Finite Group Databasebeta

← #29834536

Subgroups — #29834536

Order 15616.

674 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840193C211yesmaximal, characteristic, complemented
2C2×#16840178C211yesmaximal, characteristic, complemented
3#21455490C211yesmaximal, characteristic, complemented
4#21455484C211yesmaximal, characteristic, complemented
5#21447926C211yesmaximal, characteristic, complemented
6#21447925C211yesmaximal, characteristic, complemented
7#21447921C211yesmaximal, characteristic, complemented
8#21447920C211yesmaximal, characteristic, complemented
9#21447916C211yesmaximal, characteristic, complemented
10#21447915C211yesmaximal, characteristic, complemented
11#21447912C211yesmaximal, characteristic, complemented
12#367×D61C211yesmaximal, characteristic, complemented
13#21447530C211yesmaximal, characteristic, complemented
14#21447528C211yesmaximal, characteristic, complemented
15C61×#2217C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17C2×#14519796C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19#16840342—21no—
20#16840341—21no—
21#16840193—24no—
22C2×#14519723C2211yescharacteristic
23C2×#14519722C2211yescharacteristic
24C2×#14519718C2211yescharacteristic
25#16840178—24no—
26C2×#14519717C2211yescharacteristic
27C2×#14519716C2211yescharacteristic
28C2×#14519716C2211yescharacteristic
29C2×C16×D61C2211yescharacteristic
30C2×C16×D61C2211yescharacteristic
31#16840011—21no—
32#16840010—21no—
33#16840007—21no—
34#16840006—21no—
35#16840004C2211yescharacteristic
36#16840003C2211yescharacteristic
37#16840000C2211yescharacteristic
38#16839999C2211yescharacteristic
39#16839998C2211yescharacteristic
40#16839995C2211yescharacteristic
41#107×D61C2211yescharacteristic
42#107×D61C2211yescharacteristic
43#16839762—21no—
44#16839760—21no—
45#16839590C2211yescharacteristic
46#16839589C2211yescharacteristic
47#16839589C2211yescharacteristic
48#16839567C2211yescharacteristic
49#16839566C2211yescharacteristic
50#16839565C2211yescharacteristic
51#16839564C2211yescharacteristic
52#16839563C2211yescharacteristic
53#16839562C2211yescharacteristic
54C2×SD32×C61C2211yescharacteristic
55C22×C16×C61C2211yescharacteristic
56C61×#467C2211yescharacteristic
57C61×#466C2211yescharacteristic
58C61×#367C2211yescharacteristic
59C61×#358C2211yescharacteristic
60C61×#357C2211yescharacteristic
61C2×#11758226—21no—
62C2×#11758222D411yescharacteristic
63C2×#11758224—21no—
64#14519800—22no—
65#14519800—22no—
66#14519796—22no—
67#14519796—22no—
68C2×Dic244C2311yescharacteristic
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×D488C2311yescharacteristic
72#14519783—22no—
73#14519783—22no—
74C2×#11758194D411yescharacteristic
75C2×#11758189D411yescharacteristic
76C2×#11758189D411yescharacteristic
77C2×C8×D61C2311yescharacteristic
78C2×C8×D61C2311yescharacteristic
79#14519757—21no—
80#14519756—21no—
81#14519755—41no—
82#14519754—41no—
83#14519753—21no—
84#14519752—21no—
85#14519752—41no—
86#14519751—21no—
87#14519750—41no—
88#14519750—41no—
89#14519750—41no—
90#14519749—41no—
91#14519748—21no—
92#14519748—41no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61—21no—
95#14519723—22no—
96#14519722—22no—
97#14519718—22no—
98#14519717—22no—
