Finite Group Databasebeta

← #30596954

Subgroups — #30596954

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840733C211yesmaximal, characteristic
2C2×C4×C22⋊#6923C211yesmaximal, characteristic
3#21460700C214yesmaximal, complemented
4#21448201C211yesmaximal, characteristic
5C22×#11758213C412yescomplemented
6C22×C22⋊#6923—21no—
7C22×C4×#6923—21no—
8#16840733—21no—
9#16840733—21no—
10#16840733C412yescomplemented
11#16840733C2212yes—
12C2×#14519834—21no—
13C2×C22⋊#92420—21no—
14C4×C22⋊#6923—21no—
15C4×C22⋊#6923—21no—
16C4×C22⋊#6923C412yescomplemented
17C4×C22⋊#6923C2212yes—
18C2×(C2×#6923)⋊C4C412yescomplemented
19C23×C4×D61C2211yescharacteristic
20C2×#14519735—21no—
21#16839624C412yescomplemented
22#16839622C411yescharacteristic, complemented
23#16839619—21no—
24#16839617—21no—
25C22⋊C4×Dic61—21no—
26#16839609C2212yes—
27C61×#380C411yescharacteristic, complemented
28C23×#6923—22no—
29C2×#11758213—22no—
30C2×#11758213—44no—
31C2×#11758213C2×C414yescomplemented
32C22×#92420—22no—
33C2×C22⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—22no—
36C2×C22⋊#6923—22no—
37C2×C4×#6923—22no—
38C2×C4×#6923—22no—
39C2×C4×#6923—44no—
40#14519834—22no—
41#14519834—22no—
42C22⋊#92420—22no—
43C22⋊#92420—22no—
44(C2×#6923)⋊C4—22no—
45(C2×#6923)⋊C4C2×C414yes—
46C24×D61D411yescharacteristic
47C23×Dic61D411yescharacteristic
48C22×C4×D61—44no—
49C22×C4×D61C2×C411yescharacteristic
50C22×C4×D61C2×C411yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61D411yescharacteristic
55C22×C4×D61D411yescharacteristic
56C22×C4×D61D411yescharacteristic
57C22×C4×D61D411yescharacteristic
58C22×C4×D61Q811yescharacteristic
59C22×C4×D61Q811yescharacteristic
60C22×C4×D61C2311yescharacteristic
61#14519735—44no—
62C2×C4⋊Dic61—21no—
63C2×C22⋊Dic61—21no—
64C2×#11758198—22no—
65C2×#11758198—22no—
66C2×C4×Dic61—22no—
67#14519684—22no—
68#14519684C2×C412yescomplemented
69C23×C4×C61C2×C411yescharacteristic
70C2×C4⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72#95×C61C2×C412yescomplemented
73C24×C61C22⋊C411yescharacteristic
74C23×D61—22no—
75C23×D61—22no—
76C23×D61—42no—
77C23×D61—42no—
78C23×D61C22⋊C411yescharacteristic
79C23×D61C22⋊C411yescharacteristic
80C23×D61C22⋊C411yescharacteristic
81C23×D61C4⋊C411yescharacteristic
82C23×D61C4⋊C411yescharacteristic
83C23×D61C2×D411yescharacteristic
84C22×#6923—28no—
85C22×#6923—24no—
86C22×#6923—44no—
87C22×#6923—44no—
88C22×C4×C61—22no—
89C22×C4×C61—42no—
90C22×C4×C61C4211yescharacteristic
91C22×C4×C61C4211yescharacteristic
92C22×C4×C61C22⋊C411yescharacteristic
93C22×C4×C61C4⋊C411yescharacteristic
94C22×C4×C61C4⋊C411yescharacteristic
95C22×C4×C61C22×C411yescharacteristic
96C22×Dic61—22no—
97C22×Dic61—42no—
98C22×Dic61C22⋊C411yescharacteristic
99C22×Dic61C22⋊C411yescharacteristic
100C22×Dic61C22⋊C411yescharacteristic
101C22×Dic61C4⋊C411yescharacteristic
102C22×Dic61C4⋊C411yescharacteristic
103C22×Dic61C2×D411yescharacteristic
104C2×C4×D61—24no—
105C2×C4×D61—24no—
106C2×C4×D61—24no—
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×D61—42no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61C4211yescharacteristic
