Finite Group Databasebeta

← #30615201

Subgroups — #30615201

Order 15616.

1382 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462499C212yesmaximal, complemented
2#21461721C212yesmaximal, complemented
3#21461684C212yesmaximal, complemented
4#21461683C212yesmaximal, complemented
5#21461651C212yesmaximal
6#21461569C212yesmaximal, complemented
7C4×#14519837C212yesmaximal, complemented
8C2×#16840235C211yesmaximal, characteristic
9#16840786—28no—
10#16840765C2214yescomplemented
11C2×#14519837C2214yes—
12C2×#14519837C2214yes—
13#16840732C2214yes—
14C4×#11758217C2214yescomplemented
15#16840642C2214yescomplemented
16#16840642C2214yescomplemented
17C23×C22⋊D61C2211yescharacteristic
18#16840235—28no—
19C2×C4×C22⋊D61C411yescharacteristic
20C2×C4×C22⋊D61C411yescharacteristic
21C2×C4×C22⋊D61C2211yescharacteristic
22C2×C4×C22⋊D61C2211yescharacteristic
23C2×#14519737C411yescharacteristic
24C2×#14519737C411yescharacteristic
25C2×#14519737C2211yescharacteristic
26C2×#14519737C2211yescharacteristic
27C2×#14519733C2211yescharacteristic
28C2×#14519733C2211yescharacteristic
29C22×C22⋊Dic61C411yescharacteristic
30C2×C22⋊C4×D61C411yescharacteristic
31C2×C22⋊C4×D61C411yescharacteristic
32C22×C22⋊C4×C61C411yescharacteristic
33C2×#11758217C2318yes—
34#14519844—24no—
35C4⋊#92420—24no—
36#14519837—28no—
37#14519837—28no—
38C22⋊#92420—28no—
39#14519832—24no—
40C4×#92420—24no—
41C24×D61C2×C411yescharacteristic
42C22×C22⋊D61—24no—
43C22×C22⋊D61—24no—
44C22×C22⋊D61—24no—
45C22×C22⋊D61C2×C411yescharacteristic
46C22×C22⋊D61C2×C411yescharacteristic
47C22×C22⋊D61C2311yescharacteristic
48C22×C22⋊D61C2311yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C23×Dic61C2×C411yescharacteristic
51C23×Dic61C2311yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C4×C22⋊D61—24no—
57C4×C22⋊D61—24no—
58C4×C22⋊D61—24no—
59C4×C22⋊D61—24no—
60#14519737—24no—
61#14519737—24no—
62#14519737—24no—
63#14519737—24no—
64#14519733—24no—
65#14519733D418yes—
66C2×#11758196C2×C411yescharacteristic
67C2×#11758196C2×C411yescharacteristic
68C2×#11758196C2311yescharacteristic
69C2×#11758196C2311yescharacteristic
70C2×C22⋊Dic61—24no—
71C2×C22⋊Dic61C2×C411yescharacteristic
72C2×C22⋊Dic61C2×C411yescharacteristic
73C2×C22⋊Dic61C2×C411yescharacteristic
74C2×C22⋊Dic61C2×C411yescharacteristic
75C2×#11758198C2×C411yescharacteristic
76C2×#11758198C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2×C411yescharacteristic
79C22⋊C4×D61—24no—
80C22⋊C4×D61—24no—
81C2×C4×Dic61C2×C411yescharacteristic
82C2×C4×Dic61C2×C411yescharacteristic
83C2×C4×Dic61C2311yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C25×C61C2×C411yescharacteristic
86C23×C4×C61C2×C411yescharacteristic
87C23×C4×C61C2×C411yescharacteristic
88C2×C22⋊C4×C61—24no—
89C2×C22⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C22⋊C4×C61C2×C411yescharacteristic
92C2×C22⋊C4×C61C2×C411yescharacteristic
93C24×C61—22no—
94C24×C61—22no—
95C24×C61—22no—
96C24×C61—81no—
97C24×C61—81no—
98C24×C61C22×C411yescharacteristic
99C24×C61C22×C411yescharacteristic
100C24×C61C22×C411yescharacteristic
