Finite Group Databasebeta

← #29573385

Subgroups — #29573385

Order 15616.

940 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#380×D61C211yesmaximal, characteristic
2#21445728C211yesmaximal, characteristic
3#21444040C211yesmaximal, characteristic
4#21443699C211yesmaximal, characteristic, complemented
5#21443698C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C2×C4⋊C4×D61C411yescharacteristic, complemented
10C2×C4⋊C4×D61C411yescharacteristic, complemented
11C22×#11758198—21no—
12C2×C22⋊C4×D61—21no—
13C2×C22⋊#92418C2211yescharacteristic
14C2×#14519689—21no—
15C2×#14519689—21no—
16#16839622C2211yescharacteristic
17#16839621—21no—
18#16839620—21no—
19#16839619C411yescharacteristic, complemented
20#16839619C411yescharacteristic, complemented
21C2×#14519684—21no—
22C2×#14519684C2211yescharacteristic
23#95×D61—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C24×D61D411yescharacteristic
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C22×C4×D61—21no—
31C22×C4×D61—21no—
32C22×C4×D61—21no—
33C22×C4×D61—21no—
34C22×C4×D61—21no—
35C22×C4×D61—21no—
36C22×C4×D61—42no—
37C22×C4×D61—42no—
38C22×C4×D61C2×C411yescharacteristic
39C22×C4×D61C2×C411yescharacteristic
40C22×C4×D61D411yescharacteristic
41C22×C4×D61D411yescharacteristic
42C22×#92418—21no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C4⋊C4×D61—42no—
48C4⋊C4×D61—42no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—24no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—42no—
54C2×#11758198—42no—
55C22⋊C4×D61—42no—
56C22⋊C4×D61—42no—
57C22⋊#92418—21no—
58C22⋊#92418—21no—
59#14519689—42no—
60#14519689—42no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—21no—
65#14519684—21no—
66#14519684—42no—
67C23×C4×C61—21no—
68C23×C4×C61C2311yescharacteristic
69C22×C8×C61—21no—
70C2×C4⋊C4×C61C2×C411yescharacteristic
71C2×C4⋊C4×C61C2×C411yescharacteristic
72C2×C22⋊C4×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61—21no—
75#95×C61—21no—
76#95×C61—21no—
77#95×C61—21no—
78C24×C61C2×D411yescharacteristic
79C23×D61—21no—
80C23×D61—21no—
81C23×D61—21no—
82C23×D61—21no—
83C23×D61—22no—
84C23×D61—22no—
85C23×D61—41no—
86C23×D61—41no—
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C23×D61D812yes—
90C23×D61SD1612yes—
91C22×C4×C61—22no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—41no—
95C22×C4×C61—41no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61C22×C411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C22×C4×C61#4111yescharacteristic
107C22×C4×C61#4111yescharacteristic
108C22×Dic61—21no—
109C22×Dic61—21no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—21no—
113C22×Dic61—21no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61—41no—
120C22×Dic61—41no—
121C22×Dic61C22⋊C411yescharacteristic
122C22×Dic61C22⋊C411yescharacteristic
123C2×C4×D61—22no—
124C2×C4×D61—21no—
125C2×C4×D61—21no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—22no—
135C2×C4×D61—44no—
136C2×C4×D61—44no—
137C2×C4×D61—44no—
138C2×C4×D61—44no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×C4×D61—41no—
142C2×C4×D61—41no—
143C2×C4×D61—42no—
144C2×C4×D61—42no—
145C2×C4×D61—42no—
146C2×C4×D61—42no—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C8×C61—41no—
