Finite Group Databasebeta

← #29646322

Subgroups — #29646322

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840460C211yesmaximal, characteristic
2#21454850C212yesmaximal, complemented
3#21444187C212yesmaximal, complemented
4#21444178C212yesmaximal, complemented
5#21444166C212yesmaximal, complemented
6#21444156C211yesmaximal, characteristic, complemented
7#21444152C211yesmaximal, characteristic, complemented
8#21444149C211yesmaximal, characteristic, complemented
9#21444136C211yesmaximal, characteristic, complemented
10#21444132C211yesmaximal, characteristic, complemented
11C2×C61×#324C211yesmaximal, characteristic, complemented
12#16840460—22no—
13#16840460—22no—
14#16840460—22no—
15#16840460—22no—
16C2×#14519772C411yescharacteristic
17C2×#14519772C2211yescharacteristic
18C2×#14519768C411yescharacteristic
19C2×#14519762C411yescharacteristic
20C2×#14519762C2211yescharacteristic
21C2×#14519752C411yescharacteristic
22C2×#14519751C411yescharacteristic
23C2×#14519751C411yescharacteristic
24C2×#14519751C2211yescharacteristic
25C2×#14519739C2211yescharacteristic
26C2×C4×C22⋊D61C411yescharacteristic
27C2×C4×C22⋊D61C411yescharacteristic
28C2×C4×C22⋊D61C2211yescharacteristic
29C2×#14519735C2211yescharacteristic
30#16839837—22no—
31#16839836—22no—
32#16839833—22no—
33C8×C22⋊D61—22no—
34#16839816C2212yes—
35#16839812C2212yes—
36#16839726C2212yes—
37#16839724C2212yes—
38C22⋊C8×D61C2212yes—
39#16839488C2211yescharacteristic
40#16839488C2211yescharacteristic
41#16839488C2212yes—
42#16839485C2212yes—
43#16839485C2212yes—
44#16839485C2212yes—
45#16839485C2212yes—
46C22×C4⋊C4×C61C2211yescharacteristic
47C2×C22⋊C8×C61C2212yes—
48C61×#324C2211yescharacteristic
49C61×#324C2211yescharacteristic
50C61×#324C2212yes—
51C22×D244C2×C411yescharacteristic
52C22×D244C2×C411yescharacteristic
53C22×D244C2×C411yescharacteristic
54C22×C22⋊D61C2×C411yescharacteristic
55C22×C22⋊D61C2×C411yescharacteristic
56C22×C22⋊D61C2×C411yescharacteristic
57C22×C4×D61C2×C411yescharacteristic
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194—22no—
61C2×#11758189—22no—
62C2×C8×D61—22no—
63#14519772—22no—
64#14519772—22no—
65#14519772—22no—
66#14519772—22no—
67#14519768—22no—
68#14519768—22no—
69#14519762—22no—
70#14519762—22no—
71#14519762—22no—
72#14519762—22no—
73#14519752—22no—
74#14519752—22no—
75#14519751—22no—
76#14519751—22no—
77#14519751—22no—
78#14519751—22no—
79#14519751—22no—
80#14519751—22no—
81#14519739—22no—
82#14519739—22no—
83C4×C22⋊D61—21no—
84C4×C22⋊D61—21no—
85C4×C22⋊D61—21no—
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90C4×C22⋊D61—21no—
91C4×C22⋊D61D412yes—
92C4×C22⋊D61D412yes—
93C4×C22⋊D61D412yes—
94C4×C22⋊D61D412yes—
95#14519735—22no—
96#14519735—22no—
97C2×C4⋊Dic61C2×C411yescharacteristic
98C2×C4⋊Dic61C2×C411yescharacteristic
99C2×C4⋊Dic61C2×C411yescharacteristic
100C2×#11758196C2×C411yescharacteristic
101C2×#11758196C2×C411yescharacteristic
102C2×#11758196C2×C411yescharacteristic
103C2×C22⋊Dic61C2×C411yescharacteristic
104C2×#11758198C2×C411yescharacteristic
