Finite Group Databasebeta

← #29649242

Subgroups — #29649242

Order 15616.

610 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454775C211yesmaximal, characteristic
2#21454486C211yesmaximal, characteristic
3#21454480C211yesmaximal, characteristic
4#21444599C211yesmaximal, characteristic, complemented
5#21444596C211yesmaximal, characteristic, complemented
6#21444596C211yesmaximal, characteristic, complemented
7#21444592C211yesmaximal, characteristic, complemented
8#21444592C211yesmaximal, characteristic, complemented
9#21444581C211yesmaximal, characteristic, complemented
10#21444580C211yesmaximal, characteristic, complemented
11#21444573C211yesmaximal, characteristic, complemented
12#21444566C211yesmaximal, characteristic, complemented
13#21444565C211yesmaximal, characteristic, complemented
14#334×D61C211yesmaximal, characteristic, complemented
15C61×#1572C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16839886C411yescharacteristic
18#16839886C411yescharacteristic
19#16839827C411yescharacteristic
20#16839827C411yescharacteristic
21#16839825C411yescharacteristic
22#16839825C411yescharacteristic
23#16839825C411yescharacteristic
24#16839825C411yescharacteristic
25#16839824—21no—
26#16839821—21no—
27#16839820—21no—
28#16839820—21no—
29#16839819C2211yescharacteristic
30#16839818C2211yescharacteristic
31#16839818C2211yescharacteristic
32#16839815C2211yescharacteristic
33#16839814C2211yescharacteristic
34#16839814C2211yescharacteristic
35#16839813C2211yescharacteristic
36#16839813C2211yescharacteristic
37#16839784C2211yescharacteristic
38#16839784C2211yescharacteristic
39C4⋊C8×D61C2211yescharacteristic
40C4⋊C8×D61C2211yescharacteristic
41#16839727—21no—
42#16839727—21no—
43#16839719—21no—
44#16839716—21no—
45C2×C4×#92418C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839514C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839513C2211yescharacteristic
55#16839513C2211yescharacteristic
56#16839512C2211yescharacteristic
57#16839512C2211yescharacteristic
58#16839512C2211yescharacteristic
59#16839512C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758189—21no—
69C2×#11758189—21no—
70C22×#92418C2×C411yescharacteristic
71C22×#92418C2×C411yescharacteristic
72C2×C8×D61—21no—
73C2×C8×D61—21no—
74C2×C8×D61C2×C411yescharacteristic
75C2×C8×D61C2×C411yescharacteristic
76C2×C8×D61C2×C411yescharacteristic
77C2×C8×D61C2×C411yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122Q811yescharacteristic
80C4×D244C2×C411yescharacteristic
81C4×D244Q811yescharacteristic
82C4×C22⋊D61C2×C411yescharacteristic
83C4×C22⋊D61C2×C411yescharacteristic
84C4×C22⋊D61Q811yescharacteristic
85C4×C22⋊D61Q811yescharacteristic
86#14519736D411yescharacteristic
87#14519734D411yescharacteristic
88#14519734D411yescharacteristic
89C42×D61C2311yescharacteristic
90C42×D61C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519706—21no—
98#14519706—21no—
99#14519706C2×C411yescharacteristic
100#14519706C2×C411yescharacteristic
101#14519706C2×C411yescharacteristic
102#14519706C2×C411yescharacteristic
103C22⋊#92418—21no—
104C22⋊#92418—21no—
105#14519689—21no—
106#14519689—21no—
107#14519689—21no—
108#14519689—21no—
109#14519689C2×C411yescharacteristic
110#14519689C2×C411yescharacteristic
111#14519689C2×C411yescharacteristic
