Finite Group Databasebeta

← #29646715

Subgroups — #29646715

Order 15616.

1026 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D61C211yesmaximal, characteristic
2C2×#16839813C211yesmaximal, characteristic
3#423×D61C211yesmaximal, characteristic
4#21444275C211yesmaximal, characteristic, complemented
5#21444274C211yesmaximal, characteristic, complemented
6#21444273C211yesmaximal, characteristic, complemented
7#21444246C214yesmaximal, complemented
8#21444220C214yesmaximal, complemented
9C61×#1493C211yesmaximal, characteristic, complemented
10C2×M16×D61—21no—
11#16840319C2211yescharacteristic
12#16840318—21no—
13#16840317C411yescharacteristic
14#16840317C411yescharacteristic
15#16840316—21no—
16#16840316C2212yes—
17#16840315—21no—
18#16840314—21no—
19#16840314C412yes—
20C4⋊Q8×D61C411yescharacteristic
21C4⋊Q8×D61C411yescharacteristic
22#125×D61—21no—
23C22⋊Q8×D61—21no—
24C22⋊Q8×D61C412yes—
25C4×Q8×D61—21no—
26C4×Q8×D61C2212yes—
27#117×D61—21no—
28C2×C42×D61C2211yescharacteristic
29#16839813—21no—
30#16839813—21no—
31#16839813C2212yes—
32#16839813C2212yes—
33#16839786C2211yescharacteristic
34#16839785—21no—
35#16839784—21no—
36#16839784C2212yes—
37C2×#14519706—21no—
38C4⋊C8×D61—21no—
39C4⋊C8×D61C2212yes—
40C2×#14519689—21no—
41C2×C4×#92418C2211yescharacteristic
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#423C2211yescharacteristic
47C2×C4×C8×C61C2211yescharacteristic
48C61×Q8⋊C8C2214yescomplemented
49C2×Q8×D61—21no—
50C2×Q8×D61C2×C412yes—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C2×#11758194—21no—
55C2×#11758189—22no—
56M16×D61—44no—
57C22×#92418—21no—
58C2×C8×D61—22no—
59#14519777C2×C411yescharacteristic
60#14519777C2×C411yescharacteristic
61#14519776—21no—
62#14519776—21no—
63#14519776—21no—
64#14519776C2×C412yes—
65#14519775—21no—
66#14519775C2×C412yes—
67#14519769—21no—
68#14519768—21no—
69#14519768—21no—
70#14519767—22no—
71#14519767—22no—
72#14519757—21no—
73#14519757C2×C412yes—
74#14519756—21no—
75#14519756C2×C412yes—
76#14519755—22no—
77#14519755—22no—
78#14519754—22no—
79#14519754—22no—
80#14519753—21no—
81#14519753C2×C412yes—
82Q8×Dic61—21no—
83Q8×Dic61C2×C412yes—
84C4×Dic122—21no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122C2312yes—
88#14519742—21no—
89#14519742—22no—
90#14519742—22no—
91#14519742C2×C412yes—
92#14519736—21no—
93#14519735—21no—
94#14519735—21no—
95#14519734—22no—
96#14519733—22no—
97C4⋊C4×D61—21no—
98C4⋊C4×D61—21no—
99C4⋊C4×D61—21no—
100C4⋊C4×D61—22no—
101C4⋊C4×D61—22no—
102C4⋊C4×D61C2×C412yes—
103C22⋊C4×D61—22no—
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61D411yescharacteristic
106C2×C4×Dic61D411yescharacteristic
107C42×D61—22no—
108C42×D61C2×C411yescharacteristic
109C42×D61C2×C411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C42×D61D411yescharacteristic
114C42×D61C2311yescharacteristic
115C42×D61C2311yescharacteristic
116C4⋊#92418—21no—
117C4⋊#92418C2312yes—
118#14519706—22no—
119#14519706—22no—
120#14519706—22no—
121#14519706—22no—
122#14519689—22no—
123#14519689—22no—
124C4×#92418—21no—
125C4×#92418C2312yes—
126C2×M16×C61—21no—
127C22×C8×C61—21no—
128C4⋊Q8×C61C2×C411yescharacteristic
129C4⋊Q8×C61C2×C411yescharacteristic
