Finite Group Databasebeta

← #29667634

Subgroups — #29667634

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457139C211yesmaximal, characteristic
2#21457040C211yesmaximal, characteristic, complemented
3#21454981C211yesmaximal, characteristic, complemented
4#21445356C211yesmaximal, characteristic, complemented
5#21445349C211yesmaximal, characteristic, complemented
6#21445344C211yesmaximal, characteristic, complemented
7#21445339C211yesmaximal, characteristic, complemented
8#21445232C211yesmaximal, characteristic, complemented
9#21445225C211yesmaximal, characteristic, complemented
10#21445220C211yesmaximal, characteristic, complemented
11#21445215C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444514C211yesmaximal, characteristic, complemented
14C2×#16839511C211yesmaximal, characteristic, complemented
15C61×#3226C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168—21no—
18#16840124—21no—
19#16840092—21no—
20#16840075—21no—
21#16840062—21no—
22#16840054C2211yescharacteristic
23#16840054C2211yescharacteristic
24#16840054C2211yescharacteristic
25#16840049C2211yescharacteristic
26#16840049C2211yescharacteristic
27#16840049C2211yescharacteristic
28#16839996—21no—
29#16839989—21no—
30#16839977—21no—
31#16839959C2211yescharacteristic
32#16839954C2211yescharacteristic
33#16839892C2211yescharacteristic
34C8×Dic122C2211yescharacteristic
35#16839841C2211yescharacteristic
36#16839830—21no—
37C8×D244C2211yescharacteristic
38#16839825—21no—
39#16839822—21no—
40#16839819C2211yescharacteristic
41#16839787—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839511C2211yescharacteristic
51#16839511C2211yescharacteristic
52#16839511C2211yescharacteristic
53#16839511C2211yescharacteristic
54#16839506C2211yescharacteristic
55#16839506C2211yescharacteristic
56C61×#532C2211yescharacteristic
57C2×C4⋊Q8×C61C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#500C2211yescharacteristic
60C61×#486C2211yescharacteristic
61C61×#486C2211yescharacteristic
62C61×#480—21no—
63C61×#480—21no—
64C61×#474—21no—
65C61×#474—21no—
66C61×#431C2211yescharacteristic
67C2×#11758200—21no—
68C2×#11758199—21no—
69C2×#11758189—21no—
70C22×#92418—21no—
71C22×#92418—21no—
72C2×C8×D61—21no—
73#14519771—21no—
74#14519769D411yescharacteristic
75#14519765D411yescharacteristic
76#14519760—21no—
77#14519756D411yescharacteristic
78#14519751D411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×D244C2311yescharacteristic
81C4×C22⋊D61—21no—
82#14519734—21no—
83#14519710—21no—
84#14519710—21no—
85#14519710—21no—
86#14519708—21no—
87#14519708—21no—
88#14519708—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519698—21no—
103#14519698—21no—
104#14519697—21no—
105#14519697—21no—
106#14519697—21no—
107C22⋊#92418—21no—
108#14519689—21no—
109#14519689—21no—
110#14519688—21no—
111#14519687—21no—
112C8×Dic61—21no—
113C2×#41×C61—21no—
114C22×Q8×C61—21no—
115C4⋊Q8×C61—21no—
116C4⋊Q8×C61—21no—
117C4⋊Q8×C61—21no—
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#127×C61C2311yescharacteristic
122#124×C61—21no—
123#121×C61—21no—
124#121×C61—21no—
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C42×C61C2311yescharacteristic
130#107×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#107×C61—21no—
134C4⋊C8×C61D411yescharacteristic
135C4⋊C8×C61D411yescharacteristic
136#102×C61—21no—
137#102×C61—21no—
138#102×C61—21no—
139#102×C61—21no—
140C22⋊C8×C61D411yescharacteristic
141C22⋊C8×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144#41×C61—82no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—41no—
149C2×Q8×C61—82no—
150C2×D4×C61—21no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—41no—
154C22×C4×C61—41no—
155C22×C4×C61—41no—
156C22×C4×C61C2×D411yescharacteristic
157C22×C4×C61C2×D411yescharacteristic
158C22×C4×C61#4111yescharacteristic
159C2×C22⋊D61—21no—
160C2×D244C2×D411yescharacteristic
161C2×C4×D61—21no—
162C2×Dic122C2×D411yescharacteristic
