—611no—
646C2×C4—611no—
647C2×C4—611no—
648C2×C4—611no—
649C2×C4—611no—
650C2×C4—611no—
651C2×C4—611no—
652C2×C4—611no—
653C2×C4—611no—
654C2×C4—611no—
655C2×C4—611no—
656C2×C4—611no—
657C2×C4—611no—
658C2×C4—611no—
659C2×C4—1224no—
660C2×C4—1224no—
661C2×C4—1224no—
662C2×C4—1224no—
663C2×C4—1222no—
664C2×C4—1221no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4—2444no—
670C2×C4—2444no—
671C2×C4—2441no—
672C2×C4—2441no—
673C2×C4—2442no—
674C2×C4—2444no—
675C2×C4—2442no—
676C2×C4—2444no—
677C2×C4—2444no—
678C2×C4—2444no—
679C2×C4—2444no—
680C2×C4—2444no—
681C2×C4—2441no—
682C2×C4—2441no—
683C2×C4C2×C4×#692311yescharacteristic
684C2×C4C2×C22⋊#692311yescharacteristic
685C2×C4#1451985611yescharacteristic
686C2×C4D4×#692311yescharacteristic
687C2×C4D4×#692311yescharacteristic
688C2×C4D4×#692311yescharacteristic
689C8—41no—
690C8—2442no—
691C8—2441no—
692C22—22no—
693C22—41no—
694C22—42no—
695C22—611no—
696C22—611no—
697C22—614no—
698C22—611no—
699C22—611no—
700C22—1222no—
701C22—1222no—
702C22—1222no—
703C22—1222no—
704C22—1222no—
705C22—4882no—
706C22—4882no—
707C22—2441no—
708C22—2442no—
709C22C22⋊C4×#692311yescharacteristic
710C22#1684071011yescharacteristic
711C22#1684071211yescharacteristic
712C4—42no—
713C4—41no—
714C4—611no—
715C4—611no—
716C4—611no—
717C4—611no—
718C4—4882no—
719C4—2442no—
720C4—2444no—
721C4—2444no—
722C4—2441no—
723C4C4×C22⋊#692311yescharacteristic
724C4C22⋊C4×#692311yescharacteristic
725C4#1684071211yescharacteristic
726C4#1684071411yescharacteristic
727C2—21no—
728C2—21no—
729C2—81no—
730C2—612no—
731C2—612no—
732C2—1221no—
733C2—1221no—
734C2—4881no—
735C2#2146100011yescharacteristic
736C2#2146158412yes—
subgroupG/H
centerC2×C4D4×#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC2×#104×C61C4
socleC22×C61C4×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC22×C4×D61C23
hypercenterC2×#104#6923
hypocenterC61#10924
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
3. C2×#16840698C2semidirect
4. C2×#16840634C2semidirect
5. C2×#16840633C2semidirect
6. #21461481C2semidirect
12. C2×#14519842C4semidirect
15. C2×#14519841C4semidirect
16. (C2×#6923)⋊Q8C4semidirect
17. #16840714C4semidirect
29. C2×#14519705C4semidirect
30. C2×#14519704C4semidirect
31. C2×#14519703C4semidirect
34. C2×#104×C61C4semidirect
209. C4×#6923C22⋊C4semidirect
218. C42×C61C22⋊C4semidirect
222. C4×Dic61C22⋊C4semidirect
392. C2×#104#6923semidirect
403. C61#10924semidirect
598. C42C22⋊#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1042
#214622802
C2×#168406982
C2×#168406342
C2×#168406332
#214614812
C2×#104×D612
#1092461