Finite Group Databasebeta

← #30596650

Subgroups — #30596650

Order 15616.

986 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
1C2×D61⋊(C22⋊C8)C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460681C214yesmaximal, complemented
4#21448200C211yesmaximal, characteristic
5C22×D61⋊C8C412yescomplemented
6C2×#14519856—21no—
7C2×#14519834—21no—
8D61⋊(C22⋊C8)—21no—
9D61⋊(C22⋊C8)—21no—
10D61⋊(C22⋊C8)C412yescomplemented
11D61⋊(C22⋊C8)C2212yes—
12C2×C22⋊#92420—21no—
13#16840705C412yescomplemented
14#16840704—21no—
15#16840704C2212yes—
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519734—21no—
21#16839624C412yescomplemented
22#16839621C2212yes—
23#16839620—21no—
24#16839617—21no—
25C4×#11758198—21no—
26C4×C22⋊Dic61C411yescharacteristic, complemented
27C4×C22⋊C4×C61C411yescharacteristic, complemented
28C2×D61⋊C8—22no—
29C2×D61⋊C8—44no—
30C2×D61⋊C8C2×C414yes—
31C22×#92420—22no—
32#14519856—44no—
33C2×C4⋊#6923—22no—
34C2×C22⋊#6923—22no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38#14519834—22no—
39#14519834—22no—
40C22⋊#92420—22no—
41C22⋊#92420—22no—
42(C2×#6923)⋊C4—22no—
43(C2×#6923)⋊C4C2×C414yes—
44C24×D61D411yescharacteristic
45C23×Dic61D411yescharacteristic
46C22×C4×D61—44no—
47C22×C4×D61C2×C411yescharacteristic
48C22×C4×D61C2×C411yescharacteristic
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×D61Q811yescharacteristic
57C22×C4×D61Q811yescharacteristic
58C22×C4×D61C2311yescharacteristic
59#14519734—44no—
60C2×#11758196—22no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—21no—
65#14519684—22no—
66#14519684C2×C412yes—
67C23×C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C2×C42×C61—21no—
70#95×C61C2×C412yes—
71C24×C61C22⋊C411yescharacteristic
72C23×D61—24no—
73C23×D61—42no—
74C23×D61—42no—
75C23×D61C22⋊C411yescharacteristic
76C23×D61C22⋊C411yescharacteristic
77C23×D61C22⋊C411yescharacteristic
78C23×D61C4⋊C411yescharacteristic
79C23×D61C4⋊C411yescharacteristic
80C23×D61C2×D411yescharacteristic
81C22×#6923—24no—
82C22×C4×C61—22no—
83C22×C4×C61—42no—
84C22×C4×C61C4211yescharacteristic
85C22×C4×C61C4211yescharacteristic
86C22×C4×C61C22⋊C411yescharacteristic
87C22×C4×C61C4⋊C411yescharacteristic
88C22×C4×C61C4⋊C411yescharacteristic
89C22×C4×C61C22×C411yescharacteristic
90C22×Dic61—22no—
91C22×Dic61—42no—
92C22×Dic61C22⋊C411yescharacteristic
93C22×Dic61C22⋊C411yescharacteristic
94C22×Dic61C22⋊C411yescharacteristic
95C22×Dic61C4⋊C411yescharacteristic
96C22×Dic61C4⋊C411yescharacteristic
97C22×Dic61C2×D411yescharacteristic
98C2×C4×D61—24no—
99C2×C4×D61—24no—
100C2×C4×D61—24no—
101C2×C4×D61—42no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
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×D61C4211yescharacteristic
111C2×C4×D61C4211yescharacteristic
112C2×C4×D61C22⋊C411yescharacteristic
113C2×C4×D61C22⋊C411yescharacteristic
114C2×C4×D61C22⋊C411yescharacteristic
115C2×C4×D61C22⋊C411yescharacteristic
116C2×C4×D61C4⋊C411yescharacteristic
117C2×C4×D61C4⋊C411yescharacteristic
118C2×C4×D61C4⋊C411yescharacteristic
119C2×C4×D61C4⋊C411yescharacteristic
120C2×C4×D61C4⋊C411yescharacteristic
121C2×C4×D61C4⋊C411yescharacteristic
