Finite Group Databasebeta

← #29646146

Subgroups — #29646146

Order 15616.

960 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2#21454449C211yesmaximal, characteristic
3#432×D61C211yesmaximal, characteristic
4#21444181C214yesmaximal
5#21444173C214yesmaximal, complemented
6#21444163C211yesmaximal, characteristic, complemented
7#21444162C211yesmaximal, characteristic, complemented
8#21444162C211yesmaximal, characteristic, complemented
9C61×#1467C211yesmaximal, characteristic, complemented
10#16840316—21no—
11#16840316—21no—
12#16840316—21no—
13#16840316—21no—
14#16840316—21no—
15#16840316—21no—
16#16840316—21no—
17#16840316—21no—
18C2×#14519776C411yescharacteristic
19C2×#14519775C411yescharacteristic
20C2×#14519767C2212yes—
21C2×#14519757C411yescharacteristic
22C2×#14519755C2212yes—
23C2×#14519753C411yescharacteristic
24C2×C4×Dic122C412yes—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519734C412yes—
27C2×C42×D61C2211yescharacteristic
28#16839819C2211yescharacteristic
29#16839819C2211yescharacteristic
30#16839818—21no—
31#16839817—21no—
32#16839817—21no—
33#16839816C2212yes—
34#16839814—21no—
35#16839812C2212yes—
36#16839784—21no—
37C4⋊C8×D61—21no—
38#16839724C2212yes—
39C22⋊C8×D61C2212yes—
40#16839714—21no—
41#97×D61—21no—
42#16839488C2214yes—
43#16839487C2214yes—
44#16839487C2214yes—
45C2×C4×Q8×C61C2211yescharacteristic
46C61×#432C2211yescharacteristic
47C61×#432C2211yescharacteristic
48C61×#324C2214yes—
49C22×Dic122C2×C412yes—
50C22×Dic122C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2311yescharacteristic
54C2×#11758189—22no—
55C2×C8×D61—22no—
56#14519776—21no—
57#14519776—21no—
58#14519776—21no—
59#14519776—21no—
60#14519775—21no—
61#14519775—21no—
62#14519775—21no—
63#14519775—21no—
64#14519767—22no—
65#14519767—22no—
66#14519767—22no—
67#14519767—22no—
68#14519757—21no—
69#14519757—21no—
70#14519757—21no—
71#14519757—21no—
72#14519755—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519753—21no—
77#14519753—21no—
78#14519753—21no—
79#14519753—21no—
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—22no—
85C4×Dic122—22no—
86C4×Dic122—22no—
87C4×Dic122—22no—
88#14519734—22no—
89#14519734—22no—
90#14519734—22no—
91#14519734—22no—
92C2×C4⋊Dic61C2×C412yes—
93C2×C4⋊Dic61C2×C411yescharacteristic
94C2×#11758196C2×C412yes—
95C2×#11758196C2×C412yes—
96C2×#11758196C2×C412yes—
97C2×#11758196C2×C412yes—
98C2×#11758196C2312yes—
99C2×#11758198C2×C412yes—
100C2×#11758198C2×C412yes—
101C2×C4×Dic61C2×C412yes—
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61D411yescharacteristic
106C42×D61D411yescharacteristic
107C42×D61D411yescharacteristic
108C42×D61D411yescharacteristic
109C42×D61D411yescharacteristic
110C42×D61D411yescharacteristic
111C42×D61D411yescharacteristic
112C42×D61D411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115#14519706—22no—
116#14519706—22no—
117C22⋊#92418C2312yes—
118C22⋊#92418C2312yes—
119#14519689—22no—
120#14519689—22no—
121#14519688—21no—
122#14519688—21no—
123#14519687—22no—
124C8×Dic61—22no—
125C22×Q8×C61C2×C411yescharacteristic
126C4×Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2312yes—
132C2×C42×C61C2×C412yes—