112#14519689C2×C411yescharacteristic
113#14519688—21no—
114#14519687—21no—
115#14519687—21no—
116C4×#92418—21no—
117C4×#92418C2×C411yescharacteristic
118C4×#92418C2×C411yescharacteristic
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C8×Dic61—21no—
122C8×Dic61—21no—
123C8×Dic61C2×C411yescharacteristic
124C8×Dic61C2×C411yescharacteristic
125C8×Dic61C2×C411yescharacteristic
126C8×Dic61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61C2×C411yescharacteristic
129C4⋊C8×C61C2×C411yescharacteristic
130C4⋊C8×C61C2311yescharacteristic
131C4⋊C8×C61C2311yescharacteristic
132C4⋊C8×C61C2311yescharacteristic
133C4⋊C8×C61C2311yescharacteristic
134C22⋊C8×C61—21no—
135C22⋊C8×C61—21no—
136C22⋊C8×C61C2×C411yescharacteristic
137C22⋊C8×C61C2×C411yescharacteristic
138#97×C61—21no—
139C4×C8×C61—21no—
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C22×C4×C61C22×C411yescharacteristic
143C22×C4×C61C2×D411yescharacteristic
144C22×C4×C61C2×Q811yescharacteristic
145C2×C22⋊D61C4⋊C411yescharacteristic
146C2×C22⋊D61C4⋊C411yescharacteristic
147#11758222—22no—
148#11758222—22no—
149C2×D244C4⋊C411yescharacteristic
150C2×C4×D61C22×C411yescharacteristic
151C2×C4×D61C22×C411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×Q811yescharacteristic
155C2×C4×D61C2×Q811yescharacteristic
156C2×Dic122C4⋊C411yescharacteristic
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C42×C61C22×C411yescharacteristic
166C42×C61C2×D411yescharacteristic
167C42×C61C2×Q811yescharacteristic
168C42×C61C2411yescharacteristic
169C22⋊Dic61C4⋊C411yescharacteristic
170C22⋊Dic61C4⋊C411yescharacteristic
171#11758198C4⋊C411yescharacteristic
172#11758198C4⋊C411yescharacteristic
173#11758198C4⋊C411yescharacteristic
174#11758198C4⋊C411yescharacteristic
175C4⋊Dic61C4⋊C411yescharacteristic
176C4⋊Dic61C4⋊C411yescharacteristic
177#11758196C4⋊C411yescharacteristic
178#11758196C4⋊C411yescharacteristic
179#11758196C4⋊C411yescharacteristic
180#11758196C4⋊C411yescharacteristic
181C4×Dic61C22×C411yescharacteristic
182C4×Dic61C22×C411yescharacteristic
183C4×Dic61C2×D411yescharacteristic
184C4×Dic61C2×D411yescharacteristic
185C4×Dic61C2×Q811yescharacteristic
186C4×Dic61C2×Q811yescharacteristic
187C2×#92418—22no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—41no—
193C2×#92418C22×C411yescharacteristic
194C2×#92418C22×C411yescharacteristic
195C2×#92418C22×C411yescharacteristic
196C2×#92418C22×C411yescharacteristic
197#11758189—42no—
198#11758189—42no—
199C8×D61—22no—
200C8×D61—22no—
201C8×D61—41no—
202C8×D61—41no—
203C8×D61—42no—
204C8×D61—42no—
205C23×C61C2×C4⋊C411yescharacteristic
206C22×D61C2×C4⋊C411yescharacteristic
207C22×D61C2×C4⋊C411yescharacteristic
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61C2×C4⋊C411yescharacteristic
214C2×C4×C61C2×C4⋊C411yescharacteristic
215C2×C4×C61C2×C4⋊C411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C22×Q811yescharacteristic
219C22⋊D61—22no—
220C22⋊D61—22no—
221C2×Dic61C2×C4⋊C411yescharacteristic
222C2×Dic61C2×C4⋊C411yescharacteristic
223C2×Dic61C2×C4⋊C411yescharacteristic
224C2×Dic61C2×C4⋊C411yescharacteristic
225C2×Dic61C2×C4⋊C411yescharacteristic
226C2×Dic61C2×C4⋊C411yescharacteristic
227D244—22no—
228C4×D61—21no—
229C4×D61—21no—
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—41no—
