Finite Group Databasebeta

← #29685216

Subgroups — #29685216

Order 15616.

1142 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
1C2×#16840316C211yesmaximal, characteristic
2C2×C4×#11758189C211yesmaximal, characteristic
3#21448215C211yesmaximal, characteristic
4#21446790C212yesmaximal, complemented
5#21446637C212yesmaximal, complemented
6#21446251C212yesmaximal
7#21446249C212yesmaximal
8C4×#14519700C211yesmaximal, characteristic, complemented
9C4×#14519702C211yesmaximal, characteristic, complemented
10C4×#14519701C211yesmaximal, characteristic, complemented
11C4×#103×C61C211yesmaximal, characteristic, complemented
12C22×#11758189C2212yes—
13#16840316—24no—
14#16840316C418yescomplemented
15C2×#14519776C2211yescharacteristic
16C2×#14519775C2211yescharacteristic
17C2×#14519767—21no—
18C2×#14519757C2211yescharacteristic
19C2×#14519755—21no—
20C2×#14519753C2211yescharacteristic
21C2×C4×Dic122—21no—
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519734—21no—
24C2×C42×D61C2211yescharacteristic
25C2×#14519702C2212yes—
26C2×#14519701C2212yes—
27C2×#14519700C2212yes—
28C4×#11758189—24no—
29C2×#14519687C2212yes—
30C2×C4×#92418C2211yescharacteristic
31#16839629—21no—
32#16839627C2212yes—
33#16839624—21no—
34#16839619C2212yes—
35C4×C4⋊Dic61C2211yescharacteristic
36C4×#11758198—21no—
37#16839608—21no—
38#16839525C2212yes—
39#16839524C2212yes—
40#16839524C2212yes—
41C2×C4×Q8×C61C2211yescharacteristic
42C2×#103×C61C2212yes—
43C2×C4×C8×C61C2211yescharacteristic
44C4×C4⋊C4×C61C2211yescharacteristic
45C61×#340C2212yes—
46C22×Dic122—21no—
47C22×Dic122C2311yescharacteristic
48C22×C4×D61D411yescharacteristic
49C22×C4×D61D411yescharacteristic
50C22×C4×D61C2311yescharacteristic
51C2×#11758189—24no—
52C2×#11758189—24no—
53C2×#11758189—24no—
54C22×#92418C2312yes—
55#14519776—22no—
56#14519776C2×C414yes—
57#14519775—22no—
58#14519775C2×C414yes—
59#14519767—28no—
60#14519757—22no—
61#14519757C2×C414yes—
62#14519755—28no—
63#14519753—22no—
64#14519753C2×C414yes—
65C4×Dic122—22no—
66C4×Dic122—28no—
67C4×Dic122C2×C414yes—
68#14519734—28no—
69C2×C4⋊Dic61—21no—
70C2×C4⋊Dic61C2312yes—
71C2×C4⋊Dic61C2311yescharacteristic
72C2×#11758196—21no—
73C2×#11758196—21no—
74C2×#11758196—21no—
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758198—21no—
78C2×#11758198—21no—
79C2×#11758198—22no—
80C2×C4×Dic61—21no—
81C2×C4×Dic61—21no—
82C2×C4×Dic61D411yescharacteristic
83C2×C4×Dic61D411yescharacteristic
84C2×C4×Dic61C2311yescharacteristic
85C42×D61C2×C414yes—
86C42×D61D414yes—
87#14519702—24no—
88#14519701—24no—
89#14519700—24no—
90#14519687—24no—
91C4×#92418—22no—
92#14519684—21no—
93#14519684—22no—
94#14519684—22no—
95#14519684—22no—
96C22×Q8×C61C2311yescharacteristic
97C22×C8×C61C2312yes—
98C4×Q8×C61—22no—
99C4×Q8×C61C2×C414yes—
100C2×C4⋊C4×C61—21no—
101C2×C4⋊C4×C61C2312yes—
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C42×C61—21no—
