Finite Group Databasebeta

← #29650086

Subgroups — #29650086

Order 15616.

596 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#21455901C211yesmaximal, characteristic
2#21454964C211yesmaximal, characteristic
3#21454899C211yesmaximal, characteristic, complemented
4#21444696C211yesmaximal, characteristic, complemented
5#21444689C211yesmaximal, characteristic, complemented
6#21444668C211yesmaximal, characteristic, complemented
7#21444661C211yesmaximal, characteristic, complemented
8#21444637C211yesmaximal, characteristic, complemented
9#21444630C211yesmaximal, characteristic, complemented
10#21444625C211yesmaximal, characteristic, complemented
11#21444618C211yesmaximal, characteristic, complemented
12#21444247C211yesmaximal, characteristic, complemented
13#21444225C211yesmaximal, characteristic
14#21444119C211yesmaximal, characteristic, complemented
15C61×#1574C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18#16840093C411yescharacteristic
19#16840076C411yescharacteristic
20#16840070C411yescharacteristic
21#16840070C411yescharacteristic
22#16839985C411yescharacteristic
23#16839985C411yescharacteristic
24#16839920C411yescharacteristic
25#16839903C411yescharacteristic
26#16839889C2211yescharacteristic
27C8×Dic122—21no—
28C8×Dic122—21no—
29#16839886C2211yescharacteristic
30#16839886C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33#16839886C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×#11758190C2211yescharacteristic
37C4×#11758190C2211yescharacteristic
38#16839839C2211yescharacteristic
39#16839838—21no—
40#16839831—21no—
41#16839827C2211yescharacteristic
42#16839822—21no—
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839812—21no—
46#16839812—21no—
47#16839787—21no—
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839492C2211yescharacteristic
51#16839492C2211yescharacteristic
52#16839492C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C61×#335C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#334C2211yescharacteristic
66C61×#334C2211yescharacteristic
67C22×Dic122C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×Dic244C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×#11758190C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×C8×D61—21no—
74#14519771—21no—
75#14519769C2×C411yescharacteristic
76#14519765C2×C411yescharacteristic
77#14519760—21no—
78#14519756C2×C411yescharacteristic
79#14519751C2×C411yescharacteristic
80C4×Dic122—21no—
81C4×Dic122—21no—
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2×C411yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×D244C2311yescharacteristic
88C4×C22⋊D61—21no—
89#14519734—21no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758196—21no—
92C2×C4×Dic61—21no—
93#14519711C2×C411yescharacteristic
94#14519711C2×C411yescharacteristic
95#14519709C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97C4⋊#92418—21no—
98C4⋊#92418D411yescharacteristic
99C4⋊#92418D411yescharacteristic
100#14519706—21no—
101#14519706—21no—
102#14519706—21no—
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519702C2×C411yescharacteristic
107#14519702C2×C411yescharacteristic
108#14519702C2×C411yescharacteristic
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519699C2×C411yescharacteristic
113#14519699C2×C411yescharacteristic
114C22⋊#92418—21no—
115C22⋊#92418D411yescharacteristic
116C22⋊#92418D411yescharacteristic
117#14519689—21no—
118#14519689—21no—
119#14519687—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C2×M16×C61—21no—
130C2×C42×C61C2311yescharacteristic
131C4⋊C8×C61—21no—
132C4⋊C8×C61C2×C411yescharacteristic
133C4⋊C8×C61C2×C411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C22⋊C8×C61—21no—
139C22⋊C8×C61C2×C411yescharacteristic
140C22⋊C8×C61C2×C411yescharacteristic
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148C22×Dic61—21no—
149C22×Dic61—21no—
150C2×D244C22×C411yescharacteristic
151C2×C4×D61—21no—
152C2×Dic122—21no—
153C2×Dic122—22no—
154C2×Dic122—22no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158M16×C61—81no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—21no—
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C22×C411yescharacteristic
165C2×C8×C61C22×C411yescharacteristic
166C2×C8×C61C22×C411yescharacteristic
167C42×C61C22×C411yescharacteristic
168C42×C61C2×D411yescharacteristic
169C42×C61#4111yescharacteristic
170C42×C61C2411yescharacteristic
171C22⋊Dic61—21no—
172#11758198—21no—
173#11758198—21no—
174#11758198—21no—
175#11758198—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61C22×C411yescharacteristic
178C4⋊Dic61C22×C411yescharacteristic
179C4⋊Dic61C22×C411yescharacteristic
180C4⋊Dic61C22×C411yescharacteristic
181#11758196—21no—
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×Dic61—21no—
194C2×#92418—21no—
195C2×#92418—21no—
196C2×#92418C2×D411yescharacteristic
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200Dic244—22no—
201Dic244—22no—
202#11758190—22no—
203#11758190—22no—
204#11758189—81no—
205C8×D61—81no—
206C23×C61C4×D411yescharacteristic