133C2×C42×C61C2311yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61—21no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138#97×C61—21no—
139#97×C61—21no—
140C23×D61C22×C411yescharacteristic
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—42no—
144C22×C4×C61C22×C412yes—
145C22×C4×C61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C412yes—
148C22×C4×C61C2411yescharacteristic
149C22×Dic61C22×C412yes—
150C22×Dic61C22×C411yescharacteristic
151C22×Dic61C22×C411yescharacteristic
152C22×Dic61C22×C411yescharacteristic
153C22×Dic61C22×C412yes—
154C2×C4×D61—24no—
155C2×C4×D61—42no—
156C2×C4×D61—42no—
157C2×C4×D61C22⋊C411yescharacteristic
158C2×C4×D61C22⋊C411yescharacteristic
159C2×C4×D61C22⋊C411yescharacteristic
160C2×C4×D61C22⋊C411yescharacteristic
161C2×C4×D61C22⋊C411yescharacteristic
162C2×C4×D61C22⋊C411yescharacteristic
163C2×C4×D61C22⋊C411yescharacteristic
164C2×C4×D61C22⋊C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×D411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×Dic122—21no—
170C2×Dic122—21no—
171C2×Dic122—22no—
172C2×Dic122—22no—
173C2×Dic122—42no—
174C2×Dic122—44no—
175C2×C8×C61—22no—
176C2×C8×C61—22no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C42×C61—22no—
182C42×C61—22no—
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187#11758198—22no—
188#11758198—22no—
189#11758198—22no—
190#11758198—22no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—22no—
194C4⋊Dic61—22no—
195#11758196—22no—
196#11758196—22no—
197#11758196—22no—
198#11758196—22no—
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—22no—
205C4×Dic61—22no—
206C4×Dic61—22no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
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
219C2×#92418—22no—
220C2×#92418—22no—
221#11758189—44no—
222C8×D61—44no—
223C23×C61C23×C411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—41no—
227C22×D61C2×C22⋊C411yescharacteristic
228C22×D61C2×C22⋊C411yescharacteristic
229Q8×C61—42no—
230Q8×C61—42no—
231C2×C4×C61—22no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—24no—
236C2×C4×C61—41no—
237C2×C4×C61—42no—
238C2×C4×C61C2×C22⋊C411yescharacteristic
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C22×D411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×Dic61—22no—
245C2×Dic61—22no—
246C2×Dic61—22no—
247C2×Dic61—22no—
248C2×Dic61—22no—
249C2×Dic61—24no—
250C2×Dic61—42no—
251C2×Dic61C2×C22⋊C411yescharacteristic
252C2×Dic61C2×C22⋊C411yescharacteristic
253C2×Dic61C2×C22⋊C411yescharacteristic
254C2×Dic61C2×C22⋊C411yescharacteristic
255C2×Dic61C2×C22⋊C411yescharacteristic
256C2×Dic61C2×C22⋊C411yescharacteristic
257C4×D61—22no—
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—41no—
267C4×D61—41no—
268C4×D61#10114yes—
269Dic122—44no—
270Dic122—42no—
271Dic122—42no—
272Dic122—44no—
273C8×C61—42no—
274C8×C61—42no—
275#92418—42no—
276#92418—42no—
277#17404—611nomaximal, Sylow
278C22×C61—21no—
279C22×C61—21no—
280C22×C61C22×C22⋊C411yescharacteristic
281C22×C61#56812yes—
282C2×D61—21no—
283C2×D61—21no—
284C2×D61—21no—
285C2×D61—21no—
286C2×D61—21no—
287C2×D61—44no—
288C2×D61C2×#10112yes—
289C4×C61—21no—
290C4×C61—21no—
291C4×C61—21no—
292C4×C61—21no—
293C4×C61—21no—
294C4×C61—42no—
295C4×C61—42no—
