Finite Group Databasebeta

← #29610305

Subgroups — #29610305

Order 15616.

1194 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839692C211yesmaximal, characteristic
2C2×#16839649C212yesmaximal
3#21444080C212yesmaximal
4#21444080C212yesmaximal
5#21444054C212yesmaximal
6#21444053C212yesmaximal
7#21444051C212yesmaximal
8#21444048C211yesmaximal, characteristic
9C61×#1441C211yesmaximal, characteristic
10C22×C4⋊Dic61C2211yescharacteristic
11C22×C4⋊Dic61C2211yescharacteristic
12C22×#11758196C2212yes—
13C22×C4×Dic61C2212yes—
14C22×C4×Dic61C2211yescharacteristic
15#16839692C418yescomplemented
16#16839649—28no—
17C2×#14519684C2212yes—
18C2×#14519684C2212yes—
19C2×#14519684C2212yes—
20C2×#14519684C2212yes—
21C2×#14519684C2212yes—
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2211yescharacteristic
28C22×C4⋊C4×C61C2211yescharacteristic
29C22×C4⋊C4×C61C2211yescharacteristic
30C2×#95×C61C2212yes—
31C2×#95×C61C2212yes—
32C2×#95×C61C2211yescharacteristic
33C23×Dic61C2312yes—
34C23×Dic61C2312yes—
35C23×Dic61C2312yes—
36C23×Dic61C2312yes—
37C2×C4⋊Dic61—41no—
38C2×C4⋊Dic61—41no—
39C2×C4⋊Dic61—41no—
40C2×C4⋊Dic61—41no—
41C2×C4⋊Dic61C2×C414yes—
42C2×C4⋊Dic61D414yes—
43C2×#11758196—24no—
44C2×#11758196—24no—
45C2×#11758196C2×C418yes—
46C2×C4×Dic61—22no—
47C2×C4×Dic61—24no—
48C2×C4×Dic61—42no—
49C2×C4×Dic61—42no—
50C2×C4×Dic61—41no—
51C2×C4×Dic61—41no—
52#14519684—24no—
53#14519684—24no—
54#14519684—24no—
55#14519684—24no—
56#14519684—24no—
57#14519684—24no—
58#14519684—24no—
59#14519684—42no—
60#14519684—42no—
61#14519684C2×C414yes—
62#14519684C2×C418yes—
63C23×C4×C61C2312yes—
64C23×C4×C61C2311yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C23×C4×C61C2312yes—
67C23×C4×C61C2311yescharacteristic
68C2×C4⋊C4×C61—24no—
69C2×C4⋊C4×C61—41no—
70C2×C4⋊C4×C61—41no—
71C2×C4⋊C4×C61—41no—
72C2×C4⋊C4×C61C2×C414yes—
73#95×C61—24no—
74#95×C61—24no—
75#95×C61—41no—
76C24×C61C2411yescharacteristic
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—22no—
82C22×C4×C61—22no—
83C22×C4×C61—22no—
84C22×C4×C61—22no—
85C22×C4×C61—22no—
86C22×C4×C61—22no—
87C22×C4×C61—21no—
88C22×C4×C61—21no—
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×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×D412yes—
106C22×C4×C61#4114yes—
107C22×C4×C61#4112yes—
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×D414yes—
135C22×Dic61#4114yes—
136C4⋊C4×C61—44no—
137C4⋊C4×C61—44no—
138C4⋊Dic61—44no—
139C4⋊Dic61—44no—
140#11758196—216no—
141C4×Dic61—48no—
142C4×Dic61—44no—
143C23×C61C23×C411yescharacteristic
144C23×C61C22×D411yescharacteristic
145C23×C61C2×#4111yescharacteristic
146C23×C61C2×#4112yes—
147C23×C61C2×#4112yes—
148C23×C61H(5,𝔽2)11yescharacteristic
149C23×C61H(5,𝔽2)11yescharacteristic
150C23×C61H(5,𝔽2)11yescharacteristic
151C23×C612−1+412yes—
152C23×C612−1+412yes—
153C23×C612−1+411yescharacteristic
154C2×C4×C61—22no—
155C2×C4×C61—22no—
156C2×C4×C61—22no—
157C2×C4×C61—22no—
158C2×C4×C61—22no—
159C2×C4×C61—22no—
