Finite Group Databasebeta

← #29645555

Subgroups — #29645555

Order 15616.

970 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21444083C211yesmaximal, characteristic
2#21444080C212yesmaximal
3#21444075C212yesmaximal
4#21444075C211yesmaximal, characteristic
5#21444075C212yesmaximal
6#21444073C212yesmaximal
7#21444072C212yesmaximal
8#21444071C212yesmaximal
9C61×#1445C211yesmaximal, characteristic
10C22×C4⋊Dic61C2212yes—
11C22×C4⋊Dic61C2211yescharacteristic
12C22×C4⋊Dic61C2211yescharacteristic
13C22×#11758196C2212yes—
14C2×#14519684C2211yescharacteristic
15C2×#14519684C2212yes—
16C2×#14519684C2212yes—
17C2×#14519684C2212yes—
18C2×#14519684C2211yescharacteristic
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C22×C4⋊C4×C61C2211yescharacteristic
27C2×#95×C61C2212yes—
28C2×#95×C61C2212yes—
29C2×#95×C61C2211yescharacteristic
30C2×#95×C61C2211yescharacteristic
31C23×Dic61C2312yes—
32C23×Dic61C2312yes—
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C2×C4⋊Dic61—24no—
36C2×C4⋊Dic61—42no—
37C2×C4⋊Dic61—42no—
38C2×C4⋊Dic61—41no—
39C2×C4⋊Dic61—41no—
40C2×C4⋊Dic61—42no—
41C2×C4⋊Dic61—42no—
42C2×#11758196—24no—
43C2×#11758196—42no—
44C2×#11758196—42no—
45#14519684—22no—
46#14519684—24no—
47#14519684—22no—
48#14519684—24no—
49#14519684—24no—
50#14519684—42no—
51#14519684—42no—
52#14519684—42no—
53#14519684—42no—
54#14519684—42no—
55#14519684—42no—
56#14519684—42no—
57C23×C4×C61C2312yes—
58C23×C4×C61C2312yes—
59C23×C4×C61C2311yescharacteristic
60C23×C4×C61C2311yescharacteristic
61C23×C4×C61C2311yescharacteristic
62C2×C4⋊C4×C61—41no—
63C2×C4⋊C4×C61—41no—
64C2×C4⋊C4×C61Q814yes—
65#95×C61—41no—
66#95×C61—41no—
67#95×C61—42no—
68#95×C61—42no—
69C24×C61C2411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—21no—
73C22×C4×C61—21no—
74C22×C4×C61—22no—
75C22×C4×C61—22no—
76C22×C4×C61—21no—
77C22×C4×C61—22no—
78C22×C4×C61—21no—
79C22×C4×C61—22no—
80C22×C4×C61—22no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—21no—
85C22×C4×C61—22no—
86C22×C4×C61—21no—
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×C61C2×Q812yes—
96C22×C4×C61C2×Q814yes—
97C22×C4×C61#4112yes—
98C22×C4×C61#4112yes—
99C22×Dic61—22no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—22no—
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#4114yes—
127C4⋊C4×C61—44no—
128C4⋊Dic61—48no—
129C4⋊Dic61—44no—
130C4⋊Dic61—44no—
131#11758196—48no—
132C23×C61C22×Q811yescharacteristic
133C23×C61C2×#4111yescharacteristic
134C23×C61C2×#4112yes—
135C23×C61C2×#4111yescharacteristic
136C23×C61H(5,𝔽2)12yes—
137C23×C61H(5,𝔽2)11yescharacteristic
138C23×C61H(5,𝔽2)12yes—
139C23×C61H(5,𝔽2)11yescharacteristic
140C23×C612−1+411yescharacteristic
141C23×C612−1+412yes—
142C23×C612−1+411yescharacteristic
143C2×C4×C61—24no—
144C2×C4×C61—22no—
145C2×C4×C61—24no—
146C2×C4×C61—22no—
147C2×C4×C61—22no—
148C2×C4×C61—24no—
149C2×C4×C61—24no—
150C2×C4×C61—24no—
151C2×C4×C61—24no—
152C2×C4×C61—42no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—41no—
156C2×C4×C61—41no—
