Finite Group Databasebeta

← #30617805

Subgroups — #30617805

Order 15616.

1882 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C212yesmaximal, complemented
2#21461960C218yesmaximal, complemented
3#21461647C212yesmaximal, complemented
4#21461645C212yesmaximal, complemented
5C22×#14519750C211yesmaximal, characteristic
6C2×#14519856—22no—
7C2×#14519836C2218yescomplemented
8C2×#14519835C2218yescomplemented
9#16840705—22no—
10#16840704—22no—
11#16840704C2214yescomplemented
12#16840703C2214yes—
13C4×C22⋊#6923—22no—
14C4×C22⋊#6923C2214yescomplemented
15C23×D244C2211yescharacteristic
16C23×C22⋊D61C411yescharacteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519750—22no—
20C2×#14519750—22no—
21C2×#14519750—22no—
22C2×#14519750—22no—
23C2×#14519750C414yescomplemented
24C2×#14519750C2214yes—
25C22×#11758196C411yescharacteristic, complemented
26C22×#11758198C411yescharacteristic, complemented
27C22×C22⋊C4×C61C411yescharacteristic, complemented
28#14519856—48no—
29C2×C4⋊#6923—24no—
30C2×C22⋊#6923—24no—
31C2×C22⋊#6923—24no—
32C2×C22⋊#6923C2318yes—
33C2×C4×#6923—24no—
34#14519836—48no—
35#14519835—48no—
36(C2×#6923)⋊C4—24no—
37(C2×#6923)⋊C4—24no—
38C24×D61C2×C411yescharacteristic
39C24×D61C2311yescharacteristic
40C22×D244—22no—
41C22×D244—22no—
42C22×D244—44no—
43C22×D244C2×C412yes—
44C22×D244C2312yes—
45C22×C22⋊D61—22no—
46C22×C22⋊D61—22no—
47C22×C22⋊D61—21no—
48C22×C22⋊D61—22no—
49C22×C22⋊D61—21no—
50C22×C22⋊D61—44no—
51C22×C22⋊D61—44no—
52C22×C22⋊D61C2×C412yes—
53C22×C22⋊D61C2×C414yes—
54C22×C22⋊D61C2312yes—
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C22×C4×D61—44no—
58C22×C4×D61C2×C412yes—
59C22×C4×D61D412yes—
60C22×C4×D61D412yes—
61C22×C4×D61D412yes—
62C22×C4×D61D412yes—
63C22×C4×D61C2312yes—
64#14519750—24no—
65#14519750—24no—
66#14519750—24no—
67#14519750—24no—
68#14519750—24no—
69#14519750—24no—
70#14519750—24no—
71#14519750—24no—
72C2×#11758196—21no—
73C2×#11758196—22no—
74C2×#11758196—21no—
75C2×#11758196C2×C414yes—
76C2×#11758198—22no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198C2×C414yes—
80C25×C61C2×C411yescharacteristic
81C23×C4×C61C2×C411yescharacteristic
82C23×C4×C61C2×C411yescharacteristic
83C2×C22⋊C4×C61—22no—
84C2×C22⋊C4×C61—21no—
85C2×C22⋊C4×C61—21no—
86C2×C22⋊C4×C61C2×C414yes—
87C24×C61—21no—
88C24×C61—21no—
89C24×C61—42no—
90C24×C61—42no—
91C24×C61—42no—
92C24×C61C22×C411yescharacteristic
93C24×C61C22×C412yes—
94C23×D61—24no—
95C23×D61—21no—
96C23×D61—21no—
97C23×D61—42no—
98C23×D61—42no—
99C23×D61—42no—
100C23×D61—42no—
101C23×D61—42no—
102C23×D61C22×C412yes—
103C23×D61C22×C411yescharacteristic
104C23×D61C2×D412yes—
105C23×D61C2×D412yes—
106C23×D61C2411yescharacteristic
107C22×#6923—28no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—42no—
111C22×C4×C61—42no—
112C22×C4×C61C22⋊C412yes—
113C22×C4×C61C22⋊C411yescharacteristic
114C22×C4×C61C22⋊C411yescharacteristic
115C22×C4×C61C22×C412yes—
116C22×C4×C61C22×C412yes—
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—28no—
120C2×C22⋊D61—24no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61—44no—