160C2×C4×C61—24no—
161C2×C4×C61—24no—
162C2×C4×C61—22no—
163C2×C4×C61—22no—
164C2×C4×C61—24no—
165C2×C4×C61—24no—
166C2×C4×C61—24no—
167C2×C4×C61—42no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—41no—
171C2×C4×C61—41no—
172C2×C4×C61—42no—
173C2×C4×C61—42no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
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×C61C4×D414yes—
185C2×Dic61—24no—
186C2×Dic61—24no—
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—24no—
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—
213#14590—611nomaximal, Sylow
214C22×C61C2×C4×D411yescharacteristic
215C22×C61C4×#4112yes—
216C22×C61#51811yescharacteristic
217C22×C61#51912yes—
218C22×C61#52011yescharacteristic
219C22×C61#53411yescharacteristic
220C22×C61#53711yescharacteristic
221C22×C61#53811yescharacteristic
222C22×C61#53912yes—
223C22×C61#53912yes—
224C22×C61#53911yescharacteristic
225C22×C61#54112yes—
226C22×C61#54112yes—
227C22×C61#54712yes—
228C22×C61#54812yes—
229C22×C61#55111yescharacteristic
230C22×C61#55212yes—
231C22×C61#55312yes—
232C22×C61#55612yes—
233C22×C61#55911yescharacteristic
234C22×C61#56311yescharacteristic
235C22×C61#56311yescharacteristic
236C22×C61#56312yes—
237C4×C61—24no—
238C4×C61—42no—
239C4×C61—42no—
240C4×C61—44no—
241C4×C61—82no—
242Dic61—44no—
243Dic61—44no—
244Dic61—44no—
245Dic61—44no—
246C2×#398—611no—
247C2×#387—612no—
248#1443—612no—
249#1443—612no—
250#1441D6111yescharacteristic
251#1436—612no—
252#1436—612no—
253#1436—612no—
254C4⋊#95—611no—
255C2×C61#232511yescharacteristic
256C2×C61#233612yes—
257C2×C61#236212yes—
258C2×C61#237411yescharacteristic
259C2×C61#238111yescharacteristic
260C2×C61#272411yescharacteristic
261C2×C61#272512yes—
262C2×C61#272811yescharacteristic
263C2×C61#278712yes—
264C2×C61#278911yescharacteristic
265C2×C61#279411yescharacteristic
266C22×C4⋊C4—612no—
267C22×C4⋊C4—611no—
268C22×C4⋊C4—611no—
269C22×C4⋊C4C2×D6111yescharacteristic
270C22×C4⋊C4C2×D6111yescharacteristic
271C22×C42—611no—
272C22×C42—612no—
273#398—618no—
274#387—1228no—
275C2×#95—612no—
276C2×#95—611no—
277C2×#95—612no—
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×#95C2×D6112yes—
287C2×#95C2×D6112yes—
288C2×#95C2×D6111yescharacteristic
289C61#1459011yescharacteristic, complemented, Sylow
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—41no—
301C2×C4⋊C4—41no—
302C2×C4⋊C4—41no—
303C2×C4⋊C4—618no—
304C2×C4⋊C4—614no—
305C2×C4⋊C4—614no—
306C2×C4⋊C4—1224no—
307C2×C4⋊C4—1224no—
308C2×C4⋊C4—2441no—
309C2×C4⋊C4—2441no—
310C2×C4⋊C4—2441no—
311C2×C4⋊C4—2441no—
312C2×C4⋊C4C4×D6114yes—
313C2×C42—1224no—
314C2×C42—1222no—
315C2×C42—2441no—
316C2×C42—2441no—
317C2×C42—2442no—
318C2×C42—2442no—
319#95—24no—
320#95—24no—
321#95—41no—
322#95—614no—
323#95—618no—
324#95—1224no—
325#95—1224no—
326#95—1224no—
327#95—1224no—
328#95—1224no—
329#95—1224no—
330#95—1224no—
331#95—2442no—
332#95—2442no—
333C24C23×D6111yescharacteristic
