Finite Group Databasebeta

← #29646713

Subgroups — #29646713

Order 15616.

1026 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
1#533×D61C211yesmaximal, characteristic
2#431×D61C211yesmaximal, characteristic
3C2×#16839784C211yesmaximal, characteristic
4#21444272C214yesmaximal, complemented
5#21444246C214yesmaximal, complemented
6#21444223C211yesmaximal, characteristic, complemented
7#21444222C211yesmaximal, characteristic, complemented
8#21444221C211yesmaximal, characteristic, complemented
9C61×#1481C211yesmaximal, characteristic, complemented
10C22×#11758189—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#16839815C2211yescharacteristic
30#16839814—21no—
31#16839813C2212yes—
32#16839812—21no—
33#16839784—21no—
34#16839784—21no—
35#16839784C2212yes—
36#16839784C2212yes—
37C2×C4⋊#92418C2211yescharacteristic
38C2×#14519706—21no—
39C4⋊C8×D61—21no—
40C22⋊C8×D61—21no—
41C4×C8×D61C2212yes—
42#16839494C2214yescomplemented
43Q8⋊#92418C2214yescomplemented
44#16839492C2214yescomplemented
45C61×#533C2211yescharacteristic
46C61×#431C2211yescharacteristic
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×#11758189—22no—
55C2×#11758189—22no—
56C2×#11758189—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⋊#92418—21no—
118C4⋊#92418C2312yes—
119#14519706—22no—
120#14519706—22no—
121#14519706—22no—
122C22⋊#92418—21no—
123#14519689—22no—
124C4×#92418C2312yes—
125C8×Dic61—22no—
126C22×C8×C61—21no—
127C4⋊Q8×C61C2×C411yescharacteristic
128C4⋊Q8×C61C2×C411yescharacteristic
129#125×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61C2×C412yes—
132C4×Q8×C61—21no—
133C4×Q8×C61C2312yes—
134#117×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61—21no—
138C4⋊C8×C61C2312yes—
139C22⋊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—
174C2×C8×C61—22no—
175C2×C8×C61—22no—
176C2×C8×C61—42no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61C22×C412yes—
183C22⋊C4×C61—22no—
184C42×C61—22no—
185C42×C61C22×C411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2411yescharacteristic
189C22⋊Dic61—22no—
190#11758198—22no—
191#11758198—22no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—22no—
196C4⋊Dic61—22no—
197C4⋊Dic61C22×C412yes—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205#11758196—22no—
206C4×Dic61—22no—
207C4×Dic61—22no—
208C4×Dic61—22no—
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C411yescharacteristic
212C4×Dic61C22⋊C411yescharacteristic
213C4×Dic61C22⋊C411yescharacteristic
214C4×Dic61C22⋊C411yescharacteristic
215C4×Dic61C22×C411yescharacteristic
216C4×Dic61C22×C411yescharacteristic
217C4×Dic61C2×D411yescharacteristic
218C4×Dic61C2×D411yescharacteristic
219C4×Dic61C2×D411yescharacteristic
220C4×Dic61C2×D411yescharacteristic
221C2×#92418—22no—
222C2×#92418—22no—
223C2×#92418—42no—
224#11758189—44no—
225#11758189—44no—
226C8×D61—44no—
227C23×C61C2×C22⋊C411yescharacteristic
228C22×D61—41no—
229C22×D61—41no—
230C22×D61#10314yes—
231C22×D61C2×C22⋊C411yescharacteristic
232C22×D61C2×C22⋊C411yescharacteristic
233Q8×C61—24no—
234Q8×C61—42no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—22no—
238C2×C4×C61—41no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×SD1612yes—
243C2×C4×C61C2×Q1612yes—
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×D411yescharacteristic
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—22no—
250C2×Dic61—41no—
251C2×Dic61#10314yes—
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C2×Dic61C2×C22⋊C411yescharacteristic
258C4×D61—22no—
259C4×D61—22no—
260C4×D61—22no—
261C4×D61—22no—
262C4×D61—41no—
