Finite Group Databasebeta

← #29574113

Subgroups — #29574113

Order 15616.

702 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21448522C211yesmaximal, characteristic
2#21446134C211yesmaximal, characteristic
3#21446014C211yesmaximal, characteristic, complemented
4C2×#16839497C211yesmaximal, characteristic
5#21444083C211yesmaximal, characteristic, complemented
6#21443699C211yesmaximal, characteristic, complemented
7C61×#1280C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×C4×C22⋊D61—21no—
10C22×C4⋊Dic61C2211yescharacteristic
11C22×#11758196—21no—
12C2×#14519709—21no—
13C2×#14519699—21no—
14#16839654—21no—
15#16839647—21no—
16#16839641—21no—
17#16839640—21no—
18#16839636—21no—
19#16839622C2211yescharacteristic
20C2×#14519684—21no—
21C2×#14519684C2211yescharacteristic
22#16839525—21no—
23#16839525—21no—
24#16839497C414yescomplemented
25C2×C22⋊C8×C61C2211yescharacteristic
26C2×C22⋊C8×C61C2211yescharacteristic
27C2×#95×C61C2211yescharacteristic
28C22×D244D411yescharacteristic
29C22×C22⋊D61—21no—
30C23×Dic61—21no—
31C23×Dic61—21no—
32C22×C4×D61—21no—
33#14519751—21no—
34#14519751—21no—
35#14519751C2×C412yes—
36#14519751Q812yes—
37C4×C22⋊D61—42no—
38C4×C22⋊D61—42no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61—42no—
42C2×C4⋊Dic61D411yescharacteristic
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—42no—
47C2×#11758196—42no—
48C2×#11758196—42no—
49C2×C22⋊Dic61—21no—
50C2×#11758198—21no—
51C2×#11758198—21no—
52C2×#11758198—21no—
53C2×#11758198—21no—
54C2×C4×Dic61—21no—
55#14519709—42no—
56#14519699—42no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—42no—
62#14519684C2×C412yescomplemented
63C23×C4×C61D411yescharacteristic
64C23×C4×C61D411yescharacteristic
65C23×C4×C61C2311yescharacteristic
66C22×C8×C61—21no—
67C22×C8×C61—21no—
68C22⋊C8×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71C22⋊C8×C61C2×C412yescomplemented
72#95×C61—21no—
73#95×C61—21no—
74C24×C61C2×D411yescharacteristic
75C23×D61—21no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
78C22×C4×C61—21no—
79C22×C4×C61—21no—
80C22×C4×C61—21no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61—41no—
87C22×C4×C61SD1612yes—
88C22×C4×C61C22×C411yescharacteristic
89C22×C4×C61C2×D411yescharacteristic
90C22×C4×C61C2×D411yescharacteristic
91C22×C4×C61C2×Q811yescharacteristic
92C22×C4×C61#4111yescharacteristic
93C22×C4×C61#4111yescharacteristic
94C2×C22⋊D61—22no—
95C2×C22⋊D61—22no—
96C2×C22⋊D61—41no—
97C2×C22⋊D61—41no—
98C2×C22⋊D61—41no—
99C2×C22⋊D61—41no—
100C22×Dic61—22no—
101C22×Dic61—22no—
102C22×Dic61—22no—
103C22×Dic61—21no—
104C22×Dic61—22no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C22×Dic61—41no—
110C22×Dic61—41no—
111C22×Dic61—41no—
112C22×Dic61—41no—
113C22×Dic61—41no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—41no—
117C2×D244—21no—
118C2×D244—41no—
119C2×D244—41no—
120C2×D244C4⋊C412yescomplemented
121C2×C4×D61—42no—
122C2×C4×D61—81no—
123C2×C4×D61—81no—
124C2×C8×C61—22no—
125C2×C8×C61—41no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C2×C8×C61—41no—
129C2×C8×C61—41no—
130C22⋊Dic61—41no—
131C22⋊Dic61—41no—
132#11758198—22no—
133#11758198—22no—
134#11758198—42no—
135#11758198—81no—
136#11758198—81no—
137C4⋊Dic61—21no—
138C4⋊Dic61—22no—
139C4⋊Dic61—22no—
140C4⋊Dic61—41no—
141C4⋊Dic61—41no—
142C4⋊Dic61—41no—
143C4⋊Dic61—41no—
144C4⋊Dic61C4⋊C412yescomplemented
145#11758196—42no—
146#11758196—48no—
147C4×Dic61—42no—
148C23×C61—21no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61C4×D411yescharacteristic
153C23×C61#12011yescharacteristic
154C23×C61C22⋊Q811yescharacteristic
155C23×C61C2×SD1611yescharacteristic
156C23×C61#13511yescharacteristic
157C23×C61AGL(1,ℤ/8)11yescharacteristic
158C23×C61AGL(1,ℤ/8)11yescharacteristic
159C22×D61—22no—
160C22×D61—41no—
161C22×D61—41no—
