Finite Group Databasebeta

← #29648422

Subgroups — #29648422

Order 15616.

994 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#21459114C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic, complemented
3#431×D61C211yesmaximal, characteristic, complemented
4#21444528C212yesmaximal, complemented
5#21444521C212yesmaximal, complemented
6#21444506C212yesmaximal, complemented
7#21444493C212yesmaximal, complemented
8#21444483C211yesmaximal, characteristic, complemented
9#21444483C211yesmaximal, characteristic, complemented
10#21444481C211yesmaximal, characteristic, complemented
11C61×#1543C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840317C2211yescharacteristic
14#16840317C2211yescharacteristic
15#16840310C2211yescharacteristic
16#16840310C2211yescharacteristic
17#16840294—21no—
18#16840294—21no—
19#16840293—21no—
20#16840293—21no—
21#16840291C412yes—
22#16840291C412yes—
23#16840272—21no—
24#16840272—21no—
25#16840269C412yes—
26#41×Dic61C412yes—
27C4×#11758224—21no—
28C4×#11758224—21no—
29C2×C42×D61C2211yescharacteristic
30#16839818C2212yes—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839815C2211yescharacteristic
34#16839814C2212yes—
35#16839813—21no—
36#16839813—21no—
37#16839812—21no—
38#16839784C2212yes—
39C4⋊C8×D61C2212yes—
40#16839724—21no—
41C22⋊C8×D61—21no—
42C4×#11758189—21no—
43C4×C8×D61—21no—
44#16839511C2212yescomplemented
45#16839509C2212yescomplemented
46#16839509C2212yescomplemented
47#16839507C2212yescomplemented
48#16839507C2212yescomplemented
49#16839506C2212yescomplemented
50C61×#532C2211yescharacteristic
51C61×#431C2211yescharacteristic
52C61×#431C2211yescharacteristic
53C61×#333C2212yescomplemented
54C61×#331C2212yescomplemented
55C2×#11758224—21no—
56C2×#11758224—21no—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C2×#11758189—22no—
61C2×C8×D61—22no—
62#14519777C2311yescharacteristic
63#14519777C2311yescharacteristic
64#14519770—22no—
65#14519770—22no—
66#14519769C2×C412yes—
67#14519768—21no—
68#14519768—21no—
69#14519764—21no—
70#14519764—21no—
71#14519759—22no—
72#14519759—22no—
73#14519758—22no—
74#14519757—21no—
75#14519757—21no—
76#14519756—21no—
77#14519756—21no—
78#14519753C2×C412yes—
79#14519753C2×C412yes—
80#14519748—21no—
81#14519748—21no—
82#14519748C2×C412yes—
83#14519748C2×C412yes—
84#14519745—22no—
85Q8×Dic61C2×C412yes—
86Q8×Dic61C2×C412yes—
87C4×Dic122—21no—
88C4×Dic122—21no—
89#14519742—21no—
90#14519742—21no—
91D4×Dic61—22no—
92D4×Dic61—22no—
93D4×Dic61—21no—
94D4×Dic61—21no—
95D4×Dic61C2×C412yes—
96D4×Dic61C2×C412yes—
97C4×C22⋊D61—22no—
98C4×C22⋊D61—22no—
99#14519737—22no—
100#14519737—22no—
101#14519736—22no—
102#14519736C2×C412yes—
103#14519735—21no—
104#14519735—21no—
105#14519733—22no—
106#14519733—22no—
107C2×C4×Dic61—22no—
108C2×C4×Dic61C2×C411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C2×C4×Dic61D411yescharacteristic
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119C4⋊#92418C2312yes—
120C4⋊#92418C2312yes—
121#14519706—22no—
122#14519706—22no—
123C22⋊#92418—21no—
124C22⋊#92418—21no—
125#14519689—22no—
126#14519689—22no—
127#14519687—22no—
128C4×#92418—21no—
129C4×#92418—21no—
130C8×Dic61—22no—
131C2×#41×C61C2×C412yes—
132C4⋊Q8×C61C2311yescharacteristic
133#127×C61C2311yescharacteristic
134#124×C61C2×C412yes—
135#121×C61—21no—
136#121×C61—21no—
137C4×D4×C61—21no—
138C4×D4×C61—21no—