130#125×C61—21no—
131C22⋊Q8×C61—21no—
132C22⋊Q8×C61C2×C412yes—
133C4×Q8×C61—21no—
134C4×Q8×C61C2312yes—
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2312yes—
139C4×C8×C61—21no—
140C4×C8×C61C2312yes—
141C23×D61C22⋊C411yescharacteristic
142C2×Q8×C61—21no—
143C2×Q8×C61C22×C412yes—
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61C2×D411yescharacteristic
147C22×Dic61C22⋊C411yescharacteristic
148C22×Dic61C22⋊C411yescharacteristic
149C22×Dic61C22⋊C411yescharacteristic
150Q8×D61—44no—
151Q8×D61—44no—
152C2×C4×D61—22no—
153C2×C4×D61—22no—
154C2×C4×D61—42no—
155C2×C4×D61—42no—
156C2×C4×D61C22⋊C411yescharacteristic
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61SD1614yes—
163C2×C4×D61Q1614yes—
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C22×C411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×Dic122—21no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122C22×C412yes—
174M16×C61—42no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C2×C8×C61—42no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61C22×C412yes—
184C22⋊C4×C61—22no—
185C42×C61—22no—
186C42×C61C22×C411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189C42×C61C2411yescharacteristic
190C22⋊Dic61—22no—
191#11758198—22no—
192#11758198—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61—22no—
197C4⋊Dic61—22no—
198C4⋊Dic61C22×C412yes—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206#11758196—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×Dic61C22⋊C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C22×C411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C4×Dic61C2×D411yescharacteristic
222#11758194—42no—
223C2×#92418—22no—
224C2×#92418—22no—
225C2×#92418—42no—
226#11758189—44no—
227C8×D61—44no—
228C23×C61C2×C22⋊C411yescharacteristic
229C22×D61—41no—
230C22×D61—41no—
231C22×D61#10314yes—
232C22×D61C2×C22⋊C411yescharacteristic
233C22×D61C2×C22⋊C411yescharacteristic
234Q8×C61—24no—
235Q8×C61—42no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—22no—
239C2×C4×C61—22no—
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C2×SD1612yes—
244C2×C4×C61C2×Q1612yes—
245C2×C4×C61C23×C411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×C4×C61C22×D411yescharacteristic
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—41no—
251C2×Dic61—41no—
252C2×Dic61#10314yes—
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C2×Dic61C2×C22⋊C411yescharacteristic
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—22no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—41no—
267C4×D61—44no—
268C4×D61—44no—
269C4×D61#10314yes—
270C4×D61#10314yes—
271C4×D61C2×SD1612yes—
272C4×D61C2×SD1612yes—
273C4×D61C2×Q1612yes—
274C4×D61C2×Q1612yes—
275Dic122—24no—
276Dic122—44no—
277Dic122—44no—
278Dic122—42no—
279C8×C61—42no—
280C8×C61—42no—
281#92418—42no—
282#92418—42no—
283#17486—611nomaximal, Sylow
284C22×C61—21no—
285C22×C61—21no—
286C22×C61C2×#10312yes—
287C22×C61C22×C22⋊C411yescharacteristic
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—21no—
292C2×D61—44no—
293C2×D61C2×#10312yes—
294C2×D61C2×#10312yes—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61C2×#10312yes—
