Finite Group Databasebeta

← #30602414

Subgroups — #30602414

Order 15616.

1326 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D61⋊M16C211yesmaximal, characteristic
2C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
3C2×#16840637C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C22×#11758213C412yes—
6C2×D61⋊M16—28no—
7C2×D61⋊M16—21no—
8C2×D61⋊M16—21no—
9C2×D61⋊M16C412yes—
10C2×D61⋊M16C2212yes—
11C22×#11758217—21no—
12C22×D61⋊C8—21no—
13C22×D61⋊C8C2212yes—
14C2×#14519834—21no—
15D61⋊(C22⋊C8)—21no—
16D61⋊(C22⋊C8)—21no—
17D61⋊(C22⋊C8)C412yes—
18D61⋊(C22⋊C8)C412yes—
19C2×C22⋊#92420—21no—
20#16840637—28no—
21C23×C4×D61C2211yescharacteristic
22C2×M16×D61C2212yes—
23#16839726C411yescharacteristic
24#16839725C412yes—
25#16839724—21no—
26#16839724—21no—
27C22⋊C8×D61—21no—
28C22⋊C8×D61—21no—
29C61×#407C411yescharacteristic
30C2×#11758213—22no—
31C2×#11758213—28no—
32C2×#11758213C2×C414yes—
33D61⋊M16—28no—
34D61⋊M16—28no—
35D61⋊M16—24no—
36D61⋊M16—28no—
37D61⋊M16D418yes—
38C2×#11758217—28no—
39C2×#11758217—22no—
40C2×#11758217—22no—
41C2×D61⋊C8—28no—
42C2×D61⋊C8—22no—
43C2×D61⋊C8—22no—
44C2×D61⋊C8—24no—
45C2×D61⋊C8—24no—
46C2×D61⋊C8—22no—
47C2×D61⋊C8C2×C414yes—
48C22×#92420—22no—
49C22×#92420—22no—
50#14519834—22no—
51#14519834—22no—
52C22⋊#92420—22no—
53C22⋊#92420—22no—
54C24×D61Q811yescharacteristic
55C23×Dic61D411yescharacteristic
56C22×C4×D61—24no—
57C22×C4×D61—24no—
58C22×C4×D61C2×C411yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C22×C4×D61C2×C411yescharacteristic
63C22×C4×D61D411yescharacteristic
64C22×C4×D61D411yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61D411yescharacteristic
68C22×C4×D61Q811yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758194C2×C412yes—
71C2×#11758189—22no—
72M16×D61—24no—
73M16×D61—24no—
74C2×C8×D61—22no—
75C22⋊#92418—21no—
76C22⋊#92418—21no—
77#14519689—22no—
78#14519689—22no—
79C23×C4×C61C2×C411yescharacteristic
80C2×M16×C61C2×C412yes—
81C22⋊C8×C61—21no—
82C22⋊C8×C61—21no—
83C24×C61C4⋊C411yescharacteristic
84C23×D61—24no—
85C23×D61—24no—
86C23×D61—42no—
87C23×D61C4⋊C411yescharacteristic
88C23×D61C4⋊C411yescharacteristic
89C23×D61C4⋊C411yescharacteristic
90C23×D61C4⋊C411yescharacteristic
91C23×D61C4⋊C411yescharacteristic
92C23×D61C2×Q811yescharacteristic
93C22×C4×C61—24no—
94C22×C4×C61C4211yescharacteristic
95C22×C4×C61C4211yescharacteristic
96C22×C4×C61C22⋊C411yescharacteristic
97C22×C4×C61C22⋊C411yescharacteristic
98C22×C4×C61C4⋊C411yescharacteristic
99C22×C4×C61C22×C411yescharacteristic
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C4⋊C411yescharacteristic
107C22×Dic61C2×D411yescharacteristic
108C2×C4×D61—24no—
109C2×C4×D61—24no—
110C2×C4×D61—22no—
111C2×C4×D61—22no—
112C2×C4×D61—22no—
113C2×C4×D61—22no—
114C2×C4×D61—22no—
115C2×C4×D61—22no—
116C2×C4×D61—24no—
117C2×C4×D61—24no—
118C2×C4×D61—22no—
119C2×C4×D61—22no—
120C2×C4×D61—24no—
121C2×C4×D61—24no—
122C2×C4×D61—22no—
123C2×C4×D61—22no—
