Finite Group Databasebeta

← #29575567

Subgroups — #29575567

Order 15616.

984 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C22⋊C8×D61C211yesmaximal, characteristic
2#21454107C211yesmaximal, characteristic
3C2×#16839500C211yesmaximal, characteristic, complemented
4C2×#16839498C211yesmaximal, characteristic, complemented
5#21444040C211yesmaximal, characteristic
6#21443697C211yesmaximal, characteristic, complemented
7C61×#1294C211yesmaximal, characteristic, complemented
8C23×C4×D61C2211yescharacteristic
9C22×C8×D61—21no—
10C2×#14519757C411yescharacteristic, complemented
11C2×#14519757C411yescharacteristic, complemented
12C2×#14519756C2211yescharacteristic
13C22×#11758198—21no—
14C2×C22⋊#92418C2211yescharacteristic
15C2×#14519689—21no—
16C22⋊C8×D61—22no—
17C22⋊C8×D61—22no—
18#16839637—21no—
19#16839636—21no—
20#16839636—21no—
21#16839619C411yescharacteristic, complemented
22#16839619C411yescharacteristic, complemented
23#16839617—21no—
24C2×#14519684—21no—
25C2×#14519684C2211yescharacteristic
26#16839500—22no—
27#16839498—22no—
28C2×C22⋊C8×C61C2211yescharacteristic
29C61×#380C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C24×D61D411yescharacteristic
32C22×Dic122C2×C411yescharacteristic
33C23×Dic61—21no—
34C23×Dic61D411yescharacteristic
35C22×C4×D61—21no—
36C22×C4×D61—21no—
37C22×C4×D61—21no—
38C22×C4×D61—21no—
39C22×C4×D61—42no—
40C22×C4×D61—42no—
41C22×C4×D61C2×C411yescharacteristic
42C22×C4×D61C2×C411yescharacteristic
43C22×C4×D61D411yescharacteristic
44C22×C4×D61D411yescharacteristic
45C22×#92418—21no—
46C2×C8×D61—24no—
47C2×C8×D61—42no—
48C2×C8×D61—42no—
49#14519757—42no—
50#14519757—42no—
51#14519756—21no—
52#14519756—21no—
53#14519756—21no—
54#14519756—21no—
55C2×C4⋊Dic61—21no—
56C2×C4⋊Dic61—21no—
57C2×C4⋊Dic61C2×C411yescharacteristic
58C2×#11758196—21no—
59C2×C22⋊Dic61—21no—
60C2×#11758198—24no—
61C2×#11758198—21no—
62C2×#11758198—21no—
63C2×#11758198—21no—
64C2×#11758198—21no—
65C2×#11758198—42no—
66C2×#11758198—42no—
67C22⋊#92418—21no—
68C22⋊#92418D412yes—
69#14519689—24no—
70#14519684—21no—
71#14519684—21no—
72#14519684—21no—
73#14519684—21no—
74#14519684—42no—
75C23×C4×C61—21no—
76C23×C4×C61C2311yescharacteristic
77C22×C8×C61—21no—
78C2×C4⋊C4×C61C2×C411yescharacteristic
79C2×C4⋊C4×C61C2×C411yescharacteristic
80C2×C22⋊C4×C61—21no—
81C22⋊C8×C61—21no—
82C22⋊C8×C61D412yes—
83#95×C61—21no—
84#95×C61—21no—
85#95×C61—21no—
86C24×C61C2×D411yescharacteristic
87C23×D61—21no—
88C23×D61—21no—
89C23×D61—21no—
90C23×D61—21no—
91C23×D61—22no—
92C23×D61—22no—
93C23×D61—41no—
94C23×D61—41no—
95C23×D61C22⋊C411yescharacteristic
96C23×D61C22⋊C411yescharacteristic
97C23×D61SD1612yes—
98C23×D61Q1612yes—
99C22×C4×C61—22no—
100C22×C4×C61—21no—
101C22×C4×C61—21no—
102C22×C4×C61—41no—
103C22×C4×C61—41no—
104C22×C4×C61—41no—
105C22×C4×C61—41no—
106C22×C4×C61—41no—
107C22×C4×C61—41no—
108C22×C4×C61—41no—
109C22×C4×C61—41no—
110C22×C4×C61C22×C411yescharacteristic
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61#4111yescharacteristic
115C22×C4×C61#4111yescharacteristic
116C22×Dic61—21no—
117C22×Dic61—21no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—41no—
123C22×Dic61—41no—
124C22×Dic61—41no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C22×Dic61—41no—
128C22×Dic61—41no—
129C22×Dic61C22⋊C411yescharacteristic
130C22×Dic61C22⋊C411yescharacteristic
131C2×C4×D61—22no—
132C2×C4×D61—21no—
133C2×C4×D61—21no—
134C2×C4×D61—22no—
135C2×C4×D61—22no—