150C2×C8×C61—41no—
151C2×C8×C61—41no—
152C4⋊C4×C61—41no—
153C4⋊C4×C61—41no—
154C22⋊C4×C61—41no—
155C22⋊C4×C61—41no—
156C22⋊Dic61—41no—
157C22⋊Dic61—41no—
158#11758198—48no—
159#11758198—42no—
160#11758198—42no—
161C4⋊Dic61—41no—
162C4⋊Dic61—41no—
163#11758196—42no—
164#11758196—42no—
165C2×#92418—41no—
166C2×#92418—41no—
167C2×#92418—41no—
168C23×C61—21no—
169C23×C61—21no—
170C23×C61—21no—
171C23×C61—21no—
172C23×C61C2×C22⋊C411yescharacteristic
173C23×C61#12311yescharacteristic
174C23×C61#12311yescharacteristic
175C23×C61C2×D811yescharacteristic
176C23×C61C2×SD1611yescharacteristic
177C23×C61#13711yescharacteristic
178C23×C61#13711yescharacteristic
179C22×D61—21no—
180C22×D61—21no—
181C22×D61—21no—
182C22×D61—21no—
183C22×D61—21no—
184C22×D61—21no—
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—22no—
190C22×D61—22no—
191C22×D61—22no—
192C22×D61—22no—
193C22×D61—24no—
194C22×D61—24no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—42no—
198C22×D61—42no—
199C22×D61—42no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61#9912yes—
206C22×D61#10212yes—
207C22×D61#10212yes—
208C22×D61#10412yes—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—81no—
227C2×C4×C61—81no—
228C2×C4×C61—81no—
229C2×C4×C61—81no—
230C2×C4×C61#11711yescharacteristic
231C2×C4×C61#11711yescharacteristic
232C2×C4×C61#12311yescharacteristic
233C2×C4×C61#12311yescharacteristic
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—21no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—42no—
243C2×Dic61—42no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—81no—
251C2×Dic61—81no—
252C2×Dic61—81no—
253C2×Dic61—81no—
254C2×Dic61#9912yes—
255C4×D61—24no—
256C4×D61—24no—
257C4×D61—42no—
258C4×D61—42no—
259C4×D61—42no—
260C4×D61—42no—
261C4×D61—42no—
262C4×D61—42no—
263C4×D61—84no—
264C4×D61—84no—
265C8×C61—81no—
266#92418—81no—
267#8712—611nomaximal, Sylow
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61—21no—
274C22×C61—21no—
275C22×C61—21no—
276C22×C61—21no—
277C22×C61—21no—
278C22×C61—21no—
279C22×C61—21no—
280C22×C61#38111yescharacteristic
281C22×C61C2×#9911yescharacteristic
282C22×C61C2×#9911yescharacteristic
283C22×C61C2×#10211yescharacteristic
284C22×C61#41911yescharacteristic
285C22×C61C2×#10411yescharacteristic
286C22×C61#42111yescharacteristic
287C22×C61#48011yescharacteristic
288C22×C61#48011yescharacteristic
289C22×C61#48311yescharacteristic
290C22×C61#48311yescharacteristic
291C2×D61—22no—
292C2×D61—22no—
293C2×D61—22no—
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—44no—
301C2×D61—44no—
302C2×D61—44no—
303C2×D61—44no—
304C2×D61—41no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61#32714yes—
309C4×C61—21no—
310C4×C61—21no—
311C4×C61—21no—
312C4×C61—21no—
313C4×C61—82no—
314C4×C61—81no—
315C4×C61—81no—
316Dic61—22no—
317Dic61—41no—
318Dic61—82no—
319Dic61—81no—
320Dic61—81no—
321C2×#380—611no—
322#1779—611no—
323C22⋊#95—611no—
324#1294—611no—
325#1294—611no—
326#1294—611no—
327#1294D6111yescharacteristic, complemented
328C2×C61—21no—
329C2×C61—21no—
330C2×C61—21no—
331C2×C61—21no—
332C2×C61C2×#32711yescharacteristic
333C2×C61#150811yescharacteristic
334C2×C61#151111yescharacteristic