105C2×#11758198C2×C411yescharacteristic
106C2×#11758198C2×C411yescharacteristic
107C2×#11758198C2×C411yescharacteristic
108C2×#11758198C2×C411yescharacteristic
109C2×#11758198C2×C411yescharacteristic
110C2×#11758198C2×C411yescharacteristic
111C2×#11758198C2311yescharacteristic
112C2×#11758198C2311yescharacteristic
113C2×C4×Dic61C2×C411yescharacteristic
114C2×C4×Dic61C2×C411yescharacteristic
115C2×C4×Dic61C2311yescharacteristic
116#14519706—22no—
117#14519706—22no—
118C22⋊#92418—22no—
119C22⋊#92418C2312yes—
120C22⋊#92418C2312yes—
121#14519689—22no—
122#14519689—22no—
123#14519687—22no—
124C8×Dic61—22no—
125C23×C4×C61C2×C411yescharacteristic
126C23×C4×C61C2×C411yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C22×C8×C61—22no—
129C2×C4⋊C4×C61—22no—
130C2×C4⋊C4×C61—22no—
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61C2311yescharacteristic
135C22⋊C8×C61—22no—
136C22⋊C8×C61C2312yes—
137C22⋊C8×C61C2312yes—
138C24×C61C22×C411yescharacteristic
139C23×D61C22×C411yescharacteristic
140C23×D61C22×C411yescharacteristic
141C23×D61C22×C411yescharacteristic
142C22×C4×C61—21no—
143C22×C4×C61—21no—
144C22×C4×C61—21no—
145C22×C4×C61—21no—
146C22×C4×C61—22no—
147C22×C4×C61—41no—
148C22×C4×C61—81no—
149C22×C4×C61—81no—
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C22×C411yescharacteristic
153C22×C4×C61C22×C411yescharacteristic
154C22×C4×C61C22×C411yescharacteristic
155C22×C4×C61C2×D412yes—
156C22×C4×C61C2×D412yes—
157C22×C4×C61C2411yescharacteristic
158C2×C22⋊D61—21no—
159C2×C22⋊D61—21no—
160C2×C22⋊D61—21no—
161C2×C22⋊D61—21no—
162C2×C22⋊D61—42no—
163C2×C22⋊D61—42no—
164C2×C22⋊D61—42no—
165C2×C22⋊D61C22⋊C412yes—
166C2×C22⋊D61C22⋊C412yes—
167C22×Dic61C22×C411yescharacteristic
168C22×Dic61C22×C411yescharacteristic
169C22×Dic61C22×C411yescharacteristic
170C22×Dic61C22×C411yescharacteristic
171C22×Dic61C22×C411yescharacteristic
172C2×D244—22no—
173C2×D244—22no—
174C2×D244—22no—
175C2×D244—22no—
176C2×D244—41no—
177C2×D244—81no—
178C2×D244—81no—
179C2×C4×D61—22no—
180C2×C4×D61—21no—
181C2×C4×D61—21no—
182C2×C4×D61—21no—
183C2×C4×D61—21no—
184C2×C4×D61—41no—
185C2×C4×D61—81no—
186C2×C4×D61—81no—
187C2×C4×D61C2×D412yes—
188C2×C4×D61C2×D412yes—
189C2×C8×C61—22no—
190C2×C8×C61—22no—
191C2×C8×C61—82no—
192C4⋊C4×C61—22no—
193C4⋊C4×C61—22no—
194C4⋊C4×C61—22no—
195C4⋊C4×C61—22no—
196C22⋊Dic61C22⋊C411yescharacteristic
197C22⋊Dic61C22⋊C411yescharacteristic
198C22⋊Dic61C22⋊C411yescharacteristic
199C22⋊Dic61C22⋊C411yescharacteristic
200#11758198—22no—
201#11758198—22no—
202#11758198—22no—
203#11758198—22no—
204#11758198—22no—
205#11758198—21no—
206#11758198—21no—
207#11758198—21no—
208#11758198—21no—
209#11758198—22no—
210#11758198C22⋊C412yes—
211#11758198C22⋊C412yes—
212C4⋊Dic61—22no—
213C4⋊Dic61—22no—
214C4⋊Dic61—22no—
215#11758196—21no—
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196C22⋊C412yes—
220#11758196C22⋊C412yes—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61C2×D412yes—
226C4×Dic61C2×D412yes—
227#11758194—82no—
228C2×#92418—22no—
229C2×#92418—22no—
