Finite Group Databasebeta

← #30596951

Subgroups — #30596951

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462263C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460699C214yesmaximal, complemented
4#407×D61C211yesmaximal, characteristic
5C2×#14519856—21no—
6C22×C22⋊#6923—21no—
7C22×C4×#6923—21no—
8#16840705C412yescomplemented
9#16840704—21no—
10#16840704C412yescomplemented
11#16840703—21no—
12C4×C22⋊#6923—21no—
13C4×C22⋊#6923—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923C412yescomplemented
16C4×C22⋊#6923C2212yes—
17C4×C22⋊#6923C2212yes—
18C2×(C2×#6923)⋊C4C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×M16×D61C412yescomplemented
21#16839726C411yescharacteristic, complemented
22#16839725C2212yes—
23#16839724—21no—
24#16839724—21no—
25C22⋊C8×D61—21no—
26C22⋊C8×D61—21no—
27C61×#407C411yescharacteristic, complemented
28C23×#6923—22no—
29#14519856—44no—
30C2×C4⋊#6923—22no—
31C2×C22⋊#6923—28no—
32C2×C22⋊#6923—22no—
33C2×C22⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38C2×C4×#6923—22no—
39C2×C4×#6923—22no—
40C2×C4×#6923—44no—
41(C2×#6923)⋊C4—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yes—
44(C2×#6923)⋊C4C2×C414yescomplemented
45C24×D61D411yescharacteristic
46C23×Dic61Q811yescharacteristic
47C22×C4×D61—44no—
48C22×C4×D61C2×C411yescharacteristic
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61D411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61C2311yescharacteristic
60C2×#11758194C2×C412yescomplemented
61C2×#11758189—22no—
62M16×D61—44no—
63C2×C8×D61—22no—
64C22⋊#92418—21no—
65C22⋊#92418—21no—
66#14519689—22no—
67#14519689—22no—
68C23×C4×C61C2×C411yescharacteristic
69C2×M16×C61C2×C412yescomplemented
70C22⋊C8×C61—21no—
71C22⋊C8×C61—21no—
72C24×C61C4⋊C411yescharacteristic
73C23×D61—24no—
74C23×D61—42no—
75C23×D61—42no—
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C4⋊C411yescharacteristic
81C23×D61C2×D411yescharacteristic
82C22×#6923—28no—
83C22×#6923—24no—
84C22×#6923—24no—
85C22×#6923—44no—
86C22×#6923—44no—
87C22×C4×C61—42no—
88C22×C4×C61C4211yescharacteristic
89C22×C4×C61C4211yescharacteristic
90C22×C4×C61C22⋊C411yescharacteristic
91C22×C4×C61C22⋊C411yescharacteristic
92C22×C4×C61C4⋊C411yescharacteristic
93C22×C4×C61C22×C411yescharacteristic
94C22×Dic61—42no—
95C22×Dic61C4⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C4⋊C411yescharacteristic
98C22×Dic61C4⋊C411yescharacteristic
99C22×Dic61C4⋊C411yescharacteristic
100C22×Dic61C2×Q811yescharacteristic
101C2×C4×D61—24no—
102C2×C4×D61—24no—
103C2×C4×D61—24no—
104C2×C4×D61—42no—
105C2×C4×D61—42no—
106C2×C4×D61—42no—
107C2×C4×D61—42no—
108C2×C4×D61—42no—
109C2×C4×D61—42no—
110C2×C4×D61—42no—
111C2×C4×D61—42no—
112C2×C4×D61—42no—
113C2×C4×D61C4211yescharacteristic
114C2×C4×D61C4211yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C22⋊C411yescharacteristic
117C2×C4×D61C22⋊C411yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C22×C411yescharacteristic
126C2×C4×D61C22×C411yescharacteristic
127C2×C4×D61C2×D411yescharacteristic
128C2×C4×D61C2×D411yescharacteristic
129C22⋊#6923—28no—
130C22⋊#6923—28no—
131C22⋊#6923—44no—
132C22⋊#6923—44no—
133C22⋊#6923—44no—
134C4⋊#6923—44no—
135C4×#6923—44no—
136C4×#6923—44no—
137C4×#6923—44no—
138M16×C61—42no—
139C2×C8×C61—22no—
140#11758194—42no—
141C2×#92418—22no—
142#11758189—44no—
143C8×D61—44no—
144C23×C61—22no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61#9511yescharacteristic
148C23×C61#9511yescharacteristic
149C23×C61C2×C4⋊C411yescharacteristic
