Finite Group Databasebeta

← #29580489

Subgroups — #29580489

Order 15616.

1018 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 109 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#21456576C211yesmaximal, characteristic, complemented
2C2×#16839913C211yesmaximal, characteristic, complemented
3#21446804C211yesmaximal, characteristic, complemented
4#21445750C211yesmaximal, characteristic, complemented
5#21444387C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#2433C211yesmaximal, characteristic
8C22×#11758200—21no—
9C2×#14519756C2211yescharacteristic
10#16840092—21no—
11#16840078—21no—
12#16839989—22no—
13#16839913—22no—
14#16839913—22no—
15#16839913—21no—
16#16839900—21no—
17C2×#14519698—21no—
18C2×#14519698—22no—
19C2×C22⋊#92418C2211yescharacteristic
20C2×C22⋊#92418C2211yescharacteristic
21#16839622C2211yescharacteristic
22#16839528—22no—
23#16839496—22no—
24C23×D4×C61C2211yescharacteristic
25C2×#127×C61—21no—
26C2×#121×C61C2211yescharacteristic
27C2×#120×C61—22no—
28C61×#392—22no—
29C61×#390—21no—
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×Dic122D411yescharacteristic, complemented
32C2×#11758200—24no—
33C2×#11758200—22no—
34C2×#11758200—44no—
35C22×#92418—21no—
36C22×#92418D412yescomplemented
37#14519756—21no—
38#14519756—21no—
39#14519756—21no—
40#14519756—21no—
41C2×C4⋊Dic61—21no—
42C2×C4⋊Dic61D411yescharacteristic, complemented
43C2×#11758196—21no—
44C2×C22⋊Dic61—21no—
45C2×C22⋊Dic61—21no—
46#14519708—22no—
47#14519700—22no—
48#14519698—22no—
49#14519698—24no—
50#14519698—44no—
51C22⋊#92418—21no—
52C22⋊#92418—21no—
53C22⋊#92418—21no—
54C22⋊#92418D412yescomplemented
55#14519684—21no—
56C25×C61—21no—
57C22×D4×C61—21no—
58C22×D4×C61—24no—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×D4×C61—21no—
62C22×D4×C61—21no—
63C22×D4×C61—21no—
64C22×D4×C61—44no—
65C22×D4×C61D411yescharacteristic
66C22×D4×C61D412yes—
67C23×C4×C61C2311yescharacteristic
68#127×C61—44no—
69#121×C61—21no—
70#121×C61—21no—
71#121×C61—21no—
72#121×C61—21no—
73#120×C61—44no—
74#120×C61—44no—
75C2×C4⋊C4×C61D411yescharacteristic
76C2×C22⋊C4×C61—24no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61D412yes—
79C2×C42×C61—21no—
80#95×C61—21no—
81C24×C61—22no—
82C24×C61—21no—
83C24×C61—44no—
84C24×C61—41no—
85C24×C61—41no—
86C24×C61—42no—
87C24×C61—42no—
88C24×C61—82no—
89C24×C61C2×D411yescharacteristic
90C2×D4×C61—24no—
91C2×D4×C61—24no—
92C2×D4×C61—24no—
93C2×D4×C61—22no—
94C2×D4×C61—21no—
95C2×D4×C61—22no—
96C2×D4×C61—21no—
97C2×D4×C61—42no—
98C2×D4×C61—42no—
99C2×D4×C61—42no—
100C2×D4×C61—42no—
101C2×D4×C61—48no—
102C2×D4×C61—44no—
103C2×D4×C61—44no—
104C2×D4×C61—44no—
105C2×D4×C61—48no—
106C2×D4×C61—41no—
107C2×D4×C61—41no—
108C2×D4×C61—42no—
109C2×D4×C61—42no—
110C2×D4×C61—41no—
111C2×D4×C61—41no—
112C2×D4×C61—84no—
113C22×C4×C61—22no—
114C22×C4×C61—21no—
115C22×C4×C61—42no—
116C22×C4×C61C2×D411yescharacteristic
117C22×C4×C61C2×D411yescharacteristic
118C22×C4×C61C2×D411yescharacteristic
119C22×C4×C61C2×D411yescharacteristic
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61#4111yescharacteristic
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61—41no—
125C2×Dic122—21no—
126C2×Dic122—21no—
127C2×Dic122—42no—
128C4⋊C4×C61—21no—
129C4⋊C4×C61—21no—
130C22⋊C4×C61—22no—
131C22⋊C4×C61—48no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C22⋊C4×C61SD1614yescomplemented
135C42×C61—42no—
136C22⋊Dic61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—42no—
139#11758200—48no—
140#11758200—82no—
141C4⋊Dic61—21no—
142C4⋊Dic61—21no—
143C4⋊Dic61—42no—
144#11758196—41no—
145#11758196—41no—
146C2×#92418—22no—
147C2×#92418—22no—