117C2×C4×D61C4211yescharacteristic
118C2×C4×D61C22⋊C411yescharacteristic
119C2×C4×D61C22⋊C411yescharacteristic
120C2×C4×D61C22⋊C411yescharacteristic
121C2×C4×D61C22⋊C411yescharacteristic
122C2×C4×D61C4⋊C411yescharacteristic
123C2×C4×D61C4⋊C411yescharacteristic
124C2×C4×D61C4⋊C411yescharacteristic
125C2×C4×D61C4⋊C411yescharacteristic
126C2×C4×D61C4⋊C411yescharacteristic
127C2×C4×D61C4⋊C411yescharacteristic
128C2×C4×D61C22×C411yescharacteristic
129C2×C4×D61C22×C411yescharacteristic
130C2×C4×D61C2×D411yescharacteristic
131C2×C4×D61C2×Q811yescharacteristic
132C22⋊#6923—28no—
133C22⋊#6923—24no—
134C22⋊#6923—24no—
135C2×#92420—24no—
136C2×#92420—44no—
137C4×#6923—44no—
138C4×#6923—44no—
139#11758213—44no—
140#11758213—44no—
141C4⋊C4×C61—42no—
142C22⋊C4×C61—42no—
143C22⋊Dic61—42no—
144#11758198—44no—
145#11758198—44no—
146C4⋊Dic61—42no—
147C4×Dic61—44no—
148C23×C61—41no—
149C23×C61—41no—
150C23×C61#9511yescharacteristic
151C23×C61#9511yescharacteristic
152C23×C61#10412yes—
153C23×C61#10412yes—
154C23×C61C2×C22⋊C411yescharacteristic
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—22no—
158C22×D61—22no—
159C22×D61—22no—
160C22×D61—22no—
161C22×D61—21no—
162C22×D61—21no—
163C22×D61—21no—
164C22×D61—21no—
165C22×D61—22no—
166C22×D61—22no—
167C22×D61—22no—
168C22×D61—22no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173C22×D61—41no—
174C22×D61—41no—
175C22×D61—48no—
176C22×D61—48no—
177C22×D61#9511yescharacteristic
178C22×D61#9511yescharacteristic
179C22×D61C2×C22⋊C411yescharacteristic
180C22×D61C2×C4⋊C411yescharacteristic
181C2×#6923—28no—
182C2×#6923—44no—
183C2×#6923—416no—
184C2×#6923—44no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61—42no—
194C2×C4×C61#9511yescharacteristic
195C2×C4×C61#9511yescharacteristic
196C2×C4×C61C2×C4211yescharacteristic
197C2×C4×C61C2×C4⋊C411yescharacteristic
198C2×Dic61—22no—
199C2×Dic61—22no—
200C2×Dic61—22no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61#9511yescharacteristic
208C2×Dic61#9511yescharacteristic
209C2×Dic61C2×C22⋊C411yescharacteristic
210C2×Dic61C2×C4⋊C411yescharacteristic
211C4×D61—22no—
212C4×D61—22no—
213C4×D61—22no—
214C4×D61—22no—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—22no—
218C4×D61—22no—
219C4×D61—22no—
220C4×D61—41no—
221C4×D61—41no—
222C4×D61—41no—
223C4×D61—41no—
224C4×D61—41no—
225C4×D61—41no—
226C4×D61#9914yes—
227#92420—44no—
228#8051—611nomaximal, Sylow
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—21no—
235C22×C61—42no—
236C22×C61—42no—
237C22×C61#33912yes—
238C22×C61#33912yes—
239C22×C61C2×#9511yescharacteristic
240C22×C61C2×#10411yescharacteristic
241C22×C61C2×#10411yescharacteristic
242C2×D61—28no—
243C2×D61—21no—
244C2×D61—21no—
245C2×D61—21no—
246C2×D61—21no—
247C2×D61—21no—
248C2×D61—21no—
249C2×D61—21no—
250C2×D61—21no—
251C2×D61—21no—
252C2×D61—21no—
253C2×D61—42no—
254C2×D61—42no—
255C2×D61—44no—
256C2×D61—42no—
257C2×D61—42no—
258C2×D61—44no—
259C2×D61—44no—
260C2×D61#34212yes—
261C2×D61#42112yes—
262#6923—48no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—82no—
267C4×C61#34212yes—
