Finite Group Databasebeta

← #30614112

Subgroups — #30614112

Order 15616.

1662 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D61⋊#104C212yesmaximal
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3C2×#16840698C211yesmaximal, characteristic, complemented
4#21461583C214yesmaximal, complemented
5#21461582C214yesmaximal, complemented
6#21461495C212yesmaximal, complemented
7C4×#41×D61C211yesmaximal, characteristic
8C2×D61⋊M16C2212yes—
9C22×C4×#6923C2212yes—
10C2×#14519842C2214yes—
11D61⋊#104C4116yescomplemented
12C2×#14519841C2214yes—
13C4×#11758213C2214yescomplemented
14C4×#11758217—22no—
15#16840721—21no—
16C4×D61⋊C8—21no—
17#16840698—21no—
18#16840698—21no—
19#16840698C2214yescomplemented
20C2×(C2×#6923)⋊C4—22no—
21#16840632C2218yescomplemented
22C2×#41×D61C2211yescharacteristic
23#41×Dic61C411yescharacteristic, complemented
24C4×#11758226C2212yes—
25C4×#11758222—21no—
26C4×#11758222C411yescharacteristic, complemented
27#16840230—21no—
28#16840230C411yescharacteristic, complemented
29C4×#11758224—22no—
30C4×#11758224C2212yes—
31C4×Q8×D61C412yescomplemented
32C4×D4×D61—22no—
33C4×D4×D61C412yescomplemented
34#117×D61—21no—
35#117×D61C2211yescharacteristic
36C2×C42×D61—21no—
37C2×C42×D61C2211yescharacteristic
38C4×#41×C61C411yescharacteristic, complemented
39C23×#6923—22no—
40C2×#11758213C2314yes—
41D61⋊M16—24no—
42D61⋊M16C2×C418yescomplemented
43C2×#11758217—22no—
44C2×D61⋊C8—22no—
45C2×C4×#6923—22no—
46C2×C4×#6923—24no—
47C2×C4×#6923C2×C418yescomplemented
48C2×C4×#6923C2314yes—
49#14519842C2×C4116yescomplemented
50#14519841C2×C4116yescomplemented
51#14519832—24no—
52C4×#92420—24no—
53(C2×#6923)⋊C4—24no—
54(C2×#6923)⋊C4—24no—
55C2×#11758226C2311yescharacteristic
56C2×#11758222—21no—
57C2×#11758222C2×C411yescharacteristic
58C2×#11758224—21no—
59C2×#11758224C2311yescharacteristic
60#41×D61—24no—
61#41×D61C2×C418yes—
62C2×Q8×D61C2×C411yescharacteristic
63C2×D4×D61—21no—
64C2×D4×D61C2×C411yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—22no—
67C22×C4×D61D412yes—
68C22×C4×D61C2311yescharacteristic
69Q8×Dic61C2×C412yescomplemented
70C4×Dic122—22no—
71C4×Dic122C2×C412yescomplemented
72#14519742—22no—
73#14519742C2×C412yescomplemented
74C4×D244—22no—
75C4×D244C2×C412yescomplemented
76D4×Dic61—22no—
77D4×Dic61C2×C412yescomplemented
78#14519739—22no—
79#14519739C2×C412yescomplemented
80C4×C22⋊D61—22no—
81C4×C22⋊D61—22no—
82C4×C22⋊D61—22no—
83#14519737—22no—
84#14519737—22no—
85#14519737—22no—
86#14519736—21no—
87#14519736C2×C411yescharacteristic
88#14519735—22no—
89#14519735C2312yes—
90#14519734—21no—
91#14519734—21no—
92#14519734—21no—
93#14519733—21no—
94#14519733—22no—
95C4⋊C4×D61—22no—
96C4⋊C4×D61C2×C412yes—
97C22⋊C4×D61—21no—
98C22⋊C4×D61—22no—
99C2×C4×Dic61—21no—
100C2×C4×Dic61—22no—
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D412yes—
103C42×D61—22no—
104C42×D61—21no—
