Finite Group Databasebeta

← #29662923

Subgroups — #29662923

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456196C211yesmaximal, characteristic
2#21455860C211yesmaximal, characteristic
3#475×D61C211yesmaximal, characteristic
4#21454771C211yesmaximal, characteristic
5#21445403C211yesmaximal, characteristic, complemented
6#21445373C211yesmaximal, characteristic, complemented
7#21445371C211yesmaximal, characteristic, complemented
8#21445280C211yesmaximal, characteristic, complemented
9#21445274C211yesmaximal, characteristic, complemented
10#21445250C211yesmaximal, characteristic, complemented
11#21445248C211yesmaximal, characteristic, complemented
12#21444568C211yesmaximal, characteristic
13#21444506C211yesmaximal, characteristic
14#21444489C211yesmaximal, characteristic
15C61×#1704C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16840129—21no—
20#16840129—21no—
21#16840114C2211yescharacteristic
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840099—21no—
25#16840054C2211yescharacteristic
26#16840048C2211yescharacteristic
27#16840047C2211yescharacteristic
28#16840046—21no—
29#16840045—21no—
30#16840044C2211yescharacteristic
31#16839973C2211yescharacteristic
32#16839972C2211yescharacteristic
33#16839919—21no—
34#16839893C2211yescharacteristic
35#16839891—21no—
36#16839890—21no—
37C8×Dic122C2211yescharacteristic
38#16839886C2211yescharacteristic
39#16839856—21no—
40#16839854—21no—
41#16839814C2211yescharacteristic
42#106×D61—21no—
43#16839784—21no—
44#16839784C2211yescharacteristic
45C4⋊C8×D61C2211yescharacteristic
46#16839769—21no—
47#16839769—21no—
48#103×D61—21no—
49#16839714—21no—
50C4×#11758189C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839509C2211yescharacteristic
56#16839509C2211yescharacteristic
57#16839508C2211yescharacteristic
58#16839507C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#446C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61D411yescharacteristic
69C2×Dic244—21no—
70C2×#11758202—21no—
71C2×#11758189—21no—
72C2×#11758189D411yescharacteristic
73C2×#11758189D411yescharacteristic
74C2×C8×D61—21no—
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519776—21no—
78#14519776—21no—
79#14519775—21no—
80#14519768—21no—
81#14519757—21no—
82#14519753—21no—
83Q8×Dic61—21no—
84Q8×Dic61D411yescharacteristic
85C4×Dic122—21no—
86C4×Dic122C2311yescharacteristic
87#14519742—21no—
88#14519742—21no—
89#14519742D411yescharacteristic
90#14519735—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61—21no—
94C4⋊C4×D61D411yescharacteristic
95C42×D61—21no—
96C42×D61C2311yescharacteristic
97#14519710—21no—
98#14519709—21no—
99#14519708—21no—
100#14519708—21no—
101C4⋊#92418—21no—
102C4⋊#92418C2311yescharacteristic
103C4⋊#92418C2311yescharacteristic
104C4⋊#92418C2311yescharacteristic
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702—21no—
110#14519702—21no—
111#14519702—21no—
112#14519702—21no—
113#14519701—21no—
114#14519701—21no—
115#14519701—21no—
116#14519700—21no—
117#14519700—21no—
118#14519700—21no—
119#14519700—21no—
120#14519700—21no—
121#14519689—21no—
122#14519688—21no—
123#14519687D411yescharacteristic
124#14519687D411yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C4⋊Q8×C61C2311yescharacteristic
130C4⋊Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61—21no—
141#103×C61—21no—
142#97×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147Q8×D61—22no—
148Q8×D61—41no—
149Q8×D61—42no—
150Q8×D61—42no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—41no—
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61C2×D411yescharacteristic
156C2×C4×D61#4111yescharacteristic
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—21no—
160C2×Dic122—41no—
161C2×Dic122C2×D411yescharacteristic
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C42×C61—21no—
174C42×C61C2411yescharacteristic
175#11758202—42no—
176#11758198—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—41no—
183C4⋊Dic61C2×D411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—41no—
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202Dic244—42no—
203#11758189—22no—
204#11758189—22no—
205#11758189—42no—
206C8×D61—42no—
207C22×D61#12111yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—41no—
223C2×Dic61—41no—
224C2×Dic61#12111yescharacteristic
225C2×Dic61#12111yescharacteristic
226C2×Dic61#12111yescharacteristic
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—41no—
230C4×D61—42no—
231C4×D61—81no—
232C4×D61—82no—
233C4×D61#13512yes—
234C4×D61#13712yes—
235Dic122—21no—
236Dic122—42no—
237Dic122—41no—
238Dic122—41no—
239Dic122—41no—
240Dic122—41no—
241Dic122—82no—
242Dic122#13712yes—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#19175—611nomaximal, Sylow
254C22×C61C2×#12111yescharacteristic
255C2×D61—21no—
256C2×D61—21no—
257C2×D61#46412yes—
258C4×C61—21no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61C2×#13511yescharacteristic
264C4×C61C2×#13711yescharacteristic
265C4×C61C2×#13711yescharacteristic
266C4×C61#57511yescharacteristic
