Finite Group Databasebeta

← #29648438

Subgroups — #29648438

Order 15616.

972 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2#21454447C211yesmaximal, characteristic
3C2×#16839814C211yesmaximal, characteristic
4#21444528C212yesmaximal, complemented
5#21444526C212yesmaximal, complemented
6#21444498C212yesmaximal, complemented
7#21444489C212yesmaximal, complemented
8#21444477C211yesmaximal, characteristic, complemented
9#21444476C211yesmaximal, characteristic, complemented
10#21444474C211yesmaximal, characteristic, complemented
11C61×#1542C211yesmaximal, characteristic, complemented
12#16840319C2211yescharacteristic
13#16840318—21no—
14#16840317C2211yescharacteristic
15#16840317C2211yescharacteristic
16#16840316—21no—
17#16840316C412yes—
18#16840315—21no—
19#16840314—21no—
20#16840314C412yes—
21C4⋊Q8×D61C2211yescharacteristic
22C4⋊Q8×D61C2211yescharacteristic
23#125×D61—21no—
24C22⋊Q8×D61—21no—
25C22⋊Q8×D61C412yes—
26C4×Q8×D61—21no—
27C4×Q8×D61C412yes—
28#117×D61—21no—
29C2×C42×D61C2211yescharacteristic
30#16839818C2212yes—
31#16839816—21no—
32#16839815C2211yescharacteristic
33#16839814—21no—
34#16839814—21no—
35#16839814C2212yes—
36#16839814C2212yes—
37#16839813—21no—
38#16839784C2212yes—
39C2×C4⋊#92418C2211yescharacteristic
40#16839724—21no—
41C2×#14519689—21no—
42C4×#11758189—21no—
43C2×C8×Dic61—21no—
44#16839511C2212yescomplemented
45#16839510C2212yescomplemented
46#16839510C2212yescomplemented
47#16839509C2212yescomplemented
48#16839508C2212yescomplemented
49#16839507C2212yescomplemented
50C61×#533C2211yescharacteristic
51C61×#431C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C61×#333C2212yescomplemented
54C61×#332C2212yescomplemented
55C2×Q8×D61—21no—
56C2×Q8×D61C2×C412yes—
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C2×#11758189—22no—
61C22×#92418—21no—
62#14519777C2311yescharacteristic
63#14519777C2311yescharacteristic
64#14519776—21no—
65#14519776—21no—
66#14519776—21no—
67#14519776C2×C412yes—
68#14519775—21no—
69#14519775C2×C412yes—
70#14519769—21no—
71#14519768—21no—
72#14519768—21no—
73#14519767—22no—
74#14519767—22no—
75#14519757—21no—
76#14519757C2×C412yes—
77#14519756—21no—
78#14519756C2×C412yes—
79#14519755—22no—
80#14519755—22no—
81#14519754—22no—
82#14519754—22no—
83#14519753—21no—
84#14519753C2×C412yes—
85Q8×Dic61—21no—
86Q8×Dic61C2×C412yes—
87C4×Dic122—21no—
88C4×Dic122—22no—
89C4×Dic122—22no—
90C4×Dic122C2×C412yes—
91#14519742—22no—
92#14519742—22no—
93#14519742—21no—
94#14519742C2×C412yes—
95#14519736—21no—
96#14519735—21no—
97#14519735—21no—
98#14519734—22no—
99#14519733—22no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61—21no—
103C4⋊C4×D61—21no—
104C4⋊C4×D61—21no—
105C4⋊C4×D61C2×C412yes—
106C22⋊C4×D61—22no—
107C2×C4×Dic61C2×C411yescharacteristic
108C2×C4×Dic61D411yescharacteristic
109C2×C4×Dic61D411yescharacteristic
110C42×D61—22no—
111C42×D61C2×C411yescharacteristic
112C42×D61C2×C411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61D411yescharacteristic
115C42×D61D411yescharacteristic
116C42×D61D411yescharacteristic
117C42×D61C2311yescharacteristic
118C42×D61C2311yescharacteristic
119C4⋊#92418—21no—
120C4⋊#92418C2312yes—
121C4⋊#92418C2312yes—
122#14519706—22no—
123C22⋊#92418—21no—
124#14519689—22no—
125#14519689—22no—
126#14519689—22no—
127#14519687—22no—
128C4×#92418—21no—
129C8×Dic61—22no—
130C8×Dic61—22no—
131C22×C8×C61—21no—
132C4⋊Q8×C61C2311yescharacteristic
133C4⋊Q8×C61C2311yescharacteristic
134#125×C61—21no—
135C22⋊Q8×C61—21no—
136C22⋊Q8×C61C2×C412yes—
