Finite Group Databasebeta

← #29583324

Subgroups — #29583324

Order 15616.

570 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451632C211yesmaximal, characteristic
2#21446124C211yesmaximal, characteristic
3#21446009C211yesmaximal, characteristic
4C2×#16839500C211yesmaximal, characteristic
5#21444072C211yesmaximal, characteristic
6#21443699C211yesmaximal, characteristic
7C2×C61×#324C211yesmaximal, characteristic
8C2×#14519756C2211yescharacteristic
9C22×C4⋊Dic61C2211yescharacteristic
10C2×#14519711—21no—
11C2×#14519702—21no—
12#16839701—21no—
13#16839695—21no—
14#16839695—21no—
15#16839682—21no—
16#16839635—21no—
17#16839625—21no—
18#16839622C2211yescharacteristic
19C2×#14519684—21no—
20C2×#14519684—21no—
21C2×#14519684C2211yescharacteristic
22#16839525—21no—
23#16839525—21no—
24#16839500—22no—
25C22×C4⋊C4×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×C22⋊C8×C61C2211yescharacteristic
28C61×#324—22no—
29C22×Dic122D411yescharacteristic
30C23×Dic61—21no—
31C23×Dic61—21no—
32#14519756—21no—
33#14519756—21no—
34#14519756—21no—
35#14519756—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—21no—
38C2×C4⋊Dic61—42no—
39C2×C4⋊Dic61D411yescharacteristic
40C2×C4⋊Dic61D411yescharacteristic
41C2×C4⋊Dic61D411yescharacteristic
42C2×#11758196—21no—
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46C2×C22⋊Dic61—21no—
47#14519711—42no—
48#14519702—42no—
49#14519684—21no—
50#14519684—21no—
51#14519684—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—42no—
59#14519684—42no—
60C23×C4×C61D411yescharacteristic
61C23×C4×C61D411yescharacteristic
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C22×C8×C61—21no—
65C2×C4⋊C4×C61—21no—
66C2×C4⋊C4×C61—21no—
67C2×C4⋊C4×C61—21no—
68C2×C4⋊C4×C61—21no—
69C2×C4⋊C4×C61—21no—
70C2×C4⋊C4×C61—21no—
71C22⋊C8×C61—21no—
72C22⋊C8×C61—21no—
73C22⋊C8×C61—21no—
74C22⋊C8×C61D412yes—
75C24×C61C2×D411yescharacteristic
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—21no—
82C22×C4×C61—21no—
83C22×C4×C61—21no—
84C22×C4×C61—21no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61—41no—
88C22×C4×C61—41no—
89C22×C4×C61Q1612yes—
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×D411yescharacteristic
92C22×C4×C61C2×D411yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C22×C4×C61#4111yescharacteristic
95C22×C4×C61#4111yescharacteristic
96C22×Dic61—22no—
97C22×Dic61—22no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—21no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C2×Dic122—21no—
115C2×Dic122—21no—
116C2×Dic122—41no—
117C2×Dic122—41no—
118C2×C8×C61—22no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C2×C8×C61—41no—
122C2×C8×C61—41no—
123C2×C8×C61—41no—
124C4⋊C4×C61—41no—
125C4⋊C4×C61—41no—
126C4⋊C4×C61—41no—
127C4⋊C4×C61—41no—
128C22⋊Dic61—41no—
129C22⋊Dic61—41no—
130C22⋊Dic61—41no—
131C22⋊Dic61—41no—
132C4⋊Dic61—22no—
133C4⋊Dic61—22no—
134C4⋊Dic61—21no—
135C4⋊Dic61—21no—
136C4⋊Dic61—41no—
137C4⋊Dic61—41no—
138C4⋊Dic61—41no—
139C4⋊Dic61—41no—
140#11758196—41no—
141#11758196—41no—
142#11758196—81no—
143#11758196—81no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61—21no—
148C23×C61#12011yescharacteristic
149C23×C61#12111yescharacteristic
150C23×C61#12311yescharacteristic
151C23×C61C2×Q1611yescharacteristic
152C23×C61#13511yescharacteristic
153C23×C61AGL(1,ℤ/8)11yescharacteristic
