Finite Group Databasebeta

← #30609978

Subgroups — #30609978

Order 15616.

1738 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C212yesmaximal, complemented
2#21461077C214yesmaximal, complemented
3#21461069C212yesmaximal, complemented
4#21461066C212yesmaximal, complemented
5#21461057C214yesmaximal, complemented
6C22×#14519737C211yesmaximal, characteristic
7C22×#11758217—22no—
8#16840732—22no—
9#16840732—22no—
10#16840732C2214yes—
11#16840732C2214yescomplemented
12C2×C22⋊#92420—22no—
13C2×C22⋊#92420C2214yescomplemented
14#16840608C2218yescomplemented
15#16840606C2218yescomplemented
16C23×C22⋊D61C411yescharacteristic
17C24×Dic61C2211yescharacteristic
18C23×C4×D61C411yescharacteristic
19C2×#14519737—22no—
20C2×#14519737—22no—
21C2×#14519737—22no—
22C2×#14519737—22no—
23C2×#14519737C412yes—
24C2×#14519737C412yes—
25C2×#14519737C2212yes—
26C2×#14519737C2212yes—
27C22×#11758196C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×C4×Dic61C411yescharacteristic
30C22×C22⋊C4×C61C411yescharacteristic
31C2×#11758217—24no—
32C2×#11758217—24no—
33C2×#11758217—48no—
34C22×#92420—24no—
35C22⋊#92420—24no—
36C22⋊#92420—24no—
37C22⋊#92420—24no—
38C22⋊#92420C2318yes—
39C24×D61C2×C411yescharacteristic
40C22×C22⋊D61—22no—
41C22×C22⋊D61—22no—
42C22×C22⋊D61—28no—
43C22×C22⋊D61C2×C412yes—
44C22×C22⋊D61C2×C412yes—
45C23×Dic61—44no—
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C23×Dic61D412yes—
51C23×Dic61D412yes—
52C23×Dic61D412yes—
53C23×Dic61D412yes—
54C23×Dic61C2311yescharacteristic
55C23×Dic61C2311yescharacteristic
56C23×Dic61C2311yescharacteristic
57C22×C4×D61—21no—
58C22×C4×D61—21no—
59C22×C4×D61—21no—
60C22×C4×D61—21no—
61C22×C4×D61—44no—
62C22×C4×D61C2×C412yes—
63C22×C4×D61C2×C412yes—
64#14519737—24no—
65#14519737—24no—
66#14519737—24no—
67#14519737—24no—
68#14519737—24no—
69#14519737—24no—
70#14519737—24no—
71#14519737—24no—
72C2×#11758196—22no—
73C2×#11758196—22no—
74C2×#11758196C2×C412yes—
75C2×#11758196C2312yes—
76C2×#11758198—22no—
77C2×#11758198—22no—
78C2×#11758198C2×C412yes—
79C2×#11758198C2312yes—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61—21no—
83C2×C4×Dic61—21no—
84C2×C4×Dic61C2×C412yes—
85C2×C4×Dic61C2×C412yes—
86C25×C61C2×C411yescharacteristic
87C23×C4×C61C2×C411yescharacteristic
88C23×C4×C61C2×C411yescharacteristic
89C2×C22⋊C4×C61—22no—
90C2×C22⋊C4×C61—22no—
91C2×C22⋊C4×C61C2×C412yes—
92C2×C22⋊C4×C61C2×C412yes—
93C24×C61—24no—
94C24×C61—42no—
95C24×C61—42no—
96C24×C61C22⋊C412yes—
97C24×C61C22⋊C412yes—
98C24×C61C22×C411yescharacteristic
99C24×C61C22×C411yescharacteristic
100C24×C61C22×C411yescharacteristic
101C23×D61—21no—
102C23×D61—21no—
103C23×D61—24no—
104C23×D61—42no—
105C23×D61—42no—
106C23×D61C22×C412yes—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—42no—
112C22×C4×C61—42no—
113C22×C4×C61C22×C412yes—
114C22×C4×C61C22×C412yes—
115C2×C22⋊D61—216no—
116C2×C22⋊D61—216no—
117C2×C22⋊D61—24no—
118C2×C22⋊D61—24no—
119C2×C22⋊D61—24no—
120C2×C22⋊D61—24no—
121C2×C22⋊D61—24no—
122C2×C22⋊D61M1618yescomplemented
123C22×Dic61—21no—
124C22×Dic61—21no—
125C22×Dic61—24no—
126C22×Dic61—28no—
127C22×Dic61—24no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C22×Dic61—44no—