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—21no—
345C22×C4—22no—
346C22×C4—21no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—22no—
350C22×C4—22no—
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—614no—
360C22×C4—614no—
361C22×C4—614no—
362C22×C4—614no—
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—1222no—
387C22×C4C2×C4×D6112yes—
388C22×C4C2×C4×D6112yes—
389C22×C4C2×C4×D6112yes—
390C22×C4D4×D6112yes—
391C22×C4#1175822414yes—
392C22×C4#1175822612yes—
393C4⋊C4—44no—
394C4⋊C4—44no—
395C4⋊C4—12216no—
396C4⋊C4—2444no—
397C4⋊C4—2444no—
398C42—2444no—
399C42—2448no—
400C23C22×C4×D6111yescharacteristic
401C23C2×D4×D6111yescharacteristic
402C23#41×D6112yes—
403C23C2×#1175822412yes—
404C23C2×#1175822611yescharacteristic
405C23#1451982211yescharacteristic
406C23#1451982211yescharacteristic
407C23#1451982311yescharacteristic
408C23#1451982412yes—
409C23#1451982411yescharacteristic
410C23#1451982512yes—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—24no—
422C2×C4—24no—
423C2×C4—24no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—1224no—
442C2×C4—1224no—
443C2×C4—1224no—
444C2×C4—1224no—
445C2×C4—1224no—
446C2×C4—1224no—
447C2×C4—1224no—
448C2×C4—1224no—
449C2×C4—1224no—
450C2×C4—1224no—
451C2×C4—1224no—
452C2×C4—1224no—
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—
464C2×C4—2442no—
465C2×C4—2442no—
466C2×C4—2442no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4#1451973914yes—
470C22C2×#1451973911yescharacteristic
471C22C4×#1175822412yes—
472C22#1684023511yescharacteristic
473C22#1684023812yes—
474C22#1684024211yescharacteristic
475C22#1684032011yescharacteristic
476C22#1684033911yescharacteristic
477C22#1684035211yescharacteristic
478C22#1684035612yes—
479C22#1684036012yes—
480C22#1684036111yescharacteristic
481C22#1684036912yes—
482C22#1684037212yes—
483C22#1684041412yes—
484C22#1684041812yes—
485C22#1684044311yescharacteristic
486C22#1684045012yes—
487C22#1684045912yes—
488C22#1684048612yes—
489C22#1684049611yescharacteristic
490C22#1684051111yescharacteristic
491C22#1684051211yescharacteristic
492C22#1684051312yes—
493C4—24no—
494C4—44no—
495C4—42no—
496C4—42no—
497C4—82no—
498C4—2444no—
499C4—2444no—
500C4—2444no—
501C4—2444no—
502C2#2144851911yescharacteristic
503C2#2144862412yes—
504C2#2144884512yes—
505C2#2144895211yescharacteristic
506C2#2144899811yescharacteristic
507C2#2145274611yescharacteristic
508C2#2145275212yes—
509C2#2145278511yescharacteristic
510C2#2145355612yes—
511C2#2145358111yescharacteristic
512C2#2145364411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×#1441C2
socle, prime radical, cosocleC24×C61C24
hypercenter#1441D61
hypocenterC61#14590
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
15. #16839692C4semidirect
289. C61#14590semidirect

Maximal subgroups

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

subgroupindex
C2×#168396922
C2×#168396492
#214440802
#214440542
#214440532
#214440512
#214440482
C61×#14412
#1459061