Finite Group Databasebeta

← #29582326

Subgroups — #29582326

Order 15616.

728 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839964C211yesmaximal, characteristic, complemented
2#21450732C211yesmaximal, characteristic
3#21446781C211yesmaximal, characteristic, complemented
4C2×D4⋊#92418C211yesmaximal, characteristic, complemented
5C2×#16839489C211yesmaximal, characteristic, complemented
6#21443703C211yesmaximal, characteristic, complemented
7C2×C61×#474C211yesmaximal, characteristic, complemented
8C22×#11758201—21no—
9C2×#14519751—21no—
10C2×#14519748—21no—
11C2×C4×D244C2211yescharacteristic
12#16839964—22no—
13#16839964—22no—
14C2×C4⋊#92418C2211yescharacteristic
15C2×#14519701—21no—
16C2×C4×#92418C2211yescharacteristic
17#16839678—22no—
18#16839632C2211yescharacteristic
19#16839622—21no—
20#16839619—21no—
21#16839524—22no—
22D4⋊#92418—22no—
23#16839489—22no—
24C2×C4⋊Q8×C61C2211yescharacteristic
25C2×C4×D4×C61C2211yescharacteristic
26C61×#474—22no—
27C61×#474—22no—
28C2×#107×C61—21no—
29C2×C4⋊C8×C61C2211yescharacteristic
30C2×#102×C61—21no—
31C22×D244D411yescharacteristic
32C22×C22⋊D61—22no—
33C22×C4×D61—21no—
34C2×#11758201—24no—
35C2×#11758201—42no—
36C2×#11758201—42no—
37C22×#92418—21no—
38C22×#92418—21no—
39#14519751—42no—
40#14519751—42no—
41#14519748—42no—
42#14519748—42no—
43C4×D244—21no—
44C4×D244—21no—
45C4×D244—21no—
46C4×D244—21no—
47C2×C4⋊Dic61—21no—
48C2×C4⋊Dic61—21no—
49C2×C4⋊Dic61D411yescharacteristic
50C2×C4⋊Dic61D412yes—
51C2×C22⋊Dic61—22no—
52C2×#11758198—22no—
53C2×#11758198—21no—
54C4⋊#92418—21no—
55C4⋊#92418D412yescomplemented
56#14519701—24no—
57C4×#92418—21no—
58C4×#92418—21no—
59#14519684—22no—
60C22×Q8×C61—21no—
61C22×D4×C61D411yescharacteristic
62C23×C4×C61—21no—
63C22×C8×C61—21no—
64C4⋊Q8×C61—21no—
65C4⋊Q8×C61—21no—
66C4⋊Q8×C61—21no—
67C4⋊Q8×C61D412yescomplemented
68C4×D4×C61—21no—
69C4×D4×C61—21no—
70C4×D4×C61—21no—
71C4×D4×C61—21no—
72C2×C4⋊C4×C61—21no—
73C2×C4⋊C4×C61—21no—
74C2×C4⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61—21no—
76C2×C42×C61C2311yescharacteristic
77#107×C61—24no—
78C4⋊C8×C61—21no—
79C4⋊C8×C61D412yescomplemented
80#102×C61—24no—
81C24×C61—21no—
82C23×D61—21no—
83C2×Q8×C61—22no—
84C2×Q8×C61—41no—
85C2×Q8×C61—41no—
86C2×Q8×C61—41no—
87C2×Q8×C61—41no—
88C2×Q8×C61—41no—
89C2×D4×C61—21no—
90C2×D4×C61—21no—
91C2×D4×C61—21no—
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61SD1612yescomplemented
95C22×C4×C61—21no—
96C22×C4×C61—41no—
97C22×C4×C61—41no—
98C22×C4×C61—41no—
99C22×C4×C61—41no—
100C22×C4×C61—41no—
101C22×C4×C61—41no—
102C22×C4×C61—41no—
103C22×C4×C61C2×D411yescharacteristic
104C22×C4×C61C2×D411yescharacteristic
105C22×C4×C61C2×D411yescharacteristic
106C2×C22⋊D61—44no—
107C2×C22⋊D61—44no—
108C2×C22⋊D61—82no—
109C22×Dic61—21no—
110C22×Dic61—22no—
111C2×D244—21no—
112C2×D244—21no—
113C2×D244—21no—
114C2×D244—21no—
115C2×D244—21no—
116C2×D244D812yes—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×C4×D61—41no—
121C2×C4×D61—41no—
122C2×C4×D61—41no—
123C2×C8×C61—22no—