99#14519716—22no—
100#14519716—22no—
101C2×#11758185C2311yescharacteristic
102C2×#11758185C2311yescharacteristic
103C16×D61—22no—
104C16×D61D414yescomplemented
105#14519711C2311yescharacteristic
106#14519711C2311yescharacteristic
107#14519710—21no—
108#14519710—21no—
109#14519702—21no—
110#14519701—21no—
111#14519700—21no—
112#14519699—21no—
113#14519698—21no—
114#14519697—21no—
115C2×Q16×C61C2311yescharacteristic
116C2×D8×C61C2311yescharacteristic
117C22×C8×C61C2311yescharacteristic
118C22⋊Q8×C61—21no—
119#121×C61—21no—
120SD32×C61—22no—
121C2×C16×C61—22no—
122C2×C16×C61C2311yescharacteristic
123C2×C16×C61C2311yescharacteristic
124#107×C61C2311yescharacteristic
125#107×C61C2311yescharacteristic
126#103×C61—21no—
127#102×C61—21no—
128C2×Q8×C61—21no—
129C2×D4×C61—21no—
130C2×D4×C61—41no—
131C22×C4×C61C2×D411yescharacteristic
132C2×C22⋊D61—41no—
133C2×C22⋊D61—41no—
134C2×C22⋊D61—41no—
135C2×C22⋊D61D811yescharacteristic
136C2×C22⋊D61D811yescharacteristic
137C22×Dic61—41no—
138#11758226—42no—
139#11758226—42no—
140#11758224—42no—
141#11758224—42no—
142#11758222—22no—
143#11758222—22no—
144C2×D244—21no—
145C2×D244—41no—
146C2×D244—41no—
147C2×D244D811yescharacteristic
148C2×C4×D61—41no—
149C2×C4×D61—41no—
150C2×C4×D61—41no—
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×Dic122—21no—
154C2×Dic122D811yescharacteristic
155Q16×C61—21no—
156Q16×C61—21no—
157D8×C61—21no—
158D8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—41no—
166C22⋊C4×C61—41no—
167C22⋊C4×C61—41no—
168C22⋊Dic61—41no—
169C22⋊Dic61—41no—
170#11758201—42no—
171#11758200—42no—
172#11758198—41no—
173#11758198—41no—
174#11758198—41no—
175#11758198—41no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—41no—
179#11758196—41no—
180#11758196—41no—
181#11758196—41no—
182#11758196—41no—
183#11758194—22no—
184C2×#92418C2×D411yescharacteristic
185C2×#92418C2×D411yescharacteristic
186Dic244—21no—
187Dic244—21no—
188D488—21no—
189D488—21no—
190#11758189—22no—
191#11758189—22no—
192C8×D61—21no—
193C8×D61—21no—
194C8×D61C2×D412yes—
195C8×D61#4112yes—
196C16×C61—21no—
197C16×C61C2×D412yes—
198#11758185—21no—
199#11758185C2×D412yes—
200C23×C61—41no—
201C23×C61C2×D811yescharacteristic
202C22×D61—41no—
203C22×D61C2×D811yescharacteristic
204C22×D61C2×D811yescharacteristic
205Q8×C61—41no—
206Q8×C61—41no—
207D4×C61—41no—
208D4×C61—41no—
209D4×C61—161no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61C2×D811yescharacteristic
216C2×C4×C61C22×D411yescharacteristic
217C22⋊D61—22no—
218C22⋊D61—22no—
219C22⋊D61—82no—
220C22⋊D61—161no—
221C22⋊D61—161no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61—41no—
225C2×Dic61—82no—
226C2×Dic61C2×D811yescharacteristic
227C2×Dic61C2×D811yescharacteristic
228D244—22no—
229D244—41no—
230D244—41no—
231D244—82no—
232D244—161no—
233C4×D61—21no—
234C4×D61—21no—
235C4×D61—82no—
236C4×D61—161no—
237C4×D61—161no—
238C4×D61#12112yes—
239C4×D61#13512yes—
240Dic122—22no—
241Dic122—41no—
242Dic122—41no—
243C8×C61—21no—
244C8×C61C22×D411yescharacteristic
245C8×C61C2×#4111yescharacteristic
246#92418—21no—
247#92418#12112yes—
248#33611—611nomaximal, Sylow
249C22×C61—21no—
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—81no—