131C22×Dic61—44no—
132C22×Dic61—42no—
133C22×Dic61—42no—
134C22×Dic61—44no—
135C22×Dic61—42no—
136C22×Dic61C22⋊C411yescharacteristic
137C22×Dic61C22⋊C411yescharacteristic
138C22×Dic61C22⋊C411yescharacteristic
139C22×Dic61C22⋊C412yes—
140C22×Dic61C22⋊C412yes—
141C22×Dic61C22⋊C412yes—
142C22×Dic61C22⋊C412yes—
143C22×Dic61C22⋊C411yescharacteristic
144C22×Dic61C22×C411yescharacteristic
145C22×Dic61C22×C411yescharacteristic
146C22×Dic61C22×C412yes—
147C22×Dic61C22×C411yescharacteristic
148C22×Dic61C2×D412yes—
149C22×Dic61C2×D412yes—
150C22×Dic61C2×D412yes—
151C22×Dic61C2×D412yes—
152C22×Dic61C2×D412yes—
153C22×Dic61C2×D412yes—
154C22×Dic61C2411yescharacteristic
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—44no—
160C2×C4×D61—44no—
161C2×C4×D61—44no—
162C2×C4×D61—44no—
163C2×C4×D61—44no—
164C2×C4×D61—44no—
165#11758217—48no—
166#11758217—48no—
167C2×#92420—28no—
168C2×#92420—48no—
169C22⋊C4×C61—24no—
170C22⋊C4×C61—24no—
171#11758198—24no—
172#11758198—24no—
173#11758196—24no—
174#11758196—24no—
175C4×Dic61—22no—
176C4×Dic61—22no—
177C4×Dic61—22no—
178C4×Dic61—22no—
179C23×C61—22no—
180C23×C61—22no—
181C23×C61—22no—
182C23×C61—22no—
183C23×C61—24no—
184C23×C61—24no—
185C23×C61—24no—
186C23×C61—24no—
187C23×C61—42no—
188C23×C61—41no—
189C23×C61—41no—
190C23×C61—42no—
191C23×C61—41no—
192C23×C61—41no—
193C23×C61—416no—
194C23×C61C2×C22⋊C412yes—
195C23×C61C2×C22⋊C412yes—
196C23×C61C2×C22⋊C411yescharacteristic
197C23×C61C2×C22⋊C411yescharacteristic
198C23×C61C2×M1614yes—
199C23×C61C23×C411yescharacteristic
200C22×D61—24no—
201C22×D61—24no—
202C22×D61—22no—
203C22×D61—22no—
204C22×D61—42no—
205C22×D61—416no—
206C22×D61—42no—
207C22×D61—42no—
208C22×D61—42no—
209C22×D61—42no—
210C22×D61—42no—
211C22×D61C2×M1614yescomplemented
212C2×C4×C61—22no—
213C2×C4×C61—22no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C22⋊D61—216no—
221C22⋊D61—216no—
222C2×Dic61—24no—
223C2×Dic61—24no—
224C2×Dic61—22no—
225C2×Dic61—22no—
226C2×Dic61—24no—
227C2×Dic61—22no—
228C2×Dic61—24no—
229C2×Dic61—24no—
230C2×Dic61—22no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—24no—
235C2×Dic61—24no—
236C2×Dic61—42no—
237C2×Dic61—42no—
238C2×Dic61—41no—
239C2×Dic61—42no—
240C2×Dic61—42no—
241C2×Dic61—42no—
242C2×Dic61—41no—
243C2×Dic61#9914yes—
244C2×Dic61C2×C22⋊C411yescharacteristic
245C2×Dic61C2×C22⋊C411yescharacteristic
246C2×Dic61C2×C22⋊C412yes—
247C2×Dic61C2×C22⋊C411yescharacteristic
248C2×Dic61C2×C22⋊C411yescharacteristic
249C2×Dic61C2×M1614yescomplemented
250C2×Dic61C22×D412yes—
251C4×D61—44no—
252C4×D61—44no—
253C4×D61—44no—
254C4×D61—44no—
255#92420—48no—
256#17362—611nomaximal, Sylow
257C22×C61—28no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61—21no—
262C22×C61—22no—
263C22×C61—21no—
264C22×C61—21no—
265C22×C61—22no—
266C22×C61—22no—
267C22×C61—22no—
268C22×C61—22no—
269C22×C61—44no—
270C22×C61—48no—
271C22×C61—48no—
272C22×C61—44no—
273C22×C61#40714yes—
274C22×C61C2×#9912yes—
275C22×C61#41312yes—
276C22×C61C22×C22⋊C411yescharacteristic
277C22×C61C22×M1612yes—
278C2×D61—24no—
279C2×D61—44no—
280C2×D61—48no—
281C2×D61—48no—
