Finite Group Databasebeta

← #29608216

Subgroups — #29608216

Order 15616.

1302 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×#16839649C212yesmaximal
2C2×#16839643C212yesmaximal
3C2×#16839631C211yesmaximal, characteristic
4#21444085C212yesmaximal
5#21444085C212yesmaximal
6#21444072C211yesmaximal, characteristic
7#21444053C212yesmaximal
8#21444043C212yesmaximal
9C61×#1441C211yesmaximal, characteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758196C2212yes—
13C22×#11758196C2212yes—
14C22×C4×Dic61C2212yes—
15C22×C4×Dic61C2211yescharacteristic
16#16839649—28no—
17#16839643—28no—
18#16839631C418yescomplemented
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C2×#14519684C2212yes—
29C22×C4⋊C4×C61C2211yescharacteristic
30C22×C4⋊C4×C61C2211yescharacteristic
31C2×#95×C61C2212yes—
32C2×#95×C61C2212yes—
33C2×#95×C61C2211yescharacteristic
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C23×Dic61C2312yes—
38C2×C4⋊Dic61—24no—
39C2×C4⋊Dic61—41no—
40C2×C4⋊Dic61—41no—
41C2×C4⋊Dic61—41no—
42C2×C4⋊Dic61C2×C414yes—
43C2×#11758196—24no—
44C2×#11758196—24no—
45C2×#11758196—24no—
46C2×#11758196—24no—
47C2×#11758196C2×C418yes—
48C2×#11758196C2×C418yes—
49C2×C4×Dic61—22no—
50C2×C4×Dic61—22no—
51C2×C4×Dic61—24no—
52C2×C4×Dic61—24no—
53C2×C4×Dic61—42no—
54C2×C4×Dic61C2×C414yes—
55#14519684—24no—
56#14519684—24no—
57#14519684—24no—
58#14519684—24no—
59#14519684—24no—
60#14519684—24no—
61#14519684—24no—
62#14519684—42no—
63#14519684—41no—
64#14519684D418yes—
65C23×C4×C61C2312yes—
66C23×C4×C61C2311yescharacteristic
67C23×C4×C61C2311yescharacteristic
68C23×C4×C61C2312yes—
69C23×C4×C61C2311yescharacteristic
70C2×C4⋊C4×C61—24no—
71C2×C4⋊C4×C61—41no—
72C2×C4⋊C4×C61—41no—
73C2×C4⋊C4×C61—41no—
74C2×C4⋊C4×C61C2×C414yes—
75#95×C61—24no—
76#95×C61—24no—
77#95×C61—41no—
78C24×C61C2411yescharacteristic
79C22×C4×C61—21no—
80C22×C4×C61—21no—
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—21no—
90C22×C4×C61—21no—
91C22×C4×C61—21no—
92C22×C4×C61—22no—
93C22×C4×C61—21no—
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×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61C22×C412yes—
105C22×C4×C61C22×C412yes—
106C22×C4×C61C22×C412yes—
107C22×C4×C61C2×D414yes—
108C22×C4×C61#4112yes—
109C22×C4×C61#4112yes—
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—22no—
133C22×Dic61C22×C414yes—
134C22×Dic61C22×C414yes—
135C22×Dic61C2×D414yes—
136C22×Dic61C2×D414yes—
137C22×Dic61#4114yes—
138C4⋊C4×C61—44no—
139C4⋊C4×C61—44no—
140C4⋊Dic61—44no—
141C4⋊Dic61—44no—
142#11758196—216no—
143#11758196—216no—
144C4×Dic61—28no—
145C4×Dic61—48no—
146C23×C61C23×C411yescharacteristic
147C23×C61C22×D412yes—
148C23×C61C2×#4111yescharacteristic
149C23×C61C2×#4111yescharacteristic
150C23×C61C2×#4112yes—
151C23×C61H(5,𝔽2)11yescharacteristic
152C23×C61H(5,𝔽2)11yescharacteristic
153C23×C612−1+411yescharacteristic
154C23×C612−1+411yescharacteristic
155C23×C612−1+412yes—
156C23×C612−1+412yes—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
162C2×C4×C61—22no—