235C4×D61—41no—
236C4×D61#13512yes—
237C4×D61#13512yes—
238Dic122—22no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—41no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#92418#13112yes—
255#17827—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—21no—
259C22×C61C22×C4⋊C411yescharacteristic
260C2×D61—21no—
261C2×D61—21no—
262C2×D61—21no—
263C2×D61—21no—
264C2×D61—21no—
265C2×D61#42712yes—
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61C2×#13111yescharacteristic
271C4×C61#56811yescharacteristic
272C4×C61C2×#13511yescharacteristic
273C4×C61C2×#13511yescharacteristic
274Dic61—21no—
275Dic61—21no—
276Dic61—21no—
277Dic61—21no—
278Dic61—21no—
279Dic61#42712yes—
280C8×#41—611no—
281#2925—611no—
282#2925—611no—
283#1572—611no—
284#1572—611no—
285#1572—611no—
286#1572D6111yescharacteristic, complemented
287#1571—611no—
288#1571—611no—
289#1568—611no—
290#1568—611no—
291#1566—611no—
292#1564—611no—
293#1564—611no—
294C2×#334—611no—
295C2×C61—41no—
296C2×C61#290611yescharacteristic
297C2×C61C2×#42711yescharacteristic
298C2×C61#291611yescharacteristic
299D61—22no—
300D61—41no—
301C4×#41—611no—
302C8×Q8—611no—
303C8×Q8—611no—
304C8×D4—611no—
305C8×D4—611no—
306C8×D4—611no—
307C8×D4—611no—
308C8×D4—611no—
309C8×D4—611no—
310#433—1221no—
311#433—1221no—
312#433—1221no—
313#433—1221no—
314#432—611no—
315#432—611no—
316#432—611no—
317#432C2×D6111yescharacteristic
318#431—611no—
319#431—611no—
320#431—611no—
321#431—611no—
322#431—611no—
323#431C2×D6111yescharacteristic
324#431C2×D6111yescharacteristic
325#423—611no—
326#423—611no—
327C2×C4⋊C8—611no—
328C2×C4⋊C8—611no—
329#408—1221no—
330#408—1221no—
331#405—1221no—
332#405—1221no—
333C2×C4×C8—611no—
334C2×C4×C8—611no—
335C2×C4×C8—611no—
336#335—611no—
337#335—611no—
338#335—611no—
339#335—611no—
340#335—611no—
341#335—611no—
342#335C2×D6111yescharacteristic
343#335C2×D6111yescharacteristic
344#334—611no—
345#334—611no—
346#334—611no—
347#334—611no—
348#334—611no—
349#334—611no—
350#334C2×D6111yescharacteristic
351#334C2×D6111yescharacteristic
352C61#1782711yescharacteristic, complemented, Sylow
353C2×#41—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—611no—
357C22×C8—611no—
358C22×C8—611no—
359C22×C8—611no—
360C22×C8—611no—
361C22×C8—611no—
362C22×C8—1221no—
363C22×C8—1221no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×D4—611no—
367C4×D4—611no—
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—611no—
371C4×D4—611no—
372#117—611no—
373#117—611no—
374#117—611no—
375C2×C42—611no—
376C2×C42—611no—
377C2×C42C22×D6111yescharacteristic
378C4⋊C8—611no—
379C4⋊C8—611no—
380C4⋊C8—611no—
381C4⋊C8—611no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8C4×D6111yescharacteristic
391C4⋊C8C4×D6111yescharacteristic
392C4⋊C8C22×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C22⋊C8—21no—
397C22⋊C8—21no—
398C22⋊C8—611no—
399C22⋊C8—611no—
400C22⋊C8—611no—
401C22⋊C8—611no—
402C22⋊C8—1221no—
403C22⋊C8—1221no—
404C22⋊C8—1221no—
405C22⋊C8—1221no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8C4×D6111yescharacteristic
409C22⋊C8C4×D6111yescharacteristic
410#97—21no—
411#97—1221no—
412#97—1221no—
413#97—1221no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8—1221no—
426C4×C8C22×D6111yescharacteristic
