Finite Group Databasebeta

← #29670665

Subgroups — #29670665

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#21458598C211yesmaximal, characteristic, complemented
2#21458511C211yesmaximal, characteristic, complemented
3#21458207C211yesmaximal, characteristic, complemented
4#21445469C211yesmaximal, characteristic, complemented
5#21445356C211yesmaximal, characteristic, complemented
6#21445277C211yesmaximal, characteristic, complemented
7#21445254C211yesmaximal, characteristic
8#21445221C211yesmaximal, characteristic, complemented
9#21445026C211yesmaximal, characteristic, complemented
10#21444975C211yesmaximal, characteristic, complemented
11#21444940C211yesmaximal, characteristic, complemented
12#21444889C211yesmaximal, characteristic
13#21444669C211yesmaximal, characteristic, complemented
14SD16⋊#92418C211yesmaximal, characteristic, complemented
15C61×#3361C211yesmaximal, characteristic
16#16840490C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840134C2211yescharacteristic
20#16840129—21no—
21#16840116—21no—
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840108C2211yescharacteristic
25#16840097—21no—
26#16840095—21no—
27#16840072—21no—
28#16840062—21no—
29#16840057C2211yescharacteristic
30#16840057C2211yescharacteristic
31#16840054C2211yescharacteristic
32#16840047C2211yescharacteristic
33#16840001—21no—
34#16839981—21no—
35#16839967C2211yescharacteristic
36#16839965—21no—
37#16839959C2211yescharacteristic
38#16839892C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40#16839859—21no—
41C4×#11758202C2211yescharacteristic
42C4×#11758200—21no—
43D4×#92418C2211yescharacteristic
44C2×#14519710—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839509C2211yescharacteristic
50#16839506C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839483C2211yescharacteristic
56C61×#559C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#488—21no—
59C61×#486C2211yescharacteristic
60C61×#478—21no—
61C61×#477C2211yescharacteristic
62C61×#463—21no—
63C61×#459C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×SD16×C61C2211yescharacteristic
66C4×D8×C61—21no—
67C2×#11758202D411yescharacteristic
68C2×#11758200—21no—
69C2×#11758200—21no—
70C2×#11758200—41no—
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519775—21no—
75#14519769—21no—
76#14519768—21no—
77#14519767—41no—
78#14519756—21no—
79#14519754—41no—
80C4×Dic122—21no—
81C4×Dic122C2311yescharacteristic
82#14519742—21no—
83D4×Dic61—21no—
84C2×C4⋊Dic61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519706—21no—
97#14519702—21no—
98#14519702—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—41no—
103#14519701D411yescharacteristic
104#14519700—21no—
105#14519700—21no—
106#14519700D411yescharacteristic
107#14519698—21no—
108#14519698—21no—
109#14519698—21no—
110C22⋊#92418—21no—
111#14519687—21no—
112C4×#92418—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×SD16×C61D411yescharacteristic
116C2×D8×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118#127×C61C2311yescharacteristic
119#125×C61—21no—
120#124×C61—21no—
121#124×C61—21no—
122#123×C61—41no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61C2311yescharacteristic
126C4×Q8×C61C2311yescharacteristic
127C4×D4×C61—21no—
128C4×D4×C61—21no—
129C4×D4×C61—21no—
130C4×D4×C61C2311yescharacteristic
131C2×C4⋊C4×C61—21no—
132#107×C61—21no—
133#106×C61D411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61D411yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61—21no—
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C2×D411yescharacteristic
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61C2×D411yescharacteristic
151C22×C4×C61—21no—
152C22×C4×C61—41no—
153C22×C4×C61—41no—
154C22×Dic61—41no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C2×D411yescharacteristic
158SD16×C61—22no—
159D8×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—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61C2×D411yescharacteristic
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C42×C61—21no—
178C42×C61—21no—
179C42×C61C2411yescharacteristic
180C22⋊Dic61—41no—
181#11758202—41no—
182#11758200—42no—
183#11758200—42no—
184#11758200—82no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190C4⋊Dic61C2×D411yescharacteristic
191#11758196—21no—
192#11758196—41no—
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—42no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C23×C61—21no—
206C23×C61—41no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—81no—
212D4×C61—21no—
213D4×C61—41no—
214D4×C61—41no—
215D4×C61—41no—
216D4×C61—41no—
217D4×C61—81no—
218D4×C61#13512yes—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—161no—
228C2×C4×C61—161no—
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61H(5,𝔽2)11yescharacteristic
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—161no—
237Dic122—21no—
238Dic122—21no—
239Dic122—41no—
240Dic122—41no—