263C4×D61—41no—
264C4×D61—41no—
265C4×D61—41no—
266C4×D61—44no—
267C4×D61—44no—
268C4×D61#10314yes—
269C4×D61#10314yes—
270C4×D61C2×SD1612yes—
271C4×D61C2×SD1612yes—
272C4×D61C2×Q1612yes—
273C4×D61C2×Q1612yes—
274Dic122—24no—
275Dic122—44no—
276Dic122—42no—
277Dic122—44no—
278C8×C61—42no—
279C8×C61—42no—
280#92418—42no—
281#92418—42no—
282#17486—611nomaximal, Sylow
283C22×C61—21no—
284C22×C61—21no—
285C22×C61C2×#10312yes—
286C22×C61C22×C22⋊C411yescharacteristic
287C2×D61—21no—
288C2×D61—21no—
289C2×D61—21no—
290C2×D61—21no—
291C2×D61—44no—
292C2×D61C2×#10312yes—
293C2×D61C2×#10312yes—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—42no—
298C4×C61—42no—
299C4×C61C2×#10312yes—
300C4×C61#56812yes—
301C4×C61C22×SD1611yescharacteristic
302C4×C61C22×Q1611yescharacteristic
303Dic61—21no—
304Dic61—21no—
305Dic61—21no—
306Dic61—42no—
307Dic61—42no—
308Dic61C2×#10312yes—
309Dic61C2×#10312yes—
310Dic61#42112yes—
311C2×#533—611no—
312C2×#431—611no—
313C2×#423—611no—
314#1493—614no—
315#1487—614no—
316#1481—611no—
317#1481—611no—
318#1481—611no—
319#1481D6111yescharacteristic, complemented
320C2×C61—22no—
321C2×C61#287911yescharacteristic
322C2×C61C22×#10311yescharacteristic
323C2×C61C2×#42111yescharacteristic
324D61—22no—
325D61—22no—
326C22×M16—1221no—
327#533—611no—
328#533—611no—
329#533—612no—
330#533—612no—
331#533—611no—
332#533—1221no—
333#533—1221no—
334#533—1221no—
335#533—1221no—
336#533C2×D6111yescharacteristic
337C2×C4⋊Q8—611no—
338C2×C4⋊Q8—611no—
339C2×#125—1221no—
340C2×C22⋊Q8—612no—
341C2×C22⋊Q8—1221no—
342C2×C4×Q8—612no—
343C2×C4×Q8—1221no—
344C2×#117—1221no—
345C22×C42—611no—
346#431—611no—
347#431—612no—
348#431—1221no—
349#431—1221no—
350#431C2×D6111yescharacteristic
351#423—612no—
352#423—612no—
353#423—1221no—
354#423—1221no—
355C2×C4⋊C8—611no—
356C2×C4⋊C8—1221no—
357C2×C4⋊C8—1221no—
358C2×C4⋊C8C2×D6111yescharacteristic
359C2×C22⋊C8—1221no—
360C2×C4×C8—612no—
361Q8⋊C8—614no—
362Q8⋊C8—614no—
363Q8⋊C8—614no—
364Q8⋊C8C2×D6114yescomplemented
365C61#1748611yescharacteristic, complemented, Sylow
366C22×Q8—612no—
367C22×Q8—1221no—
368C23×C4—611no—
369C23×C4—611no—
370C23×C4—611no—
371C2×M16—1222no—
372C2×M16—1222no—
373C2×M16—2444no—
374C22×C8—21no—
375C22×C8—1222no—
376C22×C8—1221no—
377C4⋊Q8—612no—
378C4⋊Q8—612no—
379C4⋊Q8—611no—
380C4⋊Q8—611no—
381C4⋊Q8—1221no—
382C4⋊Q8—1221no—
383C4⋊Q8—1221no—
384C4⋊Q8—1221no—
385C4⋊Q8C4×D6111yescharacteristic
386C4⋊Q8C4×D6111yescharacteristic
387#125—21no—
388#125—1222no—
389#125—1222no—
390#125—1221no—
391#125—1221no—
392#125—1221no—
393C22⋊Q8—21no—
394C22⋊Q8—612no—
395C22⋊Q8—612no—
396C22⋊Q8—612no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C22⋊Q8—1222no—
400C22⋊Q8—1222no—
401C22⋊Q8—1221no—
402C22⋊Q8—1221no—
403C22⋊Q8—1221no—
404C22⋊Q8C4×D6112yes—
405C4×Q8—21no—
406C4×Q8—612no—
407C4×Q8—612no—
408C4×Q8—612no—
409C4×Q8—1222no—
410C4×Q8—1222no—
411C4×Q8—1222no—
412C4×Q8—1221no—
413C4×Q8—1222no—
414C4×Q8—1221no—
415C4×Q8—1221no—
416C4×Q8C22×D6112yes—
417#117—21no—
418#117—1222no—
419#117—1222no—
420#117—1221no—
421#117—1221no—
422#117—1221no—
423C2×C4⋊C4—612no—
424C2×C4⋊C4—1221no—
425C2×C4⋊C4—1221no—
426C2×C4⋊C4—1222no—
427C2×C4⋊C4—1222no—
428C2×C4⋊C4—1221no—
429C2×C22⋊C4—1222no—
430C2×C42—611no—
431C2×C42—611no—
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—1222no—
442C2×C42C22×D6111yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—612no—
446C4⋊C8—1222no—
447C4⋊C8—1222no—
448C4⋊C8—1222no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8C22×D6112yes—
452C22⋊C8—21no—
453C22⋊C8—1222no—
454C22⋊C8—1221no—
