Finite Group Databasebeta

← #29651278

Subgroups — #29651278

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455901C211yesmaximal, characteristic
2#21454975C211yesmaximal, characteristic
3#21454909C211yesmaximal, characteristic, complemented
4#21444727C211yesmaximal, characteristic, complemented
5#21444720C211yesmaximal, characteristic, complemented
6#21444668C211yesmaximal, characteristic, complemented
7#21444668C211yesmaximal, characteristic, complemented
8#21444661C211yesmaximal, characteristic, complemented
9#21444654C211yesmaximal, characteristic, complemented
10#21444637C211yesmaximal, characteristic, complemented
11#21444630C211yesmaximal, characteristic, complemented
12#21444277C211yesmaximal, characteristic
13C2×#16839492C211yesmaximal, characteristic, complemented
14#21444112C211yesmaximal, characteristic, complemented
15C61×#1573C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17C2×C4×Dic122C2211yescharacteristic
18#16840093C411yescharacteristic
19#16840076C411yescharacteristic
20#16840070C411yescharacteristic
21#16840070C411yescharacteristic
22#16839985C411yescharacteristic
23#16839985C411yescharacteristic
24#16839920C411yescharacteristic
25#16839903C411yescharacteristic
26#16839890—21no—
27#16839890—21no—
28#16839889C2211yescharacteristic
29#16839889C2211yescharacteristic
30#16839889C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33#16839886C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×#11758190C2211yescharacteristic
37C4×#11758190C2211yescharacteristic
38#16839839C2211yescharacteristic
39#16839833—21no—
40#16839827C2211yescharacteristic
41C8×C22⋊D61—21no—
42#16839822—21no—
43#16839816—21no—
44#16839815C2211yescharacteristic
45#16839812—21no—
46#16839787—21no—
47C2×C4×#92418C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50#16839492C2211yescharacteristic
51#16839492C2211yescharacteristic
52#16839492C2211yescharacteristic
53#16839492C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839489C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839483C2211yescharacteristic
59#16839483C2211yescharacteristic
60C61×#432C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C2×C4⋊C8×C61C2211yescharacteristic
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—
73C22×#92418—21no—
74C2×C8×D61—21no—
75#14519771—21no—
76#14519769C2×C411yescharacteristic
77#14519765C2×C411yescharacteristic
78#14519760—21no—
79#14519756C2×C411yescharacteristic
80#14519751C2×C411yescharacteristic
81C4×Dic122—21no—
82C4×Dic122—21no—
83C4×Dic122C2×C411yescharacteristic
84C4×Dic122C2×C411yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×Dic122C2311yescharacteristic
87C4×Dic122C2311yescharacteristic
88C4×D244C2311yescharacteristic
89C4×C22⋊D61—21no—
90#14519734—21no—
91C2×C4⋊Dic61C2×C411yescharacteristic
92C2×#11758196—21no—
93C2×C4×Dic61—21no—
94#14519711C2×C411yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
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⋊#92418D411yescharacteristic
115C22⋊#92418D411yescharacteristic
116#14519689—21no—
117#14519689—21no—
118#14519687—21no—
119#14519687—21no—
120#14519687—21no—
121C4×#92418—21no—
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C4×#92418C2311yescharacteristic
125C4×#92418C2311yescharacteristic
126C8×Dic61—21no—
127C8×Dic61—21no—
128C8×Dic61—21no—
129C22×C8×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
141#97×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—22no—
153C2×Dic122—21no—
154C2×Dic122—41no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
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×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×#92418—42no—
197C2×#92418C2×D411yescharacteristic
198C2×#92418C2×D411yescharacteristic
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201Dic244—22no—
202Dic244—41no—
203#11758190—22no—
204#11758190—41no—
205#11758189—81no—
206C8×D61—81no—
207C23×C61C4×D411yescharacteristic
208C22×D61—21no—
209C2×C4×C61—22no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C4×D411yescharacteristic
217C2×C4×C61C23×C411yescharacteristic
218C2×C4×C61C22×D411yescharacteristic
219C2×C4×C61C2×#4111yescharacteristic
220C22⋊D61—42no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61—42no—
229C2×Dic61—42no—
230D244—21no—
231D244—21no—
232C4×D61—41no—
233C4×D61—41no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240Dic122#13112yes—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—41no—
246C8×C61—41no—
247C8×C61—41no—
248C8×C61—41no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#18023—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61#44412yes—
259C22×C61C2×C4×D411yescharacteristic
260C2×D61—41no—
261C2×D61—41no—
262C2×D61—41no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61C2×#13111yescharacteristic
268C4×C61#56811yescharacteristic
269C4×C61#57711yescharacteristic
270C4×C61#57811yescharacteristic
