Finite Group Databasebeta

← #29645565

Subgroups — #29645565

Order 15616.

1122 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444089C211yesmaximal, characteristic
2#21444089C212yesmaximal
3#21444085C212yesmaximal
4#21444083C211yesmaximal, characteristic
5#21444072C212yesmaximal
6#21444070C212yesmaximal
7#21444069C212yesmaximal
8#21444069C212yesmaximal
9C61×#1444C211yesmaximal, characteristic
10C23×Dic122C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758196C2212yes—
13C22×#11758196C2212yes—
14C2×#14519684C2211yescharacteristic
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2211yescharacteristic
26C22×C4⋊C4×C61C2212yes—
27C22×C4⋊C4×C61C2211yescharacteristic
28C2×#95×C61C2211yescharacteristic
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C22×Dic122—42no—
32C22×Dic122—41no—
33C22×Dic122—42no—
34C22×Dic122—41no—
35C22×Dic122Q814yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C23×Dic61C2312yes—
39C23×Dic61C2312yes—
40C2×C4⋊Dic61—41no—
41C2×C4⋊Dic61—42no—
42C2×#11758196—24no—
43C2×#11758196—42no—
44C2×#11758196—42no—
45C2×#11758196—42no—
46C2×#11758196—42no—
47C2×#11758196Q818yescomplemented
48#14519684—22no—
49#14519684—42no—
50#14519684—42no—
51#14519684—42no—
52#14519684—42no—
53#14519684—42no—
54#14519684—42no—
55#14519684—42no—
56#14519684—42no—
57#14519684—41no—
58#14519684—42no—
59#14519684—42no—
60C23×C4×C61C2312yes—
61C23×C4×C61C2312yes—
62C23×C4×C61C2311yescharacteristic
63C23×C4×C61C2311yescharacteristic
64C23×C4×C61C2311yescharacteristic
65C2×C4⋊C4×C61—24no—
66C2×C4⋊C4×C61—42no—
67C2×C4⋊C4×C61—42no—
68C2×C4⋊C4×C61—41no—
69C2×C4⋊C4×C61—42no—
70#95×C61—22no—
71#95×C61—41no—
72#95×C61—42no—
73C24×C61C2411yescharacteristic
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—22no—
77C22×C4×C61—21no—
78C22×C4×C61—22no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
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—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×C61C2×Q812yes—
100C22×C4×C61C2×Q814yes—
101C22×C4×C61#4112yes—
102C22×C4×C61#4112yes—
103C22×Dic61—22no—
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×Dic61C2×Q814yes—
129C22×Dic61C2×Q814yes—
130C22×Dic61C2×Q814yes—
131C2×Dic122—48no—
132C2×Dic122—44no—
133C2×Dic122—44no—
134C2×Dic122—44no—
135C2×Dic122—48no—
136C4⋊C4×C61—48no—
137C4⋊C4×C61—44no—
138C4⋊Dic61—44no—
139#11758196—48no—
140#11758196—48no—
141C23×C61C22×Q811yescharacteristic
142C23×C61C22×Q812yes—
143C23×C61C2×#4111yescharacteristic
144C23×C61C2×#4111yescharacteristic
145C23×C61H(5,𝔽2)12yes—
146C23×C61H(5,𝔽2)12yes—
147C23×C61H(5,𝔽2)12yes—
148C23×C61H(5,𝔽2)11yescharacteristic
149C23×C61H(5,𝔽2)11yescharacteristic
150C23×C612−1+411yescharacteristic
151C23×C612−1+411yescharacteristic
152C2×C4×C61—24no—
153C2×C4×C61—24no—
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—24no—
157C2×C4×C61—24no—
158C2×C4×C61—22no—
159C2×C4×C61—24no—
160C2×C4×C61—24no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—42no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—42no—
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×Dic61—24no—
182C2×Dic61—24no—
183C2×Dic61—24no—
184C2×Dic61—24no—
185C2×Dic61—24no—
186C2×Dic61—24no—
187C2×Dic61—24no—
188C2×Dic61—24no—
189C2×Dic61—24no—
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—
209Dic122—416no—
210#17306—611nomaximal, Sylow
211C22×C61#53812yes—
212C22×C61#53812yes—
213C22×C61#53911yescharacteristic
214C22×C61#53911yescharacteristic
215C22×C61#54312yes—
216C22×C61#54312yes—
217C22×C61#54311yescharacteristic
218C22×C61#54412yes—
219C22×C61#54412yes—
220C22×C61#55412yes—
221C22×C61#55412yes—
222C22×C61#55511yescharacteristic
223C22×C61#55711yescharacteristic
224C22×C61#55711yescharacteristic
225C22×C61Q8211yescharacteristic
226C22×C61Q8212yes—
227C22×C61#56011yescharacteristic
228C22×C61#56011yescharacteristic
229C22×C61#56012yes—
230C22×C61H(3,𝔽4)11yescharacteristic
231C22×C61#56212yes—
232C22×C61#56212yes—
233C22×C61#56311yescharacteristic
234C4×C61—42no—
235C4×C61—42no—
236C4×C61—42no—
237C4×C61—44no—
238C4×C61—82no—
239Dic61—44no—
240Dic61—44no—
241Dic61—44no—
242Dic61—82no—
243#1446—612no—
244#1446—611no—
245#1445—612no—
246#1444—611no—
247#1444D6111yescharacteristic
248#1441—612no—
249#1441—612no—
250#1441—612no—
251#1441—612no—
252C2×C61#278412yes—
253C2×C61#279211yescharacteristic