137C4×Q8×C61—21no—
138C4×Q8×C61C2×C412yes—
139#117×C61—21no—
140C2×C42×C61C2311yescharacteristic
141C4⋊C8×C61—21no—
142C4⋊C8×C61C2312yes—
143C4⋊C8×C61C2312yes—
144C22⋊C8×C61—21no—
145C4×C8×C61—21no—
146C23×D61C22⋊C411yescharacteristic
147C2×Q8×C61—21no—
148C2×Q8×C61C22×C412yes—
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×Dic61C22⋊C411yescharacteristic
153C22×Dic61C22⋊C411yescharacteristic
154C22×Dic61C22⋊C411yescharacteristic
155Q8×D61—44no—
156Q8×D61—44no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—24no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—42no—
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C22⋊C411yescharacteristic
166C2×C4×D61C22⋊C411yescharacteristic
167C2×C4×D61C22⋊C411yescharacteristic
168C2×C4×D61C22⋊C411yescharacteristic
169C2×C4×D61C22×C411yescharacteristic
170C2×C4×D61C22×C411yescharacteristic
171C2×C4×D61C2×D411yescharacteristic
172C2×C4×D61C2×D411yescharacteristic
173C2×C4×D61C2×D411yescharacteristic
174C2×C4×D61C2×D411yescharacteristic
175C2×Dic122—21no—
176C2×Dic122—22no—
177C2×Dic122—22no—
178C2×Dic122C22×C412yes—
179C2×C8×C61—22no—
180C2×C8×C61—22no—
181C2×C8×C61—42no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—21no—
185C4⋊C4×C61—21no—
186C4⋊C4×C61—21no—
187C4⋊C4×C61C22×C412yes—
188C22⋊C4×C61—22no—
189C42×C61—22no—
190C42×C61C22×C411yescharacteristic
191C42×C61C2×D411yescharacteristic
192C42×C61C2×D411yescharacteristic
193C42×C61C2411yescharacteristic
194C22⋊Dic61—22no—
195#11758198—22no—
196#11758198—22no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61—22no—
201C4⋊Dic61—22no—
202C4⋊Dic61C22×C412yes—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—22no—
207#11758196—22no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211C4×Dic61—22no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22⋊C411yescharacteristic
217C4×Dic61C22⋊C411yescharacteristic
218C4×Dic61C22⋊C411yescharacteristic
219C4×Dic61C22⋊C411yescharacteristic
220C4×Dic61C22×C411yescharacteristic
221C4×Dic61C22×C411yescharacteristic
222C4×Dic61C2×D411yescharacteristic
223C4×Dic61C2×D411yescharacteristic
224C4×Dic61C2×D411yescharacteristic
225C4×Dic61C2×D411yescharacteristic
226C2×#92418—22no—
227C2×#92418—22no—
228C2×#92418—42no—
229#11758189—44no—
230C23×C61C2×C22⋊C411yescharacteristic
231C22×D61—22no—
232C22×D61—22no—
233C22×D61—41no—
234C22×D61C2×C22⋊C411yescharacteristic
235C22×D61C2×C22⋊C411yescharacteristic
236Q8×C61—42no—
237Q8×C61—42no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61—22no—
241C2×C4×C61—41no—
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×C22⋊C411yescharacteristic
244C2×C4×C61C2×C22⋊C411yescharacteristic
245C2×C4×C61#13712yes—
246C2×C4×C61#13712yes—
247C2×C4×C61C23×C411yescharacteristic
248C2×C4×C61C22×D411yescharacteristic
249C2×C4×C61C22×D411yescharacteristic
250C2×Dic61—22no—
251C2×Dic61—22no—
252C2×Dic61—22no—
253C2×Dic61—22no—
254C2×Dic61—22no—
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C2×Dic61C2×C22⋊C411yescharacteristic
260C2×Dic61C2×C22⋊C411yescharacteristic
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—21no—
264C4×D61—21no—
265C4×D61—21no—
266C4×D61—21no—
267C4×D61—22no—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—22no—
271C4×D61—22no—
272C4×D61—41no—
273C4×D61—41no—
274C4×D61—44no—
275C4×D61—44no—
276C4×D61#13514yes—
277Dic122—42no—
278Dic122—44no—
279Dic122—44no—
280Dic122—42no—
281C8×C61—42no—
282C8×C61—42no—
283#92418—42no—
284#92418—42no—
285#17718—611nomaximal, Sylow
286C22×C61—21no—