154C23×C61#13711yescharacteristic
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—21no—
159C2×C4×C61—22no—
160C2×C4×C61—22no—
161C2×C4×C61—22no—
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—42no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—81no—
175C2×C4×C61#12111yescharacteristic
176C2×C4×C61#12111yescharacteristic
177C2×C4×C61#12311yescharacteristic
178C2×C4×C61#12411yescharacteristic
179C2×Dic61—42no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—41no—
187C2×Dic61—41no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—42no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—81no—
198C2×Dic61—81no—
199C2×Dic61—81no—
200C2×Dic61—81no—
201C2×Dic61—81no—
202C2×Dic61—81no—
203C2×Dic61—81no—
204C2×Dic61—81no—
205Dic122—42no—
206Dic122—81no—
207C8×C61—42no—
208C8×C61—81no—
209#10400—611nomaximal, Sylow
210C22×C61—21no—
211C22×C61—21no—
212C22×C61—21no—
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61#39411yescharacteristic
223C22×C61#44911yescharacteristic
224C22×C61#45111yescharacteristic
225C22×C61#45411yescharacteristic
226C22×C61#45611yescharacteristic
227C22×C61B(4,𝔽2)11yescharacteristic
228C22×C61#45811yescharacteristic
229C22×C61#46711yescharacteristic
230C22×C61#46811yescharacteristic
231C22×C61#48411yescharacteristic
232C22×C61#48511yescharacteristic
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—21no—
236C4×C61—21no—
237C4×C61—42no—
238C4×C61—81no—
239Dic61—82no—
240Dic61—81no—
241Dic61—82no—
242Dic61—81no—
243Dic61—81no—
244Dic61—81no—
245#2627—611no—
246#1872—611no—
247#1852—611no—
248C2×#328—611no—
249C2×#324D6111yescharacteristic
250#1441—611no—
251#1294—611no—
252C2×C61—21no—
253C2×C61—21no—
254C2×C61—21no—
255C2×C61—21no—
256C2×C61#159711yescharacteristic
257C2×C61#160511yescharacteristic
258C2×C61#160911yescharacteristic
259C2×C61#161711yescharacteristic
260C2×C61#203611yescharacteristic
261C2×C61#203811yescharacteristic
262C2×C61#204411yescharacteristic
263C2×C22⋊Q8—611no—
264C22×C4⋊C4—611no—
265C22×C4⋊C4C2×D6111yescharacteristic
266C2×#107—1221no—
267C2×#103—1221no—
268C2×C22⋊C8C2×D6111yescharacteristic
269C2×C22⋊C8C2×D6111yescharacteristic
270#400—1221no—
271#398—1221no—
272#398—1221no—
273#395—1221no—
274#385—1221no—
275#381—1221no—
276#380—611no—
277C2×#95—611no—
278C2×#95—1221no—
279C2×#95—1221no—
280#340—1221no—
281#340—1221no—
282#328—1222no—
283#324—22no—
284C61#1040011yescharacteristic, complemented, Sylow
285C22×Q8—611no—
286C23×C4—1221no—
287C23×C4—1221no—
288C23×C4D24411yescharacteristic
289C23×C4D24411yescharacteristic
290C23×C4C22×D6111yescharacteristic
291C22×C8—21no—
292C22×C8—21no—
293C22⋊Q8—1221no—
294C22⋊Q8—1221no—
295C22⋊Q8—1221no—
296C22⋊Q8—1221no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—611no—
304C2×C4⋊C4—611no—
305C2×C4⋊C4—611no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4—1221no—
308C2×C4⋊C4—1221no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—2442no—
312C2×C22⋊C4—1221no—
313C2×C22⋊C4—1221no—
314#107—2442no—
315#103—2442no—
316C22⋊C8—21no—
317C22⋊C8—21no—
318C22⋊C8—21no—
319C22⋊C8C22⋊D6112yes—
320#95—1221no—
321#95—1221no—
322#95—1221no—
323#95—1221no—
324#95—1221no—
325#95—1221no—
326#95—1221no—
327#95—1221no—
328#95—1221no—
329#95—2442no—
330#95—2442no—
331C24C2×D24411yescharacteristic
332C2×Q8—1221no—