162C22×D61—41no—
163C22×D61—41no—
164C22×D61—41no—
165C22×D61—41no—
166C2×C4×C61—21no—
167C2×C4×C61—21no—
168C2×C4×C61—21no—
169C2×C4×C61—21no—
170C2×C4×C61—22no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—42no—
178C2×C4×C61—42no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—81no—
183C2×C4×C61—81no—
184C2×C4×C61C2×C4⋊C411yescharacteristic
185C2×C4×C61C4×D411yescharacteristic
186C2×C4×C61C22⋊Q811yescharacteristic
187C2×C4×C61#12311yescharacteristic
188C22⋊D61—42no—
189C22⋊D61—42no—
190C22⋊D61—42no—
191C22⋊D61—42no—
192C2×Dic61—24no—
193C2×Dic61—22no—
194C2×Dic61—42no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61—42no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—81no—
212C2×Dic61—81no—
213C2×Dic61—81no—
214C2×Dic61—81no—
215D244—42no—
216D244—81no—
217C4×D61—84no—
218C8×C61—42no—
219C8×C61—81no—
220#8873—611nomaximal, Sylow
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61—21no—
233C22×C61#38511yescharacteristic
234C22×C61C4×SD1611yescharacteristic
235C22×C61#44211yescharacteristic
236C22×C61#44911yescharacteristic
237C22×C61#45011yescharacteristic
238C22×C61#45311yescharacteristic
239C22×C61#45611yescharacteristic
240C22×C61B(4,𝔽2)11yescharacteristic
241C22×C61#45811yescharacteristic
242C22×C61#47611yescharacteristic
243C22×C61#47811yescharacteristic
244C2×D61—42no—
245C2×D61—42no—
246C2×D61—42no—
247C2×D61—81no—
248C2×D61—81no—
249C2×D61—81no—
250C2×D61—81no—
251C4×C61—21no—
252C4×C61—21no—
253C4×C61—21no—
254C4×C61—21no—
255C4×C61—42no—
256C4×C61—81no—
257Dic61—44no—
258Dic61—42no—
259Dic61—82no—
260Dic61—81no—
261Dic61—81no—
262#2325—611no—
263#1874—611no—
264#1853—611no—
265C2×#327—611no—
266#1444—611no—
267#1294—611no—
268#1280D6111yescharacteristic, complemented
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—21no—
273C2×C61#160011yescharacteristic
274C2×C61#160411yescharacteristic
275C2×C61#160911yescharacteristic
276C2×C61#161311yescharacteristic
277C2×C61#185911yescharacteristic
278C2×C61#186411yescharacteristic
279C2×C61#186711yescharacteristic
280D61—82no—
281C2×#121—611no—
282C2×C4×D4—1221no—
283C22×C4⋊C4—611no—
284C22×C4⋊C4—1221no—
285C2×#106—1221no—
286C2×#102—1221no—
287C2×C22⋊C8C2×D6111yescharacteristic
288C2×C22⋊C8C2×D6111yescharacteristic
289#388—1221no—
290#387—1221no—
291#386—1221no—
292#386—1221no—
293#385—1221no—
294#380—611no—
295C2×#95—611no—
296C2×#95—1221no—
297C2×#95C2×D6111yescharacteristic
298#340—1221no—
299#340—1221no—
300#327—614no—
301C61#887311yescharacteristic, complemented, Sylow
302C22×D4—611no—
303C22×D4—1221no—
304C23×C4—1221no—
305C23×C4—1221no—
306C23×C4—1221no—
307C23×C4D24411yescharacteristic
308C23×C4D24411yescharacteristic
309C23×C4C22×D6111yescharacteristic
310C22×C8—21no—
311C22×C8—21no—
312#121—612no—
313#121—612no—
314#121—1221no—
315#121—1221no—
316C4×D4—2442no—
317C4×D4—2442no—
318C2×C4⋊C4—611no—
319C2×C4⋊C4—611no—
320C2×C4⋊C4—611no—
321C2×C4⋊C4—1221no—
322C2×C4⋊C4—1221no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4—2442no—
325C2×C4⋊C4—2442no—
326C2×C4⋊C4—2442no—
327C2×C4⋊C4—2442no—
328C2×C22⋊C4—1221no—
329C2×C22⋊C4—1221no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4—1221no—
332C2×C22⋊C4—1221no—
333C2×C42—1221no—
334#106—2442no—
335#102—2442no—
336C22⋊C8—21no—
337C22⋊C8—21no—
338C22⋊C8—21no—
339C22⋊C8C4×D6112yescomplemented
340#95—21no—
341#95—21no—
342#95—612no—
343#95—1221no—
344#95—1221no—
345#95—1221no—
346#95—1221no—
347#95—2442no—
348C24—1221no—
349C24C2×D24411yescharacteristic
350C2×D4—612no—
351C2×D4—1222no—
352C2×D4—1222no—
353C2×D4—1221no—
354C2×D4—2441no—
355C2×D4—2441no—
356C2×D4—2441no—
357C2×D4—2441no—
358C2×D4—2441no—
359C2×D4—2441no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—1222no—
372C22×C4—1222no—
373C22×C4—1222no—
374C22×C4—1221no—
375C22×C4—1222no—
376C22×C4—1221no—