287C22×C61—21no—
288C22×C61#41912yes—
289C22×C61C22×C22⋊C411yescharacteristic
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—21no—
293C2×D61—21no—
294C2×D61—21no—
295C2×D61—44no—
296C2×D61#41612yes—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—21no—
300C4×C61—42no—
301C4×C61—42no—
302C4×C61#41912yes—
303C4×C61C2×#13512yes—
304C4×C61C2×#13711yescharacteristic
305C4×C61C2×#13711yescharacteristic
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—21no—
310Dic61—42no—
311Dic61—42no—
312Dic61#41312yes—
313Dic61#41612yes—
314C2×#533—611no—
315#2920—611no—
316C2×#431—611no—
317#1554—612no—
318#1554—612no—
319#1548—612no—
320#1546—612no—
321#1542—611no—
322#1542—611no—
323#1542—611no—
324#1542D6111yescharacteristic, complemented
325C2×C61—22no—
326C2×C61C2×#41311yescharacteristic
327C2×C61C2×#41611yescharacteristic
328C2×C61C2×#41911yescharacteristic
329D61—22no—
330D61—41no—
331#533—611no—
332#533—611no—
333#533—612no—
334#533—612no—
335#533—611no—
336#533—1221no—
337#533—1221no—
338#533—1221no—
339#533—1221no—
340#533C2×D6111yescharacteristic
341C2×C4⋊Q8—611no—
342C2×C4⋊Q8—611no—
343C2×#125—1221no—
344C2×C22⋊Q8—612no—
345C2×C22⋊Q8—1221no—
346C2×C4×Q8—612no—
347C2×C4×Q8—1221no—
348C2×#117—1221no—
349C22×C42—611no—
350#432—612no—
351#432—1221no—
352#431—611no—
353#431—612no—
354#431—612no—
355#431—1221no—
356#431—1221no—
357#431—1221no—
358#431C2×D6111yescharacteristic
359#423—612no—
360C2×C4⋊C8—611no—
361C2×C4⋊C8C2×D6111yescharacteristic
362#407—1221no—
363C2×C22⋊C8—1221no—
364C4×M16—1221no—
365C2×C4×C8—1221no—
366#333—612no—
367#333—612no—
368#333—612no—
369#333C2×D6112yescomplemented
370#332—612no—
371#332—612no—
372#332—612no—
373#332C2×D6112yescomplemented
374C61#1771811yescharacteristic, complemented, Sylow
375C22×Q8—612no—
376C22×Q8—1221no—
377C23×C4—611no—
378C23×C4—611no—
379C23×C4—611no—
380C2×M16—1222no—
381C22×C8—21no—
382C22×C8—1221no—
383C4⋊Q8—612no—
384C4⋊Q8—612no—
385C4⋊Q8—611no—
386C4⋊Q8—611no—
387C4⋊Q8—1221no—
388C4⋊Q8—1221no—
389C4⋊Q8—1221no—
390C4⋊Q8—1221no—
391C4⋊Q8C22×D6111yescharacteristic
392C4⋊Q8C22×D6111yescharacteristic
393#125—21no—
394#125—1222no—
395#125—1222no—
396#125—1221no—
397#125—1221no—
398#125—1221no—
399C22⋊Q8—21no—
400C22⋊Q8—612no—
401C22⋊Q8—612no—
402C22⋊Q8—612no—
403C22⋊Q8—1222no—
404C22⋊Q8—1222no—
405C22⋊Q8—1222no—
406C22⋊Q8—1222no—
407C22⋊Q8—1221no—
408C22⋊Q8—1221no—
409C22⋊Q8—1221no—
410C22⋊Q8C4×D6112yes—
411C4×Q8—21no—
412C4×Q8—612no—
413C4×Q8—612no—
414C4×Q8—612no—
415C4×Q8—1222no—
416C4×Q8—1222no—
417C4×Q8—1222no—
418C4×Q8—1221no—
419C4×Q8—1222no—
420C4×Q8—1221no—
421C4×Q8—1221no—
422C4×Q8C4×D6112yes—
423#117—21no—
424#117—1222no—
425#117—1222no—
426#117—1221no—
427#117—1221no—
428#117—1221no—
429C2×C4⋊C4—612no—
430C2×C4⋊C4—1221no—
431C2×C4⋊C4—1221no—
432C2×C4⋊C4—1222no—
433C2×C4⋊C4—1222no—
434C2×C4⋊C4—1221no—
435C2×C22⋊C4—1222no—
436C2×C42—611no—
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—1222no—
448C2×C42C22×D6111yescharacteristic
449C4⋊C8—21no—
450C4⋊C8—612no—
451C4⋊C8—612no—
452C4⋊C8—1222no—
453C4⋊C8—1221no—
454C4⋊C8C22×D6112yes—
455C4⋊C8C22×D6112yes—
456C22⋊C8—21no—
457C22⋊C8—1222no—
458C22⋊C8—1222no—
459C22⋊C8—1222no—
460C22⋊C8—1221no—
461#97—1222no—
462C4×C8—21no—
463C4×C8—1222no—
464C4×C8—1222no—
465C4×C8—1221no—
466C24—611no—
467C2×Q8—21no—
468C2×Q8—612no—
469C2×Q8—1222no—
470C2×Q8—1222no—
471C2×Q8—1221no—
472C2×Q8—2444no—
473C2×Q8—2444no—
474C2×Q8C2×C4×D6112yes—
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—611no—
