Finite Group Databasebeta

← #29582315

Subgroups — #29582315

Order 15616.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839959C211yesmaximal, characteristic, complemented
2C2×#16839954C211yesmaximal, characteristic
3#21450742C211yesmaximal, characteristic, complemented
4C2×#16839494C211yesmaximal, characteristic, complemented
5C2×#16839491C211yesmaximal, characteristic, complemented
6#21443702C211yesmaximal, characteristic, complemented
7C61×#1957C211yesmaximal, characteristic, complemented
8C22×#11758200—21no—
9C22×#11758199—21no—
10C2×#14519757—21no—
11C2×C4×Dic122C2211yescharacteristic
12C2×C4×D244C2211yescharacteristic
13#16839959—22no—
14#16839959—22no—
15#16839954—22no—
16#16839954—22no—
17C2×C4⋊#92418C2211yescharacteristic
18C2×C4⋊#92418C2211yescharacteristic
19C2×#14519698—21no—
20C2×#14519698—21no—
21#16839684—22no—
22#16839663—21no—
23#16839661—21no—
24#16839619—21no—
25#16839494—22no—
26#16839491—22no—
27C2×#127×C61C2211yescharacteristic
28C2×#102×C61—22no—
29C2×C4×C8×C61C2211yescharacteristic
30C61×#384C2211yescharacteristic
31C22×Dic122D411yescharacteristic
32C22×D244D411yescharacteristic
33C22×C4×D61—21no—
34C2×#11758200—24no—
35C2×#11758200—42no—
36C2×#11758200—42no—
37C2×#11758199—24no—
38C2×#11758199—42no—
39C2×#11758199—42no—
40C22×#92418—21no—
41C22×#92418—21no—
42#14519757—42no—
43#14519757—42no—
44C4×Dic122—21no—
45C4×Dic122—21no—
46C4×Dic122—21no—
47C4×Dic122—21no—
48C4×D244—21no—
49C4×D244—21no—
50C4×D244—21no—
51C4×D244—21no—
52C2×C4⋊Dic61—22no—
53C2×C4⋊Dic61D411yescharacteristic
54C2×C4⋊Dic61D411yescharacteristic
55C2×#11758196—21no—
56C2×#11758198—22no—
57C2×#11758198—21no—
58C2×#11758198—22no—
59C2×C4×Dic61—21no—
60C4⋊#92418—21no—
61C4⋊#92418—21no—
62C4⋊#92418D412yes—
63C4⋊#92418D412yes—
64#14519698—24no—
65#14519698—24no—
66#14519684—22no—
67C22×D4×C61—21no—
68C22×D4×C61—21no—
69C22×D4×C61—21no—
70C22×C8×C61—21no—
71#127×C61—21no—
72#127×C61—21no—
73#127×C61—21no—
74#127×C61D412yes—
75C2×C4⋊C4×C61—21no—
76C2×C4⋊C4×C61—21no—
77C2×C4⋊C4×C61D412yes—
78C2×C42×C61C2311yescharacteristic
79#102×C61—44no—
80C4×C8×C61—21no—
81C4×C8×C61—21no—
82C24×C61—41no—
83C23×D61—21no—
84C2×D4×C61—22no—
85C2×D4×C61—22no—
86C2×D4×C61—22no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—41no—
93C2×D4×C61—41no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C22×C4×C61—22no—
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61C2×D411yescharacteristic
103C22×C4×C61C2×D411yescharacteristic
104C22×Dic61—21no—
105C22×Dic61—21no—
106C22×Dic61—21no—
107C2×D244—21no—
108C2×D244—21no—
109C2×D244—21no—
110C2×D244—21no—
111C2×D244—21no—
112C2×D244SD1612yescomplemented
113C2×C4×D61—41no—
114C2×C4×D61—41no—
115C2×C4×D61—41no—
116C2×C4×D61—41no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×Dic122—21no—
120C2×Dic122—21no—
121C2×Dic122—21no—
122C2×Dic122—21no—
123C2×Dic122—21no—
124C2×Dic122D812yescomplemented
125C2×C8×C61—22no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C4⋊C4×C61—42no—
129C4⋊C4×C61—41no—
130C4⋊C4×C61—41no—
131C4⋊C4×C61—41no—
132C4⋊C4×C61—41no—
133C42×C61C2×D411yescharacteristic
134C42×C61C2×D411yescharacteristic
135C42×C61C2×D411yescharacteristic
136C42×C61#4111yescharacteristic
137#11758200—48no—
138#11758199—48no—
139#11758198—44no—
140#11758198—41no—
141#11758198—41no—
142#11758198—82no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—44no—
148#11758196—41no—
149#11758196—41no—
150C4×Dic61—41no—
151C4×Dic61—41no—
152C2×#92418—22no—
153C2×#92418—22no—
154C2×#92418—41no—
155C2×#92418—41no—
156C2×#92418—41no—
157C2×#92418—41no—
158C23×C61—42no—
159C23×C61—81no—
160C23×C61—81no—
161C23×C61—81no—
162C23×C61—81no—
163C23×C61—81no—
164C23×C61—81no—
165C23×C61#12011yescharacteristic
166C22×D61—22no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170C22×D61—41no—
171C22×D61—41no—
172C22×D61—41no—
173D4×C61—44no—
174D4×C61—42no—
175D4×C61—42no—
176D4×C61—42no—
177D4×C61—42no—
