Finite Group Databasebeta

← #29573399

Subgroups — #29573399

Order 15616.

868 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448201C211yesmaximal, 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×#14519735C411yescharacteristic, complemented
10C2×#14519735C411yescharacteristic, complemented
11C22×#11758198—21no—
12C2×C22⋊#92418C2211yescharacteristic
13C2×#14519689—21no—
14C2×#14519689—21no—
15#16839624—21no—
16#16839622C2211yescharacteristic
17#16839619C411yescharacteristic, complemented
18#16839619C411yescharacteristic, complemented
19#16839617—21no—
20C22⋊C4×Dic61—21no—
21#16839609—21no—
22C2×#14519684—21no—
23C2×#14519684C2211yescharacteristic
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—42no—
35C22×C4×D61—42no—
36C22×C4×D61C2×C411yescharacteristic
37C22×C4×D61C2×C411yescharacteristic
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×#92418—21no—
41#14519735—42no—
42#14519735—42no—
43C2×C4⋊Dic61C2×C411yescharacteristic
44C2×C4⋊Dic61C2×C411yescharacteristic
45C2×C22⋊Dic61—21no—
46C2×#11758198—24no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×#11758198—21no—
51C2×#11758198—42no—
52C2×#11758198—42no—
53C2×C4×Dic61—21no—
54C2×C4×Dic61—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57#14519689—42no—
58#14519689—42no—
59#14519684—21no—
60#14519684—21no—
61#14519684—21no—
62#14519684—21no—
63#14519684—21no—
64#14519684—42no—
65C23×C4×C61—21no—
66C23×C4×C61C2311yescharacteristic
67C22×C8×C61—21no—
68C2×C4⋊C4×C61C2×C411yescharacteristic
69C2×C4⋊C4×C61C2×C411yescharacteristic
70C2×C22⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73#95×C61—21no—
74#95×C61—21no—
75#95×C61—21no—
76C24×C61C2×D411yescharacteristic
77C23×D61—21no—
78C23×D61—21no—
79C23×D61—22no—
80C23×D61—22no—
81C23×D61—21no—
82C23×D61—21no—
83C23×D61—21no—
84C23×D61—21no—
85C23×D61—41no—
86C23×D61—41no—
87C23×D61C22⋊C411yescharacteristic
88C23×D61C22⋊C411yescharacteristic
89C22×C4×C61—22no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—41no—
93C22×C4×C61—41no—
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×C61C22×C411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C22×C4×C61#4111yescharacteristic
105C22×C4×C61#4111yescharacteristic
106C22×Dic61—21no—
107C22×Dic61—21no—
108C22×Dic61—22no—
109C22×Dic61—22no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C22×Dic61—41no—
118C22×Dic61—41no—
119C22×Dic61C22⋊C411yescharacteristic
120C22×Dic61C22⋊C411yescharacteristic
121C2×C4×D61—22no—
122C2×C4×D61—21no—
123C2×C4×D61—21no—
124C2×C4×D61—22no—
125C2×C4×D61—22no—
126C2×C4×D61—21no—
127C2×C4×D61—21no—
128C2×C4×D61—21no—
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×C4×D61—22no—
133C2×C4×D61—44no—
134C2×C4×D61—44no—
135C2×C4×D61—44no—
136C2×C4×D61—44no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×C4×D61—41no—
140C2×C4×D61—41no—
141C2×C8×C61—41no—
142C2×C8×C61—41no—
143C2×C8×C61—41no—
144C4⋊C4×C61—41no—
145C4⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊Dic61—41no—
149C22⋊Dic61—41no—
150#11758198—42no—
151#11758198—48no—
152#11758198—42no—
153#11758198—42no—
154#11758198—42no—
155C4⋊Dic61—41no—
156C4⋊Dic61—41no—
157C4×Dic61—42no—
158C4×Dic61—42no—
159C2×#92418—41no—
160C2×#92418—41no—
161C2×#92418—41no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61C2×C22⋊C411yescharacteristic
167C23×C61#12311yescharacteristic
168C23×C61#12311yescharacteristic
169C23×C61#13511yescharacteristic
170C23×C61#13511yescharacteristic
171C23×C61AGL(1,ℤ/8)11yescharacteristic
172C23×C61#13711yescharacteristic
173C22×D61—24no—
174C22×D61—24no—
175C22×D61—21no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—21no—
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—42no—
188C22×D61—42no—
189C22×D61—42no—
190C22×D61—42no—
191C22×D61—42no—
192C22×D61—42no—
193C22×D61—42no—
194C22×D61—42no—
195C22×D61—42no—
196C22×D61—42no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61#9912yes—
202C22×D61#10412yes—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—41no—
