Finite Group Databasebeta

← #30610448

Subgroups — #30610448

Order 15616.

1332 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462496C211yesmaximal, characteristic, complemented
2C4×D61⋊M16C211yesmaximal, characteristic, complemented
3#21461161C212yesmaximal, complemented
4#21461160C212yesmaximal, complemented
5#21461157C214yesmaximal, complemented
6#21461113C214yesmaximal, complemented
7C2×C4×#11758226C211yesmaximal, characteristic
8C2×D61⋊M16—21no—
9#16840784—21no—
10#16840783C2212yes—
11#16840781C2212yescomplemented
12#16840778—21no—
13#16840766C2212yescomplemented
14#16840733—21no—
15C4×#11758213—21no—
16C4×#11758213—21no—
17C4×#11758213C2212yescomplemented
18C4×#11758217—21no—
19C4×#11758217C2212yes—
20#16840721—21no—
21C4×D61⋊C8C2212yescomplemented
22Q8⋊#92420C2218yescomplemented
23#16840610C2218yescomplemented
24C22×#11758226C411yescharacteristic
25C4×#11758226—21no—
26C4×#11758226—21no—
27C4×#11758226—21no—
28C4×#11758226—21no—
29C4×#11758226C412yes—
30C4×#11758226C412yes—
31C4×#11758226C2212yes—
32C4×#11758226C2212yes—
33C2×Q8×Dic61C2211yescharacteristic
34C2×C4×D244—21no—
35C2×C4×D244C411yescharacteristic
36C2×#14519739—21no—
37C2×#14519739C2211yescharacteristic
38C2×#14519735—21no—
39C2×#14519735C411yescharacteristic
40C2×C42×D61—21no—
41C2×C42×D61C2211yescharacteristic
42C2×C4×Q8×C61C411yescharacteristic
43C2×#11758213—22no—
44C2×#11758213—22no—
45D61⋊M16—28no—
46C2×#11758217—22no—
47C2×D61⋊C8—22no—
48C4⋊#92420—22no—
49C4⋊#92420C2314yes—
50#14519834—22no—
51C22⋊#92420—22no—
52#14519832—22no—
53#14519832—22no—
54#14519832—22no—
55C4×#92420—22no—
56C4×#92420—22no—
57C4×#92420C2314yes—
58C2×#11758226—28no—
59C2×#11758226—21no—
60C2×#11758226—21no—
61C2×#11758226C2×C412yes—
62C2×#11758226C2×C412yes—
63C22×D244—21no—
64C22×D244C2×C411yescharacteristic
65C22×C4×D61—21no—
66C22×C4×D61—21no—
67C22×C4×D61—21no—
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61D411yescharacteristic
70C22×C4×D61D411yescharacteristic
71Q8×Dic61—21no—
72Q8×Dic61—21no—
73Q8×Dic61C2×C412yes—
74Q8×Dic61C2312yes—
75C4×D244—22no—
76C4×D244—22no—
77C4×D244—22no—
78C4×D244—22no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244C2×C412yes—
82C4×D244C2×C412yes—
83#14519739—22no—
84#14519739—22no—
85#14519739—22no—
86#14519739—22no—
87#14519739—21no—
88#14519739—21no—
89#14519739C2×C412yes—
90#14519739C2312yes—
91#14519735—21no—
92#14519735—21no—
93#14519735—22no—
94#14519735—22no—
95#14519735—22no—
96#14519735—22no—
97#14519735C2×C412yes—
98#14519735C2×C412yes—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2×C411yescharacteristic
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198—21no—
104C2×C4×Dic61—21no—
105C2×C4×Dic61—21no—
106C2×C4×Dic61D411yescharacteristic
107C2×C4×Dic61D411yescharacteristic
108C2×C4×Dic61C2311yescharacteristic
109C42×D61—22no—
110C42×D61—22no—
111C42×D61—22no—
112C42×D61—22no—
113C42×D61C2×C411yescharacteristic
114C42×D61C2×C411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61D411yescharacteristic
118C42×D61D411yescharacteristic
119C42×D61C2311yescharacteristic
120C42×D61C2311yescharacteristic
121C22×Q8×C61C2×C411yescharacteristic
122C4×Q8×C61—21no—
123C4×Q8×C61—21no—
124C4×Q8×C61C2×C412yes—
125C4×Q8×C61C2×C412yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C42×C61—21no—
129C2×C42×C61C2×C411yescharacteristic
130C23×D61—21no—
