Finite Group Databasebeta

← #29575990

Subgroups — #29575990

Order 15616.

580 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 91 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454858C211yesmaximal, characteristic, complemented
2#21451706C211yesmaximal, characteristic
3C4×#14519691C211yesmaximal, characteristic, complemented
4#21444336C211yesmaximal, characteristic, complemented
5#21444334C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#1284C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×C4×C22⋊D61C2211yescharacteristic
10#16839838—22no—
11#16839837—22no—
12#16839812—21no—
13C2×#14519691—21no—
14#16839726C2211yescharacteristic
15#16839724—21no—
16#16839702C411yescharacteristic, complemented
17#16839699C411yescharacteristic, complemented
18#16839680C411yescharacteristic, complemented
19#16839678—21no—
20#16839672C411yescharacteristic, complemented
21#16839671—21no—
22#16839654—21no—
23#16839640—21no—
24C4×C22⋊Dic61C2211yescharacteristic
25#16839528—21no—
26#16839497—22no—
27#16839495—22no—
28C61×#407C2211yescharacteristic
29C61×#381C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×D244—21no—
32C22×D244C2×C411yescharacteristic
33C22×C22⋊D61—21no—
34C22×C22⋊D61D411yescharacteristic
35C22×C4×D61D411yescharacteristic
36C2×#11758194—21no—
37C2×#11758189—22no—
38#14519751—21no—
39#14519751—21no—
40#14519751—21no—
41#14519751—21no—
42C4×C22⋊D61—21no—
43C4×C22⋊D61—21no—
44C4×C22⋊D61—21no—
45C4×C22⋊D61—21no—
46C2×C4⋊Dic61—21no—
47C2×C4⋊Dic61C2×C411yescharacteristic
48C2×#11758196C2×C411yescharacteristic
49C2×C22⋊Dic61—21no—
50C2×C22⋊Dic61D411yescharacteristic
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×#11758198—21no—
55C2×#11758198—21no—
56C2×#11758198C2×C411yescharacteristic
57C2×C4×Dic61—21no—
58C2×C4×Dic61D411yescharacteristic
59#14519706—22no—
60#14519691—24no—
61C22⋊#92418—21no—
62C22⋊#92418D412yescomplemented
63#14519689—22no—
64C8×Dic61—22no—
65#14519684—21no—
66#14519684—21no—
67#14519684—21no—
68C23×C4×C61C2311yescharacteristic
69C2×M16×C61—21no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C42×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yescomplemented
75#95×C61—21no—
76#95×C61—21no—
77#95×C61C2×C411yescharacteristic
78#95×C61C2×C411yescharacteristic
79C24×C61C2×D411yescharacteristic
80C23×D61—21no—
81C23×D61C22⋊C411yescharacteristic
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—41no—
85C22×C4×C61—81no—
86C22×C4×C61C22×C411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×D411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C2×C22⋊D61—21no—
93C2×C22⋊D61—21no—
94C2×C22⋊D61—22no—
95C2×C22⋊D61—41no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—81no—
99C2×C22⋊D61—81no—
100C22×Dic61—21no—
101C22×Dic61—41no—
102C22×Dic61C22⋊C411yescharacteristic
103C22×Dic61C22⋊C411yescharacteristic
104C22×Dic61C22⋊C411yescharacteristic
105C2×D244—21no—
106C2×D244—21no—
107C2×D244—42no—
108C2×D244—81no—
109C2×D244—81no—
110C2×D244—81no—
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—81no—
114M16×C61—81no—
115C2×C8×C61—22no—
116C22⋊C4×C61—22no—
117C22⋊C4×C61—41no—
118C22⋊C4×C61—81no—
119C42×C61—81no—
120C22⋊Dic61—21no—
121C22⋊Dic61—21no—
122C22⋊Dic61—22no—
123C22⋊Dic61—41no—
124#11758198—21no—
125#11758198—21no—
126#11758198—41no—
127#11758198—41no—
128#11758198—42no—
129#11758198—81no—
130#11758198—81no—
131#11758198—81no—
132C4⋊Dic61—21no—
133C4⋊Dic61—21no—
134C4⋊Dic61—81no—
135#11758196—21no—
136#11758196—21no—
137C4×Dic61—21no—
138C4×Dic61—21no—
139C4×Dic61—81no—
140#11758194—81no—
141C2×#92418—22no—
