Finite Group Databasebeta

← #29646317

Subgroups — #29646317

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840468C211yesmaximal, characteristic
2#21454856C211yesmaximal, characteristic
3#21454853C211yesmaximal, characteristic
4#21444181C212yesmaximal, complemented
5#21444181C212yesmaximal, complemented
6#21444175C211yesmaximal, characteristic, complemented
7#21444162C211yesmaximal, characteristic, complemented
8#21444147C212yesmaximal, complemented
9#21444142C211yesmaximal, characteristic, complemented
10#324×D61C212yesmaximal, complemented
11C61×#1470C211yesmaximal, characteristic, complemented
12#16840468—21no—
13#16840468—21no—
14#16840468—22no—
15#16840468—22no—
16#16840468—21no—
17#16840468—21no—
18C2×#14519776C411yescharacteristic
19C2×#14519768C411yescharacteristic
20C2×#14519757C412yes—
21C2×#14519755C412yes—
22C2×#14519755C2212yes—
23C2×C4×Dic122C2211yescharacteristic
24C2×C4×D244C2211yescharacteristic
25C2×#14519739C411yescharacteristic
26C2×#14519739C411yescharacteristic
27C2×C4⋊C4×D61C2212yes—
28#16839841—21no—
29#16839839—21no—
30#16839835—22no—
31#16839832—22no—
32C8×D244—21no—
33#16839827—21no—
34#16839819C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839724C2212yes—
37#16839724C2212yes—
38C22⋊C8×D61C2212yes—
39C22⋊C8×D61C2212yes—
40#16839488C2212yes—
41#16839488C2212yes—
42#16839487C2211yescharacteristic
43#16839487C2212yes—
44#16839487C2211yescharacteristic
45#16839487C2211yescharacteristic
46#16839487C2211yescharacteristic
47#16839487C2212yes—
48C2×#125×C61C2211yescharacteristic
49C61×#432C2211yescharacteristic
50C61×#431C2211yescharacteristic
51C61×#324C2212yes—
52C61×#324C2212yes—
53C22×Dic122C2×C411yescharacteristic
54C22×Dic122C2×C412yes—
55C22×D244C2×C411yescharacteristic
56C22×C4×D61C2×C412yes—
57C22×C4×D61C2×C412yes—
58C22×C4×D61C2312yes—
59C2×#11758189—22no—
60C2×#11758189—22no—
61C2×C8×D61—22no—
62C2×C8×D61—22no—
63#14519776—22no—
64#14519776—21no—
65#14519776—21no—
66#14519768—22no—
67#14519768—21no—
68#14519768—21no—
69#14519757—22no—
70#14519757—22no—
71#14519757—22no—
72#14519757—22no—
73#14519755—22no—
74#14519755—22no—
75#14519755—22no—
76#14519755—22no—
77#14519755—22no—
78#14519755—22no—
79#14519755—22no—
80#14519755—22no—
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122—21no—
85C4×D244D411yescharacteristic
86C4×D244D411yescharacteristic
87C4×D244D412yes—
88C4×D244D412yes—
89C4×D244D411yescharacteristic
90C4×D244D411yescharacteristic
91#14519739—22no—
92#14519739—21no—
93#14519739—21no—
94#14519739—22no—
95#14519739—21no—
96#14519739—21no—
97C2×C4⋊Dic61C2×C412yes—
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196C2×C412yes—
101C2×#11758196C2×C412yes—
102C2×#11758196C2311yescharacteristic
103C2×#11758196C2311yescharacteristic
104C4⋊C4×D61—22no—
105C4⋊C4×D61—22no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×#11758198C2×C412yes—
109C2×#11758198C2×C412yes—
110C2×#11758198C2×C412yes—
111C2×C4×Dic61C2×C411yescharacteristic
112C2×C4×Dic61C2×C411yescharacteristic
113C4⋊#92418—21no—
114C4⋊#92418—21no—
115C22⋊#92418C2311yescharacteristic
116C22⋊#92418C2312yes—
117C22⋊#92418C2311yescharacteristic
118#14519689—22no—
119#14519689—22no—
120#14519689—22no—
121#14519689—22no—
122#14519688—21no—
123C4×#92418—21no—
124#125×C61—21no—
125#125×C61—21no—
126#125×C61—21no—
127#125×C61—21no—
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C412yes—
131C2×C4⋊C4×C61C2312yes—
