Finite Group Databasebeta

← #29667631

Subgroups — #29667631

Order 15616.

580 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
1#21457157C211yesmaximal, characteristic
2#21456970C211yesmaximal, characteristic, complemented
3#21456846C211yesmaximal, characteristic
4#21454975C211yesmaximal, characteristic
5#21445376C211yesmaximal, characteristic, complemented
6#21445369C211yesmaximal, characteristic, complemented
7#21445336C211yesmaximal, characteristic, complemented
8#21445331C211yesmaximal, characteristic, complemented
9#21445252C211yesmaximal, characteristic, complemented
10#21445245C211yesmaximal, characteristic, complemented
11#21445212C211yesmaximal, characteristic, complemented
12#21445207C211yesmaximal, characteristic, complemented
13#21444602C211yesmaximal, characteristic, complemented
14#21444517C211yesmaximal, characteristic, complemented
15C2×C61×#332C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840154—21no—
21#16840130—21no—
22#16840114C2211yescharacteristic
23#16840114C2211yescharacteristic
24#16840097—21no—
25#16840097—21no—
26#16840070—21no—
27#16840054—21no—
28#16840054—21no—
29#16840048C2211yescharacteristic
30#16840043C2211yescharacteristic
31#16840003—21no—
32#16839991—21no—
33#16839985—21no—
34#16839973C2211yescharacteristic
35#16839969C2211yescharacteristic
36#16839969C2211yescharacteristic
37#16839968C2211yescharacteristic
38#16839964C2211yescharacteristic
39#16839964C2211yescharacteristic
40#16839918—21no—
41#16839901—21no—
42#16839889C2211yescharacteristic
43#16839886C2211yescharacteristic
44#16839839C2211yescharacteristic
45#16839833—21no—
46#16839827C2211yescharacteristic
47C8×C22⋊D61—21no—
48#16839822—21no—
49#16839819C2211yescharacteristic
50#16839815C2211yescharacteristic
51#16839787—21no—
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C2×C4⋊Q8×C61C2211yescharacteristic
61C2×C4⋊C8×C61C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
63C61×#332C2211yescharacteristic
64C61×#332C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Dic244—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758190—21no—
71C2×#11758201—21no—
72C2×#11758201—21no—
73C2×#11758189—21no—
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519771—21no—
78#14519769—21no—
79#14519769D411yescharacteristic
80#14519765D411yescharacteristic
81#14519760—21no—
82#14519756—21no—
83#14519756—21no—
84#14519756D411yescharacteristic
85#14519751D411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122—21no—
88C4×Dic122C2311yescharacteristic
89C4×D244C2311yescharacteristic
90C4×C22⋊D61—21no—
91#14519736—21no—
92#14519734—21no—
93#14519711—21no—
94#14519710—21no—
95#14519710—21no—
96#14519710—21no—
97#14519710—21no—
98#14519709—21no—
99C4⋊#92418D411yescharacteristic
100C4⋊#92418D411yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519702—21no—
106#14519702—21no—
107#14519702—21no—
108#14519701—21no—
109#14519701—21no—
110#14519701—21no—
111#14519701—21no—
112#14519700—21no—
113#14519700—21no—
114#14519700—21no—
115#14519700—21no—
116#14519699—21no—
117C22⋊#92418—21no—
118C22⋊#92418D411yescharacteristic
119C22⋊#92418D411yescharacteristic
120#14519689—21no—
121#14519689—21no—
122#14519688—21no—
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C22×Q8×C61—21no—
128C22×C8×C61—21no—
129C22×C8×C61—21no—
130C4⋊Q8×C61—21no—
131C4⋊Q8×C61—21no—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2311yescharacteristic
134C4⋊Q8×C61C2311yescharacteristic
135C2×C4⋊C4×C61—21no—
136C2×C4⋊C4×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61—21no—
140C4⋊C8×C61C2311yescharacteristic
141C4⋊C8×C61C2311yescharacteristic
142C4⋊C8×C61C2311yescharacteristic
143C4⋊C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—81no—
148C2×Q8×C61—81no—
