Finite Group Databasebeta

← #29580412

Subgroups — #29580412

Order 15616.

798 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 798 conjugacy classes of subgroups — too many to draw. Only its 85 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#21455079C211yesmaximal, characteristic
2#21451199C211yesmaximal, characteristic, complemented
3#21445763C211yesmaximal, characteristic
4#21444351C211yesmaximal, characteristic, complemented
5#21444149C211yesmaximal, characteristic, complemented
6#21443671C211yesmaximal, characteristic, complemented
7C61×#2406C211yesmaximal, characteristic
8C2×#14519807—21no—
9C2×#14519756C2211yescharacteristic
10#16839924—22no—
11#16839918—21no—
12#16839913—21no—
13C2×#14519704—22no—
14#16839763—21no—
15#16839726C2211yescharacteristic
16#16839726C2211yescharacteristic
17#16839692—21no—
18#16839682—21no—
19#16839657—22no—
20#16839635—21no—
21#16839635—21no—
22C4×C22⋊Dic61C2211yescharacteristic
23#16839498—22no—
24#16839488—22no—
25C22×#41×C61C2211yescharacteristic
26C2×#123×C61—21no—
27C22×C4⋊C4×C61C2211yescharacteristic
28C61×#395—21no—
29C61×#394—21no—
30C61×#386—21no—
31C61×#385—22no—
32C61×#381C2211yescharacteristic
33C22×Dic122D411yescharacteristic
34#14519807—44no—
35C2×#11758202—22no—
36C2×#11758200—22no—
37C2×#11758194—21no—
38C2×#11758194—21no—
39#14519756—21no—
40#14519756—21no—
41#14519756—21no—
42#14519756—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×#11758196—22no—
45C2×#11758196—21no—
46C2×#11758196—22no—
47C2×C22⋊Dic61—21no—
48C2×C22⋊Dic61—21no—
49C2×C4×Dic61D412yes—
50#14519704—44no—
51#14519701—22no—
52#14519698—22no—
53C22⋊#92418—21no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418D412yes—
57#14519684—22no—
58#14519684—22no—
59#14519684—21no—
60C2×#41×C61—21no—
61C2×#41×C61—21no—
62C2×#41×C61—21no—
63C2×#41×C61—21no—
64C2×#41×C61—44no—
65C22×Q8×C61D411yescharacteristic
66C22×D4×C61—21no—
67C22×D4×C61D411yescharacteristic
68C23×C4×C61—21no—
69C23×C4×C61D411yescharacteristic
70C23×C4×C61D411yescharacteristic
71C23×C4×C61C2311yescharacteristic
72#123×C61—44no—
73C2×C4⋊C4×C61—22no—
74C2×C4⋊C4×C61—21no—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61—21no—
78C2×C4⋊C4×C61—21no—
79C2×C4⋊C4×C61—21no—
80C2×C22⋊C4×C61—22no—
81C2×C22⋊C4×C61—22no—
82C2×C22⋊C4×C61—21no—
83#95×C61—22no—
84#95×C61—21no—
85#95×C61D412yes—
86C24×C61—21no—
87C24×C61C2×D411yescharacteristic
88#41×C61—24no—
89#41×C61—24no—
90#41×C61—42no—
91#41×C61—42no—
92#41×C61—42no—
93#41×C61—42no—
94#41×C61—42no—
95#41×C61—42no—
96C2×Q8×C61—21no—
97C2×Q8×C61—21no—
98C2×Q8×C61—42no—
99C2×D4×C61—24no—
100C2×D4×C61—21no—
101C2×D4×C61—21no—
102C2×D4×C61—42no—
103C2×D4×C61—42no—
104C2×D4×C61—41no—
105C2×D4×C61—41no—
106C22×C4×C61—21no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—22no—
111C22×C4×C61—21no—
112C22×C4×C61—21no—
113C22×C4×C61—21no—
114C22×C4×C61—42no—
115C22×C4×C61—42no—
116C22×C4×C61—42no—
117C22×C4×C61—42no—
118C22×C4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61—42no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61#4111yescharacteristic
127C22×Dic61—22no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C2×Dic122—21no—
131C2×Dic122—21no—
132C2×Dic122—42no—
133C4⋊C4×C61—44no—
134C4⋊C4×C61—41no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C4⋊C4×C61—41no—
138C22⋊C4×C61—44no—
139C22⋊C4×C61—42no—
