Finite Group Databasebeta

← #29670884

Subgroups — #29670884

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458690C211yesmaximal, characteristic, complemented
2#21458475C211yesmaximal, characteristic
3#21458213C211yesmaximal, characteristic, complemented
4#21445438C211yesmaximal, characteristic, complemented
5#21445347C211yesmaximal, characteristic, complemented
6#21445233C211yesmaximal, characteristic, complemented
7#21445199C211yesmaximal, characteristic, complemented
8#21445157C211yesmaximal, characteristic
9#21445031C211yesmaximal, characteristic, complemented
10#21444977C211yesmaximal, characteristic, complemented
11#21444940C211yesmaximal, characteristic, complemented
12#21444890C211yesmaximal, characteristic
13#21444653C211yesmaximal, characteristic, complemented
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3400C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840161—21no—
20#16840158C2211yescharacteristic
21#16840134C2211yescharacteristic
22#16840116—21no—
23#16840114C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840096—21no—
26#16840096—21no—
27#16840069—21no—
28#16840062—21no—
29#16840059—21no—
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840057C2211yescharacteristic
33#16840057C2211yescharacteristic
34#16840039C2211yescharacteristic
35#16840000—21no—
36#16839974—21no—
37#16839954C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C4×#11758201—21no—
41C4×#11758201C2211yescharacteristic
42C4×#11758199—21no—
43C8×D244C2211yescharacteristic
44#107×D61—21no—
45#16839513C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839510C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#559C2211yescharacteristic
57C61×#557C2211yescharacteristic
58C61×#497—21no—
59C61×#492C2211yescharacteristic
60C61×#464—21no—
61C61×#462C2211yescharacteristic
62C61×#461—21no—
63C61×#460C2211yescharacteristic
64C61×#446C2211yescharacteristic
65C61×#440—21no—
66C4×Q16×C61C2211yescharacteristic
67C2×#11758200—41no—
68C2×#11758201D411yescharacteristic
69C2×#11758199—21no—
70C2×C8×D61—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519769—21no—
74#14519769—21no—
75#14519755—41no—
76#14519755—41no—
77#14519753—21no—
78#14519753—21no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244C2311yescharacteristic
82C4⋊C4×D61—21no—
83C4⋊C4×D61—21no—
84#14519711—21no—
85#14519711—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708D411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701D411yescharacteristic
104#14519700—41no—
105#14519698—21no—
106#14519698—21no—
107#14519698—21no—
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111C4×#92418—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61—21no—
116C2×Q16×C61D411yescharacteristic
117C2×SD16×C61—21no—
118C2×SD16×C61—21no—
119C2×SD16×C61—21no—
120C4⋊Q8×C61—21no—
121C4⋊Q8×C61C2311yescharacteristic
122#127×C61C2311yescharacteristic
123#125×C61—21no—
124#125×C61—41no—
125#124×C61—21no—
126#124×C61—21no—
127#123×C61—41no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61—21no—
135#107×C61D411yescharacteristic
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61D411yescharacteristic
140#103×C61D411yescharacteristic
141#102×C61—21no—
142#97×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—22no—
159Q16×C61—81no—
160SD16×C61—42no—
161SD16×C61—81no—
162SD16×C61—81no—
163C2×C8×C61—21no—
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—41no—
172C4⋊C4×C61—41no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61C2×D411yescharacteristic
175C4⋊C4×C61C2×D411yescharacteristic
176C4⋊C4×C61C2×D411yescharacteristic
177C22⋊C4×C61—41no—
178C22⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C42×C61—21no—
181C42×C61—21no—
182C42×C61—21no—
183C42×C61—41no—
184C42×C61C2411yescharacteristic
185#11758201—22no—
186#11758200—82no—
187#11758199—42no—
188#11758198—21no—
189#11758198—41no—
190#11758198—41no—
191C4⋊Dic61—21no—
192C4⋊Dic61—21no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61C2×D411yescharacteristic
196#11758196—41no—
197#11758196—41no—
198#11758196—41no—
199#11758196—41no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C8×D61—42no—
207C23×C61—41no—
208C22×D61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—41no—
216Q8×C61—41no—
217D4×C61—41no—
218D4×C61—41no—
219D4×C61—41no—
220D4×C61—41no—
221D4×C61—81no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—161no—
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61H(5,𝔽2)11yescharacteristic
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236D244—21no—
237D244#13712yes—
238C4×D61—41no—
239C4×D61—41no—
240C4×D61—161no—
241C4×D61—161no—
242Dic122—81no—
243Dic122—81no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61#13512yes—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#19857—611nomaximal, Sylow
254C22×C61—81no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61D4211yescharacteristic
258C2×D61—22no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—21no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—81no—
269C4×C61C2×#13511yescharacteristic
270C4×C61C2×#13711yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—41no—
274Dic61—81no—
275Dic61—81no—
276#3400D6111yescharacteristic, complemented
277#3381—611no—
278#3361—611no—
279#3338—611no—
280#1714—611no—
281#1696—611no—
282#1678—611no—
283#1672—611no—
284#1665—611no—
285#1644—611no—
286#1636—611no—
287#1630—611no—
288#1622—611no—
289#1582—611no—
