Finite Group Databasebeta

← #29610825

Subgroups — #29610825

Order 15616.

1138 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839682C211yesmaximal, characteristic
2#21444089C212yesmaximal
3#21444085C212yesmaximal
4#21444079C212yesmaximal
5#21444075C212yesmaximal
6#21444069C212yesmaximal
7#21444048C211yesmaximal, characteristic
8#21444044C212yesmaximal
9C61×#1441C211yesmaximal, characteristic
10C23×Dic122C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758196C2212yes—
13C22×C4×Dic61C2211yescharacteristic
14#16839682C418yescomplemented
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2211yescharacteristic
27C22×C4⋊C4×C61C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C2×#95×C61C2212yes—
30C2×#95×C61C2212yes—
31C2×#95×C61C2211yescharacteristic
32C22×Dic122—41no—
33C22×Dic122—41no—
34C22×Dic122—42no—
35C22×Dic122—42no—
36C22×Dic122C2×C414yes—
37C23×Dic61C2312yes—
38C23×Dic61C2312yes—
39C23×Dic61C2312yes—
40C23×Dic61C2312yes—
41C2×C4⋊Dic61—22no—
42C2×C4⋊Dic61—41no—
43C2×C4⋊Dic61—41no—
44C2×#11758196—42no—
45C2×#11758196—42no—
46C2×#11758196C2×C418yes—
47C2×C4×Dic61—41no—
48C2×C4×Dic61—41no—
49C2×C4×Dic61Q814yescomplemented
50#14519684—42no—
51#14519684—42no—
52#14519684—42no—
53#14519684—42no—
54#14519684—42no—
55#14519684—42no—
56#14519684—42no—
57#14519684—42no—
58#14519684—42no—
59#14519684—42no—
60#14519684C2×C418yes—
61#14519684C2×C414yes—
62C23×C4×C61C2312yes—
63C23×C4×C61C2312yes—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2311yescharacteristic
67C2×C4⋊C4×C61—41no—
68C2×C4⋊C4×C61—41no—
69C2×C4⋊C4×C61—41no—
70C2×C4⋊C4×C61—42no—
71C2×C4⋊C4×C61C2×C414yes—
72#95×C61—24no—
73#95×C61—42no—
74#95×C61—41no—
75C24×C61C2411yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—22no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—22no—
84C22×C4×C61—21no—
85C22×C4×C61—21no—
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—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×C61C22×C412yes—
103C22×C4×C61C22×C412yes—
104C22×C4×C61C22×C412yes—
105C22×C4×C61C2×Q812yes—
106C22×C4×C61#4112yes—
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×Dic61C22×C414yes—
133C22×Dic61C22×C414yes—
134C22×Dic61C2×Q814yes—
135C2×Dic122—48no—
136C2×Dic122—44no—
137C2×Dic122—48no—
138C2×Dic122—44no—
139C2×Dic122—44no—
140C4⋊C4×C61—44no—
141C4⋊C4×C61—44no—
142C4⋊Dic61—44no—
143#11758196—48no—
144C4×Dic61—44no—
145C23×C61C23×C411yescharacteristic
146C23×C61C22×Q811yescharacteristic
147C23×C61C2×#4111yescharacteristic
148C23×C61H(5,𝔽2)11yescharacteristic
149C23×C61H(5,𝔽2)11yescharacteristic
150C23×C61H(5,𝔽2)12yes—
151C23×C61H(5,𝔽2)12yes—
152C23×C61H(5,𝔽2)11yescharacteristic
153C23×C612−1+412yes—
154C23×C612−1+412yes—
155C23×C612−1+411yescharacteristic
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—24no—
163C2×C4×C61—22no—
164C2×C4×C61—22no—
165C2×C4×C61—24no—
166C2×C4×C61—42no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
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×C61—42no—
180C2×C4×C61—42no—
181C2×C4×C61—42no—
182C2×C4×C61—42no—
183C2×C4×C61—42no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61C4×Q814yes—
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—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—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—42no—
212C2×Dic61—42no—
213C2×Dic61—42no—
214C2×Dic61—42no—
215Dic122—416no—
216#14638—611nomaximal, Sylow
217C22×C61C2×C4×Q811yescharacteristic
218C22×C61#51812yes—
219C22×C61#51811yescharacteristic
220C22×C61#51912yes—
221C22×C61#52011yescharacteristic
222C22×C61#53811yescharacteristic
223C22×C61#53911yescharacteristic
224C22×C61#54212yes—
225C22×C61#54212yes—
226C22×C61#54311yescharacteristic
227C22×C61#54412yes—
228C22×C61#54411yescharacteristic
229C22×C61#54412yes—
230C22×C61#56012yes—
231C22×C61#56011yescharacteristic
232C22×C61H(3,𝔽4)11yescharacteristic
233C22×C61#56212yes—
234C22×C61#56212yes—
235C22×C61#56311yescharacteristic
236C22×C61#56311yescharacteristic
237C22×C61#56312yes—
238C22×C61#56312yes—
239C22×C61#56312yes—
240C4×C61—24no—
241C4×C61—42no—
242C4×C61—42no—
243C4×C61—82no—
244C4×C61—82no—
245Dic61—44no—
246Dic61—44no—
247Dic61—44no—
248Dic61—82no—
249C2×#395—611no—
250#1446—612no—
251#1445—612no—
252#1443—612no—
253#1442—612no—
254#1441—612no—
255#1441D6111yescharacteristic
256C4⋊#95—611no—
257#1434—612no—
258C2×C61#232911yescharacteristic
259C2×C61#233112yes—
260C2×C61#237511yescharacteristic
261C2×C61#237812yes—
262C2×C61#238111yescharacteristic
263C2×C61#283011yescharacteristic
264C2×C61#283211yescharacteristic
