Finite Group Databasebeta

← #30596246

Subgroups — #30596246

Order 15616.

1318 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D61⋊#407C211yesmaximal, characteristic
2C22×(C2×#6923)⋊C4C211yesmaximal, characteristic
3#21460656C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C24×#6923C412yes—
6C2×D61⋊M16—21no—
7#16840734—21no—
8#16840733—21no—
9#16840733C412yescomplemented
10#16840732C412yescomplemented
11D61⋊(C22⋊C8)—21no—
12D61⋊(C22⋊C8)C2212yes—
13C2×(C2×#6923)⋊C4—21no—
14C2×(C2×#6923)⋊C4—21no—
15C2×(C2×#6923)⋊C4—21no—
16C2×(C2×#6923)⋊C4—21no—
17C2×(C2×#6923)⋊C4C412yes—
18C2×(C2×#6923)⋊C4C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61—21no—
21#16839726C411yescharacteristic, complemented
22#16839725—21no—
23#16839724—21no—
24#16839724C412yescomplemented
25C22⋊C8×D61—21no—
26C22⋊C8×D61C2212yes—
27C61×#407C411yescharacteristic, complemented
28C23×#6923—22no—
29C23×#6923—22no—
30C23×#6923—28no—
31C23×#6923—44no—
32C23×#6923—44no—
33C23×#6923C2×C414yes—
34C2×#11758213—22no—
35D61⋊M16—44no—
36C2×#11758217—22no—
37C2×D61⋊C8—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420C2×C414yescomplemented
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4—22no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4—22no—
46C24×D61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C22×C4×D61—44no—
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61D411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C22×C4×D61C2311yescharacteristic
61C2×#11758194—21no—
62C2×#11758189—22no—
63M16×D61—44no—
64C2×C8×D61—22no—
65C22⋊#92418—21no—
66C22⋊#92418C2×C412yescomplemented
67#14519689—22no—
68#14519689—22no—
69C23×C4×C61C2×C411yescharacteristic
70C2×M16×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61C2×C412yescomplemented
73C24×C61C4211yescharacteristic
74C23×D61—24no—
75C23×D61—22no—
76C23×D61—22no—
77C23×D61—24no—
78C23×D61C4211yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C23×D61C22×C411yescharacteristic
84C22×#6923—28no—
85C22×#6923—28no—
86C22×#6923—24no—
87C22×#6923—24no—
88C22×#6923—432no—
89C22×#6923—44no—
90C22×#6923—44no—
91C22×#6923—44no—
92C22×#6923—44no—
93C22×#6923—44no—
94C22×#6923—44no—
95C22×#6923M1618yescomplemented
96C22×C4×C61—42no—
97C22×C4×C61C4211yescharacteristic
98C22×C4×C61C22⋊C411yescharacteristic
99C22×C4×C61C22⋊C411yescharacteristic
100C22×C4×C61C4⋊C411yescharacteristic
101C22×C4×C61C4⋊C411yescharacteristic
102C22×C4×C61C22×C411yescharacteristic
103C22×Dic61—42no—
104C22×Dic61C4211yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C4⋊C411yescharacteristic
108C22×Dic61C4⋊C411yescharacteristic
109C22×Dic61C22×C411yescharacteristic
110C2×C4×D61—24no—
111C2×C4×D61—24no—
112C2×C4×D61—42no—
113C2×C4×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61—42no—
117C2×C4×D61—42no—
118C2×C4×D61—42no—
119C2×C4×D61—42no—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61C22⋊C411yescharacteristic
123C2×C4×D61C22⋊C411yescharacteristic
124C2×C4×D61C22⋊C411yescharacteristic
125C2×C4×D61C22⋊C411yescharacteristic
126C2×C4×D61C22⋊C411yescharacteristic
127C2×C4×D61C22⋊C411yescharacteristic
128C2×C4×D61C4⋊C411yescharacteristic
129C2×C4×D61C4⋊C411yescharacteristic
130C2×C4×D61C4⋊C411yescharacteristic
131C2×C4×D61C4⋊C411yescharacteristic
132C2×C4×D61C4⋊C411yescharacteristic
133C2×C4×D61C4⋊C411yescharacteristic
134C2×C4×D61C2×D411yescharacteristic
135C2×C4×D61C2×D411yescharacteristic
136C2×C4×D61C2×D411yescharacteristic
137C2×C4×D61C2×Q811yescharacteristic
138#11758217—44no—
139C2×#92420—24no—
140#11758213—44no—
141D61⋊C8—44no—
142M16×C61—42no—
143C2×C8×C61—22no—
144#11758194—42no—
145C2×#92418—22no—
146#11758189—44no—