178D4×C61—82no—
179D4×C61—81no—
180D4×C61—81no—
181D4×C61—81no—
182D4×C61—81no—
183C2×C4×C61—21no—
184C2×C4×C61—21no—
185C2×C4×C61—42no—
186C2×C4×C61—42no—
187C2×C4×C61—42no—
188C2×C4×C61#12011yescharacteristic
189C2×C4×C61#12011yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61#12111yescharacteristic
193C2×C4×C61#12711yescharacteristic
194C2×C4×C61C2×D811yescharacteristic
195C2×C4×C61C2×SD1611yescharacteristic
196C2×C4×C61#13511yescharacteristic
197C2×C4×C61#13511yescharacteristic
198C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
199C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
201C2×C4×C61#13711yescharacteristic
202C2×Dic61—22no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211D244—22no—
212D244—22no—
213D244—41no—
214D244—41no—
215C4×D61—81no—
216C4×D61—81no—
217C4×D61—81no—
218C4×D61—81no—
219Dic122—22no—
220Dic122—22no—
221Dic122—41no—
222Dic122—41no—
223C8×C61—42no—
224#92418—42no—
225#92418—42no—
226#10229—611nomaximal, Sylow
227C22×C61—82no—
228C22×C61—82no—
229C22×C61—82no—
230C22×C61—161no—
231C22×C61—161no—
232C22×C61—161no—
233C22×C61—161no—
234C22×C61#39211yescharacteristic
235C22×C61#44711yescharacteristic
236C22×C61#44811yescharacteristic
237C22×C61#44911yescharacteristic
238C22×C61#44911yescharacteristic
239C22×C61#45311yescharacteristic
240C22×C61#45411yescharacteristic
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—82no—
251C4×C61#44711yescharacteristic
252C4×C61#44911yescharacteristic
253C4×C61#45011yescharacteristic
254C4×C61#45211yescharacteristic
255C4×C61#46511yescharacteristic
256C4×C61#46611yescharacteristic
257C4×C61#46811yescharacteristic
258C4×C61#46911yescharacteristic
259Dic61—42no—
260Dic61—81no—
261Dic61—81no—
262C2×#460—611no—
263C2×#459—611no—
264#2538—611no—
265#1957D6111yescharacteristic, complemented
266C2×Q8⋊C8—611no—
267C2×D4⋊C8—611no—
268#1296—611no—
269C2×C61—162no—
270C2×C61#162111yescharacteristic
271C2×C61#162211yescharacteristic
272C2×C61#162711yescharacteristic
273C2×C61#162811yescharacteristic
274C2×C61#199911yescharacteristic
275C2×C61#200011yescharacteristic
276C2×C61#200611yescharacteristic
277D61—82no—
278C22×SD16—1221no—
279C22×D8—1221no—
280C2×#127C2×D6111yescharacteristic
281C2×C22⋊Q8—1221no—
282C2×C4×Q8—611no—
283C2×C4×D4—611no—
284#460—1222no—
285#460—1222no—
286#459—1222no—
287#459—1222no—
288C2×C4⋊C8—611no—
289C2×C4⋊C8—611no—
290C2×#102—22no—
291C2×#102—1221no—
292C2×#102—1221no—
293C2×C4×C8C2×D6111yescharacteristic
294#396—1222no—
295#390—1221no—
296#389—1221no—
297#384C2×D6111yescharacteristic
298#380—1221no—
299Q8⋊C8—1222no—
300D4⋊C8—1222no—
301C61#1022911yescharacteristic, complemented, Sylow
302C22×Q8—611no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4—611no—
307C23×C4—1221no—
308C2×SD16—1224no—
309C2×SD16—2442no—
310C2×SD16—2442no—
311C2×D8—1224no—
312C2×D8—2442no—
313C2×D8—2442no—
314C22×C8—21no—
315C22×C8—1221no—
316C22×C8—1221no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127D24412yes—
321C22⋊Q8—2442no—
322C22⋊Q8—2442no—
323C4×Q8—1221no—
324C4×Q8—1221no—
325C4×Q8—1221no—
326C4×Q8—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330C4×D4—1221no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—611no—
334C2×C4⋊C4—611no—
335C2×C4⋊C4—1222no—
336C2×C4⋊C4—1221no—
337C2×C4⋊C4C22⋊D6112yes—
338C2×C22⋊C4—1222no—
339C2×C22⋊C4—1222no—
340C2×C22⋊C4—1221no—
341C2×C42—1221no—
342C2×C42C22×D6111yescharacteristic
343C4⋊C8—612no—
344C4⋊C8—612no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347#102—44no—
348#102—1224no—
349#102—1224no—
350C4×C8—21no—
351C4×C8—21no—
352#95—1222no—
353C24—41no—
354C24—1221no—
355C2×Q8—612no—
356C2×Q8—1221no—
357C2×Q8—1221no—
358C2×Q8—1221no—
359C2×Q8—1221no—
360C2×Q8—1221no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—22no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—41no—
367C2×D4—41no—
368C2×D4—41no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—612no—
378C2×D4—1221no—
