Finite Group Databasebeta

← #29609001

Subgroups — #29609001

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444087C212yesmaximal
2#21444087C212yesmaximal
3#21444081C212yesmaximal
4#21444051C212yesmaximal
5#21444051C212yesmaximal
6#21444046C211yesmaximal, characteristic
7#21444046C211yesmaximal, characteristic
8#21444044C212yesmaximal
9C2×C61×#389C211yesmaximal, characteristic
10C22×C4×Dic61C2212yes—
11C2×#14519684C2212yes—
12C2×#14519684C2212yes—
13C2×#14519684C2212yes—
14C2×#14519684C2212yes—
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2211yescharacteristic
19C2×#14519684C2212yes—
20C2×#14519684C2211yescharacteristic
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2211yescharacteristic
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C22×C4⋊C4×C61C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2212yes—
29C22×C42×C61C2211yescharacteristic
30C61×#389C418yescomplemented
31C2×#95×C61C2212yes—
32C23×Dic61C2312yes—
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C2×C4×Dic61—24no—
37C2×C4×Dic61—42no—
38C2×C4×Dic61—42no—
39#14519684—24no—
40#14519684—24no—
41#14519684—24no—
42#14519684—24no—
43#14519684—24no—
44#14519684—24no—
45#14519684—24no—
46#14519684—41no—
47#14519684—41no—
48#14519684—42no—
49#14519684—42no—
50#14519684—41no—
51#14519684—41no—
52#14519684—42no—
53#14519684—42no—
54C23×C4×C61C2312yes—
55C23×C4×C61C2311yescharacteristic
56C23×C4×C61C2312yes—
57C23×C4×C61C2311yescharacteristic
58C23×C4×C61C2311yescharacteristic
59C2×C4⋊C4×C61—22no—
60C2×C4⋊C4×C61—22no—
61C2×C4⋊C4×C61—41no—
62C2×C4⋊C4×C61—41no—
63C2×C4⋊C4×C61—42no—
64C2×C4⋊C4×C61—42no—
65C2×C4⋊C4×C61C2×C414yes—
66C2×C4⋊C4×C61C2×C418yes—
67C2×C4⋊C4×C61C2×C414yes—
68C2×C42×C61—41no—
69C2×C42×C61—41no—
70C2×C42×C61C2×C414yes—
71#95×C61C2×C418yes—
72C24×C61C2411yescharacteristic
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
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—22no—
91C22×C4×C61—22no—
92C22×C4×C61—22no—
93C22×C4×C61—22no—
94C22×C4×C61—22no—
95C22×C4×C61—22no—
96C22×C4×C61—22no—
97C22×C4×C61C22×C412yes—
98C22×C4×C61C22×C414yes—
99C22×C4×C61C22×C414yes—
100C22×C4×C61C22×C412yes—
101C22×C4×C61C22×C412yes—
102C22×C4×C61#4112yes—
103C22×C4×C61#4112yes—
104C22×Dic61—22no—
105C22×Dic61—22no—
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#4114yes—
131C22×Dic61#4114yes—
132C4⋊C4×C61—28no—
133C4⋊C4×C61—44no—
134C4⋊C4×C61—48no—
135C42×C61—44no—
136C4×Dic61—48no—
137C23×C61C23×C411yescharacteristic
138C23×C61C2×#4111yescharacteristic
139C23×C61C2×#4111yescharacteristic
140C23×C61C2×#4112yes—
141C23×C61C2×#4112yes—
142C23×C61H(5,𝔽2)11yescharacteristic
143C23×C61H(5,𝔽2)12yes—
144C23×C61H(5,𝔽2)11yescharacteristic
145C23×C612−1+411yescharacteristic
146C23×C612−1+411yescharacteristic
147C23×C612−1+412yes—
148C2×C4×C61—22no—
149C2×C4×C61—22no—
150C2×C4×C61—22no—
151C2×C4×C61—22no—
152C2×C4×C61—22no—
153C2×C4×C61—22no—
154C2×C4×C61—24no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—24no—
158C2×C4×C61—24no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—24no—
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—42no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
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#11714yes—
179C2×Dic61—24no—
180C2×Dic61—24no—
181C2×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—42no—
186C2×Dic61—42no—
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—
207#14490—611nomaximal, Sylow
208C22×C61C2×#11711yescharacteristic
209C22×C61C4×#4111yescharacteristic
210C22×C61C4×#4111yescharacteristic
211C22×C61#51811yescharacteristic
212C22×C61#51811yescharacteristic
213C22×C61#51911yescharacteristic
214C22×C61#51911yescharacteristic
215C22×C61#53812yes—
216C22×C61#53912yes—
217C22×C61#53911yescharacteristic
218C22×C61#53911yescharacteristic
219C22×C61#53911yescharacteristic
220C22×C61#53911yescharacteristic
221C22×C61#54012yes—
222C22×C61#54212yes—
223C22×C61#55212yes—
224C22×C61#55212yes—
225C22×C61#55212yes—
226C22×C61#55312yes—
227C22×C61#55612yes—
228C22×C61#55912yes—
229C22×C61#56312yes—
230C22×C61#56312yes—
231C4×C61—24no—
232C4×C61—42no—
233C4×C61—42no—
234C4×C61—44no—
235C4×C61—44no—
236Dic61—44no—
237Dic61—44no—
238Dic61—82no—
239Dic61—82no—
240C2×#389D6111yescharacteristic
241#1445—612no—
242#1445—612no—
243#1443—612no—