105C42×D61—21no—
106C42×D61—21no—
107C42×D61—22no—
108C42×D61C2×C412yes—
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61C2312yes—
114C2×#41×C61C2×C411yescharacteristic
115C4×Q8×C61C2×C412yescomplemented
116C4×D4×C61—22no—
117C4×D4×C61C2×C412yescomplemented
118#117×C61—21no—
119#117×C61C2×C411yescharacteristic
120C2×C42×C61—21no—
121C2×C42×C61C2×C411yescharacteristic
122C23×D61—21no—
123C23×D61C2×D411yescharacteristic
124C22×#6923—28no—
125C22×#6923—24no—
126C22×#6923—48no—
127#41×C61—22no—
128#41×C61C4214yes—
129C2×Q8×C61C22×C411yescharacteristic
130C2×D4×C61—21no—
131C2×D4×C61C22×C411yescharacteristic
132C22×C4×C61—21no—
133C22×C4×C61—22no—
134C22×C4×C61C22⋊C412yes—
135C22×C4×C61C22×C411yescharacteristic
136C2×C22⋊D61—21no—
137C2×C22⋊D61—21no—
138C2×C22⋊D61—21no—
139C22×Dic61—21no—
140C22×Dic61—22no—
141C22×Dic61C22⋊C412yes—
142C22×Dic61C2×D411yescharacteristic
143#11758226—22no—
144#11758226C22×C414yes—
145Q8×D61—22no—
146Q8×D61C4214yes—
147#11758224—28no—
148#11758224—22no—
149#11758224C22×C414yes—
150D4×D61—28no—
151D4×D61—22no—
152D4×D61C4214yes—
153#11758222—22no—
154#11758222—28no—
155#11758222C4214yes—
156C2×D244—21no—
157C2×D244C22×C411yescharacteristic
158C2×C4×D61—21no—
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—28no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—44no—
166C2×C4×D61—48no—
167C2×C4×D61C22⋊C412yes—
168C2×C4×D61C22⋊C412yes—
169C2×C4×D61C22×C411yescharacteristic
170C2×C4×D61C22×C414yes—
171C2×C4×D61C2×D412yes—
172C2×C4×D61C2×D412yes—
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×C4×D61#4114yes—
176C2×C4×D61C2411yescharacteristic
177C2×Dic122—21no—
178C2×Dic122C22×C411yescharacteristic
179#11758217—28no—
180C2×#92420—24no—
181C4×#6923—28no—
182C4×#6923—24no—
183C4×#6923C22×C418yescomplemented
184#11758213—24no—
185#11758213C22×C418yescomplemented
186D61⋊C8—28no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61C22×C412yes—
189C22⋊C4×C61—21no—
190C22⋊C4×C61—22no—
191C42×C61—21no—
192C42×C61—22no—
193C42×C61C22⋊C411yescharacteristic
194C42×C61C22⋊C411yescharacteristic
195C42×C61C22×C412yes—
196C22⋊Dic61—21no—
197C22⋊Dic61—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—21no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61—22no—
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C412yes—
213C4×Dic61C22⋊C412yes—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C412yes—
216C4×Dic61C2×D412yes—
217C4×Dic61C2×D412yes—
218C23×C61—21no—
219C23×C61C2×C22⋊C411yescharacteristic
220C22×D61—24no—
221C22×D61—21no—
222C22×D61—24no—
223C22×D61—44no—
224C22×D61C2×C22⋊C411yescharacteristic
225C22×D61C4×D414yes—
226C22×D61C22×D411yescharacteristic
227C2×#6923—28no—
228C2×#6923—48no—
229C2×#6923—416no—
230Q8×C61—21no—
231Q8×C61C2×C4212yes—
232D4×C61—24no—
233D4×C61—21no—
234D4×C61C2×C4212yes—
235C2×C4×C61—21no—
236C2×C4×C61—24no—
237C2×C4×C61—22no—