163C2×C4×C61—24no—
164C2×C4×C61—24no—
165C2×C4×C61—22no—
166C2×C4×C61—22no—
167C2×C4×C61—24no—
168C2×C4×C61—24no—
169C2×C4×C61—24no—
170C2×C4×C61—42no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—42no—
175C2×C4×C61—42no—
176C2×C4×C61—42no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
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×C61—42no—
187C2×C4×C61#11714yes—
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—24no—
197C2×Dic61—24no—
198C2×Dic61—24no—
199C2×Dic61—24no—
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—
215C2×Dic61C4×D418yes—
216#14424—611nomaximal, Sylow
217C22×C61C2×#11711yescharacteristic
218C22×C61C2×C4×D412yes—
219C22×C61#51811yescharacteristic
220C22×C61#51912yes—
221C22×C61#51911yescharacteristic
222C22×C61#53612yes—
223C22×C61#53612yes—
224C22×C61#53911yescharacteristic
225C22×C61#53911yescharacteristic
226C22×C61#53911yescharacteristic
227C22×C61#53911yescharacteristic
228C22×C61#54112yes—
229C22×C61#54112yes—
230C22×C61D4211yescharacteristic
231C22×C61#54712yes—
232C22×C61#54712yes—
233C22×C61#55012yes—
234C22×C61#55212yes—
235C22×C61#55212yes—
236C22×C61#55911yescharacteristic
237C22×C61#56311yescharacteristic
238C22×C61#56311yescharacteristic
239C22×C61#56312yes—
240C4×C61—24no—
241C4×C61—42no—
242C4×C61—42no—
243C4×C61—44no—
244C4×C61—82no—
245Dic61—28no—
246Dic61—44no—
247Dic61—44no—
248Dic61—82no—
249C2×#387—612no—
250C2×#387—612no—
251C2×#384—611no—
252#1445—612no—
253#1445—612no—
254#1441—611no—
255#1441D6111yescharacteristic
256#1436—612no—
257#1434—612no—
258C2×C61#231311yescharacteristic
259C2×C61#232712yes—
260C2×C61#234412yes—
261C2×C61#236611yescharacteristic
262C2×C61#238111yescharacteristic
263C2×C61#268011yescharacteristic
264C2×C61#268011yescharacteristic
265C2×C61#272112yes—
266C2×C61#272112yes—
267C2×C61#279411yescharacteristic
268C2×C61#279411yescharacteristic
269C22×C4⋊C4—612no—
270C22×C4⋊C4—612no—
271C22×C4⋊C4—611no—
272C22×C4⋊C4—611no—
273C22×C4⋊C4C2×D6111yescharacteristic
274C22×C4⋊C4C2×D6111yescharacteristic
275C22×C42—611no—
276C22×C42—612no—
277#387—1228no—
278#387—1228no—
279#384—618no—
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×#95—612no—
289C2×#95—611no—
290C2×#95C2×D6112yes—
291C2×#95C2×D6112yes—
292C2×#95C2×D6111yescharacteristic
293C61#1442411yescharacteristic, complemented, Sylow
294C23×C4—612no—
295C23×C4—612no—
296C23×C4—612no—
297C23×C4—612no—
298C23×C4C22×D6112yes—
299C23×C4C22×D6111yescharacteristic
300C23×C4C22×D6111yescharacteristic
301C23×C4C22×D6112yes—
302C23×C4C22×D6111yescharacteristic
303C2×C4⋊C4—24no—
304C2×C4⋊C4—41no—
305C2×C4⋊C4—41no—
306C2×C4⋊C4—41no—
307C2×C4⋊C4—618no—
308C2×C4⋊C4—618no—
309C2×C4⋊C4—614no—
310C2×C4⋊C4—1224no—
311C2×C4⋊C4—1224no—
312C2×C4⋊C4—1224no—
313C2×C4⋊C4—1224no—
314C2×C4⋊C4—1224no—
315C2×C4⋊C4—2441no—
316C2×C4⋊C4—2441no—
317C2×C4⋊C4—2441no—
318C2×C4⋊C4C4×D6114yes—
319C2×C42—614no—
320C2×C42—1222no—
321C2×C42—1222no—
322C2×C42—1224no—
323C2×C42—1224no—
324C2×C42—2442no—
325#95—24no—
326#95—24no—