124C2×C4×D61C4211yescharacteristic
125C2×C4×D61C4211yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C22⋊C411yescharacteristic
130C2×C4×D61C22⋊C411yescharacteristic
131C2×C4×D61C22⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C4⋊C411yescharacteristic
136C2×C4×D61C22×C411yescharacteristic
137C2×C4×D61C22×C411yescharacteristic
138C2×C4×D61C2×D414yes—
139C2×C4×D61C2×D411yescharacteristic
140C2×C4×D61C2×D411yescharacteristic
141C2×C4×D61#4114yes—
142#11758217—28no—
143#11758217—28no—
144C2×#92420—28no—
145C2×#92420—24no—
146C2×#92420—24no—
147C2×#92420—42no—
148C2×#92420—42no—
149#11758213—28no—
150#11758213—24no—
151#11758213C22⋊C418yes—
152D61⋊C8—28no—
153D61⋊C8—28no—
154D61⋊C8—28no—
155D61⋊C8—44no—
156M16×C61—24no—
157C2×C8×C61—22no—
158#11758194—24no—
159C2×#92418—22no—
160#11758189—44no—
161C8×D61—42no—
162C8×D61—42no—
163C23×C61—22no—
164C23×C61—22no—
165C23×C61—41no—
166C23×C61#9511yescharacteristic
167C23×C61#9511yescharacteristic
168C23×C61C2×C4⋊C411yescharacteristic
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—22no—
175C22×D61—22no—
176C22×D61—22no—
177C22×D61—22no—
178C22×D61—22no—
179C22×D61—22no—
180C22×D61—22no—
181C22×D61—22no—
182C22×D61—41no—
183C22×D61—41no—
184C22×D61—41no—
185C22×D61—416no—
186C22×D61#9511yescharacteristic
187C22×D61#9511yescharacteristic
188C22×D61#10814yes—
189C22×D61C2×C4⋊C411yescharacteristic
190C22×D61C2×C4⋊C411yescharacteristic
191C22×D61C22⋊Q814yes—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—22no—
195C2×C4×C61—22no—
196C2×C4×C61—22no—
197C2×C4×C61#9511yescharacteristic
198C2×C4×C61#9511yescharacteristic
199C2×C4×C61C2×C4211yescharacteristic
200C2×C4×C61C2×C22⋊C411yescharacteristic
201C2×C4×C61C4×D414yes—
202C2×Dic61—22no—
203C2×Dic61—21no—
204C2×Dic61—21no—
205C2×Dic61—21no—
206C2×Dic61—21no—
207C2×Dic61—22no—
208C2×Dic61—22no—
209C2×Dic61#9511yescharacteristic
210C2×Dic61#9511yescharacteristic
211C2×Dic61C2×C22⋊C411yescharacteristic
212C2×Dic61C2×C22⋊C411yescharacteristic
213C2×Dic61#12012yes—
214C2×Dic61#12312yes—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—22no—
221C4×D61—22no—
222C4×D61—22no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—21no—
227C4×D61—22no—
228C4×D61—22no—
229C4×D61C2×C22⋊C412yes—
230C4×D61#11712yes—
231C4×D61C4×D414yes—
232C4×D61#12012yes—
233C4×D61#12114yes—
234C4×D61#12312yes—
235#92420—28no—
236#92420—44no—
237C8×C61—42no—
238#92418—42no—
239#10734—611nomaximal, Sylow
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—21no—
246C22×C61—21no—
247C22×C61—44no—
248C22×C61#34112yescomplemented
249C22×C61C2×#9511yescharacteristic
250C22×C61#38512yes—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—28no—
256C2×D61—28no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—44no—
261C2×D61—44no—
262C2×D61—44no—
263C2×D61—44no—
264C2×D61#34112yescomplemented
265C2×D61#38012yes—
266C2×D61#38512yes—
267C2×D61C2×#10812yes—
268C2×D61#43012yes—