207C22×D61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—81no—
220C2×Dic61—24no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—81no—
229D244—21no—
230D244—21no—
231C4×D61—41no—
232C4×D61—41no—
233Dic122—24no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122#13112yes—
239Dic122#13112yes—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—41no—
253#92418—41no—
254#17919—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61C2×#13111yescharacteristic
267C4×C61C2×#13111yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—22no—
271Dic61—22no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3108—611no—
278#2993—611no—
279#2982—611no—
280#1588—611no—
281#1587—611no—
282#1584—611no—
283#1583—611no—
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1574D6111yescharacteristic, complemented
289#1487—611no—
290#1482—611no—
291#1454—611no—
292C2×C61—41no—
293C2×C61#292911yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—81no—
297#529—611no—
298C2×C4×Q8—611no—
299#483—611no—
300#480—611no—
301#479—611no—
302#479—611no—
303#464—611no—
304#464—611no—
305#451—611no—
306#448—611no—
307#446—611no—
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8—1221no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319#436—611no—
320#436—1221no—
321#435—1221no—
322C8×D4—611no—
323#433—1221no—
324#431—611no—
325#431—611no—
326#431—1221no—
327#431—1221no—
328#431C2×D6111yescharacteristic
329#431C2×D6111yescharacteristic
330#424—1221no—
331#423C2×D6111yescharacteristic
332#335C2×D6111yescharacteristic
333#335C2×D6111yescharacteristic
334#334C2×D6111yescharacteristic
335#334C2×D6111yescharacteristic
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1791911yescharacteristic, complemented, Sylow
349C22×Q8—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C2×M16—21no—
355C2×M16—1221no—
356C22×C8—1221no—
357#126—1221no—
358#125—611no—
359#124—611no—
360#123—1221no—
361C22⋊Q8—611no—
362#121—611no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—1221no—
369C4×Q8—1221no—
370C4×D4—611no—
371C4×D4—1221no—
372#117—1221no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
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⋊C8C4×D6111yescharacteristic
392C4⋊C8C4×D6111yescharacteristic
393C4⋊C8C22×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#102—611no—
404#102—611no—
405C22⋊C8—21no—
406C22⋊C8—611no—
407C22⋊C8—611no—
408C22⋊C8—1221no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C4×D6111yescharacteristic
412C22⋊C8C4×D6111yescharacteristic
413#97—1221no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C2×Q8—611no—
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—1222no—
430C2×Q8—1222no—
431C2×Q8—1221no—
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4#1175822611yescharacteristic
440Q16—1222no—
441Q16—1222no—
442SD16—1222no—
443SD16—1222no—
444M16—81no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—4881no—
457C2×C8C2×C4×D6111yescharacteristic
458C2×C8C2×C4×D6111yescharacteristic
459C2×C8C2×C4×D6111yescharacteristic
460C2×C8C2×C4×D6111yescharacteristic
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42D4×D6111yescharacteristic
486C42#1175822611yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23#1451973911yescharacteristic
490Q8—612no—
491Q8—612no—
492Q8—1224no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—1221no—
497D4—1221no—
498D4—1221no—
499D4—4881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—1224no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—4881no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4#1451973911yescharacteristic
517C2×C4#1451973911yescharacteristic
518C2×C4#1451973911yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C2×D4×D6111yescharacteristic
521C2×C4C2×#1175822611yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C2×#1451973911yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—1222no—
548C4—1222no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4#131×D6111yescharacteristic
556C4#1684057211yescharacteristic
557C4#1684057811yescharacteristic
558C2—41no—
559C2—4881no—
560C2#2145451211yescharacteristic
561C2#2145466011yescharacteristic
562C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1574C2
socleC22×C61C2×C4×D4
prime radical#14519751C2×C4
cosocleC42×C61C24
hypercenter#1574D61
hypocenterC61#17919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1574

Complements

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

NH ≅ G/Ntype
3. #21454899C2semidirect
4. #21444696C2semidirect
5. #21444689C2semidirect
6. #21444668C2semidirect
7. #21444661C2semidirect
8. #21444637C2semidirect
9. #21444630C2semidirect
10. #21444625C2semidirect
11. #21444618C2semidirect
12. #21444247C2semidirect
14. #21444119C2semidirect
15. C61×#1574C2semidirect
288. #1574D61semidirect
348. C61#17919semidirect

Maximal subgroups

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

subgroupindex
#214559012
#214549642
#214548992
#214446962
#214446892
#214446682
#214446612
#214446372
#214446302
#214446252
#214446182
#214442472
#214442252
#214441192
C61×#15742
#1791961