254C2×C61#279211yescharacteristic
255C2×C61#280612yes—
256C2×C61#280612yes—
257C2×C61#280911yescharacteristic
258C2×C61#281111yescharacteristic
259C2×C61#282411yescharacteristic
260C2×C61#282411yescharacteristic
261C2×C61#284112yes—
262C2×C61#284211yescharacteristic
263C23×Q8—611no—
264C22×C4⋊C4—612no—
265C22×C4⋊C4—612no—
266C22×C4⋊C4—611no—
267C22×C4⋊C4C2×D6112yes—
268C22×C4⋊C4C2×D6111yescharacteristic
269C2×#95—611no—
270C2×#95—612no—
271C2×#95—612no—
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×D6111yescharacteristic
282C2×#95C2×D6111yescharacteristic
283C2×#95C2×D6112yes—
284C61#1730611yescharacteristic, complemented, Sylow
285C22×Q8—614no—
286C22×Q8—2442no—
287C22×Q8—2441no—
288C22×Q8—2442no—
289C22×Q8—2441no—
290C23×C4—612no—
291C23×C4—612no—
292C23×C4—612no—
293C23×C4—612no—
294C23×C4C22×D6112yes—
295C23×C4C22×D6111yescharacteristic
296C23×C4C22×D6111yescharacteristic
297C23×C4C22×D6112yes—
298C23×C4C22×D6111yescharacteristic
299C2×C4⋊C4—24no—
300C2×C4⋊C4—42no—
301C2×C4⋊C4—42no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4—618no—
305C2×C4⋊C4—1224no—
306C2×C4⋊C4—2442no—
307C2×C4⋊C4—2442no—
308C2×C4⋊C4—2442no—
309C2×C4⋊C4—2442no—
310C2×C4⋊C4—2441no—
311C2×C4⋊C4—2442no—
312#95—22no—
313#95—41no—
314#95—42no—
315#95—1222no—
316#95—2442no—
317#95—2442no—
318#95—2442no—
319#95—2442no—
320#95—2442no—
321#95—2441no—
322#95—2442no—
323#95—2442no—
324#95—2442no—
325#95—2442no—
326#95—2442no—
327C24C23×D6111yescharacteristic
328C2×Q8—2448no—
329C2×Q8—2444no—
330C2×Q8—2444no—
331C2×Q8—2444no—
332C2×Q8—2448no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
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—21no—
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—614no—
359C22×C4—614no—
360C22×C4—614no—
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×C4—1222no—
380C22×C4—1222no—
381C22×C4—1222no—
382C22×C4—1222no—
383C22×C4—1222no—
384C22×C4—1222no—
385C22×C4—1222no—
386C22×C4#1175822212yes—
387C22×C4#1175822412yes—
388C22×C4Q8×D6114yes—
389C22×C4Q8×D6112yes—
390C4⋊C4—48no—
391C4⋊C4—44no—
392C4⋊C4—2448no—
393C4⋊C4—2448no—
394C4⋊C4—2444no—
395C23C2×Q8×D6112yes—
396C23C2×Q8×D6111yescharacteristic
397C23C2×#1175822411yescharacteristic
398C23C2×#1175822211yescharacteristic
399C23#1451982212yes—
400C23#1451982211yescharacteristic
401C23#1451982212yes—
402C23#1451982312yes—
403C23#1451982311yescharacteristic
404C23#1451982411yescharacteristic
405C23#1451982511yescharacteristic
406Q8—24416no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—42no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—1224no—
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—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×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C22#1684034512yes—
465C22#1684034712yes—
466C22#1684035711yescharacteristic
467C22#1684035911yescharacteristic
468C22#1684038712yes—
469C22#1684038711yescharacteristic
470C22#1684038712yes—
471C22#1684038912yes—
472C22#1684039212yes—
473C22#1684046712yes—
474C22#1684047012yes—
475C22#1684047711yescharacteristic
476C22#1684048711yescharacteristic
477C22#1684049011yescharacteristic
478C22#1684049211yescharacteristic
479C22#1684049212yes—
480C22#1684049911yescharacteristic
481C22#1684050211yescharacteristic
482C22#1684050212yes—
483C22#1684050511yescharacteristic
484C22#1684050712yes—
485C22#1684050812yes—
486C22#1684051611yescharacteristic
487C4—42no—
488C4—42no—
489C4—42no—
490C4—44no—
491C4—82no—
492C4—4882no—
493C4—2444no—
494C4—2444no—
495C4—2444no—
496C2#2145351812yes—
497C2#2145361511yescharacteristic
498C2#2145361911yescharacteristic
499C2#2145377612yes—
500C2#2145378212yes—
501C2#2145380411yescharacteristic
502C2#2145381111yescharacteristic
503C2#2145389911yescharacteristic
504C2#2145390111yescharacteristic
505C2#2145407712yes—
506C2#2145408411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, prime radical, cosocleC24×C61C24
FittingC61×#1444C2
hypercenter#1444D61
hypocenterC61#17306
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1444

Complements

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

NH ≅ G/Ntype
47. C2×#11758196Q8semidirect
284. C61#17306semidirect

Maximal subgroups

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

subgroupindex
#214440892
#214440852
#214440832
#214440722
#214440702
#214440692
C61×#14442
#1730661