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—416no—
168C22×D61#9511yescharacteristic
169C22×D61#9511yescharacteristic
170C22×D61#10414yes—
171C22×D61C2×C22⋊C411yescharacteristic
172C22×D61C2×C22⋊C411yescharacteristic
173C2×#6923—28no—
174C2×#6923—44no—
175C2×#6923—416no—
176C2×#6923—44no—
177C2×#6923—44no—
178C2×#6923—44no—
179C2×#6923—44no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61#9511yescharacteristic
187C2×C4×C61#9511yescharacteristic
188C2×C4×C61C2×C4211yescharacteristic
189C2×C4×C61C2×C22⋊C411yescharacteristic
190C2×Dic61—22no—
191C2×Dic61—22no—
192C2×Dic61—22no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61#9511yescharacteristic
197C2×Dic61#9511yescharacteristic
198C2×Dic61C2×C4⋊C411yescharacteristic
199C2×Dic61C2×C4⋊C411yescharacteristic
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—22no—
208C4×D61—22no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215C4×D61#9914yes—
216C8×C61—42no—
217#92418—42no—
218#8051—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—44no—
228C22×C61#33912yes—
229C22×C61C2×#9511yescharacteristic
230C2×D61—28no—
231C2×D61—21no—
232C2×D61—21no—
233C2×D61—21no—
234C2×D61—21no—
235C2×D61—21no—
236C2×D61—21no—
237C2×D61—21no—
238C2×D61—21no—
239C2×D61—44no—
240C2×D61—44no—
241C2×D61—44no—
242C2×D61—44no—
243C2×D61—44no—
244C2×D61#33912yes—
245C2×D61#34212yes—
246C2×D61C2×#10412yes—
247C2×D61#42112yes—
248#6923—48no—
249#6923—84no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61C2×#9912yes—
254Dic61—21no—
255Dic61—21no—
256Dic61—21no—
257Dic61#34212yes—
258C2×#407—611no—
259#2280—611no—
260C2×C4×C22⋊C4—611no—
261#1297—614no—
262C2×C61—22no—
263C2×C61—41no—
264C2×C61—41no—
265C2×C61C2×#33911yescharacteristic
266C2×C61#173311yescharacteristic
267C2×C61C2×#34211yescharacteristic
268D61—22no—
269D61—22no—
270D61—22no—
271D61—22no—
272C24×C4—611no—
273C22×M16—612no—
274C2×#117—1221no—
275C22×C22⋊C4—1221no—
276C22×C42—1221no—
277#407—611no—
278#407—612no—
279#407—1221no—
280#407—1221no—
281#407#692311yescharacteristic, complemented
282C2×C22⋊C8—1221no—
283C2×C22⋊C8—1221no—
284#381—612no—
285#380—612no—
286#380—1221no—
287#379—1221no—
288C4×C22⋊C4—612no—
289C4×C22⋊C4—612no—
290C4×C22⋊C4—612no—
291C4×C22⋊C4—1221no—
292C4×C22⋊C4—1221no—
293C4×C22⋊C4—1221no—
294C2×#95—612no—
295C61#805111yescharacteristic, complemented, Sylow
296C25—611no—
297C23×C4—611no—
298C23×C4—611no—
299C23×C4—611no—
300C23×C4—611no—
301C23×C4—611no—
302C23×C4—611no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—611no—
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C23×C4—611no—
310C23×C4—1222no—
311C23×C4—2444no—
312C23×C4C2×#692311yescharacteristic
313C2×M16—612no—
314C2×M16—1222no—
315C2×M16—2444no—
316C2×M16C2×#692312yescomplemented
317C22×C8—1222no—
318#117—2444no—
319C2×C4⋊C4—1222no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1228no—
323C2×C22⋊C4—1222no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1222no—
326C2×C42—1222no—
327C2×C42—1222no—
328C2×C42—1222no—
329C2×C42—2444no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—1222no—
333C22⋊C8—1222no—
334C22⋊C8—1221no—
335C22⋊C8—1221no—
336#95—614no—
337#95—614no—
338#95—1222no—
339#95—1222no—
340C24—611no—
341C24—611no—
342C24—611no—
343C24—611no—
344C24—611no—
345C24—611no—
346C24—1224no—
347C24—2442no—
348C24—2442no—
349C24C4⋊#692311yescharacteristic
350C22×C4—42no—
351C22×C4—611no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—611no—
356C22×C4—611no—
357C22×C4—611no—