157C2×C4×C61—41no—
158C2×C4×C61—41no—
159C2×C4×C61—42no—
160C2×C4×C61—42no—
161C2×C4×C61—42no—
162C2×C4×C61—42no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—42no—
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×Dic61—24no—
173C2×Dic61—24no—
174C2×Dic61—24no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
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—
200#17304—611nomaximal, Sylow
201C22×C61#53812yes—
202C22×C61#53812yes—
203C22×C61#53911yescharacteristic
204C22×C61#53912yes—
205C22×C61#53911yescharacteristic
206C22×C61#54112yes—
207C22×C61#54212yes—
208C22×C61#54311yescharacteristic
209C22×C61#54412yes—
210C22×C61#55212yes—
211C22×C61#55312yes—
212C22×C61#55412yes—
213C22×C61#55511yescharacteristic
214C22×C61#55511yescharacteristic
215C22×C61#55711yescharacteristic
216C22×C61#55711yescharacteristic
217C22×C61#56011yescharacteristic
218C22×C61#56011yescharacteristic
219C22×C61#56212yes—
220C22×C61#56212yes—
221C22×C61#56311yescharacteristic
222C22×C61#56312yes—
223C22×C61#56311yescharacteristic
224C4×C61—42no—
225C4×C61—42no—
226C4×C61—42no—
227C4×C61—44no—
228C4×C61—82no—
229Dic61—44no—
230Dic61—82no—
231Dic61—82no—
232Dic61—82no—
233#1445D6111yescharacteristic
234#1444—611no—
235#1443—612no—
236#1442—612no—
237#1442—611no—
238#1442—612no—
239#1441—612no—
240#1441—612no—
241#1441—612no—
242C2×C61#276911yescharacteristic
243C2×C61#277412yes—
244C2×C61#278112yes—
245C2×C61#278411yescharacteristic
246C2×C61#279511yescharacteristic
247C2×C61#280212yes—
248C2×C61#280911yescharacteristic
249C2×C61#282611yescharacteristic
250C2×C61#283112yes—
251C2×C61#283411yescharacteristic
252C2×C61#284111yescharacteristic
253C22×C4⋊C4—612no—
254C22×C4⋊C4—612no—
255C22×C4⋊C4—611no—
256C22×C4⋊C4—611no—
257C22×C4⋊C4C2×D6111yescharacteristic
258C2×#95—612no—
259C2×#95—611no—
260C2×#95—612no—
261C2×#95—612no—
262C2×#95—611no—
263C2×#95—612no—
264C2×#95—612no—
265C2×#95—612no—
266C2×#95—612no—
267C2×#95—612no—
268C2×#95—612no—
269C2×#95—612no—
270C2×#95C2×D6112yes—
271C2×#95C2×D6112yes—
272C2×#95C2×D6111yescharacteristic
273C2×#95C2×D6111yescharacteristic
274C61#1730411yescharacteristic, complemented, Sylow
275C23×C4—612no—
276C23×C4—612no—
277C23×C4—612no—
278C23×C4—612no—
279C23×C4C22×D6112yes—
280C23×C4C22×D6112yes—
281C23×C4C22×D6111yescharacteristic
282C23×C4C22×D6111yescharacteristic
283C23×C4C22×D6111yescharacteristic
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—1224no—
287C2×C4⋊C4—1224no—
288C2×C4⋊C4—2442no—
289C2×C4⋊C4—2442no—
290C2×C4⋊C4—2442no—
291C2×C4⋊C4—2442no—
292C2×C4⋊C4—2441no—
293C2×C4⋊C4—2441no—
294C2×C4⋊C4—2442no—
295C2×C4⋊C4—2442no—
296C2×C4⋊C4Dic12214yes—
297#95—42no—
298#95—41no—
299#95—41no—
300#95—42no—
301#95—1224no—
302#95—1224no—
303#95—1222no—
304#95—1224no—
305#95—1222no—
306#95—2442no—
307#95—2442no—
308#95—2442no—
309#95—2442no—
310#95—2442no—
311#95—2442no—
312#95—2442no—
313C24C23×D6111yescharacteristic
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—614no—