139C2×C42×C61C2311yescharacteristic
140C4⋊C8×C61C2312yes—
141C4⋊C8×C61C2312yes—
142C22⋊C8×C61—21no—
143C22⋊C8×C61—21no—
144C4×C8×C61—21no—
145C4×C8×C61—21no—
146C23×D61C22⋊C411yescharacteristic
147#41×C61—44no—
148C2×Q8×C61C22×C412yes—
149C2×D4×C61—22no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61C22×C412yes—
153C22×C4×C61—22no—
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D411yescharacteristic
156C22×C4×C61C2×D411yescharacteristic
157C2×C22⋊D61—22no—
158C2×C22⋊D61—22no—
159C22×Dic61—22no—
160C22×Dic61—22no—
161C22×Dic61C22⋊C411yescharacteristic
162C22×Dic61C22⋊C411yescharacteristic
163C22×Dic61C22⋊C411yescharacteristic
164#11758224—44no—
165#11758224—44no—
166C2×C4×D61—24no—
167C2×C4×D61—42no—
168C2×C4×D61—42no—
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×D61C22×C411yescharacteristic
177C2×C4×D61C2×D411yescharacteristic
178C2×C4×D61C2×D411yescharacteristic
179C2×C4×D61C2×D411yescharacteristic
180C2×C4×D61C2×D411yescharacteristic
181C2×Dic122—21no—
182C2×Dic122—21no—
183C2×C8×C61—22no—
184C2×C8×C61—22no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C22⋊C4×C61—22no—
188C22⋊C4×C61—22no—
189C42×C61C22×C411yescharacteristic
190C42×C61C2×D411yescharacteristic
191C42×C61C2×D411yescharacteristic
192C42×C61C2411yescharacteristic
193C22⋊Dic61—22no—
194C22⋊Dic61—22no—
195C22⋊Dic61—22no—
196C22⋊Dic61—22no—
197C22⋊Dic61—22no—
198#11758198—22no—
199#11758198—22no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61—22no—
203C4⋊Dic61—22no—
204C4⋊Dic61C22×C412yes—
205C4⋊Dic61C22×C412yes—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210C4×Dic61—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22×C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C2×#92418—22no—
226C2×#92418—22no—
227#11758189—44no—
228C8×D61—44no—
229C23×C61—22no—
230C23×C61C2×C22⋊C411yescharacteristic
231C22×D61—22no—
232C22×D61—41no—
233C22×D61—41no—
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C411yescharacteristic
236Q8×C61—42no—
237D4×C61—42no—
238D4×C61—44no—
239D4×C61—42no—
240D4×C61—42no—
241C2×C4×C61—22no—
242C2×C4×C61—22no—
243C2×C4×C61—22no—
244C2×C4×C61—22no—
245C2×C4×C61—44no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C411yescharacteristic
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61C23×C411yescharacteristic
250C2×C4×C61C22×D411yescharacteristic
251C2×C4×C61C22×D411yescharacteristic
252C22⋊D61—44no—
253C22⋊D61—44no—
254C2×Dic61—22no—
255C2×Dic61—22no—
256C2×Dic61—22no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—44no—
260C2×Dic61—44no—
261C2×Dic61C2×C22⋊C411yescharacteristic
262C2×Dic61C2×C22⋊C411yescharacteristic
263C2×Dic61C2×C22⋊C411yescharacteristic
264C2×Dic61C2×C22⋊C411yescharacteristic
265C2×Dic61C2×C22⋊C411yescharacteristic
266C2×Dic61C2×C22⋊C411yescharacteristic
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—22no—
273C4×D61—22no—
274C4×D61—41no—
275C4×D61—41no—
276C4×D61—41no—
277C4×D61—41no—
278C4×D61#13514yes—
279Dic122—42no—
280Dic122—42no—
281C8×C61—42no—
282C8×C61—42no—
283#92418—42no—
284#92418—42no—
285#17716—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—42no—
290C22×C61—42no—
291C22×C61—42no—
292C22×C61C22×C22⋊C411yescharacteristic
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—21no—
296C2×D61—21no—
297C2×D61—21no—
298C2×D61—44no—
299C2×D61#41612yes—