140C22⋊C4×C61—44no—
141C22⋊Dic61—24no—
142C22⋊Dic61—41no—
143C22⋊Dic61—41no—
144#11758202—44no—
145#11758200—44no—
146C4⋊Dic61—21no—
147C4⋊Dic61—21no—
148#11758196—44no—
149#11758196—41no—
150#11758196—41no—
151#11758196—82no—
152C4×Dic61—42no—
153#11758194—42no—
154#11758194—42no—
155C2×#92418—22no—
156C2×#92418—41no—
157C23×C61—22no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—41no—
161C23×C61—42no—
162C23×C61—41no—
163C23×C61—41no—
164C23×C61—42no—
165C23×C61#12011yescharacteristic
166C23×C61#12011yescharacteristic
167C23×C61#12111yescharacteristic
168Q8×C61—22no—
169Q8×C61—22no—
170Q8×C61—41no—
171Q8×C61—41no—
172D4×C61—22no—
173D4×C61—22no—
174D4×C61—41no—
175D4×C61—41no—
176D4×C61—44no—
177D4×C61—44no—
178C2×C4×C61—22no—
179C2×C4×C61—22no—
180C2×C4×C61—22no—
181C2×C4×C61—22no—
182C2×C4×C61—22no—
183C2×C4×C61—22no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—44no—
189C2×C4×C61—44no—
190C2×C4×C61—41no—
191C2×C4×C61—41no—
192C2×C4×C61—41no—
193C2×C4×C61—41no—
194C2×C4×C61—41no—
195C2×C4×C61—41no—
196C2×C4×C61—42no—
197C2×C4×C61—42no—
198C2×C4×C61—42no—
199C2×C4×C61—41no—
200C2×C4×C61—42no—
201C2×C4×C61—42no—
202C2×C4×C61—81no—
203C2×C4×C61#12011yescharacteristic
204C2×C4×C61#12111yescharacteristic
205C2×C4×C61#12111yescharacteristic
206C2×C4×C61#12711yescharacteristic
207C2×Dic61—24no—
208C2×Dic61—42no—
209C2×Dic61—42no—
210C2×Dic61—42no—
211C2×Dic61—41no—
212C2×Dic61—41no—
213C2×Dic61—42no—
214Dic122—42no—
215Dic122—81no—
216#92418—42no—
217#92418—81no—
218#9943—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—44no—
227C22×C61—44no—
228C22×C61—42no—
229C22×C61—82no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61#39211yescharacteristic
233C22×C61#45612yes—
234C22×C61B(4,𝔽2)12yes—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—42no—
240C4×C61—42no—
241C4×C61—82no—
242C4×C61—81no—
243Dic61—44no—
244Dic61—81no—
245Dic61—81no—
246#3007—611no—
247#2583—611no—
248#2406D6111yescharacteristic
249#1789—611no—
250#1511—611no—
251#1463—611no—
252#1284—611no—
253C2×C61—22no—
254C2×C61—22no—
255C2×C61—41no—
256C2×C61—82no—
257C2×C61#200511yescharacteristic
258C2×C61#201011yescharacteristic
259C2×C61#202111yescharacteristic
260C22×#41C2×D6111yescharacteristic
261C2×#137—1221no—
262C2×#123—21no—
263C2×C22⋊Q8—611no—
264C22×C4⋊C4C2×D6111yescharacteristic
265#452—1222no—
266#451—1221no—
267#450—1221no—
268C2×#104—1222no—
269#417—1221no—
270#407—611no—
271#407—611no—
272#398—1221no—
273#395—21no—
274#395—1221no—
275#394—21no—
276#389—1222no—
277#386—21no—
278#385—22no—
279#385—1221no—
280#385—1221no—
281#381C2×D6111yescharacteristic
282C4×C22⋊C4—611no—
283#328—1222no—
284#324—1222no—
285C61#994311yescharacteristic, complemented, Sylow
286C2×#41—21no—
287C2×#41—21no—
288C2×#41—21no—
289C2×#41—21no—
290C2×#41—44no—
291C22×Q8—611no—
292C22×Q8C22⋊D6111yescharacteristic
293C22×D4—21no—
294C22×D4C22⋊D6111yescharacteristic
295C23×C4—21no—
296C23×C4C22⋊D6111yescharacteristic
297C23×C4C22⋊D6111yescharacteristic
298C23×C4C22×D6111yescharacteristic
299#137—2444no—
300C2×Q16—1222no—
301C2×SD16—1222no—
302C2×M16—1221no—
303C2×M16—1221no—
304#123—44no—
305C22⋊Q8—1221no—
306C22⋊Q8—1221no—
307C22⋊Q8—1221no—
308C22⋊Q8—1221no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312C2×C4⋊C4—21no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—611no—
317C2×C4⋊C4—1222no—
