Finite Group Databasebeta

← #29608806

Subgroups — #29608806

Order 15616.

1398 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839648C212yesmaximal
2#21444087C212yesmaximal
3#21444087C212yesmaximal
4#21444072C212yesmaximal
5#21444051C212yesmaximal
6#21444048C212yesmaximal
7#21444046C211yesmaximal, characteristic
8#21444046C211yesmaximal, characteristic
9C22×#125×C61C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C4×Dic61C2212yes—
12#16839648—28no—
13C2×#14519684C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2211yescharacteristic
24C2×#14519684C2211yescharacteristic
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#125×C61—28no—
28C2×#125×C61C418yescomplemented
29C22×C4⋊C4×C61C2212yes—
30C22×C4⋊C4×C61C2212yes—
31C22×C4⋊C4×C61C2211yescharacteristic
32C22×C4⋊C4×C61C2211yescharacteristic
33C22×C42×C61C2211yescharacteristic
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C2×C4⋊Dic61—24no—
39C2×C4⋊Dic61—24no—
40C2×C4⋊Dic61—42no—
41C2×C4×Dic61—24no—
42C2×C4×Dic61—24no—
43C2×C4×Dic61—42no—
44#14519684—24no—
45#14519684—24no—
46#14519684—24no—
47#14519684—24no—
48#14519684—24no—
49#14519684—24no—
50#14519684—24no—
51#14519684—24no—
52#14519684—41no—
53#14519684—42no—
54#14519684—41no—
55#14519684—41no—
56#14519684—42no—
57#14519684—41no—
58C23×C4×C61C2311yescharacteristic
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2312yes—
61C23×C4×C61C2312yes—
62C23×C4×C61C2311yescharacteristic
63#125×C61—232no—
64C2×C4⋊C4×C61—24no—
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—24no—
67C2×C4⋊C4×C61—24no—
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61C2×C418yes—
70C2×C4⋊C4×C61C2×C418yes—
71C2×C4⋊C4×C61C2×C414yes—
72C2×C4⋊C4×C61C2×C414yes—
73C2×C4⋊C4×C61D418yes—
74C2×C42×C61—24no—
75C2×C42×C61C2×C414yes—
76C24×C61C2411yescharacteristic
77C22×C4×C61—22no—
78C22×C4×C61—22no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—22no—
88C22×C4×C61—22no—
89C22×C4×C61—22no—
90C22×C4×C61—22no—
91C22×C4×C61—22no—
92C22×C4×C61—21no—
93C22×C4×C61—21no—
94C22×C4×C61—22no—
95C22×C4×C61—21no—
96C22×C4×C61—21no—
97C22×C4×C61—22no—
98C22×C4×C61C22×C412yes—
99C22×C4×C61C22×C412yes—
100C22×C4×C61C22×C414yes—
101C22×C4×C61C22×C412yes—
102C22×C4×C61C22×C414yes—
103C22×C4×C61C2×D414yes—
104C22×C4×C61C2×D414yes—
105C22×C4×C61C2×D414yes—
106C22×Dic61—22no—
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×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61#4114yes—
133C22×Dic61#4114yes—
134C4⋊C4×C61—216no—
135C4⋊C4×C61—216no—
136C4⋊C4×C61—28no—
137C4⋊C4×C61C22⋊C4116yes—
138C42×C61—28no—
139C4⋊Dic61—48no—
140C4×Dic61—48no—
141C23×C61C23×C411yescharacteristic
142C23×C61C22×D412yes—
143C23×C61C2×#4112yes—
144C23×C61C2×#4112yes—
145C23×C61H(5,𝔽2)11yescharacteristic
146C23×C61H(5,𝔽2)11yescharacteristic
147C23×C612−1+412yes—
148C23×C612−1+411yescharacteristic
149C23×C612−1+411yescharacteristic
150C23×C612−1+411yescharacteristic
151C23×C612−1+411yescharacteristic
152C2×C4×C61—24no—
153C2×C4×C61—22no—
154C2×C4×C61—22no—
155C2×C4×C61—24no—