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—22no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61—81no—
258C22×C61D4211yescharacteristic
259C4×C61—21no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—41no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—81no—
266C4×C61C2×#13511yescharacteristic
267C4×C61#57511yescharacteristic
268C4×C61#57811yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—41no—
271Dic61—41no—
272Dic61—81no—
273Dic61—81no—
274#3372—611no—
275#3365—611no—
276#3361D6111yescharacteristic
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—42no—
290C2×C61—161no—
291C2×C61#326911yescharacteristic
292C2×C61#328511yescharacteristic
293C2×C61#328811yescharacteristic
294#559C2×D6111yescharacteristic
295#557—611no—
296#554—611no—
297#554C2×D6111yescharacteristic
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#477C2×D6111yescharacteristic
316#475—611no—
317#467—1221no—
318#464—1221no—
319#463—21no—
320#461—611no—
321#461—1221no—
322#460—611no—
323#459C2×D6111yescharacteristic
324#446—611no—
325C8×Q8—611no—
326C8×Q8C2×D6111yescharacteristic
327#440—1221no—
328C4×Q16—611no—
329C4×SD16—1221no—
330C4×SD16C2×D6111yescharacteristic
331C4×D8—21no—
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×Q16—611no—
347C2×SD16—1221no—
348C2×SD16—1221no—
349C2×SD16—2441no—
350C2×SD16C22⋊D6111yescharacteristic
351C2×D8—21no—
352C22×C8—1221no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8C22×D6111yescharacteristic
357#127C22×D6111yescharacteristic
358#125—21no—
359#125—1221no—
360#125—1221no—
361#125—2441no—
362#124—21no—
363#124—21no—
364#123—41no—
365C22⋊Q8—21no—
366C22⋊Q8—41no—
367C22⋊Q8—1221no—
368C22⋊Q8—2441no—
369C4×Q8—611no—
370C4×Q8—1221no—
371C4×Q8—1221no—
372C4×Q8C22×D6111yescharacteristic
373C4×Q8C22×D6111yescharacteristic
374C4×D4—21no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—1221no—
378C4×D4C22×D6111yescharacteristic
379C2×C4⋊C4—21no—
380C2×C4⋊C4—1221no—
381#107—21no—
382#107—611no—
383#107—1221no—
384#107—1221no—
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#106—1221no—
389#106C22⋊D6111yescharacteristic
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—611no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—2441no—
408#103C22⋊D6111yescharacteristic
409#102—21no—
410#102—21no—
411#102—21no—
412#102—1221no—
413#102—1221no—
414#102—1221no—
415#102C22⋊D6111yescharacteristic
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—611no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×Q8D4×D6111yescharacteristic
428C2×Q8C2×C22⋊D6111yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4C2×C22⋊D6111yescharacteristic
433C22×C4—21no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—2441no—
437Q16—2441no—
438SD16—22no—
439SD16—4882no—
440SD16—2442no—
441SD16—2442no—
442D8—42no—
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—41no—
458C4⋊C4—41no—
459C4⋊C4—611no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—2441no—
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—21no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—2441no—
479C42—21no—
480C42—21no—
481C42—1221no—
482C42—2441no—
483C42C23×D6111yescharacteristic
484C23—21no—
485C23—41no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—81no—
491Q8—1221no—
492Q8—1221no—
493Q8—4881no—
494Q8—2441no—
495Q8—2441no—
496D4—21no—
497D4—41no—
498D4—41no—
499D4—41no—
500D4—41no—
501D4—81no—
502D4#1451979712yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—161no—
512C2×C4—161no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—9761no—
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—22no—
531C22—41no—
532C22—41no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22D4×C22⋊D6111yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—81no—
544C4—4881no—
545C4—4881no—
546C4—2441no—
547C4—2441no—
548C4C2×#1451979711yescharacteristic
549C4#1684055911yescharacteristic
550C4#1684057611yescharacteristic
551C4#1684057711yescharacteristic
552C2—42no—
553C2—161no—
554C2#2145737411yescharacteristic
555C2#2145755611yescharacteristic
556C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3361C2
socleC22×C61D42
prime radicalC61×#459C22
hypercenter#3361D61
hypocenterC61#19842
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3361

Complements

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

NH ≅ G/Ntype
1. #21458598C2semidirect
2. #21458511C2semidirect
3. #21458207C2semidirect
4. #21445469C2semidirect
5. #21445356C2semidirect
6. #21445277C2semidirect
8. #21445221C2semidirect
9. #21445026C2semidirect
10. #21444975C2semidirect
11. #21444940C2semidirect
13. #21444669C2semidirect
14. SD16⋊#92418C2semidirect
345. C61#19842semidirect

Maximal subgroups

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

subgroupindex
#214585982
#214585112
#214582072
#214454692
#214453562
#214452772
#214452542
#214452212
#214450262
#214449752
#214449402
#214448892
#214446692
SD16⋊#924182
C61×#33612
#1984261