104C2×C42×C61—21no—
105C2×C42×C61C2311yescharacteristic
106#103×C61—24no—
107C4×C8×C61—22no—
108#95×C61—21no—
109C23×D61C2×D411yescharacteristic
110C2×Q8×C61—21no—
111C2×Q8×C61—22no—
112C2×Q8×C61—22no—
113C2×Q8×C61C22×C412yes—
114C22×C4×C61—21no—
115C22×C4×C61—21no—
116C22×C4×C61—22no—
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2411yescharacteristic
120C22×Dic61—21no—
121C22×Dic61—21no—
122C22×Dic61—22no—
123C22×Dic61C2×D411yescharacteristic
124C22×Dic61C2×D411yescharacteristic
125C22×Dic61C2×D411yescharacteristic
126C2×C4×D61—22no—
127C2×C4×D61—22no—
128C2×C4×D61—22no—
129C2×C4×D61—22no—
130C2×C4×D61—42no—
131C2×C4×D61C22⋊C414yes—
132C2×C4×D61C22⋊C414yes—
133C2×C4×D61C22×C412yes—
134C2×C4×D61C2×D412yes—
135C2×Dic122—22no—
136C2×Dic122—22no—
137C2×Dic122—21no—
138C2×Dic122—24no—
139C2×Dic122—44no—
140C2×Dic122C22×C412yes—
141C2×C8×C61—22no—
142C2×C8×C61—22no—
143C2×C8×C61#4114yes—
144C4⋊C4×C61—24no—
145C4⋊C4×C61—21no—
146C4⋊C4×C61—22no—
147C4⋊C4×C61—22no—
148C4⋊C4×C61C22×C412yes—
149C42×C61—24no—
150C42×C61—42no—
151C42×C61C22×C412yes—
152C42×C61C2×D412yes—
153#11758198—24no—
154#11758198—24no—
155#11758198—44no—
156C4⋊Dic61—21no—
157C4⋊Dic61—24no—
158C4⋊Dic61—22no—
159C4⋊Dic61—22no—
160C4⋊Dic61C22×C412yes—
161#11758196—24no—
162#11758196—24no—
163#11758196—24no—
164#11758196—24no—
165#11758196—24no—
166C4×Dic61—24no—
167C4×Dic61—42no—
168C4×Dic61C22⋊C414yes—
169C4×Dic61C22⋊C414yes—
170C4×Dic61C22×C412yes—
171C4×Dic61C2×D412yes—
172C2×#92418—22no—
173C2×#92418—22no—
174C2×#92418#4114yes—
175#11758189—216no—
176C23×C61C22×D411yescharacteristic
177C22×D61—22no—
178C22×D61—21no—
179C22×D61—21no—
180C22×D61—22no—
181C22×D61C2×C22⋊C412yes—
182Q8×C61—22no—
183Q8×C61—22no—
184Q8×C61—42no—
185C2×C4×C61—22no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—42no—
189C2×C4×C61—42no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—42no—
193C2×C4×C61C2×C22⋊C412yes—
194C2×C4×C61C2×C22⋊C412yes—
195C2×C4×C61#13712yes—
196C2×C4×C61#13712yes—
197C2×C4×C61C23×C411yescharacteristic
198C2×C4×C61C22×D411yescharacteristic
199C2×C4×C61C2×#4112yes—
200C2×C4×C61C2×#4112yes—
201C2×Dic61—22no—
202C2×Dic61—21no—
203C2×Dic61—21no—
204C2×Dic61—22no—
205C2×Dic61—22no—
206C2×Dic61—22no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61C2×C22⋊C412yes—
213C2×Dic61C2×C22⋊C412yes—
214C2×Dic61C2×C22⋊C412yes—
215C4×D61—22no—
216C4×D61—22no—
217C4×D61—24no—
218C4×D61—28no—
219C4×D61—44no—
220Dic122—22no—
221Dic122—22no—
222Dic122—48no—
223Dic122—42no—
224C8×C61—24no—
225#92418—24no—
226#21404—611nomaximal, Sylow
227C22×C61C22×C22⋊C411yescharacteristic
228C22×C61#53212yes—
229C22×C61C2×#13711yescharacteristic
230C22×C61C2×#13711yescharacteristic
231C22×C61#57512yes—
232C2×D61—22no—
233C2×D61—22no—
234C2×D61—22no—
235C2×D61—42no—
236C2×D61—42no—
237C4×C61—22no—
238C4×C61—42no—
239C4×C61—42no—
240C4×C61—82no—
241C4×C61#41914yes—