268Dic61—21no—
269Dic61—21no—
270Dic61—21no—
271Dic61—82no—
272Dic61C2×#9912yes—
273C2×#407—611no—
274#2280—611no—
275C2×C4×C22⋊C4—611no—
276#1297—614no—
277C2×C61—21no—
278C2×C61—21no—
279C2×C61—22no—
280C2×C61—22no—
281C2×C61C2×#33911yescharacteristic
282C2×C61#173311yescharacteristic
283C2×C61C2×#34211yescharacteristic
284D61—22no—
285D61—22no—
286D61—41no—
287D61—41no—
288C24×C4—611no—
289C22×M16—612no—
290C2×#117—1221no—
291C22×C22⋊C4—1221no—
292C22×C42—1221no—
293#407—612no—
294#407—612no—
295#407—1221no—
296#407—1221no—
297C2×C22⋊C8—1221no—
298C2×C22⋊C8—1221no—
299#381—612no—
300#380—611no—
301#380—1221no—
302#380#692311yescharacteristic, complemented
303#379—1221no—
304C4×C22⋊C4—612no—
305C4×C22⋊C4—612no—
306C4×C22⋊C4—612no—
307C4×C22⋊C4—1221no—
308C4×C22⋊C4—1221no—
309C4×C22⋊C4—1221no—
310C2×#95—612no—
311C61#805111yescharacteristic, complemented, Sylow
312C25—611no—
313C23×C4—611no—
314C23×C4—611no—
315C23×C4—611no—
316C23×C4—611no—
317C23×C4—611no—
318C23×C4—611no—
319C23×C4—611no—
320C23×C4—611no—
321C23×C4—611no—
322C23×C4—611no—
323C23×C4—611no—
324C23×C4—611no—
325C23×C4—611no—
326C23×C4—1222no—
327C23×C4—2444no—
328C23×C4C2×#692311yescharacteristic
329C2×M16—614no—
330C2×M16—1222no—
331C2×M16—2444no—
332C22×C8—1222no—
333#117—2444no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—1221no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—1222no—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1224no—
340C2×C22⋊C4—1224no—
341C2×C22⋊C4—1222no—
342C2×C22⋊C4—1222no—
343C2×C22⋊C4—1221no—
344C2×C42—1222no—
345C2×C42—1222no—
346C2×C42—1222no—
347C2×C42—2444no—
348C22⋊C8—1222no—
349C22⋊C8—1222no—
350C22⋊C8—1222no—
351C22⋊C8—1222no—
352#95—614no—
353#95—612no—
354#95—1222no—
355#95—1222no—
356#95C2×#692312yescomplemented
357C24—611no—
358C24—611no—
359C24—611no—
360C24—611no—
361C24—611no—
362C24—611no—
363C24—1222no—
364C24—1222no—
365C24—2442no—
366C24—2442no—
367C24C22⋊#692311yescharacteristic
368C22×C4—22no—
369C22×C4—42no—
370C22×C4—611no—
371C22×C4—611no—
372C22×C4—611no—
373C22×C4—611no—
374C22×C4—611no—
375C22×C4—611no—
376C22×C4—611no—
377C22×C4—611no—
378C22×C4—611no—
379C22×C4—611no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—611no—
384C22×C4—611no—
385C22×C4—611no—
386C22×C4—611no—
387C22×C4—611no—
388C22×C4—611no—
389C22×C4—611no—
390C22×C4—611no—
391C22×C4—611no—
392C22×C4—1224no—
393C22×C4—1224no—
394C22×C4—1224no—
395C22×C4—1224no—
396C22×C4—1228no—
397C22×C4—1222no—
398C22×C4—2442no—
399C22×C4—2442no—
400C22×C4—2442no—
401C22×C4—2442no—
402C22×C4—2442no—
403C22×C4—2442no—
404C22×C4—2442no—
405C22×C4—2442no—
406C22×C4—2442no—
407C22×C4—2442no—
408C22×C4—2444no—
409C22×C4—2444no—
410C22×C4C4×#692311yescharacteristic
411C22×C4C4×#692311yescharacteristic
412C22×C4C4⋊#692311yescharacteristic
413C22×C4C4⋊#692311yescharacteristic
414C22×C4C22⋊#692311yescharacteristic
415C22×C4C22×#692311yescharacteristic
416M16—2444no—
417M16—2444no—
418C2×C8—1224no—
419C2×C8—2444no—
420C4⋊C4—42no—
421C4⋊C4—2442no—
422C22⋊C4—42no—
423C22⋊C4—1224no—
424C22⋊C4—1224no—
425C22⋊C4—1228no—