269C4×C61—21no—
270C4×C61—21no—
271C4×C61C4×C22⋊C412yes—
272C4×C61#38612yes—
273Dic61—21no—
274Dic61—21no—
275Dic61#37911yescharacteristic
276Dic61#38111yescharacteristic
277Dic61#38612yes—
278C23×M16—611no—
279C2×#407—611no—
280C22×C22⋊C8—611no—
281C2×#341—614no—
282C2×C61—22no—
283C2×C61—22no—
284C2×C61—41no—
285C2×C61C22⋊#9511yescharacteristic
286C2×C61C2×#34111yescharacteristic
287C2×C61#173811yescharacteristic
288D61—22no—
289D61—22no—
290D61—41no—
291D61#185514yes—
292C24×C4—611no—
293C22×M16—612no—
294C22×M16—612no—
295C22×M16—612no—
296C22×M16—612no—
297C22×M16—1228no—
298C22×M16—1221no—
299C22×M16—1221no—
300C22×M16—1221no—
301C23×C8—612no—
302C23×C8—1221no—
303#407—611no—
304#407—612no—
305#407—1221no—
306#407—1221no—
307#407#692311yescharacteristic
308C2×C22⋊C8—612no—
309C2×C22⋊C8—612no—
310C2×C22⋊C8—1221no—
311C2×C22⋊C8—1221no—
312C2×C22⋊C8—1221no—
313C2×C22⋊C8—1221no—
314C2×C22⋊C8—1221no—
315C2×C22⋊C8—1221no—
316#341—1228no—
317C61#1073411yescharacteristic, complemented, Sylow
318C25—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—611no—
327C23×C4—611no—
328C23×C4—611no—
329C23×C4—611no—
330C23×C4—611no—
331C23×C4—611no—
332C23×C4—1224no—
333C23×C4—1224no—
334C23×C4C2×#692311yescharacteristic
335C2×M16—614no—
336C2×M16—618no—
337C2×M16—612no—
338C2×M16—1222no—
339C2×M16—1228no—
340C2×M16—1228no—
341C2×M16—1222no—
342C2×M16—1222no—
343C2×M16—1224no—
344C2×M16—1222no—
345C2×M16—1228no—
346C2×M16—1228no—
347C2×M16—1228no—
348C2×M16—1224no—
349C2×M16—1224no—
350C2×M16C2×#692312yes—
351C22×C8—614no—
352C22×C8—1222no—
353C22×C8—1222no—
354C22×C8—1222no—
355C22×C8—1222no—
356C22×C8—1228no—
357C22×C8—1222no—
358C22×C8—1224no—
359C22×C8—1224no—
360C22×C8—1222no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—1222no—
364C22⋊C8—1222no—
365C22⋊C8—1222no—
366C22⋊C8—1222no—
367C22⋊C8—1222no—
368C22⋊C8—1222no—
369C22⋊C8—1221no—
370C22⋊C8—1221no—
371C24—611no—
372C24—611no—
373C24—611no—
374C24—611no—
375C24—611no—
376C24—611no—
377C24—1224no—
378C24—1224no—
379C24—2442no—
380C24C4⋊#692311yescharacteristic
381C22×C4—24no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—614no—
388C22×C4—614no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—611no—
393C22×C4—611no—
394C22×C4—611no—
395C22×C4—611no—
396C22×C4—611no—
397C22×C4—611no—
398C22×C4—611no—
399C22×C4—611no—
400C22×C4—611no—
401C22×C4—611no—
402C22×C4—611no—
403C22×C4—611no—
404C22×C4—611no—
405C22×C4—611no—
406C22×C4—1222no—
407C22×C4—1222no—
408C22×C4—1222no—
409C22×C4—1222no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—1224no—
413C22×C4—1224no—
414C22×C4—1222no—
415C22×C4—1222no—
416C22×C4—1222no—
417C22×C4—1222no—
418C22×C4—1224no—
419C22×C4—1224no—
420C22×C4—1224no—
421C22×C4—1222no—
422C22×C4—1222no—
423C22×C4—1224no—
424C22×C4C4×#692311yescharacteristic
425C22×C4C4×#692311yescharacteristic
426C22×C4C4⋊#692311yescharacteristic
427C22×C4C22⋊#692311yescharacteristic
