Finite Group Databasebeta

← #29836914

Subgroups — #29836914

Order 15616.

546 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458190C211yesmaximal, characteristic, complemented
2#21457560C211yesmaximal, characteristic
3#21448052C211yesmaximal, characteristic, complemented
4#21448026C211yesmaximal, characteristic, complemented
5#21448000C211yesmaximal, characteristic, complemented
6#21447985C211yesmaximal, characteristic, complemented
7#21447917C211yesmaximal, characteristic, complemented
8#21447907C211yesmaximal, characteristic, complemented
9#21447883C211yesmaximal, characteristic, complemented
10#21447758C211yesmaximal, characteristic, complemented
11Q32×Dic61C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic, complemented
13#21447525C211yesmaximal, characteristic, complemented
14C2×#16839566C211yesmaximal, characteristic, complemented
15C61×#2188C211yesmaximal, characteristic, complemented
16C2×#14519800C2211yescharacteristic
17#16840454—21no—
18#16840423—21no—
19C2×#14519720C2211yescharacteristic
20C22×#11758185C2211yescharacteristic
21C2×C16×D61C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840147C2211yescharacteristic
24#16840102—21no—
25#16840090—21no—
26#16840071—21no—
27#16840000C2211yescharacteristic
28#16840000C2211yescharacteristic
29#16839998C2211yescharacteristic
30#16839986—21no—
31#16839923—21no—
32#16839901—21no—
33Q16×Dic61C2211yescharacteristic
34Q16×Dic61C2211yescharacteristic
35C8×C22⋊D61C2211yescharacteristic
36#16839799C2211yescharacteristic
37C2×#14519711C2211yescharacteristic
38#16839589C2211yescharacteristic
39#16839588C2211yescharacteristic
40#16839588C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839566C2211yescharacteristic
43#16839566C2211yescharacteristic
44#16839566C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839566C2211yescharacteristic
47#16839564C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C22×Q16×C61C2211yescharacteristic
53C2×Q32×C61C2211yescharacteristic
54C2×Q32×C61C2211yescharacteristic
55C61×#467C2211yescharacteristic
56C61×#358C2211yescharacteristic
57C61×#358C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758226—21no—
60#14519800—22no—
61#14519800—41no—
62C2×#11758201—21no—
63C2×#11758201—21no—
64C2×D488C2311yescharacteristic
65C2×C8×D61C2311yescharacteristic
66#14519772—41no—
67#14519768—21no—
68#14519768—41no—
69#14519766—21no—
70#14519766—41no—
71#14519761—41no—
72#14519753—21no—
73#14519753—21no—
74#14519753—41no—
75#14519751—21no—
76#14519751—41no—
77Q8×Dic61—21no—
78Q8×Dic61—21no—
79C4×C22⋊D61—41no—
80C4×C22⋊D61D411yescharacteristic
81#14519735—21no—
82#14519733—41no—
83C2×C4⋊Dic61—21no—
84#14519720—41no—
85C2×#11758185—41no—
86C2×#11758185C2311yescharacteristic
87C2×#11758185C2311yescharacteristic
88C16×D61—41no—
89#14519711—21no—
90#14519711C2311yescharacteristic
91#14519711C2311yescharacteristic
92#14519711C2311yescharacteristic
93#14519708—21no—
94#14519708—21no—
95#14519706D411yescharacteristic