335C2×C61#151911yescharacteristic
336C2×C61#181911yescharacteristic
337C2×C61#182311yescharacteristic
338C2×C61#182611yescharacteristic
339D61—24no—
340D61—42no—
341C24×C4—611no—
342C22×C4⋊C4—611no—
343C22×C4⋊C4—611no—
344C22×C22⋊C4—1221no—
345C22×C22⋊C4—1221no—
346C2×C22⋊C8—611no—
347C2×C22⋊C8—1221no—
348C2×C22⋊C8—1221no—
349C2×C22⋊C8C2×D6111yescharacteristic
350#380—611no—
351#380—611no—
352#380—611no—
353#380—1221no—
354#380—1221no—
355#380C2×D6111yescharacteristic
356C2×#95—611no—
357C2×#95—1221no—
358C2×#95—1221no—
359C2×#95C2×D6111yescharacteristic
360C61#871211yescharacteristic, complemented, Sylow
361C25—611no—
362C23×C4—21no—
363C23×C4—611no—
364C23×C4—611no—
365C23×C4—611no—
366C23×C4—611no—
367C23×C4—611no—
368C23×C4—1221no—
369C23×C4—1221no—
370C23×C4—1221no—
371C23×C4—1221no—
372C23×C4—1221no—
373C23×C4—1221no—
374C23×C4—1221no—
375C23×C4—2442no—
376C23×C4—2442no—
377C23×C4C22×D6111yescharacteristic
378C22×C8—21no—
379C22×C8—1221no—
380C2×C4⋊C4—611no—
381C2×C4⋊C4—611no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—2442no—
385C2×C4⋊C4—2442no—
386C2×C4⋊C4C4×D6111yescharacteristic
387C2×C4⋊C4C4×D6111yescharacteristic
388C2×C22⋊C4—21no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1224no—
392C2×C22⋊C4—1221no—
393C2×C22⋊C4—2442no—
394C2×C22⋊C4—2442no—
395C2×C22⋊C4—2442no—
396C2×C22⋊C4—2442no—
397C22⋊C8—21no—
398C22⋊C8—21no—
399C22⋊C8—1221no—
400C22⋊C8—1221no—
401C22⋊C8—2442no—
402C22⋊C8—2442no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—2442no—
412C24—611no—
413C24—611no—
414C24—612no—
415C24—612no—
416C24—1222no—
417C24—1222no—
418C24—1221no—
419C24—1221no—
420C24—1221no—
421C24—1221no—
422C24—2441no—
423C24—2441no—
424C24D4×D6111yescharacteristic
425C22×C4—22no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1221no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1221no—
447C22×C4—1221no—
448C22×C4—1221no—
449C22×C4—1221no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—2441no—
457C22×C4—2441no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2444no—
461C22×C4—2444no—
462C22×C4—2444no—
463C22×C4—2444no—
464C22×C4—2442no—
465C22×C4—2442no—
466C22×C4—2442no—
467C22×C4—2442no—
468C22×C4—2442no—
469C22×C4—2442no—
470C22×C4—2441no—
471C22×C4—2441no—
472C22×C4—2441no—
473C22×C4—2441no—
474C22×C4—2441no—
475C22×C4—2441no—
476C22×C4—2441no—
477C22×C4C2×C4×D6111yescharacteristic
478C22×C4#1175822211yescharacteristic
479C22×C4#1175822211yescharacteristic
480C22×C4D4×D6111yescharacteristic
481C22×C4#1175822411yescharacteristic
482C22×C4#1175822611yescharacteristic
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—2441no—
487C2×C8—2441no—
488C2×C8—2441no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—2441no—
492C4⋊C4—2441no—
493C4⋊C4—2442no—
494C4⋊C4—2442no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—2442no—
498C22⋊C4—2442no—
499C22⋊C4—2448no—
500C22⋊C4—2441no—
501C22⋊C4—2441no—
502C23—21no—
503C23—21no—
504C23—21no—
505C23—21no—
506C23—612no—
507C23—612no—
508C23—612no—
509C23—612no—
510C23—1224no—
511C23—1224no—
512C23—1221no—
513C23—1221no—
514C23—1221no—
515C23—1221no—
516C23—1221no—
517C23—1221no—
518C23—1221no—
519C23—1221no—
520C23—1221no—
521C23—1222no—
