Finite Group Databasebeta

← #30597275

Subgroups — #30597275

Order 15616.

914 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840732C211yesmaximal, characteristic
2C2×#16840732C211yesmaximal, characteristic
3#21460720C214yesmaximal, complemented
4#21448197C211yesmaximal, characteristic
5C22×#11758217—21no—
6C22×#11758217C412yescomplemented
7#16840732—21no—
8#16840732—21no—
9#16840732—21no—
10#16840732—21no—
11#16840732C412yescomplemented
12#16840732C412yescomplemented
13#16840732C2212yes—
14#16840732C2212yes—
15C2×C22⋊#92420—21no—
16C2×C22⋊#92420—21no—
17C2×C22⋊#92420—21no—
18C2×C22⋊#92420C412yescomplemented
19C24×Dic61C2211yescharacteristic
20C2×#14519733—21no—
21#16839623—21no—
22#16839620—21no—
23#16839620C2212yes—
24#16839618C411yescharacteristic
25C22⋊C4×Dic61—21no—
26C22⋊C4×Dic61C412yes—
27C61×#379C411yescharacteristic
28C2×#11758217—22no—
29C2×#11758217—22no—
30C2×#11758217—22no—
31C2×#11758217—44no—
32C2×#11758217—44no—
33C2×#11758217C2×C414yes—
34C22×#92420—22no—
35C22×#92420—22no—
36C22⋊#92420—22no—
37C22⋊#92420—22no—
38C22⋊#92420—22no—
39C22⋊#92420—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42C22⋊#92420—22no—
43C22⋊#92420C2×C414yes—
44C23×Dic61—44no—
45C23×Dic61C2×C411yescharacteristic
46C23×Dic61C2×C411yescharacteristic
47C23×Dic61C2×C411yescharacteristic
48C23×Dic61C2×C411yescharacteristic
49C23×Dic61C2×C411yescharacteristic
50C23×Dic61D411yescharacteristic
51C23×Dic61D411yescharacteristic
52C23×Dic61D411yescharacteristic
53C23×Dic61D411yescharacteristic
54C23×Dic61D411yescharacteristic
55C23×Dic61D411yescharacteristic
56C23×Dic61Q811yescharacteristic
57C23×Dic61Q811yescharacteristic
58C23×Dic61C2311yescharacteristic
59#14519733—44no—
60C2×#11758196—22no—
61C2×C22⋊Dic61—21no—
62C2×C22⋊Dic61—21no—
63C2×C22⋊Dic61C2×C412yes—
64C2×C4×Dic61—22no—
65#14519684—22no—
66#14519684—22no—
67C25×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C22⋊C4×C61—21no—
70C2×C22⋊C4×C61C2×C412yes—
71C24×C61—42no—
72C24×C61—42no—
73C24×C61—42no—
74C24×C61C4211yescharacteristic
75C24×C61C4211yescharacteristic
76C24×C61C22⋊C411yescharacteristic
77C24×C61C22⋊C411yescharacteristic
78C24×C61C4⋊C411yescharacteristic
79C24×C61C4⋊C411yescharacteristic
80C24×C61C22×C411yescharacteristic
81C22×C4×C61—22no—
82C22×Dic61—24no—
83C22×Dic61—24no—
84C22×Dic61—24no—
85C22×Dic61—22no—
86C22×Dic61—42no—
87C22×Dic61—42no—
88C22×Dic61—42no—
89C22×Dic61—42no—
90C22×Dic61—42no—
91C22×Dic61—42no—
92C22×Dic61—42no—
93C22×Dic61—42no—
94C22×Dic61—42no—
95C22×Dic61—42no—
96C22×Dic61—42no—
97C22×Dic61C4211yescharacteristic
98C22×Dic61C4211yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C22⋊C411yescharacteristic
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C22×Dic61C22⋊C411yescharacteristic
106C22×Dic61C22⋊C411yescharacteristic
107C22×Dic61C22⋊C411yescharacteristic
108C22×Dic61C22⋊C411yescharacteristic
109C22×Dic61C4⋊C411yescharacteristic
110C22×Dic61C4⋊C411yescharacteristic
111C22×Dic61C4⋊C411yescharacteristic
112C22×Dic61C4⋊C411yescharacteristic
113C22×Dic61C4⋊C411yescharacteristic
114C22×Dic61C4⋊C411yescharacteristic
115C22×Dic61C4⋊C411yescharacteristic
116C22×Dic61C4⋊C411yescharacteristic
117C22×Dic61C4⋊C411yescharacteristic
118C22×Dic61C4⋊C411yescharacteristic
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C22×C411yescharacteristic
121C22×Dic61C2×D411yescharacteristic
