Finite Group Databasebeta

← #29650732

Subgroups — #29650732

Order 15616.

590 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#21456402C211yesmaximal, characteristic
2#21454750C211yesmaximal, characteristic
3#21454748C211yesmaximal, characteristic
4#21444672C211yesmaximal, characteristic, complemented
5#21444671C211yesmaximal, characteristic, complemented
6#21444670C211yesmaximal, characteristic, complemented
7#21444669C211yesmaximal, characteristic, complemented
8#21444668C211yesmaximal, characteristic, complemented
9#21444667C211yesmaximal, characteristic, complemented
10#21444666C211yesmaximal, characteristic, complemented
11#21444576C211yesmaximal, characteristic
12#21444272C211yesmaximal, characteristic
13#21444272C211yesmaximal, characteristic
14#322×D61C211yesmaximal, characteristic
15C61×#1584C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17#16840316C2211yescharacteristic
18#16840166C411yescharacteristic
19#16840140C411yescharacteristic
20#16840111C411yescharacteristic
21#16840111C411yescharacteristic
22#16840004C411yescharacteristic
23#16840002C411yescharacteristic
24#16840002C411yescharacteristic
25#16840000C411yescharacteristic
26#16839893C2211yescharacteristic
27#16839892C2211yescharacteristic
28#16839891—21no—
29#16839890—21no—
30#16839889C2211yescharacteristic
31Q8×#92418C2211yescharacteristic
32C8×Dic122—21no—
33C8×Dic122C2211yescharacteristic
34#16839886—21no—
35#16839886C2211yescharacteristic
36C4×Dic244C2211yescharacteristic
37C4×#11758202C2211yescharacteristic
38C4×#11758202C2211yescharacteristic
39#16839787—21no—
40#16839787—21no—
41#16839784C2211yescharacteristic
42#16839784C2211yescharacteristic
43#16839719—21no—
44#16839716—21no—
45C4×C8×D61C2211yescharacteristic
46C4×C8×D61C2211yescharacteristic
47C4×C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839514C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54Q8⋊#92418C2211yescharacteristic
55#16839492C2211yescharacteristic
56#16839492C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C8×Q8×C61C2211yescharacteristic
62C4×Q16×C61C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×Dic244C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×C8×D61—21no—
73C2×C8×D61C2×C411yescharacteristic
74C2×C8×D61C2×C411yescharacteristic
75C2×C8×D61D411yescharacteristic
76C2×C8×D61D411yescharacteristic
77#14519776C2×C411yescharacteristic
78#14519776C2×C411yescharacteristic
79#14519775C2×C411yescharacteristic
80#14519775C2×C411yescharacteristic
81#14519767—21no—
82#14519767—21no—
83#14519757C2×C411yescharacteristic
84#14519757C2×C411yescharacteristic
85#14519755—21no—
86#14519755—21no—
87#14519753C2×C411yescharacteristic
88#14519753C2×C411yescharacteristic
89C4×Dic122—21no—
90C4×Dic122—21no—
91C4×Dic122C2311yescharacteristic
92C4×Dic122C2311yescharacteristic
93#14519734—21no—
94#14519734—21no—
95C42×D61C2311yescharacteristic
96#14519711C2×C411yescharacteristic
97#14519710C2×C411yescharacteristic
98#14519710C2×C411yescharacteristic
99C4⋊#92418—21no—
100C4⋊#92418—21no—
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519701C2×C411yescharacteristic
112#14519701C2×C411yescharacteristic
113#14519700C2×C411yescharacteristic
114#14519700C2×C411yescharacteristic
115#14519688—21no—
116#14519687—21no—
117#14519687—21no—
118C4×#92418—21no—
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C8×Dic61—21no—
123C8×Dic61—21no—
124C8×Dic61—21no—
125C8×Dic61C2×C411yescharacteristic
126C8×Dic61C2×C411yescharacteristic
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C2×Q16×C61C2×C411yescharacteristic
130C4×Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61C2×C411yescharacteristic
133C4⋊C8×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#103×C61C2×C411yescharacteristic
139#97×C61—21no—
140C4×C8×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×Q8×C61C22×C411yescharacteristic
146C2×C4×D61C22×C411yescharacteristic
147C2×C4×D61C2×D411yescharacteristic