124C2×C8×C61—41no—
125C2×C8×C61—41no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61—21no—
128C4⋊C4×C61—22no—
129C4⋊C4×C61—21no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61—41no—
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61C2×D411yescharacteristic
137C42×C61#4111yescharacteristic
138C22⋊Dic61—44no—
139#11758201—48no—
140#11758198—44no—
141#11758198—41no—
142#11758198—41no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—41no—
146C4⋊Dic61—41no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C4⋊Dic61—42no—
150C2×#92418—22no—
151C2×#92418—22no—
152C2×#92418—41no—
153C2×#92418—41no—
154C2×#92418—41no—
155C2×#92418—41no—
156C23×C61—22no—
157C23×C61—41no—
158C23×C61—41no—
159C23×C61—41no—
160C23×C61—41no—
161C23×C61—41no—
162C23×C61—41no—
163C23×C61#12011yescharacteristic
164C22×D61—22no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171Q8×C61—42no—
172Q8×C61—42no—
173Q8×C61—81no—
174Q8×C61—81no—
175D4×C61—22no—
176D4×C61—22no—
177D4×C61—41no—
178D4×C61—41no—
179C2×C4×C61—21no—
180C2×C4×C61—21no—
181C2×C4×C61—41no—
182C2×C4×C61—42no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—81no—
186C2×C4×C61—81no—
187C2×C4×C61—81no—
188C2×C4×C61—81no—
189C2×C4×C61—81no—
190C2×C4×C61—81no—
191C2×C4×C61#12011yescharacteristic
192C2×C4×C61#12011yescharacteristic
193C2×C4×C61#12111yescharacteristic
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12711yescharacteristic
197C2×C4×C61C2×D811yescharacteristic
198C2×C4×C61C2×SD1611yescharacteristic
199C2×C4×C61#13511yescharacteristic
200C2×C4×C61#13511yescharacteristic
201C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
202C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C61#13711yescharacteristic
205C22⋊D61—88no—
206C2×Dic61—41no—
207C2×Dic61—42no—
208C2×Dic61—42no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—42no—
212D244—22no—
213D244—22no—
214D244—41no—
215D244—41no—
216C4×D61—81no—
217C4×D61—81no—
218C4×D61—81no—
219C4×D61—81no—
220C8×C61—42no—
221#92418—42no—
222#92418—42no—
223#10231—611nomaximal, Sylow
224C22×C61—42no—
225C22×C61—42no—
226C22×C61—42no—
227C22×C61—81no—
228C22×C61—81no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61#39211yescharacteristic
232C22×C61#44711yescharacteristic
233C22×C61#44911yescharacteristic
234C22×C61#45011yescharacteristic
235C22×C61#45211yescharacteristic
236C22×C61#45511yescharacteristic
237C22×C61#45611yescharacteristic
238C2×D61—42no—
239C2×D61—42no—
240C2×D61—42no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—81no—
248C4×C61—82no—
249C4×C61#44711yescharacteristic
250C4×C61#44811yescharacteristic
251C4×C61#44911yescharacteristic
252C4×C61#44911yescharacteristic
253C4×C61#46511yescharacteristic
254C4×C61#46611yescharacteristic
255C4×C61#46811yescharacteristic
256C4×C61#46911yescharacteristic
257Dic61—82no—
258Dic61—81no—
259C2×#474D6111yescharacteristic, complemented
260C2×#461—611no—
261#2537—611no—
262#1990—611no—
263C2×D4⋊C8—611no—
264C2×D4⋊C8—611no—
265#1296—611no—
266C2×C61—82no—
267C2×C61#163911yescharacteristic
