Finite Group Databasebeta

← #29574777

Subgroups — #29574777

Order 15616.

764 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
1C2×#16839954C211yesmaximal, characteristic
2C4⋊C4×D244C211yesmaximal, characteristic, complemented
3#21446626C211yesmaximal, characteristic, complemented
4C2×#16839489C211yesmaximal, characteristic, complemented
5#21443703C211yesmaximal, characteristic, complemented
6#21443660C211yesmaximal, characteristic, complemented
7C61×#1982C211yesmaximal, characteristic, complemented
8C22×#11758199—21no—
9C2×C4×D244—21no—
10C2×C4×D244C2211yescharacteristic
11C2×C4⋊C4×D61—21no—
12#16839954—22no—
13#16839954C414yescomplemented
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519698—21no—
16C2×#14519698—22no—
17C2×C4×#92418C2211yescharacteristic
18#16839660—21no—
19#16839636—22no—
20#16839632C2211yescharacteristic
21#16839619—21no—
22#16839489—22no—
23C2×#127×C61C2211yescharacteristic
24C2×C4⋊C8×C61C2211yescharacteristic
25C2×#102×C61—21no—
26C2×#102×C61—21no—
27C4×C4⋊C4×C61C2211yescharacteristic
28C22×D244D411yescharacteristic
29C22×C4×D61—21no—
30C22×C4×D61—22no—
31C2×#11758199—24no—
32C2×#11758199—42no—
33C2×#11758199—42no—
34C22×#92418—21no—
35C22×#92418—21no—
36C4×D244—21no—
37C4×D244—21no—
38C4×D244—42no—
39C4×D244—42no—
40C4×D244C2×C412yes—
41C4×D244D412yes—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61—21no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×C4⋊Dic61D412yes—
46C2×#11758196—22no—
47C4⋊C4×D61—42no—
48C4⋊C4×D61—42no—
49C2×#11758198—21no—
50C2×#11758198—22no—
51C4⋊#92418—21no—
52C4⋊#92418C2×C412yescomplemented
53#14519698—24no—
54#14519698—44no—
55C4×#92418—21no—
56C4×#92418—21no—
57#14519684—22no—
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—21no—
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—22no—
100C2×D244—21no—
101C2×D244—21no—
102C2×D244—21no—
103C2×D244C22⋊C412yes—
104C2×D244D812yes—
105C2×D244SD1612yes—
106C2×C4×D61—22no—
107C2×C4×D61—22no—
108C2×C4×D61—41no—
109C2×C4×D61—41no—
110C2×C4×D61—41no—
111C2×C4×D61—41no—
112C2×C4×D61—44no—
113C2×C4×D61—44no—
114C2×C4×D61—82no—
115C2×C8×C61—41no—
116C2×C8×C61—41no—
117C2×C8×C61—41no—
118C4⋊C4×C61—21no—
119C4⋊C4×C61—21no—
120C4⋊C4×C61—21no—
121C4⋊C4×C61D812yescomplemented
122C42×C61—41no—
123C42×C61—41no—
124C42×C61C22×C411yescharacteristic
125C42×C61C2×D411yescharacteristic
126C42×C61#4111yescharacteristic
127C42×C61#4111yescharacteristic
128#11758199—48no—
129#11758198—22no—
130#11758198—22no—
131#11758198—44no—
132C4⋊Dic61—21no—
133C4⋊Dic61—41no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C4⋊Dic61—41no—
137C4⋊Dic61—42no—
138C4⋊Dic61C22⋊C412yes—
139#11758196—44no—
140C2×#92418—22no—
141C2×#92418—22no—
142C2×#92418—41no—
143C2×#92418—41no—
144C2×#92418—41no—
145C2×#92418—41no—
146C23×C61—42no—
147C23×C61—81no—
148C23×C61—81no—
149C23×C61—81no—
150C23×C61—81no—
151C23×C61—81no—
152C23×C61—81no—
153C23×C61#12011yescharacteristic
154C22×D61—22no—
155C22×D61—22no—
156C22×D61—22no—
157C22×D61—41no—
158C22×D61—41no—
159C22×D61—41no—
160C22×D61—41no—
161D4×C61—44no—
162D4×C61—42no—
163D4×C61—42no—
164D4×C61—42no—
165D4×C61—42no—
166D4×C61—82no—
167D4×C61—81no—
168D4×C61—81no—
169D4×C61—81no—
170D4×C61—81no—
171C2×C4×C61—21no—
172C2×C4×C61—21no—
173C2×C4×C61—22no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61C2×C22⋊C411yescharacteristic
180C2×C4×C61C4×D411yescharacteristic
181C2×C4×C61C4×D411yescharacteristic
182C2×C4×C61#12111yescharacteristic
183C2×C4×C61#12111yescharacteristic
184C2×C4×C61#12311yescharacteristic
185C2×C4×C61C2×D811yescharacteristic
186C2×C4×C61C2×D811yescharacteristic
187C2×C4×C61C2×SD1611yescharacteristic
188C2×C4×C61#13511yescharacteristic
189C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
