Finite Group Databasebeta

← #30598872

Subgroups — #30598872

Order 15616.

742 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461674C211yesmaximal, characteristic, complemented
2C2×#16840614C212yesmaximal
3#21460997C211yesmaximal, characteristic, complemented
4#21460692C212yesmaximal, complemented
5C4×#14519752C211yesmaximal, characteristic
6C22×C4⋊#6923—21no—
7C2×C4⋊#92420—21no—
8C2×#14519834C2212yes—
9C2×(C2×#6923)⋊C4—21no—
10C2×(C2×#6923)⋊C4C2212yes—
11#16840628—21no—
12#16840614—24no—
13C2×#14519752C2211yescharacteristic
14C2×C4×D244—21no—
15C2×C4×D244C411yescharacteristic, complemented
16C2×C42×D61C2211yescharacteristic
17#16839663C411yescharacteristic, complemented
18#16839661C411yescharacteristic, complemented
19#16839654—21no—
20#16839640—21no—
21#16839619C2211yescharacteristic
22C4×#11758198—21no—
23C4×C4⋊C4×C61C411yescharacteristic, complemented
24C23×#6923—22no—
25C22×#92420—22no—
26C2×C4⋊#6923—24no—
27C2×C4⋊#6923—42no—
28C2×C4⋊#6923—42no—
29C4⋊#92420—42no—
30#14519834—22no—
31#14519834—22no—
32(C2×#6923)⋊C4—22no—
33(C2×#6923)⋊C4—22no—
34(C2×#6923)⋊C4—42no—
35C22×D244—21no—
36C22×D244C2×C411yescharacteristic
37C22×C4×D61—21no—
38C22×C4×D61D411yescharacteristic
39C22×C4×D61D411yescharacteristic
40C22×C4×D61C2311yescharacteristic
41#14519752—21no—
42#14519752—21no—
43#14519752D412yes—
44#14519752Q812yes—
45C4×D244—42no—
46C4×D244—42no—
47C4×D244—42no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61C2×C411yescharacteristic
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×C4×Dic61C2×C411yescharacteristic
56C2×C4×Dic61D411yescharacteristic
57C2×C4×Dic61D411yescharacteristic
58C42×D61—42no—
59#14519684—21no—
60#14519684—21no—
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C42×C61—21no—
64C2×C42×C61C2×C411yescharacteristic
65#95×C61—21no—
66C23×D61—21no—
67C23×D61C2×D411yescharacteristic
68C22×#6923—24no—
69C22×#6923—42no—
70C22×#6923—42no—
71C22×#6923—42no—
72C22×#6923—42no—
73C22×#6923—42no—
74C22×#6923—42no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61C22⋊C411yescharacteristic
78C22×C4×C61C22⋊C411yescharacteristic
79C22×C4×C61C22×C411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61C22⋊C411yescharacteristic
82C22×Dic61C22⋊C411yescharacteristic
83C22×Dic61C2×D411yescharacteristic
84C2×D244—22no—
85C2×D244—22no—
86C2×D244—21no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90C2×D244—41no—
91C2×D244—41no—
92C2×D244—41no—
93C2×D244C4⋊C412yescomplemented
94C2×C4×D61—22no—
95C2×C4×D61—22no—
96C2×C4×D61—21no—
97C2×C4×D61—21no—
98C2×C4×D61—41no—
99C2×C4×D61—41no—
100C2×C4×D61—41no—
101C2×C4×D61—41no—
102C2×C4×D61—42no—
103C2×C4×D61—42no—
104C2×C4×D61—42no—
105C2×C4×D61D812yes—
106C2×C4×D61SD1612yes—
107C2×C4×D61C2×D411yescharacteristic
108C2×C4×D61C2×Q811yescharacteristic
109C2×C4×D61#4111yescharacteristic
110C2×C4×D61#4111yescharacteristic
111C2×#92420—42no—
112C2×#92420—42no—
113C2×#92420—42no—
114C4⋊#6923—48no—
115C4⋊C4×C61—21no—
116C4⋊C4×C61—41no—
117C4⋊C4×C61C4⋊C412yescomplemented
118C42×C61—22no—
119C42×C61—42no—
120#11758198—22no—
121#11758198—22no—
122#11758198—42no—
123#11758198—42no—
124#11758198—41no—
125#11758198—41no—
126#11758198—42no—
127C4⋊Dic61—42no—
128C4⋊Dic61—41no—
129C4×Dic61—22no—
130C4×Dic61—41no—
131C4×Dic61—41no—
132C23×C61C2×C22⋊C411yescharacteristic
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—22no—
138C22×D61—41no—
139C22×D61—41no—
140C22×D61—41no—
141C22×D61—41no—
142C22×D61—41no—
143C22×D61—41no—
144C22×D61#12111yescharacteristic
145C22×D61C22⋊Q811yescharacteristic
146C22×D61C2×D811yescharacteristic
147C22×D61C2×SD1611yescharacteristic
148C22×D61AGL(1,ℤ/8)11yescharacteristic
149C22×D61#13711yescharacteristic
150C2×#6923—44no—