123C2×C22⋊D61—44no—
124C2×C22⋊D61—48no—
125C2×C22⋊D61—48no—
126C2×C22⋊D61—48no—
127C2×C22⋊D61—48no—
128C2×C22⋊D61—44no—
129C22×Dic61—24no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—42no—
133C22×Dic61C22⋊C411yescharacteristic
134C22×Dic61C22⋊C412yes—
135C22×Dic61C22⋊C411yescharacteristic
136C22×Dic61C22×C412yes—
137C22×Dic61C22×C412yes—
138C2×D244—24no—
139C2×D244—24no—
140C2×D244—28no—
141C2×D244—44no—
142C2×D244—48no—
143C2×D244—48no—
144C2×C4×D61—28no—
145C2×C4×D61—44no—
146C2×C4×D61—44no—
147C2×C4×D61—44no—
148C2×C4×D61—44no—
149C2×C4×D61—44no—
150C2×C4×D61C22⋊C412yes—
151C2×C4×D61C22⋊C412yes—
152C2×C4×D61C22⋊C412yes—
153C2×C4×D61C22⋊C412yes—
154C2×C4×D61C2×D412yes—
155C2×C4×D61C2×D412yes—
156C2×C4×D61C2×D412yes—
157C2×C4×D61C2×D412yes—
158C22⋊#6923—216no—
159C22⋊#6923—48no—
160C22⋊#6923—48no—
161C4⋊#6923—48no—
162C4×#6923—48no—
163C22⋊C4×C61—24no—
164C22⋊C4×C61—24no—
165#11758198—24no—
166#11758198—24no—
167#11758196—24no—
168#11758196—24no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—24no—
174C23×C61—42no—
175C23×C61—42no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—42no—
179C23×C61—42no—
180C23×C61—42no—
181C23×C61—42no—
182C23×C61—88no—
183C23×C61C2×C22⋊C411yescharacteristic
184C23×C61C2×C22⋊C411yescharacteristic
185C23×C61C23×C411yescharacteristic
186C22×D61—22no—
187C22×D61—24no—
188C22×D61—24no—
189C22×D61—24no—
190C22×D61—24no—
191C22×D61—22no—
192C22×D61—24no—
193C22×D61—41no—
194C22×D61—42no—
195C22×D61—41no—
196C22×D61—41no—
197C22×D61—42no—
198C22×D61—41no—
199C22×D61—416no—
200C22×D61—42no—
201C22×D61—42no—
202C22×D61—42no—
203C22×D61—42no—
204C22×D61—42no—
205C22×D61—42no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—88no—
209C22×D61C2×C22⋊C412yes—
210C22×D61C22×D412yes—
211C22×D61H(5,𝔽2)14yes—
212C2×#6923—48no—
213C2×#6923—48no—
214C2×#6923—48no—
215C2×C4×C61—24no—
216C2×C4×C61—22no—
217C2×C4×C61—24no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61C2×C22⋊C412yes—
224C2×C4×C61C2×C22⋊C412yes—
225C22⋊D61—48no—
226C22⋊D61—48no—
227C22⋊D61—48no—
228C22⋊D61—48no—
229C2×Dic61—22no—
230C2×Dic61—24no—
231C2×Dic61—24no—
232C2×Dic61—22no—
233C2×Dic61—24no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236C2×Dic61#9914yescomplemented
237C2×Dic61C2×C22⋊C412yes—
238C2×Dic61C2×C22⋊C412yes—
239D244—48no—
240D244—48no—
241C4×D61—24no—
242C4×D61—24no—
243C4×D61—24no—
244C4×D61—24no—
245C4×D61—42no—
246C4×D61—42no—
247C4×D61—42no—
248C4×D61—42no—
249#21793—611nomaximal, Sylow
250C22×C61—28no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—42no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61—84no—
261C22×C61—84no—
262C22×C61—84no—
263C22×C61C2×#9912yes—
264C22×C61#41012yes—
265C22×C61C22×C22⋊C411yescharacteristic
266C22×C61#51812yes—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—22no—
271C2×D61—22no—
272C2×D61—44no—
273C2×D61—48no—
274C2×D61—48no—
275C2×D61—44no—
276C2×D61—42no—
277C2×D61—42no—
278C2×D61—42no—
279C2×D61—84no—
280C2×D61—84no—
281C2×D61—84no—
282C2×D61#53514yes—
283#6923—88no—
284C4×C61—22no—
285C4×C61—22no—
