Finite Group Databasebeta

← #30602432

Subgroups — #30602432

Order 15616.

1406 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2C2×#16840704C211yesmaximal, characteristic
3C2×#16840641C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C22×#11758213—21no—
6C2×D61⋊M16—28no—
7C2×D61⋊M16—21no—
8C2×D61⋊M16—21no—
9C2×D61⋊M16C412yescomplemented
10C2×D61⋊M16C2212yes—
11C22×#11758217C412yescomplemented
12C22×D61⋊C8—21no—
13C22×C4⋊#6923C2212yes—
14C22×C22⋊#6923C412yes—
15#16840704—21no—
16#16840704—21no—
17#16840704—21no—
18#16840704—21no—
19C2×(C2×#6923)⋊C4C412yes—
20#16840641—28no—
21C23×C4×D61C2211yescharacteristic
22C2×M16×D61C2212yes—
23#16839726C411yescharacteristic, complemented
24#16839725C412yescomplemented
25#16839724—21no—
26#16839724—21no—
27C22⋊C8×D61—21no—
28C22⋊C8×D61—21no—
29C61×#407C411yescharacteristic, complemented
30C23×#6923C2×C414yes—
31C2×#11758213—28no—
32C2×#11758213—22no—
33C2×#11758213—22no—
34D61⋊M16—28no—
35D61⋊M16—28no—
36D61⋊M16—24no—
37D61⋊M16—28no—
38D61⋊M16D418yes—
39C2×#11758217—22no—
40C2×#11758217—28no—
41C2×#11758217C2×C414yes—
42C2×D61⋊C8—28no—
43C2×D61⋊C8—22no—
44C2×D61⋊C8—22no—
45C22×#92420—22no—
46C2×C4⋊#6923—22no—
47C2×C4⋊#6923—22no—
48C2×C4⋊#6923—24no—
49C2×C4⋊#6923—24no—
50C2×C22⋊#6923—22no—
51C2×C22⋊#6923—22no—
52C2×C22⋊#6923—44no—
53(C2×#6923)⋊C4—22no—
54(C2×#6923)⋊C4—22no—
55C24×D61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C22×C4×D61—24no—
58C22×C4×D61—24no—
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61D411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61Q811yescharacteristic
70C22×C4×D61C2311yescharacteristic
71C2×#11758194C2×C412yes—
72C2×#11758189—22no—
73M16×D61—24no—
74M16×D61—24no—
75C2×C8×D61—22no—
76C22⋊#92418—21no—
77C22⋊#92418—21no—
78#14519689—22no—
79#14519689—22no—
80C23×C4×C61C2×C411yescharacteristic
81C2×M16×C61C2×C412yes—
82C22⋊C8×C61—21no—
83C22⋊C8×C61—21no—
84C24×C61C4211yescharacteristic
85C23×D61—22no—
86C23×D61—22no—
87C23×D61—24no—
88C23×D61—42no—
89C23×D61C4211yescharacteristic
90C23×D61C22⋊C411yescharacteristic
91C23×D61C22⋊C411yescharacteristic
92C23×D61C4⋊C411yescharacteristic
93C23×D61C4⋊C411yescharacteristic
94C23×D61C22×C411yescharacteristic
95C22×#6923—24no—
96C22×#6923—28no—
97C22×#6923—44no—
98C22×#6923—44no—
99C22×C4×C61—24no—
100C22×C4×C61C4211yescharacteristic
101C22×C4×C61C22⋊C411yescharacteristic
102C22×C4×C61C22⋊C411yescharacteristic
103C22×C4×C61C4⋊C411yescharacteristic
104C22×C4×C61C4⋊C411yescharacteristic
105C22×C4×C61C22×C411yescharacteristic
106C22×Dic61—22no—
107C22×Dic61—22no—
108C22×Dic61C4211yescharacteristic
109C22×Dic61C22⋊C411yescharacteristic
110C22×Dic61C22⋊C411yescharacteristic
111C22×Dic61C4⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113C22×Dic61C22×C411yescharacteristic
114C2×C4×D61—24no—
115C2×C4×D61—24no—
116C2×C4×D61—22no—
117C2×C4×D61—22no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—22no—
121C2×C4×D61—22no—
122C2×C4×D61—24no—
123C2×C4×D61—24no—
124C2×C4×D61—24no—
125C2×C4×D61—24no—
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C22⋊C411yescharacteristic
133C2×C4×D61C22⋊C411yescharacteristic
134C2×C4×D61C22⋊C411yescharacteristic