148C2×C4×D61#4111yescharacteristic
149C2×Dic122—21no—
150C2×Dic122—21no—
151C2×Dic122C22×C411yescharacteristic
152C2×Dic122C22×C411yescharacteristic
153Q16×C61—41no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61C22×C411yescharacteristic
158C2×C8×C61C22×C411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61C22×C411yescharacteristic
164C4⋊C4×C61C22×C411yescharacteristic
165C42×C61—21no—
166C42×C61—21no—
167C42×C61C2411yescharacteristic
168#11758202—41no—
169#11758202—41no—
170#11758198—21no—
171#11758198—21no—
172#11758198—21no—
173#11758198—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61C22×C411yescharacteristic
177C4⋊Dic61C22×C411yescharacteristic
178#11758196—21no—
179#11758196—21no—
180#11758196—21no—
181#11758196—21no—
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61C22×C411yescharacteristic
191C4×Dic61C2×D411yescharacteristic
192C4×Dic61#4111yescharacteristic
193C2×#92418—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C22×C411yescharacteristic
197C2×#92418C22×C411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200Dic244—41no—
201#11758189—42no—
202#11758189—42no—
203C8×D61—22no—
204C8×D61—41no—
205C8×D61—41no—
206C8×D61—42no—
207C8×D61Q1614yescomplemented
208C22×D61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61C4×D411yescharacteristic
225C2×Dic61C4×D411yescharacteristic
226C2×Dic61C4×D411yescharacteristic
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—22no—
230C4×D61C2×Q1612yes—
231C4×D61#13512yes—
232Dic122—21no—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—42no—
237Dic122—42no—
238C8×C61—21no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61C2×Q1612yes—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418C2×Q1612yes—
252#17977—611nomaximal, Sylow
253C22×C61C2×C4×D411yescharacteristic
254C2×D61—21no—
255C2×D61—21no—
256C2×D61C4×Q1612yes—
257C4×C61—21no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61#56811yescharacteristic
263C4×C61#56811yescharacteristic
264C4×C61C22×Q1611yescharacteristic
265C4×C61C2×#13511yescharacteristic
266Dic61—21no—
267Dic61—41no—
268Dic61—41no—
269Dic61—41no—
270Dic61—41no—
271Dic61C4×Q1612yes—
272Dic61#44412yes—
273#3170—611no—
274#2960—611no—
275#2960—611no—
276#1584—611no—
277#1584—611no—
278#1584—611no—
279#1584—611no—
280#1584—611no—
281#1584—611no—
282#1584—611no—
283#1584D6111yescharacteristic, complemented
284#1567—611no—
285#1493—611no—
286#1493—611no—
287C2×#322—611no—
288C2×C61#293211yescharacteristic
289C2×C61C2×C4×Q1611yescharacteristic
290C2×C61C2×#44411yescharacteristic
291D61—22no—
292#533—611no—
293#533—611no—
294#500—611no—
295#494—611no—
296#487—611no—
297#487—611no—
298#467—611no—
299#467—611no—
300#467—611no—
301#467—611no—
302#446—611no—
303#446—611no—
304#446—611no—
305#446—1221no—
306#446—1221no—
307#446C2×D6111yescharacteristic
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—1221no—
312C8×Q8—1221no—
313C8×Q8C2×D6111yescharacteristic
314C4×Q16—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×Q16C2×D6111yescharacteristic
318#424—1221no—
319#424—1221no—
320#423—611no—
321#423—611no—
322#405—1221no—
323#405—1221no—
324C2×C4×C8—611no—
325C2×C4×C8—611no—
326C2×C4×C8—611no—
327#335—611no—
328#335—611no—
329#335—611no—
330#335C2×D6111yescharacteristic
331Q8⋊C8—611no—
332Q8⋊C8—611no—
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8C2×D6111yescharacteristic
338Q8⋊C8C2×D6111yescharacteristic
339#322—611no—
340#322—611no—
341#322—611no—
342#322C2×D6111yescharacteristic
343C61#1797711yescharacteristic, complemented, Sylow
344C2×Q16—611no—
345C2×Q16—611no—
346C2×Q16—611no—
347C2×Q16C4×D6111yescharacteristic
348C2×M16—1221no—
349C2×M16—1221no—
350C22×C8—611no—
351C22×C8—611no—
352C22×C8—611no—
353C22×C8—611no—
354C22×C8—1221no—
355C4⋊Q8—611no—
356C4⋊Q8—611no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360#125—1221no—
361C22⋊Q8—611no—
362C22⋊Q8—611no—
363C22⋊Q8—611no—
364C22⋊Q8—611no—
365C22⋊Q8—1221no—