427C4×C8C22×D6111yescharacteristic
428#41—1222no—
429#41—1222no—
430C2×Q8—611no—
431C2×D4—611no—
432C2×D4—611no—
433C2×D4—611no—
434C22×C4—611no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—611no—
440C22×C4C2×C4×D6111yescharacteristic
441C22×C4D4×D6111yescharacteristic
442C22×C4Q8×D6111yescharacteristic
443M16—2442no—
444M16—2442no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1222no—
454C2×C8—1222no—
455C2×C8—1222no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—2441no—
461C2×C8—2441no—
462C2×C8—2442no—
463C2×C8—2442no—
464C2×C8—2441no—
465C2×C8C2×C4×D6111yescharacteristic
466C2×C8C2×C4×D6111yescharacteristic
467C2×C8C2×C4×D6111yescharacteristic
468C2×C8C2×C4×D6111yescharacteristic
469C4⋊C4—611no—
470C4⋊C4—611no—
471C4⋊C4—611no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—611no—
475C22⋊C4—611no—
476C22⋊C4—611no—
477C22⋊C4—611no—
478C22⋊C4—611no—
479C22⋊C4—611no—
480C22⋊C4—611no—
481C42—611no—
482C42—611no—
483C42—611no—
484C42—611no—
485C42—611no—
486C42—611no—
487C42C2×C4×D6111yescharacteristic
488C42D4×D6111yescharacteristic
489C42Q8×D6111yescharacteristic
490C42C23×D6111yescharacteristic
491C23—611no—
492C23—611no—
493C23C4⋊C4×D6111yescharacteristic
494Q8—1222no—
495D4—1222no—
496D4—1222no—
497D4—1222no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—611no—
504C2×C4—612no—
505C2×C4—612no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—611no—
509C2×C4—611no—
510C2×C4—611no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—2441no—
518C2×C4—2441no—
519C2×C4C4⋊C4×D6111yescharacteristic
520C2×C4C4⋊C4×D6111yescharacteristic
521C2×C4C4⋊C4×D6111yescharacteristic
522C2×C4C22×C4×D6111yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4C2×Q8×D6111yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—612no—
534C8—1221no—
535C8—1221no—
536C8—1221no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—612no—
545C22—1221no—
546C22—1221no—
547C22—1221no—
548C22—1221no—
549C22—1221no—
550C22C2×C4⋊C4×D6111yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—612no—
556C4—1221no—
557C4—1221no—
558C4—1221no—
559C4—1221no—
560C4—1221no—
561C4#131×D6111yescharacteristic
562C4#1684052711yescharacteristic
563C4#135×D6111yescharacteristic
564C4#135×D6111yescharacteristic
565C2—41no—
566C2—1222no—
567C2—2441no—
568C2#2145438611yescharacteristic
569C2#427×D6111yescharacteristic
570C2#2145442911yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1572C2
socleC22×C61C22×C4⋊C4
prime radicalC2×#11758222D4
cosocleC42×C61C24
hypercenter#1572D61
hypocenterC61#17827
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1572

Complements

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

NH ≅ G/Ntype
4. #21444599C2semidirect
5. #21444596C2semidirect
6. #21444596C2semidirect
7. #21444592C2semidirect
8. #21444592C2semidirect
9. #21444581C2semidirect
10. #21444580C2semidirect
11. #21444573C2semidirect
12. #21444566C2semidirect
13. #21444565C2semidirect
14. #334×D61C2semidirect
15. C61×#1572C2semidirect
286. #1572D61semidirect
352. C61#17827semidirect

Maximal subgroups

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

subgroupindex
#214547752
#214544862
#214544802
#214445992
#214445962
#214445922
#214445812
#214445802
#214445732
#214445662
#214445652
#334×D612
C61×#15722
#1782761