Finite Group Databasebeta

← #29836971

Subgroups — #29836971

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458239C211yesmaximal, characteristic, complemented
2#21457576C211yesmaximal, characteristic, complemented
3#21448041C211yesmaximal, characteristic, complemented
4#21448012C211yesmaximal, characteristic, complemented
5#21447970C211yesmaximal, characteristic, complemented
6#21447906C211yesmaximal, characteristic, complemented
7#21447903C211yesmaximal, characteristic, complemented
8#21447853C211yesmaximal, characteristic, complemented
9#21447744C211yesmaximal, characteristic, complemented
10#21447743C211yesmaximal, characteristic, complemented
11#21447670C211yesmaximal, characteristic, complemented
12#21447636C211yesmaximal, characteristic, complemented
13#21447524C211yesmaximal, characteristic, complemented
14#21447523C211yesmaximal, characteristic, complemented
15C61×#2234C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519796C2211yescharacteristic
18#16840475—21no—
19#16840430—21no—
20C2×#14519722C2211yescharacteristic
21C2×D976C2211yescharacteristic
22C2×#14519718C2211yescharacteristic
23C22×#11758185C2211yescharacteristic
24C2×C16×D61C2211yescharacteristic
25#16840166C2211yescharacteristic
26#16840137C2211yescharacteristic
27#16840088—21no—
28#16840086—21no—
29#16840051—21no—
30#16839999C2211yescharacteristic
31#16839999C2211yescharacteristic
32#16839998C2211yescharacteristic
33#16839961—21no—
34#16839908—21no—
35#16839905—21no—
36#16839856C2211yescharacteristic
37#16839844C2211yescharacteristic
38C8×C22⋊D61C2211yescharacteristic
39#16839799C2211yescharacteristic
40#16839587C2211yescharacteristic
41#16839580C2211yescharacteristic
42#16839567C2211yescharacteristic
43#16839565C2211yescharacteristic
44#16839565C2211yescharacteristic
45#16839564C2211yescharacteristic
46#16839563C2211yescharacteristic
47#16839562C2211yescharacteristic
48#16839562C2211yescharacteristic
49#16839562C2211yescharacteristic
50#16839541C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#466C2211yescharacteristic
53C61×#427C2211yescharacteristic
54C61×#367C2211yescharacteristic
55C61×#366C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C61×C22⋊C16C2211yescharacteristic
59C2×#11758222—21no—
60C2×#11758224—21no—
61#14519799—22no—
62#14519799—41no—
63#14519796—22no—
64#14519796—41no—
65C2×Dic244C2311yescharacteristic
66C2×#11758190—21no—
67C2×#11758200—21no—
68C2×D488C2311yescharacteristic
69C2×D488C2311yescharacteristic
70C2×#11758199—21no—
71C2×C8×D61C2311yescharacteristic
72#14519776—21no—
73#14519773—21no—
74#14519773—41no—
75#14519765—41no—
76#14519763—41no—
77#14519752—21no—
78#14519752—21no—
79#14519751—21no—
80#14519750—41no—
81#14519750—41no—
82#14519749—41no—
83#14519742—21no—
84#14519739—21no—
85C4×C22⋊D61D411yescharacteristic
86#14519737—41no—
87#14519735—21no—
88#14519734—41no—
89#14519722—22no—
90D976—41no—
91#14519718—41no—
92C2×#11758185—41no—
93C2×#11758185C2311yescharacteristic
94C2×#11758185C2311yescharacteristic
95C16×D61—41no—
96#14519711C2311yescharacteristic
97#14519710—21no—