377C22×C4—1221no—
378C22×C4—4881no—
379C22×C4—4881no—
380C22×C4—2442no—
381C22×C4—2441no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4#1175819012yes—
392C22×C4C2×C4×D6111yescharacteristic
393C22×C4#1175822211yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4D4×D6111yescharacteristic
396C22×C4#1175822411yescharacteristic
397C22×C4Q8×D6111yescharacteristic
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—41no—
402C2×C8—41no—
403C2×C8—41no—
404C4⋊C4—612no—
405C4⋊C4—1222no—
406C4⋊C4—1222no—
407C4⋊C4—1221no—
408C4⋊C4—2441no—
409C4⋊C4—2441no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2442no—
413C4⋊C4—2448no—
414C22⋊C4—1222no—
415C22⋊C4—1222no—
416C22⋊C4—4881no—
417C22⋊C4—4881no—
418C22⋊C4—2442no—
419C22⋊C4—2441no—
420C22⋊C4—2441no—
421C42—2442no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—1222no—
427C23—2441no—
428C23—2441no—
429C23—2441no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23C4×D24411yescharacteristic
434C23#1451974711yescharacteristic
435C23#1451975711yescharacteristic
436C23C2×#1175819011yescharacteristic
437C23#1451979911yescharacteristic
438C23#1451980511yescharacteristic
439C23#1451980511yescharacteristic
440D4—4881no—
441D4—2442no—
442D4—2442no—
443D4—2442no—
444D4—2442no—
445D4—2442no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—22no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—1224no—
465C2×C4—1222no—
466C2×C4—4884no—
467C2×C4—4881no—
468C2×C4—4881no—
469C2×C4—4881no—
470C2×C4—4881no—
471C2×C4—2442no—
472C2×C4—2442no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2442no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2442no—
481C2×C4—2442no—
482C2×C4—2442no—
483C2×C4—2442no—
484C2×C4—2442no—
485C2×C4—2442no—
486C2×C4—2441no—
487C2×C4—2441no—
488C2×C4C4⋊C4×D6111yescharacteristic
489C2×C4#1451973711yescharacteristic
490C2×C4#1451975511yescharacteristic
491C2×C4#1451975911yescharacteristic
492C8—42no—
493C8—81no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—21no—
501C22—21no—
502C22—21no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—4881no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—2442no—
511C22—2442no—
512C22—2442no—
513C22#1683963611yescharacteristic
514C22C4×#1175819011yescharacteristic
515C22#1683987511yescharacteristic
516C22#1683990911yescharacteristic
517C22#1683991511yescharacteristic
518C22#1683993211yescharacteristic
519C22#1683994711yescharacteristic
520C22#1683995011yescharacteristic
521C22#1683995311yescharacteristic
522C22#1684005311yescharacteristic
523C22#1684006311yescharacteristic
524C4—21no—
525C4—21no—
526C4—21no—
527C4—21no—
528C4—42no—
529C4—81no—
530C4—4882no—
531C4—4881no—
532C4—4881no—
533C4—2444no—
534C4—2442no—
535C2—21no—
536C2—21no—
537C2—21no—
538C2—21no—
539C2—4882no—
540C2#2144476711yescharacteristic
541C2#2144479011yescharacteristic
542C2#2144481811yescharacteristic
543C2#2144484111yescharacteristic
544C2#2144604811yescharacteristic
545C2#2144608311yescharacteristic
546C2#2144610111yescharacteristic
subgroupG/H
centerC23#14519747
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1280C2
socleC23×C61#120
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenter#1280D61
hypocenterC61#8873
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1280

Complements

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

NH ≅ G/Ntype
3. #21446014C2semidirect
5. #21444083C2semidirect
6. #21443699C2semidirect
7. C61×#1280C2semidirect
24. #16839497C4semidirect
62. #14519684C2×C4semidirect
71. C22⋊C8×C61C2×C4semidirect
120. C2×D244C4⋊C4semidirect
144. C4⋊Dic61C4⋊C4semidirect
268. #1280D61semidirect
301. C61#8873semidirect
339. C22⋊C8C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214485222
#214461342
#214460142
C2×#168394972
#214440832
#214436992
C61×#12802
#887361