238C2×C4×C61—42no—
239C2×C4×C61—44no—
240C2×C4×C61C2×C4212yes—
241C2×C4×C61C2×C22⋊C412yes—
242C2×C4×C61C2×C22⋊C412yes—
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61#11712yes—
245C2×C4×C61C23×C411yescharacteristic
246C22⋊D61—24no—
247C22⋊D61—24no—
248C22⋊D61—24no—
249C2×Dic61—21no—
250C2×Dic61—24no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61—44no—
254C2×Dic61C2×C22⋊C412yes—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C4×D414yes—
258C2×Dic61C22×D411yescharacteristic
259D244—24no—
260D244—21no—
261D244C2×C4212yes—
262C4×D61—24no—
263C4×D61—24no—
264C4×D61—24no—
265C4×D61—24no—
266C4×D61—24no—
267C4×D61—42no—
268C4×D61—42no—
269C4×D61—44no—
270C4×D61—44no—
271C4×D61—44no—
272C4×D61C2×C4212yes—
273C4×D61#11712yes—
274C4×D61C4×D414yes—
275C4×D61C4×D414yes—
276C4×D61C23×C412yes—
277C4×D61C2×#4112yes—
278Dic122—21no—
279Dic122—24no—
280Dic122C2×C4212yes—
281#92420—28no—
282C2×#1759—611nomaximal, Sylow
283C22×C61—22no—
284C22×C61—22no—
285C22×C61—42no—
286C22×C61C4×C22⋊C412yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C2×D61—22no—
289C2×D61—28no—
290C2×D61—22no—
291C2×D61—42no—
292C2×D61—48no—
293C2×D61C4×C22⋊C412yes—
294C2×D61#42114yes—
295C2×D61C2×C4×D412yes—
296#6923—48no—
297C4×C61—22no—
298C4×C61—22no—
299C4×C61—22no—
300C4×C61—42no—
301C4×C61C4×C22⋊C412yes—
302C4×C61C22×C4211yescharacteristic
303C4×C61C2×#11711yescharacteristic
304Dic61—22no—
305Dic61—22no—
306Dic61—22no—
307Dic61—42no—
308Dic61C4×C22⋊C412yes—
309Dic61C2×C4×D412yes—
310C2×C4×#41—611no—
311C22×#104—612no—
312C2×C4×M16—611no—
313C2×#376—611no—
314#1759—614no—
315#1759—614no—
316C2×#339—612no—
317C2×C61—22no—
318C2×C61—42no—
319C2×C61C2×C4×C22⋊C411yescharacteristic
320C2×C61C2×#42112yes—
321D61—22no—
322D61—42no—
323D61#175914yescomplemented
324C22×#41—611no—
325C22×M16—612no—
326C4×#41—611no—
327C4×#41—612no—
328C4×#41—612no—
329C4×#41—611no—
330C4×#41—611no—
331C4×#41—1221no—
332C4×#41—1221no—
333C4×#41—1222no—
334C4×#41#692311yescharacteristic, complemented
335C2×C4×Q8—612no—
336C2×C4×D4—612no—
337C2×C4×D4—1222no—
338C2×#117—611no—
339C2×#117—1221no—
340C22×C42—611no—
341C22×C42—612no—
342C22×C42—1221no—
343C2×#104—614no—
344C2×#104—6116no—
345C2×#104—614no—
346C4×M16—614no—
347C4×M16—1222no—
348C2×#97—1221no—
349C2×C4×C8—1221no—
350#376—614no—
351#376—1221no—
352#376—1221no—
353C2×#95—1222no—
354#339—618no—
355C61C2×#175911yescharacteristic, complemented, Sylow
356C2×#41—618no—
357C2×#41—611no—
358C2×#41—611no—
359C2×#41—611no—
360C2×#41—1221no—
361C2×#41—1221no—
362C2×#41—1224no—
363C2×#41C2×#692311yescharacteristic
364C22×Q8—611no—
365C22×D4—611no—
366C22×D4—1221no—
367C23×C4—611no—
368C23×C4—612no—
369C23×C4—1221no—
370C23×C4—1222no—
371C23×C4—1222no—
372C2×M16—618no—
373C2×M16—614no—
374C2×M16—1222no—
375C2×M16—1224no—
376C22×C8—1222no—
377C4×Q8—612no—
378C4×Q8—612no—
379C4×Q8—612no—