98#14519708—21no—
99#14519706D411yescharacteristic
100#14519700—21no—
101#14519699—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418D411yescharacteristic
106#14519689D411yescharacteristic
107C8×Dic61C2311yescharacteristic
108C2×D8×C61C2311yescharacteristic
109C22×C8×C61C2311yescharacteristic
110#121×C61—21no—
111#117×C61—21no—
112C2×C16×C61C2311yescharacteristic
113C2×C16×C61C2311yescharacteristic
114#107×C61C2311yescharacteristic
115#107×C61C2311yescharacteristic
116#107×C61C2311yescharacteristic
117#106×C61—21no—
118#102×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C22×C4×C61C2×D411yescharacteristic
122C2×C22⋊D61—41no—
123C2×C22⋊D61—41no—
124C2×C22⋊D61—41no—
125C2×C22⋊D61—41no—
126C2×C22⋊D61—41no—
127C2×C22⋊D61D811yescharacteristic
128C22×Dic61—41no—
129#11758224—42no—
130#11758224—81no—
131#11758222—42no—
132#11758222—81no—
133C2×D244—21no—
134C2×D244—21no—
135C2×D244—41no—
136C2×D244—41no—
137C2×C4×D61—41no—
138C2×C4×D61—41no—
139C2×C4×D61C2×D411yescharacteristic
140C2×Dic122—21no—
141C2×Dic122—41no—
142D8×C61—21no—
143D8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61C2×D411yescharacteristic
147C2×C8×C61C2411yescharacteristic
148C4⋊C4×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C22⋊C4×C61—41no—
152C22⋊C4×C61—41no—
153C42×C61—41no—
154C22⋊Dic61D811yescharacteristic
155#11758200—42no—
156#11758199—81no—
157#11758198—41no—
158#11758198—41no—
159#11758198—41no—
160#11758198—41no—
161#11758198—41no—
162#11758198D811yescharacteristic
163C4⋊Dic61—21no—
164#11758196—41no—
165#11758196—41no—
166#11758196D811yescharacteristic
167C4×Dic61—41no—
168C4×Dic61—41no—
169C4×Dic61C2×D411yescharacteristic
170C2×#92418C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172Dic244—21no—
173Dic244#4112yes—
174D488—21no—
175D488—21no—
176D488—21no—
177D488—21no—
178#11758190—42no—
179C8×D61—21no—
180C8×D61—21no—
181C16×C61—21no—
182C16×C61—21no—
183#11758185—21no—
184#11758185—21no—
185C23×C61—41no—
186C23×C61C2×D811yescharacteristic
187C22×D61—41no—
188C22×D61—41no—
189C22×D61C2×D811yescharacteristic
190D4×C61—41no—
191D4×C61—41no—
192D4×C61—161no—
193C2×C4×C61—21no—
194C2×C4×C61—21no—
195C2×C4×C61—41no—
196C2×C4×C61—41no—
197C2×C4×C61—41no—
198C2×C4×C61C2×D811yescharacteristic
199C2×C4×C61C22×D411yescharacteristic
200C22⋊D61—22no—
201C22⋊D61—82no—
202C22⋊D61—82no—
203C22⋊D61—82no—
204C22⋊D61—161no—
205C22⋊D61—161no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—82no—
209C2×Dic61C2×D811yescharacteristic
210C2×Dic61C2×D811yescharacteristic
211C2×Dic61C2×D811yescharacteristic
212D244—41no—
213D244—41no—
214D244—41no—
215D244—41no—
216D244—161no—
217D244—161no—
218C4×D61—21no—
219C4×D61—21no—
220C4×D61—82no—
221C4×D61—82no—
222Dic122—22no—
223Dic122—41no—
224Dic122—161no—
225C8×C61—21no—
226C8×C61C2×#4111yescharacteristic
227C8×C61H(5,𝔽2)11yescharacteristic
228#92418—21no—
229#92418—21no—
230#33872—611nomaximal, Sylow
231C22×C61—21no—
232C22×C61—21no—
233C22×C61—21no—
234C22×C61—81no—
235C22×C61—81no—
236C22×C61—81no—
237C22×C61C22×D811yescharacteristic
238C2×D61—21no—
239C2×D61—21no—
