Finite Group Databasebeta

← #30596944

Subgroups — #30596944

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2#21462263C211yesmaximal, characteristic
3#21460700C214yesmaximal, complemented
4#21448199C211yesmaximal, characteristic
5C22×#11758213C412yescomplemented
6C2×#14519856—21no—
7#16840733—21no—
8#16840733—21no—
9#16840733C412yescomplemented
10#16840733C2212yes—
11C2×#14519834—21no—
12C2×C22⋊#92420—21no—
13#16840705C412yescomplemented
14#16840704—21no—
15#16840704C412yescomplemented
16#16840703—21no—
17C4×C22⋊#6923—21no—
18C4×C22⋊#6923C2212yes—
19C23×C4×D61C2211yescharacteristic
20C2×#14519733—21no—
21#16839625C411yescharacteristic, complemented
22#16839621—21no—
23#16839621C412yescomplemented
24#16839617—21no—
25#16839609—21no—
26#16839609C2212yes—
27C61×#381C411yescharacteristic, complemented
28C2×#11758213—22no—
29C2×#11758213—44no—
30C2×#11758213C2×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#14519733—44no—
60C2×#11758196—22no—
61C2×C22⋊Dic61—21no—
62C2×#11758198—22no—
63C2×#11758198—22no—
64C2×C4×Dic61—22no—
65#14519684—21no—
66#14519684C2×C412yes—
67C23×C4×C61C2×C411yescharacteristic
68C2×C22⋊C4×C61—21no—
69#95×C61—21no—
70#95×C61C2×C412yes—
71C24×C61C22⋊C411yescharacteristic
72C23×D61—42no—
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—24no—
91C22×Dic61—22no—
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—42no—
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—
133#11758213—44no—
134#11758213—44no—
135C22⋊C4×C61—42no—
136C22⋊Dic61—42no—
137#11758198—44no—
138#11758198—44no—
139#11758196—44no—
140C4×Dic61—44no—
141C23×C61—22no—
142C23×C61—22no—
143C23×C61—41no—
144C23×C61#9511yescharacteristic
145C23×C61#9511yescharacteristic
146C23×C61C2×C22⋊C411yescharacteristic
147C22×D61—22no—
148C22×D61—22no—
149C22×D61—22no—
150C22×D61—22no—
151C22×D61—22no—
152C22×D61—22no—
153C22×D61—22no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
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
170C2×#6923—44no—
171C2×#6923—44no—
172C2×#6923—44no—
173C2×C4×C61—22no—
174C2×C4×C61—22no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61#9511yescharacteristic
183C2×C4×C61#9511yescharacteristic
184C2×C4×C61C2×C4211yescharacteristic
185C2×C4×C61C2×C4⋊C411yescharacteristic
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—22no—
189C2×Dic61—22no—
190C2×Dic61—22no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61#9511yescharacteristic
195C2×Dic61#9511yescharacteristic
196C2×Dic61#9914yes—
197C2×Dic61C2×C22⋊C411yescharacteristic
198C2×Dic61C2×C4⋊C411yescharacteristic
199C4×D61—22no—
200C4×D61—22no—
201C4×D61—22no—
202C4×D61—22no—
203C4×D61—22no—
204C4×D61—22no—
205C4×D61—22no—
206C4×D61—22no—
207C4×D61—41no—
208C4×D61—41no—
209C4×D61—41no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—41no—
213C4×D61—41no—
214C4×D61—41no—
215#92420—44no—
216#8049—611nomaximal, Sylow
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—44no—
225C22×C61#34212yes—
226C22×C61C2×#9511yescharacteristic
227C22×C61#42112yes—
228C2×D61—21no—
229C2×D61—21no—
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—44no—
245C2×D61#42112yes—
246#6923—84no—
247C4×C61—21no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—82no—
252Dic61—21no—
253Dic61—21no—
254Dic61—82no—
255Dic61#34212yes—
256Dic61C2×#9912yes—
257C2×#407—611no—
258#2280—611no—
259#2280—611no—
260#1297—614no—
261C2×C61—22no—
262C2×C61—22no—
263C2×C61—41no—
264C2×C61#173311yescharacteristic
265C2×C61#173311yescharacteristic
266C2×C61C2×#34211yescharacteristic
267D61—22no—
268D61—41no—
269D61—41no—
270D61—41no—
271C24×C4—611no—
272C22×M16—612no—
273C2×#117—1221no—
274C2×#117—1221no—
275#407—612no—
276#407—612no—
277#407—1221no—
278#407—1221no—
279C2×C22⋊C8—1221no—
280C2×C22⋊C8—1221no—
281#381—612no—
282#381—611no—
283#381#692311yescharacteristic, complemented
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—612no—
292C4×C22⋊C4—1221no—
293C4×C22⋊C4—1221no—