136C2×C4×D61—21no—
137C2×C4×D61—21no—
138C2×C4×D61—21no—
139C2×C4×D61—21no—
140C2×C4×D61—21no—
141C2×C4×D61—21no—
142C2×C4×D61—22no—
143C2×C4×D61—44no—
144C2×C4×D61—44no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61—41no—
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—41no—
154C2×Dic122—41no—
155C2×C8×C61—22no—
156C2×C8×C61—41no—
157C2×C8×C61—41no—
158C4⋊C4×C61—41no—
159C4⋊C4×C61—41no—
160C22⋊C4×C61—41no—
161C22⋊C4×C61—41no—
162C22⋊Dic61—41no—
163C22⋊Dic61—41no—
164#11758198—42no—
165#11758198—48no—
166#11758198—42no—
167#11758198—42no—
168#11758198—42no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—42no—
172C4⋊Dic61—42no—
173#11758196—41no—
174#11758196—41no—
175C2×#92418—22no—
176C2×#92418—41no—
177C2×#92418—41no—
178C8×D61—48no—
179C23×C61—21no—
180C23×C61—21no—
181C23×C61—21no—
182C23×C61—21no—
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61#12111yescharacteristic
185C23×C61#12111yescharacteristic
186C23×C61C2×SD1611yescharacteristic
187C23×C61C2×Q1611yescharacteristic
188C23×C61#13511yescharacteristic
189C23×C61#13511yescharacteristic
190C22×D61—21no—
191C22×D61—21no—
192C22×D61—21no—
193C22×D61—21no—
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—21no—
199C22×D61—21no—
200C22×D61—22no—
201C22×D61—22no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—24no—
205C22×D61—24no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61—42no—
212C22×D61—42no—
213C22×D61—42no—
214C22×D61—42no—
215C22×D61—42no—
216C22×D61#9912yes—
217C22×D61#10312yes—
218C22×D61#10312yes—
219C22×D61#10412yes—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—42no—
229C2×C4×C61—42no—
230C2×C4×C61—42no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61—41no—
237C2×C4×C61—81no—
238C2×C4×C61—81no—
239C2×C4×C61—81no—
240C2×C4×C61—81no—
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61#12011yescharacteristic
244C2×C4×C61#12311yescharacteristic
245C2×Dic61—21no—
246C2×Dic61—21no—
247C2×Dic61—21no—
248C2×Dic61—21no—
249C2×Dic61—21no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—81no—
262C2×Dic61—81no—
263C2×Dic61—81no—
264C2×Dic61—81no—
265C2×Dic61#9912yes—
266C4×D61—24no—
267C4×D61—24no—
268C4×D61—42no—
269C4×D61—42no—
270C4×D61—42no—
271C4×D61—42no—
272C4×D61—42no—
273C4×D61—42no—
274Dic122—81no—
275Dic122—81no—
276C8×C61—42no—
277#92418—42no—
278#9111—611nomaximal, Sylow
279C22×C61—21no—
280C22×C61—21no—
281C22×C61—21no—
282C22×C61—21no—
283C22×C61—21no—
284C22×C61—21no—
285C22×C61—21no—
286C22×C61—21no—
287C22×C61—21no—
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—21no—
291C22×C61#38611yescharacteristic
292C22×C61C2×#9911yescharacteristic
293C22×C61C2×#9911yescharacteristic
294C22×C61C2×#10311yescharacteristic
295C22×C61#41611yescharacteristic
296C22×C61C2×#10411yescharacteristic
297C22×C61#42111yescharacteristic
298C22×C61#46511yescharacteristic
299C22×C61#46511yescharacteristic
300C22×C61#46711yescharacteristic
301C22×C61#46711yescharacteristic
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—22no—
307C2×D61—22no—
308C2×D61—22no—
309C2×D61—22no—
310C2×D61—22no—
311C2×D61—44no—
312C2×D61—44no—
313C2×D61—44no—
314C2×D61—44no—
315C2×D61—41no—
316C2×D61—41no—
317C2×D61—41no—
318C2×D61—41no—
319C2×D61#32814yescomplemented
320C4×C61—21no—
321C4×C61—21no—
322C4×C61—21no—
323C4×C61—21no—
324C4×C61—82no—
325C4×C61—81no—
326C4×C61—81no—
327Dic61—22no—
328Dic61—41no—
329Dic61—82no—
330Dic61—81no—
331Dic61—81no—