240C2×D61—21no—
241C2×D61—81no—
242C2×D61—81no—
243C2×D61—81no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C4×C61—21no—
248C4×C61—81no—
249C4×C61—81no—
250C4×C61—81no—
251C4×C61#54611yescharacteristic
252C4×C61#57711yescharacteristic
253Dic61—21no—
254Dic61—21no—
255Dic61—42no—
256Dic61—81no—
257Dic61#50812yes—
258#3341—611no—
259#3287—611no—
260#2240—611no—
261#2234—611no—
262#2234D6111yescharacteristic, complemented
263#2227—611no—
264#2215—611no—
265#2215—611no—
266#2206—611no—
267#2186—611no—
268#2186—611no—
269C4×SD32—611no—
270D4×C16—611no—
271#2138—611no—
272#2138—611no—
273C2×C61—41no—
274C2×C61—161no—
275C2×C61#329411yescharacteristic
276C2×C61C2×#50811yescharacteristic
277C2×C61#341511yescharacteristic
278D61—41no—
279D61—161no—
280D61—161no—
281C2×#135—611no—
282C2×#135—611no—
283#555—1221no—
284#550—1221no—
285C2×SD32—611no—
286C2×D16—611no—
287C2×D16—611no—
288C22×C16—611no—
289C22×C16—611no—
290#500—611no—
291#493—611no—
292#482—1221no—
293#482—1221no—
294#476—1221no—
295#466—611no—
296#466—611no—
297#466—611no—
298#466C2×D6111yescharacteristic
299#460—1221no—
300#449—1221no—
301#449—1221no—
302C4×Q16—611no—
303C4×D8—611no—
304C8×D4—611no—
305#427—611no—
306#427C2×D6111yescharacteristic
307#367C2×D6111yescharacteristic
308#366—611no—
309#366C2×D6111yescharacteristic
310C4⋊C16—611no—
311#358—611no—
312#358—611no—
313#358—611no—
314#357—611no—
315#357—611no—
316#357—611no—
317#357—611no—
318#357—611no—
319#357C2×D6111yescharacteristic
320#357C2×D6111yescharacteristic
321C22⋊C16—611no—
322C22⋊C16C2×D6111yescharacteristic
323C4×C16—611no—
324C61#3387211yescharacteristic, complemented, Sylow
325C2×#41—1221no—
326C2×#41—1221no—
327#135—1222no—
328#135—1222no—
329#135—2441no—
330#135—2441no—
331C2×Q16—611no—
332C2×SD16—1221no—
333C2×SD16—1221no—
334C2×D8—611no—
335C2×D8—611no—
336C2×D8—1221no—
337C2×D8C22×D6111yescharacteristic
338C22×C8—611no—
339C22×C8C22×D6111yescharacteristic
340C4⋊Q8—1221no—
341#127—1221no—
342#127—2441no—
343#124—2441no—
344#124—2441no—
345#121—21no—
346#121—1221no—
347#121—1221no—
348#121—1221no—
349#121—2441no—
350#121—2441no—
351#121—2441no—
352C4×Q8—1221no—
353C4×D4—611no—
354C4×D4—1221no—
355C4×D4—2441no—
356#117—21no—
357#117—1221no—
358#117—2441no—
359SD32—1222no—
360D16—2441no—
361D16—2441no—
362C2×C16—611no—
363C2×C16—611no—
364C2×C16—2441no—
365C2×C16—2441no—
366C2×C16C22×D6111yescharacteristic
367C2×C16C22×D6111yescharacteristic
368#107—611no—
369#107—1221no—
370#107C22×D6111yescharacteristic
371#107C22×D6111yescharacteristic
372#107C22×D6111yescharacteristic
373#106—21no—
374#106—1221no—
375C4⋊C8—611no—
376#103—1221no—
377#102—21no—
378#102—1221no—
379#102—1221no—
380#102—1221no—
381#102—1221no—
382C22⋊C8—611no—
383C22⋊C8—611no—
384C4×C8—611no—
385#41—4881no—
386#41—4881no—
387#41—2442no—
388#41—2442no—
389C2×Q8—1221no—
390C2×Q8—2441no—
391C2×D4—21no—
392C2×D4—41no—
393C2×D4—611no—
394C2×D4—1221no—
395C2×D4—1221no—
396C2×D4—2441no—
397C2×D4—2441no—
398C2×D4—2441no—
399C2×D4—2441no—
400C2×D4—2441no—
401C2×D4—2441no—
402C2×D4—2441no—
403C22×C4—611no—
404C22×C4—2441no—