131C23×D61C22⋊C411yescharacteristic
132C2×Q8×C61—24no—
133C2×Q8×C61—21no—
134C2×Q8×C61C22×C412yes—
135C22×C4×C61—21no—
136C22×C4×C61—21no—
137C22×C4×C61C22⋊C411yescharacteristic
138C22×C4×C61C22⋊C411yescharacteristic
139C22×C4×C61C22×C411yescharacteristic
140C22×Dic61—21no—
141C22×Dic61C22⋊C411yescharacteristic
142C22×Dic61C2×D411yescharacteristic
143C22×Dic61C2×D411yescharacteristic
144#11758226—28no—
145#11758226—28no—
146#11758226—24no—
147#11758226—24no—
148#11758226—24no—
149#11758226M1618yescomplemented
150C2×D244—28no—
151C2×D244—22no—
152C2×D244—22no—
153C2×D244—21no—
154C2×D244—24no—
155C2×D244C22×C412yes—
156C2×C4×D61—28no—
157C2×C4×D61—24no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—24no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—22no—
164C2×C4×D61—22no—
165C2×C4×D61—42no—
166C2×C4×D61—44no—
167C2×C4×D61—44no—
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22⋊C411yescharacteristic
170C2×C4×D61C22⋊C411yescharacteristic
171C2×C4×D61C22⋊C411yescharacteristic
172C2×C4×D61C22⋊C411yescharacteristic
173C2×C4×D61C22⋊C411yescharacteristic
174C2×C4×D61C22×C411yescharacteristic
175C2×C4×D61C22×C411yescharacteristic
176C2×C4×D61C2×D411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180#11758217—28no—
181C2×#92420—24no—
182C2×#92420—24no—
183#11758213—28no—
184#11758213—44no—
185D61⋊C8—28no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61—22no—
188C4⋊C4×C61—21no—
189C4⋊C4×C61C22×C412yes—
190C42×C61—22no—
191C42×C61—22no—
192C42×C61C22⋊C411yescharacteristic
193C42×C61C22⋊C411yescharacteristic
194C42×C61C22×C411yescharacteristic
195C42×C61C22×C411yescharacteristic
196#11758198—22no—
197#11758198—22no—
198#11758198—22no—
199#11758198—22no—
200#11758198—22no—
201#11758198—22no—
202C4⋊Dic61—21no—
203C4⋊Dic61—22no—
204C4⋊Dic61—22no—
205C4⋊Dic61C22×C412yes—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61—22no—
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2411yescharacteristic
222C23×C61C2×C22⋊C411yescharacteristic
223C22×D61—24no—
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—22no—
227C22×D61—41no—
228C22×D61—42no—
229C22×D61—42no—
230C22×D61C2×C22⋊C411yescharacteristic
231C22×D61C2×C22⋊C411yescharacteristic
232Q8×C61—24no—
233Q8×C61—22no—
234Q8×C61C2×M1614yescomplemented
235C2×C4×C61—24no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—41no—
240C2×C4×C61—42no—
241C2×C4×C61#10414yes—
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61C2×C22⋊C411yescharacteristic
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C23×C411yescharacteristic
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—42no—
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C22×D411yescharacteristic
258C2×Dic61C22×D411yescharacteristic
259D244—28no—
260D244—24no—
261D244—28no—
262D244—22no—
263D244C2×M1614yescomplemented
264C4×D61—28no—
265C4×D61—22no—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—28no—
274C4×D61—22no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—44no—
278C4×D61—44no—
279C4×D61—44no—
280C4×D61—44no—
281C4×D61C2×M1614yes—
282#92420—28no—
283#92420—44no—
284#17447—611nomaximal, Sylow
285C22×C61—21no—
286C22×C61—21no—
287C22×C61C2×#10412yes—
288C22×C61C22×C22⋊C411yescharacteristic
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—24no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—44no—
296C2×D61—48no—
297C2×D61—42no—