122C22×Dic61C2×D411yescharacteristic
123C22×Dic61C2×D411yescharacteristic
124C22×Dic61C2×Q811yescharacteristic
125#11758217—44no—
126#11758217—44no—
127#11758217—44no—
128#11758217—44no—
129C2×#92420—24no—
130C2×#92420—24no—
131C2×#92420—44no—
132C2×#92420—44no—
133C22⋊C4×C61—42no—
134C22⋊C4×C61—42no—
135C22⋊C4×C61—42no—
136C22⋊Dic61—42no—
137C22⋊Dic61—42no—
138C22⋊Dic61—42no—
139#11758196—44no—
140C4×Dic61—44no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61—22no—
145C23×C61—22no—
146C23×C61—22no—
147C23×C61—22no—
148C23×C61—22no—
149C23×C61—22no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—41no—
155C23×C61—41no—
156C23×C61—41no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—41no—
162C23×C61—416no—
163C23×C61#9511yescharacteristic
164C23×C61#9511yescharacteristic
165C23×C61#9511yescharacteristic
166C23×C61#9511yescharacteristic
167C23×C61C2×C4211yescharacteristic
168C23×C61C2×C22⋊C411yescharacteristic
169C23×C61C2×C4⋊C411yescharacteristic
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×Dic61—22no—
174C2×Dic61—22no—
175C2×Dic61—22no—
176C2×Dic61—22no—
177C2×Dic61—22no—
178C2×Dic61—22no—
179C2×Dic61—22no—
180C2×Dic61—22no—
181C2×Dic61—22no—
182C2×Dic61—22no—
183C2×Dic61—22no—
184C2×Dic61—22no—
185C2×Dic61—22no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61#9511yescharacteristic
204C2×Dic61#9511yescharacteristic
205C2×Dic61#9511yescharacteristic
206C2×Dic61#9511yescharacteristic
207C2×Dic61#9914yes—
208C2×Dic61C2×C22⋊C411yescharacteristic
209C2×Dic61C2×C22⋊C411yescharacteristic
210C2×Dic61C2×C4⋊C411yescharacteristic
211C2×Dic61C2×C4⋊C411yescharacteristic
212#92420—44no—
213#92420—44no—
214#8108—611nomaximal, Sylow
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
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—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—44no—
234C22×C61—44no—
235C22×C61—44no—
236C22×C61—44no—
237C22×C61—44no—
238C22×C61—44no—
239C22×C61—44no—
240C22×C61#34212yes—
241C22×C61#34412yes—
242C22×C61C2×#9511yescharacteristic
243C22×C61#41312yes—
244C4×C61—82no—
245Dic61—21no—
246Dic61—21no—
247Dic61—21no—
248Dic61—21no—
249Dic61—21no—
250Dic61—21no—
251Dic61—82no—
252Dic61#34212yes—
253Dic61C2×#9912yes—
254C2×#407—611no—
255C2×#407—611no—
256#2280—611no—
257#1305—614no—
258C2×C61—22no—
259C2×C61—22no—
260C2×C61—22no—
261C2×C61—41no—
262C2×C61—41no—
263C2×C61—41no—
264C2×C61—41no—
265C2×C61C2×#34211yescharacteristic
266C2×C61#174211yescharacteristic
267C2×C61C2×#34411yescharacteristic
268C24×C4—611no—
269C22×M16—612no—
270C22×M16—1221no—
271C2×#117—1221no—
272#407—612no—
273#407—612no—
274#407—612no—
275#407—612no—
276#407—1221no—
277#407—1221no—
278#407—1221no—
279#407—1221no—
280C2×C22⋊C8—612no—
281C2×C22⋊C8—1221no—
282C2×C22⋊C8—1221no—
283C2×C22⋊C8—1221no—
284#381—1221no—
285#380—612no—
286#380—1221no—
287#379—611no—
288#379#692311yescharacteristic
289C4×C22⋊C4—612no—
290C4×C22⋊C4—1221no—
291C61#810811yescharacteristic, complemented, Sylow
292C25C2×#692311yescharacteristic
293C23×C4—611no—
294C23×C4—611no—
295C23×C4—611no—
296C23×C4—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—2444no—
308C2×M16—614no—
309C2×M16—1222no—
310C2×M16—1222no—
311C2×M16—1222no—
312C2×M16—2444no—
313C2×M16—2444no—
314C22×C8—1222no—
315C22×C8—1222no—
316#117—2444no—