149C22×C4×C61—41no—
150C22×C4×C61C2×D411yescharacteristic
151C22×C4×C61C2×D411yescharacteristic
152C22×C4×C61#4111yescharacteristic
153C2×C22⋊D61—21no—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122C2×D411yescharacteristic
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61—81no—
164C2×C8×C61—81no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C42×C61C2×D411yescharacteristic
172C42×C61C2×D411yescharacteristic
173C42×C61#4111yescharacteristic
174C42×C61C2411yescharacteristic
175C22⋊Dic61—21no—
176C22⋊Dic61—41no—
177#11758202—81no—
178#11758202—81no—
179#11758201—81no—
180#11758201—81no—
181#11758198—21no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C2×D411yescharacteristic
190C4⋊Dic61C2×D411yescharacteristic
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—41no—
196#11758196—41no—
197C4×Dic61—21no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205Dic244—81no—
206#11758190—81no—
207#11758189—81no—
208C8×D61—81no—
209C23×C61#12111yescharacteristic
210C22×D61—21no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—82no—
216C2×C4×C61—22no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—82no—
224C2×C4×C61#12111yescharacteristic
225C2×C4×C61#12111yescharacteristic
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C22⋊D61—42no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236D244—21no—
237D244—21no—
238C4×D61—41no—
239C4×D61—41no—
240Dic122—21no—
241Dic122—21no—
242Dic122—41no—
243Dic122—41no—
244Dic122—41no—
245Dic122—41no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—21no—
254#92418—41no—
255#92418—41no—
256#19590—611nomaximal, Sylow
257C22×C61—21no—
258C22×C61—21no—
259C22×C61#47312yes—
260C22×C61C2×#12111yescharacteristic
261C2×D61—41no—
262C2×D61—41no—
263C2×D61—41no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61#57611yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277Dic61—81no—
278Dic61—81no—
279#3248—611no—
280#3230—611no—
281#3218—611no—
282#2994—611no—
283#1700—611no—
284#1699—611no—
285#1694—611no—
286#1693—611no—
287#1680—611no—
288#1679—611no—
289#1674—611no—
290#1673—611no—
291#1573—611no—
292#1552—611no—
293C2×#332D6111yescharacteristic, complemented
294C2×C61—22no—
295C2×C61#304611yescharacteristic
296C2×C61#306211yescharacteristic
297C2×C61C2×#47311yescharacteristic
298D61—81no—
299#533—611no—
300C2×C4⋊Q8C2×D6111yescharacteristic
301#529—611no—
302#500—611no—
303#500—611no—
304#497—1221no—
305#491—1221no—
306#487—611no—
307#487—611no—
308#484—1221no—
309#484—1221no—
310#479—1221no—
311#477—1221no—
312#477—1221no—
313#475—611no—
314#474—611no—
315#467—1221no—
316#465—1221no—
317#464—1221no—
318#462—611no—
319#462—611no—
320#462—611no—
321#461—611no—
322#461—611no—
323#461—611no—
324#451—1221no—
325#448—1221no—
326#446—611no—
327C8×Q8—611no—
328#436—611no—
329#435—1221no—
330C8×D4—611no—
331C8×D4—1221no—
332#433—1221no—
333#432—611no—
334#431—611no—
335#424—1221no—
336C2×C4⋊C8C2×D6111yescharacteristic
337C2×C4⋊C8C2×D6111yescharacteristic
338#335—611no—
339#335—611no—
340#334—611no—
341#334—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332C2×D6111yescharacteristic
347#332C2×D6111yescharacteristic
348#332C2×D6111yescharacteristic
349#332C2×D6111yescharacteristic
350C61#1959011yescharacteristic, complemented, Sylow
351C22×Q8—21no—
352C2×Q16—1221no—
353C2×Q16—1221no—
354C2×Q16—1221no—
355C2×SD16—1221no—
356C2×SD16—1221no—
357C2×SD16—1221no—
358C2×M16—1221no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—1221no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—611no—
366C4⋊Q8—611no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#126—1221no—
370#125—611no—
371#125—1221no—
372#124—611no—
373#123—1221no—
374C22⋊Q8—611no—
375C22⋊Q8—1221no—
376C22⋊Q8—1221no—
377#121—611no—
