Finite Group Databasebeta

← #29575287

Subgroups — #29575287

Order 15616.

822 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840138C211yesmaximal, characteristic
2#21448883C211yesmaximal, characteristic, complemented
3#21446747C211yesmaximal, characteristic, complemented
4C2×#16839505C211yesmaximal, characteristic, complemented
5#21443660C211yesmaximal, characteristic, complemented
6#21443658C211yesmaximal, characteristic, complemented
7C61×#1982C211yesmaximal, characteristic, complemented
8C22×#11758199—22no—
9C2×#14519774C2211yescharacteristic
10C2×C4×D244—21no—
11C2×#14519739—21no—
12#16840138—22no—
13#16840138C414yescomplemented
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—21no—
16C2×#14519698—21no—
17C2×C4×#92418C2211yescharacteristic
18#16839664—21no—
19#16839663—21no—
20#16839640—22no—
21C4×C4⋊Dic61C2211yescharacteristic
22#16839505—22no—
23C2×#127×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×#102×C61—21no—
26C2×#102×C61—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×D244—21no—
29C22×D244—21no—
30C22×D244D412yes—
31C22×C4×D61—22no—
32C2×#11758199—28no—
33C2×#11758199—44no—
34C2×#11758199—44no—
35C22×#92418—21no—
36C22×#92418—21no—
37#14519774—21no—
38#14519774—21no—
39#14519774C2×C412yes—
40#14519774D412yes—
41C4×D244—42no—
42C4×D244—42no—
43#14519739—42no—
44#14519739—42no—
45C2×C4⋊Dic61D411yescharacteristic
46C2×C4⋊Dic61D411yescharacteristic
47C2×#11758198—22no—
48C2×#11758198—22no—
49C2×#11758198—22no—
50C2×C4×Dic61—21no—
51C4⋊#92418—21no—
52C4⋊#92418—21no—
53#14519698—42no—
54#14519698—42no—
55C4×#92418—21no—
56C4×#92418C2×C412yescomplemented
57#14519684—21no—
58C22×D4×C61—21no—
59C22×D4×C61—21no—
60C22×D4×C61—21no—
61C22×C8×C61—21no—
62#127×C61—21no—
63#127×C61—21no—
64#127×C61—21no—
65#127×C61C2×C412yescomplemented
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C42×C61—21no—
69C2×C42×C61C2311yescharacteristic
70C4⋊C8×C61—21no—
71C4⋊C8×C61—21no—
72#102×C61—42no—
73#102×C61—42no—
74#95×C61—21no—
75C24×C61—41no—
76C23×D61—22no—
77C2×D4×C61—22no—
78C2×D4×C61—22no—
79C2×D4×C61—22no—
80C2×D4×C61—42no—
81C2×D4×C61—42no—
82C2×D4×C61—41no—
83C2×D4×C61—41no—
84C2×D4×C61—41no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61C2×D411yescharacteristic
96C22×C4×C61C2×D411yescharacteristic
97C22×C4×C61C2×D411yescharacteristic
98C22×Dic61—21no—
99C22×Dic61—21no—
100C2×D244—22no—
101C2×D244—22no—
102C2×D244—22no—
103C2×D244—22no—
104C2×D244—22no—
105C2×D244—41no—
106C2×D244—41no—
107C2×D244—41no—
108C2×D244—41no—
109C2×D244—41no—
110C2×D244—41no—
111C2×D244—41no—
112C2×D244—41no—
113C2×D244—42no—
114C2×D244—42no—
115C2×D244C22⋊C414yes—
116C2×C4×D61—44no—
117C2×C4×D61—44no—
118C2×C4×D61—82no—
119C2×C8×C61—41no—
120C2×C8×C61—41no—
121C2×C8×C61—41no—
122C4⋊C4×C61—21no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61D812yescomplemented
126C42×C61—41no—
127C42×C61—41no—
128C42×C61C22×C411yescharacteristic
129C42×C61C2×D411yescharacteristic
130C42×C61#4111yescharacteristic
131C42×C61#4111yescharacteristic
132#11758199—416no—
133#11758198—44no—
134#11758198—44no—
135#11758198—82no—
136C4⋊Dic61—21no—
137C4⋊Dic61—21no—
138C4⋊Dic61—21no—
139C4⋊Dic61D812yescomplemented
140C4×Dic61—41no—
141C4×Dic61—41no—
142C2×#92418—22no—
143C2×#92418—22no—
144C2×#92418—22no—
145C2×#92418—41no—
146C2×#92418—41no—
147C2×#92418—41no—
148C23×C61—42no—
149C23×C61—81no—
150C23×C61—81no—
151C23×C61—81no—
152C23×C61—81no—
153C23×C61—81no—
154C23×C61—81no—
155C23×C61#12011yescharacteristic
156C22×D61—24no—
157C22×D61—42no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61—42no—
162C22×D61—42no—
163D4×C61—44no—
164D4×C61—42no—
165D4×C61—42no—
166D4×C61—42no—
167D4×C61—42no—
168D4×C61—82no—
169D4×C61—81no—
170D4×C61—81no—
171D4×C61—81no—
172D4×C61—81no—
173C2×C4×C61—21no—
174C2×C4×C61—21no—