253C22×C61—81no—
254C22×C61—81no—
255C22×C61C22×D811yescharacteristic
256C2×D61—21no—
257C2×D61—21no—
258C2×D61—21no—
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—81no—
262C2×D61—81no—
263C2×D61—81no—
264C2×D61#46612yes—
265C4×C61—21no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61C2×#12111yescharacteristic
270C4×C61C2×#13511yescharacteristic
271Dic61—21no—
272Dic61—81no—
273Dic61—81no—
274Dic61—81no—
275Dic61#46612yes—
276C2×#508—611no—
277C2×#504—611no—
278#3061—611no—
279#3061—611no—
280#2219—611no—
281#2219—611no—
282#2218—611no—
283#2218—611no—
284#2217—611no—
285#2217—611no—
286#2217—611no—
287#2217D6111yescharacteristic, complemented
288C2×#367—611no—
289#2139—611no—
290#2139—611no—
291C2×C61—41no—
292C2×C61—161no—
293C2×C61C2×#46611yescharacteristic
294C2×C61#341611yescharacteristic
295C2×C61#341611yescharacteristic
296D61—22no—
297D61—41no—
298D61—161no—
299C2×#135—611no—
300C2×#135—611no—
301C2×#131—611no—
302#537—1221no—
303#537—1221no—
304#508—1224no—
305C2×Q32—611no—
306C2×SD32—611no—
307C2×SD32C2×D6111yescharacteristic
308C2×D16—611no—
309#504—1224no—
310C2×M32—611no—
311C2×M32—611no—
312C2×M32—611no—
313C22×C16—611no—
314C22×C16—611no—
315C22×C16C2×D6111yescharacteristic
316#468—1221no—
317#468—1221no—
318#468—1221no—
319#468—1221no—
320#467—611no—
321#467—611no—
322#467—611no—
323#467C2×D6111yescharacteristic
324#466—611no—
325#466—611no—
326#466—611no—
327#466C2×D6111yescharacteristic
328C2×#107—611no—
329C2×#107—611no—
330#417—1221no—
331#417—1221no—
332#367—611no—
333#367—611no—
334#367—611no—
335#367C2×D6111yescharacteristic
336#358—611no—
337#358—611no—
338#358—611no—
339#358C2×D6111yescharacteristic
340#357—611no—
341#357—611no—
342#357—611no—
343#357C2×D6111yescharacteristic
344C61#3361111yescharacteristic, complemented, Sylow
345C2×#41—611no—
346C2×#41—1221no—
347C2×#41—1221no—
348#135—1222no—
349#135—1222no—
350#135—1222no—
351#135—1222no—
352C2×Q16—611no—
353C2×Q16C22×D6111yescharacteristic
354C2×SD16—1221no—
355C2×SD16—1221no—
356C2×D8—611no—
357C2×D8C22×D6111yescharacteristic
358#131—1222no—
359#131—1222no—
360C2×M16—611no—
361C2×M16—611no—
362C2×M16—611no—
363C22×C8—611no—
364C22×C8—611no—
365C22×C8C22×D6111yescharacteristic
366C22⋊Q8—21no—
367C22⋊Q8—1221no—
368C22⋊Q8—1221no—
369C22⋊Q8—1221no—
370C22⋊Q8—2441no—
371C22⋊Q8—2441no—
372#121—21no—
373#121—1221no—
374#121—1221no—
375#121—1221no—
376#121—2441no—
377#121—2441no—
378#121—2441no—
379#121—2441no—
380#121—2441no—
381#121—2441no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384Q32—1222no—
385SD32—22no—
386SD32—1222no—
387D16—1222no—
388M32—1222no—
389M32—1222no—
390M32—1222no—
391C2×C16—22no—
392C2×C16—611no—
393C2×C16—614no—
394C2×C16—611no—
395C2×C16—1222no—
396C2×C16C22×D6111yescharacteristic
397C2×C16C22×D6111yescharacteristic
398#107—611no—
399#107—611no—
400#107—1221no—
401#107—1221no—
402#107C22×D6111yescharacteristic
403#107C22×D6111yescharacteristic
404#103—21no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#102—21no—
409#102—1221no—
410#102—1221no—
411#102—1221no—
412#41—1222no—
413#41—1222no—
414#41—2442no—
415#41—2442no—
416#41—2442no—
417#41—2442no—
418C2×Q8—21no—
419C2×Q8—611no—