300C4×C61#42112yes—
301C4×C61#56812yes—
302C4×C61C22×SD1611yescharacteristic
303C4×C61C22×Q1611yescharacteristic
304Dic61—21no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—42no—
309Dic61—42no—
310Dic61C2×#10312yes—
311Dic61C2×#10312yes—
312C2×#533—611no—
313C2×#431—611no—
314C2×#423—611no—
315#1493—611no—
316#1493—611no—
317#1493—611no—
318#1493D6111yescharacteristic, complemented
319#1487—614no—
320#1481—614no—
321C2×C61—22no—
322C2×C61#287911yescharacteristic
323C2×C61C22×#10311yescharacteristic
324C2×C61C2×#42111yescharacteristic
325D61—22no—
326D61—22no—
327C22×M16—1221no—
328#533—611no—
329#533—611no—
330#533—612no—
331#533—612no—
332#533—611no—
333#533—1221no—
334#533—1221no—
335#533—1221no—
336#533—1221no—
337#533C2×D6111yescharacteristic
338C2×C4⋊Q8—611no—
339C2×C4⋊Q8—611no—
340C2×#125—1221no—
341C2×C22⋊Q8—612no—
342C2×C22⋊Q8—1221no—
343C2×C4×Q8—612no—
344C2×C4×Q8—1221no—
345C2×#117—1221no—
346C22×C42—611no—
347#431—612no—
348#431—612no—
349#431—1221no—
350#431—1221no—
351#423—611no—
352#423—612no—
353#423—1221no—
354#423—1221no—
355#423C2×D6111yescharacteristic
356C2×C4⋊C8—612no—
357C2×C4⋊C8—1221no—
358C2×C4⋊C8—1221no—
359C2×C22⋊C8—1221no—
360C2×C4×C8—611no—
361C2×C4×C8C2×D6111yescharacteristic
362Q8⋊C8—614no—
363Q8⋊C8—614no—
364Q8⋊C8—614no—
365Q8⋊C8C2×D6114yescomplemented
366C61#1748611yescharacteristic, complemented, Sylow
367C22×Q8—612no—
368C22×Q8—1221no—
369C23×C4—611no—
370C23×C4—611no—
371C23×C4—611no—
372C2×M16—21no—
373C2×M16—1222no—
374C2×M16—1221no—
375C2×M16—2444no—
376C22×C8—21no—
377C22×C8—1222no—
378C22×C8—1221no—
379C4⋊Q8—612no—
380C4⋊Q8—612no—
381C4⋊Q8—611no—
382C4⋊Q8—611no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385C4⋊Q8—1221no—
386C4⋊Q8—1221no—
387C4⋊Q8C4×D6111yescharacteristic
388C4⋊Q8C4×D6111yescharacteristic
389#125—21no—
390#125—1222no—
391#125—1222no—
392#125—1221no—
393#125—1221no—
394#125—1221no—
395C22⋊Q8—21no—
396C22⋊Q8—612no—
397C22⋊Q8—612no—
398C22⋊Q8—612no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1222no—
402C22⋊Q8—1222no—
403C22⋊Q8—1221no—
404C22⋊Q8—1221no—
405C22⋊Q8—1221no—
406C22⋊Q8C4×D6112yes—
407C4×Q8—21no—
408C4×Q8—612no—
409C4×Q8—612no—
410C4×Q8—612no—
411C4×Q8—1222no—
412C4×Q8—1222no—
413C4×Q8—1222no—
414C4×Q8—1221no—
415C4×Q8—1222no—
416C4×Q8—1221no—
417C4×Q8—1221no—
418C4×Q8C22×D6112yes—
419#117—21no—
420#117—1222no—
421#117—1222no—
422#117—1221no—
423#117—1221no—
424#117—1221no—
425C2×C4⋊C4—612no—
426C2×C4⋊C4—1221no—
427C2×C4⋊C4—1221no—
428C2×C4⋊C4—1222no—
429C2×C4⋊C4—1222no—
430C2×C4⋊C4—1221no—
431C2×C22⋊C4—1222no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—611no—
440C2×C42—611no—
441C2×C42—611no—
442C2×C42—611no—
443C2×C42—1222no—
444C2×C42C22×D6111yescharacteristic
445C4⋊C8—21no—
446C4⋊C8—612no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1222no—
450C4⋊C8—1222no—
451C4⋊C8—1221no—
452C4⋊C8C22×D6112yes—
453C22⋊C8—1222no—
454C22⋊C8—1222no—
455C4×C8—21no—
456C4×C8—612no—
457C4×C8—1221no—
458C4×C8C22×D6112yes—
459C24—611no—
460C2×Q8—21no—
461C2×Q8—612no—
462C2×Q8—1222no—
463C2×Q8—1222no—
464C2×Q8—1221no—
465C2×Q8—2444no—
466C2×Q8—2444no—
467C2×Q8C2×C4×D6112yes—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—614no—