96#14519701—21no—
97#14519701—21no—
98#14519701—21no—
99#14519701—21no—
100#14519699—21no—
101C22⋊#92418D411yescharacteristic
102#14519689D411yescharacteristic
103C8×Dic61C2311yescharacteristic
104C22×Q8×C61—21no—
105C2×Q16×C61—22no—
106C2×Q16×C61—21no—
107C2×Q16×C61—41no—
108C2×Q16×C61C2311yescharacteristic
109C2×Q16×C61C2311yescharacteristic
110C2×Q16×C61C2311yescharacteristic
111C22×C8×C61C2311yescharacteristic
112C22⋊Q8×C61—21no—
113Q32×C61—22no—
114Q32×C61—41no—
115C2×C16×C61C2311yescharacteristic
116C2×C16×C61C2311yescharacteristic
117#107×C61C2311yescharacteristic
118#103×C61—21no—
119C2×Q8×C61—21no—
120C2×Q8×C61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—42no—
123C2×Q8×C61—41no—
124C2×Q8×C61—81no—
125C22×C4×C61—41no—
126C22×C4×C61C2×D411yescharacteristic
127C2×C22⋊D61—41no—
128C2×C22⋊D61D811yescharacteristic
129C22×Dic61—41no—
130#11758226—42no—
131#11758226—81no—
132C2×D244—21no—
133C2×D244—41no—
134C2×C4×D61—41no—
135C2×C4×D61C2×D411yescharacteristic
136Q16×C61—21no—
137Q16×C61—21no—
138Q16×C61—21no—
139Q16×C61—21no—
140Q16×C61—21no—
141Q16×C61—42no—
142Q16×C61#4112yes—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61C2×D411yescharacteristic
146C2×C8×C61C2411yescharacteristic
147C4⋊C4×C61—21no—
148C4⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C22⋊Dic61D811yescharacteristic
151#11758201—42no—
152#11758201—81no—
153#11758198—41no—
154#11758198—41no—
155#11758198—41no—
156#11758198—41no—
157#11758198—41no—
158#11758198—41no—
159#11758198D811yescharacteristic
160C4⋊Dic61—21no—
161C4⋊Dic61—21no—
162C4⋊Dic61—21no—
163C4⋊Dic61—41no—
164C4⋊Dic61—41no—
165C4⋊Dic61—41no—
166C4⋊Dic61—41no—
167#11758196—41no—
168#11758196—41no—
169#11758196—41no—
170#11758196D811yescharacteristic
171C4×Dic61—41no—
172C4×Dic61—41no—
173C4×Dic61—41no—
174C4×Dic61C2×D411yescharacteristic
175C2×#92418C2×D411yescharacteristic
176C2×#92418C2×D411yescharacteristic
177D488—21no—
178D488—21no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61C2×D811yescharacteristic
186C22×D61—41no—
187C22×D61C2×D811yescharacteristic
188Q8×C61—22no—
189Q8×C61—41no—
190Q8×C61—41no—
191Q8×C61—41no—
192Q8×C61—41no—
193Q8×C61—41no—
194Q8×C61—82no—
195C2×C4×C61—21no—
196C2×C4×C61—21no—
197C2×C4×C61—41no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—82no—
202C2×C4×C61C2×D811yescharacteristic
203C2×C4×C61C22×D411yescharacteristic
204C22⋊D61—22no—
205C22⋊D61—82no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—82no—
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212C2×Dic61C2×D811yescharacteristic
213D244—41no—
214D244—41no—
215D244—82no—
216C4×D61—21no—
217C4×D61—21no—
218C4×D61—82no—
219C8×C61—21no—
220C8×C61C2×#4111yescharacteristic
221C8×C61H(5,𝔽2)11yescharacteristic
222#92418—21no—
223#92418—21no—
224#33867—611nomaximal, Sylow
225C22×C61—21no—
226C22×C61—21no—
227C22×C61#50812yes—
228C22×C61C22×D811yescharacteristic
229C2×D61—21no—
230C2×D61—21no—
231C2×D61—21no—
232C2×D61—81no—