294C61#804911yescharacteristic, complemented, Sylow
295C25—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—611no—
308C23×C4—611no—
309C23×C4—2444no—
310C23×C4C2×#692311yescharacteristic
311C2×M16—614no—
312C2×M16—1222no—
313C2×M16—2444no—
314C22×C8—1222no—
315#117—2444no—
316#117—2444no—
317C2×C4⋊C4—1222no—
318C2×C4⋊C4—1222no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—1222no—
321C2×C22⋊C4—1222no—
322C2×C22⋊C4—1222no—
323C2×C22⋊C4—1222no—
324C2×C22⋊C4—1222no—
325C2×C22⋊C4—1221no—
326C2×C42—1222no—
327C2×C42—1222no—
328C22⋊C8—1222no—
329C22⋊C8—1222no—
330C22⋊C8—1222no—
331C22⋊C8—1222no—
332#95—21no—
333#95—614no—
334#95—612no—
335#95—1222no—
336#95—1221no—
337#95C2×#692312yes—
338C24—611no—
339C24—611no—
340C24—611no—
341C24—611no—
342C24—611no—
343C24—611no—
344C24—2442no—
345C24—2442no—
346C24—2442no—
347C24C22⋊#692311yescharacteristic
348C22×C4—22no—
349C22×C4—42no—
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—1224no—
373C22×C4—1224no—
374C22×C4—1224no—
375C22×C4—1224no—
376C22×C4—1222no—
377C22×C4—2442no—
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×C4C4×#692311yescharacteristic
388C22×C4C4×#692311yescharacteristic
389C22×C4C4⋊#692311yescharacteristic
390C22×C4C4⋊#692311yescharacteristic
391C22×C4C22⋊#692311yescharacteristic
392C22×C4C22×#692311yescharacteristic
393M16—2444no—
394M16—2444no—
395C2×C8—1224no—
396C2×C8—2444no—
397C4⋊C4—2444no—
398C4⋊C4—2444no—
399C22⋊C4—42no—
400C22⋊C4—2444no—
401C22⋊C4—2444no—
402C22⋊C4—2442no—
403C22⋊C4—2444no—
404C22⋊C4—2444no—
405C22⋊C4—2444no—
406C42—2444no—
407C42—2444no—
408C23—22no—
409C23—22no—
410C23—41no—
411C23—611no—
412C23—611no—
413C23—611no—
414C23—611no—
415C23—1222no—
416C23—1222no—
417C23—1222no—
418C23—1222no—
419C23—1222no—
420C23—1222no—
421C23—1222no—
422C23—2441no—
423C23—2441no—
424C23—2441no—
425C23—2441no—
426C23—2441no—
427C23—2441no—
428C23—2441no—
429C23—2441no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23—24416no—
434C23(C2×#6923)⋊C411yescharacteristic
435C23(C2×#6923)⋊C411yescharacteristic
436C23C2×C22⋊#692311yescharacteristic
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—614no—
447C2×C4—611no—
448C2×C4—611no—
449C2×C4—611no—
450C2×C4—611no—
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—1222no—
462C2×C4—1222no—
463C2×C4—1222no—
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—2442no—
473C2×C4—2442no—
474C2×C4—2444no—
475C2×C4—2444no—
476C2×C4—2444no—
477C2×C4—2442no—
478C2×C4(C2×#6923)⋊C411yescharacteristic
479C2×C4(C2×#6923)⋊C411yescharacteristic
480C2×C4C2×C4×#692311yescharacteristic
481C2×C4C2×C4⋊#692311yescharacteristic
482C8—2444no—
483C22—21no—
484C22—21no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—44no—
491C22—612no—
492C22—1221no—
493C22—1221no—
494C22—1221no—
495C22—1221no—
496C22—1221no—
497C22—1221no—
498C22—1221no—
499C22—1221no—
500C22—1221no—
501C22—1221no—
502C22—1221no—
503C22—2444no—
504C22—2444no—
505C22—2444no—
506C22—2444no—
507C22—2444no—
508C22—2444no—
509C22#1684063912yes—
510C22C2×(C2×#6923)⋊C411yescharacteristic
511C22#1684075912yes—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—82no—
517C4—612no—
518C4—612no—
519C4—1221no—
520C4—1221no—
521C4—4882no—
522C4—4884no—
523C2—22no—
524C2—22no—
525C2—41no—
526C2—1222no—
527C2—2441no—
528C2—2441no—
529C2—2441no—
530C2#2146149911yescharacteristic
531C2#2146150011yescharacteristic
532C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#381C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#381#6923
hypocenterC61#8049
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
3. #21460700C2semidirect
5. C22×#11758213C4semidirect
9. #16840733C4semidirect
13. #16840705C4semidirect
15. #16840704C4semidirect
21. #16839625C4semidirect
23. #16839621C4semidirect
27. C61×#381C4semidirect
283. #381#6923semidirect
294. C61#8049semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
#214622632
#214607002
#214481992
#804961