268C2×C61#164611yescharacteristic
269C2×C61#164711yescharacteristic
270C2×C61#165411yescharacteristic
271C2×C61#199911yescharacteristic
272C2×C61#200011yescharacteristic
273C2×C61#200711yescharacteristic
274D61—82no—
275C22×SD16—1221no—
276C2×C4⋊Q8C2×D6111yescharacteristic
277C2×#121—1221no—
278C2×#121—1221no—
279C2×C4×D4—611no—
280C2×C4×D4C2×D6111yescharacteristic
281#474—22no—
282#474—22no—
283#461—1222no—
284#461—1222no—
285C2×#107—21no—
286C2×C4⋊C8—611no—
287C2×C4⋊C8C2×D6111yescharacteristic
288C2×#103—1221no—
289C2×#102—21no—
290C2×C4×C8—611no—
291#394—1222no—
292#384—611no—
293#380—1221no—
294#380—1221no—
295#340—1222no—
296D4⋊C8—1222no—
297D4⋊C8—1222no—
298C61#1023111yescharacteristic, complemented, Sylow
299C22×Q8—21no—
300C22×D4—611no—
301C22×D4—1222no—
302C22×D4C22⋊D6111yescharacteristic
303C23×C4—21no—
304C23×C4—1221no—
305C2×SD16—1224no—
306C2×SD16—2442no—
307C2×SD16—2442no—
308C22×C8—21no—
309C22×C8—1221no—
310C22×C8—1221no—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8C22⋊D6112yescomplemented
315#121—2442no—
316#121—2442no—
317#121—2442no—
318#121—2442no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—21no—
322C4×D4—21no—
323C4×D4—1221no—
324C4×D4—1221no—
325C4×D4—1221no—
326C4×D4—1221no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—611no—
330C2×C4⋊C4—612no—
331C2×C4⋊C4—1221no—
332C2×C4⋊C4—1221no—
333C2×C4⋊C4C22⋊D6111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—1222no—
336C2×C22⋊C4—1222no—
337C2×C22⋊C4—1221no—
338C2×C42C22×D6111yescharacteristic
339#107—24no—
340C4⋊C8—21no—
341C4⋊C8—612no—
342C4⋊C8—1221no—
343C4⋊C8C22⋊D6112yescomplemented
344#103—1224no—
345#102—24no—
346C4×C8—1221no—
347C4×C8—1221no—
348#95—1222no—
349C24—21no—
350C24—1221no—
351C2×Q8—22no—
352C2×Q8—41no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×Q8—41no—
356C2×Q8—41no—
357C2×D4—21no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—612no—
363C2×D4—1221no—
364C2×D4—1221no—
365C2×D4—1221no—
366C2×D4—1221no—
367C2×D4—1221no—
368C2×D4—4882no—
369C2×D4—2444no—
370C2×D4—2444no—
371C2×D4#1175820112yescomplemented
372C22×C4—21no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—1221no—
381C22×C4—1222no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4D4×D6111yescharacteristic
389C22×C4D4×D6111yescharacteristic
390C22×C4C2×C22⋊D6111yescharacteristic
391SD16—2448no—
392C2×C8—22no—
393C2×C8—41no—
394C2×C8—41no—
395C2×C8—1222no—
396C2×C8—1222no—
397C2×C8—2441no—
398C2×C8—2441no—
399C2×C8—2441no—
400C2×C8—2441no—
401C4⋊C4—22no—
402C4⋊C4—21no—
403C4⋊C4—22no—
404C4⋊C4—21no—
405C4⋊C4—41no—
406C4⋊C4—41no—
407C4⋊C4—1221no—
408C4⋊C4—1221no—
409C4⋊C4—2442no—
410C4⋊C4—2441no—
411C4⋊C4—2441no—
412C4⋊C4—2441no—
413C4⋊C4—2441no—
414C22⋊C4—41no—
415C22⋊C4—41no—
416C22⋊C4—2444no—
417C22⋊C4—2444no—
418C22⋊C4—2441no—
419C22⋊C4—2441no—
420C42D4×D6111yescharacteristic
421C42#1175822411yescharacteristic
422C42C2×C22⋊D6111yescharacteristic
423C42C2×C22⋊D6111yescharacteristic
424C23—22no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—1222no—