333C2×Q8—1221no—
334C2×Q8—2441no—
335C2×Q8—2441no—
336C22×C4—21no—
337C22×C4—21no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—21no—
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—1222no—
350C22×C4—1222no—
351C22×C4—1221no—
352C22×C4—1221no—
353C22×C4—1221no—
354C22×C4—1221no—
355C22×C4—2441no—
356C22×C4—2441no—
357C22×C4—2441no—
358C22×C4—2441no—
359C22×C4—2441no—
360C22×C4—2441no—
361C22×C4—2441no—
362C22×C4—2441no—
363C22×C4—2441no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4Dic24412yes—
368C22×C4#1175822211yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C22×C4D4×D6111yescharacteristic
371C22×C4#1175822411yescharacteristic
372C22×C4#1175822411yescharacteristic
373C22×C4C2×C22⋊D6111yescharacteristic
374C2×C8—22no—
375C2×C8—41no—
376C2×C8—41no—
377C2×C8—41no—
378C2×C8—41no—
379C2×C8—41no—
380C4⋊C4—41no—
381C4⋊C4—41no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—1222no—
385C4⋊C4—1222no—
386C4⋊C4—1221no—
387C4⋊C4—1221no—
388C4⋊C4—4881no—
389C4⋊C4—4881no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4—2441no—
393C4⋊C4—2441no—
394C4⋊C4—2441no—
395C4⋊C4—2441no—
396C22⋊C4—2441no—
397C22⋊C4—2441no—
398C22⋊C4—2441no—
399C22⋊C4—2441no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23#1451974711yescharacteristic
405C23#1451975111yescharacteristic
406C23#1451976111yescharacteristic
407C23C2×Dic24411yescharacteristic
408C23#1451979911yescharacteristic
409C23#1451980511yescharacteristic
410C23#1451981011yescharacteristic
411Q8—4881no—
412Q8—2442no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—81no—
433C2×C4—4881no—
434C2×C4—4881no—
435C2×C4—4881no—
436C2×C4—4881no—
437C2×C4—4881no—
438C2×C4—4881no—
439C2×C4—4881no—
440C2×C4—4881no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2442no—
445C2×C4—2442no—
446C2×C4—2441no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2442no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4#1451974811yescharacteristic
460C2×C4#1451974911yescharacteristic
461C2×C4#1451975911yescharacteristic
462C2×C4#1451976311yescharacteristic
463C8—42no—
464C8—81no—
465C22—21no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22#1683967811yescharacteristic
478C22#1683990911yescharacteristic
479C22#1683992011yescharacteristic
480C22#1683993711yescharacteristic
481C22#1683994711yescharacteristic
482C22#1683995011yescharacteristic
483C22#1683995311yescharacteristic
484C22#1684000311yescharacteristic
485C22#1684000811yescharacteristic
486C22#1684009811yescharacteristic
487C22#1684010411yescharacteristic
488C4—21no—
489C4—21no—
490C4—21no—
491C4—21no—
492C4—42no—
493C4—81no—
494C4—4882no—
495C4—4881no—
496C4—4882no—
497C4—4881no—
498C4—4881no—
499C4—4881no—
500C2—21no—
501C2—21no—
502C2—21no—
503C2—21no—
504C2#2144475011yescharacteristic
505C2#2144479511yescharacteristic
506C2#2144481811yescharacteristic
507C2#2144486311yescharacteristic
508C2#2144702311yescharacteristic
509C2#2144703711yescharacteristic
510C2#2144706911yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenterC2×#324D61
hypocenterC61#10400
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
284. C61#10400semidirect

Maximal subgroups

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

subgroupindex
#214516322
#214461242
#214460092
C2×#168395002
#214440722
#214436992
C2×C61×#3242
#1040061