175C2×C4×C61—22no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61C2×C22⋊C411yescharacteristic
182C2×C4×C61C4×D411yescharacteristic
183C2×C4×C61C4×D411yescharacteristic
184C2×C4×C61#12111yescharacteristic
185C2×C4×C61#12111yescharacteristic
186C2×C4×C61#12311yescharacteristic
187C2×C4×C61C2×D811yescharacteristic
188C2×C4×C61C2×D811yescharacteristic
189C2×C4×C61#13511yescharacteristic
190C2×C4×C61#13511yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
194C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
195C2×Dic61—22no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—41no—
201D244—44no—
202D244—42no—
203D244—42no—
204D244—42no—
205D244—42no—
206D244—42no—
207D244—42no—
208D244—42no—
209D244—42no—
210D244—82no—
211C4×D61—88no—
212C8×C61—81no—
213#92418—24no—
214#92418—81no—
215#9061—611nomaximal, Sylow
216C22×C61—82no—
217C22×C61—82no—
218C22×C61—82no—
219C22×C61—161no—
220C22×C61—161no—
221C22×C61—161no—
222C22×C61—161no—
223C22×C61#38611yescharacteristic
224C22×C61#44711yescharacteristic
225C22×C61#44711yescharacteristic
226C22×C61#44911yescharacteristic
227C22×C61#44911yescharacteristic
228C22×C61#45311yescharacteristic
229C22×C61#45311yescharacteristic
230C2×D61—44no—
231C2×D61—44no—
232C2×D61—44no—
233C2×D61—82no—
234C2×D61—82no—
235C2×D61—82no—
236C2×D61—82no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—42no—
240C4×C61—81no—
241C4×C61C4×D811yescharacteristic
242C4×C61C4×D811yescharacteristic
243C4×C61#44211yescharacteristic
244C4×C61#44211yescharacteristic
245C4×C61#45911yescharacteristic
246C4×C61#45911yescharacteristic
247C4×C61#46311yescharacteristic
248C4×C61#46311yescharacteristic
249Dic61—42no—
250Dic61—81no—
251C2×#493—611no—
252#2366—611no—
253#1982—611no—
254#1982D6111yescharacteristic, complemented
255C2×#331—611no—
256#1279—611no—
257#1279—611no—
258C2×C61—162no—
259C2×C61#161911yescharacteristic
260C2×C61#162011yescharacteristic
261C2×C61#162111yescharacteristic
262C2×C61#162111yescharacteristic
263C2×C61#187911yescharacteristic
264C2×C61#187911yescharacteristic
265C2×C61#188711yescharacteristic
266D61—84no—
267C22×D8—1222no—
268C2×#127—611no—
269C2×#127C2×D6111yescharacteristic
270C2×C4×D4—1221no—
271C2×C4×D4—1221no—
272#493—614no—
273#493—1222no—
274C2×C4⋊C8—611no—
275C2×C4⋊C8C2×D6111yescharacteristic
276C2×#102—21no—
277C2×#102—21no—
278C2×#102—1221no—
279C2×#102—1221no—
280C2×C4×C8—611no—
281#390—1221no—
282#390—1221no—
283#386—1222no—
284C4×C4⋊C4—611no—
285C4×C4⋊C4C2×D6111yescharacteristic
286#331—1222no—
287C61#906111yescharacteristic, complemented, Sylow
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—21no—
291C22×D4—612no—
292C22×D4—1221no—
293C22×D4—1221no—
294C23×C4—1222no—
295C2×D8—1228no—
296C2×D8—2444no—
297C2×D8—2444no—
298C22×C8—21no—
299C22×C8—1221no—
300C22×C8—1221no—
301#127—21no—
302#127—21no—
303#127—21no—
304#127—612no—
305#127—612no—
306#127—1221no—
307#127—1221no—
308#127C4×D6112yescomplemented
309C4×D4—2442no—
310C4×D4—2442no—
311C4×D4—2442no—
312C4×D4—2442no—
313C2×C4⋊C4—611no—
314C2×C4⋊C4—611no—
315C2×C4⋊C4C22⋊D6111yescharacteristic
316C2×C4⋊C4C22⋊D6111yescharacteristic
317C2×C22⋊C4—1222no—
318C2×C22⋊C4—1222no—
319C2×C22⋊C4—1222no—
320C2×C42—21no—
321C2×C42—1221no—
322C2×C42C22×D6111yescharacteristic
323C4⋊C8—21no—
324C4⋊C8—21no—
325C4⋊C8—1221no—
326C4⋊C8—1221no—
327#102—42no—
328#102—42no—
329#102—2442no—
330#102—2442no—
331C4×C8—612no—
332C4×C8—1221no—
333#95—21no—
334#95—1221no—
335C24—41no—
336C24—1222no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—22no—
340C2×D4—42no—
341C2×D4—42no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—614no—
354C2×D4—1222no—
355C2×D4—1222no—
356C2×D4—1222no—
357C2×D4—1222no—
358C2×D4—1222no—
359C2×D4—2442no—
360C2×D4—2442no—
361C2×D4—2441no—
362C2×D4—2441no—
363C2×D4—2441no—
364C2×D4—2441no—
365C2×D4—2441no—