101C23×D61—22no—
102C23×D61—22no—
103C23×D61—22no—
104C23×D61—81no—
105C23×D61—81no—
106C23×D61C22×C411yescharacteristic
107C23×D61C22×C411yescharacteristic
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—81no—
111C22×C4×C61—81no—
112C22×C4×C61C22×C411yescharacteristic
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C411yescharacteristic
116C2×C22⋊D61—232no—
117C2×C22⋊D61—22no—
118C2×C22⋊D61—22no—
119C2×C22⋊D61—22no—
120C2×C22⋊D61—22no—
121C2×C22⋊D61—22no—
122C2×C22⋊D61—22no—
123C2×C22⋊D61—22no—
124C2×C22⋊D61—22no—
125C2×C22⋊D61—22no—
126C2×C22⋊D61—22no—
127C2×C22⋊D61#4114yes—
128C2×C22⋊D61#4114yes—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—81no—
134C22×Dic61—81no—
135C22×Dic61C22×C411yescharacteristic
136C22×Dic61C22×C411yescharacteristic
137C22×Dic61C22×C411yescharacteristic
138C22×Dic61C22×C411yescharacteristic
139C22×Dic61C22×C411yescharacteristic
140C22×Dic61C2×D414yes—
141C22×Dic61C2411yescharacteristic
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—81no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×C4×D61—81no—
150#11758217—28no—
151#11758217—28no—
152C2×#92420—28no—
153C22⋊C4×C61—22no—
154C22⋊C4×C61—22no—
155C22⋊C4×C61—22no—
156C22⋊C4×C61C22⋊C414yes—
157C22⋊Dic61—22no—
158C22⋊Dic61—22no—
159C22⋊Dic61—22no—
160C22⋊Dic61C22⋊C414yes—
161#11758198—22no—
162#11758198—22no—
163#11758198—22no—
164#11758198—22no—
165#11758196—22no—
166#11758196—22no—
167#11758196C22⋊C414yes—
168#11758196C22⋊C414yes—
169C4×Dic61—22no—
170C4×Dic61—22no—
171C4×Dic61C2×D414yes—
172C4×Dic61C2×D414yes—
173C23×C61—28no—
174C23×C61—21no—
175C23×C61—21no—
176C23×C61—21no—
177C23×C61—21no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61—41no—
183C23×C61—41no—
184C23×C61—41no—
185C23×C61—41no—
186C23×C61—82no—
187C23×C61—82no—
188C23×C61—84no—
189C23×C61—84no—
190C23×C61C2×C22⋊C412yes—
191C23×C61#11712yes—
192C23×C61#11712yes—
193C23×C61C23×C411yescharacteristic
194C22×D61—21no—
195C22×D61—21no—
196C22×D61—21no—
197C22×D61—21no—
198C22×D61—28no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C22×D61—82no—
204C22×D61—82no—
205C22×D61—84no—
206C22×D61—84no—
207C22×D61#11712yes—
208C22×D61#11712yes—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—82no—
216C2×C4×C61—82no—
217C2×C4×C61C2×C22⋊C412yes—
218C2×C4×C61C2×C22⋊C412yes—
219C22⋊D61—28no—
220C22⋊D61—28no—
221C22⋊D61—28no—
222C22⋊D61—28no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—28no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—82no—
233C2×Dic61—82no—
234C2×Dic61C2×C22⋊C412yes—
235C2×Dic61C2×C22⋊C412yes—
236C2×Dic61C2×C22⋊C412yes—
237C2×Dic61C22×D412yes—
238C2×Dic61C2×#4112yes—
239C2×Dic61C2×#4112yes—
240C4×D61—82no—
241C4×D61—82no—
242C4×D61—82no—
243C4×D61—82no—
244#92420—48no—
245#20729—611nomaximal, Sylow
246C22×C61—21no—
247C22×C61—21no—
248C22×C61—22no—
249C22×C61—22no—
250C22×C61—22no—
251C22×C61—22no—
252C22×C61—22no—
253C22×C61—42no—
254C22×C61—42no—
255C22×C61—42no—
256C22×C61—42no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61—41no—