148C2×#92418—42no—
149C2×#92418—42no—
150C23×C61—24no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—44no—
154C23×C61—44no—
155C23×C61—42no—
156C23×C61—44no—
157C23×C61—42no—
158C23×C61—42no—
159C23×C61—42no—
160C23×C61—44no—
161C23×C61—41no—
162C23×C61—42no—
163C23×C61—82no—
164C23×C61—82no—
165C23×C61—88no—
166C23×C61—88no—
167C23×C61—82no—
168C23×C61—81no—
169C23×C61—81no—
170C23×C61#12011yescharacteristic
171C23×C61#12111yescharacteristic
172C23×C61#12711yescharacteristic
173C23×C61C2×SD1612yes—
174C23×C61AGL(1,ℤ/8)12yes—
175D4×C61—24no—
176D4×C61—24no—
177D4×C61—42no—
178D4×C61—42no—
179D4×C61—44no—
180D4×C61—44no—
181D4×C61—42no—
182D4×C61—81no—
183D4×C61—816no—
184D4×C61—82no—
185D4×C61—81no—
186D4×C61—81no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—22no—
190C2×C4×C61—24no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—42no—
195C2×C4×C61—42no—
196C2×C4×C61—41no—
197C2×C4×C61—42no—
198C2×C4×C61#12011yescharacteristic
199C2×C4×C61#12011yescharacteristic
200C2×C4×C61#12111yescharacteristic
201C2×C4×C61#12111yescharacteristic
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—81no—
205C2×Dic61—81no—
206C2×Dic61—81no—
207C2×Dic61—81no—
208C2×Dic61—81no—
209Dic122—42no—
210Dic122—42no—
211#92418—42no—
212#92418—42no—
213#9954—611nomaximal, Sylow
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—42no—
221C22×C61—42no—
222C22×C61—48no—
223C22×C61—44no—
224C22×C61—84no—
225C22×C61—84no—
226C22×C61—88no—
227C22×C61—84no—
228C22×C61—84no—
229C22×C61—82no—
230C22×C61—82no—
231C22×C61—81no—
232C22×C61—81no—
233C22×C61—81no—
234C22×C61#39211yescharacteristic
235C22×C61#45012yes—
236C22×C61#46012yes—
237C22×C61#49211yescharacteristic
238C22×C61#49611yescharacteristic
239C4×C61—21no—
240C4×C61—21no—
241C4×C61—21no—
242C4×C61—44no—
243C4×C61—81no—
244C4×C61B(4,𝔽2)12yes—
245Dic61—81no—
246Dic61—81no—
247Dic61—161no—
248#3187—611no—
249C2×#450—611no—
250#2433D6111yescharacteristic
251#1996—611no—
252#1786—611no—
253#1519—611no—
254#1282—611no—
255C2×C61—21no—
256C2×C61—22no—
257C2×C61—22no—
258C2×C61—21no—
259C2×C61—84no—
260C2×C61—161no—
261C2×C61#200811yescharacteristic
262C2×C61#201411yescharacteristic
263C2×C61#202111yescharacteristic
264C23×D4C2×D6111yescharacteristic
265C22×SD16—1221no—
266C2×#127—21no—
267C2×C22⋊Q8—611no—
268C2×#121C2×D6111yescharacteristic
269C2×#120—22no—
270#483—1221no—
271#481—1221no—
272#465—1222no—
273#450—1222no—
274#450—1221no—
275#450—1222no—
276#448—1221no—
277C2×#102—1221no—
278C2×#102—1222no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8—611no—
281#392—22no—
282#390—21no—
283#380—611no—
284C4×C22⋊C4C2×D6111yescharacteristic
285#342—1222no—
286#327—1222no—
287C61#995411yescharacteristic, complemented, Sylow
288C25—21no—
289C22×Q8—611no—
290C22×D4—21no—
291C22×D4—24no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4—21no—
295C22×D4—21no—
296C22×D4—21no—
297C22×D4—44no—
298C22×D4C22⋊D6111yescharacteristic
299C22×D4C22⋊D6112yes—
300C23×C4C22×D6111yescharacteristic
301C2×SD16—1222no—
302C2×SD16—1224no—
303C2×SD16—2444no—
304C22×C8—612no—
305C22×C8—1221no—
306#127—44no—
307C22⋊Q8—1221no—
308C22⋊Q8—1221no—
309C22⋊Q8—1221no—
310C22⋊Q8—1221no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#120—44no—
316#120—44no—
317C2×C4⋊C4—611no—
318C2×C4⋊C4—1221no—
319C2×C4⋊C4—1221no—
320C2×C4⋊C4C22⋊D6111yescharacteristic
321C2×C22⋊C4—24no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C22⋊C4C22⋊D6112yes—
326C2×C42—21no—
327#106—1222no—
328#103—1222no—
329#102—1224no—
330#102—1222no—
331#102—2444no—
332C22⋊C8—612no—
333C22⋊C8—1221no—
334C22⋊C8—1221no—
335C22⋊C8—1221no—
336#95—21no—
337#95—1221no—
