Finite Group Databasebeta

← #29650113

Subgroups — #29650113

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455886C211yesmaximal, characteristic
2#21454926C211yesmaximal, characteristic
3#21454915C211yesmaximal, characteristic, complemented
4#21444688C211yesmaximal, characteristic, complemented
5#21444676C211yesmaximal, characteristic, complemented
6#21444671C211yesmaximal, characteristic, complemented
7#21444637C211yesmaximal, characteristic, complemented
8SD16⋊#92418C211yesmaximal, characteristic, complemented
9#21444623C211yesmaximal, characteristic, complemented
10#21444622C211yesmaximal, characteristic, complemented
11#21444601C211yesmaximal, characteristic, complemented
12#21444250C211yesmaximal, characteristic
13#21444220C211yesmaximal, characteristic, complemented
14#21444120C211yesmaximal, characteristic, complemented
15C61×#1582C211yesmaximal, characteristic, complemented
16#16840316C2211yescharacteristic
17C4×#11758224C2211yescharacteristic
18#16840106C411yescharacteristic
19#16840102C411yescharacteristic
20#16840046C411yescharacteristic
21#16840040C411yescharacteristic
22#16839971C411yescharacteristic
23#16839965C411yescharacteristic
24#16839925C411yescharacteristic
25#16839921C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839890—21no—
28#16839889—21no—
29Q8×#92418C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33C4×Dic244C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758200C2211yescharacteristic
36D4×#92418C2211yescharacteristic
37C8×C22⋊D61—21no—
38#16839825—21no—
39#16839824—21no—
40#16839822—21no—
41#16839818C2211yescharacteristic
42#16839813C2211yescharacteristic
43#16839813C2211yescharacteristic
44#16839813C2211yescharacteristic
45#16839812—21no—
46C2×#14519706—21no—
47C4⋊C8×D61C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839494C2211yescharacteristic
52#16839494C2211yescharacteristic
53Q8⋊#92418C2211yescharacteristic
54#16839492C2211yescharacteristic
55#16839492C2211yescharacteristic
56D4⋊#92418C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#446C2211yescharacteristic
61C4×SD16×C61C2211yescharacteristic
62C8×D4×C61C2211yescharacteristic
63C61×#334C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×#322C2211yescharacteristic
67C2×#11758224C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C22×#92418—21no—
72C2×C8×D61—21no—
73#14519776C2×C411yescharacteristic
74#14519775C2×C411yescharacteristic
75#14519767—21no—
76#14519757C2×C411yescharacteristic
77#14519755—21no—
78#14519753C2×C411yescharacteristic
79C4×Dic122—21no—
80C4×Dic122C2311yescharacteristic
81C4×Dic122C2311yescharacteristic
82#14519742C2×C411yescharacteristic
83D4×Dic61C2×C411yescharacteristic
84C4×C22⋊D61—21no—
85#14519737—21no—
86#14519735C2×C411yescharacteristic
87#14519734—21no—
88#14519733—21no—
89C2×C4×Dic61—21no—
90C42×D61C2311yescharacteristic
91#14519711C2×C411yescharacteristic
92#14519710C2×C411yescharacteristic
93#14519708C2×C411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519706—21no—
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706C2×C411yescharacteristic
104#14519706C2×C411yescharacteristic
105#14519706D411yescharacteristic
106#14519706D411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519701C2×C411yescharacteristic
110#14519700C2×C411yescharacteristic
111#14519700C2×C411yescharacteristic
112#14519698C2×C411yescharacteristic
113C22⋊#92418—21no—
114#14519689—21no—
115#14519689—21no—
116#14519689C2×C411yescharacteristic
117#14519689C2×C411yescharacteristic
118#14519689D411yescharacteristic
119#14519689D411yescharacteristic
120#14519687—21no—
121#14519687—21no—
122C4×#92418—21no—
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×SD16×C61C2×C411yescharacteristic
130C22×C8×C61—21no—
131C4×Q8×C61C2311yescharacteristic
132C4×D4×C61C2311yescharacteristic
133#106×C61C2×C411yescharacteristic
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137#103×C61C2×C411yescharacteristic
138#102×C61C2×C411yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61C22×C411yescharacteristic
146C22×C4×C61—21no—
147C2×C22⋊D61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150#11758224—22no—
151#11758224—22no—
152C2×C4×D61C22×C411yescharacteristic
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61#4111yescharacteristic
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158SD16×C61—22no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61C22×C411yescharacteristic
169C4⋊C4×C61C22×C411yescharacteristic
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61C2411yescharacteristic
173C22⋊Dic61—21no—
174#11758202—22no—
175#11758200—22no—
176#11758198—21no—
177#11758198—21no—
178#11758198—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C22×C411yescharacteristic
181C4⋊Dic61C22×C411yescharacteristic
182#11758196—21no—
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61C22×C411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204Dic244—22no—
205C8×D61—81no—
206C23×C61—21no—
207C22×D61C4×D411yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210D4×C61—21no—
211D4×C61#13112yes—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—21no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C22⋊D61—24no—
221C2×Dic61—24no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—81no—
227C2×Dic61C4×D411yescharacteristic
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C4×D61—21no—