191C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
192C2×C4×C61#13711yescharacteristic
193C2×Dic61—22no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—42no—
197C2×Dic61—42no—
198C2×Dic61—42no—
199D244—22no—
200D244—22no—
201D244—22no—
202D244#10214yescomplemented
203C4×D61—42no—
204C4×D61—42no—
205C4×D61—42no—
206C4×D61—42no—
207C4×D61—88no—
208C8×C61—81no—
209#92418—42no—
210#92418—42no—
211#8977—611nomaximal, Sylow
212C22×C61—82no—
213C22×C61—82no—
214C22×C61—82no—
215C22×C61—161no—
216C22×C61—161no—
217C22×C61—161no—
218C22×C61—161no—
219C22×C61#38611yescharacteristic
220C22×C61#44711yescharacteristic
221C22×C61#44711yescharacteristic
222C22×C61#44811yescharacteristic
223C22×C61#44911yescharacteristic
224C22×C61#45311yescharacteristic
225C22×C61#45411yescharacteristic
226C2×D61—24no—
227C2×D61—42no—
228C2×D61—42no—
229C2×D61—42no—
230C2×D61—42no—
231C2×D61—42no—
232C2×D61—42no—
233C4×C61—21no—
234C4×C61—21no—
235C4×C61—42no—
236C4×C61—81no—
237C4×C61C2×#10211yescharacteristic
238C4×C61#41711yescharacteristic
239C4×C61C4×D811yescharacteristic
240C4×C61#44211yescharacteristic
241C4×C61#45911yescharacteristic
242C4×C61#46311yescharacteristic
243C4×C61#48011yescharacteristic
244C4×C61#48111yescharacteristic
245Dic61—42no—
246Dic61—82no—
247C2×#459—611no—
248D4×C4⋊C4—611no—
249#1982D6111yescharacteristic, complemented
250#1957—611no—
251C2×D4⋊C8—611no—
252#1296—611no—
253#1279—611no—
254C2×C61—162no—
255C2×C61#161911yescharacteristic
256C2×C61#162211yescharacteristic
257C2×C61#162511yescharacteristic
258C2×C61#162711yescharacteristic
259C2×C61#187411yescharacteristic
260C2×C61#187911yescharacteristic
261C2×C61#188311yescharacteristic
262D61—44no—
263C22×D8—1221no—
264C2×#127C2×D6111yescharacteristic
265C2×C4×D4—611no—
266C2×C4×D4—1221no—
267C22×C4⋊C4—1221no—
268#459—614no—
269#459—1222no—
270C2×C4⋊C8—611no—
271C2×C4⋊C8C2×D6111yescharacteristic
272C2×#102—21no—
273C2×#102—21no—
274C2×#102—1221no—
275C2×#102—1222no—
276C2×C4×C8—611no—
277#389—1221no—
278#385—1222no—
279#384—611no—
280#380—1221no—
281C4×C4⋊C4C2×D6111yescharacteristic
282D4⋊C8—1222no—
283C61#897711yescharacteristic, complemented, Sylow
284C22×D4—21no—
285C22×D4—21no—
286C22×D4—21no—
287C22×D4—611no—
288C23×C4—1222no—
289C23×C4—1221no—
290C2×D8—1224no—
291C2×D8—2442no—
292C2×D8—2442no—
293C22×C8—21no—
294C22×C8—1221no—
295C22×C8—1221no—
296#127—21no—
297#127—21no—
298#127—21no—
299#127C4×D6112yescomplemented
300C4×D4—612no—
301C4×D4—612no—
302C4×D4—1221no—
303C4×D4—1221no—
304C4×D4—2442no—
305C4×D4—2442no—
306C2×C4⋊C4—611no—
307C2×C4⋊C4—612no—
308C2×C4⋊C4—1222no—
309C2×C4⋊C4—1221no—
310C2×C4⋊C4—1221no—
311C2×C4⋊C4—2442no—
312C2×C4⋊C4—2442no—
313C2×C4⋊C4C22⋊D6111yescharacteristic
314C2×C4⋊C4C22⋊D6111yescharacteristic
315C2×C22⋊C4—1221no—
316C2×C22⋊C4—1222no—
317C2×C42—21no—
318C2×C42C22×D6111yescharacteristic
319C4⋊C8—21no—
320C4⋊C8—21no—
321C4⋊C8—612no—
322C4⋊C8—1221no—
323#102—42no—
324#102—42no—
325#102—1224no—
326#102—2444no—
327C4×C8—1221no—
328C4×C8—1221no—
329#95—21no—
330#95—1222no—
331C24—41no—
332C24—1221no—
333C2×D4—22no—
334C2×D4—22no—
335C2×D4—22no—
336C2×D4—42no—
337C2×D4—42no—
338C2×D4—41no—
339C2×D4—41no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4—41no—
343C2×D4—41no—
344C2×D4—41no—
345C2×D4—41no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4—41no—
349C2×D4—612no—
350C2×D4—612no—
351C2×D4—612no—
352C2×D4—1221no—
353C2×D4—1221no—
354C2×D4—1221no—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—1221no—
358C22×C4—1222no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—4882no—
362C22×C4—2444no—
363C22×C4—2444no—
364C22×C4—2441no—
365C22×C4—2441no—
366C22×C4—2441no—
367C22×C4—2441no—
368C22×C4D4×D6111yescharacteristic