380C4×Q8—1222no—
381C4×Q8—1222no—
382C4×Q8C2×#692312yescomplemented
383C4×D4—22no—
384C4×D4—612no—
385C4×D4—612no—
386C4×D4—612no—
387C4×D4—1222no—
388C4×D4—1222no—
389C4×D4—1222no—
390C4×D4—1222no—
391C4×D4—1222no—
392C4×D4—1222no—
393C4×D4—1222no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4C2×#692312yescomplemented
397#117—21no—
398#117—611no—
399#117—612no—
400#117—1221no—
401#117—1221no—
402#117—1222no—
403#117—1222no—
404#117—1221no—
405#117—1221no—
406#117—1221no—
407#117C2×#692311yescharacteristic
408C2×C4⋊C4—612no—
409C2×C4⋊C4—1222no—
410C2×C22⋊C4—1222no—
411C2×C22⋊C4—1221no—
412C2×C42—21no—
413C2×C42—612no—
414C2×C42—611no—
415C2×C42—611no—
416C2×C42—611no—
417C2×C42—611no—
418C2×C42—611no—
419C2×C42—612no—
420C2×C42—612no—
421C2×C42—618no—
422C2×C42—614no—
423C2×C42—1222no—
424C2×C42—1221no—
425C2×C42—1221no—
426C2×C42—1222no—
427C2×C42—1222no—
428C2×C42—1221no—
429C2×C42—1222no—
430C2×C42—1224no—
431C2×C42—1221no—
432C2×C42C2×#692311yescharacteristic
433#104—6116no—
434#104—6116no—
435#97—1224no—
436C4×C8—1224no—
437#95—1224no—
438#95—1224no—
439C24—611no—
440C24—1221no—
441#41—22no—
442#41—614no—
443#41—614no—
444#41—614no—
445#41—1228no—
446#41—1228no—
447#41—1222no—
448#41—1222no—
449#41—1222no—
450#41C4×#692314yes—
451C2×Q8—614no—
452C2×Q8—611no—
453C2×Q8—1221no—
454C2×Q8—1222no—
455C2×Q8C22×#692311yescharacteristic
456C2×D4—21no—
457C2×D4—614no—
458C2×D4—611no—
459C2×D4—1221no—
460C2×D4—1222no—
461C2×D4—1221no—
462C2×D4—1228no—
463C2×D4—1221no—
464C2×D4—1221no—
465C2×D4C22×#692311yescharacteristic
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—611no—
469C22×C4—614no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—614no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—612no—
479C22×C4—612no—
480C22×C4—1221no—
481C22×C4—1228no—
482C22×C4—1222no—
483C22×C4—1221no—
484C22×C4—1222no—
485C22×C4—1221no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1224no—
489C22×C4—1228no—
490C22×C4—1222no—
491C22×C4—2444no—
492C22×C4—2448no—
493C22×C4—2448no—
494C22×C4C22⋊#692312yes—
495C22×C4C22×#692311yescharacteristic
496M16—618no—
497M16—1224no—
498M16—1228no—
499C2×C8—1224no—
500C2×C8—1228no—
501C4⋊C4—22no—
502C4⋊C4—612no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4C22×#692312yes—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1221no—
514C22⋊C4—1222no—
515C42—22no—
516C42—21no—
517C42—612no—
518C42—612no—
519C42—612no—
520C42—612no—
521C42—611no—
522C42—611no—
523C42—612no—
524C42—618no—
525C42—1222no—
526C42—1222no—
527C42—1222no—
528C42—1224no—
529C42—1228no—
530C42—1222no—
531C42—1221no—
532C42C22⋊#692311yescharacteristic
533C42C22⋊#692311yescharacteristic
534C42C22×#692312yes—
535C23—21no—
536C23—611no—
537C23—611no—
538C23—614no—
539C23—1224no—
540C23—1224no—
541C23—1221no—
542C23—2444no—
543C23C2×C22⋊#692311yescharacteristic
544Q8—21no—