332C22×C22⋊C8—611no—
333#2848—611no—
334C2×#328—611no—
335C2×#328—611no—
336C22⋊#95—611no—
337#1294—611no—
338#1294D6111yescharacteristic, complemented
339C2×C61—21no—
340C2×C61—21no—
341C2×C61—21no—
342C2×C61—21no—
343C2×C61C2×#32811yescharacteristic
344C2×C61#150111yescharacteristic
345C2×C61#151611yescharacteristic
346C2×C61#152011yescharacteristic
347C2×C61#187111yescharacteristic
348C2×C61#189211yescharacteristic
349C2×C61#189811yescharacteristic
350D61—24no—
351D61—42no—
352C24×C4—611no—
353C23×C8—1221no—
354C2×C22⋊Q8—611no—
355C2×C22⋊Q8—611no—
356C2×C22⋊Q8—611no—
357C22×C22⋊C4—1221no—
358C2×C22⋊C8—611no—
359C2×C22⋊C8—1222no—
360C2×C22⋊C8—1221no—
361C2×C22⋊C8—1222no—
362C2×C22⋊C8C2×D6111yescharacteristic
363#385—1221no—
364#385—1221no—
365#385—1221no—
366#380—611no—
367#380—611no—
368#380C2×D6111yescharacteristic
369#379—1221no—
370C2×#95—611no—
371C2×#95—1221no—
372C2×#95C2×D6111yescharacteristic
373#328—1222no—
374#328—1222no—
375C61#911111yescharacteristic, complemented, Sylow
376C25—611no—
377C22×Q8—611no—
378C23×C4—21no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—1221no—
385C23×C4—1221no—
386C23×C4—1221no—
387C23×C4—1221no—
388C23×C4—1221no—
389C23×C4—2442no—
390C23×C4—2442no—
391C23×C4C22×D6111yescharacteristic
392C22×C8—21no—
393C22×C8—1224no—
394C22×C8—1221no—
395C22×C8—2442no—
396C22×C8—2442no—
397C22⋊Q8—1221no—
398C22⋊Q8—1221no—
399C22⋊Q8—1221no—
400C22⋊Q8—1221no—
401C22⋊Q8—2442no—
402C22⋊Q8—2442no—
403C2×C4⋊C4—611no—
404C2×C4⋊C4—1221no—
405C2×C4⋊C4—1221no—
406C2×C4⋊C4—1221no—
407C2×C4⋊C4C4×D6111yescharacteristic
408C2×C4⋊C4C4×D6111yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—1221no—
411C2×C22⋊C4—1221no—
412C2×C22⋊C4—1221no—
413C2×C22⋊C4—1221no—
414C2×C22⋊C4—1224no—
415C2×C22⋊C4—1221no—
416C2×C22⋊C4—2442no—
417C2×C22⋊C4—2442no—
418C22⋊C8—21no—
419C22⋊C8—612no—
420C22⋊C8—1224no—
421C22⋊C8—1221no—
422C22⋊C8D24412yes—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—1221no—
427#95—1221no—
428#95—1221no—
429#95—1221no—
430#95—2442no—
431C24—611no—
432C24—611no—
433C24—612no—
434C24—612no—
435C24—1222no—
436C24—1222no—
437C24—1221no—
438C24—1221no—
439C24—1221no—
440C24—1221no—
441C24—2441no—
442C24—2441no—
443C24D4×D6111yescharacteristic
444C2×Q8—1221no—
445C2×Q8—1221no—
446C2×Q8—2441no—
447C2×Q8—2441no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—611no—
460C22×C4—611no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1221no—
467C22×C4—1221no—
468C22×C4—1221no—
469C22×C4—1221no—
470C22×C4—1221no—
471C22×C4—1221no—
472C22×C4—1221no—
473C22×C4—1221no—
474C22×C4—1221no—
475C22×C4—1221no—
476C22×C4—1222no—
477C22×C4—1221no—
478C22×C4—1221no—
479C22×C4—2441no—
480C22×C4—2441no—
481C22×C4—2441no—
482C22×C4—2441no—
483C22×C4—2444no—
484C22×C4—2444no—
485C22×C4—2444no—
486C22×C4—2444no—
487C22×C4—2441no—
488C22×C4—2441no—
489C22×C4—2441no—
490C22×C4—2441no—
491C22×C4—2441no—
492C22×C4—2441no—
493C22×C4—2441no—
494C22×C4C2×C4×D6111yescharacteristic
495C22×C4C2×D24411yescharacteristic
496C22×C4#1175822211yescharacteristic
497C22×C4D4×D6111yescharacteristic
498C22×C4D4×D6111yescharacteristic
499C22×C4#1175822611yescharacteristic
500C2×C8—22no—
501C2×C8—41no—
502C2×C8—41no—
503C2×C8—1222no—
504C2×C8—2448no—
505C2×C8—2441no—
506C2×C8—2441no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4—1221no—
510C4⋊C4—1221no—
511C4⋊C4—2442no—
512C4⋊C4—2442no—
513C4⋊C4—2441no—
514C4⋊C4—2441no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—2442no—