428C22×C4C22⋊#692311yescharacteristic
429C22×C4C22×#692311yescharacteristic
430M16—24no—
431M16—618no—
432M16—1224no—
433M16—1228no—
434M16—1228no—
435M16—1228no—
436M16—1224no—
437M16—2444no—
438C2×C8—22no—
439C2×C8—1228no—
440C2×C8—1224no—
441C2×C8—1228no—
442C2×C8—1228no—
443C2×C8—1224no—
444C2×C8—1228no—
445C2×C8—1222no—
446C2×C8—2442no—
447C2×C8—2442no—
448C2×C8—2444no—
449C2×C8—2442no—
450C2×C8—2442no—
451C23—22no—
452C23—22no—
453C23—41no—
454C23—611no—
455C23—614no—
456C23—614no—
457C23—611no—
458C23—611no—
459C23—611no—
460C23—1222no—
461C23—1222no—
462C23—1222no—
463C23—1222no—
464C23—1222no—
465C23—1222no—
466C23—1222no—
467C23—1222no—
468C23—1222no—
469C23—1222no—
470C23—1222no—
471C23—1222no—
472C23—1222no—
473C23—2441no—
474C23—2441no—
475C23—2441no—
476C23—24416no—
477C23(C2×#6923)⋊C411yescharacteristic
478C23(C2×#6923)⋊C411yescharacteristic
479C23C2×C4⋊#692311yescharacteristic
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—612no—
486C2×C4—612no—
487C2×C4—611no—
488C2×C4—611no—
489C2×C4—612no—
490C2×C4—614no—
491C2×C4—612no—
492C2×C4—612no—
493C2×C4—612no—
494C2×C4—614no—
495C2×C4—611no—
496C2×C4—611no—
497C2×C4—1221no—
498C2×C4—1221no—
499C2×C4—1221no—
500C2×C4—1221no—
501C2×C4—1222no—
502C2×C4—1222no—
503C2×C4—1222no—
504C2×C4—1222no—
505C2×C4—1222no—
506C2×C4—1222no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1222no—
512C2×C4—1222no—
513C2×C4—1222no—
514C2×C4—1222no—
515C2×C4—1222no—
516C2×C4—1222no—
517C2×C4—1222no—
518C2×C4(C2×#6923)⋊C411yescharacteristic
519C2×C4(C2×#6923)⋊C411yescharacteristic
520C2×C4C2×C4×#692311yescharacteristic
521C2×C4C2×C22⋊#692311yescharacteristic
522C2×C4D4×#692314yes—
523C8—42no—
524C8—1228no—
525C8—2444no—
526C8—2442no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—21no—
533C22—21no—
534C22—44no—
535C22—612no—
536C22—612no—
537C22—612no—
538C22—612no—
539C22—612no—
540C22—1228no—
541C22—1228no—
542C22—1221no—
543C22—1221no—
544C22—1221no—
545C22—1221no—
546C22—1221no—
547C22—1221no—
548C22—1221no—
549C22—2444no—
550C22—2444no—
551C22—2444no—
552C22—2444no—
553C22#1684063712yescomplemented
554C22C2×(C2×#6923)⋊C411yescharacteristic
555C22#1684070912yes—
556C4—21no—
557C4—21no—
558C4—611no—
559C4—611no—
560C4—612no—
561C4—1221no—
562C4—1221no—
563C4C22⋊C4×#692312yes—
564C4#1684071012yes—
565C2—22no—
566C2—22no—
567C2—41no—
568C2—614no—
569C2—1222no—
570C2—1222no—
571C2—2441no—
572C2#2146099211yescharacteristic
573C2C2×#1684063711yescharacteristic
574C2#2146151211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61Q8
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#10734
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. C2×#16840637C2semidirect
248. C22×C61#341semidirect
264. C2×D61#341semidirect
317. C61#10734semidirect
553. C22#16840637semidirect

Maximal subgroups

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

subgroupindex
C22×D61⋊M162
C2×D61⋊(C22⋊C8)2
C2×#168406372
#407×D612
#1073461