156C2×C4×C61—24no—
157C2×C4×C61—24no—
158C2×C4×C61—24no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—22no—
169C2×C4×C61—22no—
170C2×C4×C61—24no—
171C2×C4×C61—42no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61C2×C22⋊C414yes—
180C2×C4×C61C2×C22⋊C418yes—
181C2×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—42no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—42no—
193C2×Dic61—42no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
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—
209#14474—611nomaximal, Sylow
210C22×C61C22×C22⋊C411yescharacteristic
211C22×C61C4×#4111yescharacteristic
212C22×C61C4×#4111yescharacteristic
213C22×C61#51911yescharacteristic
214C22×C61#51911yescharacteristic
215C22×C61#52011yescharacteristic
216C22×C61#52011yescharacteristic
217C22×C61#53612yes—
218C22×C61#53612yes—
219C22×C61#53912yes—
220C22×C61#53912yes—
221C22×C61#54112yes—
222C22×C61#54112yes—
223C22×C61#54612yes—
224C22×C61#54712yes—
225C22×C61#54812yes—
226C22×C61#55012yes—
227C22×C61#55212yes—
228C22×C61#55212yes—
229C22×C61#56211yescharacteristic
230C22×C61#56311yescharacteristic
231C22×C61#56311yescharacteristic
232C22×C61#56411yescharacteristic
233C4×C61—24no—
234C4×C61—28no—
235C4×C61—42no—
236C4×C61—42no—
237C4×C61—44no—
238Dic61—44no—
239Dic61—44no—
240Dic61—82no—
241Dic61—82no—
242C22×#125D6111yescharacteristic
243C2×#387—612no—
244#1445—612no—
245#1445—612no—
246#1441—612no—
247#1436—612no—
248C4⋊#95—612no—
249#1434—611no—
250#1434—611no—
251C2×C61#231011yescharacteristic
252C2×C61#233611yescharacteristic
253C2×C61#233611yescharacteristic
254C2×C61#233911yescharacteristic
255C2×C61#234111yescharacteristic
256C2×C61#237111yescharacteristic
257C2×C61#238211yescharacteristic
258C2×C61#269012yes—
259C2×C61#269412yes—
260C2×C61#271912yes—
261C2×C61#272112yes—
262C2×#125—28no—
263C2×#125Dic6118yescomplemented
264C22×C4⋊C4—612no—
265C22×C4⋊C4C2×D6112yes—
266C22×C4⋊C4C2×D6112yes—
267C22×C4⋊C4C2×D6111yescharacteristic
268C22×C4⋊C4C2×D6111yescharacteristic
269C22×C42—612no—
270C22×C42C2×D6111yescharacteristic
271#387—1228no—
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×#95—611no—
282C2×#95—611no—
283C2×#95—611no—
284C2×#95—612no—
285C2×#95—612no—
286C61#1447411yescharacteristic, complemented, Sylow
287C23×C4—612no—
288C23×C4—612no—
289C23×C4—612no—
290C23×C4—612no—
291C23×C4C22×D6112yes—
292C23×C4C22×D6111yescharacteristic
293C23×C4C22×D6111yescharacteristic
294C23×C4C22×D6112yes—
295C23×C4C22×D6111yescharacteristic
296#125—232no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—24no—
300C2×C4⋊C4—24no—
301C2×C4⋊C4—24no—
302C2×C4⋊C4—1224no—
303C2×C4⋊C4—1224no—
304C2×C4⋊C4—2442no—
305C2×C4⋊C4C2×Dic6118yes—
306C2×C4⋊C4C2×Dic6118yes—
307C2×C4⋊C4C2×Dic6114yes—
308C2×C4⋊C4C2×Dic6114yes—
309C2×C4⋊C4C22⋊D6118yes—
310C2×C42—24no—
311C2×C42—1224no—
312C2×C42—1224no—
313C2×C42—2442no—
314C2×C42C2×Dic6114yes—
315#95—1224no—
316#95—1224no—
317#95—1224no—
318#95—1224no—
319#95—1224no—
320#95—1224no—
321#95—1224no—
322#95—1224no—