230#11758189—82no—
231C8×D61—82no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—22no—
235C23×C61—41no—
236C23×C61C2×C22⋊C411yescharacteristic
237C23×C61C2×C22⋊C411yescharacteristic
238C23×C61C23×C411yescharacteristic
239C22×D61—21no—
240C22×D61—21no—
241C22×D61—21no—
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—41no—
248C22×D61—41no—
249C22×D61—41no—
250C22×D61—41no—
251C22×D61—41no—
252C22×D61—41no—
253C22×D61C2×C22⋊C412yes—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—42no—
262C2×C4×C61—42no—
263C2×C4×C61—41no—
264C2×C4×C61—41no—
265C2×C4×C61—42no—
266C2×C4×C61—42no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—81no—
270C2×C4×C61—81no—
271C2×C4×C61C2×C22⋊C412yes—
272C2×C4×C61#13112yes—
273C2×C4×C61C22×D412yes—
274C22⋊D61—24no—
275C22⋊D61—42no—
276C22⋊D61—42no—
277C22⋊D61—42no—
278C22⋊D61—42no—
279C22⋊D61—42no—
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—41no—
285C2×Dic61—41no—
286C2×Dic61—41no—
287C2×Dic61—41no—
288C2×Dic61C2×C22⋊C411yescharacteristic
289C2×Dic61C2×C22⋊C411yescharacteristic
290C2×Dic61C2×C22⋊C411yescharacteristic
291C2×Dic61C2×C22⋊C411yescharacteristic
292C2×Dic61C2×C22⋊C412yes—
293D244—44no—
294D244—82no—
295D244—82no—
296C4×D61—42no—
297C4×D61—42no—
298C4×D61—42no—
299C4×D61—42no—
300C4×D61—81no—
301C4×D61—81no—
302C8×C61—42no—
303C8×C61—42no—
304#92418—42no—
305#92418—42no—
306#17427—611nomaximal, Sylow
307C22×C61—21no—
308C22×C61—21no—
309C22×C61—21no—
310C22×C61—21no—
311C22×C61—21no—
312C22×C61—21no—
313C22×C61—21no—
314C22×C61—42no—
315C22×C61—42no—
316C22×C61#41312yes—
317C22×C61C22×C22⋊C411yescharacteristic
318C22×C61C2×#13111yescharacteristic
319C22×C61#56811yescharacteristic
320C2×D61—22no—
321C2×D61—22no—
322C2×D61—22no—
323C2×D61—41no—
324C2×D61—41no—
325C2×D61—41no—
326C2×D61—41no—
327C2×D61—41no—
328C2×D61—41no—
329C2×D61—81no—
330C2×D61—81no—
331C2×D61—81no—
332C2×D61—81no—
333C2×D61—81no—
334C2×D61—81no—
335C4×C61—22no—
336C4×C61—22no—
337C4×C61—22no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341Dic61—21no—
342Dic61—21no—
343Dic61—21no—
344Dic61—21no—
345Dic61—22no—
346Dic61—41no—
347Dic61—41no—
348C2×#553—611no—
349#2974—612no—
350#1473—612no—
351#1471—612no—
352#1468—612no—
353#1465—611no—
354#1464—611no—
355#1463—611no—
356#1459—611no—
357#1458—611no—
358C2×#324D6111yescharacteristic, complemented
359C2×C61—21no—
360C2×C61—21no—
361C2×C61—22no—
362C2×C61—41no—
363C2×C61#288011yescharacteristic
364C2×C61#288311yescharacteristic
365C2×C61C2×#41311yescharacteristic
366D61—42no—
367D61—81no—
368D61—81no—
369#553—1222no—
370#553—1222no—
371#553—1222no—
372#553—1222no—
373C2×#126—611no—
374C2×#126—611no—
375C2×#125—611no—
376C2×#123—611no—
377C2×#123—611no—
378C2×#121—611no—
379C2×#121—611no—
380C2×#121—611no—
381C2×#121—611no—
382C2×C4×D4—611no—
383C2×C4×D4—611no—
384C2×C4×D4—611no—
385C2×C4×D4—611no—
386C2×#117—611no—
387C22×C4⋊C4C2×D6111yescharacteristic
388#436—1222no—
389#435—1222no—
390#435—1222no—
391C8×D4—1222no—
392#432—612no—
393#431—612no—
394#407—612no—
395#407—612no—