366C22⋊Q8—1221no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8C22×D6111yescharacteristic
372C4×Q8C22×D6111yescharacteristic
373#117—1221no—
374#117—1221no—
375C2×C42—611no—
376#107—611no—
377#107—611no—
378#107—611no—
379#107C4×D6111yescharacteristic
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—1221no—
385C4⋊C8—1221no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C22×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394#103—611no—
395#103—611no—
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103C4×D6111yescharacteristic
401#103C4×D6111yescharacteristic
402#97—21no—
403#97—1221no—
404#97—1221no—
405#97—1221no—
406C4×C8—21no—
407C4×C8—611no—
408C4×C8—611no—
409C4×C8—611no—
410C4×C8—611no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8—611no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8—1221no—
417C4×C8—1221no—
418C4×C8C22×D6111yescharacteristic
419C4×C8C22×D6111yescharacteristic
420C4×C8C22×D6111yescharacteristic
421C2×Q8—611no—
422C2×Q8—611no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8C2×C4×D6111yescharacteristic
426C2×Q8C2×C4×D6111yescharacteristic
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430Q16—41no—
431Q16—2441no—
432Q16—2441no—
433Q16—2441no—
434M16—2442no—
435M16—2442no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—611no—
440C2×C8—614no—
441C2×C8—611no—
442C2×C8—611no—
443C2×C8—611no—
444C2×C8—1222no—
445C2×C8—1221no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—2441no—
449C2×C8—2441no—
450C2×C8—2442no—
451C2×C8C2×C4×D6111yescharacteristic
452C2×C8C2×C4×D6111yescharacteristic
453C2×C8D4×D6111yescharacteristic
454C2×C8D4×D6111yescharacteristic
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—611no—
458C4⋊C4—611no—
459C4⋊C4—1221no—
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—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4C2×C4×D6111yescharacteristic
472C4⋊C4C2×C4×D6111yescharacteristic
473C22⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C42—21no—
478C42—21no—
479C42—611no—
480C42—611no—
481C42—611no—
482C42—1221no—
483C42—1221no—
484C42C23×D6111yescharacteristic
485C23—611no—
486Q8—21no—
487Q8—21no—
488Q8—21no—
489Q8—21no—
490Q8—1221no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—2442no—
495Q8—2442no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—612no—
503C2×C4—612no—
504C2×C4—611no—
505C2×C4—1222no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4C22×C4×D6111yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4#41×D6111yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—612no—
522C8—1221no—
523C8—1221no—
524C8—1221no—
525C8—2441no—
526C8—2441no—
527C8—2441no—
528C8Q16×D6112yes—
529C22—612no—
530C22—1221no—
531C22—1221no—
532C22C4×D4×D6111yescharacteristic
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—612no—
539C4—612no—
540C4—1221no—
541C4—2441no—
542C4—2441no—
543C4—2441no—
544C4—2441no—
545C4#1684052711yescharacteristic
546C4#1684052811yescharacteristic
547C4C2×Q16×D6111yescharacteristic
548C4#135×D6111yescharacteristic
549C2—1222no—
550C2#2145453311yescharacteristic
551C2C4×Q16×D6111yescharacteristic
552C2#444×D6111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1584C2
socleC22×C61C2×C4×D4
prime radicalC22×D61C4×D4
cosocleC42×C61C24
hypercenter#1584D61
hypocenterC61#17977
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1584

Complements

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

NH ≅ G/Ntype
4. #21444672C2semidirect
5. #21444671C2semidirect
6. #21444670C2semidirect
7. #21444669C2semidirect
8. #21444668C2semidirect
9. #21444667C2semidirect
10. #21444666C2semidirect
15. C61×#1584C2semidirect
207. C8×D61Q16semidirect
283. #1584D61semidirect
343. C61#17977semidirect

Maximal subgroups

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

subgroupindex
#214564022
#214547502
#214547482
#214446722
#214446712
#214446702
#214446692
#214446682
#214446672
#214446662
#214445762
#214442722
#322×D612
C61×#15842
#1797761