208C2×C4×C61—41no—
209C2×C4×C61—41no—
210C2×C4×C61—41no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—42no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—81no—
221C2×C4×C61—81no—
222C2×C4×C61—81no—
223C2×C4×C61—81no—
224C2×C4×C61#11711yescharacteristic
225C2×C4×C61#11711yescharacteristic
226C2×C4×C61#12311yescharacteristic
227C2×C4×C61#12311yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—42no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—81no—
245C2×Dic61—81no—
246C2×Dic61—81no—
247C2×Dic61—81no—
248C2×Dic61#9912yes—
249C4×D61—24no—
250C4×D61—24no—
251C4×D61—42no—
252C4×D61—42no—
253C4×D61—42no—
254C4×D61—42no—
255C4×D61—42no—
256C4×D61—42no—
257C8×C61—81no—
258#92418—81no—
259#8715—611nomaximal, Sylow
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—21no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—21no—
266C22×C61—21no—
267C22×C61—21no—
268C22×C61—21no—
269C22×C61—21no—
270C22×C61—21no—
271C22×C61—21no—
272C22×C61#38111yescharacteristic
273C22×C61C2×#9911yescharacteristic
274C22×C61C2×#9911yescharacteristic
275C22×C61#41611yescharacteristic
276C22×C61#41711yescharacteristic
277C22×C61C2×#10411yescharacteristic
278C22×C61#42111yescharacteristic
279C22×C61#48211yescharacteristic
280C22×C61#48211yescharacteristic
281C22×C61#48511yescharacteristic
282C22×C61#48511yescharacteristic
283C2×D61—22no—
284C2×D61—22no—
285C2×D61—22no—
286C2×D61—22no—
287C2×D61—22no—
288C2×D61—22no—
289C2×D61—44no—
290C2×D61—44no—
291C2×D61—44no—
292C2×D61—44no—
293C2×D61—41no—
294C2×D61—41no—
295C2×D61—41no—
296C2×D61—41no—
297C2×D61—41no—
298C2×D61—41no—
299C2×D61—41no—
300C2×D61—41no—
301C4×C61—21no—
302C4×C61—21no—
303C4×C61—21no—
304C4×C61—21no—
305C4×C61—82no—
306C4×C61—81no—
307C4×C61—81no—
308Dic61—22no—
309Dic61—41no—
310Dic61—82no—
311Dic61—81no—
312Dic61—81no—
313#2280—611no—
314#1779—611no—
315C22⋊#95—611no—
316#1294—611no—
317#1294—611no—
318#1294—611no—
319#1294D6111yescharacteristic, complemented
320C2×C61—21no—
321C2×C61—21no—
322C2×C61—21no—
323C2×C61—21no—
324C2×C61#150111yescharacteristic
325C2×C61#150411yescharacteristic
326C2×C61#151311yescharacteristic
327C2×C61#151611yescharacteristic
328C2×C61#181911yescharacteristic
329C2×C61#182511yescharacteristic
330C2×C61#182611yescharacteristic
331D61—42no—
332D61—42no—
333C24×C4—611no—
334C2×#117—611no—
335C2×#117—611no—
336C22×C22⋊C4—1221no—
337C2×C22⋊C8—611no—
338C2×C22⋊C8—1221no—
339C2×C22⋊C8—1221no—
340C2×C22⋊C8C2×D6111yescharacteristic
341#381—1221no—
342#380—611no—
343#380—611no—
344#380—611no—
345#380C2×D6111yescharacteristic
346#379—1221no—
347C4×C22⋊C4—1221no—
348C4×C22⋊C4—1221no—
349C2×#95—611no—
350C2×#95—1221no—
351C2×#95C2×D6111yescharacteristic
352C61#871511yescharacteristic, complemented, Sylow
353C25—611no—
354C23×C4—21no—
355C23×C4—611no—
356C23×C4—611no—
357C23×C4—611no—
358C23×C4—611no—
359C23×C4—611no—
360C23×C4—1221no—
361C23×C4—1221no—
362C23×C4—1221no—
363C23×C4—1221no—
364C23×C4—1221no—
365C23×C4—2442no—
366C23×C4—2442no—
367C23×C4C22×D6111yescharacteristic
368C22×C8—21no—
369C22×C8—1221no—
370#117—2442no—
371#117—2442no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4C4×D6111yescharacteristic
375C2×C4⋊C4C4×D6111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1221no—
380C2×C22⋊C4—1221no—
381C2×C22⋊C4—1224no—
382C2×C22⋊C4—1221no—
383C2×C22⋊C4—2442no—
384C2×C22⋊C4—2442no—
385C2×C42—1221no—
386C2×C42—1221no—
387C22⋊C8—21no—
388C22⋊C8—21no—
389C22⋊C8—1221no—
390C22⋊C8—1221no—
391C22⋊C8—2442no—
392C22⋊C8—2442no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—1221no—
397#95—1221no—
398#95—1221no—
399#95—1221no—
400#95—1221no—
401#95—2442no—
402C24—611no—
403C24—611no—
404C24—1222no—
405C24—1222no—
406C24—1221no—
407C24—1221no—
408C24—1221no—
409C24—1221no—
410C24—1221no—
411C24—1221no—
412C24—2441no—
413C24—2441no—
414C24D4×D6111yescharacteristic
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4—41no—