396C2×C22⋊C8—612no—
397C2×C22⋊C8C2×D6112yes—
398#324—611no—
399#324—611no—
400#324—612no—
401#324C2×D6111yescharacteristic
402#324C2×D6111yescharacteristic
403#324C2×D6112yes—
404#323—612no—
405#323—612no—
406#323—612no—
407#323—612no—
408C61#1742711yescharacteristic, complemented, Sylow
409C22×D4—611no—
410C22×D4—611no—
411C22×D4—611no—
412C22×D4—611no—
413C22×D4—611no—
414C22×D4—611no—
415C23×C4—611no—
416C23×C4—611no—
417C23×C4—611no—
418C23×C4C4×D6111yescharacteristic
419C23×C4C4×D6111yescharacteristic
420C23×C4C22×D6111yescharacteristic
421C2×M16—1222no—
422C2×M16—1222no—
423C22×C8—22no—
424C22×C8—1222no—
425#126—1222no—
426#126—1222no—
427#126—1222no—
428#126—1222no—
429#125—1222no—
430#125—1222no—
431#123—1222no—
432#123—1222no—
433#123—1222no—
434#123—1222no—
435#121—1222no—
436#121—1222no—
437#121—1222no—
438#121—1222no—
439#121—1222no—
440#121—1222no—
441#121—1222no—
442#121—1222no—
443C4×D4—612no—
444C4×D4—612no—
445C4×D4—612no—
446C4×D4—612no—
447C4×D4—1221no—
448C4×D4—1221no—
449C4×D4—1221no—
450C4×D4—1221no—
451C4×D4—1221no—
452C4×D4—1221no—
453C4×D4—1221no—
454C4×D4—1221no—
455C4×D4—1222no—
456C4×D4—1222no—
457#117—1222no—
458#117—1222no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—611no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4C4×D6111yescharacteristic
468C2×C4⋊C4C4×D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C22⋊C4—611no—
472C2×C22⋊C4—611no—
473C2×C22⋊C4—611no—
474C2×C22⋊C4—611no—
475C2×C22⋊C4—611no—
476C2×C22⋊C4—611no—
477C2×C22⋊C4—611no—
478C2×C22⋊C4—611no—
479C2×C22⋊C4—611no—
480C2×C22⋊C4—611no—
481C2×C42—611no—
482C2×C42—611no—
483C2×C42—611no—
484C4⋊C8—1222no—
485C4⋊C8—1222no—
486C22⋊C8—22no—
487C22⋊C8—612no—
488C22⋊C8—612no—
489C22⋊C8—1222no—
490C22⋊C8—1222no—
491C22⋊C8—1222no—
492C22⋊C8C22×D6112yes—
493C22⋊C8C22×D6112yes—
494#97—1222no—
495C4×C8—1222no—
496C24—611no—
497C24—611no—
498C24—611no—
499C24C2×C4×D6111yescharacteristic
500C2×D4—612no—
501C2×D4—612no—
502C2×D4—1222no—
503C2×D4—1222no—
504C2×D4—1221no—
505C2×D4—1221no—
506C2×D4—1221no—
507C2×D4—1221no—
508C2×D4—1222no—
509C2×D4—1222no—
510C2×D4—4881no—
511C2×D4—4881no—
512C2×D4—2441no—
513C2×D4—2442no—
514C2×D4—2442no—
515C2×D4—2442no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—41no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—611no—
525C22×C4—611no—
526C22×C4—611no—
527C22×C4—612no—
528C22×C4—612no—
529C22×C4—611no—
530C22×C4—611no—
531C22×C4—1221no—
532C22×C4—1221no—
533C22×C4—1221no—
534C22×C4—1221no—
535C22×C4—1222no—
536C22×C4—4881no—
537C22×C4—4881no—
538C22×C4—2441no—
539C22×C4C2×C4×D6111yescharacteristic
540C22×C4C2×C4×D6111yescharacteristic
541C22×C4C2×C4×D6111yescharacteristic
542C22×C4C2×C4×D6111yescharacteristic
543C22×C4C2×C4×D6111yescharacteristic
544C22×C4D4×D6112yes—
545C22×C4D4×D6112yes—
546C22×C4C23×D6111yescharacteristic
547M16—4882no—
548M16—4882no—
549C2×C8—22no—
550C2×C8—22no—
551C2×C8—82no—
552C2×C8—1222no—
553C2×C8—1222no—
554C2×C8—4882no—
555C4⋊C4—22no—
556C4⋊C4—22no—
557C4⋊C4—22no—
558C4⋊C4—22no—
559C4⋊C4—612no—