271Dic61—22no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278#3108—611no—
279#2994—611no—
280#2984—611no—
281#1593—611no—
282#1592—611no—
283#1584—611no—
284#1584—611no—
285#1583—611no—
286#1582—611no—
287#1579—611no—
288SD16⋊C8—611no—
289#1573D6111yescharacteristic, complemented
290#1494—611no—
291C2×Q8⋊C8—611no—
292#1452—611no—
293C2×C61—22no—
294C2×C61#293311yescharacteristic
295C2×C61#294711yescharacteristic
296C2×C61C2×#44411yescharacteristic
297D61—81no—
298#529—611no—
299C2×C4×Q8—611no—
300#483—611no—
301#480—611no—
302#479—611no—
303#479—611no—
304#464—611no—
305#464—611no—
306#451—611no—
307#448—611no—
308#446—611no—
309#446—611no—
310#446—611no—
311#446—1221no—
312#446—1221no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320#436—611no—
321#435—1221no—
322C8×D4—611no—
323C8×D4—1221no—
324#433—1221no—
325#432—1221no—
326#432C2×D6111yescharacteristic
327#431—611no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330#424—1221no—
331C2×C4⋊C8C2×D6111yescharacteristic
332C2×C4×C8—611no—
333#335C2×D6111yescharacteristic
334#335C2×D6111yescharacteristic
335#334C2×D6111yescharacteristic
336#334C2×D6111yescharacteristic
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343D4⋊C8—611no—
344D4⋊C8—611no—
345#322—611no—
346#322—611no—
347#322—611no—
348#322—611no—
349C61#1802311yescharacteristic, complemented, Sylow
350C22×Q8—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16—611no—
355C2×M16—1221no—
356C22×C8—21no—
357C22×C8—1221no—
358C22×C8—1221no—
359#126—1221no—
360#125—611no—
361#124—611no—
362#123—1221no—
363C22⋊Q8—611no—
364#121—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—611no—
370C4×Q8—1221no—
371C4×Q8—1221no—
372C4×D4—611no—
373C4×D4—1221no—
374#117—1221no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8C4×D6111yescharacteristic
393C4⋊C8C4×D6111yescharacteristic
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#102—611no—
405#102—611no—
406C22⋊C8—21no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C4×D6111yescharacteristic
412C22⋊C8C4×D6111yescharacteristic
413#97—21no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8C22×D6111yescharacteristic
426C4×C8C22×D6111yescharacteristic
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—1222no—
431C2×Q8—1221no—
432C2×Q8—2441no—
433C2×D4—611no—
434C2×D4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4C2×C4×D6111yescharacteristic
439C22×C4D4×D6111yescharacteristic
440C22×C4#1175822611yescharacteristic
441Q16—1222no—
442Q16—2441no—
443SD16—1222no—
444SD16—2441no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—4881no—
458C2×C8—2442no—
459C2×C8C2×C4×D6111yescharacteristic
460C2×C8C2×C4×D6111yescharacteristic
461C2×C8C2×C4×D6111yescharacteristic
462C2×C8C2×C4×D6111yescharacteristic
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—611no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42C2×C4×D6111yescharacteristic
487C42D4×D6111yescharacteristic
488C42#1175822611yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23#1451973911yescharacteristic
492Q8—612no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—1221no—
500D4—1221no—
501D4—2442no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—2442no—
515C2×C4—2442no—
516C2×C4—2441no—
517C2×C4—2441no—
518C2×C4#1451973911yescharacteristic
519C2×C4#1451973911yescharacteristic
520C2×C4#1451973911yescharacteristic
521C2×C4C22×C4×D6111yescharacteristic
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C2×#1175822611yescharacteristic
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C22—21no—
539C22—21no—
540C22—2441no—
541C22—2441no—
542C22—2441no—
543C22#1683988312yes—
544C22C2×#1451973911yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—1222no—
550C4—2441no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4#131×D6111yescharacteristic
557C4#1684052711yescharacteristic
558C4#1684057211yescharacteristic
559C4#1684057811yescharacteristic
560C2—22no—
561C2—4881no—
562C2#2145454311yescharacteristic
563C2#2145466011yescharacteristic
564C2C2×#1683988311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1573C2
socleC22×C61C2×C4×D4
prime radical#14519751C2×C4
cosocleC42×C61C24
hypercenter#1573D61
hypocenterC61#18023
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1573

Complements

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

NH ≅ G/Ntype
3. #21454909C2semidirect
4. #21444727C2semidirect
5. #21444720C2semidirect
6. #21444668C2semidirect
7. #21444668C2semidirect
8. #21444661C2semidirect
9. #21444654C2semidirect
10. #21444637C2semidirect
11. #21444630C2semidirect
13. C2×#16839492C2semidirect
14. #21444112C2semidirect
15. C61×#1573C2semidirect
289. #1573D61semidirect
349. C61#18023semidirect

Maximal subgroups

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

subgroupindex
#214559012
#214549752
#214549092
#214447272
#214447202
#214446682
#214446612
#214446542
#214446372
#214446302
#214442772
C2×#168394922
#214441122
C61×#15732
#1802361