323#95—2441no—
324#95—2442no—
325#95—2441no—
326#95—2441no—
327#95—2442no—
328#95—2441no—
329C24C23×D6111yescharacteristic
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—614no—
352C22×C4—614no—
353C22×C4—1222no—
354C22×C4—1222no—
355C22×C4—1222no—
356C22×C4—1222no—
357C22×C4—1222no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1222no—
363C22×C4—1222no—
364C22×C4—1222no—
365C22×C4—1222no—
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×C4C22×Dic6112yes—
380C22×C4C22×Dic6112yes—
381C22×C4C22×Dic6114yes—
382C22×C4C22×Dic6112yes—
383C22×C4C22×Dic6114yes—
384C22×C4C2×C22⋊D6114yes—
385C22×C4C2×C22⋊D6114yes—
386C22×C4C2×C22⋊D6114yes—
387C4⋊C4—216no—
388C4⋊C4—216no—
389C4⋊C4—28no—
390C4⋊C4—2448no—
391C4⋊C4C22⋊Dic61116yes—
392C42—28no—
393C42—2448no—
394C23C23×Dic6111yescharacteristic
395C23C22×C22⋊D6112yes—
396C23#41×D6112yes—
397C23#41×D6112yes—
398C23#1451982311yescharacteristic
399C23#1451982311yescharacteristic
400C23#1451982411yescharacteristic
401C23#1451982411yescharacteristic
402C23#1451982511yescharacteristic
403C23#1451982511yescharacteristic
404C23#1451982512yes—
405C2×C4—24no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—1224no—
436C2×C4—1224no—
437C2×C4—1224no—
438C2×C4—2442no—
439C2×C4—2442no—
440C2×C4—2442no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4—2442no—
451C2×C4—2442no—
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×C4C2×C22⋊Dic6114yes—
461C2×C4C2×C22⋊Dic6118yes—
462C22C22×C22⋊Dic6111yescharacteristic
463C22#41×Dic6111yescharacteristic
464C22#41×Dic6111yescharacteristic
465C22#1684024011yescharacteristic
466C22#1684024011yescharacteristic
467C22#1684024511yescharacteristic
468C22#1684024511yescharacteristic
469C22#1684033612yes—
470C22#1684033612yes—
471C22#1684036012yes—
472C22#1684036012yes—
473C22#1684037112yes—
474C22#1684037112yes—
475C22#1684040012yes—
476C22#1684041112yes—
477C22#1684041912yes—
478C22#1684043112yes—
479C22#1684044412yes—
480C22#1684044412yes—
481C22#1684051011yescharacteristic
482C22#1684051611yescharacteristic
483C22#1684051611yescharacteristic
484C22C61⋊#56411yescharacteristic
485C4—28no—
486C4—24no—
487C4—42no—
488C4—42no—
489C4—44no—
490C4—4882no—
491C4—4882no—
492C4—2444no—
493C4—2444no—
494C2#2144840511yescharacteristic
495C2#2144862511yescharacteristic
496C2#2144862511yescharacteristic
497C2#2144864911yescharacteristic
498C2#2144866011yescharacteristic
499C2#2144892511yescharacteristic
500C2#2144900511yescharacteristic
501C2#2145227912yes—
502C2#2145233312yes—
503C2#2145267812yes—
504C2#2145270812yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC22×#125×C61C2
socle, prime radical, cosocleC24×C61C24
hypercenterC22×#125D61
hypocenterC61#14474
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
28. C2×#125×C61C4semidirect
263. C2×#125Dic61semidirect
286. C61#14474semidirect

Maximal subgroups

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

subgroupindex
C2×#168396482
#214440872
#214440722
#214440512
#214440482
#214440462
C22×#125×C612
#1447461