474C22×C4—614no—
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—1222no—
486C22×C4—1222no—
487C22×C4—2442no—
488C22×C4—2442no—
489C22×C4C2×C4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491C22×C4D4×D6111yescharacteristic
492M16—42no—
493M16—2444no—
494M16—2442no—
495C2×C8—22no—
496C2×C8—22no—
497C2×C8—42no—
498C2×C8—1222no—
499C2×C8—1222no—
500C2×C8—2444no—
501C2×C8—2442no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—22no—
507C4⋊C4—612no—
508C4⋊C4—1222no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C4⋊C4C2×C4×D6112yes—
522C22⋊C4—22no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C42—22no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—611no—
538C42—611no—
539C42—1222no—
540C42—1222no—
541C42—1222no—
542C42C2×C4×D6111yescharacteristic
543C42D4×D6111yescharacteristic
544C42D4×D6111yescharacteristic
545C42C23×D6111yescharacteristic
546C23—611no—
547C23—611no—
548C23—614no—
549C23—2441no—
550C23—2441no—
551C23C22⋊C4×D6111yescharacteristic
552Q8—24no—
553Q8—42no—
554Q8—1224no—
555Q8—2444no—
556Q8—2444no—
557Q8—2442no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—611no—
563C2×C4—611no—
564C2×C4—614no—
565C2×C4—614no—
566C2×C4—614no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
570C2×C4—612no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—611no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1222no—
579C2×C4—1222no—
580C2×C4—1222no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2444no—
586C2×C4—2444no—
587C2×C4—2441no—
588C2×C4—2441no—
589C2×C4C22⋊C4×D6111yescharacteristic
590C2×C4C22⋊C4×D6111yescharacteristic
591C2×C4C22⋊C4×D6111yescharacteristic
592C2×C4SD16×D6112yes—
593C2×C4Q16×D6112yes—
594C2×C4C22×C4×D6111yescharacteristic
595C2×C4C2×D4×D6111yescharacteristic
596C2×C4C2×D4×D6111yescharacteristic
597C8—42no—
598C8—42no—
599C8—2442no—
600C8—2442no—
601C22—21no—
602C22—21no—
603C22—612no—
604C22—612no—
605C22—1221no—
606C22—1221no—
607C22—1221no—
608C22—1221no—
609C22—2444no—
610C22#103×D6112yes—
611C22C2×C22⋊C4×D6111yescharacteristic
612C4—21no—
613C4—21no—
614C4—42no—
615C4—42no—
616C4—612no—
617C4—612no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—1221no—
622C4—2442no—
623C4—2442no—
624C4#103×D6112yes—
625C4#1683977712yes—
626C4#1684052712yes—
627C4C2×SD16×D6111yescharacteristic
628C4C2×Q16×D6111yescharacteristic
629C2—22no—
630C2—1222no—
631C2—1222no—
632C2#2145426111yescharacteristic
633C2C2×#103×D6111yescharacteristic
634C2C2×#1683977711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1493C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1493D61
hypocenterC61#17486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
4. #21444275C2semidirect
5. #21444274C2semidirect
6. #21444273C2semidirect
7. #21444246C2semidirect
8. #21444220C2semidirect
9. C61×#1493C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
318. #1493D61semidirect
365. Q8⋊C8C2×D61semidirect
366. C61#17486semidirect

Maximal subgroups

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

subgroupindex
#533×D612
C2×#168398132
#423×D612
#214442752
#214442742
#214442732
#214442462
#214442202
C61×#14932
#1748661