Finite Group Databasebeta

← #29665106

Subgroups — #29665106

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457186C211yesmaximal, characteristic
2#21457042C211yesmaximal, characteristic
3#21456366C211yesmaximal, characteristic, complemented
4#21454817C211yesmaximal, characteristic
5#21445346C211yesmaximal, characteristic, complemented
6#21445341C211yesmaximal, characteristic, complemented
7#21445324C211yesmaximal, characteristic, complemented
8#21445317C211yesmaximal, characteristic, complemented
9#21445222C211yesmaximal, characteristic, complemented
10#21445217C211yesmaximal, characteristic, complemented
11#21445200C211yesmaximal, characteristic, complemented
12#21445193C211yesmaximal, characteristic, complemented
13#21444587C211yesmaximal, characteristic, complemented
14#21444499C211yesmaximal, characteristic, complemented
15C61×#1554C211yesmaximal, characteristic, complemented
16C2×#14519777C2211yescharacteristic
17#16840296C2211yescharacteristic
18#16840172—21no—
19#16840172—21no—
20#16840171—21no—
21#16840165C2211yescharacteristic
22#16840165C2211yescharacteristic
23#16840158C2211yescharacteristic
24#16840158C2211yescharacteristic
25#16840122—21no—
26#16840093—21no—
27#16840076—21no—
28#16840069—21no—
29#16840058C2211yescharacteristic
30#16840058C2211yescharacteristic
31#16840054C2211yescharacteristic
32#16840053C2211yescharacteristic
33#16840053C2211yescharacteristic
34#16840049C2211yescharacteristic
35#16840018—21no—
36#16840010—21no—
37#16839984—21no—
38#16839969C2211yescharacteristic
39#16839964C2211yescharacteristic
40#16839889C2211yescharacteristic
41#16839886C2211yescharacteristic
42#16839839C2211yescharacteristic
43#16839837—21no—
44#16839836—21no—
45#16839827C2211yescharacteristic
46#16839821—21no—
47#16839805—21no—
48#16839805—21no—
49#16839786C2211yescharacteristic
50#16839716—21no—
51C4×#11758194C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839512C2211yescharacteristic
55#16839512C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839510C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#333C2211yescharacteristic
64C61×#333C2211yescharacteristic
65C61×#332C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C22×Dic122—21no—
68C2×#11758202—21no—
69C2×#11758201—21no—
70C2×#11758194—21no—
71C2×#11758194D411yescharacteristic
72C2×#11758194D411yescharacteristic
73C2×#11758189—21no—
74C2×C8×D61—21no—
75#14519777—21no—
76#14519777—21no—
77#14519777—21no—
78#14519777C2311yescharacteristic
79#14519777C2311yescharacteristic
80#14519771—21no—
81#14519769D411yescharacteristic
82#14519765D411yescharacteristic
83#14519760—21no—
84#14519756D411yescharacteristic
85#14519751D411yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244C2311yescharacteristic
88C4×C22⋊D61—21no—
89#14519734—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61—21no—
92#14519711—21no—
93#14519711—21no—
94#14519710—21no—
95#14519710—21no—
96#14519710—21no—
97#14519710—21no—
98#14519710—21no—
99#14519709—21no—
100#14519709—21no—
101#14519708—21no—
102#14519708—21no—
103#14519708—21no—
104#14519708—21no—
105#14519708—21no—
106C4⋊#92418—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109#14519706—21no—
110#14519706—21no—
111#14519702—21no—
112#14519702—21no—
113#14519701—21no—
114#14519701—21no—
115#14519700—21no—
116#14519699—21no—
117#14519699—21no—
118#14519697—21no—
119#14519689—21no—
120#14519689—21no—
121#14519688D411yescharacteristic
122#14519688D411yescharacteristic
123#14519687—21no—
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C4⋊Q8×C61C2311yescharacteristic
128C4⋊Q8×C61C2311yescharacteristic
129#125×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61—21no—
132C4×Q8×C61—21no—
133C4×Q8×C61—21no—
134#117×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140C22⋊C8×C61—21no—
141C22⋊C8×C61—21no—
142#97×C61—21no—