122C2×C4×D61C22×C411yescharacteristic
123C2×C4×D61C22×C411yescharacteristic
124C2×C4×D61C2×D411yescharacteristic
125C2×C4×D61C2×Q811yescharacteristic
126C22⋊#6923—44no—
127C22⋊#6923—44no—
128C22⋊#6923—44no—
129C2×#92420—24no—
130C2×#92420—44no—
131C4⋊#6923—44no—
132C4×#6923—44no—
133D61⋊C8—44no—
134D61⋊C8—44no—
135C22⋊C4×C61—42no—
136C42×C61—42no—
137C22⋊Dic61—42no—
138#11758198—44no—
139#11758198—44no—
140#11758196—44no—
141C4×Dic61—42no—
142C23×C61—22no—
143C23×C61—22no—
144C23×C61—41no—
145C23×C61#9511yescharacteristic
146C23×C61#9511yescharacteristic
147C23×C61C2×C22⋊C411yescharacteristic
148C22×D61—22no—
149C22×D61—22no—
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—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—416no—
166C22×D61#9511yescharacteristic
167C22×D61#9511yescharacteristic
168C22×D61C2×C22⋊C411yescharacteristic
169C22×D61C2×C4⋊C411yescharacteristic
170C22×D61#13514yes—
171C2×#6923—44no—
172C2×#6923—44no—
173C2×#6923—44no—
174C2×C4×C61—22no—
175C2×C4×C61—22no—
176C2×C4×C61—22no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61#9511yescharacteristic
184C2×C4×C61#9511yescharacteristic
185C2×C4×C61C2×C4211yescharacteristic
186C2×C4×C61C2×C4⋊C411yescharacteristic
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61#9511yescharacteristic
197C2×Dic61#9511yescharacteristic
198C2×Dic61C2×C22⋊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—
216#92420—44no—
217#7982—611nomaximal, Sylow
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—44no—
226C22×C61H(3,ℤ/4)12yes—
227C22×C61C2×#9511yescharacteristic
228C22×C61#41612yes—
229C2×D61—28no—
230C2×D61—21no—
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#34212yes—
245C2×D61#41612yes—
246C2×D61#42712yes—
247#6923—84no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—82no—
252C4×C61#34212yes—
253Dic61—21no—
254Dic61—21no—
255Dic61—21no—
256Dic61—82no—
257Dic61C2×#9912yes—
258C22×C22⋊C8—611no—
259#2280—611no—
260#2280—611no—
261#1289—614no—
262C2×C61—22no—
263C2×C61—22no—
264C2×C61—41no—
265C2×C61C2×H(3,ℤ/4)11yescharacteristic
266C2×C61#173511yescharacteristic
267C2×C61C2×#34211yescharacteristic
268D61—22no—
269D61—22no—
270D61—22no—
271D61—41no—
272C24×C4—611no—
273C23×C8—612no—
274C2×#117—1221no—
275C2×#117—1221no—
276C2×C22⋊C8—612no—
277C2×C22⋊C8—612no—
278C2×C22⋊C8—1221no—
279C2×C22⋊C8—1221no—
280C2×C22⋊C8—1221no—
281C2×C22⋊C8—1221no—
282#381—612no—
283#381—612no—
284#380—612no—
285#380—612no—
286#380—1221no—
287#380—1221no—
288#379—1221no—
289#379—1221no—
290C4×C22⋊C4—612no—
291C4×C22⋊C4—611no—
292C4×C22⋊C4—1221no—
293C4×C22⋊C4—1221no—
294C4×C22⋊C4#692311yescharacteristic, complemented
295C61#798211yescharacteristic, 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—2444no—
311C23×C4C2×#692311yescharacteristic
312C22×C8—614no—
313C22×C8—1222no—
314C22×C8—1222no—
315C22×C8—2444no—
316#117—2444no—
317#117—2444no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1222no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4—1222no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1222no—
326C2×C22⋊C4—1221no—
327C2×C42—21no—
328C2×C42—1222no—