379C2×D4—1221no—
380C2×D4—1221no—
381C2×D4—1221no—
382C2×D4—1221no—
383C22×C4—22no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4—2441no—
391C22×C4—2441no—
392C22×C4—2441no—
393C22×C4D4×D6111yescharacteristic
394C22×C4D4×D6111yescharacteristic
395C22×C4C2×C22⋊D6111yescharacteristic
396SD16—2448no—
397D8—2448no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—1222no—
402C2×C8—1222no—
403C2×C8—2441no—
404C2×C8—2441no—
405C2×C8—2441no—
406C2×C8—2441no—
407C4⋊C4—42no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—1221no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C4⋊C4—1221no—
416C4⋊C4—2444no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C22⋊C4—4882no—
420C22⋊C4—2444no—
421C22⋊C4—2441no—
422C22⋊C4—2441no—
423C42—2441no—
424C42—2441no—
425C42C2×D24411yescharacteristic
426C42#1175822211yescharacteristic
427C42D4×D6111yescharacteristic
428C42D4×D6111yescharacteristic
429C23—42no—
430C23—81no—
431C23—81no—
432C23—81no—
433C23—81no—
434C23—81no—
435C23—81no—
436C23—1222no—
437C23—2441no—
438C23—2441no—
439C23—2441no—
440C23—2441no—
441C23—2441no—
442C23—2441no—
443C23#1451974511yescharacteristic
444Q8—1222no—
445Q8—1222no—
446Q8—2441no—
447Q8—2441no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—42no—
452D4—42no—
453D4—82no—
454D4—81no—
455D4—81no—
456D4—81no—
457D4—81no—
458D4—1222no—
459D4—1222no—
460D4—2441no—
461D4—2441no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—1222no—
468C2×C4—4881no—
469C2×C4—4881no—
470C2×C4—4881no—
471C2×C4—4881no—
472C2×C4—2441no—
473C2×C4—2441no—
474C2×C4—2441no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4#1451974711yescharacteristic
481C2×C4#1451974711yescharacteristic
482C2×C4#1451975011yescharacteristic
483C2×C4#1451975011yescharacteristic
484C2×C4#1451975111yescharacteristic
485C2×C4#1451977311yescharacteristic
486C2×C4D8×D6111yescharacteristic
487C2×C4SD16×D6111yescharacteristic
488C2×C4#1451979611yescharacteristic
489C2×C4#1451979811yescharacteristic
490C2×C4#1451980111yescharacteristic
491C2×C4#1451980111yescharacteristic
492C2×C4#1451980411yescharacteristic
493C2×C4#1451980611yescharacteristic
494C8—42no—
495C8—2442no—
496C8—2442no—
497C22—82no—
498C22—82no—
499C22—82no—
500C22—161no—
501C22—161no—
502C22—161no—
503C22—161no—
504C22—4881no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—2442no—
509C22—2442no—
510C22—2442no—
511C22#1683967111yescharacteristic
512C22#1683989411yescharacteristic
513C22#1683989911yescharacteristic
514C22#1683990411yescharacteristic
515C22#1683990611yescharacteristic
516C22#1683992911yescharacteristic
517C22#1683993411yescharacteristic
518C4—21no—
519C4—21no—
520C4—82no—
521C4—4881no—
522C4—4881no—
523C4—2442no—
524C4#1683989711yescharacteristic
525C4#1683990811yescharacteristic
526C4#1683991411yescharacteristic
527C4#1683992511yescharacteristic
528C4#1683999011yescharacteristic
529C4#1683999711yescharacteristic
530C4#1684000711yescharacteristic
531C4#1684001411yescharacteristic
532C2—162no—
533C2—4882no—
534C2#2144488111yescharacteristic
535C2#2144488811yescharacteristic
536C2#2144491911yescharacteristic
537C2#2144492611yescharacteristic
538C2#2144681611yescharacteristic
539C2#2144682311yescharacteristic
540C2#2144686011yescharacteristic
subgroupG/H
centerC23#14519745
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1957C2
socleC23×C61#120
prime radicalC2×#16839954C2
hypercenter#1957D61
hypocenterC61#10229
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
1. C2×#16839959C2semidirect
3. #21450742C2semidirect
4. C2×#16839494C2semidirect
5. C2×#16839491C2semidirect
6. #21443702C2semidirect
7. C61×#1957C2semidirect
112. C2×D244SD16semidirect
124. C2×Dic122D8semidirect
265. #1957D61semidirect
301. C61#10229semidirect

Maximal subgroups

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

subgroupindex
C2×#168399592
C2×#168399542
#214507422
C2×#168394942
C2×#168394912
#214437022
C61×#19572
#1022961