487C22×C4—611no—
488C22×C4—611no—
489C22×C4—611no—
490C22×C4—1224no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—2442no—
496C22×C4C2×C4×D6111yescharacteristic
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499M16—2444no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—42no—
503C2×C8—1222no—
504C2×C8—1222no—
505C2×C8—2442no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—612no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C4⋊C4—1221no—
521C4⋊C4—1221no—
522C4⋊C4—1221no—
523C4⋊C4—1222no—
524C4⋊C4—1222no—
525C4⋊C4C2×C4×D6112yes—
526C22⋊C4—22no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C22⋊C4—1222no—
530C42—22no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—611no—
540C42—611no—
541C42—611no—
542C42—611no—
543C42—1222no—
544C42—1222no—
545C42—1222no—
546C42C2×C4×D6111yescharacteristic
547C42D4×D6111yescharacteristic
548C42D4×D6111yescharacteristic
549C42C23×D6111yescharacteristic
550C23—611no—
551C23—611no—
552C23—1222no—
553C23—1222no—
554C23—2441no—
555C23C22⋊C4×D6111yescharacteristic
556Q8—42no—
557Q8—42no—
558Q8—2442no—
559Q8—2444no—
560Q8—2444no—
561Q8—2442no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—41no—
566C2×C4—611no—
567C2×C4—611no—
568C2×C4—614no—
569C2×C4—611no—
570C2×C4—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—1222no—
574C2×C4—1222no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—1222no—
582C2×C4—1222no—
583C2×C4—1221no—
584C2×C4—1221no—
585C2×C4—1221no—
586C2×C4—1221no—
587C2×C4—1222no—
588C2×C4—1222no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2444no—
592C2×C4—2444no—
593C2×C4C22⋊C4×D6111yescharacteristic
594C2×C4C22⋊C4×D6111yescharacteristic
595C2×C4C22⋊C4×D6111yescharacteristic
596C2×C4#1451980612yes—
597C2×C4#1451980912yes—
598C2×C4C22×C4×D6111yescharacteristic
599C2×C4C2×D4×D6111yescharacteristic
600C2×C4C2×D4×D6111yescharacteristic
601C8—42no—
602C8—42no—
603C8—2442no—
604C8—2442no—
605C22—21no—
606C22—21no—
607C22—612no—
608C22—1221no—
609C22—1221no—
610C22—1221no—
611C22—1221no—
612C22—1221no—
613C22—2444no—
614C22#1683976912yes—
615C22C2×C22⋊C4×D6111yescharacteristic
616C4—21no—
617C4—21no—
618C4—21no—
619C4—42no—
620C4—42no—
621C4—612no—
622C4—612no—
623C4—1221no—
624C4—1221no—
625C4—1221no—
626C4—1221no—
627C4—2442no—
628C4—2442no—
629C4#1683976912yes—
630C4#135×D6112yes—
631C4C2×#1451980611yescharacteristic
632C4C2×#1451980911yescharacteristic
633C2—22no—
634C2—1222no—
635C2—2441no—
636C2#413×D6111yescharacteristic
637C2#416×D6111yescharacteristic
638C2C2×#1683976911yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1542C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1542D61
hypocenterC61#17718
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1542

Complements

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

NH ≅ G/Ntype
4. #21444528C2semidirect
5. #21444526C2semidirect
6. #21444498C2semidirect
7. #21444489C2semidirect
8. #21444477C2semidirect
9. #21444476C2semidirect
10. #21444474C2semidirect
11. C61×#1542C2semidirect
44. #16839511C22semidirect
45. #16839510C22semidirect
46. #16839510C22semidirect
47. #16839509C22semidirect
48. #16839508C22semidirect
49. #16839507C22semidirect
53. C61×#333C22semidirect
54. C61×#332C22semidirect
324. #1542D61semidirect
369. #333C2×D61semidirect
373. #332C2×D61semidirect
374. C61#17718semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#214544472
C2×#168398142
#214445282
#214445262
#214444982
#214444892
#214444772
#214444762
#214444742
C61×#15422
#1771861