296C4×C61C2×#10112yes—
297Dic61—21no—
298Dic61—21no—
299Dic61—21no—
300Dic61—21no—
301Dic61—42no—
302Dic61—42no—
303Dic61#41012yes—
304Dic61C2×#10112yes—
305C2×#533—611no—
306#2920—611no—
307C2×#432—611no—
308#1472—614no—
309#1470—614no—
310#1467—611no—
311#1467—611no—
312#1467—611no—
313#1467D6111yescharacteristic, complemented
314C2×C61—22no—
315C2×C61#287911yescharacteristic
316C2×C61C2×#41011yescharacteristic
317C2×C61C22×#10111yescharacteristic
318D61—22no—
319D61—41no—
320#533—1221no—
321#533—1221no—
322#533—1221no—
323#533—1221no—
324#533—1221no—
325#533—1221no—
326#533—1221no—
327#533—1221no—
328C2×C4⋊Q8—611no—
329C2×C4⋊Q8—611no—
330C2×#125—612no—
331C2×C22⋊Q8—611no—
332C2×C22⋊Q8—611no—
333C2×C22⋊Q8—612no—
334C2×C4×Q8—612no—
335C2×C4×Q8—611no—
336C2×C4×Q8C2×D6111yescharacteristic
337C2×#117—612no—
338C22×C42—611no—
339#432—611no—
340#432—611no—
341#432—612no—
342#432—1221no—
343#432—1221no—
344#432—1221no—
345#432C2×D6111yescharacteristic
346#432C2×D6111yescharacteristic
347#431—612no—
348#431—1221no—
349#423—1221no—
350C2×C4⋊C8—1221no—
351#407—612no—
352C2×C22⋊C8—612no—
353C4×M16—1221no—
354C2×#97—1221no—
355#324—614no—
356#324—614no—
357#324—614no—
358#324C2×D6114yes—
359C61#1740411yescharacteristic, complemented, Sylow
360C22×Q8—612no—
361C22×Q8—611no—
362C22×Q8C4×D6111yescharacteristic
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C2×M16—1222no—
367C22×C8—1222no—
368C4⋊Q8—1221no—
369C4⋊Q8—1221no—
370C4⋊Q8—1221no—
371C4⋊Q8—1221no—
372C4⋊Q8—1221no—
373C4⋊Q8—1221no—
374C4⋊Q8—1221no—
375C4⋊Q8—1221no—
376#125—1222no—
377#125—1222no—
378#125—1222no—
379#125—1222no—
380C22⋊Q8—1222no—
381C22⋊Q8—1222no—
382C22⋊Q8—1222no—
383C22⋊Q8—1222no—
384C22⋊Q8—1221no—
385C22⋊Q8—1221no—
386C22⋊Q8—1221no—
387C22⋊Q8—1221no—
388C22⋊Q8—1221no—
389C22⋊Q8—1221no—
390C22⋊Q8—1221no—
391C22⋊Q8—1221no—
392C4×Q8—21no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—1222no—
397C4×Q8—1222no—
398C4×Q8—1222no—
399C4×Q8—1222no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×Q8—1221no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408C2×C4⋊C4—612no—
409C2×C4⋊C4—612no—
410C2×C4⋊C4—612no—
411C2×C4⋊C4—612no—
412C2×C4⋊C4—612no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4C4×D6111yescharacteristic
416C2×C4⋊C4C22×D6112yes—
417C2×C22⋊C4—612no—
418C2×C22⋊C4—612no—
419C2×C42—611no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—611no—
423C2×C42—611no—
424C2×C42—611no—
425C2×C42—611no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—612no—
431C2×C42C4×D6112yes—
432C2×C42C22×D6111yescharacteristic
433C4⋊C8—21no—
434C4⋊C8—21no—
435C4⋊C8—1222no—
436C4⋊C8—1222no—
437C4⋊C8—1221no—
438C4⋊C8—1221no—
439C22⋊C8—612no—
440C22⋊C8—612no—
441C22⋊C8—1222no—
442C22⋊C8—1222no—
443C22⋊C8C22×D6112yes—
444C22⋊C8C22×D6112yes—
445#97—21no—
446#97—21no—
447#97—1222no—
448#97—1221no—
449#97—1221no—
450C4×C8—1222no—
451C24—611no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—42no—
455C2×Q8—1222no—
456C2×Q8—1222no—
457C2×Q8—1221no—
458C2×Q8—1221no—
459C2×Q8—2442no—
460C2×Q8—2444no—
461C22×C4—611no—
462C22×C4—611no—
463C22×C4—611no—
464C22×C4—611no—
465C22×C4—611no—
466C22×C4—611no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—611no—