300C4×C61—21no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—42no—
304C4×C61#41312yes—
305C4×C61C2×#13512yes—
306C4×C61#57512yes—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—21no—
311Dic61—21no—
312Dic61—42no—
313Dic61—42no—
314Dic61#41612yes—
315#3444—611no—
316#2920—611no—
317C2×#431—611no—
318#1554—612no—
319#1553—612no—
320#1550—612no—
321#1547—612no—
322#1544—611no—
323#1544—611no—
324#1543—611no—
325#1543D6111yescharacteristic, complemented
326C2×C61—41no—
327C2×C61—82no—
328C2×C61C2×#41311yescharacteristic
329C2×C61C2×#41611yescharacteristic
330C2×C61#289611yescharacteristic
331D61—22no—
332D61—41no—
333#533—611no—
334#533—611no—
335#533—611no—
336#532—611no—
337#532—611no—
338#532C2×D6111yescharacteristic
339#529—612no—
340#529—612no—
341#529—1221no—
342#529—1221no—
343#529—1221no—
344#529—1221no—
345#525—612no—
346#525—1221no—
347#525—1221no—
348C4×#41—612no—
349C4×#41—1221no—
350C4×#41—1221no—
351C22×C42—611no—
352#432—612no—
353#432—1221no—
354#431—611no—
355#431—611no—
356#431—612no—
357#431—1221no—
358#431—1221no—
359#431—1221no—
360#431C2×D6111yescharacteristic
361#431C2×D6111yescharacteristic
362#423—612no—
363C2×C4⋊C8—612no—
364#407—1221no—
365C2×C22⋊C8—1221no—
366C4×M16—1221no—
367C2×C4×C8—1221no—
368#333—612no—
369#333C2×D6112yescomplemented
370#332—612no—
371#332—612no—
372#332—612no—
373#332—612no—
374#331—612no—
375#331C2×D6112yescomplemented
376C61#1771611yescharacteristic, complemented, Sylow
377C2×#41—1221no—
378C2×#41—1221no—
379C2×#41C4×D6112yes—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C2×M16—1222no—
384C22×C8—1222no—
385C4⋊Q8—611no—
386C4⋊Q8—611no—
387C4⋊Q8C22×D6111yescharacteristic
388#127C22×D6111yescharacteristic
389#126—1222no—
390#126—1222no—
391#125—612no—
392#125—1221no—
393#125—1221no—
394#124—1221no—
395#124—1221no—
396#124C4×D6112yes—
397#123—1222no—
398#123—1222no—
399#123—1222no—
400C22⋊Q8—612no—
401C22⋊Q8—612no—
402C22⋊Q8—1221no—
403C22⋊Q8—1221no—
404C22⋊Q8—1221no—
405C22⋊Q8—1221no—
406#121—21no—
407#121—21no—
408#121—612no—
409#121—612no—
410#121—1221no—
411#121—1221no—
412#120—1222no—
413C4×Q8—612no—
414C4×Q8—612no—
415C4×Q8—1221no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×Q8—1221no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—612no—
422C4×D4—612no—
423C4×D4—1221no—
424C4×D4—1221no—
425C4×D4—1222no—
426C4×D4—1222no—
427C4×D4—1222no—
428C4×D4—1222no—
429C4×D4—1222no—
430C4×D4—1222no—
431#117—612no—
432#117—1222no—
433#117—1222no—
434#117—1222no—
435#117—1221no—
436#117—1221no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—611no—
444C2×C42—611no—
445C2×C42—611no—
446C2×C42—611no—
447C2×C42—611no—
448C2×C42—1222no—
449C2×C42C22×D6111yescharacteristic
450C4⋊C8—612no—
451C4⋊C8—612no—
452C4⋊C8—1222no—
453C4⋊C8—1222no—
454C4⋊C8C22×D6112yes—
455C4⋊C8C22×D6112yes—
456C22⋊C8—21no—
457C22⋊C8—21no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8—1221no—
461C22⋊C8—1221no—
462#97—1222no—
463C4×C8—21no—
464C4×C8—21no—
465C4×C8—1222no—
466C4×C8—1221no—
467C4×C8—1221no—
468C24—611no—
469#41—44no—
470#41—2444no—
471#41—2444no—
472C2×Q8—1221no—
473C2×Q8—1221no—
474C2×Q8C2×C4×D6112yes—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—1222no—
479C2×D4—1222no—
480C2×D4C2×C4×D6112yes—
481C22×C4—22no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—611no—
485C22×C4—611no—
486C22×C4—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—611no—