405C22×C4—2441no—
406C22×C4—2441no—
407C22×C4D4×D6111yescharacteristic
408Q16—612no—
409Q16—1221no—
410SD16—2442no—
411SD16—2442no—
412D8—21no—
413D8—21no—
414D8—1221no—
415D8—1221no—
416D8—1221no—
417D8—1221no—
418D8—4881no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—611no—
422C2×C8—611no—
423C2×C8—1221no—
424C2×C8—1221no—
425C2×C8D4×D6111yescharacteristic
426C2×C8C23×D6111yescharacteristic
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—611no—
431C4⋊C4—1221no—
432C4⋊C4—2441no—
433C4⋊C4—2441no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—611no—
437C22⋊C4—611no—
438C22⋊C4—2441no—
439C22⋊C4—2441no—
440C22⋊C4—2441no—
441C22⋊C4—2441no—
442C22⋊C4—2441no—
443C42—41no—
444C42—611no—
445C42—2441no—
446C42—2441no—
447C16—21no—
448C16—21no—
449C16—1221no—
450C16—1221no—
451C23—41no—
452C23—611no—
453C23—2441no—
454C23—2441no—
455C23D8×D6111yescharacteristic
456Q8—1222no—
457Q8—9761no—
458Q8—2441no—
459D4—41no—
460D4—41no—
461D4—161no—
462D4—1222no—
463D4—9761no—
464D4—9761no—
465D4—9761no—
466D4—9761no—
467D4—4882no—
468D4—4882no—
469D4—4882no—
470D4—2441no—
471D4—2441no—
472D4—2441no—
473D4—2441no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—611no—
480C2×C4—611no—
481C2×C4—611no—
482C2×C4—1221no—
483C2×C4—1221no—
484C2×C4—4882no—
485C2×C4—4882no—
486C2×C4—4882no—
487C2×C4—2441no—
488C2×C4—2441no—
489C2×C4D8×D6111yescharacteristic
490C2×C4C2×D4×D6111yescharacteristic
491C8—21no—
492C8—1221no—
493C8—1221no—
494C8#41×D6111yescharacteristic
495C8#1451982311yescharacteristic
496C22—21no—
497C22—21no—
498C22—21no—
499C22—81no—
500C22—81no—
501C22—81no—
502C22—1221no—
503C22—1221no—
504C22—1221no—
505C22—4881no—
506C22—4881no—
507C22—4881no—
508C22—4881no—
509C22—4881no—
510C22—4881no—
511C22C2×D8×D6111yescharacteristic
512C4—21no—
513C4—81no—
514C4—81no—
515C4—81no—
516C4—612no—
517C4—1221no—
518C4—1221no—
519C4—4881no—
520C4—2442no—
521C4#1684040411yescharacteristic
522C4#1684057111yescharacteristic
523C2—41no—
524C2—161no—
525C2—9761no—
526C2—9761no—
527C2—2441no—
528C2#2145763011yescharacteristic
529C2#508×D6111yescharacteristic
530C2#2145895911yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2234C2
socleC22×C61C22×D8
hypercenter#2234D61
hypocenterC61#33872
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2234

Complements

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

NH ≅ G/Ntype
1. #21458239C2semidirect
2. #21457576C2semidirect
3. #21448041C2semidirect
4. #21448012C2semidirect
5. #21447970C2semidirect
6. #21447906C2semidirect
7. #21447903C2semidirect
8. #21447853C2semidirect
9. #21447744C2semidirect
10. #21447743C2semidirect
11. #21447670C2semidirect
12. #21447636C2semidirect
13. #21447524C2semidirect
14. #21447523C2semidirect
15. C61×#2234C2semidirect
262. #2234D61semidirect
324. C61#33872semidirect

Maximal subgroups

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

subgroupindex
#214582392
#214575762
#214480412
#214480122
#214479702
#214479062
#214479032
#214478532
#214477442
#214477432
#214476702
#214476362
#214475242
#214475232
C61×#22342
#3387261