263C22×C61—88no—
264C22×C61C22×C22⋊C411yescharacteristic
265C22×C61C2×#11711yescharacteristic
266C22×C61C2×#11711yescharacteristic
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—41no—
272C2×D61—41no—
273C2×D61—41no—
274C2×D61—41no—
275C2×D61—42no—
276C2×D61—42no—
277C2×D61—88no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—41no—
281C4×C61—41no—
282Dic61—22no—
283Dic61—22no—
284Dic61—22no—
285Dic61—41no—
286Dic61—41no—
287Dic61#52514yes—
288C2×#518—611no—
289#2921—612no—
290#1822—612no—
291#1800—612no—
292#1800—612no—
293#1783—612no—
294C4×#100—612no—
295C4×#100—612no—
296C2×C61—21no—
297C2×C61—21no—
298C2×C61—42no—
299C2×C61—42no—
300C2×C61—42no—
301C2×C61#228011yescharacteristic
302C2×C61#288811yescharacteristic
303C2×C61#288811yescharacteristic
304D61—42no—
305D61—42no—
306C23×D4—611no—
307#518—1228no—
308C2×C4×D4—611no—
309C2×C4×D4—611no—
310C2×C4×D4—611no—
311C2×C4×D4—611no—
312C2×C4×D4—611no—
313C2×C4×D4—611no—
314C2×C4×D4—611no—
315C2×C4×D4—611no—
316C2×#117—611no—
317C2×#117—611no—
318C22×C22⋊C4—611no—
319C22×C22⋊C4—611no—
320C22×C22⋊C4—611no—
321C22×C22⋊C4#692311yescharacteristic
322#433—1228no—
323#423—614no—
324C2×#100—614no—
325C2×#100—614no—
326#407—614no—
327C4×M16—614no—
328#343—614no—
329#343—614no—
330C61#2072911yescharacteristic, complemented, Sylow
331C25—611no—
332C25C2×#692311yescharacteristic
333C22×D4—611no—
334C22×D4—611no—
335C22×D4—611no—
336C22×D4—611no—
337C22×D4—1224no—
338C22×D4—1224no—
339C22×D4—1224no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4C2×#692311yescharacteristic
348C23×C4C2×#692311yescharacteristic
349C2×M16—618no—
350C4×D4—1224no—
351C4×D4—1224no—
352C4×D4—1224no—
353C4×D4—1224no—
354C4×D4—1224no—
355C4×D4—1224no—
356C4×D4—1224no—
357C4×D4—1224no—
358#117—618no—
359#117—1224no—
360C2×C4⋊C4—611no—
361C2×C4⋊C4—611no—
362C2×C4⋊C4—611no—
363C2×C4⋊C4—611no—
364C2×C22⋊C4—24no—
365C2×C22⋊C4—611no—
366C2×C22⋊C4—611no—
367C2×C22⋊C4—611no—
368C2×C22⋊C4—611no—
369C2×C22⋊C4—611no—
370C2×C22⋊C4—611no—
371C2×C22⋊C4—611no—
372C2×C22⋊C4—611no—
373C2×C22⋊C4—1224no—
374C2×C22⋊C4—1224no—
375C2×C22⋊C4—1224no—
376C2×C22⋊C4C2×#692311yescharacteristic
377C2×C22⋊C4C2×#692311yescharacteristic
378C2×C22⋊C4C2×#692311yescharacteristic
379C2×C22⋊C4C2×#692311yescharacteristic
380C2×C42—611no—
381C2×C42—611no—
382C2×C42—611no—
383C2×C42—611no—
384C4⋊C8—1224no—
385C4⋊C8—1224no—
386#100—1228no—
387#100—1228no—
388C22⋊C8—1228no—
389#97—1224no—
390C4×C8—1224no—
391C24—22no—
392C24—22no—
393C24—22no—
394C24—81no—
395C24—81no—
396C24—611no—
397C24—611no—
398C24—1222no—
399C24—1222no—
400C24—1222no—
401C24—4881no—
402C24—4881no—
403C24C22×#692311yescharacteristic
404C24C22×#692311yescharacteristic
405C24C22×#692311yescharacteristic
406C2×D4—614no—
407C2×D4—614no—
408C2×D4—1222no—
409C2×D4—1222no—
410C2×D4—1222no—
411C2×D4—1222no—
412C2×D4—1222no—
413C2×D4—1222no—
414C2×D4—1222no—
415C2×D4—1222no—
416C2×D4—12232no—
417C2×D4—1222no—
418C2×D4—1222no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—611no—
424C22×C4—614no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1222no—