338C24—22no—
339C24—21no—
340C24—44no—
341C24—41no—
342C24—41no—
343C24—42no—
344C24—42no—
345C24—82no—
346C24C2×C22⋊D6111yescharacteristic
347C2×Q8—1221no—
348C2×Q8—1221no—
349C2×Q8—2442no—
350C2×D4—24no—
351C2×D4—24no—
352C2×D4—24no—
353C2×D4—22no—
354C2×D4—21no—
355C2×D4—22no—
356C2×D4—21no—
357C2×D4—42no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—42no—
361C2×D4—48no—
362C2×D4—44no—
363C2×D4—44no—
364C2×D4—44no—
365C2×D4—48no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—42no—
369C2×D4—42no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—84no—
373C22×C4—22no—
374C22×C4—21no—
375C22×C4—42no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—2441no—
379C22×C4D4×D6111yescharacteristic
380C22×C4D4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4#1175822411yescharacteristic
383C22×C4C2×C22⋊D6111yescharacteristic
384C22×C4C2×C22⋊D6111yescharacteristic
385SD16—4882no—
386SD16—2448no—
387C2×C8—1222no—
388C2×C8—1222no—
389C2×C8—2442no—
390C2×C8—2442no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—1221no—
394C4⋊C4—1221no—
395C4⋊C4—2442no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—22no—
399C22⋊C4—48no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—2442no—
403C22⋊C4—2441no—
404C22⋊C4—2441no—
405C22⋊C4#1175820014yescomplemented
406C42—42no—
407C23—24no—
408C23—41no—
409C23—41no—
410C23—44no—
411C23—44no—
412C23—42no—
413C23—44no—
414C23—42no—
415C23—42no—
416C23—44no—
417C23—42no—
418C23—42no—
419C23—41no—
420C23—82no—
421C23—82no—
422C23—88no—
423C23—88no—
424C23—82no—
425C23—81no—
426C23—81no—
427C23#1451974611yescharacteristic
428C23#1451974811yescharacteristic
429C23#1451977311yescharacteristic
430C23C2×#1175820012yes—
431C23#1451980312yes—
432Q8—2442no—
433Q8—2442no—
434D4—24no—
435D4—24no—
436D4—42no—
437D4—42no—
438D4—44no—
439D4—44no—
440D4—42no—
441D4—81no—
442D4—816no—
443D4—82no—
444D4—81no—
445D4—81no—
446C2×C4—22no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—4881no—
458C2×C4—4881no—
459C2×C4—4881no—
460C2×C4—4881no—
461C2×C4—4881no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4#1451974511yescharacteristic
465C2×C4#1451974511yescharacteristic
466C2×C4#1451974911yescharacteristic
467C2×C4#1451974911yescharacteristic
468C8—2442no—
469C8—2442no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—42no—
477C22—42no—
478C22—48no—
479C22—44no—
480C22—84no—
481C22—84no—
482C22—88no—
483C22—84no—
484C22—84no—
485C22—82no—
486C22—82no—
487C22—81no—
488C22—81no—
489C22—81no—
490C22#1683967011yescharacteristic
491C22#1683991312yes—
492C22#1683995912yes—
493C22#1684013411yescharacteristic
494C22#1684014911yescharacteristic
495C4—21no—
496C4—21no—
497C4—21no—
498C4—44no—
499C4—81no—
500C4—9761no—
501C4—4881no—
502C4—4881no—
503C4#1683994812yes—
504C2—22no—
505C2—21no—
506C2—22no—
507C2—21no—
508C2—84no—
509C2—161no—
510C2#2144687211yescharacteristic
511C2#2144690711yescharacteristic
512C2#2144694211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2433C2
socleC22×C61#392
hypercenter#2433D61
hypocenterC61#9954
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. #21456576C2semidirect
2. C2×#16839913C2semidirect
3. #21446804C2semidirect
4. #21445750C2semidirect
5. #21444387C2semidirect
6. #21443667C2semidirect
31. C22×Dic122D4semidirect
36. C22×#92418D4semidirect
42. C2×C4⋊Dic61D4semidirect
54. C22⋊#92418D4semidirect
134. C22⋊C4×C61SD16semidirect
287. C61#9954semidirect
405. C22⋊C4#11758200semidirect

Maximal subgroups

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

subgroupindex
#214565762
C2×#168399132
#214468042
#214457502
#214443872
#214436672
C61×#24332
#995461