471C22×C4—611no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—611no—
476C22×C4—612no—
477C22×C4—612no—
478C22×C4—1224no—
479C22×C4—2442no—
480C22×C4—2442no—
481C22×C4C2×C4×D6112yes—
482C22×C4C2×C4×D6111yescharacteristic
483C22×C4C2×C4×D6111yescharacteristic
484C22×C4C2×C4×D6112yes—
485C22×C4C23×D6111yescharacteristic
486M16—2444no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—1222no—
490C2×C8—1222no—
491C2×C8—2444no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—1222no—
497C4⋊C4—1222no—
498C4⋊C4—1222no—
499C4⋊C4—1222no—
500C4⋊C4—1222no—
501C4⋊C4—1222no—
502C4⋊C4—1222no—
503C4⋊C4—1222no—
504C4⋊C4—1222no—
505C4⋊C4—1222no—
506C4⋊C4—1222no—
507C4⋊C4—1222no—
508C4⋊C4—1221no—
509C4⋊C4—1221no—
510C22⋊C4—1222no—
511C22⋊C4—1222no—
512C22⋊C4—1222no—
513C22⋊C4—1222no—
514C42—22no—
515C42—22no—
516C42—611no—
517C42—611no—
518C42—611no—
519C42—611no—
520C42—611no—
521C42—611no—
522C42—611no—
523C42—611no—
524C42—611no—
525C42—611no—
526C42—611no—
527C42—611no—
528C42—1222no—
529C42—1222no—
530C42D4×D6111yescharacteristic
531C42D4×D6111yescharacteristic
532C42D4×D6111yescharacteristic
533C42D4×D6111yescharacteristic
534C23—611no—
535C23—611no—
536C23—1222no—
537C23—1222no—
538C23—2441no—
539C23C22×C4×D6111yescharacteristic
540Q8—42no—
541Q8—42no—
542Q8—2442no—
543Q8—2442no—
544Q8—2444no—
545Q8—2444no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—611no—
554C2×C4—611no—
555C2×C4—614no—
556C2×C4—611no—
557C2×C4—611no—
558C2×C4—611no—
559C2×C4—611no—
560C2×C4—1222no—
561C2×C4—1222no—
562C2×C4—1222no—
563C2×C4—1222no—
564C2×C4—1222no—
565C2×C4—1222no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1222no—
570C2×C4—1224no—
571C2×C4—2441no—
572C2×C4—2441no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2442no—
578C2×C4C22⋊C4×D6111yescharacteristic
579C2×C4C22⋊C4×D6111yescharacteristic
580C2×C4C22⋊C4×D6111yescharacteristic
581C2×C4C22⋊C4×D6111yescharacteristic
582C2×C4C2×D4×D6111yescharacteristic
583C2×C4C2×D4×D6111yescharacteristic
584C8—42no—
585C8—42no—
586C8—2442no—
587C8—2442no—
588C22—21no—
589C22—21no—
590C22—612no—
591C22—1221no—
592C22—1221no—
593C22—1221no—
594C22—1221no—
595C22—1221no—
596C22—2444no—
597C22C2×C22⋊C4×D6111yescharacteristic
598C22#1684052812yes—
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—21no—
604C4—42no—
605C4—42no—
606C4—612no—
607C4—612no—
608C4—1221no—
609C4—1221no—
610C4—1221no—
611C4—1221no—
612C4—2442no—
613C4—2442no—
614C4#101×D6112yes—
615C2—22no—
616C2—1222no—
617C2—2441no—
618C2#2145426211yescharacteristic
619C2#410×D6111yescharacteristic
620C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1467C2
socleC22×C61C22×C22⋊C4
prime radicalC23×D61C22×C4
cosocleC22×C4×C61C24
hypercenter#1467D61
hypocenterC61#17404
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1467

Complements

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

NH ≅ G/Ntype
5. #21444173C2semidirect
6. #21444163C2semidirect
7. #21444162C2semidirect
8. #21444162C2semidirect
9. C61×#1467C2semidirect
313. #1467D61semidirect
359. C61#17404semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
#214544492
#432×D612
#214441812
#214441732
#214441632
#214441622
C61×#14672
#1740461