545Q8—612no—
546Q8—1224no—
547Q8—1221no—
548Q8C2×C4×#692312yes—
549D4—24no—
550D4—21no—
551D4—612no—
552D4—1224no—
553D4—1224no—
554D4—1224no—
555D4—1224no—
556D4—1221no—
557D4C2×C4×#692312yes—
558C2×C4—21no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—42no—
562C2×C4—44no—
563C2×C4—611no—
564C2×C4—611no—
565C2×C4—614no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—614no—
571C2×C4—614no—
572C2×C4—612no—
573C2×C4—612no—
574C2×C4—1224no—
575C2×C4—1224no—
576C2×C4—1224no—
577C2×C4—1224no—
578C2×C4—1224no—
579C2×C4—1221no—
580C2×C4—1224no—
581C2×C4—1228no—
582C2×C4—1222no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4—2444no—
588C2×C4—2442no—
589C2×C4—2444no—
590C2×C4—24416no—
591C2×C4—2448no—
592C2×C4C2×C4×#692312yes—
593C2×C4C2×C22⋊#692312yes—
594C2×C4C2×C22⋊#692312yes—
595C2×C4C2×C22⋊#692311yescharacteristic
596C2×C4#1451985612yes—
597C2×C4C23×#692311yescharacteristic
598C8—1228no—
599C22—22no—
600C22—22no—
601C22—42no—
602C22—614no—
603C22—612no—
604C22—612no—
605C22—1228no—
606C22—1222no—
607C22—1222no—
608C22—2448no—
609C22—2442no—
610C22C4×C22⋊#692312yes—
611C22C22×C22⋊#692311yescharacteristic
612C4—22no—
613C4—22no—
614C4—22no—
615C4—42no—
616C4—612no—
617C4—612no—
618C4—1222no—
619C4—1222no—
620C4—1222no—
621C4—2448no—
622C4—2442no—
623C4C4×C22⋊#692312yes—
624C4C22×C4×#692311yescharacteristic
625C4C2×#1451985611yescharacteristic
626C2—22no—
627C2—42no—
628C2—614no—
629C2—1222no—
630C2—2442no—
631C2C2×C4×C22⋊#692311yescharacteristic
632C2D61⋊#42112yes—
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC4×C61C22×C42
FrattiniC2×C4C23×#6923
FittingC4×#41×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#41×D61C22
cosocleC2×C4×D61C24
hypercenterC4×#41#6923
hypocenterC61C2×#1759
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. C4×D61⋊M16C2semidirect
3. C2×#16840698C2semidirect
4. #21461583C2semidirect
5. #21461582C2semidirect
6. #21461495C2semidirect
11. D61⋊#104C4semidirect
13. C4×#11758213C22semidirect
19. #16840698C22semidirect
21. #16840632C22semidirect
23. #41×Dic61C4semidirect
26. C4×#11758222C4semidirect
28. #16840230C4semidirect
31. C4×Q8×D61C4semidirect
33. C4×D4×D61C4semidirect
38. C4×#41×C61C4semidirect
42. D61⋊M16C2×C4semidirect
47. C2×C4×#6923C2×C4semidirect
49. #14519842C2×C4semidirect
50. #14519841C2×C4semidirect
69. Q8×Dic61C2×C4semidirect
71. C4×Dic122C2×C4semidirect
73. #14519742C2×C4semidirect
75. C4×D244C2×C4semidirect
77. D4×Dic61C2×C4semidirect
79. #14519739C2×C4semidirect
115. C4×Q8×C61C2×C4semidirect
117. C4×D4×C61C2×C4semidirect
183. C4×#6923C22×C4semidirect
185. #11758213C22×C4semidirect
323. D61#1759semidirect
334. C4×#41#6923semidirect
355. C61C2×#1759semidirect
382. C4×Q8C2×#6923semidirect
396. C4×D4C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1042
C4×D61⋊M162
C2×#168406982
#214615832
#214615822
#214614952
C4×#41×D612
C2×#175961