290#1579—611no—
291C2×C61—161no—
292C2×C61#327011yescharacteristic
293C2×C61#328411yescharacteristic
294C2×C61#328811yescharacteristic
295D61—42no—
296#559C2×D6111yescharacteristic
297#557C2×D6111yescharacteristic
298#554—611no—
299#554—611no—
300#500—611no—
301#499—1221no—
302#498—611no—
303#497—21no—
304#492—611no—
305#492C2×D6111yescharacteristic
306#488—1221no—
307#487—611no—
308#486—611no—
309#484—1221no—
310#484—1221no—
311#479—1221no—
312#478—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477—611no—
317#477—611no—
318#474—611no—
319#467—1221no—
320#464—21no—
321#463—1221no—
322#462C2×D6111yescharacteristic
323#461—21no—
324#460C2×D6111yescharacteristic
325#459—611no—
326#446C2×D6111yescharacteristic
327C8×Q8—611no—
328C8×Q8—611no—
329#440—21no—
330C4×Q16C2×D6111yescharacteristic
331C4×SD16—611no—
332C4×SD16—1221no—
333C4×D8—1221no—
334C8×D4—611no—
335C2×#107—1221no—
336#334—611no—
337#334—611no—
338#333—611no—
339#333—611no—
340#332—611no—
341#331—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345D4⋊C8—611no—
346#322—611no—
347C61#1985711yescharacteristic, complemented, Sylow
348C2×Q16—21no—
349C2×Q16C22⋊D6111yescharacteristic
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—611no—
354C2×SD16—2441no—
355C2×D8—1221no—
356C22×C8—1221no—
357C4⋊Q8—21no—
358C4⋊Q8—611no—
359C4⋊Q8—611no—
360C4⋊Q8C22×D6111yescharacteristic
361#127C22×D6111yescharacteristic
362#125—21no—
363#125—41no—
364#125—1221no—
365#125—1221no—
366#124—21no—
367#124—21no—
368#123—41no—
369C22⋊Q8—1221no—
370C22⋊Q8—1221no—
371C22⋊Q8—2441no—
372C22⋊Q8—2441no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8C22×D6111yescharacteristic
376C4×Q8C22×D6111yescharacteristic
377C4×Q8C22×D6111yescharacteristic
378C4×D4—21no—
379C4×D4—21no—
380C4×D4—611no—
381C4×D4—1221no—
382C4×D4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4—1221no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#107—1221no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#107C22⋊D6111yescharacteristic
393#106—611no—
394#106—1221no—
395#106—1221no—
396C4⋊C8—21no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—611no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—2441no—
410#103C22⋊D6111yescharacteristic
411#103C22⋊D6111yescharacteristic
412#102—21no—
413#102—611no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418C22⋊C8—1221no—
419#97—21no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C2×Q8—21no—
426C2×Q8—1221no—
427C2×Q8—1221no—
428C2×Q8D4×D6111yescharacteristic
429C2×Q8C2×C22⋊D6111yescharacteristic
430C2×Q8C2×C22⋊D6111yescharacteristic
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—611no—
435C22×C4—41no—
436C22×C4—1221no—
437C22×C4—2441no—
438C22×C4—2441no—
439Q16—22no—
440Q16—81no—
441SD16—42no—
442SD16—81no—
443SD16—81no—
444SD16—1222no—
445SD16—4882no—
446D8—2442no—
447C2×C8—21no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—2442no—
455C2×C8C2×C22⋊D6111yescharacteristic
456C2×C8C2×C22⋊D6111yescharacteristic
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—611no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—2441no—
471C4⋊C4—2441no—
472C4⋊C4—2441no—
473C4⋊C4—2441no—
474C4⋊C4D4×D6111yescharacteristic
475C4⋊C4C2×C22⋊D6111yescharacteristic
476C4⋊C4C2×C22⋊D6111yescharacteristic
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—1221no—
481C22⋊C4—2441no—
482C22⋊C4—2441no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—41no—
487C42C23×D6111yescharacteristic
488C23—41no—
489C23—1221no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—4881no—
499Q8—4881no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—81no—
505D4—612no—
506D4—1221no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—161no—
515C2×C4—1221no—
516C2×C4—9761no—
517C2×C4—9761no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4—2441no—
521C2×C4—2441no—
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C22×C22⋊D6111yescharacteristic
524C2×C4#1451982211yescharacteristic
525C8—21no—
526C8—41no—
527C8—1221no—
528C8—1221no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8#1451979712yes—
534C22—81no—
535C22—81no—
536C22—81no—
537C22—1222no—
538C22—2441no—
539C22—2441no—
540C22D4×C22⋊D6111yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—81no—
549C4—4881no—
550C4—4881no—
551C4—2441no—
552C4C2×#1451979711yescharacteristic
553C4#137×D6111yescharacteristic
554C4#1684057311yescharacteristic
555C4#1684057811yescharacteristic
556C2—161no—
557C2—2442no—
558C2#2145738311yescharacteristic
559C2#2145754911yescharacteristic
560C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3400C2
socleC22×C61D42
prime radical#16839954C22
hypercenter#3400D61
hypocenterC61#19857
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3400

Complements

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

NH ≅ G/Ntype
1. #21458690C2semidirect
3. #21458213C2semidirect
4. #21445438C2semidirect
5. #21445347C2semidirect
6. #21445233C2semidirect
7. #21445199C2semidirect
9. #21445031C2semidirect
10. #21444977C2semidirect
11. #21444940C2semidirect
13. #21444653C2semidirect
14. #21444638C2semidirect
15. C61×#3400C2semidirect
276. #3400D61semidirect
347. C61#19857semidirect

Maximal subgroups

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

subgroupindex
#214586902
#214584752
#214582132
#214454382
#214453472
#214452332
#214451992
#214451572
#214450312
#214449772
#214449402
#214448902
#214446532
#214446382
C61×#34002
#1985761