420C2×Q8—1221no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—611no—
424C2×D4—611no—
425C2×D4—611no—
426C2×D4—1221no—
427C2×D4—2441no—
428C2×D4—2441no—
429C2×D4—2441no—
430C2×D4—2441no—
431C2×D4—2441no—
432C22×C4—611no—
433C22×C4—611no—
434C22×C4—2441no—
435C22×C4—2441no—
436C22×C4—2441no—
437C22×C4—2441no—
438C22×C4D4×D6111yescharacteristic
439Q16—21no—
440Q16—21no—
441Q16—1221no—
442Q16—1221no—
443SD16—2442no—
444SD16—2442no—
445D8—21no—
446D8—21no—
447D8—1221no—
448D8—1221no—
449M16—1222no—
450M16—1222no—
451M16—1222no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—611no—
455C2×C8—612no—
456C2×C8—612no—
457C2×C8—611no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8D4×D6111yescharacteristic
461C2×C8C23×D6111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—2441no—
475C22⋊C4—2441no—
476C22⋊C4—2441no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C22⋊C4—2441no—
480C16—21no—
481C16—612no—
482C16—1221no—
483C16D4×D6112yes—
484C23—41no—
485C23—611no—
486C23—611no—
487C23—2441no—
488C23D8×D6111yescharacteristic
489Q8—41no—
490Q8—41no—
491Q8—1222no—
492Q8—2441no—
493Q8—2441no—
494D4—41no—
495D4—41no—
496D4—161no—
497D4—1222no—
498D4—1222no—
499D4—1222no—
500D4—9761no—
501D4—9761no—
502D4—9761no—
503D4—4882no—
504D4—4882no—
505D4—2441no—
506D4—2441no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—611no—
513C2×C4—612no—
514C2×C4—612no—
515C2×C4—611no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—9761no—
519C2×C4—9761no—
520C2×C4—4882no—
521C2×C4—4882no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4D8×D6111yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C8—21no—
528C8—612no—
529C8—1221no—
530C8C2×D4×D6111yescharacteristic
531C8#41×D6111yescharacteristic
532C22—21no—
533C22—21no—
534C22—21no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—612no—
539C22—1221no—
540C22—1221no—
541C22—1221no—
542C22—1221no—
543C22—1221no—
544C22—4881no—
545C22—4881no—
546C22—4881no—
547C22C2×D8×D6111yescharacteristic
548C4—21no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4—612no—
553C4—1221no—
554C4—4881no—
555C4—4881no—
556C4—4881no—
557C4#121×D6111yescharacteristic
558C4#135×D6111yescharacteristic
559C2—41no—
560C2—161no—
561C2—1222no—
562C2—9761no—
563C2—2441no—
564C2#466×D6111yescharacteristic
565C2#2145896111yescharacteristic
566C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2217C2
socleC22×C61C22×D8
hypercenter#2217D61
hypocenterC61#33611
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. C2×#16840193C2semidirect
2. C2×#16840178C2semidirect
3. #21455490C2semidirect
4. #21455484C2semidirect
5. #21447926C2semidirect
6. #21447925C2semidirect
7. #21447921C2semidirect
8. #21447920C2semidirect
9. #21447916C2semidirect
10. #21447915C2semidirect
11. #21447912C2semidirect
12. #367×D61C2semidirect
13. #21447530C2semidirect
14. #21447528C2semidirect
15. C61×#2217C2semidirect
104. C16×D61D4semidirect
287. #2217D61semidirect
344. C61#33611semidirect

Maximal subgroups

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

subgroupindex
C2×#168401932
C2×#168401782
#214554902
#214554842
#214479262
#214479252
#214479212
#214479202
#214479162
#214479152
#214479122
#367×D612
#214475302
#214475282
C61×#22172
#3361161