147C8×D61—44no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—22no—
151C23×C61#9511yescharacteristic
152C23×C61#9511yescharacteristic
153C23×C61C2×C4211yescharacteristic
154C22×D61—216no—
155C22×D61—216no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—22no—
162C22×D61—22no—
163C22×D61—22no—
164C22×D61—22no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—21no—
168C22×D61—21no—
169C22×D61—21no—
170C22×D61—21no—
171C22×D61—22no—
172C22×D61—22no—
173C22×D61#9511yescharacteristic
174C22×D61#9511yescharacteristic
175C22×D61#9914yes—
176C22×D61#10012yes—
177C22×D61#10112yes—
178C22×D61C2×C22⋊C411yescharacteristic
179C22×D61C2×C4⋊C411yescharacteristic
180C22×D61C2×M1614yes—
181C2×#6923—28no—
182C2×#6923—416no—
183C2×#6923—416no—
184C2×#6923—48no—
185C2×#6923—44no—
186C2×#6923—44no—
187C2×#6923—48no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61#9511yescharacteristic
195C2×C4×C61#9511yescharacteristic
196C2×C4×C61C2×C22⋊C411yescharacteristic
197C2×C4×C61C2×C4⋊C411yescharacteristic
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61#9511yescharacteristic
205C2×Dic61#9511yescharacteristic
206C2×Dic61C2×C22⋊C411yescharacteristic
207C2×Dic61C2×C4⋊C411yescharacteristic
208C4×D61—22no—
209C4×D61—22no—
210C4×D61—22no—
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—41no—
217C4×D61—41no—
218C4×D61—41no—
219C4×D61—41no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224#92420—44no—
225C8×C61—42no—
226#92418—42no—
227#7909—611nomaximal, Sylow
228C22×C61—28no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61#34212yes—
236C22×C61#34312yes—
237C22×C61C2×#9511yescharacteristic
238C22×C61C4×M1612yes—
239C2×D61—28no—
240C2×D61—28no—
241C2×D61—28no—
242C2×D61—21no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—24no—
249C2×D61—24no—
250C2×D61—24no—
251C2×D61—24no—
252C2×D61—24no—
253C2×D61—24no—
254C2×D61#34212yes—
255C2×D61#34312yes—
256C2×D61#40712yes—
257C2×D61C2×#9912yes—
258C2×D61C2×#10011yescharacteristic
259C2×D61C2×#10111yescharacteristic
260C2×D61#42312yes—
261#6923—48no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266Dic61—21no—
267Dic61—21no—
268Dic61—21no—
269Dic61—21no—
270C2×#407—611no—
271C2×#407—611no—
272C22×#95—611no—
273#1280—614no—
274C2×C61—22no—
275C2×C61—22no—
276C2×C61—22no—
277C2×C61#172811yescharacteristic
278C2×C61C2×#34211yescharacteristic
279C2×C61C2×#34311yescharacteristic
280D61—22no—
281D61—22no—
282D61—22no—
283D61#146212yes—
284D61#146312yes—
285C24×C4—611no—
286C24×C4—612no—
287C22×M16—1221no—
288C22×M16—1221no—
289#407—612no—
290#407—612no—
291#407—611no—
292#407—612no—
293#407—1221no—
294#407—1221no—
295#407—1221no—
296#407—1221no—
297#407#692311yescharacteristic, complemented
298C2×C22⋊C8—612no—
299C2×C22⋊C8—612no—
300C2×C22⋊C8—1221no—
301C2×C22⋊C8—1221no—
302C2×#95—612no—
303C2×#95—612no—
304C2×#95—1221no—
305C2×#95—1221no—
306C2×#95—1221no—
307C2×#95—1221no—
308C61#790911yescharacteristic, complemented, Sylow
309C25—611no—
310C23×C4—611no—
311C23×C4—611no—
312C23×C4—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—614no—
324C23×C4—1228no—
325C23×C4—1222no—
326C23×C4—1222no—
327C23×C4—2444no—
328C23×C4—2444no—
329C23×C4—2444no—
330C23×C4C2×#692311yescharacteristic
331C2×M16—21no—
332C2×M16—1222no—
333C2×M16—1222no—
334C2×M16—1222no—
335C2×M16—1221no—
336C2×M16—2444no—
337C2×M16—2444no—
338C22×C8—1222no—
339C22×C8—1222no—
340C22⋊C8—21no—
341C22⋊C8—614no—
342C22⋊C8—612no—
343C22⋊C8—1222no—
344C22⋊C8—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C22⋊C8—1222no—
348C22⋊C8—1221no—
349C22⋊C8C2×#692312yescomplemented
350#95—1222no—
351#95—1222no—
352#95—1222no—
353#95—1222no—
354C24—611no—
355C24—611no—
356C24—611no—
357C24—611no—