286C4×C61—42no—
287Dic61—22no—
288Dic61—42no—
289Dic61C2×#9914yes—
290C22×#121—611no—
291#2280—612no—
292#1964—618no—
293#1781—612no—
294#1781—612no—
295C2×C61—22no—
296C2×C61—22no—
297C2×C61—22no—
298C2×C61—82no—
299C2×C61#230911yescharacteristic
300C2×C61C22×#9911yescharacteristic
301C2×C61C2×#41011yescharacteristic
302D61—24no—
303D61—42no—
304D61—82no—
305C23×D4—611no—
306C23×D4—611no—
307C23×D4—611no—
308C24×C4—611no—
309C2×#121—614no—
310C2×#121—614no—
311C2×#121—1222no—
312C2×#121—1222no—
313C2×#121—1222no—
314C2×#121—1222no—
315C2×#117—1222no—
316C22×C4⋊C4—611no—
317C22×C22⋊C4—611no—
318C22×C22⋊C4#692311yescharacteristic, complemented
319C2×#99—618no—
320C2×#99—618no—
321#381—1222no—
322#380—614no—
323#380—1222no—
324#379—614no—
325C4×C22⋊C4—614no—
326C4×C22⋊C4—1222no—
327C61#2179311yescharacteristic, complemented, Sylow
328C25—611no—
329C25—611no—
330C25C2×#692311yescharacteristic
331C22×D4—612no—
332C22×D4—614no—
333C22×D4—612no—
334C22×D4—612no—
335C22×D4—612no—
336C22×D4—1222no—
337C22×D4—1222no—
338C22×D4—1221no—
339C22×D4—1222no—
340C22×D4—1221no—
341C22×D4—1222no—
342C22×D4—1222no—
343C22×D4—2444no—
344C22×D4—2444no—
345C22×D4—2444no—
346C23×C4—611no—
347C23×C4—612no—
348C23×C4—612no—
349C23×C4—612no—
350C23×C4—612no—
351C23×C4—612no—
352C23×C4—612no—
353C23×C4—611no—
354C23×C4—2444no—
355C23×C4C2×#692311yescharacteristic
356C23×C4C2×#692311yescharacteristic
357#121—1224no—
358#121—1224no—
359#121—1224no—
360#121—1224no—
361#121—1224no—
362#121—1224no—
363#121—1224no—
364#121—1224no—
365#117—2448no—
366C2×C4⋊C4—614no—
367C2×C4⋊C4—1221no—
368C2×C4⋊C4—1222no—
369C2×C4⋊C4—1221no—
370C2×C4⋊C4—1224no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—614no—
375C2×C22⋊C4—618no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1221no—
378C2×C22⋊C4—1221no—
379C2×C22⋊C4—1224no—
380C2×C22⋊C4—1224no—
381C2×C22⋊C4C2×#692314yes—
382C2×C42—1224no—
383#99—2448no—
384#99—2448no—
385#95—1224no—
386#95—1224no—
387C24—21no—
388C24—21no—
389C24—42no—
390C24—42no—
391C24—42no—
392C24—611no—
393C24—612no—
394C24—612no—
395C24—611no—
396C24—612no—
397C24—1224no—
398C24—1221no—
399C24—1221no—
400C24—2442no—
401C24—2442no—
402C24—2442no—
403C24—2442no—
404C24—2442no—
405C24C22×#692311yescharacteristic
406C24C22×#692312yes—
407C2×D4—1228no—
408C2×D4—1224no—
409C2×D4—1224no—
410C2×D4—1224no—
411C2×D4—1224no—
412C2×D4—1228no—
413C2×D4—1224no—
414C2×D4—1224no—
415C2×D4—2444no—
416C2×D4—2448no—
417C2×D4—2448no—
418C2×D4—2444no—
419C2×D4—2444no—
420C2×D4—2448no—
421C2×D4—2444no—
422C2×D4—2448no—
423C2×D4—2448no—
424C2×D4—2448no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—611no—
430C22×C4—612no—
431C22×C4—611no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—612no—
435C22×C4—612no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—1228no—
443C22×C4—1224no—
444C22×C4—1221no—
445C22×C4—1221no—
446C22×C4—1228no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4—2444no—
450C22×C4—2444no—
451C22×C4—2444no—
452C22×C4—2442no—
453C22×C4C22⋊#692312yes—
454C22×C4C22⋊#692311yescharacteristic