432C23—2441no—
433C23—2441no—
434C23—2441no—
435C23—2441no—
436C23—2441no—
437C23—2441no—
438C23#1451974511yescharacteristic
439Q8—42no—
440Q8—42no—
441Q8—81no—
442Q8—81no—
443D4—22no—
444D4—22no—
445D4—41no—
446D4—41no—
447D4—1222no—
448D4—1222no—
449D4—4888no—
450D4—2441no—
451D4—2441no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—81no—
459C2×C4—81no—
460C2×C4—81no—
461C2×C4—81no—
462C2×C4—81no—
463C2×C4—81no—
464C2×C4—4881no—
465C2×C4—4881no—
466C2×C4—4881no—
467C2×C4—4881no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2441no—
471C2×C4—2442no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4#1451974511yescharacteristic
475C2×C4#1451974611yescharacteristic
476C2×C4#1451974811yescharacteristic
477C2×C4#1451974911yescharacteristic
478C2×C4#1451974911yescharacteristic
479C2×C4#1451977311yescharacteristic
480C2×C4D8×D6111yescharacteristic
481C2×C4C2×#1175820111yescharacteristic
482C2×C4#1451979611yescharacteristic
483C2×C4#1451979711yescharacteristic
484C2×C4#1451980111yescharacteristic
485C2×C4#1451980111yescharacteristic
486C2×C4#1451980211yescharacteristic
487C2×C4#1451980811yescharacteristic
488C8—42no—
489C8—2442no—
490C8—2442no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—81no—
495C22—81no—
496C22—81no—
497C22—81no—
498C22—4881no—
499C22—4881no—
500C22—4881no—
501C22—4881no—
502C22—2442no—
503C22—2442no—
504C22—2442no—
505C22#1683967011yescharacteristic
506C22#1683989411yescharacteristic
507C22#1683990411yescharacteristic
508C22#1683991211yescharacteristic
509C22#1683992211yescharacteristic
510C22#1683993811yescharacteristic
511C22#1683994311yescharacteristic
512C4—21no—
513C4—21no—
514C4—81no—
515C4—82no—
516C4—4882no—
517C4—4881no—
518C4#1683989411yescharacteristic
519C4#1683990111yescharacteristic
520C4#1683990411yescharacteristic
521C4#1683990711yescharacteristic
522C4#1683999311yescharacteristic
523C4#1683999511yescharacteristic
524C4#1684001011yescharacteristic
525C4#1684001211yescharacteristic
526C2—82no—
527C2—4882no—
528C2#2144499711yescharacteristic
529C2#2144504611yescharacteristic
530C2#2144505311yescharacteristic
531C2#2144510211yescharacteristic
532C2#2144681411yescharacteristic
533C2#2144682011yescharacteristic
534C2#2144686411yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC2×C61×#474C2
socleC23×C61#120
prime radical#21450732C2
hypercenterC2×#474D61
hypocenterC61#10231
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#16839964C2semidirect
3. #21446781C2semidirect
4. C2×D4⋊#92418C2semidirect
5. C2×#16839489C2semidirect
6. #21443703C2semidirect
7. C2×C61×#474C2semidirect
55. C4⋊#92418D4semidirect
67. C4⋊Q8×C61D4semidirect
79. C4⋊C8×C61D4semidirect
94. C2×D4×C61SD16semidirect
259. C2×#474D61semidirect
298. C61#10231semidirect
314. C4⋊Q8C22⋊D61semidirect
343. C4⋊C8C22⋊D61semidirect
371. C2×D4#11758201semidirect

Maximal subgroups

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

subgroupindex
C2×#168399642
#214507322
#214467812
C2×D4⋊#924182
C2×#168394892
#214437032
C2×C61×#4742
#1023161