Finite Group Databasebeta

← #29670666

Subgroups — #29670666

Order 15616.

576 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458596C211yesmaximal, characteristic, complemented
2#21458475C211yesmaximal, characteristic
3#21458213C211yesmaximal, characteristic, complemented
4#21445471C211yesmaximal, characteristic, complemented
5#21445357C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445253C211yesmaximal, characteristic
8#21445223C211yesmaximal, characteristic, complemented
9#21445025C211yesmaximal, characteristic, complemented
10#21444977C211yesmaximal, characteristic, complemented
11#21444940C211yesmaximal, characteristic, complemented
12#21444890C211yesmaximal, characteristic
13#21444670C211yesmaximal, characteristic, complemented
14#21444629C211yesmaximal, characteristic, complemented
15C61×#3365C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840134C2211yescharacteristic
20#16840130—21no—
21#16840116—21no—
22#16840114C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840096—21no—
26#16840096—21no—
27#16840069—21no—
28#16840062—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840057C2211yescharacteristic
33#16840000—21no—
34#16839974—21no—
35#16839964—21no—
36#16839964C2211yescharacteristic
37#16839954C2211yescharacteristic
38#16839893C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839860—21no—
41C4×#11758201C2211yescharacteristic
42C4×#11758199—21no—
43C8×D244C2211yescharacteristic
44#107×D61—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#559C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#488—21no—
59C61×#486C2211yescharacteristic
60C61×#478—21no—
61C61×#475C2211yescharacteristic
62C61×#464—21no—
63C61×#460C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×Q16×C61C2211yescharacteristic
66C4×SD16×C61—21no—
67C2×#11758200—41no—
68C2×#11758201—21no—
69C2×#11758201D411yescharacteristic
70C2×#11758199—21no—
71C2×C8×D61—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519769—21no—
75#14519769—21no—
76#14519755—41no—
77#14519755—41no—
78#14519753—21no—
79#14519753—21no—
80C4×D244—21no—
81C4×D244—21no—
82C4×D244C2311yescharacteristic
83C4⋊C4×D61—21no—
84C4⋊C4×D61—21no—
85#14519711—21no—
86#14519711—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519708D411yescharacteristic
92C4⋊#92418—21no—
93C4⋊#92418—21no—
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519701D411yescharacteristic
105#14519700—41no—
106#14519698—21no—
107#14519698—21no—
108#14519698—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C2×SD16×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119#127×C61C2311yescharacteristic
120#125×C61—21no—
121#125×C61—41no—
122#124×C61—21no—
123#124×C61—21no—
124#123×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61—21no—
127C4×Q8×C61C2311yescharacteristic
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61—21no—
132#107×C61D411yescharacteristic
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#103×C61D411yescharacteristic
139#102×C61—21no—
140#102×C61—21no—
141#102×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C2×D411yescharacteristic
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C22×C4×C61—41no—
152C2×D244C2×D411yescharacteristic
153C2×C4×D61—21no—
154C2×C4×D61—41no—
155C2×C4×D61—41no—
156C2×Dic122—21no—
157C2×Dic122—21no—
158Q16×C61—41no—
159SD16×C61—42no—
160C2×C8×C61—21no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182#11758201—22no—
183#11758201—42no—
184#11758200—82no—
185#11758199—42no—
186#11758198—21no—
187#11758198—41no—
188#11758198—41no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197#11758196—41no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C8×D61—42no—
205C23×C61—41no—
206C22×D61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—41no—
214Q8×C61—41no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—81no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—41no—
227C2×C4×C61—161no—
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61H(5,𝔽2)11yescharacteristic
231C2×Dic61—21no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234D244—21no—
235D244#13512yes—
236C4×D61—41no—
237C4×D61—41no—
238C4×D61—161no—
239C4×D61—161no—
240Dic122—81no—
241Dic122—81no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245#92418—21no—
246#92418—21no—
247#92418—41no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#19842—611nomaximal, Sylow
252C22×C61—81no—
253C22×C61—81no—
254C22×C61—81no—
255C22×C61D4211yescharacteristic
256C2×D61—22no—
257C2×D61—41no—
258C2×D61—41no—
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—81no—
267C4×C61C2×#13511yescharacteristic
268C4×C61#57511yescharacteristic
269C4×C61#57811yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274#3372—611no—
275#3365D6111yescharacteristic, complemented
276#3361—611no—
277#3338—611no—
278#1719—611no—
279#1698—611no—
280#1684—611no—
281#1681—611no—
282#1676—611no—
283#1643—611no—
284#1636—611no—
285#1630—611no—
286#1622—611no—
287#1584—611no—
288SD16⋊C8—611no—
289C2×C61—161no—
290C2×C61#326911yescharacteristic
291C2×C61#328511yescharacteristic