317C2×C4⋊C4—1222no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—612no—
321C2×C22⋊C4—1221no—
322C2×C22⋊C4—1221no—
323C2×C22⋊C4C2×#692312yes—
324C2×C42—1222no—
325C22⋊C8—614no—
326C22⋊C8—1222no—
327C22⋊C8—1222no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332C22⋊C8—1222no—
333#95—1222no—
334#95—1222no—
335C24—42no—
336C24—42no—
337C24—42no—
338C24C4×#692311yescharacteristic
339C24C4×#692311yescharacteristic
340C24C4⋊#692311yescharacteristic
341C24C4⋊#692311yescharacteristic
342C24C22⋊#692311yescharacteristic
343C24C22⋊#692311yescharacteristic
344C24C22×#692311yescharacteristic
345C22×C4—22no—
346C22×C4—611no—
347C22×C4—611no—
348C22×C4—611no—
349C22×C4—611no—
350C22×C4—611no—
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—611no—
374C22×C4—1224no—
375C22×C4—1224no—
376C22×C4—1224no—
377C22×C4—1222no—
378C22×C4—2442no—
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—
389M16—2444no—
390M16—2444no—
391M16—2444no—
392M16—2444no—
393C2×C8—1224no—
394C2×C8—1224no—
395C2×C8—2444no—
396C2×C8—2444no—
397C4⋊C4—2444no—
398C22⋊C4—42no—
399C22⋊C4—42no—
400C22⋊C4—42no—
401C22⋊C4—2442no—
402C22⋊C4—2442no—
403C22⋊C4—2442no—
404C42—2444no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23—22no—
409C23—22no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—22no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—416no—
427C23(C2×#6923)⋊C411yescharacteristic
428C23(C2×#6923)⋊C411yescharacteristic
429C23(C2×#6923)⋊C411yescharacteristic
430C23(C2×#6923)⋊C411yescharacteristic
431C23C2×C4×#692311yescharacteristic
432C23C2×C22⋊#692311yescharacteristic
433C23C2×C4⋊#692311yescharacteristic
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—614no—
438C2×C4—611no—
439C2×C4—611no—
440C2×C4—611no—
441C2×C4—611no—
442C2×C4—611no—
443C2×C4—611no—
444C2×C4—611no—
445C2×C4—611no—
446C2×C4—1222no—
447C2×C4—1222no—
448C2×C4—1222no—
449C2×C4—1222no—
450C2×C4—1222no—
451C2×C4—1222no—
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—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
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—2442no—
474C2×C4—2442no—
475C2×C4—2442no—
476C8—2444no—
477C8—2444no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—44no—
497C22—44no—
498C22—44no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—44no—
503C22#1684063912yes—
504C22#1684064312yes—
505C22C2×(C2×#6923)⋊C411yescharacteristic
506C22#1684074912yes—
507C4—82no—
508C4—612no—
509C4—612no—
510C4—1221no—
511C4—1221no—
512C4—1221no—
513C4—1221no—
514C4—1221no—
515C4—1221no—
516C4—4882no—
517C2—22no—
518C2—22no—
519C2—22no—
520C2—41no—
521C2—41no—
522C2—41no—
523C2—41no—
524C2C2×#1684063911yescharacteristic
525C2#2146152511yescharacteristic
526C2C2×#1684064311yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC23×C61C2×C42
FrattiniC24C22×#6923
FittingC61×#379C4
socleC22×C61C2×#95
prime radicalC25×C61C2×C4
cosocleC23×Dic61C23
hypercenter#379#6923
hypocenterC61#8108
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #379

Complements

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

NH ≅ G/Ntype
3. #21460720C2semidirect
6. C22×#11758217C4semidirect
11. #16840732C4semidirect
12. #16840732C4semidirect
18. C2×C22⋊#92420C4semidirect
291. C61#8108semidirect

Maximal subgroups

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

subgroupindex
C2×#168407322
#214607202
#214481972
#810861