340C22×C4—1222no—
341C22×C4—1222no—
342C22×C4—1222no—
343C22×C4—1222no—
344C22×C4—1222no—
345C22×C4—1222no—
346C22×C4—1222no—
347C22×C4—1222no—
348C22×C4—1222no—
349C22×C4—1222no—
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×C4C2×Dic12214yes—
368C22×C4C2×Dic12212yes—
369C22×C4#1175822612yes—
370C22×C4#1175822612yes—
371C4⋊C4—44no—
372C4⋊C4—2448no—
373C4⋊C4—2448no—
374C4⋊C4—2444no—
375C4⋊C4—2444no—
376C23C22×Dic12211yescharacteristic
377C23#41×D6112yes—
378C23C2×#1175822611yescharacteristic
379C23C2×#1175822611yescharacteristic
380C23#1451982212yes—
381C23#1451982211yescharacteristic
382C23#1451982211yescharacteristic
383C23#1451982312yes—
384C23#1451982412yes—
385C23#1451982411yescharacteristic
386C23#1451982411yescharacteristic
387C2×C4—24no—
388C2×C4—24no—
389C2×C4—24no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—22no—
395C2×C4—24no—
396C2×C4—42no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—42no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—1224no—
417C2×C4—1224no—
418C2×C4—1224no—
419C2×C4—2442no—
420C2×C4—2442no—
421C2×C4—2442no—
422C2×C4—2442no—
423C2×C4—2442no—
424C2×C4—2442no—
425C2×C4—2442no—
426C2×C4—2442no—
427C2×C4—2442no—
428C2×C4—2442no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4—2442no—
432C2×C4—2442no—
433C2×C4—2442no—
434C2×C4—2442no—
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—
444C22#1684034412yes—
445C22#1684035212yes—
446C22#1684036111yescharacteristic
447C22#1684036111yescharacteristic
448C22#1684036112yes—
449C22#1684036912yes—
450C22#1684037812yes—
451C22#1684038811yescharacteristic
452C22#1684039012yes—
453C22#1684045012yes—
454C22#1684046512yes—
455C22#1684047112yes—
456C22#1684047411yescharacteristic
457C22#1684047811yescharacteristic
458C22#1684049111yescharacteristic
459C22#1684049111yescharacteristic
460C22#1684049911yescharacteristic
461C22#1684050211yescharacteristic
462C22#1684050912yes—
463C22#1684050912yes—
464C22#1684051211yescharacteristic
465C22#1684051511yescharacteristic
466C22#1684051512yes—
467C4—42no—
468C4—42no—
469C4—44no—
470C4—42no—
471C4—82no—
472C4—4882no—
473C4—4882no—
474C4—4882no—
475C4—2444no—
476C2#2145331411yescharacteristic
477C2#2145337412yes—
478C2#2145348812yes—
479C2#2145352011yescharacteristic
480C2#2145365311yescharacteristic
481C2#2145374112yes—
482C2#2145380711yescharacteristic
483C2#2145391911yescharacteristic
484C2#2145397012yes—
485C2#2145400511yescharacteristic
486C2#2145407611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutator, socle, prime radical, cosocleC24×C61C24
FittingC61×#1445C2
hypercenter#1445D61
hypocenterC61#17304
LCSG ▷ C24×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1445

Complements

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

NH ≅ G/Ntype
274. C61#17304semidirect

Maximal subgroups

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

subgroupindex
#214440832
#214440802
#214440752
#214440732
#214440722
#214440712
C61×#14452
#1730461