244#1436—612no—
245#1436—612no—
246#1434—611no—
247#1434—611no—
248#1434—612no—
249C2×C61#231311yescharacteristic
250C2×C61#233211yescharacteristic
251C2×C61#233311yescharacteristic
252C2×C61#235611yescharacteristic
253C2×C61#235711yescharacteristic
254C2×C61#237111yescharacteristic
255C2×C61#238111yescharacteristic
256C2×C61#277112yes—
257C2×C61#277312yes—
258C2×C61#277712yes—
259C2×C61#278712yes—
260C22×C4⋊C4C2×D6111yescharacteristic
261C22×C4⋊C4C2×D6111yescharacteristic
262C22×C4⋊C4C2×D6112yes—
263C22×C42—612no—
264C22×C42C2×D6111yescharacteristic
265#389Dic6118yescomplemented
266C2×#95—612no—
267C2×#95—612no—
268C2×#95—612no—
269C2×#95—612no—
270C2×#95—612no—
271C2×#95—612no—
272C2×#95—612no—
273C2×#95—611no—
274C2×#95—611no—
275C2×#95—611no—
276C2×#95—612no—
277C2×#95—611no—
278C2×#95—612no—
279C2×#95—612no—
280C2×#95—612no—
281C2×#95C2×D6112yes—
282C61#1449011yescharacteristic, complemented, Sylow
283C23×C4—612no—
284C23×C4—612no—
285C23×C4—612no—
286C23×C4—612no—
287C23×C4C22×D6112yes—
288C23×C4C22×D6111yescharacteristic
289C23×C4C22×D6112yes—
290C23×C4C22×D6111yescharacteristic
291C23×C4C22×D6111yescharacteristic
292C2×C4⋊C4—22no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—41no—
295C2×C4⋊C4—41no—
296C2×C4⋊C4—42no—
297C2×C4⋊C4—42no—
298C2×C4⋊C4C2×Dic6114yes—
299C2×C4⋊C4C2×Dic6118yes—
300C2×C4⋊C4C2×Dic6114yes—
301C2×C42—41no—
302C2×C42—41no—
303C2×C42—1224no—
304C2×C42—2442no—
305C2×C42—2442no—
306C2×C42C2×Dic6114yes—
307#95—1224no—
308#95—1224no—
309#95—1224no—
310#95—1224no—
311#95—1224no—
312#95—1224no—
313#95—1224no—
314#95—2441no—
315#95—2441no—
316#95—2441no—
317#95—2441no—
318#95—2442no—
319#95—2442no—
320#95—2442no—
321#95—2442no—
322#95C2×Dic6118yes—
323C24C23×D6111yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—614no—
349C22×C4—614no—
350C22×C4—1222no—
351C22×C4—1222no—
352C22×C4—1222no—
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#1175822212yes—
377C22×C4#1175822212yes—
378C22×C4C22×Dic6112yes—
379C22×C4C22×Dic6114yes—
380C22×C4C22×Dic6114yes—
381C22×C4C22×Dic6112yes—
382C22×C4C22×Dic6112yes—
383C4⋊C4—28no—
384C4⋊C4—44no—
385C4⋊C4—48no—
386C42—44no—
387C42—2448no—
388C23C23×Dic6111yescharacteristic
389C23#41×D6112yes—
390C23#41×D6112yes—
391C23C2×#1175822211yescharacteristic
392C23C2×#1175822211yescharacteristic
393C23#1451982212yes—
394C23#1451982211yescharacteristic
395C23#1451982211yescharacteristic
396C23#1451982512yes—
397C23#1451982511yescharacteristic
398C23#1451982511yescharacteristic
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—1224no—
430C2×C4—1224no—
431C2×C4—1224no—
432C2×C4—1224no—
433C2×C4—1224no—
434C2×C4—1224no—
435C2×C4—2442no—
436C2×C4—2442no—
437C2×C4—2442no—
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#1451973614yes—
458C22C2×#1451973611yescharacteristic
459C22#41×Dic6111yescharacteristic
460C22#41×Dic6111yescharacteristic
461C22#1684023711yescharacteristic
462C22#1684023711yescharacteristic
463C22#1684024011yescharacteristic
464C22#1684024011yescharacteristic
465C22#1684034412yes—
466C22#1684035812yes—
467C22#1684035911yescharacteristic
468C22#1684035911yescharacteristic
469C22#1684035911yescharacteristic
470C22#1684035911yescharacteristic
471C22#1684036212yes—
472C22#1684038212yes—
473C22#1684044412yes—
474C22#1684044412yes—
475C22#1684045312yes—
476C22#1684046212yes—
477C22#1684048412yes—
478C22#1684049512yes—
479C22#1684051112yes—
480C22#1684051112yes—
481C4—24no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—44no—
486C4—4882no—
487C4—4882no—
488C4—2444no—
489C4—2444no—
490C2#2144842211yescharacteristic
491C2#2144857711yescharacteristic
492C2#2144858611yescharacteristic
493C2#2144878411yescharacteristic
494C2#2144879211yescharacteristic
495C2#2144892511yescharacteristic
496C2#2144900011yescharacteristic
497C2#2145333312yes—
498C2#2145335712yes—
499C2#2145342312yes—
500C2#2145354512yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC2×C61×#389C2
socle, prime radical, cosocleC24×C61C24
hypercenterC2×#389D61
hypocenterC61#14490
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
30. C61×#389C4semidirect
265. #389Dic61semidirect
282. C61#14490semidirect

Maximal subgroups

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

subgroupindex
#214440872
#214440812
#214440512
#214440462
#214440442
C2×C61×#3892
#1449061