292C2×C61#328811yescharacteristic
293D61—42no—
294#559C2×D6111yescharacteristic
295#557C2×D6111yescharacteristic
296#554—611no—
297#554—611no—
298#500—611no—
299#492—611no—
300#491—1221no—
301#488—21no—
302#488—1221no—
303#487—611no—
304#487—611no—
305#486—611no—
306#486C2×D6111yescharacteristic
307#484—1221no—
308#484—1221no—
309#479—1221no—
310#478—21no—
311#478—1221no—
312#477—611no—
313#477—611no—
314#477—611no—
315#477—611no—
316#475C2×D6111yescharacteristic
317#467—1221no—
318#464—21no—
319#463—1221no—
320#461—611no—
321#461—1221no—
322#460C2×D6111yescharacteristic
323#459—611no—
324#446—611no—
325C8×Q8—611no—
326C8×Q8C2×D6111yescharacteristic
327#440—1221no—
328C4×Q16C2×D6111yescharacteristic
329C4×SD16—21no—
330C4×SD16—611no—
331C4×D8—1221no—
332C8×D4—611no—
333C2×#107—1221no—
334#335—611no—
335#335—611no—
336#333—611no—
337#333—611no—
338#332—611no—
339#331—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345C61#1984211yescharacteristic, complemented, Sylow
346C2×Q16C22⋊D6111yescharacteristic
347C2×SD16—21no—
348C2×SD16—611no—
349C2×SD16—1221no—
350C2×SD16—2441no—
351C2×D8—1221no—
352C22×C8—1221no—
353C4⋊Q8—21no—
354C4⋊Q8—611no—
355C4⋊Q8—611no—
356C4⋊Q8C22×D6111yescharacteristic
357#127C22×D6111yescharacteristic
358#125—21no—
359#125—41no—
360#125—1221no—
361#125—1221no—
362#124—21no—
363#124—21no—
364#123—41no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C22⋊Q8—2441no—
368C22⋊Q8—2441no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8C22×D6111yescharacteristic
372C4×Q8C22×D6111yescharacteristic
373C4×Q8C22×D6111yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—611no—
377C4×D4—1221no—
378C4×D4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#107C22⋊D6111yescharacteristic
388#106—21no—
389#106—611no—
390C4⋊C8—21no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8C22×D6111yescharacteristic
397#103—21no—
398#103—611no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—2441no—
407#103C22⋊D6111yescharacteristic
408#103C22⋊D6111yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—611no—
413#102—1221no—
414#102—1221no—
415#102—1221no—
416C22⋊C8—1221no—
417#97—1221no—
418C4×C8—21no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—1221no—
422C4×C8C22×D6111yescharacteristic
423C2×Q8—21no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8D4×D6111yescharacteristic
427C2×Q8C2×C22⋊D6111yescharacteristic
428C2×Q8C2×C22⋊D6111yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—611no—
433C22×C4—41no—
434C22×C4—1221no—
435C22×C4—2441no—
436C22×C4—2441no—
437Q16—41no—
438SD16—42no—
439SD16—1222no—
440SD16—4882no—
441SD16—2442no—
442D8—2442no—
443C2×C8—21no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—2442no—
451C2×C8C2×C22⋊D6111yescharacteristic
452C2×C8C2×C22⋊D6111yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—611no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4D4×D6111yescharacteristic
471C4⋊C4C2×C22⋊D6111yescharacteristic
472C4⋊C4C2×C22⋊D6111yescharacteristic
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—1221no—
477C22⋊C4—2441no—
478C22⋊C4—2441no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—41no—
483C42C23×D6111yescharacteristic
484C23—41no—
485C23—1221no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—4881no—
495Q8—4881no—
496D4—41no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—81no—
501D4—612no—
502D4—1221no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—161no—
511C2×C4—1221no—
512C2×C4—9761no—
513C2×C4—9761no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C22×C22⋊D6111yescharacteristic
520C2×C4#1451982211yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—1221no—
525C8—1221no—
526C8—2441no—
527C8—2441no—
528C8—2441no—
529C8—2441no—
530C22—81no—
531C22—81no—
532C22—81no—
533C22—1222no—
534C22—2441no—
535C22—2441no—
536C22D4×C22⋊D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—4881no—
546C4—4881no—
547C4—2441no—
548C4#135×D6111yescharacteristic
549C4#1684056011yescharacteristic
550C4#1684057611yescharacteristic
551C4#1684057711yescharacteristic
552C2—161no—
553C2—2442no—
554C2#2145737511yescharacteristic
555C2#2145755411yescharacteristic
556C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3365C2
socleC22×C61D42
prime radical#16839954C22
hypercenter#3365D61
hypocenterC61#19842
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3365

Complements

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

NH ≅ G/Ntype
1. #21458596C2semidirect
3. #21458213C2semidirect
4. #21445471C2semidirect
5. #21445357C2semidirect
6. #21445275C2semidirect
8. #21445223C2semidirect
9. #21445025C2semidirect
10. #21444977C2semidirect
11. #21444940C2semidirect
13. #21444670C2semidirect
14. #21444629C2semidirect
15. C61×#3365C2semidirect
275. #3365D61semidirect
345. C61#19842semidirect

Maximal subgroups

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

subgroupindex
#214585962
#214584752
#214582132
#214454712
#214453572
#214452752
#214452532
#214452232
#214450252
#214449772
#214449402
#214448902
#214446702
#214446292
C61×#33652
#1984261