518C22⋊C4—2442no—
519C22⋊C4—2448no—
520C22⋊C4—2442no—
521C22⋊C4—2442no—
522C22⋊C4—2441no—
523C22⋊C4—2441no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—612no—
529C23—612no—
530C23—612no—
531C23—612no—
532C23—1224no—
533C23—1224no—
534C23—1221no—
535C23—1221no—
536C23—1221no—
537C23—1221no—
538C23—1221no—
539C23—1221no—
540C23—1222no—
541C23—1222no—
542C23—1222no—
543C23—1222no—
544C23—1221no—
545C23—1221no—
546C23—1221no—
547C23—1221no—
548C23—2442no—
549C23—2442no—
550C23—2442no—
551C23—2442no—
552C23—2442no—
553C23—2442no—
554C23—2442no—
555C23—2442no—
556C23—2442no—
557C23—2442no—
558C23C22⋊C4×D6111yescharacteristic
559C23#1451975011yescharacteristic
560C23#1451975211yescharacteristic
561C23SD16×D6111yescharacteristic
562C23Q16×D6111yescharacteristic
563C23#1451979611yescharacteristic
564C23#1451979811yescharacteristic
565Q8—4881no—
566Q8—4881no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—42no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—81no—
585C2×C4—81no—
586C2×C4—81no—
587C2×C4—81no—
588C2×C4—612no—
589C2×C4—1224no—
590C2×C4—1224no—
591C2×C4—1221no—
592C2×C4—1221no—
593C2×C4—1221no—
594C2×C4—1221no—
595C2×C4—1221no—
596C2×C4—4881no—
597C2×C4—4881no—
598C2×C4—4881no—
599C2×C4—4881no—
600C2×C4—2442no—
601C2×C4—2442no—
602C2×C4—2442no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2442no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4—2441no—
614C2×C4—2441no—
615C2×C4—2441no—
616C2×C4—2441no—
617C2×C4#1451973911yescharacteristic
618C2×C4C4×D24411yescharacteristic
619C2×C4#1451974711yescharacteristic
620C2×C4#1451976211yescharacteristic
621C8—42no—
622C8—2442no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—21no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—614no—
636C22—1222no—
637C22—1222no—
638C22—1222no—
639C22—1222no—
640C22—1222no—
641C22—1222no—
642C22—1222no—
643C22—1222no—
644C22—1222no—
645C22—2444no—
646C22—2444no—
647C22—2444no—
648C22—2444no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22#1683964011yescharacteristic
654C22#99×D6111yescharacteristic
655C22#99×D6111yescharacteristic
656C22#103×D6111yescharacteristic
657C22#1683975511yescharacteristic
658C22#104×D6111yescharacteristic
659C22#1683977711yescharacteristic
660C22#1683999011yescharacteristic
661C22#1683999211yescharacteristic
662C22#1684000211yescharacteristic
663C22#1684000411yescharacteristic
664C4—21no—
665C4—21no—
666C4—21no—
667C4—21no—
668C4—82no—
669C4—81no—
670C4—81no—
671C4—1222no—
672C4—4882no—
673C4—4881no—
674C4—4881no—
675C4—2441no—
676C2—21no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—1224no—
681C2—2442no—
682C2#328×D6111yescharacteristic
683C2#2144430711yescharacteristic
684C2#2144437211yescharacteristic
685C2#2144438911yescharacteristic
686C2#2144612011yescharacteristic
687C2#2144624111yescharacteristic
688C2#2144627111yescharacteristic
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#9111
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
3. C2×#16839500C2semidirect
4. C2×#16839498C2semidirect
6. #21443697C2semidirect
7. C61×#1294C2semidirect
10. C2×#14519757C4semidirect
11. C2×#14519757C4semidirect
21. #16839619C4semidirect
22. #16839619C4semidirect
319. C2×D61#328semidirect
338. #1294D61semidirect
375. C61#9111semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C8×D612
#214541072
C2×#168395002
C2×#168394982
#214440402
#214436972
C61×#12942
#911161