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
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×C61—21no—
173C4⋊C4×C61—41no—
174C4⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C42×C61C2×D411yescharacteristic
178C42×C61C2×D411yescharacteristic
179C42×C61#4111yescharacteristic
180C42×C61C2411yescharacteristic
181C22⋊Dic61—21no—
182#11758200—81no—
183#11758199—81no—
184#11758198—21no—
185#11758198—21no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61C2×D411yescharacteristic
189C4⋊Dic61C2×D411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—81no—
202C2×#92418—81no—
203#11758189—81no—
204C8×D61—81no—
205C23×C61—41no—
206C23×C61#12111yescharacteristic
207C22×D61—21no—
208Q8×C61—82no—
209Q8×C61—81no—
210Q8×C61—81no—
211Q8×C61—81no—
212D4×C61—41no—
213D4×C61—41no—
214D4×C61—41no—
215D4×C61—41no—
216D4×C61—81no—
217D4×C61—82no—
218C2×C4×C61—22no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—82no—
227C2×C4×C61—82no—
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61#12111yescharacteristic
230C2×C4×C61#12111yescharacteristic
231C2×C4×C61C22×D411yescharacteristic
232C2×C4×C61C22×D411yescharacteristic
233C2×C4×C61C2×#4111yescharacteristic
234C22⋊D61—42no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238D244—21no—
239D244—21no—
240C4×D61—41no—
241C4×D61—41no—
242Dic122—21no—
243Dic122—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#19591—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—81no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61#47212yes—
261C22×C61C2×#12111yescharacteristic
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—41no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—81no—
270C4×C61—81no—
271C4×C61—81no—
272C4×C61#57711yescharacteristic
273C4×C61#57711yescharacteristic
274C4×C61#57811yescharacteristic
275C4×C61#57811yescharacteristic
276Dic61—41no—
277Dic61—41no—
278Dic61—41no—
279#3247—611no—
280#3238—611no—
281#3226D6111yescharacteristic, complemented
282#2994—611no—
283#1698—611no—
284#1697—611no—
285#1696—611no—
286#1695—611no—
287#1678—611no—
288#1677—611no—
289#1676—611no—
290#1675—611no—
291#1573—611no—
292#1551—611no—
293C2×#333—611no—
294C2×C61—22no—
295C2×C61—161no—
296C2×C61#304611yescharacteristic
297C2×C61#306311yescharacteristic
298C2×C61C2×#47211yescharacteristic
299D61—81no—
300#532C2×D6111yescharacteristic
301C2×C4⋊Q8C2×D6111yescharacteristic
302#529—611no—
303#501—1221no—
304#500C2×D6111yescharacteristic
305#500C2×D6111yescharacteristic
306#489—1221no—
307#486C2×D6111yescharacteristic
308#486C2×D6111yescharacteristic
309#483—1221no—
310#480—21no—
311#480—21no—
312#480—1221no—
313#478—1221no—
314#477—611no—
315#477—611no—
316#477—611no—
317#476—611no—
318#476—611no—
319#476—611no—
320#474—21no—
321#474—21no—
322#466—1221no—
323#465—1221no—
324#463—1221no—
325#460—611no—
326#459—611no—
327#446—611no—
328C8×Q8—611no—
329#436—611no—
330#435—1221no—
331C8×D4—611no—
332C8×D4—1221no—
333#433—1221no—
334#432—611no—
335#431C2×D6111yescharacteristic
336#424—1221no—
337C2×C4⋊C8—611no—
338C2×C4⋊C8—611no—
339#335—611no—
340#335—611no—
341#334—611no—
342#334—611no—
343#333—611no—
344#333—611no—
345#333—611no—
346#333—611no—
347#333—611no—
348#333—611no—
349#331—611no—
350#331—611no—
351C61#1959111yescharacteristic, complemented, Sylow
352C2×#41—21no—
353C22×Q8—21no—
354C2×SD16—1221no—
355C2×D8—1221no—
356C2×M16—1221no—
357C22×C8—1221no—
358C22×C8—1221no—
359C22×C8—1221no—
360C4⋊Q8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8C22×D6111yescharacteristic
364C4⋊Q8C22×D6111yescharacteristic
365C4⋊Q8C22×D6111yescharacteristic
366#127C22×D6111yescharacteristic
367#126—1221no—
368#125—611no—
369#124—21no—
370#124—611no—
371#123—1221no—
372C22⋊Q8—611no—
373#121—21no—
374#121—21no—
375#121—611no—
376C4×Q8—611no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4—611no—
380C4×D4—1221no—
381#117—1221no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C42C22×D6111yescharacteristic