426C22⋊C4—2444no—
427C22⋊C4—2444no—
428C22⋊C4—2442no—
429C42—2444no—
430C42—2444no—
431C42—2444no—
432C23—41no—
433C23—41no—
434C23—611no—
435C23—611no—
436C23—611no—
437C23—611no—
438C23—1222no—
439C23—1222no—
440C23—1222no—
441C23—1222no—
442C23—1222no—
443C23—1222no—
444C23—1222no—
445C23—1221no—
446C23—1221no—
447C23—1221no—
448C23—1221no—
449C23—1222no—
450C23—1222no—
451C23—1222no—
452C23—2441no—
453C23—2441no—
454C23—2441no—
455C23—2441no—
456C23—2441no—
457C23—2441no—
458C23—2448no—
459C23—2448no—
460C23(C2×#6923)⋊C411yescharacteristic
461C23(C2×#6923)⋊C411yescharacteristic
462C23#1451984112yes—
463C23#1451984212yes—
464C23C2×C22⋊#692311yescharacteristic
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—611no—
475C2×C4—614no—
476C2×C4—611no—
477C2×C4—611no—
478C2×C4—611no—
479C2×C4—1222no—
480C2×C4—1222no—
481C2×C4—1222no—
482C2×C4—1222no—
483C2×C4—1222no—
484C2×C4—1222no—
485C2×C4—1222no—
486C2×C4—1222no—
487C2×C4—1222no—
488C2×C4—1222no—
489C2×C4—1222no—
490C2×C4—1222no—
491C2×C4—1228no—
492C2×C4—2441no—
493C2×C4—2441no—
494C2×C4—2441no—
495C2×C4—2441no—
496C2×C4—2441no—
497C2×C4—2441no—
498C2×C4—2441no—
499C2×C4—2441no—
500C2×C4—2441no—
501C2×C4—2442no—
502C2×C4—2442no—
503C2×C4—2442no—
504C2×C4—2444no—
505C2×C4—2444no—
506C2×C4—24416no—
507C2×C4(C2×#6923)⋊C411yescharacteristic
508C2×C4(C2×#6923)⋊C411yescharacteristic
509C2×C4C2×C4×#692311yescharacteristic
510C2×C4C2×C4⋊#692311yescharacteristic
511C8—2444no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—42no—
519C22—42no—
520C22—612no—
521C22—612no—
522C22—1228no—
523C22—1221no—
524C22—1221no—
525C22—1221no—
526C22—1221no—
527C22—1221no—
528C22—1221no—
529C22—1221no—
530C22—1221no—
531C22—1221no—
532C22—1221no—
533C22—2442no—
534C22—2442no—
535C22—2442no—
536C22—2442no—
537C22—2444no—
538C22—2444no—
539C22—2444no—
540C22#1684063212yes—
541C22#1684063212yes—
542C22C2×(C2×#6923)⋊C411yescharacteristic
543C22C2×#1451984111yescharacteristic
544C22C2×#1451984211yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—82no—
549C4—612no—
550C4—1221no—
551C4—1221no—
552C4—1221no—
553C4—4882no—
554C4—2448no—
555C4#1684063912yes—
556C2—21no—
557C2—21no—
558C2—22no—
559C2—22no—
560C2—1222no—
561C2—1222no—
562C2—2441no—
563C2—2441no—
564C2C2×#1684063211yescharacteristic
565C2#2146150011yescharacteristic
566C2C2×#1684063911yescharacteristic
subgroupG/H
centerC22C2×(C2×#6923)⋊C4
commutatorC2×C4×C61C2×C42
FrattiniC22×C4C22×#6923
FittingC61×#380C4
socleC22×C61C2×#95
prime radicalC24×D61D4
cosocleC22×C4×D61C23
hypercenter#380#6923
hypocenterC61#8051
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
3. #21460700C2semidirect
5. C22×#11758213C4semidirect
10. #16840733C4semidirect
16. C4×C22⋊#6923C4semidirect
18. C2×(C2×#6923)⋊C4C4semidirect
21. #16839624C4semidirect
22. #16839622C4semidirect
27. C61×#380C4semidirect
31. C2×#11758213C2×C4semidirect
68. #14519684C2×C4semidirect
72. #95×C61C2×C4semidirect
302. #380#6923semidirect
311. C61#8051semidirect
356. #95C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168407332
C2×C4×C22⋊#69232
#214607002
#214482012
#805161