366C2×D4—2441no—
367C2×D4—2441no—
368C2×D4—2441no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—1221no—
372C22×C4—1221no—
373C22×C4—4882no—
374C22×C4—2444no—
375C22×C4—2444no—
376C22×C4D4×D6111yescharacteristic
377C22×C4D4×D6111yescharacteristic
378C22×C4C2×C22⋊D6111yescharacteristic
379D8—24416no—
380C2×C8—41no—
381C2×C8—41no—
382C2×C8—41no—
383C2×C8—1222no—
384C2×C8—1222no—
385C2×C8—1222no—
386C2×C8—2441no—
387C2×C8—2441no—
388C2×C8—2441no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—612no—
393C4⋊C4—1221no—
394C4⋊C4—1221no—
395C4⋊C4—1221no—
396C4⋊C4#1175819912yescomplemented
397C22⋊C4—4882no—
398C22⋊C4—2444no—
399C22⋊C4—2444no—
400C42—41no—
401C42—41no—
402C42—2441no—
403C42—2441no—
404C42C2×C4×D6111yescharacteristic
405C42#1175822211yescharacteristic
406C42D4×D6111yescharacteristic
407C42#1175822411yescharacteristic
408C23—42no—
409C23—81no—
410C23—81no—
411C23—81no—
412C23—81no—
413C23—81no—
414C23—81no—
415C23—1224no—
416C23—2442no—
417C23—2442no—
418C23—2442no—
419C23—2442no—
420C23—2442no—
421C23—2442no—
422C23#1451974511yescharacteristic
423D4—44no—
424D4—42no—
425D4—42no—
426D4—42no—
427D4—42no—
428D4—82no—
429D4—81no—
430D4—81no—
431D4—81no—
432D4—81no—
433D4—4882no—
434D4—2444no—
435D4—2442no—
436D4—2442no—
437D4—2442no—
438D4—2442no—
439D4—2442no—
440D4—2442no—
441D4—2442no—
442D4—2442no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—1222no—
452C2×C4—4888no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4C22⋊C4×D6111yescharacteristic
459C2×C4#1451973711yescharacteristic
460C2×C4C4×C22⋊D6111yescharacteristic
461C2×C4#1451974811yescharacteristic
462C2×C4#1451975011yescharacteristic
463C2×C4#1451975911yescharacteristic
464C2×C4D8×D6111yescharacteristic
465C2×C4C2×#1175819911yescharacteristic
466C2×C4#1451979711yescharacteristic
467C2×C4#1451979811yescharacteristic
468C2×C4#1451980111yescharacteristic
469C2×C4#1451980211yescharacteristic
470C2×C4#1451980311yescharacteristic
471C2×C4#1451980411yescharacteristic
472C8—81no—
473C8—1224no—
474C8—4881no—
475C22—82no—
476C22—82no—
477C22—82no—
478C22—161no—
479C22—161no—
480C22—161no—
481C22—161no—
482C22—4882no—
483C22—4882no—
484C22—4882no—
485C22—4882no—
486C22—2444no—
487C22—2444no—
488C22—2444no—
489C22#1683963811yescharacteristic
490C22#1683989411yescharacteristic
491C22#1683989511yescharacteristic
492C22#1683990511yescharacteristic
493C22#1683990611yescharacteristic
494C22#1683992811yescharacteristic
495C22#1683992811yescharacteristic
496C4—21no—
497C4—21no—
498C4—42no—
499C4—81no—
500C4—4881no—
501C4—2442no—
502C4#1683984211yescharacteristic
503C4C4×#1175819911yescharacteristic
504C4#1683987111yescharacteristic
505C4#1683987211yescharacteristic
506C4#1683995411yescharacteristic
507C4#1683995611yescharacteristic
508C4#1683997411yescharacteristic
509C4#1683997611yescharacteristic
510C2—162no—
511C2—4884no—
512C2#2144487211yescharacteristic
513C2#2144487711yescharacteristic
514C2#2144488211yescharacteristic
515C2#2144488311yescharacteristic
516C2#2144616411yescharacteristic
517C2#2144617011yescharacteristic
518C2#2144621411yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1982C2
socleC23×C61#120
prime radicalC2×#16840138C2
cosocleC2×C42×C61C23
hypercenter#1982D61
hypocenterC61#9061
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. #21448883C2semidirect
3. #21446747C2semidirect
4. C2×#16839505C2semidirect
5. #21443660C2semidirect
6. #21443658C2semidirect
7. C61×#1982C2semidirect
13. #16840138C4semidirect
56. C4×#92418C2×C4semidirect
65. #127×C61C2×C4semidirect
125. C4⋊C4×C61D8semidirect
139. C4⋊Dic61D8semidirect
254. #1982D61semidirect
287. C61#9061semidirect
308. #127C4×D61semidirect
396. C4⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168401382
#214488832
#214467472
C2×#168395052
#214436602
#214436582
C61×#19822
#906161