298C2×D61—42no—
299C2×D61#40712yes—
300C4×C61—24no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—42no—
305C4×C61C2×#10412yes—
306C4×C61C2×#10412yes—
307C4×C61C22×M1612yes—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—42no—
313Dic61#40712yes—
314Dic61#57512yes—
315C2×C4×#41—611no—
316#2920—611no—
317C2×C4×M16—611no—
318#1491—612no—
319#1490—612no—
320#1489—614no—
321#1476—614no—
322C2×C61—22no—
323C2×C61C2×#40711yescharacteristic
324C2×C61#289611yescharacteristic
325C2×C61C22×#10411yescharacteristic
326D61—22no—
327D61—41no—
328D61—44no—
329C22×#41—611no—
330C22×M16—1221no—
331C4×#41—612no—
332C4×#41—612no—
333C4×#41—612no—
334C4×#41—612no—
335C4×#41—1221no—
336C4×#41—1221no—
337C4×#41—1221no—
338C4×#41—1221no—
339C2×C4×Q8—611no—
340C2×C4×Q8#692311yescharacteristic
341C2×C4×D4—611no—
342C2×C4×D4—611no—
343C2×C4×D4—1221no—
344C2×C4×D4—1221no—
345C2×#117—611no—
346C2×#117—1221no—
347C22×C42—611no—
348C22×C42—1221no—
349#432—612no—
350#432—1221no—
351#431—612no—
352#431—1221no—
353#423—612no—
354#407—1221no—
355C4×M16—612no—
356C4×M16—612no—
357C4×M16—1221no—
358C4×M16—1221no—
359C4×M16—1221no—
360C2×#97—1221no—
361C2×C4×C8—612no—
362Q8⋊C8—618no—
363D4⋊C8—618no—
364C61#1744711yescharacteristic, complemented, Sylow
365C2×#41—612no—
366C2×#41—612no—
367C2×#41—1221no—
368C2×#41—1221no—
369C2×#41—1228no—
370C22×Q8C2×#692311yescharacteristic
371C22×D4—611no—
372C22×D4—1221no—
373C23×C4—611no—
374C23×C4—611no—
375C23×C4—611no—
376C23×C4—1221no—
377C23×C4—1221no—
378C23×C4—1221no—
379C2×M16—1222no—
380C2×M16—1222no—
381C2×M16—1228no—
382C2×M16—1222no—
383C22×C8—1222no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—612no—
387C4×Q8—612no—
388C4×Q8—1221no—
389C4×Q8—1221no—
390C4×Q8C2×#692312yes—
391C4×Q8C2×#692312yes—
392C4×D4—612no—
393C4×D4—612no—
394C4×D4—612no—
395C4×D4—612no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1221no—
401C4×D4—1221no—
402C4×D4—1222no—
403C4×D4—1222no—
404C4×D4—1222no—
405C4×D4—1222no—
406C4×D4—1221no—
407C4×D4—1221no—
408#117—612no—
409#117—612no—
410#117—1222no—
411#117—1222no—
412#117—1222no—
413#117—1222no—
414#117—1221no—
415#117—1221no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—611no—
418C2×C4⋊C4—1221no—
419C2×C4⋊C4C2×#692311yescharacteristic
420C2×C22⋊C4—1221no—
421C2×C22⋊C4—1221no—
422C2×C22⋊C4—1221no—
423C2×C42—21no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—1222no—
436C2×C42—1222no—
437C2×C42—1222no—
438C2×C42—1222no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42C2×#692311yescharacteristic
442C4⋊C8—614no—
443C4⋊C8—1222no—
444C22⋊C8—1222no—
445C22⋊C8—1222no—
446#97—1222no—
447#97—1222no—
448#97—1222no—
449C4×C8—614no—
450C4×C8—1222no—
451C4×C8—1222no—
452C24—611no—
453C24—1221no—
454#41—618no—
455#41—1224no—
456#41—1224no—
457#41—1228no—
458#41—1228no—
459#41—1224no—
460C2×Q8—24no—
461C2×Q8—21no—
462C2×Q8C22×#692312yes—
463C2×D4—612no—
464C2×D4—1224no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1228no—
468C2×D4—1221no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—611no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—611no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—1222no—
487C22×C4—1222no—
488C22×C4—1224no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1228no—
492C22×C4—1224no—
493C22×C4—1221no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—2442no—
497C22×C4—2444no—