265C2×C61#283812yes—
266C2×C61#284112yes—
267C2×C61#284311yescharacteristic
268C2×C61#284411yescharacteristic
269C23×Q8—611no—
270C22×C4⋊C4—612no—
271C22×C4⋊C4—611no—
272C22×C4⋊C4C2×D6111yescharacteristic
273C22×C4⋊C4C2×D6111yescharacteristic
274C22×C42—611no—
275#395—618no—
276C2×#95—612no—
277C2×#95—611no—
278C2×#95—612no—
279C2×#95—612no—
280C2×#95—612no—
281C2×#95—612no—
282C2×#95—612no—
283C2×#95—612no—
284C2×#95—612no—
285C2×#95—612no—
286C2×#95—612no—
287C2×#95—612no—
288C2×#95C2×D6112yes—
289C2×#95C2×D6112yes—
290C2×#95C2×D6111yescharacteristic
291C61#1463811yescharacteristic, complemented, Sylow
292C22×Q8—614no—
293C22×Q8—2442no—
294C22×Q8—2441no—
295C22×Q8—2441no—
296C22×Q8—2442no—
297C23×C4—612no—
298C23×C4—612no—
299C23×C4—612no—
300C23×C4—612no—
301C23×C4C22×D6112yes—
302C23×C4C22×D6112yes—
303C23×C4C22×D6111yescharacteristic
304C23×C4C22×D6111yescharacteristic
305C23×C4C22×D6111yescharacteristic
306C2×C4⋊C4—41no—
307C2×C4⋊C4—41no—
308C2×C4⋊C4—41no—
309C2×C4⋊C4—42no—
310C2×C4⋊C4—618no—
311C2×C4⋊C4—1222no—
312C2×C4⋊C4—2442no—
313C2×C4⋊C4—2442no—
314C2×C4⋊C4—2441no—
315C2×C4⋊C4—2441no—
316C2×C4⋊C4C4×D6114yes—
317C2×C42—614no—
318C2×C42—2441no—
319C2×C42—2441no—
320#95—24no—
321#95—41no—
322#95—42no—
323#95—614no—
324#95—618no—
325#95—2442no—
326#95—2442no—
327#95—2442no—
328#95—2442no—
329#95—2442no—
330#95—2442no—
331#95—2442no—
332#95—2442no—
333#95—2442no—
334#95—2442no—
335C24C23×D6111yescharacteristic
336C2×Q8—2448no—
337C2×Q8—2444no—
338C2×Q8—2448no—
339C2×Q8—2444no—
340C2×Q8—2444no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—22no—
347C22×C4—21no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
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—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—22no—
367C22×C4—614no—
368C22×C4—614no—
369C22×C4—614no—
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×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4—1222no—
393C22×C4—1222no—
394C22×C4—1222no—
395C22×C4C2×C4×D6112yes—
396C22×C4C2×C4×D6112yes—
397C22×C4C2×C4×D6112yes—
398C22×C4#1175822412yes—
399C22×C4Q8×D6112yes—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—2448no—
403C4⋊C4—2444no—
404C42—2444no—
405C23C22×C4×D6111yescharacteristic
406C23C2×Q8×D6111yescharacteristic
407C23C2×#1175822411yescharacteristic
408C23#1451982212yes—
409C23#1451982211yescharacteristic
410C23#1451982211yescharacteristic
411C23#1451982312yes—
412C23#1451982311yescharacteristic
413C23#1451982412yes—
414C23#1451982411yescharacteristic
415C23#1451982512yes—
416Q8—24416no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—24no—
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—42no—
447C2×C4—1224no—
448C2×C4—1224no—
449C2×C4—1224no—
450C2×C4—1224no—
451C2×C4—1224no—
452C2×C4—1224no—
453C2×C4—1224no—
454C2×C4—1224no—
455C2×C4—1224no—
456C2×C4—2442no—
457C2×C4—2442no—
458C2×C4—2442no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2442no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4—2442no—
474C2×C4—2442no—
475C2×C4#1451974214yes—
476C22C2×#1451974211yescharacteristic
477C22#1684023412yes—
478C22#1684023511yescharacteristic
479C22#1684023812yes—
480C22#1684024211yescharacteristic
481C22#1684034911yescharacteristic
482C22#1684035711yescharacteristic
483C22#1684037912yes—
484C22#1684038512yes—
485C22#1684038711yescharacteristic
486C22#1684038912yes—
487C22#1684039111yescharacteristic
488C22#1684039212yes—
489C22#1684050012yes—
490C22#1684050211yescharacteristic
491C22#1684050511yescharacteristic
492C22#1684050912yes—
493C22#1684051012yes—
494C22#1684051111yescharacteristic
495C22#1684051211yescharacteristic
496C22#1684051312yes—
497C22#1684051312yes—
498C22#1684051412yes—
499C4—24no—
500C4—42no—
501C4—42no—
502C4—82no—
503C4—82no—
504C4—4882no—
505C4—2444no—
506C4—2444no—
507C4—2444no—
508C2#2144854911yescharacteristic
509C2#2144856612yes—
510C2#2144895711yescharacteristic
511C2#2144898412yes—
512C2#2144899811yescharacteristic
513C2#2145396611yescharacteristic
514C2#2145399011yescharacteristic
515C2#2145405012yes—
516C2#2145407512yes—
517C2#2145408911yescharacteristic
518C2#2145409011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1441D61
hypocenterC61#14638
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
14. #16839682C4semidirect
49. C2×C4×Dic61Q8semidirect
291. C61#14638semidirect

Maximal subgroups

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

subgroupindex
C2×#168396822
#214440892
#214440852
#214440792
#214440752
#214440692
#214440482
#214440442
C61×#14412
#1463861