327#95—41no—
328#95—618no—
329#95—1224no—
330#95—1224no—
331#95—1224no—
332#95—1224no—
333#95—1224no—
334#95—1224no—
335#95—1224no—
336#95—2441no—
337#95—2442no—
338C24C23×D6111yescharacteristic
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—21no—
353C22×C4—21no—
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—614no—
365C22×C4—614no—
366C22×C4—614no—
367C22×C4—614no—
368C22×C4—614no—
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—1222no—
387C22×C4—1222no—
388C22×C4—1222no—
389C22×C4—1222no—
390C22×C4—1222no—
391C22×C4—1222no—
392C22×C4C2×C4×D6112yes—
393C22×C4C2×C4×D6112yes—
394C22×C4C2×C4×D6112yes—
395C22×C4D4×D6114yes—
396C22×C4#1175822412yes—
397C22×C4#1175822612yes—
398C4⋊C4—44no—
399C4⋊C4—44no—
400C4⋊C4—12216no—
401C4⋊C4—12216no—
402C4⋊C4—2444no—
403C4⋊C4—2444no—
404C42—1228no—
405C42—2448no—
406C23C22×C4×D6111yescharacteristic
407C23C2×D4×D6112yes—
408C23#41×D6112yes—
409C23C2×#1175822411yescharacteristic
410C23C2×#1175822611yescharacteristic
411C23#1451982211yescharacteristic
412C23#1451982211yescharacteristic
413C23#1451982412yes—
414C23#1451982411yescharacteristic
415C23#1451982411yescharacteristic
416C23#1451982512yes—
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—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—41no—
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—618no—
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—1224no—
457C2×C4—1224no—
458C2×C4—1224no—
459C2×C4—1224no—
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#1451973514yes—
476C22C2×#1451973511yescharacteristic
477C22C4×D4×D6112yes—
478C22#1684023511yescharacteristic
479C22#1684023812yes—
480C22#1684023911yescharacteristic
481C22#1684033412yes—
482C22#1684033512yes—
483C22#1684035711yescharacteristic
484C22#1684035711yescharacteristic
485C22#1684036111yescharacteristic
486C22#1684036111yescharacteristic
487C22#1684036912yes—
488C22#1684037112yes—
489C22#1684039411yescharacteristic
490C22#1684041212yes—
491C22#1684041512yes—
492C22#1684043012yes—
493C22#1684044612yes—
494C22#1684045012yes—
495C22#1684049611yescharacteristic
496C22#1684051111yescharacteristic
497C22#1684051211yescharacteristic
498C22#1684051312yes—
499C4—24no—
500C4—44no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—1228no—
505C4—4882no—
506C4—2444no—
507C4—2444no—
508C2#2144842111yescharacteristic
509C2#2144853412yes—
510C2#2144868712yes—
511C2#2144888211yescharacteristic
512C2#2144899811yescharacteristic
513C2#2145216211yescharacteristic
514C2#2145216311yescharacteristic
515C2#2145271912yes—
516C2#2145272012yes—
517C2#2145364311yescharacteristic
518C2#2145364411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1441D61
hypocenterC61#14424
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
18. #16839631C4semidirect
293. C61#14424semidirect

Maximal subgroups

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

subgroupindex
C2×#168396492
C2×#168396432
C2×#168396312
#214440852
#214440722
#214440532
#214440432
C61×#14412
#1442461