151C2×#6923—44no—
152C2×#6923—44no—
153C2×#6923—82no—
154C2×#6923—82no—
155C2×#6923—82no—
156C2×#6923—82no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61#9912yes—
169C2×C4×C61#10212yes—
170C2×C4×C61#10412yes—
171C2×C4×C61C2×C4⋊C411yescharacteristic
172C2×C4×C61#11711yescharacteristic
173C2×Dic61—21no—
174C2×Dic61—21no—
175C2×Dic61—21no—
176C2×Dic61—21no—
177C2×Dic61—21no—
178C2×Dic61—21no—
179C2×Dic61—21no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61#10212yes—
184C2×Dic61#12111yescharacteristic
185C2×Dic61C22⋊Q811yescharacteristic
186D244—42no—
187D244—42no—
188D244—42no—
189D244—42no—
190D244—42no—
191D244—42no—
192C4×D61—24no—
193C4×D61—24no—
194C4×D61—41no—
195C4×D61—41no—
196C4×D61—41no—
197C4×D61—41no—
198C4×D61—42no—
199C4×D61—42no—
200C4×D61—84no—
201#92420—82no—
202#8571—611nomaximal, Sylow
203C22×C61#38011yescharacteristic
204C22×C61C2×#9911yescharacteristic
205C22×C61#41011yescharacteristic
206C22×C61C2×#10211yescharacteristic
207C22×C61#41711yescharacteristic
208C22×C61C2×#10411yescharacteristic
209C22×C61#42111yescharacteristic
210C2×D61—21no—
211C2×D61—21no—
212C2×D61—21no—
213C2×D61—21no—
214C2×D61—21no—
215C2×D61—21no—
216C2×D61—21no—
217C2×D61—21no—
218C2×D61—21no—
219C2×D61—21no—
220C2×D61—21no—
221C2×D61—21no—
222C2×D61—42no—
223C2×D61—42no—
224C2×D61—42no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61#45911yescharacteristic
230C2×D61#46111yescharacteristic
231C2×D61#47411yescharacteristic
232C2×D61#47611yescharacteristic
233#6923—84no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—42no—
237C4×C61—41no—
238C4×C61—81no—
239C4×C61#32714yescomplemented
240Dic61—21no—
241Dic61—21no—
242Dic61—22no—
243Dic61—41no—
244Dic61—81no—
245C4×#121—611no—
246#1797—611no—
247C2×#327—612no—
248C4⋊#95—611no—
249#1294—612no—
250C2×C61C2×#32711yescharacteristic
251C2×C61#150911yescharacteristic
252C2×C61#151311yescharacteristic
253C2×C61#151711yescharacteristic
254C2×C61#179911yescharacteristic
255C2×C61#180211yescharacteristic
256C2×C61#180611yescharacteristic
257D61—21no—
258D61—21no—
259D61—21no—
260D61—21no—
261D61—82no—
262C2×#121—611no—
263C2×C4×D4—611no—
264C2×C4×D4—1221no—
265C22×C4⋊C4—1221no—
266C22×C42—611no—
267C2×C4⋊C8—1221no—
268C2×C22⋊C8—612no—
269#390—611no—
270#389—611no—
271#388—1221no—
272#386—1221no—
273#380—611no—
274C4×C4⋊C4#692311yescharacteristic, complemented
275C4×C22⋊C4—1221no—
276C2×#95—612no—
277C2×#95—1221no—
278#336—1221no—
279#327—1224no—
280C61#857111yescharacteristic, complemented, Sylow
281C22×D4—611no—
282C22×D4—1221no—
283C23×C4—611no—
284C23×C4—611no—
285C23×C4—611no—
286C23×C4—1222no—
287C23×C4—1221no—
288C22×C8—1222no—
289#121—612no—
290#121—612no—
291#121—1221no—
292#121—1221no—
293C4×D4—2442no—
294C4×D4—2442no—
295C4×D4—2442no—
296C2×C4⋊C4—611no—
297C2×C4⋊C4—1221no—
298C2×C4⋊C4—1224no—
299C2×C4⋊C4—2442no—
300C2×C4⋊C4—2442no—
301C2×C4⋊C4C2×#692311yescharacteristic
302C2×C4⋊C4C2×#692311yescharacteristic
303C2×C22⋊C4—1221no—
304C2×C22⋊C4—1221no—
305C2×C22⋊C4—1221no—
306C2×C22⋊C4—1221no—
307C2×C22⋊C4—1221no—
308C2×C42—21no—
309C2×C42—611no—
310C2×C42—611no—
311C2×C42—611no—
312C2×C42—2442no—
313C2×C42C2×#692311yescharacteristic
314C4⋊C8—2442no—
315C22⋊C8—1222no—
316C22⋊C8—1222no—
317#95—21no—
318#95—1221no—
319#95—1221no—
320#95—1222no—
321#95—1222no—
322#95—2442no—
323C24—611no—
324C24—1221no—
325C2×D4—612no—
326C2×D4—1222no—
327C2×D4—1222no—
328C2×D4—1221no—
329C2×D4—2441no—
330C2×D4—2441no—
331C2×D4—2441no—
332C2×D4—2441no—
333C2×D4—2441no—
334C2×D4—2441no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—612no—
340C22×C4—612no—
341C22×C4—611no—
342C22×C4—611no—
343C22×C4—611no—
344C22×C4—611no—
345C22×C4—611no—
346C22×C4—1221no—
347C22×C4—1221no—