233C2×D61—81no—
234C2×D61—81no—
235C4×C61—21no—
236C4×C61—42no—
237C4×C61—81no—
238C4×C61—81no—
239C4×C61—81no—
240C4×C61#54611yescharacteristic
241C4×C61#57711yescharacteristic
242Dic61—21no—
243Dic61—21no—
244Dic61—21no—
245Dic61—81no—
246Dic61—81no—
247Dic61—81no—
248#3336—611no—
249#3285—611no—
250#2242—611no—
251#2237—611no—
252#2232—611no—
253#2229—611no—
254#2217—611no—
255#2216—611no—
256#2211—611no—
257#2189—611no—
258#2188D6111yescharacteristic, complemented
259C4×Q32—611no—
260D4×C16—611no—
261#2138—611no—
262C2×#358—611no—
263C2×C61—22no—
264C2×C61#329411yescharacteristic
265C2×C61C2×#50811yescharacteristic
266C2×C61#341711yescharacteristic
267D61—41no—
268D61—161no—
269C2×#135—611no—
270C22×Q16C2×D6111yescharacteristic
271#552—1221no—
272#548—1221no—
273C2×Q32C2×D6111yescharacteristic
274C2×Q32C2×D6111yescharacteristic
275C2×SD32—611no—
276C22×C16—611no—
277C22×C16—611no—
278#499—611no—
279#495—611no—
280#485—1221no—
281#483—1221no—
282#479—1221no—
283#467—611no—
284#467—611no—
285#467C2×D6111yescharacteristic
286#466—611no—
287#464—1221no—
288#452—1221no—
289#448—1221no—
290C4×Q16—611no—
291C4×Q16—611no—
292C8×D4—611no—
293#427—611no—
294C2×#107—611no—
295#367—611no—
296#366—611no—
297#366—611no—
298C4⋊C16—611no—
299#358—611no—
300#358—611no—
301#358—611no—
302#358—611no—
303#358—611no—
304#358C2×D6111yescharacteristic
305#358C2×D6111yescharacteristic
306#357—611no—
307#357—611no—
308#357—611no—
309C22⋊C16—611no—
310C22⋊C16C2×D6111yescharacteristic
311C4×C16—611no—
312C61#3386711yescharacteristic, complemented, Sylow
313C2×#41—1221no—
314C22×Q8—21no—
315#135—1222no—
316#135—2441no—
317C2×Q16—22no—
318C2×Q16—21no—
319C2×Q16—41no—
320C2×Q16C22×D6111yescharacteristic
321C2×Q16C22×D6111yescharacteristic
322C2×Q16C22×D6111yescharacteristic
323C2×SD16—1221no—
324C2×SD16—1221no—
325C2×D8—611no—
326C22×C8—611no—
327C22×C8C22×D6111yescharacteristic
328#126—2441no—
329#125—1221no—
330#125—2441no—
331#124—1221no—
332#124—2441no—
333#123—2441no—
334C22⋊Q8—21no—
335C22⋊Q8—1221no—
336C22⋊Q8—1221no—
337C22⋊Q8—2441no—
338#121—1221no—
339#121—2441no—
340C4×Q8—1221no—
341C4×Q8—1221no—
342C4×D4—611no—
343C4×D4—2441no—
344#117—1221no—
345#117—2441no—
346C2×C4⋊C4—1221no—
347Q32—22no—
348Q32—41no—
349SD32—2441no—
350C2×C16—611no—
351C2×C16—611no—
352C2×C16—2441no—
353C2×C16—2441no—
354C2×C16C22×D6111yescharacteristic
355C2×C16C22×D6111yescharacteristic
356#107—611no—
357#107—611no—
358#107—611no—
359#107—1221no—
360#107C22×D6111yescharacteristic
361#106—1221no—
362#106—1221no—
363C4⋊C8—611no—
364#103—21no—
365#103—1221no—
366#103—1221no—
367#103—1221no—
368#103—1221no—
369#102—1221no—
370C22⋊C8—611no—
371C22⋊C8—611no—
372C4×C8—611no—
373#41—4881no—
374#41—2442no—
375C2×Q8—21no—
376C2×Q8—21no—
377C2×Q8—21no—
378C2×Q8—42no—
379C2×Q8—41no—
380C2×Q8—81no—
381C2×D4—611no—
382C2×D4—1221no—
383C2×D4—2441no—
384C2×D4—2441no—
385C22×C4—41no—
386C22×C4—611no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4D4×D6111yescharacteristic