135C2×C4×D61C22⋊C411yescharacteristic
136C2×C4×D61C4⋊C411yescharacteristic
137C2×C4×D61C4⋊C411yescharacteristic
138C2×C4×D61C4⋊C411yescharacteristic
139C2×C4×D61C4⋊C411yescharacteristic
140C2×C4×D61C4⋊C411yescharacteristic
141C2×C4×D61C4⋊C411yescharacteristic
142C2×C4×D61C2×D414yes—
143C2×C4×D61C2×D411yescharacteristic
144C2×C4×D61C2×D411yescharacteristic
145C2×C4×D61C2×D411yescharacteristic
146C2×C4×D61C2×Q811yescharacteristic
147C2×C4×D61#4114yes—
148C22⋊#6923—44no—
149C22⋊#6923—44no—
150#11758217—28no—
151#11758217—24no—
152#11758217C22⋊C418yescomplemented
153C2×#92420—28no—
154C2×#92420—24no—
155C4⋊#6923—42no—
156C4⋊#6923—44no—
157C4⋊#6923—42no—
158#11758213—28no—
159#11758213—28no—
160D61⋊C8—28no—
161D61⋊C8—28no—
162M16×C61—24no—
163C2×C8×C61—22no—
164#11758194—24no—
165C2×#92418—22no—
166#11758189—42no—
167#11758189—42no—
168C8×D61—44no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—41no—
172C23×C61#9511yescharacteristic
173C23×C61#9511yescharacteristic
174C23×C61C2×C4211yescharacteristic
175C22×D61—22no—
176C22×D61—21no—
177C22×D61—21no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—22no—
183C22×D61—22no—
184C22×D61—22no—
185C22×D61—22no—
186C22×D61—22no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—22no—
190C22×D61—41no—
191C22×D61—41no—
192C22×D61—41no—
193C22×D61—48no—
194C22×D61—48no—
195C22×D61#9511yescharacteristic
196C22×D61#9511yescharacteristic
197C22×D61#10012yes—
198C22×D61#10112yes—
199C22×D61C2×C22⋊C411yescharacteristic
200C22×D61C2×C4⋊C411yescharacteristic
201C22×D61C4×D414yes—
202C2×#6923—44no—
203C2×#6923—44no—
204C2×#6923—44no—
205C2×#6923—88no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—22no—
210C2×C4×C61—22no—
211C2×C4×C61#9511yescharacteristic
212C2×C4×C61#9511yescharacteristic
213C2×C4×C61C2×C22⋊C411yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C4×D414yes—
216C2×Dic61—22no—
217C2×Dic61—21no—
218C2×Dic61—21no—
219C2×Dic61—22no—
220C2×Dic61—22no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61#9511yescharacteristic
224C2×Dic61#9511yescharacteristic
225C2×Dic61C2×C22⋊C412yes—
226C2×Dic61C2×C22⋊C411yescharacteristic
227C2×Dic61C2×C4⋊C411yescharacteristic
228C2×Dic61#11712yes—
229C4×D61—22no—
230C4×D61—22no—
231C4×D61—22no—
232C4×D61—22no—
233C4×D61—22no—
234C4×D61—22no—
235C4×D61—22no—
236C4×D61—22no—
237C4×D61—21no—
238C4×D61—21no—
239C4×D61—22no—
240C4×D61—22no—
241C4×D61—21no—
242C4×D61—21no—
243C4×D61#12012yes—
244C4×D61#12012yes—
245C4×D61#12114yes—
246C4×D61C22⋊Q814yes—
247C4×D61#12312yes—
248C4×D61#12312yes—
249#92420—28no—
250C8×C61—42no—
251#92418—42no—
252#10739—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—44no—
261C22×C61#34312yescomplemented
262C22×C61C2×#9511yescharacteristic
263C22×C61C4×C22⋊C412yes—
264C2×D61—21no—
265C2×D61—21no—
266C2×D61—21no—
267C2×D61—21no—
268C2×D61—24no—
269C2×D61—24no—
270C2×D61—24no—
271C2×D61—24no—
272C2×D61—21no—
273C2×D61—21no—
274C2×D61—21no—
275C2×D61—44no—
276C2×D61—44no—
277C2×D61—44no—
278C2×D61—42no—
279C2×D61—42no—
280C2×D61#34312yescomplemented
281C2×D61#38512yes—
282C2×D61#38612yes—
283C2×D61C2×#10011yescharacteristic
284C2×D61C2×#10111yescharacteristic
285C2×D61#41312yes—