423C22×C4—41no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4—1221no—
443C22×C4—1222no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—2441no—
447C22×C4—2441no—
448C22×C4—2441no—
449C22×C4—2441no—
450C22×C4—2444no—
451C22×C4—2444no—
452C22×C4—2444no—
453C22×C4—2444no—
454C22×C4—2441no—
455C22×C4—2441no—
456C22×C4—2441no—
457C22×C4—2441no—
458C22×C4—2441no—
459C22×C4—2441no—
460C22×C4—2441no—
461C22×C4C2×C4×D6111yescharacteristic
462C22×C4#1175822211yescharacteristic
463C22×C4#1175822211yescharacteristic
464C22×C4D4×D6111yescharacteristic
465C22×C4#1175822411yescharacteristic
466C22×C4#1175822611yescharacteristic
467C2×C8—41no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—2441no—
471C2×C8—2441no—
472C2×C8—2441no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—2441no—
476C4⋊C4—2441no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—2442no—
480C22⋊C4—2442no—
481C22⋊C4—2448no—
482C22⋊C4—2442no—
483C22⋊C4—2442no—
484C22⋊C4—2441no—
485C22⋊C4—2441no—
486C42—2442no—
487C42—2442no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—612no—
493C23—612no—
494C23—1224no—
495C23—1224no—
496C23—1221no—
497C23—1221no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23—1221no—
503C23—1221no—
504C23—1221no—
505C23—1221no—
506C23—1221no—
507C23—1221no—
508C23—2442no—
509C23—2442no—
510C23—2442no—
511C23—2442no—
512C23—2442no—
513C23—2442no—
514C23—2442no—
515C23—2442no—
516C23—2442no—
517C23—2442no—
518C23—2441no—
519C23—2441no—
520C23—2441no—
521C23—2441no—
522C23C22⋊C4×D6111yescharacteristic
523C23#1451975911yescharacteristic
524C23#1451976211yescharacteristic
525C23#1451979811yescharacteristic
526C23#1451980011yescharacteristic
527C23#1451980111yescharacteristic
528C23#1451980611yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—81no—
549C2×C4—81no—
550C2×C4—612no—
551C2×C4—1224no—
552C2×C4—1224no—
553C2×C4—1221no—
554C2×C4—1221no—
555C2×C4—1221no—
556C2×C4—1221no—
557C2×C4—1221no—
558C2×C4—4881no—
559C2×C4—4881no—
560C2×C4—4881no—
561C2×C4—4881no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2441no—
574C2×C4—2441no—
575C2×C4—2441no—
576C2×C4—2441no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4#1451973411yescharacteristic
580C2×C4#1451973511yescharacteristic
581C2×C4#1451975911yescharacteristic
582C2×C4#1451976211yescharacteristic
583C8—81no—
584C8—4881no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—21no—
596C22—21no—
597C22—1222no—
598C22—1222no—
599C22—1222no—
600C22—1222no—
601C22—1222no—
602C22—1222no—
603C22—2444no—
604C22—2444no—
605C22—2444no—
606C22—2444no—
607C22—2441no—
608C22—2441no—
609C22—2441no—
610C22—2441no—
611C22—2441no—
612C22—2441no—
613C22—2441no—
614C22—2441no—
615C22#1683962411yescharacteristic
616C22#99×D6111yescharacteristic
617C22#99×D6111yescharacteristic
618C22#1683975711yescharacteristic
619C22#1683976011yescharacteristic
620C22#104×D6111yescharacteristic
621C22#1683977711yescharacteristic
622C22#1684008511yescharacteristic
623C22#1684008911yescharacteristic
624C22#1684010211yescharacteristic
625C22#1684010611yescharacteristic
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—82no—
631C4—81no—
632C4—81no—
633C4—1222no—
634C4—4882no—
635C4—4881no—
636C4—4881no—
637C4—2441no—
638C2—21no—
639C2—21no—
640C2—21no—
641C2—21no—
642C2—2442no—
643C2—2442no—
644C2#2144430911yescharacteristic
645C2#2144432011yescharacteristic
646C2#2144435911yescharacteristic
647C2#2144437411yescharacteristic
648C2#2144589211yescharacteristic
649C2#2144591311yescharacteristic
650C2#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#8715
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×#14519735C4semidirect
10. C2×#14519735C4semidirect
17. #16839619C4semidirect
18. #16839619C4semidirect
319. #1294D61semidirect
352. C61#8715semidirect

Maximal subgroups

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

subgroupindex
#214482012
#214457282
#214440402
#214436992
#214436982
#214436972
C61×#12942
#871561