455C4×C8—612no—
456C4×C8—1222no—
457C4×C8C22×D6112yes—
458C24—611no—
459C2×Q8—21no—
460C2×Q8—612no—
461C2×Q8—1222no—
462C2×Q8—1222no—
463C2×Q8—1221no—
464C2×Q8—2444no—
465C2×Q8—2444no—
466C2×Q8C2×C4×D6112yes—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—614no—
473C22×C4—614no—
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—1222no—
485C22×C4—1222no—
486C22×C4—2442no—
487C22×C4—2442no—
488C22×C4C2×C4×D6111yescharacteristic
489C22×C4D4×D6111yescharacteristic
490C22×C4D4×D6111yescharacteristic
491M16—2444no—
492M16—2444no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—42no—
496C2×C8—1222no—
497C2×C8—1222no—
498C2×C8—2444no—
499C2×C8—2442no—
500C4⋊C4—22no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—612no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
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—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4C2×C4×D6112yes—
520C22⋊C4—22no—
521C22⋊C4—1222no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C42—22no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—611no—
529C42—611no—
530C42—611no—
531C42—611no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—611no—
537C42—1222no—
538C42—1222no—
539C42—1222no—
540C42C2×C4×D6111yescharacteristic
541C42D4×D6111yescharacteristic
542C42D4×D6111yescharacteristic
543C42C23×D6111yescharacteristic
544C23—611no—
545C23—611no—
546C23—614no—
547C23—2441no—
548C23—2441no—
549C23C22⋊C4×D6111yescharacteristic
550Q8—24no—
551Q8—42no—
552Q8—1224no—
553Q8—2442no—
554Q8—2444no—
555Q8—2444no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—611no—
561C2×C4—611no—
562C2×C4—611no—
563C2×C4—614no—
564C2×C4—614no—
565C2×C4—614no—
566C2×C4—612no—
567C2×C4—612no—
568C2×C4—612no—
569C2×C4—612no—
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—2441no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2444no—
585C2×C4—2444no—
586C2×C4—2441no—
587C2×C4C22⋊C4×D6111yescharacteristic
588C2×C4C22⋊C4×D6111yescharacteristic
589C2×C4C22⋊C4×D6111yescharacteristic
590C2×C4SD16×D6112yes—
591C2×C4Q16×D6112yes—
592C2×C4C22×C4×D6111yescharacteristic
593C2×C4C2×D4×D6111yescharacteristic
594C2×C4C2×D4×D6111yescharacteristic
595C8—42no—
596C8—42no—
597C8—2442no—
598C8—2442no—
599C22—21no—
600C22—21no—
601C22—612no—
602C22—612no—
603C22—1221no—
604C22—1221no—
605C22—1221no—
606C22—1221no—
607C22—2444no—
608C22#103×D6112yes—
609C22C2×C22⋊C4×D6111yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—612no—
616C4—612no—
617C4—612no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—2442no—
622C4—2442no—
623C4#103×D6112yes—
624C4#1684052712yes—
625C4C2×SD16×D6111yescharacteristic
626C4C2×Q16×D6111yescharacteristic
627C2—22no—
628C2—1222no—
629C2—1222no—
630C2#2145426111yescharacteristic
631C2C2×#103×D6111yescharacteristic
632C2#421×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1481C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22⋊C4
cosocleC42×C61C24
hypercenter#1481D61
hypocenterC61#17486
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #21444272C2semidirect
5. #21444246C2semidirect
6. #21444223C2semidirect
7. #21444222C2semidirect
8. #21444221C2semidirect
9. C61×#1481C2semidirect
42. #16839494C22semidirect
43. Q8⋊#92418C22semidirect
44. #16839492C22semidirect
48. C61×Q8⋊C8C22semidirect
319. #1481D61semidirect
364. Q8⋊C8C2×D61semidirect
365. C61#17486semidirect

Maximal subgroups

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

subgroupindex
#533×D612
#431×D612
C2×#168397842
#214442722
#214442462
#214442232
#214442222
#214442212
C61×#14812
#1748661