142#11758189—82no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—41no—
146C23×C61—41no—
147C23×C61C2×C22⋊C411yescharacteristic
148C23×C61#12111yescharacteristic
149C23×C61#12111yescharacteristic
150C22×D61—21no—
151C22×D61—21no—
152C22×D61—21no—
153C22×D61—41no—
154C22×D61—41no—
155C22×D61—41no—
156C22×D61—41no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161C22×D61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—42no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—81no—
176C2×C4×C61—81no—
177C2×C4×C61C4×D411yescharacteristic
178C2×C4×C61C4×D411yescharacteristic
179C2×C4×C61#12011yescharacteristic
180C2×C4×C61#12311yescharacteristic
181C22⋊D61—42no—
182C22⋊D61—42no—
183C22⋊D61—82no—
184C22⋊D61—82no—
185C2×Dic61—21no—
186C2×Dic61—21no—
187C2×Dic61—21no—
188C2×Dic61—21no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—42no—
194C2×Dic61—41no—
195C2×Dic61—81no—
196C2×Dic61—81no—
197C2×Dic61#10412yes—
198D244—81no—
199D244—81no—
200D244—84no—
201C4×D61—42no—
202C4×D61—81no—
203C8×C61—42no—
204#92418—42no—
205#9186—611nomaximal, Sylow
206C22×C61—21no—
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—21no—
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—81no—
215C22×C61—81no—
216C22×C61#38611yescharacteristic
217C22×C61C2×#10411yescharacteristic
218C22×C61#42111yescharacteristic
219C2×D61—42no—
220C2×D61—41no—
221C2×D61—41no—
222C2×D61—41no—
223C2×D61—81no—
224C2×D61—81no—
225C2×D61—81no—
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C2×D61—81no—
230C2×D61—81no—
231C4×C61—21no—
232C4×C61—21no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—81no—
236C4×C61—81no—
237C4×C61—82no—
238Dic61—22no—
239Dic61—41no—
240Dic61—41no—
241Dic61—82no—
242Dic61—81no—
243#2975—611no—
244#2635—611no—
245C4×#99—611no—
246#1507—611no—
247#1507—611no—
248#1284—611no—
249#1284D6111yescharacteristic, complemented
250C2×C61—21no—
251C2×C61—21no—
252C2×C61—41no—
253C2×C61—41no—
254C2×C61#187111yescharacteristic
255C2×C61#191011yescharacteristic
256C2×C61#191311yescharacteristic
257D61—81no—
258D61—161no—
259C2×#121—611no—
260C2×C4×D4—611no—
261#436—1222no—
262#436—1222no—
263#431—1221no—
264C2×#99—1221no—
265#407—611no—
266#407—1221no—
267#407C2×D6111yescharacteristic
268#400—611no—
269#399—611no—
270#394—611no—
271#394—1221no—
272#392—611no—
273#392—1221no—
274#388—1221no—
275#386—1221no—
276#381C2×D6111yescharacteristic
277C4×C22⋊C4—611no—
278C4×C22⋊C4C2×D6111yescharacteristic
279#342—1221no—
280#327—1222no—
281#327—1222no—
282C61#918611yescharacteristic, complemented, Sylow
283C22×D4—611no—
284C22×D4—611no—
285C22×D4—1221no—
286C22×D4—1221no—
287C23×C4—611no—
288C23×C4C22×D6111yescharacteristic
289C2×M16—21no—
290C2×M16—1222no—
291C2×M16—1221no—
292#121—1221no—
293#121—1221no—
294#121—1221no—
295#121—1221no—
296C4×D4—1221no—
297C4×D4—1221no—
298C4×D4—1221no—
299C4×D4—1221no—
300C2×C4⋊C4—611no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—1221no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—611no—
306C2×C22⋊C4—611no—
307C2×C22⋊C4—1221no—
308C2×C22⋊C4—1221no—
309C2×C22⋊C4—1221no—
310C2×C22⋊C4—1221no—
311C2×C22⋊C4—1221no—
312C2×C22⋊C4—1221no—
313C2×C42—21no—
314C2×C42—611no—
315C2×C42—1221no—
316C4⋊C8—1222no—
317#99—1224no—
318C22⋊C8—21no—
319C22⋊C8—612no—
320C22⋊C8—1222no—
321C22⋊C8—1221no—
322C22⋊C8D24412yescomplemented
323C4×C8—1222no—
324#95—21no—
325#95—21no—
326#95—1221no—
327#95—1221no—
328#95—1221no—
329#95C4×D6111yescharacteristic
330#95C4×D6111yescharacteristic
331C24—611no—
332C24—1221no—
333C24D4×D6111yescharacteristic
334C2×D4—1222no—
335C2×D4—1221no—
336C2×D4—1221no—