282C2×D61—42no—
283C2×D61—42no—
284C2×D61—44no—
285C4×C61—42no—
286C4×C61—42no—
287Dic61—24no—
288Dic61—22no—
289Dic61—21no—
290Dic61—21no—
291Dic61—22no—
292Dic61C2×#9912yes—
293Dic61C2×#9912yes—
294C22×C4×D4—611no—
295C2×#407—612no—
296#1465—614no—
297#1463—612no—
298#1462—612no—
299#1459—614no—
300C2×C61—22no—
301C2×C61—22no—
302C2×C61—22no—
303C2×C61—24no—
304C2×C61—42no—
305C2×C61C2×#40711yescharacteristic
306C2×C61C22×#9911yescharacteristic
307C2×C61C2×#41311yescharacteristic
308D61—44no—
309C23×D4—611no—
310C24×C4—611no—
311C24×C4—611no—
312C22×M16—1222no—
313C2×C4×D4—612no—
314C2×C4×D4—612no—
315C2×C4×D4—612no—
316C2×C4×D4—612no—
317C2×C4×D4—1222no—
318C2×C4×D4—1222no—
319C2×C4×D4—1222no—
320C2×C4×D4—1222no—
321C22×C4⋊C4—611no—
322C22×C22⋊C4—611no—
323C22×C22⋊C4#692311yescharacteristic
324C22×C42—611no—
325#407—614no—
326#407—614no—
327#407—1222no—
328#407—1222no—
329C2×C22⋊C8—614no—
330C2×C22⋊C8—1222no—
331#324—618no—
332#323—618no—
333C61#1736211yescharacteristic, complemented, Sylow
334C25—611no—
335C25C2×#692311yescharacteristic
336C22×D4—612no—
337C22×D4—612no—
338C22×D4—1228no—
339C22×D4—1222no—
340C22×D4—1222no—
341C23×C4—612no—
342C23×C4—611no—
343C23×C4—612no—
344C23×C4—612no—
345C23×C4—612no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—612no—
353C23×C4—612no—
354C23×C4—1221no—
355C23×C4—1221no—
356C23×C4—1221no—
357C23×C4—1221no—
358C23×C4—2444no—
359C23×C4—2444no—
360C23×C4C2×#692311yescharacteristic
361C23×C4C2×#692311yescharacteristic
362C2×M16—1224no—
363C2×M16—1224no—
364C2×M16—2448no—
365C22×C8—1224no—
366C4×D4—1224no—
367C4×D4—1224no—
368C4×D4—1224no—
369C4×D4—1224no—
370C4×D4—1224no—
371C4×D4—1224no—
372C4×D4—1224no—
373C4×D4—1224no—
374C2×C4⋊C4—612no—
375C2×C4⋊C4—612no—
376C2×C4⋊C4—1222no—
377C2×C4⋊C4—1222no—
378C2×C22⋊C4—22no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—612no—
381C2×C22⋊C4—612no—
382C2×C22⋊C4—1222no—
383C2×C22⋊C4—1222no—
384C2×C22⋊C4C2×#692312yes—
385C2×C22⋊C4C2×#692312yes—
386C2×C42—612no—
387C2×C42—612no—
388C2×C42—1221no—
389C2×C42—1221no—
390C2×C42—1221no—
391C2×C42—1221no—
392C22⋊C8—618no—
393C22⋊C8—1224no—
394C22⋊C8—1224no—
395C22⋊C8—1224no—
396C24—24no—
397C24—42no—
398C24—42no—
399C24—612no—
400C24—1224no—
401C24—1221no—
402C24—1221no—
403C24—2442no—
404C24—2442no—
405C24C22⋊#692312yes—
406C24C22⋊#692312yes—
407C24C22×#692311yescharacteristic
408C24C22×#692311yescharacteristic
409C24C22×#692311yescharacteristic
410C2×D4—618no—
411C2×D4—1224no—
412C2×D4—1224no—
413C2×D4—12216no—
414C2×D4—12216no—
415C2×D4—1224no—
416C2×D4—1224no—
417C2×D4—1224no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—42no—
423C22×C4—42no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—611no—
428C22×C4—612no—
429C22×C4—612no—
430C22×C4—612no—
431C22×C4—612no—
432C22×C4—612no—
433C22×C4—612no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—612no—
437C22×C4—612no—
438C22×C4—612no—
439C22×C4—612no—
440C22×C4—612no—
441C22×C4—611no—
442C22×C4—611no—
443C22×C4—1222no—
444C22×C4—1222no—
445C22×C4—1222no—
446C22×C4—1222no—
447C22×C4—1228no—
448C22×C4—1224no—
449C22×C4—1224no—
450C22×C4—1221no—
451C22×C4—1221no—
