Finite Group Databasebeta

← #30596340

Subgroups — #30596340

Order 15616.

1058 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460661C214yesmaximal, complemented
4C2×#16839725C211yesmaximal, characteristic
5C2×D61⋊M16—21no—
6C22×C22⋊#6923C412yes—
7C22×C4×#6923—21no—
8#16840734—21no—
9#16840733—21no—
10#16840733C412yescomplemented
11#16840732C412yescomplemented
12D61⋊(C22⋊C8)—21no—
13D61⋊(C22⋊C8)C2212yes—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C412yes—
17C4×C22⋊#6923C2212yes—
18C2×(C2×#6923)⋊C4—21no—
19C23×C4×D61C2211yescharacteristic
20C22×#11758194C411yescharacteristic, complemented
21#16839725—21no—
22#16839725—21no—
23#16839725—21no—
24#16839725—21no—
25C2×#14519689C412yescomplemented
26C2×#14519689C2212yes—
27C22×M16×C61C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30D61⋊M16—42no—
31D61⋊M16—42no—
32C2×#11758217—22no—
33C2×D61⋊C8—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—28no—
36C2×C22⋊#6923C2×C414yes—
37C2×C4×#6923—22no—
38C2×C4×#6923—22no—
39C2×C4×#6923—42no—
40C2×C4×#6923—42no—
41#14519834—22no—
42#14519834—22no—
43C22⋊#92420—22no—
44C22⋊#92420C2×C414yescomplemented
45(C2×#6923)⋊C4—22no—
46(C2×#6923)⋊C4—22no—
47C24×D61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C22×C4×D61—42no—
50C22×C4×D61—42no—
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61D411yescharacteristic
59C22×C4×D61D411yescharacteristic
60C22×C4×D61Q811yescharacteristic
61C22×C4×D61Q811yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C2×#11758194—21no—
64C2×#11758194—21no—
65C2×#11758194—42no—
66C22×#92418C2×C412yescomplemented
67#14519689—22no—
68#14519689—22no—
69#14519689—22no—
70#14519689—22no—
71C23×C4×C61C2×C411yescharacteristic
72C2×M16×C61—21no—
73C2×M16×C61—21no—
74C2×M16×C61—42no—
75C22×C8×C61C2×C412yescomplemented
76C24×C61C4211yescharacteristic
77C23×D61—24no—
78C23×D61—42no—
79C23×D61—42no—
80C23×D61C4211yescharacteristic
81C23×D61C22⋊C411yescharacteristic
82C23×D61C22⋊C411yescharacteristic
83C23×D61C4⋊C411yescharacteristic
84C23×D61C4⋊C411yescharacteristic
85C23×D61C22×C411yescharacteristic
86C22×#6923—28no—
87C22×#6923—24no—
88C22×#6923—44no—
89C22×#6923—44no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61C4211yescharacteristic
93C22×C4×C61C22⋊C411yescharacteristic
94C22×C4×C61C22⋊C411yescharacteristic
95C22×C4×C61C4⋊C411yescharacteristic
96C22×C4×C61C4⋊C411yescharacteristic
97C22×C4×C61C22×C411yescharacteristic
98C22×Dic61—42no—
99C22×Dic61C4211yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C4⋊C411yescharacteristic
103C22×Dic61C4⋊C411yescharacteristic
104C22×Dic61C22×C411yescharacteristic
105C2×C4×D61—22no—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—22no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—41no—
112C2×C4×D61—41no—
113C2×C4×D61—42no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—42no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—42no—
122C2×C4×D61—42no—
123C2×C4×D61C22⋊C411yescharacteristic
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C22⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C4⋊C411yescharacteristic
135C2×C4×D61C2×D411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×C4×D61C2×D411yescharacteristic
138C2×C4×D61C2×Q811yescharacteristic
139C22⋊#6923—28no—
140C22⋊#6923—24no—
141C22⋊#6923M1618yescomplemented
142#11758217—44no—
143C2×#92420—24no—
144C4×#6923—44no—
145C4×#6923—42no—
146C4×#6923—42no—
147#11758213—44no—
148D61⋊C8—42no—
149D61⋊C8—42no—
150M16×C61—42no—
151M16×C61—42no—
152C2×C8×C61—22no—
153C2×C8×C61—42no—
154#11758194—42no—
155#11758194—42no—
156C2×#92418—22no—
157C2×#92418—42no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—41no—
161C23×C61#9511yescharacteristic
162C23×C61#9511yescharacteristic
163C23×C61C2×C4211yescharacteristic
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—22no—