337C2×D4—1221no—
338C2×D4—1221no—
339C2×D4—4881no—
340C2×D4—4881no—
341C2×D4—4881no—
342C2×D4—4881no—
343C2×D4—4881no—
344C2×D4—2442no—
345C2×D4—2441no—
346C2×D4—2441no—
347C2×D4—2441no—
348C22×C4—21no—
349C22×C4—21no—
350C22×C4—41no—
351C22×C4—81no—
352C22×C4—611no—
353C22×C4—611no—
354C22×C4—611no—
355C22×C4—1221no—
356C22×C4—1221no—
357C22×C4—1221no—
358C22×C4—4881no—
359C22×C4—2441no—
360C22×C4C2×C4×D6111yescharacteristic
361C22×C4C2×D24411yescharacteristic
362C22×C4#1175822211yescharacteristic
363C22×C4D4×D6111yescharacteristic
364C22×C4D4×D6111yescharacteristic
365C22×C4#1175822611yescharacteristic
366M16—81no—
367M16—4882no—
368M16—4881no—
369C2×C8—22no—
370C2×C8—1222no—
371C4⋊C4—1221no—
372C4⋊C4—1221no—
373C4⋊C4—1221no—
374C4⋊C4—1221no—
375C4⋊C4—4881no—
376C22⋊C4—22no—
377C22⋊C4—41no—
378C22⋊C4—81no—
379C22⋊C4—1221no—
380C22⋊C4—1221no—
381C22⋊C4—1221no—
382C22⋊C4—1221no—
383C22⋊C4—1222no—
384C22⋊C4—4881no—
385C22⋊C4—4881no—
386C22⋊C4—4881no—
387C22⋊C4—2442no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C42—81no—
392C42—1221no—
393C42—1221no—
394C42—4881no—
395C23—21no—
396C23—21no—
397C23—41no—
398C23—41no—
399C23—1221no—
400C23—1221no—
401C23—1221no—
402C23—2441no—
403C23—2441no—
404C23—2441no—
405C23—2441no—
406C23—2441no—
407C23—2441no—
408C23—2441no—
409C23—2441no—
410C23—2441no—
411C23C22⋊C4×D6111yescharacteristic
412C23#1451975011yescharacteristic
413C23#1451975211yescharacteristic
414D4—4881no—
415D4—4881no—
416D4—4884no—
417D4—4882no—
418D4—4882no—
419D4—2442no—
420D4—2442no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—81no—
435C2×C4—81no—
436C2×C4—612no—
437C2×C4—1221no—
438C2×C4—1221no—
439C2×C4—1221no—
440C2×C4—1221no—
441C2×C4—4881no—
442C2×C4—4881no—
443C2×C4—4881no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4#1451973911yescharacteristic
452C2×C4C4×D24411yescharacteristic
453C2×C4#1451974711yescharacteristic
454C2×C4#1451976211yescharacteristic
455C8—42no—
456C8—2442no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—21no—
464C22—21no—
465C22—81no—
466C22—81no—
467C22—4881no—
468C22—4881no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22—4881no—
473C22—4881no—
474C22—4881no—
475C22—2442no—
476C22—2441no—
477C22—2441no—
478C22—2441no—
479C22#1683964011yescharacteristic
480C22#104×D6111yescharacteristic
481C22#1683977711yescharacteristic
482C4—21no—
483C4—21no—
484C4—21no—
485C4—21no—
486C4—81no—
487C4—81no—
488C4—82no—
489C4—1222no—
490C4—4882no—
491C4—4881no—
492C4—2441no—
493C4—2441no—
494C2—21no—
495C2—21no—
496C2—41no—
497C2—41no—
498C2—9761no—
499C2—4881no—
500C2#2144612011yescharacteristic
501C2#2144634511yescharacteristic
502C2#2144636011yescharacteristic
subgroupG/H
centerC22#16839640
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1284C2
socleC22×C61#386
prime radical#21451706C2
cosocleC23×C4×C61C23
hypercenter#1284D61
hypocenterC61#9186
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1284

Complements

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

NH ≅ G/Ntype
1. #21454858C2semidirect
3. C4×#14519691C2semidirect
4. #21444336C2semidirect
5. #21444334C2semidirect
6. #21443671C2semidirect
7. C61×#1284C2semidirect
16. #16839702C4semidirect
17. #16839699C4semidirect
18. #16839680C4semidirect
20. #16839672C4semidirect
62. C22⋊#92418D4semidirect
74. C22⋊C8×C61D4semidirect
249. #1284D61semidirect
282. C61#9186semidirect
322. C22⋊C8D244semidirect

Maximal subgroups

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

subgroupindex
#214548582
#214517062
C4×#145196912
#214443362
#214443342
#214436712
C61×#12842
#918661