369C22×C4D4×D6111yescharacteristic
370C22×C4C2×C22⋊D6111yescharacteristic
371D8—2448no—
372C2×C8—41no—
373C2×C8—41no—
374C2×C8—41no—
375C2×C8—1222no—
376C2×C8—1222no—
377C2×C8—2441no—
378C2×C8—2441no—
379C2×C8—2441no—
380C2×C8—2441no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—21no—
384C4⋊C4—612no—
385C4⋊C4—1221no—
386C4⋊C4—2442no—
387C4⋊C4—2444no—
388C4⋊C4—2441no—
389C4⋊C4—2441no—
390C4⋊C4—2441no—
391C4⋊C4—2441no—
392C4⋊C4#1175819912yescomplemented
393C22⋊C4—1222no—
394C22⋊C4—1222no—
395C22⋊C4—2444no—
396C42—41no—
397C42—41no—
398C42C2×C4×D6111yescharacteristic
399C42#1175822211yescharacteristic
400C42D4×D6111yescharacteristic
401C42#1175822411yescharacteristic
402C23—42no—
403C23—81no—
404C23—81no—
405C23—81no—
406C23—81no—
407C23—81no—
408C23—81no—
409C23—1222no—
410C23—1222no—
411C23—1222no—
412C23—2441no—
413C23—2441no—
414C23—2441no—
415C23—2441no—
416C23#1451974511yescharacteristic
417D4—44no—
418D4—42no—
419D4—42no—
420D4—42no—
421D4—42no—
422D4—82no—
423D4—81no—
424D4—81no—
425D4—81no—
426D4—81no—
427D4—614no—
428D4—1222no—
429D4—1222no—
430D4—1222no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—1222no—
440C2×C4—4888no—
441C2×C4—2442no—
442C2×C4—2442no—
443C2×C4—2442no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4—2442no—
447C2×C4—2442no—
448C2×C4—2442no—
449C2×C4—2442no—
450C2×C4C22⋊C4×D6111yescharacteristic
451C2×C4#1451973711yescharacteristic
452C2×C4C4×C22⋊D6111yescharacteristic
453C2×C4#1451974811yescharacteristic
454C2×C4#1451975011yescharacteristic
455C2×C4#1451975911yescharacteristic
456C2×C4D8×D6111yescharacteristic
457C2×C4C2×#1175819911yescharacteristic
458C2×C4SD16×D6111yescharacteristic
459C2×C4#1451979711yescharacteristic
460C2×C4#1451980111yescharacteristic
461C2×C4#1451980211yescharacteristic
462C2×C4#1451980311yescharacteristic
463C2×C4#1451980611yescharacteristic
464C8—81no—
465C8—2442no—
466C8—2442no—
467C22—82no—
468C22—82no—
469C22—82no—
470C22—161no—
471C22—161no—
472C22—161no—
473C22—161no—
474C22—1224no—
475C22—2442no—
476C22—2442no—
477C22—2442no—
478C22—2442no—
479C22—2442no—
480C22—2442no—
481C22#1683963811yescharacteristic
482C22#1683989411yescharacteristic
483C22#1683989511yescharacteristic
484C22#1683989911yescharacteristic
485C22#1683990511yescharacteristic
486C22#1683992811yescharacteristic
487C22#1683993311yescharacteristic
488C4—21no—
489C4—21no—
490C4—42no—
491C4—81no—
492C4—4882no—
493C4—2442no—
494C4#102×D6111yescharacteristic
495C4#1683976011yescharacteristic
496C4C4×#1175819911yescharacteristic
497C4#1683987211yescharacteristic
498C4#1683995411yescharacteristic
499C4#1683997411yescharacteristic
500C4#1684007411yescharacteristic
501C4#1684007911yescharacteristic
502C2—162no—
503C2—2444no—
504C2#2144487211yescharacteristic
505C2#2144489011yescharacteristic
506C2#2144490711yescharacteristic
507C2#2144492011yescharacteristic
508C2#2144613311yescharacteristic
509C2#2144617011yescharacteristic
510C2#2144619211yescharacteristic
subgroupG/H
centerC23#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1982C2
socleC23×C61#120
prime radicalC2×#16839954C2
cosocleC2×C42×C61C23
hypercenter#1982D61
hypocenterC61#8977
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. C4⋊C4×D244C2semidirect
3. #21446626C2semidirect
4. C2×#16839489C2semidirect
5. #21443703C2semidirect
6. #21443660C2semidirect
7. C61×#1982C2semidirect
13. #16839954C4semidirect
52. C4⋊#92418C2×C4semidirect
65. #127×C61C2×C4semidirect
121. C4⋊C4×C61D8semidirect
202. D244#102semidirect
249. #1982D61semidirect
283. C61#8977semidirect
299. #127C4×D61semidirect
392. C4⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
C2×#168399542
C4⋊C4×D2442
#214466262
C2×#168394892
#214437032
#214436602
C61×#19822
#897761