132C2×C42×C61C2311yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C22⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2311yescharacteristic
138#97×C61—21no—
139C4×C8×C61—21no—
140C23×D61C22×C412yes—
141C22×C4×C61C22×C412yes—
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C22×C411yescharacteristic
144C22×C4×C61C22×C412yes—
145C22×C4×C61C2411yescharacteristic
146C22×Dic61C22×C411yescharacteristic
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C22×C411yescharacteristic
149C22×Dic61C22×C411yescharacteristic
150C22×Dic61C22×C412yes—
151C2×D244—24no—
152C2×D244C22⋊C412yes—
153C2×D244C22⋊C411yescharacteristic
154C2×D244C22⋊C411yescharacteristic
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—24no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—42no—
161C2×C4×D61—82no—
162C2×C4×D61—82no—
163C2×C4×D61C2×D412yes—
164C2×C4×D61C2×D412yes—
165C2×C4×D61C2×D412yes—
166C2×C4×D61C2×D412yes—
167C2×Dic122—21no—
168C2×Dic122—21no—
169C2×Dic122—22no—
170C2×Dic122—22no—
171C2×Dic122—22no—
172C2×Dic122—41no—
173C2×Dic122—82no—
174C2×C8×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—22no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—22no—
182C4⋊C4×C61—22no—
183C4⋊C4×C61—22no—
184C4⋊C4×C61—22no—
185C42×C61C2×D411yescharacteristic
186C42×C61C2×D411yescharacteristic
187C42×C61C2×D411yescharacteristic
188C42×C61C2×D411yescharacteristic
189#11758198—22no—
190#11758198—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198C22⋊C412yes—
194#11758198C22⋊C412yes—
195#11758198C22⋊C412yes—
196#11758198C22⋊C412yes—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—22no—
200C4⋊Dic61—22no—
201C4⋊Dic61C22⋊C412yes—
202C4⋊Dic61C22⋊C411yescharacteristic
203C4⋊Dic61C22⋊C411yescharacteristic
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207#11758196—21no—
208#11758196—22no—
209#11758196—22no—
210#11758196—22no—
211#11758196—22no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—22no—
219#11758189—82no—
220#11758189—82no—
221C8×D61—82no—
222C8×D61—82no—
223C23×C61C23×C411yescharacteristic
224C22×D61—22no—
225C22×D61—22no—
226C22×D61—24no—
227C22×D61—42no—
228C22×D61C2×C22⋊C412yes—
229C22×D61C2×C22⋊C412yes—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—22no—
233C2×C4×C61—22no—
234C2×C4×C61—22no—
235C2×C4×C61—22no—
236C2×C4×C61—22no—
237C2×C4×C61—41no—
238C2×C4×C61—42no—
239C2×C4×C61C2×C22⋊C411yescharacteristic
240C2×C4×C61C2×C22⋊C411yescharacteristic
241C2×C4×C61C2×C22⋊C411yescharacteristic
242C2×C4×C61C2×C22⋊C411yescharacteristic
243C2×C4×C61C22×D411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—21no—
251C2×Dic61—21no—
252C2×Dic61—42no—
253C2×Dic61—41no—
254C2×Dic61—41no—
255C2×Dic61C2×C22⋊C412yes—
256C2×Dic61C2×C22⋊C412yes—
257C2×Dic61#13112yes—
258D244—24no—
259D244—22no—
260D244#10114yes—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61—42no—
264C4×D61—42no—
265C4×D61—44no—
266C4×D61—44no—
267C4×D61—82no—
268C4×D61—82no—
269Dic122—42no—
270Dic122—42no—
271Dic122—82no—
272Dic122—82no—
273C8×C61—41no—
274C8×C61—42no—
275C8×C61—41no—
276#92418—41no—
277#92418—42no—
278#92418—41no—
279#17426—611nomaximal, Sylow
280C22×C61—21no—
281C22×C61—21no—
282C22×C61C22×C22⋊C411yescharacteristic
283C22×C61C2×#13111yescharacteristic
284C22×C61#56811yescharacteristic
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—22no—
290C2×D61—44no—
291C2×D61—44no—
292C2×D61C2×#10114yes—