170C22×D61—22no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61—22no—
174C22×D61—41no—
175C22×D61—41no—
176C22×D61—41no—
177C22×D61—41no—
178C22×D61—41no—
179C22×D61—41no—
180C22×D61—41no—
181C22×D61—416no—
182C22×D61#9511yescharacteristic
183C22×D61#9511yescharacteristic
184C22×D61C2×C22⋊C411yescharacteristic
185C22×D61C2×C4⋊C411yescharacteristic
186C22×D61C2×M1614yes—
187C2×#6923—28no—
188C2×#6923—44no—
189C2×#6923—416no—
190C2×#6923—44no—
191C2×C4×C61—22no—
192C2×C4×C61—22no—
193C2×C4×C61—22no—
194C2×C4×C61—21no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—21no—
198C2×C4×C61#9511yescharacteristic
199C2×C4×C61#9511yescharacteristic
200C2×C4×C61#9912yes—
201C2×C4×C61#9912yes—
202C2×C4×C61C2×C22⋊C411yescharacteristic
203C2×C4×C61C2×C4⋊C411yescharacteristic
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61#9511yescharacteristic
211C2×Dic61#9511yescharacteristic
212C2×Dic61C2×C22⋊C411yescharacteristic
213C2×Dic61C2×C4⋊C411yescharacteristic
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—21no—
221C4×D61—21no—
222C4×D61—21no—
223C4×D61—21no—
224C4×D61—21no—
225C4×D61—21no—
226C4×D61—41no—
227C4×D61—41no—
228C4×D61—41no—
229C4×D61—41no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—41no—
233C4×D61—41no—
234#92420—44no—
235C8×C61—42no—
236#92418—42no—
237#7929—611nomaximal, Sylow
238C22×C61—21no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—21no—
244C22×C61—21no—
245C22×C61—44no—
246C22×C61#34212yes—
247C22×C61C2×#9511yescharacteristic
248C22×C61C4×M1612yes—
249C2×D61—28no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—21no—
254C2×D61—21no—
255C2×D61—21no—
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—44no—
260C2×D61—44no—
261C2×D61—44no—
262C2×D61—44no—
263C2×D61—44no—
264C2×D61#34412yes—
265C2×D61#40712yes—
266C2×D61#42312yes—
267#6923—48no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61#34212yes—
271C4×C61C2×#9911yescharacteristic
272C4×C61C2×#9911yescharacteristic
273Dic61—21no—
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277C2×#407—611no—
278C2×#407—611no—
279C2×C4×C22⋊C4—611no—
280#1282—614no—
281C2×C61—22no—
282C2×C61—22no—
283C2×C61—41no—
284C2×C61#172811yescharacteristic
285C2×C61C2×#34211yescharacteristic
286C2×C61C2×#34411yescharacteristic
287D61—22no—
288D61—22no—
289D61—22no—
290D61—41no—
291C24×C4—611no—
292C22×M16—611no—
293C22×M16—1221no—
294C22×M16#692311yescharacteristic, complemented
295C22×C22⋊C4—612no—
296C22×C42—1221no—
297#407—612no—
298#407—612no—
299#407—1221no—
300#407—1221no—
301#407—1221no—
302#407—1221no—
303#407—1221no—
304#407—1221no—
305C2×C22⋊C8—612no—
306C2×C22⋊C8—612no—
307C2×C22⋊C8—612no—
308C2×C22⋊C8—1221no—
309C4×C22⋊C4—612no—
310C4×C22⋊C4—612no—
311C4×C22⋊C4—1221no—
312C4×C22⋊C4—1221no—
313C2×#95—1221no—
314C61#792911yescharacteristic, complemented, Sylow
315C25—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—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—1222no—
330C23×C4—2442no—
331C23×C4—2442no—
332C23×C4C2×#692311yescharacteristic
333C2×M16—21no—
334C2×M16—21no—
335C2×M16—42no—
336C2×M16—1222no—
337C2×M16—1222no—
338C2×M16—1221no—
339C2×M16—1221no—
340C2×M16—2442no—
341C2×M16—2442no—
342C2×M16—2442no—
343C22×C8—612no—
344C22×C8—1222no—
345C22×C8C2×#692312yescomplemented
346C2×C22⋊C4—614no—
347C2×C22⋊C4—1228no—
348C2×C22⋊C4—1222no—
349C2×C42—1222no—
350C2×C42—1222no—
351C2×C42—2442no—
352C2×C42—2442no—
353C22⋊C8—614no—
354C22⋊C8—1222no—
355C22⋊C8—1222no—
356C22⋊C8—1222no—
357C22⋊C8—1222no—
358C22⋊C8—1222no—
359C22⋊C8—1222no—
360C22⋊C8—1222no—
361#95—1222no—
362#95—1222no—
363C24—611no—
364C24—611no—
365C24—611no—
366C24—611no—
367C24—611no—
368C24—611no—
369C24—1224no—
370C24—2442no—
371C24—2442no—
372C24C4×#692311yescharacteristic
373C22×C4—22no—
374C22×C4—22no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