231C4×D61—21no—
232C4×D61—21no—
233C4×D61—21no—
234C4×D61—41no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—81no—
239Dic122#13112yes—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#17921—611nomaximal, Sylow
255C22×C61—22no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—21no—
260C2×D61—21no—
261C2×D61—21no—
262C4×C61—21no—
263C4×C61—41no—
264C4×C61—41no—
265C4×C61—41no—
266C4×C61C2×#13111yescharacteristic
267C4×C61C2×#13111yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—22no—
271Dic61—21no—
272Dic61—21no—
273Dic61—21no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3107—611no—
278#2988—611no—
279#2985—611no—
280#1587—611no—
281#1585—611no—
282#1584—611no—
283#1582D6111yescharacteristic, complemented
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1573—611no—
289#1488—611no—
290#1481—611no—
291#1454—611no—
292C2×C61—42no—
293C2×C61#292911yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—41no—
297#533—611no—
298C4×#41—611no—
299#485—611no—
300#485—611no—
301#475—611no—
302#474—611no—
303#462—611no—
304#461—611no—
305#452—611no—
306#452—611no—
307#446—611no—
308#446—1221no—
309#446—1221no—
310#446C2×D6111yescharacteristic
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C8×Q8—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16C2×D6111yescharacteristic
319C8×D4—611no—
320C8×D4—1221no—
321C8×D4—1221no—
322C8×D4C2×D6111yescharacteristic
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431—611no—
327#431—611no—
328#431—611no—
329#431—1221no—
330C2×C4⋊C8—611no—
331C2×C4⋊C8—1221no—
332#335—611no—
333#335—611no—
334#334—611no—
335#334C2×D6111yescharacteristic
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8C2×D6111yescharacteristic
342D4⋊C8—611no—
343D4⋊C8C2×D6111yescharacteristic
344#322—611no—
345#322—611no—
346#322C2×D6111yescharacteristic
347C82—611no—
348C61#1792111yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16C4×D6111yescharacteristic
354C22×C8—21no—
355C22×C8—1221no—
356C22×C8—1221no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360C22⋊Q8—611no—
361C22⋊Q8—611no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368C4×D4—611no—
369C4×D4—1221no—
370C4×D4—1221no—
371C4×D4C22×D6111yescharacteristic
372#117—611no—
373#117—1221no—
374#117—1221no—
375C2×C42—611no—
376C2×C42—1221no—
377#107—611no—
378#107—611no—
379#106—611no—
380#106C4×D6111yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
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⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103C4×D6111yescharacteristic
403#102—611no—
404#102C4×D6111yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—1221no—
415#97—1221no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—1222no—
427#41—1222no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—1221no—
431C2×Q8C2×C4×D6111yescharacteristic
432C2×D4—1221no—
433C2×D4C2×C4×D6111yescharacteristic
434C22×C4—21no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—611no—
438C22×C4—1221no—
439C22×C4—1221no—
440Q16—1222no—
441Q16—1222no—
442SD16—22no—
443SD16—1222no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—81no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—4881no—
456C2×C8—4881no—
457C2×C8C2×C4×D6111yescharacteristic
458C2×C8C2×C4×D6111yescharacteristic
459C2×C8D4×D6111yescharacteristic
460C2×C8D4×D6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—21no—
480C42—611no—
481C42—611no—
482C42—611no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42—1221no—
487C42C23×D6111yescharacteristic
488C23—21no—
489C23—611no—
490Q8—21no—
491Q8—21no—
492Q8—612no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497D4—21no—
498D4—1224no—
499D4#1451978512yes—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—611no—
506C2×C4—611no—
507C2×C4—611no—
508C2×C4—1224no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—1221no—
517C2×C4—4881no—
518C2×C4—2441no—
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4#41×D6111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—22no—
537C22—41no—
538C22—41no—
539C22—1221no—
540C22—1221no—
541C22—1221no—
542C22C4×D4×D6111yescharacteristic
543C4—21no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—1221no—
548C4—1221no—
549C4—1221no—
550C4—1222no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4C2×#1451978511yescharacteristic
556C4#1684056811yescharacteristic
557C4#1684057611yescharacteristic
558C2—42no—
559C2—2441no—
560C2#2145451011yescharacteristic
561C2#2145465511yescharacteristic
562C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1582C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758224C2×C4
cosocleC42×C61C24
hypercenter#1582D61
hypocenterC61#17921
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
3. #21454915C2semidirect
4. #21444688C2semidirect
5. #21444676C2semidirect
6. #21444671C2semidirect
7. #21444637C2semidirect
8. SD16⋊#92418C2semidirect
9. #21444623C2semidirect
10. #21444622C2semidirect
11. #21444601C2semidirect
13. #21444220C2semidirect
14. #21444120C2semidirect
15. C61×#1582C2semidirect
283. #1582D61semidirect
348. C61#17921semidirect

Maximal subgroups

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

subgroupindex
#214558862
#214549262
#214549152
#214446882
#214446762
#214446712
#214446372
SD16⋊#924182
#214446232
#214446222
#214446012
#214442502
#214442202
#214441202
C61×#15822
#1792161