358C24—611no—
359C24—611no—
360C24—1224no—
361C24—1224no—
362C24—1222no—
363C24—1222no—
364C24C4×#692311yescharacteristic
365C22×C4—42no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
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—618no—
389C22×C4—1224no—
390C22×C4—1224no—
391C22×C4—1224no—
392C22×C4—1224no—
393C22×C4—1228no—
394C22×C4—1228no—
395C22×C4—2442no—
396C22×C4—2442no—
397C22×C4—2442no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2444no—
407C22×C4—2444no—
408C22×C4—2444no—
409C22×C4—2444no—
410C22×C4—24432no—
411C22×C4—2444no—
412C22×C4—2444no—
413C22×C4C4×#692311yescharacteristic
414C22×C4C4⋊#692311yescharacteristic
415C22×C4C4⋊#692311yescharacteristic
416C22×C4C22⋊#692311yescharacteristic
417C22×C4C22⋊#692311yescharacteristic
418C22×C4C22×#692311yescharacteristic
419M16—42no—
420M16—2444no—
421M16—2442no—
422M16—2444no—
423M16—2444no—
424C2×C8—22no—
425C2×C8—1224no—
426C2×C8—1222no—
427C2×C8—2444no—
428C2×C8—2444no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—611no—
433C23—614no—
434C23—614no—
435C23—612no—
436C23—612no—
437C23—611no—
438C23—611no—
439C23—611no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1221no—
445C23—1221no—
446C23—1222no—
447C23—1222no—
448C23—1221no—
449C23—1222no—
450C23—1221no—
451C23—1222no—
452C23—1222no—
453C23—1222no—
454C23—12216no—
455C23—12216no—
456C23—1222no—
457C23—1222no—
458C23—1222no—
459C23(C2×#6923)⋊C411yescharacteristic
460C23(C2×#6923)⋊C411yescharacteristic
461C23C2×C4×#692311yescharacteristic
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—611no—
469C2×C4—611no—
470C2×C4—611no—
471C2×C4—611no—
472C2×C4—1222no—
473C2×C4—1222no—
474C2×C4—1222no—
475C2×C4—1222no—
476C2×C4—1222no—
477C2×C4—1222no—
478C2×C4—1222no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1228no—
483C2×C4—2441no—
484C2×C4—2441no—
485C2×C4—2441no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4—2441no—
490C2×C4—2441no—
491C2×C4—2441no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2444no—
496C2×C4—2444no—
497C2×C4—2448no—
498C2×C4—24416no—
499C2×C4—24416no—
500C2×C4—2448no—
501C2×C4(C2×#6923)⋊C411yescharacteristic
502C2×C4(C2×#6923)⋊C411yescharacteristic
503C2×C4C2×C22⋊#692311yescharacteristic
504C2×C4C2×C4⋊#692311yescharacteristic
505C8—42no—
506C8—2442no—
507C8—2444no—
508C22—28no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—612no—
516C22—611no—
517C22—611no—
518C22—612no—
519C22—612no—
520C22—612no—
521C22—612no—
522C22—1224no—
523C22—1224no—
524C22—1224no—
525C22—1224no—
526C22—1224no—
527C22—1224no—
528C22—1228no—
529C22—1228no—
530C22—1228no—
531C22—1221no—
532C22—1221no—
533C22—1221no—
534C22—1221no—
535C22—1221no—
536C22—1221no—
537C22#1684063912yes—
538C22#1684064112yes—
539C22C2×(C2×#6923)⋊C411yescharacteristic
540C22M16×#692312yes—
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—1221no—
546C4—1221no—
547C4—1221no—
548C4—1221no—
549C4—2448no—
550C2—22no—
551C2—22no—
552C2—22no—
553C2—612no—
554C2—612no—
555C2—1222no—
556C2—1222no—
557C2—1222no—
558C2#2146148111yescharacteristic
559C2C2×#1684063911yescharacteristic
560C2C2×#1684064111yescharacteristic
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#7909
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. #21460656C2semidirect
9. #16840733C4semidirect
10. #16840732C4semidirect
21. #16839726C4semidirect
24. #16839724C4semidirect
27. C61×#407C4semidirect
41. C22⋊#92420C2×C4semidirect
66. C22⋊#92418C2×C4semidirect
72. C22⋊C8×C61C2×C4semidirect
95. C22×#6923M16semidirect
297. #407#6923semidirect
308. C61#7909semidirect
349. 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
C22×(C2×#6923)⋊C42
#214606562
#407×D612
#790961