498C22×C4—2444no—
499C22×C4C22⋊#692311yescharacteristic
500C22×C4C22⋊#692311yescharacteristic
501C22×C4C22×#692311yescharacteristic
502M16—1228no—
503M16—1228no—
504M16—2444no—
505C2×C8—1224no—
506C2×C8—1228no—
507C2×C8—1224no—
508C4⋊C4—22no—
509C4⋊C4—22no—
510C4⋊C4—21no—
511C4⋊C4—612no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1221no—
515C4⋊C4C22×#692312yes—
516C22⋊C4—1222no—
517C22⋊C4—1222no—
518C22⋊C4—1222no—
519C22⋊C4—1222no—
520C22⋊C4—1222no—
521C22⋊C4—1222no—
522C42—22no—
523C42—22no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—1222no—
537C42—1222no—
538C42—1222no—
539C42—1222no—
540C42C22⋊#692311yescharacteristic
541C42C22⋊#692311yescharacteristic
542C42C22×#692311yescharacteristic
543C42C22×#692311yescharacteristic
544C23—611no—
545C23—611no—
546C23—1222no—
547C23—1224no—
548C23—1222no—
549C23—1222no—
550C23—2441no—
551C23—2442no—
552C23—2442no—
553C23C2×C22⋊#692311yescharacteristic
554Q8—24no—
555Q8—22no—
556Q8D61⋊M1614yescomplemented
557D4—614no—
558D4—1228no—
559D4—1228no—
560D4—1224no—
561D4—1222no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—41no—
567C2×C4—42no—
568C2×C4—611no—
569C2×C4—611no—
570C2×C4—614no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1228no—
579C2×C4—1222no—
580C2×C4—1228no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1222no—
584C2×C4—1222no—
585C2×C4—1222no—
586C2×C4—1222no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—1222no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2444no—
593C2×C4—2444no—
594C2×C4—2442no—
595C2×C4—2444no—
596C2×C4—2444no—
597C2×C4#1451984214yes—
598C2×C4C2×C22⋊#692311yescharacteristic
599C2×C4C2×C22⋊#692311yescharacteristic
600C2×C4C2×C22⋊#692311yescharacteristic
601C2×C4C2×C22⋊#692311yescharacteristic
602C2×C4C2×C22⋊#692311yescharacteristic
603C2×C4C23×#692311yescharacteristic
604C8—1228no—
605C8—2444no—
606C22—21no—
607C22—21no—
608C22—612no—
609C22—1221no—
610C22—1221no—
611C22—1224no—
612C22—1221no—
613C22—1221no—
614C22—1221no—
615C22—2444no—
616C22—2448no—
617C22—2442no—
618C22—2442no—
619C22C2×#1451984212yes—
620C22C22×C22⋊#692311yescharacteristic
621C4—24no—
622C4—21no—
623C4—21no—
624C4—21no—
625C4—42no—
626C4—612no—
627C4—612no—
628C4—1221no—
629C4—1221no—
630C4—1221no—
631C4—1221no—
632C4—2442no—
633C4C2×#1451984212yes—
634C4C2×#1451984212yes—
635C4C2×D61⋊M1612yes—
636C2—22no—
637C2—1222no—
638C2—2441no—
639C2—2444no—
640C2D61⋊#40711yescharacteristic
641C2#2146243911yescharacteristic
642C2C22×#1451984211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×C4×Q8×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758226C4
cosocleC4×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#17447
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. #21462496C2semidirect
2. C4×D61⋊M16C2semidirect
3. #21461161C2semidirect
4. #21461160C2semidirect
5. #21461157C2semidirect
6. #21461113C2semidirect
11. #16840781C22semidirect
13. #16840766C22semidirect
17. C4×#11758213C22semidirect
21. C4×D61⋊C8C22semidirect
22. Q8⋊#92420C22semidirect
23. #16840610C22semidirect
149. #11758226M16semidirect
234. Q8×C61C2×M16semidirect
263. D244C2×M16semidirect
364. C61#17447semidirect
556. Q8D61⋊M16semidirect

Maximal subgroups

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

subgroupindex
#214624962
C4×D61⋊M162
#214611612
#214611602
#214611572
#214611132
C2×C4×#117582262
#1744761