267Dic61—22no—
268Dic61—21no—
269Dic61—21no—
270Dic61—41no—
271Dic61—81no—
272Dic61—81no—
273Dic61#46412yes—
274#3139—611no—
275#3104—611no—
276C2×#475—611no—
277Q8×M16—611no—
278#1704—611no—
279#1704D6111yescharacteristic, complemented
280#1700—611no—
281#1700—611no—
282#1684—611no—
283#1684—611no—
284#1680—611no—
285#1680—611no—
286#1565—611no—
287#1550—611no—
288#1546—611no—
289C2×C61C2×#46411yescharacteristic
290C2×C61#305611yescharacteristic
291C2×C61#306911yescharacteristic
292D61—22no—
293#533—611no—
294C2×C4⋊Q8—611no—
295C2×C4×Q8—611no—
296#491—1221no—
297#491—1221no—
298#487—611no—
299#487—611no—
300#487—611no—
301#487C2×D6111yescharacteristic
302#484—1221no—
303#477—611no—
304#477C2×D6111yescharacteristic
305#475—611no—
306#475—611no—
307#475—611no—
308#475—1221no—
309#475—1221no—
310#475C2×D6111yescharacteristic
311#462—611no—
312#462—611no—
313#451—1221no—
314#446—611no—
315#446—1221no—
316#446—1221no—
317#446C2×D6111yescharacteristic
318C8×Q8—611no—
319C8×Q8—611no—
320C4×Q16—1221no—
321C4×Q16—1221no—
322#431—611no—
323C2×#106—1221no—
324#423—611no—
325#423—1221no—
326C2×C4⋊C8—611no—
327#419—1221no—
328#419—1221no—
329C2×#103—1221no—
330C4×M16—611no—
331C4×M16—1221no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334C2×D6111yescharacteristic
336#333—611no—
337#333C2×D6111yescharacteristic
338#332—611no—
339#332—611no—
340#332—611no—
341#332—611no—
342#332—611no—
343#332C2×D6111yescharacteristic
344C61#1917511yescharacteristic, complemented, Sylow
345C22×Q8—611no—
346C22×Q8—1221no—
347C2×Q16—1221no—
348C2×Q16—1221no—
349C2×M16—611no—
350C2×M16—611no—
351C2×M16—1221no—
352C22×C8—1221no—
353C4⋊Q8—611no—
354C4⋊Q8—611no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8—1221no—
358C4⋊Q8C22×D6111yescharacteristic
359C4⋊Q8C22×D6111yescharacteristic
360#125—1221no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×Q8C22×D6111yescharacteristic
371#117—1221no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—1221no—
374C2×C4⋊C4—1221no—
375C2×C4⋊C4—1221no—
376C2×C42—611no—
377C2×C42—1221no—
378#107—21no—
379#107—1221no—
380#106—21no—
381#106—1221no—
382#106—1221no—
383#106—1221no—
384C4⋊C8—21no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—611no—
415#97—611no—
416#97—1221no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8C22×D6111yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—611no—
425C2×Q8—1221no—
426C2×Q8—1222no—
427C2×Q8—1221no—
428C2×Q8—1221no—
429C2×Q8—2441no—
430C2×Q8—2442no—
431C2×Q8—2442no—
432C2×Q8—2441no—
433C2×Q8D4×D6111yescharacteristic
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—2441no—
440Q16—2442no—
441Q16—2442no—
442M16—1222no—
443M16—1222no—
444M16—2442no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—2442no—
454C2×C8D4×D6111yescharacteristic
455C2×C8D4×D6111yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—611no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
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
475C22⋊C4—2441no—
476C42—21no—
477C42—611no—
478C42—611no—
479C42—611no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—2441no—
484C42C23×D6111yescharacteristic
485C23—611no—
486Q8—21no—
487Q8—21no—
488Q8—41no—
489Q8—41no—
490Q8—81no—
491Q8—612no—
492Q8—1221no—
493Q8—4882no—
494Q8—2442no—
495Q8—2441no—
496Q8—2441no—
497Q8—2441no—
498Q8—2441no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—611no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4881no—
513C2×C4—4882no—
514C2×C4—2441no—
515C2×C4—2442no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C2×D4×D6111yescharacteristic
520C2×C4#41×D6111yescharacteristic
521C8—21no—
522C8—21no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—1221no—
527C8—1221no—
528C8—2441no—
529C8—2441no—
530C8—2441no—
531C22—612no—
532C22—1221no—
533C22—1221no—
534C22#121×D6111yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—612no—
541C4—1221no—
542C4—1222no—
543C4—1221no—
544C4—4881no—
545C4—4881no—
546C4—2441no—
547C4#135×D6111yescharacteristic
548C4#137×D6111yescharacteristic
549C4#137×D6111yescharacteristic
550C4#1684056111yescharacteristic
551C2—1222no—
552C2#464×D6111yescharacteristic
553C2#2145544811yescharacteristic
554C2#2145555111yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1704C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1704D61
hypocenterC61#19175
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1704

Complements

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

NH ≅ G/Ntype
5. #21445403C2semidirect
6. #21445373C2semidirect
7. #21445371C2semidirect
8. #21445280C2semidirect
9. #21445274C2semidirect
10. #21445250C2semidirect
11. #21445248C2semidirect
15. C61×#1704C2semidirect
279. #1704D61semidirect
344. C61#19175semidirect

Maximal subgroups

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

subgroupindex
#214561962
#214558602
#475×D612
#214547712
#214454032
#214453732
#214453712
#214452802
#214452742
#214452502
#214452482
#214445682
#214445062
#214444892
C61×#17042
#1917561