Finite Group Databasebeta

← #29610101

Subgroups — #29610101

Order 15616.

1358 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839682C211yesmaximal, characteristic
2C2×#16839666C212yesmaximal
3C2×#16839644C212yesmaximal
4#21444080C212yesmaximal
5#21444077C212yesmaximal
6#21444051C211yesmaximal, characteristic
7#21444050C212yesmaximal
8#21444043C212yesmaximal
9C61×#1445C211yesmaximal, characteristic
10C23×Dic122C2211yescharacteristic
11C22×#11758196C2212yes—
12C22×#11758196C2212yes—
13C22×C4×Dic61C2211yescharacteristic
14C22×C4×Dic61C2212yes—
15#16839682C418yescomplemented
16#16839666—28no—
17#16839644—28no—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C22×C4⋊C4×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C2×#95×C61C2211yescharacteristic
34C22×Dic122—24no—
35C22×Dic122—24no—
36C22×Dic122—41no—
37C22×Dic122—41no—
38C22×Dic122C2×C414yes—
39C23×Dic61C2312yes—
40C23×Dic61C2312yes—
41C23×Dic61C2312yes—
42C23×Dic61C2312yes—
43C2×#11758196—24no—
44C2×#11758196—24no—
45C2×#11758196—24no—
46C2×#11758196—24no—
47C2×#11758196—42no—
48C2×#11758196C2×C418yes—
49C2×C4×Dic61—24no—
50C2×C4×Dic61—24no—
51C2×C4×Dic61—24no—
52C2×C4×Dic61—41no—
53C2×C4×Dic61—42no—
54#14519684—24no—
55#14519684—24no—
56#14519684—24no—
57#14519684—24no—
58#14519684—24no—
59#14519684—24no—
60#14519684—24no—
61#14519684—41no—
62#14519684C2×C414yes—
63#14519684C2×C418yes—
64#14519684D418yes—
65C23×C4×C61C2312yes—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2311yescharacteristic
69C23×C4×C61C2312yes—
70C2×C4⋊C4×C61—41no—
71C2×C4⋊C4×C61—41no—
72C2×C4⋊C4×C61C2×C414yes—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—41no—
76#95×C61—41no—
77C24×C61C2411yescharacteristic
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—21no—
86C22×C4×C61—21no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
89C22×C4×C61—22no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61C22×C412yes—
104C22×C4×C61C22×C412yes—
105C22×C4×C61C22×C412yes—
106C22×C4×C61C2×D414yes—
107C22×Dic61—22no—
108C22×Dic61—22no—
109C22×Dic61—22no—
110C22×Dic61—22no—
111C22×Dic61—22no—
112C22×Dic61—22no—
113C22×Dic61—22no—
114C22×Dic61—22no—
115C22×Dic61—22no—
116C22×Dic61—22no—
117C22×Dic61—22no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—22no—
121C22×Dic61—22no—
122C22×Dic61—22no—
123C22×Dic61—22no—
124C22×Dic61—22no—
125C22×Dic61—22no—
126C22×Dic61—22no—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61C22×C414yes—
130C22×Dic61C22×C414yes—
131C22×Dic61C2×D414yes—
132C22×Dic61C2×D414yes—
133C22×Dic61#4114yes—
134C22×Dic61#4114yes—
135C2×Dic122—216no—
136C2×Dic122—44no—
137C2×Dic122—44no—
138C2×Dic122—48no—
139C2×Dic122—44no—
140C4⋊C4×C61—44no—
141#11758196—216no—
142#11758196—48no—
143C4×Dic61—44no—
144C4×Dic61—48no—
145C23×C61C23×C411yescharacteristic
146C23×C61C22×D412yes—
147C23×C61C2×#4112yes—
148C23×C61C2×#4112yes—
149C23×C61H(5,𝔽2)11yescharacteristic
150C23×C61H(5,𝔽2)11yescharacteristic
151C23×C612−1+412yes—