143C4×C8×C61—21no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C22×C4×C61C2×D411yescharacteristic
147C22×C4×C61C2×D411yescharacteristic
148C22×C4×C61#4111yescharacteristic
149C2×C22⋊D61—21no—
150C22×Dic61—41no—
151C2×D244C2×D411yescharacteristic
152C2×C4×D61—21no—
153C2×Dic122—21no—
154C2×Dic122—21no—
155C2×Dic122—41no—
156C2×Dic122—82no—
157C2×Dic122C2×D411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C22⋊C4×C61—41no—
169C42×C61—41no—
170C42×C61C2×D411yescharacteristic
171C42×C61C2×D411yescharacteristic
172C42×C61#4111yescharacteristic
173C42×C61C2411yescharacteristic
174C22⋊Dic61—21no—
175#11758202—81no—
176#11758201—81no—
177#11758198—21no—
178#11758198—21no—
179#11758198—21no—
180#11758198—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—41no—
186C4⋊Dic61—41no—
187C4⋊Dic61C2×D411yescharacteristic
188C4⋊Dic61C2×D411yescharacteristic
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193C4×Dic61—21no—
194#11758194—22no—
195#11758194—22no—
196#11758194—81no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203#11758189—42no—
204C8×D61—42no—
205C23×C61#12111yescharacteristic
206C22×D61—21no—
207Q8×C61—41no—
208Q8×C61—41no—
209Q8×C61—81no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61#12111yescharacteristic
218C2×C4×C61#12111yescharacteristic
219C2×C4×C61#12111yescharacteristic
220C2×C4×C61C22×D411yescharacteristic
221C2×C4×C61C22×D411yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C22⋊D61—81no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—82no—
230D244—21no—
231D244—21no—
232C4×D61—41no—
233C4×D61—41no—
234Dic122—21no—
235Dic122—21no—
236Dic122—82no—
237Dic122—81no—
238Dic122—81no—
239C8×C61—41no—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243#92418—21no—
244#92418—21no—
245#92418—41no—
246#92418—41no—
247#92418#13712yes—
248#92418#13712yes—
249#19379—611nomaximal, Sylow
250C22×C61—21no—
251C22×C61—21no—
252C22×C61—21no—
253C22×C61C2×#12111yescharacteristic
254C2×D61—41no—
255C2×D61—41no—
256C2×D61—41no—
257C4×C61—21no—
258C4×C61—21no—
259C4×C61—21no—
260C4×C61—21no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61C2×#13711yescharacteristic
264C4×C61C2×#13711yescharacteristic
265C4×C61#57711yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—41no—
268Dic61—41no—
269Dic61—41no—
270Dic61—81no—
271Dic61—81no—
272#3252—611no—
273#3238—611no—
274#3165—611no—
275#2969—611no—
276#1696—611no—
277#1695—611no—
278#1692—611no—
279#1691—611no—
280#1676—611no—
281#1675—611no—
282#1672—611no—
283#1671—611no—
284#1569—611no—
285#1554D6111yescharacteristic, complemented
286#1548—611no—
287C2×C61—41no—
288C2×C61#303911yescharacteristic
289C2×C61#306311yescharacteristic
290C2×C61#306811yescharacteristic
291D61—81no—
292#533C2×D6111yescharacteristic
293C2×C4⋊Q8—611no—
294#529—611no—
295#501—1221no—
296#501—1221no—
297#501—1221no—
298#500—611no—
299#500—611no—
300#498—611no—
301#498—611no—
302#489—1221no—
303#483—1221no—
304#480—1221no—
305#479—1221no—
306#477—611no—
307#477—611no—
308#477—611no—
309#476—611no—
310#476—611no—
311#476—611no—
312#470—1221no—
313#468—1221no—
314#464—1221no—
315#462—611no—
316#461—611no—
317#446—611no—
318C8×Q8—611no—
319#436—611no—
320#436—1221no—
321#435—1221no—
322C8×D4—611no—
323#433—1221no—
324#432C2×D6111yescharacteristic
325#431C2×D6111yescharacteristic
326#428—1221no—
327#428—1221no—
328#423—611no—
329#405—1221no—
330C4×M16—611no—
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335#333—611no—
336#333—611no—
337#333—611no—
338#333—611no—
339#333C2×D6111yescharacteristic
340#333C2×D6111yescharacteristic
341#332C2×D6111yescharacteristic
342#332C2×D6111yescharacteristic
343C61#1937911yescharacteristic, complemented, Sylow
344C22×Q8—1221no—
345C2×Q16—1221no—
346C2×SD16—1221no—
347C2×M16—611no—
348C2×M16—611no—
349C2×M16—1221no—
350C2×M16—1221no—
351C22×C8—1221no—
352C4⋊Q8—611no—
353C4⋊Q8—611no—
354C4⋊Q8—1221no—
355C4⋊Q8—1221no—