452C22×C4—2444no—
453C22×C4—2444no—
454C22×C4—2444no—
455C22×C4—2444no—
456C22×C4—2444no—
457C22×C4—2444no—
458C22×C4—2442no—
459C22×C4—2444no—
460C22×C4—2442no—
461C22×C4—2444no—
462C22×C4—2442no—
463C22×C4—2442no—
464C22×C4—2442no—
465C22×C4—2444no—
466C22×C4C22×#692312yes—
467C22×C4C22×#692312yes—
468M16—2448no—
469M16—2448no—
470C2×C8—1228no—
471C2×C8—2448no—
472C4⋊C4—1224no—
473C4⋊C4—1224no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—1224no—
477C22⋊C4—1224no—
478C42—1222no—
479C42—1222no—
480C42—1222no—
481C42—1222no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—24no—
486C23—24no—
487C23—24no—
488C23—24no—
489C23—22no—
490C23—42no—
491C23—41no—
492C23—41no—
493C23—42no—
494C23—41no—
495C23—41no—
496C23—416no—
497C23—614no—
498C23—1224no—
499C23—1224no—
500C23—1222no—
501C23—1222no—
502C23—2442no—
503C23—2442no—
504C23—2442no—
505C23—24416no—
506C23—2442no—
507C23—2442no—
508C23—2442no—
509C23C2×C22⋊#692312yes—
510C23C2×C22⋊#692312yes—
511C23C2×C22⋊#692311yescharacteristic
512C23C2×C22⋊#692311yescharacteristic
513C23D61⋊M1614yes—
514C23C23×#692311yescharacteristic
515D4—12216no—
516D4—12216no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—614no—
526C2×C4—611no—
527C2×C4—611no—
528C2×C4—611no—
529C2×C4—611no—
530C2×C4—612no—
531C2×C4—612no—
532C2×C4—614no—
533C2×C4—1224no—
534C2×C4—1224no—
535C2×C4—1224no—
536C2×C4—1224no—
537C2×C4—1222no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1222no—
541C2×C4—1224no—
542C2×C4—1224no—
543C2×C4—1224no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—2444no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4—2441no—
552C2×C4—2442no—
553C2×C4—2442no—
554C2×C4—2442no—
555C2×C4—2441no—
556C2×C4—2442no—
557C2×C4—2442no—
558C8—2448no—
559C22—28no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—44no—
572C22—48no—
573C22—48no—
574C22—44no—
575C22—1224no—
576C22—2444no—
577C22—2448no—
578C22—2448no—
579C22—2444no—
580C22—2442no—
581C22—2442no—
582C22#1684073414yes—
583C22D61⋊#9912yes—
584C22#1684074912yes—
585C22C22×C22⋊#692311yescharacteristic
586C22C2×D61⋊M1612yes—
587C4—42no—
588C4—42no—
589C4—612no—
590C4—612no—
591C4—1224no—
592C4—1222no—
593C4—1222no—
594C4—1221no—
595C4—1221no—
596C2—22no—
597C2—22no—
598C2—22no—
599C2—24no—
600C2—42no—
601C2—2444no—
602C2C2×#1684073411yescharacteristic
603C2C2×D61⋊#9911yescharacteristic
604C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC22×C22⋊C4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×C22⋊D61C4
cosocleC22×Dic61C24
hypercenterC22×C22⋊C4#6923
hypocenterC61#17362
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16840732C2semidirect
2. #21461077C2semidirect
3. #21461069C2semidirect
4. #21461066C2semidirect
5. #21461057C2semidirect
11. #16840732C22semidirect
13. C2×C22⋊#92420C22semidirect
14. #16840608C22semidirect
15. #16840606C22semidirect
122. C2×C22⋊D61M16semidirect
211. C22×D61C2×M16semidirect
249. C2×Dic61C2×M16semidirect
333. C61#17362semidirect

Maximal subgroups

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

subgroupindex
C2×#168407322
#214610772
#214610692
#214610662
#214610572
C22×#145197372
#1736261