318C2×C4⋊C4—1222no—
319C2×C4⋊C4—1221no—
320C2×C22⋊C4—22no—
321C2×C22⋊C4—22no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—1221no—
324C2×C22⋊C4—1221no—
325C2×C42—612no—
326#104—2444no—
327#103—1222no—
328#102—1222no—
329C22⋊C8—612no—
330C22⋊C8—1221no—
331C22⋊C8—1221no—
332C22⋊C8—1221no—
333#95—22no—
334#95—21no—
335#95—1222no—
336#95—1222no—
337#95—1221no—
338#95C22⋊D6112yes—
339C24—21no—
340C24C2×C22⋊D6111yescharacteristic
341#41—24no—
342#41—24no—
343#41—42no—
344#41—42no—
345#41—42no—
346#41—42no—
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—42no—
352C2×Q8—1221no—
353C2×Q8—1221no—
354C2×Q8—2442no—
355C2×D4—24no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—42no—
359C2×D4—42no—
360C2×D4—41no—
361C2×D4—41no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—21no—
366C22×C4—21no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—42no—
377C22×C4—1222no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4D4×D6111yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4D4×D6111yescharacteristic
383C22×C4#1175822411yescharacteristic
384C22×C4C2×C22⋊D6111yescharacteristic
385C22×C4C2×C22⋊D6111yescharacteristic
386Q16—2444no—
387SD16—2444no—
388M16—2442no—
389M16—2442no—
390C2×C8—1222no—
391C2×C8—2441no—
392C4⋊C4—44no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—1221no—
398C4⋊C4—1221no—
399C4⋊C4—4882no—
400C4⋊C4—2444no—
401C4⋊C4—2441no—
402C4⋊C4—2441no—
403C22⋊C4—44no—
404C22⋊C4—42no—
405C22⋊C4—44no—
406C22⋊C4—1224no—
407C22⋊C4—2441no—
408C22⋊C4—2441no—
409C42—2442no—
410C23—22no—
411C23—22no—
412C23—22no—
413C23—41no—
414C23—42no—
415C23—41no—
416C23—42no—
417C23—41no—
418C23#1451974511yescharacteristic
419C23#1451974611yescharacteristic
420C23#1451974911yescharacteristic
421Q8—22no—
422Q8—22no—
423Q8—41no—
424Q8—41no—
425Q8—4881no—
426Q8—2442no—
427D4—22no—
428D4—22no—
429D4—41no—
430D4—41no—
431D4—44no—
432D4—44no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—44no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—42no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—41no—
457C2×C4—81no—
458C2×C4—1224no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4#1451974511yescharacteristic
466C2×C4#1451974811yescharacteristic
467C2×C4#1451974911yescharacteristic
468C2×C4#1451977311yescharacteristic
469C8—4881no—
470C8—2442no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—44no—
479C22—44no—
480C22—42no—
481C22—82no—
482C22—81no—
483C22—81no—
484C22#1683967011yescharacteristic
485C22#1683994512yes—
486C22#1683994812yes—
487C4—21no—
488C4—21no—
489C4—21no—
490C4—21no—
491C4—42no—
492C4—42no—
493C4—82no—
494C4—81no—
495C4—4881no—
496C4—4881no—
497C4—2444no—
498C2—22no—
499C2—22no—
500C2—41no—
501C2—82no—
502C2#2144685311yescharacteristic
503C2#2144688411yescharacteristic
504C2#2144694211yescharacteristic
subgroupG/H
centerC22#16839670
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#2406C2
socleC22×C61#392
prime radicalC22×#41×C61C22
hypercenter#2406D61
hypocenterC61#9943
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. #21451199C2semidirect
4. #21444351C2semidirect
5. #21444149C2semidirect
6. #21443671C2semidirect
285. C61#9943semidirect

Maximal subgroups

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

subgroupindex
#214550792
#214511992
#214457632
#214443512
#214441492
#214436712
C61×#24062
#994361