434C22×C4—1222no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1222no—
438C22×C4—4881no—
439C22×C4—4881no—
440C22×C4—4881no—
441C22×C4—4881no—
442C22×C4—4881no—
443C22×C4—4881no—
444C22×C4C22×#692311yescharacteristic
445C22×C4C22×#692311yescharacteristic
446C22×C4C22×#692311yescharacteristic
447C22×C4C22×#692311yescharacteristic
448M16—1228no—
449M16—1228no—
450C2×C8—1228no—
451C4⋊C4—614no—
452C4⋊C4—614no—
453C4⋊C4—1222no—
454C4⋊C4—1222no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—22no—
458C22⋊C4—614no—
459C22⋊C4—1222no—
460C22⋊C4—1222no—
461C22⋊C4—1222no—
462C22⋊C4—1222no—
463C22⋊C4—1222no—
464C22⋊C4—1222no—
465C22⋊C4—1222no—
466C22⋊C4C22⋊#692314yes—
467C42—614no—
468C42—614no—
469C42—1222no—
470C42—1222no—
471C23—28no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23—41no—
483C23—41no—
484C23—82no—
485C23—82no—
486C23—84no—
487C23—84no—
488C23—612no—
489C23—612no—
490C23—1228no—
491C23—1221no—
492C23—1221no—
493C23—1221no—
494C23—1221no—
495C23—4882no—
496C23—4882no—
497C23—4884no—
498C23—4884no—
499C23—2441no—
500C23—2441no—
501C23—2441no—
502C23—2441no—
503C23C2×C22⋊#692312yes—
504C23#1451985612yes—
505C23#1451985612yes—
506C23C23×#692311yescharacteristic
507D4—1228no—
508D4—1228no—
509D4—1228no—
510D4—1228no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—612no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—1228no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—4882no—
531C2×C4—4882no—
532C2×C4—4882no—
533C2×C4—4882no—
534C2×C4—4882no—
535C2×C4—4882no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4C2×C22⋊#692312yes—
541C2×C4C2×C22⋊#692312yes—
542C8—2448no—
543C22—21no—
544C22—21no—
545C22—22no—
546C22—22no—
547C22—22no—
548C22—22no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—88no—
561C22—1222no—
562C22—1222no—
563C22—4888no—
564C22—2442no—
565C22—2442no—
566C22—2442no—
567C22—2442no—
568C22—2441no—
569C22—2441no—
570C22—2441no—
571C22—2441no—
572C22C22×C22⋊#692311yescharacteristic
573C22C2×#1451985611yescharacteristic
574C22C2×#1451985611yescharacteristic
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—614no—
580C4—1222no—
581C4—1222no—
582C4—1222no—
583C4—2441no—
584C4—2441no—
585C2—21no—
586C2—21no—
587C2—42no—
588C2—42no—
589C2—42no—
590C2—2442no—
591C2—2442no—
592C2#2146226311yescharacteristic
593C2#2146242911yescharacteristic
594C2#2146242911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C22
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#20729
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462499C2semidirect
2. #21461721C2semidirect
3. #21461684C2semidirect
4. #21461683C2semidirect
6. #21461569C2semidirect
7. C4×#14519837C2semidirect
10. #16840765C22semidirect
14. C4×#11758217C22semidirect
15. #16840642C22semidirect
16. #16840642C22semidirect
330. C61#20729semidirect

Maximal subgroups

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

subgroupindex
#214624992
#214617212
#214616842
#214616832
#214616512
#214615692
C4×#145198372
C2×#168402352
#2072961