378C4×Q8—611no—
379C4×Q8—1221no—
380C4×Q8—1221no—
381C4×D4—611no—
382C4×D4—1221no—
383#117—1221no—
384#117—1221no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C42C22×D6111yescharacteristic
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107—1221no—
393#106—1221no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403C4⋊C8C22×D6111yescharacteristic
404C4⋊C8C22×D6111yescharacteristic
405C4⋊C8C22×D6111yescharacteristic
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#102—1221no—
418C22⋊C8—611no—
419C22⋊C8—611no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8—1221no—
423#97—1221no—
424#97—1221no—
425C4×C8—611no—
426C4×C8—611no—
427C4×C8—1221no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8—81no—
432C2×Q8—81no—
433C2×Q8—611no—
434C2×Q8—1221no—
435C2×Q8—1221no—
436C2×D4—611no—
437C2×D4—1221no—
438C22×C4—41no—
439C22×C4—1221no—
440C22×C4#1175822211yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4D4×D6111yescharacteristic
443Q16—4881no—
444Q16—4881no—
445Q16—4881no—
446SD16—4881no—
447SD16—4881no—
448SD16—4881no—
449M16—4881no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—81no—
455C2×C8—81no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—611no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—4881no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—611no—
470C4⋊C4—611no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—1221no—
479C4⋊C4—2441no—
480C4⋊C4—2441no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C22⋊C4—1221no—
486C22⋊C4—2441no—
487C42—1221no—
488C42—2441no—
489C42#1175822211yescharacteristic
490C42D4×D6111yescharacteristic
491C42D4×D6111yescharacteristic
492C42C23×D6111yescharacteristic
493C23—1221no—
494C23#1451975011yescharacteristic
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—82no—
500Q8—1221no—
501Q8—1221no—
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—1221no—
507D4—1221no—
508D4—2442no—
509C2×C4—22no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—1221no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4—2441no—
524C2×C4#1451975011yescharacteristic
525C2×C4#1451975011yescharacteristic
526C2×C4#1451975011yescharacteristic
527C2×C4C2×D4×D6111yescharacteristic
528C2×C4C2×D4×D6111yescharacteristic
529C2×C4C2×#1175822211yescharacteristic
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—1221no—
538C8—2441no—
539C8—2441no—
540C22—21no—
541C22—21no—
542C22—2441no—
543C22—2441no—
544C22—2441no—
545C22#1684003612yes—
546C22C2×#1451975011yescharacteristic
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—81no—
552C4—81no—
553C4—4881no—
554C4—4881no—
555C4—2441no—
556C4—2441no—
557C4—2441no—
558C4#1684056311yescharacteristic
559C4#1684056811yescharacteristic
560C4#1684056811yescharacteristic
561C4#1684057511yescharacteristic
562C2—22no—
563C2—4881no—
564C2#2145537411yescharacteristic
565C2#2145549711yescharacteristic
566C2C2×#1684003611yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC2×C61×#332C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenterC2×#332D61
hypocenterC61#19590
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
2. #21456970C2semidirect
5. #21445376C2semidirect
6. #21445369C2semidirect
7. #21445336C2semidirect
8. #21445331C2semidirect
9. #21445252C2semidirect
10. #21445245C2semidirect
11. #21445212C2semidirect
12. #21445207C2semidirect
13. #21444602C2semidirect
14. #21444517C2semidirect
15. C2×C61×#332C2semidirect
293. C2×#332D61semidirect
350. C61#19590semidirect

Maximal subgroups

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

subgroupindex
#214571572
#214569702
#214568462
#214549752
#214453762
#214453692
#214453362
#214453312
#214452522
#214452452
#214452122
#214452072
#214446022
#214445172
C2×C61×#3322
#1959061