522C23—1222no—
523C23—1222no—
524C23—1222no—
525C23—1221no—
526C23—2442no—
527C23—2442no—
528C23—2442no—
529C23—2442no—
530C23—2442no—
531C23—2442no—
532C23—2442no—
533C23—2442no—
534C23—2442no—
535C23—2442no—
536C23C22⋊C4×D6111yescharacteristic
537C23#1451975911yescharacteristic
538C23#1451976211yescharacteristic
539C23D8×D6111yescharacteristic
540C23SD16×D6111yescharacteristic
541C23#1451980611yescharacteristic
542C23#1451980911yescharacteristic
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—81no—
561C2×C4—81no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—612no—
565C2×C4—1224no—
566C2×C4—1224no—
567C2×C4—1221no—
568C2×C4—1221no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—4884no—
573C2×C4—4884no—
574C2×C4—4881no—
575C2×C4—4881no—
576C2×C4—4881no—
577C2×C4—4881no—
578C2×C4—2442no—
579C2×C4—2442no—
580C2×C4—2442no—
581C2×C4—2442no—
582C2×C4—2442no—
583C2×C4—2442no—
584C2×C4—2442no—
585C2×C4—2442no—
586C2×C4—2442no—
587C2×C4—2442no—
588C2×C4—2442no—
589C2×C4—2441no—
590C2×C4—2441no—
591C2×C4—2441no—
592C2×C4—2441no—
593C2×C4—2441no—
594C2×C4—2441no—
595C2×C4#1451973411yescharacteristic
596C2×C4#1451973511yescharacteristic
597C2×C4#1451975911yescharacteristic
598C2×C4#1451976211yescharacteristic
599C8—81no—
600C8—4881no—
601C22—21no—
602C22—21no—
603C22—21no—
604C22—21no—
605C22—21no—
606C22—21no—
607C22—21no—
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—614no—
614C22—1222no—
615C22—1222no—
616C22—1222no—
617C22—1222no—
618C22—1222no—
619C22—1222no—
620C22—1222no—
621C22—1222no—
622C22—1222no—
623C22—2444no—
624C22—2444no—
625C22—2444no—
626C22—2444no—
627C22—2441no—
628C22—2441no—
629C22—2441no—
630C22—2441no—
631C22#1683962411yescharacteristic
632C22#99×D6111yescharacteristic
633C22#99×D6111yescharacteristic
634C22#102×D6111yescharacteristic
635C22#1683976911yescharacteristic
636C22#104×D6111yescharacteristic
637C22#1683977711yescharacteristic
638C22#1684007411yescharacteristic
639C22#1684007711yescharacteristic
640C22#1684009111yescharacteristic
641C22#1684009411yescharacteristic
642C4—21no—
643C4—21no—
644C4—21no—
645C4—21no—
646C4—82no—
647C4—81no—
648C4—81no—
649C4—1222no—
650C4—4882no—
651C4—4881no—
652C4—4881no—
653C4—2441no—
654C2—21no—
655C2—21no—
656C2—21no—
657C2—21no—
658C2—1224no—
659C2—2442no—
660C2#327×D6111yescharacteristic
661C2#2144433711yescharacteristic
662C2#2144435011yescharacteristic
663C2#2144438511yescharacteristic
664C2#2144589211yescharacteristic
665C2#2144590411yescharacteristic
666C2#2144591711yescharacteristic
subgroupG/H
centerC23C22⋊C4×D61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61C2×C22⋊C4
prime radicalC24×D61D4
cosocleC23×C4×C61C23
hypercenter#1294D61
hypocenterC61#8712
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
4. #21443699C2semidirect
5. #21443698C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
9. C2×C4⋊C4×D61C4semidirect
10. C2×C4⋊C4×D61C4semidirect
19. #16839619C4semidirect
20. #16839619C4semidirect
327. #1294D61semidirect
360. C61#8712semidirect

Maximal subgroups

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

subgroupindex
#380×D612
#214457282
#214440402
#214436992
#214436982
#214436972
C61×#12942
#871261