242C4×C61C4×#4111yescharacteristic
243C4×C61C4×#4111yescharacteristic
244C4×C61#52512yes—
245Dic61—22no—
246Dic61—22no—
247Dic61—22no—
248Dic61—42no—
249Dic61—42no—
250Dic61—82no—
251C2×#533—611no—
252C2×C4×M16—611no—
253#2283—611no—
254#1993—612no—
255#1960—612no—
256#1894—612no—
257#1894—612no—
258C4×#103—611no—
259C4×#103—611no—
260C4×#103—611no—
261C4×#103D6111yescharacteristic, complemented
262C2×C61#229711yescharacteristic
263C2×C61C2×#41911yescharacteristic
264C2×C61#289611yescharacteristic
265C2×C61#317212yes—
266C2×C61#317212yes—
267D61—42no—
268C22×M16—612no—
269#533—618no—
270#533—1224no—
271C2×C4⋊Q8—611no—
272C2×C4⋊Q8—611no—
273C2×#125—1221no—
274C2×C22⋊Q8—611no—
275C2×C22⋊Q8—611no—
276C2×C22⋊Q8—1221no—
277C2×C4×Q8—611no—
278C2×C4×Q8—1221no—
279C2×C4×Q8C2×D6111yescharacteristic
280C2×#117—1221no—
281C22×C42—611no—
282C2×#103—612no—
283C2×#103—612no—
284C2×#103—612no—
285C2×#103C2×D6112yes—
286C4×M16—1224no—
287C2×#97—612no—
288C2×C4×C8—611no—
289C2×C4×C8C2×D6111yescharacteristic
290#383—1221no—
291#382—612no—
292#381—1221no—
293#380—612no—
294C4×C4⋊C4—611no—
295C4×C4⋊C4C2×D6111yescharacteristic
296C4×C22⋊C4—1221no—
297#376—1221no—
298#340—612no—
299#340—612no—
300#340—612no—
301#340C2×D6112yes—
302C61#2140411yescharacteristic, complemented, Sylow
303C22×Q8—611no—
304C22×Q8—1221no—
305C22×Q8C22×D6111yescharacteristic
306C23×C4—611no—
307C23×C4—611no—
308C23×C4—611no—
309C2×M16—1224no—
310C2×M16—1224no—
311C2×M16—1224no—
312C22×C8—612no—
313C22×C8C22×D6112yes—
314C4⋊Q8—614no—
315C4⋊Q8—614no—
316C4⋊Q8—1222no—
317C4⋊Q8—1222no—
318#125—1228no—
319C22⋊Q8—614no—
320C22⋊Q8—614no—
321C22⋊Q8—1222no—
322C22⋊Q8—1228no—
323C22⋊Q8—1222no—
324C4×Q8—22no—
325C4×Q8—614no—
326C4×Q8—1228no—
327C4×Q8—1222no—
328C4×Q8C4×D6114yes—
329#117—1228no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—611no—
332C2×C4⋊C4—612no—
333C2×C4⋊C4—1221no—
334C2×C4⋊C4—1221no—
335C2×C4⋊C4—1221no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4—1221no—
338C2×C4⋊C4—1221no—
339C2×C4⋊C4C22×D6112yes—
340C2×C4⋊C4C22×D6111yescharacteristic
341C2×C22⋊C4—1221no—
342C2×C22⋊C4—1221no—
343C2×C22⋊C4—1222no—
344C2×C42—21no—
345C2×C42—21no—
346C2×C42—611no—
347C2×C42—611no—
348C2×C42—611no—
349C2×C42—614no—
350C2×C42—614no—
351C2×C42—1221no—
352C2×C42—1221no—
353C2×C42C22×D6111yescharacteristic
354#103—24no—
355#103—1224no—
356#103—1224no—
357#103—1224no—
358#97—1224no—
359C4×C8—22no—
360C4×C8—1222no—
361#95—21no—
362#95—1222no—
363#95—1222no—
364#95—1222no—
365#95—1221no—
366C24—611no—
367C2×Q8—21no—
368C2×Q8—22no—
369C2×Q8—22no—
370C2×Q8—612no—
371C2×Q8—1224no—
372C2×Q8—1221no—
373C2×Q8—1222no—
374C2×Q8—1222no—
375C2×Q8—2444no—
376C2×Q8C2×C4×D6112yes—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—611no—
383C22×C4—612no—
384C22×C4—612no—
385C22×C4—614no—
386C22×C4—614no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1221no—