560C4⋊C4—612no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1222no—
566C4⋊C4—1222no—
567C4⋊C4—1222no—
568C22⋊C4—611no—
569C22⋊C4—611no—
570C22⋊C4—611no—
571C22⋊C4—611no—
572C22⋊C4—612no—
573C22⋊C4—612no—
574C22⋊C4—1222no—
575C22⋊C4—1221no—
576C22⋊C4—1221no—
577C22⋊C4—1221no—
578C22⋊C4—1221no—
579C22⋊C4—1222no—
580C22⋊C4—1222no—
581C22⋊C4—1222no—
582C22⋊C4—1222no—
583C22⋊C4—1222no—
584C42—612no—
585C42—612no—
586C42—1221no—
587C42—1221no—
588C42—1221no—
589C42—1221no—
590C23—22no—
591C23—21no—
592C23—21no—
593C23—41no—
594C23—612no—
595C23—1221no—
596C23—1221no—
597C23—1221no—
598C23—1221no—
599C23—1221no—
600C23—1221no—
601C23—1221no—
602C23—1221no—
603C23—2441no—
604C23—2441no—
605C23—2441no—
606C23—2441no—
607C23—2441no—
608C23—2441no—
609C23C22⋊C4×D6111yescharacteristic
610C23C22⋊C4×D6111yescharacteristic
611C23C22×C4×D6111yescharacteristic
612D4—1224no—
613D4—4882no—
614D4—4882no—
615D4—2444no—
616D4—2442no—
617D4—2442no—
618D4—2442no—
619D4—2442no—
620D4—2442no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—81no—
637C2×C4—81no—
638C2×C4—611no—
639C2×C4—611no—
640C2×C4—612no—
641C2×C4—611no—
642C2×C4—611no—
643C2×C4—1221no—
644C2×C4—1221no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—4881no—
648C2×C4—4881no—
649C2×C4—2442no—
650C2×C4—2442no—
651C2×C4—2442no—
652C2×C4—2442no—
653C2×C4—2441no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4C22⋊C4×D6112yes—
658C2×C4#1451978312yes—
659C2×C4C2×D4×D6112yes—
660C8—42no—
661C8—42no—
662C8—2442no—
663C8—2442no—
664C22—21no—
665C22—21no—
666C22—21no—
667C22—21no—
668C22—21no—
669C22—21no—
670C22—21no—
671C22—42no—
672C22—42no—
673C22—1222no—
674C22—1222no—
675C22—1222no—
676C22—4881no—
677C22—4881no—
678C22—4881no—
679C22—4881no—
680C22—4881no—
681C22—4881no—
682C22—2441no—
683C22—2441no—
684C22—2441no—
685C22—2441no—
686C22—2441no—
687C22—2441no—
688C22#1683974512yes—
689C22C2×C22⋊C4×D6111yescharacteristic
690C22C2×#1451978311yescharacteristic
691C22#1684052811yescharacteristic
692C4—22no—
693C4—22no—
694C4—22no—
695C4—41no—
696C4—41no—
697C4—41no—
698C4—1221no—
699C4—1221no—
700C4—1221no—
701C4—1221no—
702C4—1222no—
703C4—2441no—
704C4—2441no—
705C2—21no—
706C2—21no—
707C2—22no—
708C2—41no—
709C2—4881no—
710C2—4881no—
711C2—2442no—
712C2#2145426511yescharacteristic
713C2#2145427711yescharacteristic
714C2C2×#1683974511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#324C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840460C2
cosocleC22×C4×C61C24
hypercenterC2×#324D61
hypocenterC61#17427
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21444187C2semidirect
4. #21444178C2semidirect
5. #21444166C2semidirect
6. #21444156C2semidirect
7. #21444152C2semidirect
8. #21444149C2semidirect
9. #21444136C2semidirect
10. #21444132C2semidirect
11. C2×C61×#324C2semidirect
358. C2×#324D61semidirect
408. C61#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404602
#214548502
#214441872
#214441782
#214441662
#214441562
#214441522
#214441492
#214441362
#214441322
C2×C61×#3242
#1742761