293C4×C61—21no—
294C4×C61—21no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—42no—
299C4×C61—42no—
300C4×C61C2×#10112yes—
301Dic61—22no—
302Dic61—22no—
303Dic61—22no—
304Dic61—41no—
305Dic61—41no—
306Dic61—41no—
307C2×#554—611no—
308#2974—611no—
309#2974—611no—
310#1472—612no—
311#1472—612no—
312#1470—611no—
313#1470D6111yescharacteristic, complemented
314#1467—611no—
315#1463—612no—
316#1461—611no—
317C2×#324—612no—
318C2×C61—21no—
319C2×C61—21no—
320C2×C61#288011yescharacteristic
321C2×C61#288311yescharacteristic
322C2×C61C22×#10111yescharacteristic
323D61—24no—
324D61—42no—
325#554—1221no—
326#554—1221no—
327#554—1222no—
328#554—1222no—
329#554—1221no—
330#554—1221no—
331C2×C4⋊Q8—611no—
332C2×#125—611no—
333C2×#125C2×D6111yescharacteristic
334C2×C22⋊Q8—612no—
335C2×C22⋊Q8—612no—
336C2×C22⋊Q8—612no—
337C2×C4×Q8—611no—
338C2×C4×D4—611no—
339C2×C4×D4—611no—
340C2×C4×D4—611no—
341C22×C4⋊C4—612no—
342#436—1221no—
343#436—1221no—
344#435—1222no—
345#435—1222no—
346C8×D4—1221no—
347C8×D4—1221no—
348#432—611no—
349#432C2×D6111yescharacteristic
350#431—611no—
351#431C2×D6111yescharacteristic
352#407—612no—
353#407—612no—
354C2×C22⋊C8—612no—
355C2×C22⋊C8—612no—
356#324—612no—
357#324—612no—
358#324—611no—
359#324—612no—
360#324—611no—
361#324—611no—
362#324—611no—
363#324—612no—
364#324C2×D6112yes—
365#324C2×D6112yes—
366C61#1742611yescharacteristic, complemented, Sylow
367C22×Q8—611no—
368C22×Q8—612no—
369C22×D4—611no—
370C23×C4—612no—
371C23×C4—612no—
372C23×C4—612no—
373C2×M16—1222no—
374C2×M16—1222no—
375C22×C8—1222no—
376C22×C8—1222no—
377C4⋊Q8—1222no—
378C4⋊Q8—1221no—
379C4⋊Q8—1221no—
380#125—21no—
381#125—21no—
382#125—21no—
383#125—21no—
384#125—1222no—
385#125—1221no—
386#125—1221no—
387C22⋊Q8—1222no—
388C22⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C22⋊Q8—1222no—
392C22⋊Q8—1222no—
393C22⋊Q8—1222no—
394C22⋊Q8—1222no—
395C22⋊Q8—1222no—
396C22⋊Q8—1222no—
397C22⋊Q8—1222no—
398C22⋊Q8—1222no—
399C4×Q8—1221no—
400C4×Q8—1221no—
401C4×Q8—1221no—
402C4×Q8—1221no—
403C4×D4—611no—
404C4×D4—611no—
405C4×D4—612no—
406C4×D4—612no—
407C4×D4—611no—
408C4×D4—611no—
409C4×D4—1221no—
410C4×D4—1222no—
411C4×D4—1221no—
412C4×D4—1221no—
413C4×D4—1222no—
414C4×D4—1221no—
415C2×C4⋊C4—611no—
416C2×C4⋊C4—612no—
417C2×C4⋊C4—612no—
418C2×C4⋊C4—611no—
419C2×C4⋊C4—612no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—1222no—
423C2×C4⋊C4—1222no—
424C2×C4⋊C4—1222no—
425C2×C4⋊C4—1222no—
426C2×C4⋊C4C4×D6111yescharacteristic
427C2×C4⋊C4C4×D6111yescharacteristic
428C2×C4⋊C4C4×D6112yes—
429C2×C4⋊C4C22×D6112yes—
430C2×C22⋊C4—612no—
431C2×C22⋊C4—612no—
432C2×C22⋊C4—612no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42C22×D6111yescharacteristic
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—1221no—
439C4⋊C8—1221no—
440C22⋊C8—611no—
441C22⋊C8—612no—
442C22⋊C8—611no—
443C22⋊C8—1222no—
444C22⋊C8—1222no—
445C22⋊C8—1222no—
446C22⋊C8—1222no—
447C22⋊C8C22×D6111yescharacteristic
448C22⋊C8C22×D6112yes—
449C22⋊C8C22×D6111yescharacteristic
450#97—21no—
451#97—1221no—
452C4×C8—21no—
453C4×C8—1221no—
454C24—612no—
455C2×Q8—1222no—
456C2×Q8—1222no—
457C2×Q8—1222no—
458C2×Q8—1221no—
459C2×Q8—1221no—
460C2×Q8—4882no—
461C2×Q8—2441no—
462C2×D4—611no—
463C2×D4—612no—
464C2×D4—611no—
465C2×D4—1224no—
466C22×C4—611no—
467C22×C4—612no—
468C22×C4—612no—
469C22×C4—612no—
470C22×C4—612no—
471C22×C4—612no—
472C22×C4—611no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1224no—