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—1222no—
398C22×C4—1222no—
399C22×C4—1222no—
400C22×C4—1222no—
401C22×C4—1224no—
402C22×C4—1228no—
403C22×C4—2441no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4—2441no—
408C22×C4—2441no—
409C22×C4—2441no—
410C22×C4—2441no—
411C22×C4—2442no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2442no—
415C22×C4—2442no—
416C22×C4—2442no—
417C22×C4—2442no—
418C22×C4—2444no—
419C22×C4—2444no—
420C22×C4C4×#692311yescharacteristic
421C22×C4C4⋊#692311yescharacteristic
422C22×C4C4⋊#692311yescharacteristic
423C22×C4C22⋊#692311yescharacteristic
424C22×C4C22⋊#692311yescharacteristic
425C22×C4C22×#692311yescharacteristic
426M16—42no—
427M16—42no—
428M16—2442no—
429M16—2444no—
430M16—2444no—
431M16—2442no—
432C2×C8—22no—
433C2×C8—42no—
434C2×C8—1224no—
435C2×C8—1222no—
436C2×C8—2442no—
437C2×C8—2442no—
438C2×C8—2442no—
439C22⋊C4—618no—
440C22⋊C4—1224no—
441C22⋊C4—1228no—
442C42—2442no—
443C42—2442no—
444C42—2444no—
445C23—22no—
446C23—22no—
447C23—41no—
448C23—611no—
449C23—611no—
450C23—611no—
451C23—614no—
452C23—611no—
453C23—1222no—
454C23—1222no—
455C23—1222no—
456C23—1222no—
457C23—1222no—
458C23—1222no—
459C23—1222no—
460C23—1222no—
461C23—1222no—
462C23—1222no—
463C23—2441no—
464C23—2441no—
465C23—2441no—
466C23—2441no—
467C23—2441no—
468C23—2441no—
469C23—2441no—
470C23—24416no—
471C23(C2×#6923)⋊C411yescharacteristic
472C23(C2×#6923)⋊C411yescharacteristic
473C23C2×C4×#692311yescharacteristic
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—611no—
482C2×C4—611no—
483C2×C4—611no—
484C2×C4—611no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1221no—
488C2×C4—1221no—
489C2×C4—1221no—
490C2×C4—1221no—
491C2×C4—1221no—
492C2×C4—1221no—
493C2×C4—1221no—
494C2×C4—1221no—
495C2×C4—1222no—
496C2×C4—1222no—
497C2×C4—1222no—
498C2×C4—1222no—
499C2×C4—1228no—
500C2×C4—2441no—
501C2×C4—2441no—
502C2×C4—2441no—
503C2×C4—2441no—
504C2×C4—2441no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4—2444no—
513C2×C4—24416no—
514C2×C4—2444no—
515C2×C4(C2×#6923)⋊C411yescharacteristic
516C2×C4(C2×#6923)⋊C411yescharacteristic
517C2×C4#1451983512yes—
518C2×C4#1451983612yes—
519C2×C4C2×C22⋊#692311yescharacteristic
520C2×C4C2×C4⋊#692311yescharacteristic
521C8—42no—
522C8—2444no—
523C8—2442no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—44no—
532C22—612no—
533C22—612no—
534C22—612no—
535C22—1228no—
536C22—1221no—
537C22—1221no—
538C22—1221no—
539C22—1221no—
540C22—1221no—
541C22—1221no—
542C22—1221no—
543C22—1221no—
544C22—1221no—
545C22—2444no—
546C22—2444no—
547C22—2444no—
548C22—2444no—
549C22—2444no—
550C22#1684064012yes—
551C22C2×(C2×#6923)⋊C411yescharacteristic
552C22M16×#692312yes—
553C4—21no—
554C4—21no—
555C4—1221no—
556C4—1221no—
557C4—1221no—
558C4—1221no—
559C4—2448no—
560C4#1684064012yes—
561C4C2×#1451983511yescharacteristic
562C4C2×#1451983611yescharacteristic
563C2—22no—
564C2—22no—
565C2—41no—
566C2—1222no—
567C2—1222no—
568C2—1222no—
569C2—2441no—
570C2#2146148111yescharacteristic
571C2C2×#1684064011yescharacteristic
572C2#2146152911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC23×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC22×M16×C61C4
socleC22×C61C2×#95
prime radicalC24×D61C2×C4
cosocleC22×C4×D61C23
hypercenterC22×M16#6923
hypocenterC61#7929
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
3. #21460661C2semidirect
10. #16840733C4semidirect
11. #16840732C4semidirect
20. C22×#11758194C4semidirect
25. C2×#14519689C4semidirect
27. C22×M16×C61C4semidirect
44. C22⋊#92420C2×C4semidirect
66. C22×#92418C2×C4semidirect
75. C22×C8×C61C2×C4semidirect
141. C22⋊#6923M16semidirect
294. C22×M16#6923semidirect
314. C61#7929semidirect
345. C22×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
D61⋊#4072
C2×C4×C22⋊#69232
#214606612
C2×#168397252
#792961