286#6923—84no—
287C4×C61—21no—
288C4×C61—21no—
289C4×C61#38512yes—
290C4×C61#38612yes—
291Dic61—21no—
292Dic61—21no—
293Dic61#37911yescharacteristic
294Dic61#38012yes—
295Dic61#38111yescharacteristic
296C23×M16—611no—
297C2×#407—611no—
298C2×#380—611no—
299C2×#343—614no—
300C2×C61—22no—
301C2×C61—22no—
302C2×C61—41no—
303C2×C61C22⋊#9511yescharacteristic
304C2×C61C2×#34311yescharacteristic
305C2×C61#174211yescharacteristic
306D61—22no—
307D61—22no—
308D61—41no—
309D61#190012yes—
310D61#190112yes—
311C24×C4—611no—
312C22×M16—612no—
313C22×M16—612no—
314C22×M16—612no—
315C22×M16—612no—
316C22×M16—1228no—
317C22×M16—1221no—
318C22×M16—1221no—
319C22×M16—1221no—
320C23×C8—1221no—
321C22×C4⋊C4—612no—
322C22×C22⋊C4—612no—
323#407—611no—
324#407—612no—
325#407—1221no—
326#407—1221no—
327#407#692311yescharacteristic, complemented
328C2×C22⋊C8—1221no—
329C2×C22⋊C8—1221no—
330#380—1221no—
331#380—1221no—
332#380—1221no—
333#380—1221no—
334C2×#95—612no—
335#343—1228no—
336C61#1073911yescharacteristic, complemented, Sylow
337C25—611no—
338C23×C4—611no—
339C23×C4—611no—
340C23×C4—611no—
341C23×C4—611no—
342C23×C4—611no—
343C23×C4—611no—
344C23×C4—611no—
345C23×C4—611no—
346C23×C4—611no—
347C23×C4—611no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—614no—
352C23×C4—1224no—
353C23×C4—1224no—
354C23×C4C2×#692311yescharacteristic
355C2×M16—614no—
356C2×M16—618no—
357C2×M16—612no—
358C2×M16—1222no—
359C2×M16—1228no—
360C2×M16—1228no—
361C2×M16—1222no—
362C2×M16—1224no—
363C2×M16—1222no—
364C2×M16—1222no—
365C2×M16—1228no—
366C2×M16—1228no—
367C2×M16—1228no—
368C2×M16—1224no—
369C2×M16—1224no—
370C2×M16C2×#692312yes—
371C22×C8—1222no—
372C22×C8—1222no—
373C22×C8—1222no—
374C22×C8—1222no—
375C22×C8—1228no—
376C2×C4⋊C4—1224no—
377C2×C4⋊C4—1224no—
378C2×C4⋊C4—1222no—
379C2×C4⋊C4—1222no—
380C2×C22⋊C4—1222no—
381C2×C22⋊C4—1222no—
382C2×C22⋊C4—2444no—
383C22⋊C8—21no—
384C22⋊C8—21no—
385C22⋊C8—1222no—
386C22⋊C8—1222no—
387C22⋊C8—1221no—
388C22⋊C8—1221no—
389#95—1222no—
390#95—1222no—
391C24—611no—
392C24—611no—
393C24—611no—
394C24—611no—
395C24—611no—
396C24—611no—
397C24—1222no—
398C24—1224no—
399C24—1222no—
400C24—2442no—
401C24C4×#692311yescharacteristic
402C22×C4—24no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—611no—
407C22×C4—611no—
408C22×C4—614no—
409C22×C4—614no—
410C22×C4—611no—
411C22×C4—611no—
412C22×C4—611no—
413C22×C4—611no—
414C22×C4—611no—
415C22×C4—611no—
416C22×C4—611no—
417C22×C4—611no—
418C22×C4—611no—
419C22×C4—611no—
420C22×C4—611no—
421C22×C4—611no—
422C22×C4—611no—
423C22×C4—611no—
424C22×C4—611no—
425C22×C4—611no—
426C22×C4—611no—
427C22×C4—1222no—
428C22×C4—1222no—
429C22×C4—1222no—
430C22×C4—1222no—
431C22×C4—1222no—
432C22×C4—1222no—
433C22×C4—1224no—
434C22×C4—1224no—
435C22×C4—1222no—
436C22×C4—1222no—
437C22×C4—1224no—
438C22×C4—1224no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1224no—
442C22×C4—1222no—
443C22×C4—1222no—
444C22×C4—1224no—
445C22×C4—1228no—
446C22×C4—1224no—
447C22×C4—2444no—
448C22×C4—2444no—
449C22×C4C4×#692311yescharacteristic
450C22×C4C4⋊#692311yescharacteristic
451C22×C4C4⋊#692311yescharacteristic
452C22×C4C22⋊#692311yescharacteristic