476C22×C4—1222no—
477C22×C4—1222no—
478C22×C4—1222no—
479C22×C4—1222no—
480C22×C4—4882no—
481C22×C4—4882no—
482C22×C4—2442no—
483C22×C4C2×C4×D6112yes—
484C22×C4C2×C4×D6111yescharacteristic
485C22×C4C2×C4×D6111yescharacteristic
486C22×C4C2×C4×D6112yes—
487C22×C4C23×D6111yescharacteristic
488M16—4882no—
489M16—4882no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—22no—
493C2×C8—1221no—
494C2×C8—1221no—
495C2×C8—1222no—
496C2×C8—4882no—
497C2×C8—4882no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—22no—
505C4⋊C4—22no—
506C4⋊C4—612no—
507C4⋊C4—611no—
508C4⋊C4—611no—
509C4⋊C4—1222no—
510C4⋊C4—1222no—
511C4⋊C4—1222no—
512C4⋊C4—1222no—
513C4⋊C4—1222no—
514C4⋊C4—1222no—
515C4⋊C4—1221no—
516C4⋊C4—1221no—
517C4⋊C4—1221no—
518C4⋊C4—1221no—
519C4⋊C4—1221no—
520C4⋊C4—1221no—
521C22⋊C4—612no—
522C22⋊C4—612no—
523C22⋊C4—612no—
524C22⋊C4—612no—
525C22⋊C4—1222no—
526C22⋊C4—1222no—
527C22⋊C4—1222no—
528C22⋊C4—1222no—
529C42—1221no—
530C42—1221no—
531C42—1221no—
532C42—1221no—
533C42D4×D6111yescharacteristic
534C42D4×D6111yescharacteristic
535C42D4×D6111yescharacteristic
536C42D4×D6111yescharacteristic
537C23—612no—
538C23—612no—
539C23—1224no—
540C23—1222no—
541C23—1222no—
542C23—2442no—
543C23C22×C4×D6111yescharacteristic
544Q8—4882no—
545Q8—4882no—
546Q8—2442no—
547Q8—2442no—
548D4—614no—
549D4—1224no—
550D4—1222no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—612no—
561C2×C4—612no—
562C2×C4—612no—
563C2×C4—1221no—
564C2×C4—1221no—
565C2×C4—1221no—
566C2×C4—1221no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—4882no—
571C2×C4—4882no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2444no—
577C2×C4—2444no—
578C2×C4—2442no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4C22⋊C4×D6111yescharacteristic
582C2×C4C22⋊C4×D6111yescharacteristic
583C2×C4C22⋊C4×D6111yescharacteristic
584C2×C4C22⋊C4×D6111yescharacteristic
585C2×C4C2×D4×D6111yescharacteristic
586C2×C4C2×D4×D6111yescharacteristic
587C8—41no—
588C8—42no—
589C8—41no—
590C8—2441no—
591C8—2442no—
592C8—2441no—
593C22—21no—
594C22—21no—
595C22—614no—
596C22—1222no—
597C22—1222no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—2444no—
602C22—2444no—
603C22C2×C22⋊C4×D6111yescharacteristic
604C22#131×D6111yescharacteristic
605C22#1684052711yescharacteristic
606C4—21no—
607C4—21no—
608C4—21no—
609C4—21no—
610C4—21no—
611C4—42no—
612C4—42no—
613C4—1222no—
614C4—1222no—
615C4—1222no—
616C4—2441no—
617C4—2441no—
618C4—2441no—
619C4#101×D6112yes—
620C2—21no—
621C2—21no—
622C2—1224no—
623C2—2442no—
624C2#2145426711yescharacteristic
625C2#2145427811yescharacteristic
626C2C2×#101×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1470C2
socleC22×C61C22×C22⋊C4
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1470D61
hypocenterC61#17426
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1470

Complements

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

NH ≅ G/Ntype
4. #21444181C2semidirect
5. #21444181C2semidirect
6. #21444175C2semidirect
7. #21444162C2semidirect
8. #21444147C2semidirect
9. #21444142C2semidirect
10. #324×D61C2semidirect
11. C61×#1470C2semidirect
313. #1470D61semidirect
366. C61#17426semidirect

Maximal subgroups

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

subgroupindex
C2×#168404682
#214548562
#214548532
#214441812
#214441752
#214441622
#214441472
#214441422
#324×D612
C61×#14702
#1742661