329C2×C42—1221no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332C22⋊C8—1222no—
333C22⋊C8—1222no—
334#95—614no—
335#95—612no—
336#95—1222no—
337#95—1222no—
338#95C2×#692312yes—
339C24—611no—
340C24—611no—
341C24—611no—
342C24—611no—
343C24—611no—
344C24—611no—
345C24—1224no—
346C24—2442no—
347C24—2442no—
348C24C22⋊#692311yescharacteristic
349C22×C4—22no—
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—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×C4C4×#692311yescharacteristic
389C22×C4C4×#692311yescharacteristic
390C22×C4C4⋊#692311yescharacteristic
391C22×C4C4⋊#692311yescharacteristic
392C22×C4C22⋊#692311yescharacteristic
393C22×C4C22×#692311yescharacteristic
394C2×C8—1224no—
395C2×C8—2444no—
396C2×C8—2444no—
397C2×C8—2444no—
398C4⋊C4—2444no—
399C4⋊C4—2444no—
400C22⋊C4—42no—
401C22⋊C4—2444no—
402C22⋊C4—2444no—
403C22⋊C4—2442no—
404C22⋊C4—2444no—
405C22⋊C4—2444no—
406C22⋊C4—2444no—
407C42—42no—
408C42—2442no—
409C42—2444no—
410C23—22no—
411C23—22no—
412C23—41no—
413C23—611no—
414C23—611no—
415C23—611no—
416C23—614no—
417C23—611no—
418C23—1222no—
419C23—1222no—
420C23—1222no—
421C23—1222no—
422C23—1222no—
423C23—1222no—
424C23—1222no—
425C23—1222no—
426C23—1222no—
427C23—1222no—
428C23—2441no—
429C23—2441no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—24416no—
436C23(C2×#6923)⋊C411yescharacteristic
437C23(C2×#6923)⋊C411yescharacteristic
438C23C2×C22⋊#692311yescharacteristic
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—42no—
448C2×C4—611no—
449C2×C4—614no—
450C2×C4—611no—
451C2×C4—611no—
452C2×C4—611no—
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—1222no—
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—2442no—
475C2×C4—2442no—
476C2×C4—2444no—
477C2×C4—2444no—
478C2×C4—2444no—
479C2×C4—2442no—
480C2×C4(C2×#6923)⋊C411yescharacteristic
481C2×C4(C2×#6923)⋊C411yescharacteristic
482C2×C4C2×C4×#692311yescharacteristic
483C2×C4C2×C4⋊#692311yescharacteristic
484C8—2444no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—612no—
494C22—612no—
495C22—612no—
496C22—1228no—
497C22—1221no—
498C22—1221no—
499C22—1221no—
500C22—1221no—
501C22—1221no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—1221no—
506C22—2444no—
507C22—2444no—
508C22—2444no—
509C22—2444no—
510C22—2444no—
511C22#1684062912yes—
512C22C2×(C2×#6923)⋊C411yescharacteristic
513C22#1684075212yes—
514C4—21no—
515C4—21no—
516C4—21no—
517C4—82no—
518C4—612no—
519C4—1221no—
520C4—1221no—
521C4—1221no—
522C4—4882no—
523C4—4884no—
524C4#1684063912yes—
525C2—22no—
526C2—22no—
527C2—41no—
528C2—1222no—
529C2—1222no—
530C2—1222no—
531C2—2441no—
532C2C2×#1684062911yescharacteristic
533C2#2146150411yescharacteristic
534C2C2×#1684063911yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61#7982
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #21460681C2semidirect
5. C22×D61⋊C8C4semidirect
10. D61⋊(C22⋊C8)C4semidirect
13. #16840705C4semidirect
18. C4×C22⋊#6923C4semidirect
21. #16839624C4semidirect
26. C4×C22⋊Dic61C4semidirect
27. C4×C22⋊C4×C61C4semidirect
294. C4×C22⋊C4#6923semidirect
295. C61#7982semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊(C22⋊C8)2
#214622632
#214606812
#214482002
#798261