152C23×C612−1+412yes—
153C23×C612−1+412yes—
154C2×C4×C61—24no—
155C2×C4×C61—24no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—24no—
162C2×C4×C61—24no—
163C2×C4×C61—24no—
164C2×C4×C61—42no—
165C2×C4×C61—42no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—24no—
190C2×Dic61—24no—
191C2×Dic61—24no—
192C2×Dic61—24no—
193C2×Dic61—24no—
194C2×Dic61—24no—
195C2×Dic61—24no—
196C2×Dic61—24no—
197C2×Dic61—24no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—42no—
201C2×Dic61—42no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—42no—
205C2×Dic61—42no—
206C2×Dic61—42no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61C4×D418yes—
211Dic122—416no—
212#14574—611nomaximal, Sylow
213C22×C61C2×C4×D412yes—
214C22×C61C4×#4111yescharacteristic
215C22×C61#51811yescharacteristic
216C22×C61#51912yes—
217C22×C61#51911yescharacteristic
218C22×C61#53612yes—
219C22×C61#53612yes—
220C22×C61#53912yes—
221C22×C61#54112yes—
222C22×C61#54112yes—
223C22×C61#54212yes—
224C22×C61D4211yescharacteristic
225C22×C61#54612yes—
226C22×C61#54712yes—
227C22×C61#54812yes—
228C22×C61#55111yescharacteristic
229C22×C61#55212yes—
230C22×C61#55612yes—
231C22×C61#56311yescharacteristic
232C22×C61#56311yescharacteristic
233C22×C61#56312yes—
234C4×C61—42no—
235C4×C61—42no—
236C4×C61—42no—
237C4×C61—44no—
238C4×C61—82no—
239Dic61—28no—
240Dic61—44no—
241Dic61—44no—
242Dic61—44no—
243C2×#395—611no—
244C2×#391—612no—
245C2×#387—612no—
246#1445D6111yescharacteristic
247#1443—612no—
248#1442—612no—
249#1436—612no—
250#1436—611no—
251#1434—612no—
252C2×C61#232712yes—
253C2×C61#233211yescharacteristic
254C2×C61#235811yescharacteristic
255C2×C61#236212yes—
256C2×C61#238111yescharacteristic
257C2×C61#267412yes—
258C2×C61#268912yes—
259C2×C61#269012yes—
260C2×C61#276212yes—
261C23×Q8—611no—
262C22×C4⋊C4—612no—
263C22×C4⋊C4—612no—
264C22×C4⋊C4C2×D6111yescharacteristic
265C22×C42—612no—
266C22×C42—611no—
267#395—618no—
268#391—1228no—
269#387—1228no—
270C2×#95—612no—
271C2×#95—611no—
272C2×#95—612no—
273C2×#95—612no—
274C2×#95—612no—
275C2×#95—612no—
276C2×#95—612no—
277C2×#95—612no—
278C2×#95—612no—
279C2×#95—612no—
280C2×#95—611no—
281C2×#95C2×D6112yes—
282C2×#95C2×D6112yes—
283C2×#95C2×D6111yescharacteristic
284C2×#95C2×D6111yescharacteristic
285C61#1457411yescharacteristic, complemented, Sylow
286C22×Q8—614no—
287C22×Q8—1224no—
288C22×Q8—1224no—
289C22×Q8—2441no—
290C22×Q8—2441no—
291C23×C4—612no—
292C23×C4—612no—
293C23×C4—612no—
294C23×C4—612no—
295C23×C4C22×D6112yes—
296C23×C4C22×D6111yescharacteristic
297C23×C4C22×D6111yescharacteristic
298C23×C4C22×D6111yescharacteristic
299C23×C4C22×D6112yes—
300C2×C4⋊C4—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—618no—
303C2×C4⋊C4—1224no—
304C2×C4⋊C4—1224no—
305C2×C4⋊C4—1224no—
306C2×C4⋊C4—1224no—
307C2×C4⋊C4—2442no—
308C2×C4⋊C4C4×D6114yes—
309C2×C42—1224no—
310C2×C42—1224no—
311C2×C42—1224no—
312C2×C42—2442no—
313C2×C42—2441no—
314#95—24no—
315#95—24no—
316#95—41no—
317#95—41no—