455C22×C4C22⋊#692311yescharacteristic
456C22×C4C22×#692312yes—
457C22×C4C22×#692312yes—
458C4⋊C4—1224no—
459C4⋊C4—1224no—
460C4⋊C4—2448no—
461C22⋊C4—24no—
462C22⋊C4—24no—
463C22⋊C4—1224no—
464C22⋊C4—1224no—
465C22⋊C4—12216no—
466C22⋊C4—2448no—
467C22⋊C4—2448no—
468C42—2448no—
469C23—22no—
470C23—22no—
471C23—22no—
472C23—22no—
473C23—24no—
474C23—42no—
475C23—42no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—42no—
480C23—42no—
481C23—42no—
482C23—88no—
483C23—612no—
484C23—614no—
485C23—612no—
486C23—1224no—
487C23—1224no—
488C23—1224no—
489C23—1224no—
490C23—1222no—
491C23—1224no—
492C23—1222no—
493C23—4888no—
494C23—2442no—
495C23—2441no—
496C23—2441no—
497C23—2442no—
498C23—2441no—
499C23—2441no—
500C23—2442no—
501C23—2442no—
502C23—2442no—
503C23—2442no—
504C23—2442no—
505C23—2442no—
506C23—24416no—
507C23—2442no—
508C23—2442no—
509C23C2×C22⋊#692311yescharacteristic
510C23C2×C22⋊#692311yescharacteristic
511C23C23×#692311yescharacteristic
512D4—2448no—
513D4—2448no—
514D4—2448no—
515D4—2448no—
516D4—2448no—
517D4—2448no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—614no—
527C2×C4—612no—
528C2×C4—612no—
529C2×C4—1224no—
530C2×C4—1224no—
531C2×C4—1224no—
532C2×C4—1224no—
533C2×C4—1224no—
534C2×C4—1224no—
535C2×C4—1222no—
536C2×C4—1222no—
537C2×C4—1224no—
538C2×C4—2442no—
539C2×C4—2442no—
540C2×C4—2442no—
541C2×C4—2442no—
542C2×C4—2448no—
543C2×C4—2448no—
544C2×C4—2448no—
545C2×C4—2442no—
546C2×C4—2442no—
547C2×C4C2×C22⋊#692312yes—
548C2×C4C2×C22⋊#692312yes—
549C22—28no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—42no—
557C22—42no—
558C22—42no—
559C22—84no—
560C22—84no—
561C22—84no—
562C22—614no—
563C22—1222no—
564C22—1222no—
565C22—1222no—
566C22—1222no—
567C22—1222no—
568C22—4884no—
569C22—4884no—
570C22—4884no—
571C22—2444no—
572C22—2448no—
573C22—2448no—
574C22—2444no—
575C22—2442no—
576C22—2442no—
577C22—2442no—
578C22D61⋊#9912yes—
579C22#1684074112yes—
580C22C22×C22⋊#692311yescharacteristic
581C22#1684082912yes—
582C4—22no—
583C4—22no—
584C4—42no—
585C4—614no—
586C4—1222no—
587C4—4888no—
588C4—2442no—
589C2—22no—
590C2—22no—
591C2—22no—
592C2—82no—
593C2—1224no—
594C2—4882no—
595C2—2442no—
596C2#2146229211yescharacteristic
597C2C2×D61⋊#9911yescharacteristic
598C2C2×#1684074111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#14519750C2
cosocleC23×D61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#21793
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #21462263C2semidirect
2. #21461960C2semidirect
3. #21461647C2semidirect
4. #21461645C2semidirect
7. C2×#14519836C22semidirect
8. C2×#14519835C22semidirect
11. #16840704C22semidirect
14. C4×C22⋊#6923C22semidirect
16. C23×C22⋊D61C4semidirect
23. C2×#14519750C4semidirect
25. C22×#11758196C4semidirect
26. C22×#11758198C4semidirect
27. C22×C22⋊C4×C61C4semidirect
236. C2×Dic61#99semidirect
318. C22×C22⋊C4#6923semidirect
327. C61#21793semidirect

Maximal subgroups

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

subgroupindex
#214622632
#214619602
#214616472
#214616452
C22×#145197502
#2179361