491C22×C4—611no—
492C22×C4—611no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—1224no—
498C22×C4—1222no—
499C22×C4—1222no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4C2×C4×D6111yescharacteristic
503C22×C4D4×D6111yescharacteristic
504C22×C4D4×D6111yescharacteristic
505M16—2444no—
506C2×C8—22no—
507C2×C8—22no—
508C2×C8—1222no—
509C2×C8—1222no—
510C2×C8—2444no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—612no—
514C4⋊C4—612no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4—1222no—
522C4⋊C4—1222no—
523C22⋊C4—22no—
524C22⋊C4—22no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C22⋊C4—1222no—
531C22⋊C4—1222no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—611no—
544C42—1222no—
545C42—1222no—
546C42—1222no—
547C42C2×C4×D6111yescharacteristic
548C42D4×D6111yescharacteristic
549C42D4×D6111yescharacteristic
550C42C23×D6111yescharacteristic
551C23—22no—
552C23—611no—
553C23—611no—
554C23—1222no—
555C23—2441no—
556C23—2441no—
557C23C22⋊C4×D6111yescharacteristic
558Q8—42no—
559Q8—2442no—
560Q8—2442no—
561D4—42no—
562D4—44no—
563D4—42no—
564D4—42no—
565D4—2444no—
566D4—2444no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4—611no—
573C2×C4—614no—
574C2×C4—611no—
575C2×C4—611no—
576C2×C4—611no—
577C2×C4—611no—
578C2×C4—611no—
579C2×C4—1222no—
580C2×C4—1222no—
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—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2444no—
594C2×C4—2441no—
595C2×C4—2441no—
596C2×C4—2444no—
597C2×C4C22⋊C4×D6111yescharacteristic
598C2×C4C22⋊C4×D6111yescharacteristic
599C2×C4C22⋊C4×D6111yescharacteristic
600C2×C4C22×C4×D6111yescharacteristic
601C2×C4C2×D4×D6111yescharacteristic
602C2×C4C2×D4×D6111yescharacteristic
603C8—42no—
604C8—42no—
605C8—2442no—
606C8—2442no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—612no—
614C22—1221no—
615C22—1221no—
616C22—1221no—
617C22—1221no—
618C22—1221no—
619C22—2444no—
620C22C2×C22⋊C4×D6111yescharacteristic
621C4—21no—
622C4—21no—
623C4—21no—
624C4—42no—
625C4—612no—
626C4—1221no—
627C4—1221no—
628C4—1221no—
629C4—1221no—
630C4—1221no—
631C4—2442no—
632C4—2442no—
633C4#1683974312yes—
634C4#135×D6112yes—
635C4#1684055912yes—
636C2—41no—
637C2—82no—
638C2—1222no—
639C2—2441no—
640C2C2×#1683974311yescharacteristic
641C2#416×D6111yescharacteristic
642C2#2145433411yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1543C2
socleC22×C61C22×C22⋊C4
prime radical#21459114C2
cosocleC42×C61C24
hypercenter#1543D61
hypocenterC61#17716
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
2. #21454447C2semidirect
3. #431×D61C2semidirect
4. #21444528C2semidirect
5. #21444521C2semidirect
6. #21444506C2semidirect
7. #21444493C2semidirect
8. #21444483C2semidirect
9. #21444483C2semidirect
10. #21444481C2semidirect
11. C61×#1543C2semidirect
44. #16839511C22semidirect
45. #16839509C22semidirect
46. #16839509C22semidirect
47. #16839507C22semidirect
48. #16839507C22semidirect
49. #16839506C22semidirect
53. C61×#333C22semidirect
54. C61×#331C22semidirect
325. #1543D61semidirect
369. #333C2×D61semidirect
375. #331C2×D61semidirect
376. C61#17716semidirect

Maximal subgroups

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

subgroupindex
#214591142
#214544472
#431×D612
#214445282
#214445212
#214445062
#214444932
#214444832
#214444812
C61×#15432
#1771661