392C22×C4—1221no—
393C22×C4—1222no—
394C22×C4—2442no—
395C22×C4D4×D6111yescharacteristic
396C22×C4D4×D6111yescharacteristic
397C22×C4C23×D6111yescharacteristic
398M16—12216no—
399C2×C8—22no—
400C2×C8—22no—
401C2×C8—614no—
402C2×C8—1222no—
403C2×C8—1222no—
404C2×C8#1175822214yes—
405C4⋊C4—21no—
406C4⋊C4—24no—
407C4⋊C4—22no—
408C4⋊C4—22no—
409C4⋊C4—612no—
410C4⋊C4—1224no—
411C4⋊C4—1224no—
412C4⋊C4—1224no—
413C4⋊C4—1224no—
414C4⋊C4—1224no—
415C4⋊C4—1221no—
416C4⋊C4—1224no—
417C4⋊C4—1222no—
418C4⋊C4—1222no—
419C4⋊C4C2×C4×D6112yes—
420C22⋊C4—1224no—
421C22⋊C4—1224no—
422C22⋊C4—2444no—
423C42—24no—
424C42—42no—
425C42—612no—
426C42—612no—
427C42—614no—
428C42—614no—
429C42—1224no—
430C42—2442no—
431C42C2×C4×D6112yes—
432C42D4×D6112yes—
433C23—612no—
434C23—1221no—
435C23—1221no—
436C23—1222no—
437C23—1222no—
438C23C2×D4×D6111yescharacteristic
439Q8—22no—
440Q8—22no—
441Q8—42no—
442Q8—1222no—
443Q8—1222no—
444Q8—2448no—
445Q8—2442no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—42no—
450C2×C4—42no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—612no—
455C2×C4—612no—
456C2×C4—612no—
457C2×C4—1221no—
458C2×C4—1221no—
459C2×C4—1222no—
460C2×C4—1222no—
461C2×C4—1222no—
462C2×C4—1222no—
463C2×C4—1224no—
464C2×C4—1228no—
465C2×C4—1222no—
466C2×C4—1222no—
467C2×C4—2444no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4C22⋊C4×D6112yes—
474C2×C4C22⋊C4×D6112yes—
475C2×C4#1451980612yes—
476C2×C4#1451980912yes—
477C2×C4C22×C4×D6111yescharacteristic
478C2×C4C2×D4×D6111yescharacteristic
479C2×C4#41×D6112yes—
480C2×C4C2×#1175822212yes—
481C8—24no—
482C8—1224no—
483C22—1222no—
484C22—1222no—
485C22—1222no—
486C22—2442no—
487C22—2442no—
488C22C2×C22⋊C4×D6111yescharacteristic
489C22#1684030912yes—
490C22C2×#1451980611yescharacteristic
491C22C2×#1451980911yescharacteristic
492C22#1684055912yes—
493C4—22no—
494C4—42no—
495C4—42no—
496C4—82no—
497C4—1222no—
498C4—1222no—
499C4—1222no—
500C4—4882no—
501C4—2442no—
502C4—2442no—
503C4#1683976914yes—
504C4#1684023011yescharacteristic
505C4C4×#1175822211yescharacteristic
506C4#1684027112yes—
507C2—2442no—
508C2#2144830511yescharacteristic
509C2C2×#1683976911yescharacteristic
510C2#2145433411yescharacteristic
511C2#2145642112yes—
512C2#2145642312yes—
subgroupG/H
centerC22×C4D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×#103×C61C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC4×#103D61
hypocenterC61#21404
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. #21446790C2semidirect
5. #21446637C2semidirect
8. C4×#14519700C2semidirect
9. C4×#14519702C2semidirect
10. C4×#14519701C2semidirect
11. C4×#103×C61C2semidirect
14. #16840316C4semidirect
261. C4×#103D61semidirect
302. C61#21404semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×C4×#117581892
#214482152
#214467902
#214466372
#214462512
#214462492
C4×#145197002
C4×#145197022
C4×#145197012
C4×#103×C612
#2140461