385#107—21no—
386#107—21no—
387#107—21no—
388#107—21no—
389#107—1221no—
390#107—1221no—
391#107—1221no—
392#106—1221no—
393#106—1221no—
394#106—1221no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—611no—
401C4⋊C8—1221no—
402C4⋊C8—1221no—
403C4⋊C8—1221no—
404C4⋊C8—1221no—
405C4⋊C8C22⋊D6111yescharacteristic
406C4⋊C8C22⋊D6111yescharacteristic
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#102—21no—
411#102—21no—
412#102—21no—
413#102—21no—
414#102—1221no—
415#102—1221no—
416#102—1221no—
417#102—1221no—
418#102—1221no—
419C22⋊C8—1221no—
420C22⋊C8—1221no—
421C22⋊C8—1221no—
422C22⋊C8C22⋊D6111yescharacteristic
423C22⋊C8C22⋊D6111yescharacteristic
424#97—1221no—
425#97—1221no—
426C4×C8—1221no—
427C4×C8C22×D6111yescharacteristic
428C4×C8C22×D6111yescharacteristic
429#41—82no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—41no—
434C2×Q8—82no—
435C2×Q8—611no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4—611no—
441C2×D4—1221no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—1221no—
445C22×C4D4×D6111yescharacteristic
446C22×C4#1175822411yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448SD16—4881no—
449D8—4881no—
450M16—4881no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—4881no—
458C2×C8—4881no—
459C2×C8—4881no—
460C2×C8C2×C22⋊D6111yescharacteristic
461C2×C8C2×C22⋊D6111yescharacteristic
462C2×C8C2×C22⋊D6111yescharacteristic
463C2×C8C2×C22⋊D6111yescharacteristic
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—1221no—
481C22⋊C4—1221no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C42—1221no—
486C42D4×D6111yescharacteristic
487C42#1175822411yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—41no—
491C23—1221no—
492C23#1451974811yescharacteristic
493Q8—81no—
494Q8—81no—
495Q8—81no—
496Q8—82no—
497Q8—1221no—
498Q8—1221no—
499D4—41no—
500D4—41no—
501D4—41no—
502D4—41no—
503D4—81no—
504D4—82no—
505D4—1221no—
506D4—1221no—
507D4—2442no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—1221no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—2441no—
522C2×C4—2441no—
523C2×C4#1451974811yescharacteristic
524C2×C4#1451974811yescharacteristic
525C2×C4#1451974811yescharacteristic
526C2×C4C2×D4×D6111yescharacteristic
527C2×C4C22×C22⋊D6111yescharacteristic
528C2×C4C2×#1175822411yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C22—21no—
540C22—21no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—2441no—
545C22—2441no—
546C22—2441no—
547C22#1684002912yes—
548C22C2×#1451974811yescharacteristic
549C4—21no—
550C4—21no—
551C4—21no—
552C4—21no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4—2441no—
557C4—2441no—
558C4—2441no—
559C4#1684057011yescharacteristic
560C4#1684057111yescharacteristic
561C4#1684057711yescharacteristic
562C4#1684057811yescharacteristic
563C2—22no—
564C2—161no—
565C2—4881no—
566C2#2145536511yescharacteristic
567C2#2145550411yescharacteristic
568C2C2×#1684002911yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3226C2
socleC22×C61C2×#121
prime radical#21457139C2
hypercenter#3226D61
hypocenterC61#19591
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3226

Complements

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

NH ≅ G/Ntype
2. #21457040C2semidirect
3. #21454981C2semidirect
4. #21445356C2semidirect
5. #21445349C2semidirect
6. #21445344C2semidirect
7. #21445339C2semidirect
8. #21445232C2semidirect
9. #21445225C2semidirect
10. #21445220C2semidirect
11. #21445215C2semidirect
12. #21444604C2semidirect
13. #21444514C2semidirect
14. C2×#16839511C2semidirect
15. C61×#3226C2semidirect
281. #3226D61semidirect
351. C61#19591semidirect

Maximal subgroups

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

subgroupindex
#214571392
#214570402
#214549812
#214453562
#214453492
#214453442
#214453392
#214452322
#214452252
#214452202
#214452152
#214446042
#214445142
C2×#168395112
C61×#32262
#1959161