356C4⋊Q8—1221no—
357C4⋊Q8C22×D6111yescharacteristic
358C4⋊Q8C22×D6111yescharacteristic
359#126—1221no—
360#125—21no—
361#125—611no—
362#124—611no—
363#123—1221no—
364C22⋊Q8—21no—
365C22⋊Q8—21no—
366C22⋊Q8—611no—
367#121—611no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×Q8—611no—
371C4×D4—611no—
372C4×D4—1221no—
373#117—21no—
374#117—1221no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C42C22×D6111yescharacteristic
378#107—1221no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388#106—1221no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#102—1221no—
407#102—1221no—
408#102—1221no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—611no—
415#97—611no—
416#97—1221no—
417C4×C8—21no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—611no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—4882no—
427C2×Q8—2441no—
428C2×D4—611no—
429C2×D4—1221no—
430C22×C4—1221no—
431C22×C4—2441no—
432C22×C4#1175822211yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4D4×D6111yescharacteristic
435Q16—4881no—
436SD16—4881no—
437M16—1222no—
438M16—1222no—
439M16—4881no—
440M16—2442no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—611no—
446C2×C8—611no—
447C2×C8—611no—
448C2×C8—611no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—2442no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—611no—
459C4⋊C4—611no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C22⋊C4—41no—
471C22⋊C4—1221no—
472C22⋊C4—1221no—
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C42—41no—
477C42—1221no—
478C42#1175822211yescharacteristic
479C42D4×D6111yescharacteristic
480C42D4×D6111yescharacteristic
481C42C23×D6111yescharacteristic
482C23—1221no—
483C23#1451975011yescharacteristic
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—1221no—
488Q8—1221no—
489Q8—4881no—
490Q8—4881no—
491Q8—4882no—
492D4—1221no—
493D4—1221no—
494D4—4881no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—4882no—
506C2×C4—2441no—
507C2×C4—2441no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4#1451975011yescharacteristic
511C2×C4#1451975011yescharacteristic
512C2×C4#1451975011yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4C2×D4×D6111yescharacteristic
515C2×C4C2×#1175822211yescharacteristic
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—612no—
521C8—612no—
522C8—1221no—
523C8—1221no—
524C8—2441no—
525C8—2441no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—2441no—
530C22—2441no—
531C22—2441no—
532C22C2×#1451975011yescharacteristic
533C4—21no—
534C4—21no—
535C4—21no—
536C4—21no—
537C4—81no—
538C4—81no—
539C4—4881no—
540C4—4881no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4#137×D6111yescharacteristic
545C4#137×D6111yescharacteristic
546C4#1684056911yescharacteristic
547C4#1684057611yescharacteristic
548C2—41no—
549C2—4881no—
550C2#2145530511yescharacteristic
551C2#2145551311yescharacteristic
552C2#2145555011yescharacteristic
subgroupG/H
centerC22C2×#14519750
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1554C2
socleC22×C61C2×#121
prime radical#14519751D4
hypercenter#1554D61
hypocenterC61#19379
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1554

Complements

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

NH ≅ G/Ntype
3. #21456366C2semidirect
5. #21445346C2semidirect
6. #21445341C2semidirect
7. #21445324C2semidirect
8. #21445317C2semidirect
9. #21445222C2semidirect
10. #21445217C2semidirect
11. #21445200C2semidirect
12. #21445193C2semidirect
13. #21444587C2semidirect
14. #21444499C2semidirect
15. C61×#1554C2semidirect
285. #1554D61semidirect
343. C61#19379semidirect

Maximal subgroups

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

subgroupindex
#214571862
#214570422
#214563662
#214548172
#214453462
#214453412
#214453242
#214453172
#214452222
#214452172
#214452002
#214451932
#214445872
#214444992
C61×#15542
#1937961