358C22×C4—611no—
359C22×C4—611no—
360C22×C4—611no—
361C22×C4—611no—
362C22×C4—611no—
363C22×C4—611no—
364C22×C4—611no—
365C22×C4—611no—
366C22×C4—611no—
367C22×C4—611no—
368C22×C4—611no—
369C22×C4—611no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—1224no—
374C22×C4—1224no—
375C22×C4—1224no—
376C22×C4—1224no—
377C22×C4—1228no—
378C22×C4—1224no—
379C22×C4—2442no—
380C22×C4—2442no—
381C22×C4—2442no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4—2442no—
386C22×C4—2442no—
387C22×C4—2442no—
388C22×C4—2442no—
389C22×C4—2444no—
390C22×C4—2444no—
391C22×C4C4×#692311yescharacteristic
392C22×C4C4×#692311yescharacteristic
393C22×C4C4⋊#692311yescharacteristic
394C22×C4C22⋊#692311yescharacteristic
395C22×C4C22⋊#692311yescharacteristic
396C22×C4C22×#692311yescharacteristic
397M16—42no—
398M16—2444no—
399M16—2442no—
400C2×C8—22no—
401C2×C8—1222no—
402C2×C8—2444no—
403C4⋊C4—2444no—
404C22⋊C4—1228no—
405C22⋊C4—1228no—
406C22⋊C4—2444no—
407C22⋊C4—2444no—
408C22⋊C4—2444no—
409C42—2444no—
410C42—2444no—
411C42—2444no—
412C23—22no—
413C23—41no—
414C23—41no—
415C23—611no—
416C23—611no—
417C23—611no—
418C23—611no—
419C23—614no—
420C23—1222no—
421C23—1222no—
422C23—1222no—
423C23—1222no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—1222no—
429C23—1222no—
430C23—1222no—
431C23—2441no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—24416no—
438C23(C2×#6923)⋊C411yescharacteristic
439C23(C2×#6923)⋊C411yescharacteristic
440C23C2×C4⋊#692311yescharacteristic
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—611no—
448C2×C4—614no—
449C2×C4—611no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—1222no—
453C2×C4—1222no—
454C2×C4—1222no—
455C2×C4—1222no—
456C2×C4—1222no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1222no—
464C2×C4—1228no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2441no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2444no—
475C2×C4—2444no—
476C2×C4—2444no—
477C2×C4—2444no—
478C2×C4—2444no—
479C2×C4—24416no—
480C2×C4(C2×#6923)⋊C411yescharacteristic
481C2×C4(C2×#6923)⋊C411yescharacteristic
482C2×C4C2×C4×#692311yescharacteristic
483C2×C4C2×C22⋊#692311yescharacteristic
484C8—42no—
485C8—2442no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—44no—
495C22—612no—
496C22—612no—
497C22—612no—
498C22—612no—
499C22—1228no—
500C22—1221no—
501C22—1221no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—1221no—
507C22—1221no—
508C22—2444no—
509C22—2444no—
510C22—2444no—
511C22—2444no—
512C22—2444no—
513C22#1684063412yes—
514C22C2×(C2×#6923)⋊C411yescharacteristic
515C4—21no—
516C4—21no—
517C4—21no—
518C4—612no—
519C4—1221no—
520C4—1221no—
521C4—1221no—
522C4—4884no—
523C4—2448no—
524C4D61⋊#9912yes—
525C2—22no—
526C2—41no—
527C2—41no—
528C2—1222no—
529C2—1222no—
530C2—1222no—
531C2—1222no—
532C2C2×#1684063411yescharacteristic
533C2#2146150111yescharacteristic
534C2#2146151611yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#407#6923
hypocenterC61#8051
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
3. #21460699C2semidirect
8. #16840705C4semidirect
10. #16840704C4semidirect
15. C4×C22⋊#6923C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
20. C2×M16×D61C4semidirect
21. #16839726C4semidirect
27. C61×#407C4semidirect
44. (C2×#6923)⋊C4C2×C4semidirect
60. C2×#11758194C2×C4semidirect
69. C2×M16×C61C2×C4semidirect
281. #407#6923semidirect
295. C61#8051semidirect
316. C2×M16C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214622632
C2×C4×C22⋊#69232
#214606992
#407×D612
#805161