453C22×C4C22⋊#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455M16—24no—
456M16—618no—
457M16—1228no—
458M16—1224no—
459M16—1228no—
460M16—1228no—
461M16—1224no—
462M16—2442no—
463M16—2442no—
464C2×C8—22no—
465C2×C8—1228no—
466C2×C8—1224no—
467C2×C8—1228no—
468C2×C8—1228no—
469C2×C8—1222no—
470C2×C8—2444no—
471C4⋊C4—2442no—
472C4⋊C4—2442no—
473C4⋊C4—2444no—
474C22⋊C4—2444no—
475C22⋊C4—2444no—
476C23—22no—
477C23—22no—
478C23—41no—
479C23—611no—
480C23—612no—
481C23—612no—
482C23—611no—
483C23—611no—
484C23—614no—
485C23—611no—
486C23—1222no—
487C23—1221no—
488C23—1222no—
489C23—1221no—
490C23—1222no—
491C23—1221no—
492C23—1222no—
493C23—1222no—
494C23—1222no—
495C23—1222no—
496C23—1221no—
497C23—1222no—
498C23—1222no—
499C23—1222no—
500C23—1222no—
501C23—2441no—
502C23—2441no—
503C23—2441no—
504C23—2448no—
505C23—2448no—
506C23(C2×#6923)⋊C411yescharacteristic
507C23(C2×#6923)⋊C411yescharacteristic
508C23C2×C4×#692311yescharacteristic
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—612no—
517C2×C4—612no—
518C2×C4—612no—
519C2×C4—614no—
520C2×C4—612no—
521C2×C4—612no—
522C2×C4—614no—
523C2×C4—612no—
524C2×C4—611no—
525C2×C4—611no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1222no—
529C2×C4—1222no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1222no—
533C2×C4—1222no—
534C2×C4—1222no—
535C2×C4—1222no—
536C2×C4—1221no—
537C2×C4—1221no—
538C2×C4—1222no—
539C2×C4—1222no—
540C2×C4—1221no—
541C2×C4—1221no—
542C2×C4—1222no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—4888no—
548C2×C4—2444no—
549C2×C4—2444no—
550C2×C4—2444no—
551C2×C4(C2×#6923)⋊C411yescharacteristic
552C2×C4(C2×#6923)⋊C411yescharacteristic
553C2×C4C2×C22⋊#692311yescharacteristic
554C2×C4C2×C4⋊#692311yescharacteristic
555C2×C4D4×#692314yes—
556C8—42no—
557C8—1228no—
558C8—2442no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—44no—
567C22—612no—
568C22—611no—
569C22—611no—
570C22—612no—
571C22—612no—
572C22—612no—
573C22—1224no—
574C22—1224no—
575C22—1224no—
576C22—1224no—
577C22—1221no—
578C22—1221no—
579C22—1221no—
580C22—1221no—
581C22—1221no—
582C22—1221no—
583C22—1221no—
584C22—2444no—
585C22—2444no—
586C22—2442no—
587C22—2442no—
588C22—2444no—
589C22#1684064112yescomplemented
590C22C2×(C2×#6923)⋊C411yescharacteristic
591C22C22⋊C4×#692312yes—
592C4—21no—
593C4—21no—
594C4—611no—
595C4—612no—
596C4—611no—
597C4—1221no—
598C4—1221no—
599C4—4884no—
600C4#1684070912yes—
601C4#1684071012yes—
602C2—22no—
603C2—22no—
604C2—41no—
605C2—612no—
606C2—612no—
607C2—1222no—
608C2—1222no—
609C2—2441no—
610C2#2146099211yescharacteristic
611C2C2×#1684064111yescharacteristic
612C2#2146152311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#10739
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. C2×#16840641C2semidirect
9. C2×D61⋊M16C4semidirect
11. C22×#11758217C4semidirect
23. #16839726C4semidirect
24. #16839725C4semidirect
29. C61×#407C4semidirect
152. #11758217C22⋊C4semidirect
261. C22×C61#343semidirect
280. C2×D61#343semidirect
327. #407#6923semidirect
336. C61#10739semidirect
589. C22#16840641semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×#168407042
C2×#168406412
#407×D612
#1073961