318#95—618no—
319#95—614no—
320#95—618no—
321#95—1224no—
322#95—1224no—
323#95—1224no—
324#95—1224no—
325#95—1224no—
326#95—1224no—
327#95—1224no—
328#95—2441no—
329C24C23×D6111yescharacteristic
330C2×Q8—12216no—
331C2×Q8—2444no—
332C2×Q8—2444no—
333C2×Q8—2448no—
334C2×Q8—2444no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—614no—
361C22×C4—614no—
362C22×C4—614no—
363C22×C4—614no—
364C22×C4—614no—
365C22×C4—614no—
366C22×C4—1222no—
367C22×C4—1222no—
368C22×C4—1222no—
369C22×C4—1222no—
370C22×C4—1222no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4—1222no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1222no—
378C22×C4—1222no—
379C22×C4—1222no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4—1222no—
387C22×C4—1222no—
388C22×C4C2×C4×D6112yes—
389C22×C4C2×C4×D6112yes—
390C22×C4C2×C4×D6112yes—
391C22×C4D4×D6114yes—
392C4⋊C4—44no—
393C4⋊C4—12216no—
394C4⋊C4—2448no—
395C42—2448no—
396C42—2444no—
397C23C22×C4×D6111yescharacteristic
398C23C2×D4×D6112yes—
399C23#41×D6112yes—
400C23#41×D6112yes—
401C23#1451982211yescharacteristic
402C23#1451982211yescharacteristic
403C23#1451982412yes—
404C23#1451982412yes—
405C23#1451982512yes—
406Q8—24416no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—618no—
437C2×C4—1224no—
438C2×C4—1224no—
439C2×C4—1224no—
440C2×C4—1224no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1224no—
444C2×C4—1224no—
445C2×C4—1224no—
446C2×C4—1224no—
447C2×C4—1224no—
448C2×C4—1224no—
449C2×C4—1224no—
450C2×C4—1224no—
451C2×C4—1224no—
452C2×C4—2442no—
453C2×C4—2442no—
454C2×C4—2442no—
455C2×C4—2442no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C22C4×D4×D6112yes—
465C22#1684023011yescharacteristic
466C22#1684023511yescharacteristic
467C22#1684023812yes—
468C22#1684023911yescharacteristic
469C22#1684033412yes—
470C22#1684033512yes—
471C22#1684035512yes—
472C22#1684036912yes—
473C22#1684037112yes—
474C22#1684038012yes—
475C22#1684039711yescharacteristic
476C22#1684040112yes—
477C22#1684041012yes—
478C22#1684042212yes—
479C22#1684044211yescharacteristic
480C22#1684044412yes—
481C22#1684047912yes—
482C22#1684051111yescharacteristic
483C22#1684051211yescharacteristic
484C22#1684051312yes—
485C4—42no—
486C4—42no—
487C4—42no—
488C4—44no—
489C4—82no—
490C4—1228no—
491C4—2444no—
492C4—2444no—
493C4—2444no—
494C2#2144853412yes—
495C2#2144857211yescharacteristic
496C2#2144880011yescharacteristic
497C2#2144884112yes—
498C2#2144899811yescharacteristic
499C2#2145210512yes—
500C2#2145227612yes—
501C2#2145229112yes—
502C2#2145322812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1445C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1445D61
hypocenterC61#14574
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
15. #16839682C4semidirect
285. C61#14574semidirect

Maximal subgroups

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

subgroupindex
C2×#168396822
C2×#168396662
C2×#168396442
#214440802
#214440772
#214440512
#214440502
#214440432
C61×#14452
#1457461