390Q16—21no—
391Q16—21no—
392Q16—21no—
393Q16—21no—
394Q16—21no—
395Q16—42no—
396Q16#1175822412yes—
397SD16—4881no—
398SD16—2442no—
399D8—1221no—
400D8—1221no—
401C2×C8—21no—
402C2×C8—21no—
403C2×C8—611no—
404C2×C8—611no—
405C2×C8—1221no—
406C2×C8—1221no—
407C2×C8D4×D6111yescharacteristic
408C2×C8C23×D6111yescharacteristic
409C4⋊C4—21no—
410C4⋊C4—41no—
411C4⋊C4—611no—
412C4⋊C4—1221no—
413C4⋊C4—1221no—
414C4⋊C4—1221no—
415C4⋊C4—2441no—
416C4⋊C4—2441no—
417C4⋊C4—2441no—
418C4⋊C4—2441no—
419C4⋊C4—2441no—
420C4⋊C4—2441no—
421C4⋊C4—2441no—
422C22⋊C4—41no—
423C22⋊C4—611no—
424C22⋊C4—611no—
425C22⋊C4—2441no—
426C22⋊C4—2441no—
427C22⋊C4—2441no—
428C22⋊C4—2441no—
429C22⋊C4—2441no—
430C22⋊C4—2441no—
431C42—611no—
432C42—2441no—
433C42—2441no—
434C42—2441no—
435C16—21no—
436C16—21no—
437C16—1221no—
438C16—1221no—
439C23—611no—
440C23—2441no—
441C23D8×D6111yescharacteristic
442Q8—22no—
443Q8—41no—
444Q8—41no—
445Q8—41no—
446Q8—41no—
447Q8—41no—
448Q8—82no—
449D4—1222no—
450D4—4882no—
451D4—4882no—
452D4—2441no—
453D4—2441no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—82no—
461C2×C4—611no—
462C2×C4—611no—
463C2×C4—611no—
464C2×C4—1221no—
465C2×C4—1221no—
466C2×C4—4882no—
467C2×C4—4882no—
468C2×C4—2441no—
469C2×C4—2441no—
470C2×C4—2441no—
471C2×C4D8×D6111yescharacteristic
472C2×C4C2×D4×D6111yescharacteristic
473C8—21no—
474C8—1221no—
475C8—1221no—
476C8C2×#1175822411yescharacteristic
477C8#1451982211yescharacteristic
478C22—21no—
479C22—21no—
480C22—1221no—
481C22—1221no—
482C22—1221no—
483C22—4881no—
484C22—4881no—
485C22—4881no—
486C22#1684019512yes—
487C22C2×D8×D6111yescharacteristic
488C4—21no—
489C4—42no—
490C4—81no—
491C4—81no—
492C4—81no—
493C4—1221no—
494C4—1221no—
495C4—1221no—
496C4—4881no—
497C4—4881no—
498C4—4881no—
499C4#1684039911yescharacteristic
500C4#1684057211yescharacteristic
501C2—22no—
502C2—9761no—
503C2—2441no—
504C2#2145762511yescharacteristic
505C2C2×#1684019511yescharacteristic
506C2#2145897111yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2188C2
socleC22×C61C22×D8
prime radical#21457560C2
hypercenter#2188D61
hypocenterC61#33867
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2188

Complements

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

NH ≅ G/Ntype
1. #21458190C2semidirect
3. #21448052C2semidirect
4. #21448026C2semidirect
5. #21448000C2semidirect
6. #21447985C2semidirect
7. #21447917C2semidirect
8. #21447907C2semidirect
9. #21447883C2semidirect
10. #21447758C2semidirect
11. Q32×Dic61C2semidirect
12. #21447636C2semidirect
13. #21447525C2semidirect
14. C2×#16839566C2semidirect
15. C61×#2188C2semidirect
258. #2188D61semidirect
312. C61#33867semidirect

Maximal subgroups

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

subgroupindex
#214581902
#214575602
#214480522
#214480262
#214480002
#214479852
#214479172
#214479072
#214478832
#214477582
Q32×Dic612
#214476362
#214475252
C2×#168395662
C61×#21882
#3386761