348C22×C4—1222no—
349C22×C4—1222no—
350C22×C4—1224no—
351C22×C4—1221no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355C22×C4—2441no—
356C22×C4—2442no—
357C22×C4—2442no—
358C22×C4—2442no—
359C22×C4—2442no—
360C22×C4—2442no—
361C22×C4—2442no—
362C22×C4—2442no—
363C22×C4—2442no—
364C22×C4—2442no—
365C22×C4C22⋊#692311yescharacteristic
366C22×C4C22⋊#692311yescharacteristic
367C22×C4C22×#692311yescharacteristic
368C2×C8—2442no—
369C2×C8—2442no—
370C2×C8—2442no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—2441no—
374C4⋊C4—2442no—
375C4⋊C4—2448no—
376C4⋊C4C4⋊#692312yescomplemented
377C22⋊C4—1222no—
378C22⋊C4—1222no—
379C22⋊C4—2442no—
380C22⋊C4—2442no—
381C22⋊C4—2442no—
382C22⋊C4—2441no—
383C22⋊C4—2441no—
384C42—22no—
385C42—42no—
386C42—1222no—
387C42—2441no—
388C42—2441no—
389C23—611no—
390C23—611no—
391C23—611no—
392C23—611no—
393C23—611no—
394C23—611no—
395C23—1221no—
396C23—1221no—
397C23—1221no—
398C23—1221no—
399C23—1222no—
400C23—2441no—
401C23—2441no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23C2×C22⋊#692311yescharacteristic
407D4—2442no—
408D4—2442no—
409D4—2442no—
410D4—2442no—
411D4—2442no—
412D4—2442no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—22no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—611no—
425C2×C4—611no—
426C2×C4—612no—
427C2×C4—1221no—
428C2×C4—1221no—
429C2×C4—1221no—
430C2×C4—1221no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1221no—
434C2×C4—1221no—
435C2×C4—1221no—
436C2×C4—4882no—
437C2×C4—4882no—
438C2×C4—4882no—
439C2×C4—4882no—
440C2×C4—4884no—
441C2×C4—2441no—
442C2×C4—2441no—
443C2×C4—2441no—
444C2×C4—2441no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2444no—
448C2×C4—2444no—
449C2×C4—2444no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4#1451983612yes—
454C2×C4#1451983912yes—
455C2×C4#1451984212yes—
456C2×C4C2×C4⋊#692311yescharacteristic
457C2×C4#1451985611yescharacteristic
458C8—4882no—
459C22—611no—
460C22—611no—
461C22—611no—
462C22—611no—
463C22—1221no—
464C22—1221no—
465C22—1221no—
466C22—1221no—
467C22—1221no—
468C22—1221no—
469C22—1221no—
470C22—1221no—
471C22—1221no—
472C22—1221no—
473C22—1221no—
474C22—1221no—
475C22—4881no—
476C22—4881no—
477C22—4881no—
478C22—4881no—
479C22—2442no—
480C22—2442no—
481C22—2442no—
482C22#1684070411yescharacteristic
483C22C2×#1451983611yescharacteristic
484C22#1684074111yescharacteristic
485C22C2×#1451983911yescharacteristic
486C22#1684075311yescharacteristic
487C22C2×#1451984211yescharacteristic
488C22#1684075911yescharacteristic
489C4—21no—
490C4—21no—
491C4—42no—
492C4—41no—
493C4—81no—
494C4—1221no—
495C4—1221no—
496C4—1222no—
497C4—4884no—
498C4—4881no—
499C4—2441no—
500C4#1684061414yescomplemented
501C2—1221no—
502C2—1221no—
503C2—1221no—
504C2—1221no—
505C2—4882no—
506C2C2×#1684061411yescharacteristic
507C2#2146122311yescharacteristic
508C2#2146123611yescharacteristic
509C2#2146124911yescharacteristic
510C2#2146168011yescharacteristic
511C2#2146168711yescharacteristic
512C2#2146169211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519752C22
cosocleC22×C4×D61C23
hypercenterC4×C4⋊C4#6923
hypocenterC61#8571
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #21461674C2semidirect
3. #21460997C2semidirect
4. #21460692C2semidirect
15. C2×C4×D244C4semidirect
17. #16839663C4semidirect
18. #16839661C4semidirect
23. C4×C4⋊C4×C61C4semidirect
93. C2×D244C4⋊C4semidirect
117. C4⋊C4×C61C4⋊C4semidirect
239. C4×C61#327semidirect
274. C4×C4⋊C4#6923semidirect
280. C61#8571semidirect
376. C4⋊C4C4⋊#6923semidirect
500. C4#16840614semidirect

Maximal subgroups

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

subgroupindex
#214616742
C2×#168406142
#214609972
#214606922
C4×#145197522
#857161